考虑蠕变影响的堆载作用下被动排桩受力变形分析

Analysis on Deformation of a Passive Pile under Surcharge Load Conditions Considering Creep Effects

为分析堆载作用下被动桩受力变形的时间效应,首先引入分数阶Merchant模型描述土体的蠕变特性,然后根据对应性原理和Laplace变换推导Boussinesq黏弹性解,计算堆载引发水平附加应力,并通过Terzaghi土拱模型将附加应力传递到桩上,得到堆载作用在桩上的被动荷载.其次,将桩简化为黏弹性Pasternak地基上的欧拉梁,建立桩身挠曲微分方程,并采用有限差分法及Laplace逆变换求解,随后通过与已有试验结果的对比分析,验证了本文方法的可行性.最后,对分数阶Merchant模型参数(虎克体的弹性模量Eh、Kelvin体的弹性模量Ek及黏滞系数η、分数阶阶次α)、堆载-桩身水平距离以及堆载荷载对桩身水平位移的影响进行了分析,分析结果表明:Eh越大,桩身初始水平位移越小;Ek越大,桩身水平位移随时间的增量越小;η越大,桩身到达最终变形量的时间越长;α越大,Kelvin体的黏滞性越大;堆载-桩身水平距离越小、堆载荷载越大,桩身水平位移越大;且随时间的增加,桩身水平位移对Eh的敏感度降低,对堆载-桩身水平距离和堆载荷载的敏感度会增大.

To analyze the time effect of passive pile deformation under the action of surcharge load,this paper first introduces the fractional-order Merchant model to describe the creep characteristics of the soil.Then,based on the correspondence principle and Laplace transform,the Boussinesq viscoelastic solution is derived to calculate the additional horizontal stress induced by the load.The Terzaghi arching model is used to transfer the additional stress to the pile,obtaining the passive load on the pile due to the action of the load.Next,the pile is simplified as an Euler beam on a viscoelastic Pasternak foundation,and the differential equation calculating the deflection of the pile is established.The finite difference method and Laplace inverse transform are used to solve the equation.Subsequently,by comparing the results with existing experimental data,the feasibility of the method proposed in this paper is validated.Finally,the effects of fractional-order Merchant model parameters(elastic modulus Eh of Hooke body,elastic modulus Ek of Kelvin body,viscosity coefficientη,and fractional-order orderα),surcharge load-pile horizontal distance,and surcharge load on pile horizontal displacement are analyzed.The analysis results show that the larger Eh is,the smaller the initial pile horizontal displacement is.The greater Ek is,the smaller the increment of pile horizontal displacement with time,and the greaterηresults in the longer time for the pile to reach the final deformation.The largerαis,the greater the viscosity of Kelvin body is.The smaller surcharge load-pile horizontal distance and larger load lead to larger horizontal displacement of piles.With increasing time,the sensitivity of pile horizontal displacement to Eh decreases,and the sensitivity of surcharge load-pile horizontal distance and surcharge load increases.