1er · 2014. 10. 22. · Ha resultado ganador del 1er Premio Abertis 2013 en la categoría...

sobre gestión deinfraestructurasd e l t r a n s p o r t e

Premio Internacional

Abertis de investigación

Rheological and mechanical characterization of portland cement

mixes containing micro and nano amorphous silica particles

Luis Eduardo Zapata Orduz

1- PUERTO RICO -

er

Pórtico

La red internacional de Cátedra Abertis convoca un año más, junto a prestigiosas universidades, los premios que reconocen a los mejores trabajos de final de carrera, tesinas o tesis doctorales relacionadas con la gestión de infraestructuras de transporte, desarrollados por universitarios de los distintos países en los que opera el grupo Abertis.

A partir de la creación en el año 2003 de la primera Cátedra Abertis junto a la Universitat Politècnica de Catalunya-UPC (BarcelonaTech), la red ha ido creciendo y ganando presencia internacional en Francia, Puerto Rico, Brasil y recientemente en Chile.

Este modelo de gestión del conocimiento tiene su origen en la firme voluntad de Abertis de colaborar con las universidades, los centros de excelencia y los expertos más destacados en cada materia con el fin de ayudar a generar y a divulgar el conocimiento, poniéndolo al servicio de la investigación y de toda la sociedad. El trabajo distinguido por los Premios Abertis de investigación que ahora tiene en sus manos, quiere ser una muestra más de esta vocación de servicio a los investigadores, a la comunidad educativa y de los profesionales con responsabilidades en el campo dela gestión de las infraestructuras.

Esta visión, que se integra en la responsabilidad social de Abertis, aspira también a ofrecer vías de progreso, de colaboración, de diálogo y de interacción en todos los territorios en los que Abertis está presente, ayudando a desarrollar de forma responsable y sostenible las actividades del Grupo. Más información sobre las actividades de la Cátedra Abertis en la web: www.catedrasabertis.com.

PresentaciónLa Cátedra Abertis de la Universidad de Puerto Rico (UPR) promueve la realización de seminarios y conferencias y la investigación sobre la gestión de infraestructuras del transporte estructurada en los ejes de actividad de la corporación: carreteras y autopistas, tráfico, seguridad vial y sistemas de transporte inteligentes. Asimismo, con objeto de potenciar el interés de los universitarios residentes en la isla, la Cátedra Abertis establece anualmente el Premio Abertis, al mejor trabajo de investigación inédito en gestión del transporte realizado por estudiantes en Puerto Rico.

Este año fue muy especial para nosotros ya que por primera vez la entrega del Premio Internacional se llevó a cabo en Puerto Rico, lo cual fue una oportunidad excelente para el intercambio de ideas con ejecutivos de Abertis, funcionarios del Gobierno de Puerto Rico, sector privado y de la Universidad de Puerto Rico. Esperamos continuar esta relación con la Fundación Abertis en los años venideros y estamos seguros que este premio redundará en mejoras en las infraestructuras de transporte en Puerto Rico y en motivar a futuros profesionales de la ingeniería y gerencia a cursar estudios en gestión de transporte.

Ha resultado ganador del 1er Premio Abertis 2013 en la categoría doctoral, la Tesis titulada “Rheological and Mechanical Characterization of Portland Cement Mixes Containing Micro and Nano Amorphous Silica Particles” por el Dr. Luis E. Zapata Orduz, Ingeniero de Ingeniería Civil por la Universidad de Puerto Rico- Recinto de Mayagüez.

La tesis emplea nano-SiO2 (nS), ceniza volante (FA), humo de sílice (SF) y superplastificantes tipo polycarboxilatos (SP) para determinar las características reológicas en estado fresco y las propiedades macro-mecánicas en estado endurecido. El estado fresco de las pastas de cemento usando el cono de Marsh (MCT) mostró que las adiciones minerales mejoraron la fluidez, pero los resultados mostraron que los análisis del MCT se deben interpretar cuidadosamente cuando hay adiciones minerales, por posibles distorsiones ocasionadas por la viscosidad plástica del material. Además, se estudió el estado endurecido de morteros a w/b=0.35 que contenían nano/micro-SiO2. Los análisis SEM mostraron que sistemas con nano-SiO2 presentaron mejoras por densificación y gradación. El estudio de concretos con nS, SF, FA y SP fue más complejo y requirió técnicas estadísticas (DOE) y redes neuronales (ANN). Los resultados DOE en compresión y tensión indicaron que las mezclas binarias de nS-SF son la mejor opción para ganar resistencia. Finalmente, desde ensayos de tensión indirecta en concretos se estimaron los parámetros de Weibull usando técnicas no-lineales. Los resultados estadísticos mostraron que algunos sistemas de silica amorfa exhibían valores del módulo Weibull mayores que las muestras de control. La novedad es que pese a la importancia del modulo Weibull en el análisis de materiales quebradizos, la mayoría de los estudios se basan en concretos simples.

En este categoría de tesis doctoral, se presentaron además, contribuciones técnicas relacionadas con el desarrollo de un modelo sistemodinámico para pronosticar, jerarquizar y distribuir cítricos durante operaciones de ayuda en caso de huracán, integración de sistemas de información geográfica, la síntesis, formación y caracterización de peróxido en la fabricación de explosivos caseros, el desarrollo de una tipología de los dos mecanismos de apoyo fiscal directo e indirecto e identificar las jurisdicciones donde se han empleado estos mecanismos y emplear el nano-SiO2, la ceniza volante , el humo de sílice y superplastificantes tipo de polucarboxilatos para determinar las características reológicas en estado fresco y propiedades macro-mecánicas en estado endurecido.

Dr. Benjamín Colucci RíosDirector de la Cátedra Abertis-UPR

RHEOLOGICAL AND MECHANICAL CHARACTERIZATION OF PORTLAND

CEMENT MIXES CONTAINING MICRO AND NANO AMORPHOUS SILICA

PARTICLES

By

Luis Eduardo Zapata Orduz

A dissertation submitted in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

IN

CIVIL ENGINEERING

UNIVERSITY OF PUERTO RICO

MAYAGÜEZ CAMPUS

2013

Approved by:

___________________________________ ____________

Arsenio Cáceres Fernández, PhD Date

Member, Graduate Committee

___________________________________ ____________

Omar I. Molina Bas, PhD Date


___________________________________ ____________

O. Marcelo Suárez, PhD Date


___________________________________ ____________

Genock Portela Gauthier, PhD Date

President, Graduate Committee

___________________________________ ____________

Ruben E. Díaz, PhD Date

Representative of Graduate Studies

___________________________________ ____________

Ismael Pagán Trinidad, MSCE Date

Chairperson of the Department

ii

ABSTRACT

In concrete technology, it is common to use fly ash (FA) and micro-SiO2 (SF) as mineral admixtures. This

has resulted in improvements in the fresh and hardened states. On the other hand, nano-SiO2 (nS) is

industrially produced for diverse applications due to their unique characteristics. Nevertheless, its use in

the concrete industry is not yet common and their physical-chemical effects as well as mechanical and

durability capacities are subject of interest in recent research. Thus, the current study employed nS, FA,

SF and polycarboxylate-type superplasticizer (SP) to determine their rheological characteristics at early

age and their macro-mechanical properties in the hardened state. The rheological properties of grouts

using the Marsh cone test (MCT) approach showed that mineral admixtures could improve the fluidity.

Nevertheless, results also showed that MCT must be interpreted carefully when mineral additions are

applied, because nonlinearities of the plastic viscosity could cause distortions in the MCT analyses. On

the other hand, the hardened state of mortar samples containing nano/micro-SiO2 at w/b=0.35 was

studied. SEM examinations in the ITZ suggested that compressive strengths of nano-SiO2-systems

presented densification and filler effects, whereas micro-SiO2-systems only showed filler effects.

Nevertheless, the study of concretes containing nS, SF, FA, and SP was more complex and statistical

tools (DOE) and artificial neural simulations (ANN) were required. DOE results of compressive and

tensile strength indicated that nS-SF binary mixes are the optimal choice to gain strength. However, DOE

results also showed lack-of-fit of the second-order. But, the ANN could effectively explain the lack-of-fit

inherit in the DOEs. Finally, splitting tensile failures were carried out on concretes to investigate the

accuracy of the Weibull models. The estimated Weibull parameters were obtained by using modern

advanced nonlinear methodologies. Statistical analysis indicated that some specific combinations of

amorphous silica exhibited Weibull modulus higher than the control case. The novelty in these analyses is

that despite the importance of the Weibull modulus in reliability analyses of brittle materials, the majority

of the studies are on plain concretes. The data is especially scarce for nano-SiO2 on binary, ternary, and/or

quaternary concretes mixes.

iii

RESUMEN

En tecnología del concreto, el uso de ceniza volante (FA) y humo de sílice (SF) como aditivo mineral es

muy común. Su implementación ha demostrado mejoras en el estado fresco y el endurecido. Además,

debido a sus propiedades únicas, el uso de nano-SiO2 (nS) ha presentado varias aplicaciones industriales.

Sin embargo, su uso en la industria del concreto no es común y sus efectos físico-químicos, capacidades

mecánicas y durabilidad son aún tema de investigación. Por consiguiente, el presente estudio emplea nS,

FA, SF y superplastificantes tipo polycarboxilatos (SP) para determinar las características reológicas en

estado fresco y las propiedades macro-mecánicas en estado endurecido. El estado fresco de las pastas de

cemento usando el cono de Marsh (MCT) mostró que las adiciones minerales mejoraron la fluidez. Pero

los resultados también mostraron que los análisis del MCT se deben interpretar cuidadosamente cuando

hay adiciones minerales, por posibles efectos de distorsión ocasionados por la viscosidad plástica en el

material. Por otra parte, se estudió el estado endurecido de morteros a w/b=0.35 que contenían

nano/micro-SiO2. Los análisis SEM en la interface mostraron que sistemas con nano-SiO2 presentaron

mejoras por densificación y gradación, mientras que en micro-SiO2 sólo la gradación fue importante. Sin

embargo, el estudio de concretos que contenían nS, SF, FA and SP fue más complejo y requirió usar

técnicas estadísticas (DOE) y redes neuronales (ANN). Los resultados desde DOE en compresión y

tensión indicaron que las mezclas binarias de nS-SF son la mejor opción para ganar resistencia. No

obstante, también se encontró falta-de-ajuste de segundo orden. Pero los análisis con ANN pudieron

eficazmente explicar esta falta-de-ajuste de los DOEs. Finalmente, desde ensayos de tensión indirecta en

concretos se estimaron los parámetros de Weibull usando modernas técnicas no-lineales. Los resultados

estadísticos mostraron que algunos sistemas de silica amorfa exhibían valores del módulo Weibull

mayores que las muestras de control. La novedad es que pese a la importancia del modulo Weibull en el

análisis de materiales quebradizos, la mayoría de los estudios se basan en concretos simples. Y los datos

son especialmente escasos para concretos que poseen nS en diseños binarios, terciarios y/o cuaternarios.

iv

Time ago Sir I. Newton said: “If I have seen further than others, it is by standing upon the

shoulders of giants”. To my parents Flor Elva and Eduardo, they patiently were my own giants during

these long academic years. Also, this thesis is dedicated to researchers in the field of concrete sciences,

because I used their shoulders.

v

ACKNOWLEDGEMENTS

I owe thanks to Prof. Genock Portela Gauthier, who trusted on my work four years ago and

accepted me as PhD student. Also, thanks by the supervision of the entire experimental and computational

process of this thesis and thanks by giving me much confidence to perform the cases studied. Also, I

would like to express my warm thanks to Drs. O. Marcelo Suárez, Omar I. Molina Bas, and Arsenio D.

Cáceres, who accepted to be co-examiners. In numerous discussions they helped to provide guidance to

this thesis and helped thoroughly reviewing this manuscript.

The materials employed in the present thesis were partially based on work supported by Essroc

San Juan, Puerto Rico, W. R. Grace & Co-Conn, Sika Corporation (PR-USA), and the staff of the

Construction Materials laboratory of the Department of Civil Engineering and Surveying of the

University of Puerto Rico at Mayagüez. The author would like to thank specially the National Science

Foundation (NSF) under Grant HRD 0833112 (CREST program) and Dr. O. Marcelo Suárez, because the

technical and financial support along these two last years of hard work. Without the help of CREST

program this work would not be as complete. I would like to extend me gratitude to the Geotechnical and

Structures Laboratory of the Engineer Research and Development Center, US Army Corps of Engineers

(Vicksburg, MS, USA), for supported at the beginning of the experiments and for advice during the

development of the majority of the topics in the present thesis.

I owe deep thanks to Dr. Ricardo López, who in numerous opportunities patiently advised me in

administrative situations. I am thankful to Dr. Luis E. Suárez, who inspired me as a Matlab® user during

the time involved in the course INCI-6029 and Dr. Antonio González-Quevedo who inspired me to read

papers on automation in construction during the time involved in the course INCI-6208. These two things

played an important role in a chapter of the present thesis. Special thanks are due to the construction

materials laboratory technician Mr. Monserrate Cruz, who spent much time finding solutions in the set up

devices required in the present investigation.

I thank to my graduate friends Fabio M. Upegüi, Diego Aguirre, Jorge A. Caro, and Ulises

Barajas, because they disinterestedly supported the present project in many ways. Finally, I am in

thankful with the entire undergraduate students who helped me with the cumbersome experimental

program carried out in the present thesis along the last four years.

vi

TABLE OF CONTENTS

ABSTRACT .................................................................................................................................................. ii

RESUMEN .................................................................................................................................................. iii

ACKNOWLEDGEMENTS .......................................................................................................................... v

TABLE OF CONTENTS ............................................................................................................................. vi

LIST OF FIGURES ..................................................................................................................................... ix

LIST OF TABLES ....................................................................................................................................... xi

LIST OF ABBREVIATIONS .................................................................................................................... xiii

CHAPTER I .................................................................................................................................................. 1

1 INTRODUCTION ..................................................................................................................................... 1

1.1 Justification ........................................................................................................................................ 1

1.2 Objectives .......................................................................................................................................... 2

1.3 Materials used in this research ........................................................................................................... 4

1.3.1 Portland cement type I ............................................................................................................... 4

1.3.2 Chemical admixtures ................................................................................................................. 4

1.3.3 Mineral admixtures .................................................................................................................... 4

1.3.4 Fine aggregate ............................................................................................................................ 5

1.3.5 Coarse aggregate ........................................................................................................................ 6

1.3.6 Water ......................................................................................................................................... 6

1.4 Literature review ................................................................................................................................ 6

1.4.1 Amorphous silica particles ........................................................................................................ 6

1.4.2 Fresh state properties in cementitious mixes ............................................................................. 8

1.4.3 Hardened state properties in mortar and concrete samples ........................................................ 9

1.4.4 Statistical design of experiments (DOE) ................................................................................... 9

1.4.5 Artificial neural networks (ANN) simulations ......................................................................... 10

1.4.6 Weibull statistical analysis ...................................................................................................... 11

1.5 General methodology ....................................................................................................................... 11

1.6 Scope of the research work .............................................................................................................. 13

1.7 General organization of the present thesis ....................................................................................... 14

1.7.1 Compatibility analyses and rheological performance between Portland cement Type I

and micro/nano-SiO2 particles in presence of polycarboxylate-type superplasticizers ....... 15

1.7.2 Fresh state analyses and compressive strength of superplasticized mortar containing

micro/nano-SiO2 particles .................................................................................................... 15

vii

CHAPTER II ............................................................................................................................................... 17

2 COMPATIBILITY ANALYSIS AND RHEOLOGICAL PERFORMANCE BETWEEN

PORTLAND CEMENT TYPE I AND MICRO/NANO-SIO2 PARTICLES IN PRESENCE

OF POLYCARBOXYLATE-TYPE SUPERPLASTICIZER ........................................................ 17

2.1 Introduction ...................................................................................................................................... 17

2.2 Theoretical background ................................................................................................................... 17

2.3 Methods used to analyze PC-SP systems ......................................................................................... 18

2.3.1 Marsh apparatus ....................................................................................................................... 18

2.3.2 Marsh test procedure ................................................................................................................ 19

2.4 Results and discussion ..................................................................................................................... 19

2.4.1 Marsh cone test analysis on plain grout mixtures .................................................................... 19

2.4.2 Marsh cone test analysis on PC-SP2-SF-0.35 system ............................................................. 22

2.4.3 Marsh cone test analysis on PC-SP2-SF-0.40 system ............................................................. 24

2.4.4 Marsh cone test analysis on PC-SP2-nS-0.35 system .............................................................. 26

2.4.5 Marsh cone test analysis on PC-SP2-nS-0.40 system .............................................................. 27

2.4.6 Marsh cone test: effects of the water-binder ratio ................................................................... 29

2.4.7 Marsh cone test: effects of the mineral admixture ................................................................... 30

2.5 Chapter final remarks ....................................................................................................................... 30

CHAPTER III ............................................................................................................................................. 32

3 FRESH STATE ANALYSIS AND MECHANICAL STRENGTH ON SUPERPLASTICIZED

MICRO/NANO-SiO2 SYSTEMS .................................................................................................. 32

3.1 Introduction ...................................................................................................................................... 32


3.3 Proportions, casting and testing for cementitious samples .............................................................. 33

3.3.1 Mortar samples: proportions, casting and testing .................................................................... 33

3.3.2 Concrete samples: proportions, casting and testing ................................................................. 34


3.4.1 Fresh state properties of mortar samples ................................................................................. 35

3.4.2 Hardened state properties of mortar samples ........................................................................... 38

3.4.3 Fresh concrete properties: validation of the MCT measurements ............................................ 42

3.4.4 Hardened concrete properties .................................................................................................. 44


CHAPTER IV ............................................................................................................................................. 48

viii

4 NONLINEAR STATISTICAL ANALYSIS IN COMPRESSIVE AND TENSILE STRENGTHS

OF CONCRETE CONTAINING AMORPHOUS SILICA ........................................................... 48

4.1 Introduction ...................................................................................................................................... 48


4.3 Proportions, casting and testing for concrete samples ..................................................................... 49

4.3.1 Concrete mixture proportions and specimen fabrication ......................................................... 49

4.3.2 Compressive and splitting tensile strength tests ...................................................................... 49

4.4 Development of the DOE and ANN models .................................................................................... 50


4.5.1 DOE analysis for compressive strength ................................................................................... 54

4.5.2 DOE analysis for tensile strength ............................................................................................ 60

4.5.3 ANN simulations ...................................................................................................................... 67


CHAPTER V .............................................................................................................................................. 78

5 WEIBULL ANALYSIS ON TENSILE STRENGTH OF CONCRETE CONTAINING

AMORPHOUS SILICA ................................................................................................................. 78

5.1 Introduction ...................................................................................................................................... 78

5.2 Proportions, casting and testing for concrete samples ..................................................................... 78

5.2.1 Concrete proportions ............................................................................................................... 78

5.2.2 Specimen fabrication ............................................................................................................... 79

5.2.3 Testing procedures ................................................................................................................... 79


5.3.1 Splitting tensile strength test .................................................................................................... 81

5.3.2 Statistical background .............................................................................................................. 81



CHAPTER VI ........................................................................................................................................... 101

6 GENERAL CONCLUSIONS AND RECOMMENDATIONS ............................................................. 101

6.1 Summary of the chapters ............................................................................................................... 101

6.2 Principal conclusions ..................................................................................................................... 102

6.3 Recommendations for future works ............................................................................................... 104

6.4 References ...................................................................................................................................... 106

ix

LIST OF FIGURES

Figure 1-1. XRD pattern of MA obtained with CuKα radiation. .................................................................. 5

Figure 2-1. Scheme of the Marsh cone apparatus. ...................................................................................... 18

Figure 2-2. Flow time as a function of SP-dosage at 5 min. ....................................................................... 21

Figure 2-3. Flow time as a function of SP-dosage at 60 min. ..................................................................... 21

Figure 2-4. Flow time as a function of SP2-dosage at 5 min (w/b=0.35). .................................................. 23

Figure 2-5. Flow time as a function of SP2-dosage at 60 min (w/b=0.35). ................................................ 23

Figure 2-6. Flow time as a function of SP2-dosage at 5 min (w/b=0.40). .................................................. 24

Figure 2-7. Flow time as a function of SP2-dosage at 60 min (w/b=0.40). ................................................ 25

Figure 2-8. Flow time for nS systems as a function of SP2-dosage at 5 min (w/b=0.35). .......................... 26

Figure 2-9. Flow time for nS systems as a function of SP2-dosage at 60 min (w/b=0.35). ........................ 27

Figure 2-10. Flow time for nS systems as a function of SP2 dosage at 5 min (w/b = 0.40). ...................... 28

Figure 2-11. Flow time for nS systems as a function of SP2-dosage at 60 min (w/b = 0.40). .................... 29

Figure 3-1. Constant contour plot for FA: (a) SF (wt%) and (b) nS (wt%). ............................................... 37

Figure 3-2. Constant contour plot for UW (kg/m3): (a) SF (wt%) and (b) nS (wt%). ................................. 37

Figure 3-3. Constant contour plot for AC (%): (a) SF (wt%) and (b) nS (wt%). ........................................ 38

Figure 3-4. Contour plots for Sc (MPa): (a) SF (wt%) and (b) nS (wt%). .................................................. 39

Figure 3-5. SEM micrographs of CA sample at SD=1, w/b=0.35 and t=90-days. ..................................... 40

Figure 3-6. SEM micrographs of S15A sample at SD=1, w/b=0.35 and t=90-days. .................................. 41

Figure 3-7. SEM micrographs of n3A sample at SD=1, w/b=0.35 and t=90-days. .................................... 41

Figure 3-8. Compressive and tensile strengths at w/b = 0.35. ..................................................................... 45

Figure 4-1. Schematic of a multilayer feed-forward/back-propagation network model. ............................ 51

Figure 4-2. Compressive strength of concretes at 3 days: (a) for DOE I and (b) for DOE II. .................... 55

Figure 4-3. Compressive strength of concretes at 7 days: (a) for DOE I and (b) for DOE II. .................... 55

Figure 4-4. Compressive strength of concretes at 28 days: (a) for DOE I and (b) for DOE II. .................. 56

x



Figure 4-7. Compression tests: DOE III (3-days): (a) principal effects and (b) interactive effects. ........... 58

Figure 4-8. Compression tests: DOE III (7-days): (a) principal effects and (b) interactive effects. ........... 58

Figure 4-9. Compression tests: DOE III (28-days): (a) principal effects and (b) interactive effects. ......... 58

Figure 4-10. Compression tests: DOE III (56-days): (a) principal effects and (b) interactive effects. ....... 59

Figure 4-11. Compression tests: DOE III (90-days): (a) principal effects and (b) interactive effects. ....... 59

Figure 4-12. Tensile strength of concretes at 3 days: (a) for DOE I and (b) for DOE II. ........................... 62

Figure 4-13. Tensile strength of concretes at 7 days: (a) for DOE I and (b) for DOE II. ........................... 63

Figure 4-14. Tensile strength of concretes at 28 days: (a) for DOE I and (b) for DOE II. ......................... 63



Figure 4-17. Tension analysis: DOE III at 3 days: (a) principal effects and (b) interactive effects. .......... 65

Figure 4-18. Tension analysis: DOE III at 7 days: (a) principal effects and (b) interactive effects. .......... 65

Figure 4-19. Tension analysis: DOE III at 28 days: (a) principal effects and (b) interactive effects. ........ 65



Figure 4-22. Actual compression and ANN-simulated-LMBP [12:15:1] (a) trained (b) tested. ................. 71

Figure 4-23. Actual tensile strength and ANN-simulated-LMBP [12:16:1] (a) trained (b) tested. ............. 71

Figure 4-24. Actual compressive strength and ANN-simulated-BRA [12:3:1] (a) trained (b) tested. ........ 72

xi

LIST OF TABLES

Table 1-1. Physical-chemical and mineralogical characteristics of the cement ............................................ 4

Table 1-2. Principal physical and chemical characteristics of FA, SF and nS .............................................. 5

Table 2-1. Results of saturation dosage and compatibility of the PC-SP systems ...................................... 19

Table 2-2. Physical and chemical properties of the chemical admixtures .................................................. 20

Table 2-3. Rheological parameters in PC-SP2-SF systems at w/b=0.35 and 0.40 ...................................... 26

Table 2-4. Rheological parameters in PC-SP2-nS systems at w/b=0.35 and 0.40 ...................................... 27

Table 3-1. MCT parameters in PC-SP (SD=1) at w/b=0.35 and 0.40 ......................................................... 33

Table 3-2. Mixtures proportions for the mortar cubes at w/b=0.35 ............................................................ 34

Table 3-3. Mix proportions of the concrete specimens ............................................................................... 35

Table 3-4. Fresh state properties for SF variable ........................................................................................ 36

Table 3-5. Fresh state properties for nS variable ........................................................................................ 36

Table 3-6. Compressive strength after 90 days ........................................................................................... 39

Table 3-7. Fresh properties of concrete binary mixtures (w/b=0.35) .......................................................... 42

Table 3-8. Fisher LSD for the difference in compressive and splitting tensile strength ............................. 45

Table 4-1. Concrete proportions, DOE compositions, and mechanical strengths of samples .................... 50

Table 4-2. Statistical results from DOEs in compression tests ................................................................... 54

Table 4-3. Summary from DOE analysis: optimized values for compressive strength .............................. 60

Table 4-4. Statistical results from DOEs in tension tests ............................................................................ 61

Table 4-5. Summary from DOE analysis of nS, SF and FA optimized values for tensile strength ............ 67

Table 4-6. Design parameters of ANN models ............................................................................................ 68

Table 4-7. Performance of ANN architectures (average of twelve simulations) ......................................... 68

Table 4-8. Results between the adjusted model from DOEs analyses and ANN-models ............................ 69

Table 4-9. Results between the predictive model from DOEs analyses and ANN-models ......................... 70

Table 4-10. Normalized ranking order from sensitivity analysis on ANN-simulations .............................. 73

xii

Table 4-11. Actual compression values and simulated ANN using LMBP [12:15:1] ................................. 74

Table 4-12. Actual compression values and simulated from ANN using BRA [12:3:1] ............................. 75

Table 4-13. Actual tension values and simulated from ANN using LMBP [12:16:1] ................................. 76

Table 5-1. Laboratory proportions and mechanical results of concrete samples ........................................ 80

Table 5-2. Statistical results and estimated parameters at 3-days ............................................................... 94

Table 5-3. Statistical results and estimated parameters at 7-days ............................................................... 95

Table 5-4. Statistical results and estimated parameters at 28-days ............................................................. 95



Table 5-7. Relationship between estimated Weibull parameters and average splitting strength ................ 98

Table 5-8. φ and λ estimated parameters versus r and the first order statistic ............................................ 99

xiii

LIST OF ABBREVIATIONS

ΔFT: fluidity loss

Ca(OH)2: Calcium hydroxide

C-S-H: Calcium silicate hydrate

CO: control or plain samples

C3A: tricalcium aluminate

C3S: tricalcium silicate

C4AF: tetracalcium ferroaluminate

GBFS: ground granulated blast-furnace slag

ITZ: interfacial transition zone

LSD: Fisher Least Significant Difference

MA: mineral admixtures

MSE: Error mean square

MCT: Marsh cone test

FT: flow time

FA: fly ash

NP: natural pozzolans

PC: Portland cement

XRD: x-ray diffraction

Na2O-eq: sodium oxide equivalent

nS: nano-SiO2

SD: saturation dosage

SEM: scanning electron micrographs

xiv

SG: specific gravity

SiO2: silica

SP: superplasticizer

SF: micro-SiO2

SSD: saturated surface dried

w/b: water-to-binder ratio

wt%: weight of cementitious materials (%)

1

CHAPTER I

1 INTRODUCTION

1.1 Justification

Increasing use of nano-modified high-performance materials in the construction industry such as

smart carbon nano-tubes, nano-titania, nano-calcium carbonate and nano-alumina produce systems with

higher strength, improved durability and reduced environmental impact (Gopalakrishnan et al., 2011).

Specifically, among recent advances in the concrete industry aiming to make concrete more sustainable

are the increasing use of binary, ternary, and quaternary binders. In effect, such modified cementitious

materials result not only in the production of high strength concretes but also in more durable, sustainable,

and economical concrete structures (Aïtcin and Mindess, 2011).

In concrete technology, it is common to use fly ash (FA) and silica fume or micro-SiO2 (SF) in

concrete mixes as mineral admixtures (MA) or supplementary cementitious materials (SCM). This has

resulted in improvements on the porosity, permeability, bleeding, and secondary C-S-H gel gained by the

reaction between the amorphous SiO2 with the calcium hydroxide in the cement hydration process

(Aïtcin, 1998; Mehta and Monteiro, 2003; Nazari and Riahi, 2011; Senff et al., 2010; Siddique and Khan,

2011). On the other hand, colloidal silica or nano-SiO2 (nS) particles are industrially produced for a

diverse array of applications. Nevertheless, the use of nS in concrete industry is not yet very common

practice because it is often too expensive (van de Griend et al., 2012) and their physical-chemical effects

as well as mechanical and durability capacities are being matter of recent research in concrete technology

(Jalal et al., 2012; Ltifi et al., 2011; Nazari and Riahi, 2011; Stefanidou and Papayianni, 2012; Zyganitidis

et al., 2011).

The present thesis is focused on the study of cementitious mixes containing amorphous silica at

both micro and nano scales. The samples contain replacement levels from zero to forty-six percent by

weight of cementitious material (wt%). The additions consist of Class F FA and SF as amorphous micro

particles and colloidal-silica as amorphous nS. In this thesis, the pertinent modifications for the binary,

ternary, and quaternary designs containing amorphous silica particles by the implementation of the

Absolute Volume Method are developed, adopting general plain concrete guides suggested by ACI 211.1

(1991).

2

The current study aims to employ nS in conjunction with other amorphous silica products (FA

and SF) at the micro scale and study the basic fresh characteristics and the principal hardened properties

in concrete samples. The cementitious systems will be experimentally analyzed to determine their

rheological characteristics at early age and their macro-mechanical properties (compressive and tensile

strength) in the hardened state at different maturity ages.

In the fresh state, the majority of the analyses are based on the Marsh cone test procedure. This

test has been widely supported by experiments on grouts without mineral admixtures hence, in the present

research a series of experimental programs incorporating SF and nS are developed. In addition, despite

the importance in reliability analyses of brittle materials, many studies in the literature evaluate the

Weibull modulus, only for plain concrete specimens while there are only a few studies in binary mixes.

Thus, concretes containing nano-SiO2 additions on binary, ternary and/or quaternary mixes are especially

scarce. Therefore, in the present thesis the accuracy of the two- and three-parameter Weibull models will

be investigated using the tensile strength of plain, binary, ternary and quaternary designs containing FA,

SF, and/or nS. The estimated Weibull parameters will be obtained by using modern nonlinear statistical

methodologies. Therefore, experimental and computational achievements will be provided to the concrete

technology area regarding the use of complex and novelty systems containing colloidal-amorphous silica

in conjunction with FA, SF and chemical polycarboxylate-type superplasticizers. On the other hand, in

the hardened state, results must reveal the effects on strength, strength gain and Weibull parameters

produced by additions of amorphous silica at micro and nano scales as well as the effects produced by

ternary and quaternary additions containing nano-SiO2 as an active ingredient.

1.2 Objectives

To study cementitious systems containing chemical and mineral admixtures via rheological and

mechanical characterization in the fresh and hardened states, respectively; in order to get mix proportions

classified as high-strength concretes as per the American Concrete Institute Committee ACI 363 R-92

(1997). The results will be analyzed by using advanced statistical tools including both theoretical

conditions and computational simulations.

The research work will focus on the following specific objectives:

Study the compatibility between Portland cement type I locally produced and a large range of

commercial polycarboxylate-type superplasticizers in grouts containing micro and nano particles of

SiO2 via the Marsh Cone Test procedure.

3

Study mortar specimens (ASTM C109, 2008) utilizing tested chemical and mineral admixtures

showing compatibility characteristics to be employed in mortar designs in order to both check the

rheological characteristics and investigate the water/binder range resulting most appropriate to cast

concrete samples.

Design plain, binary, ternary, and quaternary concrete mixes containing chemical and several

amorphous silica additions as mineral admixtures (fly ash, silica fume, and nano-SiO2) and

characterize their properties using the following techniques:

Fresh state: The entrapped air content (ASTM C138, 2010), the slump-cone test (ASTM

C143,2010), the flow table test (ASTM C1437), the fresh density or unit weight (ASTM

C138, 2010).

Hardened state: Compressive strength (ASTM C39, 2011) and tensile splitting test (ASTM

C496, 2004) for mechanical characterization, and scanning electron microscopy for the

microstructural properties.

Produce a computational model to simulate the behavior of the plain, binary, ternary, and quaternary

compressive strength of the concrete samples using Artificial Neural Networks based on Matlab®

script programs.

Produce a computational model to simulate the behavior of the plain, binary, ternary, and quaternary

splitting tensile strength of the concrete samples using Artificial Neural Networks based on Matlab®

script programs.

Obtain optimal design parameters from statistical analyses for the compression and tension states of

the plain, binary, ternary and quaternary high-strength concrete samples taking into account both

theoretical conditions and selected experimental ranges.

Obtain for the plain, binary, ternary, and quaternary high-strength concrete samples failed in splitting

tension test the Scale and Shape Weibull parameters via statistical analysis using script programs

developed in Mathematica® software to analyze the stochastic behavior of the samples containing fly

ash, micro and nano-SiO2.

4

1.3 Materials used in this research

In this thesis the materials listed below were employed for the experimental designs. The

proportions and recipes were varied for each particular experiment. Also, the source of fine and coarse

aggregate was the same through the experimental program to obtain comparative results. The brand and

source of the chemical and mineral admixtures as well as the Portland cement (PC) Type I was the same

for all the experimental programs. The exception is explained on Chapter I, where five different chemical

admixtures are used, but this variety of products was in fact the central axis of the experiment in that

chapter. Particular details are given below and additional information is provided through the chapters

when it is needed or relevant.

1.3.1 Portland cement type I

The cement is a PC Type I (ASTM C150, 2009). In the present thesis the grouts, mortars and

concrete samples were prepared using the same Portland cement type I. Table 1-1 shows the properties of

the cement.

Table 1-1. Physical-chemical and mineralogical characteristics of the cement

CHEMICAL COMPOSITION (wt%) BOGUE COMPOSITION (wt%)

SiO2 20.29 C3S 55.4

Al2O3 6.40 C2S 16.4

Fe2O3 3.51 C3A 11.0

CaO 65.13 C4AF 10.7

SO3 2.65 PHYSICAL PROPERTIES

MgO 1.03 Blaine (m2/kg) 394

K2O 0.48 Specific Gravity 2.90

Na2O 0.12 Normal consistency (%) 26.5

Loss of ignition 3.13 Compressive strength on cubes (MPa)

Alkalis Na2O eq.=0.44% 1 d 14.2

Free CaO 1.2 3 d 24.3

Insoluble residue 0.31 7 d 31.5

1.3.2 Chemical admixtures

This study employs five different polymer-based chemical admixtures of third generation (Rixom

and Mailvaganam, 2002). The doses vary in each particular experiment. All doses through the thesis are

expressed as the ratio by weight between the solid active matter and the cementitious content (wt%). The

physical-chemical properties of the admixtures were supplied by the manufacturers (Chapter II).

1.3.3 Mineral admixtures

The mineral admixtures employed were nano-SiO2 consisted of nanoparticles that were in the

form of opalescent amorphous silica dispersed in water (slurry). The nano-SiO2 particles were employed

5

at levels up to 6 (wt%). The micro-SiO2 powder (ASTM C1240, 2010) was in the form of uncondensed

particles, and it was employed at different levels from 5 to 20 (wt%). Finally, this thesis employed Class

F FA (low-calcium) (ASTM C618, 2008). Table 1-2 shows the principal physical-chemical characteristics

of nS, SF, and FA and Figure 1-1 shows results of X-ray diffraction (XRD) confirming the amorphous

nature of the materials.

Table 1-2. Principal physical and chemical characteristics of FA, SF and nS

FA SF nS

Chemical composition (wt%) SiO2 54.3 91.3 99.9

H2O 0.7 0.3 ---

pH value --- --- 9.0

Loss of ignition 1.28 --- 0.1

Physical properties

Specific gravity 2.1 2.3 2.1

Mean size (nm) 25000 200 25

Retained #325 (%) 15.5 --- ---

SSA* (m2/kg) 320 25000 109000

*SSA = specific surface area

Figure 1-1. XRD pattern of MA obtained with CuKα radiation.

1.3.4 Fine aggregate

The fine aggregate was in accordance to ASTM C33 (2003) with specific gravity (SSD) of 2.53,

and absorption capacity of 3.92%. The fine aggregate was oven dried before being used in the

experiments. Also, following recommendations for the design of high-strength concrete (Aïtcin, 1998;

Caldarone, 2009) the fineness modulus of the fine aggregate was 3.0.

5 15 25 35 45

Arb

itra

ry I

nte

nsi

ty U

nit

s

2θ

nS

SF

F

6

1.3.5 Coarse aggregate

The crushed gravel incorporated as coarse aggregate in the mixes has a maximum diameter of 9.5

mm, SSD specific gravity of 2.7, and absorption capacity of 4.2%. This material was in accordance to

ASTM C33 (2003). The coarse aggregate was oven dried before being used in the experiments.

1.3.6 Water

The water employed in the casting of grouts, mortar and concrete samples was tap water. The

source of the water was the system available at the University of Puerto Rico, specifically in the

construction materials laboratory located in Mayagüez, PR-USA.

1.4 Literature review

1.4.1 Amorphous silica particles

There are several studies on incorporation of SCM in cement-based composites; most of which

focus on FA and SF. These materials are used on different basis, for instance, environmental and energy-

related costs because they are cheaper than PC and its replacement helps to reduce the overall CO2

consumption (Mehta and Monteiro, 2003; Vejmelková et al., 2009). Also, SCM are attractive due to

improvements in the rheology, durability and strength of the concrete (Rao, 2003). Hence, FA and/or SF

additions are common in the production of high-strength concretes (Aïtcin, 1998; Caldarone, 2009; Rao,

2003). Nowadays the use of nS has gained special attention in civil engineering applications because

some improvements in chemical, physical and mechanical properties of concrete have been obtained

(Qing et al., 2007; Jalal et al., 2012; Nazari and Riahi, 2011; Li et al., 2004; Lin et al., 2008; Senff et al.,

2010; Stefanidou and Papayianni, 2012; Zhang and Islam, 2012; Zyganitidis et al., 2011).

FA is the most widely used SCM in concrete production (Kosmatka et al., 2003). FA is a finely

divided powder consisting of spherical glassy particles which resemble Portland cement. FA particles are

a by-product of the combustion of pulverized coal in electric power-generating plants collected by

electrostatic precipitators or bag filters. FA particles are primarily silicate glass containing silica, alumina,

iron, sodium, potassium, carbon and small amount of crystalline compounds. ASTM C618 (2008) Class F

and Class C FA are commonly used as pozzolanic admixture for concrete. Class F FA is often used at

dosages of 15 to 25 wt% and Class C FA is used at dosages of 15 to 40 wt% (Kosmatka et al., 2003).

During the last decade, considerable attention has been given to the use of SF as a partial

replacement of cement to produce high-strength concrete. Silica fume is also referred as micro-silica (or

micro-SiO2) is a mineral addition by-product of the ferrosilicon alloy industries obtained in an electric arc

7

furnace. SF rises as an oxidized vapor from 2000 °C furnaces. When it cools it condenses and is collected.

The condensed silica fume is then processed to remove impurities and to control particle size which is

extremely fine, about 100 times smaller than average cement particles (Kosmatka et al., 2003). SF is

essentially amorphous silica (usually more than 85%). SF is used in amounts between 5 and 10 wt%

where a high degree of impermeability and/or high-strength concrete is required.

In comparison to normal Portland cement-concretes, the addition of SF provide the following: i)

particles with two orders of magnitude finer than Portland cement, ii) highly pozzolanic reactive

chemistry, iii) increase the water requirement in concrete unless SPs are used (Siddique and Khan, 2011).

In addition, SF in concrete results in lower: porosity, permeability, and bleeding because amorphous SiO2

react and consume calcium hydroxide from the hydration process (Mindess et al., 2003). Silica fume

concrete has been found to be extremely strong, impermeable, and very durable against freezing-thawing,

salt water, and abrasion resistance. In concrete technology incorporation of SF is one of the methods of

enhancing the strength of concrete, particularly when the aggregates are of low quality (Almusallam et al.,

2004).

On the other hand, nano-SiO2 particles are industrially produced for a diverse array of

applications such as, paper treatment, anti-corrosion, painting, coatings, and textile industry among

others. In general, the variety of applications are due to their unique characteristics such as large surface

area, binding capacity, basic pH, heat resistance, large quantities of amorphous silica and high free

energy. Nowadays, the use of nS particularly has gained attention in civil engineering applications

because the potential improvements produced in chemical, physical and mechanical properties of concrete

(Björnström et al., 2004; Chen and Lin, 2009; Jalal et al., 2012; Jo et al., 2007; Li et al., 2004; Lin et al.,

2008; Nazari and Riahi, 2011; Zhang and Islam, 2012; Stefanidou and Papayianni, 2012; Zyganitidis et

al., 2011).

Results have shown that, like SF particles, addition of nS provide potentially enlarged strength,

lower porosity, improved permeability, and reduced bleeding. The reaction of the amorphous silica with

the Ca(OH)2 induces formation of secondary C-S-H (Jo et al., 2007; Mehta and Monteiro, 2003; Mindess

et al., 2003; Siddique and Khan, 2011). Therefore, since the major reactivity with the Ca(OH)2 phase and

the better improvement in the interfacial transition zone (ITZ), the potential effect of nS has been found to

be more efficient in enhancing strength than SF particles (Qing et al., 2007; Sanchez and Sobolev, 2010).

8

1.4.2 Fresh state properties in cementitious mixes

Polycarboxylate-type superplasticizers (SP) represent one of the most employed chemical

admixtures for concrete. The SP presence is related to its capacity of producing concrete with: i) high-

fluidity, ii) high-strength, and iii) superior dispersing force and retention effects even at low w/b ratios

(Yamada et al., 2001). However, the dispersing force of the SP and its power of retention seem to be

affected by some components of the PC or even by variations in the sequence of the mixing conditions

(Hallal et al., 2010).

Specifically, the behavior of the blended systems formed by PC and SPs may be altered due to

changes in the sequence in which the SP admixture is added (Agulló et al., 1999; Aïtcin, 1998; Hallal et

al., 2010). Even when a particular kind of cement and a particular SP is satisfactory with respect to the

specifications of an adopted standard (e.g. ASTM) the resultant PC-SP couple may not be necessarily

compatible from a rheological point of view (Aïtcin, 1998; Dodson and Hayden, 1989). Hence, one

approach to amend this problem is to select the most efficient PC-SP couple between the different brands

of cements and/or SP available in a particular location (Hallal et al., 2010).

In technical literature, rheology studies the laws governing the flow behavior (de Larrard, 1999).

In this sense, the Marsh cone test (MCT) is a “dynamic” indicator of rheological behavior in a particular

PC-SP couple by studying the performance of the grout (Aïtcin, 1998). The Marsh cone method is widely

used as a preliminary test before calibrating particular mixture designs with trial batches or with

quantitative studies by employing more complex instrumentation based on shear stress and plastic

viscosity measurements (Agulló et al., 1999; Aïtcin, 1998; Hallal et al., 2010). This procedure becomes

significant when high-performance concrete is the target, since its low w/b ratios require (usually w/b≤

0.35) the use of compatible PC-SP systems as an initial step (Aïtcin, 1998; Hallal et al., 2010).

In addition to the MCT procedure, in this research the slump cone, air content, unit weight and

flow table test are proposed on the fresh state of cementitious samples. The slump-cone test (ASTM

C143, 2010) is a measure the consistency. The literature (Li, 2011) defines consistency as a property

which describes how easily fresh cementitious mixes flows. The flow table test is described in ASTM

C1437 (2007). In general the flow area of a cementitious material is related to the degree in dispersion of

the cement particles (Chandra and Björnström, 2002); the fresh density or unit weight, as defined in

ASTM C138 (2010), is a measure of compactness (Chandra and Björnström, 2002); and the entrapped air

content (ASTM Standard C138) is a measure of the voids in concretes.

9

1.4.3 Hardened state properties in mortar and concrete samples

At any stage of hydration, the hardened cement paste of concrete or mortar samples consists of

(Illston and Domone, 2001): (1) a residue of unhydrated cement, at the center of the original grains; (2)

the hydrates, primarily calcium silicates hydrates (C-S-H) but also some calcium aluminates,

sulfoaluminates and ferrites; (3) crystals of calcium hydroxide; (4) the unfilled residues of the spaces

between the cement grains, called the capillary pores. The strength of the hardened cement paste derives

from van der Waals type forces between the hydrate fibers. Although these forces are of relatively low

magnitude, the integrated effect over the enormous surface area is considerable.

The compressive strength at a specified age, usually 28 days, measured on standard test

specimens, has traditionally been the criterion of acceptance of concrete. Also, the compressive strength

of concrete is, in most cases, the most suitable and effective tool for the control of concrete quality, even

when the compressive strength is not the most important quality to be controlled in a mix design. On the

other hand, indirect tensile test on concrete such as the splitting tensile test (ASTM C496, 2004) are

carried out in lieu of performing direct tensile test on brittle materials because the samples tend to break

where they are gripped by the testing machine. This is due to contact stresses exceed the fracture strength

of the material, leading to premature failure at the grips (Ashby and Jones, 2005).

1.4.4 Statistical design of experiments (DOE)

The statistical designed experiments which will be referred from now on as DOE are very useful,

because with a minimum of well-planned and developed experimental trials using an specialized software

it is possible to detect the principal and/or interactive effects between the factors under study (Aïtcin and

Mindess, 2011; Akalin et al., 2010; Caldarone, 2009; Senff et al., 2010). In civil engineering applications,

Senff et al. (2010) reported the effects of w/b, nS and SF on rheology, spread on flow table, compressive

strength, water absorption, apparent porosity, unrestrained shrinkage and weight loss of mortars up to 28

days using a 22 factorial design experiment with central points. Specifically, when values of compressive

strength were analyzed, the results showed that the curvature was statistically significant, suggesting that

the compressive strength variation did not follow a linear model. By using a robust statistical treatment

(32 factorial), they showed that the concavity of curve is positive when w/b varies and nS or SF was kept

constant, while negative curve concavities were obtained when nS or SF vary and w/b was kept constant.

In addition, when the above models were tested for lack-of-fit, the result was statistically significant. In a

similar study (Senff et al., 2009), the authors showed that it is possible to adjust the data to a second order

model reducing the range of the w/b ratio, thus the lack-of-fit condition could be successfully overcome.

10

Finally, the authors also could identify the interactive effects between the factors (w/b, SF o nS) which

were explained in detail in the document (Senff et al., 2009).

Ayan et al. (2011) carried out a parameter optimization of compressive strength of steel fiber

reinforced high-strength concrete (SFRHSC) by statistical design of experiments. The results showed that

among several factors affecting the compressive strength, five parameters that maximize all the responses

were: age of testing, binder type, binder amount, curing type and steel fiber volume fraction. In this study

was clearly demonstrated that current factors used in concrete technology, except steel fiber, significantly

contributed to the compressive strength being the age and binder type the most significant contributors.

Akalin et al. (2010) stated that concrete design is a hard and expensive job which takes too much time,

being the selection of an appropriate chemical admixture a very important criterion to achieve the desired

specification for concrete. Therefore, the cited authors proposed statistical mixtures experiments in order

to study the effects of admixture components and admixture dosage on the response variables examined.

In their experiments, the target was to reach an optimum point by obtaining maximum compressive

strength and maximum water reduction for concrete with minimum cost of the admixture. The results

from the statistical treatments were validated in laboratory experiments on mortar and concretes showing

that application of mixture experiments in concrete industry can result in lower product costs, shorter

product design and development time, and product with enhanced field performance.

1.4.5 Artificial neural networks (ANN) simulations

Artificial neural networks simulations (ANNs) are a powerful tool extremely useful in situations

for which the rules are unknown or when response surfaces are highly complex. Hence, the use of ANN is

especially advantageous when traditional predictive mathematical models are not feasible (El-Kassas et

al., 2002). However, the ANN flexibility is linked to one of the most important of their disadvantages:

they are not able to provide explanations and justifications for their answers (El-Kassas et al., 2002).

Therefore, ANN are often called “black box” (Arsenovic´ et al., 2013; Lee and Hsiung, 2009) but a

mathematical treatment on the trained network called sensitivity analysis can clarify considerably the

behavior of the parameters involved (Das and Basudhar, 2006; Guler and Artir, 2007; Lee and Hsiung,

2009; Madandoust et al., 2012).

In civil engineering, ANN approach has been widely used to model and analyze a diversity of

topics, such as soil behavior (Khanlari et al., 2012), torsion in concrete beams (Arslan, 2010), and the

effects of ground-granulated blast furnace slag and calcium nitrite-based corrosion inhibitor on the

chloride ion permeability and the compressive and tensile strength of concrete specimens (Boğa et al.,

11

2013). Also, flexural capacity of fiber-reinforced polymer concrete columns were determined, the ANN

predictions were more satisfactory than approaches used currently in the literature (Köroğlu et al., 2012).

Finally, the split tensile strength and water permeability of concrete containing Fe2O3 nanoparticles was

studied by Nazari et al., (2011) using ANN and genetic programming. According to their results, both

models have strong predicting potential, although ANN exhibited better performance. Nevertheless, the

computational work of the ANNs was more difficult to be carried out.

1.4.6 Weibull statistical analysis

In concrete technology the Weibull statistic has been used in research dealing with failure

analysis and fatigue tests. For example, Man and van Mier (2011) studied the size effect of concrete

subjected to three-point bending using the lattice model. The numerical analyses showed that a size effect

can be approximated with a Weibull model, where the Weibull modulus, depends on the concrete

composition. Also, in Germany Toasa Caiza and Ummenhofer (2011) stated that there are several

methods to determine the Weibull parameters. Nevertheless, they emphasized that there is no consensus

about which is the most appropriate method. The authors presented a general formulation of the

Probability Weighted Moments to estimate the three-parameter Weibull distribution. The study also

contains an application with experimental and simulated data from concrete specimens.

Similarly, a research dealing with the probability of failure of concrete components under

multiaxial stress states was developed in Japan by Li et al. (2003). This work presented a simplified

measurement method for determining the parameters of the governing Weibull distribution. Finally, a

recent study developed by Peiying et al. (2012) where the damage probability in concrete was analyzed

based on detection test and numerical simulation. In their research the authors assumed that concrete

strength obeyed a two parameter Weibull distribution and based on the results of numerical simulation,

the local damage probability analyses were developed.

1.5 General methodology

To estimate the rheological behaviors of PC-SP systems, two simplified methods are widely used

(Aïtcin, 1998): i) the mini-slump test and ii) the Marsh cone test. The present thesis will employ the

Marsh cone test (MCT) due to the dynamic characterization of the systems. Thus, typical water-to-binder

(w/b) ratios for experiments in high-strength concrete will be adopted in the grouts to obtain rheological

parameters indicating an acceptable chemical compatibility between the local Portland cement Type I and

the available chemical admixtures for this thesis. Also, in order to be consistent with Aïtcin (1998) it is

12

important to define a grout as a material different to mortar or concrete, that is, the combination of water,

PC, and mineral admixtures (when applied).

Specifically, in the fresh state the MCT would assist in the design of grouts with several chemical

admixtures to obtain a chemically compatible Portland cement and superplasticizers couples, which

permits to study mineral additions (fly ash, micro-SiO2 and nano-SiO2) in posterior stages. Thus, by using

the MCT, the effects of the following parameters are studied: i) type and dosage of the mineral

admixtures, ii) dosage of polycarboxylate-based superplasticizer, and iii) at two different w/b ratios

typical for high-strength concrete: 0.35 and 0.40.

Since the incorporation of amorphous silica in different size particles (micro and nano) could

have different rheological results, as a second stage the rheological behavior of the best PC-SP selected in

the previous stage will be studied but now with micro and nano-SiO2 additions. This posterior stage aims

to estimate the effects of different dosage levels of SP and the potential w/b ratios to be adopted in the

design of concrete mixes containing SF and/or nS.

Once the chemical couples (PC-SP) and the most adequate w/b ratios are tested and selected in

the fresh state, the next step consists in the design of more complex cementitious mixes, using a series of

fresh tests commonly employed in concrete technology to characterize the PC-SP-SF/nS systems. In this

stage, the experimental program will address the relationship between the fresh and hardened states in

mortar cements, which include superplasticized mineral admixtures in the range of micro and nanometer

scales. In this case, the SP levels will vary in dosage to characterize the behavior of the systems in their

rheological properties and their mechanical compressive strengths in mortar specimens.

Once the rheological analyses between PC-SP-SF/nS have been carried out in the fresh state and

the mortar samples studied in the hardened state by means of compressive strength, the results will be

analyzed to design more complex systems but now using concrete mixes and incorporating Class F FA as

a third amorphous silica product to produce binary, ternary and quaternary mixes: PC-SP, FA-PC-SP, SF-

PC-SP, nS-PC-SP, FA-SF-PC-SP, FA-nS-PC-SP, and FA-SF-nS-PC-SP.

In the hardened state, the mechanical test of the concrete samples will be carried out using both

compressive and tensile strength analyses. Different ages of failure will be conducted to monitor the

strength gained over time, which is an important issue when mineral admixtures are employed. In this

stage, statistical tools such as designs of experiments are employed in order to analyze in a more efficient

way the complex systems formed.

13

The next and final steps include the incorporation of experimental results as input data in

computational models, based on both artificial intelligence and advanced failure analyses based on the

Weibull statistics. The purpose is to understand the effects of the amorphous silica and correlate

theoretical concepts with experimental results.

As a final remark, it is important to clarify a couple of points in the fresh and hardened states. For

the fresh state: even though a particular system (mortar or concrete) would be cast without

superplasticizer (SP) based on its fresh behavior during the earlier minutes; all mortars and concretes in

this thesis will include SPs. The use of SP is based on two main reasons: first, validation in the prediction

of SP content in concrete from the MCT methodology based on grouts. Second, when validation

experiments are not the topic being studied, the environmental conditions and the high reactivity of the

materials employed (SF and nS) could affect retention effects of the fresh state; therefore the casting

process would be disadvantageous for some mixes in comparison with superplasticized-mixes.

Respect to the hardened state, the general objective of this study is related to the high-strength

concrete based on the ACI 363 (1997). The official document (ACI 363-97) states that a concrete is

referred as high strength when it reaches 40 MPa at 28 days in 6x12 inches cylinders. Nevertheless, the

present thesis is based on 2x4 inches cylinders. In order to reduce the geometrical-scale effects in

unpublished trials carried out in the laboratory at the beginning of the experimental program, 6x12 inches

cylinders were cast and the strength values were recorded. For calibration purposes, 2x4 inches cylinders

were cast in the same mixes and the loading rate was changed to obtain similar results as those obtained

using 6x12 inches cylinders. Notice from Chapter III how the strength gain rate of the 2x4 cylinders is in

the middle of the expected ranges from literature when using the larger 6x12 inches molds.

1.6 Scope of the research work

This research is restricted to the study of grouts at w/b=0.35 and 0.40, mortars at w/b=0.35 and

concretes at w/b=0.35 using Portland cement Type I and Polycarboxylate-type superplasticizers.

Nanoparticles of silica and silica fume are employed as mineral admixtures in grouts and mortars,

whereas micro- and nano-particles of silica and fly ash are employed in concrete samples. The principal

idea in the implementation of computational tools in this thesis is in assisting the analyzer in the physical

phenomenon, i.e., in determining and understanding the role of the mineral additions and aging effects on

concrete samples.

14

The activities to be performed as part of this thesis include:

(1) Perform the Marsh cone test method to study the rheological properties in the fresh state of the

cementitious systems. In addition to the Marsh cone test procedure, in this research the slump cone, air

content, unit weight and flow table test are used on the fresh state of cementitious samples.

(2) Perform compression and scanning electron micrographs (SEM) tests in mortar samples at 90

days and compressive and tensile strength measurements on concrete samples at specified ages of 3, 7,

28, 56 and 90 days. The compressive strength of mortar and concrete samples are treated as both an

output research variable and an indicator for the control of concrete quality. On the other hand, the

indirect tensile tests on concrete samples are performed using the splitting tensile test. The measurements

of this test are used only as an output research variable.

(3) Execute factorial experiments on mortar samples at 90 days and response surface analyses

from designed experiments on concrete specimens at 3, 7, 28, 56 and 90 days. These treatments are

carried out since the analyses of the nonlinear effects between the studied variables are more efficient

using statistical tools. Also, the response surface methodology permits determine the optimal dosages of

mineral admixtures in order to gain compression and tension strength in the concrete specimens.

(4) Develop artificial neural networks models for concretes failed in compression and tension

tests at 3, 7, 28, 56 and 90 days. The aim of incorporating artificial neural simulations in this study is to

correlate fresh and hardened concrete properties, as well as, to predict compressive and tensile strength of

concrete samples containing nano-particles of silica along with micro silica and/or fly ash in presence of

polycarboxylate-type superplasticizer as a tool complementary to response surface analyses.

(5) Address experiments in both plain and binary-ternary-quaternary systems in tension test

failures to determine Weibull parameters in concretes containing amorphous silica, especially, nano-

particles of silica as an active ingredient of the concrete samples.

1.7 General organization of the present thesis

The present thesis assesses the rheological and mechanical characterization of PC mixes

containing amorphous-SiO2 in presence of polycarboxylate-type SP. The present thesis is organized in six

chapters, where the first is being discussed in this section, and a summary of Chapter II-VI is presented as

follows:

15

1.7.1 Compatibility analyses and rheological performance between Portland cement Type I

and micro/nano-SiO2 particles in presence of polycarboxylate-type superplasticizers

In Chapter II, five PC-SP systems are analyzed at w/b=0.40 and the best PC-SP couple on

rheological basis using the MCT is selected. Once the best PC-SP is found, it is now cast at w/b=0.35 and

0.40 but adding SF(5,10,15 wt%) and nS(1,2,3 wt%). The rheological properties of these grouts

containing mineral admixtures are discussed.

1.7.2 Fresh state analyses and compressive strength of superplasticized mortar containing

micro/nano-SiO2 particles

In Chapter III, the best PC-SP previously found in Chapter II is now used in the casting of mortar

and concrete specimens at w/b=0.35 containing SF(5,10,15 wt%) and nS(1,2,3 wt%). For mortar

specimens, the saturation dosage (SD) for each system was obtained according to MCT results previously

found in Chapter II. Furthermore, two overdose levels consisting of two times (SD=2) and four times

(SD=4) the SD from the MCT were used to study the compressive behavior of mortar samples containing

mineral admixtures. Statistical experimental designs at w/b=0.35 on mortar samples are conducted to

study the fresh state properties. In the hardened state of the mortar samples, compressive strength and

SEM examinations in the ITZ are carried out. Also, validation of the results of Chapter II from the MCT

in plain and mineral grouts is carried out using concrete mixes based on several trials with the best PC-SP

couple found in Chapter II on mortar samples, but now acting in binary concrete blends of PC-nS(1,2,3

wt%)/SF(5,10,15 wt%) at w/b=0.35. Finally, mechanical tests of these concrete samples are analyzed in

compression and tension conditions. Compressive and tensile strength of concretes containing amorphous

silica analyzed by designed experiments and artificial neural networks simulations

In Chapter IV mechanical and rheological applications of Chapters II and III is carried out using

the best PC-SP (Chapter II) in plain, binary, ternary, and quaternary concrete blends containing PC-SP-

FA/SF/nS at w/b=0.35. This chapter also presents experimental and computational treatments related to

compressive and tensile strength of concrete specimens. At different ages (3, 7, 28, 56 and 90 days), three

different central-composite experimental designs (DOE) are performed. Also, by ANN, the compressive

and tensile strength of the systems are modeled and additional mathematical analyses of the ANNs are

carried out to explain complex mathematical phenomena presented in the DOEs. Failure statistical

analysis on tensile strength of concretes containing amorphous silica

Chapter V investigates the tensile strength of concrete compositions tested in Chapter IV: PC-SP-

FA/SF/nS at w/b=0.35. Splitting tensile failures are carried out to investigate the accuracy of two and

three-parameters Weibull models. Finally, the estimated Weibull parameters are obtained by using

16

different advanced nonlinear methodologies. Summary, conclusions and recommendation for future

studies

In chapter VI, summary, final conclusions and recommendations for future researches are

developed, according to the results obtained on chapters II through V. Finally, the literature cited through

chapters I to V is shown.

17

CHAPTER II

2 COMPATIBILITY ANALYSIS AND RHEOLOGICAL PERFORMANCE BETWEEN

PORTLAND CEMENT TYPE I AND MICRO/NANO-SIO2 PARTICLES IN PRESENCE

OF POLYCARBOXYLATE-TYPE SUPERPLASTICIZER

2.1 Introduction

The present chapter assesses the interaction between a locally-produced PC type I and five

commercial polycarboxylate type SP in grouts containing SF or nS. The experimental procedure

comprises the evaluation of five PC-SP systems analyzed at w/b=0.40 and the best PC-SP couple on

rheological basis using the MCT methodology is selected. Once the best PC-SP couple at w/b=0.40 is

known, the rheological behavior is evaluated at w/b=0.35 and 0.40 but adding 5, 10 and 15 wt% and 1, 2,

and 3 wt% of SF and nS, respectively. Thus, by using the MCT, the effects of the following parameters

were studied: i) type and dosage of the MA, ii) dosage of carboxylate-based SP, and iii) two w/b ratios.

2.2 Theoretical background

The MCT is a “dynamic” indicator of rheological behavior in a particular PC-SP couple by

studying the performance of the paste (Aïtcin, 1998). The MCT is considered to reveal the same trends as

the yield shear stress, by assuming that the cement paste under study follows a Bingham model (Agulló et

al., 1999; Banfill, 1991; de Larrard, 1999; Tattersall, 1991). This becomes relevant when high-

performance concrete is the target, since its low w/b (generally, w/b ≤ 0.35) require the use of compatible

PC-SP systems (Hallal et al., 2010). Nevertheless, this method must be used as a preliminary test prior to

calibrate particular mixture designs incorporating aggregates with field trial batches.

The term compatibility is understood as that which characterizes the PC-SP-SF/nS interaction

reflected in: low flow time (FT) at 5 min, low saturation dosage (SD) and negligible fluidity loss (ΔFT) at

60 min. Where, the difference between the FT at 60 and 5 min is defined as the ΔFT (Hallal et al., 2010).

Plain compatible couples require an FT between 60 and 90 sec in combination with ΔFT tending to zero

and values of SD in the 0.0-1.0 range by mass of solid content (wt%) of SP with respect to the cement

weight (Aïctin, 1998). SD is defined as the point beyond which at 5 min age there is no significant

18

increase in fluidity (Agulló et al., 1999; Aïctin, 1998; Hallal et al., 2010). Furthermore, under ideal

conditions the intersection of the curves describing the rheological behavior reflected in the FT at 5 and

60 min corresponds to the SD (Aïctin, 1998). Nevertheless, when the ideal conditions of the intersection

are not reached, the break point in the curve FT vs. SP dosage at 5 min is commonly accepted as the SD.

Polycarboxylate-type SPs are one of the most employed chemical admixtures for concrete. This is

due to its capacity of producing concrete with: i) high fluidity, ii) high strength, and iii) superior

dispersing force and retention effects even at low w/b (Yamada et al., 2001). However, the dispersing

force of the polycarboxylate-type SPs and its power of retention seem to be affected by some components

of the cement (Hallal et al., 2010; Yamada et al., 2001) or even by variations in the sequence of the

mixing conditions (Agulló et al., 1999; Aïctin, 1998; Hallal et al., 2010; Yamada et al., 2001). Recently,

the reasons for the incompatibility between cement and some SPs have been of interest in concrete

technology (Felekoğlu et al., 2011; Plank, 2009; Plank, 2010; Zingg, 2009).

2.3 Methods used to analyze PC-SP systems

2.3.1 Marsh apparatus

The Marsh funnel viscometer (1.5 L) is shown in Figure 2-1. The calibration of the viscometer

was conducted as part of each experimental scheme following the manufacturer´s instructions.

Figure 2-1. Scheme of the Marsh cone apparatus.

19

2.3.2 Marsh test procedure

During the process 1.2 L of cement paste is employed (Aïctin, 1998). The pastes were mixed in a

1.7 L Hamilton-Beach blender with 550 Watt peak-power motor 120V, 60Hz, and 3.5A. Following

literature recommendations (Aïctin, 1998; Ferraris et al., 2001; Helmuth et al., 2006) a blender is used

instead of a Hobart mixer. The sample preparation comprised the following steps (Aïctin, 1998):

Step 1: Record the water temperature before starting the mixing process, as it must range between

20-23 °C in order to represent normal initial hydration conditions. Step 2: Pour the water, SP and nS (if

used) into the jar and start the mixing process during 10 sec. Step 3: Progressively, add the amount of

cement within a time interval not exceeding 2 min. In the case of PC-SP-SF systems, the cement and the

SF were previously mixed by hand in dry conditions for 3 min. Step 4: Stop the mixing process for 15 sec

in order to clean the cement adhered to the jar. Step 5: Mixing For 60 sec and then monitor the

temperature: 20-23 °C. If the temperature is not within the range, the experiment had to be repeated from

step 1. Step 6: Fill the Marsh cone to about 1.4 L, and then proceed to record the time it takes to fill the

1.2 L beaker with grout.

2.4 Results and discussion

2.4.1 Marsh cone test analysis on plain grout mixtures

Table 2-1 summarizes the results obtained from the rheological analysis of the systems. Results

show that SD, FT and ΔFT present important variations among the systems studied even though the same

cement was employed and all five SP employed rely on the latter polymer technology (Rixom and

Mailvaganam, 2002). Table 1.2 (Zapata et al., 2013a) shows the principal properties of the SP used in the

present couples. In general, a poor compatibility was observed in these PC-SP couples. In order to save

efforts, an adequate SP in conjunction with a particular kind of cement must be selected following careful

experiments in laboratory before applying these materials in field and massive conditions.

Table 2-1. Results of saturation dosage and compatibility of the PC-SP systems

Rheological Parameters PC-SP1 PC-SP2 PC-SP3 PC-SP4 PC-SP5

T average (°C) 21.0 21.8 20.2 20.0 20.0

SD (wt% of cementitious) 0.60 0.80 0.60 1.40 ----

FT at SD (s) 111 83 135 164 ----

ΔFT at SD (s) +116 -9.0 ∞ ∞ ∞

Compatibility criterion NO YES NO NO NO

20

Figure 2-2 and Figure 2-3 present the results of FT from SP1 to SP5 at 5 and 60 min, respectively.

Figure 2-2 shows PC-SP1 system where the SD presents the smallest dosage of this study: 0.6 (wt%) with

FT=111 sec. This same point at 60 min (Figure 2-3) shows a FT=227 sec. Thereby, this system represents

a case of incompatibility due to low capability of dispersion at 1 hour age. PC-SP2 system (Figure 2-2)

demonstrated the best performance between the SPs tested. This couple presented SD=0.8 wt% with

FT≈83 sec and negative ΔFT at the SD. Then, this system can be classified as compatible following the

rules above explained, i.e., a plain compatible couple requires FT between 60 and 90 sec in combination

with ΔFT tending to zero and values of SD in the 0.0-1.0 wt% range (Zapata et al., 2013a).

Table 2-2. Physical and chemical properties of the chemical admixtures

SP1 SP2 SP3* SP4* SP5

Solid content (%) 35 40 30 35 35

Physical state Liquid Liquid Liquid Liquid Liquid

Color Brown Blue Brown Brown Blue

pH 4.4 – 4.9 4.8 – 6.8 8.0 - 10 8.0 - 10 3.0 – 5.0

Specific gravity 1.08 1.08 1.08 1.10 1.08

Chemical

family

Carboxylated

polyether

Carboxylated

polyether

Carboxylated

polyether

Carboxylated

polyether

Polycarboxylate

solution

Chemical

ingredient

Polyacrylate

aqueous solution

Carboxylated

polyether

copolymer

Triethanolamine

Triethanolamine

Aqueous

polycarboxylate

Standard

ASTM C494

types A and F;

ASTM C1017

type I

ASTM C494

types A and F;

ASTM C1017

type I

Not Available

Not Available

ASTM C494

types A and F

PC-SP3 couple presents SD=0.6 wt% in conjunction with a stable behavior through the

experimental range (Figure 2-2). However, Figure 2-3 shows that values of FT at SD as well as FT at

SP=0.4 and SP=0.8 wt% the grout did not flow through the MCT. Hence, this system is incompatible due

to its poor fluidity at the SD. PC-SP4 exhibit SP=1.4 wt% with FT=164 sec at SD. This system has values

of FT and SD higher than found in the literature for plain systems. PC-SP5 did not present a defined point

of SD, that is, this couple presents an erratic behavior typical in incompatible systems. In addition, this

couple did not exhibit flow at 60 min (Figure 2-3). Thereby, both PC-SP4 and PC-SP5 systems are

incompatibles because they did not satisfy any of the condition for PC-SP couples (Agulló et al., 1999;

Aïtcin, 1998; Hallal et al., 2010). Finally, the case of PC-SP4 and PC-SP5 systems may be interpreted as

a chemical incompatibility and it is possible to argue that the cement particles were not efficiently

dispersed (Zapata et al., 2013a).

21

Figure 2-2. Flow time as a function of SP-dosage at 5 min.

Figure 2-3. Flow time as a function of SP-dosage at 60 min.

50

150

250

350

450

550

650

750

850

950

0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2 2,4 2,6

FT

(s)

SP (wt%)

SP1 SP2 SP3 SP4 SP5

50

250

450

650

850

1050

1250

1450

1650

0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2 2,4 2,6

FT

(s)

SP (wt%)

SP1 SP2 SP3 SP5

22

With the exception of PC-SP2 system, it is possible to argue that the other cement and the

chemical admixtures are not compatible to be adopted in concrete mixture designs. In these particular

cases the SPs could not prevent the cement particles reaction with water and hydration products were

formed. There are several possible parameters involved, for example, the SP compositions and physical-

chemical properties such as fineness of the cement grains and C3A content (Table 1-1).

It is important to note the active chemical ingredient of the SP4 is comparable to that of SP3

(Table 2-2), nevertheless only the SP3 showed experimental points at 60 min, that is, SP4 did not flow at

1 hour age. This observation reveals the high chemical sensitive of the PC-SP couples in concrete designs.

The PC-SP1, PC-SP2 and PC-SP5 systems showed that in high SP-dosages tended to reduce the paste

fluidity (Figure 2-2. Flow time as a function of SP-dosage at 5 minand Figure 2-3. Flow time as a

function of SP-dosage at 60 min). The present results are in agreement with those of other works (Agulló

et al., 1999; Hallal et al., 2010;) who found that some systems are prone to suffer negative effects caused

by excessive amount of SP dosage. In general, systems like SP1, SP3, SP4 and SP5 are difficult to

improve from the rheological point of view by using economical solutions (Zapata et al., 2013a).

2.4.2 Marsh cone test analysis on PC-SP2-SF-0.35 system

Once the most satisfactory PC-SP couple had been identified, the following analysis was

performed at w/b of 0.35 by using SP2 as chemical admixture and SF as MA. Figure 2-4 and Figure 2-5

show the rheological behavior of the system at 5 and 60 min, respectively (Zapata et al., 2011). This

system will be designated hereafter as PC-SP2-SF-0.35. Figure 2-4 reveals a high FT=1340 sec at SP=0.4

wt%, which was developed by the system with SF=5 wt%. The rheological behavior in this particular

point (SF=5 wt%) has been found troubled by several investigators (Hallal et al., 2010; Nehdi and

Mindess, 1998) because high dosage of SP is required. In this study this may be explained as follows: ii)

the packing density of the materials, particularly at SF5 wt% replacement level, on which the granular

particles presented the worst packing between them, ii) It is known that at low w/b ratios the aluminates

phases are highly reactive (Chandra and Björnström, 2002) however, the presence of gypsum is expected

to suppress the reactivity of these phases (Mehta and Monteiro, 2003). For some reason the low MA

concentrations tended to accelerate the solubility of the aluminates phases, which permit that the anionic

SP molecules were more likely adsorbing on these phases. In addition, the vacancy gypsum molecules

tend to accelerate the C3S hydration. Note that in this particular research the cement used (Table 1-1.

Physical-chemical and mineralogical characteristics of the cement) has a high value of C3A+C4AF, which

23

could worsen the situation (Zapata et al., 2013b). However, more specialized studies are required, such as,

Z-potential measurements in order to validate this hypothesis.

Figure 2-4. Flow time as a function of SP2-dosage at 5 min (w/b=0.35).


0

200

400

600

800

1000

1200

1400

1600

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)

PC SF = 5 wt% SF = 10 wt% SF = 15 wt%

0

200

400

600

800

1000

1200

1400

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)

PC SF = 5 wt% SF = 10 wt% SF = 15 wt%

24

At large SP dosages, the curve exhibits a satisfactory and constant behavior along the

experimental range (Figure 2-4). At 60 min, like at 5 min in Figure 2-4 the same troubled point (SP=0.4

and SF=5 wt%) presented an extreme value FT=1998 sec which is not shown in Figure 2-5 due to scale

reasons. In general, at w/b=0.35 and at the SD, the presence of the MA improved the FT of the PC-SP2

couple, with respect to the value obtained in the plain condition. Nevertheless, the following observations

must be taken into account: in Table 2-1. Results of saturation dosage and compatibility of the PC-SP

systems it is possible to observe that SF addition only improved the FT at 5 min, but the ΔFT is a relative

measure, therefore care should be put. At SF=5.0 wt% the SD is increased from 0.7 to 1.0 (wt%) with

respect to the plain case and the ΔFT reached the most critical “relative” value (+12.0) between the PC-

SP2-SF-0.35 systems (Zapata et al., 2013a).

2.4.3 Marsh cone test analysis on PC-SP2-SF-0.40 system

Figure 2-6 and Figure 2-7 display the rheological behavior of the PC-SP2-SF-0.40 systems at 5

and 60 min, respectively. In general, conversely to PC-SP2-SF-0.35 systems, these couples tended to be

in the SD improved by the MA. As in PC-SP2-SF-0.35, the FT is very long in the PC-SP2-SF5 system at

5 and 60 min (Figure 2-4 and Figure 2-7). In Table 2-1 (Zapata et al., 2013b), the qualitative description

is based taking into account simultaneously parameters such as FT, ΔFT and SD which define the

compatibility of a system, as explained above. With regard to FT it is important to notice that there is not

a unique numerical criterion of the MCT when MA is added. Then, the criterion employed was based on

the times for plain systems reported in the literature as cited earlier (Aïtcin, 1998; Hallal et al., 2010).


0

50

100

150

200

250

300

350

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)

PC SF = 5 wt% SF = 10 wt% SF = 15 wt%

25


All eight systems analyzed presented acceptable values of SD ranging from 0.40 to 1.0 (wt%).

Also, the PC-SP2-SF5-0.35 system showed high ΔFT=+12 sec, and the PC-SP2-SF15-0.40 system

showed the highest ΔFT of +35 sec. Thus, the compatibility criterion for the eight systems was only

successful for three of them, namely: SF = 0.0, 5.0 and 10.0 (wt%) only at w/b=0.40. The other systems

were found as incompatible applying the conventional criteria from the MCT without MA (Table 2-3).

With the exception of point SF=5 wt% at w/b=0.35, Table 2-3 shows how the addition of SF allowed

smaller both FT values at 5 min and SD values (Zapata et al., 2013a).

Above behavior counteracts other works (Agulló et al., 1999; Zenati et al., 2009), where the

addition of SF led to an increase in the FT (Zapata et al., 2011). In that literature, the results were

attributed to the high fineness of the MA, which caused an increment on the water requirement. In the

present study, the improvement in FT as SF content increases is attributed to the gradation in the packing

density of the granular phase. It occurs as a result of the finest SF particles, as long as the SP is present to

avoid earlier chemical reactions, between the cement products and the SF particles (Zapata et al., 2013b).

0

50

100

150

200

250

300

350

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)

PC SF = 5 wt% SF = 10 wt% SF = 15 wt%

26

Table 2-3. Rheological parameters in PC-SP2-SF systems at w/b=0.35 and 0.40

w/b

SF

(wt%)

SD

(wt%)

FT

(s)

ΔFT

(s)

Observation

[High value]

Compatibility

[Qualitative]

0.35

0.0 0.7 380 -42.0 FT NO

5.0 1.0 (43%) 298 (22%) +12.0 FT - ΔFT NO

10.0 0.7 (0.0%) 304 (20%) -14.0 FT NO

15.0 0.7 (0.0%) 173 (55%) -16.0 FT NO

0.40

0.0 1.0 83 -9.0 ----- YES

5.0 0.7 (43%) 94 (13%) -5.0 ----- YES

10.0 0.4 (60%) 74 (11%) +3.0 ----- YES

15.0 0.4 (60%) 81 (2 %) +35.0 ΔFT NO

2.4.4 Marsh cone test analysis on PC-SP2-nS-0.35 system

Figure 2-8 reveals that the fluidity of the grouts keeps close values for nS=1 wt% (N1) and nS=2

wt% (N2) samples, being N2 more fluid than N1 samples; whereas nS=3 wt% (N3) samples exhibited

longer FT values than both N1 and N2. Also, CO samples presented the poorest rheological behavior. On

the other hand, the fluidity at 60 min (Figure 2-9) shows similar trend as FT at 5 min, that is, one group is

formed by the behaviors of N1 and N2, and a second group is formed by N3 and CO samples. These

results are unexpected because additions of nS, which have an extremely high surface area compared to

cement particles, are expected to increase the FT and ΔFT at long time even in the SP presence. It is

argued that this beneficial effect is caused by an improvement in the packing density of the grouts.

Nevertheless, after nS=2 wt% the reaction of the nanoparticles is evident and the FT and ΔFT suffered a

detrimental effect (Figure 2-8 and Figure 2-9) (Zapata et al., 2013b).

Figure 2-8. Flow time for nS systems as a function of SP2-dosage at 5 min (w/b=0.35).

0

100

200

300

400

500

600

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)

Plain nS = 1 wt% nS = 2 wt% nS = 3 wt%

27

Figure 2-9. Flow time for nS systems as a function of SP2-dosage at 60 min (w/b=0.35).

2.4.5 Marsh cone test analysis on PC-SP2-nS-0.40 system

Figure 2-10 and Figure 2-11 display the rheological behavior of the PC-SP2-nS-0.40 systems at 5

and 60 min, respectively. Compared to PC-SP2-nS-0.35 systems, at 5 min age N1 and N2 suffered an

increase in FT whereas CO samples improved its fluidity. In a similar fashion, the fluidity loss at this

specific w/b ratio had a beneficial effect only for the N3 and CO samples. These results seem to exhibit a

detriment on the rheological properties in N1 and N2 samples as the w/b ratio increased from 0.35 to 0.40;

while the result was exactly the opposite for CO and N3. In fact, as presented in Table 2-4, the amounts of

SP increased as the w/b ratio increased. These rheological results suggest a complex behavior in PC-SP-

N1/N2 systems, because a dilution effect is expected to keep away the cement and nS particles and their

subsequent interactions (Zapata et al., 2013a).

Table 2-4. Rheological parameters in PC-SP2-nS systems at w/b=0.35 and 0.40

w/b

nS

(wt%)

SD

(wt%)

FT

(s)

ΔFT

(s)

Observation

[High value]

Compatibility

[Qualitative]

0.35

0.0 0.7 380 -42.0 FT NO

1.0 1.6 (129%) 161 (58%) -31 SD - FT NO

2.0 0.7 (0.0%) 134 (65%) -16 FT NO

3.0 1.0 (43%) 269 (29%) +70 FT - ΔFT NO

0.40

0.0 1.0 83 -9.0 ----- YES

1.0 1.6 (60%) 207 (149%) -7 FT NO

2.0 1.0 (0.0%) 207 (149%) -5 FT NO

3.0 1.0 (0.0%) 199 (140%) +18 FT - ΔFT NO

0

200

400

600

800

1000

1200

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)


28

At w/b=0.40 for low nS replacements the FT increased compared to w/b=0.35; that is, at higher

w/b ratio, PC-SP-N1/N2 systems showed a decreased in the rheological behavior. Nevertheless, N3 and

CO samples were in agreement conforming to the dilution effect (Figure 2-8 and Figure 2-10), that is, the

FT decreased. This phenomenon is attributed to deviation from the linear Bingham behavior induced by

changes of the plastic viscosity (Zapata et al., 2013a). This behavior could suggest that MCT in nS

systems captured effects not only from the yield stress, but also interactions from the liquid phase. In

addition, it is important to note that for nS systems at both 5 and 60 min age after SP=1.0 wt% the FT of

the systems appeared to converge to a unique value independent of the nS replacement (Figure 2-10 and

Figure 2-11). Since this particular behavior was not observed at w/b=0.35 it is attributed to dilution

effects. This interesting behavior was also reported by Hallal et al. (2010) in experiments with blended

cements on the MCT when the w/b ratios were changed between 0.35, 0.40 and 0.45.

Figure 2-10. Flow time for nS systems as a function of SP2 dosage at 5 min (w/b = 0.40).

0

50

100

150

200

250

300

350

400

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)


29

Figure 2-11. Flow time for nS systems as a function of SP2-dosage at 60 min (w/b = 0.40).

2.4.6 Marsh cone test: effects of the water-binder ratio

For control grout mixtures, the FT increased with a decrease in the w/b ratio from 0.40 to 0.35, as

expected due to water reduction. Observations of the FT compared to the controls reveal that SF additions

could improve the fresh properties at both w/b ratios, while nS additions only at w/b=0.35. This behavior

contrasts with plain conditions. The better flow rates are expected, because dilution tends to resemble an

ideally Newtonian fluid with respect to its viscosity. This suggests a nonlinear nature of the rheological

behavior in complex systems such as PC-SP-nS (Zapata et al., 2013b).

The SD for each system was considered as the lowest FT value obtained at 5 min. The SD are

similar to those of the plain condition for nS=2 and nS=3 wt% at w/b=0.35. Conversely, the highest value

of 1.6% was obtained in nS=1.0 wt% (Table 2-4) for both w/b ratios. PC-SP-MA couples with low

mineral contents consumed larger amounts of SP (Table 2-3 and Table 2-4)(Nehdi et al., 1998). Also, it is

shown (Table 2-4) that due to the high nS-surface reactivity, more SP is required compared to SF particles

(Senff et al., 2010). With respect to the superplasticized control systems, it should be noted that besides

the specific surface area of the nS, at nS=1 and 2 wt%, the FT values were not increased when nS

contents were raised neither at w/b=0.35 nor at w/b=0.40. This result differs with other researches (Agulló

et al., 1999; Zenati et al., 2009) for which both parameters the SD and/or the FT were increased because

of MA additions (Zapata et al., 2013b).

0

100

200

300

400

500

600

700

800

900

1000

0,4 0,7 1,0 1,3 1,6 1,9 2,2 2,5

FT

(s)

SP (wt%)


30

In mix designs, behaviors such as those listed above are attributed to different interactions

between the raw materials, the PC, and chemical configuration of the SP employed. Consequently, there

is a very complex chemical interaction in the PC-SP-MA systems. Moreover, due to structural

instabilities in the materials employed and proportions used, variations of the nS in the nucleation and

interaction with Ca(OH)2 crystals at early and later ages are expected (Zapata et al., 2013b). Eqs. (2.1)-

(2.2) show the principal reactions conducted in this matter. Also, recent literature reported that more rapid

hydration at early age of cement in the presence of nS has not yet been established (Ltifi et al., 2011).

Cement reaction: C3S + H2O → C-S-H + Ca(OH)2 (2.1)

Pozzolanic reaction: Ca(OH)2 + Pozzolan + H2O → C-S-H (2.2)

2.4.7 Marsh cone test: effects of the mineral admixture

Even though at w/b=0.35, both MA grouts were diagnosed as incompatibles (Table 2-3 and Table

2-4), the behavior of the nS-grouts was better than SF-grouts, except for ΔFT at nS=3 wt%. On the other

hand, at w/b=0.40 the opposite trend was obtained, that is, the FTs for SF systems were less than the FTs

for nS systems. Note that in nS-systems at an early age (i.e., 5 min.), the FT at w/b=0.35 performed better

than at w/b=0.40 (except N3). Contrarily, at w/b=0.40 the adsorption of the SP efficiently worked at a

later age (i.e., 60 min in N3). Then, taking into account the behavior of the nS in the MCT, it is possible to

argue that under saturation levels of SP in the pore solution and low MA replacements levels (nS≤ 2

wt%), nS-grouts perform better than under SP dilution conditions. But at high levels of replacements

(N3), the performance is better under SP dilution rather than in SP saturation conditions (Zapata et al.,

2013b).

2.5 Chapter final remarks

The purpose of this chapter was to analyze PC-SP systems at w/b=0.40 and the best PC-SP

couple on rheological basis using the MCT is selected. Then, the best PC-SP was cast at w/b=0.35 and

0.40 but adding micro-SiO2 and nano-SiO2. The principal results can be summarized as follows:

The PC-SP1, PC-SP2 and PC-SP5 systems showed that high SP-dosages tend to reduce the paste

fluidity. These results confirm that some systems are prone to suffer negative effects caused by

excessive amount of SP dosage.

31

Among the five chemical admixtures employed, only the PC-SP2 couple presents a compatibility

case with acceptable saturation dosage, low flow time at 5 min and negative fluidity loss.

The MCT measurements show that saturation dosage, flow time and loss of fluidity exhibited a

nonlinear behavior in grouts with micro- and nano-SiO2 particles and chemical additions, as when

compared to the control samples.

The highest values of saturation dosages were obtained at the lowest levels of the micro- and

nano-SiO2 additions. This was found independently of either the type of mineral admixture or the

w/b ratio.

The flow time at early age (5 min) improved in nS-additions at w/b=0.35, reaching values about

65% of the control case. The nS-additions at w/b=0.40 exhibited an increase on the flow time

about 150% respective to the control case. Also, the loss of fluidity was detrimental at both w/b

ratios; it tends to cause positive values with an increase in the mineral addition levels.

The results obtained here suggest that under superplasticized conditions nS-grouts improved its

rheological behavior at low both w/b ratios and replacements levels, while high replacements

levels of nS tend to exhibit better fluidity at high w/b ratios.

32

CHAPTER III

3 FRESH STATE ANALYSIS AND MECHANICAL STRENGTH ON

SUPERPLASTICIZED MICRO/NANO-SiO2 SYSTEMS

3.1 Introduction

This chapter studies mortar samples cast with the best PC-SP couple found on grouts in Chapter

II. The program addresses the relationship between the fresh and hardened states in mortar cements,

which include MA in the range of micro and nanometer scales and SP in diverse dosages. The mortar

samples are designed with SP dosage obtained from the MCT in Chapter II and two over-dosages to

investigate possible improvements in the fresh and/or hardened states. Factorial experimental designs at

w/b=0.35 are carried out on mortar samples to understand the relationship between the variables in the

fresh state: flow area, unit weight and air content. In the hardened state, compressive strength and SEM

analysis are developed in the micro/nano-SiO2-systems to obtain mechanical and microstructural

information of the mortars. Furthermore, at the end of this chapter using concrete mixes validation of the

MCT results from Chapter II and validation of the mortar analysis developed in this chapter are carried

out. These concretes are based on several trials with the best PC-SP couple from Chapter II cast in binary

blends: PC-nS(1,2,3 wt%)/SF(5,10,15 wt%) at w/b=0.35. Finally, mechanical tests of the concrete

specimens are analyzed in compression and tension conditions.


Currently, the extended use of SP improves the workability of cementitious mixtures.

Superplasticizers are adsorbed onto the surface in order to deflocculate cement particles, which release

trapped water from cement flocks (Chandra and Björnström, 2002). Furthermore, it is known that mixes

containing silica as cement replacement increase the strength due to a pozzolanic and filler effect

(Siddique and Khan, 2011). However, the compaction necessary to produce a mixture as homogeneous as

possible is directly related to its rheological behavior, which depends on the chemical compatibility

between the materials. In fact, the presence of MA in conjunction with SP additions affects the

workability in the fresh state of grouts and concretes (Chandra and Björnström, 2002).

33

3.3 Proportions, casting and testing for cementitious samples

3.3.1 Mortar samples: proportions, casting and testing

Mortar samples were prepared in a 5 L Hobart with two speeds (120 and 60 rpm). The total

mixing time was fixed to 5 min. Mortars were prepared where water, SP and nS (if used) were mixed for

1.5 min at 120 rpm. Fine aggregate, cement and SF (if used) were added to the mixer for 2 min at 60 rpm.

The process was followed by addition of previously mixed water and SP. Thereafter, the materials were

mixed for 1.5 min at 120 rpm. The formwork removal occurred 24 h after casting. The samples were

cured in limewater at 23-25 °C. In the mortar samples the compressive tests were conducted on standard

50x50 mm cubes at 90-days using a 3000 kN Forney universal testing machine in load-controlled (0.35

MPa/s) (ASTM C109, 2008). Fixed 3:1 solid content of sand and cementitious materials in mortars at

w/b=0.35 were used. The fineness modulus of the sand was 3.0. The SD for each system was obtained

according to MCT results (Chapter II). Furthermore, two overdose levels consisting of two times (SD=2)

and four times (SD=4) the SD were used to study the compressive behavior of MA. Table 3-1 and Table

3-2 show the rheological parameters and material proportions used, respectively (Zapata et al., 2013b).

Table 3-1. MCT parameters in PC-SP (SD=1) at w/b=0.35 and 0.40

Grout

mixture

Addition

(wt%)

Sat. dosage

(SD)(wt%)

Flow time:

FT(s)

Fluidity loss:

ΔFT (s)

Observation:

[High value]

Compatibility

[Criterion]

w/b

0.35

w/b

0.40

w/b

0.35

w/b

0.40

w/b

0.35

w/b

0.40

w/b

0.35

w/b

0.40

w/b

0.35

w/b

0.40

plain 0.0 0.7 1.0 380 83 -42 -9 FT ---- NO YES

SF

5.0 1.0 0.7 298 94 +12 -5 FT-ΔFT ---- NO YES

10.0 0.7 0.4 304 74 -14 +3 FT ---- NO YES

15.0 0.7 0.4 173 81 -16 +35 FT ΔFT NO NO

nS

1.0 1.6 1.6 161 207 -31 -7 SD-FT FT NO NO

2.0 0.7 1.0 134 207 -16 -5 FT FT NO NO

3.0 1.0 1.0 269 199 +70 +18 FT-ΔFT FT-ΔFT NO NO

The flowability, air content, and fresh density of mortars were tested using three replicates for

different MA and SP additions at w/b=0.35. Flow area was measured at 23 °C by pull-out spread of the

mortar from the adapted mini-slump cone (38.1 mm and 88.9 mm top and bottom diameters, respectively

and 76.2 mm height). The measured spread (F) in mm was the average of two perpendicularly crossing

diameters at 3 min age. The relative flow area (FA) was calculated by using Eq. (3.1) (Chandra and

Björnström, 2002) where the radius at the bottom cone section is ro=44.45 mm

(3.1)

34

Table 3-2. Mixtures proportions for the mortar cubes at w/b=0.35

Mixture

Reference*

Mixture proportions (g)

Water Cement Sand SF nS SP (slurry)

Control A 120.3 354.1 1062.4 ---- ---- 6.0

Control B 116.6 354.1 1062.4 ---- ---- 12.0

Control C 109.1 354.1 1062.4 ---- ---- 24.0

S5A 118.3 335.2 1060.4 17.7 ---- 8.60

S10A 119.6 316.7 1057.1 35.5 ---- 6.0

S15A 119.2 298.3 1055.1 52.7 ---- 6.0

n1A 111.8 349.9 1062.5 ---- 7.0 13.7

n2A 113.0 346.4 1061.4 ---- 6.0 6.0

n3A 107.9 342.8 1060.2 ---- 21.2 8.60

S5B 113.0 335.2 1060.4 17.7 ---- 17.2

S10B 116.0 316.7 1057.1 35.5 ---- 12.0

S15B 115.5 298.3 1055.1 52.7 ---- 11.9

n1B 103.3 349.9 1062.5 ---- 7.0 27.5

n2B 109.3 346.4 1061.4 ---- 6.0 12.0

n3B 102.6 342.8 1060.2 ---- 21.2 17.2

S5C 102.4 335.2 1060.4 17.7 ---- 34.3

S10C 108.6 316.7 1057.1 35.5 ---- 24.0

S15C 108.2 298.3 1055.1 52.7 ---- 23.8

n1C 86.3 349.9 1062.5 ---- 7.0 54.9

n2C 101.9 346.4 1061.4 ---- 6.0 24.0

n3C 92.0 342.8 1060.2 ---- 21.2 34.3

*S=silica fume, n=nano-SiO2, A=saturation dosage (wt%), B=two times the saturation dosage (wt%) and C=four times the

saturation dosage (wt%).

3.3.2 Concrete samples: proportions, casting and testing

The concrete samples were prepared with an effective w/b ratio of 0.35 and a coarse/fine

aggregate ratio of 1.50. A total cementitious material content of 465 kg/m3 was kept constant. The SP

dosage for each system was obtained from trial batches. The making and curing of the samples proceeded

as per (ASTM C192, 2009). The water contents of the nS (slurry) and the SP were taken into account in

the mix designs. Relative amounts of materials used are shown in Table 3-3 where the first symbols are

CO, N or S, indicating CO for control (or plain) samples, N for nS samples and S for SF-systems. The

second symbol for N and S designs is the amount used, i.e. 1, 2 a 3 wt% of nS and 5, 10 and 15 wt% of

SF. The amounts of nS and SP are expressed in solid contents (Zapata et al., 2013a).

The mechanical tests for concrete samples were carried out according to ASTM procedures for

compressive (ASTM C39, 2011) and tensile (ASTM C496, 2004) strength of the concrete cylinders. The

experimental samples consisted of standard 50x100 mm cylinders (ASTM C470, 2008) cured in

limewater until the day of the test. Three different ages of testing were conducted in this program: 3, 7

and 28 days using a 3000 kN capacity Forney universal test machine operated under load control

conditions.

35

Table 3-3. Mix proportions of the concrete specimens

Mix ID

kg/m3

PC nS SF Fine Coarse SP Water

CO 468.7 ---- ---- 673 1000 9.1 219

N1 463.9 4.8 ---- 665 989 9.9 212

N2 459.2 9.6 ---- 664 989 8.0 213

N3 455.1 14.3 ---- 662 983 10.8 206

S5 445.1 ---- 23.4 664 986 4.2 224

S10 421.9 ---- 46.9 658 980 2.8 226

S15 398.3 ---- 70.3 659 979 3.3 221


3.4.1 Fresh state properties of mortar samples

The results discussed on Chapter II showed how complex it is to analyze the behavior of the

factors included in the present thesis. For this reason in the present chapter the experimental program was

aided by using a statistical approach based on multilevel factorial design: nS (0.0, 1.0, 2.0, 3.0 wt%) and

SD (1.0, 2.0 4.0 times) with three replicates, 36 total random runs in one block. In this thesis section the

selected limits of the factors studied were chosen in accordance to the most typical field ranges and

literature found for SF (5-15 wt%) and nS (1-3 wt%), respectively. The SP levels were chosen based on

the SD from the MCT experiments (Table 3-1) (Zapata et al., 2013a).

The response variables herein were two different kinds, that is, fresh and hardened state. In the

fresh state are: (i) flow area (FA), which is related to the degree in dispersion of the cement particles

(Chandra and Björnström, 2002; Hallal et al., 2010); (ii) fresh density or unit weight (UW in kg/m3)

(ASTM C138, 2010), which represents a measure of compactness (Chandra and Björnström, 2002); and

(iii) entrapped air content (AC in %) (ASTM C138, 2010), which is a measure of the voids in mortars. For

the hardened state, the compressive strength (MPa) represents the response variable. The compressive

strength was measured at long term (90-days) due to the presence of MA. Three measurements of each

response variable are summarized in Table 3-4 and Table 3-5 in order to be employed in the factorial

design (Zapata et al., 2013b).

36

3.4.1.1 Fresh mortar flow area

The statistical analysis showed that SF, nS and SD as main factors, as well as its interactions were

significant with p-value=0.000 with R2=0.9492 and R

2=0.9767 for SF and nS systems, respectively.

Figure 3-1 shows the effect of each variable plotted for constant FA contours (Zapata et al., 2013c).

Table 3-4. Fresh state properties for SF variable

Mortar

sample

SF

(wt%)

SP

(SD-times)

Flow area: FA

Dimensionless

Fresh density: UW

(kg/m3) Air content: AC

(%) CA ---- 1 3.01±0.46 2201±25.76 10.88±1.04

CB ---- 2 3.12±0.12 2260± 5.62 8.50±0.23 CC ---- 4 3.00±0.23 2264± 8.26 8.36±0.33 S5A 5 1 3.47±0.24 2303± 6.99 6.74±0.28

S5B 5 2 7.67±0.50 2321±6.65 5.65±0.27 S5C 5 4 6.84±0.32 2323±11.01 5.16±0.45

S10A 10 1 2.89±0.11 2317±3.28 5.79±0.13 S10B 10 2 6.38±0.78 2325±10.48 5.50±0.43 S10C 10 4 7.67±0.50 2318±6.92 5.37±0.28 S15A 15 1 3.35±0.12 2315±9.60 5.50±0.39 S15B 15 2 6.87±1.28 2329±13.61 4.95±0.56 S15C 15 4 5.05±0.56 2316±8.19 5.07±0.34

Table 3-5. Fresh state properties for nS variable

Mortar

sample

nS

(wt%)

SP

(SD-times)

Flow area: FA

Dimensionless

Fresh density: UW

(kg/m3) Air content: AC

(%) CA ---- 1 3.01±0.46 2201±25.76 10.88±1.04

CB ---- 2 3.12±0.12 2260± 5.62 8.50±0.23 CC ---- 4 3.00±0.23 2264± 8.26 8.36±0.33 n1A 1 1 3.36±0.36 2294±7.90 7.13±0.32

n1B 1 2 6.84±0.32 2300±8.59 6.87±0.35 n1C 1 4 8.52±0.35 2300±13.97 6.14±0.57 n2A 2 1 3.01±0.46 2288±10.67 7.74±0.43 n2B 2 2 3.72±0.25 2305±16.41 6.67±0.66 n2C 2 4 6.53±0.31 2310±14.43 6.47±0.58 n3A 3 1 3.00±0.00 2310±3.69 6.87±0.15 n3B 3 2 3.72±0.50 2314±4.70 6.32±0.19 n3C 3 4 5.47±0.44 2312±17.92 6.39±0.73

The systems at SD=1.0 reached poor values (FA≈3) for all SF/nS levels (Figure 3-1). At SD=2,

all SF-systems improve their behavior (FA≈7), whereas only nS=1 wt% reached high value (FA=7). At

SD=4, the performance of the MA-systems was only improved at specific combinations. FA≈8 was the

best performance for both MA, i.e., SF→6wt% (Figure 3-1a) and nS→1.0 wt% (Figure 3-1b). At MA

lower concentrations, possibly the Ca2+

ion concentration in the pore solution is reduced, thereby reducing

the fluidity of the system. Similarly, at higher concentrations of MA, both the excess of SF or nS and the

presence of SP particles apparently blocked the Ca2+

ions accelerating the hydration reaction.

37

SF (wt%)

SD

(n

-tim

es)

14121086420

4,0

3,5

3,0

2,5

2,0

1,5

1,0

FA = 6-7

FA > 8 FA = 7-8

FA = 6-7

FA = 5-6

FA = 4-5FA = 3-4(a)

nS (wt%)

SD

(n

-tim

es)

3,02,52,01,51,00,50,0

4,0

3,5

3,0

2,5

2,0

1,5

1,0

FA = 3-4

FA < 3

FA = 4-5

5-6

FA =

FA = 6-7

FA = 7-8

FA > 8

(b)

Figure 3-1. Constant contour plot for FA: (a) SF (wt%) and (b) nS (wt%).

3.4.1.2 Unit weight of mortars

The statistical analysis showed that SF, nS and SD as main factors, as well as its interactions were

significant (p-value=0.000) with R2=0.9424 and R

2=0.8960 for SF and nS, respectively. Figure 3-2 shows

each variable plotted as constant contours (Zapata et al., 2013b). UW behavior improves 3% from SD=1

to SD=2 or its statistical equivalent SD=4. At SD=1, SF-systems (SF=10 and 15 wt%) could slightly

enhance their UW-values (2320 kg/m3) with regard to the value found at SF=5 wt% (2300 kg/m

3).

Nevertheless, the performance was substantially improved by 6% with respect to the control case. On the

other hand, in the nS-systems all levels remained constant for all SD variations. The cohesiveness reached

in the mass of nS-systems is the same as those reached in SF-systems (Fig. 2.3a-b). This improvement is

attributed to a better packing density reached due to the filler effect of MA (Rao, 2003).

SF (wt%)

SD

(n

-tim

es)

14121086420

4,0

3,5

3,0

2,5

2,0

1,5

1,0

UW > 2320

UW = 2280-2320

UW = 2240-2280

UW < 2240

(a)

nS (wt%)

SD

(n

-tim

es)

3,02,52,01,51,00,50,0

4,0

3,5

3,0

2,5

2,0

1,5

1,0

UW = 2280-2320

UW = 2240-2280

UW < 2240(b)

Figure 3-2. Constant contour plot for UW (kg/m3): (a) SF (wt%) and (b) nS (wt%).

38

3.4.1.3 Air content of mortars

The ANOVA analysis showed that SF, nS, and SD as main factors, as well as their interaction

were significant at the p-value=0.000. The data variability was well explained with R2=0.9570 and

R2=0.9002 for SF and nS, respectively. Figure 3-3 shows each variable plotted as constant contours.

SF (wt%)

SD

(n

-tim

es)

14121086420

4,0

3,5

3,0

2,5

2,0

1,5

1,0

AC = 6-7

AC = 6-8

AC =8-10

AC > 10

(a)

nS (wt%)

SD

(n

-tim

es)

3,02,52,01,51,00,50,0

4,0

3,5

3,0

2,5

2,0

1,5

1,0

AC = 6-7

AC = 7-8

AC = 8-9

AC = 9-10

AC > 10

(b)

Figure 3-3. Constant contour plot for AC (%): (a) SF (wt%) and (b) nS (wt%).

For all SD values, both MA types showed lower AC-values than their respective control systems

(Figure 3-3). Notice from Figure 3-3 that for SF≥5 wt% and nS≥1 wt%, an increase in SP dosage from

SD=1 to at least SD≈1.5 showed the smallest AC values obtained by these systems. In addition, the effect

of SP increments is especially noticed in the control samples when the values for AC varied up to 30%.

However, these systems reached larger AC values than those observed in MA-systems. The improvement

in AC is attributed to the satisfactory compaction of the mortars as a result of their enhanced fluidity in

the presence of MA into target SP dosages. Although the nS and SF-systems reached the same peak

density value, the SF-systems exhibited an AC lower than the values found in nS-systems with constant

SD (Figure 3-2 and Figure 3-3). This is attributed to better compaction reached by the SF filler effect.

3.4.2 Hardened state properties of mortar samples

3.4.2.1 Mortar compression tests after 90 days

Table 3-6 shows the compressive strength (Sc) of the samples after 90 days (Zapata et al., 2013b).

The ANOVA analysis showed that only SF and nS as main factors were significant. The variability in the

data was explained with R2=0.8689 and R

2=0.6076 for SF and nS systems, respectively. Figure 3-4(a-b)

shows the effect of each variable plotted as constant contours. The results show that mortars containing

both MA developed higher Sc than control systems (Figure 3-4). These results are in agreement with

39

other research involving SF in cementitious systems (Almusallam et al., 2004; Qing et al., 2007; Jalal et

al., 2012; Senff et al., 2010; Shih et al., 2006; Zhang and Islam, 2012). This fact can be attributed to the

pozzolanic reaction, the filler effect, or both actions reached with nS at 1 or 2 wt%, which are statistically

comparable to the SF additions at 5 or 10 wt%.

In the present thesis, Figure 3-4b shows how an increase in SD at the lowest value of nS

replacement reaches the highest Sc. But at higher values of nS content, the compressive strength was

dropped, even though the SP dosage was elevated up to four times with respect to its associated SD. That

weak zone formation induced by poor dispersion of the nS particles is accepted in the present experiment

is noteworthy. It is in agreement with the idea (Ltifi et al., 2011) that large quantities of materials which

have great surface energy will be difficult to be uniformly dispersed as explained on Chapter II (Zapata et

al., 2013b).

Table 3-6. Compressive strength after 90 days

Mortar

sample

SF

(wt%)

SP

(SD-times)

Sc

(MPa)

Mortar

sample

nS

(wt%)

SP

(SD-times)

Sc

(MPa)

CA ---- 1 58.16±4.70 CA ---- 1 58.16±4.70

CB ---- 2 61.55±2.40 CB ---- 2 61.55±2.40 CC ---- 4 60.77±2.12 CC ---- 4 60.77±2.12 S5A 5 1 76.28±3.05 n1A 1 1 70.35±2.07

S5B 5 2 78.82±3.52 n1B 1 2 74.09±3.83 S5C 5 4 73.17±2.46 n1C 1 4 74.18±3.39

S10A 10 1 78.43±1.35 n2A 2 1 72.92±9.80 S10B 10 2 78.97±7.73 n2B 2 2 71.77±3.00 S10C 10 4 77.53±5.39 n2C 2 4 70.02±1.35 S15A 15 1 81.37±4.07 n3A 3 1 71.74±1.43 S15B 15 2 83.56±5.21 n3B 3 2 66.12±10.43 S15C 15 4 86.46±4.87 n3C 3 4 68.06±6.28

SF (wt%)

SD

(n

-tim

es)

14121086420

4,0

3,5

3,0

2,5

2,0

1,5

1,0

Sc = 80-90Sc = 70-80

Sc = 60-70

(a)

nS (wt%)

SD

(n

-tim

es)

3,02,52,01,51,00,50,0

4,0

3,5

3,0

2,5

2,0

1,5

1,0

Sc = 70-75

Sc = 65-70

Sc = 65-70

Sc = 75-80

Sc = 60-65 (b)

Figure 3-4. Contour plots for Sc (MPa): (a) SF (wt%) and (b) nS (wt%).

40

3.4.2.2 Scanning electron microscopy analysis

Secondary electron image analyses (JEOL JSM-510LV) were carried out on post-test cube

specimens in order to observe the properties in the ITZ of PC-SP-MA-systems. Figure 3-5 to Figure 3-7

are micrographs of cement paste samples (SD=1) with: i) plain condition, ii) SF additions, and iii) nS

additions, respectively. The ITZ of CA samples (Figure 3-5) shows massive crystals of

C3A.3CaSO4.32H2O (AFt) and platy-Ca(OH)2. These effects are explained by internal bleeding due to a

high local w/b ratio at the ITZ. The morphology structure in control samples, when compared with MA

systems, is in agreement with the poor properties in the fresh state and with the compressive results

(Figure 3-4) (Zapata et al., 2013b).

Figure 3-6 shows a micrograph of the SF-family (S15A), which was the system that reached the

highest compressive strength. This sample has an ITZ denser than those on the control sample. The ITZ is

denser, because SF particles can fill the space between cement grains, so they can improve the behavior in

two different ways: i) due to packing effect and ii) due to reacting with Ca(OH)2 to form secondary C-S-H

(Senff et al., 2010; Jalal et al., 2012; Mazloom et al., 2004; Li, 2011). Nevertheless, long and slender AFt

and AFm crystals were observed (Zapata et al., 2013b). CH

Figure 3-5. SEM micrographs of CA sample at SD=1, w/b=0.35 and t=90-days.

CH

AFt

41

Figure 3-6. SEM micrographs of S15A sample at SD=1, w/b=0.35 and t=90-days.

Finally, nS-systems (Figure 3-7) showed aggregation of AFm and a vitreous phase (Zapata et al.,

2013b). The latter is associated to the pozzolanic reaction. Nevertheless, this morphology, compared to

that found in plain and SF-systems, exhibited the densest ITZ aspect. Similar results have been found by

other studies (Nazari and Riahi, 2011; Qing et al., 2007).

Figure 3-7. SEM micrographs of n3A sample at SD=1, w/b=0.35 and t=90-days.

AFm

Vitreous

phase

AFm

AFt

C-S-H

Vitreous

phase

42

3.4.3 Fresh concrete properties: validation of the MCT measurements

Table 3-7 lists the test results performed on fresh experimental concrete samples. Fresh properties

of concrete samples were measured by slump, air content, unit weight, and flow table area. The purpose

of the concrete measurements was to validate the conclusions drawn from the MCT obtained in the

cement paste for each type and dosage of MA. The concrete rheological behavior was principally tested

using the standard slump cone test. The initial slump of all mixtures was in the range of 108-130 mm,

except the SF=15 wt% which reported the lowest value of 83 mm. The air content of all mixtures was in

the range of 3.6-5.2 (%), the unit weight was in the 2352-2392 (kg/m3) range, and the flow area was

within the 103 to 150% range. The unit weight for all nS-systems showed steady value very similar to CO

samples. The unit weight for SF-systems exhibited a variable value from 2392 (kg/m3) at SF=5 wt% to

2352 (kg/m3) at SF=15 wt%. This behavior is expected because of the relative high replacement level of

PC being of 15% (cementitious material) as well as the different specific gravities of both materials, i.e.,

SG(SF)=2.1 (Table 1-2) < SG(PC)=2.9 (Table 1-1) (Zapata et al., 2013a).

Table 3-7. Fresh properties of concrete binary mixtures (w/b=0.35)

Mixture

type

Unit

Weight

(kg/m3)

Flow

area

(%)

SP

(wt%)

Air

(%)

t=0 min

slump

(mm)

t=10 min

slump

(mm)

t=30 min

slump

(mm)

t=60 min

slump

(mm)

t=90 min

slump

(mm)

t=120 min

slump

(mm)

CO 2382 138 1.94 4.7 114 111 98 89 44 22

N1 2386 125 2.11 3.8 108 108 102 95 95 89

N2 2382 142 1.71 4.3 114 114 114 105 102 95

N3 2391 108 2.30 4.3 108 108 89 89 32 13

S5 2392 150 0.90 3.6 114 102 83 32 13 0

S10 2370 119 0.60 4.8 130 89 25 0 0 0

S15 2352 103 0.70 5.2 83 32 0 0 0 0

Note from Table 3-3 that, whenever possible, in all designs the quantities of fine/coarse aggregate

were maintained constant. Nevertheless, the unit weight in CO specimens was smaller than those in nS-

systems; this indicates that nS concrete acquired a better cohesion when compared to plain concretes. The

same is observed for the lower SF level of 5 wt% (Table 3-3) (Zapata et al., 2013a). The incorporation of

amorphous silica in different size particle has very different rheological results as shown in Table 3-7.

The SF systems presented SP dosage lower than both CO and nS specimens. Nonetheless, these SF

samples exhibited slump loss higher than both CO and nS systems. The SF=5 wt% (S5) sample was the

SF system with better behavior in slump loss (Table 3-7), because it was the sample that admitted the

highest SP dosage before increase in the initial slump, segregation or excess bleeding were observed.

43

It is important to note that the particular point of SF=5 wt% presented the highest SP requirement

in the developing of the MCT on Chapter II (Table 2.1). This is in agreement with Nehdi et al. (1998) who

found increments in the SP dosage at replacement values of 5% SF. Finally referent to SF, it should be

note that the general graphical behavior from MCT at w/b=0.40 (Table 2-3) also corresponds adequately

to the experimental results found in this chapter. Nevertheless, the numerical results registered from the

MCT (Table 2-3) are written taken only minimum values, hence this fact make some misleading the good

global performance registered in Figure 2-6 and Figure 2-7. As a consequence, in MA systems the use of

MCT methodology seems to be an option to predict concrete behavior, as long as the w/b employed is the

same in both cases: grouts and concretes (Zapata et al., 2013a).

Additions of nS tended to maintain the same SP dosage requirement as the CO samples. This fact

is unexpected because the specific surface areas of both materials are extremely different (Table 1-2). In

fact, the slump loss at nS=1 and nS=2 wt% was better than both CO and SF systems. This fact is

attributed this to a synergistic effect between both enhancements in the packing density and effective

adsorption of the SP. A recent study carried out by Zhang and Islam, (2012) conducted on calorimeter

curves at early age of the hydration reaction demonstrated that nS tend to reduce the calcium and

hydroxyl ion concentration. A variable effect on the SP dosage appears as the nS amount was varied,

which is attributed to the fluidification effect in the packing density for this particular cement and nS

contents for the specific chemical and physical properties of the materials employed. The concrete field

experiments are in accordance with the MCT graphical analysis on Chapter II (Figure 2-8 to Figure 2-11).

Moreover, these results agree with the two different groups formed in the rheological measurements on

the MCT at w/b=0.35 (Figure 2-8 and Figure 2-9) (Zapata et al., 2013a).

It can be concluded that MCT-grout analyses and field concrete trials are not at all in agreement in

their numerical answers. Moreover, this observation is true for both cases (i) when the results are

tabulated as the minimum values obtained from the MCT analysis and (ii) when there exists a break point

in the MCT graphical behavior. Nevertheless, one important feature is that the general graphical behavior

at w/b=0.35 could effectively reflect the experimental trend found in field concrete investigations. For

example, from the MCT curves the fluidity at both 5 min (Figure 2-8) and 60 min (Figure 2-9) showed

that one group is formed by the behaviors of N1 and N2, and a second group is formed by N3 and CO

samples. This agrees with the fresh state experiments carried out on concrete samples (Table 3-7).

Therefore, as in the case for SF, in nS systems the use of MCT seems to be an option to predict the

behavior of concrete mixes, as long as the w/b employed be the same in both cases: grouts and concretes.

44

Finally, considering all those results it is possible conclude that the MCT analysis is an effective

preliminary test to understand the global behavior of couples between PC-SP-nS/SF. However, the

tabulated values must be analyzed cautiously because they can easily lead to erroneous conclusions.

Conversely, here was found that the graphical global behavior at 5 min is a better indication of the field

and/or laboratory experiments on actual concrete samples. On the other hand, the behavior of MCT

method at 60 min at w/b=0.40 did not reflect the findings in concrete specimens carried out at w/b=0.35.

However, for nS systems the graphical behavior at 60 min was almost representative of the concrete

specimens (Fig. 10.2) at w/b=0.35. In part, this statement can be explained by the fact that mixing

conditions of the grout in MCT analysis are not necessarily the same as the mixing conditions of the

concrete, and this latter contains two additional materials (fine and coarse aggregates) which were not

taken into account in the developing of MCT analysis (Zapata et al., 2013a).

3.4.4 Hardened concrete properties

In ¡Error! No se encuentra el origen de la referencia. is summarized the average compressive

nd splitting tensile strength of three specimens at several age of testing. The analyses were performed

using the Fisher Least Significant Difference (LSD) methodology at 5% level. By using LSD

(Montgomery, 2001) the null hypotheses to be tested is as follows

Ho: μi = μj for all i ≠ j (3.1)

Assuming a two-sided alternative, the pair of means μi and μj is declared statistical significantly

different if

|

(3.2)

The term N-a refers to the degrees of freedom, ni and nj are the sample sizes and MSE is the error

mean square. Present procedure consisting in compares the observed difference between each pair of

averages to the corresponding LSD. If Eq. (3.2) is satisfied then, the conclusion is that population means

differ. The results are summarized in Table 3-8 where the letters from “A” to “F” are related to

homogeneous groups within the same age of testing (Zapata et al., 2013a).

45

Table 3-8. Fisher LSD for the difference in compressive and splitting tensile strength

Mixture

type

Compressive strength (MPa) Splitting tensile strength (MPa)

3 days 7 days 28 days 3 days 7 days 28 days

CO 28.8 (A) 31.9 (A) 50.3 (A) 4.3 (A) 5.3 (A) 5.2 (A) N1 27.9 (A) 37.1 (B) 49.7 (A) 3.3 (B) 6.1 (A) 7.0 (B) N2 30.6 (A) 43.5 (C) 53.3 (B) 3.6 (B) 6.8 (A) 6.7 (B) N3 36.7 (B) 54.1 (D) 67.8 (C) 5.2 (A) 6.5 (A) 6.8 (B) S5 37.9 (B) 47.9 (E) 65.2 (D) 5.8 (A) 5.8 (A) 6.6 (B)

S10 26.3 (A) 40.8 (C) 56.2 (E) 4.4 (A) 6.3 (A) 6.4 (B) S15 28.3 (A) 45.1 (C) 60.6 (F) 5.1(A) 5.4 (A) 6.2 (B)

Figure 3-8 shows the behavior in the hardened state of the concrete samples through the time and

between the different mixes. The strength gained at early ages for SF samples was slightly higher than in

nS specimens. This means that the ratio of 3-7 days strength for nS samples ranged from 0.68 to 0.75

whereas for SF-systems it was between 0.63-0.79. In a similar manner, the 7-28 days strength for nS-

systems ranged from 0.75-0.82, whereas for SF-systems was between 0.73-0.74. This latter result is in

agreement with those of Almusallan et al. (2004) who reported a ratio of 7-28 days strength ranged from

0.74 to 0.80 for concrete samples made with SF=10 and 15 wt% at w/b=0.35. In the same research

(Almusallan et al., 2004) a ratio of 7-28 days strength between 0.60 and 0.65 is reported for normal

strength concrete, which perfectly enclosed the ratio herein for control samples of 0.63 (Zapata et al.,

2013a).

Figure 3-8. Compressive and tensile strengths at w/b = 0.35.

CO CO CO N1 N1 N1 N2 N2 N2 N3 N3 N3 S5 S5 S5 S10 S10 S10 S15 S15 S15

CO

CO CO

N1 N2

N3

S5

S10

S15

0

1

2

3

4

5

6

7

8

0

10

20

30

40

50

60

70

80

3-days 7-days 28-days

St

(Mp

a)

Sc

(MP

a)

Lines --> Tension

Bars --> Compression

46

Generally, for all ages the compressive strength improvement was higher in the N3 and S5

samples. As the whole, samples containing MA exhibited higher compressive strength values than CO

mixtures, which agree with research involving nS or other amorphous silica additions in cementitious

systems (Almusallam et al., 2004; Qing et al., 2007; Shih et al., 2006;). Regarding splitting tensile

strength (Figure 3-8), the highest value was reached at 28 days by the N1 samples; compared to CO

samples the strength value increased by 35%. At 28-days the splitting tensile strength was in general

increased for all mixtures as compared to control samples and compared to compressive strength. These

results agree with published literature on the use of nS and SF in tensile strength (Almusallam et al.,

2004; Senff et al., 2010).

The improvements in compressive and splitting tensile strength are attributed to the reaction of

amorphous silica with Ca(OH)2 liberated during the cement hydration, then formation of secondary C-S-

H is expected. It is well known (Aïtcin, 1998; Almusallam et al., 2004; Mehta and Monteiro, 2003; Zhang

and Islam, 2012) that formation of secondary C-S-H helps to fill up the pores in concrete, which leads to

denser cement matrix and ITZs. Finally, it is important to be noted that the tensile strength of concrete is

one of the parameters which are used as indicator to predict the potential for an increase in the useful-

service life of the concrete structures (Almusallam et al., 2004). Then, results here presented revealed that

additions of nS in small amounts (up to 3 wt%) are compared to additions of relative high amounts of SF

(up to 15 wt%) (Zapata et al., 2013a).


This chapter presented mechanical and rheological validation of experiments explained in

Chapter II using binary mortar and concrete blends of PC-nS(1,2,3 wt%)/SF(5,10,15 wt%) at w/b=0.35.

The principal results can be summarized as follows:

The optimal unit weights and air contents reached in the nS and SF systems show similar values,

but the SF systems exhibited the best values for these parameters. This is attributed to an uneven

compaction of the mortar due to poor fluidity associated with the high surface reaction of the nS

particles. Even so, the performance of both parameters is better than in the control case.

Flow area, fresh density and air content in the fresh state of mortar samples exhibited a nonlinear

dependence with respect to the replacement levels of mineral and chemical admixtures. In all

systems a unit weight increase was in agreement with a decrease in the air content. Lower values

47

of unit weight and higher values of air content were found in control samples than in samples

with mineral additions. Moreover, better fluidity and hence, better mortar compactions were

attained with the micro and nano SiO2 additions.

The micro and nano SiO2 additions in combination with the appropriate use of superplasticizers

could increase the compressive strength of the mortar systems. The maximum strength in nS-

system was reached at 1.0 wt%, whereas in SF-systems, it was at a level of replacement in the

order of 15 wt%. In addition, the highest compressive strength was obtained in SF-systems.

Nevertheless, evidence from SEM analysis showed that improvement in compressive strength of

SF-systems was primarily by filler effect, whereas in nS-systems it was due to both densification

and filler effect of the ITZ.

Compressive and splitting tensile strength improved rather significantly in all concrete mixtures

containing amorphous silica. In particular, the compressive strength improvement was higher in

the samples containing SF=5 wt%. On the other hand, the nS=3 wt% mixture had the highest

compressive strength, 35% higher than the control samples. Also, the highest splitting tensile

strength was measured at 28 days in all the nS samples; this again represented an increase of 35%

with respect to the control samples.

Based on the results of the current study it is possible to conclude that the MCT method must be

interpreted carefully when mineral additions are applied in concrete mixes. In the present

research, the true behavior found in the fresh concrete tests was effectively anticipated by the

graphical trend observed in the MCT analysis. Nevertheless, the numerical results registered from

neither the minimum values nor the break points in the curves effectively reflected the SP

amounts between grouts and concrete samples.

MCT analysis must be carried out in conjunction with trial batches, even though performing trial

batches is time, material and energy consuming. But it is based on the fact that mixing conditions

of the grout in MCT analysis are not necessary the same as the mixing conditions of the concrete.

Also, concrete compared with grouts contains two additional materials (fine and coarse

aggregate) which are not taking into account in the developing of MCT analysis.

48

CHAPTER IV

4 NONLINEAR STATISTICAL ANALYSIS IN COMPRESSIVE AND TENSILE

STRENGTHS OF CONCRETE CONTAINING AMORPHOUS SILICA

4.1 Introduction

This chapter presents experimental and computational findings related to the compressive and

tensile strength of concrete containing nS, SF, FA, and polycarboxylate-SP. Three central-composite

experimental designs were performed at different days of aging, to assess the role of the variables. Also,

ANNs were implemented to assist in understanding the complex nature of the systems. Finally,

mathematical sensitivity analyses on the ANN-simulations are implemented to quantify the influence of

the input variables on the model´s response.


Statistically based experimental design techniques are particularly useful in the engineering world

for solving many important and complex problems. This is because most processes can be described in

terms of several controllable variables, such as temperature, pressure, rate, etc. Therefore, by using

designed experiments, engineers can determine which subset of the process variables has the greatest

influence on process performance. The statistical methods used in design techniques aimed in the

mathematical optimization processes. It is very common that the final objective of any particular

experiment is optimization, that is, to determine which levels of the critical variables result in the best

process performance either maximum or minimum. In this sense, statistically designed experiments

permit efficiency and economy in the experimental process, and the use of statistical methods when

adequately employed in examining the data results in scientific objectivity when drawing conclusions

(Montgomery and Runger, 2011).

On the other hand, an artificial neural network is a mathematical or computational model that is

inspired by the structure and function of biological neural networks in the human brain. An artificial

neural network consists of a number of nonlinear processing units which act as artificial neurons. These

processing units are connected each other via synaptic weights. In fact, it is by the dynamic behavior of

49

their weights that the artificial neural network can “learn” a task. An artificial neural network is a

powerful and versatile modern computational tool. The high versatility of artificial neural networks comes

from its high capability and learning function. Artificial neural networks have been successfully used in

various applications such as biological, economical, engineering and social fields (Suzuki, 2011).

4.3 Proportions, casting and testing for concrete samples

4.3.1 Concrete mixture proportions and specimen fabrication

All the data presented in this section was obtained from laboratory experiments and concrete

samples were cast in different batches using data from previous chapters. Nevertheless, the raw materials

were the same (Table 1-1 and Table 1-2). All the concrete cylinders were cast, cured (ASTM C192,

2007), and failed in the same way in order to attain comparable results. The coarse-to-fine aggregate ratio

was 1.50. The amount of cementitious materials was 465±5 kg/m3 at w/b=0.35. The concrete constituents

were mixed in a commercial laboratory mixture at two speeds, 120 and 60 rpm. The total mixing time was

fixed at 5 min. The concrete samples were prepared using the same steps in which 50% of the water and

100% of the fine and coarse materials were mixed for 1.5 min at 120 rpm. Cement was mixed in dry

condition with SF (if used) and/or FA (if used), and then this powder mix was added to the mixer for 2

min at 60 rpm. The process was followed by addition of previously mixed remainder water with slurry nS

(if used) and the corresponding SP dosage. Thereafter, the materials were mixed for 1.5 min at 120 rpm.

The water content of the SP was accounted in all the mix designs. The fresh concrete was poured into 50

mm of diameter and 100 mm in height standard cylinders (ASTM C470, 2008) for testing procedures.

After pouring, finishing and previously consolidation was carried out by the rodding method (ASTM

C192, 2008). The formwork removal occurred 24 h after casting. The samples were cured in limewater at

23-25 °C until the prescribed period of failure.

4.3.2 Compressive and splitting tensile strength tests

The mechanical tests were carried out as per the ASTM procedures for compressive (ASTM C39,

2011) and splitting tensile strength (ASTM C496, 2004). Five different ages of testing were conducted in

this research: 3, 7, 28, 56 and 90 days of curing using a 3000 kN Forney universal test machine in load-

controlled setting. The data were obtained from laboratory experiments following ASTM procedures, and

testing conformed to the DOE approach for random experiments. The total number of samples tested was

360 cylinders for each mechanical test i.e., compressive and tensile analysis. Mix proportions and

mechanical strengths results are shown in Table 4-1 (Zapata et al., 2013c).

50

Table 4-1. Concrete proportions, DOE compositions, and mechanical strengths of samples

Mix

compositions

{nS:SF:FA}*

DOE

Compressive and tensile strength (MPa)**

3 days 7 days 28 days 56 days 90 days

{0.0:0.0:0.0} I-II-III 24.37 4.34 31.90 5.31 50.30 5.22 52.84 5.57 54.91 6.96

{3.0:0.0:0.0} I-II-III 36.68 5.23 54.06 6.50 67.84 6.77 70.95 8.98 74.81 8.72

{6.0:0.0:0.0} I-II 30.84 4.52 51.98 6.76 65.13 8.28 70.39 8.79 73.48 7.39

{0.0:0.0:20} I-III 22.90 3.67 29.39 4.69 43.70 6.14 51.51 7.18 54.92 7.22

{0.0:0.0:40} I 13.75 2.73 20.29 3.53 35.62 5.74 43.25 6.62 51.65 5.38

{3.0:0.0:40} I 18.74 3.59 28.99 4.74 40.78 6.14 44.90 6.94 50.46 5.36

{3.0:0.0:20} I-III 27.58 4.49 38.68 4.89 52.70 6.23 53.91 7.20 61.25 7.17

{6.0:0.0:40} I 26.31 4.77 36.00 6.07 46.19 6.29 51.67 6.57 58.53 6.21

{6.0:0.0:20} I 35.01 4.40 45.04 6.21 54.83 6.33 60.13 6.57 62.36 6.54

{0.0:10:0.0} II-III 26.29 4.36 40.84 6.26 56.16 4.86 59.78 5.55 65.42 8.96

{0.0:20:0.0} II 29.02 5.15 45.31 6.70 63.28 6.76 75.09 8.21 75.29 8.77

{3.0:20:0.0} II 31.37 5.07 46.98 6.70 63.36 6.70 68.71 8.28 76.85 8.98

{3.0:10:0.0} II-III 34.94 5.29 47.97 6.35 62.72 6.92 66.96 7.98 70.01 8.79

{6.0:20:0.0} II 36.65 5.73 50.89 6.71 64.67 8.01 71.65 6.92 70.63 8.70

{6.0:10:0.0} II 37.64 5.93 51.50 5.93 60.30 7.81 68.29 7.01 69.78 8.20

{1.5:0.0:10} III 26.96 4.60 37.27 6.29 47.97 6.42 53.67 7.27 55.97 6.87

{0.0:10:20} III 21.08 3.72 34.34 5.74 48.40 7.39 58.74 7.87 61.85 7.87

{0.0:5.0:10} III 28.43 3.99 37.61 5.93 56.99 7.64 63.52 7.23 65.71 7.06

{1.5:5.0:0.0} III 31.71 4.49 44.80 6.89 58.14 8.05 63.83 7.50 63.08 6.91

{1.5:10:10} III 27.10 4.49 39.79 6.16 56.50 8.01 65.44 8.01 68.00 7.49

{1.5:5.0:10} III 26.86 4.88 39.35 6.10 54.57 8.08 61.99 6.99 64.80 7.67

{1.5:5.0:20} III 22.36 4.14 36.56 5.83 51.48 6.00 57.16 6.97 61.97 8.62

{3.0:5.0:10} III 32.67 5.03 47.44 6.60 59.41 6.08 64.09 6.64 68.41 7.76

{3.0:10:20} III 24.96 4.35 39.92 6.32 53.39 7.96 59.74 7.56 65.46 7.79 * Mix proportions are expressed as percentage of cementitious materials. ** The symbols

or

stand for average of three replicates for

compression and tension tests, repectively.

4.4 Development of the DOE and ANN models

Several back-propagation (BP) algorithms were tested in developing the ANN simulations in this

thesis. The BP learning law consists of adjusting the weights and bias values from the output layer toward

the input vector by means of an iterative process (Ince, 2004). Mathematically, the functioning of the nth

neuron in the yth layer is represented by Eq. (4.1), where m is the number of inputs that arrive at a neuron

and the output of the neuron is the target that is being sought (Fig. 4.1) (Zapata et al., 2013c).

(4.1)

51

Figure 4-1. Schematic of a multilayer feed-forward/back-propagation network model.

Finding the optimum number of neurons in the hidden layer, the number of hidden layers, and the

type of transfer function are part of the most complex tasks in ANN simulations (Khanlari et al., 2012).

The training process of an ANN can be regarded as solving a complex nonlinear least-square

mathematical problem with the difference between the actual and simulated outputs acting as the

performance for the problem (He and Li, 2009). In creating an effective network, the training step must be

carefully developed because the error surface can converge to a false minimum or to a true minimum but

very slowly (El-Kassas et al., 2002). The accuracy of the network predictions is strongly related to the

selection of the weights used by the algorithm (Sidhu et al., 2012). Nevertheless, once the optimum

architecture is found, the ANN model is an extremely efficient nonlinear statistical tool for use in complex

problems (Alshihri et al., 2009; Arslan, 2010; El-Kassas et al., 2002; Khanlari et al., 2012; Sidhu et al.,

2012).

Many authors (Arslan, 2010; Ince, 2004; Rafiq et al., 2001; Graham et al., 2006; Ashour and

Alqedra, 2005) widely recommend that data be normalized before training to prevent extreme numerical

values or ranges of any particular parameter from distorting the influence of the other parameters. Hence,

the input and output values were normalized (Eq. 4.2) (Ashour and Alqedra, 2005) in the range of [-1,+1]

before any numerical simulation were conducted.

(4.2)

52

In the normalization function (Eq. 4.2), and are the normalized and un-normalized

values, respectively, of the input/output variables, and and are the variable minimum and

maximum values, respectively, of the dataset under normalization. In this study, multilayer feed-forward

back-propagation neural network is used with a nonlinear logistic sigmoid function (Eq. 4.3) as the

transfer function for the input vector-hidden layer and the identity function as the transfer function for the

hidden layer-output layer. The sigmoid activation function is a continuous function often utilized in

nonlinear problems (Sarıdemir et al., 2009).

(4.3)

The ANN was implemented using scripts in MATLAB®

v. 7.1. During training, the stopping

criterion was set to finish when one of the following was met, i.e., the MSE ≤ 1x10-4

, the gradient value

was less than 1x10-9

, or the iteration was larger than 1000 (Zapata et al., 2013c). In this study, three

statistical criteria were selected to compare the ANN simulations results (Sp) with the laboratory results

(Sm) at training, validation, and testing steps, i.e., the root-mean-square error (RMSE) in MPa (Eq. 4.5),

the coefficient of efficiency (CE) (Eq. 4.6), and the Pearson’s correlation coefficient (r) (Eq. 4.4).

(4.4)

(4.5)

(4.6)

and represent the average of the measured values for mechanical strength (Sc or in St MPa)

from ANN simulations and laboratory experiments, respectively. N is the total number of observations in

training, validation, or testing datasets.

Regard the development of the DOEs, three independent design of experiments were conducted in

the present study for each age of testing (3, 7, 28, 56 and 90 days), referenced hereafter as the following,

i.e., DOE I consisting of nS(0.0-6.0 wt%)-FA(0.0-40.0 wt%), DOE II consisting of nS(0.0-6.0 wt%)-

SF(0.0-20.0 wt%), and DOE III consisting of nS(0.0-3.0 wt%)-SF(0.0-10.0 wt%)-FA(0.0-20.0 wt%). The

DOEs I and II consisted of three replicates with 12 cube points, 3 center points, and 12 axial points with 2

53

factors (nS/SF, nS/FA). DOE III consisted of three replicates with 24 cube points, 3 center points, and 18

axial points with 3 factors (nS/SF/FA). A total of 27 and 45 runs were conducted randomly within a unit

statistical block for DOEs I-II and DOE III, respectively. DOE compositions are shown in Table 4-1 and

the statistical criterion for factor effect rejection was when their p-values were greater than 0.05. The

DOE models were developed in MINITAB®

v. 16 statistical software and STATGRAPHICS®

CENTURION XV of StatPoint Co. statistical software.

A key reason behind the development of the ANN models is related to their potential applicability

in conjunction with DOEs. The major importance lies at the moment of making a decision about the

pertinence of the most common variables employed in concrete technology in the DOE analysis and their

possible relationship with the LOF generally exhibited by some complex cementitious systems. Finally,

the optimized values for the nS, SF and FA variables in tension and compression tests were found by

using the second order model (Eq. 4.7) and the concept of eigenvalues Hessian matrix (Montgomery,

2001) as follows

The general second order regression model in matrix form is given by Eq. (4.7)

or Eq. (4.8) described this model in vector form

Therefore, the analysis of the stationary points is carried out as shown in Eq. (4.9)

where,

54

In this way, the analysis of the sufficient conditions is satisfied through the eigenvalues of the

Hessian matrix as shown in Eq. (4.10)

where n is the number of active variables. The Hessian matrix could be definite positive, definite

negative, nonpositive, nonnegative or neither if the associated eigenvalues are all positive, all negative,

negative and zero, positive and zero or one positive and one negative, respectively. Above conditions

define a single strong minimum, a single strong maximum, either a weak maximum/minimum or no

stationary point and the finally condition refers to a saddle point, respectively.


4.5.1 DOE analysis for compressive strength

Table 4-2 shows the mechanical results from the DOE analysis applied in compression tests. In

this table, the sign associated with the p-values indicates the positive/negative contribution of each

particular term to the strength development. The results show the input variables exhibited through the

time a variety of p-values, Pearson’s values, and linear, interactive, and/or quadratic effects (Zapata et al.,

2013c).

Table 4-2. Statistical results from DOEs in compression tests

Age

(days)

DOE nS SF FA nS.SF nS.FA SF.FA nS.nS SF.SF FA.FA LOF r

3

I 0.00(+) --- 0.00(-) --- 0.08(+) --- 0.08(-) --- 0.01(-) 0.00 0.9341

II 0.00(+) 0.20(+) --- 0.88(+) --- --- 0.01(-) 0.29(-) --- 0.00 0.8174

III 0.00(+) 0.14(-) 0.00(-) 0.08(-) 0.00(-) 0.07(-) 0.00(+) 0.01(-) 0.01(-) 0.00 0.9567

7

I 0.00(+) --- 0.00(-) --- 0.23(-) --- 0.00(-) --- 0.70(-) 0.00 0.9668

II 0.00(+) 0.28(+) --- 0.00(-) --- --- 0.01(-) 0.95(+) --- 0.00 0.8954

III 0.00(+) 0.00(+) 0.00(-) 0.00(-) 0.00(-) 0.28(+) 0.02(+) 0.00(-) 0.78(-) 0.00 0.9661

28

I 0.00(+) --- 0.00(-) --- 0.19(-) --- 0.00(-) --- 0.61(+) 0.00 0.9722

II 0.00(+) 0.08(+) --- 0.00(-) --- --- 0.00(-) 0.04(+) --- 0.00 0.8603

III 0.00(+) 0.00(+) 0.00(-) 0.00(-) 0.02(-) 0.29(+) 0.00(+) 0.00(-) 0.59(-) 0.00 0.9246

56

I 0.00(+) --- 0.00(-) --- 0.10(-) --- 0.40(-) --- 0.80(+) 0.01 0.9100

II 0.00(+) 0.01(+) --- 0.00(-) --- --- 0.21(-) 0.11(+) --- 0.02 0.8099

III 0.00(+) 0.00(+) 0.00(-) 0.04(-) 0.00(-) 0.09(+) 0.23(+) 0.04(-) 0.18(-) 0.01 0.8570

90

I 0.00(+) --- 0.00(-) --- 0.02(-) --- 0.08(-) --- 0.48(+) 0.00 0.9160

II 0.00(+) 0.00(+) --- 0.00(-) --- --- 0.00(-) 0.03(+) --- 0.00 0.9271

III 0.00(+) 0.00(+) 0.00(-) 0.00(-) 0.01(-) 0.27(+) 0.01(+) 0.06(-) 0.15(-) 0.00 0.8872

55

The continuous changing of the surface responses as the concrete aged makes the ANN models

plausible candidates to be employed as an auxiliary nonlinear statistical tool. The continuous changing on

curvature can be seen in Figure 4-2 to Figure 4-6 (Zapata et al., 2013c) for compressive analyses. Also,

the study employing ANN is motivated because in compressive tests all the models showed a LOF of

second-order (Table 4-2); while in tension analysis eleven out of fifteen exhibited the same characteristic

(Table 4-4). Regard compressive analysis, in the development of the second-order polynomial models, the

ANOVA results in Table 4-2 showed that the most important parameters (p-value < 0.05) influencing the

compressive strength at all ages were the linear terms of nS and FA and the interactive term nS·SF. Also,

the quadratic term of the nS variable (nS·nS) was important for most ages, with minor participation of the

quadratic term (SF·SF) of the SF. The quadratic term of FA variable (FA·FA) and the interaction between

the SF and the FA (SF·FA) played a less important role on the strength development in the present study.

Figure 4-2. Compressive strength of concretes at 3 days: (a) for DOE I and (b) for DOE II.


nS (wt%)FA (wt%)

Sc

(MP

a)

(a)

0 1 2 3 4 5 60

1020

3040

12

16

20

24

28

32

36

nS (wt%)SF (wt%)

Sc

(MP

a)

(b)

0 1 2 3 4 5 60

48

1216

20

25

27

29

31

33

35

37

nS (wt%)FA (wt%)

Sc

(MP

a)

(a)

0 1 2 3 4 5 60

1020

3040

19

29

39

49

59

nS (wt%)SF (wt%)

Sc

(MP

a)

(b)

0 1 2 3 4 5 60

48

1216

20

34

38

42

46

50

54

58

56




nS (wt%)FA (wt%)

(a)

Sc

(MP

a)

0 1 2 3 4 5 60

1020

3040

34

44

54

64

74

nS (wt%)SF (wt%)

Sc

(MP

a)

(b)

0 1 2 3 4 5 60

48

1216

20

52

55

58

61

64

67

(a) nS (wt%)FA (wt%)

Sc

(MP

a)

0 1 2 3 4 5 60

1020

3040

42

52

62

72

82

nS (wt%)SF (wt%)

Sc

(MP

a)

(b)

0 1 2 3 4 5 60

48

1216

20

54

58

62

66

70

74


Sc

(MP

a)

0 1 2 3 4 5 60

1020

3040

50

55

60

65

70

75

80

(b) nS (wt%)SF (wt%)

Sc

(MP

a)

0 1 2 3 4 5 60

48

1216

20

56

60

64

68

72

76

80

57

In the present work the statistical results showed that nS particles produced a negative effect on

compressive strength development when combined with the FA, as revealed by the nS·FA interactions (p-

value < 0.05) in Table 4-2. Thus, when the FA replacement is at the highest level, i.e., 40 wt% (DOE I),

the presence of nS either at the highest (nS = 6.0 wt%) or lowest level (nS = 0.0 wt%) is not statistically

significant at early ages (p-value ≥ 0.05). Only at 90 days does this effect become significant with a

negative contribution to strength development. Conversely, at lower FA and nS replacement levels (DOE

III), the interaction effect of these two input variables is effectively significant (p-value < 0.05) at all

ages. Nevertheless, as in the DOE I, the interaction effect is negative on the strength gain (Figure 4-7b to

Figure 4-11b) (Zapata et al., 2013c).

In general terms, it can be noted that, based in the p-value, the most influential linear terms in all

models at all ages were the nS and FA contents. The contribution of nS to compression strength gain is

notable while the FA input variable was related to negative influence at all ages. The negative effect of

FA is expected at early ages due to the high replacement levels of cementitious material (up to 40 wt%)

and the recognized low reactivity of the FA at those early ages. The SF had a positive effect being the

third ranking linear term in participation on strength development. The statistical significance of the SF

variable was noted at 56 days old (Figure 4-5b) for high amounts of both nS and SF (DOE II). For small

amounts of both nS and SF (DOE III), the SF started to be important at 7 days (Figure 4-8b). This latter

age is related to the normal rate for the pozzolanic development in SF systems (Almusallam et al., 2004).

Laboratory compressive strength values and data from DOEs I and II (Table 4-2) at all ages

exhibited a strong correlation, as reflected by the large r-values (i.e., r > 0.80) (Gunaydin et al., 2010).

From a statistical point of view, this represents a good agreement between the model outputs and the

experimental results. Nevertheless, the LOF tests revealed that points different from those defined in the

inputs cannot be properly represented by the surface generated by the second-order model. Also, DOE III,

which has reduced the highest values of the input variables, induced a change only in the interactive and

quadratic effects (Figure 4-7 to Figure 4-11), altering some answers regarding the DOEs I and II.

However, the LOF condition remained unchanged (Zapata et al., 2013c).

58

Figure 4-7. Compression tests: DOE III (3-days): (a) principal effects and (b) interactive effects.



(a)

Sc

(MP

a)

0

SF (wt%)

10 20

23

25

27

29

31

33

35

nS (wt%)

3 0

FA (wt%)

0(b)

Sc

(MP

a)

0

-+

0 3

FA-

-

FA+

-

+20

23

26

29

32

35

38

nS.SF (wt%)

3

SF-

SF+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-

FA+

0

SF (wt%)

10 20

Sc

(MP

a)

(a)

36

38

40

42

44

46

48

nS (wt%)

3 0

FA (wt%)

0 0

SF-

SF+

0 3

FA-

-

FA+

-

+

Sc

(MP

a)

(b)

30

34

38

42

46

50

54

nS.SF (wt%)

3

-+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-

FA+

Sc

(MP

a)

0

SF (wt%)

10 20(a)

50

53

56

59

62

65

nS (wt%)

3 0

FA (wt%)

0

Sc

(MP

a)

0

SF-

SF+

0 3

FA-

-

FA+

-

+

(b)

44

48

52

56

60

64

68

nS.SF (wt%)

3

-+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-

FA+

59



The simultaneous incorporation of nS, SF, and FA in the DOE III analysis can be seen in Figure

4-7 to Figure 4-11. In part (b), the sign of the variable indicates the low (-) or high (+) level replacement

for each one. The surface response for the DOE III in the replacement levels employed here showed

statistically significant curvature effects (Table 4-2 shows the corresponding p-values). These effects are

more pronounced as the concrete gained pozzolanic activity, i.e., from 7 days of testing (Figure 4-8b to

Figure 4-11b). The weighted statistical participation of the nS as principal effect is again noticeable. As

for DOEs I and II, the nS presence had a positive effect on strength development. The FA as a linear

variable was also significant, but unlike to nS, FA particles induced a negative effect on strength gain at

all ages. The complete analysis through the time of the optimal parameters (Eqs. 4-7 to 4-10) in

compression tests is shown in Table 4-3.

From Table 4-3 it is shown that the nS-SF-FA system and the nS-SF couple exhibited high

performance through the ages studied. In compression tests the highest strength value was 78.34 MPa at

90-days for nS = 2.3 and SF = 20 wt%. Therefore, the improvement by using the best couple is 43% with

0

SF (wt%)

10 20

Sc

(MP

a)

(a)

56

58

60

62

64

66

68

nS (wt%)

3 0

FA (wt%)

0 0

SF-

SF+

0 3

-

-

FA+

-

+Sc

(MP

a)

(b)

50

54

58

62

66

70

74

nS.SF (wt%)

3

-

+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-

FA+

0

SF (wt%)

10 20(a)

Sc

(MP

a)

59

61

63

65

67

69

71

nS (wt%)

3 0

FA (wt%)

0 0

SF-

SF+

0 3

-

-

FA+

-

+

Sc (

MP

a)

(b)

54

58

62

66

70

74

nS.SF (wt%)

3

-+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-

FA+

60

regard to the plain system at the same age (Table 4-1). This is an important quantity of strength gain in a

concrete system. Nevertheless, the LOF condition at this extreme point was statistical significant,

therefore the conclusion deduced should be treated carefully. Finally, in this segment research, the SF was

the least statistically active variable, although its contribution was positive on the strength development.

Another important feature regarding the SF additions is that, at higher levels of replacements (DOE II),

this variable is active only after 56 days of age. On the other hand, at lower levels of replacements (DOE

III), the SF variable is statistically active from the early age of 7 days (Figure 4-8a to Figure 4-11a)

(Zapata et al., 2013c). This can be attributed to more effective particle dispersion at lower dosages (DOE

III).

Table 4-3. Summary from DOE analysis: optimized values for compressive strength

Age

(days)

DOE

LOF

r

nS

(wt%)

SF

(wt%)

FA

(wt%)

Sc

(MPa)

3

I 0.00 0.9341 6.0 --- 3.7 35.94

II 0.00 0.8174 4.9 13.5 --- 36.78

III 0.00 0.9567 3.0 4.3 0.0 37.28

7

I 0.00 0.9668 6.0 --- 0.0 54.04

II 0.00 0.8954 6.0 0.0 --- 54.23

III 0.00 0.9661 3.0 3.3 0.0 53.59

28

I 0.00 0.9722 5.4 --- 0.0 66.95

II 0.00 0.8603 3.0 20.0 --- 66.86

III 0.00 0.9246 3.0 4.2 0.0 67.50

56

I 0.01 0.9100 6.0 --- 0.0 72.23

II 0.02 0.8099 2.1 20.0 --- 73.73

III 0.01 0.8570 3.0 5.0 0.0 70.99

90

I 0.00 0.9160 6.0 --- 0.0 75.21

II 0.00 0.9271 2.3 20.0 --- 78.34

III 0.00 0.8872 3.0 4.8 0.0 73.46

4.5.2 DOE analysis for tensile strength

Table 4-4 shows the mechanical results from the DOE analysis applied in tension tests. As in the

case of compressive tests, in Table 4-4 the sign associated with the p-values indicates the

positive/negative contribution of each particular term to the tensile strength development. The

orthogonality condition was successfully found in all DOEs. The independence, equal-variance, and

normality assumptions were carefully checked for each DOE. The linear, interactive, and quadratic

regression effects are shown with their associated p-values and Pearson's correlation coefficients. The

constant term is not shown but was significant (p-value < 0.05) at all ages and for all designs. The results

show the input variables exhibited through the time a variety of p-values, Pearson’s values, and linear,

interactive, and/or quadratic effects.

61

Table 4-4. Statistical results from DOEs in tension tests

Age

(days)

DOE nS SF FA nS.SF nS.FA SF.FA nS.nS SF.SF FA.FA LOF r

3

I 0.00(+) --- 0.00(-) --- 0.00(+) --- 0.03(-) --- 0.94(+) 0.06 0.8896

II 0.01(+) 0.03(+) --- 0.54(+) --- --- 0.42(-) 0.43(-) --- 0.02 0.6526

III 0.00(+) 0.83(-) 0.00(-) 0.76(-) 0.44(-) 0.72(-) 0.96(-) 0.78(+) 0.07(-) 0.18 0.8708

7

I 0.00(+) --- 0.00(-) --- 0.02(+) --- 0.75(+) --- 0.17(+) 0.02 0.9440

II 0.08(+) 0.02(+) --- 0.01(-) --- --- 0.20(-) 0.15(+) --- 0.06 0.7110

III 0.00(+) 0.00(+) 0.00(-) 0.28(-) 0.45(-) 0.02(+) 0.12(-) 0.07(-) 0.34(-) 0.00 0.8405

28

I 0.00(+) --- 0.01(-) --- 0.00(-) --- 0.83(-) --- 0.43(+) 0.01 0.8432

II 0.00(+) 0.23(+) --- 0.03(-) --- --- 0.92(+) 0.14(+) --- 0.20 0.8694

III 0.12(+) 0.01(+) 0.27(+) 0.52(+) 0.06(-) 0.04(+) 0.10(-) 0.55(-) 0.25(-) 0.00 0.6731

56

I 0.03(+) --- 0.01(-) --- 0.00(-) --- 0.02(-) --- 0.41(+) 0.00 0.7935

II 0.00(+) 0.94(+) --- 0.00(-) --- --- 0.00(-) 0.00(+) --- 0.34 0.8887

III 0.00(+) 0.62(+) 0.44(+) 0.35(-) 0.00(-) 0.15(+) 0.30(-) 0.22(+) 0.95(-) 0.08 0.7116

90

I 0.56(+) --- 0.00(-) --- 0.62(+) --- 0.11(-) --- 0.28(-) 0.00 0.8280

II 0.64(-) 0.00(+) --- 0.48(-) --- --- 0.01(-) 0.12(-) --- 0.00 0.7470

III 0.22(+) 0.03(+) 0.34(-) 0.21(-) 0.27(-) 0.61(-) 0.66(+) 0.81(-) 0.15(+) 0.04 0.5389

Respect to the tensile strength (St) ANOVA analysis showed that the linear terms of nS and FA

and its interactive terms nS·FA were the most important parameters taken into account the 95% of

confidence statistical level. As can be seen from the data (Table 4-4), where the nS are acting along with

other MA in a mix design, the behavior through the time of the system is predominantly dominated by the

effect of these nanoparticles. Although for both outputs in some systems at some ages, the full quadratic

terms were the dominant effects, e.g DOE III (Sc) at 3 days (Table 4-1), DOE II (Sc) at 28 days (Table

4-1), DOE II (St) at 56 days (Table 4.4). On the other hand, in tension analysis (Table 4-4) the FA turns to

be the most important variable. As in compression tests, additions of FA tended to deplete the tensile

strength at all ages. The nS variable is the second important linear variable. The effect on strength gain is

opposite to the FA. Nevertheless, the statistical significance of nS vanished to long term (90 days).

Finally, the SF was the third variable influencing the tensile strength. At all ages their additions tended to

favor the tensile strength gain.

From an statistical point of view, for DOEs I and II Table 4-4 shows the p-values for St at 28

days, where the correlation coefficients are higher than 0.80 indicating a good agreement between the

model outputs and the actual values. Nevertheless, for DOE I the test for LOF is showing that points

different of the defined in the inputs cannot be suitable represented by the surface generated by the second

order model. Also, DOE III which has the characteristic of reduce the highest values of the input

variables induced a changed only in the interactive effect of the nS·SF, modifying the answer regard to

DOE II. Also, the Pearson’s correlation of this analysis is the lowest registered at 28 days (r=0.6731).

However, in this particular case changing the upper limits for both nS and SF input variables the LOF

62

between DOEs II and DOE III was statistically different (Table 4-4). In addition, when the replacement

levels of nS and SF are higher (DOE II) the behavior of the system is statistically positive depending on

the nS content (p-value < 0.05). Also, the nS·SF interaction effect is statistically significant with a

negative contribution. Contrarily, at lower replacement levels of nS and SF (DOE III) the interaction

effect of these two input variables do not effectively contributes (p-value ≥ 0.05) to the tensile strength

development (Table 4-4).

Figure 4-12. Tensile strength of concretes at 3 days: (a) for DOE I and (b) for DOE II shows that

the performance of the systems in tension could not be improved by the nS when even a small amount of

FA was added (Figure 4-12 a to Figure 4-16 a). This behavior is similar to those reported for compressive

strength. Hence, the presence of FA content regardless of the nS content has a negative effect on the

output variable (Table 4-4). Also, the interaction effect between these two variables does not improve the

tensile strength behavior. The surface response is dominated by the linear and interactive effect of these

two mineral admixtures. The only positive contribution was the nS variable. Even though the relatively

simple surface response, as in the case for the compression analysis previously explained, a LOF of

second order is again present (Table 4-4). The maximum values of tensile strength at 28 days were found

when the nS content was 6.0 wt% and FA replacement was null. At last, should be noted that for all

combinations of the two mineral admixtures, the performance of the system was better than the control

case, showing that the nS additions on tensile strength are satisfactory.

Figure 4-12. Tensile strength of concretes at 3 days: (a) for DOE I and (b) for DOE II.

nS (wt%)FA (wt%)

St

(MP

a)

(a)

0 1 2 3 4 5 60

1020

3040

2,6

3

3,4

3,8

4,2

4,6

5

nS (wt%)SF (wt%)

St

(MP

a)

(b)

0 1 2 3 4 5 60

48

1216

20

4,3

4,6

4,9

5,2

5,5

5,8

63




nS (wt%)FA (wt%)

St

(MP

a)

(a)

0 1 2 3 4 5 60

1020

3040

3,5

4,5

5,5

6,5

7,5

nS (wt%)SF (wt%)

(b)

St

(MP

a)

0 1 2 3 4 5 60

48

1216

20

5,5

5,8

6,1

6,4

6,7

7

nS (wt%)FA (wt%)

St

(MP

a)

(a)

0 1 2 3 4 5 60

1020

3040

5,4

5,9

6,4

6,9

7,4

7,9

8,4

nS (wt%)SF (wt%)

St

(MP

a)

(b)

0 1 2 3 4 5 60

48

1216

20

5

6

7

8

9


St

(MP

a)

0 1 2 3 4 5 60

1020

3040

5,9

6,4

6,9

7,4

7,9

8,4

8,9

nS (wt%)SF (wt%)

St

(MP

a)

(b)

0 1 2 3 4 5 60

48

1216

20

5,4

6,4

7,4

8,4

9,4

64


On the other hand, the surface response containing the SF variable (Figure 4-12b to Figure 4-16b)

exhibits an unexpected mechanical behavior where the interactive effect of nS and SF has a small but

negative outcome on the tensile strength output at large SF contents. It can be attributed to excessive

micro-cracking in the ITZ or even phenomena associated with the cement matrix relate to deficient

dispersion of the nS. This is in agreement with other technical literature who reported that excessive

amounts of SiO2 tend to lower the strength in ceramic materials (Arsenovic´ et al., 2013). Finally, from

Table 4-1 and Table 4-4 it can be seen that the simultaneously employment of nS, SF, and FA present

very different behaviors. For compression analysis only the SF·FA and FA·FA interactions were not

active. Contrarily, for tension analysis DOE III showed that the only significant effects were the SF

variable and its interaction with FA. Also, it should be noted that DOE III in tension analysis had the

lowest Pearson´s value registered in the present thesis. These latter facts will be discussed in the next

section in conjunction with the ANN outputs.

The simultaneously employment of nS-SF-FA can be seen from Figure 4-17 to Figure 4-21. For

tension analysis the surface response for the DOE III in the replacement levels here employed did not

show statistically significant curvature effects at any age of testing. Being the SF and the interaction

SF·FA the only influent variables, both acting in positive form. It is important to note that at 28-day

Figure 4-18b showed that nS variable when testing from 0.0 to 3.0 wt% exhibits a peak value (nS≈2.3

wt%) but then, the strength improvement is depleted at nS=3.0 wt%. The complete analysis of the optimal

parameters in tension test in the present work is shown in Table 4-5. A similar behavior as depicted in

Figure 4-19b was recently reported by Nazari and Riahi (2011) by using Fe2O3 nanoparticles in normal

concrete samples at w/b=0.40, where the maximum peak was reached at the level replacement of 1.0 wt%

and then after the split tensile strength was decreased.


St

(MP

a)

0 1 2 3 4 5 60

1020

3040

5,7

6,1

6,5

6,9

7,3

7,7

8,1

(b) nS (wt%)SF (wt%)

St

(MP

a)

0 1 2 3 4 5 60

48

1216

20

7,6

8

8,4

8,8

9,2

9,6

65

Figure 4-17. Tension analysis: DOE III at 3 days: (a) principal effects and (b) interactive effects.



0

SF (wt%)

10 20(a)

St

(MP

a)

4

4,2

4,4

4,6

4,8

5

5,2

nS (wt%)

3 0

FA (wt%)

0(b)

St

(MP

a)

0

-+

nS.FA (wt%)

0 3

FA-

-

FA+

-

+

3,6

4

4,4

4,8

5,2

nS.SF (wt%)

3

SF-SF+

+

SF.FA (wt%)

0 10

FA-

FA+

0

SF (wt%)

10 20(a)

St

(MP

a)

5,8

6

6,2

6,4

6,6

6,8

nS (wt%)

3 0

FA (wt%)

0 0

SF-

SF+

0 3

FA-

-

FA+

-

+

(b)

St

(MP

a)

5,1

5,4

5,7

6

6,3

6,6

6,9

nS.SF (wt%)

3

-

+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-

FA+

St

(MP

a)

0

SF (wt%)

10 20(a)

6,7

6,9

7,1

7,3

7,5

7,7

7,9

nS (wt%)

3 0

FA (wt%)

0

St

(MP

a)

0

SF-

SF+

0 3

FA-

-FA+

-

+

(b)

5,7

6,1

6,5

6,9

7,3

7,7

8,1

nS.SF (wt%)

3

-

+

nS.FA (wt%)

+

SF.FA

0 10

FA-

FA+

66



From Table 4-5 it is shown that nS-SF couple was the best at all ages, being the highest tensile

strength value of 9.31 MPa at 90-days for nS=2.6 and SF=18 wt%. As can be seen, the improvement by

using the best couple is 38% regard the plain system at 90-day (Table 4-2). Even though the improvement

in tensile strength by using the best system is not as large as the improvement reached in the case of

compression tests, the 38% is an important strength gain value for a concrete system. Nevertheless, as in

the case for compression tests the LOF at this extreme point in tension systems was statistical significant,

therefore the conclusion deduced should be treated carefully. It is important to note that, in both cases the

compression and tension tests, the best optimized system was the nS-SF couple. Also, more important is

the fact that both cases presented almost the same level of replacements. Hence, in general terms for the

present systems here investigated it can be deduced that a mix having nS → 2.4 wt% and SF → 19 wt% is

0

SF (wt%)

10 20(a)

St

(MP

a)

6,3

6,6

6,9

7,2

7,5

7,8

nS (wt%)

3 0

FA (wt%)

0 0

SF-

SF+

0 3

FA-

-

FA+ -

+

(b)

St

(MP

a)

5,4

5,9

6,4

6,9

7,4

7,9

8,4

nS.SF (wt%)

3

-+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-FA+

0,0

SF

10,0 20,0(a)

St

(MP

a)

6,8

7

7,2

7,4

7,6

7,8

8

nS

3,0 0,0

FA

0,0 0

SF-

SF+

0 3

FA-

-

+

-

+

(b)

St

(MP

a)

6,5

6,9

7,3

7,7

8,1

8,5

8,9

nS.SF (wt%)

3

-

+

nS.FA (wt%)

+

SF.FA (wt%)

0 10

FA-FA+

67

an excellent candidate to satisfy simultaneously both mechanical demands, i.e., compression and tension

stresses. However, the LOF condition could be an important technical limitation in order to effectively

satisfy these theoretical results.

Table 4-5. Summary from DOE analysis of nS, SF and FA optimized values for tensile strength

Age

(days)

DOE

LOF

r

nS

(wt%)

SF

(wt%)

FA

(wt%)

St

(MPa)

3

I 0.06 0.8896 3.1 --- 0.0 4.95

II 0.02 0.6526 6.0 20.0 --- 5.75

III 0.18 0.8708 3.0 0.0 1.0 5.25

7

I 0.02 0.9440 6.0 --- 0.0 6.85

II 0.06 0.7110 2.0 20.0 --- 6.90

III 0.00 0.8405 2.6 5.4 0.0 6.80

28

I 0.01 0.8432 6.0 --- 0.0 7.98

II 0.20 0.8694 6.0 0.0 --- 8.40

III 0.00 0.6731 1.7 10.0 16.9 8.01

56

I 0.00 0.7935 5.2 --- 0.0 8.69

II 0.34 0.8887 4.8 0.0 --- 9.20

III 0.08 0.7116 3.0 0.0 0.0 8.73

90

I 0.00 0.8280 0.0 --- 0.0 7.80

II 0.00 0.7470 2.6 18.0 --- 9.31

III 0.04 0.5389 3.0 10.0 0.0 8.75

4.5.3 ANN simulations

Since the experimental ranges and/or the input variables were changed in all the DOE analyses, it

can be concluded that changing the experimental intervals is not a plausible option in order to overcome

the technical difficulties associated with the LOF. Then, the ANN models are expected to help in the

understanding of the physical phenomenon by including other input variables in addition to those taken

into account in the DOE analysis. In Table 4-6 the input variables are nS, SF, FA, PC (Portland cement

type I), WT (added water), AG (the sum of fine and coarse aggregate contents), SP (superplasticizer), UW

(unit weight conforming to ASTM C138 (2010)), AC (entrapped air content conforming to ASTM C138

(2010)), FT (flow table test ) ASTM C1437 (2007), IS (initial slump) ASTM C143 (2010), SL (slump

loss) and MA (maturity age). It is important to say that the highest performance in the algorithms tested

was reached with different input variables for tension and compression tests. The difference between

compression and tension systems is that PC is present only in the former and SL in the latter. The output

of the ANN models is compressive strength (Sc) or tensile strength (St) both in MPa, as a function of the

mix design components, fresh state properties, and the age at mechanical testing. The full set of old and

new input variables along with their ranges and units are shown in Table 4-6 (Zapata et al., 2013c).

68

Table 4-6. Design parameters of ANN models

Variables minimum maximum Unit

Inputs

nS 0.0 34.2 kg/m3

SF 0.0 113.9 kg/m3

FA 0.0 227.8 kg/m3

PC 253.0 469.1 kg/m3

WT 223.9 267.1 kg/m3

AG 1938.5 2098.8 kg/m3

SP 3.4 21.1 kg/m3

UW 2284.0 2391.0 kg/m3

AC 3.9 7.1 %

SL 18.1 100.0 %

FT 84.0 138.0 %

IS 101.6 130.2 mm

MA 3.0 90.0 days Outputs

Sc 13.8 76.8 MPa

St 2.7 9.0 MPa

Based on the parameters shown in Table 4-6, back-propagation algorithms (BPA) such as

gradient descent with momentum BPA, resilient BPA, Fletcher-Reeves and Polak-Ribiére conjugate

gradient BPAs, quasi-Newton BPA, and one-step secant BPA were tested (not shown here). Nevertheless,

for compressive strength two algorithms converged while for tensile strength only one of them converged.

The performances of the remaining algorithms were not satisfactory because the convergence rate was

very slow and/or the output showed low precision (not shown here). The average results for twelve

randomly initial points and internal arrays between training, validation and testing datasets are shown in

Table 4-7 (Zapata et al., 2013c).

Table 4-7. Performance of ANN architectures (average of twelve simulations)

Output

variable

(MPa)

ANN

model

Training dataset Validation dataset Testing dataset

RMSE

(MPa)

CE

r

RMSE

(MPa)

CE

r

RMSE

(MPa)

CE

r

Sc

LM[12:15:1]

1.5775

0.9894

0.9949

1.4994

0.9889

0.9962

2.3840

0.9723

0.9865

Sc

BR[12:3:1]

1.7548

0.9871

0.9935

1.5837

0.9891

0.9955

2.3007

0.9744

0.9875

St

LM[12:16:1]

0.4498

0.9002

0.9486

0.5075

0.8570

0.9375

0.6278

0.7566

0.8701

69

From Table 4-7 it is possible to conclude that, in the present work, ANN simulations were suitable

computer tools and could adequately predict strength behavior up to quaternary mixes with values being

very close to the actual data (Zapata et al., 2013c). This is in accordance to similar works using ANN to

predict compressive strength (Boğa et al., 2013; Alshihri et al., 2009; Madandoust et al., 2012; Sarıdemir

et al., 2009; Duan et al., 2013; Słoński, 2010). Also, for both compressive and tensile strength the results

from ANN simulations resulted in better performance than results from the fifteen simultaneously DOEs,

when compared with the Pearson’s correlation coefficients in both aspects as adjusted and predictive

models (Table 4-8 and Table 4-9). With regard to the tensile strength data, the analyses are more

complicated due to the geometry of the surface response. Almost one thousand simulations were carried

out in the development of the present work, being the major part with the objective of improving the

predicted values in tension data. Nevertheless in the present thesis, the results for tension analysis are

acceptable, considering the relative limited amount of data and the inherent large variability of the

concrete specimens in tension tests. In addition, as can be seen from Figure 4-23, the p-value was found

to be less than 0.05, indicating a linear statistical significant relationship at the 95% level of confidence

between the data from laboratory experiments and the predicted values for tensile strength from ANN

simulations. Even though in compression tests the ANN-results had higher performance than in tension

analyses, the results here shown are consistent with other studies (Khan, 2012; Boğa et al., 2013).

Table 4-8. Results between the adjusted model from DOEs analyses and ANN-models

Compression tests Tension test

Levenberg-Marquardt Bayesian Regularization Levenberg-Marquardt r-ANN* r-ANN/r-DOE r-ANN* r-ANN/r-DOE r-ANN* r-ANN/r-DOE

DOE I

3- days 0.9886 1.0584 0.9842 1.0537 0.9432 1.0597

7- days 0.9927 1.0268 0.9936 1.0277 0.8983 0.9499

28- days 0.9789 1.0069 0.9831 1.0112 0.9195 1.0905

56- days 0.9865 1.0841 0.9874 1.0851 0.9771 1.2314

90- days 0.9878 1.0784 0.9894 1.0801 0.8546 1.0321

DOE II

3- days 0.9800 1.1989 0.9732 1.1906 0.8731 1.3379

7- days 0.9797 1.0942 0.9837 1.0986 0.7520 1.0577

28- days 0.9454 1.0989 0.9468 1.1005 0.9010 1.0363

56- days 0.9673 1.1944 0.9782 1.2078 0.8733 0.9827

90- days 0.9641 1.0399 0.9761 1.0528 0.7868 1.0533

DOE III

3- days 0.9661 1.0098 0.9582 1.0015 0.9532 1.0946

7- days 0.9793 1.0136 0.9747 1.0089 0.7670 0.9126

28- days 0.9533 1.0310 0.9513 1.0289 0.7227 1.0737

56- days 0.9524 1.1113 0.9647 1.1257 0.8739 1.2283

90- days 0.9489 1.0696 0.9500 1.0708 0.6858 1.2726

average 1.0744 average 1.0763 average 1.0944 * Average of twelve simulations

70

Table 4-9. Results between the predictive model from DOEs analyses and ANN-models

Compression tests Tension test

Levenberg-Marquardt Bayesian Regularization Levenberg-Marquardt r-ANN* r-ANN/r-DOE r-ANN* r-ANN/r-DOE r-ANN* r-ANN/r-DOE

DOE I

3- days 0.9886 1.1107 0.9842 1.1057 0.9432 1.1782

7- days 0.9927 1.0497 0.9936 1.0507 0.8983 0.9897

28- days 0.9789 1.0273 0.9831 1.0317 0.9195 1.2944

56- days 0.9865 1.1734 0.9874 1.1745 0.9771 1.5241

90- days 0.9878 1.1502 0.9894 1.1521 0.8546 1.2331

DOE II

3- days 0.9800 1.4577 0.9732 1.4476 0.8731 3.9362

7- days 0.9797 1.1885 0.9837 1.1934 0.7520 1.6406

28- days 0.9454 1.2619 0.9468 1.2637 0.9010 1.1621

56- days 0.9673 1.5152 0.9782 1.5323 0.8733 1.0933

90- days 0.9641 1.1004 0.9761 1.1141 0.7868 1.5136

DOE III

3- days 0.9661 1.0426 0.9582 1.0341 0.9532 1.2334

7- days 0.9793 1.0408 0.9747 1.0359 0.7670 1.0668

28- days 0.9533 1.0897 0.9513 1.0874 0.7227 2.0490

56- days 0.9524 1.2942 0.9647 1.3109 0.8739 1.8460

90- days 0.9489 1.1793 0.9500 1.1807 0.6858 9.8987

average 1.1788 average 1.1810 average 2.1106

4.5.3.1 Levenberg-Marquardt algorithm

Using the LM algorithm twelve input variables and one output neuron were used as fixed

numbers and the best architecture consisted of one hidden layer with fifteen hidden neurons (HN); all

these parameters are symbolized hereafter as LMBP[12:15:1] (Zapata et al., 2013c). This architecture was

the most stable. Table 4-12 and Table 4-13 present the laboratory and simulated data for compression and

tension tests using the LM algorithm, respectively. Figure 4-22 shows a graphical representation of one of

the twelve architectures LMBP [12:15:1] of the trained (Figure 4-22a) and tested (Figure 4-23Figure

4-23b) datasets. The values obtained from the trained and tested datasets using ANN simulations are very

close to the experimental values obtained in laboratory conditions.

71

Figure 4-22. Actual compression and ANN-simulated-LMBP [12:15:1] (a) trained (b) tested.

Figure 4-23. Actual tensile strength and ANN-simulated-LMBP [12:16:1] (a) trained (b) tested.

In a similar fashion, for tension analysis comparison plots for trained and tested datasets are

shown graphically in Figure 4-23(a-b). As can be seen from Figure 4-22 to Figure 4-24, the values

obtained from the trained and tested datasets using ANN-simulations are very close to the experimental

values obtained in laboratory conditions. In the r-values from DOEs analysis versus LMBP ANN

simulations, the result was satisfactory with all the r-values from the net’s architecture being higher than

those obtained from DOE analysis (Table 4-8 and Table 4-9). Also, Table 4-9 shows the better

performance of the ANN simulations as predictive models when compared with the predictive capacity of

the DOEs.

Sc - lab experiments- (MPa)

Sc -

AN

N s

imu

lati

on

s- (

MP

a)

y = 0.3365 + 0.9936 x

r = 0.9972 P-value < 0.05

(a)0 20 40 60 80

0

20

40

60

80


Sc -

AN

N s

imu

lati

on

s- (

MP

a)

y = 1.1980 + 0.9811 x

r = 0.9894 P-value < 0.05

(b)20 30 40 50 60 70 80

23

33

43

53

63

73

83

St - lab experiments- (MPa)

St

-AN

N s

imu

lati

on

s- (

MP

a)

y = 0.5872 + 0.9080 x

r = 0.9486 P-value < 0.05

2 4 6 8 10

2

4

6

8

10

St - lab experiments- (MPa)

St

-AN

N s

imu

lati

on

s- (

MP

a)

y = 1.6389 + 0.7396 x

r = 0.8701 P-value < 0.05

4 5 6 7 8 9

4

5

6

7

8

9

72

4.5.3.2 Bayesian regularization algorithm

The Bayesian regularization method only converged for compressive tests. Using the BR

algorithm, twelve input variables and one output neuron were set as fixed numbers while the best

architecture consisted of one hidden layer with three HN, that is, BRA[12:3:1]. An ANN model of the

BRA [12:3:1] architecture is represented in Figure 4-24. In the figure are shown the results of the trained

(Figure 4-24a) and tested (Figure 4-24b) datasets. Table 4-12 presents the laboratory and simulated data

for compression tests using the BR algorithm, respectively. With regard to DOEs analysis versus ANN

simulations, the results were satisfactory with all the r values from the BRA being higher than the r

values from DOE analysis (Table 4-8 and Table 4-9) (Zapata et al., 2013c). In a similar fashion, the

performance of the BRA was slightly better than the LMBP as compared with the average r-value ratios

from Table 4-8 and Table 4-9, i.e., LMBP(r-ANN/r-DOE) < BRA(r-ANN/r-DOE). Even though the

particular run illustrated in Figure 4-22 to Figure 4-24 for LMBP and BRA, respectively; seems to show

that the precision of the LMBP was higher than the BRA, in general terms (average), the result is

opposite.

Figure 4-24. Actual compressive strength and ANN-simulated-BRA [12:3:1] (a) trained (b) tested.

4.5.3.3 Sensitivity analysis for ANN models

The sensitivity analysis was based on the Olden et al. (2004) connection weights and biases

approach. In this method, the actual values of weights and biases between input vector-hidden layers and

hidden layers-output layers are considered and the products across all the HN are added (Das and

Basudhar, 2006). Since the information is presented with the algebraic signs, the connection weight-bias

approach permits the analyzer to know if the contribution was directly or inversely related to the output.


Sc -

AN

N s

imu

lati

on

s- (

MP

a)

y = 0.9386 + 0.9825 x

r = 0.9936 P-value < 0.05

(a)0 20 40 60 80

0

20

40

60

80


Sc -

AN

N s

imu

lati

on

s- (

MP

a)

y = 0.6735 + 0.9924 x

r = 0.9878 P-value < 0.05

(b)20 30 40 50 60 70 80

23

33

43

53

63

73

83

73

The relative importance of the input variables related to the output variables is determined using Eq.

(4.11) (Dai et al., 2011)

For i = 1, 2, 3, …, n; j = 1, 2, 3, …, m (4.11)

In this equation, βi is the relative importance of ith input variable, j is the index number of the

HN, Wij is the connection weight between the ith input variable and jth HN, and Wjk is the connection

weight between the jth HN and the kth output node. Finally, algebraic summation was carried out in order

to rank the relative importance of each input variable (Table 4-10). Each normalized ranking number is

accompanied by the algebraic sign within parentheses after the Arabic number. This easily identifies the

nature (directly or inversely) of the relationship between the input and output variables. Regardless of the

algebraic sign, when the number increases, the relationship between both variables becomes less

significant.

Table 4-10. Normalized ranking order from sensitivity analysis on ANN-simulations

ANN

Compression tests

nS (kg/m3)

SF (kg/m3)

FA (kg/m3)

PC

(kg/m3)

WT

(kg/m3)

AG

(kg/m3)

SP

(kg/m3)

UW (kg/m3)

AC (%)

FT (%)

IS (mm)

MA (days)

LM 5(+) 4(-) 2(-) 3(-) 6(+) 11(-) 7(-) 12(+) 10(-) 9(+) 8(-) 1(+)

BR 4(+) 6(-) 3(-) 5(-) 2(+) 12(-) 7(+) 11(+) 9(-) 10(+) 8(-) 1(+)

ANN

Tension tests

nS (kg/m3)

SF (kg/m3)

FA (kg/m3)

SL

(%)

WT (kg/m3)

AG

(kg/m3)

SP

(kg/m3)

UW

(kg/m3)

AC

(%)

FT

(%)

IS

(mm)

MA

(days)

LM 2(+) 3(+) 12(-) 6(-) 7(-) 4(+) 8(-) 10(-) 11(-) 9(-) 5(+) 1(+)

According to the DOE methodology (Table 4-2), the LOF condition appeared 100% of the time,

while tension tests exhibited this condition only 60% of the time (Table 4-4). This latter decreased

number of 60% in tension tests could be relate to the fact that from ANN sensitivity analysis for tension

samples nS, SF, and FA variables had a high participation (Table 4-4). Whilst, for compression analysis

these input variables occupied lesser important positions than in the tension tests (Table 4-2). Therefore, it

is related to the fact that from ANN sensitivity analysis the nS, SF, and FA inputs were not necessarily the

most important contributing variables to compressive strength. From Table 4-10 it is seen that the input

variable MA (maturity age) had the highest positive contribution in both algorithms and both mechanical

tests. This result is expected because the hydration/pozzolanic reactions are time dependent. Nevertheless,

this important (the most significant) input variable was not considered, since by technical considerations

the ANN simulations were conducted using all the data at all ages while the DOE analysis was performed

74

at specific ages of 3, 7, 28, 56 and 90 days. Finally, for the present experimental and computational

research, it can be argued that statistical analysis in conjunction with ANN simulations and an adequate

sensitivity analysis effectively improved the understanding of the system´s overall behaviors.

Table 4-11. Actual compression values and simulated ANN using LMBP [12:15:1]

Mix

proportions

{nS:SF:FA}*

3 days

Actual

3 days

ANN

7 days

Actual

7 days

ANN

28 days

Actual

28 days

ANN

56 days

Actual

56 days

ANN

90 days

Actual

90 days

ANN

{0.0:0.0:0.0} 24.37 23.52 31.90 34.27 50.30 45.58 52.84 50.46 54.91 55.71

{3.0:0.0:0.0} 36.68 38.26 54.06 53.56 67.84 67.57 70.95 70.26 74.81 72.94

{6.0:0.0:0.0} 30.84 31.61 51.98 49.95 65.13 67.10 70.39 69.88 73.48 72.66

{0.0:0.0:20} 22.90 20.97 29.39 30.55 43.70 42.85 51.51 48.94 54.92 54.71

{0.0:0.0:40} 13.75 13.45 20.29 23.88 35.62 37.19 43.25 43.68 51.65 49.90

{3.0:0.0:40} 18.74 18.90 28.99 28.93 40.78 39.99 44.90 45.27 50.46 51.18

{3.0:0.0:20} 27.58 28.00 38.68 39.37 52.70 51.29 53.91 56.24 61.25 61.68

{6.0:0.0:40} 26.31 26.83 36.00 36.20 46.19 46.37 51.67 51.56 58.53 57.74

{6.0:0.0:20} 35.01 34.59 45.04 44.53 54.83 54.93 60.13 59.49 62.36 64.48

{0.0:10:0.0} 26.29 26.40 40.84 40.22 56.16 56.06 59.78 61.39 65.42 65.67

{0.0:20:0.0} 29.02 29.46 45.31 44.48 63.28 64.15 75.09 73.65 75.29 78.31

{3.0:20:0.0} 31.37 32.20 46.98 45.96 63.36 64.18 68.71 71.61 76.85 75.43

{3.0:10:0.0} 34.94 35.55 47.97 48.65 62.72 62.50 66.96 66.58 70.01 69.99

{6.0:20:0.0} 36.65 36.37 50.89 49.66 64.67 64.92 71.65 69.61 70.63 72.81

{6.0:10:0.0} 37.64 38.44 51.50 49.95 60.30 61.77 68.29 65.56 69.78 69.09

{1.5:0.0:10} 26.96 24.63 37.27 36.58 47.97 48.94 53.67 53.66 55.97 58.61

{0.0:10:20} 21.08 20.63 34.34 34.02 48.40 50.66 58.74 57.13 61.85 62.13

{0.0:5.0:10} 28.43 27.05 37.61 39.17 56.99 55.28 63.52 62.08 65.71 66.90

{1.5:5.0:0.0} 31.71 31.08 44.80 45.15 58.14 59.62 63.83 63.86 63.08 67.78

{1.5:10:10} 27.10 27.75 39.79 38.95 56.50 55.58 65.44 63.82 68.00 68.92

{1.5:5.0:10} 26.86 27.77 39.35 40.76 54.57 54.91 61.99 59.85 64.80 64.41

{1.5:5.0:20} 22.36 24.36 36.56 37.12 51.48 51.58 57.16 57.04 61.97 62.07

{3.0:5.0:10} 32.67 32.69 47.44 45.99 59.41 59.75 64.09 64.09 68.41 68.21

{3.0:10:20} 24.96 25.92 39.92 38.35 53.39 54.14 59.74 60.51 65.46 65.37 * Mix proportions expressed as percentage of cementitious materials.

75

Table 4-12. Actual compression values and simulated from ANN using BRA [12:3:1]

Mix

proportions

{nS:SF:FA}*

3 days

Actual

3 days

ANN

7 days

Actual

7 days

ANN

28 days

Actual

28 days

ANN

56 days

Actual

56 days

ANN

90 days

Actual

90 days

ANN

{0.0:0.0:0.0} 24.37 23.99 31.90 33.13 50.30 46.67 52.84 50.95 54.91 56.10

{3.0:0.0:0.0} 36.68 40.33 54.06 50.33 67.84 65.64 70.95 70.44 74.81 75.41

{6.0:0.0:0.0} 30.84 34.52 51.98 47.36 65.13 67.19 70.39 70.87 73.48 73.90

{0.0:0.0:20} 22.90 21.04 29.39 30.34 43.70 44.80 51.51 50.05 54.92 55.66

{0.0:0.0:40} 13.75 13.85 20.29 23.39 35.62 37.91 43.25 42.84 51.65 48.55

{3.0:0.0:40} 18.74 19.00 28.99 27.41 40.78 40.59 44.90 45.94 50.46 51.81

{3.0:0.0:20} 27.58 28.21 38.68 37.57 52.70 52.01 53.91 56.92 61.25 61.91

{6.0:0.0:40} 26.31 27.27 36.00 35.13 46.19 47.49 51.67 52.56 58.53 57.85

{6.0:0.0:20} 35.01 34.84 45.04 42.38 54.83 54.07 60.13 58.62 62.36 63.18

{0.0:10:0.0} 26.29 27.10 40.84 38.09 56.16 55.09 59.78 59.95 65.42 64.72

{0.0:20:0.0} 29.02 29.35 45.31 43.62 63.28 66.99 75.09 72.05 75.29 76.82

{3.0:20:0.0} 31.37 32.28 46.98 45.24 63.36 65.65 68.71 70.09 76.85 74.07

{3.0:10:0.0} 34.94 36.09 47.97 46.35 62.72 61.98 66.96 66.45 70.01 70.76

{6.0:20:0.0} 36.65 36.86 50.89 48.37 64.67 65.80 71.65 69.61 70.63 72.93

{6.0:10:0.0} 37.64 40.82 51.50 49.81 60.30 63.15 68.29 66.89 69.78 70.33

{1.5:0.0:10} 26.96 24.73 37.27 34.32 47.97 49.07 53.67 54.10 55.97 59.57

{0.0:10:20} 21.08 22.50 34.34 34.05 48.40 51.89 58.74 56.78 61.85 62.19

{0.0:5.0:10} 28.43 27.36 37.61 38.78 56.99 56.53 63.52 61.42 65.71 66.25

{1.5:5.0:0.0} 31.71 33.79 44.80 44.23 58.14 60.14 63.83 64.57 63.08 68.79

{1.5:10:10} 27.10 27.51 39.79 39.62 56.50 58.42 65.44 62.85 68.00 66.86

{1.5:5.0:10} 26.86 28.94 39.35 39.45 54.57 55.62 61.99 60.34 64.80 64.94

{1.5:5.0:20} 22.36 24.69 36.56 35.55 51.48 52.42 57.16 57.43 61.97 62.47

{3.0:5.0:10} 32.67 33.45 47.44 43.49 59.41 58.81 64.09 63.34 68.41 67.73


76

Table 4-13. Actual tension values and simulated from ANN using LMBP [12:16:1]

Mix

proportions

{nS:SF:FA}*

3 days

Actual

3 days

ANN

7 days

Actual

7 days

ANN

28 days

Actual

28 days

ANN

56 days

Actual

56 days

ANN

90 days

Actual

90 days

ANN

{0.0:0.0:0.0} 4.34 4.51 5.31 5.21 5.22 5.40 5.57 5.51 6.96 6.82

{3.0:0.0:0.0} 5.23 5.14 6.50 6.40 6.77 6.98 8.98 8.23 8.72 8.57

{6.0:0.0:0.0} 4.52 4.59 6.76 6.34 8.28 8.15 8.79 8.47 7.39 7.52

{0.0:0.0:20} 3.67 3.68 4.69 4.94 6.14 6.23 7.18 7.06 7.22 7.06

{0.0:0.0:40} 2.73 2.69 3.53 4.05 5.74 5.31 6.62 6.07 5.38 6.14

{3.0:0.0:40} 3.59 3.53 4.74 4.81 6.14 5.96 6.94 6.80 5.36 6.71

{3.0:0.0:20} 4.49 4.47 4.89 5.86 6.23 7.01 7.20 7.13 7.17 7.13

{6.0:0.0:40} 4.77 4.23 6.07 5.53 6.29 6.13 6.57 6.14 6.21 6.14

{6.0:0.0:20} 4.40 4.81 6.21 5.75 6.33 6.14 6.57 6.14 6.54 6.14

{0.0:10:0.0} 4.36 4.55 6.26 5.72 4.86 6.19 5.55 6.60 8.96 8.16

{0.0:20:0.0} 5.15 4.72 6.70 6.34 6.76 7.06 8.21 8.06 8.77 9.22

{3.0:20:0.0} 5.07 5.68 6.70 6.80 6.70 7.41 8.28 8.92 8.98 9.43

{3.0:10:0.0} 5.29 5.13 6.35 6.09 6.92 7.23 7.98 8.26 8.79 8.25

{6.0:20:0.0} 5.73 5.73 6.71 6.80 8.01 7.87 6.92 7.87 8.70 7.71

{6.0:10:0.0} 5.93 5.96 5.93 6.56 7.81 7.18 7.01 7.85 8.20 7.61

{1.5:0.0:10} 4.60 4.65 6.29 5.75 6.42 6.37 7.27 7.35 6.87 7.04

{0.0:10:20} 3.72 3.79 5.74 5.63 7.39 7.39 7.87 7.59 7.87 7.40

{0.0:5.0:10} 3.99 4.07 5.93 5.76 7.64 7.03 7.23 7.13 7.06 7.14

{1.5:5.0:0.0} 4.49 4.90 6.89 6.47 8.05 7.67 7.50 7.62 6.91 7.42

{1.5:10:10} 4.49 4.49 6.16 5.76 8.01 6.76 8.01 8.04 7.49 8.12

{1.5:5.0:10} 4.88 4.69 6.10 6.47 8.08 7.73 6.99 7.65 7.67 7.43

{1.5:5.0:20} 4.14 4.13 5.83 6.05 6.00 7.11 6.97 7.14 8.62 7.13

{3.0:5.0:10} 5.03 4.94 6.60 6.43 6.08 7.13 6.64 7.14 7.76 7.14



This chapter presents experimental and computational findings related to compressive and tensile

strength of concrete containing nano-SiO2, micro-SiO2, fly ash, and polycarboxylate-superplasticizer. The

principal results can be summarized as follows:

The simultaneous used of SF and nS additions in concrete induced a pronounced nonlinear effect

on the compressive/tensile strength response variable. Also, the curvature exhibited by the

response surfaces continuously switched from positive to negative. This complex behavior could

contribute to generate the lack-of-fit of the second-order presented in the DOEs with nS-SF-FA as

inputs.

For compression strength analysis, the replacement of cement by either SF or nS particles could

effectively improve the strength gain with respect to control systems. This is attributed to the

pozzolanic reaction between the amorphous-SiO2 and Ca(OH)2. In addition, the higher

77

mechanical performance obtained from the addition of the nano-silica particles compared to silica

fume addition was statistically demonstrated by both the DOE analysis and ANN-models.

For tension analysis, using the DOE methodology and ANN model is concluded that the input

variable FA (low calcium), exhibited the highest negative contribution to the strength

development. The performance in tension could not be improved by the nS when even FA small

amount was added. Contrarily, the nS were ranked in the second position with positive influence

on tensile strength. Whereas, the SF was ranked in the third positive place following both ANN

simulations and DOE methodology where all the experimental points, with both p-values higher

and lesser than 0.05 showed that SF induced a positive effect on tensile strength gain.

For tension tests the trained ANN models utilized to study the effects of mix proportions on

strength development were better than using the DOE methodology. The input variables used for

the development of the ANN-models were the amounts of nS, SF, FA, slump loss, added water,

aggregates, superplasticizer, air content, flow area (flow table), initial slump, and the unit weight

in the fresh state. From the results, it is possible to conclude that ANN simulations were suitable

computer tools and can adequately predict tensile strength behavior of up to quaternary concrete

mixes with values being very close to the experimental data.

The general results from response surface methodology indicate that, in the developing of the

second-order polynomial models, the analysis of variance taken into account the 95% of

confidence level showed that the most important parameters influencing compressive strength

were the linear terms of nS and FA and the interactive terms nS·SF and nS·FA for both

compression and tension tests. These behaviors were also observed by means of two independent

algorithms using ANN simulations.

DOE analysis of the maximum strength value from 3 to 90 age showed that in

tension/compression tests the nS-SF couple was the best system. In tension this couple was the

best at all ages being 38% better than controls at the same age. While in compression this system

was three of five times the best couple being 43% better than controls. In general, it was found

that nS → 2.4 wt% and SF → 19 wt% is an excellent candidate to satisfy simultaneously both

mechanical demands. However, in both cases the LOF at the extreme value of strength was

statistical significant, therefore the conclusion deduced should be treated carefully.

78

CHAPTER V

5 WEIBULL ANALYSIS ON TENSILE STRENGTH OF CONCRETE CONTAINING

AMORPHOUS SILICA

5.1 Introduction

This chapter investigates the tensile strength of plain, binary, ternary and quaternary designs

containing replacements to Type I PC by FA, SF and nS. Splitting tensile failures were carried out at 3, 7,

28, 56 and 90 days. Quadratic class goodness-of-fit test of composite hypothesis was applied to

investigate the accuracy of the two- and three-parameter Weibull models. The estimated Weibull

parameters are obtained by using modern nonlinear methodologies. In addition, deviations from the

Weibull behavior such as Gamma and Log-Normal models are also investigated. The novelty in the

present study is that despite the importance of the Weibull modulus in reliability analyses of brittle

materials, there are only a few researches related with binary, ternary and/or quaternary concretes; being

the data especially scarce for concretes containing nano-SiO2 as an active mineral admixture.

5.2 Proportions, casting and testing for concrete samples

5.2.1 Concrete proportions

All the data in this chapter was casted independently of the previous chapters, but the same

designs and raw materials were used in order to give continuity to the entire thesis (Table 1-1 and Table

1-2). The ranges of the interval values used in each experimental design were selected according to field

and literature considerations as explained in previous chapters. The ranges used for the studied variables

are as follows: SF from 5 to 20 wt%, FA from 10 to 40 wt%, and nS 1 to 6 wt%. The coarse-to-fine

aggregate ratio was kept constant to 1.50. The cementitious materials’ amount was 465±5 kg/m3 at

w/b=0.35. The water content of the nS and the SP was considered in all the mix designs. The SCM

proportions are shown in Table 5-1 (Zapata et al., 2013d).

79

5.2.2 Specimen fabrication

The concrete constituents were mixed in a commercial mixer at two speeds: 120 and 60 rpm. The

total mixing time was fixed at 5 min. The concrete samples were prepared using the same steps in which

50% of the water and 100% of the fine and coarse materials were mixed for 1.5 min at 120 rpm. Cement

was mixed in dry condition with SF (when applied) and/or FA (when applied), and then this powder mix

was added to the mixer for 2 min at 60 rpm. The process was followed by addition of previously mixed

remainder water with slurry nS (when applied) and the corresponding SP dosage. After, the materials

were mixed for 1.5 min at 120 rpm. The fresh concrete was poured into 50-mm-diameter by 100–mm-

high standard cylinders (ASTM C470, 2008). Consolidation was performed by the rodding method

(ASTM C192, 2007). The formwork was removed 24 h after casting. The samples were cured in

limewater at 23-25 °C until the age of testing. All the concrete cylinders were casted, cured, and failed in

the same mode, in order to ensure comparable results (ASTM C192, 2007). Mix proportions and

mechanical results are shown in Table 5-1 (Zapata et al., 2013d).

5.2.3 Testing procedures

The experimental testing of five different curing ages (i.e., 3, 7, 28, 56 and 90 days) was

conducted with a 3000-kN Forney universal test machine using a load-controlled setting. The material

supplies, casting technique, curing conditions, specimen geometry, testing machine and loading rate were

all kept constant during the entire experimental study of cylindrical specimens. Compressive and splitting

tensile tests were performed in accordance to ASTM C39 (2011) and ASTM C496 (2004), respectively.

Five specimens were used in each age of testing in compression tests and, twenty-three in tension tests.

For the tensile testing experiments, thin plywood bearing strips (Baboon of 3.2 mm thickness, 25

mm wide and 150 mm length) were placed between the specimen and the upper and lower bearing blocks

of the testing machine to uniformly distribute the applied load (ASTM C496, 2004). For tension tests,

each concrete sample was fractured at a loading rate of 75-80 kN/min (ASTM C496, 2004) under wet

conditions. Also, in the tension tests a preload of 100-150 N was induced to the specimen to eliminate the

error caused by poor contact. Marking, measurements and positioning of the samples were conducted in

accordance with ASTM C496 (2004). Compressive and tensile mechanical results are shown in Table 5-1.

80

Table 5-1. Laboratory proportions and mechanical results of concrete samples

Mix

compositions

{nS:SF:FA}*

Compressive and tensile strength (MPa)**

3 days 7 days 28 days 56 days 90 days

{0.0:0.0:0.0} 29.1

(3.2)

5.6

(0.6)

34.7

(2.9)

5.6

(0.7)

54.6

(4.9)

7.1

(1.1)

57.9

(7.0)

6.9

(1.2)

63.2

(9.0)

7.6

(0.9)

{3.0:0.0:0.0} 34.2

(2.6)

5.8

(0.5)

51.2

(2.9)

6.1

(0.7)

65.7

(2.1)

7.9

(0.8)

71.1

(2.4)

8.3

(0.7)

72.5

(2.9)

7.3

(1.2)

{6.0:0.0:0.0} 31.5

(4.2)

5.3

(0.5)

50.9

(1.2)

5.9

(1.3)

64.7

(1.4)

7.8

(0.6)

70.8

(3.0)

7.7

(0.8)

74.1

(1.6)

6.9

(1.0)

{0.0:0.0:20} 24.3

(2.0)

4.5

(0.6)

29.5

(4.1)

4.7

(0.8)

46.7

(3.9)

7.2

(0.6)

52.5

(3.3)

6.6

(0.9)

55.3

(3.8)

7.4

(1.0)

{0.0:0.0:40} 13.2

(1.1)

3.0

(0.4)

19.0

(2.6)

3.9

(0.8)

36.9

(1.6)

6.0

(0.2)

42.3

(2.2)

6.2

(0.7)

51.5

(5.5)

6.8

(1.0)

{3.0:0.0:40} 19.4

(4.2)

4.0

(0.4)

27.5

(2.7)

4.6

(0.7)

43.4

(2.5)

6.4

(0.4)

46.7

(3.2)

6.3

(0.6)

52.3

(4.0)

6.9

(1.0)

{3.0:0.0:20} 27.2

(1.4)

5.0

(0.5)

40.7

(2.8)

6.3

(0.7)

54.5

(4.6)

6.6

(1.2)

58.3

(6.2)

7.7

(0.8)

65.8

(4.4)

7.9

(0.7)

{6.0:0.0:40} 25.1

(2.3)

4.3

(0.5)

36.6

(3.5)

5.2

(0.7)

50.9

(4.7)

6.9

(0.5)

54.5

(4.7)

6.9

(0.7)

60.8

(2.5)

7.5

(0.8)

{6.0:0.0:20} 33.2

(3.2)

5.1

(0.6)

46.0

(2.1)

6.6

(0.6)

56.7

(3.1)

7.1

(1.0)

63.6

(4.3)

7.7

(0.9)

67.5

(5.4)

7.6

(1.1)

{0.0:10:0.0} 32.2

(6.0)

5.3

(0.7)

42.8

(2.4)

5.4

(0.6)

58.7

(4.2)

7.2

(1.2)

65.5

(6.7)

7.8

(1.0)

68.2

(3.2)

8.0

(0.9)

{0.0:20:0.0} 33.2

(4.1)

5.2

(0.5)

47.9

(2.5)

6.1

(0.5)

64.5

(2.9)

7.9

(0.8)

74.4

(2.6)

7.9

(1.3)

79.9

(4.3)

8.7

(0.8)

{3.0:20:0.0} 32.7

(1.4)

5.4

(0.4)

51.3

(4.2)

6.5

(0.7)

68.1

(4.7)

8.0

(1.0)

76.0

(7.1)

8.3

(1.1)

81.3

(4.7)

8.8

(0.6)

{3.0:10:0.0} 37.0

(4.7)

5.7

(0.4)

49.4

(3.9)

6.8

(0.5)

66.2

(3.4)

7.4

(1.1)

72.6

(5.9)

8.8

(0.8)

75.5

(5.7)

8.6

(0.8)

{6.0:20:0.0} 37.2

(1.9)

5.3

(0.6)

54.0

(3.2)

7.0

(0.5)

68.8

(5.1)

7.7

(1.0)

78.5

(7.6)

7.6

(1.0)

78.3

(8.2)

9.0

(0.6)

{6.0:10:0.0} 38.1

(1.5)

5.6

(0.4)

53.2

(2.6)

7.2

(0.6)

59.7

(7.3)

7.5

(1.0)

74.6

(6.1)

7.7

(1.3)

78.0

(8.0)

8.3

(1.0)

{1.5:0.0:10} 31.8

(5.9)

5.3

(0.8)

37.2

(0.6)

6.4

(0.5)

53.2

(5.3)

7.4

(0.8)

59.0

(5.3)

8.4

(0.9)

63.5

(7.4)

8.2

(1.0)

{0.0:10:20} 25.5

(5.0)

4.3

(0.5)

36.2

(1.9)

6.0

(0.8)

51.2

(2.8)

7.2

(0.6)

61.5

(3.1)

7.9

(0.8)

64.2

(3.9)

8.2

(0.8)

{0.0:5.0:10} 32.0

(3.8)

4.9

(0.6)

37.5

(1.0)

5.8

(1.1)

57.9

(1.8)

7.4

(0.7)

63.4

(6.4)

7.4

(0.8)

65.7

(2.3)

8.0

(1.0)

{1.5:5.0:0.0} 35.5

(4.8)

5.6

(0.6)

41.7

(4.0)

6.7

(0.8)

60.6

(3.2)

7.9

(0.9)

71.7

(7.6)

8.1

(0.8)

72.3

(9.1)

7.7

(1.2)

{1.5:10:10} 31.3

(4.2)

5.0

(0.5)

42.9

(3.3)

6.4

(1.0)

59.0

(3.1)

7.6

(0.7)

67.4

(3.6)

7.4

(0.7)

71.9

(3.9)

7.8

(0.9)

{1.5:5.0:10} 31.2

(4.3)

5.4

(0.4)

38.5

(4.0)

6.6

(0.7)

55.4

(3.4)

7.8

(0.6)

67.0

(5.0)

6.8

(1.1)

68.6

(3.9)

7.8

(0.7)

{1.5:5.0:20} 26.5

(3.9)

4.8

(0.4)

35.7

(1.5)

6.0

(0.5)

53.5

(3.1)

7.5

(0.8)

62.1

(4.6)

6.2

(0.9)

65.1

(4.0)

7.7

(0.8)

{3.0:5.0:10} 35.9

(3.2)

5.7

(0.5)

46.8

(3.1)

6.6

(0.6)

60.2

(2.4)

7.6

(0.9)

66.4

(3.2)

7.7

(1.1)

70.0

(3.2)

8.4

(0.9)

{3.0:10:20} 27.9

(2.8)

4.9

(0.4)

42.2

(2.4)

6.2

(0.8)

53.7

(3.3)

6.9

(1.2)

64.9

(4.9)

7.3

(0.8)

67.5

(3.8)

8.0

(0.8) * Mix proportions are expressed as percentage of cementitious materials. ** The numbers in parenthesis are the standard deviation in MPa. The

symbols

or

stand for the average of three and twenty-three replicates, respectively.

81


Together with the Normal, Exponential, Chi-squared, t-Student, and F-statistic the Weibull

distribution is the most popular model used in modern statistics. There always exists at least one physical

model behind each statistical distribution. With respect to the Weibull distribution there are a lot of

several physical models doing the Weibull statistic a very useful tool in engineering applications. Perhaps

the most popular model evoked in engineering applications is the model of the weakest link. This model

is connected with the extreme value origin of the Weibull model. That is, given a physical system

consisting of n identical units connected in series, and it fails with the first failure of one these units. Also,

the Weibull model is attractive in engineering applications because in some reliability studies, it is

possible to measure physical degradation as a function of time. And most failures can be traced to an

underlying degradation process. Finally, engineers are interested in studying wearing styles and these may

be expressed by a suitable chosen hazard rate. This latter is the Weibull distribution written with some

specific set of parameters which have specific physical meanings (Rinne, 2009).

5.3.1 Splitting tensile strength test

The splitting tensile test is and indirect method employed for brittle materials, as these tend to

break when gripped by the testing machine. This is caused by contact stresses that exceed the fracture

strength of the material, leading to a premature failure at the grips (Ashby and Jones, 2005). This test

method consists of applying a diametral compressive force along the length of a cylindrical concrete

specimen. This setup induces tensile stresses on the plane where this force is distributed, since the areas

of load application are in a state of triaxial compression. Thus, tensile failure is expected rather than

compressive failure. The splitting tensile strength is obtained by using Eq. (5.1) (ASTM C496, 2004)

(5.1)

where; T = splitting tensile strength [MPa], P = maximum applied load by the testing machine [N], l =

length [mm], and d = diameter of the concrete specimen [mm].

5.3.2 Statistical background

5.3.2.1 Weibull distribution

The fracture strength of brittle materials such as concrete, on repeated measurements of

macroscopically similar samples, usually exhibits significant statistical scatter (Smallman and Ngan,

82

2007). In addition, for structural engineering applications, the tensile strength of concrete is normally

neglected in design calculations (McCormac and Nelson, 2006). In 1939 the Swedish engineer Waldoddi

Weibull introduced its empirically distribution function based on tensile, bending and torsional test,

mostly carried out on brittle materials. Weibull was a pioneer in statistical research leading with failures

in brittle materials whose probability distributions present a large tail on the high-strength side (Meyers

and Chawla, 2009). Herein, a general mathematical nomenclature to describe the distributions was

adopted and a modern version of the three-parameter Weibull distribution function (DF)

(5.2)

where ≥ φ; φ ϵ ; β and λ ϵ +. In a similar fashion, the Weibull cumulative distribution function (CDF)

is given by Eq. (5.3)

(5.3)

where ≥ φ; φ ϵ ; β and λ ϵ +. In Eqs, (5.2)-(5.3) φ, β, and λ represent the location, scale, and shape

Weibull parameter, respectively. The distribution of X given by Eq. (5.2) is noted in technical literature as

X We(φ, β, λ). Eq. (5.3) represents the failure probability of the samples and in this study, the variable X

physically represents the tensile strength of the concrete samples measured in MPa units. The location

parameter represents the minimum strength (MPa). The scale parameter represents the characteristic

strength (MPa), often approximated as the mean strength (Meyers and Chawla, 2009). And the shape

parameter, also called the Weibull modulus, is a dimensionless quantity that represents the scatter in

tensile strength measures of the concrete systems. In this sense, the lower λ, the greater will be the

variability of strength and vice versa (Ashby and Jones, 2005; Peiying et al., 2012).

5.3.2.2 Goodness-of-fit tests

The goodness-of-tests are used to compare the exactitude in the fitting of parameters from the

distribution models proposed. For all tests, the hypotheses of interest are

Ho: data are independent samples from the estimated distribution

HA: data are not independent samples from the estimated distribution

83

The first step is to decide whether the data come from a Weibull distribution. In order to make a

goodness-of-fit test for a Weibull distribution, a logarithmic transformation of the supposed Weibull data

is required. Thus, if φ =0 and Y= Ln(X) the distribution is called the extreme-value distribution type I for

the minimum (Mann et al., 1971), where φ *

= Ln(β) and β *

= 1/ λ and at this stage the distribution is the

location-scale family. Herein, generally ordered data are required, which will be denoted as X(i:n). Then, in

order to get the percentage points, the following one-sided statistic is used:

where r = [(m-1)/2], and the brackets denotes the greatest integer. The denominator of the term into the

braces in Eq. (5.4) represents the expected values of the reduced extreme order statistics defined in Eq.

(5.5) as

(5.5)

In this research the expected values were obtained by using a recurrence formula given in general

form by Eqs. (5.6)-(5.7)

(5.6)

Values of S greater than Sn,m,1-α are evidence against the null hypothesis: H0: “X We(φ=0, β, λ)”.

In this study, in order to test the hypothesis involved from (Mann et al., 1971) tabulated percentiles of S

statistics based on Monte-Carlo simulations were programmed. The results for the best fitted distribution

at each age of testing are shown from Table 5-2 to Table 5-6 (Zapata et al., 2013d).

84

5.3.2.3 Discrimination problem

Once the viability of the data as a Weibull distribution function has been carried out (assuming

the two-parameter as a first trial from 5.3.2.2), the next step consists in determine whether the data comes

from whether a two-parameter distribution, or the more complex, three-parameter Weibull distribution. In

the present work an indirect procedure was employed, in which the minimum value of the statistic

associated to the particular adjusted distribution was used as a ranking criterion. Three different tests were

used to determine whether or not the dataset could reasonably have come from the distribution been

tested. Since the Weibull distribution usually relies upon the empirical distribution function (EDF) or

functions based on ordered statistics, in this work the Anderson-Darling, the Cramer von Mises and the

Watson statistic were employed. These tests rely on the quadratic class of the EDF.

5.3.2.3.1 The empirical distribution function (EDF)

The EDF (Murthy et al., 2004) is a nonparametric procedure consisting of a plot of the cumulative

proportion of the data that lie below t, with t (-∞ < t < ∞) and denoted by . In the case of n-

uncensored data points, the EDF is a step function having steps of height 1/n at each data point xi. In

general terms, the EDF can be carried out by using the order statistics t(1), …, t(n) with t(0) = 0 and t(n+1) = ∞

so that .

5.3.2.3.2 The Cramér-von Mises statistic (W2)

According to D’Agostino and Stephens (1986) this test is more powerful than the Kolmogorov-

Smirnov statistic which is the most known EDF test. The Cramér-von Mises statistic is a test based on the

difference between the hypothesized CDF given by and EDF. The test statistic is given by Eq. (5.8)

Percentiles pα of the W2 were programmed from D’Agostino and Stephens (1986). If W

2 > pα,

is rejected at level of significance α.

85

5.3.2.3.3 The Watson statistic (U2)

The Watson test is based on the difference between the hypothesized CDF given by and

EDF. The Watson test is showed in Eq. (5.9)

Percentiles pα of the U2 were programmed from D’Agostino and Stephens (1986). If U

2 > pα,


5.3.2.3.4 The Anderson-Darling statistic (A2)

The Anderson-Darling statistic is a powerful statistical tool in analyzing the three-parameter

Weibull distribution (Evans et al., 1989). This test is specially accepted in engineering applications

related to structural reliability (Alqam et al., 2002) because it is highly sensitive to the tail behavior

(Alqam et al., 2002; Rinne, 2009). Also, the Anderson-Darling test is recommended for statistical

analyses of composite materials (Alqam et al., 2002). The Anderson-Darling test is based on the

difference between the hypothesized CDF given by and EDF. This test is described in Eq. (5.10)

Percentiles pα of the A2 were programmed from D’Agostino and Stephens (1986). If A

2 > pα,


In this research, three distribution functions of the scale-shape type (two-parameter Weibull,

Gamma and Log-Normal) were analyzed and one of the shape-scale-location type (three-parameter

Weibull). It is known (Basu et al., 2009; Rinne, 2009) that the Gamma, Exponential and Log-Normal

distributions are natural competitors to the Weibull distribution. Nevertheless, only the Gamma and Log-

Normal distributions were chosen based on a previous research (Basu et al., 2009) in which they were the

most common competitors to the Weibull distribution applied to brittle materials.

In a similar fashion, three alternates’ procedures were selected for estimating the three-parameter

Weibull distribution because the complexity generated in the computational solution of the parameter

86

estimation do some algorithms to fail (Rinne, 2009). In total 1440 processes were developed to rank the

accuracy of any particular distribution function to each dataset. The tension test were carried out on 24

mixes, each one with 23 replicates failed through 5 different maturity ages, then a total of 2760 concrete

cylindrical specimens were used in the experimental program (failed in tension). In addition, there were

240 cylindrical specimens failed in compression to check the designs (24 mixes with 2 replicates through

5 days of testing), therefore, this chapter employed 3000 samples. All the computational work was

developed using Mathematica® software and the values for the statistical tests were taken from specific

references, usually tabulated from Monte Carlo simulations. The results W2, U

2, and A

2 for the best fitted

distribution at each age of testing are shown from Table 5-2 to Table 5-6 (Zapata et al., 2013d).

5.3.2.4 Brief review of the maximum likelihood approach

The versatile and reliability of the maximum likelihood do this method the most popular for

parameter estimation (Basu et al., 2009; Rinne, 2009). The maximum likelihood (ML) estimators (MLE)

are those parameter values that maximize the likelihood function or its logarithm (the log-likelihood

function). The likelihood is a function of the unknown parameters collected in a vector θ. If n is the total

number of data points, the likelihood is a product of n simple factors called likelihood elements where Li

is expressing the likelihood of an individual observation. The likelihood function describes, for each set

of distribution parameters, the chance that the true distribution has those parameters based on the sample

data. Eq. (5.11) represents the likelihood elements for the case of uncensored observations (xi) of a

continuous variate X with density function f(x|θ) and CDF F(x|θ)

(5.11)

The likelihood and log-likelihood function of an independent sample of size n is represented by

Eq. (5.12) and Eq. (5.13), respectively

(5.12)

(5.13)

The key point of the ML approach is to find that vector , which maximizes Eq. (5.12) or

its logarithm Eq. (5.13). Thus, each one of the partial derivatives with respect to parameters θi (i = 1, … ,

m) of the term in the left hand on Eq. (5.13) is called a likelihood equation or normal equations (Rinne,

2009) and the system of all m likelihood equations is given by Eq. (5.14)

87

where, the symbol ο is used to represent a vector of zeros. Finally, the solution vector is formed

by stationary points of the log-likelihood function and might include the MLE as the global maximum. In

the present work, the maximum likelihood approach will be applied to the two- and three-parameter

Weibull, Gamma, and Log-Normal distributions as an estimating method.

5.3.2.5 Two parameter Weibull distribution

Typically, the two-parameter Weibull distribution (We2) is used, knowing that the three-

parameter Weibull distribution is more robust and usually provide a better characterization of the datasets

(Alqam et al., 2002). The two-parameter Weibull distribution consists when the location parameter

(minimum strength) is fixed to zero (φ = 0) or is set to a known number, ao, which has been previously

obtained (φ = ao). There are a variety of methods to find the two Weibull parameters, being the graphical,

moments, and maximum likelihood methods the most used (Rinne, 2009). In the present thesis the scale

and shape parameters for the two-parameter Weibull distribution is obtained by using the maximum

likelihood approach explained above.

5.3.2.5.1 MLE applied to two-parameter Weibull distribution

In the particular case of the We2 distribution, the corresponding log-likelihood function is given

by Eq. (5.15) as follows

And the associated system of likelihood equations is given by Eqs. (5.16)-(5.17)

88

The vector is formed by the estimated parameters ( , ) that maximize Eq. (5.15) and

provide the solution of the problem. In the present thesis, the Newton-Raphson algorithm was used to

solve the iterative nonlinear equations.

5.3.2.6 Three-parameter Weibull distribution

Eqs. (5.2) and (5.3) represent the general form of the three-parameter Weibull distribution (We3)

as a member of the family of extreme value distributions. Nevertheless, when compared with We2, the

mathematical estimate of the three parameters is not a straightforward task (Abbasi et al., 2011). But,

once the three parameters are successfully calculated by using any one of the seventeen numerical

techniques available (Zanakis, 1979), the distribution offers a great flexibility to fit and interpret datasets.

In the present work, three methods were explored for parameter estimation in the We3: (i) the Maximum

Likelihood Method (MLE), (ii) the Modified Moment Method (MMM), and (iii) the Probability Weighted

Moments (PWM).

5.3.2.6.1 MLE applied to three-parameter Weibull distribution

For the case of the We3 the corresponding log-likelihood function is given by Eq. (5.18)

Eq. (5.18) is maximized with respect to φ, β, and λ as showed in Eqs. (5.19)-(5.20)

89

The solution vector is formed by the estimated parameters that maximize

Eq. (5.18) being the solution of the problem. Nevertheless, as in the case of We2, the exact distribution of

the MLE of the We3 is unknown. Therefore, a system of interdependent and nonlinear equations should

be solved simultaneously by numerical iterative techniques. However, in the case of the We3, the

introduction of the location parameter causes computational complexities by the geometry of Eq. (5.18).

In addition, other possible complications can arise from large or low values of the scale parameter.

Whereas values of the shape parameter less than 2 may favor non-concavity of Eq. (5.18), and high values

may cause slow convergence (Rinne, 2009). Despite the large list of algorithms available in literature, the

determination of MLE in the case of the We3 is considered a nontrivial problem because of the

complexity of the nonlinear likelihood equations (Rinne, 2009). In the present thesis, the Newton-

Raphson algorithm was the numerical technique used to solve the nonlinear iterative equations.

5.3.2.7 Modified moment method

The principles of the moment’s methods are based on equating sample moments to the

corresponding distribution moments, in this particular case referred to the moments of the We3.

Nevertheless, improvements have been made to the basic moment method, resulting in the Modified

Moment Method (MMM) (Alqam et al., 2002). Therefore, in the present study, the Modified Moment

Method described in Dodson (1994) is employed. In this sense, parameters of the We3 are estimated from

the following equations:

90

In Eqs. (5.21)-(5.23) a hat indicates the estimate of the respective parameter under consideration,

n is the total number of data points, and x1 represents the first order statistic of X(i:n).

5.3.2.8 Probability weighted moments

The Probability Weighted Moments (PWM) of a random variable X with CDF type F is the

quantities represented in Eq. (5.24)

where p,r,s . Replacing p = 1 and r = 0 in Eq. (5.24) gives the PWM represented in Eq. (5.25)

where, λ > 0 and Γ(z) is the complete Gamma function defined in Eq. (5.26)

with ζ > 0. Now, the first three PWMs are considered in order to estimate the Weibull parameters φ, β and

λ. Following the work of Toasa Caiza and Ummenhofer (2011) it could be demonstrated that denoting Ms

=M1,0,s, s = 0, 1, 2 is obtained the system of equations represented by Eqs. (5.27)-(5.29)

91

Nevertheless, it is required to know the value of the PWMs Mo, M1, M2 to solve the Eqs. (5.27)-

(5.29) and extract the Weibull parameters. Then, are established estimators dependent on the ordered

experimental dataset. For this reason, let X(i:n) be the order sample of the experimental splitting strength

results when ordering from smallest to largest. Then using estimators (denoted by the hat symbol) of the

first three PWMs Ms (Toasa Caisa et al., 2011) and after some mathematical arrangements, are estimated

values of the φ, β, and λ Weibull parameters. These can be determined by Eqs. (5.30)-(5.32) as follows

92

5.3.2.9 Gamma distribution

The Gamma distribution includes the Chi-squared, the Erlang and the Exponential distributions as

special cases, but the shape parameter of the Gamma is not confined to integer values (Forbes et al.,

2011). Eq. (5.33) represents the two-parameter Gamma distribution function

with x ≥ 0 and β, λ > 0. In Eq. (5.33) β and λ represent the scale and shape parameters, respectively, and

Γ(λ) is the complete Gamma function defined previously in Eq. (5.26). The corresponding log-likelihood

function of the Gamma distribution is given by Eq. (5.34)

Continuing with the partial derivatives with respect to the unknown parameters and after some

rearrangements, the MLE are solutions of the simultaneous nonlinear expressions given by Eqs. (5.37)-

(5.38)

5.3.2.10 Log-Normal distribution

The density function of the two-parameter log-Normal distribution with scale parameter β and

shape parameter λ is given in Eq. (5.39)

93

with x, λ > 0. The corresponding log-likelihood function of the Log-Normal distribution is given by Eq.

(5.40)

In the case of the Log-Normal distribution, the MLE are explicit solutions of the expressions

given by Eqs. (5.41)-(5.42)


After the programming of the full set of equations above showed and applied these equations to

the dataset for tension tests, the Weibull statistical analyses: Weibull modulus, the minimum strength, and

characteristic strength of the concrete systems at each age of testing are shown in Table 5-2 to Table 5-6.

Moreover, these tables show the statistical information and estimated parameters for samples exhibiting a

non-Weibull behavior such as Gamma or Log-Normal distributions. Nevertheless, the following

discussion is limited to the systems which fitted to a Weibull distribution either three or two parameters.

The Weibull modulus varied from 7.47 (minimum) to 18.91 (maximum) for the We2 at the ages of 56 and

90 days, respectively. In the case of the We3, the modulus ranged from 1.42 (minimum) to 11.87

(maximum) at the ages of 90 and 28 days, respectively. In average, the Weibull modulus estimated from

the We2 models was 11.6, which fits well with other researches where values ranging from 8 to 14 have

been reported (Man and van Mier, 2011). On the other hand, an average value of the Weibull modulus of

94

5.0 was estimated from the We3 models (Table 5-2 to Table 5-6) (Zapata et al., 2013d). This fact

demonstrated that the methodology of statistical estimation of the Weibull parameters could present

differences in the magnitudes even in similar systems. Therefore, when comparing Weibull modulus from

different sources, special attention should be put in the type of model used.

Within the Weibull models, from Table 5-2 to Table 5-6 it is noted a slight difference between the

MMM and the MLE for the We3 distribution. Where We3-MLE was the best fitting 20% of the time and

the We3-MMM resulted as the best adjusting technique 14% of the time. This result is in agreement with

other research carried out on brittle materials (Alqam et al., 2002). It is extremely important to note that

the PWM estimated 67% of the time the three-parameters in the We3 model. Thus, the PWM provided

the best fitting curve between the techniques included in this study. This pattern occurs even for

parameters not presenting a physical sense, i.e., φ < 0 or values up to 7 orders of the magnitude higher

than the common found in concrete samples (shown as dashed lines in Table 5-2 and Table 5-5). Also, it

is important to note that fails in the S static (p-value < 0.05) were not necessarily associated with fails in

the We3 models. Therefore, we recommend the three-parameter Weibull model fracture analysis in

concrete specimens taking advantage of its flexibility even when the We2 model failed.

Table 5-2. Statistical results and estimated parameters at 3-days

{nS:SF:FA}

(wt%)

Best Goodness-of-fit test (p-value) Estimated parameters

fitting Method S W2 U2 A2 φ β λ

{0.0:0.0:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 5.82 12.16

{3.0:0.0:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.48 4.60 9.98

{6.0:0.0:0.0} We3 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.05 4.45 9.48

{0.0:0.0:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.69 4.07 7.39

{0.0:0.0:40} We3 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.12 2.06 6.37

{3.0:0.0:40} We3 PWM < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.93 1.15 2.38

{3.0:0.0:20} We3 PWM < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.09 1.03 1.79

{6.0:0.0:40} We3 PWM ≥ 0.10 < 0.10 < 0.10 ≥ 0.10 0.83 3.71 7.39

{6.0:0.0:20} We3 PWM ≥ 0.10 < 0.10 < 0.10 < 0.10 2.96 2.35 4.19

{0.0:10:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 < 0.10 ----- ----- -----

{0.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.72 1.66 2.93

{3.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.60 3.98 9.94

{3.0:10:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.97 1.92 4.70

{6.0:20:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 5.54 12.35

{6.0:10:0.0} Gamma MLE < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 0.03 215.00

{1.5:0.0:10} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 5.57 9.38

{0.0:10:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 4.56 10.41

{0.0:5.0:10} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 5.17 9.97

{1.5:5.0:0.0} We3 PWM ≥ 0.10 < 0.05 < 0.05 < 0.05 ----- ----- -----

{1.5:10:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.10 2.10 4.10

{1.5:5.0:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.24 1.30 3.24

{1.5:5.0:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 4.98 16.11

{3.0:5.0:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.62 2.25 5.06

{3.0:10:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.05 1.97 5.73

95


{nS:SF:FA}

(wt%)



{0.0:0.0:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.42 2.42 3.61

{3.0:0.0:0.0} We3 PWM < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.35 1.99 2.62

{6.0:0.0:0.0} We3 PWM < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.01 2.14 1.49

{0.0:0.0:20} We3 PWM < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.29 1.58 1.68

{0.0:0.0:40} We3 MMM < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.97 1.02 1.18

{3.0:0.0:40} We3 MLE < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.35 1.42 1.79

{3.0:0.0:20} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.28 5.34 8.33

{6.0:0.0:40} We3 MLE ≥ 0.10 < 0.10 < 0.10 < 0.10 1.95 3.56 5.15

{6.0:0.0:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.06 2.74 4.67

{0.0:10:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 5.67 11.33

{0.0:20:0.0} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.69 1.62 2.89

{3.0:20:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 6.86 10.77

{3.0:10:0.0} We3 MMM < 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.69 1.29 2.32

{6.0:20:0.0} LN MLE < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.03 0.07

{6.0:10:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.15 2.31 4.05

{1.5:0.0:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.76 4.86 11.60

{0.0:10:20} LN MLE < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 5.95 0.12

{0.0:5.0:10} We3 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.84 3.33 3.18

{1.5:5.0:0.0} Gamma MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 0.10 68.28

{1.5:10:10} Gamma MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 0.15 45.83

{1.5:5.0:10} We3 MLE < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.32 1.41 1.83

{1.5:5.0:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.66 1.47 2.61

{3.0:5.0:10} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 6.83 12.83

{3.0:10:20} We3 MLE < 0.01 < 0.05 < 0.05 < 0.05 4.77 1.63 1.91


{nS:SF:FA}

(wt%)



{0.0:0.0:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.51 7.88

{3.0:0.0:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.64 4.61 5.96

{6.0:0.0:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.25 2.82 4.83

{0.0:0.0:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.36 6.13 11.27

{0.0:0.0:40} We3 PWM < 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.39 0.74 2.88

{3.0:0.0:40} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.47 1.06 2.70

{3.0:0.0:20} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.93 3.04 2.49

{6.0:0.0:40} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.17 17.25

{6.0:0.0:20} We3 PWM < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.80 2.59 2.55

{0.0:10:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.63 8.52

{0.0:20:0.0} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.53 5.64 8.36

{3.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.74 7.74 8.25

{3.0:10:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.18 6.68 6.40

{6.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.57 7.58 7.84

{6.0:10:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.93 10.46

{1.5:0.0:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.53 3.15 4.05

{0.0:10:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.76 6.76 11.61

{0.0:5.0:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.50 5.24 7.75

{1.5:5.0:0.0} We3 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.57 5.71 7.19

{1.5:10:10} We3 PWM < 0.05 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.36 2.54 3.43

{1.5:5.0:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.24 6.84 11.87

{1.5:5.0:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.79 12.45

{3.0:5.0:10} We3 MLE ≥ 0.10 < 0.01 < 0.01 < 0.01 0.84 7.12 8.52

{3.0:10:20} We2 MLE ≥ 0.10 < 0.10 < 0.10 < 0.10 0.00 7.34 7.80

96


{nS:SF:FA}

(wt%)



{0.0:0.0:0.0} We3 PWM < 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.44 2.73 2.08

{3.0:0.0:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 6.42 2.17 2.69

{6.0:0.0:0.0} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.40 3.61 4.72

{0.0:0.0:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.05 3.88 4.65

{0.0:0.0:40} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.76 5.77 9.55

{3.0:0.0:40} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.37 4.17 7.42

{3.0:0.0:20} We3 PWM ≥ 0.10 < 0.01 < 0.01 < 0.01 4.87 3.17 4.01

{6.0:0.0:40} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.00 3.14 4.39

{6.0:0.0:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.09 13.03

{0.0:10:0.0} We3 PWM ≥ 0.10 < 0.01 < 0.01 < 0.01 ----- ----- -----

{0.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.47 4.93 3.64

{3.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.20 3.46 3.11

{3.0:10:0.0} We3 PWM ≥ 0.10 < 0.01 < 0.01 < 0.01 ----- ----- -----

{6.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.10 2.81 2.48

{6.0:10:0.0} We3 MLE < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.11 2.92 2.15

{1.5:0.0:10} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.77 11.73

{0.0:10:20} We3 PWM ≥ 0.10 < 0.10 < 0.10 ≥ 0.10 5.17 2.98 4.10

{0.0:5.0:10} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.73 11.32

{1.5:5.0:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.19 4.19 5.29

{1.5:10:10} We3 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.03 2.60 4.07

{1.5:5.0:10} We2 MLE ≥ 0.10 < 0.10 < 0.10 ≥ 0.10 0.00 7.20 7.47

{1.5:5.0:20} We3 PWM < 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.74 2.79 2.80

{3.0:5.0:10} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.11 9.79

{3.0:10:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.65 11.48


{nS:SF:FA}

(wt%)



{0.0:0.0:0.0} We3 MLE < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.98 1.80 1.77

{3.0:0.0:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.51 3.18 2.48

{6.0:0.0:0.0} We3 MLE < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.46 1.55 1.50

{0.0:0.0:20} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.97 2.73 2.47

{0.0:0.0:40} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 1.16 6.06 6.52

{3.0:0.0:40} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.35 9.00

{3.0:0.0:20} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.38 3.79 5.95

{6.0:0.0:40} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 7.81 13.03

{6.0:0.0:20} We3 MLE < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.99 1.75 1.43

{0.0:10:0.0} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 5.05 3.29 3.80

{0.0:20:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 9.10 13.67

{3.0:20:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 2.95 6.14 11.62

{3.0:10:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.99 12.74

{6.0:20:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 9.25 18.91

{6.0:10:0.0} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 4.66 4.05 4.19

{1.5:0.0:10} We3 MMM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.43 8.19 9.64

{0.0:10:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.51 15.61

{0.0:5.0:10} We3 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.77 7.66 9.29

{1.5:5.0:0.0} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.19 8.13

{1.5:10:10} We3 PWM ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.38 4.81 5.62

{1.5:5.0:10} We3 MLE < 0.01 ≥ 0.10 ≥ 0.10 ≥ 0.10 6.73 1.17 1.42

{1.5:5.0:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.09 11.96

{3.0:5.0:10} We3 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 3.60 5.21 6.19

{3.0:10:20} We2 MLE ≥ 0.10 ≥ 0.10 ≥ 0.10 ≥ 0.10 0.00 8.31 12.62

97

In average the Gamma and Log-normal distributions were the models providing the best fit with

2.5% and 1.7% of the time; respectively (Zapata et al., 2013d). It is worthwhile to note that the 25% of

the time the We2 was the model with best fit against a 70% for the case of the We3 (Table 5-2 to Table

5-46). The present results on high strength concrete samples are consistent with other researches

(Abdallah et al., 1996; Alqam et al., 2002) who have reported the prevalence of the We3 when compared

with the We2 model in composite materials. From a statistical point of view, once the possible

computational technical difficulties have been solved, these results are expected since the We3 model is

an extremely flexible distribution (Abbasi et al., 2011; Rinne, 2009). In addition, these results confirm the

accuracy of the We3 model when applied to relatively small datasets (Peiying et al., 2012).

It is accepted that the mathematical treatment required in fitting the three-parameters in the We3

model is more complex than in the case when the location parameter is set to zero (Rinne, 2009; Alqam et

al., 2002; Abdallah et al., 1996; Toasa Caiza and Ummenhofer, 2011). Indeed, in the present work the

statistical estimation techniques were developed using modern and powerful approaches such as the

MMM and PWM, in addition to the classical MLE. Table 5-7 shows the sample size and additional

statistical information related to the post-fitting Weibull procedures measured by both the p-value and the

Pearson’s correlation coefficient (r) Eq. (5.43)

In Eq. (5.43) the ψ represents the estimated Weibull parameters for each dataset and is the

average splitting tensile strength (MPa) from laboratory experiments. From Table 5-7 it is observed that

the scale parameter of the We2 presents a closer statistical relationship (p-value < 0.05) than location or

shape parameters. This fact is expected because the Weibull scale parameter is related to the characteristic

strength in a physical sense. That is, the strength value with failure probability of 1-e-1

. In fact, the scale

parameter is often taken to be approximately the mean strength (Meyers and Chawla, 2009). However,

from Table 5-7 the p-value was not always significant and for the We3 model only one time it was

statistically relevant (at 28-days), and the Pearson’s value (r = 0.6597) was not as high as in the case of

the We2 (r ≥ 0.9620) when the p-value < 0.05. It is attributed to the fact that the β parameter is the

strength value with failure probability is 1-e-1

when φ = 0. Hence, the former value is relatively close to

the average strength and sometimes the β parameter is associated with the mean strength. Although,

98

strictly this latter is the strength value which failure probability is exactly 0.50. Then, a larger deviation of

the Pearson’s linearity could be expected when φ ≠ 0, i.e., when the We3 model is applied (Table 5-7).

Table 5-7. Relationship between estimated Weibull parameters and average splitting strength

Age

(days)

Weibull

type

N°

samples vs. φ vs. β vs. λ

P-value r P-value r P-value r

3 We2 6 ----- ----- 0.0000 0.9971 0.9902 -0.0065

We3 15 0.1256 0.4134 0.5231 0.1791 0.6769 0.1174

7 We2 3 ----- ----- 0.0619 0.9953 0.7882 0.3267

We3 16 0.1011 0.4246 0.3065 0.2729 0.1804 0.3526

28 We2 6 ----- ----- 0.0021 0.9620 0.8924 -0.0719

We3 17 0.0640 -0.4587 0.0040 0.6597 0.0453 0.4911

56 We2 6 ----- ----- 0.0000 0.9983 0.1828 0.6269

We3 15 0.0010 0.7604 0.2994 -0.2872 0.0692 -0.4815

90 We2 9 ----- ----- 0.0000 0.9942 0.0181 0.7575

We3 15 0.5179 -0.1813 0.1180 0.4211 0.0214 0.5870

Contrarily, significant statistical relationships were not observed between the location parameter

(only valid for the We3) and the average fracture strength. The exception was at 56-days when a positive

linear relationship (r = 0.7604 with p-value = 0.0010) could be established, indicating that higher values

of the average fracture strength are associated with higher values of minimum strength. Finally, from

Table 5-7, showing relationship between the average fracture strength and the Weibull modulus, it is

noted that the We2 and We3 models were statistically significant only one and two times, respectively,

and the Pearson’s values were positive. Indicating that lower scatter in the measured strength is associated

with higher values of splitting strength. Nevertheless, the r-values are not large enough, being the highest

0.7575 when We2 model was used. While for We3 models, the deviation from the linearity between these

two variables were markedly predominant (when significant).

Table 5-8 reports statistical information concerned with the location and shape estimated Weibull

parameters against the coefficient of variation and the first order statistic (x1:n) of the splitting tension

tests. The results show that the maximum estimated value of the location parameter is generally less than

the minimum split tension point. Nevertheless, there is not a strong linear relationship between these

variables as measured by the Pearson´s correlation and the relationship was statistically significant in

three out five days of testing (3, 7, and 56-days). On the other hand, when this value is compared with the

average fracture stress, the results showed that the location parameter is approximately one half of the

average splitting strength (Table 5-8). The average values of φ/x1:n and φ/ are 0.67 and 0.53,

respectively. The fact that the location parameter was lesser than the first order statistic (φ ≈ 0.7 x1:n) is

partially explained by the majority of the datasets adjusted to We3 instead of We2 (Zapata et al., 2013d).

99

Table 5-8. φ and λ estimated parameters versus r and the first order statistic

Age

(days)

Weibull

type

N°

samples

CV vs. λ x1:n vs. φ

φ/ X1

φ/ P-value r P-value r

3 We2 6 0.0083 -0.9245 ----- ----- ----- -----

We3 15 0.9060 -0.0334 0.0250 0.5747 0.62 0.51

7 We2 3 0.1693 -0.9648 ----- ----- ----- -----

We3 16 0.1039 -0.4215 0.0215 0.5687 0.80 0.63

28 We2 6 0.0016 -0.9676 ----- ----- ----- -----

We3 17 0.5995 -0.1372 0.5423 0.1590 0.52 0.43

56 We2 6 0.0234 -0.8722 ----- ----- ----- -----

We3 15 0.0980 -0.4432 0.0030 0.7111 0.73 0.56

90 We2 9 0.0015 -0.8848 ----- ----- ----- -----

We3 15 0.1332 -0.4060 0.2298 0.3299 0.66 0.52

Another important relationship investigated in the present study was the couple between the

coefficient of variation from laboratory experiments and the Weibull modulus from computational

analyses. In Table 5-8 it is shown that the only statistical significant relationships were found by using

We2. And also, the degree of linear association is very high and negative. This implies that high values of

dispersion are associated with small values of the shape parameter, as expected. Unfortunately, at least

from a statistical significance level of 5% one possible disadvantage from Table 5-8 deals with the fact

that the Weibull modulus in the We3 models was not directly related to the scatter observed in the

strength values using a Gaussian approach (Table 5-1). This latter fact could result in a strong point of

decision at the moment of choice between the We2 or We3 models, because the physical sense of the

Weibull modulus is of great concern in the analysis and reliability of civil engineering structures.


In the present chapter splitting tensile failures on concrete samples presented in Chapter IV were

investigated using Weibull models. The estimated Weibull parameters were obtained by using different

advanced nonlinear methodologies. The principal results can be summarized as follows:

The Weibull modulus available in the literature by using supplementary cementitious materials is

scarce and using nano-particles alone or in conjunction with other mineral addition is specially

limited. Thus, the Weibull parameters obtained from nS or nS-SF/nS-FA-SF as supplementary

cementitious materials as reported in the present study are novel.

If a three-parameter Weibull distribution is to be used to characterize data in concrete samples

containing supplementary cementitious materials such as SF, FA and nS, it is recommended to

apply the Probability Weighted Moment technique. This recommendation is based in the

100

likelihood when obtaining a better fitting in the estimated parameters when compared to the

classical maximum likelihood method.

Based on the latter observation, it could also be concluded that the use of alternative procedures

i.e., Probability Weighted Moment and/or Modified Moment Method in conjunction with

maximum likelihood in an integrated form, reduced the chance of divergences and/or parameter

estimations without physical sense. However, the simultaneous evoked of each one of the

algorithms in a single program require that higher levels of computational efficiency should be

provided in order to solve the complex equations. This mechanism only reduced the likelihood of

failure but not solved the problem in a general form, because the nonzero lower bound, when

dealing with the three-parameter Weibull estimation, could not be avoided.

The two-parameter Weibull distribution could not be rejected at the 5% level of significance only

for the 25% of the datasets investigated in the present work. Nevertheless, the relative simplicity

in the mathematical application of the two-parameter Weibull model when compared with any

method used to estimate the three-parameter Weibull models provides an advantage.

The average results (at 5% of significance) showed that one disadvantage of the Weibull modulus

estimated from the three-parameter Weibull models consisted in the fact that, this parameter did

not allow direct relationship with the scatter in the strength values obtained from laboratory

experiments. Contrary, this behavior was not observed in the two-parameter Weibull model.

Therefore, it could result in certain degree of rejection of the three-parameter Weibull distribution

against the simplest two-parameter Weibull model. Furthermore, the physical sense of the

Weibull modulus has great importance in structural and reliability analysis.

101

CHAPTER VI

6 GENERAL CONCLUSIONS AND RECOMMENDATIONS

6.1 Summary of the chapters

The present thesis assessed the rheological and mechanical characterization of Portland cement

(PC) mixes containing amorphous-SiO2 in presence of polycarboxylate-type superplasticizer (SP). The

work comprised six chapters, where Chapters II, III, IV and V were related to the experimental and

computational treatments to get the proposed objectives.

A summary of the chapters II, III, IV and V is presented as follows:

In Chapter II, five PC-SP systems were analyzed at w/b=0.40 and the best PC-SP couple on

rheological basis using the MCT was found. Then, the best PC-SP was cast at w/b=0.35 and 0.40 but

adding micro-SiO2 (SF) and nano-SiO2 (nS). The rheological properties in the fresh state showed that

Mineral admixtures in superplasticized grouts decreased the flow times and the saturation dosages when

compared to the superplasticized-control specimens.

Chapter III mechanical and rheological validation of Chapter II was carried out using the best PC-

SP found in Chapter II but now in binary mortar and concrete blends of PC-nS(1,2,3 wt%)/SF(5,10,15

wt%) at w/b=0.35. In the fresh state factorial experimental designs at w/b=0.35 on mortar samples

produced flow area, unit weight and air content in mineral admixture-systems better than in

superplasticized-control samples. In the hardened state, the maximum compressive strength was obtained

in SF=15 wt% and nS=1 wt%. Also, SEM examinations in the ITZ suggested that compressive strengths

of nano-SiO2-systems presented densification and filler effects, whereas micro-SiO2-systems only filler

effects. From validation of the rheological properties on concrete sample the results showed that MCT

must be interpreted carefully when mineral additions are applied in concrete mixes.

Chapter IV presents experimental and computational findings related to compressive and tensile

strength of concrete containing nano-SiO2, micro-SiO2, fly ash, and polycarboxylate-superplasticizer. At

different ages, three central-composite experimental designs (DOE) were performed. The statistical

102

results indicated that binary mixes composed of nS-SF are the optimal choice to gain compressive and

tensile strength. However, results also showed lack-of-fit of the second-order. Hence, by using artificial

neural simulations (ANN), the compressive and tensile strength of the systems could be successfully

modeled and ANN-sensitivity analysis could effectively explain the lack-of-fit inherit in the DOE. Due to

this latter condition, the ANN results were more representative of the surface responses than the results

from DOE. Consequently, ANN simulations brought forth better understanding of the overall behavior

because the evolution through the time of the systems.

In Chapter V the tensile strength of concrete compositions tested in Chapter IV was investigated.

Splitting tensile failures were carried out to investigate the accuracy of three-parameters Weibull models.

The estimated Weibull parameters were obtained by using different advanced nonlinear methodologies.

This strategy when applied to the three-parameter models permitted to overcome technical divergences in

some datasets associated with the solely used of the usually employed maximum likelihood method.

Finally, statistical analysis pointed out that some specific combinations of amorphous silica exhibited

higher Weibull modulus than the control case.

6.2 Principal conclusions

The present thesis assesses the rheological and mechanical characterization of Portland cement

(PC) mixes containing amorphous-SiO2 in presence of polycarboxylate-type superplasticizer (SP). The

work comprised six chapters, where Chapters II, III, IV and V were related to the experimental and

computational treatments. The principal conclusions for chapters II, III, IV and V are presented as

follows:

Chapter II: Compatibility analysis and rheological performance between Portland cement Type I

and micro/nano-SiO2 particles in presence of polycarboxylate-type superplasticizer.

The MCT measurements show that saturation dosage, flow time and loss of fluidity exhibited a

nonlinear behavior in grouts with micro- and nano-SiO2 particles and chemical additions, as when

compared to the control samples.

The results obtained here suggest that under superplasticized conditions nS-grouts improved its

rheological behavior at low both w/b ratios and replacements levels, while high replacements

levels of nS tend to exhibit better fluidity at high w/b ratios.

103

Chapter III: Fresh state analysis and compressive strength on superplasticized micro/nano-SiO2

mortars (w/b=0.35).

The micro and nano SiO2 additions in combination with the appropriate use of superplasticizers

could increase the compressive strength of the mortar systems. The maximum strength in nS-

system was reached at 1.0 wt%, whereas in SF-systems, it was at a level of replacement in the

order of 15 wt%. In addition, the highest compressive strength was obtained in SF-systems.

Nevertheless, evidence from SEM analysis showed that improvement in compressive strength of

SF-systems was primarily by filler effect, whereas in nS-systems it was due to both densification

and filler effect of the ITZ.

Based on the results of the current study it is possible to conclude that the MCT method must be

interpreted carefully when mineral additions are applied in concrete mixes. In the present research

the true behavior found in the fresh concrete tests was effectively anticipated by the graphical

trend observed in the MCT analysis. Nevertheless, the numerical results registered from neither

the minimum values nor the break points in the curves effectively reflected the SP amounts

between grouts and concrete samples.

Chapter IV: Nonlinear statistical analysis in compressive and tensile strengths of concrete

containing amorphous silica.

The simultaneous used of SF and nS additions in concrete induced a pronounced nonlinear effect

on the compressive and tensile strength response variable. Also, the curvature exhibited by the

response surfaces continuously switched from positive to negative curvature. This complex

behavior could help to resolve the lack-of-fit of the second-order model presented in the DOEs

with nS, SF, and FA as inputs.

The general results from response surface analysis of the design of experiments indicate that, in

the developing of the second-order polynomial models, the analysis of variance taken into

account the 95% of confidence statistical level showed that the most important parameters

influencing compressive strength were the linear terms of nS and FA and the interactive terms

nS·SF and nS·FA for both compression and tension tests. These behaviors were also observed by

means of two independent algorithms using ANN simulations.

104

The optimal levels of mineral admixtures at later age (90-days) from designed experiments

showed that compressive and tensile strengths were 43 and 38% better than the control concrete

samples. For both cases, i.e. compression and tension states, the nS-SF couple was the best

system (nS → 2.4 and SF → 19 wt%). From an environmental point of view, this result is

extremely important since the silica fume presence in its optimum case can be easily related with

reductions in the clinker factor. On the other hand, the nanosilica presence in this ternary system

(PC-SF-nS) could bring not only mechanical but additional benefits in the durability of the

concretes.

Chapter V: Weibull analysis on tensile strength of concrete containing amorphous silica.

The Weibull modulus available in the literature by using supplementary cementitious materials is

scarce and using nano-particles alone or in conjunction with other mineral addition is specially

limited. Thus, the Weibull parameters obtained from nS or nS-SF/nS-FA-SF as supplementary

cementitious materials as reported in the present study are novel.

The average results (at 5% of significance) showed that one disadvantage of the Weibull modulus

estimated from the three-parameter Weibull models consisted lies in the fact that, this parameter

did not allow direct relationship with the scatter in the mean value obtained from laboratory

experiments. Behavior was not observed in the two-parameter Weibull model. Therefore, it could

result in certain degree of rejection of the three-parameter Weibull distribution against the

simplest two-parameter Weibull model. Furthermore, the physical sense of the Weibull modulus

has great importance in structural and reliability analysis.

6.3 Recommendations for future works

The environmental capabilities and the fresh state benefits of the fly ash motivate the employment

of this material solely or in conjunction with nanosilica particles. On the other hand, based on the

extremely high reactivity capacity of the amorphous nanosilica particles, the use of nanosilica

could be expected to compensate for the negative effect induced by the high replacement of

cement for fly ash. Nevertheless, at least under the present experimental w/b conditions, type of

fly ash employed, age of testing (up to 90 days) and proportions of the combined use of nS and

fly ash particles, the latter did not show favorable conditions. That is, the fly ash employed did

105

not work as expected neither acting solely or in fly ash-nanosilica concrete systems. Therefore, it

is recommended in new experiments use at least two different commercial types of fly ash, and

tests each one at least in two different w/b ratios.

In the present thesis the micro and nano SiO2 additions could increase the compressive strength of

the mortar systems (w/b=0.35). The maximum strength in SF-mortars was reached at 15 wt%,

whereas in nS-systems it was at 1.0 wt%. In addition, the highest compressive strength was

obtained in SF-systems (at SF=15 wt%) when compared to control and nS-samples. Nevertheless,

evidence from SEM analysis showed that improvement in compressive strength of SF-systems

was primarily by filler effect, whereas in nS-systems it was due to both densification and filler

effect of the ITZ. This result motivates the study of the durability properties in these particular

systems, because an important source of discussion in concrete technology is related to the fact

concerning compressive strength and its relationships with durability properties.

All the results and conclusions presented in this thesis related to concrete samples were obtained

at w/b ratio of 0.35. Thus, it is suggested to perform more analyses using different w/b ratios, in

other typical ranges employed in high-strength concretes such as 0.30 or 0.25. Although based on

the author experience dealing with local materials, it could not be easy to find compatible

Portland cement and superplasticizer couples. Nevertheless, the implementation of the procedure

described on Chapter II in conjunction with new sources of materials could overcome the possible

troubles.

Finally, since the present thesis deal with a widely range of cementitious samples: grouts, mortars

and concretes as naturally expected there were a series of techniques which were carried out in

each one of the above systems. For example, the fresh state of grouts was analyzed on the basis of

physical rheology; however, these experiments could be carried out using a most sophisticate

apparatus such as a rheometer. In a similar manner, in this work the effect induced by packing

density was evolved. Nevertheless, this process was not developed. Therefore, it is widely

recommended that future studies deal with specific cementitious systems; for instance, only

grouts. However, this extensive study could be useful like a preliminary source of ideas and

possible new ways to be explored.

106

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