A new probabilistic approach to analysis of compressive strength test data of rock specimens

Abstract

In this paper, a new probabilistic approach has been proposed for dealing with the wide scatter in laboratory values of compressive strength test (uni-axial and tri-axial compressive strength tests) data of rock specimens. This wide scatter is essentially due to randomness in number as well as orientation of micro-cracks. In the proposed methodology, Stanley's approach, which uses Weibull's theory based on the weakest link model, has been modified to analyse the compressive strength test data. Stanley's approach is applicable to poly-axial tensile stress conditions. Design of all underground excavations requires, as input data, uni-axial compressive strength and the strength under poly-axial stress conditions. Data from compressive strength tests have been analysed using Weibull's theory and the proposed approach. Corresponding cumulative distribution functions of the state variable, i.e., the applied stress level, have been obtained and goodness-of-fit tests performed to check the fitness of test data to these statistical distributions. These cumulative distribution functions have been subsequently invoked to correlate the applied stress level at failure and the associated risk of failure. The analysis finds its application in specifying the design strength of rocks or rock masses for a permissible probability of failure.

Keywords:

• Weibull's theory
• Stanley's approach
• probability of failure
• compressive strength

Acknowledgements

The authors wish to express their sincere thanks to Professor (Retd.) Bhawani Singh, University of Roorkee (currently Indian Institute of Technology Roorkee), Roorkee, India, and Professor Deepak Kashyap, Indian Institute of Technology Roorkee, Roorkee, India, for the precious suggestions and discussion during the development of the present work.