The impact of high-velocity sand columns against rigid and deformable structures based on the smoothed particle hydrodynamics method

Highlights

• The high velocity soil-solid interaction is modeled base on two regimes of behavior

• A novel 2D algorithm based on the SPH method is proposed for soil-solid interaction

• Using FCSPH approach to model high-velocity soil slug impact on targets

• The rate-dependent plastic TLSPH approach is applied to simulate structure

• Impact of a sand slug on beam and rigid target is conducted against other studies.

Abstract

The response of a structure subjected to the impact of a dry sand slug has been studied using a fully coupled approach, in which a novel algorithm based on the smoothed particle hydrodynamics (SPH) method is proposed for soil-solid interaction (SSI). The proposed algorithm is a hybrid continuum/discrete approach that can determine two regimes of contact behavior. When the granular assembly has a high relative velocity in dealing with the structure, initially, the short-term particle-to-particle contacts take place, resembling molecular collisions in a fluid and referred to as regime I. Then, the increase of the relative density of aggregate particles leads to semi-permanent contacts, referred to as regime II. The present aim is development of a coupling model that includes both regimes. The simulation of impact of granular slug into a rigid or deformable target leads to large numerical errors and even divergences. To overcome the limitation of traditional SPH approach that the density estimate is a major challenge in high-rate deformation problems, the number-density scheme is extended to the fully compressible approach. Finally, the proposed SSI Algorithm is validated with Liu et al.’s results [1] to simulate the interaction of a structure with sand slugs traveling at high velocities.

Introduction

The study of the high velocity impact of granular media to deformable structure with the aim of optimal design of monolithic structures is worthwhile. The several experimental studies [2], [3], [4], [5], [6] have been done to determine the dynamic properties of fully consolidated soil. The dynamic compressibility of soil has studied over a wide strain rate range and load amplitudes. Bragov et al. [3] studied the dynamic properties of soils at high strain rates using a modified Kolsky method. They determined the volume compressibility curve and the uniaxial stress–strain curve for the development of mathematical models of soft soils [4], [6]. The main parameters in the high strain-rate compression of soils with different compressive stress levels up to 500 MPa determined to develop mathematical models of soft soils [6]. Omidvar et al. [7] reviewed the laboratory studies conducted by various researchers on the response of soil under high strain rates and showed that the strain rate, pressure, saturation, initial porosity ratio, shape, and size of soil grains are effective on the dynamic response of the soil. Park et al. [8] developed a laboratory-based method to measure the pressure exerted on a rigid stationary target by the sand slugs. Their results expressed that the transmitted momentum was approximately equal to incident momentum. Uth and Deshpande [9] and Uth et al. [10] employed this setup to study the response of monolithic structures impacted by sand slugs. The numerical analysis capabilities have made it possible to simulate complex loads created in the soil related to interaction with structure. The availability of interaction models is significant to characterize dispersing and compacting soils interacted with structure. There are limited attempts at developing interaction models between soils subjected to dynamic loading with structure, with the aim of the employment of these algorithms in numerical codes to predict the response of structure. Previous studies are limited to developing constitutive models for soil within an Eulerian numerical code and coupled to Lagrangian finite element method to simulate structure.

Most of soil models are limited to a regime where the relative density of soil mass is high enough that the contacts between particles are semi-permanent. For this reason, their applicability is questioned when the soil is widely dispersed due to impact on a structure. Besides, because dry soil grains do not support tensile stress, their behavior changes from a dense plastic media to a disconnected state during the process, a sensitive switch which is difficult to express in a unified modeling and numerical framework. For this purpose, the discrete element method (DEM), first described in Cundall and Strack [11], has been used to simulate granular flow. The rheology of granular flows based on DEM is influenced by the particle–particle interactions. Despite conceptual simplicity of DEM, unfortunately, it results in unjustified computational expense over the large physical domains in geomechanical applications. In addition, the determination of mechanical properties such as stress history and plastic effects is ambiguous; moreover the valid treatment for determining these parameters has not been provided so far. Inspired by particle–particle interactions, Deshpande et al. [12] presented a constitutive model according to a continuous approach that could be applied for granular flow in both their densely packed and disconnected states. Nevertheless, the successful performance of this model has been questioned for a coupled soil-structure interaction modeling because of computational problems that arise in analysis of a loose aggregate of particles impacts the target.

Pingle et al. [13] have employed a discrete particle model to investigate the interaction of spatially uniform granular slugs impacting rigid targets. Liu et al. [1] used coupled discrete particle/continuum simulation methodology to investigate the response of structures impacted by high-velocity granular materials. The sand is modeled as discrete circular particles while a Lagrangian finite element framework is used to model structure. They demonstrated that the response of structure is characterized by the initial velocity of the sand particles, and the height of the slug.

On the other hand, mesh-free particle methods seem to provide a more efficient way to deal with soil-structure interaction problems. The Smoothed Particle Hydrodynamics (SPH) is firstly proposed by Lucy [14] and by Gingold and Monaghan [15] for astrophysical applications. In this method, time derivatives of physical variables in the governing equations can be derived through interaction between particles, which is fundamentally different from the grid-based methods. The granular flowing has several modeling challenges when considering a continuous approach. The dry granular mass in the dense flow regime can be modeled as an elastic-viscoplastic material [16]. Regarding the nature of the SPH method that is based on a continuous approach; the impact of granular slug into a rigid or deformable target that is associated with severe dispersion leads to large numerical errors and even divergences. The weakly compressible approach (WCSPH) uses a general scheme such that the mass of particles corresponds to their initial density [17]. However, in the fully compressible approach, equivalent mass particles are considered, so that the calculated density of each particle is related to the local number density. In the present work, a fully compressible approach within the standard SPH framework is employed. Additionally, the number-density scheme for governing equations is considered as an efficient computational alternative to regulate resolution of the lowest-density region [18].

SPH has also received much attention in geotechnical engineering problems involving soil–structure interaction. In SPH simulations of fluid or granular flow interacting with deformable structures, (i) normalizing conditions [19], (ii) ghost particles [20], or (iii) boundary particle forces [21] techniques are proposed to model the contact between two media. The description of contact behaviors is generally expressed based on particle-to-surface contact or particle-to-particle contact with determining an optimal contact force which depends on the amount of overlap and the displacement rate [22], [23], [24]. The proposed contact force requires the tuning of a scaling parameter to be optimized. Due to the high sensitivity of these models to the scaling parameter, it is difficult to select the correct value for different problems. Also, to our knowledge, all these methods are applicable in low-velocity impact, but, they are not capable of modeling the aggregate behavior of particles in contact, which commonly occurs in high relative velocities. For this purpose, novel algorithms have been presented to extend the application of SPH in geomechanics including soil-structure interaction.

This paper presents a unified explicit SPH algorithm for soil-structure interaction problems to study the response of structures subjected to the impact of high velocity granular media. For this purpose, firstly, the impact of sand column to a rigid target is simulated with high accuracy. Also, the use of a fully compressible approach for modeling soil impact on structures, for the first time, can be used as an innovation to investigate granular flows in mixed regimes. In the following, a novel 2D algorithm for soil-structure interaction related to deformable structures is presented with comprehensive validations and performance investigations.