One-Dimensional Consolidation Of Saturated Soil With Continuous Drainage Boundary Under Cyclic Loadings

Based on four soil nonlinear constitutive models of Merchant Model,Fractional Order Modified Model,Semi-Logarithmic Model and Hyperbolic Model,the continuous drainage boundary is introduced to construct the one-dimensional consolidation under cyclic loadings.The consolidation equations of the corresponding models are established.The semi-analytic solutions or analytical solutions of the effective stress and consolidation settlement of the corresponding models under cyclic loading and continuous drainage boundary conditions are obtained by performing Laplace transform and separation variable method.Then,the obtained solutions are degraded to permeable boundary of Terzaghi,which is consistent with existing literatures,and verifies the reliability of the solutions.In addition,the influence of various parameters on the consolidation characteristics of these models are analyzed,the research results show that:?1?The law of the settlement of soft soil foundation is similar to effective stress under cyclic loading,both of which increase oscillating and lag relative to the cyclic loadings.When considering the continuous drainage boundary conditions,the development of effective stress and settlement of the soil layer increases significantly with the increase of boundary permeability,and the amplitude of oscillation under cyclic loadings also increases.Among them,in semi-logarithmic consolidation model,when the permeability reaches a certain level,the greater the permeability in the early stage,the faster the effective stress increases,but in the later stage,the law is reversed.In addition,the lag time of effective stress or settlement of Merchant viscoelastic foundation,semi-log nonlinear foundation,and hyperbolic nonlinear foundation with loadings will decrease as the boundary permeability increases.The degree of boundary permeability has a great influence on the consolidation characteristics of saturated soil.Therefore,the boundary conditions of consolidation cannot be ignored.?2?In Merchant model,the larger the elastic modulus of the spring in the Kelvin body E,the elastic modulus of the isolated spring ₁E,and permeability coefficient k_v,the faster the effective stress increases,and?increases,which accelerates the effective stress growth in the middle and early stage of consolidation,but in the late stage,the increase of?slows down the effective stress growth.?3?In the fractional-order modified Kelvin model,the oscillating amplitude of settlement curve under cyclic loading decreases with increasing fractional order?.The increase of?slows down the settlement development in the early stage of consolidation,but in the later stage,the value has the opposite effect on the settlement,and the final consolidation settlement time decreases with the increase of?.The larger the elastic modulus E,the smaller the final settlement,and the smaller the oscillation amplitude of the consolidation settlement under cyclic loading;the greater the delay time F of the viscoelastic body,the slower the rate of change of consolidation settlement,but it has little effect on the oscillation amplitude.?4?Under the semi-logarithmic model,the increase of initial effective stress and consolidation coefficient will cause the development rate and the oscillation amplitude of the effective stress to increase,and the time to reach stabilization will be shortened.?5?In hyperbolic model,the change of initial porosity has little effect on the development of consolidation settlement.The increase of initial compression modulus E₀ and the slope n of the compression curve will cause the development of the consolidation settlement to slow down,and the amplitude of the curve fluctuations to decrease.This research will help readers to understand the consolidation mechanical behavior of saturated soils,and the use of continuous drainage boundary can more reasonably reflect the consolidation characteristics of soils in actual engineering,and provide useful ideas for accurate prediction of consolidation settlement and related research.