考虑主应力轴旋转作用的一个增量模型

An incremental model considering the effect of rotation of principal stress axes

为了探究主应力轴旋转作用下土体的变形规律,采用如下思路构建模型:(1)分析二维铝棒的单剪试验结果可知,剪应力与正应力之比(剪应力比)与剪应变的类似双曲线关系,采用威布尔函数作为描述上述二者的关系表达式,不仅可反映双曲线型关系,还能充分考虑到应力比的应变软化现象。(2)利用应力莫尔圆上的应力比表达式,与威布尔函数联立得到了剪应变的隐函数。该隐函数认为有3个影响剪应变的因素:反映等向压缩或偏压作用下产生剪应变的球应力p,对于一般剪切作用下产生相应剪应变的滑动摩擦角φm,在莫尔圆上剪应力与大主应力之间的夹角半角a。(3)通过对上述隐函数求导可得到剪应变与剪应力比之间的增量表达式,联立Rowe剪胀方程,建立二维条件下的考虑主应力轴旋转的增量本构模型,上述二维方程可通过SMP准则拓展为三维增量本构模型。所提WB模型不仅能反映土体的压硬性、剪切体缩、体胀、应变硬化、软化,还能充分反映主应力轴旋转作用下的土体一般应力–应变关系。通过莫尔圆圆周应力路径以及单剪试验和等向压缩试验的结果与预测结果对比,验证了所提模型的适用性及合理性。

In order to explore the deformation of soil due to the rotation of principal stress axes,the following ideas are adopted to establish a model.（1） The results of single shear test on two dimensional aluminum rods are analyzed. The relationship of the ratio of the shear stress to the normal stress（shear stress ratio） with the shear strain is similar to the hyperbolic curve. The Weibull function is adopted to describe the relationship of shear stress ratio and shear strain which describes both the strain hardening and softening.（2） An implicit function about the shear strain is established by combining the shear stress ratio equation in Mohr＇s circle and Weibull function. There are three factors influencing the shear strain,including the mean stress p under isotropic or deviatoric compressions, the mobilized friction anglemj corresponding to the general deviatoric stress state and the half of angle a between the shear stress and larger principal stress axe.（3） An incremental equation about the shear strain and shear stress ratio is established by differentiating the above implicit equation. A two dimensional incremental constitutive equation is established by combining the above stress ratio equation and Rowe dilatancy equation. A three-dimensional incremental constitutive equation is derived by expanding the above model adopted by SMP criterion. The compression hardening,shear shrinkage,shear dilation,hardening and softening are reflected in the proposed model（WB）. A general stress-strain relationship considering the rotation of principal stress axes is thus derived. The applicability and rationality of the proposed model are verified by comparison of the experimental and calculated results.