• Journal of Korean Tunnelling and Underground Space Association
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• v.3 no.2
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• pp.23-32
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• 2001

Rock masses are usually discontinuous in nature, as a result of various geological processes they have underdone and they contain rock joints and bridges. Crack propagation and coalescence processes mainly cause rock failures in tunnels. In this study, we focused on the crack initiation, propagation and coalescence process of rock materials containing two pre-existing open cracks arranged in different geometries. During uniaxial compression, wing crack initiation stress, wing crack propagation angle, and crack coalescence stress of Diastone gypsum and Yeosan Marble specimens were examined. And crack initiation, propagation, and coalescence processes were observed. Shear, tensile and mixed (shear+tensile) types of crack coalescence occurred. To compare the experimental results with Ashby & Hallam model, crack coalescence stress was normalized and it generally agreed with the experimental results.

• Tunnel and Underground Space
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• v.11 no.3
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• pp.217-224
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• 2001

Rock masses are usually discontinuous in nature due to various geological processes and contain rock joints and bridges. Crack propagation and coalescence processes in rock bridge mainly cause rock failures in slopes, foundations, and tunnels. In this study, we focused on the crack initiation, propagation and coalescence process of rock materials containing two pre-existing open cracks arranged in different geometries. Specimens of 120${\times}$60${\times}$25 mm in size, which were made of Yeoman Marble, were prepared. In the specimens, two artificial cracks were cut with pre-existing crack angle ${\alpha}$, bridge angle ${\beta}$, pre-existing crack length 2c and bridge length 2b. Wing crack initiation stress, wing crack propagation angle, and crack coalescence stress were measured and crack initiation, propagation and coalescence processes were observed during uniaxial compression. Crack coalescence types were classified and analytical study using Ashby and Hallam model (1986) was performed to be compared with the experimental results.

• Geomechanics and Engineering
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• v.8 no.4
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• pp.541-557
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• 2015

This research aims to analyze the fracture coalescence characteristics of brittle sandstone specimen ($80{\times}160{\times}30mm$ in size) containing various flaws (a single fissure, double squares and combined flaws). Using a rock mechanics servo-controlled testing system, the strength and deformation behaviours of sandstone specimen containing various flaws are experimentally investigated. The results show that the crack initiation stress, uniaxial compressive strength and peak axial strain of specimen containing a single fissure are all higher than those containing double squares, while which are higher than those containing combined flaws. For sandstone specimen containing combined flaws, the uniaxial compressive strength of sandstone increase as fissure angle (${\alpha}$) increases from $30^{\circ}$ to $90^{\circ}$, which indicates that the specimens with steeper fissure angles can support higher axial capacity for ${\alpha}$ greater than $30^{\circ}$. In the entire deformation process of flawed sandstone specimen, crack evolution process is discussed detailed using photographic monitoring technique. For the specimen containing a single fissure, tensile wing cracks are first initiated at the upper and under tips of fissure, and anti-tensile cracks and far-field cracks are also observed in the deformation process; moreover anti-tensile cracks usually accompanies with tensile wing cracks. For the specimen containing double squares, tensile cracks are usually initiated from the top and bottom edge of two squares along the direction of axial stress, and in the process of final unstable failure, more vertical splitting failures are observed in the ligament region. When a single fissure and double squares are formed together into combined flaws, the crack coalescence between the fissure tips and double squares plays a significant role for ultimate failure of the specimen containing combined flaws.

• Korea-Australia Rheology Journal
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• v.17 no.3
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• pp.125-130
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• 2005

Coalescence process of binary immiscible fluid mixtures having bimodal size distributions, prepared by mixing two pre-sheared samples at different shear rates, ${\gamma}_{pre1}\;and\;{\gamma}_{pre2}$, under shear flow at a final shear rate, ${\gamma}_f$, are examined by transient shear stress measurements and microscopic observations in comparison with the results for simply pre-sheared samples having narrow size distributions (unimodal distribution samples). Component fluids are a silicone oil (PDMS) and a hydrocarbon-formaldehyde resin (Genelite) and their viscosities are 14.1 and 21.0 $pa{\cdot}sec$ at room temperature $(ca.\;20^{\circ}C)$, respectively. The weight ratio of PDMS: Genelite was 7:3. Three cases, $({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;({\gamma}_{pre1}=0.8sec^{-1},\;{\gamma}_{pre2}=4.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;and\;({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0^sec^{-1}\;and\;{\gamma}_f=7.2sec^{-1})$ the first case, transient shear stress did not show any significant difference but domains larger than the initial state are observed at short times. In the latter cases, there exist undershoot of shear stress, reflecting existence of deformed large domains, which is confirmed by the direct observation. It is concluded that coalescence between large and small domains more frequently occur than coalescence between the domains with similar size in the bimodal distribution samples.

• Geomechanics and Engineering
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• v.17 no.1
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• pp.47-56
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• 2019

Crossing (X-type) flaws are commonly encountered in rock mass. However, the crack coalescence and failure mechanisms of rock mass with X-type flaws remain unclear. In this study, we investigate the compressive failure process of rock-like specimens containing two X-type flaws aligned in the loading direction. For comparison purposes, compressive failure behavior of specimens containing two aligned single flaws is also studied. By examining the crack coalescence behavior, two characteristics for the aligned X-type flaws under uniaxial compression are revealed. The flaws tend to coalesce by cracks emanating from flaw tips along a potential path that is parallel to the maximum compressive stress direction. The flaws are more likely to coalesce along the coalescence path linked by flaw tips with greater maximum circumferential stress if there are several potential coalescence paths almost parallel to the maximum compressive stress direction. In addition, we find that some of the specimens containing two aligned X-type flaws exhibit higher strengths than that of the specimens containing two single parallel flaws. The two underlying reasons that may influence the strengths of specimens containing two aligned X-type flaws are the values of flaw tips maximum circumferential stresses and maximum shear stresses, as well as the shear crack propagation tendencies of some secondary flaws. The research reported here provides increased understanding of the fundamental nature of rock/rock-like material failure in uniaxial compression.

• Geomechanics and Engineering
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• v.15 no.5
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• pp.1047-1059
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• 2018

This paper focuses on the cracking and fragmentation process in rock materials containing a pair of non-parallel flaws, which are through the specimen thickness, under vertical compression. Several numerical experiments are conducted with varying flaw arrangements that affect the initiation and tensile wing cracks, shear crack growth, and crack coalescing behaviors. To obtain realistic numerical results, a parallelized peridynamics formulation coupled with a finite element method, which is able to capture arbitrarily occurring cracks, is employed. From previous studies, crack initiation and propagation of tensile wing cracks, horsetail cracks, and anti-wing cracks are well understood along with the coalescence between two parallel flaws. In this study, the coalescence behaviors, their fragmentation sequences, and the role of an x-shaped shear band in rock material containing two non-parallel flaws are discussed in detail on the basis of simulation results strongly correlated with previous experimental results. Firstly, crack initiation and propagation of tensile wing cracks and shear cracks between non-parallel flaws are investigated in time-history and then sequential coalescing behavior is analyzed. Secondly, under the effect of varying inclination angles of two non-parallel flaws and overlapping ratios between a pair of non-parallel flaws, the cracking patterns including crack coalescence, fragmentation, and x-shaped shear band are investigated. These numerical results, which are in good agreement with reported physical test results, are expected to provide insightful information of the fracture mechanism of rock with non-parallel flaws.

• Geomechanics and Engineering
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• v.12 no.3
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• pp.541-560
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• 2017

In this research, experimental and numerical simulations were adopted to investigate the effects of ligament angle on compressive strength and failure mode of rock-like material specimens containing two non-coplanar filled fissures under uniaxial compression. The experimental results show that with the increase of ligament angle, the compressive strength decreases to a nadir at the ligament angle of $60^{\circ}$, before increasing to the maximum at the ligament angle of $120^{\circ}$, while the elastic modulus is not obviously related to the ligament angle. The shear coalescence type easily occurred when ${\alpha}$ < ${\beta}$, although having the same degree difference between the angle of ligament and fissure. Numerical simulations using $PFC^{2D}$ were performed for flawed specimens under uniaxial compression, and the results are in good consistency with the experimental results. By analyzing the crack evolution process and parallel bond force field of rock-like material specimen containing two non-coplanar filled fissures, we can conclude that the coalescence and propagation of crack are mainly derived from parallel bond force, and the crack initiation and propagation also affect the distribution of parallel bond force. Finally, the displacement vectors in ligament region were used to identify the type of coalescence, and the results coincided with that obtained by analyzing parallel bond force field. These experimental and numerical results are expected to improve the understanding of the mechanism of flawed rock engineering structures.

• Geomechanics and Engineering
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• v.12 no.6
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• pp.919-933
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• 2017

A series of Brazilian tests under diameter compression for disc specimens was carried out to investigate the strength and failure behavior by using acoustic emission (AE) and photography monitoring technique. On the basis of experimental results, load-displacement curves, AE counts, real-time crack evolution process, failure modes and strength property of granite specimens containing two pre-existing holes were analyzed in detail. Two typical types of load-displacement curves are identified, i.e., sudden instability (type I) and progressive failure (type II). In accordance with the two types of load-displacement curves, the AE events also have different responses. The present experiments on disc specimens containing two pre-existing holes under Brazilian test reveal four distinct failure modes, including diametrical splitting failure mode (mode I), one crack coalescence failure mode (mode II), two crack coalescences failure mode (mode III) and no crack coalescence failure mode (mode IV). Compared with intact granite specimen, the disc specimen containing two holes fails with lower strength, which is closely related to the bridge angle. The failure strength of pre-holed specimen first decreases and then increases with the bridge angle. Finally, a preliminary interpretation was proposed to explain the strength evolution law of granite specimen containing two holes based on the microscopic observation of fracture plane.

• Journal of The Korean Astronomical Society
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• v.40 no.4
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• pp.157-160
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• 2007

I present a model to explain the mass segregation and shallow mass functions observed in the central parts of starburst stellar clusters. The model assumes that the initial pre-stellar cores mass function resulting from the turbulent fragmentation of the proto-cluster cloud is significantly altered by the cores coalescence before they collapse to form stars. With appropriate, yet realistic parameters, this model based on the competition between cores coalescence and collapse reproduces the mass spectra of the well studied Arches cluster. Namely, the slopes at the intermediate and high mass ends, as well as the peculiar bump observed at $6M_{\bigodot}$. This coalescence-collapse process occurs on a short timescale of the order of the free fall time of the proto-cluster cloud (i.e., a few $10^4$ years), suggesting that mass segregation in Arches and similar clusters is primordial. The best fitting model implies the total mass of the Arches cluster is $1.45{\times}10^5M_{\bigodot}$, which is slightly higher than the often quoted, but completeness affected, observational value of a few $10^4M_{\bigodot}$. The model implies a star formation efficiency of ${\sim}30$ percent which implies that the Arches cluster is likely to a gravitationally bound system.

• Smart Structures and Systems
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• v.22 no.6
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• pp.675-687
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• 2018

In the previous studies on the porous rock strength the effect of pore number and its diameter is not explicitly defined. In this paper crack initiation, propagation and coalescence in Brazilian model disc containing a single cylindrical hole and or multiple holes have been studied numerically using PFC3D. In model with internal hole, the ratio of hole diameter to model diameter was varied between 0.03, 0.17, 0.25, 0.33, and 0.42. In model with multiple hole number of holes was different in various model, i.e., one hole, two holes, three holes, four holes, five holes, six holes, seven holes, eight holes and nine holes. Diameter of these holes was 5 mm, 10 mm and 12 mm. The pre-holed Brazilian discs are numerically tested under Brazilian test. The breakage load in the ring type disc specimens containing an internal hole with varying diameters is measured. The mechanism of cracks propagation in the wall of the ring type specimens is also studied. In the case of multi-hole Brazilian disc, the cracks propagation and b cracks coalescence are also investigated. The results shows that breaking of the pre-holed disc specimens is due to the propagation of radially induced tensile cracks initiated from the surface of the central hole and propagating toward the direction of diametrical loading. In the case of disc specimens with multiple holes, the cracks propagation and cracks coalescence may occur simultaneously in the breaking process of model under diametrical compressive loading. Finally the results shows that the failure stress and crack initiation stress decreases by increasing the hole diameter. Also, the failure stress decreases by increasing the number of hole which mobilized in failure. The results of these simulations were comprised with other experimental and numerical test results. It has been shown that the numerical and experimental results are in good agreement with each other.