Oblique bearing capacity of shallow foundations placed near slopes determined by the method of rigorous characteristics

Abstract

The ultimate bearing capacity of shallow foundations placed near slopes has long been a critical issue, especially for the obliquely loaded case. However, it is too complicated to find a statically and kinematically admissible field and then present a rigorous solution. Herein, the method of rigorous characteristics is applied to establish a slip line field that satisfies the stress and velocity boundary conditions simultaneously. Meanwhile, five one-sided failure modes combined with basic boundary value problems are presented to consider a variation in the failure mechanism. The application of boundary value problems avoids an arbitrary assumption of the failure shape and identifies the failure region automatically. The analytical solutions are located in the narrow range determined by the upper bound and lower bound solutions found in the literature, and hence they are rigorous. The ultimate bearing capacity is estimated by accounting for the load inclination, soil properties and the geometry model. The variation in the ultimate bearing capacity and the failure mechanism of obliquely loaded cases shows great non-linearity, due to the complicated boundary conditions.

Oblique and eccentric bearing capacity of embedded strip footings using the method of rigorous characteristics

“…Geometry equation 19–21 $$\begin{equation}{\lambda _x} = \frac{{\partial {v_x}}}{{\partial x}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\lambda _y} = \frac{{\partial {v_y}}}{{\partial y}}{\kern 1pt} ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\varpi _{xy}} = (\frac{{\partial {v_x}}}{{\partial y}} + \frac{{\partial {v_y}}}{{\partial x}})\end{equation}$$…”

“… Geometry equation 19–21 $$\begin{equation}{\lambda _x} = \frac{{\partial {v_x}}}{{\partial x}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\lambda _y} = \frac{{\partial {v_y}}}{{\partial y}}{\kern 1pt} ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\varpi _{xy}} = (\frac{{\partial {v_x}}}{{\partial y}} + \frac{{\partial {v_y}}}{{\partial x}})\end{equation}$$ where $${\lambda _x}$$ and $${\lambda _y}$$ are the linear strain rates along the x‐axis and y‐axis directions, respectively; $${\varpi _{xy}}$$ is the shear strain rate in the x‐y plane; $${v_x}$$ and $${v_y}$$ are the basic velocity components along the x‐axis and y‐axis directions, respectively. Plastic flow rule 19–21 $$\begin{equat...$$…”

“…Finally, the residual points in the mixed boundary value problem can be directly determined by solving Equations (17) and (18). More details about the boundary value problems can refer to the literature 21,37 …”

“…In the following analyses, the footing width 𝑏 is 2.0 m and the self-unit weight of soils 𝛾 is 20.0 kN/m 3 . The smooth and fully rough soil-footing interfaces are first considered under the associated flow rule to validate Equation (21). Then, the application of the stress discontinuity line to consider the shear strength of embedded soils is verified by comparing with the existing methods.…”

Estimating the Ultimate Bearing Capacity for Strip Footing Near and within Slopes Using AI (GP, ANN, and EPR) Techniques

“…In frictional soils, the bearing capacity is mainly governed by foundation failure, while in cohesive soils, the bearing capacity of the foundation is controlled by the stability of the soil structure [6][7][8][9]. Recently, methods proposed by the researchers available to find the bearing capacity of shallow foundations on or near slopes include limit equilibrium analysis [10,11], slip line analysis [12], variational calculus [13], the method of rigorous characteristics [14], improved movement optimization [15], finite element analysis [16,17], and multiblock analysis [9]. Determining the bearing capacity of a shallow substructure is a very important component of geotechnical engineering study and practice.…”