Showing papers in "International Journal for Numerical and Analytical Methods in Geomechanics in 1992"

Cavity expansion in sands under drained loading conditions

Abstract: Solutions for the expansion of cylindrical and spherical cavities in sands are presented. The sand is modelled using recently proposed critical-state models in which the values of the friction and dilation angles depend on the deformation history. Similarity solutions are obtained which enable the limit pressure to be calculated as a function of the initial conditions. Comparisons with existing perfectly plastic theories are made and consequences for the interpretation of cone penetrometer measurements are indicated.

Numerical treatment of progressive localization in relation to borehole stability

Abstract: Results of large-scale finite element computations are presented for the problem of borehole failure due to the high stresses at great depths. Rock is modelled by an extension of the Mohr–Coulomb flow theory of plasticity for material with Cosserat micro-structure. The introduction of internal length (grain size) improves the computational stability and allows for robust post-localization computations. The presented results show clearly a progressive failure mechanism and the computed failure modes are in a good qualitative agreement with laboratory and field observations.

Resilient characterization of pavement materials

Abstract: The paper presents an approach for characterizing pavement materials using the modified linear elastic behaviour. The secant modulus of elasticity is expressed in terms of the stress invariants and an expression for the secant Poisson's ratio is derived using path independence of the total work along a closed loading cycle. Triaxial test results of granular base–subbase materials which exhibit strong non-linear behaviour and dilatancy are analysed and presented. The constitutive law is included in a finite element program and results of pavement analyses are discussed. It is found that the secant Poisson's ratio of granular base materials reaches values between 0·6 and 0·7, indicating a volume increase under high stress ratios. The pavement response predicted using the above material characterization is compatible with non-destructive test results.

A study on one-dimensional consolidation of layered systems

Abstract: A general analytical solution, which is more explicit than the one given by Schiffman and Stein,1 for the problem of one-dimensional consolidation of layered soils is presented. A relevant computer program is developed and the computed results on some examples are included. From these results, an in-depth study on the one-dimensional consolidation behaviour of layered systems is then made. It is demonstrated through these examples that both the solution technique and the computer program developed are very efficient. It is found that the effects of coefficients of permeability and volume compressibility of soil on the consolidation of layered systems are different and cannot be embodied into the coefficient of consolidation of soil. The stiffness of soil layer also plays an important role on the rate of consolidation.

A non‐linear numerical model for soil mechanics

Abstract: A new computer program (CONBAL-2) is developed for 2D numerical simulations of granular soil by random arrays of spheres. CONBAL-2 uses the discrete-element method and is based on 3D program TRUBAL, previously presented by Cundall. As in TRUBAL, the new program models a random array of elastic spheres in a periodic space. The main modification of TRUBAL is the implementation by the authors of a rigorous solution for the force–displacement relation at the interparticle contacts. This force-displacement relation is a function of the elastic constants, friction coefficient and sizes of the spheres, with the properties of quartz used to simulate sand. Other specific features of CONBAL-2 include its 2D character, the lack of particle rotation and its capability to simulate shear loading on any plane. Simulated laboratory test results are presented using CONBAL-2 and several random arrays of 531 spheres having two particle sizes. These simulations include monotonic loading drained and undrained (constant volume) ‘triaxial’ experiments, as well as a cyclic-loading, constant-volume ‘torsional shear’ test. The stress–strain curves, effective stress paths, volume changes, as well as the ‘pore water pressure’ build-up behaviour obtained in the simulations compare favourably—qualitatively and in some aspects quantitatively—with similar laboratory results on sands. However, the simulated soil is somewhat stiffer and stronger due to the perfectly rounded particles, limited range of grain sizes, lack of particle rotation and 2D character of the model.

Implicit integration in soil plasticity under mixed control for drained and undrained response

Abstract: An algorithm is outlined for the implicit integration of isotropic plasticity models for an arbitrary choice of mixed stress and strain control variables. Drained as well as undrained behaviour is considered. The closest-point-projection method in conjunction with a completely strain-driven format is used in a core algorithm. In the drained case strain response variables are determined via iterations to satisfy equilibrium of prescribed and calculated stresses that correspond to the strain response variables. In the undrained case, on the other hand, strains and pore pressure are determined via simultaneous iterations to satisfy equilibrium and the incompressibility condition. The algorithm is applied to a new generalized cam-clay model, and various iteration techniques are assessed. In particular, Newton iterations which employ the matrix of algorithmic tangent stiffness moduli are shown to compete favourably with more conventional methods.

Finite-element analysis of time-dependent large-deformation problems

Abstract: An updated Lagrangian finite-element formulation has been developed for time-dependent problems of soil consolidation involving finite deformations. Large plastic strains as well as rotations occur in such problems and nominal stress measures are introduced in the formulation to redefine stresses. This leads to corrective terms for equilibrium and yield violations in addition to geometric stiffening terms in the governing integral equations. The soil is considered to be either a linear elastic or an elastoplastic, critical-state material. Some simple numerical examples are studied to validate the formulation, followed by a detailed analysis of the problem of penetration of a pile into soil. The results of this problem are viewed with emphasis on the physical interpretation and practical significance.

Dynamic response of concrete gravity dams including dam–water–foundation interaction

Abstract: In this paper, the gravity dam–water–foundation system including the physical and mechanical properties of the sediment at the reservoir bottom is modelled using a finite element and infinite element coupling model. The sediment at the reservoir bottom has been assumed to be a viscoelastic solid medium. The effects of thickness, elastic modulus, Poisson's ratio and material damping of the sediment on the response of the dam have been studied. The related numerical results from this study illustrated that the existence of the sediment at the bottom of the reservoir has significant effects on the response of concrete gravity dams since the soft layer of the sediment plays two main roles in the dam–water–foundation system, the energy dissipation of the system and the amplification of the incident wave on the water–sediment interface. It is the amplified acceleration on the water–sediment interface that results in different mechanisms of the effect of the sediment on the response of the dam. Therefore, apart from the incident wave, the thickness, the softness and the damping ratio of the sediment can also affect the response of the dam.

Modelling and analysis of non‐random uncertainties—fuzzy‐set approach

Abstract: This paper addresses the issue of uncertainty treatment in geotechnical engineering. Emphasis is placed on modelling and analysis of non-random uncertainties using fuzzy sets. Although uncertainties were modelled with fuzzy sets in this study, subsequent analysis or processing of the uncertain information was performed using traditional, non-fuzzy techniques. These techniques, including the vertex method and Monte Carlo simulation, are discussed in detail. An example application using soil liquefaction susceptibility is presented. The paper concludes that non-random uncertainties can be successfully modelled and processed using fuzzy sets.

Numerical analysis of sampling disturbances in clay soils

Abstract: In this paper, an insight is provided into the quality of soil samples during the penetration of soil samplers. An updated Lagrangian finite element formulation with the second Piola–Kirchhoff stress rate (the Truesdell stress increment) to account for the large deformation behaviour near the sampling tube is used to determine the mechanical disturbances to a soft clay. The penetration of the sampler is simulated by splitting a group of nodes ahead of the penetration route up to a sufficient depth and applying incremental displacements to match the geometric configuration of the sampling tube. Consolidation effect is included to account for the rate of penetration. Thin-layer elements are added at the inside wall of the sampling tube to model the soil–sampler interface. The numerical results show that the central core of the sample is subjected to three distinct stages of vertical strain history, compression–extension–recompression, with the primary irrecoverable disturbances due to the compression stage ahead of the sampler. The degree of disturbance for a frictionless sampler was found to be constant after a penetration depth of 75 per cent of the sample tube diameter, while for a frictional sampler the degree of disturbances keeps increasing as the penetration proceeds. The results of a parametric study to determine the influence on sampling disturbances due to the rate of penetration, the thickness and the tip angle of the sample tube and sampler type are also presented.

A finite element analysis of direct shear tests on stiff clays

Abstract: A finite element analysis is presented of some direct shear tests carried out on samples of a stiff, heavily overconsolidated clay. The effects of softening are accounted for through a simple material model which views this phenomenon as a consequence of an intrinsic loss of strength of the material taking place when plastic strains increase. After illustrating the main characteristics of the finite element approach, with particular reference to the correct determination of the non-reversible strains, its use in the interpretation of the mentioned shear tests is discussed. Some comments are also presented on the mesh dependence of the numerical results, and on the use of a relation between material parameters and element size which reduces this negative effect. Finally, the solution procedure is applied to the simulation of a compression test in order to investigate the possibility of numerically detecting the ‘spontaneous’ (i.e. not directly induced by the boundary conditions) formation of shear zones within the specimen.

A finite element slideline approach for calculating tunnel response in jointed rock

Abstract: The general purpose finite element code DYNA2D is used to calculate the response of an unlined tunnel in jointed rock, with sliding interfaces used to represent the joints. The model problem selected for analysis closely follows a calculation using the discrete element code UDEC. Results for two cases [(1) jointed rock with lubricated joints (no joint friction) and (2) jointed rock with frictional resistance to joint motion] are presented and compared with each other and the UDEC results.

Simulation of excavation in a poro-elastic material

Abstract: A method is presented which allows the computation of the displacements and pore pressures which are generated in an elastic soil when excavation is carried out. The formulation is based on Biot's theory and is fully coupled, with consideration also given to the effects of the lowering of the water table which often accompanies the excavation of soil. Example problems are solved to illustrate the theory which has been presented.

A note on non-linear elasticity of isotropic overconsolidated clays

Abstract: An empirically established rule of Wroth1 for the dependence of the shear modulus on the mean effective pressure and the overconsolidation ratio in clays is investigated within the framework of non-linear elasticity. The resulting isotropic-deviatoric coupling is derived and compared to experiments.

Modelling of vibratory pile driving in sand

Abstract: A model for vibro-driving of rigid piles in sand is proposed incorporating the interaction of the vibrator–pile–soil system. The vibro-driver force and the non-linear soil resistance (dynamic f–w and q–w relationships) have been quantified in terms of in situ stress, relative density and particle size. The influence of relative density (0·65 and 0·90), particle size (effective grain size of 0·2 mm and 1·2 mm) and in situ stress (up to 20 psi) on the vibro-driving of a closed-ended pipe pile was investigated experimentally using a large-scale laboratory testing system. The vibro-driving model predicted the observed driving history reasonably well. A computer program (UHVIBRO) has been developed to analyse vibratory pile driving using the dynamic soil resistance relationships developed along with correlation factors from the systematic laboratory study.

Influence of construction technique on the performance of a braced excavation in marine clay

Abstract: Finite element analyses are used to quantify the effects of construction technique on the performance of braced excavations. It is first shown that the computations can be continued to ‘collapse’ and that the results agree with limit plasticity solutions. A case study involving stratified deposits of marine clay and sand is used to carry out a Class C1 ‘prediction’ of field performance. The influence of construction technique on deformations and strut loads is shown. The results of the computations are in agreement with field observations, assuming a relatively ‘flexible’ construction technique. However, even if much ‘stiffer’ techniques had been used, large field deformations would have been unavoidable under certain circumstances.

Pore‐pressure response due to penetration through layered media

Abstract: SUMMARY A solution is developed for a point dislocation traversing a slab of saturated porous material under prescribed upper and lower hydraulic boundary conditions as an analogue to penetration in a layer of finite thickness. Pressure response is conditioned by geometrical parameters and those of dimensionless penetration rate U,, dimensionless time following penetration initiation t,, and dimensionless time followiiig penetration arrest t6. The extended set of dimensionless parameters controlling the response makes parameter determination problematic and questionably non-unique. Pressure response in the proximity of a lower permeable or impermeable boundary is indistinguishable from the homogeneous case for coefficients of consolidation c in excess of 2 cm2/s. Below this threshold, penetration-generated pore pressures are visibly modified in the presence of a discrete boundary. In situ parameters inferred directly from pressure magnitudes, without due consideration for the influence of layering, may therefore be in considerable error. In the hydraulically visible range, the influence of layering on the generated tip pressures is apparent at a separation of the order of 1.5 cm for standard penetration. Although absolute pressure magnitudes are strongly modified in the presence of boundaries, dissipation rates remain relatively unaffected and are consistent with those recorded in the absence of boundaries. The monitoring of dissipation rates, post-arrest, is suggested as the most reliable and accurate method of extricating parameters, in situ.

Effect of adjoining structures on seismic response of tunnels

Abstract: In this paper the seismic behaviour of buried concrete tunnels is studied using the finite element method. The numerical tool employed is the well-known soil–structure interaction computer program FLUSH and thus analyses are carried out in the frequency domain. The seismic environment is supposed to consist of vertically propagating shear and compression waves that reproduce artificial accelerograms of a broad frequency content at selected control points. The effect of near or adjacent massive structures, such as those of nuclear power plants, is evaluated showing their influence on tunnel response. The results calculated for acceleration levels, internal structural loads, response spectra, etc., are analysed and compared either with those obtained from soil free-field response or with others computed using an alternative simplified methodology, providing useful information for preliminary design purposes.

Prediction of dilation and permeability changes in rock salt

Abstract: A numerical procedure has been developed for predicting dilation (porosity) and gas permeability changes in rock salt. The hierarchical single-surface constitutive model of Desai and co-workers is used a finite element program to calculate the state of stress and strain surrounding excavations in rock salt. The elastoplastic constitutive model accounts for strain hardening, a non-associative volumetric response and stress-path-dependent behaviour. The calculated stress and strain fields are used in a flow model based on the equivalent channel concept to predict permeability. Parameters for both the mechanical and permeability models are developed from laboratory test results. Two field experiments adjacent to underground excavations are modelled. The extent of the dilated rock zone around the excavation is predicted well, but the magnitude of the porosity and gas permeability is underpredicted very near the excavations. This discrepancy is attributed to model parameters derived from loading-only laboratory tests, whereas significant unloading occurs in the field. The shape of the yield surface was found to be an important factor in dilation and permeability predictions. Similar stress, strain and permeability fields were obtained with different model types (plane strain or axisymmetric) and initial stress states, and with instantaneous and progressive excavation.

Three‐dimensional modelling of junctions at the Channel Tunnel project

Abstract: The present paper deals with a three-dimensional FE analysis for the Channel Tunnel project. The main objective is to describe the application and the results of a FE calculation and the impact of it's results on engineering practice especially on the design of the permanent lining. The tunnel excavation was executed in accordance with the principles of the shotcrete tunnelling method (NATM). The paper represents a report from the practical engineer's point of view.

Application of non‐linear elastic model

Abstract: The properties of a previously published isotropic non-linear elastic model with an elastic potential are illustrated in detail. Its parameter determination is elaborated and a parameter list is composed on the basis of published experimental data. The formulation with the elastic potential is shown to enable the minimization of numerical drift in incremental calculations of the deformation for alternating loading.

Subsidence due to pumping from layered soil—a perturbation theory

Abstract: Persistent pumping of groundwater is known to cause subsidence of the ground surface. When the soil is composed of alternating layers of sand and clay, subsidence is, in general, a consequence of pressure change in and deformation of all layers. Even with various simplifications, the mathematical task for the mechanics of a layered soil is complex and, in the past, many idealizations have been introduced in the literature. Among the existing approximations, a well-known approximation by Hantush1 for well-hydraulics in leaky aquifers is intuitively attractive. He used the fact known to be strictly true for simple flows in a soil system with horizontal layers, that the flow must be mainly horizontal in a relatively porous aquifer and mainly vertical in a highly impervious aquitard, and invoked the same approximation for transient flows induced by well-pumping. In this paper we shall apply a perturbation analysis to give a mathematical confirmation of the hydrological approximation and to show its degree of accuracy. In particular, we treat a three-layered system, where the middle layer is a relatively soft aquitard, and the well withdraws water from the artesian aquifer at the bottom. The upper aquifer has a phreatic surface. Physically, we examine the often ignored effects of self-weight which is important for thick aquitards. The perturbation theory is worked out for sufficiently weak pumping rates and small soil deformation. Subsidence in the vertical direction due mainly to the deformation of the soft aquitard is studied. Results show that the common assumption of constant total stress with respect to depth is valid only when the storage coefficient is very small.

Stress distribution beneath rigid circular foundations on sands

Abstract: The calculation of stresses induced inside the soil mass by the foundation loads forms an essential step in most of the geotechnical engineering problems dealing with the probable behaviour of foundations. The distribution of stresses on horizontal planes containing reinforcements at various depths is required in the analysis and design of reinforced soil foundations. An accurate evaluation of contact pressure distribution at the interface is a prerequisite for the computation of stresses inside the soil mass. Of the several approaches the elastic-plastic approach of computing the contact pressure distribution appears to be reasonable. Using this approach non-dimensional equations have been derived for calculating the contact pressure distribution beneath rigid circular foundations on sands. The contact pressure distribution so derived has been used for computing the stresses at various points using elastic theory. The results have been graphically presented and are compared with Boussinesq's distribution for uniform contact pressure.

A consistent formulation of a dilatant interface element

Abstract: The paper considers a plane joint or interface element suitable for implementation into a standard non-linear finite element code. The element is intended to model discontinuities with rough contact surfaces, such as rock joints, where dilatant behaviour is present. Of particular concern is the formulation of a constitutive model which fully caters for all possible histories of opening, closing and sliding (accompained by dilation or contraction) in any direction. The non-linear incremental constitutive equations are formulated in a manner appropriate for a back-ward difference discretization in time along the path of loading. The advantage of such an approach is that no essential distinction need be drawn between opening, closing and sliding. Further, a convenient formulation of the constitutive equations is facilitated by representing the different contact conditions in relative displacement space. The state diagram in relative displacement space, however, changes from one time step to the next, and evolution equations for the updating must be formulated. These concepts are illustrated for two rock-joint models: a sawtooth asperity model and a limited dilation model. The models are based on a penalty formulation to enforce the contact constraints, and explicit equations for the tangent stiffness matrix and for the corrector step of the standard Newton–Raphson iterative algorithm are derived. These equations have been implemented as an user element into the finite element code ABAQUS7. Three examples are presented to illustrate the predictions of the formulation.

A boundary integral method for steady flow in unsaturated porous media

Abstract: The governing equation for steady flow in a homogeneous, partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function which varies exponentially with capillary-pressure head. The resulting linear field equation is a steady Fokker–Planck equation and is well-suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is often used in soil physics and is known to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM for obtaining numerical solutions is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code and a finite element code that solves the fully non-linear problem is excellent, and is achieved at a substantial advantage in computer processing time. As an illustrative example, the code is applied to determine the distribution of moisture in the vicinity of a tunnel.

Accuracy of four-node standard finite element

Abstract: In this note the accuracy of the elastic standard 4-node plane-strain finite element is investigated by comparing numerically calculated eigenvalues of the element stiffness matrix to those according to higher-order algebraic approximations. From this study it may be concluded that the ‘hourglass’ eigenmodes are the only inaccurate ones. For selective reduced numerical integration the hourglass eigenvalues may be expected to be of the order of 1/2 to 2/3 of the analytical values.