Statistical damage model with strain softening and hardening for rocks under the influence of voids and volume changes

2010 ◽  
Vol 47 (8) ◽  
pp. 857-871 ◽  
Author(s):  
Wen-Gui Cao ◽  
Heng Zhao ◽  
Xiang Li ◽  
Yong-Jie Zhang
Keyword(s):  
Constitutive Model ◽  
Strain Softening ◽  
Triaxial Compression ◽  
Damage Model ◽  
Damage Threshold ◽  
Model Parameters ◽  
Volume Changes ◽  
Conventional Triaxial Compression ◽  
Damage Constitutive Model ◽  
Statistical Damage

With regards to the composition of natural rocks including voids or pores, deformation behavior is strongly affected by variation in porosity. By using a statistical damage-based approach, the characteristics of strain softening and hardening under the influence of voids and volume changes are investigated in the present paper. Suppose that a rock consists of three parts: voids, a damaged part, and an undamaged part. The effects of voids and volume changes on rock behavior are first analyzed through determination of the porosity and an associated damage model is then developed. Later, a statistical evolution equation describing the influence of the damage threshold on the propagation condition of rock damage is formulated based on measurement of the mesoscopic element strength. A statistical damage constitutive model reflecting strain softening and hardening behavior for rocks loaded in conventional triaxial compression is further developed and a corresponding method for determining the model parameters is also provided. Theoretical results of this proposed model are then compared with those observed experimentally. Finally, several aspects of the present constitutive model, which affect the relevant behavior of rocks, are particularly discussed.

A Statistical Damage Constitutive Model for Brittle Rocks Based on the Lade-Duncan Failure Criterion

2014 ◽  
Vol 919-921 ◽  
pp. 632-636 ◽  
Author(s):  
Zhen Yuan Tian ◽  
Wei Wang ◽  
Xue Hao Li ◽  
Wei Ya Xu
Keyword(s):  
Constitutive Model ◽  
Failure Criterion ◽  
Elastic Characteristic ◽  
Damage Threshold ◽  
Model Parameters ◽  
Brittle Rocks ◽  
Good Accord ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

Micro-unit strength of rock is randomly distributed based on Lemaitres strain equivalence assumptions. The paper presents a method for measuring micro-unit strength taking into account the damage threshold. Assuming that the micro-unit strength obeys the Weibull distribution, combined with the Lade-Duncan failure criterion, a new statistical damage constitutive model for brittle rocks is established and the model parameters m and F0 are determined. The model can simulate the stress-strain relation of full process of rock failure well, especially reflects the influence of different stress on damage threshold and the linear elastic characteristic under low stress for rock. The good accord verifies the validity and feasibility of the new model.

Statistical Damage Constitutive Model for Concrete under Biaxial Tension

2013 ◽  
Vol 438-439 ◽  
pp. 183-186
Author(s):  
Wei Feng Bai ◽  
Jun Hong Zhang ◽  
Jun Feng Guan ◽  
Ying Cui
Keyword(s):  
Constitutive Model ◽  
Biaxial Tension ◽  
Damage Model ◽  
Damage Mechanism ◽  
Deformation Properties ◽  
Damage Constitutive Model ◽  
Strength And Deformation ◽  
Statistical Damage Constitutive Model ◽  
Damage Theory ◽  
Statistical Damage

Based on the statistical damage theory and the experimental phenomena, the statistical damage constitutive model for concrete under biaxial tension is proposed. The two meso-scale damage modes, rupture and yield are considered, and the whole damage evolution process is driven by the principal tensile damage strain. The results show that the proposed statistical damage model can accurately predict the constitutive behavior in the uniform damage phase for concrete under biaxial tension. The damage mechanism is discussed in the view point of biaxial strength and deformation properties.

scholarly journals Statistical Damage Constitutive Model for Cemented Sand considering the Residual Strength and Initial Compaction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Cai Tan ◽  
Ming-dao Yuan ◽  
Yong-sheng Shi ◽  
Bing-sheng Zhou ◽  
Hao Li
Keyword(s):  
Constitutive Model ◽  
Residual Strength ◽  
Damage Mechanics ◽  
Triaxial Compression ◽  
Triaxial Stress ◽  
Cemented Sand ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Initial Compaction ◽  
Statistical Damage

Based on continuum damage mechanics and the assumption of volume invariance, a damage constitutive model of cemented sand under triaxial stress was established while considering residual strength. Statistical theory was then introduced into this model. Assuming that the microunit strength of cemented sand obeys a Weibull random distribution, an expression of microunit strength based on the Mohr–Coulomb criterion was derived. Additionally, a damage evolution equation and a statistical damage constitutive model of cemented sand under triaxial stress were established. In order to consider the nonlinear deformation and volume change in the initial pore compaction stage, the critical point reflecting the completion of the initial compaction stage was determined. This was done by applying the volume invariance assumption to the linear portion of the stress and strain curve and performing a coordinate transformation. The nonlinearity of the initial compaction stage was fitted by a quadratic function. A triaxial compression test of cemented sand was then carried out to verify this proposed method. The results show that the calculated values by the damage constitutive model fit well with the actual experimental values and that the calculated results can reflect the stress softening, residual strength, and initial compaction characteristics of cemented sand, which shows the rationality and feasibility of the model.

Study on Statistical Damage Softening Constitutive Model and Determination of Parameters for Rock Based on Lognormal Distribution

2011 ◽  
Vol 69 ◽  
pp. 33-38
Author(s):  
Jian Hua Wen ◽  
Cui Ying Zhou ◽  
Li Huang ◽  
Ye Cheng ◽  
Lin Chong Huang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Lognormal Distribution ◽  
Strain Softening ◽  
Model Parameters ◽  
Kolmogorov Smirnov ◽  
Random Distributions ◽  
Determination Of Parameters ◽  
Smirnov Test ◽  
Statistical Damage

Based on the property that micro-cells strength is consistent with lognormal distribution function, this paper presented a new statistical damage softening constitutive model simulating the full process of strain softening for rock. Through discussing the characteristics of random distributions for rock micro-cells strength, lognormal distribution assumption is tested by Kolmogorov-Smirnov test in statistics, and the reasonable method of geometry boundary condition is selected to determine model parameters that can be easily applied to the situations under different complex conditions. Gabbro experiment comparative analyses show that the new damage softening constitutive model is rational and convenient in engineering.

scholarly journals Study of Damage Constitutive Model of Brittle Rocks considering Stress Dropping Characteristics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fei Li ◽  
Shuang You ◽  
Hongguang Ji ◽  
Hao Wang
Keyword(s):  
Constitutive Model ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Brittle Rock ◽  
Model Parameters ◽  
Deformation And Failure ◽  
Brittle Rocks ◽  
Whole Process ◽  
Confining Pressures ◽  
Damage Constitutive Model

Deep brittle rock exhibits characteristics of rapid stress dropping rate and large stress dropping degree after peak failure. To simulate the whole process of deformation and failure of the deep brittle rock under load, the Lemaitre strain equivalent theory is modified to make the damaged part of the rock has residual stress. Based on the damage constitutive model considering residual strength characteristics, a correction factor reflecting stress dropping rate is added, the Weibull distribution is used to describe the inhomogeneity of rock materials, and Drucker–Prager criterion is used to quantitatively describe the influence of stress on damage; a damage constitutive model of deep brittle rock considering stress dropping characteristics is established. According to the geometric features of the rock stress-strain curve, the theoretical expressions of model parameters are derived. To verify the rationality of the model, triaxial compression experiments of deep brittle rock under different confining pressures are conducted. And the influence of model parameters on rock mechanical behaviour is analysed. The results show that the model reflects the stress dropping characteristics of deep brittle rock and the theoretical curve is in good agreement with the experimental results, which indicates that the proposed constitutive model is scientific and feasible.

scholarly journals Study on Damage Constitutive Model of High-Concentration Cemented Backfill in Coal Mine

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Baogui Yang ◽  
Haigang Yang
Keyword(s):  
Constitutive Model ◽  
Coal Mine ◽  
Damage Evolution ◽  
Triaxial Compression ◽  
Failure Process ◽  
Model Parameters ◽  
High Concentration ◽  
Deformation And Failure ◽  
Cemented Backfill ◽  
Damage Constitutive Model

In order to construct the damage constitutive model (DCM) of high-concentration cemented backfill (HCCB) in coal mine, the generalized Hoek-Brown strength criterion was used as the failure criterion. For the difference of theoretical derivation of constitutive relation, a new DCM based on residual strength was proposed. Combined with the conventional triaxial compression test, the correctness and rationality of the DCM were verified. The damage evolution characteristics of HCCB were analyzed, and the physical meaning of model parameters was clarified. The results show that (a) the theoretical curves of stress-strain relation are in good agreement with its experimental curves, which means DCM can simulate the deformation and failure process of HCCB. (b) The damage evolution curve of HCCB is S -shaped. To some extent, the confining pressure can inhibit the development of damage. (c) The parameter F 0 reflects the position of the peak point of the DCM, and parameter n is the slope of the straight line segment in the postpeak strain softening stage, which are, respectively, used to characterize the strength level and brittleness of HCCB. The establishment of DCM of HCCB is helpful to reveal its deformation and failure mechanism and provides theoretical basis for its strength design.

scholarly journals A Creep Damage Constitutive Model for a Rock Mass with Nonpersistent Joints under Uniaxial Compression

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shuran Lv ◽  
Wanqing Wang ◽  
Hongyan Liu
Keyword(s):  
Rock Mass ◽  
Constitutive Model ◽  
Mechanical Behavior ◽  
Uniaxial Compression ◽  
Damage Model ◽  
Creep Damage ◽  
Model Parameters ◽  
Damage Constitutive Model ◽  
Set Up ◽  
Creep Damage Model

As part of the rock mass, both the mesoscopic and macroscopic flaws will affect the creep mechanical behavior of the rock mass with nonpersistent joints. This study focuses on this kind of rock mass and establishes a creep damage model to account for the effect of the joint on its creep mechanical behavior. First, on basis of analyzing the rock element creep mechanism and the typical creep deformation curve, a new creep damage constitutive model for the rock element is set up by introducing the damage theory and Kachanov damage evolution law into the classic creep constitutive model such as J body model. Second, the determination method of the proposed model parameters is studied in detail. Third, the calculation method of the macroscopic damage caused by the joint proposed by others is introduced which can consider the joint geometry, strength, and deformation parameters at the same time. Finally, the creep damage model for the rock mass with nonpersistent joints under uniaxial compression is proposed. The calculation examples indicate that it can present the effect of the joint on the rock mass creep mechanical behavior.

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