A creep model for ultra-deep salt rock considering thermal-mechanical damage under triaxial stress conditions

To investigate the specific creep behavior of ultra-deep buried salt during oil and gas exploitation,a set of triaxial creep experiments was conducted at elevated temperatures with constant axial pressure and unloading confining pressure conditions.Experimental results show that the salt sample deforms more significantly with the increase of applied temperature and deviatoric loading.The accelerated creep phase is not occurring until the applied temperature reaches 130℃,and higher temperature is beneficial to the occurrence of accelerated creep.To describe the specific creep behavior,a novel three-dimensional(3D)creep constitutive model is developed that incorporates the thermal and mechanical variables into mechanical elements.Subsequently,the standard particle swarm optimization(SPSO)method is adopted to fit the experimental data,and the sensibility of key model parameters is analyzed to further illustrate the model function.As a result,the model can accurately predict the creep behavior of salt under the coupled thermo-mechanical effect in deep-buried condition.Based on the research results,the creep mechanical behavior of wellbore shrinkage is predicted in deep drilling projects crossing salt layer,which has practical implications for deep rock mechanics problems.

Triaxial creep damage characteristics of sandstone under high crustal stress and its constitutive model for engineering application

The creep characteristics of rock under high crustal stress are of important influence on the long‐term stability of deep rock engineering.To study the creep characteristics and engineering application of sandstone under high crustal stress,this study constructed nonlinear creep damage(NCD)constitutive mode based on the triaxial graded loading‒unloading creep test of sandstone in the Yuezhishan Tunnel.A numerical NCD constitutive model and a breakable lining(BL)model were developed based on FLAC3D and then applied to the stability analysis of the Yuezhishan Tunnel.Based on the creep test results of sandstone,a power function of creep rate and stress level was constructed,by which the long‐term strength was solved.The results show that the long‐term strength of the red sandstone based on the related function of the steady‐state creep rate and stress level is close to the measured stress value in engineering.The NCD model considering damage factors reflects the instantaneous and viscoelastic plasticity deformation characteristics of the red sandstone.The numerical NCD constitutive model and the BL model can reflect surrounding rock deformation characteristics and lining failure characteristics in practical engineering.The research results provide theoretical references for long‐term stability analysis of rock engineering and the deformation control of surrounding rock under high crustal stress.

Non-linear creep damage model of sandstone under freeze-thaw cycle

To study rock damage characteristics under long-term freeze-thaw cycles and loads,rock freeze-thaw and creep damage factors were defined based on nuclear magnetic resonance porosity and volume strain,respectively.The damage factor is introduced into the basic rheological element,and the non-linear creep damage constitutive model and freeze-thaw rock equation are established to describe non-linear creep characteristics under a constant load.Simultaneously,the creep test of freeze-thaw rock under step loading is performed.Based on the test data,the applicability and accuracy of the creep damage freeze-thaw rock model are analyzed and verified.The results show that freeze-thaw cycles result in continuous rock pore structure damage and deterioration,and nuclear magnetic resonance porosity enhancement.The constant load induces increasing rock plastic deformation,volume,and creep aging damage.As the loading stress increases,the instantaneous rock elastic parameters increase,and the rheological elastic and viscosity parameters decrease.Furthermore,the damage degradation of freeze-thaw cycles weakens the rock viscoplasticity,resulting in a rapid decrease in the viscosity parameter with an increase in freeze-thaw cycles.Generally,the continuous damage of the rock is degraded,and the long-term strength decreases continuously.

DAMAGE AND CREEP MODEL FOR ROCK SALT AS WELL AS ITS VALIDATION

The constitutive model Hou/Lux,based on continuum damage mechanics and on the material model Lubby2 is presented and the damage,the healing of damage,the tertiary creep and the creep rupture of rock salt described. An application shows how phenomena observed in laboratory tests on axially perforated cylinder sample, such as softening, dilatancy, spalling and radial deformation into the axial bore as well as spalling can be numerically simulated with the model Hou/Lux. Furthermore,it is then evaluated against the measured permeability and stress profiles of a 37-year-old drift at the Sondershausen minein,Germany. Satisfactory agreement is obtained between the calculated and measured data.

Visco-elastoplastic damage constitutive model for compressed asphalt mastic

In order to describe the three-stage creep behavior of compressed asphalt mastic, a visco-elastoplastic damage constitutive model is proposed in this work. The model parameters are treated as quadratic polynomial functions with respect to stress and temperature. A series of uniaxial compressive creep experiments are performed at various stress and temperature conditions in order to determine these parameter functions, and then the proposed model is validated by comparison between the predictions and experiments at the other loading conditions. It is shown that very small permanent deformation at low stress and temperature increases rapidly with elevated stress or temperature and the damage may initiate in the stationary stage but mainly develops in the accelerated stage. Compared with the visco-elastoplastic models without damage, the predictions from the proposed model is in better agreement with the experiments, and can better capture the rate-dependency in creep responses of asphalt mastic especially below its softening point of 47 ℃

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process,nonlinear elements and creep damage are generally introduced in the model to resolve this issue.However,several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution.Nevertheless,the creep damage mechanism of rocks is still not clearly understood.In this study,a reasonable representation of the damage variables of solid materials is presented.Specifically,based on the Gurson damage model,the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established.Further,the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model.Finally,the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite.And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite.Overall,this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern,which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

MESO APPROACHES FOR THE CREEP DAMAGE BEHAVIOR OF NICKEL-BASE DIRECTIONALLY SOLIDIFIED SUPERALLOYS

A self-consistent creep damage constitutive model and a finite element model have been developed for nickel-base directionally solidified superalloys. Grain degradation and grain boundary voiding are considered. The model parameters are determined from the creep test data of a single crystal and a directionally solidified superalloy with a special crystallographic orientation. The numerical analysis shows that the modeled creep damage behaviors of nickel-base directionally solidified super-alloys with different crystallographic orientations are in good agreement with the experimental data.

A CREEP DAMAGE EQUATION FOR ROCKS

In this paper,based on many experimental results,a creep damage equation for rocks with a creep modulus that can describe the history of damage has been deduced.According to the equation,a creep damage model for rock materials is constructed,and it is shown that the extent of their damage,or damage degree,during creep can be determined by means of simple experiments.

Creep characteristics and constitutive model for frozen mixed soils

The uniform settle caused by the permafrost creep is still the primary problem of engineering construction in cold region.To investigate the creep characteristics of frozen soils mixed with silty clay and coarse-grained sand,several triaxial creep tests of frozen mixed soils under different conditions(temperature,confining pressure,coarse-grained particle content) were performed,and the effects of the temperature,confining pressure and coarse particle content on the creep characteristics of frozen mixed soils were also analyzed.The results of the experiments indicated that when the confining pressure was low,the specimen exhibited an attenuation creep under a low-stress level(0.4-0.7) and a non-attenuation creep under a high-stress level(0.7-0.9).In contrast,when the confining pressure was high,the specimen had both initial and stable creep stages,but no the accelerated creep stage.The higher the content of coarse grains,the shorter the stable creep stage,and the easier to enter the accelerated creep stage for the specimen.Further,the long-term strength of frozen soils decreased with an increase in the content of coarse grains.Finally,a newly improved Nishihara model was proposed to consider both the hardening effect and damage effect by introducing both the hardening and damage variables,which can model the entire creep process of frozen soils modeled relatively easily.It was found that with the increasing content of coarse particle,both the strengthening and damaged effects in the creep process are reduced。

A power function model for simulating creep mechanical properties of salt rock

In this paper,a new micro-creep model of salt rock is proposed based on a linear parallel bonded model(LPBM)using the two-dimensional particle flow code(PFC2D).The power function weakening form is assumed to describe the variation of the parallel bonded diameter(PBD)over time.By comparing with the parallel-bonded stress corrosion(PSC)model,a smaller stress fluctuation and smoother creep strain−time curves can be obtained by this power function model at the same stress level.The validity and adaptability of the model to simulate creep deformation of salt rock are verified through comparing the laboratory creep test curves and the Burgers model fitting result.The numerical results reveal that this model can be capable of capturing the creep deformation and damage behavior from the laboratory observations.

高地应力-化学侵蚀耦合作用下炭质板岩蠕变试验及非线性蠕变损伤模型

为克服高程障碍并降低施工风险,可采用长大隧道穿越崇山峻岭,但这些隧道往往处于深埋高地应力环境,并受到化学侵蚀影响。为了解决此问题,以丽江—香格里拉炭质板岩大变形隧道为研究对象,采用室内试验和理论推导,研究深埋炭质板岩隧道受化学侵蚀作用下的围岩变形特性。在Poyting-Thomson体蠕变体的基础上,根据模型元件的力学特性,叠加了损伤元件、化学损伤元件和非线性元件,提出高地应力-化学侵蚀耦合作用下炭质板岩非线性蠕变损伤本构关系。研究结果表明:1)炭质板岩试样受化学侵蚀影响显著,侵蚀90 d试样所产生的轴向蠕变应变为侵蚀0 d试样的2.02倍,侵蚀60 d试样所产生的径向蠕变为侵蚀0 d试样的1.85倍;2)受侵蚀的炭质板岩试样在三轴压缩状态下破裂以斜向贯通裂隙为主,并产生一定的滑移错动裂隙,且沿轴线的拉伸劈裂破坏受围压作用抑制明显,未产生竖向贯通裂隙。

深部硬脆性岩石分数阶蠕变损伤模型研究

硬脆性岩石与软弱岩石一样会发生蠕变破坏,因此研究其蠕变特性对围岩的稳定性具有重要意义。假设黏滞系数与初始弹性模量的幂次方成正比,以此表征岩石初始的软硬和致密状态对其蠕变行为的影响,提出一种改进的分数阶非线性黏滞体,以描述衰减和稳定蠕变阶段的黏弹性特征;根据连续损伤力学理论,引入损伤因子,建立了考虑时效损伤的分数阶非线性损伤黏塑性体,以描述加速蠕变阶段的力学行为。将胡克体、改进分数阶非线性黏滞体和分数阶非线性损伤黏塑性体串联,建立一个硬脆性岩石非线性蠕变损伤模型,并验证其合理性,试验曲线与模型理论曲线吻合良好,说明该模型能较好描述硬脆性岩石蠕变全过程。对模型参数进行敏感性分析,讨论其对蠕变行为的影响,结果表明相关参数对准确描述硬脆性岩石的蠕变特征有重要作用。

卸围压下弱胶结软岩分数阶蠕变损伤本构模型

为研究地下硐室开挖卸荷诱发的软岩蠕变损伤特征,以西部矿区弱胶结软岩为研究对象,利用GDS HPTAS开展了分级卸围压蠕变试验,研究了不同含水条件下弱胶结软岩卸围压下蠕变特征和蠕变速率特征。基于稳态蠕变速率倒数的方法,确定了弱胶结软岩长期强度和含水率的数学指数函数关系。基于蠕变速率曲线特征提出了一种确定衰减蠕变与等速蠕变分界点t_1和等速蠕变与加速蠕变分界点t_2的新方法。引入Riemann-Liouville分数阶积分算子和负时间指数损伤演化变量,定义了非线性损伤Abel黏壶,建立了一个包括弹性元件、黏弹性损伤元件、黏性元件和非线性黏塑性损伤元件的六元件分数阶蠕变损伤本构模型。基于试验结果,采用Trust-Region算法进行了模型参数识别和敏感性分析。结果表明,所建立的模型具有物理意义明确、与试验值吻合度较高等特点,可较为准确地反映开挖卸荷条件下弱胶结软岩蠕变损伤特性,对保障地下工程长期稳定性具有重要的意义。

强扰煤岩体蠕变过程中跨尺度非连续结构演化研究进展

【目的和方法】巷道围岩时效变形破坏、蠕变型冲击地压等灾害是深井面临的重大威胁,加之深部采动与结构变化的影响,亟需研究强扰煤岩体蠕变过程中跨尺度非连续结构演化规律,系统回顾煤岩体力学性质的尺度效应、非连续结构与多物理场效应,以及煤岩体长时稳定性、蠕变演化规律与力学模型。【结果和结论】强调不同尺度(细观-宏观-工程尺度)、不同尺寸(REV范围内)煤岩变形破裂过程中非连续结构(包括裂隙和矿物)与物理力学性质存在密切的关联特征。指出煤岩体跨尺度非连续结构导致应力场非均匀分布,造成力学各向异性、尺度效应及尺寸效应,进而出现非协调宏观破裂现象。透明解析与推演煤岩变形破裂过程中跨尺度非连续结构与多物理场演化规律,是认识煤岩灾变内禀机制的关键。明确指出现有蠕变实验与蠕变模型在煤岩表面变形及破裂方面具有优势,但无法预测煤岩内部变形与非连续结构;为此提出了全尺寸CT扫描重构、数字体图像相关(DVC)、跨尺度等效岩体-等效晶质建模(SRM-GBM)相结合的破解方法。对扰动煤岩体蠕变前沿问题进行了讨论,阐明了非连续结构与应力引起内部变形损伤诱发蠕变这一新观点,指出非连续结构和应力是煤岩非协调蠕变的主控因素,最后建立了强扰煤岩体蠕变过程中跨尺度非连续结构与多物理场演化的精细化建模及透明解析新方法。研究成果为相关矿山灾害的发生机理、预警与防控提供理论基础。

基于分数阶黏壶元件的岩石损伤蠕变模型

目的为了建立一个能描述岩石蠕变全过程的蠕变模型。方法首先以分数阶黏壶元件描述岩石的黏弹性,采用基于Kachanov损伤率公式的损伤体描述岩石的粘塑性并串联一个胡克体建立成只有四个元件的蠕变模型。然后,将其本构方程推广到三维应力状态,考虑球应力,并引入一个屈服函数来准确判断岩石是否发生非稳定蠕变。最后,采用最小二乘法分析得到模型参数,用红砂岩和砂质泥岩的蠕变实验数据验证模型的有效性。结果新的蠕变模型理论曲线与实验数据曲线吻合较好,可以描述岩石蠕变的全过程。结论新的蠕变模型解决了经典模型在描述岩石蠕变时的模型复杂和参数较多的问题,对研究岩石蠕变特性具有一定的参考价值。

动态冲击下红砂岩蠕变特性及损伤本构模型

为研究岩石在动态扰动下的蠕变特性,在自行研发的冲击扰动蠕变试验装置上,对细粒红砂岩开展了多级冲击扰动蠕变试验,分析了不同蠕变应力与扰动能量下瞬时变形与蠕变行为,结合间接法得到了扰动能量对长期强度的影响。结果表明:动态扰动在较低的蠕变应力下使试样致密,而当蠕变应力超过一定的应力阈值后加剧试样内部的损伤恶化,其引起的瞬时变形与蠕变应变则随蠕变应力表现出先减后增的规律;随着动态扰动能量的增加,试样的破坏应变越大,但长期强度越低;引入长期强度与扰动能量的相关性、动态扰动单元和扰动-损伤黏性元件,建立了黏塑性扰动损伤蠕变模型,结合试验数据验证了该模型的准确性,该模型可以准确地描述砂岩在静态恒载和动态扰动组合作用下的瞬态变形和蠕变行为。该研究成果对于钻爆法隧道的支护设计以及安全生产具有重要的理论意义与应用前景。

钛合金室温受压蠕变损伤本构模型

为了解决工程上在评估深潜器耐压壳体安全可靠性时不考虑拉压蠕变破坏机理产生的差异,会导致较大计算误差问题,本文提出了适用于室温蠕变的蠕变损伤本构模型。通过分析钛合金材料蠕变特性,考虑了室温环境下位错堆积造成的蠕变阻力,并且位错堆积的现象与时间有关。基于微分自洽法提出了适用于室温环境下的钛合金蠕变本构模型,得到受压情况下TC4ELI的相关材料参数,并将该模型用USDFLD和CREEP子程序进行定义。研究表明:对于受压结构而言,使用通过拉伸蠕变实验得到的本构模型的计算结果会过于保守,对于含V型缺口平板受压时等效蠕变应变的相对误差为168.20%。本文所提出的模型适用于环肋耐压壳结构的蠕变损伤分析。

温度-应力耦合作用下深部盐岩蠕变损伤模型

随着我国盐岩储库工程的兴建,浅部适宜矿床逐渐利用殆尽,盐岩储库向深部发展成为必然趋势。为了研究深部盐岩储库实际运营过程中,围岩在三向地应力和温度耦合作用下的蠕变损伤特征,进行了不同温度和应力耦合作用下深部盐岩的三轴蠕变试验。考虑温度和应力对深部盐岩蠕变损伤的影响,认为温度损伤伴随蠕变全过程,所处应力状态达到屈服极限时应力损伤开始发挥作用,且温度和应力与损伤变量之间分别满足Weibull分布和负指数函数的关系。引入分数阶Abel黏壶改进西原正夫模型,建立了一种新的考虑温度-应力耦合效应的黏弹塑性蠕变损伤模型。该模型不仅形式简单,且每个参数都有明确的物理意义,方便模型在数值计算和工程实践中的应用。结果表明:深部盐岩的稳态蠕变率是偏应力和温度的函数,拟合出稳态蠕变应变率本构方程中材料参数A=32.39 MPa-4.83/h、激活自由能Q=7.84×10^(4) kJ/mol、蠕变应力指数n=4.83;不同温度和应力下的黏弹塑性蠕变损伤模型的理论解析解与对应试验数据有良好的吻合度,验证了模型的正确性和精确度。通过蠕变损伤模型各力学元件拟合参数结果验证了温度和应力对岩石蠕变性能的影响规律,证明了所建模型的合理性。所建模型不仅可以精确表征岩石的衰减和稳态蠕变阶段,也能较好地描述加速蠕变阶段的变形特性。

浸水条件下含水率对粉砂质泥岩蠕变特性的影响研究

泥岩具有强度低、遇水易软化的特点,尤其是富水泥岩地层,对工程岩体的长期稳定性影响较大,但相关研究少有报道,因此亟待深入研究泥岩遇水蠕变特性。开展了不同初始含水率泥岩试样在天然和浸水条件下的分级加载蠕变试验,研究了水对岩体蠕变特性的影响机理,结合广义Kelvin模型,构建了考虑含水劣化效应的蠕变损伤本构模型,并将新模型嵌入FLAC3D有限差分软件中,模拟了不同工况下泥岩蠕变变形特性,并与室内试验结果进行了对比。结果表明:随着含水率的增大,岩体蠕变应变量增大,长期强度降低;相比天然条件,浸水环境使得岩体长期强度劣化更为严重,试样初始含水率越小,浸水条件对其蠕变变形影响越大;将岩体因水的劣化效应定义为蠕变参数的损伤因子,损伤因子随着含水率的增加而提高;考虑含水劣化效应的蠕变损伤本构模型数值模拟结果与室内试验结果基本吻合,验证了新模型的合理性。

含埋藏裂纹结构的拘束效应和蠕变裂纹孕育期研究

以含埋藏椭圆形裂纹的高温试样结构为研究对象,基于延性耗散模型,用三维(3D)有限元方法对其拘束效应和蠕变裂纹孕育期进行了研究。结果表明,对于裂尖前沿拘束水平,拘束参量Q的最大值总是分布在椭圆形裂纹的长轴端点处,且随着裂纹横向长度c和纵向长度a的增加,拘束参量Q越大,意味着应力集中越严重,该处位置更为危险;对于蠕变裂纹孕育期,椭圆形裂纹深度比a/t越大或长度比a/c越小,或者载荷越大,则蠕变裂纹损伤率越高,结构发生蠕变裂纹萌生的孕育期越短,结构越危险。此外,建立了拘束参量和蠕变裂纹孕育期的预测公式和工程计算方法,并验证了蠕变裂纹孕育期工程计算模型的有效性。