Inherently anisotropic rocks occur in abundance at many rock engineering project sites in Himalayan region. These rocks pose difficulty in analysis and design due to their direction dependent strength behaviour. Moreover the strength varies in a non-linear manner with confining pressure. Mohr- Coulomb strength criterion is widely used by geotechnical engineers for defining strength of rocks subjected to given confining pressure. However, the conventional Mohr-Coulomb (MC) criterion suffers from the limitation that the strength is treated to be linearly dependent on confining pressure. In the present article, the MC criterion has been modified by incorporating non-linear term while retaining the original parameters c and Φ. The non-linearity with confining stress level has been imbibed through critical state concept (Barton, 1976). The criterion has been applied to a triaxial test data base comprising of more than 1140 triaxial tests conducted world-wide on anisotropic rocks. Statistical evaluation of the goodness of fit of the proposed criterion to the data-base has been carried out. Further the predictive capabilities have been evaluated by determining the error in estimation of triaxial strength if only few triaxial test data are available for determining the criterion parameters. The data base has also been back-analysed to assess the critical confining pressure for anisotropic rocks. Statistically the critical confining pressure, for the present criterion, may be taken nearly equal to 1.25σcmax, where σcmax is the maximum value of the UCS out of all orientations of planes of anisotropy. It is concluded that reasonably good estimates of the anisotropic strength are possible through the proposed criterion.
Many rocks encountered in Himalayan region like shale, slate, schist and phyllite are inherently anisotropic and exhibit direction dependency in their strength behaviour. In addition, the strength of the rock also depends on the confining pressure and, the strength response is non-linear especially when the confining pressure may vary over large range. Conventionally, Mohr-Coulomb criterion is the most widely used criterion for rocks. However, the limitation of this criterion in its present form is that the strength is treated to be linearly dependent on the confining pressure. The present study attempts to address the following two main objectives: i) Include nonlinear response in the Mohr-Coulomb criterion while retaining parameters c and Φ in their original form; and ii) consider anisotropic response of the rock for a given confining pressure. A nonlinear strength criterion, which uses shear strength parameters c and Φ as per Mohr-Coulomb criterion, has been suggested based on critical state concept for rocks.
This paper focuses on evaluation of three models; 1) Bussian (1983), 2) Mixture (Korvin, 1982; Technov, 1998) and 3) Glover et al. (2000) for electrical conductivity response of shaly sand reservoir based on volumetric approach and looking for some scheme to solve corresponding equations better than the used schemes so far in literature. As all the models result in non-linear equations, so, there was a need of non-linear scheme to solve these equations. Genetic algorithm (GA), implementing the concept of stretching (Stoffa and Sen, 1991) has been applied to solve non-linear equations and to interpret experimental data of the sample C-26 from Waxman and Smits (1968) paper. The same job has been done by Lima et al. (1995), using the grid search method by minimizing the chi-square error (Bevington, 1969) with a relative RMS error 10.11% for Bussian model and 14.03% for Mixture model. A great improvement is obtained using GA with a relative RMS error 2.47% for Bussian model and 3.92% for mixture model. For Glover’s model which was not evaluated by Lima et al., it was difficult to obtain a relative RMS error less than 13% using GA. Lima et al. (2005) have pointed out that Bussian model shows anomalous behaviour in low salinity range, so, a modified Bussian equation is proposed for low salinity range which is tested for two cases; 1) matrix conductivity ~ fluid conductivity, leads to bulk conductivity ~ fluid conductivity ~ matrix conductivity irrespective of values of other parameters because the system turns to a single phase system and 2) For very small value of porosity, bulk density tends to matrix conductivity for low salinity range.