Coupled smoothed particle hydrodynamics-discrete element method simulations of soil liquefaction and its mitigation using gravel drains

Highlights

• A SPH-DEM approach is utilized to evaluate the responses of loose and dense granular deposits to seismic excitations.

• Gravel drains were then introduced to the loose deposit and its effect on mitigating pore pressure buildup was examined.

• The loose deposit exhibited liquefaction while the dense deposit barely showed any considerable buildup of pore pressure.

• Liquefaction of the loose deposit resulted in significant settlement while that of the dense deposit was tolerable.

• Gravel drains effectively reduced pore-pressure buildup but did not reduce the overall settlement to acceptable levels.

Abstract

In this paper, a fully Lagrangian particle-based method for coupled fluid-particle interaction is utilized to evaluate liquefaction of saturated granular soils subjected to dynamic base excitations. The discrete element method (DEM) is employed to model the solid particles and the fluid motion is simulated using the smoothed particle hydrodynamics (SPH). A coupled SPH-DEM scheme is achieved through local averaging techniques and well-established semi-empirical formulas for fluid-particle interaction. A key feature of the employed technique is that it does not presume undrained conditions for the granular deposit and allows for spatial fluid movements within the deposit. The responses of loose and dense granular deposits to seismic excitation are first analyzed. As expected, the loose deposit exhibited significant pore pressure development and liquefaction while the dense deposit barely showed any considerable buildup of pore pressure and did not liquefy. Liquefaction of the loose deposit resulted in significant surface settlement while that experienced by the dense deposit was within tolerable limits. A liquefaction mitigation technique through the installation of gravel drains was then introduced to the loose deposit and its effect on mitigating pore pressure buildup was examined. Results of conducted simulations show that the installation of gravel drains effectively reduced pore-pressure buildup and, for the most part, the soil maintained its strength. However, the drains did not reduce the overall surface settlement of the deposit to acceptable levels.

Introduction

Over the past five decades, the U.S. and other seismically active areas have sustained considerable damage resulting from earthquake-induced site liquefaction that was associated with very costly damage to port facilities, bridges, dams, buried pipes, and buildings of all types. The 2011 Tohoku (Japan) earthquake caused an estimated $300 billion in damage. Evidence of wide spread of liquefaction and lateral spreading at unprecedented scale has been observed in many locations and port facilities [1]. Similarly, the 2010–2011 earthquakes that hit the Christchurch city and its surrounding areas (Canterbury Earthquakes, New Zealand) resulted in a devastating damage due to liquefaction. The most common definition of sand liquefaction is that it is a result of water pressure buildup due to squeezing of pore space during rapid earthquake loading, without sufficient time for water to flow through the grains and drain the pressure [e.g., 2]. That is, when the sand is loosely packed, there would be a tendency for the grains to get into a denser configuration during earthquake motion, squeezing pore-water and rapidly increasing the pressure owing to the high bulk modulus of water.

Liquefaction resistance can be improved by: increasing the soil density through compaction, stabilizing the soil skeleton, reducing the degree of saturation possibly by introducing air bubbles into the void space, dissipation of the generated excess pore pressure, and intercepting the propagation of excess pore pressures buildup, among other techniques. Herein, the focus is on gravel drains as one of the widely used liquefaction hazards mitigation method. Sadrekarimi and Ghalandarzadeh [3] argue that the potential benefits of gravel drains include densification of the surrounding granular soil, dissipation of excess pore water pressure, and redistribution of earthquake-induced or pre-existing stress. They also note that the relatively high internal friction resistance of the gravel imparts a significant frictional component to the treated composite, improving both its strength and its deformational behavior.

Computational modeling offers effective means to predict and assess soil behavior in response to earthquakes. In this regard, the coupled (solid-fluid) response of saturated granular soils is commonly modeled using continuum formulations derived based on phenomenological considerations (e.g., the mixture or Biot theories) or homogenization of the micro-mechanical equations of motion [[4], [5], [6]]. Each of these different formulations requires a constitutive model to describe the relationship between effective stresses and strains of the solid phase. For liquefaction problems, constitutive models based on plasticity theory are most commonly used. Several constitutive models have been presented to describe the behavior of saturated granular soils during cyclic loading [e.g, [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]]. These constitutive relations can be employed in a finite element method or a finite difference formulation to predict the seismic response of a saturated granular deposit. High performance parallel computing simulations have also been presented using continuum-based methods [e.g., 20, 21].

The discrete element method (DEM) provides an alternative effective tool to model granular soils and other geomaterials based on micromechanical idealizations. This method [22] simulates these media as assemblages of interacting discrete particles, and has shown great capability to reproduce the actual behavior of granular soils with simple parameters at the microscale. Numerous attempts have been made at incorporating fluid-particle interaction equations into the discrete element method formulation. One of the popular coupling techniques is to describe the fluid flow by averaged Navier-Stokes equation based on mean multiphase mixture properties and employ well-established semi-empirical equations to calculate the fluid particle interaction forces (e.g. Ref. [23,24]). The fluid equations are discretized over a fixed mesh and solved using a technique known as the finite volume method (FVM). This method has proven to yield satisfactory results in simulating different geotechnical phenomena such as soil liquefaction. It has since gained momentum and was adopted by researchers to model several problems in geomechanics [e.g., [25], [26], [27], [28], [29]]. However, the usage of fixed coarse grid mesh limits its scope and application to the fixed boundary problems.

A more elaborate approach is to model fluid at the pore-scale level to investigate the development of pore pressure due to actual changes in the shape and volume of the pore space caused by particle movements. Zhu et al. [30] developed a pore-scale numerical model using smoothed particle hydrodynamics (SPH) to investigate the flow through porous media. They conducted two-dimensional simulation of flow through periodic arrangements of cylinders and validated the proposed method by comparing the results with those obtained from finite element method. Potapov et al. [31] presented a coupled DEM-SPH method to analyze flows of liquid-solid mixtures. The fluid-particle interaction was obtained by applying no-slip boundary conditions at the solid particles surface. Han and Cundall [32] combined DEM and lattice Boltzmann method (LBM) to simulate flow through porous media at the pore scale. El Shamy and Abdelhamid [33] investigated liquefaction of saturated granular soil deposits by idealizing soil grains through DEM and modeling the pore fluid using LBM. Abdelhamid and El Shamy [34] presented a fully coupled DEM-LBM model to investigate the mechanism of fine particle migration in granular filters. The high accuracy of the pore scale models comes at the price of being computationally expensive, to a degree that makes it impractical to perform numerical simulations with realistic particle sizes using typical desktop computers.

As an alternative to modeling the fluid at the pore scale, SPH could be used to approximate the set of partial differential equations represented by an averaged form of Navier-Stokes equations [35,36] that accounts for the presence of the solid phase and the momentum transfer between the phases. Indeed, SPH is a method that could be generalized to approximate any set of partial differential equations and not necessarily for fluids. For instance, large deformation models of granular materials in a continuum framework have been presented by Chen and Qiu [37], where the saturated soil equations of motions were approximated using SPH. Coupling SPH for the fluid and DEM for the solid phase offers the benefits of overcoming the need for a constitutive model for the solid phase while maintaining the robustness of DEM for large deformation problems and SPH for tracking the fluid motion. Sun et al. [38] presented a Lagrangian-Lagrangian DEM-SPH coupled model for the multiphase flows with free surfaces. They performed dam break and rotational cylindrical tank simulations to showcase the proposed method abilities. Robinson et al. [39] presented a meshless simulation technique based on coupled DEM-SPH algorithm and validated the model by conducting simulations of single particle and constant porosity block sedimentation in a fluid column. Many more examples of coupled DEM-SPH application to various science and engineering problems can be found in the recent literature [[40], [41], [42], [43], [44], [45], [46], [47]].

In this paper, the results of a novel application of SPH-DEM to model soil liquefaction is presented. A key feature of the employed technique is that it does not presume undrained conditions for the granular deposit and allows for spatial fluid movements within the deposit. The responses of loose and dense granular deposits to seismic excitation are first analyzed. As expected, the loose deposit exhibited significant pore pressure development and liquefaction while the dense deposit barely showed any considerable buildup of pore pressure and did not liquefy. A liquefaction mitigation technique through the installation of gravel drains was then introduced to the loose deposit and its effect on mitigating pore pressure buildup was examined.