Abstract: 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.

Key words: expansive soils, stress relaxation, fractional calculus, damage degradation, relaxation model