Abstract A manifold Lagrangian integration point method is proposed by combining the manifold coverage algorithm and a Lagrangian integral point finite element method, aiming to simulate the large deformation failure in slope engineering. The model is established based on the dual-discrete method with a fixed Eulerian background mesh and moving material particles. The method adopts the Eulerian mesh as the fixed background mesh and describes the deformation behaviour of macroscopic objects via particle motion between meshes, thus avoiding the problem of grid distortion in the calculation process and eliminating particle motion constraints in the set region. A strain softening strain energy density failure criterion is introduced for the first time to determine the failure of the continuum, such that the process of discontinuous failure can be addressed by a continuous method. Finally, the method is verified by simulating the post-excavation failure evolution of a slope engineering case for highway reconstruction and expansion. The results found that the obtained slope slip surface is essentially consistent with the theoretical solution.

中文翻译：

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岩质边坡大变形破坏建模的流形拉格朗日积分点法

摘要 针对边坡工程大变形破坏的模拟，将流形覆盖算法与拉格朗日积分点有限元法相结合，提出了流形拉格朗日积分点法。该模型是基于对偶离散方法建立的，欧拉背景网格固定，物质粒子运动。该方法采用欧拉网格作为固定背景网格，通过网格之间的质点运动来描述宏观物体的变形行为，避免了计算过程中出现的网格畸变问题，消除了设定区域内质点运动的约束。首次引入应变软化应变能密度失效准则来确定连续体的失效，这样可以通过连续方法解决不连续故障的过程。最后，通过模拟某公路改扩建边坡工程案例的开挖后破坏演化对该方法进行验证。结果发现，得到的斜坡滑移面与理论解基本一致。