Lower Bound Bearing Capacity of Strip Footings on Jointed Rock Masses: A Reliability-Based Approach

The bearing capacity of foundations on rock masses is complex because it is mostly a function of both the intact rock material and the rock discontinuities. The allowable bearing capacity of foundations of structures resting on jointed rock masses with one and two sets of discontinuities is of prime interest to rock mechanics engineers. Jointed rock mass properties are generally spatially variable. The uncertainties may exist due to the laboratory estimation of in situ rock properties. The factor of safety concept in rock mechanics in the estimation of allowable bearing capacity is inadequate to account variability. Reliability based design optimization (RBDO) is accomplished using statistical parameters and probability density functions for each discontinuity parameter. Deterministic bearing capacity is estimated using a lower bound bearing capacity model which is known as the Bell model coupled with a simple discontinuity strength model. Allowable bearing capacity of strip foundations resting on jointed rock masses is computed by considering the variability associated with the jointed rock mass properties, namely discontinuity orientation (θ₁), rock material cohesion (c_r), rock material frictional angle (ϕ_r), discontinuity cohesion (c_i) and discontinuity frictional angle (ϕ_i) and uniaxial compressive strength of intact rock (σ_ci). The design charts for the estimation of allowable bearing capacity factor are presented for the discontinuity orientation of joints in rock mass for the target reliability indices ranging from 1 to 6.