任意荷载下连续排水边界分数阶黏弹性地基一维固结模型

One-dimension consolidation mode of fractional order viscoelastic subgrade with continuous drainage boundary under time-dependent loading

以基于Caputo分数阶导数的弹壶元件修正Kelvin模型来描述饱和土体一维固结的力学行为,并引入连续排水边界条件,通过Laplace变换,联立求解得到任意荷载下连续排水边界分数阶黏弹性地基有效应力及固结沉降的解析解。采用Laplace逆变换,获得了其时域内的理论解,并分析了梯形循环荷载及施工荷载作用下相关参数对固结沉降的影响。研究结果表明:循环荷载作用下,黏土地基的沉降变化呈振荡增长,且振荡幅值随着边界透水性的增大而增大;分数阶次α增大,使固结前期沉降速率减慢,而在固结后期,α值对沉降的影响正好相反;循环荷载下沉降变化曲线的振荡幅值随着分数阶次α的增大而减小。此外,一维固结沉降的发展还与土体力学参数及荷载参数相关,弹性模量E越大,最终沉降量越小;黏弹性体的延迟时间F越大,固结沉降变化越慢。

The Kelvin constitutive model is modified by the spring-pot element based on the Caputo fractional derivative to describe the mechanical behavior of one-dimensional consolidation of saturated soil.After introducing the continuous drainage boundary condition,the analytical solutions of the effective stress and the settlement under time-dependent loading are derived by performing Laplace transformation.The Laplace inverse transformation is used to obtain the theoretical solutions in time domain,and the influences of relevant parameters on the settlement under trapezoidal cyclic loading and construction loading are studied.The results show that the settlement of viscoelastic soil under cyclic loading increases in an oscillating manner,and the amplitude of the oscillation increases with the boundary permeability.A higher value of the fractional orderαslows the development of settlement in the early stage of consolidation.However,in the later stage of consolidation,the effect ofαon settlement is reversed.The oscillation amplitude of the settlement under cyclic loading decreases with increase ofα.Furthermore,detailed analysis indicates that the development of one-dimensional consolidation settlement is also related to mechanical properties of soil and loading parameters.The larger the elastic modulus E is,the smaller the final settlement,and the greater the delay time of viscoelastic is,the slower the settlement occurs.