Numerical simulation of dynamic pore fluid-solid interaction in fully saturated non-linear porous media

In this paper, a large deformation formulation for dynamic analysis of the pore fluid-solid interaction in a fully saturated non-linear medium is presented in the framework of the Arbitrary Lagrangian-Eulerian method. This formulation is based on Biot’s theory of consolidation extended to include the momentum equations of the solid and fluid phases, large deformations and non-linear material behaviour. By including the displacements of the solid skeleton, u, and the pore fluid pressure, p, a (u-p) formulation is obtained, which is then discretised using finite elements. Time integration of the resulting highly nonlinear equations is accomplished by the generalized–α method, which assures second order accuracy as well as unconditional stability of the solution. Details of the formulation and its practical implementation in a finite element code are discussed. The formulation and its implementation are validated by solving some classical examples in geomechanics

Advanced Soil Constitutive Models and Their Applications to Offshore Geotechnical Problems

Advanced simulation of geotechnical problems involving clay may require sophisticated constitutive models in order to accurately capture the mechanical response of soil under various loading conditions, initial states and strain levels. This is of particular importance when numerical analyses involve an interaction of soil and structure possibly including large deformations and dynamic (cyclic) and impact loadings prevalent in most offshore geotechnical applications. Accordingly, some advanced soil models have been implemented into a bespoke finite element code and then applied to several dynamic coupled problems of geomechanics. This has provided more realistic numerical analyses for which different features of soil behavior have been taken into account. This paper presents some of these numerical simulations highlighting the importance of advanced soil constitutive models in geomechanics

Pore pressure response to dynamically installed penetrometers

Potentially, a seabed may be characterized rapidly and economically by using dynamically installed free-falling penetrometers (FFPs). Because of their relatively rapid deployment and recovery, FFPs may be preferred over conventional full-flow or cone penetrometers for characterizing seabeds. However, despite several successful field trials of FFPs, significant uncertainty still exists about the data interpretation, mainly because of the fast nature of the penetration process, during which regions of the soil body close to the penetrometer experience very high strain rates. The consequence of such high strain rates on pore pressure measurement is not well known. Furthermore, the rigorous numerical analysis of the problem is notoriously difficult because it involves large deformations, dynamics, hydrodynamic coupling, highly nonlinear material behavior, rate dependency, and contact mechanics. A finite-element procedure was developed and used in this study to provide a dynamic coupled solution for the penetrometer impact and burial into saturated clay. Subsequently, some mechanisms involved in the generation of excess pore pressures were investigated with specific attention given to the effects of the penetrometer tip geometry and the location of the pore pressure measuring devices. An important numerical challenge in modeling this problem is highlighted in this paper. It concerns the numerical diffusion that can occur because of the remeshing process required in this large deformation, moving boundary problem

Machine learning aided stochastic reliability analysis of spatially variable slopes

© 2020 This paper presents machine learning aided stochastic reliability analysis of spatially variable slopes, which significantly reduces the computational efforts and gives a complete statistical description of the factor of safety with promising accuracy compared with traditional methods. Within this framework, a small number of traditional random finite-element simulations are conducted. The samples of the random fields and the calculated factor of safety are, respectively, treated as training input and output data, and are fed into machine learning algorithms to find mathematical models to replace finite-element simulations. Two powerful machine learning algorithms used are the neural networks and the support-vector regression with their associated learning strategies. Several slopes are examined including stratified slopes with 3 or 4 layers described by 4 or 6 random fields. It is found that with 200 to 300 finite-element simulations (finished in about 5 ~ 8 h), the machine-learning generated model can predict the factor of safety accurately, and a stochastic analysis of 105 samples takes several minutes. However, the same traditional analysis would require hundreds of days of computation

Numerical analysis of torpedo anchors

This paper presents the development of a numerical framework based on the finite element method and its application in the analysis of torpedo anchors. The procedure is based on a mixture theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of soil is represented by the Modified Cam Clay material model and the interface between the soil and the structure is modelled by a mortar segment-to-segment frictional contact method. An Arbitrary Lagrangian-Eulerian (ALE) method is adopted to avoid mesh distortion throughout the numerical simulation. The generalised-α method is utilised to integrate the governing equations of motion in the time domain. Results obtained from the installation phase of a torpedo anchor reveal that the anchor decelerates at a constant rate during most of its penetration. Analysis results show a typical distribution of excess pore-water pressure during free falling installation, having higher magnitudes at the face and lower magnitudes along the shaft. The computational results for the setup phase indicate that for soil elements located within a radial distance of approximately one diameter from the centreline of the torpedo, 90% of consolidation takes place in a few days after installation, depending on the value of soil permeability

One-dimensional test problems for dynamic consolidation

Closed-form solutions are presented for some one-dimensional problems involving the dynamic response of saturated porous media. These solutions are useful for validating finite element codes for dynamic consolidation of soil. While they consider only elasticity and small strains, they do allow a check on the concurrent wave transmission and consolidation processes

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

A two-surface plasticity model for clay; numerical implementation and applications to large deformation coupled problems of geomechanics

This paper presents numerical treatments of elastoplasticity relations for a previously developed critical state two-surface plasticity model and its implementation into a bespoke finite element code as well as the commercial software Abaqus via the user defined subroutine, UMAT. The model is implemented with an efficient integration scheme based on the explicit modified Euler scheme with automatic substepping and error control. Validation of the implemented model is assessed through simulation of several laboratory tests comprising a variety of initial states and loading conditions followed by a study on the accuracy and efficiency of the integration scheme. Subsequently, the model is employed to analyse some sophisticated boundary value problems involving finite deformations, inertia effects, soil-structure interactions and saturated porous media. The constitutive model captures particular features of clay behaviour, such as the prediction of strain rate dependence, small-strain stiffness degradation, the development of residual strength at very large shear strains and stress anisotropy. The effects of these features on the behaviour of two important geotechnical problems – including pipe-seabed interaction under lateral motion and dynamically installed anchors – are specifically investigated using two advanced finite deformation schemes: one based on the Arbitrary Lagrangian Eulerian (ALE) method and another on the Particle Finite Element Method (PFEM). The study illustrates the robustness of the proposed integration scheme and successful application of the soil model, indicating that the use of such complex soil models may be useful for realistic analyses of geotechnical problems

Coupled analysis of dynamically penetrating anchors

The development of a numerical procedure for the finite element analysis of anchors dynamically penetrating into saturated soils is outlined, highlighting its unique features and capabilities. The mechanical behaviour of saturated porous media is predicted using mixture theory. An algorithm is developed for frictional contact in terms of effective normal stress. The contact formulation is based on a mortar segment-to-segment scheme, which considers the interpolation functions of the contact elements to be of order N, thus overcoming a numerical deficiency of the so-called node-to-segment (NTS) contact algorithm. The nonlinear behaviour of the solid constituent is captured by the Modified Cam Clay soil model. The soil constitutive model is also adapted so as to incorporate the dependence of clay strength on strain rate. An appropriate energy-absorbing boundary is used to eliminate possible wave reflections from the artificial mesh boundaries. To illustrate the use of the proposed computational scheme, simulations of dynamically penetrating anchors are conducted. Results are presented and discussed for the installation phase followed by 'setup', i.e., pore pressure dissipation and soil consolidation. The results, in particular, reveal the effects of strain rate on the generation of excess pore pressure, bearing resistance and frictional forces. The setup analyses also illustrate the pattern in which pore pressures are dissipated within the soil domain after installation. Hole closure behind a dynamic projectile is also illustrated by an example

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