Fig. 1

Model schematic and force analysis. (a) Schematic diagram of the model; (b) Force analysis on the soil and water columns. The forces acting on the columns include gravity (\({G_n}\)), support force (\({N_n}\)), frictional resistance (\({S_n}\)), lateral pressure (\({P_n}\)), and buoyancy (B). \(n=1\) and \(n=2\) represent the water body and sliding mass, respectively. \(\alpha\) and \(\beta\)represent the angles of the ground surface with respect to the XOZ plane and the YOZ plane, respectively. \(\Delta x\) and \(\Delta y\) denote the cell sizes in the x- and y-directions, respectively.