COMPARATIVE STUDY OF STATISTICAL STRENGTH CRITERIA FOR ROCKS

Abstract

There is a great demand for new solution techniques to rock engineering problems for safe and sound design of structures founded on rock masses. Analysis and design of such structures is carried out based on physical properties of rocks and rock masses which can be obtained by various in-situ and laboratory tests. Unlike other engineering materials, rocks and rock masses pose unforeseen problems giving tremendous challenges to the designers. These difficulties affect not only the cost and schedule of the project, but also the basic integrity of the design of structures. The computational methods used for rock engineering design typically do not consider the variability of rock properties measured or estimated to be representative of the rock mass characteristics. This assumption can grossly mislead the results depending upon the distributive character of the rock property variations. There is therefore the need for methods which takes into account variability in the properties of rocks and rock masses. In the present study, along with Weibull's statistical strength theory (1939), a new probabilistic approach has been proposed for dealing the wide scatter in laboratory values of uni-axial compressive strength test and tri-axial test data. This wide scatter is essentially due to randomness in number as well as orientation of micro-cracks. In the proposed methodology, Stanley's approach (1978), which uses Weibull's theory based on the weakest link model, has been modified to analyze the compressive strength test data. Stanley's approach is applicable to poly-axial tensile stress conditions. Design of all underground excavations requires, as an input data, uni-axial compressive strength and the strength under poly-axial stress conditions. Data from uni-axial compressive strength tests have been analyzed using Weibull's theory and the proposed approach. Triaxial compressive strength test data has been analyzed using proposed tri-axial approach. Corresponding to cumulative distribution functions of state variable, applied stress levels have been obtained and goodness-of-fit tests performed to check the fitness of tests data to these statistical distributions. These cumulative distribution functions have been subsequently invoked to correlate applied stress level at failure and 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. ii