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.

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 triaxial creep model for coal containing gas and its stability analysis

Triaxial creep tests on CCG specimens were systematically performed using aself-made creep seepage experimental apparatus for determining the creep law of CCG.An improved triaxial creep model of CCG was established on the basis of a Nishiharamodel and another visco-elasto-plastic model,parameters of which were fitted on test data.Furthermore,the creep model is validated according to the result of triaxial creep experiments,and the outcome shows that the proposed triaxial creep model can properly characterizethe properties of various creep deformation phases of CCG,especially the acceleratingcreep phase.At the same time,the instability conditions of CCG were presentedbased on the discussion of the improved model's stability in terms of stability theories ofdifferential equation solution.

Study on Unloading Creep Characteristics of the Soil and Application of the Stress-Dependent Creep Model in Suction Caisson Foundation

As the anchoring foundation of the tension leg platform(TLP),suction caisson foundation is subjected to the long-term vertical pullout loads.But there are few studies on the mechanism of the unloading creep of soft clay and long-term uplift bearing capacity of suction caisson foundations.To address this problem,unloading creep tests of soft clay were carried out to analyze the strain development with time under different confining pressures.The test results show that the creep curve rapidly develops in the early stage and tends to stabilize in the later stage.The unloading deviator stress is higher,the unloading creep deformation is greater and the soft clay has typical nonlinear creep characteristics.Therefore,by introducing the creep model and considering the influence of the deviator stress,the stress-dependent Merchant model is proposed to describe the unloading creep of soft clay.Then,the stress-dependent Merchant model is extended to a three-dimension constitutive model,and a finite element subroutine is developed to establish a finite element analysis method for analyzing the long-term uplift capacity of suction caisson foundations and validated with the long-term uplift bearing capacity results of caisson model.

Evaluation of creep models for frozen soils

To model the creep behavior of frozen soils, three creep stages have to be reasonably described （i.e., primary, secondary and tertiary stages）. Based on a series of uniaxial creep test results, three creep models were evaluated. It was shown that hypoplastic creep model has high prediction accuracy for both creep strain and strain rate in a wide stress range. The elementary rheological creep model can only be used for creep strains at low stress levels, because of the restraints of its mathematical construction. For the soft soil creep model, the progressive change from the primary to secondary and tertiary stages cannot be captured at high stress levels. Therefore, the elementary rheological and soft soil creep models can only be used for low stress levels without a tertiary stage; while the hypoplastic creep model is applicable at high stress levels with the three creep stages.

Generic creep behavior and creep modeling of an aged surface support liner under tension

Polymer-based materials have been motivated to be an alternative support system element in the mining/tunneling industry due to their logistic and geotechnical benefits.Thin spray-on liner(TSL),a term to define the application of the material on the rock surface with a layer ranging from 2 mm to10 mm in thickness,shows some promising results.TSLs are mainly composed of plastic,polymer,or cement-based ingredients to a certain proportion.This study intends to reveal the time-dependent response of TSL specimens,cured throughout 500 d,under four constant stress levels for stable laboratory conditions.The results were correlated using two interrelated equations to predict the material’s service life(creep-rupture envelopes).The proposed correlations offered an insight into both the effective permanent support time and the strain amount at the liner failure.The time-dependent deformation of TSL,whose performance is highly responsive to creep behavior,was obtained so that the design engineers may use the findings to avoid the severe problems of material creep.Experimental data were also used to develop a Burgers(four-element)creep model.Since the liner has a nonlinear time-dependent behavior,creep models were built for each stress level separately.Subsequently,a generic equation was obtained using the nonlinear parametric dependencies.There is a good agreement between the proposed model and the experimental results.The proposed model can be used as a basis for future numerical studies related to the support behavior of aged surface support liners.

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

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

Creep Model of High-Strength High-Performance Concrete Under Cyclic Loading

Concrete creep under both static and cyclic loading conditions was investigated. Four groups of high-strength high-performance concrete(HSHPC) prism specimens were fabricated, and three of these specimens were loaded periodically by the MTS Landmark Fatigue Testing Machine System. Creep characteristics and creep coefficients of HSHPC under static loading and cyclic loading, respectively, were obtained and compared. The experimental results show that the creep strains under cyclic loading with a mean stress of 0.4 fcp and an amplitude of 0.2 fcp increase significantly compared with the creep strains under static loading, and the maximum value was 1.2-2.3 times at early stages. In addition, the creep coefficient increases nonlinearly with the number of cyclic loading repetitions. The influence coefficient for cyclic loading γcyc=1.088×(N/N0)0.078 was introduced based on the previous HSHPC creep model, and then the modified creep model under cyclic loading was established. Finally, the residual method, the CEB coefficient of variation method and the B3 coefficient of variation method were applied to evaluate the modified creep model. The statistical results demonstrate that the modified creep model agrees well with the experimental measurements. Hence, it has important theoretical and practical values for accurately predicting the deflection of concrete bridges under cyclic traffic loading.

An improved Mesri creep model for unsaturated weak intercalated soils

The weak intercalated soils in redbed soft rocks of Badong formation have obvious creep characters. In order to predict the unsaturated creep behaviors of weak intercalated soils, an unsaturated creep model was established based on the unsaturated creep tests of weak intercalated soils by using GDS triaxial apparatus. The results show that the creep behaviors of intercalated soils are apparent and significantly affected by matric suction. Based on this, an empirical Mesri creep model for intercalated soils under varying matric suctions was built. The fitting results show that the parameters Ed and m of this model are in good power relations with matric suction s and stress level Dr, respectively. An improved Mesri creep model was established involving stress-matric suction-strain-time, which is more precise than the Mesri creep model in predicting the unsaturated creep behaviors of weak intercalated soils.

Creep model for unsaturated soils in sliding zone of Qianjiangping landslide

The mechanical behavior of sliding zone soils plays a significant role in landslide. In general, the sliding zone soils are basically in unsaturated state due to rainfall infiltration and reservoir water level fluctuation. Meanwhile, a large number of examples show that the deformation processes of landslides always take a long period of time, indicating that landslides exhibit a time-dependent property. Therefore, the deforma- tion of unsaturated soils of landslide involves creep behaviors. In this paper, the Burgers creep model for unsaturated soils under triaxial stress state is considered based on the unsaturated soil mechanics. Then, by curve fitting using the least squares method, creep parameters in different matric suction states are obtained based on the creep test data of unsaturated soils in the sliding zones of Qianjiangping landslide. Results show that the predicted results are in good agreement with the experimental data, Finally, to fur- ther explore the creep characteristics of the unsaturated soils in sliding zones, the relationships between parameters of the model and matric suction are analyzed and a revised Burgers creep model is developed correspondingly. Simulations on another group of test data are performed by using the modified Burgers creep model and reasonable results are observed,

Creep Modeling of Magnesia-chromite Bricks in a RH Snorkel During a Process Cycle

In this paper both experimental and analytical approaches to provide the inputs for creep modeling of refractories including a newly developed high temperature compressive creep machine and an inverse estimation procedure of creep law parameters are briefly introduced.Besides,a modified shear test is applied to determine the cohesion and friction angle of refractories under shear state. A RH snorkel equipped with magnesia- chromite bricks is chosen for a case study of thermomechanical simulation applying the classical creep model and Drucker-Prager creep model available in the finite element code ABAQUS,respectively. Afterwards,thermal stresses and joint opening of magnesia- chromite bricks during a process cycle are compared to distinguish the impact of these two creep models.

Elevated temperature creep model of parallel wire strands

T Parallel wire strands(PWSs),which are widely used in prestressed steel structures,are typically in highstress states.Under fire conditions,significant creep effects occur,reducing the prestress and influencing the mechanical behavior of PWSs.As there is no existing approach to analyze their creep behavior,this study experimentally investigated the elevated temperature creep model of PWSs.A charge-coupled camera system was incorporated to accurately obtain the deformation of the specimen during the elevated temperature creep test.It was concluded that the temperature level had a more significant effect on the creep strain than the stress level,and 450℃ was the key segment point where the creep rate varied significantly.By comparing the elevated temperature creep test results for PWSs and steel strands,it was found that the creep strain of PWSs was lower than that of steel strands at the same temperature and stress levels.The parameters in the general empirical formula,the Bailey–Norton model,and the composite timehardening model were fitted based on the experimental results.By evaluating the accuracy and form of the models,the composite time-hardening model,which can simultaneously consider temperature,stress,and time,is recommended for use in the fire-resistance design of pre-tensioned structures with PWSs.

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.

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.

Unsaturated creep tests and empirical models for sliding zone soils of Qianjiangping landslide in the Three Gorges

Creep of sliding zone soils may cause significant displacement in large-scale landslides in the Three Gorges reservoir area.To investigate the effects of water on the soil creep behavior of the Qianjiangping landslide,a series of unsaturated triaxial creep tests on the sliding zone soils were performed.Based on the analyses of testing results,a new stress intensity incorporating matric suction was defined and an unsaturated Singh-Mitchell creep model was developed.Predicted results are in good agreement with the experimental results,which indicates that the established unsaturated model can reasonably simulate the effects of water on the soil creep behavior of the landslide.Finally,relationships between matric suction and the parameters of the model were analyzed.This study provides a calculation model and parameters for the evaluation of long-term stability of landslides under the influence of water.

Creep of Concrete in Contemporary Code-Type Models

The paper presents and compares the conventional models for creep in cement concrete included in the ACI （American Concrete Institute） guide, Eurocode 2 andfib （International Federation for Structural Concrete） Model Code 2010. For the presentation and comparison of the creep models, creep coefficients are developed. The main factors affecting the prediction of creep in concrete are outlined, comparing the influence of concrete grade, environmental conditions, member size and loading conditions. Most of the conventional models currently used for creep in cement concrete develop the code-type procedures and are calibrated for normal- and high-strength concretes. They enable a more accurate analysis and better assessment of the time-dependent deformation of concrete structures at the design stage. Their complexity is significantly reduced and a range of influencing parameters are excluded from the models for simplicity and easy adaptation. The comparison of the models shows that thefib Model Code 2010 model is more consistent and calibrated to avoid shortcomings in the previous models.

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.

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

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

Viscoelastoplastic constitutive model for creep deformation behavior of asphalt sand

A uniaxial viscoelastoplastic model that can describe whole creep behaviors of asphalt sand at different temperatures was presented.The model was composed of three submodels in series,which describe elastoplastic,viscoelastic and viscoplastic characteristics respectively.The constitutive equation was established for uniaxial loading condition,and the creep representation was also obtained.The constitutive parameters were determined by uniaxial compression tests under controlled-stress of 0.1 MPa with five different test temperatures of 20,40,45,50 and 60 ℃.Expressions of the model parameters in terms of temperatures were also given.The model gave prediction at various temperatures consistent with the experimental results,and can reflect the total deformation characterization of asphalt sands.

Creep behaviour and constitutive model of coal filled with gas

Coal exhibits different creep behaviours when filled with different amounts of gas. Creep tests of coal filled with 0 and 0.5 MPa gas were performed, and strain under different axial stress was compared.The three creep constitutive models which were analysed using the method fitting experimental data for determining which creep model can reflect the creep process of the test best. The results show that the deformation of coal filled with 0.5 MPa gas is more higher than that of coal filled with 0 MPa gas under the same axial stress. Gas plays a positive effect on the deformation of coal process and will accelerate creep process. And gas will reduce coal intensity and change coal creep properties.Compared with Nishihara Model and Extensional Nishihara Model, Burgers Model can reflect the three stages of creep process of coal filled with gas better. The research results can contribute to reveal coal and gas outburst mechanism.