Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste,an underground research laboratory(URL)was constructed by Andra in the Callovo-Oxfordian(COx)claystone formation at the Meuse/Haute-Marne(MHM).The construction of URL induced the excavation damage of host formations,and the ventilation in the galleries desaturated the host formation close to the gallery wall.Moreover,it is expected that the mechanical behaviour of COx claystone is time-dependent.This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone.In this model,the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten(VG)water retention model.In terms of the viscoplastic behaviour,the nonstationary flow surface(NSFS)theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress.A progressive hardening law is adopted.Meanwhile,a non-associated flow rule is used,which is similar to that in Barcelona basic model(BBM).In addition,to describe the damage effect induced by suction change and viscoplastic loading,a damage function is defined based on the crack volume proportion.This damage function contains two variables:unsaturated effective stress and viscoplastic volumetric strain,with the related parameters determined based on the mercury intrusion porosimetry(MIP)tests.For the model validation,different tests on COx claystone under different loading paths are simulated.Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone,including swelling/shrinkage,triaxial extension and compression,and triaxial creep.

A STUDY OF B-P UNIFIED VISCOPLASTIC CONSTITUTIVE MODEL

By combining the Bodner-Partom constitutive model and equivalent stressfunction, finite element methods and program on analyzing non-elastic deformation and stress forthermal viscoplastic material are studied in this paper, and it's the first time that this materialmodel is used in a kind of engineering software-MARC. Thermal viscoplastic behavior of hightemperature alloy GH536 specimen with gap is analyzed by this program. The research results show itis feasible to analyze thermal viscoplastic behavior of specimen or structure by applying B-P model.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS

Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior＇s material properties （e.g. strain rate sensitivity） characterize the competitions between plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.

A nonlinear creep model for surrounding rocks of tunnels based on kinetic energy theorem

The initiating condition for the accelerated creep of rocks has caused difficulty in analyzing the whole creep process.Moreover,the existing Nishihara model has evident shortcomings in describing the accelerated creep characteristics of the viscoplastic stage from the perspective of internal energy to analyze the mechanism of rock creep failure and determine the threshold of accelerated creep initiation.Based on the kinetic energy theorem,Perzyna viscoplastic theory,and the Nishihara model,a unified creep constitutive model that can describe the whole process of decaying creep,stable creep,and accelerated creep is established.Results reveal that the energy consumption and creep damage in the process of creep loading mainly come from the internal energy changes of geotechnical materials.The established creep model can not only describe the viscoelasticeplastic creep characteristics of rock,but also reflect the relationship between rock energy and creep deformation change.In addition,the research results provide a new method for determining the critical point of creep deformation and a new idea for studying the creep model and creep mechanical properties.

Viscoplastic solutions of time-dependent deformation for tunnels in swelling rock mass considering stress release

Excavation and control of tunneling responses in swelling soft-rock tunnels of Sichuan-Tibet railway under seepage conditions were studied.For this,a fractional viscoplastic(FVP)model for swelling soft rocks was established by introducing Abel dashpot and unsteady viscosity coefficient,considering additional swelling deformation and damage of rock caused by humidity effect.In view of the FVP model,the viscoplastic deformation solutions for rock mass surrounding tunnel under seepage conditions were derived and long-term mechanical responses of swelling rocks upon tunnel excavation were analyzed.Next,a stress release coefficient considering seepage and creep was proposed,based on which control responses considering stress release and failure mechanism of stress release measures were analyzed.The results showed that:(i)The one-dimensional(1D)FVP model has a good application for swelling rock and the three-dimensional(3D)FVP model could well describe the whole creep process of rock mass despite a much higher creep attenuation rate in the first stage of creep;and(ii)An appropriate stress release and deformation of surrounding rocks could effectively reduce the supporting resistance.However,upon a large stress release,the radius of plastic region could increase significantly,and the strength of the surrounding rock mass decreases greatly.The proposed solution could provide a theoretical framework for capturing the excavation and support responses for tunneling in swelling rock mass in consideration of time effect.

Modeling and Numerical Simulation of Yield Viscoplastic Fluid Flow in Concentric and Eccentric Annuli

Numerical solution of yield viscoplastic fluid flow is hindered by the singularity inherent to the Herschel-Bulkley model. A finite difference method over the boundary-fitted orthogonal coordinate system is util- ized to investigate numerically the fully developed steady flow of non-Newtonian yield viscoplastic fluid through concentric and eccentric annuli. The fluid rheology is described with the Herschel-Bulkley model. The numerical simulation based on a continuous viscoplastic approach to the Herschel-Bulkley model is found in poor accordance with the experimental data on volumetric flow rate of a bentonite suspension. A strict mathematical model for Herschel-Bulkley fluid flow is established and the corresponding numerical procedures are proposed. However, only the case of flow of a Herschel-Bulkley fluid in a concentric annulus is resolved based on the presumed flow stnicture by using the common optimization technique. Possible flow structures in an eccentric afinulus are presumed, and further challenges in numerical simulation of the Herschel-Bulkley fluid flow are suggested.

A VISCOPLASTIC MODEL BASED ON NO-YIELD-SURFACE CONCEPT

The elasticjviscoplastic constitutive equation which describes deformation law of metal materials was suggested based on no-yield-surface concept and thermal activation theory of dislocation. The equation which takes account of effects of strain-rate, strain history, strain-rate history, hardening and temperature has stronger physical basis.Comparison of the theoretical prediction with experimental results of mechanical behaviours of Ti under conditions of uniaxial stress and room temperature shows good consistency.

锚固条件下煤系地层裂隙岩体蠕变力学特性研究

为探究煤系地层裂隙岩体锚固状态下的蠕变特性,开展不同裂隙倾角(15°、30°、45°、60°、90°)下裂隙加锚试件、裂隙无锚试件、完整试件的单轴蠕变试验。试验结果表明:相同应力加载等级时,裂隙无锚试件的瞬时应变量大于完整试件的瞬时应变量,而裂隙加锚试件与完整试件的瞬时应变量之差随着裂隙倾角的增加逐渐减小;随着应力加载等级的增加,各岩石试件的稳态蠕变量也逐级增大;含裂隙试件的稳态蠕变速率随着裂隙倾角增大呈先下降再上升的趋势,但裂隙加锚试件的稳态蠕变速率小于相同应力等级下裂隙无锚试件的稳态蠕变速率;在裂隙倾角较低时,裂隙无锚试件和裂隙加锚试件的裂纹贯通发展规律差异较大;基于CVISC蠕变模型进行参数反演,得出Maxwell和Kelvin相关系数随应力加载等级的变化趋势;采用应力-应变等时曲线法和非稳定流变判别法研究裂隙试件的长期强度变化规律。该研究结果为煤矿巷道长期稳定性分析及锚杆支护方案提供了试验依据。

基于损伤力学分析的汽轮机转子寿命损耗计算方法

在ANSYS有限元软件中使用耦合损伤的Chaboche黏塑性本构模型对1000 MW超超临界汽轮机转子在不同起动工况下的热机械力学响应进行了数值模拟。基于转子表面危险区域应力和损伤的分析结果,建立了汽轮机起动参数与转子最大损伤之间的函数关系,并以此提出了一种适用于复杂起动及升负荷工况下的转子寿命损耗计算方法。结果表明:在标准起动工况下模型计算结果与汽轮机寿命损耗分配表中的数据基本一致,验证了模型的有效性;采用所提方法后,对实际起动曲线进行简单处理,可快速计算出转子的寿命损耗率以及危险区域的热应力。

GH4169合金多轴热机械粘塑性本构模型及验证

为了更加精确地描述GH4169合金的多轴热机械力学行为,以Chaboche粘塑性本构模型为基础,引入了Lemaitre损伤模型、基于临界面理论的非比例强化因子和粘塑性势函数修正系数,提出建立了一种适用于GH4169合金的多轴热机械疲劳粘塑性本构模型,来描述材料的循环软化、非比例硬化和非玛辛效应,并给出了本构模型各参数的获取方法。采用此本构模型,对GH4169合金的多轴和热机械力学行为进行了模拟研究,结果表明:在20℃时,分别对轴向加载、扭转加载、比例加载、45°非比例加载以及90°非比例加载这5种加载条件下的第200次循环的迟滞回线进行模拟,轴向的应力峰谷值均与试验值结果吻合;在650℃时,模拟比例加载、45°非比例加载和90°非比例加载这3种加载条件下的第200次循环的迟滞回线,结果与试验值基本吻合,证明了建立的模型适用于高温条件;模拟300℃、550℃和650℃这3种温度下的单轴轴向加载和圆形路径加载的迟滞回线,结果与试验值基本吻合;模拟同相位与反相位加载条件下的第200次循环迟滞回线,修正后的本构模型的模拟值与试验值吻合良好。

基于触发式黏塑性元件的黏性土黏弹塑性动本构模型

基于黏性、弹性和塑性元件构造的动本构模型往往存在预测效果较差,不能完全反映黏性土的黏性、弹性、塑性的缺点。通过引入一种触发式的黏塑性元件Ψ,以残余变形为切入点,提出了一个考虑振动稳定和振动衰化现象的黏性土黏弹塑性动本构模型,并通过动三轴试验进行了验证。该动本构模型不但能够描述动荷载作用下黏性土残余应变的发展规律,且能合理地预测动应变的发展情况。结果表明,试样在动荷载作用下,存在元件Ψ的黏滞系数随振动周期增长而衰减的现象,且衰减情况和含水率密切相关。最优含水率是影响振动稳定和振动衰化现象的重要参数,当含水率小于最优含水率时,试样变形表现为振动稳定,此时元件Ψ黏滞系数的变化可以忽略不计;当含水率大于最优含水率时,试样变形表现为振动衰化,此时元件Ψ黏滞系数的变化不可忽略。

考虑基质吸力的非饱和土弹黏塑性本构模型

为了描述可控基质吸力下的非饱和土时效变形特征,提出一种考虑非饱和土基质吸力影响的弹黏塑性本构模型。新模型借鉴BBM模型对压缩特征曲线进行修正,给出非饱和土的压缩指数与基质吸力的关系函数,并将该指数引入到能描述土体超固结的下负荷模型,得到非饱和土的修正下负荷面;又以该下负荷面为参考屈服面,利用相对应力关系,建立了非饱和超固结土的弹黏塑性本构模型,并通过非饱和的三轴率敏性试验确定新模型中两个时效参数m′和c_(0)。结果表明:①模型能较好地表征非饱和土超固结比、基质吸力对其变形特征的影响;②由非饱和土的三轴率敏性试验确定的模型参数能较好地模拟其蠕变等时效变形。

Intelligent back analysis of geotechnical parameters for time-dependent rock mass surrounding mine openings using grey Verhulst model

In this paper,we present a new method of intelligent back analysis(IBA)using grey Verhulst model(GVM)to identify geotechnical parameters of rock mass surrounding tunnel,and validate it via a test for a main openings of−600 m level in Coal Mine“6.13”,Democratic People's Republic of Korea.The displacement components used for back analysis are the crown settlement and sidewalls convergence monitored at the end of the openings excavation,and the final closures predicted by GVM.The non-linear relation between displacements and back analysis parameters was obtained by artificial neural network(ANN)and Burger-creep viscoplastic(CVISC)model of FLAC3D.Then,the optimal parameters were determined for rock mass surrounding tunnel by genetic algorithm(GA)with both groups of measured displacements at the end of the final excavation and closures predicted by GVM.The maximum absolute error(MAE)and standard deviation(Std)between calculated displacements by numerical simulation with back analysis parameters and in situ ones were less than 6 and 2 mm,respectively.Therefore,it was found that the proposed method could be successfully applied to determining design parameters and stability for tunnels and underground cavities,as well as mine openings and stopes.

Finite element modelling of the geodynamic processes of the Central Andes subduction zone:A Reference Model

This paper presents preliminary results of three-dimensional thermomechanical finite-element models of a parameter study to compute the current temperature and stress distribution in the subduction zone of the central Andes （16°S-26°S） up to a depth of 400 km, the bottom of the asthenosphere. For this purpose a simulation running over c. 50,000 years will be realized based on the geometry of a generic subduction zone and an elasto-viscoplastic Drucker-Prager rheology. The kinematic and thermal boundary conditions as well as the rheological parameters represent the current state of the study area. In future works the model will be refined using a systematic study of physical parameters in order to estimate the influence of the main parameters （e.g. viscosity, fault friction, velocity, shear heating） on the results of the reference model presented here. The reference model is kept as simple as possible to be able to estimate the influence of the parameters in future studies in the best possible way, whilst minimizing comnutational time.

DISSIPATION-BASED CONSISTENT RATE-DEPENDENT MODEL FOR CONCRETE

An energy-dissipation based viscoplastic consistency model is presented to describe the performance of concrete under dynamic loading. The development of plasticity is started with the thermodynamic hypotheses in order that the model may have a sound theoretical background. Independent hardening and softening and the rate dependence of concrete are described separately for tension and compression. A modified implicit backward Euler integration scheme is adopted for the numerical computation. Static and dynamic behavior of the material is illustrated with certain numerical examples at material point level and structural level, and compared with existing experimental data. Results validate the effectiveness of the model.

3-D consistency dynamic constitutive model of concrete

Based on the consistency-viscoplastic constitutive model,the static William-Warnke model with three-parameters is modified and a consistency-viscoplastic William-Warnke model with three-parameters is developed that considers the effect of strain rates. Then,the tangent modulus of the consistency viscoplastic model is introduced and an implicit backward Elure iterative algorithm is developed. Comparisons between the numerical simulations and experimental data show that the consistency model properly provides the uniaxial and biaxial dynamic behaviors of concrete. To study the effect of strain rates on the dynamic response of concrete structures,the proposed model is used in the analysis of the dynamic response of a simply-supported beam and the results show that the strain rate has a significant effect on the displacement and stress magnitudes and distributions. Finally,the seismic responses of a 278 m high arch dam are obtained and compared by using the linear elastic model,as well as rate-independent and rate-dependent William-Warnke three-parameter models. The results indicate that the strain rate affects the first principal stresses,and the maximal equivalent viscoplastic strain rate of the arch dam. Numerical calculations and analyses reveal that considering the strain rate is important in the safety assessments of arch dams located in seismically active areas.

Comparative Study on Constitutive Modeling of Tantalum and Tantalum Tungsten Alloy

As a model bee metal, tantalum and its alloys have wide applications in defense-related fields. The KHL （Khan, Huang, Liang, 1999） model and the constitutive model proposed by Nemat-Nasser et al （Nemat-Nasser and Kapoor, 2001） for tantalum and its alloys were analyzed and compared with each other. A set of published data recorded during elastic-plastic deformations of tantalum, tantalum alloy containing tungsten of 2.5% （Ta-2.5W）, over a wide range of strains, strain rates, and temperatures were used to correlate the two models. Overall, it can be concluded that KHL model correlates much better with the data than the model used by Nemat-Nasser et al.

On a Constitutive Material Model to Capture Time Dependent Behavior of Cortical Bone

It is commonly known that cortical bone exhibits viscoelastic-viscoplastic behavior which affects the biomechanical response when an implant is subjected to an external load. In addition, long term effects such as creep, relaxation and remodeling affect the success of the implant over time. Constitutive material models are commonly derived from data obtained in in vitro experiments. However during function, remodeling of bone greatly affects the bone material over time. Hence it is essential to include long term in vivo effects in a constitutive model of bone. This paper proposes a constitutive material model for cortical bone incorporating viscoelasticity, viscoplasticity, creep and remodeling to predict stress-strain at various strain rates as well as the behavior of bone over time in vivo. The rheological model and its parameters explain the behavior of bone subjected to longitudinal loading. By a proper set of model parameters, for a specific cortical bone, the present model can be used for prediction of the behavior of this bone under specific loading conditions. In addition simulation with the proposed model demonstrates excellent agreement to in vitro and in vivo experimental results in the literature.

基于热-水-力数值模拟的饱和正常固结黏土热压缩现象

既有饱和正常固结土体加热试验研究表明,温度升高时,土体的体积变化表现为体积收缩,这与热胀冷缩基本通识相违背。针对这一问题,通过热-水-力(THM)完全耦合有限元程序对饱和正常固结黏土的加热试验进行了数值模拟。结果表明,由于黏土的热传导系数及渗透系数都比较低,在升温过程中,试样内部会形成温度差,进而产生超孔隙水压,随着超孔隙水压的消散,最终使土体表现为热压缩现象。当增大土体的渗透系数时,土体内部不产生超孔隙水压,这时土体表现为热膨胀。因此,饱和正常固结土体升温引起的热压缩现象并非土体基本力学特性,而是一个边界值问题。