Evaluating the performance of an explicit dynamic relaxation technique in analyzing non-linear geotechnical engineering problems

Explicit dynamic relaxation is an efficient tool that has been used to solve problems involving highly non-linear differential equations. The key feature of this method is the ability to use explicit dynamic algorithms in solving static problems. Few attempts have been made to date to apply this technique in conventional geotechnical engineering. In this study, an algorithm that incorporates the application of a stiffness dependent time step scheme is proposed. The algorithm has been successfully used to solve 2D and 3D non-linear geotechnical engineering problems. To calibrate the developed algorithm, numerical simulations have been conducted for a strip and square footings supported by Mohr–Coulomb material. Performance of four different types of brick elements used in collapse load calculation is examined in terms of convergence speed and accuracy. In addition, the role of employing adaptive time steps in reducing the number of iterations needed for convergence is also evaluated.     

Implicit integration of a mixed isotropic–kinematic hardening plasticity model for structured clays

In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Genetic algorithms in probabilistic finite element analysis of geotechnical problems

In application to numerical analysis of geotechnical problems, the limit-state surface is usually not known in any closed form. The probability of failure can be assessed via the so-called reliability index. A minimization problem can naturally be formed with an implicit equality constraint defined as the limit-state function and optimization methods can be used for such problems. In this paper, a genetic algorithm is proposed and incorporated into a displacement finite element method to find the Hasofer–Lind reliability index. The probabilistic finite element method is then used to analyse the reliability of classical geotechnical systems. The performance of the genetic algorithm (GA) is compared with simpler probability methods such as the first-order-second-moment Taylor series method. The comparison shows that the GA can produce the results fairly quickly and is applicable to evaluation of the failure performance of geotechnical problems involving a large number of decision variables.     

Fully coupled elastoplastic hydro-mechanical analysis of unsaturated porous media using a meshfree method

This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.     

非饱和土化学-塑性耦合本构行为的数值模拟

基于Hueckel提出的饱和黏土化学-塑性本构模型和Gallipoli提出的非饱和土弹塑性本构模型,提出了一个新的非饱和多孔介质的化学-塑性本构模型,并建立了该模型的隐式积分算法,算法中考虑了化学软化和非饱和吸力的影响。在已有的非饱和多孔介质有限元分析程序平台上进行了程序研发,对孔隙水中化学污染物浓度变化对非饱和土力学行为的影响进行数值模拟,使所研制的程序能够进行岩土工程问题的化学-力学耦合非线性分析。     

Large deformation dynamic analysis of saturated porous media with applications to penetration problems

This paper outlines the development as well as implementation of a numerical procedure for coupled finite element analysis of dynamic problems in geomechanics, particularly those involving large deformations and soil-structure interaction. The procedure is based on Biot’s theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of the soil is represented by either the Mohr Coulomb or Modified Cam Clay material model. The interface between soil and structure is modelled by the so-called node-to-segment contact method. The contact algorithm uses a penalty approach to enforce constraints and to prevent rigid body interpenetration. Moreover, the contact algorithm utilises a smooth discretisation of the contact surfaces to decrease numerical oscillations. An Arbitrary Lagrangian–Eulerian (ALE) scheme preserves the quality and topology of the finite element mesh throughout the numerical simulation. The generalised-α method is used to integrate the governing equations of motion in the time domain. Some aspects of the numerical procedure are validated by solving two benchmark problems. Subsequently, dynamic soil behaviour including the development of excess pore-water pressure due to the fast installation of a single pile and the penetration of a free falling torpedo anchor are studied. The numerical results indicate the robustness and applicability of the proposed method. Typical distributions of the predicted excess pore-water pressures generated due to the dynamic penetration of an object into a saturated soil are presented, revealing higher magnitudes of pore pressure at the face of the penetrometer and lower values along the shaft. A smooth discretisation of the contact interface between soil and structure is found to be a crucial factor to avoid severe oscillations in the predicted dynamic response of the soil.     

Development of an implicit material point method for geotechnical applications

An implicit material point method (MPM), a variant of the finite element method (FEM), is presented in this paper. The key feature of MPM is that the spatial discretisation uses a set of material points, which are allowed to move freely through the background mesh. All history-dependent variables are tracked on the material points and these material points are used as integration points similar to the Gaussian points. A mapping and re-mapping algorithm is employed, to allow the state variables and other information to be mapped back and forth between the material points and background mesh nodes during an analysis. In contrast to an explicit time integration scheme utilised by most researchers, an implicit time integration scheme has been utilised here. The advantages of such an approach are twofold: firstly, it addresses the limitation of the time step size inherent in explicit integration schemes, thereby potentially saving significant computational costs for certain types of problems; secondly, it enables an improved algorithm accuracy, which is important for some constitutive behaviours, such as elasto-plasticity. The main purpose of this paper is to provide a unified MPM framework, in which both quasi-static and dynamic analyses can be solved, and to demonstrate the model behaviour. The implementation closely follows standard FEM approaches, where possible, to allow easy conversion of other FEM codes. Newton’s method is used to solve the equation of motion for both cases, while the formation of the mass matrix and the required updating of the kinematic variables are unique to the dynamic analysis. Comparisons with an Updated Lagrangian FEM and an explicit MPM code are made with respect to the algorithmic accuracy and time step size in a couple of representative examples, which helps to illustrate the relative performance and advantages of the implicit MPM. A geotechnical application is then considered, illustrating the capabilities of the proposed method when applied in the geotechnical field.     

Analysis of stone-column reinforced foundations

A numerical model is proposed to analyse elastic as well as elastoplastic behaviour of stone-column reinforced foundations. The stone-columns are assumed to be dispersed within the in situ soil and a homogenization technique is invoked to establish equivalent material properties for in situ soil and stone-column composite. The difficulties encountered in carrying out elastoplastic analyses of composite materials are overcome by adopting a separate yield function for each of the constituent materials and a sub-iteration procedure within an implicit backward Euler stress integration scheme. In the proposed procedure, equilibrium as well as kinematic conditions implied in the homogenization procedure are satisfied for both elastic as well as elastoplastic stress states. The proposed model is implemented in an axi-symmetric finite element code and numerical prediction is made for the behaviour of model circular footings resting on stone-column reinforced foundations. This prediction indicates good agreement with experimental observation. Finally, a new scheme in which the length of stone-column is variable is proposed and its behaviour is examined through a numerical example. © 1998 John Wiley & Sons, Ltd.     

An edge-based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

To solve large deformation geotechnical problems, a novel strain-smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge-based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node-based smoothed PFEM when lower-order triangular element is used. Compared with the node-based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super-convergent and very accurate solutions due to the implementation of edge-based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.     

On the estimation of scale of fluctuation in geostatistics

Describing how soil properties vary spatially is of particular importance in stochastic analyses of geotechnical problems, because spatial variability has a significant influence on local material and global geotechnical response. In particular, the scale of fluctuation θ is a key parameter in the correlation model used to represent the spatial variability of a site through a random field. It is, therefore, of fundamental importance to accurately estimate θ in order to best model the actual soil heterogeneity. In this paper, two methodologies are investigated to assess their abilities to estimate the vertical and horizontal scales of fluctuation of a particular site using in situ cone penetration test (CPT) data. The first method belongs to the family of more traditional approaches, which are based on best fitting a theoretical correlation model to available CPT data. The second method involves a new strategy which combines information from conditional random fields with the traditional approach. Both methods are applied to a case study involving the estimation of θ at three two-dimensional sections across a site and the results obtained show general agreement between the two methods, suggesting a similar level of accuracy between the new and traditional approaches. However, in order to further assess the relative accuracy of estimates provided by each method, a second numerical analysis is proposed. The results confirm the general consistency observed in the case study calculations, particularly in the vertical direction where a large amount of data are available. Interestingly, for the horizontal direction, where data are typically scarce, some additional improvement in terms of relative error is obtained with the new approach.     

A comparative study of ANN and Neuro-fuzzy for the prediction of dynamic constant of rockmass

Physico-mechanical properties of rocks have great significance in all operational parts in mining activities, from exploration to final dispatch of material. Compressional wave velocity (p-wave velocity) and anisotropic behaviour of rocks are two such properties which help to understand the rock response under varying stress conditions. They also influence the breakage mechanism of rock. There are different methods to determine thep-wave velocity and anisotropyin situ and in the laboratory. These methods are cumbersome and time consuming. Fuzzy set theory, Fuzzy logic and Neural Networks techniques seem very well suited for typical geotechnical problems. In conjunction with statistics and conventional mathematical methods, hybrid methods can be developed that may prove to be a step forward in modeling geotechnical problems. Here, we have developed and compared two different models, Neuro-fuzzy systems (combination of fuzzy and artificial neural network systems) and Artificial neural network systems, for the prediction of compressional wave velocity.     

对岩土工程数值分析的几点思考

首先,介绍了笔者对我国岩土工程数值分析现状的调查结果及分析,然后,分析了采用连续介质力学分析岩土工程问题的关键,并讨论分析了岩土本构理论发展现状,提出对岩土本构理论发展方向的思考,最后对数值分析在岩土工程分析中的地位作了分析。分析表明,岩土工程数值分析结果是岩土工程师在岩土工程分析过程中进行综合判断的重要依据之一;采用连续介质力学模型求解岩土工程问题的关键是如何建立岩土的工程实用本构方程;建立多个工程实用本构方程结合积累大量工程经验才能促使数值方法在岩土工程中由用于定性分析转变到定量分析。     

Finite deformation analysis of geomaterials

The mathematical structure and numerical analysis of classical small deformation elasto–plasticity is generally well established. However, development of large deformation elastic–plastic numerical formulation for dilatant, pressure sensitive material models is still a research area. In this paper we present development of the finite element formulation and implementation for large deformation, elastic–plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process. The algorithm is tested in conjunction with the novel hyperelasto–plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto–plastic problems in geomechanics. We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS‐89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching. Copyright © 2001 John Wiley & Sons, Ltd.     

Three-dimensional RITSS large displacement finite element method for penetration of foundations into soil

The Remeshing and Interpolation Technique with Small Strain (RITSS) approach has been developed to deal with 3-D geotechnical problems in this paper. Unstructured 20-node hexahedral element is found to work well for predicting collapse loads accurately for 3-D undrained geotechnical problems involving material incompressibility. Remeshing is automatically accomplished by ANSYS program. With remeshing and interpolation, small fluctuations appear in the load–deformation results. In order to minimize these fluctuations, different increment sizes and remeshing frequencies are explored. Meanwhile, various 3-D interpolation methods are compared, and the unique element division method is found to work best. The results of two numerical applications are presented for a 3-D strip footing penetrating deeply into uniform clay and a square foundation into normally consolidated clay. The computed bearing capacity responses are compared with other numerical or conventional results. The results show that the present method is accurate and efficient for 3-D large displacement foundation penetration problems.     

Slope stability analyzing using recent swarm intelligence techniques

Slope stability analysis of soil with a weak layer sandwiched between two strong layers is considered as a complex geotechnical problem. In this problem, the objective function is non‐convex and discontinuous with the presence of multiple strong local minima. Classical optimization techniques fail to converge to a valid solution unless a proper initial trial is adopted. Even though many new optimization algorithms have emerged, they have not been applied to geotechnical problems yet. In the present study, some recent swarm intelligence algorithms are adopted for some complicated example of slope stability problems and benchmarked with the traditional particle swarm optimization algorithm. From the results, it seems the levy flight krill herd algorithm is the most efficient method over proposed algorithms for this kind of problem. Copyright © 2014 John Wiley & Sons, Ltd.     

A critical state model for overconsolidated structured clays

This paper presents a generalised critical state model with the bounding surface theory for simulating the stress–strain behaviour of overconsolidated structured clays. The model is formulated based on the framework of the Structured Cam Clay (SCC) model and is designated as the Modified Structured Cam Clay with Bounding Surface Theory (MSCC-B) model. The hardening and destructuring processes for structured clays in the overconsolidated state can be described by the proposed model. The image stress point defined by the radial mapping rule is used to determine the plastic hardening modulus, which varies along loading paths. A new proposed parameter h, which depends on the material characteristics, is introduced into the plastic hardening modulus equation to take the soil behaviour into account in the overconsolidated state. The MSCC-B model is finally evaluated in light of the model performance by comparisons with the measured data of both naturally and artificially structured clays under compression and shearing tests. From the comparisons, it is found that the MSCC-B model gives reasonable good simulations of mechanical response of structured clays in both drained and undrained conditions. With its simplicity and performance, the MSCC-B model is regarded as a practical geotechnical model for implementation in numerical analysis.     

A boundary element method for identifying orthotropic material parameters

A new approach is proposed for identifying elastic constants for orthotropic material bodies by using the boundary element method. The material parameters which must be determined are two Young's moduli, a shear modulus and two Poisson's ratios. The method is applied to geotechnical engineering problems.     

A Methodology for the Definition of Geotechnical Mine Sectors Based on Multivariate Cluster Analysis

This paper offers a new method for the definition of geotechnical sectors in open pit mines based on multivariate cluster analysis. A geological-geotechnical data set of a manganese open pit mine was used to demonstrate the methodology. The data set consists of a survey of geological and geotechnical parameters of the rock mass, measured directly in several points of the mine, structured initially in twenty-eight variables. After the preprocessing of the data set, the clustering technique was applied using the k-Prototype algorithm. The squared Euclidean distance was used to quantify the proximity between numerical variables, and the Jaccard's coefficient of similarity was used to quantify the proximity between the nominal variables. The different cluster results obtained were validated by the multivariate analysis of variance. The identification of cluster structures was achieved by plotting them on the mine map for spatial visualization and definition of geotechnical sectors. These sectors are spatially contiguous and relatively homogeneous regarding their geological–geotechnical properties, indicated by a high density of points of the same group. It was possible to observe a great adherence of the proposed sectors to the mine geology, demonstrating the practical representativeness of the clustering results and the proposed sectors.

     

Numerical identification of soil-structure interaction pressures

A numerical approach is presented for the ‘identification’ (or back calculation) of the earth pressure acting on embedded or retaining structures. The procedure is applicable to structures of any shape and requires a set of in situ measurements that may include displacements of points on the structure, values of concentrated forces, values of distributed loads at some locations, etc. Possible limiting values of the unknown loads, non-linear structural behaviour, varying accuracies of the input data are accounted for in the problem formulation. Depending upon the type of problem, the solution is reached by means of the unconstrained or constrained minimization of a suitably defined error function. As an example, the proposed approach is applied to the identification of the earth pressure acting on some typical geotechnical engineering structures.     

Mechanics of a sandy subsoil subjected to cyclic loadings

A simple model for compaction of a sand, that may be useful in various geotechnical applications is presented. The model has been formulated in terms of the cyclic stress and strain amplitudes. The compaction properties of a dry sand are characterized by a common compaction curve described by two coefficients. The second aim of this paper is to show some applications of the theory proposed. The attention has been restricted to the two extreme cases of practical importance, namely to the behaviour of a dry sand (or a saturated sand but in free draining conditions), and to the behaviour of saturated sand in undrained conditions. Some numerical algorithms showing how to deal with those problems are presented and illustrated on the following examples: settlement and pore pressure generation in a soil stratum subjected to an earthquake, settlement of a foundation, pore pressure generation and liquefaction in a sea-bed. The results obtained suggest that the model proposed, as well as a method of dealing with boundary value problems can serve as a useful tool for the analysis of a sandy subsoil subjected to cyclic loadings.