基于分数阶导数的冻土蠕变本构模型

冻土的蠕变特性与所受应力水平及蠕变应变有关,在高应力水平下会表现出加速蠕变特性。本文在分数阶的非线性黏壶基础上提出了可以描述加速蠕变特性的应力-应变双控元件。传统Nishihara模型难以描述加速蠕变,通过将Nishihara模型中的黏弹性体替换为分数阶的Abel黏壶,将黏塑性体替换为提出的应力-应变双控元件,得到了冻土的一维蠕变本构模型,并将其推广到三维应力状态。提出的模型对冻土的单轴和三轴蠕变试验数据进行了预测分析,和传统Nishihara模型相比,该模型只增加了一个参数,不仅能够反映冻土在低应力水平下冻土衰减蠕变和稳定蠕变特性,而且还可以较好地反映冻土在高应力水平下加速蠕变规律。说明了该模型对于描述冻土在不同应力条件下不同蠕变状态的适用性。

A Creep Constitutive Model for Frozen Soil Based on Fractional Derivative

Creep characteristic of frozen soil is related to the stress level and the accumulated creep strain. Frozen soil exhibits accelerated creep behavior under high stress level. Traditional Nishihara model is not suitable for this kind of material. A stress-strain triggered element is proposed to describe the accelerated creep based on the fractional derivative non-linear dashpot. The visco-elastic part and visco-plastic part in Nishihara model are replaced by fractional derivative Abel dashpot and the proposed stress-strain triggered element respectively. One dimensional constitutive relation can be derived from the equilibrium equation of the elements and then the relation is extended to three dimensional stress states. The creep behaviors of frozen soil in one dimension and three dimensions are fitted by the proposed model. Compared with traditional Nishihara model, the model can describe not only the decayed and stable creep under low stress level, but also the accelerated creep under high stress level by adding only one new parameter. The proposed creep model for frozen soil is suitable for different creep behavior under different stress level.