Note on measured values for the state of stress in the Earth's crust

Abstract

Although no totally satisfactory methods for measuring the complete state of stress have been devised yet, many efforts have been made to determine the state of stress at different locations. From a compilation of many in situ stress measurements, 50 which yielded the complete state of stress and in which one of the principal stresses is vertical have been selected for a statistical analysis in an endeavor to define the nature of the state of stress in the crust. These data have been analyzed as a whole and divided into three groups depending upon whether the vertical stress is the maximum, minimum, or intermediate principal stress. Linear regression analysis of the values of half the maximum stress difference as a function of half the sum of the maximum and minimum principal stresses have been made. The correlation coefficients for these fits are 0.786 for the data as a whole and 0.848, 0.790, and 0.383 for each of the groups. The slopes of these lines interpreted as a Coulomb friction, range from 0.625 (for those measurements where the vertical stress is the maximum principal stress) through 0.427 (for those cases where the vertical stress is the minimum principal stress), to 0.220 (for those cases where vertical stress is the intermediate principal stress). The 98% confidence limits for these values lie within +19.4% to −16.6%. The 98% confidence limits include the origin, except for the case where the vertical stress is the minimum principal stress, where the mean value of the intercept is 1.3 MPa. This suggests that the value of the cohesion is virtually negligible. Also, the bound to the maximum value of the ratio of the average of the horizontal stresses to the vertical stress suggests that there is a maximum stress difference which the crust can resist near surface which is at least 37.5 MPa, given a normal stress sufficient to generate such a stress difference by friction.