Literature Review of Estimating the Bearing Capacity of Rough Footings by the Stress Characteristic Lines Method

The footing of all buildings will be located on the ground. Thus, civil engineers are always faced with the problem of estimating the bearing capacity of shallow foundations. So far, various analytical and numerical methods such as stress characteristic lines method, limit equilibrium method, lower and upper boundary limit analysis methods, as well as finite difference and finite element methods, have been utilized to evaluate the bearing capacity of shallow foundations.In the meantime, the stress characteristic method, also known as the “slip-line method”, has been shown to be an efficient and useful technique for solving the bearing capacity problem due to its simplicity, high speed in calculations, and no need for neither meshing nor complex soil behavior models. These advantages attracted the attention of many researchers over the past three decades to the stress characteristic lines method.Obviously, the bearing capacity of footings would be reduced, if they are subjected to seismic loadings or if they are located on slopes or adjacent to them. On the other hand, experimental as well as numerical studies reported in the literature revealed that the roughness of the footing would have an important effect on its bearing capacity. Hence, estimating the bearing capacity of a footing taking into consideration the roughness of its contact surface constitutes one of the important issues in foundation engineering, which of course has been studied only by a small number of researchers.This paper intends to review the most important works reported in the literature concentrated on the estimation of the bearing capacity of rough shallow foundations by the stress characteristic lines method. We wanted to find the answer to the question that how different researchers considered the roughness factor in evaluating the bearing capacity of footings by the stress characteristic lines method? For this purpose, firstly the mathematical formulation of the stress characteristics method was briefly reviewed. After that, the numerical algorithm of implementing this method to estimate the bearing capacity of smooth as well as rough footings, the corresponding boundary conditions, and calculation procedure for determining the bearing capacity coefficients 𝑁𝑐, 𝑁𝑞, and 𝑁𝛾 were discussed. Various techniques for taking into consideration the roughness factor, especially their assumptions, were investigated and compared with the smooth footing case.An important point to keep in mind when calculating the bearing capacity of rough footing is the non-uniformity of the contact pressure inclination. Various researchers employed different assumptions and obtained quite different results. Some researchers considered uniform roughness by regarding different inclination for the contact pressure along the soil-footing interface or by placing a non-plastic curved wedge immediately beneath the footing. Some other researchers adopted the non-uniform roughness and solved the roughness problem by assigning a non-plastic curved wedge under the footing, or by considering it as a line and two types of parabolic equations, or even without regarding any pre-assumption failure pattern. The influences of these assumptions and methods on estimating the bearing capacity of rough footings were investigated in detail and discussed. Finally, the most important challenges ahead in evaluating the bearing capacity coefficients of rough footing by the stress characteristic lines method were summarized and explained.