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.     

Measurement of small strain behavior of a local soil by fiber Bragg grating-based local displacement transducers

The small strain stiffness of soils has a significant role in geotechnical design and analysis. In laboratory, the small strain behavior is examined by different techniques including the bender element method for measuring the maximum shear modulus and local displacement transducer (LDT) for measuring Young’s modulus at small strains. However, most commonly used LDTs are based on electrical components and have limitations, such as electromagnetic interference and possibility of short circuit in the presence of water. To overcome these limitations, in the present study, a conventional triaxial apparatus has been modified to measure and study the stress–strain behavior of soils at small strains. The major modifications include addition of piezoceramic sensors (bender elements) for measuring the maximum shear modulus and fiber Bragg grating (FBG) sensor-based local displacement transducers (FBG–LDTs) for measuring the stress–strain behavior at small strains. The modified triaxial apparatus has been used to conduct several tests on a completely decomposed granite soil from a site in Hong Kong. The stress–strain behaviors measured by the newly developed FBG–LDTs and an external displacement transducer are compared and discussed. In particular, the shear modulus values obtained using the bender elements, FBG–LTDs, and the external displacement transducer are also compared, discussed, and evaluated. The comparison and assessment show that the FBG–LTDs are more suitable for measuring the small strain behavior of soils.     

A kinematic hardening based model for unsaturated soils considering different hydraulic conditions

At present, several of the existing elastoplastic constitutive models are adapted for describing the stress–strain behavior of unsaturated soils. However, most of them present certain limitations in this field. These limitations can be related to the basic model and/or added unsaturated state variables and formulations. In this regard, inability to model the hydro‐mechanical behavior in constant water (CW) conditions is an example of these limitations. In this paper, an advanced version of CJS model is selected for adaptation to the unsaturated states. Adaptation to unsaturated states is achieved in the framework of effective stress approach. Effective stress equation and unsaturated state variables are selected based on the recent research existing in the literature. The developed model is capable of describing the complex behavior of unsaturated soil in the CW condition in addition to predicting the behavior at failure and post–failure, nonlinear elastoplastic behavior at low levels of stress and strain (by selecting a very small elastic domain), as well as wetting and collapse behaviors. In order to validate the model, results of triaxial tests in CD and CW conditions are used. The validation results indicate the good capability of the proposed model. Behavior of the unsaturated soils during wetting is an important issue. For this reason, the model is also evaluated based on the results of wetting and collapse triaxial tests. A comparison between the tests and simulation results shows that the model is able to predict the soil behavior under the wetting path. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled hydro-mechanical model for partially saturated soils predicting small strain stiffness

In the paper, we present newly developed hydro-mechanical hypoplastic model for partially saturated soils predicting small strain stiffness. Hysteretic void ratio dependent water retention model has been incorporated into the existing hypoplastic model. This required thorough revision of the model structure to allow for the hydro-mechanical coupling dependencies. The model is formulated in terms of degree of saturation, rather than of suction. Subsequently, the small strain stiffness effects were incorporated using the intergranular strain concept modified for unsaturated conditions. New features included degree of saturation-dependent size of the elastic range and an updated evolution equation for the intergranular strain. The model has been evaluated using two comprehensive data sets on completely decomposed tuff from Hong-Kong and Zenos Kaolin from Iran. It has been shown that the modified intergranular strain formulation coupled with the hysteretic water retention model correctly reproduces the effects of both the stress and suction histories on small strain stiffness evolution. The model can correctly predict also different other aspects of partially saturated soil behaviour, starting from the very small strain range up to the asymptotic large-strain response.     

Shear Modulus and Damping Ratio of Organic Soils

The paper presents results from a laboratory investigation into the dynamic properties of natural intact and model organic soils by means of resonant-column tests. The natural intact organic soils were sands, cohesive soils and peats with varying content of calcium carbonate. The model organic soils were formed in laboratory by mixing kaolinite and paper pulp. The influence of various soil parameters, such as strain level, confining stress, void ratio, plasticity index, organic content and secondary consolidation time on shear modulus, G, and damping ratio, DT, is presented and discussed. The test results on natural organic soils show that only high organic contents (OC ≥ 25%) have significant influence on G and DT at both small and high shear strains. For the model organic soils, however, a significant influence of even lower values of organic content (5% ≤ OC ≤ 20%) on G at small strains and DT at both small and high strains is observed.     

冻融循环对黏质粗粒土单轴抗压性能影响的试验研究

循环冻融作用下粗粒土的力学性质对于高寒地区边坡稳定性分析意义重大。以藏区某一排土场土体作为依托,开展了不同冻融循环次数后不同级配黏质粗粒土的单轴压缩试验,研究冻融循环作用对黏质粗粒土单轴抗压性能的影响。结果表明：冻融循环作用对黏质粗粒土应力-应变关系曲线性状及破坏模式有一定的影响,可使其应变呈现由脆性破坏（软化）向塑性流动（硬化）变化的规律。当提高冻融循环次数时,该类土体的弹模和抗压强度均显著减小,其中5~9次冻融循环前减小幅度较大,之后基本保持不变。单轴抗压性能的弱化与土样循环冻融过程中伴随的细颗粒团聚、大中孔隙增多、密实度下降有关。20次冻融循环后,该土质土样抗压强度、弹模最大降低幅度各自高达43%和77%。可见随着提高细砾组的含量,土样的抗压强度和弹模均呈现下降的趋势,这与该土样内粗、细土颗粒的比例及强度发挥机理密切相关。粗粒土单轴抗压破坏应变随冻融循环次数和细砾组含量的增加有一定的增加趋势。     

Modelling the initial shear stiffness of unsaturated soils as a function of the coupled effects of the void ratio and the degree of saturation

Existing models for predicting the small strain behaviour of unsaturated soil are not capable of predicting the initial shear stiffness during suction reduction under normally consolidated conditions. This problem has been addressed in the present study by combining an existing elastoplastic model and recent experimental data to provide a new model for the initial shear stiffness. The model, which is similar to that typically adopted for saturated soils, uses the average skeleton stress and an additional function of the degree of saturation. This new model not only captures the behaviour of the new experimental results, but it also describes a unique relationship between saturated and unsaturated soils.     

On a multilaminate model for soil incorporating small strain stiffness

In this paper a constitutive model for soils incorporating small strain stiffness formulated in the multilaminate framework is presented. In the multilaminate framework, the stress–strain behaviour of a material is obtained by integrating the mechanical response of an infinite number of randomly oriented planes passing through a material point. Such a procedure leads to a number of advantages in describing soil behaviour, the most significant being capture of initial and induced anisotropy due to plastic flow in a physically meaningful manner. In the past, many soil models of varying degree of refinement in the multilaminate framework have been presented by various authors. However, the issue of high initial soil stiffness in the range of very small strains and its degradation with straining, commonly referred to as ‘small strain stiffness’, has not been addressed within the multilaminate framework. In this paper, we adopt a micromechanics‐based approach to derive small strain elastic stiffness of the soil mass. Comparison of laboratory test data with results obtained from numerical simulations based on the proposed constitutive model incorporating small strain stiffness is performed to demonstrate its predictive capabilities. The model is implemented in a finite element code and numerical simulations of a deep excavation are presented with and without incorporation of small strain stiffness to demonstrate its importance in predicting profiles of deformation. Copyright © 2008 John Wiley & Sons, Ltd.     

A bounding surface model for unsaturated soils considering the microscopic pore structure and interparticle bonding effect due to water menisci

The interparticle bonding effect due to water menisci plays an important role in the hydromechanical coupling properties of unsaturated soils. This paper presents an unsaturated hydromechanical coupling model that considers the influence of matric suction, degree of saturation, and microscopic pore structure on the interparticle bonding effect. The enhanced effective stress and bonding variable are selected as constitutive variables. The bonding variable is correlated with the ratio between unsaturated void ratio and saturated void ratio. The deformation characteristics of unsaturated soils are described based on the bounding surface plasticity theory. A soil–water characteristic model that considers deformation and hydraulic hysteresis is integrated into the constitutive model to achieve hydromechanical coupling. The proposed model can effectively describe the hydromechanical coupling characteristics and the meniscus bonding force of unsaturated bimodal structure soils; the model parameters can be easily obtained through routine experiments. The experimental results of unsaturated isotropic compression, the wetting/drying cycle, and unsaturated triaxial shear tests are used to validate the capability of the proposed model.

     

A small‐strain overlay model

The paper begins with a discussion of the phenomenon of small‐strain stiffness and presents the small‐strain overlay model, a simple model that takes into account the non‐linear stiffness of soils at small strains. The new model can enhance already established elastoplastic formulations for non‐linear stiffness variation at small strains in a similar way that intergranular strain enhances the hypoplastic model. The overlay model is driven by the material's strain history and only two additional material constants, both with clear physical meaning. Therefore, the proposed model is a step towards the incorporation of small‐strain stiffness into routine design. In this paper, the new small‐strain overlay model is formulated. Its ability to take into account the influence of various strain histories on soil stiffness is illustrated in several examples. Copyright © 2008 John Wiley & Sons, Ltd.     

非饱和土的新非线性模型及其应用

为描述非饱和土的应力-应变特性,基于非饱和土三轴剪切试验,提出泊松比变化率（即切线泊松比随轴向应变的变化速率）的概念,发现非饱和土的切线模量和泊松比变化率均随轴向应变的增加呈指数衰减规律,基于此提出了一种描述非饱和土应力-应变关系的新非线性模型。该模型不仅能描述应变硬化,而且能描述应变软化;能对非饱和土三轴不固结不排水剪、固结排水剪、固结不排水剪试验的应力-应变关系进行描述;模型共包含6个参数,物理意义明确,确定方法简便。利用提出的模型对国内外文献中的三轴试验进行了模拟,结果表明,模拟结果与试验数据有很好的吻合度,从而验证了模型对试验数据的合理性和适用性。     

高吸力下黏性土的抗剪强度和体变特性

非饱和土中土-水之间的相互作用可区分为毛细作用和吸附作用,已有的非饱和土力学特性的研究大都局限于较低吸力、毛细作用占优范围。实践中由于环境的变化,地表土体常经历干湿循环及处在低含水率、高吸力状态,此时吸附作用占优。针对高岭土-河砂配制的非膨胀性黏性土,采用饱和盐溶液蒸汽平衡法,从脱湿和吸湿两种吸力路径下对土体施加高吸力。测试了高吸力下土体的强度和变形特性,试验中选用了0（接近无侧限）、25、50、100 kPa共4组小围压。试验结果表明,高吸力下土体表现为应变软化型破坏和剪胀性。随着围压的施加,土体从沿纵向开裂的张裂破坏过渡为剪切破坏。验证了修正后的Bishop非饱和土强度公式不适用于描述高吸力时峰值抗剪强度的变化,得到了高吸力下峰值抗剪强度可用相对于净应力的临界状态强度和剪胀作用来表示。分析发现,高吸力时土体的抗剪强度和比表面积直接相关,吸力对土体抗剪强度的作用取决于土体集聚体组构的形成和发展程度及其导致的剪胀作用。     

A bounding surface model for saturated and unsaturated soil-structure interfaces

In many geotechnical systems, such as reinforced slopes and embankments, soil-structure interfaces are often unsaturated. Shear behaviour of unsaturated interfaces is strongly dependent on their matric suctions, as revealed by the results of extensive laboratory tests. So far, constitutive models for unsaturated interfaces are very limited in the literature. This paper reports a new bounding surface model for saturated and unsaturated interfaces. New formulations were developed to incorporate suction effects on the flow rule and plastic modulus. To examine the capability of the proposed model, it was applied to simulate suction- and stress-controlled direct shear tests on unsaturated soil–cement, soil–steel and soil–geotextile interfaces. Measured and computed results are well matched, demonstrating that the proposed model can well capture key features of the shear behaviour of unsaturated interfaces, including suction-dependent dilatancy, stress–strain relation and peak and critical state shear strengths.     

考虑温度影响的重塑非饱和膨胀土非线性本构模型

以非饱和土的非线性模型为基础,通过对土性参数的修正和考虑温度本身引起的土的变形,建立了考虑温度效应的重塑非饱和膨胀土的本构模型。该模型包括土骨架的本构关系和水量变化的本构关系两个方面,涉及18个参数,都可用非饱和土三轴试验确定。共做了13个重塑非饱和膨胀土温控三轴试验,分析了温度对土的强度和变形的影响,研究了模型参数的变化规律。     

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

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.     

循环荷载下黏土应变积累积强化模型研究

循环加载历史是影响土的动力特性的一个重要因素。通过对一种原状粉质黏土进行高循环次数单剪试验,研究了黏土体应变随剪应变幅值及循环次数的变化规律,以及由于体应变的累积对黏土动力特性产生的影响。试验结果表明,黏土的体应变随着循环次数的增多和循环剪应变幅值的增大而增大,而土的动力特性则随着体应变的不断累积而出现强化现象,表现为动剪模量增加,阻尼比减小。对累积体应变与动剪模量、阻尼比之间的关系进行了研究,提出了相应的强化关系式。在常用的非线性模型基础上,通过引入动剪模量的强化系数和阻尼比的衰减系数,建立了一种能考虑循环应变历史影响的土动力模型。     

A simple critical state interface model and its application in prediction of shaft resistance of non-displacement piles in sand

A simple semi-hyperbolic state-dependent constitutive model for sand-structure interfaces is proposed. The model formulation is consistent with critical state soil mechanics since void ratio evolves continuously with shear strain from initial state towards asymptotic critical state at extremely large shear strains. The model takes into account influence of normal stiffness on volume change and stress path. The proposed interface model is implemented in a pile segment analysis scheme for simulation of shaft resistance mobilization in non-displacement piles. Results reveal that the proposed pile segment analysis can well predict shaft resistance of model piles embedded in different sands.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

荆门非饱和膨胀土的变形与强度特性试验研究

通过压力板试验,对比分析了荆门原状膨胀土与石灰改良土持水特征的差异性;应用非饱和土三轴仪,开展了原状膨胀土、石灰改良膨胀土与重塑膨胀土的变形及强度特性试验。结果表明：①石灰改良膨胀土与原状膨胀土相比,其进气值有显著降低,残余含水率显著升高,土-水特征曲线两个特征点的斜率较为平缓,说明其水稳定性较好,土体性状更为稳定;②原状膨胀土和石灰改良膨胀土在非饱和与饱和状态的应力-应变关系曲线均呈应变软化型,随净围压的增大,应变软化的程度趋缓;随含水率的减小,峰值应力增大,应力峰值点有所提前,应变软化现象更加显著。饱和重塑膨胀土的应力-应变关系呈应变强化型,非饱和重塑膨胀土则呈现为应变软化型,但其应变软化的程度较前两类土大为趋缓;③经石灰改性后,膨胀土强度参数值有大幅度提高,即使在湿化饱和后,石灰改良膨胀土仍保持了相对稳定的力学性质和较高的抗剪强度参数值。相比之下,无论是重塑膨胀土,还是原状膨胀土,对湿化作用均十分敏感,其强度参数值或波动较大,或整体水平较低。     

Universal model forms for predicting the shear modulus and material damping of soils

Numerous model forms have been used to predict the dynamic behaviours of soils, mainly the shear modulus and material damping. These models are used to represent normalised shear modulus reduction and material damping curves. The majority of the existing models are empirical and were proposed for specific soil types, strain ranges, etc. Some are limited to the data used in fitting, but fail to provide a good fit to other sets of data. The available model functions are not universal, which means that a model developed for one soil type may not be applicable for use with other soil types. In this paper, two universal mathematical models were proposed to predict the normalised shear modulus reduction and material damping curves. The mathematical model forms are sufficiently flexible to be widely used with different soil types. The models were evaluated using verification data of eight different soil types, i.e., data that were not used to fit the model parameters. The results indicate that the proposed model forms can accurately model the dynamic soil properties within the typical earthquake range. The advantage of developing the two universal models are two-fold, first the forms are applicable for sand, clay, and fibre-soil composite and second with further testing of soils, the model coefficients could ultimately be used to further understand the physical processes in soil behaviour, especially damping.