P. A. Vermeer

Non-Associated Plasticity for Soils, Concrete and Rock

With reference to practical engineering problems it is shown that considerable differences may be encountered between the results from associated and those from nonassociated plasticity theories. Next, the need for a non-associated plasticity theory is demonstrated by considering test results for sand, concrete and rock. Elementary material parameters are discussed such as Youngs modulus and Poissons ratio for the description of the elastic properties; and a cohesion and a friction angle for the determination of the strength. The salient difference from associated plasticity theory concerns the introduction of a dilatancy angle which controls the inelastic (plastic) volume changes. This dilatancy angle is not only a suitable parameter for the description of soils, but also appears to be useful for concrete and rock. Basically, the paper consists of three parts as we consider three types of models of increasing complexity. The first model is a perfectly-plastic model, which employs the five aforementioned parameters. It is based on test data rather than on Druckers hypothesis of material stability. The consequences thereof are examined. The second model is a straightforward extension of the first model by augmenting it with friction hardening and cohesion softening. This novel idea is introduced to account for the degradation of the cohesion of cemented granular materials with increasing inelastic deformation. The model is employed in an analysis which shows that plastic deformations tend to localize in thin shear bands, which may occur even before peak strength is reached. Finally, a review is given of concepts for modelling hysteresis and strain accumulation in cyclic loading. The concept of a bounding surface in addition to a yield surface is discussed and is adapted for use in a sophisticated model for loose and cemented granular materials under cyclic loading.

Continuous and discontinuous modelling of cohesive-frictional materials

Computational models for failure in cohesive-frictional materials with stochastically distributed imperfections.- Modeling of localized damage and fracture in quasibrittle materials.- Microplane modelling and particle modelling of cohesive-frictional materials.- Short-term creep of shotcrete - thermochemoplastic material modelling and nonlinear analysis of a laboratory test and of a NATM excavation by the Finite Element Method.- Thermo-poro-mechanics of rapid fault shearing.- A view on the variational setting of micropolar continua.- Macromodelling of softening in non-cohesive soils.- An experimental investigation of the relationships between grain size distribution and shear banding in sand.- Micromechanics of the elastic behaviour of granular materials.- On sticky-sphere assemblies.- Cohesive granular texture.- Micro-mechanisms of deformation in granular materials: experiments and numerical results.- Scaling properties of granular materials.- Discrete and continuum modelling of granular materials.- Difficulties and limitation of statistical homogenization in granular materials.- From discontinuous models towards a continuum description.- From solids to granulates - Discrete element simulations of fracture and fragmentation processes in geomaterials.- Microscopic modelling of granular materials taking into account particle rotations.- Microstructured materials: local constitutive equation with internal lenght, theoretical and numerical studies.- Damage in a composite material under combined mechanical and hygral load.

Soil collapse computations with finite elements

SummaryThe elastic-plastic finite element method is reviewed with a view to predict collapse loads of geotechnical constructions. The basic technique of using an incremental-iterative approach with a constant stiffness matrix is well-known, but we fill a gap by proving that the procedure converges not only for small steps but also for large load increments. Here restriction is made to associated plasticity, as uniqueness of solution is not ensured for non-associated plasticity problems. Differences between associated and nonassociated problems are illustrated by showing results of numerical analyses. Finally, a number of practical aspects associated with the method are discussed.ÜbersichtIm Hinblick auf die Vorhersage der Versagenlasten von Erdbauten wird ein Überblick über die elastisch-plastische Finite-Element-Methode gegeben. Das grundlegende Verfahren mit inkrementelliterativem Vorgehen mit einer konstanten Steifigkeitsmatrix ist wohlbekannt. Durch den Beweis, daß das Verfahren nicht nur bei kleinen Schrittweiten, sondern auch bei großen Laststufen konvergiert, werden jedoch neuartige Erkenntnisse vorgestellt. Hierbei muß einschränkend assoziierte Plastizität gelten, da bei nicht-assoziierter Plastizität die Eindeutigkeit von Lösungen nicht gewährleistet ist. Anhand von numerischen Ergebnissen werden Unterschiede zwischen Aufgabenstellungen mit assoziierter und nichtassoziierter Plastizität aufgezeigt. Schließlich werden auch noch praktische Gesichtspunkte des Verfahrens erörtert.

ARCHING EFFECTS BEHIND A SOLDIER PILE WALL

Abstract A wall consisting of anchored steel piles with horizontal timber laggings was selected to support a 16 m deep excavation with a length of more than three kilometres near Cologne in Germany. Vertical holes were bored on the wall line, at 4 m centres, and steel piles were placed within these holes. Good contact between the piles and the surrounding soil was ensured by concreting the remaining space in the holes. In this way the earth pressure behind the wall was transferred to the piles through horizontal arching, so relieving the timber laggings. As a result, lighter timber laggings could be used and the economy of the wall construction could be increased. In situ tests as well as non-linear 3D finite element (FE) analyses were carried out. Horizontal arching was promoted by means of flexible horizontal lagging timbers and solid contact between the piles and the surrounding soil. Vertical arching was induced by high pre-stress forces in the upper ground anchors. FE analyses were based on both the elasto-plastic Mohr–Coulomb model and a more advanced hardening-soil model.

Macromodelling of softening in non-cohesive soils

Considering non-cohesive material, the void ratio is used to control softening on the friction angle. In order to obtain well-posed boundary-value problems, the softening parameter is defined as a nonlocal state parameter, so that computational results remain independent of the FEM-discretization. The model is evaluated through a comparison of numerical analysis and experimental data on Hostun sand. For a calibration of the constitutive model triaxial tests and oedometer tests with near-homogeneous deformations were used. Biaxial tests with strong shear-banding for dense sand were used to study the evolution of strain localization. The resulting shear band thickness, the role of the internal length and the input of combining both material and geometric softening are discussed.

Time integration of a constitutive law for soft clays

This article presents an elasto/viscoplastic constitutive law that accounts for the creep behaviour of soft soils, and examines the performance of an implicit time-stepping algorithm. It is demonstrated that the update of stresses on the integration point level is most efficiently performed by using a scheme similar to that developed by Borja and Lee for plasticity.

Soil-structure interaction: FEM computations

Publisher Summary The chapter reviews aspects of the soil–structure interface behavior at the element level and the numerical integration of the corresponding interface constitutive models. The design of structures subjected to soil–structure interaction and to contact with friction should be tackled using soil–structure interface constitutive equations. These laws differ from the laws for soils because of three main features: the size of the relative displacements and of relative rotations between grains, the high level of dilatancy and contraction under shearing, and the presence of an intense degradation effect resulting from localization in the pattern of a shear band. The elastoplastic interface constitutive equations are easy to use but do not modelize all these effects. The incrementally non-linear interface constitutive equations are versatile for modeling all these interdependent phenomena. In addition, applications to piles under tension loading are presented to illustrate the results of these procedures.

Numerical simulation of unsaturated soil behaviour

The mechanical behaviour of unsaturated soils is one of the challenging topics in the field of geotechnical engineering. The use of finite element techniques is considered to be a promising method to solve settlement and heave problems, which are associated with unsaturated soil. Nevertheless, the success of the numerical analysis is strongly dependent on the constitutive model being used. The well-known Barcelona Basic Model is considered to be a robust and suitable model for unsaturated soils and has, thus, been implemented into the PLAXIS finite element code (Vermeer and Brinkgreve, 1995). This paper provides the results of numerical analyses of a shallow foundation resting on an unsaturated soil using the implemented model. Special attention is given to the effect of suction variation on soil behaviour.

Simulation of Incompressible Problems in Geomechanics

This article presents techniques for solving problems involving incompressibility in the context of low-order linear elements. It begins with describing a weak formulation that applies to both finite element and material point methods. Iterative solution schemes, including relaxation and explicit time stepping, are summarized. A strain enhancement procedure that is useful when incompressibility is introduced through plasticity is presented next, followed by a slope stability example that compares the iteration characteristics and vertical crest displacement corresponding to explicit and implicit matrix-free algorithms. Two procedures for dealing with pore pressure generation related to incompressibility and undrained conditions are described and an example is presented to compare pore pressures.

A fast 3D tunnel analysis

Publisher Summary This chapter considers a 3D finite element analysis for predicting surface settlements. Results of such a 3D analysis are shown for the computation of surface settlements from a full excavation of a circular new Austrian tunnel method (NATM). A new method is presented, in which similar results are obtained from a much more simple 3D analysis. It has been shown that a full 3D analysis of tunnel excavation is carried out to predict the settlement trough. Therefore, an extremely large number of excavation steps are needed. Because of this requirement, computer runtime gets excessive, and it is obvious that such a full 3D analysis is not feasible for engineering practice. It has been shown that the settlement trough that responds to a full 3D analysis is obtained from a simple 3D analysis that requires little computational effort. This method is applicable for constitutive laws with both liner elastic and constant plastic soil behavior.