scholarly journals Mechanical Mechanism and Propagation Law of Fissure-Tip Cracks of Large-Size Rock Specimens with Two Precut Fissures

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Liming Yin ◽  
Ming Li ◽  
Wenbin Sun ◽  
Juntao Chen ◽  
Bin Liu ◽  
...  
Keyword(s):  
Rock Mass ◽  
Tensile Stress ◽  
Crack Propagation ◽  
Main Crack ◽  
Similarity Theory ◽  
Three Dimensional ◽  
Structural Defects ◽  
Two Dimensional ◽  
Propagation Law ◽  
Balance State

The rock is a kind of geological medium with damages of different degrees including fissures, faults, joints, and other structural defects. Many underground rock engineering projects, such as mining and tunnel excavation, can break the three-dimensional stress balance state of rock mass and make it subject to two-dimensional or even one-dimensional stress, thus inducing stress concentration which leads to rapid failure. In order to investigate the failure law of the rock mass with such defects under two-dimensional stress, based on the similarity theory, we first prepared rocklike specimens with fissures featuring actual mechanical properties and then systematically analyzed the fissure-tip crack propagation and specimen failure law and mechanical mechanism under two-dimensional stress in view of the stress field theory. The results demonstrate that with the increase of load, the microcracks developed and propagated gradually, during which a number of branch paths were generated from the fissure tips of the specimens; the upper and lower cracks were connected first due to the main crack propagation, forming a sliding surface which caused the failure of the specimens, and the strengths of the specimens also fluctuated according to the different combinations of the fissure dip angles and rock bridge dip angles. In view of acoustic emission (AE), we calculated and obtained the spatial positions of stress peaks in each direction at the fissure tips; through comparison and analysis, the angle corresponding to the negative angle peak of the maximum circumferential tensile stress and the maximum radial tensile stress is basically the same as the angle of the main crack propagation direction generated from the preexisting fissure; it can be inferred that the tensile stress is the main stress inducing crack initiation and specimen failure, which is consistent with the physical characteristics of rock (resistant to compression but not tension). This may serve as a guidance for judging the direction along which new cracks are generated in a rock mass with double structural planes.

scholarly journals A modified maximum tangential tensile stress criterion for three-dimensional crack propagation

2012 ◽  
Vol 4 (1) ◽  
pp. 62-72 ◽  
Author(s):  
Dunfu Zhang ◽  
Weishen Zhu ◽  
Shucai Li ◽  
Bo Zhang ◽  
Weidong Wang
Keyword(s):  
Tensile Stress ◽  
Crack Propagation ◽  
Three Dimensional ◽  
Stress Criterion

scholarly journals Crack Propagation Law and Failure Characteristics of Coal-Rock Combined Body with the Different Inclination Angle of Prefabricated Fissure

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Chunlei Zhang ◽  
Yun Dong ◽  
Ruimin Feng ◽  
Ningbo Peng ◽  
Jihua Zhang ◽  
...  
Keyword(s):  
Fracture Surface ◽  
Crack Propagation ◽  
Failure Mode ◽  
Inclination Angle ◽  
Main Crack ◽  
Failure Characteristics ◽  
Secondary Cracks ◽  
Propagation Law ◽  
Inclination Angles ◽  
Coal Rock

Few studies have been conducted on the crack propagation law and failure characteristics of coal-rock combined body (CRCB) with prefabricated fissure. A sliding crack model was firstly presented to analyze the failure law of rock with a single fracture and the influence of the inclination angle of the fracture on the strength of the rock. The RFPA numerical models of the CRCB with different inclination angles of prefabricated fracture were then established to simulate the dynamic change process of crack propagation and shear stress of the CRCB with prefabricated fracture under uniaxial compression. The influence of the inclination angle of the fracture in the rock on the fracture expansion and failure characteristics of CRCB was further analyzed based on the acoustic emission data. The results showed that (1) when 2 β = arctan 1 / μ , σ cw takes the minimum value, and crack initiation is most likely to occur; (2) the strength of coal-rock assemblage shows different changing trends with the fracture inclination angle; (3) the secondary cracks of CRCB with prefabricated fracture of 0°, 15°, and 30° initiated and expanded near the tip of the main crack, and the secondary cracks of 45°, 60°, and 75° initiated and expanded from the tip of the main crack; (4) there are three failure modes of CRCB with prefabricated crack, the double-shear failure mode Λ , the tensile-shear composite failure mode along the fracture surface, and the tensile failure mode along the fracture surface; and (5) intact CRCB and CRCB with prefabricated crack when α = 75 ° and α = 90 ° have strong brittleness, and other CRCB with different prefabricated fracture inclination angles show a certain degree of postpeak plasticity. The results on the mechanical properties and damage characteristics of CRCB are of great significance for the safety and efficient mining of deep coal resources.

scholarly journals Experimental Study of Three-Dimensional Propagation of Crack in Transparent Rock Mass

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhende Zhu ◽  
Yuan Tian ◽  
Xinyu Liu
Keyword(s):  
Rock Mass ◽  
Crack Propagation ◽  
Pore Pressure ◽  
Mechanical Stability ◽  
Water Pressure ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Peak Strength ◽  
Primary Crack ◽  
Good Transparency

Three-dimensional crack propagation in a rock mass was investigated using a specifically designed material with good transparency and elastoplasticity. The material has properties that are similar to those of the nature sandstone. Hydromechanical tests were conducted to simulate pore pressure in the paper to study the influence of the angle of the primary crack and the water pressure on the mechanical stability of the rock mass. The results indicated that the water pressure accelerated the crack propagation and the failure of the samples. The influence of water pressure on initiation crack strength was not significant but had a significant impact on the peak strength. With the increase in water pressure, the crack initiation strength, penetration strength, and peak strength all decrease in varying degrees. The penetration strength did not only depend on the pore pressure but also exhibited high sensitivity to the inclination angle of the primary crack. The extended finite element method is used to simulate hydraulic fracturing. The simulation results show that the stress near the tip exhibited a cycle of energy accumulation-crack expansion-stress relaxation as the crack expanded, and this finding was consistent with Griffith’s energy theory.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

An Image Reconstruction System Applied to High Voltage Microscopy

1975 ◽  
Vol 33 ◽  
pp. 292-293
Author(s):  
D. E. Johnson
Keyword(s):  
High Voltage ◽  
Prior Information ◽  
Block Diagram ◽  
Three Dimensional ◽  
Real Space ◽  
Two Dimensional ◽  
Efficient Manner ◽  
Fourier Methods ◽  
Tilt Series ◽  
Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

Computer Assisted Image Reconstruction of Oligomer Structure

1976 ◽  
Vol 34 ◽  
pp. 472-473
Author(s):  
A.M. Jones ◽  
A. Max Fiskin
Keyword(s):  
Three Dimensional ◽  
Depth Of Field ◽  
Computer Assisted ◽  
Projection Data ◽  
Two Dimensional ◽  
Single Particles ◽  
Dimensional Reconstruction ◽  
Computer Assisted Image ◽  
The Fourier Transform ◽  
Space Approach

If the tilt of a specimen can be varied either by the strategy of observing identical particles orientated randomly or by use of a eucentric goniometer stage, three dimensional reconstruction procedures are available (l). If the specimens, such as small protein aggregates, lack periodicity, direct space methods compete favorably in ease of implementation with reconstruction by the Fourier (transform) space approach (2). Regardless of method, reconstruction is possible because useful specimen thicknesses are always much less than the depth of field in an electron microscope. Thus electron images record the amount of stain in columns of the object normal to the recording plates. For single particles, practical considerations dictate that the specimen be tilted precisely about a single axis. In so doing a reconstructed image is achieved serially from two-dimensional sections which in turn are generated by a series of back-to-front lines of projection data.

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