Large deformation dynamic analysis of saturated porous media with applications to penetration problems

This paper outlines the development as well as implementation of a numerical procedure for coupled finite element analysis of dynamic problems in geomechanics, particularly those involving large deformations and soil-structure interaction. The procedure is based on Biot’s theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of the soil is represented by either the Mohr Coulomb or Modified Cam Clay material model. The interface between soil and structure is modelled by the so-called node-to-segment contact method. The contact algorithm uses a penalty approach to enforce constraints and to prevent rigid body interpenetration. Moreover, the contact algorithm utilises a smooth discretisation of the contact surfaces to decrease numerical oscillations. An Arbitrary Lagrangian–Eulerian (ALE) scheme preserves the quality and topology of the finite element mesh throughout the numerical simulation. The generalised-α method is used to integrate the governing equations of motion in the time domain. Some aspects of the numerical procedure are validated by solving two benchmark problems. Subsequently, dynamic soil behaviour including the development of excess pore-water pressure due to the fast installation of a single pile and the penetration of a free falling torpedo anchor are studied. The numerical results indicate the robustness and applicability of the proposed method. Typical distributions of the predicted excess pore-water pressures generated due to the dynamic penetration of an object into a saturated soil are presented, revealing higher magnitudes of pore pressure at the face of the penetrometer and lower values along the shaft. A smooth discretisation of the contact interface between soil and structure is found to be a crucial factor to avoid severe oscillations in the predicted dynamic response of the soil.     

Improved numerical algorithms for frictional contact in pile penetration analysis

This paper presents a numerical formulation for frictional contact problems associated with pile penetration. The frictional contact at the soil–pile interface is formulated using the theory of hardening/softening plasticity, so that advanced models for the interface can be dealt with. A smooth discretisation of the pile surface is proposed using Bézier polynomials. An automatic load stepping scheme is proposed, which features an error control algorithm and automatic subincrementation of the load increments. The numerical algorithms are then used to analyse the installation process of pushed-in axial piles. It is shown that the smooth discretisation of the pile surface is effective in reducing the oscillation in the predicted pile resistances and the automatic load stepping scheme outperforms the classical Newton–Raphson scheme for this type of problem.     

Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd.     

Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model

The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non-linear stress–strain behaviour of soil. The Cam Clay model is revised to model the stress–strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.     

二维饱和土体动态孔隙率及相关动力响应特性研究

饱和多孔介质的动力响应研究在众多工程领域具有重要意义。充分考虑孔隙率的变化规律与影响因素,有利于合理揭示饱和多孔介质的相关力学行为。为此,将动态孔隙率模型与用于表征饱和多孔介质动力特性的u-U-p型方程结合,构建相应的非线性力学模型,利用Comsol Multiphysis PDE求取相应的数值解,以此研究不同透水条件下,受谐波载荷激励的二维饱和土体的孔隙率、变形量及孔隙水压力的变化规律。结果表明：孔隙率的变化与土骨架的体应变及孔隙水压力直接相关,土体压缩过程中,孔隙率相应减小,土骨架与孔隙流体的相互作用增强,土体运动时所受阻力增大,其无量纲竖向位移小于孔隙率被视为常数时的情况,在此条件下,由于土体的变形量减小,其孔隙水压力也相对减小。故充分考虑动态孔隙率,有利于更加精确地研究等饱土体和多孔介质的相关力学行为。此外,土体上表面透水条件下,孔隙流体可以从土体表面自由排出,土骨架承受的载荷更大,与不透水条件相比,土体孔隙率、竖向位移、孔隙水压力等变化更为显著。     

Numerical analysis of the installation effect of diaphragm walls in saturated soft clay

The construction of diaphragm wall panels can cause the stress change and soil movements in adjacent ground. In this paper, the construction sequence of a typical diaphragm wall panel in saturated soft clay is simulated with a 3D finite element program. The soil is assumed to behave as an isotropic linear elastic/Mohr–Coulomb plastic material with a soil–water coupled consolidation response. Influence of the pore water pressure is concerned to consider the consolidation behavior of the saturated soft clay. The analysis shows that the changes in effective horizontal stress and pore water pressure during diaphragm wall installation depend on arching mechanism and permeability. The variation in stresses and movements of ground computed by the coupled consolidation analysis and the total stress analysis are compared. Influences of the permeability coefficient on the installation effects are discussed by parametric studies. Finally, a case study of a diaphragm wall construction in Shanghai, in which the ground settlements were monitored, is presented to illustrate the prediction procedure of coupled consolidation analysis.     

A continuum‐discrete model using Darcy's law: formulation and verification

This paper presents a numerical scheme for fluid‐particle coupled discrete element method (DEM), which is based on poro‐elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one‐dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time‐step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid‐particle coupled DEM to simulate the mechanical behavior of saturated granular materials. Copyright © 2014 John Wiley & Sons, Ltd.     

Large deformation elastic electro-osmosis consolidation of clays

This paper presents the theoretical background of an elastic electro-osmosis consolidation model for saturated soils experiencing large strains, which considers volumetric strains induced by changes in both the hydraulic and electric driven pore water flows. Three fully coupled governing equations, considering the soil mechanical behaviour, pore water transport and electrical field, and their numerical implementation within an updated Lagrangian finite element formulation, are presented. The proposed model is first verified against a classical one-dimensional analytical solution for electro-osmosis consolidation to demonstrate its accuracy and efficiency. Then, various numerical examples are investigated to study the deformation characteristics and time dependent evolution of excess pore pressure. Finally, the importance of considering large strains in a consistent and proper way is demonstrated, and differences compared to models based on small strain theory are highlighted.     

Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity

The disturbance of a clay mass, due to either the installation of a driven pile or the expansion of a pressuremeter membrane, is often modelled as a cylindrical cavity expansion. In addition, it is usual (and convenient) to assume that the expansion occurs under conditions of plane strain. For this problem a method of analysis is presented which considers the soil to be a saturated two-phase material with a pore fluid which flows according to Darcy's Law. Non-linearity in material behaviour is permitted as long as the effective stress–strain law can be written in an incremental or rate form. The use of a consolidation analysis allows the changes in effective stress and pore pressure to be determined at any stage during both the cavity expansion and the subsequent period of reconsolidation. Expansions may occur at any prescribed rate, including the very fast (undrained) and the very slow (fully drained) case. The technique is illustrated by considering the expansion of a cavity in two different types of elastoplastic soil. It is shown how these solutions may be used to model the disturbance of the soil due to pile driving.     

A residual force finite element approach to soil–structure interaction analysis

An iterative process based upon a hybrid ‘residual force’ method is presented for solving elasto–plastic soil–structure interaction problems. In this approach the soil and the structure are treated as separate bodies and related only by compatibility of displacements and equilibrium of forces at the soil–structure interface. This scheme enables a significant improvement in numerical stability and rate of convergence over the conventional initial stress method. It is also shown that various interface conditions such as shear failure, slip and breakaway, and frictional and dilatant behaviour can be readily accounted for. Some practical aspects associated with the proposed scheme are emphasized for a number of numerical examples.     

Solutions of pore pressure build up due to progressive waves

The analytical solution of soil pore pressure accumulations due to a progressive wave is examined in detail. First of all, the errors contained in a published analytical solution for wave‐induced pore pressure accumulation are addressed, and the correct solution is presented in a more general form. The behaviour of the solution under different soil conditions is then investigated. It is found that the solution for deep soil conditions is sensitive to the soil shear stress in the top thin layer of the soil. However the solution is significantly influenced by the shear stress in the thin layer of soil near the impermeable base, for shallow and finite depth soil conditions. It is also found that a small error in the soil shear stress can lead to a large error in the accumulated pore pressure. An error analysis reveals the relationships between the accuracy of the pore pressure accumulation and the accuracy of the soil shear stress. A numerical solution to the simplified Biot consolidation equation is also developed. It is shown that the error analysis is of significant value for the numerical modelling of pore pressure buildup in marine soils. Both analytical and numerical examples are given to validate the error estimation method proposed in the present paper. Copyright © 2001 John Wiley & Sons, Ltd.     

Mechanics of a sandy subsoil subjected to cyclic loadings

A simple model for compaction of a sand, that may be useful in various geotechnical applications is presented. The model has been formulated in terms of the cyclic stress and strain amplitudes. The compaction properties of a dry sand are characterized by a common compaction curve described by two coefficients. The second aim of this paper is to show some applications of the theory proposed. The attention has been restricted to the two extreme cases of practical importance, namely to the behaviour of a dry sand (or a saturated sand but in free draining conditions), and to the behaviour of saturated sand in undrained conditions. Some numerical algorithms showing how to deal with those problems are presented and illustrated on the following examples: settlement and pore pressure generation in a soil stratum subjected to an earthquake, settlement of a foundation, pore pressure generation and liquefaction in a sea-bed. The results obtained suggest that the model proposed, as well as a method of dealing with boundary value problems can serve as a useful tool for the analysis of a sandy subsoil subjected to cyclic loadings.     

混凝土芯砂石桩的单桩承载力时间效应分析

在饱和软黏土地基沉桩过程中,挤土桩桩周土体将遭受相当大的挤压应力并引起很高的超静孔隙水压力,桩周土体超静孔隙水压力的消散,使桩周土体有效应力相应地增长,单桩承载力在间歇期内也会随着时间而逐渐增加。基于挤土桩沉桩过程所产生的挤土效应,运用圆孔扩张理论和固结理论分析了新型软基处理技术-混凝土芯砂石桩的挤土性状,并与软基处理中常用的CFG桩作了比较,从单桩侧摩阻力的时间效应方面分析了混凝土芯砂石桩的优越性。     

Model for large strain consolidation with compressible pore fluid

A numerical model, called CCPF1 (C onsolidation with C ompressible P ore F luid 1 ), is presented for one‐dimensional large strain consolidation of a saturated porous medium with compressible pore fluid. The algorithm includes all the capabilities of a previous large strain consolidation code, CS2, written for incompressible pore fluid. In addition, fluid density and fluid viscosity are functions of fluid pressure in CCPF1. Generalization of the numerical approach to accommodate these functions requires several modifications to the CS2 method, including phase relationships, intrinsic permeability, pore pressure, fluid potential, and mass flux. Inertial forces are neglected and isothermal conditions are assumed. The development of CCPF1 is first presented, followed by an example that illustrates the effects of pore fluid compressibility on the mechanics of consolidation of saturated porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamic response and pore pressure model of the saturated soft clay around the tunnel under vibration loading of Shanghai subway

This paper studies the saturated soft clay around the tunnel between Jingansi Station and Jiangsu Station of Shanghai subway line No.2. The continuous dynamic monitoring is conducted by means of embedded earth pressure piezometers and pore piezometers around the tunnel. The response frequency and stress amplitude of the saturated soft clay are studied with the distance from the tunnel due to the subway vibration loading. A formula is proposed for the attenuation of the dynamic pressure response in the soil. Then, based on the continuous field monitored data, and using the laboratory GDS (Global Digital System) test apparatus, the developing law of the pore water pressure of the saturated soft clay around tunnel is explored with the distance. By the GDS test, the model of the increasing pore water pressure of the saturated soft clay is put forward under the vibration loading. It is also amended by field monitored data. Finally the model is obtained. The result offers a valuable reference to the design, construction and the safe operation of the subway tunnel.     

Numerical analysis of the miniature piezocone penetration tests (PCPT) in cohesive soils

An analytical model to simulate the penetration of the piezocone penetrometer in cohesive soils is presented here. The elasto-plastic coupled field equations of the saturated cohesive soils (given by Voyiadjis and Abu-Farsakh) is used in this analysis. The numerical simulation of the piezocone penetration is implemented into a finite element program. The analytical model is used to analyze the miniature piezocone penetration tests (PCPT) conducted at LSU calibration chambers. Simulation of the piezocone penetration is done for two cases. In the first case, the soil–penetrometer interface friction is neglected, while in the second case, the soil–penetrometer interface friction is taken into consideration. The constraint approach is used to model the soil–piezocone interface friction in which the Mohr–Coulomb frictional model is used to define the sliding potential. Analysis is done for three different soil specimens with different stress histories. The results of the numerical simulations are compared with the experimental measurements of the miniature piezocone penetration tests (PCPT) in cohesive soil specimens conducted in LSU calibration chambers. The resulting excess pore pressure distribution and its dissipation using the numerical model are compared with some available prediction methods. © 1998 John Wiley & Sons, Ltd.     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical Investigation of the Inclined Pullout Behavior of Anchors Embedded in Clay

Two-dimensional plane strain finite element analysis has been used to simulate the inclined pullout behavior of strip anchors embedded in cohesive soil. Previous studies by other researchers were mainly concerned with plate anchors subjected to loads perpendicular to their longest axis and applied through the centre of mass. This paper investigates the behavior of vertical anchors subjected to pullout forces applied at various inclinations with respect to the longest anchor axis, and applied at the anchor top and through the centre of mass. The effects on the pullout behavior of embedment depth, overburden pressure, soil–anchor interface strength, anchor thickness, rate of clay strength increase, anchor inclination, load inclination and soil disturbance due to anchor installation were all studied. Anchor capacity is shown to increase with load inclination angle for anchors loaded through the centre of mass; greater effects are found for higher embedments. The results also show that anchor capacity improves at a decreasing rate with higher rates of increase of soil shear strength with depth. In addition, the capacity of vertically loaded anchors is shown to approximately double when the soil–anchor interface condition changes from fully separated to fully bonded. Similarly, disturbed clay strengths adjacent to the anchor following installation cause a significant reduction in anchor capacity. The results showed a significant effect of the point of load application for anchors inclined and normally loaded. The effects of other parameters, such as anchor thickness, were found to be less significant.     

Modelling of fluid expulsion and deformation behaviour of dewatering sediments

A finite element model is developed for modelling coupled fluid expulsion/deformation behaviour of dewatering sediments subjected to external loadings under isothermal conditions. The non-linear deformation behaviour of the sediment (soil) skeleton is based on the force equilibrium equation in which the constitutive relationship of stress and strain is implemented by the modified Cam-Clay model in soil plasticity. The fluid flow behaviour in the model is described by the generalized porous media flow equation. The model allows temporal and spatial variations of porosity and permeability. The fluid viscosity and density are assumed to be temperature-dependent. The model also allows the development of single and multiple faults, depending upon the material (sediment and fluid) properties, loading and boundary conditions. Procedures are implemented for (1) updating the material properties such as porosity, permeability, fluid density and viscosity and (2) the development of faults which allow the formation of high-permeability conduits for fluid flow. The solution algorithm for displacements of the sediments and the excess pore (fluid) pressure is based on a residual load technique to handle the non-linear (elastic-plastic) deformation behaviour of the sediment skeleton. The model can be applied to one- and two-dimensional problems. Examples of a plane strain saturated sediment layer subjected to stepwise horizontal tractions versus time are given.     

Assessment of the dynamic behaviour of saturated soil subjected to cyclic loading from offshore monopile wind turbine foundations

The fatigue life of offshore wind turbines strongly depends on the dynamic behaviour of the structures including the underlying soil. To diminish dynamic amplification and avoid resonance, the eigenfrequency related to the lowest eigenmode of the wind turbine should not coalesce with excitation frequencies related to strong wind, wave and ice loading. Typically, lateral response of monopile foundations is analysed using a beam on a nonlinear Winkler foundation model with soil–pile interaction recommended by the design regulations. However, as it will be shown in this paper, the guideline approaches consequently underestimate the eigenfrequency compared to full-scale measurements. This discrepancy leads the authors to investigate the influence of pore water pressure by utilising a numerical approach and consider the soil medium as a two-phase system consisting of a solid skeleton and a single pore fluid. In the paper, free vibration tests are analysed to evaluate the eigenfrequencies of offshore monopile wind turbine foundations. Since the stiffness of foundation and subsoil strongly affects the modal parameters, the stiffness of saturated soil due to pore water flow generated by cyclic motion of monopiles is investigated using the concept of a Kelvin model. It is found that the permeability of the subsoil has strong influence on the stiffness of the wind turbine that may to some extent explain deviations between experimental and computational eigenfrequencies.