膨胀土应力松弛的分数阶模型

Stress relaxation model of expansive soils based on fractional calculus

为了更准确地描述膨胀土应力松弛的力学特性,应用分数阶微积分理论构造的软体元件取代传统元件模型中的理想黏滞元件,并考虑黏滞系数的损伤劣化,建立了可以更加准确地反映南宁膨胀土非线性应力松弛特性的三元件模型。通过一系列室内试验研究,探索了在不同含水率条件下南宁膨胀土的应力松弛规律,并根据对试验结果的分析,确定了相关的模型参数,得到了膨胀土在不同含水率条件下的应力松弛方程。与整数阶西原模型和整数阶St.Venant模型进行对比,其结果表明所提出的改进模型能更有效地模拟膨胀土应力松弛的全过程,且模型具有结构简单、计算参数少、计算精度高和便于实际应用等优点。研究结果为膨胀土在长期荷载作用下的应力松弛分析提供了理论基础。

To accurately describe the mechanical behavior of stress relaxation of expansive soils, the software element is constructed by applying the theory of fractional calculus to replace the ideal viscous element in the traditional element model. The damage degradation of viscosity coefficient is considered. A new three-element model is established to better reflect the nonlinear stress relaxation behaviors of Nanning expansive soils. The stress relaxation of Nanning expansive soil under different water contents is studied by a series of indoor tests. The relevant model parameters and stress relaxation equations are determined according to the analysis of the tested results. By comparing the proposed model with the traditional integer order models （such as the traditional St.Venant model and Nishihara model）, the results show that the proposed model can more effectively simulate the whole process of the stress relaxation of the expansive soils. Furthermore, the proposed model has advantages on simple structure, few calculation parameters, high accuracy, easy to practical application. The research results provide a theoretical basis for the analysis of the stress relaxation of expansive soils under long term load.