Fractal dimension evolution of microcrack net in disordered materials

Carpinteri, Alberto; Yang, Guoping

doi:10.1016/0167-8442(96)00009-2

Cited by 27 publications

(15 citation statements)

References 3 publications

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“…The fractal dimension also increases with axial stress until the peak stress is reached, and it continues to increase with the decreasing axial stress beyond the peak stress. This behavior is consistent with Carpinteri and Yang's observations of disordered materials [51]. No critical value is found for the fractal dimension even when the simulated Fontainebleau sandstone fails.…”

Section: B Simulated Experiments Resultssupporting

confidence: 91%

“…Efforts have been made by many researchers to analyze the micro-crack development in stressed rock, e.g., Refs. [38,[49][50][51][52]. To understand rock deformation and fracture behavior [53][54][55][56][57][58][59], we quantify the evolution of micro-cracks in the simulated rock in a compressional test, and characterize patterns in the spatial distribution of these micro-cracks by using a box-counting technique [36].…”

Section: Rock Mechanical Propertiesmentioning

confidence: 99%

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Reconstruction of Sedimentary Rock Based on MechanicalProperties

Jin¹,

Patzek²,

Silin³

2004

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We describe a general, physics-based approach to numerical reconstruction of the geometrical structure and mechanical properties of natural sedimentary rock in 3D. Our procedure consists of three main steps: sedimentation, compaction, and diagenesis, followed by the verification of rock mechanical properties. The dynamic geologic processes of grain sedimentation and compaction are simulated by solving a dimensionless form of Newton's equations of motion for an ensemble of grains. The diagenetic rock transformation is modeled using a cementation algorithm, which accounts for the effect of rock grain size on the relative rate of cement overgrowth.Our emphasis is on unconsolidated sand and sandstone. The main input parameters are the grain size distribution, the final rock porosity, the type and amount of cement and clay minerals, and grain mechanical properties: the inter-grain friction coefficient, the cement strength, and the grain stiffness moduli. We use a simulated 2D Fontainebleau sandstone to obtain the grain mechanical properties. This Fontainebleau sandstone is also used to study the initiation, growth, and coalescence of microcracks under increasing vertical stress. The box fractal dimension of the micro-crack distribution, and its variation with the applied stress are estimated.

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Section: B Simulated Experiments Resultssupporting

confidence: 91%

Section: Rock Mechanical Propertiesmentioning

confidence: 99%

Reconstruction of Sedimentary Rock Based on MechanicalProperties

Jin¹,

Patzek²,

Silin³

2004

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“…More exactly, the coalescence condition in equation (1) should be calculated based on the stress intensity factors at each crack tip [24,25]. Meanwhile, the nominal (normal or uniaxial) stress was assumed to be a scalar rather than a tensor through the geometrical approximation made for the coalesced microcracks.…”

Section: Modelmentioning

confidence: 99%

Fractals and scaling in fracture induced by microcrack coalescence

Mai

Bai

2005

Philosophical Magazine Letters

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A numerical model is proposed to simulate fracture induced by the coalescence of numerous microcracks, in which the condition for coalescence between two randomly nucleated microcracks is determined in terms of a load-sharing principle. The results of the simulation show that, as the number density of nucleated microcracks increases, stochastic coalescence first occurs followed by a small fluctuation, and finally a newly nucleated microcrack triggers a cascade coalescence of microcracks resulting in catastrophic failure. The fracture profiles exhibit self-affine fractal characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatiotemporal distribution of nucleated microcracks in the vicinity of critical failure follows a power-law behaviour, which implies that the microcrack system may evolve to a critical state.

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“…To understand deformation and fracture behavior of a rock, [32][33][34][35][36] it is useful to observe evolution of micro-cracks in the rock, and characterize patterns in the spatial distribution of these micro-cracks. Efforts have been made by many researchers to observe and analyze the micro-crack development in stressed rocks, e.g., Refs., 27,[37][38][39][40] just to name a few.…”

Section: Rock Damage Analysismentioning

confidence: 99%

Physics-based Reconstruction of Sedimentary Rocks

2003

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TX 75083-3836, U.S.A., fax 01-214-952-9435. AbstractWe develop a depositional model that reconstructs numerically the geometrical structure and mechanical properties of natural sedimentary rocks in two and three dimensions. Our emphasis is on unconsolidated sands and sandstones. Our model has the following distinctive features: (1) it accounts for the dynamic geologic processes of grain sedimentation and compaction, and the diagenetic rock transformations; and (2) it reproduces the mechanical rock properties. The main input parameters are the grain size distribution, the final rock porosity, the type and amount of cement and clay minerals, the coefficient of friction, the bond strength parameters, and the grain stiffness moduli. The initial grain shapes are circular in 2D and spherical in 3D. Our depositional model can also be used to study the initiation, growth, and coalescence of micro-cracks in the rock. The proposed approach makes it possible to model the accumulation of rock damage and fracture propagation. The development of micro-cracks in, for example, a 2D marble rock model is studied under increasing vertical stress. Both the box fractal dimension of the micro-crack distribution and its variation with the applied stress are estimated.

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Fractal dimension evolution of microcrack net in disordered materials

Cited by 27 publications

References 3 publications

Reconstruction of Sedimentary Rock Based on MechanicalProperties

Reconstruction of Sedimentary Rock Based on MechanicalProperties

Fractals and scaling in fracture induced by microcrack coalescence

Physics-based Reconstruction of Sedimentary Rocks

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