【作者】 杨江海；

【导师】 黄茂松；

【作者基本信息】 同济大学 ， 岩土工程， 2007， 硕士

【摘要】 基于极限分析理论的特征线法是一种令人熟知并被广泛应用的数值方法。本文即采用特征线法，对不同粗糙程度基础下的地基承载力问题进行了分析研究。 首先将土体视为理想刚塑性材料，并认为服从库仑屈服准则，综合考虑土的粘聚力c、内摩擦角φ、土重γ及超载q，以平均应力σ和方向角θ为基本变量，引入摩尔圆半径R，重新推导出了地基土在极限荷载作用下所产生塑性区域的平衡微分方程，即地基承载力问题的控制方程。 用特征线法求解上述控制方程的关键在于如何处理基础与土体接触面处的边界条件。本文研究了完全光滑基础、完全粗糙基础和不完全粗糙基础与土体接触面的边界条件，运用有限差分方法，并充分利用对称性条件，提出了一种适合于粗糙基础的构造应力场的方法，使得计算粗糙基础下的地基承载力成为可能。根据构造应力场的思路，编制相应的计算机程序，经过一些典型算例的验证，自编程序能够得出较为精确的结果。 为了扩展应用范围，本文提出了计算地基承载力系数N_c、N_q、N_γ的方法，并计算了部分φ值对应的N_c、N_q、N_γ，进一步说明了基底粗糙度对N_γ显著的影响。同时综合考虑土重参数G(=γB／2c)、基础埋深D和内摩擦角φ，分析了基底粗糙度对地基承载力的影响。更多还原

【Abstract】 The method of characteristics (also known as the slip line method) is a traditional method to solve the classical geotechnical bearing capacity problem of a rigid foundation, resting on a cohesive-frictional soil mass, loaded to failure by a central vertical force. This paper describes the use of the method of characteristics to establish plastic collapse loads of footings with arbitrary roughness.On the assumption that the soil is at yield, the two-dimensional stress state at a point can be fully specified in terms of two auxiliary variables, namely the mean stress σ and the orientation θ of the major principal stress, together with the radius of Mohr’s circle R. The governing equation can be then obtained after associating Coulomb yield criterion with the equilibrium equation.Considerable importance should be attached to the treatment of boundary conditions of soil-footing interface. In this paper, boundary conditions of footings with faculative roughness are analyzed in detail, which makes it possible to apply the finite difference scheme to solve the governing equation with any combination of the parameters c,φ,γ,B and q.When constructing stress field under rough footings, it is convenient to adopt a new technique which makes the most of the symmetry condition. A computer progam is then developed to testify the validity of the technique and solve several example problems.In practical engineering, bearing capacity factors N_c、 N_q、 N_γ are widely used to calculate ultimate bearing capacity of foundations. Therefore, a simple and effective method is adopted to obtain values of N_c、 N_q、 N_γ regarding footings with different roughness.Finally, the problems requiring further studies are discussed.更多还原