Research paperNumerical simulation of electro-osmotic consolidation coupling non-linear variation of soil parameters
Introduction
Electro-osmotic consolidation is an effective technique for the improvement of soft soil, which involves the movement of pore water in a soil-water system from the anode toward cathode under an external electrical field. Laboratory experiments and field applications have been conducted to investigate the dewatering and consolidation behavior of soil subjected to electro-osmosis, and these investigations have generated significant knowledge pertaining to this process (Bjerrum et al., 1967, Esrig and Gemeinhardt, 1967, Casagrande, 1983, Lockhart, 1983, Lo et al., 1991, Micic et al., 2001, Burnotte et al., 2004, Glendinning et al., 2007, Jeyakanthan et al., 2011, Hu et al., 2013, Wu and Hu, 2014, Wu et al., 2015a, Wu et al., 2015b, Wu et al., 2016). Based on the knowledge, theoretical models are developed to describe the behavior of soil upon electro-osmotic consolidation, and analytical solutions for pore water pressure and degree of consolidation are obtained. Esrig (1968) first proposed a one-dimensional (1D) theoretical model and derived the solution for the excess pore water pressure under different boundary conditions. Wan and Mitchell (1976) investigated the coupling effect of surcharge preloading and electro-osmotic consolidation. Following their pioneering work, two-dimensional (2D) and axisymmetric models were further developed and the corresponding analytical solutions were derived by assuming constant soil parameters and ignoring the stress-strain behavior (Shang, 1998, Su and Wang, 2003, Li et al., 2010, Xu et al., 2011; Wu and Hu, 2013b). The obtained analytical solutions from the above models can only be applied to problems with simple boundary conditions and geometries, and cannot account for the non-linear variation of soil parameters and the coupling effect of the multi-fields including pore-water movement, electrical current, stresses and displacements. Moreover, the complex geological conditions and irregular electrode configuration in field applications cannot be considered with the developed analytical methods.
Numerical approach has proved to be a useful method to predict the behavior of soil upon electro-osmotic consolidation with complex boundary conditions and geometries. Up to now, many numerical models have been proposed to simulate the dewatering and consolidation processes of the treated soil (Lewis and Humpheson, 1973, Rittirong and Shang, 2008, Hu et al., 2010, Hu et al., 2012, Wang et al., 2012, Zhou et al., 2013, Jeyakanthan and Gnanendran, 2013, Hu and Wu, 2014, Deng and Zhou, 2015, Yuan and Hicks, 2015). Lewis and Humpheson (1973) applied the finite element method to analyze the development of pore water pressure during electro-osmotic consolidation in a 2D model. Rittirong and Shang (2008) used the finite difference model to simulate the field test reported by Bjerrum et al. (1967). Jeyakanthan and Gnanendran (2013) developed a finite element formulation integrated with the elastoplastic modified cam clay model. Hu and Wu (2014) proposed a three-dimensional (3D) numerical model for electro-osmotic consolidation and analyzed the effect of electrode configuration and electrode depth. Yuan and Hicks (2015) came up with a numerical solution at large strains and verified the solution by comparing with the field test conducted by Burnotte et al. (2004). With these proposed numerical approaches, the development of pore water pressure and soil deformation can be analyzed. However, most of the previous numerical simulations ignore the non-linear variation of soil parameters during electro-osmotic consolidation. In fact, both the laboratory experiments and field tests have confirmed the change of soil parameters such as electro-osmosis conductivity, coefficient of volume compressibility and hydraulic conductivity during electro-osmotic consolidation (Burnotte et al., 2004, Jeyakanthan et al., 2011, Wu and Hu, 2013a). These changes, although being recognized, have been rarely considered in the numerical analysis.
In this paper, the effect of the stress-strain field and the non-linear variation of soil parameters was analyzed with a multi-field coupling numerical model for electro-osmotic consolidation, in which empirical formulas describing the non-linear variation of soil parameters were incorporated. Moreover, a field test reported by Burnotte et al. (2004) was back analyzed with the numerical model. The variation of electro-osmosis conductivity and coefficient of compressibility was summarized from the literature and incorporated in the numerical simulations. The complex boundary conditions and geometry, the irregular electrode configuration and the intermittence of current were also considered in the numerical simulations to investigate the capability of the numerical approach to solve practical problems with complex operating conditions.
Section snippets
Numerical model for electro-osmotic consolidation
The multi-field coupling numerical model for electro-osmotic consolidation in this study is developed from the theoretical model proposed by Hu and Wu (2014). The adopted assumptions include: 1) the soil is saturated and the soil skeleton is linear elastic; 2) the velocity of water flow due to electro-osmosis is directly proportional to the voltage gradient; 3) the water movement in soil is linear superposition of water flows due to electro-osmosis and hydraulic gradient; 4) the influence of
Effect of the stress-strain field and the non-linear variation of soil parameters
Wu and Hu (2013b) proposed an analytical solution for electro-osmotic consolidation under axisymmetric condition. However, the soil deformation was not considered during the mathematical derivation of the analytical solutions for pore water pressure and degree of consolidation. In order to analyze the coupling effect of stress-strain field on electro-osmosis, an axisymmetric model for electro-osmotic consolidation was developed as shown in Fig. 1. The top boundary and the cathode in the center
Geological conditions of the field
Burnotte et al. (2004) reported a large field test located near Mont St-Hilaire in the St. Lawrence valley, about 40 km east of Montréal, Canada. The main purpose of this field test was to improve the strength of the soft clay in the foundation of an existing embankment and eliminate ongoing long-term settlement of the embankment. On the top of the treated area, there was a 2 m deep granular fill layer from the elevation of 40.5–38.5 m. Beneath the granular fill layer was a 3.5 m deep silty soil
Results and discussion
Fig. 8 compared the surface settlement from field measurements (S6) and the calculation results from the four numerical simulations. Although slightly larger in the early period, the settlements from the numerical simulation considering both the non-linear variations of electro-osmosis conductivity and coefficient of compressibility (N4) coincided well with the field measurements, and the prediction of the settlement from N4 was more accurate than that from N1, N2 and N3, especially in the
Conclusions
A 3D multi-field coupling numerical model for electro-osmotic consolidation was employed to analyze the effect of the non-linear variation of soil parameters during the consolidation process. The complex operating conditions, including boundary conditions and geometry, irregular electrode configuration, and current intermittence were simulated. A case study was performed to further verify the effectiveness of the numerical model. The following conclusions can be drawn based on the above studies.
Acknowledgements
Financial support from the National Natural Science Foundation of China (Project No. 51579132, 51323014, 51609123), the Ministry of Education (Project No. THZ-02-2), and the China Postdoctoral Science Foundation (Grant No. 2015M581104) are gratefully acknowledged.
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