Viscoplastic Body Research Articles

Features and Constitutive Model of Hydrate-Bearing Sandy Sediment’s Triaxial Creep Failure

In the longstanding development of hydrate-bearing sediment (HBS) reservoirs, slow and permanent deformation of the formation will occur under the influence of stress, which endangers the safety of hydrate development projects. This paper takes hydrate-bearing sandy sediment (HBSS) as the research object and conducts triaxial compression creep tests at different saturation degrees (20%, 30%, and 40%). The results show that the hydrate-containing sandy sediments have strong creep characteristics, and accelerated creep phenomenon will occur under the long-term action of high stress. The longstanding destructive power of the specimen progressively raises with the increase in hydrate saturation, but the difference in the triaxial strength of the specimen progressively increases. This indicates that the damage to the hydrate structure during long-term loading is the main factor causing the strength decrease. Further, a new nonlinear creep constitutive model was developed by using the nonlinear Burgers model in series with the fractional-order viscoplastic body model, which can well describe the creep properties of HBSS at different saturation levels.

A memory-dependent three-dimensional creep model for concrete

The study of creep models for concrete is of great significance in analyzing and predicting the long-term stability of concrete structures. Based on the theory of memory-dependent derivatives, memory-dependent viscous dashpots that can describe the characteristics of decaying creep and accelerating creep are constructed based on the varying characteristics of the creep process in different stages. The Kelvin body was replaced with a stable memory-dependent dashpot and the Newtonian dashpot in the visco-plastic body was transformed into an unstable memory-dependent dashpot by drawing on the component combination form of the Nishihara model. A three-dimensional concrete creep model based on memory-dependent derivatives was established. By adjusting the model parameters of stable and unstable memory-dependent viscous dashpots, the model can simulate the creep process of concrete with different decaying creep characteristics and accelerating creep characteristics, and it has good universality. Multiple sets of experimental data on concrete creep verify that the memory-dependent concrete creep model corresponds well to the experimental data. Compared with five other concrete creep models, this model has fewer parameters and higher fitting accuracy, especially in characterizing the accelerating creep characteristics of concrete.

Nonlinear Nishihara model of soft rock based on damage mechanics and its parameter identification

The traditional Nishihara model is difficult to describe the nonlinear primary and accelerated creep characteristics of soft rock. Based on this, an improved nonlinear Nishihara model is established by modifying the unsteady dashpot and a nonlinear damaged viscoplastic body in series. The one-dimensional and three-dimensional creep constitutive equations of soft rock are derived. Levenberg-Marquardt algorithm is used to identify model parameters of creep test data of Cretaceous soft rock and red sandstone. The results show that the correlation coefficient between the fitted results of the improved nonlinear Nishihara model and the creep test data is above 0.97. The sensitive parameters λ,η′1 and a of the model are all within a reasonable range. It shows that the model can accurately reflect the characteristics of the unsteady primary creep stage and the nonlinear damage accelerated creep stage of soft rock, which is better than the traditional Nishihara model. The research results can provide theoretical guidance for similar soft rock creep model research.

Influence of pore water pressure on concrete creep and a creep model considering the effect of cohesion and internal friction angle

AbstractA new nonlinear viscoplastic body considering cohesion and internal friction coefficient versus time is proposed by considering cohesion and internal friction angle. A new creep model for concrete considering cohesion and internal friction angle is obtained by interlocking it with the conventional model. The results show that the creep model can properly reflect the creep development of soft‐cut concrete at the pile head by comparing the creep model with the three‐dimensional creep test data trends under various levels of loading. The model can well describe the whole process of creep deformation and also better compensate for the shortcomings of the traditional creep model that cannot describe the characteristics of accelerated creep deformation.

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 damage-state 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.

Creep characteristics and damage model of coal–rock combinations with different height ratios

Numerous coal pillars are left after the coal mining process. The composite structure comprising a roof and coal pillar has prominent creep characteristics, which threaten safe underground mining. Therefore, the creep characteristics of coal-rock combinations should be studied to ensure the safety of quarry and surface. Uniaxial creep tests under static load axial pressure and different height ratios were performed using a self-designed rock creep disturbance test device to determine the effect of height ratio and axial pressure on the creep characteristics of coal–rock combinations. From the test results, a creep damage model for coal–rock combinations was established by combining the elastomer, fractional Kelvin body, plastic body, Abel dashpot, and modified nonlinear viscoplastic body; introducing damage variables D related to stress, height ratio, and time; and deriving a one-dimensional creep equation. An improved nonlinear least squares method based on pattern search was utilized to invert the creep parameters. The results of the creep equation calculation were fitted with the experimental results with good results. The creep curve with a height ratio of 2:1 was predicted with good results. The research results provide theoretical references for long-term stability analysis of rock engineering.

A nonlinear creep model for transversely isotropic rock based on fractional calculus theory

A nonlinear creep model based on fractional calculus theory is proposed to better describe the creep characteristics of transversely isotropic rock. The model includes a Hooke elastomer, a fractional Abel dashpot, a Kelvin body, and a nonlinear viscoplastic body, which effectively capture the three stages of creep (including the primary, steady-state, and accelerating creep stages) while also reflect the influence of different bedding angles on creep behavior. The parameters of the model are identified by the Levenberg–Marquardt algorithm. Compared to previous models assuming constant Poisson’s ratio for transversely isotropic rock, our nonlinear creep model demonstrates improved accuracy and rationality.

Analysis of an improved Nishihara creep model considering plastic strain accumulation

Rock-engineering structures, particularly subway excavation rock-engineering structures, are subjected to the long-term effects of external loading that may gradually damage and cause creep and severe plastic deformations or even progressive failure. The traditional Nishihara creep model cannot accurately describe the accelerated creep stage of rock with particularly obvious nonlinear characteristics. Based on this model, a damage variable that can consider the plastic strain accumulation is introduced in this study to replace the viscoplastic body in the traditional model with a damaged viscoplastic body and establish an improved Nishihara creep model. Using the superposition principle, the creep equations of the improved model in the one- and three-dimensional stress states are derived. The accuracy and rationality of the improved model are verified using uniaxial and conventional triaxial creep tests of mudstone and sandstone under different confining pressures. The improved model can not only accurately reflect the nonlinear characteristics of the creep curve in the decay and constant velocity stages but also describe the accelerated creep characteristics of mudstone and sandstone in a high-stress state. Its applicability and accuracy are superior to those of the traditional model. This study can provide a theoretical reference for subway tunnel excavation and stability analysis of deep roadway surrounding rocks.

Mechanical Properties of Gas Storage Sandstone under Uniaxial Cyclic Loading and Unloading Condition

In order to study the mechanical properties and damage evolution of the gas storage surrounding rock under the periodic injection-production process, the uniaxial cyclic loading and unloading tests of sandstone were carried out by TFD-2000 microcomputer servo-controlled rock triaxial testing machine. Results shown that the compressive strength of gas storage sandstone specimens were gradually decreases with increasing of the stress amplitude after 200 cycles. The stress-strain curve under uniaxial cyclic loading and unloading condition formed hysteresis loops, and the hysteresis loop presented sparse-dense-sparse when the stress amplitude was relative higher. The residual strains can be divided into three stages of decay deformation stage, stable deformation stage and accelerated deformation stage when the stress amplitude is 8~32 MPa, this phenomenon is very similar to the creep behavior of rocks. The energy evolution of sandstone under cyclic loading and unloading was analyzed and the damage evolution low of which was also discussed in detail, the damage variable defined by energy dissipative ratio accumulation can well reflect the damage development of sandstone under uniaxial cyclic loading and unloading. A nonlinear visco-plastic body was proposed by considering the accelerate stage of curves of the axial residual strains, and used the nonlinear visco-plastic body to replace the visco-plastic body of the traditional Nishihara model, a nonlinear viscoelastic-plastic model for cyclic loads was established and the applicability of the model is verified. The research results provide certain reference value for the construction and maintenance of gas storage.

A creep-fatigue model of rock salt and its application to the deformation analysis of CAES salt caverns

The rock surrounding salt caverns used in a compressed air energy storage (CAES) system experiences the combined creep and fatigue load during an operation period, which includes the injection, idle and production stages. To ensure the safety of the CAES salt caverns over the course of the service life, investigating the mechanical response of rock salt under creep-fatigue load is critical. In this study, creep-fatigue tests of rock salt under different conditions were performed in a stress-controlled pattern. The salt axial strain under creep-fatigue load includes initial, steady and accelerated phases. The axial strain presents a continuous increment during the high stress holding time. A fatigue damage body was established to describe the effect of cyclic load on deterioration of mechanical behavior of salt rock. A novel creep-fatigue model of rock salt is proposed by connecting the elastic body, Kelvin model, fatigue damage body and nonlinear viscoplastic body in series. The test data were used to validate the established model and they correlate well with the model data. Subsequently, the proposed model was implemented in the FLAC3D software and a creep-fatigue simulation test of a cylindrical specimen wase performed. The simulation test presents a similar variation trend compared with the test data regarding the axial strain. Finally, a three-dimensional geotechnical model was proposed to analyze the deformation of CAES salt caverns during operation and the proposed law was used as the creep model of rock salt during the simulation. The simulation results between the proposed creep-fatigue model and static Norton power model are further compared.

Deformation constitutive model of subgrade soil under intermittent cyclic loading

During the actual operation of subways, high-speed railway, and other infrastructure, subgrade soil will be subjected to periodic vibration and intermittent loading, i.e., intermittent cyclic load. To study the deformation characteristics of subgrade soil under intermittent cyclic loading, the Newtonian dashpot in the generalized Kelvin model is replaced by the fractional Abel dashpot, a fractional generalized Kelvin model is established. Then, a nonlinear viscoplastic body model considering damage is proposed, which is connected in series with the improved fractional generalized Kelvin model, and the deformation constitutive model of soil under intermittent cyclic loading is obtained. Finally, the effectiveness and applicability of the model are analyzed, and the model is compared with other constitutive models. The results show that the constitutive model established in the paper can reflect the combined effect of confining pressure, frequency, dynamic stress amplitude and other factors on the cumulative plastic strain of soil, and can well characterize the development law of three types of cumulative plastic strain curves of soil: stable, critical, and failure. The fitting parameters alpha and eta tend to decay and rise, respectively, with the increase in loading stage N, which reflects the rationality and accuracy of the model.

ANALYSIS OF VISCOPLASTIC CONTACT PROBLEM

In this paper, we analyze a quasistatic problem modeling frictional contact between a viscoplastic body and an obstacle, the so called foundation. The material constitutive relation is assumed to be non-linear. The boundary conditions of contact and friction are modeled respectively by the \textit{Signorini} conditions and the generalized Coulomb's non-local law. We derive a variational formulation for the problem and prove the existence of its unique weak solution. The proof use, essentially, classical arguments of compactness, variational inequalities and Banach’s fixed point theorem.

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.

Study on the Nonlinear Damage Creep Model of the Weak Interlayer

The weak interlayer has become a weak link in slope engineering due to its rheological effect. It is of great significance to study the nonlinear creep model of weak interlayer for long‐term stability of the slope. In this paper, based on the creep curve characteristics of weak interlayer and considering the influence of aging damage, the nonlinear improvement of a classical viscoplastic body under stress and time‐double threshold conditions is carried out, so that it can more accurately reflect the accelerated creep characteristics of the weak interlayer. By analyzing the relationship between failure load and time, the accelerated creep time threshold of the weak interlayer is obtained. On this basis, a nonlinear damage creep constitutive model of the weak interlayer is constructed and its creep equation is derived. By using the self‐defined function fitting tool of Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data of weak interlayer are fitted and compared. The fitting curve is in good agreement with the test data, which shows the rationality and applicability of the nonlinear creep model. The results show that the nonlinear damage creep model constructed in this paper can well describe the creep characteristics of the weak interlayer and the model has important theoretical reference significance for the study of long‐term stability of slope with the weak interlayer.

Nonlinear Creep Model for Rocks Considering Damage Evolution Based on the Modified Nishihara Model

In general, the microdefects in rocks obey Weibull distribution. Based on the laws of statistics of microdefects in rocks, the relationship between the damage and the strain is established. Moreover, by considering characteristics of the viscoelastic–plastic and the damage evolution in rocks, a nonlinear creep model for rocks considering damage evolution is proposed to predict the creep behaviors of rocks based on the modified Nishihara model. In the proposed model, a dashpot element and a nonlinear viscoplastic body are added into the classical Nishihara model to simulate the accelerating creep stage of soft rocks. Moreover, the damage of rocks is considered in the process of creep. The effects of the shape parameter, the scale parameter, the peak stress, the peak strain, and the confining stress on the damage are investigated using the proposed method. The novel model is suitable to predict the creep behaviors of hard rocks and soft rocks simultaneously, and the difficulty to simulate the accelerating creep stage using the traditional creep model is overcome. To verify the robustness and precision of the proposed model, the creep behaviors of granite, coal, and red sandstone at different stresses are investigated. The predicted creep behaviors of soft and hard rocks using the proposed method are in good agreement with the experimental data, especially for the nonlinear accelerating creep stage.

Numerical analysis of a viscoplastic contact problem with normal compliance, unilateral constraint, memory term and friction

In this paper, we consider a model which describes the quasistatic contact between a viscoplastic body and a foundation. The material’s behavior is modeled with a rate-type viscoplastic constitutive law with an internal state variable. The contact is modeled with normal compliance, unilateral constraint, memory term, and friction which is under a total slip-dependent version of Coulomb’s law. For the weak formulation of the problem, which is in the form of a system coupling two nonlinear integral equations with a history-dependent variational–hemivariational inequality, we introduce a fully discrete scheme and derive an error estimate. Under appropriate regularity assumptions, we obtain an optimal-order error estimate in finite element spaces. Finally, numerical results are reported to show the performance of the numerical method.

Research on the high temperature performance of asphalt pavement based on field cores with different rutting development levels

Rutting is one of the main distresses of highway asphalt pavement in China. Evaluating the high temperature performance of asphalt pavement during its service period is a major problem for road management departments. The purpose of this paper is to investigate the effect of rutting development levels on the high temperature performance of each layer in asphalt pavement and provide guidance for rutting distress evaluation of highway asphalt pavement. The field cores were obtained from the sections with different rutting development levels (different Equivalent Single Axle Loads and rutting depths) under the same service life. Based on the thickness measurement of field cores, the rutting contribution rate (RCR) of each layer was calculated. Dynamic creep test was performed on the surface layer SMA-13 and binder layer SUP-20 mixtures. Finally, dynamic modulus test was conducted to analyze the influence of rutting development levels on the viscoelastic properties of the binder layer asphalt mixture. The results show that the surface layer is largely responsible for the rutting in the initial rutting stage (rutting depth is less than 10 mm), the RCR of the binder layer increases gradually and exceeds that of the surface layer as the rutting develops. For the selected pavement structure, when the rutting depth of whole pavement is more than 15 mm, the binder layer SUP-20 behaves more like viscoplastic body in high-temperature/low-frequency range. The RCR value of binder layer is more than 40% and its resistance to deformation at high temperature starts to degrade rapidly. The high temperature performance of the surface layer remains relatively stable under different rutting depths.

Creep mechanical properties and creep model of high water material under step loading

AbstractHigh water material, a kind of filling and supporting material, is widely used in underground engineering, whose creep mechanical properties are directly related to the underground engineering stability. In this paper, creep tests of different types of high water material are carried out. The results show that: for the complete specimen and the single and double crack specimens with crack inclination angles of 0°, 30°, and 60°, the curves present initial elastic, creep attenuation and creep stabilization in the first four stages, and the creep acceleration appears in the fifth stage, leading to the final failure of the specimen; for the single and double crack specimens with a crack inclination angle of 90°, no creep acceleration appears. According to the test results, a new nonlinear viscoplastic body is proposed, and connected with the traditional Nishihara model, forming the nonlinear Nishihara model. The new model can clearly describe the creep characteristics of complete and cracked specimens at different stages. Finally, according to the new creep model, crack parameters are discussed with the creep rate index and the starting time of accelerated failure.

Bifurcation theory of plasticity, damage and failure

I developed a comprehensive theory of plasticity, damage and failure, which is independent of the micromechanical mechanism of plasticity. It includes all major components of the mechanical behavior of ductile materials, e.g. strain/work-hardening and Bauschinger effect, and covers all regimes of viscoplastic tensile/compressive loading/unloading. The theory is based on the concepts of free energy and damage parameter and has the attributes of both rate-dependent and rate-independent plasticity, kinematic and isotropic hardening. The ultimate failure of a specimen is defined as a point of critical value of the damage parameter. The theory provides justification for Drucker’s ad hoc condition of instability. The theory describes diverse phenomena of Lüders stress, creep, internal friction, and fatigue on the same self-consistent basis. In quasi-static low-cycle fatigue, I derive a Paris-type equation between the rate of degradation and cyclic plastic work and reveal a Coffin-Manson power-law relationship between the number of cycles to failure and plastic-strain amplitude. In dynamic fatigue, I find two regimes—low-cycle and high-cycle—whose loading amplitudes are separated by the yield point. The two regimes have significantly different dependencies on the frequency and viscosity. In this publication, I present the theory and computer simulations of a homogeneous viscoplastic body subjected to various conditions of isothermal strain-controlled uniaxial loading. In the follow-up publications, I will expand the theory on the cases of inhomogeneous three-dimensional bodies subjected to multiaxial loading at variable temperatures and compare the results to the experiments. Complete version of the theory can be used for the full-cycle cradle-to-grave design of new materials in service.

A piezoelectric contact problem with slip dependent friction and damage

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.