Analytical solution of consolidation considering initial hydraulic gradient and continuous drainage boundary under variable load

LI Quanjun; CHEN Yu; JIN Dandan; LI Chuanxun

doi:10.11835/j.issn.2096-6717.2021.086

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Analytical solution of consolidation considering initial hydraulic gradient and continuous drainage boundary under variable load

Civil Engineering | 更新时间：2023-06-25

- Analytical solution of consolidation considering initial hydraulic gradient and continuous drainage boundary under variable load
- Journal of Civil and Environmental Engineering Vol. 45, Issue 1, Pages: 122-134(2023)
- 作者机构：
  
  1.江苏省地矿局第三地质大队，江苏镇江 212001
  2.江苏大学土木工程与力学学院，江苏镇江 212013
- 作者简介：
  
  LI Quanjun (1969- ), senior engineer, main research interest: geotechnical engineering, E-mail: jsdzcz@sina.com.
  LI Chuanxun （corresponding author）， professor， E-mail： lichuanxun@yeah.net.
- 基金信息：
  
  National Natural Science Foundation of China(51878320)
- DOI：10.11835/j.issn.2096-6717.2021.086
  CLC： TU433
- Received：05 January 2021，
  
  Published：25 February 2023
- 稿件说明：
移动端阅览
LI Quanjun, CHEN Yu, JIN Dandan, et al. Analytical solution of consolidation considering initial hydraulic gradient and continuous drainage boundary under variable load[J]. Journal of Civil and Environmental Engineering, 2023, 45(1): 122-134.
DOI：

LI Quanjun, CHEN Yu, JIN Dandan, et al. Analytical solution of consolidation considering initial hydraulic gradient and continuous drainage boundary under variable load[J]. Journal of Civil and Environmental Engineering, 2023, 45(1): 122-134. DOI： 10.11835/j.issn.2096-6717.2021.086.

摘要

采用连续排水边界的必要性及软黏土中水的渗流存在着起始水力坡降(

)的现象已逐渐被认识，但变荷载下同时考虑连续排水边界条件和起始水力坡降的一维固结解析解还鲜见报道。针对外荷载随时间逐渐增加的实际情况，建立变荷载下同时考虑连续排水边界和起始水力坡降的固结模型。采用傅里叶变换及拉普拉斯变换获得模型的近似解析解，利用该解答分析动边界移动规律、超静孔隙水压力随时间的消散规律及平均固结度的增长规律。结果表明：在加载速率不变的情况下，起始水力坡降下排水面透水情况对固结性状的影响与其在达西定律下相同，透水情况越好，孔压消散速率越快；透水情况越差，超静孔隙水压力消散速度越慢。与完全透水边界条件下相比，连续排水条件下起始水力坡降

对固结性状影响无明显改变，

越大，移动边界到达土层底部的时间越长，固结完成时土中残留的超静孔压越大，按孔压定义的平均固结度越小；

值越小，移动边界到达土层底部的时间越短，固结完成时土中残留的超静孔压越小，按孔压定义的平均固结度越大。在起始水力坡降和边界排水条件不变的情况下，随着加载时间的增加，超静孔隙水压力峰值越小，超静孔隙水压力达到峰值的时间越长，但加载时间对超静孔压残留值及按孔压定义的最终平均固结度无影响。

Abstract

It has been gradually recognized of the existing of initial hydraulic gradient（

）during water seepage in soft clay and the necessity of considering continuous drainage boundary is being accepted more and more. However

the analytical solution of one-dimensional consolidation under variable load

considering both continuous drainage boundary condition and initial hydraulic gradient has rarely been reported. Based on the actual situation that the external load increases with time

taking variable load into account

a consolidation model considering both continuous drainage boundary and initial hydraulic gradient is established. The approximate analytical solution of the one-dimensional consolidation model is obtained by using Fourier transform and Laplace transform

from which

the moving law of dynamic boundary

dissipation law of excess pore water pressure as well as the growth characteristics of average consolidation degree are analyzed. The results show that

with the same loading rate

the influence of permeability of drainage surface under initial hydraulic gradient on consolidation behavior is just the same with that according to Darcy's law. The better the permeability is

the faster the dissipation rate of pore water pressure comes

and conversely

the worse the permeability is

the slower the dissipation rate of excess pore water pressure becomes. The effect of initial hydraulic gradient on consolidation behavior under continuous drainage boundary presents consistent with that under fully permeable boundary

of which the fact is

a larger value of

may lead to

larger residual excess pore pressure when consolidation is completed

and smaller average degree of consolidation defined by pore pressure. On the other side

the smaller value of

the shorter time it takes for the moving boundary reaching to the bottom of soil layer

the smaller the residual excess pore pressure becomes

and the larger the average degree of consolidation defined by pore pressure is. When under the same initial hydraulic gradient case and boundary drainage conditions

the peak value of excess pore water pressure decreases with the growth of loading time

and correspondingly takes longer time for the excess pore water pressure reaching to the peak value. However

the loading time has no influence on the residual value of excess pore water pressure and the final average cohesion defined by pore pressure.

关键词

Keywords

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