Effect of surface crack on the bearing capacity of strip footing placed on rock mass

In hilly regions, the existence of surface cracks in rock mass induces a potential threat to structural stability. Thus, the present research aims to explore the impact of surface cracks on the loadbearing capacity of strip footing placed on the rock mass. By taking into account the various boundary constraints across the surface of crack edges, the study investigates the presence of two categories of surface cracks, namely（1） separated crack, and（2） fine crack. The lower bound limit analysis is employed in conjunction with the finite element method（LBFELA） to conduct the numerical analysis. In order to evaluate rock mass yielding, the power conic programming（PCP） method is utilized to implement the generalized Hoek-Brown（GHB） failure criterion. The stability of the strip footing is analyzed by determining the bearing capacity factor(Nσγ), which is presented in the form of design charts by varying the strength parameters of rock, including the Geological Strength Index（GSI）, Hoek-Brown material parameter（mi）, Disturbance factor（D）, and Normalised Uniaxial Compressive Strength(σci/γB), where γ is the unit weight of rock mass, and B is the width of strip footing. The study also investigates the impact of cracks on strip footings, considering different positions of the crack（LC） and depths of the crack（DC）. The results demonstrate that the influence of the fine crack is only noticeable until the LC/B ratio reaches 6. However, for the separated crack, its impact remains significant even when the LC/B ratio exceeds 16. The appearance of fine crack at the edge of the footing results in a decrease in the magnitude Nσγ of up to 45%, indicating a substantial reduction in the stability of the footing. The failure patterns are presented and discussed in detail for various cases in this study to examine the effect of surface cracks on the strip footing and to address the extent of the plastic collapse.