Elastoplastic Model For Unsaturated Soils Research Articles

Numerical integration of the Glasgow Coupled Model (GCM)

This paper presents the derivation of the incremental constitutive relations of the Glasgow Coupled Model (GCM), an established elasto-plastic model for unsaturated soils intended to represent their mechanical and water retention behaviour. The set of incremental equations derived defines an initial value problem (IVP) that needs to be solved at each integration step once the initial (or previous) state and theincrements of suction and strain are known. To solve this IVP effectively, a small reformulation of the GCM (not involving any modification of the model, but simply presenting it differently) has been adopted withthe aim to facilitate the development of a robust algorithm capable to identify unambiguously the correct model response activated by a given stress path (i.e. elastic, mechanical yielding, water retention yielding or simultaneous mechanical and water retention yielding). Subsequent to the description of this algorithm, the paper presents an explicit substepping integration scheme with automatic error control able to integrate the incremental constitutive equations of the model for each possible response, including unsaturated and saturated conditions. The numerical capabilities of the substepping scheme in terms of accuracy and efficiency are then demonstrated in the context of the performance maps proposed originally for saturated soil models.

Calibration of BBM Parameters using the Modified State Surface Approach

The Barcelona Basic Model (BBM) developed by Alonso et al. [1] is the first and the mostwidely used elasto-plastic model for unsaturated soils. The BBM successfully explained many key features of unsaturated soils and received extensive acceptance. However, there is lack of a well-establishedmethod for selecting parameter values for the BBM from laboratory tests, although a variety of methods have been recently developed for calibrating model parameters for the BBM. Concerns still exist on the correctness and robustness of such parameter value selection procedures. The above statements were evidenced by a recent benchmark exercise on selection of parameter values for the BBM organized within a "Marie Curie" Research Training Network on "Mechanics of Unsaturated Soils for Engineering"(MUSE)[2]. Experienced constitutive modelers in unsaturated soils from 7 prestigious teams were provided with the same experimental results on an unsaturated soil to calibrate the parameter values in the BBM. Theoretically, the calibrated parameters from different teams are expected to be the same or at leastvery close. However, the selected parameter values by the 7 teams are surprisingly widely different. This paper first discussed the limitations in the existing methods to calibrate the parameter values in the BBM. A novel approach was then proposed to calibrate the parameter values for the BBM. The approach takes advantage of the close-form solution of the BBM, which is derived based upon a newly proposed Modified State Surface Approach to study the unsaturated soils [3-6]. The same experimental data, used in the MUSE benchmark exercise, were reanalysed using the proposed approach to calibrate parameters for the BBM. The results were compared with those in the MUSE benchmark exercise from which thesimplicity, effectiveness, and robustness of the proposed method were evaluated.

Undrained Spherical Cavity Expansion in Unsaturated Soils: Semianalytical Solution Coupling Hydraulic and Mechanical Behaviors

A coupled hydromechanical solution to undrained spherical cavity expansion problem in unsaturated soil is proposed with an elastoplastic model for unsaturated soil. The mechanical response and hydraulic behavior of soil during expansion are coupled together through a soil–water characteristic curve (SWCC) that evolves with the void ratio. A system of four first-order differential governing equations is derived based on the equilibrium equation, large stain theory and coupled hydromechanical constitutive relationship of soil. The present solution can reduce to unified hardening parameter model based solution under saturated condition, which validates the proposed solution. The effects of overconsolidation ratio and initial suction on expansion responses are explored based on extensive parametric studies. Special attention is paid to investigate the distributions of the principal stresses, suction, and saturated degree of soil around the expanded cavity; the stress trajectory of a representative element at the cavity surface; and cavity pressure–displacement curves. The proposed analytical solution can serve as a theoretical framework for modelling of some fundamental geotechnical problems in unsaturated soils using critical state soil models.

Stability Analysis and Size Optimization of Retaining Walls on Unsaturated Soil

This study proposes a general methodology for an elasto-plastic model for unsaturated soil and proves its feasibility through a set of experimental calculations. The method can be used to estimate the stability and optimize the size of retaining walls on unsaturated soil.

Simulation of liquefaction of unsaturated soil using critical state soil model

SummarySeveral researchers have reported that the mean effective stress of unsaturated soils having a relatively high degree of saturation gradually decreases under fully undrained cyclic loading conditions, and such soils can be finally liquefied like saturated soils. This paper describes a series of simulations of fully undrained cyclic loading on unsaturated soils, conducted using an elastoplastic model for unsaturated soils. This model is a critical state soil model formulated using effective stress tensor for unsaturated soils, which incorporates the following concepts: (a) the volumetric movement of the state boundary surface containing the critical state line owing to the variation in the degree of saturation; (b) the soil water characteristic curve considering the effects of specific volume and hydraulic hysteresis; and (c) the subloading surface concept for considering the effect of density. Void air is assumed to be an ideal gas obeying Boyle's law. The proposed model is validated through comparisons with past results. The simulation results show that the proposed model properly describes the fully undrained cyclic behavior of unsaturated soils, such as liquefaction, compression, and an increase in the degree of saturation. Finally, the effects of the degree of saturation, void ratio, and confining pressure on the cyclic strength of unsaturated soils are described by the simulation results. The liquefaction resistance of unsaturated soils increases as the degree of saturation and the void ratio decrease, and as the confining pressure increases. Furthermore, the degree of saturation has a greater effect on the liquefaction resistance than the confining pressure and void ratio. Copyright © 2017 John Wiley & Sons, Ltd.

Incorporating anisotropy in the Barcelona basic model

The paper presents an elasto-plastic model for unsaturated soils that extends the Barcelona basic model to introduce a dependency of mechanical behaviour on material anisotropy. The model builds upon a previous proposal by Al-Sharrad and Gallipoli [1] by linking material anisotropy to both the distortion and aspect ratio of the elliptical yield curve in the constant suction plane of deviator versus mean net stress. In order to take into account anisotropic behaviour, an additional constitutive equation is therefore proposed to uniquely relate the aspect ratio and the distortion of the yield ellipse. The new model is calibrated and validated against the experimental data by Al-Sharrad [2] via the simulation of triaxial tests conducted at various suctions on compacted kaolin samples. These simulations show that the new model predicts yield stresses and shear strains during anisotropic loading with greater accuracy compared to the model of Al-Sharrad and Gallipoli [1].

Fully undrained cyclic loading simulation on unsaturated soils using an elastoplastic model for unsaturated soils

Several researchers have reported that Bishop’s mean effective stress decreases in unsaturated soils under fully undrained cyclic loading conditions, and unsaturated soils are finally liquefied in a similar manner as saturated soils. This paper presents a series of simulations of such fully undrained cyclic loading on unsaturated soils using an elastoplastic model of the unsaturated soil. This model is formulated using the Bishop’s effective stress tensor incorporating the following concepts: the volumetric movement of the state boundary surface containing the normal consolidation line and the critical state line due to the variation in the degree of saturation, a soil water characteristic curve model considering the effect of specific volume and hysteresis, the subloading surface model, and Boyle’s law. Comparisons between the simulation results and the experimental ones show that the model agreed well with the unsaturated soil behavior under cyclic loading. Finally, the typical cyclic behavior of unsaturated soils under fully undrained conditions, such as the mechanism of liquefaction of unsaturated soils, the compression behavior, and an increase in the degree of saturation, are described through the proposed simulation results.

Explicit formulation of at-rest coefficient and its role in calibrating elasto-plastic models for unsaturated soils

Normally, suction-controlled triaxial tests are used to characterize soil behavior in constitutive modeling of unsaturated soils. However, this type of tests requires sophisticated equipment and is time-consuming. This has been one of the major obstacles to the implementation and dissemination of unsaturated soil mechanics beyond the research context.In contrast to suction-controlled triaxial tests, the suction-controlled oedometer test requires simpler equipment and a shorter testing period. Oedometer tests represent the at-rest earth pressure (K0) condition, which is an important stress state in any simulation. The major disadvantage of the oedometer test is that its lateral stress is controlled by the condition of zero lateral strain and remains unknown during the testing process. At present, no well-established, simple, and objective methods are available that take advantage of oedometer test results for constitutive modeling purposes.This paper derives an explicit formulation of the at-rest coefficient for unsaturated soils and develops an optimization approach for simple and objective identification of material parameters in elasto-plastic models for unsaturated soils using the results from suction-controlled oedometer tests. This is achieved by combining a modified state surface approach (MSSA), recently proposed to model the elasto-plastic behavior of unsaturated soils, with the quasi-Newton method to simultaneously calibrate all parameters governing virgin behavior in elasto-plastic models. The Barcelona Basic Model (BBM) is used to demonstrate the application of the proposed explicit formulation and calibration method. Results predicted using obtained parameters are compared with laboratory test results for the same stress paths in order to evaluate the simplicity and objectivity of the proposed method.

Coupled hydro-mechanical analysis of slope under rainfall using modified elasto-plastic model for unsaturated soils

Two modifications for the basic Barcelona model (BBM) are present. One is the replacement of the net stress by the average skeleton stress in unsaturated soil modeling, and the other is the adoption of an expression for the load−collapse (LC) yield surface that can match flexibly the normal compression lines at different suctions. The predictions of the modified BBM for the controlled-suction triaxial test on the unsaturated compacted clay are presented and compared with the experimental results. A good agreement between the predicted and experimental results demonstrates the reasonability of the modified BBM. On this basis, the coupled processes of groundwater flow and soil deformation in a homogeneous soil slope under a long heavy rainfall are simulated with the proposed elasto-plastic model. The numerical results reveal that the failure of a slope under rainfall infiltration is due to both the reduction of soil suction and the significant rise in groundwater table. The evolution of the displacements is greatly related to the change of suction. The maximum collapse deformation happens near the surface of slope where infiltrated rainwater can quickly reach. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.

A bounding surface plasticity model for unsaturated soil at small strains

Most existing hydromechanical models for unsaturated soils are not able to fully capture the nonlinearity of stress–strain curves at small strains (less than 1%). They cannot therefore, for example, accurately predict ground movements and the performance of many earth structures under working conditions. To tackle this problem, a state-dependent bounding surface plasticity model has been newly developed. Particularly, the degradation of shear modulus with strain at small strains ranging from 0.001% to 1% is focused. The proposed model is formulated in terms of mean average skeleton stress, deviator stress, suction, specific volume and degree of saturation. Void ratio-dependent hydraulic hysteresis is coupled with the stress–strain behaviour. Different from other elastoplastic models for unsaturated soils, plastic strains are allowed inside bounding surfaces. In this paper, details of model formulations and calibration procedures of model parameters are presented. To evaluate the capability of the new model, it is applied to simulate a series of triaxial compression tests on compacted unsaturated silt at various suctions. Effects of suction, drying and wetting as well as net stress on unsaturated soil behaviour are well captured. The model shows good predictions of the degradation of shear modulus with strain over a wide range of strains from 0.001% to 1%. Copyright © 2015 John Wiley & Sons, Ltd.

A hydro-mechanical elastoplastic model for unsaturated soils under isotropic loading conditions

This paper presents an elastoplastic constitutive model for the coupling of hydraulic and stress–strain behavior of unsaturated soils under isotropic loading conditions. The proposed model is capable of considering the influence of irrecoverable changes in water volume fraction on stress–strain behavior and plastic strain on hydraulic behavior. Bounding surface and subloading surface plasticity frameworks are employed to describe hydraulic and mechanical behavior, respectively. The appropriate coupled hardening rules are introduced to fully describe the coupling effects between hydraulic and stress–strain behavior. Model predictions for unsaturated highly expansive and collapsible soils are compared with test data, and reasonable agreement is achieved.

Experimental behaviour of compacted marls

Jurassic marls from Abadia, Portugal, were used in the construction of some motorway embankments. Large fragments of this evolving material remained after the construction process, and their degradation was of concern because of the expected change of the engineering properties of the compacted material. The material exhibits a very complex behaviour, which is difficult to reproduce with existing constitutive models for unsaturated structured materials. This paper focuses on understanding and providing data on the interaction between the pure marls (rock) and the aggregate behaviour. It presents the main results of tests performed to characterise the hydro-mechanical behaviour of compacted marls in specimens prepared with different grading size distributions and subjected to oedometer tests where both stress and suction changes were applied. The experimental data obtained were analysed, considering the presence of fragments and their degradation. The marl matrix was characterised to complete the existing data previously published for this material, but now with the purpose of providing a better explanation for the volumetric behaviour of the aggregate. The discussion is assisted by the explanation provided by a simple elasto-plastic model for unsaturated soils. Discrepancies with model predictions help to highlight the singularity of the marl aggregate. Compacted marls behave as materials in the transition between rockfill (when the fragments remain brittle) and a clayey soil (when the degradation accumulates). Therefore the compacted marl exhibits a dual behaviour. If it is dry, deformations are explained by the breakage of particles and rearrangement of the structure. If it is wet, the compacted marl is dominated by bond degradation of the material, the release of swelling potential and simultaneous changes in the stiffness and strength of the fragments. It appears that the transition from dry to wet can be identified by the current suction; moreover, it is rather abrupt.

Calibration of elasto-plastic models for unsaturated soils under isotropic stresses

This paper presents a new method for selecting parameter values in elasto-plastic models for unsaturated soils under isotropic stress states. The proposed method is an improvement over more traditional calibration approaches as it explicitly takes into account experimental yielding behavior when defining the unsaturated normal compression surface. This is achieved by “enriching” measured yield stresses with corresponding values of specific volume (estimated from the observed elastic and virgin responses), which generates experimental points that can be interpolated together with virgin compression data. The proposed methodology is general and independent of the chosen mathematical forms of normal compression surface, elastic law and constitutive variables. The validity of the method is demonstrated by calibrating a reference model from a set of constant suction isotropic compression tests. Both improved and traditional calibration approaches are employed to select model parameter values which are then used to predict yield curves in the mean net stress–suction plane. Because of the incorporation of yielding data in the interpolation of the normal compression surface, the improved calibration method produces a more accurate prediction of yield stresses at different suctions compared with the standard method. Due to its generality and limited subjectivity, the proposed method provides an unbiased tool to compare strengths and weaknesses of different constitutive models.

Effect of suction on volume change and shear behaviour of an overconsolidated unsaturated silty soil

This paper presents the results of an experimental study on the effect of suction on compressibility and shear behaviour of unsaturated silty soil under various types of loading. A series of laboratory experiments were conducted in a double-walled triaxial cell on samples of a compacted silty soil. In the experiments the soil samples were subjected to isotropic consolidation followed by unloading and subsequent reloading under constant suction and prescribed overconsolidated ratio. The experimental results are presented in the context of an elasto-plastic model for unsaturated soil. The effects of suction on mechanical behaviour of unsaturated silty soil are presented and discussed. It is shown that increasing suction affects the shear behaviour of unsaturated soils, but there is a limit beyond which, further increase in suction will not result in any significant change in the behaviour.

An Improved Elasto-Plastic Model for Unsaturated Soils

The strength and deformation behaviors of unsaturated soil can be approximately described by elasto-plastic constitutive model that was proved by abundance academic and test researches. The Barcelona elastic-plastic model is an excellent model that can simulate the strength and deformation of unsaturated soil. But their calculated result of shear strength is low. So an improved Barcelona model is settled by using drop-shaped shear yield surface and hardening theory of dual stress. The results show that the improved model can more accurately predict the strength and deformation behaviors of unsaturated soil under suction-controlled triaxial compression stress states.

Model Test and Consolidation Analysis of Failure of a Loose Sandy Embankment Dam During Seepage

Failures of earth dam embankments and river dikes, which are constructed of sandy soils with low dry densities, have been observed to occur during rising of water levels. In this paper, a large-scale physical model test was conducted in order to investigate the behavior of a small dam embankment as water levels rose. The test results were simulated by use of a consolidation analysis method coupled with an elastoplastic model for unsaturated soils. All parameters used in the simulation were obtained from element tests; oedometer, triaxial compression, soil water retention, and permeability tests. First, in order to verify the parameters identified, direct shear tests were simulated using the consolidation analysis method; results of the simulation and the tests were consistent. From the embankment model test it was found that the crest of the embankment moved upstream at the first stage of impounding and then moved back. After a seepage surface appeared on the downstream slope, tension cracks occurred on the downstream slope, and sliding occurred through the crack and the downstream toe. The results of the simulation were consistent with those of the model test. This consolidation analysis method could be used to simulate the complex deformations induced by saturation collapse and shear strains and even failure behavior. Old embankments constructed with loose densities might have histories in which cracks occurred on the downstream slopes when the reservoir water level rose, and their stabilities might have decreased.

Hydro-mechanical constitutive model for unsaturated compacted bentonite–sand mixture (BSM): Laboratory tests, parameter calibrations, modifications, and applications

A bentonite–sand mixture (BSM) is one of the clay-based sealing components proposed for use in a Canadian deep geological repository (DGR) for used nuclear fuel. Numerical modelling to assess the overall design of the proposed DGR requires characterisation of the hydraulic–mechanical (H–M) of each of the components of the sealing system, including the BSM. The BSM currently under consideration is a 50/50 mixture (by dry mass) of bentonite and well-graded silica sand, compacted to a dry density of at least 1.67 Mg/m 3. This paper presents the H–M constitutive model parameters, calibrated for BSM specimens under saturated and unsaturated conditions, based on various laboratory tests. A set of parameters for an elastoplastic model for unsaturated soil, Basic Barcelona Model (BBM), have been determined to simulate the mechanical behaviour of the BSM specimen. A set of parameters for van Genuchten’s Soil–Water Characteristic Curve (SWCC) and Kozeny’s hydraulic permeability model have been determined to simulate the hydraulic behaviour of the BSM specimen. Using a finite element computer code, CODE_BRIGHT, these sets of parameters have been used to simulate H–M processes in BSM specimens during water infiltration under constant volume (CV) and constant mean stress (CMS) boundary conditions. The key features of the selected constitutive models that are different from the laboratory tests of the BSM specimen have been summarised. The functions to improve the capability of the selected constitutive models to match the laboratory test results of the BSM specimen have been proposed.

Evaluation method of dam behavior during construction and reservoir filling and application to real dams

In this paper we analyzed a real fill-type dam, named the Minami-Aiki Dam, to verify a numerical consolidation method with an elastoplastic model for unsaturated soils. The validities were conducted by comparing the analyzed and measured values during construction and impounding. The settlements calculated showed good agreement to those observed. Though the changing patterns of the measured and calculated pore water pressures were similar, the amounts of pore water pressures induced by the self-weights of embankment and the dissipation speeds were different. The earth pressures measured at the bottom of the core zone showed good agreement with those calculated. This method is valid for estimating behavior of fill-type dams during construction and impounding.

Explicit stress integration with error control for the Barcelona Basic Model.: Part II: Algorithms efficiency and accuracy

The paper compares the accuracy and efficiency of explicit stress integration schemes for elasto-plastic unsaturated soil models with automatic error control. Numerical tests are performed with reference to the Barcelona Basic Model (BBM), one of the most popular elasto-plastic models for unsaturated soils, by using eight explicit Runge–Kutta algorithms of various order as well as a novel application of the extrapolation method described in the companion paper. Initially, the results obtained from the lowest order Runge–Kutta scheme (i.e. Modified Euler) as well as the extrapolation method are checked against accurate solutions of a number of BBM paths involving changes of strains and suction. Subsequently, the efficiency and accuracy of all algorithms are assessed for generic increments of strains and suction, while the difference between two alternative error control methods is also analysed. The results presented, although strictly valid for the Barcelona Basic Model, are expected to be general and relevant to other similar unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.

Explicit stress integration with error control for the Barcelona Basic Model: Part I: Algorithms formulations

The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.