A New Rock Strength Criterion from Microcracking Mechanisms Which Provides Theoretical Evidence of Hybrid Failure

Based on the assumption that rock strength follows the log normal distribution statistically, this paper establishes a damage constitutive model of rock under uniaxial stress conditions in combination with the Mohr–Coulomb strength criterion and damage mechanical theory. Experiments were carried out to investigate the damage evolution process of rock material, which can be categorized into nondamaging, accelerated growth, constant-speed, similar growth, and speed-reducing growth stages. The evolution process had a good corresponding relationship with the rock stress-strain curves. Based on the statistical damage constitutive model proposed in this paper, a numerical fitting analysis was conducted on the uniaxial compression testing data of laboratory sand rock and on experimental data from other literature, in order to validate the rationality of the constitutive equation and the determination of its parameters and to analyze the effect of internal friction variables on damage variables and compression strength. The research outcomes presented in this paper can provide useful reference for the theory of rock mechanics and for rock engineering.

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

Mathematical Problems in Engineering ◽

10.1155/2015/301241 ◽

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.

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Unification of Hoek-Brown Criterion on the Basis of United Strength Theory

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.501-504.415 ◽

2014 ◽

Vol 501-504 ◽

pp. 415-418

Author(s):

Yuan Li ◽

Qi Liang Liu ◽

Qing Chi Cai

Keyword(s):

Rock Mass ◽

Rock Strength ◽

Hard Rock ◽

Strength Criterion ◽

Strength Reduction ◽

Strength Theory ◽

Unified Strength Theory ◽

Rock Mass Strength ◽

Decomposition Formula ◽

Theory Formula

Based on twin failure mechanism of fracture and shear , the bilinear transitional strength decomposition formula reflecting the nonlinear strength of rock material is proposed,.The decomposed brittle shear formula is integrated and finally the unified strength theory formula characterized by nonlinearity of Hoek-Brown criterion is established. It makes the unified strength theory characterized by nonlinearity of empirical strength criterion, rock mass strength reduction, etc. Besides, it contributes to promote the accuracy and applicability of unified strength theory in rock strength and rock mass strength,especially for the hard rock failure analysis.

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Failure Probability Model considering the Effect of Intermediate Principal Stress on Rock Strength

Mathematical Problems in Engineering ◽

10.1155/2015/960973 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 4

Author(s):

Yonglai Zheng ◽

Shuxin Deng

Keyword(s):

Principal Stress ◽

Failure Probability ◽

Rock Strength ◽

Probability Model ◽

Strength Criterion ◽

Intermediate Principal Stress ◽

Stress Effect ◽

New Model ◽

Uniformity Coefficient ◽

Intermediate Principal Stress Effect

A failure probability model is developed to describe the effect of the intermediate principal stress on rock strength. Each shear plane in rock samples is considered as a micro-unit. The strengths of these micro-units are assumed to match Weibull distribution. The macro strength of rock sample is a synthetic consideration of all directions’ probabilities. New model reproduces the typical phenomenon of intermediate principal stress effect that occurs in some true triaxial experiments. Based on the new model, a strength criterion is proposed and it can be regarded as a modified Mohr-Coulomb criterion with a uniformity coefficient. New strength criterion can quantitatively reflect the intermediate principal stress effect on rock strength and matches previously published experimental results better than common strength criteria.

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Solvent-Ligand Interactions in Colloidal Nanocrystals

10.26434/chemrxiv.6447884 ◽

2018 ◽

Author(s):

Jonathan De Roo ◽

Nuri Yazdani ◽

Emile Drijvers ◽

Alessandro Lauria ◽

Jorick Maes ◽

...

Keyword(s):

Direct Method ◽

Line Broadening ◽

H Nmr ◽

Size Dependent ◽

Line Shape Analysis ◽

Wide Range ◽

Nanocrystal Synthesis ◽

Ligand Interactions ◽

Indispensable Tool ◽

Theoretical Evidence

<p>Although solvent-ligand interactions play a major role in nanocrystal synthesis, dispersion formulation and assembly, there is currently no direct method to study this. Here we examine the broadening of <sup>1</sup>H NMR resonances associated with bound ligands, and turn this poorly understood descriptor into a tool to assess solvent-ligand interactions. We show that the line broadening has both a homogeneous and a heterogeneous component. The former is nanocrystal-size dependent and the latter results from solvent-ligand interactions. Our model is supported by experimental and theoretical evidence that correlates broad NMR lines with poor ligand solvation. This correlation is found across a wide range of solvents, extending from water to hexane, for both hydrophobic and hydrophilic ligand types, and for a multitude of oxide, sulfide and selenide nanocrystals. Our findings thus put forward NMR line shape analysis as an indispensable tool to form, investigate and manipulate nanocolloids.</p>

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In-Situ Stresses, Rock Strength, Fluid Pressure, And Implications For Wellbore Stability And Oil And Gas Development In The Seboro and Tiaka Fields, Sulawesi, Indonesia

10.29118/ipa.0.12.e.073 ◽

2018 ◽

Author(s):

William Power

Keyword(s):

Oil And Gas ◽

Rock Strength ◽

Fluid Pressure ◽

Wellbore Stability ◽

Oil And Gas Development ◽

In Situ Stresses

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STRUCTURAL RELIABILITY ANALYSIS BASED ON P-BOXES

Building and reconstruction ◽

10.33979/2073-7416-2020-92-6-51-58 ◽

2020 ◽

Vol 92 (6) ◽

pp. 51-58

Author(s):

S.A. SOLOVYEV ◽

Keyword(s):

Probability Distribution ◽

Reliability Analysis ◽

Structural Reliability ◽

Epistemic Uncertainty ◽

Random Variable ◽

Strength Criterion ◽

Structural Elements ◽

Structural Element ◽

Limit States ◽

Distribution Shape

The article describes a method for reliability (probability of non-failure) analysis of structural elements based on p-boxes. An algorithm for constructing two p-blocks is shown. First p-box is used in the absence of information about the probability distribution shape of a random variable. Second p-box is used for a certain probability distribution function but with inaccurate (interval) function parameters. The algorithm for reliability analysis is presented on a numerical example of the reliability analysis for a flexural wooden beam by wood strength criterion. The result of the reliability analysis is an interval of the non-failure probability boundaries. Recommendations are given for narrowing the reliability boundaries which can reduce epistemic uncertainty. On the basis of the proposed approach, particular methods for reliability analysis for any structural elements can be developed. Design equations are given for a comprehensive assessment of the structural element reliability as a system taking into account all the criteria of limit states.

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