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Predicting the Compressive
Strength of High­Performance
Silica Fume Concrete by
Bayesian Methods
JOINT C­SHRP/NEWFOUNDLAND BAYESIAN APPLICATION
Prepared for: Canadian Strategic Highway Research Program (C­SHRP)

Prepared by:
Joe English, P. Eng.
Pavement Management Engineer
Department of Works, Services and Transportation
Government of Newfoundland and Labrador

October, 1995

EXECUTIVE SUMMARY

This report describes the evolution of a model to predict the compressive strength of high performance silica fume concrete using Bayesian Regression. This document fulfils the requirements of the agreement between this Department and C­SHRP concerning the Joint C­SHRP /Agency Bayesian Applications Project.

High­performance silica fume concrete is a product that is being used in Newfoundland to achieve high early strength in concrete structures. Contractors have the option of using this product to speed up construction activities such as the removal of false work and form work. As the product is new to the Department, it was suggested that a model should be created to predict its compressive strength based on the properties of the concrete mix.

As Department personnel had little experience with the product, it was decided to initially obtain Prior information only from laboratory tests and old mix designs of normal Portland cement and silica fume concretes. Sample data was selected from the project files of two structures constructed with silica fume concrete in 1994.

Several variables were identified and a Bayesian regression model was created by the computer program XLBAYES using the Data ­ Prior method. Sensitivity analysis of the model suggested that the laboratory data should only be concerned with silica fume cement. Additional laboratory testing was carried out on silica fume concrete and the data on portland cement concrete was removed.

Examination of Model 2 suggested an improvement in the predictive equation. . However, the coefficient of the variable for the fine to total aggregate ratio did not have the correct sign. Laboratory data indicated that the compressive strength of the concrete would increase if the amount of fine aggregate in the mix increases. The observations from the construction of the two structures and conventional practice predicted otherwise.

A third model was developed using an Expert Judgement Prior where three experts were asked to predict the compressive strengths. Posterior equations for two of the experts agreed that the compressive strength would decrease when the fine aggregate content increases. The third expert based his estimates on the laboratory data and predicted otherwise.

It was concluded that Bayesian analysis can be a vital tool when developing predictions. Sometimes soliciting expert judgement is more valuable than collecting data.

Acknowledgements

I would like to thank the following people who contributed to the preparation and completion of this report:

Mr. Keith Foster, P. Eng., Manager of Materials Engineering, who suggested the topic for the report and provided concrete expertise and direction.

Mr. Colin Crane, Senior Concrete Technician, who provided most of the laboratory and field data on the silica fume concrete mix designs and acted as one of the experts.

Mr. Dennis Coffin, Manager of Laboratory and Field Services with Newfoundland Geosciences Ltd.,who contributed expert analysis and the best predictive model.

Mr. Chris Walsh, Engineering Student, who acted as data manager for the first model iteration and wrote the working paper on factors influencing the compressive strength of concrete.

Mr. Mark Nickeson and Mr. Lyle Kajner, associates with VEMAX Management Inc., who provided valuable feedback and assistance with interpretations of the model.

Mr. Luc Frechette and Mr. Greg Williams, Project Managers with C­SHRP who organized the training sessions and workshops on Bayesian analysis.

Mr. Cory Williams, Engineering Student, who proof read most of the report and made several constructive suggestions.

TABLE OF CONTENTS
Introduction
Need for a Model
Staffing
Methodology
 
Model 1
Model Definition
Dependent Variable
Independent Variables
Model Type and Functional Form
Model Inputs
Analysis
Water Cement Ratio
Air Content
Fine to Total Aggregate Ratio
Silica Fume Content
Super Plasticizer Dosage
Constant (Intercept)
Model Statistics
Sensitivity Analysis
Recommendations for Model 1
Model 2
Model Definition
Dependent Variable
Independent Variables
Model Type and Functional Form
Model Inputs
Analysis
Water Cement Ratio
Air Content
Fine to Total Aggregate Ratio
Super Plasticizer Dosage
Constant
Model Statistics and Comparison of Models
Sensitivity Analysis
Recommendations for Model 2
 
Model 3
Model Definition
Dependent Variable
Independent Variables
Model Type and Functional Form
Model Inputs
Analysis
Sensitivity Analysis
Water Cement Ratio: Expert Dennis Coffin
Air Content (2)
Fine to Total Aggregate Ratio: Expert Dennis Coffin
Constant (Intercept): For Expert Dennis Coffin
Recommendations for Model 3

Conclusions

References

 
List of Figures
Figure 1: Probability Distribution Functions for Water Cement Ratio
Figure 2: Probability Distribution Functions for Air Content
Figure 3: Probability Distribution Functions for Fine to Total Aggregate Ratio
Figure 4: Probability Distribution Functions for Silica Fume
Figure 5: Probability Distribution Functions for Super Plasticizer Dosage
Figure 6: Probability Distribution Functions for Constant
Figure 7: Sensitivity of Predictions for Model I
Figure 8: Probability Distribution Functions for Water Cement Ratio ­ Model 2
Figure 9: Probability Distribution Functions for Air Content ­ Model 2
Figure 10: Probability Distribution Functions for Fine to Total Aggregate Ratio ­ Model 2
Figure I 1: Probability Distribution Functions for Super Plasticizer Dosage ­ Model 2
Figure 12: Probability Distribution Functions for Constant ­ Model 2
Figure 13: Sensitivity of Predictions for Model 2
Figure 14: Residual Plot for "Old" Data
Figure 15: Sensitivity of Prior Predictions Across Experts
Figure 16: Sensitivity of Posterior Predictions Across Experts
Figure 17: Probability Distribution Functions for Water Cement Ratio ­ Model 3
Figure 18: Probability Distribution Functions for Air Content 2 _ Model 3
Figure 19: Probability Distribution Functions for Fine to Total Aggregate Ratio ­ Model 3
Figure 20: Probability Distribution Functions For Constant ­ Model 3
List of Tables
Evaluation Table 1: Case Study ­ Concrete Strengths ­ First Run
Evaluation Table 2: Case Study ­ Concrete Strengths ­ Second Run
Table 3: Comparison of Coefficients From Experts
Table 4: Comparison of T­Statistics From Experts

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