特征应力空间中土的分数阶临界状态模型

Fractional-order critical state model for soils in characteristic stress space

分数阶微分具有连续描述零阶微分到一阶微分的特性,曲线的分数阶梯度方向不再与曲线切线垂直。分数阶微分的梯度非正交性质,可用于描述土的塑性流动方向与屈服面非正交的特性。基于特征应力与临界状态理论,在特征应力空间中利用非正交流动法则描述土的塑性应变增量方向,从而建立土的分数阶临界状态本构模型。所建立的模型首次将分数阶微分与特征应力统一于临界状态理论框架内,一方面模型可以同时描述三轴压缩和三轴伸长试验条件下土的变形和强度特性,另一方面也给出了利用三轴试验确定分数阶阶次的方法。所建立的本构模型只有5个材料参数,参数物理意义清晰,可通过常规室内土工试验确定,且模型可退化为修正剑桥模型。通过对典型应力路径条件下的试验结果进行预测表明,所建的模型能够合理地描述土的变形与强度特性。

The fractional derivative possesses the properties of describing the zero-order differential to the first-order one consecutively, and the fractional gradient direction of the curve is no longer perpendicular to its tangent. The non-orthogonal gradient law of fractional differential can be used to describe the non-associated flow rules between the plastic flow direction and the yield surface of soils. Based on the concept of characteristic stress and the critical state theory, the fractional-order flow law is used to describe the direction of plastic strain increment of soils in the characteristic stress space, and the fractional-order critical state model is then established. The fractional-order differential and the characteristic stress are unified by using the established constitutive model in the framework of the critical state theory. On the one hand, the deformation and strength properties of soils under triaxial compression and extension can be directly described by the established constitutive model. On the other hand, the method for determining the fractional order by triaxial tests is also given. There are only 5 material parameters with clear physical meanings in the established constitutive model, and they can be easily determined by the conventional triaxial tests. Moreover, the proposed constitutive model can also be simplified into the modified Cam-clay model.Finally, the new model is validated by means of the test results from the conventional triaxial tests.