One-dimensional Consolidation Of Viscoelastic Saturated Soils With Fractional Order Derivative

Terzaghi has established one-dimensional consolidation theory of elastic saturated soils in the twenties of last century,which laid the foundation for investigating the consolidation behavior of soils.Therefore,he is known as the father of modern soil mechanics.However,in engineering practice,the properties of soils and the applied external loads are sometimes inconsistent with the elastic assumption of Terzaghi's consolidation theory.This often leads to a certain deviation between the predicted values and the actual results.Hence,many researchers have made efforts to improve the elastic consolidation theory from many aspects so as to better predict the consolidation behavior of soils and guide the practical engineering.It's known that the soils subjected to long-term loads usually display creep behavior.Under this circumstance,the conventional elastic consolidation theory cannot reflect adequately the time-dependent behavior of saturated soils.Herein,if the saturated soils are regarded as viscoelastic porous media,the predicted data shall be much closer to the results of realistic consolidation.However,it is found that the predicted values obtained from the integer-order viscoelastic model cannot match well the experimental data of the early stage and the inflection point.Meanwhile,the theory of fractional calculus has made great progress and has been applied to many fields.People find that it can be used to deal with mechanical models and has the advantages of higher fitting precision and fewer parameters But,the constitutive model of fractional order derivative for the consolidation of viscoelastic saturated soils is rarely reported in the literature.Considering the deficiencies in the previous studies concerning the consolidation of viscoelastic saturated soils,we elaborate on the one-dimensional consolidation problem of fractional derivative viscoelastic saturated soils in detail in this thesis.First,based on the framework of Terzaghi's consolidation theory,the theory of fractional calculus is introduced to Kelvin-Voigt constitutive model for viscoelastic saturated soils.Then the semi-analytical solution of one-dimensional consolidation of Kelvin-Voigt constitutive model for fractional derivative viscoelastic saturated soils under instantaneous loading is obtained after implementing Laplace numerical inversion by using Crump method.As for the two classical cases of elasticity and viscoelasticity,the simplified semi-analytical solutions in this study are the same as those of the two classical cases.It indicates that the analytical solutions of two classical cases can be considered as the special cases of the solutions presented in this paper.Second,besides the case of instantaneous loading,the semi-analytical solution of one-dimensional consolidation of Kelvin-Voigt constitutive model for fractional derivative viscoelastic saturated soils subjected to arbitrary loading is obtained.As the case of viscoelasticity,the simplified semi-analytical solution for exponential loading in this study is the same as available analytical solutions in literatures.It indicates that the proposed solution under arbitrary loading is reliable.Then parameter studies were conducted to analyze the effects of the various parameters on the consolidation settlement of fractional derivative viscoelastic saturated soils.Finally,the standard consolidation experiments were carried out and the experimental data were recorded.Mathematica was employed to fit the nonlinear data to determine the fractional order of Kelvin-Voigt constitutive model,and the experimental data were analyzed.The results show that there exists a significant deviation between the theoretical values predicted from the integer-order viscoelastic model and the experimental results of the early consolidation period.Conversely,the presented fractional order derivative viscoelastic consolidation theory in this study can give much closer predictions to the experimental results.Therefore,considering the saturated soils as fractional order viscoelastic porous media can help us to better depict the time-dependent effect of its mechanical behavior.