Analytical Investigation of Effect of Vertical Drains to Consolidation Settlement Process in Isotropic Soils

Document Type : Research Paper


shahid chamran univercity of ahwaz


     Vertical drains installation can be used to accelerate the consolidation settlement. In this research, three dimension equation of consolidation in cylindrical coordinate with certain boundary condition was obtained and the analytical solution was performed. Then, the results at the MATLAB were written and the variation of degree of the settlement versus time was investigated. The results with experimental data of odoemeter test were also compared. The account of radial drains in this model were considered 0.5, 1, 1.5 and 2 cm. To verify the analytical solution, in the isotropic soils and zero radius of the vertical drain, the results and the traditional Terzaghi’s method were fully established with suitable satisfactory. The results showed. The most difference of 100% settlement velocity between of Terzaghi method and radial-vertical method was related to 40kg loads at the drain’s with 2 cm radius. This amount was 6 hr, however, the least of difference time of 100% settlement velocity was related to 5 kg loads at the drains with 0.5 cm radius and this time is 1 hr. However, results showed the analytical solution in comparison to numerical methods are predicted less time of average degree of consolidation as more accuracy.


1-    Abbasi, N., Rahimi, H., Javadi, A. A. and A. Fakher. 2007. Finite difference approach for consolidation with variable compressibility and permeability. Computers and Geotechnics, 34: 41-52.
2-    Di Rado, H. A., Beneyto, P. A., Mroginski, J. L. and A. M. Awruch. 2009. Influence of the saturation–suction relationship in the formulation of non-saturated soil consolidation models. Mathematical and Computer Modelling, 49: 1058–1070.
3-    Liu, J. C, Lei, G. H. and M. X. Zheng. 2014. General solutions for consolidation of multilayered soil with a vertical drain system. Geotextiles and Geomembranes,42:  267-276.
4-    Lu, M. M., Xie, K. H. and S. Y. Wang. 2011. Consolidation of vertical drain with depth-varying  stress induced by multi-stage loading. Computers and Geotechnics, 38: 1096–1101.
5-    McKinley, J. D. 1998. Coupled consolidation of a solid, infinite cylinder using a Terzaghi formulation. Computers and Geotechnics, 23: 193-204.
6-    Menendez, C., Nieto, P. J. G., Ortega, F. A. and A. Bello. 2010. Non-linear analysis of the consolidation of an elastic saturated soil with incompressible fluid and variable permeability by FEM. Applied Mathematics and Computation, 216: 458–476.
7-    Ong, C. Y., Chai, J. C., T. Hino. 2012. Degree of consolidation of clayey deposit with partially penetrating vertical drains. Geotextiles and Geomembranes, 34: 19-27.
8-    Qin, A., Sun, D., Yang, L. and Y. Weng. 2010. (a) A semi-analytical solution to consolidation of unsaturated soils with the free drainage well. Computers and Geotechnics, 37: 867–875.
9-    Qin, A., Sun, D., and Y. Tan. 2010.(b) Analytical solution to one-dimensional consolidation in unsaturated soils under loading varying exponentially with time. Computers and Geotechnics, 37:  233–238.
10- Rani, S., Kumar, R. and S. J. Singh. 2011. Consolidation of an anisotropic compressible poroelastic clay layer by axisymmetric surface loads. International Journal of Geomechanics, 11: 65-71.
11- Tang, X., Niu, B., Cheng, G. and H. Shen. 2013. Closed-form solution for consolidation of three-layer soil with a vertical drain system. Geotextiles and Geomembranes, 36: 81–91.
12- Terzaghi, K. 1943. Theoritical soil mechanics, John wily and Sons Inc., NewYork.
13- Wan-Huan, Z. and T. Shuai. 2012. Unsaturated Consolidation in a Sand Drain Foundation by Differential Quadrature Method. Procedia Earth and Planetary Science, 5: 52-57.
14- Xie, K. H., Wang, K., Wang, Y. L. and C. X. Li. 2010. Analytical solution for one-dimensional consolidation of clayey soils with a threshold gradient. Computers and Geotechnics, 37: 487–493.
15- Zheng, J. J., Lu, Y. E., Yin, J. H. and J. Guo. 2010. Radial consolidation with variable compressibility and permeability following pile installation. Computers and Geotechnics, 37: 408-12.
16- Zhu, G. F., and J. H. Yin. 2011. Analysis and mathematical solutions for consolidation of a soil layer with depth-dependent parameters under confined compression. International Journal of Geomechanics, 12(4): 451-461.
Volume 40, 1-1
Special Issue
June 2017
Pages 61-72
  • Receive Date: 15 November 2014
  • Revise Date: 07 June 2017
  • Accept Date: 10 February 2016
  • First Publish Date: 10 February 2016