Figure 1
Hybrind finite-discrete element model under different stress conditions (red line represents edges of joint element).
Figure 2
Relationship between the bonding stress and opening/sliding displacement under tension and shear condition
Figure 3
Failure criteria for Mixed I-II fracture mode.
Figure 4
Rock sample for UCS test and BTS test: (a) Rock specimen for UCS test; (b) Rock specimen under UCS test; (c) Rock specimen for BTS test; (d) Rock specimen under BTS test.
Figure 5
Rock fracture patterns in UCS and BTS tests: (a) UCS tests fracture pattern; (b) BTS tests fracture pattern
Figure 6
Geometrical and numerical model of UCS test: (a) Geometrical model; (b) Numerical model
Figure 7
Modelled failure process during uniaxial compression test under the loading rate of constant displacement of 0.1m/s: (a) Evolution of minor principal stress in the vertical direction; (b) Crack initiation and propagation (red: shear failure; Blue: tensile failure)
Figure 8
Stress-loading displacement curve during the uniaxial compression test under a loading rate of 0.1m/s
Figure 9
Geometrical and numerical models for the Brazilian tensile disc test: is the applied load, is the disc radius, is the distance from the center of the disc, is the disc thickness, 2 is the angular distance of load arc, and are stresses along the horizontal and vertical directions respectively.
Figure 10
Evaluation of minor principal stress and the fracture initiation and propagation for BTS test under the loading rate of 0.1m/s: (a) Evolution of minor principal stress; (b) Fracture initiation and propagation.
Figure 11
Force-loading displacement curve for during BTS test unde a quasi-static load (0.1m/s).(a) Top force-loading displacement curve; (b) Bottom force-loading displacement curve
Figure 12
Comparison of the modelled and experimental fracture pattern for BTS test: (a) modelled result; (b) experimental results.
Figure 13
Comparison of the numerical and analytical stress along the loading diameter for BTS test under the loading rate of 0.1m/s
Figure 14
Geometrical mode of notched Brazilian disc: a is the half crack length; R is the diameter; and is the orientation angle
Figure 15
Stress intensity factor(SIF) in diametral compression of the NBD at a=15.4mm ,R=54mm,a/R = 15.4/54(after Whittaker et al., 1992Whittaker, B. N., R. N. Singh and G. Sun (1992). Rock fracture mechanics: principles, design, and applications, Elsevier Amsterdam.)(Barry, Raghu et al. 1992Barry, N. W., N. S. Raghu and S. Gexin (1992). Rock fracture mechanics principles design and applications, Amsterdam: ELSEVIER.)
Figure 16
Geometrical and numerical model for diametral compression of the notched Brazilian Dis tests: (a) Geometrical model; (b) numerical model; Angles for model A, B, and C are, respectively.
Figure 17
Rock fracture initiation and propagation for pure mode-I NBD test under quasi-static loading (red color represents tensile failure while the blue color indicates the shear failure, pre-fabricated notch and the boundaries)
Figure 18
Numerical and experimental results obtained in the diametral compression of NBD tests in pure mode-I loading: i) Simulated by the code(Liu, Kou et al. 2007Liu, H., S. Kou, P.-A. Lindqvist and C. Tang (2007). Numerical modelling of the heterogeneous rock fracture process using various test techniques. Rock mechanics and rock engineering 40:2: 107-144.) ii) Experimental result (Jia, Castro-Montero et al. 1996Jia, Z., A. Castro-Montero and S. P. Shah (1996). Observation of mixed mode fracture with center notched disk specimens. Cement & Concrete Research 26:1: 125-137.); iii) Experimental and numerical result(Chen, Pan et al. 1998Chen, C. S., E. Pan and B. Amadei (1998). Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method. International Journal of Rock Mechanics and Mining Sciences 35:2: 195-218.)
Figure 19
Force loading-displacement curve for pure mode-I NBN test
Figure 20
Rock fracture initiation and propagation for pure mode-II NBD test under quasi-static loading
Figure 21
Numerical and experimental results obtained in the diametral compression of NBD tests in pure mode-II loading: i) Simulated by the code (Liu, Kou et al. 2007Liu, H., S. Kou, P.-A. Lindqvist and C. Tang (2007). Numerical modelling of the heterogeneous rock fracture process using various test techniques. Rock mechanics and rock engineering 40:2: 107-144.) ii) Experimental result (Jia, Castro-Montero et al. 1996Jia, Z., A. Castro-Montero and S. P. Shah (1996). Observation of mixed mode fracture with center notched disk specimens. Cement & Concrete Research 26:1: 125-137.); iii) Experimental and numerical result (Chen, Pan et al. 1998Chen, C. S., E. Pan and B. Amadei (1998). Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method. International Journal of Rock Mechanics and Mining Sciences 35:2: 195-218.)
Figure 22
Force loading-displacement curve for pure mode-II NBN test
Figure 23
Rock fracture initiation and propagation for pure mixed-mode I-II NBD test under quasi-static loading (red color represents tensile failure while the blue color indicates the shear failure, pre-fabricated notch and the boundaries)
Figure 24
Force loading-displacement curve for mixed-mode I-II NBN test
Figure 25
Modelled failure process during uniaxial compression test under the loading rate of constant displacement of 1m/s: (a) Evolution of minor principal stress in the vertical direction; (b) Crack initiation and propagation (red: shear failure; Blue: tensile failure)
Figure 26
Force-loading displacement curve during the uniaxial compression test under a loading rate of 1m/s
Figure 27
Modelled failure process during uniaxial compression test under the loading rate of (a) 5m/s, (b) 10m/s and (c) 50m/s, respectively.
Figure 28
Force-loading displacement curve during the uniaxial compression test under the loading rates of (a) 5m/s, (b) 10m/s and (c) 50m/s, respectively.
Figure 29
Evaluation of minor principal stress and the fracture initiation and propagation for BTS test under the loading rate of 1m/s: (a) Evolution of minor principal stress; (b) Fracture initiation and propagation
Figure 30
Force-loading displacement curve for during BTS test unde the loading rate of 1m/s :(a) Top force-loading displacement curve; (b) Bottom force-loading displacement curve
Figure 31
Dynamic rock fracture during BTS test under loading rate of 5m/s, 10m/s and 50m/s.
Figure 32
Force-loading displacement curves during BTS test under the loading rate of 5m/s, 10m/s and 50m/s, respectively: (a) Top force-loading displacement curve; (b) Bottom force-loading displacement curve
Figure 33
Comparison of the force-loading displacements of the BTS test curves under various loading rates
Figure 34
Relationship of tensile strength and the loading rate
Figure 35
Dynamic strength increasing factors obtained from hybrid modelling and their compassion with the existing results from literatures (Parts of them are taken from Asprone et al. 2009Asprone, D., E. Cadoni and A. Prota (2009). Experimental analysis on tensile dynamic behavior of existing concrete under high strain rates. ACI Structural Journal 106:1: 106. and Cho et al. 2003Cho, S. H., Y. Ogata and K. Kaneko (2003). Strain-rate dependency of the dynamic tensile strength of rock. International Journal of Rock Mechanics and Mining Sciences 40:5: 763-777.).
Figure 36
Numerical model for UCS test with structural mesh
Figure 37
Hybrid finite-discrete element modelling of rock fracture during UCS test with structural mesh for the models
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