Abstract
To better study rock blasting in engineering and the initiation and propagation behavior of the pre-existing crack under blasting stress waves, large-scale rock models containing a thorough centric crack were numerically blasted, using the LS-DYNA and HYPERMESH software for solving, modeling and meshing as well as adding keywords, respectively. The rock material chosen for the present study was granite, and the Holmquist–Johnson–Cook (HJC) model was applied to carry out numerical simulations. To study the influence of incident angle of blasting stress wave, there were four groups of modes in all designed with different borehole positions, labeled as M-1, M-2, M-3 and M-4. Based on the theoretical wavefront reconstruction, the reflection and diffraction of blasting-induced waves at a finite crack and highly complex interaction with crack were explained in detail. Furthermore, the maximum circumferential stress criterion was used to analyze the crack initiation and propagation. The results are in accordance with the experiment results, which show that the incident angles of blasting stress waves have a significant effect on the propagation characteristics of waves at the pre-existing crack and the model failure modes. As the incident angle increases, the initiating time of crack tip B decreases, but the deflecting angle increases, and damage near the pre-existing crack is more serious. In addition, reflected and diffracted waves cause stress concentration at the crack tip, which plays a dominant role in crack initiation and propagation. While the pre-existing crack hinders stress wave propagation and reduces its amplitude and inhibits the formation and development of cracks around the borehole, thereby resulting in that the model damage is mainly concentrated at the crack ends and around the borehole, no obvious damage occurs in other areas.
Similar content being viewed by others
Data Availability
Data and material will be preserved and will be available upon request.
Code availability
Software used is commercially available. If needed, authors can help readers in finding the companies providing software used in this work.
Abbreviations
- ρ :
-
Density
- ρ 0 :
-
Reference density
- V :
-
Relative volume
- D :
-
Detonation speed
- P cj :
-
Detonation pressure
- A,B, R 1, R 2, ω :
-
Basic parameters of equation of state
- C 0∼C 6 :
-
Coefficients of linear polynomial equation of state
- E :
-
Internal energy per unit volume
- α :
-
Included angle between the incident wave and crack surface
- σ θθ :
-
Circumferential stress at a certain position
- σ rr :
-
Radial stress
- σx, σy and τ xy :
-
X-stress, Y-stress and shear stress
- θ :
-
Polar angle
- PrP:
-
Reflected waves generated by P wave
- Pd AP, Sd AP:
-
Diffracted waves generated by P wave at the crack tip A
- Pd BP, Sd BP:
-
Diffracted waves generated by P wave at the crack tip B
- V + P, V_P:
-
Schmidt head waves
- R + P, R_P:
-
Rayleigh waves
- Pd BPd AP, Sd BPd AP:
-
Secondary diffracted waves generated by PdAP and SdAP waves at the crack tip B
- V + Pd AP, V_Pd AP:
-
Schmidt head waves generated by PdAP and SdAP waves
References
Bi CC (2018) Calibration of HJC constitutive parameters of Huashan granite and its blasting damage numerical simulation. Hefei University of Technology
Chen C, Yang RS, Xu P et al (2022) Experimental study on the interaction between oblique incident blast stress wave and static crack by dynamic photoelasticity. Opt Lasers Eng 148(3):106764
Chen PE, Sih GC (1977) Chapt. l and 3 of Elastodynamic Crack Problems. In: Mechanics of Fracture 4 (ed. by G.C. Sih), Noordhoj Int. Publ, Leyden
Dally JW (1980) An introduction to dynamic photoelasticity. Exp Mech 20(12):409–416
Dally JW, Fourney WL, Holloway DC (1975) Influence of containment of the bore hole pressures on explosive induced fracture, lnt. J. Rock Mech. Mix. Sci. Geomech. Abstr. 12:5–12
Fan LF, Zhou XF, Wu ZJ et al (2019) Investigation of stress wave induced cracking behavior of underground rock mass by the numerical manifold method. Tunnel Underground Space Technol 92:103032–103032
Gao XN, Wu YJ (2015) Numerical calculation of TNT explosion and its influencing factors. Chin J Explos Propell 38(3):32–39
Harris JG (1980) Diffraction by a crack of a cylindrical longitudinal pulse. J Appl Math Phys 31(3):367–383
Herakovich CT (2016) A concise introduction to elastic solids. Springer, Berlin
Hoop AT (1958) Representation theorems for the displacement in an elastic solid and their application to elastodynamic diffraction theory. PhD Thesis. Delft University of Technology, The Netherland
Hu R, Zhu ZM, Xie J et al (2015) Numerical study on crack propagation by using softening model under blasting. Adv Mater Sci Eng 2015:108580–108580
Jing L (2003) A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. Int J Rock Mech Min Sci 40(3):283–353
Jing L, Hudson JA (2002) Numerical methods in rock mechanics. Int J Rock Mech Min Sci 39(4):409–427
Lalegname A, Sändig AM (2011) Wave-crack interaction in finite elastic bodies. Int J Fract 172(2):131–149
Li JC, Ma GW (2010) Analysis of Blast Wave Interaction with a Rock Joint. Rock Mech Rock Eng 43(6):777–787
Li XB, Li CJ, Cao WZ et al (2018) Dynamic stress concentration and energy evolution of deep-buried tunnels under blasting loads. Int J Rock Mech Min Sci 104:131–146
Li Q, Xu WL, Wang K et al (2021) Study on the mechanical behavior of crack propagation effect at the end of defect under explosive load[J]. Int J Rock Mech Min Sci 138(3):104624
Qiu P, Yue ZW, Yang RS (2019) Mode I stress intensity factors measurements in PMMA by caustics method: A comparison between low and high loading rate conditions. Polym Testing 76:273–285
Qiu P, Yue ZW, Yang RS et al (2021) Modified mixed-mode caustics interpretation to study a running crack subjected to obliquely incident blast stress waves. Int J Impact Eng 150(3):103821
Rossmanith HP, Shukla A (1981a) Photoelastic investigation of stress wave diffraction about stationary crack-tips. J Mech Phys Solids 29(5–6):397–412
Rossmanith HP, Shukla A (1981b) Dynamic photoelastic investigation of interaction of stress waves with running cracks. Exp Mech 21(11):415–422
Saharan MR, Mitri HS, Jethwa JL (2006) Rock fracturing by explosive energy: review of state-of-the-art. Fragblast 10(1/2):61–81
Smith DG (1971) A Photoelastic Investigation of Stress-wave Loading of a Crack" SESA Spring Meeting 1971, Salt Lake City, Utah.
Theocaris PS, Katsamanis P (1978) Response of cracks to impact by caustics. Eng Fract Mech 10(2):197–210
Wang ZJ (2003) Experimental investigation on tamped and cavity decoupled explosion in rock-soil by mili-explosive charge.Changsha:National University of Defense Technology
Wang CY, Sun AY, Yang XY et al (2018) Numerical simulation of the interaction of laser-generated rayleigh waves with subsurface cracks. Appl Phys A 124(9):613
Woods RD (1969) A new tool for soil dynamics. J Soil Mech Found Div Asce, 94
Yang RS, Chen C, Yue ZW et al (2018) Dynamic photoelastic investigation of interaction of normal incidence blasting stress waves with running cracks. J China Coal Soc 43(3):638–645
Yang RS, Xu P, Chen C (2019) Interaction between blast stress waves and cracks. Explos Shock Waves 39(8):081102–081111
Yue ZW, Qiu P, Yang RS et al (2017) Stress analysis of the interaction of a running crack and blasting waves by caustics method. Eng Fract Mech 184:339–351
Yue ZW, Qiu P, Yang RS et al (2019) Experimental study on a Mach cone and trailing Rayleigh waves in a stress wave chasing running crack problem. Theor Appl Fract Mech 104:102371
Zhao J, Cai JG, Zhao XB et al (2003) Transmission of elastic P-waves across single fracture with nonlinear normal deformation behavior. Chin J Rock Mech Eng 22(1):9–17
Zhu ZH (1988) Dynamic photoelastic study of stress wave effect on crack propagation. J PLA Univ Sci Technol 04:78–84
Zhu ZH (1993) Dynamic photoelastic investigations of the effect of explosive stress waves on an extending-high speed crack. Explos Shock Waves 13(002):178–185
Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 51974316) and the Fundamental Research Funds for Central Universities (Nos. 2022JCCXLJ01 and 2023ZKPYLJ04).
Funding
This research was supported by the National Natural Science Foundation of China (No. 51974316) and the Fundamental Research Funds for Central Universities (Nos. 2022JCCXLJ01 and 2023ZKPYLJ04). Awards were granted to the author Liyun Yang.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Liu, H., Yang, L., Chen, C. et al. Study on the Interaction Between Blasting Stress Waves with Different Incidence Angles and Crack. Iran J Sci Technol Trans Civ Eng 47, 3591–3608 (2023). https://doi.org/10.1007/s40996-023-01197-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40996-023-01197-5