scholarly journals An Extension Failure Criterion for Brittle Rock

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Aizhong Lu ◽  
Ning Zhang ◽  
Guisen Zeng
Keyword(s):  
Principal Stress ◽  
Poisson’S Ratio ◽  
Compressive Strain ◽  
Strength Criterion ◽  
Maximum Principal Stress ◽  
Intermediate Principal Stress ◽  
Brittle Rock ◽  
Poisson's Ratio ◽  
Triaxial Tests ◽  
True Triaxial

Under the triaxial compressive state, the compressive strain is supposed to happen in the direction of the maximum principal stress, but tensile strain happens in the direction of the minimum principal stress. Moreover, as the intermediate principal stress is not too high, the corresponding strain can also be tensile. If the brittle rock is assumed as linear elastic in the prefailure stage, a new strength criterion based on the sum of the two tensile strains was presented. The new criterion considers the differences in mechanical parameters (i.e., elastic modulus and Poisson’s ratio) under tension and compression. The parameters of the criterion only include Poisson’s ratio and uniaxial strength. And the effect of the intermediate principal stress σ 2 can be reflected. Certain featured failure phenomenon of rock material can be explained well by the proposed criterion. The results of conventional and true triaxial tests can verify the criterion well. Finally, the criterion is compared with the Mohr–Coulomb and Drucker–Prager criteria.

scholarly journals Three dimensional statistical damage constitutive model of rock based on Griffith strength criterion

2021 ◽  
Author(s):  
Song Chen ◽  
Xiuling Cao ◽  
Zhao Yang
Keyword(s):  
Constitutive Model ◽  
Principal Stress ◽  
Damage Mechanics ◽  
Brittle Materials ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
True Triaxial ◽  
Damage Constitutive Model ◽  
Two Parameters ◽  
The Relationship

Abstract According to the damage mechanics theory and Lemaitre strain equivalence theory, because most rock materials are brittle materials, Griffith strength criterion has good applicability to describe the fracture failure of brittle materials from the perspective of energy. Using a new method to describe the rock micro-element strength based on Griffith strength criterion, and assuming the micro-element strength obeys the Weibull distribution, a true triaxial constitutive model of damage softening reflecting the whole process of rock failure is established. On this basis, the influence of the two parameters in the model on the curve of the constitutive model is analyzed, and the relationship between the two parameters and the intermediate principal stress in the model is established, and the model is revised reasonably. Finally, a true triaxial damage constitutive model of rock is established. The results are in good agreement with the experimental curve, which verifies its validity and rationality. At the same time, the relationship between the damage evolution and the strain and stress is discussed, and the influence of the size of the intermediate principal stress on the relationship is analyzed in detail.

scholarly journals Development of a polyaxial platen for testing true triaxial behavior of rocks

2021 ◽  
Author(s):  
Prasoon Garg ◽  
Bhardwaj Pandit ◽  
Brijes Mishra ◽  
G.L. Sivakumar Babu
Keyword(s):  
Stress State ◽  
Principal Stress ◽  
Axial Stress ◽  
Intermediate Principal Stress ◽  
Intact Rock ◽  
Triaxial Stress ◽  
Triaxial Tests ◽  
True Triaxial ◽  
True Triaxial Tests

Mining at greater depths can lead to stress-induced failure, especially in areas of high horizontal in-situ stress. The induced stresses around the opening are known to be in a poly-axial stress state where, σ_1≠ σ_2≠ σ_3 with special case of σ_3= 0 and σ_1, σ_2 ≠ 0 at its boundary. The conventional triaxial testing does not represent the actual in-situ strength of the rock in regions of high horizontal stress, as it ignores the influence of intermediate principal stress (σ_2). The typical poly-axial testing (biaxial and true-triaxial tests) of intact rock mostly requires sophisticated and expensive loading systems. This study investigated the mechanical behavior of intact rock under a poly-axial stress state using a simple and cost-effective design. The apparatus consists of biaxial frame and a confining device. The biaxial frame has two platens that apply equal stress in both directions (σ_1=σ_2) on a 50.8 mm cubical specimen when placed inside the uniaxial loading device. The confining device performed separate biaxial tests under constant intermediate principal stress (σ_2 = constant) and true-triaxial tests when used along with the biaxial frame. This study then compared the failure modes and peak strength of Berea Sandstone specimens with other biaxial/triaxial devices to validate the design of the poly-axial apparatus. We also performed uniaxial tests on both standard cylindrical samples and prismatic specimen of different slenderness ratios. These tests provided a complete understanding of the failure mode transition from standard uniaxial compressive tests to triaxial stress conditions on cubical specimen. Additionally, this study determined best-fitted strength envelopes for biaxial and triaxial stress state. Based on regression analysis, we found a quadratic polynomial to be a good fit to biaxial strength envelope. For true-triaxial strength envelope, we found the 3D failure criterion by Nadai (1950) to be a good fit with R^2 of 0.964

scholarly journals The Behavior of a Coarse Granular Material under Complex Stress Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yuefeng Zhou ◽  
Jiajun Pan ◽  
Zhanlin Cheng ◽  
Yongzhen Zuo
Keyword(s):  
Granular Material ◽  
Principal Stress ◽  
Stress Ratio ◽  
Intermediate Principal Stress ◽  
Friction Reduction ◽  
Western China ◽  
Triaxial Tests ◽  
Confining Stress ◽  
True Triaxial ◽  
Prediction Approach

In recent years, dozens of high rockfill dams are under construction or planning for hydropower exploration in western China. In dam construction, the mechanical behavior of coarse granular material greatly affects the compatible deformation of dam body. In this article, an indirect in situ density prediction approach for coarse granular material is firstly proposed to solve the technical obstacle on prediction of the material density in thick overburden layer of a dam site in southwest China. Adopting a self-developed large-scale true triaxial apparatus with a special friction-reduction technique, four series of true triaxial tests were then performed to investigate the behavior of a coarse granular material with a maximum particle diameter of 60 mm. Test results show that the peak strength of the material increases together with the increasing confining stress and the increasing intermediate principal stress ratio. The material dilatancy is restricted by both the confining stress and the intermediate principal stress ratio. With the increase in intermediate principal stress ratio, the internal friction angle increases firstly and then decreases slightly, but the slope of stress path reduces gradually. The tested peak states were compared with several well-known strength criteria under the framework of generalized stress, showing a good fitness with the Lade–Duncan criterion and underestimation by the Mohr–Coulomb criterion and the Matsuoka–Nakai criterion. The strength envelope in the π plane shrinks with the increasing confining stress.

scholarly journals Bifurcation analysis of shear band in sand under true triaxial conditions with hypoplasticity

2021 ◽  
Author(s):  
Jun Liu ◽  
shun wang ◽  
Yang Wu ◽  
Wei Wu
Keyword(s):  
Shear Band ◽  
Principal Stress ◽  
Stress Ratio ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
True Triaxial ◽  
Acoustic Tensor ◽  
Strain Relationship ◽  
Bifurcation Behaviour ◽  
Hypoplastic Constitutive Model

Predicting the onset of shear band is of significance in understanding the failureof geomaterials. The prediction accuracy is dictated by the constitutive modelused for the description of the pre-bifurcation behaviour. In this study, we firstmodify a recently proposed hypoplastic constitutive model by incorporating ageneral strength criterion and a stiffness function. We proceed to consider theonset of shear band in sand under true triaxial conditions. We demonstrate thatour analyses capture the pre-bifurcation stress–strain relationship at differentvalues of intermediate principal stress and predict fairly well the onset ofshear band. The acoustic tensor criterion generally adopted in elastoplasticapproaches is inadequate for hypoplastic approaches. No special non-coaxialtreatment is required for the present approach to yield a reasonable variationtrend of bifurcation strain with intermediate principal stress ratio 𝑏.

Anisotropic Behavior of Geomaterial under Three-Dimensional Stress States

2010 ◽  
Vol 160-162 ◽  
pp. 1425-1431
Author(s):  
Kun Yong Zhang ◽  
Yan Gang Zhang ◽  
Chi Wang
Keyword(s):  
Stress State ◽  
Principal Stress ◽  
Three Dimensional ◽  
Complex Stress State ◽  
Triaxial Tests ◽  
Induced Anisotropy ◽  
Principal Stresses ◽  
True Triaxial ◽  
Stress Effects ◽  
Stress Induced Anisotropy

Most soil constitutive models were developed based on the traditional triaxial tests with isotropic assumption, in which the load is applied as the major principal stress direction and the other two principal stresses are symmetric. When such isotropic models are applied to practical analysis, stress induced anisotropy under complex stress state and the middle principal stress effects are often neglected, thus there are many disagreements between the calculated results and the infield testing data. To simulate the practical loading process, true triaxial tests were carried out on geomaterial under three-dimensional stress state. It was found that the stress induced anisotropy effects are remarkable and the middle principal stress effects are obvious because of the initial three-dimensional stress state. Such kind of stress-induced anisotropy could have important impact on the numerical analysis results and should be taken into consideration when developing the constitutive model.

scholarly journals Rational modelling of elastic soil behaviour in 3D condition

2019 ◽  
Vol 92 ◽  
pp. 15003
Author(s):  
Teruo Nakai ◽  
Hossain Md. Shahin ◽  
Akira Ishikawa
Keyword(s):  
Principal Stress ◽  
Linear Relation ◽  
Poisson’S Ratio ◽  
Elastic Strain ◽  
Volumetric Strain ◽  
Poisson's Ratio ◽  
Elastic Component ◽  
Principal Stresses ◽  
Strain Relation ◽  
Proposed Model

A simple and rigorous formulation of elastic component of elastoplastic model for geomaterials is presented. Although linear relation between elastic volumetric strain and mean principal stress in log scale is assumed in most of the usual models, linear relation between each principal stress and the corresponding principal elastic strain in log scale is assumed. Incorporating Poisson's ratio, three principal stresses vs. three elastic principal strain relation is obtained. Also, assuming coaxially between stresses and elastic strains, this relation can be transformed to stress- elastic strain relation in general coordinate. The material parameters of the proposed model of the elastic component are the same as those of the usual models, i.e., swelling index κ and Poisson's ratio ν. This proposed model can describe typical unloading behaviour of various shear tests and constant stress ratio unloading tests reported before.

scholarly journals Three-Dimensional Numerical Analysis of the Tunnel for Polyaxial State of Stress

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Wenge Qiu ◽  
Chao Kong ◽  
Kai Liu
Keyword(s):  
Numerical Simulation ◽  
Mechanical Behavior ◽  
Principal Stress ◽  
Failure Criterion ◽  
Rock Strength ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
State Of Stress ◽  
Coulomb Failure ◽  
Coulomb Failure Criterion

The aim of this study is to have a comprehensive understanding of the mechanical behavior of rock masses around excavation under different value of intermediate principal stress. Numerical simulation was performed to investigate the influence of intermediate principal stress using a new polyaxial strength criterion which takes polyaxial state of stress into account. In order to equivalently substitute polyaxial failure criterion with Mohr-Coulomb failure criterion, a mathematical relationship was established between these two failure criteria. The influence of intermediate principal stress had been analyzed when Mohr-Coulomb strength criterion and polyaxial strength criterion were applied in the numerical simulation, respectively. Results indicate that intermediate principal stress has great influence on the mechanical behavior of rock masses; rock strength enhanced by intermediate principal stress is significant based on polyaxial strength criterion; the results of numerical simulation under Mohr-Coulomb failure criterion show that it does not exert a significant influence on rock strength. Results also indicate that when intermediate principal stress is relatively small, polyaxial strength criterion is not applicable.

The Changing Rule of Rock Strength under True Triaxial Condition

2014 ◽  
Vol 522-524 ◽  
pp. 1410-1413
Author(s):  
Ze Kang Wen ◽  
Ke Min Wei ◽  
Jia Quan Hu ◽  
You Ling Fang
Keyword(s):  
Principal Stress ◽  
Rock Strength ◽  
Quadratic Function ◽  
Intermediate Principal Stress ◽  
Stress Effect ◽  
True Triaxial Test ◽  
True Triaxial ◽  
Minimum Principal Stress ◽  
Stress Coefficient ◽  
Intermediate Principal Stress Effect

The intermediate principal stress effect of the rock has been demonstrated. By analyzing true triaxial test results of Dunham dolomite and Mizuho trachyte, we studied relationship between minimum principal stress and the rock strength under the same intermediate principal stress coefficient, and the relationship between intermediate principal stress and the rock strength under the same minimum principal stress condition. Research shows that the minimum principal stress has a linear relation with the rock strength, the intermediate principal stress coefficient of a quadratic function relation with the rock strength. And the mathematic expression of the intermediate principal stress effect function was calculated.

scholarly journals The suction,yield and strength characteristics of unsaturated intact loess based on true tri-axial tests

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Jinjin Fang
Keyword(s):  
Principal Stress ◽  
Stress Ratio ◽  
Shear Failure ◽  
Confining Pressure ◽  
Intermediate Principal Stress ◽  
True Triaxial ◽  
Yield Stress Increase ◽  
Isotropic Consolidation ◽  
The Relationship ◽  
Intact Loess

To simulate the failure of loess under undrained condition in the actual engineering,a series of isotropic consolidation and shear tests with different intermediate principal stress ratio b under constant water content were performed on intact loess with various initial suctions using the true tri-axial apparatus for unsaturated soil. The relationship between the saturations and initial suctions,the characteristics of yield,suction and strength of unsaturated intact loess were studied. The results show that the initial suctions and the suctions after the isotropic consolidation decrease with the increase of saturations. The suctions increase with the increase of the intermediate principal stress ratio b at the true triaxial shear failure. The net mean yield stress increase with the increase of the initial suction. The yield suction is a constant,but not always equal to the maximum suction that the soil specimen experienced in the history. The strength of soil increase with the increase of the net confining pressure,initial suction and the intermediate principal stress ratio b.

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