Two-Parameter Parabolic Mohr Strength Criterion and Its Damage Regularity

2006 ◽  
Vol 306-308 ◽  
pp. 327-332 ◽  
Author(s):  
Chun Guang Li ◽  
Xiu Run Ge ◽  
Hong Zheng ◽  
Shui Lin Wang
Keyword(s):  
Uniaxial Tension ◽  
Principal Stress ◽  
Uniaxial Compression ◽  
Strength Criterion ◽  
Friction Angle ◽  
Tensile Failure ◽  
Compression Tests ◽  
Uniaxial Compression Strength ◽  
Griffith Criterion ◽  
Two Parameter

A series of formulas about two-parameter parabolic Mohr strength criterion(2-PP Mohr criterion) are derived. Based on the results of uniaxial tension and uniaxial compression tests, the parameters involved in the criterion can be easily determined, then the criterion in terms of the major principal stress and the minor principal stress is derived, and the damage pattern is also discussed. At last, the formulas about the rupture angle and the friction angle are presented, and their relationship is also given. 2-PP Mohr criterion can describe not only shear but also tensile failure. In this criterion the ratio of the uniaxial compression strength and the uniaxial tension strength is not confined as in Griffith criterion. The formula about the rupture angle provides steady theoretical foundation for determining the direction of crack faces and damage patterns in the computation of macro crack propagation. In fact, Griffith criterion is only a special case of the two-parameter parabolic Mohr strength criterion proposed in this present paper.

scholarly journals The Effect of Bedding Structure on Mechanical Property of Coal

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zetian Zhang ◽  
Ru Zhang ◽  
Guo Li ◽  
Hegui Li ◽  
Jianfeng Liu
Keyword(s):  
Mechanical Property ◽  
Uniaxial Compression ◽  
Peak Stress ◽  
Natural Fracture ◽  
Test Results ◽  
Compression Tests ◽  
Average Amount ◽  
Uniaxial Compression Strength ◽  
Bedding Planes ◽  
Close Relationship

The mechanical property of coal, influencing mining activity considerably, is significantly determined by the natural fracture distributed within coal mass. In order to study the effecting mechanism of bedding structure on mechanical property of coal, a series of uniaxial compression tests and mesoscopic tests have been conducted. The experimental results show that the distribution characteristic of calcite particles, which significantly influences the growth of cracks and the macroscopic mechanical properties of coal, is obviously affected by the bedding structure. Specifically, the uniaxial compression strength of coal sample is mainly controlled by bedding structure, and the average peak stress of specimens with axes perpendicular to the bedding planes is 20.00 MPa, which is 2.88 times the average amount of parallel ones. The test results also show a close relationship between the bedding structure and the whole deformation process under uniaxial loading.

EXPERIMENTAL AND THEORETICAL STUDY ON FREEZE-THAWING DAMAGE PROPAGATION OF SATURATED ROCKS

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1853-1858 ◽  
Author(s):  
QUANSHENG LIU ◽  
GUANGMIAO XU ◽  
XIAOYAN LIU
Keyword(s):  
Uniaxial Compression ◽  
Influence Factors ◽  
Compression Tests ◽  
Freezing And Thawing ◽  
Uniaxial Compression Strength ◽  
Red Sandstone ◽  
Damage Propagation ◽  
Freeze Thaw ◽  
Thaw Cycle ◽  
Damage Process

The freezing and thawing cycles tests were conducted on red sandstone and shale. In this paper, freezing-thawing damage propagation processes are analyzed, and two deterioration modes, i.e. scaling mode for red sandstone and fracturing mode for shale, are suggested. The uniaxial compression tests are also conducted on the two types of rock subjected to different freeze-thaw cycles at room temperature. It is shown that the uniaxial compression strength and the elastic modulus of rocks at low-temperature depended on the number of freeze-thaw cycles. The mechanism and influence factors of rock deterioration due to freeze-thaw are analyzed, and the damage process of rock should be divided into two coupled parts: rocks damage due to freeze-thaw cycle as well as the damage propagation caused by stress erosion. The damage evolvement equations for the two rocks are established, and the constitutive equations for the two types of rock subjected to freeze-thaw are deduced, accordingly. It is approved that the constitutive model considering the freeze-thaw damage is credible and can be used for the following theory analysis.

scholarly journals Mechanical Characteristics and Failure Mechanism of Siltstone with Different Joint Thickness

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Huigui Li ◽  
Zhengkai Yang ◽  
Huamin Li
Keyword(s):  
Elastic Modulus ◽  
Failure Mechanism ◽  
Uniaxial Compression ◽  
Compression Strength ◽  
Damage Model ◽  
Strain Curve ◽  
Compression Tests ◽  
Uniaxial Compression Strength ◽  
Stress Strain ◽  
Joint Thickness

The mechanics of rock mass is significantly affected by joints, but many existing studies of jointed rocks make simplifications that do not consider the joint thickness. To further study the influence of joint thickness on rock mechanics (mechanical properties, failure mechanism, damage model, etc.), we fabricated jointed siltstone specimens with different joint thickness (5, 10, 15, and 20 mm) and the specimens were subjected to uniaxial compression tests. The effects of joint thickness on the uniaxial compression strength (UCS), the strain at UCS, the elastic modulus, and the stress-strain curves were thus analyzed. For the stress-strain curve, with rising joint thickness, the upper concave in the initial compression stage intensified, the slope of the stress-strain in the elastic stage decreased, and the sudden stress drop after peak strength became more obvious. Both the peak compression strength and the elastic modulus gradually decreased with rising joint thickness, but a positive correlation was found between the strain at UCS and the joint thickness.

scholarly journals Experimental Study on the Anisotropic Characteristics and Engineering Application of Tight Sandstone

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yuanlong Wei ◽  
Wei Liu ◽  
Zhenkun Hou
Keyword(s):  
Uniaxial Compression ◽  
Inclination Angle ◽  
Shear Fracture ◽  
Triaxial Compression ◽  
Compression Tests ◽  
Gas Reservoirs ◽  
Tight Sandstone ◽  
Uniaxial Compression Strength ◽  
Xujiahe Formation ◽  
Inclination Angles

The anisotropy of tight sandstone (a type of unconventional gas reservoirs) is a significant factor influencing the characteristics of cracks network under hydrofracturing; thus, it also has a large influence on the final production capacity of the gas reservoirs. To improve the understanding of anisotropy degree and mechanical properties of the tight sandstone of Xujiahe Formation and thus to provide reliable reference for the establishment of hydrofracture model and parameter designing in fracture field, a series of experiments including ultrasonic wave velocity and uniaxial and triaxial compression tests of the tight sandstone samples obtained from Xujiahe Formation with different inclination angles (the angle between sample drilling direction and bedding plane) have been conducted. With the increase of inclination angle, the velocity of the longitudinal wave and elastic modulus both show the tendency of decreasing, whereas the compressive strength shows a “U” shape varying pattern, which is high on sides and low in the middle region. The values of uniaxial compression strength (UCS) are the lowest of sandstone with the inclination angles of 30° and 45°. The fracture patterns are dominant by splitting fracture under uniaxial compression tests. However, shear fracture and dilatancy morphology is the main pattern under triaxial compression test. But the local morphology of the failure surfaces behaves different if the inclination angle is changed. Combining the mechanic theory of transversely isotropic material, the anisotropy parameters of the tight sandstone are analyzed, as well as the influence on the hydrofracturing technology for tight sandstone in the field.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

scholarly journals Investigation of Microcrack Propagation and Energy Evolution in Brittle Rocks Based on the Voronoi Model

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2108
Author(s):  
Guanlin Liu ◽  
Youliang Chen ◽  
Xi Du ◽  
Peng Xiao ◽  
Shaoming Liao ◽  
...  
Keyword(s):  
Uniaxial Compression ◽  
Damage Evolution ◽  
Rock Sample ◽  
Rock Fracture ◽  
Damage Threshold ◽  
Crack Development ◽  
Energy Evolution ◽  
Shear Cracks ◽  
Compression Tests ◽  
Microcrack Propagation

The cracking of rock mass under compression is the main factor causing structural failure. Therefore, it is very crucial to establish a rock damage evolution model to investigate the crack development process and reveal the failure and instability mechanism of rock under load. In this study, four different strength types of rock samples from hard to weak were selected, and the Voronoi method was used to perform and analyze uniaxial compression tests and the fracture process. The change characteristics of the number, angle, and length of cracks in the process of rock failure and instability were obtained. Three laws of crack development, damage evolution, and energy evolution were analyzed. The main conclusions are as follows. (1) The rock’s initial damage is mainly caused by tensile cracks, and the rapid growth of shear cracks after exceeding the damage threshold indicates that the rock is about to be a failure. The development of micro-cracks is mainly concentrated on the diagonal of the rock sample and gradually expands to the middle along the two ends of the diagonal. (2) The identification point of failure precursor information in Acoustic Emission (AE) can effectively provide a safety warning for the development of rock fracture. (3) The uniaxial compression damage constitutive equation of the rock sample with the crack length as the parameter is established, which can better reflect the damage evolution characteristics of the rock sample. (4) Tensile crack requires low energy consumption and energy dispersion is not concentrated. The damage is not apparent. Shear cracks are concentrated and consume a large amount of energy, resulting in strong damage and making it easy to form macro-cracks.

scholarly journals Tensile Strength and Failure Types of Direct and Indirect Resin Composite Copings for Perio-Overdentures Luted Using Different Adhesive Cementation Modalities

Materials ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 3517
Author(s):  
Raffaele Cesca ◽  
Vera Colombo ◽  
Bruna Ernst ◽  
Luigi Maria Gallo ◽  
Mutlu Özcan
Keyword(s):  
Resin Composite ◽  
Periodontal Diseases ◽  
Tensile Load ◽  
Resin Cement ◽  
Tensile Failure ◽  
Human Teeth ◽  
Abutment Teeth ◽  
Adhesive Cementation ◽  
To Receive ◽  
Two Parameter

Perio-overdenture design helps to reduce periodontal diseases and secondary caries on abutment teeth. Composite copings can be cemented adhesively to the abutment teeth with different techniques. In this study, direct/indirect resin composite copings for perio-overdentures, luted using different adhesive cementation modalities were compared. Human teeth (N = 40) were prepared to receive spherical attachment copings and randomly divided into four groups: (1) resin-composite copings bonded directly (DC), (2) composite copings made indirectly, luted with dual-polymerized resin cement (ICV), (3) composite copings made indirectly, bonded with resin composite (ICT), (4) composite copings made indirectly, bonded with resin composite after the immediate dentin sealing method (IDS). Specimens were tested for tensile failure and one-way ANOVA (alpha = 0.05) was performed and the two-parameter Weibull modulus, scale (m) and shape (0) were calculated. Mean tensile load (N) was significantly higher for Group IDS (238 ± 81) than for the other groups (144 ± 53–184 ± 46) (p < 0.05). Group IDS (0.54 ± 0.25 mm) showed significantly higher deformation (mm) than other groups (0.2 ± 0.1–0.32 ± 0.15) (p < 0.05). Weibull distribution presented lower shape (0) for DC (3.33) compared to other groups (3.57–4.99). Cohesive coping failures were more frequent in Group IDS (60%) and mixed failures in other groups (40–60%). In conclusion, IDS copings could be preferred over other fabrication and adhesion modalities.

scholarly journals Strength Assessment of Broken Rock Postgrouting Reinforcement Based on Initial Broken Rock Quality and Grouting Quality

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Hongfa Xu ◽  
Hansheng Geng ◽  
Feng Chen ◽  
Xiao Chen ◽  
Liangliang Qi
Keyword(s):  
Rock Mass ◽  
Internal Friction ◽  
Growth Rates ◽  
Strength Criterion ◽  
Friction Angle ◽  
Uniaxial Tensile ◽  
Strength Assessment ◽  
Uniaxial Tensile Strength ◽  
Quantitative Calculation ◽  
Grouting Reinforcement

To estimate postgrouting rock mass strength growth is important for engineering design. In this paper, using self-developed indoor pressure-grouting devices, 19 groups of test cubic blocks were made of the different water cement ratio grouting into the broken rock of three kinds of particle sizes. The shear strength parameters of each group under different conditions were tested. Then this paper presents a quantitative calculation method for predicting the strength growth of grouted broken rock. Relational equations were developed to investigate the relationship between the growth rates of uniaxial compressive strength (UCS), absolute value of uniaxial tensile strength (AUTS), internal friction angle, and cohesion for post- to pregrouting broken rock based on Mohr-Coulomb strength criterion. From previous test data, the empirical equation between the growth rate of UCS and the ratio of the initial rock mass UCS to the grout concretion UCS has been determined. The equations of the growth rates of the internal friction coefficient and UCS for grouting broken rock with rock mass rating (RMR) and its increment have been established. The calculated results are consistent with the experimental results. These observations are important for engineered design of grouting reinforcement for broken rock mass.

scholarly journals Quantitative 3D imaging of partially saturated granular materials under uniaxial compression

2021 ◽  
Author(s):  
Marius Milatz ◽  
Nicole Hüsener ◽  
Edward Andò ◽  
Gioacchino Viggiani ◽  
Jürgen Grabe
Keyword(s):  
Granular Materials ◽  
Uniaxial Compression ◽  
Water Clusters ◽  
Local Strain ◽  
Confining Pressure ◽  
Mechanical Effect ◽  
Compression Tests ◽  
Initial Water ◽  
Interfacial Areas ◽  
Membrane Effects

AbstractGauging the mechanical effect of partial saturation in granular materials is experimentally challenging due to the very low suctions resulting from large pores. To this end, a uniaxial (zero radial stress) compression test may be preferable to a triaxial one where confining pressure and membrane effects may erase the contribution of this small suction; however, volume changes are challenging to measure. This work resolves this limitation by using X-ray imaging during in situ uniaxial compression tests on Hamburg Sand and glass beads at three different initial water contents, allowing a suction-dependent dilation to be brought to the light. The acquired tomography volumes also allow the development of air–water and solid–water interfacial areas, water clusters and local strain fields to be measured at the grain scale. These measurements are used to characterise pertinent micro-scale quantities during shearing and to relate them to the measured macroscopic response. The new and well-controlled data acquired during this experimental campaign are hopefully a useful contribution to the modelling efforts—to this end they are shared with the community.

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