土体结构极限承载力的有限元分析

 在平面应变条件下，采用增量加载有限元方法求解土体结构的极限承载力，以弹塑性有限元计算不收敛作为达到极限破坏状态的判别标准；在得到土体应力场的基础上，用有限元边坡稳定分析中的滑面应力分析法验算土体结构在达到极限破坏状态时安全系数是否趋近于1.0，同时搜索相应的临界滑动面，与增量加载直到土体结构破坏获得的滑动面比较，并分析二者与经典Prandtl解破坏机构的差异。计算结果表明：屈服准则的选取对计算结果的影响很大，对于无自重的边坡和地基，在非关联流动法则下采用 Mohr-Coulomb 匹配圆准则或者在关联流动法则下采用Mohr-Coulomb内切圆屈服准则时，所得到的结果与经典Prandtl解相近；但是在非关联流动法则下采用Mohr-Coulomb匹配圆准则得到的滑动面与经典Prandtl解破坏机构不一致，极限状态下的安全系数也不为1.0；在关联流动法则下采用Mohr-Coulomb 内切圆屈服准则时，其极限状态下的滑动面与有限元稳定分析方法搜索得到的滑动面相近，与经典Prandtl解破坏机构一致，同时在该极限荷载下土体结构沿临界滑动面的安全系数Fs趋近于1.0。对于有自重的边坡，同样在关联流动法则下采用Mohr-Coulomb内切圆屈服准则时，其极限状态下的滑动面与有限元稳定分析方法搜索得到的滑动面一致，在该极限荷载下土体结构沿临界滑动面的安全系数Fs趋近于1.0，说明此屈服准则下求得的极限承载力是土体结构严格意义上的真正的承载力。

FINITE ELEMENT ANALYSIS OF ULTIMATE BEARING CAPACITY OF SOIL MASS STRUCTURE

The ultimate bearing capacity of soil mass is analysed by elastoplastic finite element method through step loading under plane strain condition；and non-convergence in finite element program is taken as discriminant criterion of failure. Slip surface stress analysis method in finite element analysis of slope stability is used to validate whether the safety factor tends to 1.0 when soil mass arrives at the state of limit equilibrium and to search for the critical slip surface. The critical slip surface given by the method is compared with that obtained by the classical Prandtl solution. The example shows that different yield criteria affect the results greatly. Namely，for slope and foundation without self-weight，the solution obtained by Mohr-Coulomb inside-tangent circle yield criterion under associated flow rule or Mohr-Coulomb matched D-P yield criterion under non-associated flow rule is close to the classical Prandtl solution. But the critical slip surface obtained by Mohr-Coulomb matched D-P yield criterion under non-associated flow rule is not in accordance with the classical Prandtl solution；and the corresponding safety factor is not tend to 1.0. The solution obtained by Mohr-Coulomb inside-tangent circle yield criterion under associated flow rule makes the safety factor tend to 1.0 along critical slip surface and the corresponding slip surface accord with the classical Prandtl solution. For the slope with self-weight，the solution obtained by Mohr-Coulomb inside-tangent circle yield criterion makes the safety factor tend to 1.0 along critical slip surface and the critical slip surface in the limit state accord with that obtained by finite element stability analysis. These show that the solution obtained by Mohr-Coulomb inside-tangent circle yield criterion under associated flow rule is the true ultimate bearing capacity of soil mass structure.