基于GIS的边坡稳定性计算方法研究

结合GIS（地理信息系统）的空间分析能力和滑动面正应力分布假定模型，建立了基于栅格单元的三维边坡极限平衡模型，提出了基于GIS的边坡稳定性计算方法。该方法首先建立了基于栅格柱体单元的三维边坡稳定性分析模型，给出了模型参数在GIS中的空间表达式；其次，在极限平衡条件下，推导出滑体在GIS中的3个力平衡方程式和1个力矩平衡方程式，形成了用于求解三维安全系数的方程组；最后，基于摩尔-库仑强度准则，以及滑动面正应力分布的假定，求解三维安全系数。同时利用COM（组件对象模型）技术开发出一个基于GIS的三维边坡稳定性分析扩展模块，该模块可实现复杂的算法计算以及多种组合荷载下的稳定性计算，并通过算例验证了该模块的正确性和便利性。

Research on slope stability calculation method based on GIS

Combined with the assumption of normal stress distribution on sliding surface and the spatial analysis capability of Geographic Information Systems (GIS), a three-dimensional (3D) slope equilibrium model based on grid cells is established, and a GIS-based slope stability calculation method is proposed. In this method, a 3D slope stability analysis model based on grid cylinder elements is firstly established, and the spatial computational expression of each parameter in GIS is clearly articulated. Secondly, under the condition of limit equilibrium, a set of stability analysis equations, including three force equilibrium equations and one moment equilibrium equation of the sliding body, are derived for solving the three-dimensional safety factor. Finally, following the Mohr-Coulomb strength criterion and the assumption of normal stress distribution on the sliding surface, the three-dimensional safety factor is solved. Moreover, the component object model (COM) technology is used to develop a GIS-based 3D slope stability analysis module, which can be implemented for the complex algorithms and the calculation of multiple stratigraphic slopes and multiple combinations of factors in 3D slope stability analyses. The correctness and feasibility of the module are verified by three typical cases.