循环加-卸载岩石本构模型研究

循环加-卸载岩石本构模型是预测压气储能洞室长期稳定性的关键,但目前还没有适用的本构模型,因此,提出了一种能够描述岩石循环加载和卸载的本构模型。鉴于岩石在循环作用下损伤不断累积,将基于Weibull分布的岩石损伤软化模型进行拓展,并用内变量疲劳本构模型描述每个循环的初始模量和卸载模量的变化,进而得到循环加-卸载作用下的岩石本构模型,然后将该模型与现有的试验结果进行对比。该模型物理意义明确,涉及的参数较少,且便于拟合。提出的循环加-卸载下岩石本构模型对试验数据拟合效果较好,能较准确地反映循环荷载上、下限值对应的轴向应变,也能反映出循环内部变形模量衰减的趋势。该模型的成功建立为循环加-卸载下岩石本构模型的研究提供了新思路。     

Numerical modeling of cyclic mobility based on fuzzy-set concepts in plasticity theory

In this paper, the application of an efficient, transparent and accurate kinematic-cyclic constitutive model based on the fuzzy-set concepts and incremental plasticity theory is presented to show its capability in modeling cyclic mobility of saturated granular soil. The nature and kinematic mechanism of the membership functions in the fuzzy-set constitutive model are illustrated. The model’s capability of modeling soil dilatancy is investigated. Important features of volume change and pore water pressure build-up related to soil cyclic mobility are captured. The formulation of the proposed model is relatively simple and it can be readily implemented in finite element codes. The enhanced fuzzy-set model is capable of simulating ground motion problems particularly related to cyclic mobility, soil liquefaction, and spreading behavior.     

不同应力路径下饱和黏土耦合循环剪切特性

地基土单元体在波浪荷载的作用下将发生主应力轴连续旋转,这对土的强度和变形特性会产生显著的影响。针对饱和黏土,利用土工静力－动力液压三轴－扭转多功能扭剪仪进行了均等固结下的耦合循环剪切试验,着重研究了不同循环应力路径对应力-应变关系和强度特性的影响。试验结果表明,耦合循环荷载下黏土扭转剪切分量和正向偏差分量的应力-应变关系曲线与应力路径有关,且随着振动次数的增加逐渐疏松,割线模量 和 不断衰减,这与不固结不排水条件下的应力-应变关系曲线的变化规律明显不同;扭转剪切分量大的椭圆应力路径的动强度略小于正向偏差分量大的动强度。饱和黏土在不同应力路径下的力学特性的试验研究可以为建立复杂应力路径下的本构模型提供试验依据。     

A two-mechanism soil–structure interface model for three-dimensional cyclic loading

A three-dimensional (3D) soil–structure interface model is proposed within the two-mechanism constitutive theory and bounding surface theory originally established for soils. The proposed model has two main characteristics: first, the model is formulated based on two different and superposed deformation mechanisms. The first mechanism is due to the stress ratio increment, and the second is due to the normal stress increment. Each mechanism induces a shear strain component and a normal strain component. The proposed model can be reduced to the conventional single-mechanism interface model. Second, the plastic modulus and stress dilatancy are defined using the bounding surface theory. The plastic flow rule under cyclic loading is modified and assumed to be dependent on both the stress state of the mapping point and the stress reversal loading direction. The proposed model was validated against the available 3D interface tests and was found to satisfactorily reflect the salient features of the interfaces under monotonic and cyclic loading paths with different normal boundaries. The problem in which the elastic normal stiffness in conventional single-mechanism interface models is often underestimated to enhance the simulation performance under varying normal stress conditions is solved by incorporating the second mechanism. And the effect of the second mechanism on the modeling behavior is discussed. The modified plastic flow direction accurately simulates the 3D cyclic shear response, and the difference between the model simulation and test result increases with the number of cycles by use of the plastic flow direction defined in conventional bounding surface theory.     

考虑循环软化的非线性动力本构模型在FLAC3D中的实现

已有震害研究表明,震后边坡会因持续变形而破坏,且伴随着土体强度逐渐降低的现象,即土的循环软化行为。因此,有必要研究考虑循环软化的非线性动力本构模型以用于复杂条件下地震边坡稳定性分析。在已有的非线性动力本构模型基础上,提出了考虑循环软化的处理方法。同时,在FLAC3D平台上实现了本构模型二次开发,并通过了理论公式与已有文献中试验数据的验证。结果表明：计算出的骨干曲线与理论公式一致,且计算出的动剪切模量比及阻尼比与试验数据吻合较好,能够克服Hardin-Drnevich模型和Davidenkov模型在较大应变处（>0.01%）过高地估算阻尼比的缺陷;考虑了循环软化后,计算出的剪切强度有明显降低,且当遇到骨干曲线剪应力可以连续地过渡到软化后的主干曲线上,模型的收敛性较好。所开发的本构模型可为大应变条件下软土场地及边坡地震灾害评估提供支持。     

A NON-LINEAR SEISMIC RESPONSE ANALYSIS METHOD FOR SATURATED SOIL–STRUCTURE SYSTEM WITH ABSORBING BOUNDARY

A non-linear seismic response analysis method for 2-D saturated soil–structure system with an absorbing boundary is presented. According to the 3-D strain space multimechanism model for the cyclic mobility of sandy soil, a constitutive expression for the plane strain condition is first given. Next, based on Biot's two-phase mixture theory, the finite element equations of motion for a saturated soil–structure system with an absorbing boundary during earthquake loadings are derived. A simulation of the shaking table test is performed by applying the proposed constitutive model. The effectiveness of the absorbing boundary is examined for the 2-D non-linear finite element models subjected to random inputs. Finally, a numerical seismic response analysis for a typical saturated soil–structure system is performed as an application of the proposed method.     

Analysis of liquefaction susceptibility of nearly saturated sands

A new constitutive formulation for simulating the behaviour of nearly saturated sands under seismic loads is presented. The formulation is based on combining the Henry's law for dissolution of gas in water, the ideal or perfect gas law and the law of conservation of mass. The effects of transient air dissolution in water on the compressibility of partially saturated soils are also taken into account. The model was calibrated based on numerical simulations of isotropically consolidated cyclic triaxial tests conducted on partially saturated samples of Toyoura sand. A multi‐yield plasticity soil constitutive model implemented in the finite element code DYNAFLOW was used for these numerical simulations. It is shown that the formulation proposed here is able to reasonably predict the soil cyclic undrained behaviour at various degrees of saturation (95% and higher). Copyright © 2006 John Wiley & Sons, Ltd.     

Application of a Hill-Climbing technique to the formulation of a new cyclic nonlinear elastic constitutive model

In the field of constitutive modelling of soil behaviour, optimisation techniques have been mostly employed as a calibration tool, particularly when several model parameters lack clear physical meaning. In this paper, however, a procedure based on a Hill-Climbing optimisation algorithm is presented as a form of improving the performance of constitutive models. Specifically, a simple cyclic nonlinear elastic model, which is shown to be unable to simulate adequately the damping ratio measured under small and large strain amplitudes, is modified by applying the Hill-Climbing technique to the determination of a new relationship describing the unloading/reloading behaviour of soil under cyclic loading. The performance of the proposed model is assessed by evaluating its parameters based on three distinct sets of empirical damping ratio curves and computing the corresponding error in their simulation. It is shown that the introduction of the new unloading/reloading expression formulated based on the outcome of the optimisation procedure increases substantially the precision of the constitutive model.     

循环荷载下砂土的剪切硬化边界面本构模型

基于临界状态土力学框架,建立了一个适用于往返循环荷载作用的砂土边界面本构模型。采用无纯弹性域假设,认为受到反向荷载的瞬时土体就产生塑性变形,砂土的弹性区域退化为一个点。屈服面为倒子弹头型,由于砂土孔隙比与压力之间不存在惟一对应的关系,使得屈服面大小无法与体积应变直接耦合,故采用塑性偏应变而不是剑桥模型那种塑性体应变作为硬化参数。流动法则采用加入状态参数的修正的Rowe应力剪胀关系,体现了依赖状态的剪胀思想。屈服面大小的比值 反映了塑性模量的演化,并推导了 的表达式。只用1套参数,该模型就能合理地模拟砂土在不同密度和固结压力下循环荷载的应力-应变关系曲线。     

Liquefaction and cyclic mobility model for saturated granular media

A new constitutive law for the behaviour of undrained sand subjected to dynamic loading is presented. The proposed model works for small and large strain ranges and incorporates contractive and dilative properties of the sand into the unified numerical scheme. These features allow to correctly predict liquefaction and cyclic mobility phenomena for different initial relative densities of the soil. The model has been calibrated as an element test, by using cyclic simple shear data reported in the literature. For the contractive sand behaviour a well‐known endochronic densification model has been used, whereas a plastic model with a new non‐associative flow rule is applied when the sand tends to dilate. Both dilatancy and flow rule are based on a new state parameter, associated to the stiffness degradation of the material as the shaking goes on. Also, the function that represents the rearrangement memory of the soil takes a zero value when the material dilates, in order to easily model the change in the internal structure. Proceeding along this kind of approach, liquefaction and cyclic mobility are modelled with the same constitutive law, within the framework of a bi‐dimensional FEM coupled algorithm developed in the paper. For calibration purposes, the behaviour of the soil in a cyclic simple shear test has been simulated, in order to estimate the influence of permeability, frequency of loading, and homogeneity of the shear stress field on the laboratory data. Copyright © 2006 John Wiley & Sons, Ltd.     

An Elasto-Plastic Constitutive Model for Rock Joints Under Cyclic Loading and Constant Normal Stiffness Conditions

An elasto-plastic constitutive model is introduced for rock joints under cyclic loading, considering the additional shear resistance generated by the asperity damage in the first forward shear cycle and sliding mechanism for further shearing. A series of cyclic loading direct shear tests was conducted on artificial joints with triangular asperities and replicas of a real rock asperity surface under constant normal stiffness (CNS) conditions. The model was calibrated and then validated using selected data sets from the experimental results. Model simulations were found to be in good agreement with the rock joints behaviour under cyclic loading and CNS conditions both in stress prediction and dilation behaviour. In addition, dynamic stability analysis of an underground structure was carried out, using Universal Distinct Element Code and the proposed constitutive model.     

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。     

基于Hardin曲线的土体边界面本构模型在ADINA软件中的实现

为了提出一种适合于岩土地震数值模拟的土体本构模型,基于土体动应力-应变关系的Hardin曲线及其在非等幅往返荷载下的Pyke修正,采用von Mises准则在偏应力平面上构造边界面,以反向加载点和当前应力点的连线在边界面上投影的比例作为硬化参数,推导了塑性硬化模量并给出该边界面本构的具体增量表述。在有限元软件ADINA中通过自定义材料的二次开发实现了该本构模型,并利用动三轴试验对该本构模型进行了验证。数值模拟与试验结果的对比表明,本构模型能如实反映土体的应力-应变关系。针对实际工程场地的地震反应,应用边界面本构模型在ADINA中进行了二维数值模拟,与SHAKE91的计算结果进行了对比,说明了该本构模型应用于岩土地震工程问题的合理性。     

考虑孔压积累-消散耦合的等效有限元方法

交通荷载往复作用下饱和软土路基会发生显著的工后沉降,并引起不均匀沉降。采用基于室内循环三轴或空心圆柱扭转试验建立的经验显式模型与等效有限元相结合方式,在预测路基长期沉降方面取得了较好的效果。然而,其采用的瞬时积累、逐步消散的孔压模型与实际工程中孔压积累与消散同时进行有着明显的差异。忽略这种差异将会使得计算结果低于实际值。采用能反映自然排水条件下震动孔压长消规律的解析公式,对以上的不足作出改进,并用改进的孔压模型计算了上海浦东国际机场第一跑道的长期运营沉降。分析表明,与瞬时积累、逐步消散的孔压模型相比,考虑孔压积累与消散耦合效应的孔压模型,计算结果更接近实测资料。     

基于颗粒物质力学与连续介质热力学的岩土本构模型初探

首先简要介绍颗粒物质力学与模拟岩土材料本构特性的热力学方法,其次对力链及其对应的强弱网络的形成、力学特性与能量耗散特点与机制进行深入地分析,随后在Collins提出的土体热力学模型的基础上,考虑强弱网络结构的应力应变特征,引入合理的假设,探讨建立符合热力学原理的宏细观结合的岩土本构模型的思路与步骤     

A unified constitutive model for unsaturated soil under monotonic and cyclic loading

This study presents a sophisticated elastoplastic constitutive model for unsaturated soil using Bishop-type skeleton stress and degree of saturation as state variables in the framework of critical state soil mechanism. The model is proposed in order to describe the coupled hydromechanical behavior of unsaturated soil irrespective of what kind of the loadings or the drainage conditions may be. At the same time, a water retention characteristic curve considering the influence of deformation on degree of saturation is also proposed. In the model, the superloading and subloading concepts are introduced to consider the influences of overconsolidation and structure on deformation and strength of soils. The proposed model only employs nine parameters, among which five parameters are the same as those used in Cam-Clay model. The other four parameters have the clear physical meanings and can be easily determined by conventional soil tests. The capability and accuracy of the proposed model have been validated carefully through a series of laboratory tests such as isotropic loading tests and triaxial monotonic and cyclic compression tests under different mechanical and hydraulic conditions.

     

基于广义塑性力学的土体次加载面循环塑性模型(Ⅱ):本构方程与验证

按广义塑性力学原理，导出了土体次加载面循环塑性模型的本构方程，建立了相应的加卸载准则以及模型参数的确定方法。通过多种应力路径下土的本构响应的模拟，表明次加载面循环塑性模型能较好地反映循环荷载作用下土体呈现的非线性、滞回性与变形的积累性三方面主要特征，初步验证了模型的有效性。     

Clay minerals in fluvial shaley sandstone of upper Triassic reservoir (TAGS)—Toual field SE Algeria: identification from wireline logs and core data

The creep property of rock under cyclic loading is very important in civil engineering. In order to establish a novel constitutive equation for rock under cyclic loading, a fractional-order viscoplastic body under cyclic loading was constructed based on fractional-order viscous element. A fractional-order visco-elastoplastic model (FVEPM) for rock was established by connecting constructed fractional-order viscoplastic body with Burgers model. The model was a Burgers model when the maximum value of cyclic loading was less than the critical strength of rock; otherwise, it was a FVEPM which can be used to reflect the transient, steady-state, and tertiary creep phases of rock. The cyclic loading was decomposed into a static load and a cyclic loading with a zero average stress. According to rheological mechanics theory, the rheology constitutive equation of rock under the static load can be derived. According to viscoelastic mechanics theory, the constitutive equation under cyclic loading with a zero average stress was established by introducing the variation parameters of energy storage and energy dissipation compliance caused by rock damage and fracture. Finally, a new dynamic constitutive equation of rock cyclic loading can be obtained by superimposing the constitutive equation under static load and cyclic loading with a zero average stress. Compared with existing test results of rock under cyclic loading, the proposed constitutive model can be used to describe the creep characteristics of rock under cyclic loading and reflect the presented fluctuation of strain curve of rock under cyclic loading.     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

结构性土UH模型

在描述重塑土的统一硬化模型（UH模型）基础上,以动态地移动正常固结线（MNCL）代替静态的正常固结线（NCL）作为参考线来确定参考应力,将土的结构性衰减体现在MNCL的演化中,从而把UH模型扩展为可考虑土结构性的结构性土UH模型。结构性土UH模型可以合理地并连续光滑地描述结构性土的等向压缩规律、应变硬化、应变软化、剪切体积收缩、剪切体积膨胀、不排水剪切减压软化以及结构性和密度耦合影响等力学特性。相比于UH模型,结构性土UH模型新增3个参数,分别用于描述结构性的程度、衰减速度、以及塑性流动规律。通过3种天然土的试验结果与模型预测对比验证了结构性土UH 模型的合理性。