Strength modelling of geomaterials with random systems of structural joints

Strong-geomaterial samples–such as monolithic rock, concrete, and firm clay–are often weakened by random discontinuities called weak joints (fissures, cracks). The paper focuses on a theoretical strength evaluation of such samples using standard methods of series reliability systems; it is assumed that the shearing failure modes generated by structural joints are independent elements of the system. Special attention is paid to the number k of elements in the system which is randomized by making use of the Poisson probability distribution. Closed-form solutions for the random strength of samples, i.e. distribution functions, are derived for randomly equivalent continua, both anisotropic and isotropic. In particular, such solutions can yield the average strength of the structured sample (the homogenized or the effective one) and its higher-order moments, etc. The examples reveal a strong reduction of the strength if weak joints concentrate around some critical angles, but primarily if the number of discontinuities increases.