A damage mechanics based on the constitutive model for strain-softening rocks

Shen, Ping; Tang, Huiming; Ning, Yibing; Xia, Ding

doi:10.1016/j.engfracmech.2019.106521

Cited by 49 publications

(25 citation statements)

References 28 publications

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“…Except for the parameters in equation (24), derived from the 'Extremum Method', the other two equations were obtained by the fitting method.…”

Section: Parameters In the Modelsmentioning

confidence: 99%

“…Due to random distribution of the rock micro-element strength, a certain intensity distribution needs to be employed, and generally the log-normal distribution, normal distribution, and Weibull distribution find their application. e Weibull distribution is the most reasonable among the three distributions [21], and if properly applied, the whole deformation process of the rocks, including the statistical damage, strain softening, and damage weakening, can be well described [24]. Unfortunately, the plastic deformation in the initial compression stage cannot be reflected by these models, since for each micro-element, the stress-strain relationship is deemed to obey Hooke's law when the stress is small, ignoring the fact that the plastic deformation process due to the initial voids is compacted.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Development of a Model for Initial Compaction Stage in Rock Based on Energy Dissipation

Nie

Cai

et al. 2022

Advances in Materials Science and Engineering

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An accurate model is essential for the numerical simulation of the rock failure occurring under different conditions. However, the expression of the initial compression stage is often overlooked in the widespread constitutive models. In this pursuit, several models considering the initial compression stage were gathered from the previous studies, and a model based on the energy dissipation principle was proposed in the present study. Subsequently, the experimental data of five different types of rock under uniaxial load was collected from the literature to verify the validity of the proposed model, and the performance was compared with the other models. It was found that all the models listed in this study exhibited good performance in expressing the stress-strain curve during the initial compression stage.

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“…Except for the parameters in equation (24), derived from the 'Extremum Method', the other two equations were obtained by the fitting method.…”

Section: Parameters In the Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Development of a Model for Initial Compaction Stage in Rock Based on Energy Dissipation

Nie

Cai

et al. 2022

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

show abstract

“…Therefore, it is important to select a constitutive model to study the mechanical characteristics of coal accurately. At present, strain-softening models and Mohr-Coulomb models are typically used in mechanical testing of coal/rock masses with FLAC3D [35][36][37][38].…”

Section: Constitutive Model Selectionmentioning

confidence: 99%

Influence Analysis and Stepwise Regression of Coal Mechanical Parameters on Uniaxial Compressive Strength Based on Orthogonal Testing Method

et al. 2020

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Uniaxial compressive strength (UCS) and peak strain (PS) are essential indices for studying the mechanical properties of coal and rock masses, and they are closely related to mechanical parameters such as the elastic modulus (E), Poisson’s ratio (υ), cohesion (C) and internal friction angle (Φ) of coal and rock masses. This study took the No. 2-1 coal seam of Zhaogu No. 2 Mine, in Henan Province, China, as the research object. An RMT-150B servo testing machine was used to test all mechanical parameters, including the E, υ, C and Φ of coal and rock masses. Based on the principle of orthogonal testing, Three Dimensions Fast Lagrangian Analysis of Continua (FLAC3D) was used to select E, υ, C, Φ, tensile strength (Rm) and dilation angle (Ψ) as initial participation factors. Using these six parameters and a five-level combination scheme (L25 (56)), the influence of coal mechanical parameters on UCS and PS was investigated, using the software SPSS for stepwise regression analysis, and a uniaxial pressure-resistant regression prediction equation was established. The research showed that, under uniaxial compression conditions, the main parameters controlling UCS of coal masses are C and Φ; conversely, the main parameters controlling PS are E and C. UCS and PS exhibit significant linear relationships with these main controlling parameters. Here, a stepwise regression prediction equation was established through reliability verification analysis using the main controlling parameters. This prediction method produces very small errors and a good degree of fit, thus allowing the rapid prediction of UCS. The precision of the stepwise regression model depends on the number of test samples, which can be increased in the later stages of a design project to further improve the precision of the projection model.

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“…These models can be separated into two categories, stochastic and phenomenological models. The stochastic method mainly uses a probability distribution function (e.g., Normal distribution, Poisson distribution, or Exponential distribution) to mimic the distribution of certain rock mass properties (e.g., strength) and, therefore, the overall non-linear loading behaviour (Tang et al 1997;Li and Chen 2009;Li et al 2012;Chen et al 2018;Shen et al 2019). However, this type of model is less convincing since the true internal heterogeneity of rock samples is hard to be directly verified.…”

Section: Introductionmentioning

confidence: 99%

A Pre-peak Elastoplastic Damage Model of Gosford Sandstone Based on Acoustic Emission and Ultrasonic Wave Measurement

et al. 2022

Rock Mech Rock Eng

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The determination of internal material damage is always an arduous challenge. Non-destructive monitoring methods show great potential in quantitatively determining the internal material properties, whereas most of the studies relying on external observations remain in a qualitative stage. They either violate the basic thermodynamic assumptions or are difficult to guide engineering practice. In this paper, following the theory of continuum mechanics, an elastoplastic damage model based on non-destructive monitoring methods (i.e., acoustic emission and ultrasonic wave velocity measurement) has been developed. To capture the continuous and precise damage evolution inside rock mass, P wave velocity obtained by ultrasonic wave measurement was utilised and then considered as an input for the proposed elastoplastic damage model. Triaxial loading test results on six Gosford sandstone samples were analysed first to characterise critical stresses along the stress–strain loading curves, such as crack closure stress, stable crack propagation stress and unstable crack propagation stress. The drop of ultrasonic wave velocity can be seen as an indicator to represent the damage evolution inside rock material. Damage initiation is also closely related to the confining stress and dilation induced volumetric expansion. The test results also suggested that the Drucker–Prager criterion is sufficient to describe the plastic yielding surface and the following material hardening. A non-associated plastic flow assumption was adopted, considering the essence of microcrack shearing in rock failure and the effect of hydrostatic pressure on plastic deformation. A modified Drucker–Prager plastic potential was also introduced to track the orientation of plastic increment with material hardening. A scalar damage variable was derived from ultrasonic wave measurement results to indirectly represent the deterioration of rock properties (modulus). The proposed model was used to match lab test results with high consistency, and the main features of rock behaviour in triaxial loading tests were successfully captured by the model. Finally, the damage evolution of rock samples was analysed, which indicates that damage is dependent on its conjugate force, namely damage energy release rate Y. This study proves that P wave velocity can be an effective approach to measure and forecast the internal damage evolution inside rock mass, which has broad prospects for engineering applications.

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A damage mechanics based on the constitutive model for strain-softening rocks

Cited by 49 publications

References 28 publications

Development of a Model for Initial Compaction Stage in Rock Based on Energy Dissipation

Development of a Model for Initial Compaction Stage in Rock Based on Energy Dissipation

Influence Analysis and Stepwise Regression of Coal Mechanical Parameters on Uniaxial Compressive Strength Based on Orthogonal Testing Method

A Pre-peak Elastoplastic Damage Model of Gosford Sandstone Based on Acoustic Emission and Ultrasonic Wave Measurement

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