Study On Stress And Displacement Fields In Semi-Infinite Foundations Under Different Loads

There exist various layered foundations in geotechnical engineering. Some methods have been proposed for the analysis of the stresses and displacements in the layered foundations. However, there are some disadvantages for these methods in engineering applications. In this thesis, a new numerical method with good accuracy and high efficiency has been developed.The fundamental solutions for layered solids are utilized and coupled in integral equations for obtaining the stress and displacements in the layered solutions. The fundamental solutions are stress and displacement fields in the layered solids of infinite extent subjected to the concentrated forces. First, the integral equations are developed using the fundamental solutions. The stresses and displacements at any point in the foundation of semi-infinite extent can be calculated using these integral equations. Second, the eight-node isoperimetric elements are used to discretize the loading area. Because of thefundamental solutions, there are weakly and strongly singular integrals (0(1/r)and 0(1/r~2)) in the integral equations, where r is the distance between the sourceand the field points. In calculating the stress and displacement on the loading surface, these singular integrals must be carefully solved. In order to calculating the weak singular integral, the coordinate transform method is used. The strongly singular integral can not be calculated by using the constitutive and equilibrium equations. The stresses on the loading surface are indirectly obtained by solving linear equations.In order to verify the present method, two examples, which have the exact solutions, are analyzed. The relative errors are calculated. It can be found that the numerical solutions with good accuracy can be obtained.In addition, the present method is also used to analyze three in-situ examples,...