Stress-integration algorithms for geomechanics problems involving large deformations

In nonlinear finite element analysis, loads are usually applied in increments and the corresponding incremental displacements are obtained by solving the global equilibrium equations. The incremental strains can be computed from the incremental displacements in the usual way. A set of ordinary differential equations must then be solved to find the stress increment based upon the known strain increment

Flow rule effects in the Tresca model

The Tresca failure criterion is used regularly in geotechnical engineering to compute the failure loads of clay soils deforming under undrained conditions. When this criterion is used together with the finite element method a plastic flow rule must also be incorporated in the elasto-plastic soil model. The effects of the flow rule on the performance of a non-linear analysis using an elastic perfectly plastic soil model obeying the Tresca failure criteria are discussed in this note. Application of this model in a three-dimensional analysis causes computational difficulties, due to the gradient discontinuities that exist at the corner of the Tresca yield surface. Such discontinuities can be removed from the yield (or failure) surface using different methods. Two of the most widely used methods in removing singularities from the yield surface and their overall performances in a three-dimensional finite element analysis are discussed. The motivation for this study comes from a concern raised by Randolph and Puzrin [Randolph MF and Puzrin AM Upper bound limit analysis of circular foundations on clay under general loading. Geotechnique, (2003);53(9):785-796, [5]] about reported instances of under predictions of the collapse loads by finite element analysis [Taiebat HA and Carter JP Numerical studies of the bearing capacity of shallow foundations on cohesive soil subjected to combined loading. Geotechnique, (2000);50(4):409-418, [7]] and [Taiebat HA and Carter JP Bearing capacity of strip and circular foundations on undrained clay subjected to eccentric loads. Geotechnique, (2002);52(1):61-64, [8]], [Gourvenec S and Randolph M Effect of strength non-homogeneity on the shape of failure envelopes for combined loading of strip and circular foundations on clay, Geotechnique, (2003);53(6):575-586, [4]], when it is usually expected that finite element results should overestimate the true collapse loads. The intent of this study is to demonstrate and reiterate that although the finite element method is an extremely powerful analytical tool for solution of engineering problems, it is nevertheless subjected to approximation errors due to simplifications that are necessarily made to prevent other numerical difficulties

Parametric study of a free-falling penetrometer in clay-like soils

A free-falling penetrometer (FFP) is a useful apparatus for providing information on the mechanical properties of soil layers, especially where the site in question is inaccessible, which is normally the situation for many seabed, river and swamp deposits. FFP tests can provide useful data such as the total depth and time of penetration and the deceleration characteristics of the penetrometer, provided it is suitably instrumented. The main quantities of interest measured in FFP tests, viz., the time and depth of penetration, depend on the mechanical properties of the soil, such as its shear strength and rigidity index, as well as those parameters associated exclusively with the penetrometer, such as its geometry and the energy with which it first impacts the soil. Potentially, these penetration data can be used to deduce strength parameters for the soil in situ, either through empirical correlations or else by application of a rigorous numerical solution for the ideal penetration problem. Arobust finite element analysis procedurewas developed at the University of Newcastle, Australia, especially for the analysis of geotechnical problems, including problems that involve soil penetration. This method of analysis is based upon the Arbitrary Lagrangian Eulerian (ALE) finite element technique and takes into account material nonlinearity and rate dependence, large deformations, changing boundary conditions, and time-dependent loading, including an allowance for dynamic forces when necessary. The present study aims to provide some numerical results describing the effect of the mechanical properties of the soil and the energy of the penetrometer on the penetration response. This goal has been achieved by performing a wide range of FFP analyses using the proposed ALE finite element method

Numerical investigation of dynamic penetration factors for a free falling penetrometer

Free falling penetrometers (FFPs) are being used increasingly to determine the geotechnical properties of the soil at sites where the static cone penetration test (CPT) cannot be conducted easily, if at all, due to inaccessibility. Examples include many seabed sites, particularly in deep water. FFPs can provide the total time and depth of penetration as well as the deceleration characteristic of the penetrometer, which can then be used to infer some fundamental soil properties. This study employs a validated fi nite element technique based on the Arbitrary Lagrangian-Eulerian method to investigate numerically the dynamic penetration factor, Ndp, for a free falling penetrometer, and to fi nd the relation between this factor and the geotechnical properties of a layer of cohesive soil. It is demonstrated that the dynamic soil resistance can be obtained as the product of its undrained shear strength and the dynamic cone penetration factor, and the latter depends on several parameters such as the rigidity index of the soil, the rate of loading and the rate of shear strength increase with depth of the soil. A wide range of numerical predictions is discussed here and a closed-form expression is derived for the dynamic penetration factor. Comparisons are also made between the deduced values of Ndp and published values of the conventional cone factor, Nc

Lateral displacements due to installation of soil-cement columns

A method for predicting the lateral displacement of the ground induced by the installation of soil-cement columns is briefly summarized and then applied to two field tests conducted in Japan in the 1990s. The prediction method was developed by Chai et al. in 2009 using cavity expansion theory. This method can consider explicitly the effect of the amount of injected admixture and the stiffness and strength of the deposit as well as empirically account for the construction method. The two field tests were conducted at two different sites where, in each case, sandy layers exist at the ground surface underlain by a clayey layer, which in turn is underlain by another sandy layer. A comparison of the predicted and measured lateral displacement profiles indicates that the calculation method under-estimated the lateral displacement of the clayey layers but generally over-estimated the displacements of the sandy layers in cases where the volumetric strain (Δ) of the soil was assumed to be zero. When it was assumed that Δ = 2% in the sandy layers, the calculated values of lateral displacement provide a good match to the measured data for the sandy surface layer, which indicates that during the column installation process, the soil may deform under conditions of partial drainage

Modelling the dependency of soil-water characteristic curves on initial density

This paper presents a simple approach to quantify the effect of initial soil density on the soil-water characteristic curve (SWCC) of unsaturated soils. This approach is based on an incremental relationship between the degree of saturation and the initial voids ratio, which satisfies the intrinsic constraints for three-phase porous materials. The incremental relationship can be incorporated into existing SWCC equations to model the water retention behaviour for deformable soils. Only one additional parameter is introduced, which can be conveniently calibrated via conventional water retention tests. The SWCCs for the same soil at different initial voids ratios can be found using the proposed approach. The proposed approach is validated against experimental data from drying tests for both compacted and reconstituted soils

On the compression behaviour of structured soils

Structured soils exhibit an apparent non-linear normal compression line in the semi-log compression plane, which dominates the difference in the mechanical behaviour between structured soils and their reconstituted counterparts. The effect of soil structure is investigated via the change of compression stiffness with structure degradation. A differential expression of the normal compression line is then established and applied to a large number of different types of soil. Satisfactory results are obtained, illustrating the validity and applicability of the proposed approach

Analysis of soil penetration problems by high-order elements

This paper addresses the application of high-order elements in the analysis of soil penetration problems, particularly those involving inertia forces and large deformations. Among others, 15-node triangular elements are formulated within an Arbitrary Lagrangian-Eulerian finite element method. Preliminary studies indicate that high-order elements can significantly decrease the analysis time without significant loss of accuracy

Hysteretic seepage analysis in unsaturated soil covers

This paper aims to study numerically the effect of hysteresis on the hydraulic behaviour of unsaturated soil covers. The Richards equation is coupled with the hysteretic soil water retention curve (SWRC), to describe the flow in unsaturated soils. A linear scanning curve is used to describe the hydraulic behaviour within the main hysteretic loop in unsaturated seepage problems. The proposed approach is implemented with the finite difference method. A comparison of the proposed hysteretic model with the traditional non-hysteretic model is carried out first. The non-hysteretic model using the main drying SWRC leads to significantly different results than the hysteretic model, further demonstrating the necessity of accounting for hysteresis in seepage analysis. A sensitivity analysis on the hysteresis ratio and the slope of the scanning curve is then carried out with the hysteretic model. Results show that hydraulic hysteresis cannot be neglected in the seepage analysis of soil covers composed of soils exhibiting significant hydraulic hysteresis. The proper determination of both the scanning curve and the initial hydraulic state plays a crucial role in the reliability of numerical simulations of soil covers subjected to cyclic drying and wetting. It is suggested that the proposed hysteretic model may be applied in the design and evaluation of the hydraulic performance of soil covers

Determination of effective elastic properties of microcracked rocks based on asymptotic approximation

In this paper, we present a study on the effective elastic properties of finely fractured rock based on the concept of energy equivalence. The effective elastic properties a rock body weakened by many penny-shaped microcracks, such as the apparent Young's modulus, shear modulus and Poisson's ratio, are particularly important in many applications. To determine these macroscopic parameters, we first adopt the dilute solution approach outlined in Kachanov (1992), where a crack compliance tensor is defined and used extensively to express the energy perturbation caused by the presence of the cracks. In parallel, a self-consistent method is employed where an asymptotic form of the Eshelby's tensor (Eshelby, 1957) is developed to treat a penny-shaped microcrack as an extreme case of a spheroid-shaped inhomogeneity. The asymptotic approximation permits the local Eshelby tensor as well as its global expression to be derived analytically, and to be further used to construct an equivalent eigenstrain problem based on energy equivalence. The effective values for the parameters of interest can then be evaluated. The formulation and results obtained through the asymptotic self-consistent approach are compared to those predicted using a non-interacting scheme