XFEM对土体三维张拉破坏过程的模拟

土体的张拉破坏是岩土工程中常见的破坏形式之一，属于典型的非连续问题，扩展有限元法（XFEM）因在模拟这类问题方面具有更大的灵活性和兼容性近年来发展很快。然而，XFEM在模拟岩土工程中的三维张拉破坏方面还很少见。除了几何上的复杂性以外，开裂方向的判断是个难点。文章在已有的XFEM程序中引入开裂势函数方法以从宏观上更准确地追踪开裂方向，给出了三维裂缝的积分方案，建立了一套能够方便模拟三维条件下土体开裂过程的方法。首先介绍所使用的XFEM程序的理论基础，其次介绍开裂势函数方法在XFEM程序中的实现，再次介绍裂缝面的处理和积分，最后用加入开裂势函数法的XFEM程序对土石坝心墙横向开裂进行模拟，以验证方法的有效性。

Simulation of 3D tensile failure in soil using XFEM

As a typical strong discontinuity, tensile soil crack is a popular failure mode in geotechnical engineering. In recent years, such failure problems are usually solved using an extended finite element method (XFEM) due to its flexibility and compatibility, but its application to three-dimensional tensile soil failure is lacking. Besides geometrical complexity, the 3D applications also meet the difficulty of determining the developing direction of the front. This paper describes a crack tracking algorithm that can be integrated into a XFEM code, and presents a scheme of integrating crack planes for rather accurate and convenient simulations of 3D tensile failure. We first review the theoretical basis for XFEM, then discuss implementation of this new algorithm and describe a geometric treatment and quadrature scheme for crack interface calculation, and finally present simulations of a cross cracking process in the core wall of an earth-rockfill dam to demonstrate the efficiency of our new algorithm.