The creep of potash salt rocks from Saskatchewan

Summary The results of creep tests on the Esterhazy-and the Patience-Lake-types of potash salt rocks from Saskatchewan, Canada are presented. The investigations involved over 6 years of time-dependent experiments in uniaxial compression using potash from the Rocanville and the Lanigan mines of the Potash Corporation of Saskatchewan. A creep test at a given load would last from 2 to 8 months, with most tests conducted over a 4-month period.Since the yield stress of both types of potash lies between 9 and 11 MPa, there is very little creep below 11 MPa. Between 11 and 13 MPa, creep strain production increases sharply through plastic deformation. Above about 13 MPa, however, plastic creep is dominated by brittle creep caused by microcracking. As a result, the lateral and volume creep strain curves may then display the transient and the steady-state, or all three stages of creep, while the axial strain, which is not affected by microcracking, usually attenuates for the whole duration.Two different interpretations of the results are offered. Identifying the last (the fourth) month of testing with the steady-state model, the stress dependence of the steady-state rate has been established for both rock types. A unimodal rate model for the axial strain and a bimodal model for the lateral strain are suggested. The alternate interpretation proceeds on the assumption that under 13 MPa, both the axial and the lateral strain can be modelled through the power function formulation of transient strain.     

Microstructure and fabric development in ice: Lessons learned from in situ experiments and implications for understanding rock evolution

In this contribution we present a review of the evolution of microstructures and fabric in ice. Based on the review we show the potential use of ice as an analogue for rocks by considering selected examples that can be related to quartz-rich rocks. Advances in our understanding of the plasticity of ice have come from experimental investigations that clearly show that plastic deformation of polycrystalline ice is initially produced by basal slip. Interaction of dislocations play an essential role for dynamic recrystallization processes involving grain nucleation and grain-boundary migration during the steady-state flow of ice. To support this review we describe deformation in polycrystalline ‘standard’ water-ice and natural-ice samples, summarize other experiments involving bulk samples and use in situ plane-strain deformation experiments to illustrate the link between microstructure and fabric evolution, rheological response and dominant processes. Most terrestrial ice masses deform at low shear stresses by grain-size-insensitive creep with a stress exponent (n ≤ 3). However, from experimental observations it is shown that the distribution of plastic activity producing the microstructure and fabric is initially dominated by grain-boundary migration during hardening (primary creep), followed by dynamic recrystallization during transient creep (secondary creep) involving new grain nucleation, with further cycles of grain growth and nucleation resulting in near steady-state creep (tertiary creep). The microstructural transitions and inferred mechanism changes are a function of local and bulk variations in strain energy (i.e. dislocation densities) with surface grain-boundary energy being secondary, except in the case of static annealing. As there is a clear correspondence between the rheology of ice and the high-temperature deformation dislocation creep regime of polycrystalline quartz, we suggest that lessons learnt from ice deformation can be used to interpret polycrystalline quartz deformation. Different to quartz, ice allows experimental investigations at close to natural strain rate, and through in-situ experiments offers the opportunity to study the dynamic link between microstructural development, rheology and the identification of the dominant processes.     

坝基碎屑岩三轴蠕变特性及长期强度试验研究

基于物理和常规变形特性分析,认为某水电站坝基碎屑岩力学特性异常复杂,故采用岩石三轴伺服仪开展了系列的蠕变力学特性试验研究。首先,探讨了轴向、侧向及体积蠕变特性和速率变化规律;其次,分析了蠕变对偏应力-应变特性影响并开展了破坏岩样微细观电镜扫描试验;最后,在采用等时曲线簇法确定长期强度的基础上,以实际延性扩容为依据,认为岩石侧向体积扩容速率大于轴向压缩速率的临界点为快速蠕变破坏的标志,提出确定长期强度的新方法。结果表明,碎屑岩表现出显著的蠕变特性,蠕变曲线主要分为初始衰减和稳态蠕变两阶段,且最后一级应力施加后呈现加速蠕变现象;应力增加导致蠕变变形加剧,最终破坏表现出轴向压缩变形过大、体积延性扩容明显、稳态蠕变速率较大等特点,且蠕变速率与应力符合指数函数关系。岩样长期强度与三向稳态蠕变速率交点和侧向体积扩容应力阀值基本一致,为常规强度的54%～80%。试验结果旨在为相关岩石工程长期稳定分析及蠕变模型构建提供可靠的依据。     

基于承压板试验的岩体蠕变参数反演统一解析公式法

由于岩体性状的复杂性和多样性,现场试验是进行岩石力学研究的重要手段。以往的现场承压板试验,由于试验条件的限制,试验荷载的设定将使岩体蠕变呈衰减蠕变形态,却难以反映岩体的等速蠕变和加速蠕变。坝基软弱岩体的力学特性是影响大坝及地下结构长期稳定性的重要因素。通过对坝基软弱岩体现场承压板试验曲线中表现出的衰减蠕变和等速蠕变两阶段特性,辨识了蠕变模型。并推导了刚、柔性承压板深部岩体的黏弹性一般解,给出了Maxwell模型、广义Kelvin模型、Burgers模型的黏弹性位移的统一表达式。结合试验数据,以理论解析反演法得到相关的蠕变参数,为以后的坝基长期稳定性计算奠定基础。     

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。     

Cumulative Benioff strain-release, modified Omori's law and transient behaviour of rocks

Irreversible thermodynamic theories with internal state variables can be used to derive a general constitutive law for both transient and steady-state behaviours of rocks. This constitutive law can represent the concepts of damage and damage evolution in either the fibre-bundle model or continuum damage mechanics. We have previously proposed an empirically based constitutive law for both the transient and steady-state behaviours of rocks ultimately derived from laboratory experimental data. We show here that this law is concordant with the general constitutive law derived from irreversible thermodynamic theories, and that the relaxation modulus has a temporal power–law that depends on a structural fractal property of rocks. Our constitutive law predicts forms for the cumulative Benioff strain-release for precursory seismic activations and the modified Omori's laws of aftershocks, both aspects of the temporal fractal properties of seismicity. These seismic properties can also be derived by the fibre-bundle model or continuum damage mechanics. Our model suggests that these time-scale invariant processes of seismicity may be regulated by the fractal structures of crustal rocks.     

Finite element modelling of pressuremeter tests and footings on frozen soils

A finite element code is developed to model the structure-frozen soil/ice interaction using a time incrementing, fully implicit, iterative algorithm, and a constitutive model based on the concept that total strain tensor consists of an elastic and a creep component. The code is used to investigate the applicability and limitations of the power law as the creep model for frozen soil by simulating two pressuremeter tests. Two extended phenomenological models based on the generalized power law are used in axisymmetric finite element analyses to simulate two, long-term, stage-loaded pressuremeter tests, and comparison of results with test data indicates that one model demonstrates a better ability to approximate the actual response to subsequent load steps, under certain restrictions. Stress analyses demonstrate the ability of the constitutive model to show transient as well as subsequent quasi-stationary stress stages in creep analysis. Additional simulations of short-term pressuremeter tests on ice are performed to further illustrate some limitations of the power-law model. Examples for prediction of creep settlements on frozen geomaterials are demonstrated by considering the interaction of fully flexible circular footings and concrete cylindrical footings (of different embedment depths) with frozen sands.     

三轴压缩蠕变试验下石英云母片岩各向异性蠕变特性研究

对石英云母片岩进行三轴压缩蠕变试验,研究丹巴水电站石英云母片岩的三轴蠕变特性及其各向异性特性。按轴向荷载与层理面关系加工成平行组和垂直组2组试件,开展分级加载方式进行不同围压条件下的蠕变试验。试验研究表明,石英云母片岩具有蠕变特性,包括瞬时变形、衰减蠕变、稳定蠕变和加速蠕变阶段;采用带Kachanov蠕变损伤律的蠕变模型来描述石英云母片岩的蠕变特性,并进行蠕变参数辨识,拟合结果显示此模型能很好地描述石英云母片岩的蠕变特性;根据试验结果获得2组试件的长期屈服强度、破坏形态、瞬时变形参数和稳定蠕变速率,分析表明石英云母片岩的蠕变力学特性具有明显的各向异性特性。层理面与轴向荷载垂直的试件较层理面与轴向荷载平行的试件的强度、弹性剪切模量、体积模量和黏性系数相对较大,表现出较高的抗变形和抗破坏能力;平行组以剪切破坏为主,垂直组破坏时出现侧向鼓胀现象,显示出延性破坏的特点;2组石英云母片岩试件的瞬时应变量和稳定蠕变速率都随着应力水平的提高而增大。     

角闪斜长片麻岩流变力学特性研究

为了解小湾水电站枢纽区角闪斜长片麻岩的流变力学特性,采用岩石全自动三轴流变伺服仪对角闪斜长片麻岩进行三轴流变力学试验。试验结果表明,强度较高的角闪斜长片麻岩会发生流变现象,尤其在高应力水平条件下,其流变特性明显;外荷载超过岩样的长期强度时,随着时间的逐渐增加试样变形经历典型流变3个阶段,并最终加速流变破裂。依据岩样稳态流变阶段的流变速率与应力水平的关系,提出了一种确定长期强度的方法。在Burgers流变模型中加入统计损伤,并用Mohr-Coulomb准则确定的岩石长期强度作为开始进入非线性加速流变阶段的阀值,得到相应的非线性损伤流变模型。利用岩石全程三轴流变试验结果,采用优化后的算法,对非线性损伤流变模型相应的参数进行了辨识,结果表明,建立的岩石统计损伤非线性流变变模型与流变试验结果吻合较为理想,可以较为准确地反映角闪斜长片麻岩的流变力学特征     

川东气田盐岩、膏盐岩蠕变特性试验研究

对川东气田盐岩、膏盐岩进行了矿物组分测定,采用TAW-1000深水孔隙压力伺服试验系统进行了蠕变试验,分析了固有的矿物组分及偏应力、温度、围压对蠕变的影响,结合蠕变曲线和岩石参数,提出了稳态蠕变速率本构方程。研究表明：川东气田盐岩、膏盐岩矿物组分以NaCl、CaSO4为主,其中NaCl含量最高可达93%以上;岩石固有的矿物组分是影响岩石蠕变特性的内因,随NaCl含量增加,瞬态蠕变、稳态蠕变速率相应增大;随偏应力、温度的增加稳态蠕变速率增大,围压对其影响不大;通过试验数据拟合得出赫德（Heard）蠕变本构方程中的参数,求出不同偏应力、温度下盐岩、膏盐岩的稳态蠕变速率,为川东气田盐岩、膏盐岩地层安全钻进泥浆密度窗口计算和套管非正常变形分析提供了理论依据。     

A comparative study of different model families for the constitutive simulation of viscous clays

The simulation of the viscous behavior of some clays is of high importance in many geotechnical problems. The literature offers a vast amount of constitutive models able to simulate the rate dependence observed on these materials. Although most of these models are calibrated to very similar experimental observations and share similar definitions of material parameters, some discrepancies of their response have been detected, which are related to their mathematical formulations. In this work, the causes of these discrepancies are carefully studied. To that end, four different model families are analyzed, namely, nonstationary flow surface (NSFS) models, viscoplasticity with overstress function (OVP), viscoplasticity with Norton's power law (NVP), and visco-hypoplasticity (VHP). For the sake of a fair comparison, single constitutive models using the same set of material parameters, and following other requirements, are developed for each model family. Numerical implementations of the four resulting models are performed. Their response at different tests are carefully analyzed through simulation examples and direct examination of their constitutive equations. The set includes some basic tests at isotropic stress states and others as responses envelopes, undrained creep rupture, and an oedometer test with loading, unloading-reloading, creep, and relaxation. The article is concluded with some remarks about the observed discrepancies of these model families.     

高渗透压脆性岩石蠕变宏−细观力学模型研究

高渗透压对深部地下工程脆性岩石蠕变力学特性有着重要影响。然而,能够解释高渗透压作用脆性岩石完整减速、稳态及加速三级蠕变过程中,细观裂纹扩展与宏观变形关系的宏细观力学模型研究很少。基于考虑含有初始裂纹与新生成翼型裂纹影响的裂纹尖端应力强度模型,引入渗透水压与初始裂纹及新生成翼型裂纹之间的力学关系,建立了考虑渗透水压作用的裂纹尖端应力强度模型;然后结合亚临界裂纹扩展法则,与裂纹及应变损伤关系模型,推出了考虑渗透水压影响的脆性岩石蠕变裂纹扩展与宏观变形关系的宏细观力学模型。当施加轴向应力小于岩石裂纹启裂应力时,岩石近似表现为线弹性变形;当施加轴向应力大于裂纹启裂应力且小于岩石峰值强度,岩石表现为塑性蠕变变形。研究了不同渗透压作用下,分级轴向应力加载岩石蠕变应变时间演化曲线,并通过试验结果验证了模型的合理性。分别讨论了恒定渗透压与分级渗透压,对脆性岩石蠕变过程中裂纹长度、裂纹扩展速率、轴向应变及轴向应变率的影响。该模型为高渗透压深部地下工程围岩稳定性评价提供了重要理论依据。     

地壳脆塑性转化带非稳态流变与震后松弛变形机制

大陆浅源地震密集分布层称为地震层,该深度处于石英脆塑性转化带,其变形除受温度控制外,地震周期各阶段变形随应变速率和应力发生变化,从间震期的稳态蠕变转化为同震破裂和震后松弛阶段非稳态蠕变。与间震期长期蠕变相关的野外塑性变形和稳态流变实验研究非常多,而与震后松弛相关的地壳深部脆塑性转化和非稳态蠕变研究非常有限,更缺少非稳态流变的本构方程。震后松弛阶段的断层滑动研究和基于GPS观测数据反演地壳形变研究都依赖于非稳态蠕变实验数据及其流变模型。本文介绍了野外断层脆塑性转化带非稳态流变和高温高压非稳态流变实验研究进展,分析震后松弛阶段断层脆塑性转化带的变形特征与变形模式,讨论了非稳态流变与脆塑性转化带强度定量化研究中存在的问题。     

黏土岩温度-渗流-应力耦合特性试验与本构模型研究进展

高放废物处置库、垃圾填埋场等工程中常常涉及到温度场（T）、渗流场（H）和应力场（M）的耦合作用的问题。从试验和理论模型两个角度综述国内外黏土岩温度-渗流-应力耦合特性的研究进展,主要包括其传热特性、温度影响下的渗流特性、变形、强度、蠕变特性。在此基础上,重点分析了黏土岩水-热迁移模型以及热-力耦合本构模型的适应性。基于上述认识,通过试验研究了比利时Boom clay在温度作用下的强度、渗透性、蠕变性等特征。结果表明：随着温度升高,Boom clay的强度有所降低,渗透性显著增强,蠕变速率明显加快。提出了适用于Boom clay的THM耦合弹塑性损伤模型,计算结果验证了模型能合理反映温度的影响。最后,探讨了黏土岩THM耦合机理研究的不足和今后的研究方向。     

海相沉积软土蠕变BP神经网络本构模型

海相沉积软土具有很强的蠕变特性,传统分级构建蠕变本构模型方法不实用,且很难真正反映岩土流变的非线性特性。为此,本文引入具有超强非线性映射和容错能力的BP神经网络模型,通过改进BP算法,根据江门软土的室内直剪蠕变试验结果,建立了海相沉积软土BP神经网络蠕变本构模型,避免了传统方法为满足试验曲线变化规律和蠕变特性而需要建立复杂的本构数学表达式。最后,利用上海地区软土蠕变实验结果对本文提出的方法进行了验证,并对BP神经网络蠕变模型在描述软土流变方面的特点进行了讨论。结果表明,本文建模方法简单,并能很好地描述软土的非线性蠕变问题。     

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     

冻融循环作用下砂岩蠕变特性及损伤模型研究

青藏高原高寒地区岩体长期稳定性受冻融作用影响显著,有必要开展冻融岩石的时效性特征研究。为探讨砂岩在冻融循环作用下的蠕变劣化特性,基于不同冻融循环次数后石英砂岩及红砂岩单轴蠕变试验结果,深入分析了冻融循环对砂岩各蠕变阶段的影响特征。研究表明,在非屈服应力条件下,试样在衰减蠕变阶段的蠕变时长随着冻融循环次数的增加而明显减小,对应蠕变量及蠕变速率增大;在屈服应力条件下,试样进入加速蠕变阶段的应力阈值随着冻融循环次数的增加而逐渐降低,对应从稳定蠕变到加速破坏所经历的时间更短,破坏时累计的应变增量更大;在长期荷载作用下,试样的宏观破裂形态随循环次数的增加逐步由单一斜剪切破坏模式向共轭断面拉剪复合型破坏模式演化。根据试验结果,提出了具有冻融与长期受荷劣化特征的非定常性黏弹性系数损伤演化方程,将其引入西原模型构建了考虑冻融损伤的砂岩蠕变本构模型。利用冻融后红砂岩蠕变试验数据对模型进行了参数辨识与比较分析,验证了模型的正确性及适用性。通过对模型参数进行拟合分析,揭示了黏弹性冻融损伤系数随冻融循环次数的变化规律,表明了长期受荷损伤参数具有控制加速蠕变幅度的重要作用。研究结果对于高寒山区岩体长期稳定性评价具有一定意义。     

热−水−力耦合条件下黏土岩蠕变特性研究

黏土岩作为放射性核废料处置的备选介质,长期处于热-水-力耦合的复杂条件下。为研究围岩的长期稳定性,开展了一系列不同围压和偏应力下的黏土岩加温-降温排水蠕变试验。得出以下结论：温度的升高会提升黏土岩的蠕变速率,延长衰减蠕变阶段的时间,但是降温过程中试样主要以冷缩变形为主,并未见明显的蠕变变形;围压的降低以及偏应力的增加会提高黏土岩的蠕变速率,并且这种影响会随温度的升高明显加剧。基于试验结果,在Perzyna过应力理论的基础上引入蠕变硬化、蠕变损伤以及热损伤,建立了黏土岩热-水-力耦合蠕变模型。通过ABAQUS软件及其子程序对该模型进行数值实现,模拟结果与试验结果的对比初步表明该模型可以很好地描述热-水-力耦合条件下黏土岩的蠕变特性。     

万福煤矿不同含水率砂岩蠕变力学特性试验研究

为研究深部巷道围岩在地下水作用下的长期蠕变力学特性,采用自主研制的深部软岩五联流变试验系统,开展不同含水率(0%、0.8%、1.6%、2.4%、3.3%)下砂岩吸水软化单轴压缩试验及单轴蠕变试验。通过试验结果研究表明：砂岩的单轴抗压强度、弹性模量和蠕变破坏应力与含水率呈指数下降关系,蠕变破坏应力与单轴抗压强度的比值在0.76～0.84之间;砂岩衰减蠕变阶段时间随着含水率的增加而减少,随应力水平的增加而增加。径向应变比轴向应变先进入稳态蠕变阶段,破坏应力下径向应变的加速蠕变阶段开始时间要先于轴向应变;基于稳态蠕变速率曲线确定了砂岩的长期强度,径向稳态蠕变速率确定的值略小于轴向,长期强度与含水率之间满足负指数关系;将蠕变试验中径向应变与轴向应变之比定义为μ_c,提出了基于μ_c值的岩石长期强度确定方法且μ_c值与含水率无关,对于本次砂岩样品可以认为μ_c值大于0.3时样品会在一定时间内发生加速蠕变破坏;随着含水率的增加,样品破坏形态由单斜面剪切破坏逐渐演变至X状共轭斜面剪切破坏。研究结果为地下水作用下巷道长期稳...     

Comparison of two creep degradation modeling approaches for soft structured soils

The creep degradation is a common phenomenon for soft structured clays. In this paper, the creep degradation behavior for soft structured clays is first studied by combining intrinsic creep behavior and the structure indicator. A creep-implicit model and a creep-explicit model corresponding to a stress-based and a creep-based structure indicators are developed, respectively, under one-dimensional condition. Parameters determination for both models is straightforward from oedometer tests. Coupled with consolidation theory, both models are used to simulate oedometer tests with different structural levels and load durations on three clays. The predictive ability of the two models on creep behavior, creep degradation behavior and evolution of structure indicator is analyzed. The relationship between the two structure indicators is discussed based on experimental results. The comparison between experimental and numerical results demonstrates that both models can accurately describe the creep degradation behavior of soft structured clay under one-dimensional loading.