三维边坡稳定分析的有限元弹塑性迭代解法

Elastoplastic finite element iteration method for stability analysis of three-dimensional slope

针对已知滑动面的三维边坡稳定分析问题,在塑性力学上限定理的基础上,提出了求解安全系数的三维有限元弹塑性迭代解法。对于滑动面的非线性特性,采用常规的矩形(平面)或立方体(空间)单元来描述,应力则符合相关联流动法则的Mohr-Coulomb强度准则。通过对弹塑性增量理论中流动法则的分析,证明了当结构达到极限状态时,滑动面内切向应力的方向与滑体的主滑方向一致,说明最终以滑动面内的切向应力作为滑体滑动力的有效性。通过迭代的方式,逐步降低滑动面材料的抗剪参数,使边坡达到极限状态,不仅快速求得了滑动面的安全系数,且能够得到边坡在接近临界失稳状态时滑动面内切向应力的分布情况和边坡的变形规律,为边坡采取加固措施提供了参考依据。最后,以椭球面滑动和楔形滑动2个经典算例和工程实例,验证了该方法的有效性和正确性。

For the stability analysis of three-dimensional slope with known slip surface, based on the upper-bound theory of plasticity, an elastoplastic finite element iteration method for stability factor is suggested. The contact surface is simulated by rectangle element for plane problems or cubic element for dimensional problems with small thickness; and the Mohr-Coulomb associated flow rule criterion for the stresses is adopted. Based on analyzing the associated flow rule in the incremental elastoplastic theory, it is proven that the direction of the tangential stress on the slip surface and the sliding direction of the slope are consistent when the slope reaches ultimate state; so it is accurate that the tangential stress is regarded as the sliding force. In the process of calculation, the shear strength parameter is reduced step by step based on the iterative method, until the slip slope reaches ultimate state. Not only the stability factor can be got by this method rapidly, but also the tangential stress distribution on the slip surface and the deformation law of the slope can be obtained as well, which provides reference for taking reinforcement measures to the slope. At last two typical problems, i.e. ellipsoid slide and wedge slide, and a project example are given to verify its availability and rightness.