A Fractional Order Creep Damage Model for Microbially Improved Expansive Soils

Microbial Induced Calcite Precipitation method was used to improve the expansive soils of Nanning, Guangxi. The nonlinear shear creep behavior of microbially improved expansive soil was studied by triaxial consolidation drainage shear test. The results show that when the expansive soil was applied a small partial stress, the creep curve of soil exhibits transient deformation and decay creep. When the partial stress reaches a certain value, there is decay creep, steady-state creep and accelerated creep successively showed on the creep curve. The stress-strain isochronous curves reflect there are obvious nonlinear characteristics in the creep process of improved expansive soils. The degree of this nonlinearity is related to the creep time and stress level. The longer the creep time as well as the higher the stress level, the higher the degree of nonlinearity. Based on the fractional calculus theory and statistical damage theory, the probability density function of Weibull distribution was introduced, and the damage degradation of soft component viscosity coefficient was considered. As a result, a fractional-order damage creep model which can describe the shear creep evolution of microbially improved expansive soils is established. Compared with the Kelvin creep model of integer order and the Burgers creep model of fractional order, the fractional order damage creep model has not only better comparative evaluation results but also more higher computational accuracy. It indicates that the fractional-order damage creep model can better describe the whole process of shear creep in microbially improved expansive soils. The above findings provide a theoretical basis for the study of deformation analysis of microbially improved expansive soils under long-term loading.