Abstract: Disasters induced by rock creep in engineering are common, and soft rock creep is also more common in actual engineering. In order to explore the soft rock creep characteristics and accurately predict the soft rock creep deformation. In this study, firstly, a one-dimensional secondary consolidation creep test was carried out on the soft mudstone in Lund area of Guyuan City, Ningxia, and the creep characteristics of soft mudstone under the one-dimensional secondary consolidation creep test were analyzed. Secondly, the concept of fractional order theory was introduced to derive the fractional order Burgers model constitutive equation which can describe the nonlinear creep characteristics. Finally, the lsqcurvefit algorithm in Matlab was used to numerically solve the one-dimensional secondary consolidation creep test data of soft mudstone, and the effect of fractional order number on the one-dimensional secondary consolidation creep curve of soft mudstone was analyzed. One-dimensional secondary consolidation creep test shows that the creep mechanism of soft mudstone conforms to the three stages of transient deformation, consolidation deformation, and stable deformation in consolidation creep, and shows obvious nonlinear characteristics. And the undisturbed sample, remodeled sample in the consolidation process produced a large degree of secondary consolidation creep, the maximum deformation can account for 59% of the total deformation. Numerical simulation results show that the fractional order Burgers model can better describe the nonlinear characteristics of the sub-consolidation creep; Model fractional order γ has a strong sensitivity to reflect the elasticity of the fitted curve and the nonlinear viscoelasticity after the stage, and fractional order  β  sensitivity is poorer than the viscoelasticity stage of the creep tendency to make a subtle response.

Key words: soft mudstone, fractional order theory, rock creep, Burgers model, Guyuan City,Ningxia