Hill稳定条件在有限元法计算地基承载力中的应用

APPLICATION OF HILL'S STABILITY CONDITION TO BEARING CAPACITY COMPUTATION OF FOUNDATION WITH FINITE ELEMENT METHOD

对大型有限元分析软件ABAQUS进行二次开发,以条形地基极限承载力问题为例,探讨有限元方法结合Hill稳定充分条件在求解岩土工程承载力问题中的应用。根据Hill稳定充分条件,当系统局部二阶功小于0时,地基局部潜在失稳;当整体二阶功小于0时,地基达到极限状态,可能发生整体失稳。探讨剪胀角对地基承载力的影响,并将有限元方法结合Hill稳定充分条件的计算结果和常规有限元法计算的结果与已有的数值、理论结果进行比较。结果表明:在剪胀角比摩擦角小很多时,与常规有限元法计算结果相比,有限元方法结合Hill稳定条件,计算得到的地基极限承载力更加接近理论解;当剪胀角和摩擦角接近时,二者计算结果基本一致,均能得到较为合理的结果。有限元方法结合Hill稳定条件,能较好地预测地基潜在失稳区域,可以判定结构的局部稳定性和整体稳定性,能同时描述地基的面破坏模式和场破坏模式,而且有理论基础和明确的物理意义,应用方便,是一种值得推荐的方法。

Based on the secondary development ofABAQUS, the Hill＇s sufficient stability condition is applied, with finite element method, to limit bearing capacity calculation of strip foundation on cohesive frictional soils. The limit bearing capacity of the foundation as well as the potential instability regions of the soil is studied. According to Hill＇s sufficient stability condition, when the local second order work of the soil system is negative, the local region becomes potentially instable： when the global second order work of the system is negative, the system arrives limit state, and becomes potentially instable, thus the limit bearing capacity of the system is the load applied to the system at the moment. The influence of dilatancy angle on the bearing capacity is studied. Results show that, when the dilatancy angle is much smaller than the frictional angle, the limit bearing capacity computed by finite element method（FEM） with Hill＇s sufficient stability condition is close to theoretical solution of the equivalent material, and smaller than that of regular FEM. When the dilatancy angle is close to the frictional angle, the results of FEM with Hill＇s sufficient stability condition and the regular FEM are close and both can give preferable solution. The FEM with Hill＇s sufficient stability condition can also give the potential instability regions of the soil system, which can depict the surface failure mode and field failure mode simultaneously. Since the FEM with Hill＇s sufficient stability condition has a solid and clear theoretical background and therefore it is convenient to use, it is a deserved method for recommendation.