岩土材料在非关联流动法则下剪胀角选取探讨

岩土材料属于摩擦型材料，其强度特性时参数指标的选取至关重要。当前对剪胀角存在模糊认识，导致在理论分析和数值模拟分析中常会产生较大误差。在分析传统的滑移线场理论的基础上，采用广义塑性理论，证明了岩土材料在非关联流动法则条件下的剪胀角应取? /2，且此时体变必为0。通过对具有精确理论解的经典Prandtl地基承载力课题的数值模拟分析，分别对关联流动法则、非关联流动法则剪胀角取? /2及非关联流动法则剪胀角取0三种情况下地基的承载力进行了计算。结果表明，上述3种情况下得到的极限荷载的误差为2 %，但滑移线场与理论解有较大差异。其中，在非关联流动法则条件下，采用剪胀角? =? /2所得到的滑移线场与Prandtl理论解一致，而采用? =0所得到的滑移线场与理论解有较大的偏差。这说明目前在非关联流动法则条件下采用? = 0虽然可得到相应的正确的极限荷载，但是相应的滑移线场具有较大的误差，同时也证明了岩土材料在非关联流动法则条件下的剪胀角应该选取? /2，而不是目前通常采用的0。

Determination of dilatancy angle for geomaterials under non-associated flow rule

Geomaterials are frictional materials, and their strength indexes play a key role in depicting strength characteristics. Illegible knowledge on dilatancy angle has existed for a long time, which caused large errors in theoretical analysis and numerical simulation. It was proved with the generalized geotechnical plastic mechanics principle that the angle of dilatancy should be ? /2 and the corresponding volumetric strain is zero for geomaterials under non-associated flow rule, based on traditional slip line theory. The classic foundation bearing capacity topic of Prandtl’s solution, which has accurate theoretical interpretation, was analyzed systemetically with step loading finite elements under the following three conditions: 1) associated flow rule, 2) non-associated flow rule with the dilatancy of ? /2 and 3) non-associated flow rule with the dilatancy of 0. Results showed that the errors of ultimate capacity obtained under the above three conditions were within 2 %, but the slip line fields were quite different. The slip line field obtained under conditon 2) was identical with that by Prandtl’s solution, but a large deviation existed between condition 3) and Prandtl’s solution. Thus a correct ultimate load and a slip line field with a great error can be acquired under condition 3), but both are precise under condition 2). Therefore, the angle of dilatancy should be ? /2, not 0 widely used at present when non-associated flow rule is applied.