Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses

Zhou, Xiaoping; Yang, Haiqing

doi:10.1016/j.ijrmms.2012.06.001

Cited by 83 publications

(18 citation statements)

References 27 publications

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“…Additionally, the Young's modulus is 32.5 GPa, Poisson's ratio is 0.24, and fracture toughness is 1 MPa·√m. The maximum tangential stress criterion is employed as the failure criterion, which can be expressed as

cos \frac{{normalθ}_{normalc}}{2} ((), K_{I} {cos}^{2} \frac{{normalθ}_{normalc}}{2} - \frac{3}{2} K_{II} sin θ_{c}) = K_{IC}

where K I is the SIF for mode I loading, K II is the SIF for mode II loading, and K IC is the fracture toughness for mode I loading. The crack initiation angle with respect to the pre‐existing crack (θ c ) is defined as

θ_{c} = 2 arctan ([], \frac{1}{4} ((), \frac{{normalK}_{normalI}}{{normalK}_{II}} - sign ((), {normalK}_{II}) \sqrt{{(\frac{{normalK}_{normalI}}{{normalK}_{II}})}^{2} + 8}))

where the sign function is defined as

sign ((), {normalK}_{II}) = ({, \begin{matrix} 1 K_{II} > 0 \\ - 1 K_{II} < 0 \end{matrix})

…”

Section: Comparative Studymentioning

confidence: 99%

“…Hence, the XFEM had been employed in many fields. Zhou and Yang employed the XFEM to model the deformation and failure of surrounding rock mass around the underground cavern. Patil et al used the XFEM to evaluate the elastic properties of heterogeneous materials.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is complex for the XFEM. Zhou and Yang solved the same problems by combining the displacement projecting method and the displacement loading method in the framework of XFEM, but it leads to the distortion of the mesh when the boundary is not regular. Fortunately, with the development of the computational science, the mesh technology makes considerable advances in recent years, particularly the triangular mesh.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method

Chen

Zhou

Berto

2018

Fatigue Fract Eng Mat Struct

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In this paper, a novel geometric method combined with the piecewise linear function method is introduced into the extended finite element method (XFEM) to determine the crack tip element and crack surface element. Then, by combining with the advanced mesh technique, a novel method is proposed to improve the modelling of crack propagation in triangular 2D structure with the XFEM. The numerical tests show that the accuracy, the convergence, and the stability of the XFEM can be improved using the proposed method. Moreover, the applicability of the conventional multiple enrichment scheme is discussed. Compared with the proposed method, the conventional multiple enrichment scheme has deficiency in mixed mode I and II crack. Finally, a comparative study shows that the performance of the XFEM by using the proposed method to model the crack propagation can be greatly improved.

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cos \frac{{normalθ}_{normalc}}{2} ((), K_{I} {cos}^{2} \frac{{normalθ}_{normalc}}{2} - \frac{3}{2} K_{II} sin θ_{c}) = K_{IC}

θ_{c} = 2 arctan ([], \frac{1}{4} ((), \frac{{normalK}_{normalI}}{{normalK}_{II}} - sign ((), {normalK}_{II}) \sqrt{{(\frac{{normalK}_{normalI}}{{normalK}_{II}})}^{2} + 8}))

where the sign function is defined as

sign ((), {normalK}_{II}) = ({, \begin{matrix} 1 K_{II} > 0 \\ - 1 K_{II} < 0 \end{matrix})

…”

Section: Comparative Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method

Chen

Zhou

Berto

2018

Fatigue Fract Eng Mat Struct

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“…Liang et al [7] and Li et al [8] discussed the mechanical mechanism of the growth of surface crack using the rock failure process analysis (RFPA) program. Except the above literatures, other researchers using other different numerical methods, like discrete element method (DEM) [9,10], discontinuous deformation analysis (DDA) [11], finite element method (FEM) [12,13], and extended finite element method (XFEM) [14], modeled the fracture propagation process and obtained different fracture propagation mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Fracture Propagation Characteristic and Micromechanism of Rock-Like Specimens under Uniaxial and Biaxial Compression

Liu

Huang

et al. 2016

Shock and Vibration

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This paper presents a set of uniaxial and biaxial compression tests on the rock-like material specimens with different fracture geometries through a rock mechanics servo-controlled testing system (RMT-150C). On the basis of experimental results, the characteristics of fracture propagation under different fracture geometries and loading conditions are firstly obtained. The newly formed fractures are observed propagating from or near the preexisting crack tips for different specimens, while the propagation paths are affected by the loading condition obviously. Then, by adopting acoustic emission (AE) location technique, AE event localization characteristics in the process of loading are investigated. The locations of AE events are in good agreement with the macroscopic fracture propagation path. Finally, the micromechanism of macroscopic fracture propagation under uniaxial and biaxial compression conditions is analyzed, and the fracture propagation can be concluded as a result of microdamage accumulation inside the material. The results of this paper are helpful for theory and engineering design of the fractured rock mass.

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“…Goncalves da Silva and Einstein (2013) implemented a strain-based and a normal stress-dependent criterion in FROCK to model the crack initiation, propagation, and coalescence through rock bridges, which appeared to yield better results than Bobet's stress-based criterion (Bobet and Einstein 1998). Based on the extended finite element method and global-local analysis, Zhou and Yang (2012) proposed a new multi-scale numerical model, in which the maximum circumferential stress criterion is used and the interaction integral method is employed to calculate the modes I and II SIFs, to model the crack initiation, propagation, and coalescence of multiple cracks in rock masses. Haeri et al (2014a) studied the crack propagation and coalescence based on modes I and II stress SIFs by a modified higher-order displacement discontinuity method.…”

Section: Introductionmentioning

confidence: 99%

Step-path failure of rock slopes with intermittent joints

et al. 2014

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Step-path failure is a typical instable mode of rock slopes with intermittent joints. To gain deeper insight into the step-path failure mechanism, six rock slopes with different intermittent joints are studied using the 2D Particle Flow Code (PFC). Three different step-path failure modes, i.e., shear, tensile, and mixed tensile-shear failure, are observed by focusing on the crack initiation, propagation, and coalescence in the rock bridges. The cracks develop progressively in the rock bridges, which induce the intermittent joints to coalesce one by one from bottom to top under the action of gravity. The tensile cracks that often appear in the main body and at the crown are nearly vertical to the step-path failure surface. The step-path failure in a rock slope with intermittent joints can be divided into four stages in terms of both stress and crack development in the rock bridges, i.e., elastic deformation, failure of rock bridges at a lower position, progressive failure of rock bridges upward, and final block slide. Therefore, reinforcement is suggested to be applied to the lower part of the slopes. Three equations for calculating the factors of safety are derived with respect to the three failure modes, in which the degree of joint coalescence is considered.

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Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses

Cited by 83 publications

References 27 publications

The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method

The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method

Fracture Propagation Characteristic and Micromechanism of Rock-Like Specimens under Uniaxial and Biaxial Compression

Step-path failure of rock slopes with intermittent joints

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