一种非线性强度准则及转换应力法

岩土材料在二维破坏模式下具有较强烈的曲线形态,在一般剪应力与正应力空间中提出用幂参数曲线来表达上述曲线,该曲线与摩尔圆的外切点即对应为破坏应力点,则利用该点的外切直线斜率的反正切值来得到有效滑移角.对于三维单元体,共存在三个有效滑移角,利用三个有效滑移角确定出空间有效滑移面.基于岩土材料为摩擦型材料这一基本特性,利用空间有效滑移面上的应力比为一定值作为衡量材料破坏与否的判断准则,基于上述思路推导得到了t强度准则,在偏平面上,t准则开口形状为介于Von-Mises圆形曲线到SMP曲边三角形形态.在子午面上,引入开口的幂函数作为反映静水压力效应以及剪切破坏的曲线,而闭口的水滴型屈服面函数作为反映体积压缩屈服曲线,反映了岩土材料的压剪耦合特性.基于所提出的t强度准则, 推导了变换应力公式,可将以$p,q$为应力量的二维模型简单方便的转换为三维应力状态本构模型.通过强度以及多种应力路径的测试对比,验证了所提t准则及基于该准则的变换应力公式的合理性. 

A NONLINEAR STRENGTH CRITERION AND TRANSFORMATION STRESS METHOD 1)

The curve is expressed by a power parameter curve in the space of normal stress and shear stress. The outer tangent point of the curve and the mohr's circle corresponds to the point of failure stress point. Then, the inverse tangent value of the slope of the outer tangent line at the point is used to obtain the effective slip Angle.There are three effective slip angles for a three-dimensional element, and three effective slip angles are used to determine the effective slip surface of space. Based on the basic features of geotechnical materials as friction materials, the stress ratio on the effective slip surface is taken as a certain value to judge whether the material is damaged or not. The t strength criterion was derived based on the above ideas, in deviatoric plane, the shape of t criterion is a closed curve between Von-Mises criterion and SMP criterion. In the meridian plane, the introduction of open power function as a reflection of the curve of the effect of hydrostatic pressure and shear failure, and closed droplet type yield criterion function is adopted to reflect volume compression yield curve, reflect the compression-shear coupling characteristics of geotechnical material. Based on the proposed t strength criterion, the transformation stress formula is derived, which can easily transform the two-dimensional model by using $p$ and $q$ as the stress variables into a three-dimensional stress state constitutive model. Through the test and comparison of strength and various stress paths, the rationality of the proposed t criterion and the transformation stress formula based on the criterion is verified.