Numerical simulation of pile installations in a hypoplastic framework using an SPH based method

Abstract

This paper presents a tool to estimate the stresses, and thus the expected forces, at a retaining wall by the installation of piles. The solution method is based on Smoothed Particle Hydrodynamics (SPH) and the soil is modeled using a simplified hypoplastic material law. In order to correctly compute the forces on the soil due to the contact between the pile and the soil, a formulation for imposing frictional boundary conditions using SPH is developed. Modeling the soil with the chosen hypoplastic approach also allows for tensile forces in the soil. However, these are not physical. Therefore, an alternative formulation is presented which directly eliminates unphysical tensile stresses in the cohesionless soil without any additional numerical parameters. The numerical code is firstly validated against benchmark problems. Then several test cases are simulated including monotonic and cyclic penetration of piles into the soil. A good agreement with the experimental observation is found. Additionally, the impact of pile driving in the presence of sheetpiles (retainers) is investigated to see how the pile driving can alter the applied forces on the sheet piles. The simulation of such complex geotechnical problems that involve large deformation, material nonlinearity, and moving boundary conditions demonstrates the applicability and versatility of the proposed numerical tool in this field.

Introduction

The dense settlement in cities often places strong demands on the geotechnical production methods for new buildings. Especially when building excavation pits, the usability of the surrounding infrastructure must be guaranteed at all times. For this purpose, the effects of geotechnical manufacturing processes on the soil must be understood. The soil as a material is characterized by the storage of the prehistory as long as the processes do not lead to a swept out of memory. Soils with different load history therefore react differently to the same loads.

When designing or dimensioning excavation pits, the influence of geotechnical production methods, such as pile driving, vibrating, pressing, grouting or prestressing of construction aids as well as concreting and draining is neglected. Measurements at Potsdamer Platz in Berlin during the construction phase show that production methods lead to significant ground movements inside and outside the excavation pit (Triantafyllidis, 1998). Especially the insertion of piles by vibrating led to a very strong deformation of nearby retaining walls. The real behavior was partly higher by a factor of 4 than assumed in the original dimensioning. The deformation behavior also clearly exceeded the deformations caused by the underwater excavation and draining of the excavation pit. The design of the construction could therefore not correctly capture all phases leading to the final deformations (Triantafyllidis, 1998).

An alternative that can contribute to the correct design of excavation pits is numerical simulation. By means of a realistic reproduction of the pile installation process, the deformations of neighboring buildings or retaining walls can be calculated. In addition to accurate constitutive models for the soil and contact conditions between the structure and the soil (Weißenfels and Wriggers, 2015), stable and efficient numerical solution methods able to represent the piles installation process are required.

Different approaches are available for modeling the constitutive behavior of soils. Mostly, the concept of elasto-plasticity is used in geotechnical simulations, like the Mohr Coulomb or the Drucker Prager model. A generalization able to include the dependency of soil behavior on the Lode angle is given in Ehlers (1995). Additionally, Cam Clay models based on the critical state concept are also used quite often. An introduction to these models can be found in Desai and Siriwardane (1984) and a numerical realization of the Mohr Coulomb and the Drucker Prager model is given in de Souza Neto et al. (2008). An extension of the critical soil state concept applicable to cyclic loadings is proposed by means of the SANISAND model (Taiebat and Dafalias, 2008). Since some soil characteristics can hardly be included into the elasto-plastic framework, recently hypoplastic models were developed where the material behavior is considered as inelastic from the onset of loading. Kolymbas (2000) gives a general introduction into hypoplasticity and von Wolffersdorff (1996) proposes a simple but accurate model where the material parameters can be determined by standard experimental tests (Herle, 1997).

When piles are installed using the penetration method, for instance by means of hammer dropping, part of the soil is displaced during the process. The simulation with mesh-based methods in a Lagrange description of the differential equations leads to very strong deformations of the mesh. These can either falsify the results or cause the simulation to be aborted. Solution methods based on the Euler description are based on a transport of the material through fixed control volumes. However, the definition of the interface between pile and soil requires further algorithms. Meshfree particle methods, on the other hand, allow deformations of any size in a Lagrange description. Therefore, these methods are suitable for numerically representing the installation of piles. A large number of different meshfree methods are available. As a fully Lagrangian mesh-less method, Smoothed Particle Hydrodynamics (SPH) has been successfully applied to various physical problems in astrophysical application (Gingold and Monaghan, 1977), reactive transport and precipitation (Tartakovsky et al., 2007), solid deformation (Gray et al., 2001) and heat transport (Cleary and Monaghan, 1999). In particular, it has become well established for the simulation of fluids with free surfaces (Monaghan, 1994). By describing the material behavior on the basis of the symmetrical velocity gradient, the hypoplastic material formulation can be easily integrated into the algorithms of SPH for fluid flow in order to tailor such algorithms to non-liquid materials. The first author has already developed a numerical code in the SPH framework for the simulation of biomechanical system in an aqueous environment (Soleimani et al., 2016). The aim is to tailor the existing SPH computer code to the new geomechanical application through incorporating a hypoplastic constitutive behaviour along with the required modifications which are appropriate for soil modellling. The SPH method has recently drawn the attention of researchers in geomechanical community (Peng et al., 2019, Wang et al., 2019, Wang and Wei, 2020). Moreover, the hypoplastic approch has proven to be a successful method in modeling the response of soils and granular materials (Gudehus, 2019, Fuentes et al., 2019, Tafili and Triantafyllidis, 2020). In (Bui et al., 2007) an multiphase SPH based model has been presented for the water saturated soil. The failure and collapse mechanisms of cohesive soil has been studied in (Zhang et al., 2019) via incorporating a softenning behaviour in an elasto-plastic framework. Slope stability analysis, which is closely related to the soil failure, using SPH method is also a matter of research among researchers, see for examples (Nonoyama et al., 2015, Wu et al., 2015).

The outline of this paper is as follows: First, the balance equations, the hypoplastic material description, and the kinematic relations are presented which are necessary to formulate the corresponding differential equations. Section 3 introduces the Smoothed Particle Hydrodynamics discretization concept which is applied to the equations from Section 2. In Section 4, the new algorithm to impose traction vectors resulting from friction within the SPH framework is proposed together with a new correction scheme to suppress tensile stresses. Three different test cases are presented in Section 5 to validate the new formulations. In addition, the benefit of using a meshfree solution scheme to design the right pattern for the insertion of piles in order to avoid strong movements of the surrounding retaining walls and buildings is also demonstrated. A conclusion of this work is given in Section 6.