Modeling the behavior of sandstone based on generalized plasticity concept

With the concept of generalized plasticity, a constitutive model for describing the deformation behavior of sandstone is proposed in this paper. This proposed model is characterized by the following features: (i) nonlinear elasticity under hydrostatic and shear loading; (ii) associated flow rule for pre‐peak simulation; (iii) substantial plastic deformation during shear loading; and (iv) significant shear dilation and distortion prior to the failure state. This model requires 10 material parameters, including three for elasticity and seven for plasticity. All of the parameters can be determined, in a straightforward manner, by the suggested procedures. The proposed model has been validated by comparing the triaxial test results of the Mushan sandstone under different hydrostatic stress, different stress paths, and cyclic loading condition. It is also versatile in simulating the deformation behaviors of two other sandstones. Upon slight modification of the model, the post‐peak behavior of sandstone can be reasonably predicted using proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical and Laboratory Analysis of Relaxation Tests for Determining Time-Dependent Properties of Rock

Roof falls in coal mines may occur within a few months to a few years after excavation. In this paper, we proposed the use of relaxation tests as a substitute for time-dependent tests. The relation between creep behavior and relaxation behavior was numerically investigated and demonstrates that the material assigned with creep model can show relaxation behavior. Then the relaxation model was developed by modifying the Burgers creep model. Numerical simulation of a relaxation test on a simulated rock model in 3DEC yielded results that were similar to theoretical prediction. A relaxation test was performed on two groups of specimens under varying load conditions. Results from the laboratory tests validated the approach of using relaxation test to determine time-dependent properties. Finally, time-dependent properties were investigated by performing relaxation tests at different stages of a complete stress–strain curve. The relaxation test during strain-softening was unsuccessful; however, the relaxation behavior at residual stage in post-failure region was more significant than that in pre-failure region and the sudden drop in stress indicated there was strength deterioration due to the accumulation of viscous strain.     

岩石内变量蠕变模型研究

通过一系列砂岩、页岩和辉绿岩室内蠕变试验,获得了不同应力和初始应变状态下岩石蠕变特性。通过误差分析讨论了计算蠕变速率时如何选择时间增量。讨论了复杂加、卸载条件下时间相关蠕变模型的局限性,提出采用不可恢复应变作为内变量来描述复杂条件下岩石蠕变性质,并据此提出了岩石的内变量蠕变模型。试验数据与模型拟合结果对比表明,内变量蠕变模型较好地反映了3种岩石的蠕变行为。此外,还初步讨论了模型在岩石率相关性质研究中的适用性,并利用相关试验数据进行了验证。     

Long-term Non-linear creep and swelling behavior of Hong Kong marine deposits in oedometer condition

The time-dependent stress-strain behavior of clayey soil is a great concern for predicting long-term settlement especially for large-scale land reclamation projects. In this paper, long-term time-dependent behavior of Hong Kong Marine Deposits (HKMD) under the loading stage and unloading stage is investigated by multi-staged loading oedometer test. Special emphasis has been given to study creep and swelling behavior. It is found that the clayey soil demonstrates the creep behavior during the loading stage, whereas it shows the swelling behavior during the unloading stage. The analysis of the creep behavior shows that there exists a linear trend between creep strain and time (in log-scale) within a certain period, whereas a nonlinear relationship in a long term view. Similar result is found for the swelling behavior. A nonlinear function is found to be suitable to predict the long-term creep and swelling behavior. The creep strain limit and swelling strain limit can be obtained if the nonlinear function is adopted to fit the experimental data. In addition, a new modified Elastic Visco-Plastic model considering Swelling (EVPS model) is proposed and presented, which considers the nonlinear creep and swelling behavior. In this modified EVPS model, the final creep and swelling equilibrium stress-strain state can also be obtained when the time is infinite.     

结构性软黏土时效特性的一维弹黏塑性模拟

为了研究土体结构破坏对软黏土一维变形的时效特性的影响,在Bjerrum的等时间线体系基础上,提出了等黏塑性应变率线等黏塑性应变率线概念,建立了非结构性软黏土的一维弹黏塑性模型;为了描述土体结构渐进破坏特征,定义了结构性参数--结构应变,在非结构性模型的基础上推导了结构性软黏土一维弹黏塑性模型;讨论了通过试验法直接确定模型参数的方法,并利用新建模型对温州天然软黏土的一维常规压缩试验、天然Ariake 黏土的分级快速固结试验、结构性Berthierville黏土的一维等应变率压缩试验及长期蠕变试验进行模拟。模拟与试验结果的对比表明,该模型能较好地描述结构性软黏土一维压缩变形的时效特征。     

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。     

软岩流变的一种新力学模型

软岩在低应力水平下表现为弹性和粘弹性;在较高的应力水平下表现为弹性、塑性和粘弹性;在高应力水平下表现为弹性、塑性、粘弹性和粘塑性。为了对其进行全面描述,首先,提出了两种非线性元件-蠕变体和裂隙塑性体,并将它们和描述衰减蠕变特性的开尔文体及描述瞬弹性的虎克体相结合,得到了一种新的复合流变力学模型。然后,通过其采用的软岩蠕变的分级增量循环加卸载试验证明,该模型可很好地描述软岩在不同应力水平下的蠕变特性特别是裂隙闭合阶段和加速蠕变阶段的特性,可在工程实际中推广应用。     

不同含水率软弱结构面剪切蠕变试验及模型研究

软弱结构面的蠕变特性是岩体重要力学特性之一,其蠕变特性常控制着岩体的蠕变变形和长期强度。软弱结构面中充填物的含水率是影响其蠕变特性的重要因素之一,通过开展不同含水率砂岩软弱结构面剪切蠕变试验,得到了具不同含水率的砂岩软弱结构面剪切蠕变试验曲线。基于得到的剪切蠕变试验曲线,分析了含水率对软弱结构面剪切蠕变特性及长期抗剪强度的影响规律。最后通过模型辨识,采用改进的粘弹塑性模型来描述考虑含水率变化的砂岩软弱结构面蠕变特性。     

Interface creep behavior of grouted anchors in clayey soils: effect of soil moisture condition

This study aims at investigating the influence of moisture conditions on interface shear behavior of element-grouted anchor specimens embedded in clayey soils. The tests involved comparatively short embedment lengths and a device that was specially designed to facilitate moisture conditioning. Rapidly loaded pullout tests as well as pullout tests under sustained (creep) loading were conducted to characterize both the short-term and long-term ultimate shear strength of anchor–soil interfaces. Both values of the interface shear strength were found to decrease exponentially with increasing moisture content values, although their ratio was found to show a linearly decreasing trend with increasing moisture content. The interface shear creep response under pullout conditions was characterized by a rheological hybrid model that could be calibrated using experimental measurements obtained under increasing stress levels. The accuracy of the hybrid model was examined by evaluating the stress-dependent prediction model as well as its governing parameters. This investigation uncovers the coupled impact of soil moisture condition and external stress state on the time-dependent performance of grouted anchors embedded in clayey soils by correlating the interface shear strength with soil moisture content and associating the creep model with stress levels applied to the grout–soil interface.

     

考虑水化学损伤的砂岩流变损伤本构模型

通过对已有的水化学溶液腐蚀作用后红砂岩三轴蠕变试验结果的分析,可知水化学作用能够加快岩石损伤的发展,增强红砂岩的蠕变效应。根据水岩化学作用的动力学理论,将红砂岩中可溶解胶结物的流失作为水化学腐蚀作用下岩石力学性能劣化的根本原因。通过化学反应速率方程和测定浸泡过程中溶液pH值的变化,定义了考虑初始pH值和时间的化学损伤因子。考虑流变过程中的应力损伤,基于广义Kelvin模型,提出了考虑水化学作用的砂岩流变损伤本构模型。通过对水化学作用下红砂岩流变试验结果进行模拟,对该模型进行了参数辨识和验证。结果表明,所提出的模型能够较好地反映水化学作用下砂岩的流变特性,具有有效性和合理性。     

软弱结构面剪切蠕变特性与含水率关系研究

软弱结构面往往控制着岩体的蠕变变形,含水率又是影响软弱结构面蠕变特性的重要因素,通过开展不同含水率条件下砂岩软弱结构面剪切蠕变试验,得到了不同含水率条件下剪切蠕变曲线,并考虑加载历史对试验曲线进行了修正。在此基础上,通过模型辨识选取Burgers模型描述砂岩软弱结构面蠕变的黏弹性特性。分析了含水率对砂岩软弱结构面剪切蠕变特性的影响,并对含水率影响软弱结构面剪切蠕变特性的机制进行了探讨。     

孔隙水压力分级加载砂岩蠕变特性研究

采用RLW－2000 M微机控制煤岩流变仪,以细粒砂岩为研究对象,对三轴压缩条件下岩石孔隙水压力分级加载蠕变试验进行了蠕变特性及模型研究,重点分析了孔隙水压力分级加载时蠕变条件下岩石的应变（应变速率）、等效孔隙体积（体积速率）演化曲线,同时对不同孔隙水压力分级加载条件下的岩石蠕变演化曲线进行了模型分析和对比。试验结果表明,逐级加载孔隙水压作用下细粒砂岩的蠕变曲线符合蠕变演化3阶段特征;分级加载水压力的孔隙体积演化规律符合微孔洞的损伤过程的3个阶段规律;利用西原体模型进行理论与试验蠕变曲线对比,蠕变方程曲线与试验曲线的演化规律吻合。     

复杂应力路径下流体饱和砂岩本构模型

高孔隙率砂岩在不同围压及被不同流体（水及油）饱和时表现出不同的应力-应变特性及不同的破坏过程。复杂应力路径下油和水饱和砂岩的力学试验表明,存在某一临界围压,随着围压的增加,饱和砂岩从以压剪破坏为主,逐渐转变为以孔隙坍塌破坏为主的破坏机制。通过力学试验结果的分析,以两种破坏理论对油和水饱和砂岩的破坏特征进行了力学解释,并应用经典塑性力学的盖帽模型建立了相应的本构模型,应用非线性有限元法进行了数值验证,研究结果表明,提出的模型与试验资料吻合良好,能较好地模拟复杂应力路径下油和水饱和砂岩的破坏机制及模拟注水采油引起的砂岩附加沉降。     

Effects of cyclic loading on the rheological properties of sandstones

This paper presents some results of the laboratory tests on the time-dependent behaviour of three types of sandstone. Research into the rheological properties of rocks is mostly done under static (quasistatic) loading. In nature, however, rocks are also often subjected to cyclic (vibration) loading as a result of vibrations from traffic or the propagation of seismic waves due to, for example, earthquakes, rock bursts, blasting operations and such like. On this account, the research presented is focused on the study of rheological rock properties during vibration (cyclic) loading. The tests of the rheological properties of a cyclic load were conducted both in creep regime and in relaxation regime, at various levels of average load or strain and for various parameters of vibration (frequency, amplitude). The measured values of different parameter settings were compared and evaluated so that it was possible to set the dependence of cyclical rock loading in the rheological regime. For the purpose of the comparison of rock behavior during vibration and static loading, other tests were also carried out. The results of the research show that, in the course of cyclical loading, the rock rheological properties depend, to a significant extent, on the parameters of this loading, especially the amplitude and frequency.     

A nonstationary parameter model for the sandstone creep tests

The rock masses of hydro-fluctuation belt experience seepage pressure following impoundment in the Three Gorges Reservoir; its creep behaviors are significant for reservoir bank slopes. To study the creep behaviors under seepage pressure (0, 1.45, and 1.75 MPa), we performed creep tests using representative landslide sandstone in the Three Gorges Reservoir and investigated the sandstone creep behaviors under the coupling effects of seepage pressure and stress. Previous researches on rocks have usually regarded the creep constitutive parameter as a constant; however, in this study, a nonlinear, nonstationary, plastic-viscous (NNPV) creep model which can describe the curve of sandstone creep tests is proposed. The rock-creep parameters under three levels of seepage pressure were identified, and theoretical curves using the NNPV model agreed well with the experimental data, indicating that the new model cannot only describe the primary creep and secondary creep stages under varying seepage pressures but also, in particular, perfectly describes the tertiary creep stage. Finally, the sensitivity of the NNPV model parameters is analyzed, and the result shows that the nonstationary coefficient α and the nonlinear coefficient m are main parameters affecting the tertiary creep stage.     

不同含水状态砂岩分级循环荷载试验研究

为探究不同含水状态砂岩在循环荷载作用下的力学行为差异,对干燥、天然以及饱和三种含水状态下的砂岩进行了单轴分级循环加卸载试验。研究结果表明:由于水对砂岩的物理化学软化作用,饱水、天然以及干燥状态下的强度依次递减,而变形依次增加;卸载模量随着循环周次的增加呈先增大后减小的整体趋势,同一循环周次下,含水量越高,其卸载模量越小;体积应变开始出现拐点时的循环周次正好与卸载模量转折点所处的加卸载周次相对应;能量值随循环周次的增加均呈幂函数型增长,同一循环周次下,含水率越高的砂岩各项能量值越大;基于能量耗散的损伤定义表明:砂岩初始损伤值不为零,且均经历了一个先减小后增大的损伤演化过程,相同循环周次下,饱和、天然以及干燥砂岩的损伤量依次增大。     

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。     

Nonstationary flow surface theory for modeling the viscoplastic behaviors of soils

This paper presents a three-dimensional elastic viscoplastic model that can describe the time-dependent behaviors of soft clays. The constitutive model is formulated based on the nonstationary flow surface theory and incorporates new developments, including (i) an improved definition of the nonstationary flow surface that is capable of capturing the stress–strain behaviors under different loading paths, (ii) a unique stress–strain—viscoplastic-strain-rate equation that is able to explicitly describe the nonstationary flow surface, and (iii) a final stable state concept that identifies the final equilibrium state at the end of creep and stress relaxation, which is also used to simplify the loading criteria. The consistency condition is validated for the proposed model, and the viscoplastic multipliers are calculated by solving the consistency equations. The model performance is investigated and validated via simulation of both oedometer and triaxial tests. The numerical results demonstrate that the proposed model is able to reproduce the main viscoplastic behaviors of soils, including creep, undrained creep rupture, stress relaxation, rate effect and accumulated effect.     

深层膏质泥岩蠕变特性及非线性蠕变模型研究

泥岩作为油气储层常见复杂介质,在深部高温、高压环境下蠕变力学特性异常复杂,是引起套管损伤破坏的重要因素。以深部油气藏工程含膏质泥岩为研究对象,首先开展了高温为130 ℃、高围压为30 MPa、不同偏应力水平下多试样、单级加载三轴蠕变试验。该泥岩呈显著的时效力学特性,蠕变应力阀值较低,应力和持时对蠕变特性存在显著影响,低应力、长时间作用下泥岩亦呈现明显的稳态蠕变和加速蠕变破坏,且加速蠕变起始时间随应力增加呈指数降低关系。其次探讨了泥岩加速蠕变和强度损伤特性,提出了蠕变损伤起始时间概念,认为泥岩内部蠕变损伤变量可用指数函数予以描述。最后,基于蠕变损伤变量和起始时间,构建考虑泥岩加速蠕变的非线性改进Burgers蠕变模型,对蠕变参数开展辨识和分析,所选模型可准确地对深层膏质泥岩蠕变特性进行描述。研究成果旨在为深部泥岩油气藏套管工程长期稳定分析及安全评价提供可靠的依据。     

盐岩循环加卸载过程中的速率效应试验研究

作为一种典型软岩,盐岩力学特性的时间相关性显著,准确预测和评估盐穴储气库加卸载过程中的变形损伤能力,关系到能源储备库的长期安全稳定运行。为研究盐岩的速率效应,进行了不同加卸载速率的疲劳试验。基于现有蠕变本构模型,构建了速率效应方程,区分了加卸载过程中的蠕变塑性变形与加载塑性变形。研究结果表明：（1）盐岩的整体疲劳寿命、稳定变形阶段（即第2阶段）疲劳寿命占比基本随加卸载速率的增大而增大。（2）减速变形阶段（即第1阶段）疲劳寿命占比、稳定变形阶段平均残余应变基本随加卸载速率增大而减小。（3）速率耦合疲劳试验中,加卸载速率越大,残余应变越小,蠕变塑性变形随加卸载速率的增大而减小,当加卸载速率由0.04 kN/s增加至5 kN/s时,蠕变塑性变形在循环中的占比由85%下降至36%,呈现出负指数的关系。（4）整个循环加卸载过程中,加载塑性变形、蠕变塑性变形均呈现U型发展趋势,与盐岩疲劳过程的三阶段相对应。该研究结果可以为进一步分析盐岩蠕变塑性与加载塑性奠定基础。