# Semi-analytical and semi-numerical method for the single soil layer consolidation problem

Tao Cheng (Institute of Geotechnical and Underground Engineering, Huazhong University of Science and Technology, Wuhan, China and School of Civil Engineering, Hubei Polytechnic University, Huangshi, China)
Keqin Yan (School of Civil Engineering, Hubei Polytechnic University, Huangshi, China)
Jun-Jie Zheng (Institute of Geotechnical and Underground Engineering, Huazhong University of Science and Technology, Wuhan, China)
Xian-Feng Luo (School of Civil Engineering, Hubei Polytechnic University, Huangshi, China)
Ding-Bang Zhang (School of Civil Engineering, Hubei Polytechnic University, Huangshi, China)
Wan-Hui Xu (School of Civil Engineering, Hubei Polytechnic University, Huangshi, China)
Ren-Jie Hu (School of Civil Engineering, Hubei Polytechnic University, Huangshi, China)
Yi Zhang (School of Civil Engineering, Hubei Polytechnic University, Huangshi, China, and Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan)

ISSN: 0264-4401

Article publication date: 2 May 2017

153

## Abstract

### Purpose

This paper aims to present a simplified solution method for the elasto-plastic consolidation problem under different stress paths.

### Design/methodology/approach

First, a double-yield-surface model is introduced as the constitutive model framework, and a partial derivative coefficient sequence is obtained by using numerical approximation using Gauss nuclear function to construct a discretization constitutive model which can reflect the influence of different stress paths. Then, the model is introduced to Biot’s consolidation theory. Volumetric strain of each step as the right-hand term, the continuity equation is simplified as a Poisson equation and the fundamental solution is derived by the variable separation method. Based on it, a semi-analytical and semi-numerical method is presented and implemented in a finite element program.

### Findings

The method is a simplified solution that is more convenient than traditional coupling stiffness matrix method. Moreover, the consolidation of the semi-infinite foundation model is analyzed. It is shown that the numerical method is sufficiently stable and can reflect the influence of stress path, loading distribution width and some other factors on the deformation of soil skeleton and pore water pressure.

### Originality/value

Original features of this research include semi-numerical semi-analytical consolidation method; pore water pressure and settlements of different stress paths are different; maximum surface uplift at 3.5a; and stress path is the main influence factor for settlement when loading width a > 10 m.

## Acknowledgements

The study was supported by the Natural Science Foundation of Hubei Province under Grant 2013CFC103, the Natural Science Foundation of Hubei Polytechnic University under Grant 13xjz03A, the National Natural Science Foundation of China under Grant 51478201, the Natural Science Foundation of Hubei Province under Grant 2012FKC14201, Scientific Research Foundation of Hubei Provincial Education Department D20134401 and the Innovation Foundation in Youth Team of Hubei Polytechnic University under Grant Y0008. Their financial support is gratefully acknowledged.

## Citation

Cheng, T., Yan, K., Zheng, J.-J., Luo, X.-F., Zhang, D.-B., Xu, W.-H., Hu, R.-J. and Zhang, Y. (2017), "Semi-analytical and semi-numerical method for the single soil layer consolidation problem", Engineering Computations, Vol. 34 No. 3, pp. 960-987. https://doi.org/10.1108/EC-10-2015-0297

## Publisher

:

Emerald Publishing Limited Bingley, United Kingdom