Rigorous Solution Method Of Earth Pressure Against The Rotating Retaining Wall And Its Application

For the limit equilibrium problems of soil mass under complex stress and velocity boundary conditions, their exact solutions need to satisfy the limit balance equations, the plastic flow equations, the stress boundary conditions and the velocity boundary conditions. Such general exact solutions can not be obtained by the analytically mathematical methods. Numerical simulation methods can be applied to solve such problems and give rather exact solutions.The present paper constructed a so called "rigorous solution theory" for solving the first and the second classes of the limit equilibrium problem of soil mass by the applications of the bound limit theorems and numerical simulation methods. The rigorous solution theory are applied to obtain the numerical solutions of the earth pressure against the rotating retaining wall, the ultimate bearing capacity of soil foundation and the slope bearing capacity of soil mass. The method by means of the rigorous solution theory for the numerical solutions are called "rigorous solution method"The conclusions of the present study in the present paper are as follows:(1) Including the slip-line rigorous solution method and the upper and lower bound finite element rigorous solution method, the rigorous solution methods are presented for solving the limit equilibrium problems of soil mass under complex stress and velocity boundary conditions. The methods are derived from the geometry conditions, stress admissible conditions and kinetic admissible conditions on the discontinuous stress line and discontinuous velocity line and the upper bound and lower bound theorems on the discontinuous surfaces of stress and velocity. The methods are based on the rigorous theory system, and their solutions are unique for a real problem. It can be called "the rigorous solution methods". The numerical methods based the rigorous solution methods can obtain rather exact numerical results.(2) The ultimate earth pressure problems of the retaining wall under complicated boundary conditions are solved by the slip-line rigorous solution method. By constructing the mechanical models of the retaining wall under discontinuous loading and velocity distributions, the computer arithmetic of the slip-line rigorous solution method are presented for the walls under translation mode, rotation around the wall bottom or a specific wall-point. Their active and passive earth pressures, discontinuous stress fields and discontinuous velocity fields are calculated with the computer arithmetic. The numerical results can show themselves are rigorous, i.e., the complicated stress and velocity boundary conditions are satisfied by the numerical results. In addition, the present solution of the ultimate earth pressure under the wall movement mode with rotation around a specific wall-point can not be solved by the classical analytical methods.(3) The upper bound limit finite element method applied usually in the stability analysis of slop is revised by the use of the upper and lower bound finite element rigorous solution method. It is firstly introduced to the ultimate earth pressure problems of the retaining wall under various modes of movement. The upper limit values of the earth pressures of the four retaining modes are solved. The revised upper bound limit finite element method is based on the rigorous theoretical system. The upper limit value obtained by the revised method is the minimum of the upper ultimate values of earth pressure, and then is belong to exact solution and can be called the rigorous solution. Complicated loadings, geometry shape of soil mass, material properties, complicated stress boundary condition and complicated velocity boundary conditions can be take account into easily by the revised method. Hence, the ultimate earth pressure, stress fields and velocity fields can be calculated successfully. It can be applied well to the limit equilibrium problem of rock and soil mass under complicated environment.(4) The ultimate bearing capacity of soil foundation is solved by the slip-line rigorous solution method. The shearing strength of over loaded soil mass, partially loading and friction between soli and wall can be involved. With slick foundation surface and vertically loading, the ultimate bearing capacity of soil foundation under the weightless and the gravity of soil are compared. However, the simplified formulae applied in the engineering design have not been obtained.(5) The soil slope bearing capacity is solved by the slip-line rigorous solution method. An iterative arithmetic of the slip-line rigorous solution method is presented. Although it will be computed many times, but the numerical solution can satisfied all the traction boundary conditions and the velocity boundary conditions. Hence, it is an exact solution. In addition, the influences of the soil properties on the slop bearing capacity are numerically investigated.(6) By the use of the theory of generalized plasticity, the slip-line rigorous solution method under the associated and non-associated flow rules are discussed in the limit analysis in the soil-rock engineering.