Phương pháp để phân tích những áp lực đất của Coulomb xem xét điều kiện khắc nghiệt, trong đó đất là trên bờ vực của sự thất bại. Đây là loại phân tích có thể được cung cấp một cơ sở vững chắc lý thuyết của lý thuyết dẻo. Điều này cũng cho phép khái quát phương pháp, và để điều tra những hạn chế có thể xảy ra và tính hợp lệ của phương pháp này. Trong phân tích của áp lực và căng thẳng trong cơ học liên tục ba loại phương trình cần thiết: điều kiện cân. | Chapter 39 LIMIT ANALYSIS Coulomb s method for the analysis of soil pressures considers extreme conditions in which the soil is on the verge of failure. This type of analysis can be given a firm theoretical basis by the theory of plasticity. This also enables to generalize the method and to investigate the possible limitations and the validity of the method. In the analysis of stresses and strains in continuum mechanics three types of equations are needed equilibrium conditions constitutive relations and compatibility equations. The general purpose is to determine the stresses and strains in a certain body under the influence of given stresses and displacements on the surface of that body. Even for the simplest type of material a linear elastic body for which the constitutive relations are linear relations between stresses and strains Hooke s law this is a formidable task which can be solved only for simple cases such as a half space a perfect sphere or a cylindrical body. Approximate solutions may be found for various materials including linear elastic materials using advanced numerical methods such as the finite element method. Such numerical methods will not be considered in this book however. An alternative may be formed by limit analysis on the basis of plasticity theory which aims not to give the complete field of actual stresses and deformations but is restricted to give a possible upper or lower limit of the stresses or the deformations. Basic theorems of plasticity theory In considerations of limit analysis not all the details of the constitutive relations are taken into account but one aspect is given priority namely the failure criterion of the material. For soils this may be the Mohr-Coulomb criterion described by a cohesion c and a friction angle Ộ. Also not all the conditions of equilibrium and compatibility equations are taken into account but only a subset of these equations. The purpose of limit analysis is not to determine the complete field
