A damage-softening statistical constitutive model considering rock residual strength

Wang, Zhiliang; Yong-chi, LI; Wang, J. G.

doi:10.1016/j.cageo.2006.02.011

Cited by 209 publications

(109 citation statements)

References 11 publications

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“…There are four common distributions which have been used in rock mechanics: power function distribution [40], Weibull distribution [41], normal distribution [42], and normal logarithmic distribution [43]. According to Wu et al [30], the power function distribution and Weibull distribution are chosen to model the stress-strain curves of shale samples.…”

Section: Statistical Damage Constitutive Models Of Rocks Undermentioning

confidence: 99%

A Damage Constitutive Model for the Effects of CO₂-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

et al. 2018

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CO 2 is a very promising fluid for drilling and nonaqueous fracturing, especially for CO 2 -enhanced shale gas recovery. Brittleness is a very important characteristic to evaluate the drillability and fracability. However, there is not much relevant research works on the influence of CO 2 and CO 2 -based fluids on shale's brittleness been carried out. Therefore, a series of strength tests were conducted to obtain the stress-strain characteristics of shale soaked in different phases of CO 2 including subcritical or supercritical CO 2 with formation of water for different time intervals (10 days, 20 days, and 30 days). Two damage constitutive equations based on the power function distribution and Weibull distribution were established to predict the threshold stress for both intact and soaked shale samples. Based on the results, physical and chemical reactions during the imbibition cause reductions of shales' peak axial strength (20.79%~61.52%) and Young's modulus (13.14%~62.44%). Weibull distribution-based constitutive model with a damage threshold value of 0.8 has better agreement with the experiments than that of the power function distribution-based constitutive model. The energy balance method together with the Weibull distribution-based constitutive model is applied to calculate the brittleness values of samples with or without soaking. The intact shale sample has the highest BI value of 0.9961, which is in accordance with the high percentage of brittleness minerals of the shale samples. The CO 2 -NaCl-shale interactions during the imbibition decrease the brittleness values. Among the three soaking durations, the minimum brittleness values occur on samples with 20 days' imbibition in subcritical and supercritical CO 2 + NaCl solutions and the reductions of which are 2.08% and 2.49%, respectively. Subcritical/supercritical CO 2 + NaCl imbibition has higher effect on shale's strength and Young's modulus than on the brittleness. The low-clay shale still keeps good fracture performance after imbibition.

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Section: Statistical Damage Constitutive Models Of Rocks Undermentioning

confidence: 99%

A Damage Constitutive Model for the Effects of CO₂-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

et al. 2018

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“…Thus, a damage statistical constitutive model for rock can be set up. Till now, much progress in the study of damage statistical constitutive models has been made [16,17]. The establishment of a rock damage statistical constitutive model is mainly based on the following two aspects: (1) choose strength criteria for the rock mesoscopic element, for instance, the maximum principle strain criterion, Mohr-Coulomb criterion and Drucker-Prager criterion; and (2) determine the distribution law of the rock mesoscopic element strength, for example power function distribution and Weibull distribution.…”

Section: A Damage Constitutive Model For Rock With Mesoscopic Flawsmentioning

confidence: 99%

“…But for convenience in engineering analysis, it is necessary to classify these two kinds of damages and then calculate their coupling effect [15]. Now the existing study on rock mesoscopic damage mechanics is often based on the statistical damage constitutive model [16,17], which is well developed. However, the study on rock mass damage constitutive model is comparatively not enough, because the most existing studies mainly adopt the damage tensor to describe the anisotropic damage in the rock mass caused by the joints [10,11], in which only the joint geometrical property such as its length and dip angle is considered, while its mechanical property such as the shear strength is not.…”

Section: Introductionmentioning

confidence: 99%

A Damage Constitutive Model for Rock Mass with Nonpersistently Closed Joints Under Uniaxial Compression

Liu

Zhang

2015

Arab J Sci Eng

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As part of the rock mass, both the macroscopic flaws such as joints and the mesoscopic flaws such as microcracks affect the strength and the deformational behavior of rock mass. Existing models can either handle any one of them alone, and a model which can consider the co-effect of these two kinds of flaws on rock mass mechanical behavior is not yet available. This study focusses on rock mass with nonpersistently closed joints and establishes a new damage constitutive model for it. Firstly, the damage model for the intact rock which contains only the mesoscopic flaws is introduced. Second, the expression of the macroscopic damage variable (tensor) which can consider the joint geometrical and mechanical properties at the same time is obtained based on the energy principle and fracture theory. Third, the damage variable based on coupling the macroscopic and mesoscopic flaws is deduced based on Lemaitre strain equivalence hypothesis, and then the corresponding damage constitutive model for rock mass with nonpersistently closed joints under uniaxial compression is set up. Finally, the test data for the intact rock under uniaxial compression are adopted to validate the proposed model. A series of calculation examples verify that the proposed model is capable of presenting the

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“…Symbolizing the state variable of the extent of rock failure, a damage variable can be defined by statistical theory as follows (Wang et al, 2007;Cao et al, 2008):…”

Section: Damage Variablementioning

confidence: 99%

Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements

Lyu

Zhang

et al. 2015

J. Zhejiang Univ. Sci. A

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It is difficult to establish a constitutive model of damage for rock materials due to the complex meso-mechanism of the rock deterioration process. In this paper, by analysis of the damage mechanism, the reason for the existence of a rock damage threshold is explained and we conclude that damaged rock elements of micro scale can still bear stress. The correlation between damaged and undamaged elements is examined in relation to stress distribution. Rocks under different initial conditions can be defined as undamaged materials with different properties, to avoid the issue of the solution of the undamaged condition and to simplify the damage model. On the basis of the Mohr-Coulomb criterion and theories of continuum damage and statistical mechanics, a constitutive model of rock materials affected by the load-bearing capacity of damaged elements under triaxial compression is established. Compared with previous experimental data and theoretical results, we show that this model can reflect the stress-strain relationship of the whole process of rock failure. In particular, the description of the strain softening stage after peak strength is proved to be more reasonable. Programming of the constitutive model applied to stability analysis of the Qingdao subway station is achieved by secondary development of FLAC 3D. The computing results compare very well with field monitoring data, indicating that the constitutive model of damaged rock can reflect the deterioration effect of weathered rock at the site. This constitutive model of rock damage may provide a useful reference for practical application.

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A damage-softening statistical constitutive model considering rock residual strength

Cited by 209 publications

References 11 publications

A Damage Constitutive Model for the Effects of CO₂-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

A Damage Constitutive Model for the Effects of CO₂-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

A Damage Constitutive Model for Rock Mass with Nonpersistently Closed Joints Under Uniaxial Compression

Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements

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A damage-softening statistical constitutive model considering rock residual strength

Cited by 209 publications

References 11 publications

A Damage Constitutive Model for the Effects of CO2-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

A Damage Constitutive Model for the Effects of CO2-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

A Damage Constitutive Model for Rock Mass with Nonpersistently Closed Joints Under Uniaxial Compression

Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements

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A Damage Constitutive Model for the Effects of CO₂-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

A Damage Constitutive Model for the Effects of CO₂-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale