Viscoelastic Mechanics Analysis Of Foundation Settlement Based On Fractional Differential Theory

Both rock mass and soil have viscoelastic properties.Under the action of longterm loads such as building loads,the foundation will have the creep phenomenon that the settlement increases with time.When the settlement is too large,the stability of the structure will be adversely affected.Therefore,the influence of viscoelastic deformation on settlement must be considered in settlement calculation and design.In this paper,the fractional-order generalized Kelvin model is used to simulate the soil layer,and the viscoelastic solution of the foundation settlement under two working conditions,the independent foundation acting on the infinite soil layer and the strip foundation acting on the finite soil layer,is deduced based on the elastic-viscoelastic correspondence principle in viscoelasticity.The main research contents and results of this paper are as follows:(1)For the case of an independent foundation working on an infinitely thick soil layer,this article derived the viscoelastic solution for the foundation settlement based on Boussinesq’s displacement elastic solution and the elastic-viscoelastic correspondence principle in viscoelastic mechanics.On this basis,the effects of four main parameters,including differential order,on the settlement were analyzed,and a sensitivity analysis was conducted.The results showed that the fractional generalized Kelvin model has greater flexibility compared to the traditional integer-order generalized Kelvin model,as it can consider the rate of deceleration of creep and describe a wider range of viscoelastic material mechanical properties using fewer parameters.Additionally,the sensitivity of the differential order was greater than the other three parameters.Finally,the model was used for parameter identification and fitting of field pressure plate creep test data,and the comparative results showed that the viscoelastic solution of the fractional-order generalized Kelvin model is closer to the actual measurement results compared to the integer-order generalized Kelvin model and can more accurately describe the rheological behavior of rocks.(2)When a strip foundation acts on a finite thickness soil layer,this article uses the complex variable function method to obtain the elastic displacement solution as a basis.The analytical function is considered as a function of time,and the Laplace transform is applied to the displacement boundary conditions to solve the equation in the Laplace domain.The image function of the analytical function is obtained,and the expression of the analytical function at different times is obtained using the Iseger numerical Laplace inverse transform formula,which is used to obtain the viscoelastic solution for the settlement of the foundation when a strip foundation acts on a finite thickness soil layer.The obtained results are compared with ANSYS,and good agreement is obtained,which verifies the correctness of the derivation process.Then the boundary conditions are verified,and the results show that both the stress boundary conditions of the surface and the displacement boundary at the bottom of the soil layer satisfy well.In addition,this paper also analyzes and discusses the influence of soil layer thickness,distributed load type and distributed load range width on the settlement,and draws the following conclusions:For the generalized Kelvin model adopted,the settlement will gradually stabilize with the increase of time.Furthermore,when the form of the load distribution is different,the vertical displacement curves of different loads under the same total distributed load and other parameters are basically the same at the two sides of the foundation but have some differences near the foundation,and the maximum difference occurs at the center of the foundation.When the soil layer thickness is different,under the same parameters,the settlement and the range of the area where vertical displacement occurs with the uniformly distributed load obviously increase as the thickness of the soil layer increases at the same time.When the width of the foundation action is different,under the same total distributed load and other parameters,the vertical displacement curves at both sides of the foundation are basically the same at the same time,only the vertical ground displacement near the foundation has a significant difference,and the smaller the settlement at the center of the foundation is,when the width of the range of the distributed load action is larger.