Relationship between point load index and compressive strength of foliated metamorphic rocks at different loading angles

Point load index strength of rock samples is a simple method to estimate the compressive strength of the rock and has been studied by a host of researchers in terms of linear correlations. Although the strength of the rocks has been proven to vary with change in foliation planes, a model with a loading angle with respect to such planes is lacking. This study attempts to correlate the point load index with compressive strength while incorporating the angle of anisotropy. Samples of four metamorphic rocks of foliated nature obtained from the Nepal Himalaya were tested for point load and compressive strengths at different angles ranging from 0 to 90° with an interval of 15°. An investigation carried out on four such rock types showed that the “root mean square error” of the prediction, using around twenty-three published equations for estimation of compressive strength from point load tests that varied between 7.97 and 36.99, despite a high R2 of 0.88 to 0.90. Such variability is due to the angle of anisotropy which is not included in such equations. Simple regression and advanced nonlinear ANOVA using response surface analysis were deployed to ascertain the reasons for the variability of the results. A new model for determining compressive strength with the help of point load index while incorporating the angle of anisotropy, providing interactions of the independent variables, could thus be developed in the process and is reported for the first time. The model showed a very high R2 of 0.93 with an adjusted R2 of 0.92, a predicted R2 of 0.92, and a “root mean square error” of 5.27. The equation developed can thus be used for predicting compressive strength with a high degree of confidence. This analysis can be quite useful in projects frequented by anisotropic rocks where strength estimation has to be done frequently owing to recurrent directional effects of the orientation of the excavation and related rock mass anisotropy.