Influence of a nonlinear failure criterion on the bearing capacity of a strip footing resting on rock mass using a lower bound approach

The strength envelope of almost all geomaterials is nonlinear when one considers a wide range of stresses. Therefore, a nonlinear failure criterion needs to be used in stability analysis whenever the effects of nonlinearity are too significant to be neglected. This paper presents a lower bound solution to the bearing capacity calculation of a strip footing resting on a homogenous weightless rock mass using the nonlinear Hoek-Brown (HB) failure criterion. Two types of admissible stress fields are used to develop solutions. The first stress field has three stress legs. The second stress field has a spiral-like shape with n stress legs, where n may vary from 9 to 18 000 (even to infinity). Using two admissible stress fields, equations are derived and used for the calculation of lower bound bearing capacity values of a strip footing on rock mass. The influences of the admissible stress leg number n and the material parameter s in the nonlinear HB failure criterion are investigated. It is found that the lower bound bearing capacity calculated using the spiral-like shape admissible stress field approaches to the true optimum value as the stress leg number n increases, and the nonlinear material parameter s has a strong influence on the bearing capacity of the footing.