Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

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.

Effect of Interface Form on Creep Failure and Life of Dissimilar Metal Welds Involving Nickel-Based Weld Metal and Ferritic Base Metal

For dissimilar metal welds(DMWs)involving nickel-based weld metal(WM)and ferritic heat resistant steel base metal(BM)in power plants,there must be an interface between WM and BM,and this interface suffers mechanical and microstructure mismatches and is often the rupture location of premature failure.In this study,a new form of WM/BM interface form,namely double Y-type interface was designed for the DMWs.Creep behaviors and life of DMWs containing double Y-type interface and conventional I-type interface were compared by finite element analysis and creep tests,and creep failure mechanisms were investigated by stress-strain analysis and microstructure characterization.By applying double Y-type interface instead of conventional I-type interface,failure location of DMW could be shifted from the WM/ferritic heat-affected zone(HAZ)interface into the ferritic HAZ or even the ferritic BM,and the failure mode change improved the creep life of DMW.The interface premature failure of I-type interface DMW was related to the coupling effect of microstructure degradation,stress and strain concentrations,and oxide notch on the WM/HAZ interface.The creep failure of double Y-type interface DMW was the result of Type IV fracture due to the creep voids and micro-cracks on fine-grain boundaries in HAZ,which was a result of the matrix softening of HAZ and lack of precipitate pinning at fine-grain boundaries.The double Y-type interface form separated the stress and strain concentrations in DMW from the WM/HAZ interface,preventing the trigger effect of oxide notch on interface failure and inhibiting the interfacial microstructure cracking.It is a novel scheme to prolong creep life and enhance reliability of DMW,by means of optimizing the interface form,decoupling the damage factors from WM/HAZ interface,and then changing the failure mechanism and shifting the failure location.

Numerical analysis on the factors affecting post-peak characteristics of coal under uniaxial compression

The post-peak characteristics of coal serve as a direct reflection of its failure process and are essential parameters for evaluating brittleness and bursting liability.Understanding the significant factors that influence post-peak characteristics can offer valuable insights for the prevention of coal bursts.In this study,the Synthetic Rock Mass method is employed to establish a numerical model,and the factors affecting coal post-peak characteristics are analyzed from four perspectives:coal matrix mechanical parameters,structural weak surface properties,height-to-width ratio,and loading rate.The research identifies four significant influencing factors:deformation modulus,density of discrete fracture networks,height-to-width ratio,and loading rate.The response and sensitivity of post-peak characteristics to single-factor and multi-factor interactions are assessed.The result suggested that feasible prevention and control measures for coal bursts can be formulated through four approaches:weakening the mechanical properties of coal pillars,increasing the number of structural weak surfaces in coal pillars,reducing the width of coal pillars,and optimizing mining and excavation speed.The efficacy of measures aimed at weakening the mechanical properties of coal is successfully demonstrated through a case study on coal burst prevention using large-diameter borehole drilling.

Creep constitutive model considering nonlinear creep degradation of fractured rock

Stability analysis of underground constructions requires a model study of rock masses’ long-term performance. Creep tests under different stress conditions was conducted on intact granite and granite samples fractured at 30° and 45° angles. The experimental results indicate that the steady creep strain rates of intact and fractured rock present an exponential increase trend with the increase of stress level. A nonlinear creep model is developed based on the experimental results, in which the initial damage caused by fracture together with the damage caused by constant load have been taken into consideration. The fitting analysis results indicated that the model proposed is more accurate at identifying the full creep regions in fractured granite, especially the accelerated stage of creep deformation. The least-square fit error of the proposed creep model is significantly lower than that of Nishihara model by almost an order of magnitude. An analysis of the effects of elastic modulus, viscosity coefficient, and damage factors on fractured rock strain rate and creep strain is conducted. If no consideration is given to the effects of the damage, the proposed nonlinear creep model can degenerate into to the classical Nishihara model.

High density dislocations enhance creep ageing response and mechanical properties in 2195 alloy sheet

The creep strain of conventionally treated 2195 alloy is very low,increasing the difficulty of manufacturing Al-Cu-Li alloy sheet parts by creep age forming.Therefore,finding a solution to improve the creep formability of Al-Cu-Li alloy is vital.A thorough comparison of the effects of cryo-deformation and ambient temperature large pre-deformation(LPD)on the creep ageing response in the 2195 alloy sheet at 160℃with different stresses has been made.The evolution of dislocations and precipitates during creep ageing of LPD alloys are revealed by X-ray diffraction and transmission electron microscopy.High-quality 2195 alloy sheet largely pre-deformed by 80%without edge-cracking is obtained by cryo-rolling at liquid nitrogen temperature,while severe edge-cracking occurs during room temperature rolling.The creep formability and strength of the 2195 alloy are both enhanced by introducing pre-existing dislocations with a density over 1.4×10^(15)m^(−2).At 160℃and 150 MPa,creep strain and creep-aged strength generally increases by 4−6 times and 30−50 MPa in the LPD sample,respectively,compared to conventional T3 alloy counterpart.The elongation of creep-aged LPD sample is low but remains relevant for application.The high-density dislocations,though existing in the form of dislocation tangles,promote the formation of refined T1 precipitates with a uniform dispersion.

Calculation of Mass Concrete Temperature and Creep Stress under the Influence of Local Air Heat Transfer

Temperature-induced cracking during the construction of mass concrete is a significant concern.Numerical simulations of concrete temperature have primarily assumed that the concrete is placed in an open environment.The problem of heat transfer between the air and concrete has been simplified to the concrete’s heat dissipation boundary.However,in the case of tubular concrete structures,where air inlet and outlet are relatively limited,the internal air temperature does not dissipate promptly to the external environment as it rises.To accurately simulate the temperature and creep stress in tubular concrete structures with enclosed air spaces during construction,we establish an air–concrete coupled heat transfer model according to the principles of conjugate heat transfer,and the accuracy of the model is verified through experiments.Furthermore,we conduct a case study to analyze the impact of airflow within the ship lock corridor on concrete temperature and creep stress.The results demonstrate that enhancing airflow within the corridor can significantly reduce the maximum concrete temperature.Compared with cases in which airflow within the corridor is neglected,the maximum concrete temperature and maximum tensile stress can be reduced by 12.5℃ and 0.7 MPa,respectively,under a wind speed of 4 m/s.The results of the traditional calculation method are relatively close to those obtained at a wind speed of 1 m/s.However,the temperature reduction process in the traditional method is faster,and the method yields greater tensile stress values for the corridor location.

Improving creep strength of the fine-grained heat-affected zone of novel 9Cr martensitic heat-resistant steel via modified thermo-mechanical treatment

The infamous type Ⅳ failure within the fine-grained heat-affected zone (FGHAZ) in G115 steel weldments seriously threatens the safe operation of ultra-supercritical (USC) power plants.In this work,the traditional thermo-mechanical treatment was modified via the replacement of hot-rolling with cold rolling,i.e.,normalizing,cold rolling,and tempering (NCT),which was developed to improve the creep strength of the FGHAZ in G115 steel weldments.The NCT treatment effectively promoted the dissolution of preformed M_(23)C_(6)particles and relieved the boundary segregation of C and Cr during welding thermal cycling,which accelerated the dispersed reprecipitation of M_(23)C_(6) particles within the fresh reaustenitized grains during post-weld heat treatment.In addition,the precipitation of Cu-rich phases and MX particles was promoted evidently due to the deformation-induced dislocations.As a result,the interacting actions between precipitates,dislocations,and boundaries during creep were reinforced considerably.Following this strategy,the creep rupture life of the FGHAZ in G115 steel weldments can be prolonged by 18.6%,which can further push the application of G115 steel in USC power plants.

Decadal Forecasts of Large Earthquakes along the Northern San Andreas Fault System, California: Increased Activity on Regional Creeping Faults Prior to Major and Great Events

The three largest earthquakes in northern California since 1849 were preceded by increased decadal activity for moderate-size shocks along surrounding nearby faults. Increased seismicity, double-difference precise locations of earthquakes since 1968, geodetic data and fault offsets for the 1906 great shock are used to re-examine the timing and locations of possible future large earthquakes. The physical mechanisms of regional faults like the Calaveras, Hayward and Sargent, which exhibit creep, differ from those of the northern San Andreas, which is currently locked and is not creeping. Much decadal forerunning activity occurred on creeping faults. Moderate-size earthquakes along those faults became more frequent as stresses in the region increased in the latter part of the cycle of stress restoration for major and great earthquakes along the San Andreas. They may be useful for decadal forecasts. Yearly to decadal forecasts, however, are based on only a few major to great events. Activity along closer faults like that in the two years prior to the 1989 Loma Prieta shock needs to be examined for possible yearly forerunning changes to large plate boundary earthquakes. Geodetic observations are needed to focus on identifying creeping faults close to the San Andreas. The distribution of moderate-size earthquakes increased significantly since 1990 along the Hayward fault but not adjacent to the San Andreas fault to the south of San Francisco compared to what took place in the decades prior to the three major historic earthquakes in the region. It is now clear from a re-examination of the 1989 mainshock that the increased level of moderate-size shocks in the one to two preceding decades occurred on nearby East Bay faults. Double-difference locations of small earthquakes provide structural information about faults in the region, especially their depths. The northern San Andreas fault is divided into several strongly coupled segments based on differences in seismicity.

Pore-pressure and stress-coupled creep behavior in deep coal:Insights from real-time NMR analysis

Understanding the variations in microscopic pore-fracture structures(MPFS) during coal creep under pore pressure and stress coupling is crucial for coal mining and effective gas treatment. In this manuscript, a triaxial creep test on deep coal at various pore pressures using a test system that combines in-situ mechanical loading with real-time nuclear magnetic resonance(NMR) detection was conducted.Full-scale quantitative characterization, online real-time detection, and visualization of MPFS during coal creep influenced by pore pressure and stress coupling were performed using NMR and NMR imaging(NMRI) techniques. The results revealed that seepage pores and microfractures(SPM) undergo the most significant changes during coal creep, with creep failure gradually expanding from dense primary pore fractures. Pore pressure presence promotes MPFS development primarily by inhibiting SPM compression and encouraging adsorption pores(AP) to evolve into SPM. Coal enters the accelerated creep stage earlier at lower stress levels, resulting in more pronounced creep deformation. The connection between the micro and macro values was established, demonstrating that increased porosity at different pore pressures leads to a negative exponential decay of the viscosity coefficient. The Newton dashpot in the ideal viscoplastic body and the Burgers model was improved using NMR experimental results, and a creep model that considers pore pressure and stress coupling using variable-order fractional operators was developed. The model’s reasonableness was confirmed using creep experimental data. The damagestate adjustment factors ω and β were identified through a parameter sensitivity analysis to characterize the effect of pore pressure and stress coupling on the creep damage characteristics(size and degree of difficulty) of coal.

Mechanical behavior of sandstone during post-peak cyclic loading and unloading under hydromechanical coupling

This paper investigates mechanical behaviours of sandstone during post-peak cyclic loading and unloading subjected to hydromechanical coupling effect, confirming the peak and residual strengths reduction laws of sandstone with water pressure, and revealing the influence of water pressure on the upper limit stress and deformation characteristics of sandstone during post-peak cyclic loading and unloading.Regarding the rock strength, the experimental study confirms that the peak strength σ_(p) and residual strength σ_(r) decrease as water pressure P increases. Especially, the normalized strength parameters σ_(p)/σ_(pk) and σ_(r)/σ_(re) was negatively and linearly correlated with the P/σ_(3). Moreover, the Hoek-Brown strength criterion can be applied to describe the relationship between effective peak strength and effective confining stress. During post-peak cyclic loading and unloading, both the upper limit stress σ_(p(i)) and crack damage threshold stress σ_(cd(i)) of each cycle tend to decrease with the increasing cycle number. A hysteresis loop exists among the loading and unloading stress–strain curves, indicating the unloading deformation modulus E_(unload) is larger than the loading deformation modulus E_(load). Based on experimental results,a post-peak strength prediction model related to water pressure and plastic shear strain is established.

Magnesium-based nanocomposites:A review from mechanical,creep and fatigue properties

The addition of nanoscale additions to magnesium(Mg)based alloys can boost mechanical characteristics without noticeably decreasing ductility.Since Mg is the lightest structural material,the Mg-based nanocomposites(NCs)with improved mechanical properties are appealing materials for lightweight structural applications.In contrast to conventional Mg-based composites,the incorporation of nano-sized reinforcing particles noticeably boosts the strength of Mg-based nanocomposites without significantly reducing the formability.The present article reviews Mg-based metal matrix nanocomposites(MMNCs)with metallic and ceramic additions,fabricated via both solid-based(sintering and powder metallurgy)and liquid-based(disintegrated melt deposition)technologies.It also reviews strengthening models and mechanisms that have been proposed to explain the improved mechanical characteristics of Mg-based alloys and nanocomposites.Further,synergistic strengthening mecha-nisms in Mg matrix nanocomposites and the dominant equations for quantitatively predicting mechanical properties are provided.Furthermore,this study offers an overview of the creep and fatigue behavior of Mg-based alloys and nanocomposites using both traditional(uniaxial)and depth-sensing indentation techniques.The potential applications of magnesium-based alloys and nanocomposites are also surveyed.

Creep behavior and permeability evolution of coal pillar dam for underground water reservoir

Using goof as water storage space plays a vital role in the ecological environment and economic development of arid mining areas,while the rock strength and the stability of coal pillars in underground water reservoirs are closely related to creep process.In this work,triaxial creep-seepage tests were conducted for coal samples to develop new insights into the creep behavior and permeability evolution.The results showed that the creep deformation and permeability evolution of coal samples exhibit three stages,namely,the compaction hardening stage before the stress threshold,volumetric compaction stage,and volumetric dilatancy stage.The coal permeability decreases first and then increases with the creep strain and it is well correlated with the variation of volumetric strain.

A post-peak dilatancy model for soft rock and its application in deep tunnel excavation

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy(PPD)behavior and simulate surrounding rock deformation;however,simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms.This study developed a PPD model for rocks(rock masses)based on the Alejanoe-Alonso(A-A)dilatancy model.The developed model comprehensively reflects the influences of confining pressure(σ_(3))and plastic shear strain(γ^(p)),with the advantages of a simple mathematical form,while requiring fewer parameters and demonstrating a clear physical significance.The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A-A model,particularly for Witwatersrand quartzite and jointed granite.The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated,and the model was found to be more suitable for the soft and large-scale rocks,e.g.deep rock mass.The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass,and the developed semi-analytical solution was compared and verified with existing analytical solutions.The sensitivities of the rock dilatancy to γ^(p) and σ_(3) showed significant spatial variabilities along the radial direction of the surrounding rock,and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elasticeplastic boundary to the tunnel wall,thereby presenting the σ3-or γ^(p)-dominated differential effects of rock dilatancy.Tunnel deformation parabolically or exponentially increased with increasing in situ stress(buried depth).The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling,which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.

Supporting structure failure caused by the squeezing tunnel creep and its reinforcement measure

Tunnels deeply buried have high crustal stress and are prone to large deformation disasters when encountering soft rock.The large deformation phenomenon during the construction process of the Maoxian Tunnel on the Chengdu-Lanzhou Railway is particularly evident.This article focuses on the large deformation problem of the No.1 inclined shaft of the Maoxian Tunnel,and uses on-site monitoring methods to explore the reasons for tunnel structure failure,and analyzes the mechanical behavior of the tunnel structure.By using numerical simulation methods,the effectiveness of the second-layer support in resisting creep loads in tunnels was studied,and the influence of the construction time of the secondlayer support on the mechanical properties of the tunnel was discussed.The results indicate that the first-layer support in the tunnel is a structural failure caused by asymmetric deformation caused by creep,while the second-layer support has a good effect on resisting creep loads.The research results can provide a technical reference for deformation control of squeezing tunnels.

Tailoring the microstructural characteristics and enhancing creep properties of as-cast Mg-5Bi-5Sn alloy through Mn addition

The creep properties, microstructural characteristics and creep mechanisms of as-cast Mg-5Bi-5Sn(BT55) alloy without and with Mn(BTM550) addition were investigated via creep at 423, 448, and 473 K as well as stresses of 30, 50 and 75 MPa. The results indicate that adding Mn can result in the formation of primary and the dynamic precipitated α-Mn phases. In addition, the morphology of the precipitated Mg_(3)Bi_(2) phase and the orientation relationship between Mg_(2)Sn precipitates and α-Mg can be effectively modified. Tailoring the microstructural characteristics is responsible for the improved creep performance of BTM550 alloy. The dominant creep mechanisms in BT55 and BTM550 alloys are dislocation cross-slip and climb, respectively. Furthermore, twinning and pyramidal slip play an assisting part in both alloys during creep process.

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.

Anisotropic creep behavior of soft-hard interbedded rock masses based on 3D printing and digital imaging correlation technology

Three-dimensional(3D)printing technology is increasingly used in experimental research of geotechnical engineering.Compared to other materials,3D layer-by-layer printing specimens are extremely similar to the inherent properties of natural layered rock masses.In this paper,soft-hard interbedded rock masses with different dip angles were prepared based on 3D printing(3DP)sand core technology.Uniaxial compression creep tests were conducted to investigate its anisotropic creep behavior based on digital imaging correlation(DIC)technology.The results show that the anisotropic creep behavior of the 3DP soft-hard interbedded rock mass is mainly affected by the dip angles of the weak interlayer when the stress is at low levels.As the stress level increases,the effect of creep stress on its creep anisotropy increases significantly,and the dip angle is no longer the main factor.The minimum value of the long-term strength and creep failure strength always appears in the weak interlayer within 30°–60°,which explains why the failure of the layered rock mass is controlled by the weak interlayer and generally emerges at 45°.The tests results are verified by comparing with theoretical and other published studies.The feasibility of the 3DP soft-hard interbedded rock mass provides broad prospects and application values for 3DP technology in future experimental research.

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.

Static Bending Creep Properties of Glass Fiber Surface Composite Wood

To study the static bending creep properties of glass fiber reinforced wood,glass fiber reinforced poplar(GFRP)specimens were obtained by pasting glass fiber on the upper and lower surfaces of Poplar(Populus euramevicana,P),the performance of Normal Creep(NC)and Mechanical Sorptive Creep(MSC)of GFRP and their influencing factors were tested and analyzed.The test results and analysis show that:(1)The MOE and MOR of Poplar were increased by 17.06%and 10.00%respectively by the glass fiber surface reinforced composite.(2)The surface reinforced P with glass fiber cloth only exhibits the NC pattern of wood and loses the MSC characteristics of wood,regardless of the constant or alternating changes in relative humidity.(3)The instantaneous elastic deformation,viscoelastic deformation,viscous deformation and total creep deflection of GFRP are positively correlated with the stress level of the external load applied to the specimen.Still,the specimen’s creep recovery rate is negatively correlated with the stress level of the external load applied to the specimen.The static creep deflection and viscous deformation of GFRP increase with the increase of the relative humidity of the environment.(4)The MSC maximum creep deflection of GFRP increased by only 7.41%over the NC maximum creep deflection,but the MSC maximum creep deflection of P increased by 199.25%over the NC maximum creep deflection.(5)The Burgers 4-factor model and the Weibull distribution equation can fit the NC and NC recovery processes of GFRP well.