Estimating Far-Field Stress Using the Mean of Local Stresses

Reliable estimates of far-field stresses are indispensable for robust rock engineering analysis. Here, by using the combined finite-discrete element method, we simulate a series of stress fields of a natural fracture network to examine whether the Euclidean mean of local stresses can be used to estimate the far-field stress. The calculations show that given a large number of local stress measurements, their Euclidean mean gives a close approximation of the far-field stress state. Whereas when only a limited number of local stresses are available, the probability of obtaining a practically acceptable estimate of far-field stress increases with the increasing number of stress measurements. The required number of stress measurements for deriving an acceptable estimate varies with the geomechanical condition; in general, the larger the overall stress variability is, the more local stress measurements are needed. Our research findings suggest that given a limited number of stress measurements, which is often encountered in rock engineering projects, attention is needed when deriving the far-field stress state based on them, and simply using their mean as far-field stress for further rock structure design and numerical analysis may yield erroneous results.