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Three-dimensional limit equilibrium method based on a TIN sliding surface

Liu, Zhen-ping, Liu, Jian, Bian, Kang, Ai, Fei
Engineering geology 2019
digital elevation models, geographic information systems, soil, surface area
The three-dimensional limit equilibrium method (3D LEM) is an important approach for analysing slope stability, and the rationality of simulations for sliding surfaces directly affects the factor of safety (FoS) accuracy. Typically, the grid model containing grid elements with fixed size and uniform distribution in a digital elevation model (DEM) is used to simulate sliding surfaces. However, it is difficult to accurately express the real sliding surface shape unless a sufficient number of grid elements are used. Moreover, the four vertexes in each grid with different elevations are assumed to be located in the same plane, which may result in incorrect slope parameters and degraded FoS accuracy. To overcome these shortcomings, the triangulated irregular network (TIN) model is adopted to construct sliding surfaces, making full use of the flexibility and accuracy of triangular elements in describing surfaces and the uniqueness of the plane determined by three vertexes. A method to generalize and simplify TIN sliding surfaces is proposed based on Visualization Toolkit (VTK) open source library modules. Furthermore, combined with the Hovland method, a 3D LEM model based on a TIN is presented, and the corresponding calculation module is written and compiled in Python. To compare the FoS precision and computational efficiency, several classic examples with ellipsoidal and planar sliding surfaces are used to analyse the slope stability. The results show that, under the condition of obtaining nearly the same FoS, the number of triangles needed can be ordered from lowest to highest as follows: the simplified TIN sliding surface, unsimplified TIN, and grid model. In addition, the computation time required for the grid model is many times higher than that of the TIN sliding surface. Therefore, compared with the grid model, the TIN sliding surface adopted in the 3D LEM can effectively improve the accuracy and efficiency of FoS calculations.