三类边坡失稳判据的统一性

The unity of three types of slope failure criteria

将热力学理论中材料破坏的能量机制引入边坡工程中,推导了强度折减过程中边坡的能量方程,利用FLAC^(3D)二次开发了能量的计算程序,并应用于某经典边坡算例中。通过与Spencer法的计算结果对比发现:强度折减法中边坡的稳定性与能量变化关系紧密,由此提出了4种新的失稳判据——能量突变失稳判据,且4种能量突变失稳判据理论上是统一的。通过对比发现:动能突变判据与数值计算收敛性判据、重力势能降突变判据与特征点垂直位移突变判据、耗散能增量突变判据与塑性区贯通判据分别存在对应关系,证明了常见的3类失稳判据也是统一的。通过算例试算发现,3类判据判定结果不相等主要是由收敛标准和网格精度等人为因素造成的,本质上是因为数值计算是一种近似解。工程应用中,可通过3类失稳判据判定结果的一致性来自评安全系数的计算精度,一致性越好,精度越高。提高计算精度的根本办法是严格收敛标准和精细网格划分,但应同时兼顾数值计算的时长,从而实现计算效率最大化。

The energy mechanism of material damage in thermodynamic theory was introduced to slope engineering. An energy conservation equation that was applicable in strength reduction period was deduced. Then, a calculation procedure for the slope energy was developed with FLAC3D, which was applied to a traditional slope example. Compared with the result from Spencer method, the slope＇s energy change was closely related to its stability in the strength reduction method, hence four new slope failure criteria-energy catastrophe criteria which were theoretically in unity were proposed. By comparison, the criterion of the kinetic energy catastrophe is in correspondence with the criteria of numerical calculation non-convergence, the loss of gravitational potential energy catastrophe is in correspondence with the criteria of dramatic increase in the marked nodal displacements, and the dissipated energy catastrophe is in correspondence with the criteria of a plastic zone going through the slope. In summary, the aforementioned correspondences demonstrate the unity of the three common failure criteria. Several examples demonstrate that the different results from the three common failure criteria are because of artificial factors such as mesh generation precision and numerical convergence criteria. In essence, the different results stem from the fact that numerical calculation is a kind of approximate solution. In application, the accuracy of safety factor can be evaluated by the consistency of the results from various slope failure criteria. The better the consistency is, the higher the accuracy is. The basic method of improving the accuracy of safety factor is strict convergence standard and fine mesh precision, but achieving strict convergence standard and fine mesh precision may require extremely long numerical calculation time. Therefore, a moderate numerical calculation time should be chosen to maximize the computational efficiency.