张拉-剪切破坏模式下边坡三维临界滑面的Cauchy问题

Cauchy problem of three-dimensional critical slip surface of slope under tension-shear failure mode

边坡失稳常表现为压剪-张拉破坏等复杂形态。基于有限元-强度折减法,获得边坡的极限应力场和应变场,从三维边坡的极限应力场出发,考虑剪切-张拉两种破坏模式,将边坡临界滑面定位问题转化为求解一阶拟线性偏微分方程的初值问题,即Cauchy问题。在边坡后缘等拉应力区采用张拉破坏模式,在被动滑动区域采用Mohr-Coulomb屈服准则的剪切破坏模式,在未假定滑面几何形式和未指定滑动模式的前提下自动确定临界滑面。分别研究了缓倾结构面的三维边坡和陡倾结构面的三维边坡,描述了二者的几何特征和分布形态,并与无节理均质边坡进行了对比分析。结合物理模型试验,开展了均布荷载作用下均质边坡在极限应力状态下的破坏特征研究,验证了方法的正确性和可靠性。

The failure mechanism of slope instability is complex,and the characteristics of sliding surface often show complex forms such as compression shear-tension failure.Based on the finite element strength reduction method,the limit stress field and strain field of slope are obtained.Starting from the limit stress field of three-dimensional slope,and considering tension-shear composite failure,the positioning problem of slope critical sliding surface is transformed into the initial value problem for solving the first-order quasilinear partial differential equation,namely,the Cauchy problem.The tensile failure mode is adopted in the equal tensile stress area at the scarp of the slope,and the shear failure mode of Mohr-Coulomb yield criterion is adopted in the passive sliding area.In this way,the critical slip surface is determined without assuming the geometry of the slip surface and specifying the slip mode automatically.The three-dimensional slope of gently inclined structural plane and steeply inclined structural plane are studied respectively.Not only the geometric characteristics and distribution of the two are described,but also compared with the jointed homogeneous slope.Finally,combined with the physical model test,the failure characteristics of homogeneous slope under uniformly distributed load in ultimate stress state are studied to verify the correctness and reliability of the method.