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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 law of the soil under the rotation of the principal stress axis, the following train of thought was used to build the model: (1) Analyzing the single-shear test results of the two-dimensional aluminum rod, it is found that the ratio of shear stress to normal stress (shear stress ratio) Similar hyperbolic relationship, the use of Weibull function as a description of the relationship between the two expressions, not only reflect the hyperbolic relationship, but also take full account of the stress than the strain softening phenomenon. (2) Using the stress ratio expression on the Mohr circle of the stress, the implicit function of shear strain is obtained by combining with the Weibull function. The implicit function assumes that there are three factors that affect the shear strain: the spherical stress p that produces the shear strain under isotropic compression or bias, the sliding friction angle φm for the corresponding shear strain under normal shear, Angle between the shear stress and the main stress half-angle a. (3) Through the derivation of the above implicit function, the incremental expressions of shear strain and shear stress ratio and the simultaneous Rowe dilatancy equation can be obtained, and an incremental constitutive model considering principal axis rotation under two-dimensional conditions is established , The two-dimensional equation can be extended to a three-dimensional incremental constitutive model through the SMP criterion. The proposed WB model can not only reflect the compressive rigidity, shear shrinkage, body bulge, strain hardening and softening of soil, but also fully reflect the general stress-strain relationship of soil under the rotation of principal stress axis. The applicability and rationality of the proposed model are verified by comparing the results of the stress circle along the Mohr circle with the shear tests and the isotropic compression tests with the predicted results.