Spatial Distribution Of Cracks Research Articles

Study on crack propagation mechanism of coal under the different orientation between prefabricated slots and true triaxial stress

In engineering, the interrelationship between hydraulic slots and in-situ stress affects the efficiency of the relief stress of coalbeds. In this research, true triaxial experiments were carried out on coal with prefabricated slots parallel to the σ2 (FP-σ2) and the σ3 (FP-σ3). The results show that the modulus of elasticity and Poisson's ratio of the specimens change dynamically with the increase of cycles, and the peak strength and peak strain of the FP-σ3 specimen is larger than the FP-σ2 specimen. The cracks of FP-σ2 specimens were mainly distributed in the X-Z plane, while the cracks of FP-σ3 specimens were more uniformly distributed inside the specimens. For FP-σ3 specimens, a crack's stable expansion orientation of the slot exists, which influences the competitive extension of cracks in the slot-plane with the σ1-σ3 plane. In this orientation, the cracks are distributed in a complex manner. The effects of the horizontal stress difference Kn and the horizontal deflection angle ω of slot on the spatial distribution of cracks were further analyzed by numerical simulation. It can change the slot's horizontal deflection angle ω to make the cracks' distribution uniform. The optimisation method of hydraulic slotting in deep coalbeds is discussed based on research results.

Stress interactions in cracked media during the closure of prestressed cracks

Abstract With the increasing pressure, a crack in a medium will be gradually closed, which is affected by stress interactions. The closing process of parallel cracks under vertical stress is simulated here. The coplanar and stacked cracked models are constructed to analyze the influence of two types of stress interaction on the closing process. The spatial distribution of cracks, demonstrated by numerical experiments, has a significant impact on stress interactions and thus the process of crack closure. The mechanisms underlying the delay of crack closure caused by stress interactions are different for the two models. Furthermore, according to the stress dependence of crack microscopic parameters (crack porosity, aperture, and length of major axis), the process of crack closure can be divided into three stages: the linear deformation stage, the contact stage, and the closure stage. In the first stage, no contact is permitted inside the crack. The shielding effect directly leads to a closure lag, and thus a linear stress dependence of the microscopic crack parameter. In the second stage, the shielding effect determines the increasing rate for the stress dependence of microscopic crack parameters in regularly distributed cracked models. However, for the randomly distributed cracked model, local stress interactions result in the eccentric closure of cracks, and thus the crack closure lag. In the last stage, the crack is closed and stress interactions disappear both in the regularly and randomly distributed models.

Thermal conductivity of crack-containing media: A numerical study

The present study aims to evaluate the effective thermal conduction behavior of crack-containing media through micromechanical modeling. Numerical analyses were performed using the finite element method, first using periodic arrays of elliptical pores and then reducing the elliptical minor axis to reach the crack limit. This parametric approach was seen to be able to capture the effect of discontinuity across the crack face in a straightforward manner. The overall thermal conductivity of the model structures, encompassing a range of crack densities and spatial distributions, was investigated. It was found that, for cracks with mixed orientations, the effective thermal conductivity is insensitive to the actual crack alignment and can be uniquely represented by the crack density. The mixed-orientation periodic crack configurations are also representative of random sizes, orientations, and spatial distributions of cracks, thus exhibiting a high degree of generality. The modeling analyses can also be used to determine simple empirical expressions for two- and three-dimensional media containing random cracks.

Developing an approach for measuring the intensity of cracking based on geospatial analysis using GIS and automated data collection system

ABSTRACT Determination and measurement of the characteristics of surface distresses such as cracking are the important tasks of pavement maintenance authorities. The measurement of main characteristics including the extent, severity, and intensity of cracking, results in a better assessment of pavement condition. The cracking intensity (crack spacing) can be expressed and developed based on the spatial distribution of cracks. Due to the difficulty of measuring the cracking intensity, the importance of this main attribute has been rarely considered. In addition, a practical method has not been provided for measuring and determining the distribution of cracking in the selected pavement section. In this paper, using the locations of pavement surface cracks and GIS, a practical method is proposed for representing and determining the intensity of cracking through identifying the spatial distribution of pavement cracks at the project level to evaluate the proposed method, longitudinal, transverse, and alligator cracks were investigated in several pavement sections. The cracking assessment was performed by the use of an automated data collection system and the location-based image processing technique in GIS. The results of the study show that through the usage of the proposed method, the intensity of cracking can be determined and considered practically as the main attribute of cracking.

3D microstructure reconstruction of casting aluminum alloy based on serial block-face scanning electron microscopy

In this work, the inner microstructure of aluminum-silicon casting alloy was experimentally investigated to reveal the spatial morphology and phase distribution. Its industrial use is as a light-weight structural material. As a powerful three-dimensional (3D) imaging tool at the nano-scale, the serial block-face scanning electron microscopy (SBFSEM) was employed to investigate the specimens. After being 3D reconstructed, the images were visualized to identify preference for several specific intermetallics by quantitative analysis. It was found that these phases have certain relationships in spatial distribution and differences in spatial shapes. The spatial distribution of cracks was studied to understand their propagation and growth.

Measuring Crack Porosity using Three‐Dimensional Electrical Resistivity Tomography

Core Ideas Desiccation cracks in Vertisols and shrink‐swell soils greatly alter soil hydrology Electrical Resistivity Tomography (ERT) may be used to measure crack porosity ERT images were measured on a cracked Vertisol Crack porosity was measured directly by filling cracks with cement ERT images were well correlated with measurements of crack porosity Desiccation cracks in Vertisols and other shrink‐swell soils greatly alter the hydrological properties of the soil by intercepting runoff and increasing evaporation. Nondestructive monitoring and measuring of soil crack volume or porosity is difficult. Typically, crack porosity is predicted from measurements of soil subsidence or shrinkage; however, these measurements require installation of permanent equipment in the field. In this paper, we demonstrate the use of electrical resistivity tomography (ERT) to monitor soil crack porosity. Electrical resistivity tomography is a noninvasive geophysical technique that generates maps or images of the subsurface electrical resistivity of a soil. We conducted ERT surveys during the seasonal drying cycle of a Vertisol in Central Texas. Crack porosity near the end of a drying cycle was measured by filling cracks with cement and photographic analysis of horizontal cross‐sections. Measured crack porosity was correlated to crack indicators on ERT images (r2 = 0.63). Total shrinkage porosity for each date of the study was predicted from soil water content loss. Measured crack porosity accounted for roughly one third of total shrinkage porosity. For dates where cracks were present, average total shrinkage porosity was well correlated with ERT indicators (r2 = 0.96). Our results suggest that ERT could be a viable, non‐invasive tool for measuring crack porosity. ERT‐based methods have several advantages over traditional shrinkage‐based methods, mainly that ERT does not require installation of permanent field equipment and can provide data on the spatial distribution of cracks over pedon‐scale areas.

Damage Assessment of the 2010 Chile Earthquake and Tsunami Using Terrestrial Laser Scanning

In the wake of the 2010 Chile earthquake and tsunami, a reconnaissance survey recorded earthquake and tsunami damage using terrestrial laser scanning (TLS), which is capable of detecting details that most traditional reconnaissance methods cannot. TLS enables precise measurements of structural deformations and damage (including shear cracking of concrete walls, concrete spalling, and damage of rebars), as well as soil deformations and damage (including erosion, scour, liquefaction, lateral spread, slope failure, and ground displacement). Advanced measurements such as minute structural rotations, spatial distribution of cracks, volumetric and positional change calculations can also be obtained. Herein, we present various types of detailed measurements and analyses using TLS data obtained at several sites that were damaged by the earthquake and/or tsunami in Concepción, Constitución, Dichato, and Talcahuano. Moreover, this high-resolution data has enabled a unique avenue for virtual, post-visit analysis, providing additional insights that were not readily observable during the field visit.

Spatial and orientational distribution of cracks in crystalline photovoltaic modules generated by mechanical load tests

Cracks in crystalline silicon solar cells influence the photovoltaic (PV) module power output in accelerated aging tests. A detailed insight into the formation of cracks offers the potential to optimize the PV module design in order to reduce the risk of power degradation in its lifetime. In this paper we present a statistical analysis on the crack formation in 27 crystalline silicon PV modules caused by a standard mechanical load test according to IEC 61215 10.16. The criticality of cracks depends strongly on the crack orientation, therefore we analyze both the spatial distribution of cracks and its dependence on the orientation of the cracks in the tested PV modules. We find that 50% of the damaged cells are cracked parallel to the busbars, which is a crack orientation with high potential impact on the power output of the PV module. A simplified numerical analysis is used to give an explanation for the statistical data and we propose a strategy for the reduction of the crack criticality.

Use of X-ray computed tomography to investigate crack distribution and mineral dissemination in sphalerite ore particles

As the trends in mineral processing move towards the beneficiation of finer grained and more complex ore bodies, so too do the methods needed to understand and model these processes. During the heap leaching of low-grade ore bodies, the crack distribution and mineral dissemination in ore particles are important characteristics that determine the performance of sub-processes, such as the diffusion of reagents in and out of particle pores. Recent developments in X-ray computed tomography (CT) as an advanced diagnostic and nondestructive technique have indicated the potential for the technology to become a tool for the acquisition of 3-D mineralogical and structural data. The spatial distribution of cracks and mineral dissemination in particles derived from a sphalerite ore in the Northern Cape, South Africa, was characterized using a high-resolution industrial X-ray CT system. This paper describes the use of image analysis techniques including image segmentation, which uses a combination of thresholding and other methods to characterize and quantify crack and mineral dissemination in the sphalerite particles. The results are validated with those obtained using traditional techniques such as physical gas (with N 2) adsorption, mercury intrusion porosimetry, SEM and QEMSCAN. A comparison of the effect of different comminution devices (HPGR and Cone crusher) on crack generation is also given.

Critical Scaling in Standard Biased Random Walks

The spatial coverage produced by a single discrete-time random walk, with an asymmetric jump probability p not equal 1/2 and nonuniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at p=p(c). Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit p-->p(c), the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model.

Scattering attenuation, dispersion and reflection ofSHwaves in two-dimensional elastic media with densely distributed cracks

We compute the synthetic seismograms of multiply scattered SH waves in 2-D elastic media with densely distributed parallel cracks. We assume randomly distributed cracks in a rectangular-bounded region, which simulate a cracked zone. The crack surfaces are assumed to be stress-free. When the incident wavelength is longer than the crack size, the delay in the arrival of the primary wave is observed at stations beyond the cracked zone and the amplitude of the primary wave is amplified in the cracked zone in the synthetic seismograms. This is because the cracked zone behaves as a low velocity and soft material to the incident long-wavelength wave due to the crack distribution. When the half-wavelength of the incident wave is shorter than the crack length, the scattered waves are clearly observed in the synthetic seismograms and the amplitude of the primary wave is largely attenuated beyond the cracked zone. The calculated attenuation coefficient Q−1 of the primary wave is directly proportional to the crack density in the range of νa2≤ 0.1, where ν and a are the number density and half the length of cracks, respectively. This is consistent with that obtained by a stochastic analysis based on Foldy's approximation. A periodic distribution of cracks in a zone is considered as an utterly different model in order to investigate the effect of spatial distributions on the attenuation and dispersion of seismic waves. When cracks are distributed densely, the values of Q−1 for the periodic crack distribution appear to differ from those for the random distribution of cracks in the low wavenumber range. This suggests that the effect of multiple interactions among densely distributed cracks depends on not only the density but also the spatial distribution of cracks at low wavenumbers. The calculated phase velocity of the primary wave is consistent with that from the stochastic analysis in the range of νa2≤ 0.1 and does not depend on the spatial distribution of cracks. This suggests that the multiple crack interactions have a smaller effect to the phase velocity. Therefore, the crack density can be estimated from the values of the phase velocity for the cases of densely distributed cracks even if the effect of the multiple crack interactions is not considered. We can clearly observe the reflected waves in the synthetic seismograms. The elastic constant of a single anisotropic layer equivalent to the cracked zone is derived from the crack density at the long-wavelength limit. The reflection coefficients calculated from the synthetic seismograms are consistent with those of the anisotropic layer calculated from its elastic constants and thickness in low wavenumber range. This means that a fracture zone distributed parallel cracks is considered as an anisotropic layer for long incident wavelengths. Therefore, the elastic constants, crack density and the thickness of the fracture zone can be estimated from the frequency dependence of the reflection coefficients for long incident wavelengths. On the contrary the wavenumber dependence of the reflection coefficients cannot be explained theoretically in the high wavenumber range.

A model for crack connectivity in rocks, a discussion

We reanalyzed a model introduced by T. R. Madden for the evaluation of the state of connectivity among the microcrack population existing inside crystalline rocks. The model assumes that cracks are distributed randomly in a cubic lattice with a basic occupation probability, p.Depending on the value of p, the stale of connectivity can give rise to macroscopic paths, which allow electrical conduction of the sample, or to extended crack surfaces, which would be responsible for rock failure. The position of the phase boundaries, that is, the threshold values of pfor the onset of conductivity or macroscopic fracture, are estimated by a real-space renormalizalion-group (RG) technique. By identifying all the relevant configurations of the lattice model, we have been able to provide explicit analytic formulae for the critical lines. The criterion used by Madden to “accept” the existence of microscopic linear connectivity is modified and the new consequences discussed. We analyze the limitations of simple versions of the RG technique, in particular when concerned with anisotropic spatial distributions of cracks. Finally, we emphasize the interest of acquiring experimental data, especially to test the position of the conduction thresholds.