A hypoplastic constitutive model for debris materials

Debris flow is a very common and destructive natural hazard in mountainous regions. Pore water pressure is the major triggering factor in the initiation of debris flow. Excessive pore water pressure is also observed during the runout and deposition of debris flow. Debris materials are normally treated as solid particle–viscous fluid mixture in the constitutive modeling. A suitable constitutive model which can capture the solid-like and fluid-like behavior of solid–fluid mixture should have the capability to describe the developing of pore water pressure (or effective stresses) in the initiation stage and determine the residual effective stresses exactly. In this paper, a constitutive model of debris materials is developed based on a framework where a static portion for the frictional behavior and a dynamic portion for the viscous behavior are combined. The frictional behavior is described by a hypoplastic model with critical state for granular materials. The model performance is demonstrated by simulating undrained simple shear tests of saturated sand, which are particularly relevant for the initiation of debris flows. The partial and full liquefaction of saturated granular material under undrained condition is reproduced by the hypoplastic model. The viscous behavior is described by the tensor form of a modified Bagnold’s theory for solid–fluid suspension, in which the drag force of the interstitial fluid and the particle collisions are considered. The complete model by combining the static and dynamic parts is used to simulate two annular shear tests. The predicted residual strength in the quasi-static stage combined with the stresses in the flowing stage agrees well with the experimental data. The non-quadratic dependence between the stresses and the shear rate in the slow shear stage for the relatively dense specimens is captured.     

Modelling the time‐dependent behaviour of granular material with hypoplasticity

This paper presents a constitutive model for time‐dependent behaviour of granular material. The model consists of 2 parts representing the inviscid and viscous behaviour of granular materials. The inviscid part is a rate‐independent hypoplastic constitutive model. The viscous part is represented by a rheological model, which contains a high‐order term denoting the strain acceleration. The proposed model is validated by simulating some element tests on granular soils. Our model is able to model not only the non‐isotach behaviour but also the 3 creep stages, namely, primary, secondary, and tertiary creep, in a unified way.     

A stabilized extended finite element framework for hydraulic fracturing simulations

We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto‐plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction‐separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the ‘cubic’ law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak‐off model. We propose a ‘local’ U‐P (displacement‐pressure) formulation to discretize the fluid‐solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The ‘local’ U‐P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton‐Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projection method to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

基于CLoE与Gudehus-Bauer亚塑性模型的颗粒材料应变局部化对比研究

基于CLoE与Gudehus-Bauer亚塑性模型数值模拟了平面应变条件下Hostun砂的应变局部化现象。从侧向压力和初始缺陷两个方面对比研究了两种模型所预测应变局部化的产生及演化模式。结果表明：（1）两种模型均能反映Hostun砂刚度随着侧向压力提高而增大的现象。（2）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得出的应变局部化形态与试验结果更加一致。（3）CLoE亚塑性模型能够反映随着荷载增加,砂的体积先膨胀后缩小的特点。（4）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得到的应变-应力曲线能够更明显地反映应变局部化带中单元的软化现象。（5）CLoE亚塑性模型能够更好地模拟由初始缺陷导致的不均匀应变。总的来说,所得的数值结果表明,CLoE亚塑性模型能够较好地模拟侧向压力和初始缺陷对应变局部化的影响,在模拟应变局部化现象方面较Gudehus-Bauer更有优势。然而,现有CLoE亚塑性模型无法考虑孔隙比,也未包含颗粒材料内尺度变量,有待进一步完善。     

A 1D Hypoplastic constitutive model for expansive soils

This paper presents a simple hypoplastic constitutive model that describes the essential features of the material behaviour of partially saturated clayey soils observed in oedometric compression tests. The model is formulated in terms of net stress and degree of saturation. The total strain rate is decomposed into a portion related to the changes in saturation and a portion for the evolution of net stress. However, no distinction is made between plastic and elastic strains. With this strain rate decomposition, the maximum swelling strain/stress are obtained by simulating wetting processes under constant stress/strain conditions. In addition to the void ratio, the model includes two scalar variables to track the loading history (preloading). The calibration of the model constants using common laboratory tests is discussed. Confined and unconfined swelling tests under oedometric conditions with subsequent loading and unloading phases carried out on three different materials were satisfactorily simulated by the model. Its promising results call for an extension to a 3D formulation.

     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

堆石料Gudehus-Bauer亚塑性本构模型改进及参数确定方法

研究了Gudehus-Bauer亚塑性本构模型和模型参数的求取方法。采用侧限压缩试验曲线求取模型参数颗粒硬度hs和指数n。根据模型方程的推导,建立了拟合指数 和 与围压之间的关系,并提出了新的拟合参数。考虑到堆石料具有明显的剪胀、剪缩性,在Gudehus-Bauer模型线性项中增加了主要控制体积应变项 ,以改善模型对堆石料体积应变曲线的描述。采用堆石料大型侧限压缩试验、常规三轴试验分别验证了新的拟合参数和改进后的Gudehus-Bauer亚塑性本构模型。与堆石料试验成果比较,提出的新拟合参数与改进后的Gudehus-Bauer亚塑性本构模型可以较好地模拟堆石料的应力-应变特性,并较好地改善了堆石料体变曲线的模拟结果。对改进后的模型作了常规三轴加、卸载模拟,模拟结果反映了改进的Gudehus-Bauer亚塑性本构模型具有一定的卸载适应性。     

Predictions of a continuous hyperplasticity model for Bangkok clay

The performance of a new constitutive model called ‘kinematic hardening modified Cam clay’ (KHMCC) is presented. The model is described using the ‘continuous hyperplasticity’ framework. Essentially this involves an infinite number of yield surfaces, thus allowing a smooth transition between elasticity and plasticity. The framework allows soil models to be developed in a relatively succinct mathematical form, since the entire constitutive behaviour can be determined through the specification of two scalar potentials. An implementation of the continuous hyperplasticity model is also described. The model requires eight parameters plus a viscosity coefficient for rate-dependent analysis. The model is defined in terms of triaxial stress–strain variables for this study, and is used to model monotonic triaxial tests on Bangkok clay. Comparisons of the theoretical predictions with the results of cyclic undrained triaxial compression tests on Bangkok clay are also presented.     

Unified modelling of granular media with Smoothed Particle Hydrodynamics

In this paper, we present a unified numerical framework for granular modelling. A constitutive model capable of describing both quasi-static and dynamic behaviours of granular material is developed. Two types of particle interactions controlling the mechanical responses, frictional contact and collision, are considered by a hypoplastic model and a Bagnold-type rheology relation, respectively. The model makes no use of concepts like yield stress or flow initiation criterion. A smooth transition between the solid-like and fluid-like behaviour is achieved. The Smoothed Particle Hydrodynamics method is employed as the unified numerical tool for both solid and fluid regimes. The numerical model is validated by simulating element tests under both quasi-static and flowing conditions. We further proceed to study three boundary value problems, i.e. collapse of a granular pile on a flat plane, and granular flows on an inclined plane and in a rotating drum.     

A basic hypoplastic constitutive model for sand

Hypoplastic constitutive models are based on nonlinear tensor functions and are characterized by simple formulation and few parameters. In its early stage, mainly basic hypoplastic constitutive equations were concerned, where the stress tensor is assumed as the only state variable. There followed some enhanced models based on the basic constitutive equation by including void ratio as an additional state variable. In this paper, we first show that the widely used hypoplastic model by Wolffersdorff is seriously flawed because the underlying basic equation does not perform properly. We proceed to develop a basic hypoplastic constitutive equation by introducing a new tensorial term, which preserves the critical state at large strain. The model performance is demonstrated by parameter study for some element tests. This simple and robust basic equation is well suited to build more sophisticated models.     

The effect of heterogeneous stress and strain on metamorphic fluid flow,Mary Kathleen,Australia, and a model for large-scale fluid circulation *

In the Proterozoic Mary Kathleen Fold Belt, northern Australia, infiltration of large volumes of externally derived fluid occurred synchronously with regional amphibolite-facies metamorphism and deformation. This paper develops a model of structurally controlled fluid migration by comparing the distribution of fossil fluid pathways with the inferred stress and strain patterns during the deformation. Intense fluid flow was localized within strong, relatively brittle meta-intrusive bodies, and in discrete, veined, brecciated and altered zones around their margins. In metasediments folded in a ductile manner outside these areas, fluid infiltration was negligible. The direct correlation between structural styles and the magnitude of veining and metasomatism suggests control of permeability enhancement, and hence fluid flow, by deformation. Finite difference modelling of a strong body in a weaker matrix has been used to evaluate the variation of stresses during the deformation, from which it is clear that stress and strain heterogeneities have systematically influenced the development and maintenance of metamorphic fluid pathways. Particular regions in which mean stress may be significantly lower than the average lithostatic pressures include the ‘strain shadow’zones adjacent to the strong bodies, other dilatant zones around the bodies, and the bodies themselves. This geometry is favourable not only for localized brittle deformation under amphilobite facies conditions, but also for focused fluid flow in the low mean stress regions, as evidenced by the abundance of veins. Fluid access through these metamorphic aquifers occurred during tensile failure episodes, with particularly large dilations and decimetre-scale veining in areas of strain incompatibility. It appears likely that fluid circulated many times through the Fold Belt, with flow concentrated in the metamorphic aquifers. A model is developed that explains both the structurally focused fluid flow and the postulated multi-pass recirculation by dilatancy pumping, the ‘pump engines’comprising the low mean stress zones.     

An intergranular strain concept for material models formulated as rate equations

The intergranular strain concept was originally developed to capture the small-strain behaviour of the soil with hypoplastic models. A change of the deformation direction leads to an increase of the material stiffness. To obtain elastic behaviour for smallstrains, only the elastic part of the material stiffness matrix is used. Two different approaches for an application of this concept to nonhypoplastic models are presented in this article. These approaches differ in the determination of the elastic stress response, which is used for reversible deformations. The first approach determines an elastic response from the original material model, and the second one uses an additional elastic model. Both approaches are applied on barodesy. The simulations are compared with experimental results and with simulations using hypoplastic models with the original intergranular strain concept.     

Simplified numerical modelling of pile penetration – the press‐replace technique

This paper presents a simplified finite element analysis technique, the ‘Press‐Replace’ technique, to model pile penetration problems in geotechnical engineering, particularly, pile jacking. The method is employed in standard finite element analysis software. The method involves a straining and a consequent geometry update phase. First, a cone penetration test in (undrained) clay is modelled and compared with the results of analytical, semi‐analytical and more advanced finite element techniques. The model sensitivity for the step size and mesh is investigated using a hypoplastic constitutive model. An optimum way of modelling based on the numerical performance is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

Primary Ore Mineral Assemblage and Fluid Inclusion Study of the Batu Hijau Porphyry Cu-Au Deposit, Sumbawa, Indonesia

Abstract. The Batu Hijau porphyry Cu‐Au deposit, Sumbawa Island, Indonesia, is associated with a tonalitic intrusive complex. The temperature‐pressure condition of mineralization at the Batu Hijau deposit is discussed on the basis of fluid inclusion microthermometry. Then, the initial Cu‐Fe sulfide mineral assemblage is discussed. Bornite and chalcopyrite are major copper ore minerals associated with quartz veinlets. The quartz veinlets have been classified into ‘A’ veinlets associated with bornite, digenite, chalcocite and chalcopyrite, ‘B’ veinlets having chalcopyrite bornite along vuggy center‐line, rare ‘C’ chalcopyrite‐quartz veinlets, and late ‘D’ veinlets consisting of massive pyrite and quartz (Clode et al., 1999). Copper and gold mineralization is associated with abundant ‘A’ quartz veinlets. Abundant fluid inclusions are found in veinlet quartz consisting mainly of gas‐rich inclusions and polyphase inclusions throughout the veinlet types. The hydrothermal activity occurred in temperature‐pressure conditions of aqueous fluid immiscibility into hypersaline brine and dilute vapor. The halite dissolution (Tm[halite]) and liquid‐vapor homogenization (Th) temperatures of the polyphase inclusions in veinlet quartz range from 270 to 472d?C and from 280 to 454d?C, respectively. The estimated salinity ranges from 36 to 47 wt% (NaCl equiv.). The apparent pressures lower than 300 bars are estimated to have been along the liquid‐vapor‐halite curve for the fluid inclusions having the Th lower than the Tm that trapped the brine saturated with halite, or at slightly higher pressure relative to liquid‐vapor‐halite curve for the fluid inclusions having the Th higher than the Tm that trapped the brine unsaturated with halite. The actual temperature and pressure during the hydrothermal activity at the Batu Hijau deposit are estimated to have been around 300d?C and 50 bars. At such temperature‐pressure conditions, the principal and initial Cu‐Fe sulfide mineral assemblages are thought to be chalcopyrite + bornite solid solution (bnss) for the chalcopyrite‐bearing assemblage, and chalcocite‐digenite solid solution and bnss for the chalcopyrite‐free assemblage.     

Numerical modelling of dynamic consolidation on granular soils

The application of Pastor–Zienkiewicz constitutive model for sands to dynamic consolidation problems is presented in this paper. This model is implemented in a coupled code formulated in terms of displacements for both solid and fluid phases (u?w formulation), which is firstly compared with u?p_w formulation for some simple examples. Its range of validity, previously established for elastic problems and harmonic loading, is explored. Once the suitability of the u?w formulation has been ascertained for this kind of dynamic problems in soils, one‐ and two‐dimensional (plane strain) dynamic consolidation numerical examples are provided, aiming to give some light into the physics of this ground improvement technique. A ‘wave of dryness’, observed at the soil surface during the impact in field cases, is numerically reproduced and justified. Some hints on the influence of the loading zone size are also given. Copyright © 2007 John Wiley & Sons, Ltd.     

Hypoplastic modelling of moisture-sensitive weathered rockfill materials

For broken rock materials under stress the process of weathering and consequently the degradation of the solid hardness may be accelerated under water. Thus, the resistance of particles against abrasion and breakage can be strongly influenced by a change of the moisture content of the grains. The focus of this paper is on modelling the essential mechanical properties of moisture-sensitive weathered coarse-grained rockfill materials using a hypoplastic constitutive model. The model takes into account the current void ratio, the effective stress, the strain rate and a moisture-dependent degradation of the solid hardness. Creep and stress relaxation during the process of degradation of the solid hardness are also included. It is shown that the results obtained from numerical simulations are in good agreement with experiments carried out with weathered granite.     

二氧化碳注入下岩层变形和流体运移分析:(Ⅱ)实例分析

第I部分[1]提出了一个两相流-岩层流固耦合模型,为了应用该模型对超临界二氧化碳注入过程中岩层力学响应和流体运移进行评估,采用Comsol商业程序,提出了相应的数值分析方法。给出了模型参数的确定方法,并采用室内试验数据对模型进行了验证;通过现场的温度和压力条件以及岩层的Van Genuchten参数,确定了二氧化碳的密度和黏度。基于三轴压缩试验、有效应力系数试验和渗透性试验,对力学模型及耦合关系中的参数进行了验证。最后给出一个应用实例,该岩层位于地下680⁷00 m深度,宽度为100 m,分析了不同二氧化碳注入速率下注入压力的演化规律,得到了岩层中孔隙压力、竖向应变和损伤变量的分布,并对二氧化碳的运移规律也进行了分析。研究结果为超临界二氧化碳注入过程中岩层力学响应和流体运移的评估提供了理论基础。     

A dilatant,two-layer debris flow model validated by flow density measurements at the Swiss illgraben test site

We propose a dilatant, two-layer debris flow model validated by full-scale density/saturation measurements obtained from the Swiss Illgraben test site. Like many existing models, we suppose the debris flow consists of a matrix of solid particles (rocks and boulders) that is surrounded by muddy fluid. However, we split the muddy fluid into two fractions. One part, the inter-granular fluid, is bonded to the solid matrix and fills the void space between the solid particles. The combination of solid material and inter-granular fluid forms the first layer of the debris flow. The second part of the muddy fluid is not bonded to the solid matrix and can move independently from the first layer. This free fluid forms the second layer of the debris flow. During flow the rocky particulate material is sheared which induces dilatant motions that change the location of the center-of-mass of the solid. The degree of solid shearing, as well as the amount of muddy fluid and of solid particles, leads to different flow compositions including debris flow fronts consisting of predominantly solid material, or watery debris flow tails. De-watering and the formation of muddy fluid washes can occur when the solid material deposits in the runout zone. After validating the model on two theoretical case studies, we show that the proposed model is able to capture the streamwise evolution of debris flow density in time and space for real debris flow events.

     

A comparative study of the hypoplasticity and the fabric‐dependent dilatant double shearing models for granular materials

In this paper, we consider the mechanical response of granular materials and compare the predictions of a hypoplastic model with that of a recently developed dilatant double shearing model which includes the effects of fabric. We implement the constitutive relations of the dilatant double shearing model and the hypoplastic model in the finite element program ABACUS/Explicit and compare their predictions in the triaxial compression and cyclic shear loading tests. Although the origins and the constitutive relations of the double shearing model and the hypoplastic model are quite different, we find that both models are capable of capturing typical behaviours of granular materials. This is significant because while hypoplasticity is phenomenological in nature, the double shearing model is based on a kinematic hypothesis and microstructural considerations, and can easily be calibrated through standard tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Validation of Hyperbolic Model by the Results of Triaxial and Direct Shear Tests of Municipal Solid Waste

The increasing demand of engineering landfills requires that designers propose a framework for landfill design, construction, repair and maintenance. As municipal solid waste (MSW) is a major part of a landfill, the analysis should consider MSW mechanical behavior using a constitutive model. To investigate this, 18 direct shear (DS) and triaxial (TX) tests were conducted on MSW samples with different fiber contents. Different shearing mechanisms lead to understand effects of fibers on stress–strain response. Based on obtained results the hyperbolic model Duncan and Chang (J Soil Mech Found Div 96(5):1629–1653, 1970) has been employed to simulate the TX results indicating the ability of the model to predict stress–strain behavior of MSW. This model could also be employed to the DS test results with some assumptions. The model can capture DS stress–strain response well whereas for TX tests the predictions were just enough. The experimental results and two sets of proposed MSW parameters of hyperbolic model have been compared and discussed.