A two-surface plasticity model for clay

This paper presents a two-surface plasticity constitutive model for clays based on critical-state soil mechanics. The model reproduces the mechanical response of clays under multi-axial loading conditions and predicts both drained and undrained behavior at small and large strains. The constitutive model also captures both the strain-rate-dependent behavior of clays and the drop in strength towards a residual value at very large shear strains using novel approaches. The paper also describes a hierarchical process for the determination of the model parameters relying more on simple curve fitting of model equations to experimental data points corresponding to specific soil states instead of trial-and-error simulations of entire experiments. Model parameter values are determined for London Clay, San Francisco Bay Mud, Boston Blue Clay and Lower Cromer Till, and the performance of the model in simulating mechanical response of clays is demonstrated for a variety of initial states and loading conditions.     

A two-surface plasticity model for cyclic behavior of saturated clay

This paper presents a two-surface plasticity model for describing some important features of saturated clay under cyclic loading conditions, such as closed hysteresis loops, cyclic shakedown and degradation, and different stress–strain relations for two-way loading. The model, namely ACC-2-C, is based on the elastoplastic model ACC-2 (an adapted Modified Cam Clay model with two yield surfaces) developed by Hong et al. (Acta Geotech 11(4):871–885, 2015). The small-strain nonlinearity concept is adopted to achieve the nonlinear characteristics of clay during unloading–loading stage. The new hardening law related to accumulated deviatoric plastic strain is proposed for the inner surface to describe the cyclic shakedown and degradation. Following the advantages of the ACC-2 model, the constitutive equations are simply formulated based on the consistency condition for the inner yield surface. The model is conveniently implemented in a finite element code using a stress integration scheme similar to the Modified Cam Clay model. The simulation results are highly consistent with experimental data from drained and undrained isotropic cyclic triaxial tests in normally consolidated saturated clay under both one-way and two-way loadings.

     

A two-surface thermomechanical plasticity model considering thermal cyclic behavior

In thermal-related engineering such as thermal energy structures and nuclear waste disposal, it is essential to well understand volume change and excess pore water pressure buildup of soils under thermal cycles. However, most existing thermo-mechanical models can merely simulate one heating–cooling cycle and fail in capturing accumulation phenomenon due to multiple thermal cycles. In this study, a two-surface elasto-plastic model considering thermal cyclic behavior is proposed. This model is based on the bounding surface plasticity and progressive plasticity by introducing two yield surfaces and two loading yield limits. A dependency law is proposed by linking two loading yield limits with a thermal accumulation parameter n_c, allowing the thermal cyclic behavior to be taken into account. Parameter n_c controls the evolution rate of the inner loading yield limit approaching the loading yield limit following a thermal loading path. By extending the thermo-hydro-mechanical equations into the elastic–plastic state, the excess pore water pressure buildup of soil due to thermal cycles is also accounted. Then, thermal cycle tests on four fine-grained soils (natural Boom clay, Geneva clay, Bonny silt, and reconstituted Pontida clay) under different OCRs and stresses are simulated and compared. The results show that the proposed model can well describe both strain accumulation phenomenon and excess pore water pressure buildup of fine-grained soils under the effect of thermal cycles.

     

A critical state two-surface plasticity model for gravelly soil-structure interfaces under monotonic and cyclic loading

An elasto-plastic model is proposed for modeling the constitutive behavior of the interface between gravelly soils and structural materials. This model is based on the two-surface plasticity formulation and it is compatible with the concept of critical state soil mechanics. The model requires the same set of eight calibration parameters for predicting the monotonic and cyclic responses of both loose and dense interfaces. The model simulates cyclic densification, shear degradation and the effects of normal pressure, soil density, and stress path. The performance of the proposed constitutive model is validated by tests data under different normal stresses and boundary conditions.     

Modeling sand response using two-surface plasticity

This paper presents a two-surface plasticity constitutive model based on critical-state soil mechanics and describes a practical process for the determination of its parameters. Determination of the constitutive model parameters can be done in a hierarchical manner, starting with the model parameters that have the most bearing on sand behavior and that can be determined using routine experimental procedures. Most parameters can be determined through simple curve fitting through experimental data points. The constitutive model is calibrated against experimental data for Toyoura sand, clean Ottawa sand and mixtures of Ottawa sand with non-plastic silt. The model simulates closely the mechanical response of sands under various loading conditions and predicts both drained and undrained behavior of sands at small and large strains using the actual small-strain shear modulus, as measured in resonant column or bender elements tests, along with realistic values of Poisson’s ratio. Performance of the model in simulating sand response is demonstrated for a variety of initial states and loading conditions.     

A plasticity model for the mechanical behaviour of anisotropically consolidated clay

An incremental plasticity theory has been developed to describe the mechanical behaviour of anisotropically consolidated clays. The theory removes some of the shortcomings of the existing critical state models by incorporating the effects of the initial anisotropy due to a known depositional stress history and its subsequent alteration during further plastic deformation under a general stress system. From the extensive comparisons with the reported results in the literature, it is established that the model is satisfactory in predicting the various aspects of drained as well as undrained behaviour of K₀-consolidated clays.     

A landslide in stiff,intact clay

A landslide in a stiff clay formation, interrupting the excavation of a tunnel for a major railway in Sicily, is reported. Limit equilibrium and FEM undrained and drained analyses of the slope before tunnel excavation agree in showing that the slope was stable with a relatively high factor of safety and the critical slip surface is located well above the tunnel. The undrained stability of the tunnel checked both via FEM and via standard analytical solutions for face stability is also verified. The FEM analyses of the slope have been repeated considering the excavation of the tunnel in undrained and drained conditions. The advancement of the tunnel face is simulated in a plane strain analysis by the Panet method. In undrained conditions, the system keeps stable. In drained conditions with a stress release factor of 50 %, the slope is on the verge of failing with a very low safety factor, while with a stress release factor of 80 %, it fails following a complex mechanism that matches the observed failure surface. These findings are discussed and some conclusions attempted.     

考虑饱和黏土初始各向异性的循环边界面塑性模型

天然土体的初始各向异性通常可对其后继循环特性产生显著影响。现有考虑循环载荷作用的土体弹塑性模型,往往采用类似修正剑桥模型的椭圆形屈服面,已有研究表明,该椭圆形屈服面因其拉伸弹性区域偏大,针对天然K0固结状态的土体,其计算精度较差。基于新近提出的广义各向同性硬化准则,在边界面方程中引入初始各向异性张量,并采用空间滑动面破坏准则（SMP）的变换应力法,建立了能考虑饱和黏土初始各向异性的循环边界面塑性模型。分别针对等压和偏压固结的饱和黏土静、动三轴试验进行模拟,结果表明,该模型能合理反映土体的初始各向异性及其后继循环动力特性。     

SANICLAY: simple anisotropic clay plasticity model

SANICLAY is a new simple anisotropic clay plasticity model that builds on a modification of an earlier model with an associated flow rule, in order to include simulations of softening response under undrained compression following K_o consolidation. Non‐associativity is introduced by adopting a yield surface different than the plastic potential surface. Besides, the isotropic hardening of the yield surface both surfaces evolve according to a combined distortional and rotational hardening rule, simulating the evolving anisotropy. Although built on the general premises of critical state soil mechanics, the model induces a critical state line in the void ratio–mean effective stress space, which is a function of anisotropy. To ease interpretation, the model formulation is presented firstly in the triaxial stress space and subsequently, its multiaxial generalization is developed systematically, in a form appropriate for implementation in numerical codes. The SANICLAY is shown to provide successful simulation of both undrained and drained rate‐independent behaviour of normally consolidated sensitive clays, and to a satisfactory degree of accuracy of overconsolidated clays. The new model requires merely three constants more than those of the modified Cam clay model, all of which are easily calibrated from well‐established laboratory tests following a meticulously presented procedure. Copyright © 2006 John Wiley & Sons, Ltd.     

An anisotropic plasticity clay model accounting for structural effects and overconsolidation

Natural soils such as clays exhibit a variety of features including anisotropy, destruction and overconsolidation. In this work, a constitutive model that is able to replicate those salient features of natural clays is presented. The model is based on the classical S-CLAY1 model, where the anisotropy of the soil is captured through the initial inclination and rotation of the yield surface. To account for overconsolidation, a parabolic Hvorslev envelope is adopted. The compression curve of the reconstituted soil is taken as the reference to describe the structural of the soil. Parameters of the proposed constitutive model all have clear physical meanings and can be conveniently determined from conventional triaixal tests. Numerical examples using the proposed model to simulate overconsolidated natural soils are presented and compared with existing experimental data, demonstrating the capability of the model.     

Class A predictions of a NATM tunnel in stiff clay

The paper demonstrates the application of a hypoplastic model in class A predictions of a NATM tunnel in an urban environment. The tunnel, excavated in a stiff clay, is 14 m wide with 6 m to 21 m of overburden thickness. The constitutive model was calibrated using laboratory data (oedometric and triaxial tests) and the parameters were optimised using monitoring data from an exploratory drift. Based on the optimised data set, the future tunnel was simulated. After the tunnel excavation, it could be concluded that the model predicted correctly surface settlements, surface horizontal displacements, and the distribution of vertical displacements with depth. It overpredicted horizontal displacements in the vicinity of the tunnel.     

Anisotropic bounding-surface plasticity model for the cyclic shakedown and degradation of saturated clay

The cyclic behaviours of embedded offshore structures under different cyclic loading levels are related to the cyclic shakedown and degradation of the surrounding soils. In the present study, a damage-dependent bounding-surface model based on a newly proposed hardening rule was developed to predict the cyclic shakedown and degradation of saturated clay and the effect of the initial anisotropic stress state. By extending the Masing’s rule to the bounding-surface plasticity theory, the stress reversal point is taken as the generalised homological centre of the bounding surface. With movement of the generalised homological centre, at lower stress amplitudes, the cyclic process ends at a steady state, and cyclic shakedown is reached. At higher stress amplitudes, a damage parameter related to the accumulated deviatoric plastic strain is incorporated into the form of the bounding surface, which is hence able to contract to model degradations in stiffness and strength. To take into account the effects of initial anisotropic conditions on the cyclic behaviour of soils, an initial anisotropic tensor is introduced in the bounding surface. The developed model is validated through undrained isotropic and anisotropic cyclic triaxial tests in normally consolidated and overconsolidated saturated clay under both one-way and two-way loadings. Both cyclic shakedown and degradation are well reproduced by the model, as is the anisotropy effect induced by the initial anisotropic consolidation process.     

On yielding and flow of sand; A generalized two-surface model

This paper presents an extension to the concepts and ideas put forward in three articles by the first author and his colleagues during the 1966–1967 period [1].An isotropic-kinematic hardening rule for sand is proposed applicable to both monotonic and cyclic loading conditions. It is based on the theory of bounding surface plasticity incorporating, as in the previous studies, a non-associated flow rule. A three dimensional formulation of the constitutive relation is provided and a comparison of the predicted behaviour and observed responses for a number of undrained loading programs is presented.     

上海市浅部数层硬土的沉积环境、时代及划分对比

上海市陆域东部滨海平原区埋深三、五十米以上及西部湖沼平原区埋深二十多米以上分布有数层“硬土”,现在可以确定,均属于晚更新世晚期的陆相沉积。     

Weathering of Valle Ricca stiff and jointed clay

The study proposes a weathering model of Pliocene–Pleistocene stiff and jointed blue-grey clay transforming into yellow clay. Physical, mineralogical, chemical and textural changes, as well as the weathering profile were investigated in a quarry of central Italy. Based on geological records and inferences, these changes are likely to have occurred within a time-span of about 50,000 years BP, upon overburden stress unloading and in a stress regime that is locally controlled by suction. Weathering propagated into the clay at a rate of about 0.3 mm/year and was enhanced by the enlargement of the pre-existing tectonic discontinuities and by the formation of new joints. A mass loss of about 22–25 wt.% was calculated. Considering Fe and P as immobile elements, the individual oxides contribute to mass loss in the following order: SiO₂ > CaO = CO₂ > Al₂O₃ > MgO > K₂O > S > Na₂O > TiO₂ > MnO. The Fe₂O₃ / (Fe₂O₃ + FeO) ratio varies from 9–29% in the blue-grey clay to 75–82% in the yellow one. Oxidation and/or dissolution of 7 Å-Fe²⁺-bearing clay minerals, mica-like minerals and calcite and parallel increase of smectite and Fe-hydroxides play a critical role in the chemical changes and explain the higher plasticity of the yellow clay with respect to the blue-grey one. The role of water during the weathering process was inferred to occur in cyclical steps: 1) seepage of meteoric water; 2) dissemination of highly oxidizing meteoric water; 3) triggering of oxidation and dissolution of minerals; 4) water evaporation; 5) partial migration of the elements contained in the aqueous solution and consequent deposition of minerals in the joints.     

循环荷载下非饱和结构性黏土的弹塑性双面模型

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。     

A hypoplastic model for clay and sand

The theory of hypoplasticity was developed initially for non-cohesive soils. However, sand and clay have many common properties; therefore arose the idea to extend the hypoplastic model to clay. The proposed model is able to describe the behaviour of cohesive soils with the incorporation of an appropriate structure tensor into the constitutive equation. This tensor is a stress-like internal parameter, also called back stress. This enables us to describe the behaviour of cohesive soils with the same material parameters for several states of consolidation and also to model barotropy and pycnotropy of sand. Numerical simulations of element tests are performed in order to check the performance of this hypoplastic model. Experimental data obtained with normally and overconsolidated clay and sand specimens with various densities are taken for comparison, and it is shown that the model is capable of describing the material behaviour of clay and sand. The determination of the material constants, the calibration method, is also presented in this paper.     

一种改进的粘土亚塑性本构模型

简要地介绍了Herle和Kolymbas针对黏土建立的亚塑性本构模型的方法。结合黏土的特性以及对响应包络线的分析,详细地列出了HK模型几个尚未解决的问题,并对该模型3个参数分别进行了改进,建立了改进后的HK亚塑性公式以及参数的确定方法。改进后的模型继承了HK模型参数少、易确定以及公式简洁等特点,使HK模型不仅具有严密的数学和力学基础,而且具有较好的实际意义。     

描述饱和黏性土应变软化的弹塑性双面模型

常规三轴压缩试验中具有较强结构性的黏性土在围压较低时其应力−应变关系会呈现应变软化现象,一般还伴有塑性变形,通常土体内部结构损伤是应变软化产生的主要原因。考虑到采用经典塑性理论描述材料的应变软化不仅会违背 Drucker 的稳定性假设,而且也不能描述卸载塑性。因此,基于修正剑桥模型及 Li 和 Meissner 提出的塑性硬化准则,建立了一个描述饱和黏性土不排水应变软化的弹塑性双面模型。该模型以应力−应变曲线的峰值点分界,将应变硬化和应变软化分别作为独立的加载事件进行分析,同时引入新的结构性参数表征剪切过程中土体结构损伤导致的塑性刚度衰退。对不同固结状态饱和结构性黏土的三轴固结不排水压缩试验结果的模拟表明,所建模型能够较好地描述饱和黏性土的不排水应变软化特性。