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In a FE analysis of transient heat transfer, a lower limit of the time-step size exists below which numerical oscillations of temperatures may occur. Although time-step constraints for simulating 1D heat diffusion have been well established in the literature, the conclusions cannot be directly applied to 2D cases. In this paper, both analytical and computational studies are carried out to obtain the time-step constraints for 2D linear and quadratic elements. It is noted that in the simulation of 2D heat diffusion employing quadratic elements is not always beneficial. Recommendations are provided on selecting the numerical scheme to minimise numerical oscillations.

A new Petrov-Galerkin finite element method for two-dimensional (2D) highly advective flows in porous media, which removes numerical oscillations and retains its precision compared to the conventional Galerkin finite element method, is presented. A new continuous weighting function for quadratic elements is proposed. Moreover, a numerical scheme is developed to ensure the weighting factors are accurately determined for 2D non-uniform flows and 2D distorted elements. Finally, a series of numerical examples are performed to demonstrate the capability of the approach. Comparison against existing methods in the simulation of a benchmark problem further verifies the robustness of the proposed method.

The accurate reproduction of the hysteretic behaviour exhibited by soils under cyclic loading is a crucial aspect of dynamic finite element analyses and is typically described using the concept of damping ratio. In this paper, a general algorithm is presented for assessing the damping ratio simulated by any constitutive model based on the registered behaviour in three-dimensional stress–strain space. A cyclic nonlinear elastic model capable of accurately reproducing a wide range of features of soil behaviour, including the variation of damping ratio with deformation level, is chosen to illustrate the capabilities of the proposed algorithm. The constitutive model is described and subsequently employed in two sets of finite element analyses, one involving the dynamic response of a sand deposit subjected to different types of motion and another focussing on the simulation of a footing subjected to cyclic vertical loading. The application of the presented algorithm provides insight into the processes through which energy is dissipated through hysteresis.

This paper discusses several considerations related to appropriate numerical modelling of the reservoir hydrodynamic pressures on dams. The reservoir is modelled with 8-noded isoparametric displacement based solid finite elements. The study includes both stiff and flexible dams with vertical and sloped upstream faces under ramp, harmonic and random acceleration loads. The numerical results were compared and found to be in good agreement with available closed-form solutions. The same approach may be used in analyses of other waterfront structures such as quay walls.

Constitutive models for unsaturated soils are most commonly based on conventional critical state type models for saturated soils. The ellipse of the modified Cam-clay model is usually adopted for the formulation of the yield and the plastic potential surfaces in the mean stress – deviatoric stress plane. Despite the wide use of this ellipse it has long been shown that the peak deviatoric stress observed for highly overconsolidated states may be largely overestimated. For fully saturated conditions, a planar surface, termed the Hvorslev surface, has been employed in the literature in order to overcome this shortcoming on the dry side of the critical state. In addition, by employing a no-tension cut-off, stress states are restricted within the compressive region. In unsaturated conditions and due to the effect of suction the soil may be subjected to tensile total stresses which should not, however, exceed a model dependent limit. Nonetheless, adopting a planar surface and in the absence of any provision, illegal tensile stresses may be obtainable. For this reason, a new expression for the Hvorslev surface, which restricts the stress state within acceptable boundaries, is proposed, based on a small number of model parameters. The new surface is curved rather than planar and can also be used in combination with critical state type constitutive models developed for saturated conditions. The new surface is calibrated based on fully saturated undrained triaxial compression and extension tests and on unsaturated drained triaxial tests. The superiority of the new surface in comparison with commonly adopted shapes for the yield and the plastic potential functions – such as the ellipse and the bullet shape of the modified and the original Cam clay models – is demonstrated through numerical analyses of the unsaturated drained triaxial laboratory tests.

While the evolution with time of the factor of safety against slope failure is well understood for excavations performed under fully saturated conditions, this evolution has not been extensively studied for excavations carried out in unsaturated soils. The objective of this paper is to investigate the relationship between the factor of safety and time for an excavation performed in an unsaturated silty soil, employing the finite element method. A hypothetical boundary value problem is considered and two types of analyses performed; in the first one, unsaturated soil behaviour is modelled through appropriate constitutive and soil–water retention curve models, whereas in the second one full saturation is assumed. The effect that the saturated soil permeability, its variation with suction, the increase of apparent cohesion due to suction, the depth of the groundwater table and the hydraulic hysteresis have on the results of the unsaturated analysis is examined in a parametric study. The analyses results demonstrate that for unsaturated soils the factor of safety may increase with time, in contrast to what is commonly accepted to be the case in fully saturated soils. Furthermore, it is not possible to know in advance which one of the two types of analysis performed (i.e. the saturated or the unsaturated) will produce conservative results. It is, therefore, advisable to perform unsaturated analysis in geotechnical practice, when dealing with excavations in such soils.

In the field of constitutive modelling of soil behaviour, optimisation techniques have been mostly employed as a calibration tool, particularly when several model parameters lack clear physical meaning. In this paper, however, a procedure based on a Hill-Climbing optimisation algorithm is presented as a form of improving the performance of constitutive models. Specifically, a simple cyclic nonlinear elastic model, which is shown to be unable to simulate adequately the damping ratio measured under small and large strain amplitudes, is modified by applying the Hill-Climbing technique to the determination of a new relationship describing the unloading/reloading behaviour of soil under cyclic loading. The performance of the proposed model is assessed by evaluating its parameters based on three distinct sets of empirical damping ratio curves and computing the corresponding error in their simulation. It is shown that the introduction of the new unloading/reloading expression formulated based on the outcome of the optimisation procedure increases substantially the precision of the constitutive model.

This paper presents a numerical study on the short-term bearing capacity of preloaded footings on soft clay. In practice, this situation needs to be addressed when re-using an existing foundation for a new building or when extra load is to be transmitted to an existing foundation. Previous studies have estimated the bearing capacity in this situation, allowing simply for the increase in the soil undrained strength due to the increase in effective stresses imposed by the preload. However, field and laboratory observations corroborate that there is a continuous increase in the stiffness and strength soil properties with time, even after the dissipation of the excess pore water pressures generated during the initial loading is complete. This paper quantifies the short-term bearing capacity of existing foundations allowing for the occurrence of creep deformations and associated soil hardening. The problem is investigated by means of a series of plane-strain coupled finite element analyses of a 2 m wide rough strip footing, in which the foundation soil is modelled using an overstress based elastic-viscoplastic model. The study investigates the effect of the level of preload, the applied loading rate, the creep characteristics of the foundation soil (magnitude and creep law type) and the footing geometry. It is shown that the time dependent nature of soil (e.g. occurrence of creep) accounts for a significant increase in bearing capacity.

This paper examines the seismic response of a large and complex system comprising a Lock chamber and three neighbouring water saving basins (WSBs). The developed two-dimensional plane strain finite element model included the entire system in order to explore the interaction of the various structures. The first set of analyses was undertaken under static conditions to simulate the construction sequence and to establish the stress regime prior to the examined seismic event. Subsequently, dynamic time domain analyses were performed to examine the response of the system to seismic loading. The ground motion was applied into the finite element mesh employing a sub-structuring technique which enables economic modelling of large computation domains and accurate representation of the semi-infinite half-space. The paper explores some aspects of the numerical modelling of such complex systems, such as the impact on the predicted seismic response of the adopted constitutive model and the modelling of hydrodynamic effects. The discussion of the dynamic analyses results focuses on the main Lock structure, looking at the prevailing modes of deformation, the potential lift-off of the base of the Lock walls and the interaction of the main wall with the other retaining structures.

This paper presents a three-dimensional elastic viscoplastic constitutive model that is able to reproduce the time dependent behaviour of soils with isotach viscosity. This constitutive law is based on the overstress theory and incorporates some important features, namely: (i) a non-linear creep law with a limit for the amount of creep deformation under isotropic stress conditions; (ii) a flexible loading surface that is capable of reproducing a wide range of shapes in p ′ − J stress space and incorporates the Matsuoka–Nakai failure criterion in the deviatoric stress space and (iii) assumes that the viscoplastic scalar multiplier is constant on a given loading surface to ensure that critical state conditions are reached. A full description of the model, its governing equations and implementation in a finite element program are presented. The model is then used to simulate the results of laboratory tests, highlighting the model’s abilities and shortcomings in reproducing the time dependent behaviour of soft clays. Furthermore, the paper investigates the importance of accounting for creep non-linearity and the consequences of isotach viscosity on the critical state line.

The shear strength of loose soils and soils which have reached critical state is not significantly affected by the value of the intermediate principal stress and can therefore be approximated sufficiently by the Mohr–Coulomb hexagon in the deviatoric plane. The Mohr–Coulomb hexagon, however, tends to underestimate the peak shear strength of dense soils for any stress state other than triaxial compression. Other failure surfaces have been proposed which take account of the influence of the relative magnitude of the intermediate principal stress. Two of the best-known surfaces, the Matsuoka–Nakai and Lade surfaces, are considered in this paper. These two surfaces were evaluated for plane strain conditions. Comparison with experimental results showed that the Matsuoka–Nakai surface approximates well the peak shear strength of dense soils, while the Lade yield surface overestimates it. Based on this study a new yield surface expression is proposed which can equally be applied to loose or dense soils. More importantly the proposed expression allows the yield surface to change shape as shearing progresses and reduces to the Mohr–Coulomb hexagon once critical state is reached.