Creep Deformation Characteristics Research Articles

Investigating the Creep Damage and Permeability Evolution Mechanism of Phyllite Considering Non-Darcy’s Flow

AbstractThis study investigates the intricate interplay of hydraulic coupling, creep damage, and permeability evolution mechanisms in phyllite, focusing on their relevance to tunnel engineering design and long-term stability in soft rock formations. To achieve this, conventional triaxial tests were conducted on saturated phyllite specimens under creep-seepage acoustic emission conditions. The results were systematically analyzed to unveil the inherent characteristics of creep deformation, seepage rate evolution, and damage progression in phyllite when subjected to stress–seepage coupling. Furthermore, a permeability model for representative volume element (RVE) was developed based on meso-mechanics principles, considering the distinctive attributes of low-permeability non-Darcy’s flow in rock. Consequently, a novel relationship between effective damage and permeability was established. We determined that seepage pressure induces three key effects on the creep damage mechanism of phyllite samples: (1) It adds to the existing stress through the superposition of osmotic pressure and axial load, (2) it induces tensile expansion stress because of pore water pressure, and (3) it softens the fracture surfaces to some extent. More importantly, this study validates the relationship between effective damage and permeability through the fitting of creep and damage parameters, which were obtained from the test results, and it reveals a square relationship between subsequent damage and permeability under stress conditions. The findings of this study provide a robust theoretical foundation for comprehending the evolution of damage and permeability characteristics during the creep process of rock under seepage conditions. We obtained essential insights and quantitative analyses for comprehending the damage mechanisms in rock creep under hydraulic coupling, which has significant implications for tunnel engineering and long-term rock stability assessments in soft rock environments.

Anisotropic characteristics and creep model for thin-layered rock under true triaxial compression

The failure phenomenon of thin-layered rock tunnels not only exhibits asymmetric spatial characteristics, but also significant time-dependent characteristics under high in-situ stress, which is attributed to the time-dependent fracture of thin-layered rocks. This paper conducted a series of true triaxial creep compression tests on typical thin-layered rock siliceous slate with acoustic emission technique to reveal its anisotropic time-dependent fracture characteristics. The anisotropic long-term strength, creep fracturing process, and fracture orientation characteristics of thin-layered rocks under different loading angles (β, ω) and intermediate principal stress were summarized. A three-dimensional (3D) non-linear visco-plastic creep model for thin-layered rock was developed to simulate its anisotropic creep behavior. The time-dependent fracturing of rocks during true triaxial creep loading is reflected through the change of equivalent strain based on an improved Euler iteration method. By constructing the plastic potential function and overstress index related to loading angles and stress state, the anisotropic time-dependent fracturing process and propagation of thin-layered rocks under different loading angles and intermediate principal stress are expounded. The model was validated experimentally to show it can reflect the long-term strength and creep deformation characteristics of thin-layered rocks under true triaxial compression.

Strength and creep characteristics of methane hydrate-bearing clayey silts of the South China Sea

Natural gas hydrates are abundantly detected in the clayey-silty deposits of the South China Sea (SCS). The long-term hydrate extraction process may trigger creep deformation and failure of the clayey-silty reservoir. Hence, it is essential to evaluate the creep properties of the clayey-silty hydrate reservoir for safe production. Current research mainly focused on rapid failure, while neglecting time-dependent creep deformation of the clayey-silty hydrate reservoir. In this study, a number of triaxial shear and creep experiments were carried out on methane hydrate-bearing clayey silts (HBCSs) in the SCS in order to investigate their strength and creep deformation characteristics. The results indicated that: (1) the increase of effective stress enhances the shear strength and deformation, and the presence of hydrates enhances the shear strength while reducing the deformation; (2) the creep strain and strain rate increase as the creep stress ratio and effective stress rise; (3) the accelerated creep stage only occurs at higher effective stress in HBCSs and not in hydrate-free clayey silts (HFCSs), and the creep strain and strain rate of the HBCSs are lower than those of the HFCSs. The experimental data will contribute to the construction and verification of creep constitutive models for HBCSs in the SCS.

A Fractional-Order Creep Model of Water-Immersed Coal

The long-term stability of a coal pillar dam is a serious concern for coal mine underground reservoirs because of the creep behavior of coal in complex water immersion and mechanical environments. In order to investigate the characteristics of creep deformation of water-immersed coal and develop a proper creep model, this paper implemented a series of creep experiments of coal via multistage loading at various water-immersion times. The experiment data were analyzed, in terms of immersion-induced damage, elasto-plastic performance, creep behavior, etc., suggesting obvious mechanical properties’ degradation of coal by water. The elastic modulus and peak strength of water-immersed coal decrease exponentially with the immersion time, while the creep rate of coal shows an upward tendency with the promoted immersion time. According to the remarked relationships of elastic, viscoelastic, and viscoplastic properties versus the stress levels and water-immersion time, a creep model based on conformable fractional derivatives is proposed, considering the influence of the water-immersion time and variable stress level. The proposed model was verified using the experiment data, showing a good capacity of the creep model for reproducing the creep process of water-immersed coal. This paper provides a fundamental model for further studying the stability of coal pillars and their influence on the safety of underground water reservoirs.

A novel time-dependent damage constitutive model for hard rock materials

The mechanical behavior of deep hard rocks plays a crucial role in the long-term safety and stability of engineering structures. This work focuses on studying the instantaneous and time-dependent fracture propagation of hard rock materials from a theoretical perspective. A new unified constitutive model, based on a modified Mohr–Coulomb (M-C) criterion, is proposed to accurately represent the short and long-term mechanical properties of hard rocks. To capture the strain hardening and strain softening behaviors, damage is utilized as an internal mechanism-driven variable, controlling the expansion and contraction of the plastic yield surface. Additionally, a combination of time-dependent damage law and viscoplastic theory is employed to account for nonlinear creep deformation characteristics. By considering the time-dependent effects, the model can be applied to both instantaneous loading and creep conditions. The general algorithm format is derived in detail, and an explicit integration algorithm is utilized to update the time-dependent damage evolution. Finally, the proposed model is validated by comparing its predictions with the short and long-term mechanical responses of Beishan granite and Rumei dacite. This comprehensive constitutive model improves our understanding of continuum damage mechanics and provides a scientific basis for analyzing and evaluating the long-term safety and stability of deep hard rock engineering projects.

Creep deformation and damage characteristics of nickel-based superalloy GH4169

To further understand the creep behavior of nickel-based superalloys, creep deformation and damage characteristics of nickel-based superalloy GH4169 were investigated systematically by using SEM, EBSD and TEM characterizations in this study. Creep tests were conducted at 650 °C under 820 MPa.The results indicated that the fractions of low-, high-angle, and twin grain boundaries changed significantly after creep. Due to the grain rotation mechanism, the overall microstructure changed from random to preferred crystallographic orientation. <110>//loading direction (LD) oriented grains were rotated to <100>//LD and <111>//LD fibers, resulting in the decrease of <110> fiber, and the increase of <100> and <111> fibers. Cases of <110> oriented grains rotating into <100> and <111> orientations were also provided. Deformation twin and stacking faults were determined as the main deformation mechanisms. The failure of the specimen was induced by intergranular brittle fracture. The grain boundaries with special characteristics, namely high Schmid factor m and low Schmid factor mismatch Δm of neighbouring grains, and low geometric compatibility factor m’, exhibited high susceptibility to cracking.

The Secondary Development and Application of the Improved Nishihara Creep Model in Soft Rock Tunnels

Given the complexity and diversity of rock formations, existing constitutive models struggle to accurately portray their mechanical properties, leading to substantial discrepancies between numerical simulation outcomes and reality. This inadequacy fails to meet the demands of numerical analysis in practical engineering. This study first analyzes the physical and mechanical properties of thin-layered carbonaceous phyllite. Subsequently, an improved Nishihara rheological constitutive model is established based on these analyses. Utilizing the secondary development function offered by FLAC3D, the proposed model is further developed. The program’s correctness and reliability are confirmed through a numerical simulation using the triaxial creep test from existing research. Finally, the established constitutive model is applied in the numerical simulation of an actual soft rock tunnel engineering, obtaining results compared to real monitoring data. The results demonstrate that the improved Nishihara model is more effective at describing the creep deformation characteristics of soft rock. Moreover, the findings from this study can serve as a theoretical reference for predicting deformation in soft rock tunnel engineering.

A nonlinear creep model of rocks based on memory-dependent derivative

The creep behavior of soil and rock exhibits significant time-dependence and non-linearity, which are difficult to capture using traditional composite element models. In the framework of memory-dependent derivative theory, a memory-dependent visco-pot element with non-linear creep behavior, no instantaneous deformation, elastic after-effect, and stress relaxation is proposed. By connecting a memory-dependent visco-pot element with strain triggering to the Nishihara model, a memory-dependent derivative creep model is developed and its constitutive equation is derived. The creep test data pertaining to coal, salt, sandstone, and olivine rock are used to validate the model, which can describe the initial creep, steady-state creep, and non-linear accelerated creep deformation characteristics of various soil and rock materials. Comparison with fractional-order models, improved Nishihara models, and Hehai models shows that our model has better fitting results and is more advantageous in characterizing the non-linear features of soil and rock during the accelerated creep stage.

Plasticity analysis and constitutive model of salt rock under different loading speeds

Salt rock is recognized as an ideal source for oil, natural gas and compressed air due to its good deformation and low permeability. The injection–production frequency/rate under different working conditions greatly influences various mechanical behaviours, such as the deformation and convergence of the reservoir. Therefore, it is crucial to analyse the rate correlation of the mechanical characteristics of salt rock and to establish the corresponding constitutive model; this model accurately evaluates reservoir safety and reasonably designs reservoir operating pressure. According to the experimental deformation characteristics of salt rock under different loading and unloading rates, the time correlation, stage characteristics and evolution law of salt rock deformation were analysed, and a viscoplastic constitutive model of salt rock in the whole process was constructed based on loading plasticity and rate-related plasticity. The prediction effect of the model was verified by graded creep tests and different rate cyclic loading and unloading tests, revealing the good adaptability of the model for salt rock under complex loading paths. The results showed that the plastic (unrecoverable) deformation of salt rock could be divided into loading plasticity caused by stress state change and creep plasticity generated over a long period by stress accumulation. The creep deformation characteristics of salt rock could be better described using hardened damping elements, classical Norton elements and fracture damage variables; the relationship between loading plasticity and stress path changes was linear. The model had a high accuracy in predicting the deformation of salt rock under complex cyclic loading paths. For radial strain and volume strain, the accelerating point that protended the rapid growth of microcracks was used to distinguish the accelerated creep stage from the steady state creep stage. The number of events with an average frequency in the range of 0–50 kHz after the accelerating point suddenly increased significantly, which could be regarded as a precursor to the primary fracture of the rock.

Research on creep characteristics of loading and unloading of hard Flint limestone

The hard Flint limestone of Shuibuya hydropower station underground construction cavern is utilized as a research object to investigate the creep problem caused by excavation of rock masses such as caverns. In order to perform a triaxial compression grade-unloading creep test, the actual adjustment path of stress during excavation of underground cavern surrounding rock is used. Limestone under different confistiff pressures is then evaluated. Based on the Nishihara model, the elastic damage element considering time-dependent damage is introduced, and the unloading creep constitutive model of stiff Flint limestone is established and verified by experiments. The results show: 1) Deformation and creep strain appear at all stress levels. 2) As the unloading amount increased from 2 to 4 MPa, the quasi-destructive stresses of the samples were smaller from 83 to 79 MPa, indicating that the unloading amount affected the final creep damage strength of the rock samples. In other words, the higher the unloading amount, the lower the ultimate creep failure strength. 3) When entering the accelerated creep stage, the axial and lateral creep strains of the sample increase non-linearly, and the rupture duration of the sample is very short. Therefore, the creep deformation and creep rate characteristics of this stage should be paid attention to in practical engineering. 4) Different from the loading stress path, the failure mode of the Flint limestone rock sample is different. When the unloading amount is 2 and 4 MPa, the creep failure mode of the Flint limestone rock sample is shear failure, showing a significant oblique section crack. 5) The non-linear creep model curve of aging damage and the fitting effect of the unloading creep test curve are acceptable. The rationality of the established non-linear creep model is illustrated.

The creep model based on nonlinear Newton body under different temperature conditions

Mastering the creep deformation characteristics of rock under different temperature conditions is of great significance for studying the long-term stability and deformation mechanism of geotechnical engineering. Based on the classical Burgers model, the creep model under different temperature conditions is established by introducing a nonlinear Newton body. The parameters of the creep model are identified and the influence law of different parameters on rock creep deformation is analyzed. The relationship between model parameters and temperature is quantitatively expressed. The results show that the newly established model can describe the characteristics of the rock in the decay creep stage and the constant creep stage, especially can quantitatively characterize the relationship between the strain and the time of the rock in the tertiary creep under different temperatures conditions. The model fitting curve is highly consistent with the test data, and the correlation coefficient R2 is above 0.98, which thoroughly verifies the accuracy and rationality of the model. It is found that when the temperature is constant, the creep increases with the increase of the shear modulus of the elastomer G1, the shear modulus of the viscoelastic body G2, and the viscosity coefficient of the viscous body η1 in the constant creep stage. The decay creep property of rock is more obvious with the increase of the viscosity coefficient η2, and the axial strain tends to a constant value. The achievement can be used to predict the deformation trend of geotechnical engineering with time under different temperature conditions and provide the theoretical basis for long-term stability analysis.

Creep Characteristic Test and Creep Model of Frozen Soil

In order to research the creep deformation characteristics of frozen soil and the effect of various influencing factors on creep, indoor uniaxial creep tests were carried out on frozen soil specimens at temperatures of −5, −4, −3 and −2 °C under loads of 0.25, 0.5, and 0.75 σt, respectively. The creep deformation characteristics of frozen soil under different temperatures and load conditions are analyzed under unconfined conditions. The results show that under the uniaxial creep test conditions, when the load is low, there is no accelerated creep stage in the creep curve, which belongs to the decaying type creep; when the load is 0.75 σt, the creep curve enters the stage of accelerated creep, and the creep turns non-attenuated; temperature is the most important external factor affecting permafrost soil creep, and the proportion of ice is the key internal factor for affecting permafrost soil creep, the temperature is negatively correlated with the proportion of ice and the sensitivity of creep rate to temperature and load increases with the decrease of the proportion of ice; the damage variable D is introduced to modify the creep constitutive equation of the frozen soil, the creep process of frozen soil is well described by the modified creep constitutive equation for frozen soil.

Fractional viscoelastic-plastic constitutive model for frozen soil based on microcosmic damage mechanism

Frozen soil is a kind of composite geotechnical material with significant creep properties. To develop a creep constitutive model that can consider the composite properties and internal microcosmic damage mechanism of frozen soil, it is first conceptualized as a binary medium material containing both bonded elements and frictional elements, and the creep breakage mechanism of frozen soil is analyzed. Then, the relationship between micro-strain and macro-strain is established based on the homogenization theory. The creep constitutive relations of bonded elements and frictional elements are established, respectively, based on the creep breakage mechanism and the fractional calculus theory. In addition, the breakage ratio is defined as a function of creep time. Finally, a new fractional constitutive model with a composite structure is established. The three-dimensional model is also derived to facilitate its extensive application. Reasonable agreement is achieved comparing the model prediction results with the creep experimental results, and the proposed model can accurately capture the creep deformation characteristics of each phase. The results of the parameter sensitivity analysis further demonstrate the applicability of the definition of composite structure for the frozen soil.

Experimental characterization of flat indentation creep behaviour of Inconel 617

To analyse the creep deformation characteristics of Inconel 617, vacuum flat indentation creep test and microstructure analysis were completed in this study. With an increase in the creep load and temperature, limiting primary creep deflection and power law coefficient increased. An apparent indentation primary creep stage was observed and proven to be about 15–25 h in flat indentation creep test here. To describe the macro–deformation of Inconel 617, a modified theta–projection model was proposed and proven to be a feasible method to predict flat indentation creep curve accurately. Subsequently, a creep life prediction method based on deformation control was proposed. Based on the Larson – Miller parameter, reasonable conversion relationship between indentation creep stress and uniaxial creep equivalent stress was established. Finally, the microstructure analysis was completed to investigate the creep deformation characteristic. A hemispherical region along with significant extended grains and increase in hardness were observed. Considerable amount of Cr-rich precipitates and a small amount of Mo-rich precipitates were observed. Meanwhile, the precipitates were found to be discontinuous and granular for short indentation creep times.

Study on Creep Behavior of Silty Clay Based on Fractal Derivative

Soft soil is widely distributed in the riverside area of southern China. The creep deformation characteristics of the soft soil affect the long-term stability of the structure foundation, which cannot be ignored. Through the triaxial drainage creep test, the creep characteristics of riverside soil with a soft interlayer from Jiangsu Province were studied. The test results show that the creep procedure of the soft soil is divided into two stages, exhibiting steady-state creep and shear shrinkage characteristics with time and stress growth, which presents typical nonlinear behavior. Additionally, the confining pressure and stress are critical factors affecting creep characteristics. The fractal dashpot based on fractal derivative theory is introduced in place of the Abel dashpot in the classical fractional Burgers model; a fractal Burgers creep model with few parameters, high precision, and clear physical significance is established. Additionally, an analytical solution to the creep model is given. The model parameters are determined by fitting the test results, and the comparison shows that the results estimated with the model are more accurate than those estimated with the traditional model. The sensitivity analyses of the model parameters reveal the influence of key parameters on the creep characteristics of the soil. The results further confirm that the proposed fractal Burgers model can characterize the creep behavior of viscoelastic soil. These observations are extremely important for predicting the foundation displacement and formulating measures to prevent the deformation, which can provide a reference for engineering applications in the riverside area of southern China.

Model test on creep deformation and failure characteristics of soft rock roadways

This paper studies the creep deformation and failure characteristics of a soft rock roadway under the condition of combined support through a model test that lasted for 30 days. Under the action of high stress, the soft rock roadways present a tendency of continuous failure and nonconvergence, and the cross-sectional area shrinks to 52.3 % of the original roadway. The failure of the anchorage zone causes the bolt to lose its supporting function, and the continuous extrusion leads to the cracking of the lining and the shrinkage of the arch. Floor heave is the superposition of geometric deformation and loose deformation. The floor is continuously replenished by the movement of the surrounding rock below and to the two sides and moves upward under the combined action of high-level stress and vertical stress. Finally, the model test conclusion is verified by field tests, and deformation control schemes are proposed.

Time-Dependent Creep Constitutive Model of Roadway Surrounding Rock Based on Creep Parameters

In order to better study the creep deformation characteristics of rock under different stresses, the generalized Burgers model was used as the basic model after analyzing the creep characteristics of rock and its relationship with stress and strain, and its application scope was verified. Based on the damage mechanics theory, a viscoplastic body considering aging damage was established, which was connected with the generalized Burgers model in series. A new nonlinear creep constitutive model was obtained, which was extended to three dimensions. In addition, the relationship between model parameters and damage variables was established by introducing damage variables that considered damage effects. The unsteady creep constitutive model of rock is obtained, and the correctness and rationality of the model are verified by test data. The results show that this model not only accurately reflects the creep characteristics of attenuation and steady creep stage but also overcomes the defect that the generalized Burgers model is difficult to describe the accelerated creep. Considering the deterioration of creep parameters with time, the creep damage process of rock under different stress states can be better described, which provides a new idea for establishing unsteady creep model and determining model parameters.

Experimental Study on the Short-Term Uniaxial Creep Characteristics of Sandstone-Coal Composite Samples

In this investigation, the uniaxial short-term creep tests with multi-step loading were conducted on the sandstone-coal composite samples, and the characteristics of creep strength, creep deformation, acoustic emission (AE), and creep failure of composite samples were studied, respectively. The creep strength of the composite sample decreased with the stress-level duration, which was mainly determined by the coal and influenced by the interactions with the sandstone. The creep deformation and damage of sandstone weakened the deformation and damage accumulation within the coal, resulting in the larger strength for the composite sample compared with the pure coal sample. The axial creep strain of composite sample generally increased with the stress-level or the stress-level duration under same conditions. The AE characteristics of composite sample were related to the creep strain rate, the stress level, the stress level duration, and the local failure or fracture during creep loading. The micro or macro failure and fracture within the composite sample caused the rise in the axial creep strains and the frequency and intensity of AE signals, especially the macro failure and fracture. The creep failures of composite samples mainly occurred within the coal with the splitting ejection failure accompanied by the local shear failure, and no obvious failures were found within the sandstone. The coal in the composite sample became more broken with the stress-level duration.

Creep deformation characteristics of rubberised structural concrete

The influence of replacement of fine mineral aggregates with crumb tyre rubber of different particle sizes (2.36, 1.18 and 0.425 mm) on creep and shrinkage of structural rubberised concrete (rubcrete) is investigated. Rubcrete specimens were made using plain Portland cement (PC), 0.60 w/b ratio, crushed andesite coarse aggregate and a 90/10 blend of, respectively, crushed fine andesite and crumb rubber aggregate. The crumb rubber sizes were not blended in the concrete, resulting in three rubcrete mixes. Drying shrinkage and creep was monitored for approximately 1 year. The results show that compared to mineral aggregate concrete (MAC) both drying shrinkage and creep of the rubcretes increased, respectively, by up to 20% and 10% with decrease in crumb rubber particle size. Minimal differences were observed between the drying shrinkage and creep of the rubcretes made with the 1.18 and 2.36 mm crumb rubber aggregates. The results also showed that the introduction of crumb tyre rubber in concrete did not alter the micro-cracking potential of the rubcretes. Ultimately, the findings clearly show that structural rubcrete has similar creep and shrinkage deformation characteristics to that of MAC of similar strength.

Development and Application of a New Triaxial Testing System for Subzero Rocks

Abstract To face the challenges of coal production today, the mechanical behaviors of rock in subzero and disturbed environments are critical in the geomechanics of coal mining and artificial freezing engineering. Disturbances significantly affect the long-term mechanical properties and nonlinear viscoelastic-plastic deformation characteristics of frozen soft rock. This article summarizes current rock triaxial test systems, which cannot concurrently solve the problems of subzero temperatures, creep, disturbance, and high sampling rates. Based on existing equipment limitations and the current research aims, an innovative, applicable, and scalable measurement/control system based on National Instruments hardware is integrated into LabVIEW to design and construct a new triaxial testing system capable of achieving both dynamic disturbances and subzero temperatures. The testing system can produce a basic environment with confining pressures up to 30 MPa, axial forces up to 500 kN, and lowest temperatures of −30°C. The system has a 51.2 kS/s sampling using 5-channel closed-loop control. By changing the transfer valve between the supercharger and the servo valve, both conventional triaxial compression and creep tests can be carried out. The triaxial creep tests are performed on frozen rock specimens under step loading and graded disturbances to analyze the creep deformation characteristics and failure modes of the specimens. The results show that at low stress levels, the disturbance load closes and reorganizes microcracks in the rock specimens, reducing the specimen deformation rate. With increasing stress levels or disturbance intensities, the specimen cracks expand rapidly, the creep rate increases, the disturbance energy stored in the rock specimen releases, and the specimens rapidly fail. Therefore, this disturbance creep phenomenon must be considered, and timely support should be provided for exposed frozen rock wall to guarantee construction safety. Moreover, the test results also verify that the design of the new testing system is reliable, feasible, and useful.