Automatic calibration of soil–water characteristic curves using genetic algorithms

An automatic technique for the determination of the coefficients of models for soil–water characteristic curves (SWCC) or water retention curves (WRC) is presented. The technique is based on optimisation using genetic algorithms, in which the error between predictions and experimental data is minimised by varying the model parameters. The method is powerful and reasonably efficient in finding the best parameters. Four models are analysed including one accounting for hysteresis behaviour. Details of a simple genetic algorithm (SGA) and its complete application are explained. To account for the hysteresis of the SWCC, the models are programmed in a rate form, in which numerical integration is employed to advance the state variables. One advantage of the optimisation presented is that the best curves averaging both the drying and wetting paths are obtained when hysteresis is present.     

The optimisation of flotation networks

The generalised optimisation of a flotation network is studied by means of using variable connections (structural parameters) and variable enhancement factors which are used instead of a flotation model to describe the separation process. The enhancement factors are functions of variables affecting the flotation process. These functional relationship may be derived by means of using a flotation model. Bounds are placed on the enhancement factors by means of either using a flotation model or by inspection of existing pilot or commercial plant data. These bounds, together with external, system and mass balance constraints and an appropriate objective function, define the general optimisation problem for a flotation network.The optimisation problem above may be solved by non-linear programming methods, however, it is easily transformable into a Linear Programme which is easy to solve. The procedure has been applied to a flotation circuit comprising three banks of cells for which an optimal set of connections and enhancement factors has been computed for varying constraints.A simulation procedure based on a gamma flotation model has been applied to one of the optimal circuits so as to compute the flotation variables.     

Application of a Hill-Climbing technique to the formulation of a new cyclic nonlinear elastic constitutive model

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.     

Single‐and multi‐objective genetic algorithm optimization for identifying soil parameters

This paper discusses the quality of the procedure employed in identifying soil parameters by inverse analysis. This procedure includes a FEM‐simulation for which two constitutive models—a linear elastic perfectly plastic Mohr–Coulomb model and a strain‐hardening elasto‐plastic model—are successively considered. Two kinds of optimization algorithms have been used: a deterministic simplex method and a stochastic genetic method. The soil data come from the results of two pressuremeter tests, complemented by triaxial and resonant column testing. First, the inverse analysis has been performed separately on each pressuremeter test. The genetic method presents the advantage of providing a collection of satisfactory solutions, among which a geotechnical engineer has to choose the optimal one based on his scientific background and/or additional analyses based on further experimental test results. This advantage is enhanced when all the constitutive parameters sensitive to the considered problem have to be identified without restrictions in the search space. Second, the experimental values of the two pressuremeter tests have been processed simultaneously, so that the inverse analysis becomes a multi‐objective optimization problem. The genetic method allows the user to choose the most suitable parameter set according to the Pareto frontier and to guarantee the coherence between the tests. The sets of optimized parameters obtained from inverse analyses are then used to calculate the response of a spread footing, which is part of a predictive benchmark. The numerical results with respect to both the constitutive models and the inverse analysis procedure are discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Automatic Variogram Modeling by Iterative Least Squares: Univariate and Multivariate Cases

In this paper, we propose a new methodology to automatically find a model that fits on an experimental variogram. Starting with a linear combination of some basic authorized structures (for instance, spherical and exponential), a numerical algorithm is used to compute the parameters, which minimize a distance between the model and the experimental variogram. The initial values are automatically chosen and the algorithm is iterative. After this first step, parameters with a negligible influence are discarded from the model and the more parsimonious model is estimated by using the numerical algorithm again. This process is iterated until no more parameters can be discarded. A procedure based on a profiled cost function is also developed in order to use the numerical algorithm for multivariate data sets (possibly with a lot of variables) modeled in the scope of a linear model of coregionalization. The efficiency of the method is illustrated on several examples (including variogram maps) and on two multivariate cases.     

基于SFG模型的统一屈服面本构模型与试验研究

将SFG模型中的加载湿陷屈服面（LC屈服面）与BBM模型中提出的吸力增加屈服面（SI屈服面）统一成为单独光滑的屈服面,基于弹塑性理论框架,推导出相应的弹塑性本构模型。通过非饱和固结直剪试验对江西红土的模型计算参数的应力-应变曲线与试验结果进行对比。结果表明：模型对多种应力路径下非饱和三轴试验的计算结果与相应试验的测定结果较为吻合,验证了模型能较好地模拟非饱和土在多种应力路径下的体应变行为。统一屈服面简化了加载湿陷屈服面与吸力增加屈服面之间的耦合分析,解决了因双屈服面的不连续而造成计算不便问题,拓宽了SFG模型的适用性。     

Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates

Geologic CO₂ sequestration in deep saline aquifers is a promising technique to mitigate the effect of greenhouse gas emissions. Designing optimal CO₂ injection strategy becomes a challenging problem in the presence of geological uncertainty. We propose a surrogate assisted optimisation technique for robust optimisation of CO₂ injection strategies. The surrogate is built using Adaptive Sparse Grid Interpolation (ASGI) to accelerate the optimisation of CO₂ injection rates. The surrogate model is adaptively built with different numbers of evaluation points (simulation runs) in different dimensions to allow automatic refinement in the dimension where added resolution is needed. This technique is referred to as dimensional adaptivity and provides a good balance between the accuracy of the surrogate model and the number of simulation runs to save computational costs. For a robust design, we propose a utility function which comprises the statistical moment of the objective function. Numerical testing of the proposed approach applied to benchmark functions and reservoir models shows the efficiency of the method for the robust optimisation of CO₂ injection strategies under geological uncertainty.     

Computer-aided calibration of a soil plasticity model

A non-linear optimization technique based on the quasi-Newton approach is employed to back-calculate certain model parameters of a simple, bounding surface, soil plasticity model from in situ pressuremeter data. The theoretical response corresponding to a given set of parameters is generated by finite element analysis. A semi-analytical procedure is developed for the accurate and efficient evaluation of the gradient of objective function with respect to the model parameters of interest. The BFGS update is used to update the Hessian. Results of a series of numerical experimentation using artificial pressuremeter responses is first reported and discussed. A set of laboratory cavity expansion data is then used to calibrate the constitutive model.     

Predictive potential of Perzyna viscoplastic modelling for granular geomaterials

This paper reappraises Perzyna-type viscoplasticity for the constitutive modelling of granular geomaterials, with emphasis on the simulation of rate/time effects of different magnitude. An existing elasto-plastic model for sands is first recast into a Perzyna viscoplastic formulation and then calibrated/validated against laboratory test results on Hostun sand from the literature. Notable model features include (1) enhanced definition of the viscous nucleus function and (2) void ratio dependence of stiffness and viscous parameters, to model the pycnotropic behaviour of granular materials with a single set of parameters, uniquely identified against standard creep and triaxial test results. The comparison between experimental data and numerical simulations points out the predicative capability of the developed model and the complexity of defining a unique viscous nucleus function to capture sand behaviour under different loading/initial/boundary and drainage conditions. It is concluded that the unified viscoplastic simulation of both drained and undrained response is particularly challenging within Perzyna's framework and opens to future research in the area. The discussion presented is relevant, for instance, to the simulation of multiphase strain localisation phenomena, such as those associated to slope stability problems in variably saturated soils.     

Slope stability analysis in 3D using numerical limit analysis (NLA) and elasto-plastic analysis (EPA)

The present paper addresses the problem of factor of safety (FS) determination in 3D slope stability analysis. For that purpose, use is made of two numerical methods/techniques in three benchmark problems: numerical limit analysis (NLA) and elasto-plastic analysis (EPA). Finite elements are used in both techniques. The primary objective of the study is, by comparing the two techniques, to establish the feasibility of using NLA in the evaluation of 3D slope stability problems and to establish its practical applicability and competitiveness in relation to EPA. Because of their geometry or their boundary conditions, the problems cannot be analysed as plane strain state problems or using the 2D limit equilibrium technique. In both methods, an FS is determined for the slopes by reducing the strength parameters of the geological materials using a scalar factor, known as the strength reduction factor. From the comparison of the FSs and of the computational efforts required for the two numerical techniques, it was possible to establish NLA’s competiveness and viability for the analysis of real 3D slope stability problems when implemented in an efficient manner.     

Numerical Modelling of a Shaking Table Test for Soil-Foundation-Superstructure Interaction by Means of a Soil Constitutive Model Implemented in a FEM Code

Dynamic soil-structure interaction (DSSI) plays a fundamental role in many geotechnical and/or structural design situations, as clearly shown by the damage which occurred during several recent earthquakes (Kobe 1995; Koaceli 1999; Chi-Chi 1999; L’Aquila 2009). For a long time civil engineering researchers have devoted increasing attention to this subject. Thanks to their efforts, several technical regulations, such as EC8 (2003), have taken DSSI into account. However, many steps are still necessary in order to increase our knowledge regarding this complex phenomenon, as well as to make all the results achieved known to academics and practitioners. This paper presents the results of a shaking table test performed on a scaled physical model consisting of a 3-D steel frame resting on a bed of sand. The experimental results are compared with the numerical ones obtained using a sophisticated elasto-plastic constitutive model recently implemented in the FEM code utilised. The solution of geotechnical problems requires the use of appropriate constitutive models. Many interesting constitutive models have been developed, but only a few of these have been implemented into commercial numerical codes; which is particularly so when dynamic analyses are required. The described experimental results, as well as the comparison between them and the numerical results, allow interesting considerations to be drawn on dynamic soil-structure interaction and on its numerical simulation.     

A new data assimilation procedure to develop a debris flow run-out model

Parameter calibration is one of the most problematic phases of numerical modeling since the choice of parameters affects the model’s reliability as far as the physical problems being studied are concerned. In some cases, laboratory tests or physical models evaluating model parameters cannot be completed and other strategies must be adopted; numerical models reproducing debris flow propagation are one of these. Since scale problems affect the reproduction of real debris flows in the laboratory or specific tests used to determine rheological parameters, calibration is usually carried out by comparing in a subjective way only a few parameters, such as the heights of soil deposits calculated for some sections of the debris flows or the distance traveled by the debris flows using the values detected in situ after an event has occurred. Since no automatic or objective procedure has as yet been produced, this paper presents a numerical procedure based on the application of a statistical algorithm, which makes it possible to define, without ambiguities, the best parameter set. The procedure has been applied to a study case for which digital elevation models of both before and after an important event exist, implicating that a good database for applying the method was available. Its application has uncovered insights to better understand debris flows and related phenomena.     

Full-scale Modelling of Falling Rock Protection Barriers

Full-scale impact tests, carried out to evaluate the behaviour of flexible falling rock protection barriers, are described and relevant results presented and discussed. Falling rock protection barriers, which may be numbered among passive measures against rockfall, are designed to intercept and stop falling rocks by dissipation of impact energies through the elasto-plastic deformation of a system made up of metallic nets and supporting and connecting components. The testing programme involved models of barriers subjected to the impact of free-falling blocks of kinetic energy ranging from 500 to 5,000 kJ. The experimental test site, set-up in Fonzaso (Italy), and the experimental procedure were developed according to the new European testing standards (ETAG 027) on falling rock protection kits. The paper is aimed at presenting an extensive and high quality database, which can be extremely useful for a better understanding of the actual response of such structures and for any subsequent analytical and numerical modelling.     

Numerical stability of non-local viscoplastic FEM analyses for the study of localisation processes

As is well known, numerically handling, by means of finite element codes, localisation problems involving softening materials is still quite delicate. As soon as strain localisation occurs, mesh dependence and serious problems of convergence take place. This paper deals with this type of problem in the case where localisation occurs in an ideal naturally cemented granular specimen tested under plane strain conditions. Different versions (a local elasto-plastic, a local viscoplastic and a non-local viscoplastic) of the same strain softening model are taken into consideration and the relative numerical results are critically discussed and compared. The snap-back problem is numerically taken into account and it has been demonstrated to be affected not only by the softening parameters but also by the viscous nucleus definition. To highlight the relationship between viscosity and non-locality, the results of a numerical parametric analysis are finally discussed.     

Unsaturated structured soils: constitutive modelling and stability analyses

The paper presents a new single-surface elasto-plastic model for unsaturated cemented soils, formulated within the critical state soil mechanics framework, which should be considered as an extension to unsaturated conditions of a recently proposed constitutive law for saturated structured soils. The model has been developed with the main purpose of inspecting the mechanical instabilities induced in natural soils by bond degradation resulting from the accumulation of plastic strains and/or the changes in pore saturation. At this scope, the constitutive equations are used to simulate typical geotechnical testing conditions, whose results are then analysed in light of the controllability theory. The results of triaxial tests on an ideal fully saturated cemented soil and on the corresponding unsaturated uncemented one are first discussed, aiming at detecting the evidence of potentially unstable conditions throughout the numerical simulations. This is followed by similar analyses considering the combined effects of both the above features. For each analysed case, a simple analytical stability criterion is proposed and validated against the numerical results, generalizing the results, and highlighting the crucial role of state variables and model parameters on the possible occurrence of failure conditions.

     

Optimised design of jet-grouted raft using response surface method

The use of jet grouting as a foundation supporting element has brought about the need to define the design strategies for jet-grouted raft (JGR) system which differs from the traditional raft design due to the effects of jet-grouted columns (JGCs). Paper tackles this important aspect by combining the previously defined design strategies on piled raft and JGC to achieve an optimised design of complete JGR system. Initially, a single JGC has been analysed by means of three dimensional finite element (3D FE) analysis accounting for the previously measured actual trial JGC’s geometrical variation with depth. The image processing technique allowing the complex 3D FE modelling of JGC system is utilised and the results are validated by the back-analysis of the well-known experimental results reported in the literature. In a parametric study, extension of the numerical analysis to the complete JGR system is accomplished by considering the mutual interaction between the foundation elements. The effects of design factors that are interlayer thickness, JGC spacing and lengths on the design responses of vertical stresses, bending moments, average and differential settlements are presented. Response Surface Method is utilised in the multi objective optimisation analysis to present the optimised design solution by accounting for the design constraints previously defined for the considered factors and the responses. The significance of design constraints and their relative influences on the optimised design of JGR are finally discussed.     

Three dimensional Finite Element modeling of seismic soil–structure interaction in soft soil

Earthquakes in regions underlain by soft clay have amply demonstrated the detrimental effects of soil–structure interaction (SSI) in such settings. This paper describes a new three dimensional Finite Element model utilizing linear elastic single degree of freedom (SDOF) structure and a nonlinear elasto-plastic constitutive model for soil behavior in order to capture the nonlinear foundation–soil coupled response under seismic loadings. Results from an experimental SSI centrifuge test were used to verify the reliability of the numerical model followed by parametric studies to evaluate performance of linear elastic structures underlain by soft saturated clay. The results of parametric study demonstrate that rigid slender (tall) structures are highly susceptible to the SSI effects including alteration of natural frequency, foundation rocking and excessive base shear demand. Structure–foundation stiffness and aspect ratios were found to be crucial parameters controlling coupled foundation–structure performance in flexible-base structures. Furthermore, frequency content of input motion, site response and structure must be taken into account to avoid occurrence of resonance problem.     

Study on coupled thermo-hydro-mechanical processes in column bentonite test

An unconventional numerical scheme is developed to simulate coupled thermo-hydro-mechanical (THM) processes in partially saturated medium. The non-isothermal, unsaturated fluid flow and mechanical processes are sequentially coupled by updating all the state variables using cellular automaton technique and finite difference method on spatial and temporal scale, respectively. A new cellular automaton updating scheme is proposed by introducing a fast successive relaxation index, which greatly improves the computational efficiency in the simulation of THM coupling process. This is implemented in a self-developed numerical system, i.e., an elasto-plastic cellular automaton (EPCA^3D), which was used to numerically reproduce the coupled THM behavior of bentonite pellets in a column experiment that was heated up to 140 °C firstly and then was hydrated simulating the resaturation of the backfilling. By using the cellular automaton technique in EPCA^3D, the challenging courses of the changing boundary conditions over time and space during the experiment are conveniently implemented. The EPCA^3D was able to reproduce the main physical processes of the in laboratory column bentonite experiment within the heating and hydration phase. The modeling results for the evolution of temperature, relative humidity, water uptake and axial pressure are consistent with the experimental data in terms of trends and magnitudes, which verifies the realistic simulation with the developed model and contributes to a deeper understanding of the observed phenomena.     

Cohesive‐frictional model for bond and splitting action of prestressing wire

This paper presents a numerical procedure for bond between indented wires and concrete, and the coupled splitting process of the surrounding concrete. The bond model is an interface, non‐associative, plasticity model. It is coupled with a cohesive fracture model for concrete to take into account the splitting of such concrete. Bond between steel and concrete is fundamental for the transmission of stresses between both materials in precast prestressed concrete. Indented wires are used to improve the bond in these structural elements. The radial component of the prestressing force, increased by Poisson's effect, may split the surrounding concrete, decreasing the wire confinement and diminishing the bonding. The combined action of the bond and the splitting is studied with the proposed model. The results of the numerical model are compared with the results of a series of tests, such as those which showed splitting induced by the bond between wire and concrete. Tests with different steel indentation depths were performed. The numerical procedure accurately reproduces the experimental records and improves knowledge of this complex process. Copyright © 2010 John Wiley & Sons, Ltd.