Fractional Order Relaxation Model And Numerical Study Of Lime Treated Expansive Soil In Hefei

In this paper,the lime treated expansive soil is taken as the research object.First of all,based on the theory of fractional order differential,We discuss the two stage of the fractional order relaxation constitutive model which can consider whether the test specimen destroyed or not.And then apply test data to fit the formula of theory,found that building model has good applicability,and the sensitivity of the model parameters were analyzed.Inside,the theoretical formula is derived for the incremental form based on FLAC3D numerical calculation method,and internal constitutive model is developed.By simulating the consolidation,loading and relaxation process of the sample in the relaxation test,the rationality and reliability of the program are good.Finally,the transformation law of relaxation is simulated and analyzed under different loading rates,confining pressure,loading strain and pore water pressure.The main conclusions of this paper are as follows:（1）The Fractional Nishihara relaxation model was established by using the fractional calculus theory,and the constitutive equations were solved by series decomposition and Laplace transform.When the loading strain was small,the model was a Fractional three-element relaxation model;when the loading strain is large,the model is a fractional Burgers relaxation model.Then,the stress relaxation test data of Hefei lime-treated expansive soil were fitted,and it was found that the results have better applicability than the traditional component model.By sensitivity analysis of the parameters in the model,the results show that:the larger the viscosity coefficient is,the slower the relaxation rate is.The larger the fractional order is,the smaller the initial stress value and the smaller the overall relaxation.When the shear modulus increases,the stress relaxation rate slows down and the initial stress value increases slightly.In the fractional order Burgers relaxation model,the fractional order,the viscosity coefficient and the damage characteristic parameters have a great influence on the stress relaxation quantity and rate,while the shear modulus has a little influence on the stress relaxation quantity and rate.（2）Based on the display constitutive equation of the fractional original model,the explicit formula is first rewritten into an incremental form according to the first-order approximation method in the fractional theory.Then,based on the C++language environment in Visual Studio 2020,the explicit formula is compiled into a DLL（Dynamic Library）file form that can be called by internal statements of FLAC3D.Finally,a standard cylinder triaxial specimen model was established by FLAC3D to simulate external conditions such as confining pressure and loading rate,and the stress was corrected by using the Mole-coulomb plasticity theory in the loading process.In the stress relaxation process,a custom constitutive model was called to solve the problem.The increment form of fractional relaxation constitutive equation and the rationality of FLAC3D program are verified by comparing the calculation examples with the experimental data from the aspects of stress-strain curve,stress relaxation curve and stress cloud diagram.It can be seen from the stress-strain curve that the brittle failure occurred to the specimen,which is consistent with the characteristics of the expansive soil treated by lime.（3）From the relaxation curve and stress contour obtained by numerical calculation,it can be seen that if the relaxation of the model occurs under the condition that the specimen is not damaged,the relaxation curve roughly has three stages,namely,the rapid stress descending stage,the gentle stress descending stage and the equilibrium stage;It can be seen from the stress contour that the internal stress of the specimen is constantly adjusted and uniform.Finally,the stress at the bottom of the specimen is small and the stress is approximately uniform.If the relaxation curve of the specimen after failure can be divided into two stages:the rapid stress descending stage and the equilibrium stage.In the cloud image,the initial stress is rapidly adjusted,and then the stress rapidly reaches equilibrium within the model element.（4）Through numerical simulation of the influence of test conditions such as loading rate,confining pressure,loading strain and pore water pressure on the relaxation process,we can get:When the loading rate varies between 4×10^-7m/s-1.2×10^-6m/s and the strain level is low,the initial stress value and stress relaxation increase with the increase of the loading rate,and the relaxation rate first increases and then decreases with the increase of the loading rate.When the confining pressure varies between 100 and 300k Pa,the initial stress and stress relaxation increase with the increase of the confining pressure.When the confining pressure is the same and the strain level is low,the initial stress,residual stress and stress relaxation all increase with the increase of the strain level.When the strain level is higher,the initial stress and residual stress decrease.When the pore water pressure varies from 100 to 200k Pa and the strain level is low,the initial stress,residual stress and residual stress ratio increase with the increase of pore water pressure,and the stress relaxation decreases with the increase of pore water pressure.When the strain level is high,the initial stress,residual stress and stress relaxation decrease with the increase of pore water pressure,and the residual stress ratio decreases with the increase of pore water pressure.