A constitutive law for rock salt based on creep and relaxation tests

Summary The paper deals with uniaxial relaxation tests on rock salt which are the basis for a constitutive equation. Since so far no regard was paid to relaxation behaviour, corresponding test results are not available and hence a special device for performing of uniaxial relaxation tests had to be constructed. Some interesting test results are discussed in the paper. These results are useful for the verification of constitutive equations. A critical analysis of conventional constitutive laws and their fundamentals shows that these material laws have considerable imperfections and are rested on substantial restrictions. Particularly, they are not able to describe relaxation behaviour sufficiently. Consequently, a constitutive law is proposed consisting of a strain hardening approach with separate creep and relaxation functions. By post-calculation of different laboratory tests it could be shown that in comparison to conventional steady-state creep equations this material law describes the viscous behaviour of rock salt more realistically.     

盐岩蠕变特性和本构关系研究

对金坛盐岩蠕变规律进行了试验研究,分析了不同应力状态和温度对盐岩蠕变特性的影响,通过试验获取了蠕变曲线和蠕变特征参数。根据其蠕变曲线特征,用黏弹塑性理论建立了盐岩蠕变本构模型。试验结果表明,稳态蠕变率是偏应力和温度的非线性函数关系,并提出盐岩的稳态蠕变本构方程。通过试验数据拟合得到本构方程中的参数,将理论和试验结果进行比较,结果表明两者的吻合性较好。     

深部盐岩蠕变特性研究

通过对湖北云应的盐岩和泥岩,以及江苏金坛盐岩的单轴、三轴蠕变试验结果的分析,研究了包括应力、围压等外在条件以及内部组成结构对盐岩蠕变特性的影响。发现盐岩无论在何种围压下,稳态蠕变率都随偏应力的增加而显著地增大;围压起到限制变形的作用,而随着围压增高,围压对稳态蠕变率的影响越来越小;晶粒越大和杂质含量越多,盐岩的蠕变属性越弱。盐岩的蠕变变形是应变硬化和回复效应等内部变形机制共同作用的结果,选用内应力作为内变量可用来描述这种内部微观结构的演化过程。对云应盐岩的多级加载蠕变试验数据进行拟合,确定了非线性蠕变本构方程中的参数,理论与试验结果的比较表明,两者吻合性较好。     

盐岩储气库蠕变损伤分析

通过对盐岩本构关系的实验研究,对Norton Power 盐岩蠕变本构模型引入损伤变量,在损伤等效应力中引入考虑偏应力和围压影响的函数,建立了一种能反映盐岩蠕变和加速蠕变的本构模型。通过对某盐矿盐岩实验数据进行拟合,获得了本构模型的参数,理论曲线与实验曲线吻合得较好。通过三维数值模拟方法,应用该本构模型对某盐矿天然气储存库进行了数值模拟研究,探讨了该盐矿盐岩储气库最低内压工况下,腔周损伤区的扩展、变形规律及最长持续运行时间。研究结果表明：（1）盐岩本构模型在盐岩加速蠕变期具有较好的数值稳定性;（2）在最低运行压力下,腔周盐岩进入加速蠕变期后,储气库损伤区的扩展速度非常快,储气库最危险部位位于腔体顶部;（3）腔周盐岩进行加速蠕变期后,盐岩的腔体体积收敛变形主要表现为损伤蠕变体积收敛,稳态蠕变体积收敛趋于稳定;（4）该盐矿盐岩储气库在该压力下最长持续运行时间约为3个月。     

New Viscoplastic Model for Design Analysis of Tunnels in Squeezing Conditions

Summary  This paper is intended to describe the SHELVIP (Stress Hardening ELastic VIscous Plastic) model, a new viscoplastic constitutive law which has been developed to incorporate the most important features of behaviour observed in tunnels excavated in severe to very severe squeezing conditions. This model couples the elastoplastic and time-dependent behaviour by using a plastic yield surface, as frequently adopted in tunnel design analysis, and the definition of a state of overstress referred to a viscoplastic yield surface. The model is formulated in all its detailed aspects. The related analytical closed-form solution for representing triaxial creep deformations is developed. Also developed is an incremental numerical solution for describing the triaxial stress–strain behaviour under constant strain rate conditions. The model is shown to fit very satisfactorily the results of creep tests on clay shales and relaxation tests on coal specimens, as recently performed for design analysis of tunnels in squeezing conditions. Correspondence: D. Debernardi, Department of Structural and Geotechnical Engineering, Politecnico di Torino, Torino, Italy     

层状盐岩蠕变变形相互作用研究

考虑泥岩夹层和盐岩的弹性性质和稳态蠕变性质,通过数值试验方法计算层状复合盐岩体在单轴和低围压三轴荷载作用下蠕变变形过程中力学相互作用和变形时效规律,分析泥岩夹层和盐岩层因蠕变率不匹配对层状盐岩蠕变的影响,初步讨论了层状复合岩体的复合材料研究方法。结果表明,层状盐岩中泥岩夹层与盐岩因弹性参数不匹配产生的初始应力集中在蠕变过程中发生松弛,因泥岩夹层与盐岩层蠕变率不匹配导致两者之间应力重分布,泥岩夹层对盐岩层的蠕变有明显抑制作用。这些分析体现了层状盐岩蠕变过程的非线性性质,为建立层状盐岩体合理本构模型奠定了基础。     

Viscoplastic model for geologic materials with generalized flow rule

The general yield function in the hierarchical approach for constitutive modelling of materials is used with Perzyna's theory to characterize viscoplastic behaviour of geologic materials: a sand and rock salt. Particular attention is given to determination of the constants from laboratory quasistatic or short term, and creep tests. The proposed model is verified with respect to observed laboratory response of the sand and salt. It is implemented in a non-linear finite element procedure and applied to analyse time-dependent behaviour of a cavity in the rock salt.     

A viscoplastic model including anisotropic damage for the time dependent behaviour of rock

This paper presents a new constitutive model for the time dependent mechanical behaviour of rock which takes into account both viscoplastic behaviour and evolution of damage with respect to time. This model is built by associating a viscoplastic constitutive law to the damage theory. The main characteristics of this model are the account of a viscoplastic volumetric strain (i.e. contractancy and dilatancy) as well as the anisotropy of damage. The latter is described by a second rank tensor. Using this model, it is possible to predict delayed rupture by determining time to failure, in creep tests for example. The identification of the model parameters is based on experiments such as creep tests, relaxation tests and quasi‐static tests. The physical meaning of these parameters is discussed and comparisons with lab tests are presented. The ability of the model to reproduce the delayed failure observed in tertiary creep is demonstrated as well as the sensitivity of the mechanical response to the rate of loading. The model could be used to simulate the evolution of the excavated damage zone around underground openings. Copyright © 2005 John Wiley & Sons, Ltd.     

FINITE ELEMENT MODELLING OF A DEEP SEA CLAY IN LONG-TERM LABORATORY CREEP TESTS

A new finite element program is introduced and its predictive capabilities are compared to results from two long-term, drained laboratory creep tests on a deep sea clay. The constitutive behaviour is based on Cam clay critical state plasticity theory with creep and time-dependent hardening. Creep is computed using either Singh–Mitchell's three-dimensional equation or Taylor's secondary compression relationship. The experimental creep data include a triaxial specimen subjected to two deviatoric stress increments and a one-dimensional consolidation specimen subjected to three vertical stress increments. In addition, the pore pressure behaviour following an increase in stress is examined in the triaxial sample. Predictions compare favourably to test data, which provide confidence for applying the chosen constitutive model and numerical formulation to solve seabed-related problems on the continental slope that are of interest to geologists, the oil industry and the navy, among others.     

Discrete element modelling of creep of asphalt mixtures

Creep tests on asphalt mixtures have been undertaken under four stress levels in the laboratory while the discrete element model (DEM) has been used to simulate the laboratory tests. A modified Burger’s model has been used to represent the time-dependent behaviour of an asphalt mixture by adding time-dependent moment and torsional resistance at contacts. Parameters were chosen to give the correct stress-strain response for constant strain rate tests in Cai et al. (2013). The stress-strain response for the laboratory creep tests and the simulations were recorded. The DEM results show reasonable agreement with the experiments. The creep simulation results proved to be dependent on both bond strength variability and positions of the particles. Bond breakage was recorded during the simulations and used to investigate the micro-mechanical deformation behaviour of the asphalt mixtures. An approach based on dimensional analysis is also presented in this paper to reduce the computational time during the creep simulation, and this analysis is also a new contribution.     

Deformation of natural gypsum rock: Mechanisms and questions

The deformation mechanisms of a natural gypsum rock were investigated in instantaneous and long-term laboratory tests. The mechanical behaviour of this rock is strongly influenced by the relative humidity, but this influence seems to be more important on the long-term behaviour. Apart from classical plastic mechanisms, we identify a damage-like mechanism assisted by the variation in relative humidity. Even though this mechanism contributes to the increase of creep strain rate, laboratory evidence shows that it is unrelated to oriented cracking, as usually is the case with stress-induced damage. This mechanism is thought to be due to the migration of water molecules from their sites in the crystalline structure of gypsum (CaSO₄·2H₂O) while under stress. By entering the capillary space, these molecules contribute to the formation of adsorbed water layers and the increased thickness of these layers, thus reducing the interaction between neighbouring faces of gypsum crystals. So, more than effective stress, a complex mechanism reducing the creep activation energy, assisted by relative humidity and stress, is considered as the principal mechanism controlling the long-term behaviour of natural gypsum rock. Such a mechanism would also explain the traces of dissolution observed in pillars of underground gypsum quarries, where, because of the absence of water table, a dissolution-precipitation creep seems improbable.     

深井蠕变地层钻井液密度优化技术

深部地层盐岩钻井是钻井工程中的重大技术难题之一。由于盐岩性能的特殊性,当钻开井眼后盐岩蠕变,常造成井眼失稳、卡钻、固井后挤毁套管等事故,给钻井带来重大经济损失。结合山东胜科1井钻井工程,对深部地层盐岩及软泥岩等岩层的蠕变速率进行测试,采用三维数值模拟方法获得了盐岩及软泥岩的蠕变参数。并通过所获得的蠕变参数,对胜利油田东营区块盐岩及软泥岩井眼不同深度、不同钻井液密度下地层的蠕变速率进行了分析,获得了盐岩及软泥岩井眼许可钻井液密度。研究成果可以为钻井工程钻井液密度选用提供指导意义。     

低频循环荷载下盐岩轴向蠕变的Burgers模型分析

为了研究盐岩在低频循环荷载作用下的蠕变特性,采用恒轴压、循环围压的应力加载方式对盐岩开展了低频循环荷载蠕变试验。试验结果显示,当蠕变时间较短时,盐岩轴向蠕变曲线近似为平滑曲线,波动性不大;当时间增加到一定程度以后,盐岩变形随围压变化而发生明显的波动。总体来看,循环荷载下盐岩轴向蠕变曲线与Burgers模型蠕变曲线较为相似。将Burgers模型分解为Maxwell模型和Kelvin模型,忽略材料的疲劳效应,分别推导了恒轴压、循环围压应力加载方式下Maxwell模型和Kelvin模型的轴向蠕变方程,分析了荷载循环周期对模型蠕变性的影响规律;将循环荷载下Maxwell模型和Kelvin模型的轴向蠕变方程进行叠加,得到了循环荷载下Burgers模型的轴向蠕变方程,并利用盐岩蠕变试验结果对其合理性进行了验证。结果表明:拟合曲线和试验曲线吻合良好,该模型能够较好地反映盐岩在循环荷载作用下的蠕变特性和荷载变化对盐岩蠕变性的重要影响,特别是能够反映出不同荷载循环周期下盐岩变形随荷载变化而发生的明显的波动现象。     

Creep of saturated materials as a chemically enhanced rate‐dependent damage process

Material behaviour that exhibits characteristics of creep induced by a spontaneous mineral dissolution enhanced by material damage is studied. It is believed that the characteristic rates of the chemical processes involved determine the time‐rate dependence of the resulting strain. A basic model of a combined chemo‐plastic softening and chemically enhanced deviatoric strain hardening for saturated geomaterials is presented. Chemical softening is postulated to occur as a consequence of the net mass removal resulting from dissolution and precipitation of specific minerals occurring at the damage‐generated inter‐phase interfaces. Closed and open systems are discussed. In the former case, deformation at constant stress results entirely from a local compensation mechanism between the chemical softening and strain hardening. The classical three stages of creep are interpreted in terms of mechanisms of dissolution and precipitation, as well as the variation in the reaction surface areas involved in the mass exchange. In an open system, the above local mechanism is enhanced by the removal of mass via diffusion of species affecting the mass balance. Such a system is addressed via a boundary value problem as shown in an example. Copyright © 2007 John Wiley & Sons, Ltd.     

软岩的强度—变形—时间之间关系的试验分析

对软岩和有不连续面的软岩试样进行一系列固结不排水三轴压缩和蠕变试验,测定并分析了它们在正常固结和超固结状态下的应变软化性状、蠕变特性和残余强度的变化规律。探讨了软岩中存在的不连续面对应力－应变关系、残余强度特性和蠕变应变速率的影响。     

石油钻井工程中岩层蠕变速率及蠕变参数分析

石油勘探开发工程中,盐膏岩层及含膏泥岩由于具有较低的渗透特性,往往是大型油气藏的封闭层。由于盐层具有较大的流变特性,盐层钻井技术成为钻井工程中的重大技术难题。通过对某一勘探井盐岩层及含膏泥岩井眼不同时间间隔下的井眼测试,获得了井眼地层盐岩及软泥岩等岩层的蠕变速率。采用幂指数流变本构模型对盐岩及软泥岩的蠕变速率进行了分析,通过反演获得了该地质区块盐岩及软泥岩的蠕变参数。该参数能进一步用于对盐岩钻井过程中钻井液密度的优化分析中。     

Deformation Behavior of Chalk Studied Close to In Situ Reservoir Conditions

A laboratory test program, which simulated reservoir conditions of pressure and temperature, was conducted on outcrop and reservoir chalk samples of various porosities. All the samples experienced a stress path following uniaxial strain condition K ₀ that led to compaction failure, i.e. pore collapse. The experiments were loaded by depletion of pore pressure conducted under load controlled conditions. This depletion phase was followed by a creep period, where time-dependent deformation was monitored. The intention of creating such reservoir condition in these laboratory experiments was to gain knowledge of the nature of chalk compaction. Chalk is an important reservoir rock for the oil and gas industry with unique storage capability with porosities up toward 50%. However, this rock is also very weak which has resulted in significant reservoir compaction and in turn severe seabed subsidence and casing failure. Mapping of the mechanical behavior of chalk in terms of deformation is thus decisive for a proper understanding of these reservoirs. The results of this study show that chalk is indeed a rate-dependent material under laboratory loading conditions as time effects were revealed as the loading rate was varied. However, the results raise uncertainty about the importance of rate dependency for chalk under completely drained conditions. Further, such high-porosity chalk suffers for substantial plastic strains and obvious strain hardening. Indeed, a relation between deformation/porosity and hardening is proposed by the introduction of real-time modulus values. Time-dependent deformation, also called creep was influenced by the depletion phase, as consolidation or transient creep influenced the deformation response for as much as 175 h after a change in load. This indicates that transient creep is dependent on the stress history. However, observations suggest the existence of a universal mechanism for steady state creep, governed by neither the initial porosity nor the stress history or chalk type, which thus seems to be an independent strain contributor. Finally, time dependence is found on the K ₀ development for chalk tested at typically laboratory rates, which has been discussed as a reflection of the nature of the grain re-arrangement during failure and plastic deformation. Ultimately, such time dependence of the K ₀ may contribute to the understanding of stress path data deduced from field data.     

大岗山坝区岩体现场剪切蠕变试验及参数反演

现场剪切蠕变试验是了解岩体剪切蠕变特性的最重要手段。针对大岗山水电站坝区"硬、脆、碎"辉绿岩脉进行了现场剪切蠕变试验,分析了岩体的剪切蠕变变形规律和剪切蠕变速率特性。试验结果表明,在剪应力较小时坝区岩体剪切蠕变仅呈现出减速蠕变和稳态蠕变2个阶段;当剪应力接近屈服强度时,坝区岩体剪切蠕变速率由渐变增长转为突变增长,岩体在短时间内即发生破坏,呈现出加速蠕变特性。恒定正应力下辉绿岩体的稳态流变速率与剪应力之间可用指数关系来表征。根据剪切蠕变试验曲线,进行了岩体剪切蠕变模型辨识。辨识表明,西原模型可以较好反映坝区辉绿岩脉的剪切蠕变特性。通过优化反演获得坝区岩体的剪切蠕变参数,为坝基边坡工程稳定性分析和设计提供了重要的力学依据。     

Mechanical properties of altered granite gneiss considering time effect

The altered granite gneiss is a special rock with loosely-structured and well-developed pores and cavities. The microstructure and mineral composition of the rock were analysed by SEM-EDS and creep triaxial tests were carried out and the axial and lateral deformations over time were discussed. Both the axial and the lateral creep curves show the typical three distinct creep stages (decay creep, steady state creep, accelerated creep). At a low stress level, the axial creep strain is unnoticeable, and only when loaded at a high stress level will the creep strain increase at an increasing rate until the rock specimen fails. The lateral creep strain is smaller than the axial creep strain, but the creep rate (dε/dt) in the lateral direction is higher than that in the axial direction at all stress levels. The failure pattern, which is affected by many factors, shows a shear failure with rather broken and rough failure surfaces.