Elsevier

Computers and Geotechnics

Volume 125, September 2020, 103686
Computers and Geotechnics

Research Paper
Evaluation of dynamic compaction to improve saturated foundation based on the fluid-solid coupled method with soil cap model

https://doi.org/10.1016/j.compgeo.2020.103686Get rights and content

Abstract

This paper presented a dynamic fluid-solid coupled finite element (FE) method incorporating the soil cap yield hardening model to analyze the improvement on saturated foundation under dynamic compaction (DC). Biot’s dynamic u–U–p formulation was employed to describe the coupling of pore fluid and solid phases, which was discretized into finite elements by application of the Galerkin method and viscous Cartesian connectors. The proposed numerical model showed reasonably good agreement with the existing analytical solutions of one-dimensional transient loading problems and field measurement of dynamic compaction. The effects of groundwater table and soil permeability were examined via the development of excess pore water pressure, effective soil stress and void ratio. Results showed that groundwater table had a significant effect on the foundation improvement by DC. Higher groundwater table resulted in larger excess pore water pressure, and effective soil stress was not found to develop under the groundwater table during the compaction process. The decrement in the void ratio was only limited to soils located above the groundwater table, and a critical depth of groundwater table existed for the DC reinforcement in fine soil foundation, which was suggested to be 6 m for the DC reinforcement with the tamping energy of 2500 kN·m per blow. Four soil permeability coefficients of k = 10−2 m/s, 10−3 m/s, 10−5 m/s and 10−7 m/s were chosen in the parametric analysis, which represented gravel, coarse sand, silt and silty clay, respectively. Higher permeability resulted in lower excess pore water pressure and larger decrease in void ratio. However, the saturated foundation was not suitable to reinforce by dynamic compaction, no matter how much the soil permeability was. Compared to the increase in soil permeability, it was more crucial to lower the groundwater table before implementing dynamic compaction. Moreover, the gravel columns were preferred to be used to accelerate the drainage of groundwater than the sand columns.

Introduction

Dynamic compaction is a common and economical ground improvement technique, which has been widely applied in various types of soil including loosely packed sand (Mayne et al., 1984), silt (Yingren et al., 1998, Nashed, 2006), clayey soil (Menard and Broise, 1975), landfill waste (Van Impe and Bouazza, 1997) and even collapsible loess in their dry/moist states (Feng et al., 2015). Therefore, current researches mainly focus on the DC treatment on dry soils to estimate the dynamic stress distribution (Mayne and Jones, 1983, Michalowski and Nadukuru, 2012, Scott and Pearce, 1975); crater depth (Mullins et al., 2000, Feng et al., 2010, Feng et al., 2013) and influencing depth (Feng et al., 2015, Feng et al., 2015). However, at some coastal areas, dynamic compaction is also reported to extend its usage to reinforce the foundation with high groundwater table, such as offshore land reclamation and airport construction (Wang et al., 2019). As a matter of fact, a high proportion of the dynamic impact is first transferred to the pore water, and the densification effectiveness for saturated deposit is dominated by the soil permeability that controls the dissipation speed of excess pore water pressure (Ghassemi et al., 2010, Lukas, 1995). Consequently; in order to obtain reasonable design parameters of dynamic compaction against the high groundwater table, it is necessary to examine the effects of soil permeability and groundwater table on the dissipation of excess pore water and development of effective soil stress and void ratio.

Biot pointed that relative motion existed between soil skeleton and pore fluid even when there is no drainage of pore fluid. Hence, the well-known dual-phase formulations were proposed to describe solid–fluid interaction by inertial, viscous and volumetric coupling under dynamic loads (Biot, 1956, Biot, 1956). Ghassemi et al. (2010) modelled a fully-coupled analysis of dynamic compaction using the u(displacement of the soil skeleton)–p(pore pressure) formulation on granular soils. They revealed that most of the DC improvement occurred during the undrained phase at the initial stage, and high oscillation of pore pressure appeared. Results also indicated that the improvement zone diminished when the degree of saturation increased. Although the u-p formulation is sufficient for lower-frequency problems, López-Querol et al. (2008)) found that since the u–p formulation neglected the relative fluid acceleration, it lacked accuracy in the computation of excess pore water pressure compared with the u–w(displacement of pore fluid) formulation. In order to overcome this problem, Ye et al. (2014)) developed an implementable method for fully coupled u–U type analysis using ABAQUS software. The solid and pore fluid phases were realized by two overlapping meshes with collocated elements and nodal points. A three-dimensional elasto-plastic model involving impulsive surface loading on dry sand overlying saturated sand was validated to analyze the dynamic compaction problem. The numerical results highlighted the importance role of the slow dilatational wave in dynamic compaction process. Furthermore, the soil should be sufficiently permeable and the loading duration sufficiently long for the slow wave to be more effective. Nevertheless, most numerical simulations of dynamic compaction focused on sandy soils using elastic or simple soils constitutive relationships without plastic flow rules. Additionally, considering the important effect of soil permeability at the situation of high saturation, a series of dewatering techniques, such as prefabricated vertical drains(PVD) (Wang et al., 2000) and vibro-stone columns (Shenthan et al., 2004); have been proposed for densification of saturated low-permeability soils. Cao and Wang (2007) confirmed an effective practice of heavy tamping after rockfilling displacement to improve seabed sediments in coastal reclamation area. Thevanayagam et al. (2009) studied the compaction processes and concurrent densification on the basis of the energy principle method, and concluded that the use of wick drains can greatly enhance densification and depth of improvement in non-plastic silty sands. Although increasing soil permeability is beneficial to improve foundation by dynamic compaction, its suitability to the soil types and groundwater tables is still ambiguous.

The objective of this paper is to develop a fully coupled fluid–solid model to simulate dynamic compaction for various soil types, especially for fine soils with large plastic deformation. Therefore, a dynamic fluid–solid coupled FE method was first proposed to reveal the elastic, viscous and plastic behaviors during the dynamic compaction process in saturated soil. The Biot’s dynamic u–U–p formulation was employed to describe the coupling of pore fluid and solid phases, which was discretized into finite elements by application of the Galerkin method and viscous Cartesian connectors. The soil behavior was simulated based on the cap yield hardening model with the principle of effective stress, which was programmed as a subroutine into the ABAQUS software. A comprehensive comparison between the proposed method and previous analytical solutions and field measurement was performed, which showed reasonably good agreement. Then the proposed fluid–solid coupled FE method was used to evaluate the improvement effect of dynamic compaction on saturated foundation considering various groundwater tables and soil types. Some engineering solutions were also suggested to effectively improve the fine soil foundation with high groundwater tables.

Section snippets

Biot’s dynamic u–U/u–U–p formulation

Biot (Biot, 1956, Biot, 1956) proposed the well-known u-U-π formulations together with the elastic constitutive relations to solve the three dimensional solid–fluid coupled problems under dynamic loading. By introducing the effective stress principle, the u-U-π formulation can be converted to the u-U-p formulation, which isLTσ-1-np+cU̇-u̇-1-nρsu¨=0np-cU̇-u̇-nρfU¨=0where L denotes the directional derivative matrix; σ and p denote the effective stress and pore pressure macroscopically; U,U̇

Validation of the fluid–solid coupled method with linear elastic model

Firstly, the implementation of the fluid–solid coupled model on ABAQUS is verified with simple linear elastic soil model. Hiremath et al. (Hiremath et al., 1988) deduced analytical solutions for the problem of a fully saturated porous layer with a finite thickness subjected to velocity loading. The soil column is 0.5 m long and the bottom boundary is rigid and impermeable as illustrated in Fig. 1. Two plane-strain overlapping meshes are used, namely, the solid mesh and the fluid mesh, each

Numerical analysis

In this section, the effects of groundwater table and soil permeability on the DC improvement are analyzed based on the proposed numerical model as shown in Fig. 5. Results on four different groundwater tables, i.e., h = 0 m, 2 m, 4 m and 6 m below ground surface, are compared with those of dry soil foundation. The soil permeability coefficients used in the analysis are k = 10−2 m/s, 10−3 m/s, 10−5 m/s and 10−7 m/s, representing gravel, coarse sand, silt and silty clay, respectively.

Conclusions

This study investigates the potential application of dynamic fluid–solid coupled FE method with cap model used for the study of dynamic response characteristics on the saturated foundation under dynamic compaction. The proposed numerical model shows reasonably good agreement with the published analytical solutions of one-dimensional transient loading problems and field measurement of dynamic compaction. The effects of groundwater table and soil permeability are examined via the development of

CRediT authorship contribution statement

Zhou Chong: Methodology, Software, Validation, Writing - original draft. Jiang Hongguang: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Yao Zhanyong: Conceptualization, Supervision, Project administration. Li Hui: Software, Validation. Yang Chenjun: Software, Investigation. Chen Luchuan: Project administration, Funding acquisition. Geng Xueyu: Conceptualization, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

Financial supports from the National Natural Science Foundation for Young Scientists of China (Grant No. 51608306), Shandong Transportation Science and Technology Foundation (2016B20, 2019B47_2), and Young Scholar Future Plan Funds of Shandong University are gratefully acknowledged.

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