岩土类工程材料π平面的蛋形强度准则

Egg-Shaped Strength Criterion on the Plane for Geotechnical Engineering Materials

岩土类工程材料在三维应力状态下表现出偏平面各向异性的强度特征,而常见的强度理论在这方面存在一定局限。文中将蛋形屈服函数从子午面扩展至平面,提出了偏平面的蛋形强度准则,整个模型仅需α2和β2个参数,分别表征蛋形角隅函数的曲率变化以及三轴拉伸与三轴压缩强度之比。首先从数学角度论证蛋形函数作为平面形状函数的可行性,其次结合真三轴试验结果对蛋形角隅函数的有效性进行分析与讨论,相关数值比较结果表明:根据模型参数的不同,蛋形函数可表征多种不同形态的平面强度包线。在β一定的情形下,蛋形角隅函数与包括SMP准则在内的一些常见角隅函数均能较好地再现试验结果。当α2趋向于0时,蛋形强度包线与SMP准则趋于一致;而当α2趋向于1时,蛋形强度包线与Mohr-Coulomb准则趋于一致。

Yield and failure properties on the deviatoric plane for geotechnical engineering materials under three-dimensional stress state are characterized by anisotropy,which can not be reflected by most classical strength criteria.This paper extended the egg-shaped function from the meridional plane to the plane and proposed the egg-shaped strength criterion for the deviatoric plane.Only 2 parametersα2 andβare required,which represent the curvature of egg-shaped function and the ratio of triaxial tensile strength to triaxial compressive strength,respectively.First of all,the feasibility of the egg-shaped function as yield/failure envelopes of deviatoric plane was mathematically demonstrated.Then the validity of the egg-shaped criterion was then analyzed and discussed combined with the results of several true triaxial tests.The numerical results show that the egg-shaped function can well simulate the strength envelopes with different geometric types depend on the defining parameters.Whenβis well determined,the egg-shaped function can successfully reproduce the test results as well as some other g(θ)expressions including the SMP criterion.And asα2 approaches 0,the egg-shaped strength envelope tends to be consistent with the SMP criterion.When it approaches 1,the egg-shaped strength envelope tends to be consistent with that of the Mohr-Coulomb criterion.