Nonlinear creep damage constitutive model for soft rocks

Liu, Huai-Zhong; Xie, Hehan; He, Jian; Xiao, Ming; Li, Zhuo

doi:10.1007/s11043-016-9319-7

Cited by 103 publications

(47 citation statements)

References 27 publications

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“…As shown in Figure 4, the traditional Nishihara model is composed of a Hooke body, a Kelvin body, and an ideal visco-plastic body in series, 45 where E 0 stands for the elastic modulus, E 1 denotes the viscoelastic modulus, and η 1 and η 2 are the viscosity coefficients of the dashpot.…”

Section: One-dimensional Nonlinear Creep Model For Coal or Rockmentioning

confidence: 99%

“…27,29,36,37,45 For 3-D problems, the total strain can be given by. 27,29,36,37,45 For 3-D problems, the total strain can be given by.…”

Section: Three-dimensional Creep Equations For Coal Containing Gasmentioning

confidence: 99%

“…The one-dimensional creep equations can be generalized to construct three-dimensional (3-D) creep equations using an analogy method. 27,29,36,37,45 For 3-D problems, the total strain can be given by.…”

Section: Three-dimensional Creep Equations For Coal Containing Gasmentioning

confidence: 99%

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Creep characteristics and constitutive model of coal under triaxial stress and gas pressure

Zhang

Gao

et al. 2019

Energy Science & Engineering

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Creep behavior is one of the most important mechanical behaviors of coal. In the present study, we systematically carried out a series of creep experiments of briquette samples under triaxial compression and gas pressure. The experimental results showed that the creep deformation characteristics of coal were related to deviatoric stress and gas pressure. The accelerating creep stage initiated when the deviatoric stress reached or exceeded the yield stress until failure took place. In contrast, when the deviatoric stress was less than the yield strength, only transient and steady creep stage occurred. Besides, gas pressure played a positive role in the creep process of coal. The axial strain of coal slightly increased with gas pressure (range from 0.13 to 0.40 MPa) when the effective triaxial stress remained constant. For example, in the steady creep stage (σ 1 = 9 MPa, p = 0.13 MPa), the axial strain of sample S 1 is 2.710% and that of sample S 2 is 3.361%, that is, coal samples with high gas pressure have higher axial strain. Moreover, gas pressure has two main effects on the mechanical behavior of coal. One is that the coal adsorbs gas molecules resulting in swelling strain and swelling stress, and the other is that the gas pressure may compress the coal particles. Considering the swelling stress and gas pressure, we intensively studied the effective stress formula of coal containing gas. Then, the effective stress was taken into consideration in the nonlinear Nishihara creep model. Furthermore, the tertiary creep factor n was introduced in the nonlinear model to control the creep deformation evolution with time so that the nonlinear model could accurately describe the full creep stage of coal. In contrast, due to the lack of such a controlling parameter, the Nishihara model failed to reproduce the accelerating creep stage. K E Y W O R D Scoal, creep model, effective stress, gas pressure, swelling stress, triaxial compression | INTRODUCTIONCreep behavior is one of the fundamental mechanical properties of coal or rock, associated with the stability of many buildings and underground structures in mining and rock engineering, such as roadways, tunnels, and dams. It is important to have a precise understanding of the creep or timedependent behavior of coal or rock, which may prevent coal 502 | ZHANG et Al. Highlights• The coupling effect of triaxial stress and gas pressure on coal was investigated. • The gas pressure played a positive role in the creep process of coal. • The effective stress of gas-filled coal was intensively studied. • The effective stress was considered in the nonlinear Nishihara creep model of coal, which could accurately reproduce the three creep stages, especially the accelerating creep stage.How to cite this article: Zhang L, Li X-C, Gao J-X, An Z-X, Yang X-H, Nie B-S. Creep characteristics and constitutive model of coal under triaxial stress and gas pressure. Energy Sci Eng. 2020;8:501-514. https ://doi.

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Section: One-dimensional Nonlinear Creep Model For Coal or Rockmentioning

confidence: 99%

“…27,29,36,37,45 For 3-D problems, the total strain can be given by. 27,29,36,37,45 For 3-D problems, the total strain can be given by.…”

Section: Three-dimensional Creep Equations For Coal Containing Gasmentioning

confidence: 99%

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Creep characteristics and constitutive model of coal under triaxial stress and gas pressure

Zhang

Gao

et al. 2019

Energy Science & Engineering

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“…Previous studies have shown that the viscosity coe cient of rock will decrease when stress exceeds the long-term ultimate strength [17][18][19]; since an exponential function can better re ect the relationship between the damage variables and the strain (Figure 10), we assume that the damage variables in the cycle creep stage can be expressed as an exponential function (as shown in (4)), and based on the characteristic of the Burgers creep model [20], a new viscoelastic-plastic creep model was proposed, as shown in Figure 13.…”

Section: Creep Model and Parameter Identi Cation Formmentioning

confidence: 99%

Mechanical Behavior of Shale Rock under Uniaxial Cyclic Loading and Unloading Condition

Zhao

Liu

et al. 2018

Advances in Civil Engineering

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In order to investigate the mechanical behavior of shale rock under cyclic loading and unloading condition, two kinds of incremental cyclic loading tests were conducted. Based on the result of the short-term uniaxial incremental cyclic loading test, the permanent residual strain, modulus, and damage evolution were analyzed firstly. Results showed that the relationship between the residual strains and the cycle number can be expressed by an exponential function. e deformation modulus E 50 and elastic modulus E S first increased and then decreased with the peak stress under the loading condition, and both of them increased approximately linearly with the peak stress under the unloading condition. On the basis of the energy dissipation, the damage variables showed an exponential increasing with the strain at peak stress. e creep behavior of the shale rock was also analyzed. Results showed that there are obvious instantaneous strain, decay creep, and steady creep under each stress level and the specimen appears the accelerated creep stage under the 4th stress of 51.16 MPa. Based on the characteristics of the Burgers creep model, a viscoelastic-plastic creep model was proposed through viscoplastic mechanics, which agrees very well with the experimental results and can better describe the creep behavior of shale rock better than the Burgers creep model. Results can provide some mechanics reference evidence for shale gas development.

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“…However, the parameters 2 and Shock and Vibration Figure 11 that the axial and the lateral creep curves show obvious nonlinear behavior; the instantaneous strain, decay creep, and steady creep reveal a trend of increase with the cycle number and cycle loading, indicating that both the cycle number and the level of the stress are the primary reason for the nonlinear behavior of the red stone under uniaxial cyclic loading. In order to better describe the creep behavior of red sandstone material under cyclic incremental uniaxial compressive and tensile stress, by adopting the decreasing hypothesis of viscosity coefficient [21][22][23], an improved Burgers creep model of rock material can be proposed, as shown in Figure 13.…”

Section: Creep Model and Parameter Identificationmentioning

confidence: 99%

Mechanical Behavior of Red Sandstone under Incremental Uniaxial Cyclical Compressive and Tensile Loading

Zhao

Liu

Huang

et al. 2017

Shock and Vibration

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Uniaxial experiments were carried out on red sandstone specimens to investigate their short-term and creep mechanical behavior under incremental cyclic compressive and tensile loading. First, based on the results of short-term uniaxial incremental cyclic compressive and tensile loading experiments, deformation characteristics and energy dissipation were analyzed. The results show that the stress-strain curve of red sandstone has an obvious memory effect in the compressive and tensile loading stages. The strains at peak stresses and residual strains increase with the cycle number. Energy dissipation, defined as the area of the hysteresis loop in the stress-strain curves, increases nearly in a power function with the cycle number. Creep test of the red sandstone was also conducted. Results show that the creep curve under each compressive or tensile stress level can be divided into decay and steady stages, which cannot be described by the conventional Burgers model. Therefore, an improved Burgers creep model of rock material is constructed through viscoplastic mechanics, which agrees very well with the experimental results and can describe the creep behavior of red sandstone better than the Burgers creep model.

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Nonlinear creep damage constitutive model for soft rocks

Cited by 103 publications

References 27 publications

Creep characteristics and constitutive model of coal under triaxial stress and gas pressure

Creep characteristics and constitutive model of coal under triaxial stress and gas pressure

Mechanical Behavior of Shale Rock under Uniaxial Cyclic Loading and Unloading Condition

Mechanical Behavior of Red Sandstone under Incremental Uniaxial Cyclical Compressive and Tensile Loading

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