To investigate the seismic performance of hollow reinforced concrete （RC） bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametri...To investigate the seismic performance of hollow reinforced concrete （RC） bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametric study is carried out for different axial load ratios, longitudinal reinforcement ratios and lateral reinforcement ratios. The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity, which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns. Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations, and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance. However, the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design. The hollow RC rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations, and may be considered as a substitute for current hollow RC rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges （JTG/T B02-01-2008）. The length of the plastic hinge region was found to approach one sixth of the hollow RC rectangular bridge column height for all specimen columns, and it was much less than those specified in the current JTG/T. Thus, the length of the plastic hinge region is more concentrated for RC rectangular hollow bridge columns.展开更多
The Norwegian Public Roads Administration(NPRA) is planning for an upgrade of the E39 highway route at the westcoast of Norway. Fixed links shall replace ferries at seven fjord crossings. Wide spans and large depths a...The Norwegian Public Roads Administration(NPRA) is planning for an upgrade of the E39 highway route at the westcoast of Norway. Fixed links shall replace ferries at seven fjord crossings. Wide spans and large depths at the crossings combined with challenging subsea topography and environmental loads call for an extension of existing practice. A variety of bridge concepts are evaluated in the feasibility study. The structures will experience significant loads from deadweight, traffic and environment. Anchoring of these forces is thus one of the challenges met in the project. Large-size subsea rock anchors are considered a viable alternative. These can be used for anchoring of floating structures but also with the purpose of increasing capacity of fixed structures. This paper presents first a thorough study of factors affecting rock anchor bond capacity. Laboratory testing of rock anchors subjected to cyclic loading is thereafter presented. Finally, the paper presents a model predicting the capacity of a rock anchor segment, in terms of a ribbed bar, subjected to a cyclic load history. The research assumes a failure mode occurring in the interface between the rock anchor and the surrounding grout. The constitutive behavior of the bonding interface is investigated for anchors subjected to cyclic one-way tensile loads. The model utilizes the static bond capacity curve as a basis, defining the ultimate bond sbuand the slip s1 at τ. A limited number of input parameters are required to apply the model. The model defines the bond-slip behavior with the belonging rock anchor capacity depending on the cyclic load level(τcy/τ), the cyclic load ratio(R= τcy/τcy), and the number of load cycles(N). The constitutive model is intended to model short anchor lengths representing an incremental length of a complete rock anchor.展开更多
The attenuation of the acoustic activity in marble specimens under uniaxial compressive loadingunloading loops is quantified in juxtaposition to that of the electric activity.In parallel,the existence of"pre-fail...The attenuation of the acoustic activity in marble specimens under uniaxial compressive loadingunloading loops is quantified in juxtaposition to that of the electric activity.In parallel,the existence of"pre-failure indiceso"warning about entrance into a critical stage,that of impending fracture,is explored.The acoustic activity is quantified in terms of the normalized number of acoustic hits,their average rate of production and their cumulative energy,and,the cumulative counts and their average rate of change.The electric activity is studied in terms of the pressure stimulated currents and the electric charge released.The analysis revealed that the acoustic and electric activities are linearly correlated to each other,suggesting that they are different manifestations of the same damage mechanisms.In addition,Kaiser's effect,governing the acoustic activity,is found to govern,also,the electric activity.Moreover,it is concluded that entrance into the critical stage is safely predicted by means of a simple criterion,based on the evolution of the average rate of change of the normalized cumulative counts in the natural time domain.These predictions are almost identical with those of the criterion based on the "varianceo" and the "entropies" of the time series of acoustic events in this domain.展开更多
This paper presents an ultralow-frequency cyclic loading creep test system for rock salt.The system comprises five subsystems:a cyclic load generation system,a triaxial pressure chamber,a pressure and deformation moni...This paper presents an ultralow-frequency cyclic loading creep test system for rock salt.The system comprises five subsystems:a cyclic load generation system,a triaxial pressure chamber,a pressure and deformation monitoring system,a signal acquisition and load control integrated system,and an automatic oil replenishment and discharge system.This test system overcomes the limitations of traditional electrohydraulic servo creep testing machines and gravity loading creep testing machines when conducting low-frequency cyclic load creep tests.This allows for long-term(1-2 years)creep tests under extremely-low-frequency cyclic loading conditions,which simulate the actual operating conditions of salt cavern gas storage.The cyclic load generation system converted constant-weight loads into a continuously variable hydraulic oil pressure and amplified the oil pressure using a pressure intensifier,which provided a stable load source for the test system.Using this test system,creep tests were performed under low-frequency cyclic loading with periods of 1 d and 7 d.The results showed that the test system performed well,as evidenced by the validation of the loading capacity,loading stability,and temperature control stability.Comparing the creep deformation of rock salt samples with the cyclic periods of 1 d and 7 d,it was observed that,within this cyclic period range,the creep deformation of the sample increased with higher loading frequencies,provided that the cyclic loading waveform and stress remained constant.展开更多
Red clay,widely used as a subgrade material in southern China,requires a reliable evaluation of its dynamic behavior to ensure infrastructure safety.Long-term cyclic triaxial tests were conducted on red clay from typi...Red clay,widely used as a subgrade material in southern China,requires a reliable evaluation of its dynamic behavior to ensure infrastructure safety.Long-term cyclic triaxial tests were conducted on red clay from typical,complex subway subgrades to investigate its dynamic properties and shakedown behavior under intermittent cyclic loading.Results show that intermittent cyclic loading,especially with multiple amplitudes,causes greater axial plastic strain and lower post-cyclic strength than continuous loading.These effects diminish with increasing confining pressure.Notably,axial strain partially recovers during loading intervals,with recovery ratios depending on the number and sequence of pauses.Based on the rules of cumulative plastic strain rates and cumulative plastic strain increments,shakedown behavior for red clay under intermittent cyclic loading is divided into three categories:plastic shakedown,critical shakedown,and plastic creep.A quantitative shakedown limit criterion is proposed using the Boltzmann function.Shakedown behavior significantly influences the post-cyclic strengths,and the influence diminishes as confining pressure increases.Samples exhibiting plastic creep and plastic shakedown behavior have the lowest and highest strengths,and those with critical shakedown behaviors have medium strengths.Cyclic loading with relatively low-stress amplitude causes a hardening effect,while cyclic loading intermittence or cyclic loading with relatively high-stress amplitude causes a degradation effect,and both effects are mitigated by higher confining pressures.展开更多
It is important to analyze the damage evolution process of surrounding rock under different water content for the stability of engineering rock mass.Based on digital speckle correlation(DSCM),acoustic emission(AE)and ...It is important to analyze the damage evolution process of surrounding rock under different water content for the stability of engineering rock mass.Based on digital speckle correlation(DSCM),acoustic emission(AE)and electromagnetic radiation(EMR),uniaxial hierarchical cyclic loading and unloading tests were carried out on sandstones with different fracture numbers under dry,natural and saturated water content,to explore the fracture propagation,failure precursor characteristics and damage response mechanism under the influence of water content effect.The results show that with the increase of water content,the peak stress and crack initiation stress decrease gradually,and the decreases are 15.28%-21.11%and 17.64%-23.04%,respectively.The peak strain and crack initiation strain increase gradually,and the increases are 19.85%-44.53%and 19.15%-41.94%,respectively.The precracked rock with different water content is mainly characterized by tensile failure at different loading stages.However,with the increase of water content,the proportion of shear cracks gradually increases,while acoustic emission events gradually decrease,the dissipative energy and energy storage limits of the rock under peak load gradually decrease,and the charge signal increases significantly,which is because the lubrication effect of water reduces the friction coefficient between crack surfaces.展开更多
Preexisting cracks inside tight sandstones are one of the most important properties for controlling the mechanical and seepage behaviors.During the cyclic loading process,the rock generally exhibits obvious memorabili...Preexisting cracks inside tight sandstones are one of the most important properties for controlling the mechanical and seepage behaviors.During the cyclic loading process,the rock generally exhibits obvious memorability and irreversible plastic deformation,even in the linear elastic stage.The assessment of the evolution of preexisting cracks under hydrostatic pressure loading and unloading processes is helpful in understanding the mechanism of plastic deformation.In this study,ultrasonic measurements were conducted on two tight sandstone specimens with different bedding orientations subjected to hydrostatic loading and unloading processes.The P-wave velocity was characterized by a similar response with the volumetric strain to the hydrostatic pressure and showed different strain sensitivities at different loading and unloading stages.A numerical model based on the discrete element method(DEM)was proposed to quantitatively clarify the evolution of the crack distribution under different hydrostatic pressures.The numerical model was verified by comparing the evolution of the measured P-wave velocities on two anisotropic specimens.The irreversible plastic deformation that occurred during the hydrostatic unloading stage was mainly due to the permanent closure of plastic-controlled cracks.The closure and reopening of cracks with a small aspect ratio account for the major microstructure evolution during the hydrostatic loading and unloading processes.Such evolution of microcracks is highly dependent on the stress path.The anisotropy of the crack distribution plays an important role in the magnitude and strain sensitivity of the P-wave velocity under stress conditions.The study can provide insight into the microstructure evolution during cyclic loading and unloading processes.展开更多
Cyclic changes in the internal pressure of compressed air energy storage reservoirs in abandoned coal mines result in complex alternating loads on the rocks surrounding the energy storage reservoirs.These complex alte...Cyclic changes in the internal pressure of compressed air energy storage reservoirs in abandoned coal mines result in complex alternating loads on the rocks surrounding the energy storage reservoirs.These complex alternating loads can be regarded as multi-stage constant-amplitude cyclic loads following simplification.In this paper,the mechanical responses and acoustic emission(AE)characteristics of red sandstone with five bedding dip angles(0°,30°,45°,60°,and 90°)under such loads are investigated,and the damage evolution processes of the five specimens are revealed from both quantitative and microscopic perspectives.The results show that the fatigue deformation characteristics of the specimens are affected by the bedding dip angle.Under cyclic loads,the axially irreversible plastic deformations of the rocks increase,their elastic stiffness increases,their crack volumetric strain increases and then decreases,and their AE cumulative count/energy curves exhibit a ladder shape.A damage evolution model based on the crack volumetric strain is proposed,and the damage evolution process is divided into two stages:a rapid increase stage and a tendency toward stabilization stage.Through cluster analysis,the AE events are used to classify the damage into three categories:small-sized localized damage,large-sized tensile damage,and large-sized shear damage.Finally,the MohreCoulomb criterion is applied to analyze the relationship between the failure modes of the red sandstone specimens and the dip angle of the bedding.The results of this study will help to predict the stability and safety of compressed air energy storage reservoirs in abandoned coal mines.展开更多
To mitigate the challenges in managing the damage level of reinforced concrete(RC)pier columns subjected to cyclic reverse loading,this study conducted a series of cyclic reverse tests on RC pier columns.By analyzing ...To mitigate the challenges in managing the damage level of reinforced concrete(RC)pier columns subjected to cyclic reverse loading,this study conducted a series of cyclic reverse tests on RC pier columns.By analyzing the outcomes of destructive testing on various specimens and fine-tuning the results with the aid of the IMK(Ibarra Medina Krawinkler)recovery model,the energy dissipation capacity coefficient of the pier columns were able to be determined.Furthermore,utilizing the calibrated damage model parameters,the damage index for each specimen were calculated.Based on the obtained damage levels,three distinct pre-damage conditions were designed for the pier columns:minor damage,moderate damage,and severe damage.The study then predicted the variations in hysteresis curves and damage indices under cyclic loading conditions.The experimental findings reveal that the displacement at the top of the pier columns can serve as a reliable indicator for controlling the damage level of pier columns post-loading.Moreover,the calibrated damage index model exhibits proficiency in accurately predicting the damage level of RC pier columns under cyclic loading.展开更多
This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstruc...This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstructural degradation is decomposed into two parts:an instantaneous part arising from monotonic loading and a fatigue-related one induced by cyclic loading,relating to the initiation and propagation of microcracks.The inelastic deformation arises directly from frictional sliding along microcracks,inherently coupled with the damage effect.A fractional plastic flow rule is introduced using stress-fractional plasticity operations and covariant transformation approach,instead of classical plastic flow function.Additionally,the progression of fatigue damage is intricately tied to subcracks and can be calculated through application of a convolution law.The number of loading cycles serves as an integration variable,establishing a connection between inelastic deformation and the evolution of fatigue damage.In order to verify the accuracy of the proposed model,comparison between analytical solutions and experimental data are carried out on three different rocks subjected to conventional triaxial compression and cyclic loading tests.The evolution of damage variables is also investigated along with the cumulative deformation and fatigue lifetime.The improvement of the fractional model is finally discussed by comparing with an existing associated fatigue model in literature.展开更多
This work aims to reveal the mechanical responses and energy evolution characteristics of skarn rock under constant amplitude-varied frequency loading paths.Testing results show that the fatigue lifetime,stress−strain...This work aims to reveal the mechanical responses and energy evolution characteristics of skarn rock under constant amplitude-varied frequency loading paths.Testing results show that the fatigue lifetime,stress−strain responses,deformation,energy dissipation and fracture morphology are all impacted by the loading rate.A pronounced influence of the loading rate on rock deformation is found,with slower loading rate eliciting enhanced strain development,alongside augmented energy absorption and dissipation.In addition,it is revealed that the loading rate and cyclic loading amplitude jointly influence the phase shift distribution,with accelerated rates leading to a narrower phase shift duration.It is suggested that lower loading rate leads to more significant energy dissipation.Finally,the tensile or shear failure modes were intrinsically linked to loading strategy,with cyclic loading predominantly instigating shear damage,as manifest in the increased presence of pulverized grain particles.This work would give new insights into the fortification of mining structures and the optimization of mining methodologies.展开更多
The fatigue characteristics of rock materials significantly impact the economy and safety of underground structures during construction.Hence,it is essential to conduct further investigation into the progressive damag...The fatigue characteristics of rock materials significantly impact the economy and safety of underground structures during construction.Hence,it is essential to conduct further investigation into the progressive damage processes of rocks under cyclic loading conditions.This research utilised both laboratory experiments and discrete element simulations to investigate how confining pressure and fatigue upper limit stress influence the mechanical behaviour and crack development of marble under low-cycle fatigue conditions.By introducing synthetic displacement and reasonable assumptions,the classical damage evolution law was updated,resulting in a fatigue life prediction formula applicable to various rock materials and loading conditions.The results indicate that lower fatigue upper limit stress can delay the accumulation of damage and extend the fatigue life of the rock,but it results in more severe ultimate failure.The damage variable’s correlation with the relative number of loading cycles for different fatigue load upper limits under the same confining pressure can be approximated by the same functional relationship.The modified damage evolution model provides an effective characterisation of this trend.The proposed fatigue life prediction method comprehensively accounts for different rock materials,confining pressures,loading frequencies,and initial damage,showing a close match with actual results.展开更多
During underground excavation,the surrounding rock mass is subjected to complex cyclic stress,significantly impacting its long-term stability,especially under varying water content conditions where this effect is ampl...During underground excavation,the surrounding rock mass is subjected to complex cyclic stress,significantly impacting its long-term stability,especially under varying water content conditions where this effect is amplified.However,research on the mechanical response mechanisms of surrounding rock mass under such conditions remains inadequate.This study utilized acoustic emission(AE)and resistivity testing to monitor rock fracture changes,revealing the rock’s damage state and characterizing the damage evolution process during uniaxial cyclic loading and unloading.First,a damage variable equation was established based on AE and resistivity parameters,leading to the derivation of a corresponding damage constitutive equation.Uniaxial cyclic loading and unloading tests were then conducted on sandstone samples with varying water contents,continuously monitoring AE signals and resistivity,along with computed tomography scans before and after failure.The predictions from the damage constitutive equation were compared with experimental results.This comparison shows that the proposed damage variable equation effectively characterizes the damage evolution of sandstone during loading and unloading,and that the constitutive equation closely fits the experimental data.This study provides a theoretical basis for monitoring and assessing the responses of surrounding rock mass during underground excavation.展开更多
In order to research the concrete archaized buildings with lintel-column joint,2 specimens were tested under dynamic experiment.The failure characteristics,skeleton curves,mechanical behavior such as the load-displace...In order to research the concrete archaized buildings with lintel-column joint,2 specimens were tested under dynamic experiment.The failure characteristics,skeleton curves,mechanical behavior such as the load-displacement hysteretic loops,load carrying capacity,degradation of strength and stiffness,ductility and energy dissipation of the joints were analyzed.The results indicate that comparies with the lintel-column joints,the loading capacity and energy dissipation of the concrete archaized buildings with dual lintel-column joints are higher,and the hysteretic loops is in plump-shape.However,the displacement ductility coefficient is less than that of lintel-column joints.Both of them of the regularity of rigidity degeneration are basically the same.Generally,the joints have the good energy dissipation capacity.And the concrete archaized buildings with lintel-column joints exhibit excellent seismic behavior.展开更多
In this study,a uniaxial cyclic compression test is conducted on coal-rock composite structures under two cyclic loads using MTSE45.104 testing apparatus to investigate the macro-mesoscopic deformation,damage behavior...In this study,a uniaxial cyclic compression test is conducted on coal-rock composite structures under two cyclic loads using MTSE45.104 testing apparatus to investigate the macro-mesoscopic deformation,damage behavior,and energy evolution characteristics of these structures under different cyclic stress disturbances.Three loading and unloading rates(LURs)are tested to examine the damage behaviors and energy-driven characteristics of the composites.The findings reveal that the energy-driven behavior,mechanical properties,and macro-micro degradation characteristics of the composites are significantly influenced by the loading rate.Under the gradual cyclic loading and unloading(CLU)path with a constant lower limit(path I)and the CLU path with variable upper and lower boundaries(path II),an increase in LURs from 0.05 to 0.15 mm/min reduces the average loading time by 32.39%and 48.60%,respectively.Consequently,the total number of cracks in the samples increases by 1.66-fold for path I and 1.41-fold for path II.As LURs further increase,the energy storage limit of samples expands,leading to a higher proportion of transmatrix and shear cracks.Under both cyclic loading conditions,a broader cyclic stress range promotes energy dissipation and the formation of internal fractures.Notably,at higher loading rates,cracks tend to propagate along primary weak surfaces,leading to an increased incidence of intermatrix fractures.This behavior indicates a microscopic feature of the failure mechanisms in composite structures.These results provide a theoretical basis for elucidating the damage and failure characteristics of coal-rock composite structures under cyclic stress disturbances.展开更多
Salt cavern energy storage technology contributes to energy reserves and renewable energy scale-up.This study focuses on salt cavern gas storage in Jintan to assess the long-term stability of its surrounding rock unde...Salt cavern energy storage technology contributes to energy reserves and renewable energy scale-up.This study focuses on salt cavern gas storage in Jintan to assess the long-term stability of its surrounding rock under frequent operation.The fatigue test results indicate that stress holding significantly reduces fatigue life,with the magnitude of stress level outweighing the duration of holding time in determining peak strain.Employing a machine learning approach,the impact of various factors on fatigue life and peak strain was quantified,revealing that higher stress limits and stress holding adversely impact the fatigue index,whereas lower stress limits and rate exhibit a positive effect.A novel fatigue-creep composite damage constitutive model is constructed,which is able to consider stress magnitude,rate,and stress holding.The model,validated through multi-path tests,accurately captures the elasto-viscous behavior of salt rock during loading,unloading,and stress holding.Sensitivity analysis further reveals the time-and stress-dependent behavior of model parameters,clarifying that strain changes stem not only from stress variations but are also influenced by alterations in elasto-viscous parameters.This study provides a new method for the mechanical assessment of salt cavern gas storage surrounding rocks.展开更多
Understanding the shear mechanical behaviors and instability mechanisms of rock joints under dynamic loading remains a complex challenge.This research conducts a series of direct shear tests on real rock joints subjec...Understanding the shear mechanical behaviors and instability mechanisms of rock joints under dynamic loading remains a complex challenge.This research conducts a series of direct shear tests on real rock joints subjected to cyclic normal loads to assess the influence of dynamic normal loading amplitude(F_(d)),dynamic normal loading frequency(f_(v)),initial normal loading(F_(s)),and the joint roughness coefficient(JRC)on the mechanical properties and instability responses of these joints.The results show that unstable sliding is often accompanied by friction weakening due to dynamic normal loads.A significant negative correlation exists between cyclic normal loads and the normal displacement during the shearing process.Dynamic normal load paths vary the contact states of asperities on the rough joint surfaces,impacting the stick-slip instability mechanism of the joints,which in turn affects both the magnitude and location of the stress drop during the stick-slip events,particularly during the unloading phases.An increasing F_(d) results in a more stable shearing behavior and a reduction in the amplitude of stick-slip stress drops.The variation in f_(v) influences the amplitude of stress drop for the joints during shear,characterized by an initial decrease(f_(v)=0.25-2 Hz)before exhibiting an increment(f_(v)=2-4 Hz).As F_(s) increases,sudden failures of the interlocked rough surfaces are more prone to occur,thus producing enhanced instability and a more substantial stress drop.Additionally,a larger JRC intensifies the instability of the joints,which would induce a more pronounced decline in the stick-slip stress.The Rate and state friction(RSF)law can provide an effective explanation for the unstable sliding phenomena of joints during the oscillations of normal loads.The findings may provide certain useful references for a deeper comprehension of the sliding behaviors exhibited by rock joints when subjected to cyclic dynamic disturbances.展开更多
The mechanical properties of red sandstone subjected to cyclic point loading were investigated. Tests were conducted using MTS servohydraulic landmark test system, under cyclic loadings with constant amplitudes and in...The mechanical properties of red sandstone subjected to cyclic point loading were investigated. Tests were conducted using MTS servohydraulic landmark test system, under cyclic loadings with constant amplitudes and increasing multi-level amplitudes. The frequencies range from 0.1 to 5 Hz and lower limit load ratios range from 0 to 0.60. Laboratory investigations were performed to find the effect of the frequency and the lower limit load ratio on the fatigue life and hysteresis properties of sandstone. The results show that the fatigue life of sandstone decreases first and then increases with the increase of frequency and lower limit load ratio. Under the same cycle number, the spacing between hysteresis loops increases with rising frequency and decreasing lower limit load ratio. The existence of “training” and “memory” effects in red sandstone under cyclic point loading was proved.展开更多
A discussion of several kinematic hardening rules based on nonproportional cyclic experiments of 42CrMo steel is presented. They include Prager, Ziegler, Chaboche, Mroz and Tseng Lee hardenin...A discussion of several kinematic hardening rules based on nonproportional cyclic experiments of 42CrMo steel is presented. They include Prager, Ziegler, Chaboche, Mroz and Tseng Lee hardening rules. It shows that Mroz and Tseng Lee rule related to a two surface model has the latent potentiality to describe the nonproportional cyclic hardening behaviors, and a simple two surface model is presented.展开更多
This paper describes low cyclic loading testing of nine angle-steel concrete column （ASCC） specimens. In the tests, the influence of the shear-span ratio, axial compression ratio and shear steel plate ratio on the h...This paper describes low cyclic loading testing of nine angle-steel concrete column （ASCC） specimens. In the tests, the influence of the shear-span ratio, axial compression ratio and shear steel plate ratio on the hysteretic behavior, energy dissipation, strength degradation, stiffness degradation, skeleton curve and ductility of the ASCCs is studied. Based on the test results, some conclusions are presented. The P-A and sectional M -φ hysteretic models for the ASCCs are presented in a companion paper （Zheng and Ji, 2008）.展开更多
基金National Natural Science Foundation of China under Grant No.51178008,No.50908005National Basic Research Program of China under Grant No.2011CB013600+1 种基金the International Cooperative Project of NSFC-JST under Grant No.51021140003a Joint Research Project between the Beijing University of Technology and the University at Buffalo with Partial Support from the U.S.Federal Highway Administration under Contract No.DTFH61-07-C-00020
文摘To investigate the seismic performance of hollow reinforced concrete （RC） bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametric study is carried out for different axial load ratios, longitudinal reinforcement ratios and lateral reinforcement ratios. The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity, which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns. Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations, and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance. However, the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design. The hollow RC rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations, and may be considered as a substitute for current hollow RC rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges （JTG/T B02-01-2008）. The length of the plastic hinge region was found to approach one sixth of the hollow RC rectangular bridge column height for all specimen columns, and it was much less than those specified in the current JTG/T. Thus, the length of the plastic hinge region is more concentrated for RC rectangular hollow bridge columns.
基金sponsored by the Norwegian Public Roads Administration(NPRA)
文摘The Norwegian Public Roads Administration(NPRA) is planning for an upgrade of the E39 highway route at the westcoast of Norway. Fixed links shall replace ferries at seven fjord crossings. Wide spans and large depths at the crossings combined with challenging subsea topography and environmental loads call for an extension of existing practice. A variety of bridge concepts are evaluated in the feasibility study. The structures will experience significant loads from deadweight, traffic and environment. Anchoring of these forces is thus one of the challenges met in the project. Large-size subsea rock anchors are considered a viable alternative. These can be used for anchoring of floating structures but also with the purpose of increasing capacity of fixed structures. This paper presents first a thorough study of factors affecting rock anchor bond capacity. Laboratory testing of rock anchors subjected to cyclic loading is thereafter presented. Finally, the paper presents a model predicting the capacity of a rock anchor segment, in terms of a ribbed bar, subjected to a cyclic load history. The research assumes a failure mode occurring in the interface between the rock anchor and the surrounding grout. The constitutive behavior of the bonding interface is investigated for anchors subjected to cyclic one-way tensile loads. The model utilizes the static bond capacity curve as a basis, defining the ultimate bond sbuand the slip s1 at τ. A limited number of input parameters are required to apply the model. The model defines the bond-slip behavior with the belonging rock anchor capacity depending on the cyclic load level(τcy/τ), the cyclic load ratio(R= τcy/τcy), and the number of load cycles(N). The constitutive model is intended to model short anchor lengths representing an incremental length of a complete rock anchor.
文摘The attenuation of the acoustic activity in marble specimens under uniaxial compressive loadingunloading loops is quantified in juxtaposition to that of the electric activity.In parallel,the existence of"pre-failure indiceso"warning about entrance into a critical stage,that of impending fracture,is explored.The acoustic activity is quantified in terms of the normalized number of acoustic hits,their average rate of production and their cumulative energy,and,the cumulative counts and their average rate of change.The electric activity is studied in terms of the pressure stimulated currents and the electric charge released.The analysis revealed that the acoustic and electric activities are linearly correlated to each other,suggesting that they are different manifestations of the same damage mechanisms.In addition,Kaiser's effect,governing the acoustic activity,is found to govern,also,the electric activity.Moreover,it is concluded that entrance into the critical stage is safely predicted by means of a simple criterion,based on the evolution of the average rate of change of the normalized cumulative counts in the natural time domain.These predictions are almost identical with those of the criterion based on the "varianceo" and the "entropies" of the time series of acoustic events in this domain.
基金funding support from the General Program of the National Natural Science Foundation of China(Grant No.52374069)the Excellent Young Scientists Fund Program of the National Natural Science Foundation of China(Grant No.52122403)the Youth Innovation Promotion Association CAS(Grant No.Y2023089).
文摘This paper presents an ultralow-frequency cyclic loading creep test system for rock salt.The system comprises five subsystems:a cyclic load generation system,a triaxial pressure chamber,a pressure and deformation monitoring system,a signal acquisition and load control integrated system,and an automatic oil replenishment and discharge system.This test system overcomes the limitations of traditional electrohydraulic servo creep testing machines and gravity loading creep testing machines when conducting low-frequency cyclic load creep tests.This allows for long-term(1-2 years)creep tests under extremely-low-frequency cyclic loading conditions,which simulate the actual operating conditions of salt cavern gas storage.The cyclic load generation system converted constant-weight loads into a continuously variable hydraulic oil pressure and amplified the oil pressure using a pressure intensifier,which provided a stable load source for the test system.Using this test system,creep tests were performed under low-frequency cyclic loading with periods of 1 d and 7 d.The results showed that the test system performed well,as evidenced by the validation of the loading capacity,loading stability,and temperature control stability.Comparing the creep deformation of rock salt samples with the cyclic periods of 1 d and 7 d,it was observed that,within this cyclic period range,the creep deformation of the sample increased with higher loading frequencies,provided that the cyclic loading waveform and stress remained constant.
基金the support of the National Natural Science Foundation of China(Grant No.52108319)the Natural Science Foundation of Jiangxi Province(20224BAB214069)。
文摘Red clay,widely used as a subgrade material in southern China,requires a reliable evaluation of its dynamic behavior to ensure infrastructure safety.Long-term cyclic triaxial tests were conducted on red clay from typical,complex subway subgrades to investigate its dynamic properties and shakedown behavior under intermittent cyclic loading.Results show that intermittent cyclic loading,especially with multiple amplitudes,causes greater axial plastic strain and lower post-cyclic strength than continuous loading.These effects diminish with increasing confining pressure.Notably,axial strain partially recovers during loading intervals,with recovery ratios depending on the number and sequence of pauses.Based on the rules of cumulative plastic strain rates and cumulative plastic strain increments,shakedown behavior for red clay under intermittent cyclic loading is divided into three categories:plastic shakedown,critical shakedown,and plastic creep.A quantitative shakedown limit criterion is proposed using the Boltzmann function.Shakedown behavior significantly influences the post-cyclic strengths,and the influence diminishes as confining pressure increases.Samples exhibiting plastic creep and plastic shakedown behavior have the lowest and highest strengths,and those with critical shakedown behaviors have medium strengths.Cyclic loading with relatively low-stress amplitude causes a hardening effect,while cyclic loading intermittence or cyclic loading with relatively high-stress amplitude causes a degradation effect,and both effects are mitigated by higher confining pressures.
基金financially supported by National Natural Science Foundation of China(No.52304136)Young Talent of Lifting Engineering for Science and Technology in Shandong,China(No.SDAST2024QTA060)Key Project of Research and Development in Liaocheng(No.2023YD02)。
文摘It is important to analyze the damage evolution process of surrounding rock under different water content for the stability of engineering rock mass.Based on digital speckle correlation(DSCM),acoustic emission(AE)and electromagnetic radiation(EMR),uniaxial hierarchical cyclic loading and unloading tests were carried out on sandstones with different fracture numbers under dry,natural and saturated water content,to explore the fracture propagation,failure precursor characteristics and damage response mechanism under the influence of water content effect.The results show that with the increase of water content,the peak stress and crack initiation stress decrease gradually,and the decreases are 15.28%-21.11%and 17.64%-23.04%,respectively.The peak strain and crack initiation strain increase gradually,and the increases are 19.85%-44.53%and 19.15%-41.94%,respectively.The precracked rock with different water content is mainly characterized by tensile failure at different loading stages.However,with the increase of water content,the proportion of shear cracks gradually increases,while acoustic emission events gradually decrease,the dissipative energy and energy storage limits of the rock under peak load gradually decrease,and the charge signal increases significantly,which is because the lubrication effect of water reduces the friction coefficient between crack surfaces.
基金supported by the National Natural Science Foundation of China(Grant No.U2244215)the Knowledge Innovation Program of Wuhan-Basic Research(Grant No.2022010801010159)the Major Project of Inner Mongolia Science and Technology(Grant No.2021ZD0034).
文摘Preexisting cracks inside tight sandstones are one of the most important properties for controlling the mechanical and seepage behaviors.During the cyclic loading process,the rock generally exhibits obvious memorability and irreversible plastic deformation,even in the linear elastic stage.The assessment of the evolution of preexisting cracks under hydrostatic pressure loading and unloading processes is helpful in understanding the mechanism of plastic deformation.In this study,ultrasonic measurements were conducted on two tight sandstone specimens with different bedding orientations subjected to hydrostatic loading and unloading processes.The P-wave velocity was characterized by a similar response with the volumetric strain to the hydrostatic pressure and showed different strain sensitivities at different loading and unloading stages.A numerical model based on the discrete element method(DEM)was proposed to quantitatively clarify the evolution of the crack distribution under different hydrostatic pressures.The numerical model was verified by comparing the evolution of the measured P-wave velocities on two anisotropic specimens.The irreversible plastic deformation that occurred during the hydrostatic unloading stage was mainly due to the permanent closure of plastic-controlled cracks.The closure and reopening of cracks with a small aspect ratio account for the major microstructure evolution during the hydrostatic loading and unloading processes.Such evolution of microcracks is highly dependent on the stress path.The anisotropy of the crack distribution plays an important role in the magnitude and strain sensitivity of the P-wave velocity under stress conditions.The study can provide insight into the microstructure evolution during cyclic loading and unloading processes.
基金supported by the National Natural Science Foundation of China(Grant No.52374078)the Fundamental Research Funds for the Central Universities(Grant No.2023CDJKYJH021)the Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(Grant No.2024TIAD-CYKJCXX0011).
文摘Cyclic changes in the internal pressure of compressed air energy storage reservoirs in abandoned coal mines result in complex alternating loads on the rocks surrounding the energy storage reservoirs.These complex alternating loads can be regarded as multi-stage constant-amplitude cyclic loads following simplification.In this paper,the mechanical responses and acoustic emission(AE)characteristics of red sandstone with five bedding dip angles(0°,30°,45°,60°,and 90°)under such loads are investigated,and the damage evolution processes of the five specimens are revealed from both quantitative and microscopic perspectives.The results show that the fatigue deformation characteristics of the specimens are affected by the bedding dip angle.Under cyclic loads,the axially irreversible plastic deformations of the rocks increase,their elastic stiffness increases,their crack volumetric strain increases and then decreases,and their AE cumulative count/energy curves exhibit a ladder shape.A damage evolution model based on the crack volumetric strain is proposed,and the damage evolution process is divided into two stages:a rapid increase stage and a tendency toward stabilization stage.Through cluster analysis,the AE events are used to classify the damage into three categories:small-sized localized damage,large-sized tensile damage,and large-sized shear damage.Finally,the MohreCoulomb criterion is applied to analyze the relationship between the failure modes of the red sandstone specimens and the dip angle of the bedding.The results of this study will help to predict the stability and safety of compressed air energy storage reservoirs in abandoned coal mines.
基金supported by National Natural Science Foundation of China(Project No.51878156)EPC Innovation Consulting Project for Longkou Nanshan LNG Phase I Receiving Terminal(Z2000LGENT0399).
文摘To mitigate the challenges in managing the damage level of reinforced concrete(RC)pier columns subjected to cyclic reverse loading,this study conducted a series of cyclic reverse tests on RC pier columns.By analyzing the outcomes of destructive testing on various specimens and fine-tuning the results with the aid of the IMK(Ibarra Medina Krawinkler)recovery model,the energy dissipation capacity coefficient of the pier columns were able to be determined.Furthermore,utilizing the calibrated damage model parameters,the damage index for each specimen were calculated.Based on the obtained damage levels,three distinct pre-damage conditions were designed for the pier columns:minor damage,moderate damage,and severe damage.The study then predicted the variations in hysteresis curves and damage indices under cyclic loading conditions.The experimental findings reveal that the displacement at the top of the pier columns can serve as a reliable indicator for controlling the damage level of pier columns post-loading.Moreover,the calibrated damage index model exhibits proficiency in accurately predicting the damage level of RC pier columns under cyclic loading.
基金Fundamental Research Funds for the Central Universities(Grant No.B230201059)for the support.
文摘This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstructural degradation is decomposed into two parts:an instantaneous part arising from monotonic loading and a fatigue-related one induced by cyclic loading,relating to the initiation and propagation of microcracks.The inelastic deformation arises directly from frictional sliding along microcracks,inherently coupled with the damage effect.A fractional plastic flow rule is introduced using stress-fractional plasticity operations and covariant transformation approach,instead of classical plastic flow function.Additionally,the progression of fatigue damage is intricately tied to subcracks and can be calculated through application of a convolution law.The number of loading cycles serves as an integration variable,establishing a connection between inelastic deformation and the evolution of fatigue damage.In order to verify the accuracy of the proposed model,comparison between analytical solutions and experimental data are carried out on three different rocks subjected to conventional triaxial compression and cyclic loading tests.The evolution of damage variables is also investigated along with the cumulative deformation and fatigue lifetime.The improvement of the fractional model is finally discussed by comparing with an existing associated fatigue model in literature.
基金Project(52174069) supported by the National Natural Science Foundation of ChinaProject(8202033) supported by the Beijing Natural Science Foundation,ChinaProject(KCF2203) supported by the Henan Key Laboratory for Green and Efficient Mining&Comprehensive Utilization of Mineral Resources (Henan Polytechnic University),China。
文摘This work aims to reveal the mechanical responses and energy evolution characteristics of skarn rock under constant amplitude-varied frequency loading paths.Testing results show that the fatigue lifetime,stress−strain responses,deformation,energy dissipation and fracture morphology are all impacted by the loading rate.A pronounced influence of the loading rate on rock deformation is found,with slower loading rate eliciting enhanced strain development,alongside augmented energy absorption and dissipation.In addition,it is revealed that the loading rate and cyclic loading amplitude jointly influence the phase shift distribution,with accelerated rates leading to a narrower phase shift duration.It is suggested that lower loading rate leads to more significant energy dissipation.Finally,the tensile or shear failure modes were intrinsically linked to loading strategy,with cyclic loading predominantly instigating shear damage,as manifest in the increased presence of pulverized grain particles.This work would give new insights into the fortification of mining structures and the optimization of mining methodologies.
基金supported by the Key Supported Project of the Joint Fund of the National Natural Science Foundation of China for Geology(No.U2444220)the National Natural Science Foundation of China(Nos.52374090 and 52278351)+1 种基金the Scientific Research(on Science and Technology)Projects for Young and Middle-aged Teachers in Fujian(No.JAT220464)the Engineering Innovation Center for Urban Underground Space Exploration and Evaluation,Ministry of Natural Resources of the People’s Republic of China(No.USEEOS-2024-01)。
文摘The fatigue characteristics of rock materials significantly impact the economy and safety of underground structures during construction.Hence,it is essential to conduct further investigation into the progressive damage processes of rocks under cyclic loading conditions.This research utilised both laboratory experiments and discrete element simulations to investigate how confining pressure and fatigue upper limit stress influence the mechanical behaviour and crack development of marble under low-cycle fatigue conditions.By introducing synthetic displacement and reasonable assumptions,the classical damage evolution law was updated,resulting in a fatigue life prediction formula applicable to various rock materials and loading conditions.The results indicate that lower fatigue upper limit stress can delay the accumulation of damage and extend the fatigue life of the rock,but it results in more severe ultimate failure.The damage variable’s correlation with the relative number of loading cycles for different fatigue load upper limits under the same confining pressure can be approximated by the same functional relationship.The modified damage evolution model provides an effective characterisation of this trend.The proposed fatigue life prediction method comprehensively accounts for different rock materials,confining pressures,loading frequencies,and initial damage,showing a close match with actual results.
基金Projects(52279117,52325905)supported by the National Natural Science Foundation of ChinaProject(DJ-HXGG-2023-16)supported by the Technology Project of PowerChinaProject(SKLGME-JBGS2401)supported by the State Key Laboratory of Geomechanics and Geotechnical Engineering,China。
文摘During underground excavation,the surrounding rock mass is subjected to complex cyclic stress,significantly impacting its long-term stability,especially under varying water content conditions where this effect is amplified.However,research on the mechanical response mechanisms of surrounding rock mass under such conditions remains inadequate.This study utilized acoustic emission(AE)and resistivity testing to monitor rock fracture changes,revealing the rock’s damage state and characterizing the damage evolution process during uniaxial cyclic loading and unloading.First,a damage variable equation was established based on AE and resistivity parameters,leading to the derivation of a corresponding damage constitutive equation.Uniaxial cyclic loading and unloading tests were then conducted on sandstone samples with varying water contents,continuously monitoring AE signals and resistivity,along with computed tomography scans before and after failure.The predictions from the damage constitutive equation were compared with experimental results.This comparison shows that the proposed damage variable equation effectively characterizes the damage evolution of sandstone during loading and unloading,and that the constitutive equation closely fits the experimental data.This study provides a theoretical basis for monitoring and assessing the responses of surrounding rock mass during underground excavation.
基金supported by Crosswise Tasks of Enterprise Entrusted(JG-ZH-A-202411-003)High-level Talents Program of Hainan Basic and Applied Basic Research Program of China(520RC543)。
文摘In order to research the concrete archaized buildings with lintel-column joint,2 specimens were tested under dynamic experiment.The failure characteristics,skeleton curves,mechanical behavior such as the load-displacement hysteretic loops,load carrying capacity,degradation of strength and stiffness,ductility and energy dissipation of the joints were analyzed.The results indicate that comparies with the lintel-column joints,the loading capacity and energy dissipation of the concrete archaized buildings with dual lintel-column joints are higher,and the hysteretic loops is in plump-shape.However,the displacement ductility coefficient is less than that of lintel-column joints.Both of them of the regularity of rigidity degeneration are basically the same.Generally,the joints have the good energy dissipation capacity.And the concrete archaized buildings with lintel-column joints exhibit excellent seismic behavior.
基金Project(2023YFC3009003) supported by the National Key R&D Program of ChinaProjects(52130409, 52121003, 52374249, 52204220) supported by the National Natural Science Foundation of ChinaProject(2024JCCXAQ01) supported by the Fundamental Research Funds for the Central Universities,China。
文摘In this study,a uniaxial cyclic compression test is conducted on coal-rock composite structures under two cyclic loads using MTSE45.104 testing apparatus to investigate the macro-mesoscopic deformation,damage behavior,and energy evolution characteristics of these structures under different cyclic stress disturbances.Three loading and unloading rates(LURs)are tested to examine the damage behaviors and energy-driven characteristics of the composites.The findings reveal that the energy-driven behavior,mechanical properties,and macro-micro degradation characteristics of the composites are significantly influenced by the loading rate.Under the gradual cyclic loading and unloading(CLU)path with a constant lower limit(path I)and the CLU path with variable upper and lower boundaries(path II),an increase in LURs from 0.05 to 0.15 mm/min reduces the average loading time by 32.39%and 48.60%,respectively.Consequently,the total number of cracks in the samples increases by 1.66-fold for path I and 1.41-fold for path II.As LURs further increase,the energy storage limit of samples expands,leading to a higher proportion of transmatrix and shear cracks.Under both cyclic loading conditions,a broader cyclic stress range promotes energy dissipation and the formation of internal fractures.Notably,at higher loading rates,cracks tend to propagate along primary weak surfaces,leading to an increased incidence of intermatrix fractures.This behavior indicates a microscopic feature of the failure mechanisms in composite structures.These results provide a theoretical basis for elucidating the damage and failure characteristics of coal-rock composite structures under cyclic stress disturbances.
基金supported by the National Natural Science Foundation of China(Nos.52374078,U24A20616 and 52074043)the Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(No.2024TIAD-CYKJCXX0011)the Fundamental Research Funds for the Central Universities(No.2023CDJKYJH021)。
文摘Salt cavern energy storage technology contributes to energy reserves and renewable energy scale-up.This study focuses on salt cavern gas storage in Jintan to assess the long-term stability of its surrounding rock under frequent operation.The fatigue test results indicate that stress holding significantly reduces fatigue life,with the magnitude of stress level outweighing the duration of holding time in determining peak strain.Employing a machine learning approach,the impact of various factors on fatigue life and peak strain was quantified,revealing that higher stress limits and stress holding adversely impact the fatigue index,whereas lower stress limits and rate exhibit a positive effect.A novel fatigue-creep composite damage constitutive model is constructed,which is able to consider stress magnitude,rate,and stress holding.The model,validated through multi-path tests,accurately captures the elasto-viscous behavior of salt rock during loading,unloading,and stress holding.Sensitivity analysis further reveals the time-and stress-dependent behavior of model parameters,clarifying that strain changes stem not only from stress variations but are also influenced by alterations in elasto-viscous parameters.This study provides a new method for the mechanical assessment of salt cavern gas storage surrounding rocks.
基金funding support from the National Natural Science Foundation of China(Grant Nos.52174092,and 51904290)open fund of Key Laboratory of Safety and High-efficiency Coal Mining,Ministry of Education(Anhui University of Science and Technology)(Grant No.JYBSYS202311).
文摘Understanding the shear mechanical behaviors and instability mechanisms of rock joints under dynamic loading remains a complex challenge.This research conducts a series of direct shear tests on real rock joints subjected to cyclic normal loads to assess the influence of dynamic normal loading amplitude(F_(d)),dynamic normal loading frequency(f_(v)),initial normal loading(F_(s)),and the joint roughness coefficient(JRC)on the mechanical properties and instability responses of these joints.The results show that unstable sliding is often accompanied by friction weakening due to dynamic normal loads.A significant negative correlation exists between cyclic normal loads and the normal displacement during the shearing process.Dynamic normal load paths vary the contact states of asperities on the rough joint surfaces,impacting the stick-slip instability mechanism of the joints,which in turn affects both the magnitude and location of the stress drop during the stick-slip events,particularly during the unloading phases.An increasing F_(d) results in a more stable shearing behavior and a reduction in the amplitude of stick-slip stress drops.The variation in f_(v) influences the amplitude of stress drop for the joints during shear,characterized by an initial decrease(f_(v)=0.25-2 Hz)before exhibiting an increment(f_(v)=2-4 Hz).As F_(s) increases,sudden failures of the interlocked rough surfaces are more prone to occur,thus producing enhanced instability and a more substantial stress drop.Additionally,a larger JRC intensifies the instability of the joints,which would induce a more pronounced decline in the stick-slip stress.The Rate and state friction(RSF)law can provide an effective explanation for the unstable sliding phenomena of joints during the oscillations of normal loads.The findings may provide certain useful references for a deeper comprehension of the sliding behaviors exhibited by rock joints when subjected to cyclic dynamic disturbances.
基金Projects(51322403,51274254)supported by the National Natural Science Foundation of ChinaProject(2015CB060200)supported by the National Basic Research Program of China
文摘The mechanical properties of red sandstone subjected to cyclic point loading were investigated. Tests were conducted using MTS servohydraulic landmark test system, under cyclic loadings with constant amplitudes and increasing multi-level amplitudes. The frequencies range from 0.1 to 5 Hz and lower limit load ratios range from 0 to 0.60. Laboratory investigations were performed to find the effect of the frequency and the lower limit load ratio on the fatigue life and hysteresis properties of sandstone. The results show that the fatigue life of sandstone decreases first and then increases with the increase of frequency and lower limit load ratio. Under the same cycle number, the spacing between hysteresis loops increases with rising frequency and decreasing lower limit load ratio. The existence of “training” and “memory” effects in red sandstone under cyclic point loading was proved.
文摘A discussion of several kinematic hardening rules based on nonproportional cyclic experiments of 42CrMo steel is presented. They include Prager, Ziegler, Chaboche, Mroz and Tseng Lee hardening rules. It shows that Mroz and Tseng Lee rule related to a two surface model has the latent potentiality to describe the nonproportional cyclic hardening behaviors, and a simple two surface model is presented.
基金the New Century Excellent Talents in University Under Grant No.290Heilongjiang Key Program on Science and Technology Under Grant No.GC04A609Harbin Key Program on Science and Technology Under Grant No.2004AA9CS187
文摘This paper describes low cyclic loading testing of nine angle-steel concrete column （ASCC） specimens. In the tests, the influence of the shear-span ratio, axial compression ratio and shear steel plate ratio on the hysteretic behavior, energy dissipation, strength degradation, stiffness degradation, skeleton curve and ductility of the ASCCs is studied. Based on the test results, some conclusions are presented. The P-A and sectional M -φ hysteretic models for the ASCCs are presented in a companion paper （Zheng and Ji, 2008）.
