Granular materials: Parameter identification and modelling of localisation problems

The prediction of landsliding requires an exact knowledge of the mechanical behaviour of granular materials. This kind of materials, e. g., sand, have a very complex deformation behaviour, which depend on the stress state and on the loading history. In this work, the deformation behaviour of the solid skeleton is characterised via homogeneous triaxial tests on dry sand specimens. Additionally, an appropriate elasto-plastic material law to describe the solid skeleton in the frame of Theory of Porous Media (TPM) is used, which is implemented in the FE tool PANDAS. Furthermore, a single-surface yield criterion with isotropic hardening, which limits the elastic domain, and a non-associated plastic flow are employed. The determination of the material parameters of the linear elasticity law as well as the single-surface yield criterion are based on test data of triaxial experiments. The material parameters are identified using a derivative-based optimisation method (donlp2), which is coupled with PANDAS. Finally, a simulation of a benchmark test is presented to show shear band localisation effects, where the material behaviour is described by a triphasic porous media model based on the TPM, where the constituents are a deformable solid skeleton and two pore fluids, water and air. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase transition processes of pore fluids in porous materials

Taking a closer look on, e. g., storage processes of greenhouse gases in deep geological aquifers or pressure decreases in dilatant shear bands, the observation can be made that pressure and temperature changes in porous materials can induce phase transition processes of the respective pore fluids. For a numerical simulation of this behaviour, a continuum mechanical model based on a multiphasic formulation embedded in the well-founded framework of the Theory of Porous Media (TPM) is presented in this contribution. The single phases are an elasto-viscoplastic solid skeleton, a materially compressible pore gas consisting of the components air and gaseous pore water (water vapour) and a materially incompressible pore liquid, i. e., liquid pore water. The numerical treatment is based on the weak formulations of the governing equations, whereas the primary variables are the temperature of the mixture, the displacement of the solid skeleton and the effective pressures of the pore fluids. An initial boundary-value problem is discussed in detail, where the resulting system of strongly coupled differential-algebraic equations is solved by the FE tool PANDAS. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On coupled problems in geomechanics

Geomechanical problems are generally based on the category of granular, cohesive-frictional materials with a fluid pore content. At the macroscopic scale of continuum mechanics, these materials can be successfully described on the basis of the well-founded Theory of Porous Media (TPM) [1]. The present contribution touches fundamental problems of coupled media by investigating the interacting behaviour of an elasto-viscoplastic porous solid skeleton, the soil, and two pore fluids, water and air. Furthermore, electro-chemical reactions are considered in order to include the swelling behaviour of active soil. In conclusion, this leads to a system of strongly coupled partial differential equations (PDE) that can be solved by use of the finite element method (FEM). In particular, the presentation includes fluid-flow situations in the fully or the partially saturated range, swelling phenomena of active clay [3] as well as localisation phenomena [2] as a result of fluid flow or heavy rainfall events. The computations are carried out by use of the single-processor FE tool PANDAS [4] and, in case of large 3-d problems, by coupling PANDAS with the multi-processor solver M++. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameteridentification of Hostun-Sand and Shear-Band Simulation of Landsliding

The simulation of deformation process of landsliding needs the knowledge of the very complex behaviour of granular materials, e. g., sand. The triax experiments on sand show a highly non-linear elasto-plastic material behaviour. Therefore, it is necessary to use a yield criteria, e. g., single-surface yield criteria with isotropic hardening and non-associated plastic potential, which satisfies adequately the requirements of the material properties. This kind of material behaviour can be described by an elasto-plastic material law in the frame of Theory of Porous Media, which is implemented in the FE tool PANDAS. By means of the data of Hostun-Sand, the material parameters of the singlesurface yield criteria are determined by use of a optimization algorithm, namely Sequential Quadratic Programming (SQP) a gradient based optimization method, which is coupled with PANDAS. Using this optimized material parameters, a simulation of a initial boundary-value problem of landsliding is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element simulation of deformation behaviour of cellular rubber components

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using porous hyperelastic material model. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The new material model which is based on Danielsson et al [1] decouples the influence of porosity from the mechanical properties of the solid material by introducing volume fraction of the pores as an explicit scalar variable. The finite element simulations are then followed by experiments on complex model to validate the material model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Description of Partially Saturated Soils by the Theory of Porous Media

In this contribution, a multi‐phase soil model based on the Theory of Porous Media (TPM) is presented. The model is fully coupled in the following constitutive phases: An elasto‐plastic or elasto‐viscoplastic solid skeleton, a materially incompressible pore‐liquid (water) and a materially compressible pore‐gas (air). The interaction of the solid skeleton and the pore‐fluids is specified by a capillary pressure‐saturation relation, whereas the mobilities of the fluid phases in the pore‐space of the solid skeleton are described by the so‐called relative permeabilities. Finally, a gravity governed initial‐boundary‐value problem solved by the FE method is presented.     

Coupled Problems of Dynamics in Materially Incompressible Saturated Porous Media

The mechanical behavior of saturated porous materials is largely governed by the interaction between the solid skeleton and the pore fluid. This interaction is particularly strong in dynamic problems and leads to numerical challenges especially in the case of incompressible constituents. In fact, the permeability plays a significant role in this coupling and influences the choice of a proper time integration scheme. Proceeding from the macroscopic Theory of Porous Media (TPM) within the isothermal and geometrical linear regime, the governing balance equations of the dynamic binary solid–fluid model are the solid and fluid momentum balances, and the overall volume balance of the biphasic mixture. This set of coupled partial differential equations (PDEs) is solved within the framework of the mixed Finite Element Method (FEM) applying two different time solution methods, viz., a monolithic implicit and a splitted implicit–explicit scheme. The time stepping algorithms are implemented into the FE program PANDAS and a Scilab FE routine and compared on a one–dimensional wave propagation example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Two‐Phasic Flow Problems in Elasto‐Plastic Porous Materials

In the present contribution, the formulation of the governing equations of coupled flow and deformation processes in porous materials is based on the well‐founded Theory of Porous Media (TPM) [2, 3]. Embedded in this concept, the model under consideration represents a triphasic medium of a cohesive‐frictional elasto‐plastic solid skeleton and a binary pore‐fluid, which is composed of a materially incompressible wetting phase (here water) and a materially compressible non‐wetting phase (here air). The unsaturated domain (saturation in terms of liquid saturation) of the porous medium is included in the model by the application of a suitable capillary‐pressure‐saturation relation, which takes into account the interaction of the solid skeleton and the two pore‐fluids. Furthermore, the interaction is described by Darcy's filter law including a relative permeability, which depends on the deformation of the pore space and the degree of saturation.     

The theoretical treatment of cooling processes in porous rocket thrustchambers

One of the most promising approaches for future high pressure rocket combustion chambers is the application of porous carbon fiber reinforced ceramics in conjunction with the effusion cooling in fluid‐cooled rocket engines. In order to determine the coolant mass flow through the porous material, the influences of the temperature have to be taken into account additionally. Thus, one has to deal with interacting continua governed by non‐isothermal processes, when designing a porous rocket combustion chamber for realistic operating conditions such as extremely high temperatures. Describing coupled solid‐fluid problems efficiently, it is generally convenient to utilize macroscopic strategies like the Theory of Porous Media (TPM). While in the past, most of the multiphase problems based on the TPM have been treated isothermally, the present contribution extends the theoretical treatment to non‐isothermal problems. This is achieved by proceeding from a thermoelastic solid skeleton saturated by a compressible viscous pore‐fluid, whereas a separate temperature field has to be established for each constituent. Finally, the efficiency of the developed model will be briefly discussed by computing some simple non‐isothermal physical effects, which are solved by the FE tool PANDAS. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of a biphasic and a multicomponent model describing viscoelastic swelling phenomena

Biological soft tissues like articular cartilage and their artificial replacement hydrogel have a multicomponent microstructure, consisting of a charged viscoelastic solid matrix saturated by a fluid, which is composed of the liquid solvent and the dissolved anions and cations. Such charged multiphasic materials exhibit a swelling behaviour under varying chemical conditions. These materials are best described by a macroscopic approach like the Theory of Porous Media (TPM). Starting from this point, a standard two-phase model is extended by dividing the fluid into the above mentioned components. Therein, the chemical relations describing the behaviour of the ions and their interaction with the other mixture constituents are incorporated. The resulting model covers mechanical as well as osmotic and electrostatic effects. For numerical and simplicity reasons, it is possible to describe the swelling phenomena by a simplified biphasic model, where the ions as a third degree of freedom and their time-dependent diffusion are neglected. Furthermore, the viscoelastic solid matrix can be replaced by an elastic material. Note that using the multicomponent model generally results in numerical problems, since the boundary conditions depend on the internal fixed charge density. It is shown that this problem can be solved by including the boundary conditions into the weak formulation. Finally, to compare the different behaviour of the above mentioned models by means of an swelling example, they are implemented into the FE tool PANDAS using stable Taylor-Hood elements for the spatial discretization. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Swelling with Weakly Fulfilled Boundary Conditions

Biological soft tissues exhibit a swelling behaviour and consist of multiple phases, a solid phase composed of collgagen fibers and charged PGA chains and a fluid phase composed of the liquid solvent and the ions of dissolved salt. In this contribution, the Theory of Porous Media (TPM) model consists of four constituents, a charged solid and an aqueous solution composed of water and the ions of dissolved salt. The solid is modelled by a finite elasticity law accounting for the multiphasic micro structure, whereas the fluid is considered as a viscous Newtonian fluid. One finally ends up with the volume balance of the fluid, the concentration balance of the cations, the momentum balance of the overall mixture. The resulting set of partial differential equations is solved within the framework of the FEM. Therefore, the weak forms are derived and the resulting set of equations for the primary variables pore pressure p, cation concentration c and solid displacement u _S , is implemented into the FE tool PANDAS. Finally, a three dimensional example of a swelling hydrogel disc is shown. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of Swelling Phenomena in Charged Hydrated Porous Media

Biological tissues like articular cartilage and geomaterials like clay have a multicomponent microstructure. The charged solid is saturated by a viscous fluid, which itself is composed of several components: the liquid solvent and the dissolved ions, namely, water, anions and cations. These charged multiphase materials exhibit a swelling behaviour under varying chemical conditions. The model describing such materials combines electrochemical and mechanical effects like osmosis and electrostatics within a macroscopic formulation. Starting from the Theory of Porous Media (TPM), a four component model is presented, wherein all constituents are materially incompressible and mass exchanges are excluded. This isothermal model leads to a set of equations which consists of three primary variables: the solid displacement u _S, the pore‐pressure p and the molar ion concentration c_m, since the ion concentrations always depend on each other because of the electroneutrality condition. For the numerical treatment, the weak formulations of governing equations are implemented in the FE tool PANDAS, wherein Taylor‐Hood elements are used for the spatial discretization. Finally, a simulation of a 3‐d swelling experiment is shown. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress-dependent Failure Surface of Granular Materials

Numerical computations of geotechnical problems will become increasingly important because of the growing complexity of geotechnical applications. Therefore, a well-founded prediction of stability statements requires appropriate models, which are able to realistically depict the stress-strain behaviour of non-cohesive-frictional granular materials. On several stress paths, drained triaxial compression experiments on compact dense sand specimen exhibited that the size of the failure surface is not independent from the hydrostatic pressure. The failure surface and, thus, the maximal shear stresses at a specific confining pressure σ₃^exp can be increased by a compression preload at a level higher than σ₃^exp. This means that granular materials own several failure surfaces in dependence of the hydrostatic pressure. Consequently, the failure criteria based on the assumption of a compression stress-path-independent single-failure surface cannot recover the newly detected plastic yielding behaviour of granular materials. An improved approach for modelling the plastic hardening and softening behaviour coupled with the new yield properties at the limit state will be presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of macroscopical transient frost processes and microscopical driving forces

The artificial saturation phenomenon due to freeze–thaw cycles is described by a multi–phase and multiscale model [1,2,3] formulated within the Theory of Porous Media, [4]. It represents partially saturated concrete as a mixture of 5 interacting constituents φ^α, namely the solid skeleton φ^s, the bulk water φ^l, the pore volume occupied by vapour φ^v, the ice φⁱ and the gel water phase φ^p. Most relevant for the model is the distinction between two length scales and their characteristic time scales. The boundary is marked where macroscopic bulk conditions change to surface physics and chemistry. Surface physics and chemistry acting on the nano–scale affect fundamental properties of concrete and consequently the durability of concrete against freeze–thaw. At the macroscopic scale the model describes transient conditions (i.e. water–uptake, heat transport, volume dilatation of 9%, phase change of first order considering hysteresis) which are characterized by a relatively long time period to reach equilibrium in contrast to the processes modelled on the microstructure. At the microscopic scale the model represents the nanoscopic CSH–gel system consisting of solid CSH and water as a linked system of both components basing on the concept of the “Solid–Liquid Gel System” [5]. In the constribution the numerical results of the model are presented with focus on the evaluation of the process zone during the penetration of the melting front into the matrix. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulations of swelling media by weakly fulfilled Dirichlet boundary conditions

Charged hydrated porous media, which are found in biomechanics as well as in geomechanics, have the capability to change their volume under varying chemical conditions of the environment. In this contribution, these materials are modelled in the framework of the thermodynamically consistent Theory of Porous Media (TPM). The underlying model consists of four constituents, a charged solid and an aqueous solution composed of water and the ions of dissolved salt. The solid is modelled by a finite elasticity law accounting for the multiphasic micro structure, whereas the fluid is considered as a viscous Newton ian fluid. One finally ends up with four balance relations, the volume balance of the fluid, the concentration balance of the cations, the momentum balance and the balance of charges of the overall mixture. The resulting set of partial differential equations is solved within the framework of the FEM. Therefore, the weak forms are derived and the resulting set of equations for the primary variables pore pressure p, cation concentration c_m and solid displacement u _S is implemented into the FE tool PANDAS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Liquefaction in fluid-saturated soils

Liquefaction phenomena can be observed if fluid-saturated soils are subjected to transient loading conditions, as they arise, for instance, during earthquakes. The term “liquefaction” comprises more specific liquefaction phenomena, such as flow liquefaction, which is an instability phenomenon in loose soils, and cyclic mobility, which is associated with medium-dense to dense soils, where, in contrast to flow liquefaction, the overall stability of the granular assembly is maintained. However, soil liquefaction is always associated with a pore-pressure build-up, which consequently reduces the intergranular frictional forces, and thus, the load bearing capacity of the fluid-saturated soil. In order to model these particular liquefaction phenomena, we proceed from a continuum-mechanical framework based on the Theory of Porous Media (TPM), where the solid skeleton is described as an elasto-(visco)plastic material with isotropic hardening and a stress-dependent failure surface. The numerical solution of the resulting coupled system of partial differential equations is carried out by the finite-element method (FEM). (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)