Barcelona Basic Model Research Articles

Multiphysics implementation of advanced soil mechanics models

Using multiphysics computer codes has become a useful tool to solve systems of partial differential equations. However, these codes do not always allow for the free introduction of implicitly defined state functions when automatic differentiation is used to compute the iteration matrix. This makes it considerably more difficult to solve geomechanical problems using non-linear constitutive models. This paper proposes a method for overcoming this difficulty based on multiphysics capabilities. The implementation of the well-known Barcelona basic model is described to illustrate the application of the method. For this purpose, without including formulation details addressed by other authors, the fundamentals of its implementation in a finite element code are described. Examples that demonstrate the scope of the proposed methodology are also presented.

Small Scale Slope Failure Benchmark Test. Modelling and Prediction

A benchmark was designed with the aim of evaluating the capabilities of current modelling techniques and computational codes to reproduce slope failures. Laboratory tests and three instrumented small scale experiments of slopes initially unsaturated and subjected to a controlled rainfall up to failure were performed. The objective of the benchmark was to predict one of the slope failures knowing the rest of the data. The paper presents the modelling strategy and the results obtained using the finite element code Code_Bright and the Barcelona Basic Model as the constitutive model for the unsaturated soils.

Rainfall-induced differential settlements of foundations on heterogeneous unsaturated soils

This study stochastically investigates the rainfall-induced differential settlement of a centrally loaded, rigid strip foundation on an unsaturated soil with spatially varying values of either preconsolidation stress or porosity. The differential settlement (between the two foundation ends) is calculated at various times during rainfall by way of a coupled, hydro-mechanical, finite-element analysis. The Barcelona basic model describes the mechanical behaviour of the soil, and the van Genuchten relationships describe water retention and permeability. The variability of soil properties is modelled by means of random fields with spatial correlation in the framework of a Monte Carlo simulation. The study demonstrates that the occurrence of rainfall-induced differential settlements can be consistently analysed using concepts of unsaturated soil mechanics and random field theory. Results show that differential settlements can be vastly underpredicted (or even completely missed) if random heterogeneity and partial saturation are not simultaneously considered. The variation of differential settlements and their statistics during the rainfall depend on the magnitude of the applied load and the statistics of soil variability. Moreover, the transient phase of infiltration and a spatial correlation length equal to the width of the foundation pose the highest risk of differential settlement.

Aspects of Mechanical Behavior and Modeling of a Tropical Unsaturated Soil

The research studies the applicability of two elastoplastic models for the collapse prediction of the lateritic soil profile from Southeastern Brazil. These tropical soils have peculiar geotechnical behavior, due to their mineralogical composition and porous structure coming from intense process of formation. Two elastoplastic models were analyzed: the Barcelona Basic Model (BBM) and another one based on BBM, however developed for tropical soils. Oedometric tests with suction control were performed at three distinct depths of the soil profile. The BBM was not suitable for the upper layer of the soil profile, because BBM considers the compressible behavior of the soil in function of the reduction of the elastoplastic compressibility index with the increase of the matric suction. The model developed for tropical soils showed better suited to the compressible behavior of the soil profile, resulting in good prediction of the collapse potential, mainly by accepting increasing values of the elastoplastic compressibility index of the soil profile with the matric suction rise.

Modeling of Coupled Thermo-Hydro-Mechanical Processes with Links to Geochemistry Associated with Bentonite-Backfilled Repository Tunnels in Clay Formations

This paper presents simulation results related to coupled thermal-hydraulic-mechanical (THM) processes in engineered barrier systems (EBS) and clay host rock, in one case considering a possible link to geochemistry. This study is part of the US DOE Office of Nuclear Energy's used fuel disposition campaign, to investigate current modeling capabilities and to identify issues and knowledge gaps associated with coupled THMC processes and EBS- rock interactions associated with repositories hosted in clay rock. In this study, we simulated a generic repository case assuming an EBS design with waste emplacement in hor- izontal tunnels that are back-filled with bentonite-based swelling clay as a protective buffer and heat load, derived for one type of US reactor spent fuel. We adopted the Barcelona basic model (BBM) for modeling of the geo- mechanical behavior of the bentonite, using properties corresponding to the FEBEX bentonite, and we used clay host rock properties derived from the Opalinus clay at Mont Terri, Switzerland. We present results related to EBS host-rock interactions and geomechanical performance in general, as well as studies related to peak temperature, buffer resaturation and thermally induced pressurization of host rock pore water, and swelling pressure change owing to variation of chemical composition in the EBS. Our ini- tial THM modeling results show strong THM-driven interactions between the bentonite buffer and the low- permeability host rock. The resaturation of the buffer is delayed as a result of the low rock permeability, and the fluid pressure in the host rock is strongly coupled with the temperature changes, which under certain circumstances could result in a significant increase in pore pressure. Moreover, using the BBM, the bentonite buffer was found to have a rather complex geomechanical behavior that eventually leads to a slightly nonuniform density distribu- tion. Nevertheless, the simulation shows that the swelling of the buffer is functioning to provide an adequate increase in confining stress on the tunnel wall, leading to a stabil- ization of any failure that may occur during the tunnel excavation. Finally, we describe the application of a pos- sible approach for linking THM processes with chemistry, focusing on the evolution of primary and secondary swelling, in which the secondary swelling is caused by changes in ionic concentration, which in turn is evaluated using a transport simulation model.

Parameter identification for elasto-plastic modelling of unsaturated soils from pressuremeter tests by parallel modified particle swarm optimization

This paper presents a methodology for the identification of parameter values in the Barcelona Basic Model (BBM) by inverse analysis of the experimental cavity pressure–cavity strain curve from pressuremeter tests in unsaturated soils. This methodology involves a high-dimensional optimization process which is particularly challenging due to the existence of a large number of local minima caused by the nonlinearity of the BBM. A novel parallel modified particle swarm optimization algorithm is utilized to minimize the difference between measured and computed values on the cavity pressure–cavity strain curve. The computed cavity pressure–cavity strain curve is obtained by using a finite element model of an unsaturated soil whose mechanical behaviour is described by the BBM. An example is presented to validate the proposed methodology making use of artificial experimental results that had been calculated by a finite element simulation of pressuremeter tests. Finally, the application to a real case is presented by showing that the proposed methodology can safely identify the values of at least six BBM parameters via inverse analysis of pressuremeter tests at different suction levels.

Using modified state surface approach to select parameter values in the Barcelona basic model

SUMMARYThe Barcelona basic model (BBM) successfully explained many key features of unsaturated soils and received extensive acceptance. It is also one of the few elastoplastic constitutive models for unsaturated soils that have been implemented within finite element codes and applied to the analysis of real boundary value problems. The BBM was proposed in incremental forms according to theories of soil plasticity in which individual aspects of the isotropic virgin behavior are controlled by multiple parameters, whereas at the same time, a single parameter controls more than one aspect of soil behavior. Although a variety of methods have been recently developed for calibrating model parameters for elastoplastic soil models, at present, there are no well‐established, simple, and objective methods for selecting parameter values in the BBM from laboratory tests. This has been one of the major obstacles to the dissemination of this constitutive model beyond the research context.This article presents an optimization approach especially developed for simple and objective identification of material parameters in the BBM. This is achieved by combining a modified state surface approach, recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic stress conditions, with the Newton or quasi‐Newton method to simultaneously determine the five parameters governing isotropic virgin behavior in the BBM. The comparison between results using the proposed method and an existing method for the same laboratory tests was discussed from which the simplicity and objectivity of the proposed method were evaluated. Copyright © 2012 John Wiley & Sons, Ltd.

A comparative study of stress integration methods for the Barcelona Basic Model

The paper compares the accuracy and stability of implicit and explicit stress integration schemes applied to the Barcelona Basic Model. In addition, the effect of the integration scheme on the convergence of Newton–Raphson algorithm is studied. By running a Newton–Raphson algorithm for a single stress point, the number of iterations required to reach convergence gives some insight on the convergence of the finite element solution at the global level. The explicit algorithms tested incorporate substepping with error control and are based on Runge–Kutta methods of different orders or on the Richardson extrapolation method. The implicit return-mapping algorithms follow the procedures of Simo and Hughes [1] and Hofmann [2].

Shear Modulus and Damping Ratio of Unsaturated Kaolin Measured by New Suction-Controlled Cyclic Triaxial Device

Abstract The cyclic triaxial test is the most widely used way to measure the cyclic stress–strain properties of saturated soils because of its availability in most geotechnical laboratories. Further, it can be viewed as a suitable tool with which to analyze the cyclic behavior of unsaturated soils in a wide strain range. In this study, a new stress path suction-controlled cyclic triaxial device is presented. It is fitted for suction-controlled testing by the axis-translation technique. Pore-air and pore-water pressures are applied at the top and bottom of the specimen by using two electro-pneumatic regulators. The capability of the new apparatus is demonstrated in this paper with the results of some suction-controlled cyclic triaxial tests. The tests are carried out on compacted specimens of lean clay that are prepared in the same initial condition and tested following different stress paths. The stress paths include suction equalization, constant suction ramped isotropic compression, series of constant suction cyclic loading, and post-cyclic constant suction ramped isotropic compression stages. Volumetric behavior and evolution of the yield curves along suction equalization, constant suction ramped isotropic compression, and post-cyclic compression stages are discussed on the basis of the Barcelona Basic Model elasto-plastic framework. The stiffness and damping ratio of the specimens are subsequently presented, highlighting the dependency of the Young’s modulus (E), shear modulus (G), and damping ratio (D) on the shear strain amplitude, number of cycles, and suction. The results show that E and G increase, whereas D decreases significantly by increasing suction at similar strain levels and number of cycles.

Equivalent stress approach in modelling unsaturated soils

SUMMARY This article presents an equivalent stress approach that can be used in many elastoplastic constitutive models for unsaturated soils. The use of the equivalent stress leads to a modified yield locus that is independent of the suction. In addition, the equivalent stress becomes the major stress variable, with suction required only as an additional variable in calculations. The model on the basis of equivalent stress predicts exactly the same soil behaviour, with the sole difference being the use of equivalent stress instead of original stress variables. This article also presents the equivalent stress formulations of several constitutive models for unsaturated soils, including the Barcelona Basic Model. The predictions from these models remain unchanged, with the only difference being in their implementation. Finally, the equivalent stress approach and the net stress approach are compared for the Barcelona Basic Model. Copyright © 2011 John Wiley & Sons, Ltd.

Modeling Unsaturated Soil Response under Suction-Controlled True Triaxial Stress Paths

AbstractResults from a comprehensive series of suction-controlled hydrostatic compression, conventional triaxial compression, triaxial compression, triaxial extension, and simple shear tests, conducted on statically compacted specimens of poorly graded sand with clay, are presented. The experiments were accomplished in a newly developed true triaxial apparatus to test cubical, 7.62 cm (3 in.) side, specimens of unsaturated soil under controlled-suction states and for a wide range of stress paths that are not readily achievable in a cylindrical cell. The key features of the apparatus and a thorough performance verification test program have been documented in a first companion paper. Results from suction-controlled tests performed in the present work were used to calibrate and further validate two of the most popular elastoplastic critical state-based frameworks postulated to date for unsaturated soils, namely, the Barcelona Basic Model and the Oxford Model. In general, predictions of unsaturated soil resp...

Some aspects of the compression and collapse behaviour of an unsaturated natural loess

The compression and collapse behaviour of a natural unsaturated loess from northern France was investigated by running a series of constant rate of strain oedometric compression tests (together with some step loading tests) while monitoring suction by means of a high-capacity tensiometer. The reasonably constant suction measured during constant water compression tests was linked to the collapse of the largest dry pores. Time-dependent behaviour was also observed, with different responses obtained at different strain rates. In a standard fashion, collapse tests appeared to bring the representative point from the constant water content curve to the zero suction compression curve, indicating the existence of a maximum collapse stress. Data were qualitatively interpreted using the loading collapse (LC) yield curve of the Barcelona basic model. Changes in the LC yield curve inclinations could account for the existence of a maximum collapse value.

Special Section on Advanced Modeling and Numerical Simulations in Geomechanics

This special section of the International Journal of Geomechanics contains selected papers that are based on the presentations at the GeoHunan International Conference: Challenges and Recent Advances in Pavement Technologies and Transportation Geotechnics, held in Changsha, Hunan, China, on August 3–6, 2009. The subject of geomechanics has come a long way in developing constitutive models for geomaterials, including nontraditional materials. Yet, there are complex geomechanics problems that do not have well-defined constitutive models and solutions. Recently, advanced modeling and numerical simulation techniques such as neural network, bound theorem, and centrifuge modeling have been employed to solve some of those geomechanics problems. Owing to the rapid expansion in the use of computer software, nonlinear numerical analysis or neural network modeling has become very popular among researchers and practicing engineers in recent years. Although theoretical models have been around for a long time, it has always been challenging to develop such models. Recently, small-scale centrifuge-based simulations have shown a promising capability of modeling prototype geostructures without a gravityinduced in situ stress field. This special section contains six full-length papers covering such advanced modeling and numerical simulations, different from traditional constitutive modeling, in geomechanics. The paper contributed by Xiang et al. discusses settlement prediction on a chimney foundation by a neural network. In their work, seven models with different input series were developed. The optimal model was determined by comparing the forecasting performance. Xiao et al. carried out numerical simulations of a single pile in expansive soil and extensively studied the load transfer mechanism and soil-pile interaction. Chen and Yu present a study on centrifuge modeling, in which staged construction on a reinforced lime-stabilized embankment was simulated by spinning the model at various g-levels. Centrifuge test results were used to verify and validate their numerical analysis. A comprehensive literature review on constitutive modeling of unsaturated soil is presented by Zhang and Li. Some limitations in the framework of the Barcelona Basic Model are discussed, and a new approach is proposed to overcome the limitations. Fu et al. investigated the compressive behavior of anchored rock masses through a series of physical model tests. The test results were compared with specimens without anchor bolts. It was concluded that the improvement attributable to vertical bolts is more effective. Zhao et al. employed an upper bound limit analysis to evaluate the ultimate pullout capacity of horizontal shallow plate anchors. Dilation and nonlinear behavior of soil was found to have profound effects on the ultimate pullout capacity.

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

SUMMARYThe Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction.According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.

Extended Barcelona Basic Model for unsaturated soils under cyclic loadings

The Barcelona Basic Model (BBM) is an extension of the Cam clay model that has become popular in applications involving unsaturated soils and, in particular, in simulations using the finite element method. Partially saturated soils can be loaded in different ways, for instance, mechanically and/or hydraulically. In addition, cycles of loading and unloading can be applied. The present work introduces a modification of the BBM in order to simplify its computer implementation and also to allow the simulation of elastoplastic behaviour during cycles of both mechanical and hydraulic loading. A unique smooth yield surface is introduced and a two-yield surfaces concept is applied in order to represent the cyclic behaviour. The influence of the intermediate principal stress on the strength is also accounted for. Finally, the numerical integration (stress update) of the extended BBM is briefly discussed.

Thermo-hydro-mechanical model of the Canister Retrieval Test

The paper presents a 2-D axisymmetric numerical simulation of the Canister Retrieval Test (CRT). The main objectives of this analysis are the study of the canister–buffer and buffer–host rock interfaces; and the evaluation of the mathematical models used to predict the THM behaviour of the buffer and interface. The THM simulation was performed using the finite element program Code-Bright. The constitutive law adopted to represent the mechanical behaviour of bentonite and pellets is the Barcelona Basic Model (BBM) with a non-linear elastic component accounting for swelling. A joint element with a non-linear elastic mechanical law was implemented in the code for the simulation of the opening–closure of the interface canister–buffer. The formulation of this element also incorporates appropriate thermal and hydraulic laws. The evolution of temperatures, relative humidities and stresses recorded during the test were compared with the simulation results. Comparing the results measured in situ with the results of numerical analysis shows that the formulation used is able to reproduce satisfactorily the phenomena involved in the test as well as their interactions. In addition, the final dry density and degree of saturation measured in samples of bentonite and pellets extracted during the test dismantling were also in agreement with the calculated values.

Implementation of the Barcelona Basic Model into TOUGH–FLAC for simulations of the geomechanical behavior of unsaturated soils

This paper presents the implementation of the Barcelona Basic Model (BBM) into the TOUGH–FLAC simulator analyzing the geomechanical behavior of unsaturated soils. We implemented the BBM into TOUGH–FLAC by (1) extending an existing FLAC 3D module for the Modified Cam-Clay (MCC) model in FLAC 3D and (2) adding computational routines for suction-dependent strain and net stress (i.e., total stress minus gas pressure) for unsaturated soils. We implemented a thermo-elasto-plastic version of the BBM, wherein the soil strength depends on both suction and temperature. The implementation of the BBM into TOUGH–FLAC was verified and tested against several published numerical model simulations and laboratory experiments involving the coupled thermal–hydrological–mechanical (THM) behavior of unsaturated soils. The simulation tests included modeling the mechanical behavior of bentonite-sand mixtures, which are being considered as back-fill and buffer materials for geological disposal of spent nuclear fuel. We also tested and demonstrated the use of the BBM and TOUGH–FLAC for a problem involving the coupled THM processes within a bentonite-backfilled nuclear waste emplacement tunnel. The simulation results indicated complex geomechanical behavior of the bentonite backfill, including a nonuniform distribution of buffer porosity and density that could not be captured in an alternative, simplified, linear-elastic swelling model. As a result of the work presented in this paper, TOUGH–FLAC with BBM is now fully operational and ready to be applied to problems associated with nuclear waste disposal in bentonite-backfilled tunnels, as well as other scientific and engineering problems related to the mechanical behavior of unsaturated soils.

A sequential method for selecting parameter values in the Barcelona basic model

The popularity of the Barcelona basic model (BBM) has grown steadily since its publication in 1990, due to its ability to capture key aspects of unsaturated soil behaviour. Nevertheless, the BBM is still rarely employed by practitioners, partly because of the absence of simple and objective methods for selecting parameter values from laboratory tests. One difficulty is that, in the BBM, individual aspects of the isotropic virgin behaviour are controlled by multiple parameters, while at the same time a single parameter controls more than one aspect of soil behaviour. This has led to iterative procedures where parameter values are adjusted in turn to match experiments, which requires significant experience and can lead to the selection of widely varying parameter values depending on the user. The proposed method streamlines parameter selection with a view to increasing the appeal of the BBM for practitioners. The method adopts a “sequential” procedure where the five parameters governing isotropic virgin behaviour are matched to degrees of freedom in the BBM, which are then fixed one at a time, in a specific order, without any assumption about other parameters. The simplicity and reduced subjectivity of the method in comparison with iterative procedures is demonstrated by selecting parameter values from laboratory tests.

Coupled solid-fluid FE-analysis of an embankment dam

A coupled solid-fluid FE-model for partially saturated soils, characterized by modeling the soil as a three-phase material consisting of a deformable soil skeleton and the fluid phases water and air, is reviewed briefly. As a constitutive model for the soil skeleton, the well-known Barcelona Basic model (BBM) is employed, which is formulated in terms of net stress and matric suction. For the BBM, a computationally efficient return mapping algorithm is proposed, which only requires the solution of a scalar nonlinear equation at the integration point level. The coupled FE-model is applied to the coupled transient numerical simulation of the water flow and the deformations and stresses in an embankment dam.

A 13-parameter model for unsaturated soil based on bounding surface plasticity

A few constitutive models for unsaturated soils have already been proposed, however, many classic models such as the Barcelona basic model can simulate neither complex volumetric soil behaviour (without forgetting its supreme merit of being the first consistently and rigorously formulated model) nor post-peak softening, and most advanced models generally comprise a large number of parameters making them more difficult to be applied to practical situations. In this paper, we present a new model for unsaturated soils based on an existing model developed originally for saturated soils. It comprises a minimum number of constitutive parameters. The extension to unsaturated state is achieved by following a general methodology previously developed in our laboratory. The capacities of this simple model are tested. With only 13 parameters, it can reproduce the basic behaviour of unsaturated soils such as rebound or collapse upon wetting, depending on the stress levels. It can also reproduce post-peak softening and transition from contractant to dilatant volumetric behaviour during undrained shear. Overall, the first tentative of validation gives a good correlation between simulations and experimental data, and shows encouraging signs for future developments.