Variance of Intact Rock Strength Determined by Triaxial Tests

"Given the results of triaixial tests, regressions are commonly used to evaluate the parameters of failure criteria that model intact rock strength and to perform statistical inferences used to evaluate characteristic values defined in EC7. Statistical robustness of these inferences is affected if the basic hypothesis underlying regression are not met, namely homoscedasticity (constant variance of the errors). This paper presents analyses of 23 sets of triaxial tests, starting by the evaluation of the regression parameters of the Mohr-Coulomb linear criterion and of the Hoek-Brown non-linear criterion, followed by carrying several statistical tests to check the homoscedasticity null hypothesis of independence between the variance of intact rock strength and the confining stress.INTRODUCTIONThough rock engineering design is clearly included in the scope of Eurocode 7(EN1997-1), its implementation raised a wide discussion regarding the applicability of structural safety concepts to geotechnical design of construction works in or on rock masses. The basis of the limit state design philosophy adopted in EC7 is that, for each particular design situation, all the possible limit states for a structure, or part of it, shall be considered and that it shall be demonstrated that the likelihood of any limit state being exceeded is sufficiently small. Though EC7 allows the limit states to be verified by one or a combination of methods, use of calculations is by far the most used, and it is often confused with the EC7 itself. It involves using characteristic values of actions, ground properties and geometrical data, as well as obtaining their design values by the partial factor method.Characteristic value of a given material property is defined in Eurocode (EN 1990) as: “value of a material or product property having a prescribed probability of not being attained in a hypothetical unlimited test series. This value generally corresponds to a specified fractile of the assumed statistical distribution of the particular property of the material or product”. As regards the design value of a material or product property, according to the Eurocode it is a “value obtained by dividing the characteristic value by a partial factor”."