用于岩土极限分析的非线性能量耗散理论

Nonlinear energy dissipation theory for limit analysis in geotechnical engineering

在岩土工程中广泛应用MohrCoulomb或Tresca破坏准则,该破坏准则为线性破坏准则。然而,大量的岩土试验结果表明:岩土破坏准则是非线性的,而线性破坏准则只是其中的一个特例。在上限定理的基础上,提出用于岩土极限分析的非线性能量耗散理论,并从应用方面证明该理论的正确性。研究结果表明:对于一般边坡稳定性,应用该理论所得结果与应用变分法所得结果一致;对于存在竖直裂缝的边坡稳定性,应用该理论所得结果与下限解一致;对主动或被动土压力,应用该理论所得结果与广义Rankine解一致。

Linear Mohr-Coulomb and Tresca failure criteria are widely used in geotechnical engineering. However, the experimental results show that the strength envelopes of almost all geomaterials have the nature of nonlinearity, and that linear Mohr-Coulomb failure criterion is a special case of failure criteria. According to the nonlinear failure criterion, nonlinear theory for limit analysis was proposed. From the numerical results, it is found that the solutions using the new theory agree well with the solutions using variational calculus method for general slopes, that the solutions using the new theory agree well with the solutions using lower bound theorem for vertical cut, and that the solutions using the new theory agree well with the solution of the active and passive earth pressures using the extended Rankine solution for rigid retaining walls.