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1.
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. 相似文献
2.
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. 相似文献
3.
The paper discusses some aspects of the Barcelona Basic Model (BBM), which is one of the most widely used elasto‐plastic models for unsaturated soils. In addition to modelling those unsaturated soils where the collapse potential increases with increasing net stress (as envisaged by the original authors), the BBM can also be used to model soils where the collapse potential decreases with increasing net stress, by selecting suitable values for the model parameters r and pc. A practical procedure is suggested for selecting a value for the important model parameter pc from laboratory test data. Problems with use of the BBM are discussed, including the difficulty of correctly matching the locations of the normal compression lines for different values of suction and the possibility of non‐convexity of the yield curve. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
4.
Julio César Beltrame Benatti Roger Augusto Rodrigues Miriam Gonçalves Miguel 《Geotechnical and Geological Engineering》2013,31(5):1569-1585
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. 相似文献
5.
Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm and a fully implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed. 相似文献
6.
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. 相似文献
7.
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。 相似文献
8.
A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use of a unique ‘effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here. 相似文献
9.
非饱和黏土的结构性能够显著影响其力学特性。基于非饱和土经典模型BBM（Barcelona basic model）和一种可描述循环塑性的硬化法则,引入体积破损率的作为标准土体结构破损的参数,建立了一个描述常吸力下非饱和结构性黏土静态及动态力学特性的弹塑性双面模型。模型在应力空间中包含与重塑非饱和土屈服面几何相似的结构性边界面和加载面,采用径向映射法则和可移动的记忆中心原理,通过结构性边界面和加载面在应力空间中的演化来反映循环加载过程中非饱和结构性黏土的循环塑性特征和结构损伤过程。通过与相关非饱和黏土控制吸力试验数据的比较,表明该模型能够较好地反映静态加载下非饱和结构性黏土的力学特性,而模型预测的循环荷载下的应力?应变特征也具有一定的合理性。 相似文献
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11.
The 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. 相似文献
12.
The finite‐element formulation and integration algorithms developed in Part I are used to analyse a number of practical problems involving unsaturated and saturated soils. The formulation and algorithms perform well for all the cases analysed, with the robustness of the latter being largely insensitive to user‐defined parameters such as the number of coarse time steps and error control tolerances. The efficiency of the algorithms, as measured by the CPU time consumed, does not depend on the number of coarse time steps, but may be influenced by the error control tolerances. Based on the analyses presented here, typical values for the error control tolerances are suggested. It is also shown that the constitutive modelling framework presented in Part I can, by adjusting one constitutive equation and one or two material parameters, be used to simulate soils that expand or collapse upon wetting. Treating the suction as a strain variable instead of a stress variable proves to be an efficient and robust way of solving suction‐dependent plastic yielding. Moreover, the concept of the constitutive stress is a particularly convenient way of handling the transition between saturation and unsaturation. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
13.
Bounding surface‐based modeling of compacted silty sand exhibiting suction dependent postpeak strain softening 
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下载免费PDF全文 Ujwalkumar D. Patil Laureano R. Hoyos Mathilde Morvan Anand J. Puppala 《国际地质力学数值与分析法杂志》2018,42(14):1741-1761
This article focuses on modeling the strain hardening‐softening response of statically compacted silty sand as observed from a comprehensive series of suction‐controlled, consolidated‐drained triaxial tests accomplished in a fully automated, double‐walled triaxial test system via the axis‐translation technique. The constitutive model used in this work is based on the theory of Bounding Surface (BS) plasticity and is formulated within a critical state framework. The essential BS model parameters are calibrated using the full set of triaxial test results and then used for predictions of compacted silty sand response at matric suction states varying from 50 to 750 kPa. Complementary simulations using the Barcelona Basic Model have also been included, alongside BS model predictions, in order to get further enlightening insights into some of the main limitations and challenges facing both frameworks within the context of the experimental evidence resulting from the present research effort. In general, irrespective of the value of matric suction applied, the Barcelona Basic Model performs relatively well in predicting response at peak and critical state failure under low net confining pressure while the Bounding Surface Model performs relatively well under high net confining pressures. 相似文献
14.
This paper involves an evaluation of a relationship describing the evolution in yield stress of unsaturated soils during hydraulic hysteresis, and an application of this relationship in an elasto-plastic framework to predict the compression curves of unsaturated soils under drained (free outflow of air and water with constant suction) or undrained (constant water content with no outflow of water and varying suction) conditions. The yield stress was quantified as the apparent mean effective preconsolidation stress obtained from compression tests reported in the literature on specimens that had experienced different hydraulic paths. It was observed that the preconsolidation stress does not follow a hysteretic path when plotted as a function of matric suction, but does when plotted as a function of the degree of saturation. Accordingly, an existing logarithmic relationship between the preconsolidation stress and matric suction normalized by the air entry suction was found to match the experimental preconsolidation stress results. This same relationship was also able to satisfactorily predict the trends in preconsolidation stress with degree of saturation by substituting the hysteretic soil–water retention curve (SWRC) into the place of the matric suction. The relationship between preconsolidation stress and suction was combined with an elasto-plastic framework to predict the compression curves of soils during drained compression, while the wetting-path relationship between preconsolidation stress and degree of saturation was combined with the framework to predict the compression curves of soils during undrained (constant water content) compression. A good match was obtained with experimental data from the literature, indicating the relevance of considering the hysteretic SWRC and preconsolidation relationships when simulating the behavior of unsaturated soils following different hydro-mechanical paths. 相似文献
15.
The 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. 相似文献
16.
This paper presents a complete finite‐element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress–strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time‐stepping scheme which automatically adjusts the time‐step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non‐linearity caused by suction‐dependent plastic yielding, suction‐dependent degree of saturation, and saturation‐dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress–strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
17.
应力路径对土的强度和变形性质具有重要影响。相对于饱和土而言,控制吸力条件下的非饱和土三轴压缩状态的应力路径研究更加复杂。随着非饱和土本构理论的不断发展,理论和试验研究结果表明,非饱和土弹塑性本构模型可以用来近似地描述非饱和土的强度和变形性质。因而,运用非饱和土弹塑性本构模型对控制吸力条件下的3种非饱和土三轴压缩应力路径试验进行数值模拟是一种有效的理论研究手段。采用Barcelona模型能够对此类试验进行较好的数值模拟,其研究结果表明,在控制吸力条件的三轴压缩状态下应力路径对非饱和土的强度和变形性质具有重要影响。 相似文献
18.
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. 相似文献
19.
Implicit integration under mixed controls of a breakage model for unsaturated crushable soils 下载免费PDF全文
下载免费PDF全文 This paper discusses a series of stress point algorithms for a breakage model for unsaturated granular soils. Such model is characterized by highly nonlinear coupling terms introduced by breakage‐dependent hydro‐mechanical energy potentials. To integrate accurately and efficiently its constitutive equations, specific algorithms have been formulated using a backward Euler scheme. In particular, because implementation and verification of unsaturated soil models often require the use of mixed controls, the incorporation of various hydro‐mechanical conditions has been tackled. First, it is shown that the degree of saturation can be replaced with suction in the constitutive equations through a partial Legendre transformation of the energy potentials, thus changing the thermomechanical state variables and enabling a straightforward implementation of a different control mode. Then, to accommodate more complex control scenarios without redefining the energy potentials, a hybrid strategy has been used, combining the return mapping scheme with linearized constraints. It is shown that this linearization strategy guarantees similar levels of accuracy compared with a conventional strain–suction‐controlled implicit integration. In addition, it is shown that the use of linearized constraints offers the possibility to use the same framework to integrate a variety of control conditions (e.g., net stress and/or water‐content control). The convergence profiles indicate that both schemes preserve the advantages of implicit integration, that is, asymptotic quadratic convergence and unconditional stability. Finally, the performance of the two implicit schemes has been compared with that of an explicit algorithm with automatic sub‐stepping and error control, showing that for the selected breakage model, implicit integration leads to a significant reduction of the computational cost. Such features support the use of the proposed hybrid scheme also in other modeling contexts, especially when strongly nonlinear models have to be implemented and/or validated by using non‐standard hydro‐mechanical control conditions. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
20.
This paper presents a numerical model for the elasto‐plastic electro‐osmosis consolidation of unsaturated clays experiencing large strains, by considering electro‐osmosis and hydro‐mechanical flows in a deformable multiphase porous medium. The coupled governing equations involving the pore water flow, pore gas flow, electric flow and mechanical deformation in unsaturated clays are derived within the framework of averaging theory and solved numerically using finite elements. The displacements of the solid phase, the pressure of the water phase, the pressure of the gas phase and the electric potential are taken as the primary unknowns in the proposed model. The nonlinear variation of transport parameters during electro‐osmosis consolidation are incorporated into the model using empirical expressions that strongly depend on the degree of water saturation, whereas the Barcelona Basic Model is employed to simulate the elasto‐plastic mechanical behaviour of unsaturated clays. The accuracy of the proposed model is evaluated by validating it against two well‐known numerical examples, involving electro‐osmosis and unsaturated soil behaviour respectively. Two further examples are then investigated to study the capability of the computational algorithm in modelling multiphase flow in electro‐osmosis consolidation. Finally, the effects of gas generation at the anode, the deformation characteristics, the degree of saturation and the time dependent evolution of the excess pore pressure are discussed. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献