Please wait a minute...
Shopping Cart Email List Chinese
Advanced Search Fig/Tab
Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

Postal Subscription Code 80-968

2018 Impact Factor: 1.272

Featured Articles  |  Most Downloaded  |  Most Reading
Online Submission Subscribe to Our RSS Content Feed
Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (6) : 1350-1362    https://doi.org/10.1007/s11709-019-0559-x
RESEARCH ARTICLE
Centrifuge experiment and numerical analysis of an air-backed plate subjected to underwater shock loading
Zhijie HUANG1,2,3,4, Xiaodan REN4(), Zuyu CHEN1,2,3, Daosheng LING1,2
1. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058, China
2. Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China
3. China Institute of Water Resources and Hydropower Research, Beijing 100048, China
4. School of Civil Engineering, Tongji University, Shanghai 200092, China
 Download: PDF(2809 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

In this study, systematic centrifuge experiments and numerical studies are conducted to investigate the effect of shock loads due to an underwater explosion on the dynamic responses of an air-backed steel plate. Numerical simulations with three different models of pressure time history generated by underwater explosion were carried out. The first model of pressure time history was measured in test. The second model to predict the time history of shock wave pressure from an underwater explosion was created by Cole in 1948. Coefficients of Cole’s formulas are determined experimentally. The third model was developed by Zamyshlyaev and Yakovlev in 1973. All of them are implemented into the numerical model to calculate the shock responses of the plate. Simulated peak strains obtained from the three models are compared with the experimental results, yielding average relative differences of 21.39%, 45.73%, and 13.92%, respectively. The Russell error technique is used to quantitatively analyze the correlation between the numerical and experimental results. Quantitative analysis shows that the simulated strains for most measurement points on the steel plate are acceptable. By changing the scaled distances, different shock impulses were obtained and exerted on the steel plate. Systematic numerical studies are performed to investigate the effect of the accumulated shock impulse on the peak strains. The numerical and experimental results suggest that the peak strains are strongly dependent on the accumulated shock impulse.
Keywords underwater explosion      centrifuge experiment      shock load      dynamic response      accumulated shock impulse     
Corresponding Author(s): Xiaodan REN   
Just Accepted Date: 24 June 2019   Online First Date: 27 August 2019    Issue Date: 21 November 2019
 Cite this article:   
Zhijie HUANG,Xiaodan REN,Zuyu CHEN, et al. Centrifuge experiment and numerical analysis of an air-backed plate subjected to underwater shock loading[J]. Front. Struct. Civ. Eng., 2019, 13(6): 1350-1362.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-019-0559-x
https://academic.hep.com.cn/fsce/EN/Y2019/V13/I6/1350
Fig.1  Test model. (a) 1/2 schematic of model with dimensions (in mm) [36]; (b) actual model.
Fig.2  Layout of transducers on the downstream surface.
group UNDEX- W (g) G (g) D (m) R (mm) Pm (MPa) q (ms) L (mm)
I 3 1.025 40 0.30 350 17.62 8.175 300
4 1.023 40 0.30 350 18.17 7.437 300
6 1.015 40 0.30 300 21.48 9.621 200
9 1.024 40 0.30 250 25.45 9.206 250
10 1.010 40 0.30 175 36.99 7.684 150
11 1.025 40 0.30 150 49.32 7.344 50
II 1 1.020 20 0.30 350 19.44 9.514 300
2 1.021 30 0.30 350 18.31 10.077 300
5 1.038 50 0.30 350 19.34 10.233 300
7 1.040 40 0.20 300 21.29 9.900 200
8 1.016 20 0.20 300 20.19 9.229 200
15 0.050 20 0.30 350 3.47 8.953 300
13 0.050 30 0.25 353.6 3.07 9.192 300
12 0.150 20 0.375 357.9 5.83 10.639 300
14 0.150 40 0.30 350 4.99 10.429 300
Tab.1  Test cases
Fig.3  History of the measured shock wave pressure of UNDEX-9.
Fig.4  Relationship between (a) peak pressure (data come from Group I) and (b) time delay constant with scaled distance.
Fig.5  Histories of the shock loads.
item measured Cole Zamyshlyaev
peak pressure (MPa) 25.45 26.12 22.30
relative difference Dr – 2.6% 12.4%
Tab.2  Peak pressure
Fig.6  Numerical model of the experiments.
material density (kg/m3) Young’s/bulk modulus (GPa) Poisson’s ratio
steel plate 8714 206 0.3
cement sand 2400 29.5 0.3
water 1000 2.14 –
Tab.3  Material parameters
Fig.7  Strain time histories of the steel plate with different element sizes. (a) 4-2-x and (b) 4-2-y.
Fig.8  The strain contour of the steel plate on the upstream surface. (a) t = 0.015 ms; (b) t = 0.030 ms; (c) t = 0.076 ms. For the downstream surface: (d) t = 0.015 ms; (e) t = 0.030 ms; (f) t = 0.076 ms.
Fig.9  The time histories of the strain. (a) 3-2-x; (b) 3-2-y; (c) 4-2-x; (d) 4-2-y; (e) 4-3-x; (f) 4-3-y; (g) 5-2-x; (h) 5-2-y; (i) 5-3-x; (j) 5-3-y.
item test (10−6) numerical: measured (10−6) Dr-M (%) numerical: Cole (10−6) Dr-C (%) numerical: Zamyshlyaev (10−6) Dr-Z (%)
3-2-x 137.57 171.57 24.71 54.30 60.53 141.39 2.78
3-2-y 155.68 218.92 40.62 103.87 33.28 186.97 20.10
4-2-x 123.56 147.29 19.21 72.92 40.98 119.11 3.60
4-2-y 216.17 207.82 3.86 108.91 49.62 184.03 14.87
4-3-x 170.14 270.20 58.81 78.07 54.11 218.71 28.55
4-3-y 187.47 242.19 29.19 139.05 25.83 226.56 20.85
5-2-x 115.92 106.14 8.43 52.96 54.31 90.75 21.71
5-2-y 170.50 186.79 9.56 100.66 40.96 171.26 0.45
5-3-x 190.93 203.21 6.43 63.60 66.69 163.84 14.19
5-3-y 184.48 208.55 13.05 127.23 31.03 206.76 12.08
Tab.4  Peak strains of the experimental and numerical results
item measured assessment Cole assessment Zamyshlyaev assessment
3-2-x 0.207 acceptable 0.645 poor 0.222 acceptable
3-2-y 0.287 poor 0.473 poor 0.210 acceptable
4-2-x 0.189 good 0.657 poor 0.218 acceptable
4-2-y 0.267 acceptable 0.538 poor 0.211 acceptable
4-3-x 0.210 acceptable 0.634 poor 0.217 acceptable
4-3-y 0.260 acceptable 0.504 poor 0.173 good
5-2-x 0.335 poor 0.757 poor 0.354 poor
5-2-y 0.245 acceptable 0.534 poor 0.197 good
5-3-x 0.297 poor 0.718 poor 0.319 poor
5-3-y 0.239 acceptable 0.540 poor 0.216 acceptable
Tab.5  Comprehensive errors RC of the strains of three numerical results
Fig.10  The time histories of the (a) pressure impulse and (b) the accumulated shock impulse.
Fig.11  The time histories of the (a) accumulated shock impulse and (b) the corresponding strain 4-2-x.
item Z
(m/kg1/3)		 L (m) W (g) 4-2-x 4-2-y 4-3-x 4-3-y
Ia (Pa·s2) Sm
(10−6)		 Ia (Pa·s2) Sm
(10−6)		 Ia (Pa·s2) Sm
(10−6)		 Ia (Pa·s2) Sm
(10−6)
numerical 1.46 0.25 5.000 0.70 438.51 0.43 493.24 0.63 792.67 0.39 635.39
1.57 0.25 4.000 0.63 381.92 0.38 439.33 0.56 714.43 0.35 563.93
1.73 0.25 3.000 0.54 316.36 0.33 377.74 0.48 615.84 0.30 481.39
1.98 0.25 2.000 0.40 202.70 0.24 270.85 0.36 410.22 0.22 342.83
2.00 0.20 1.000 0.44 157.44 0.22 216.29 0.33 267.71 0.19 287.21
2.50 0.25 1.000 0.34 117.00 0.16 181.54 0.28 213.35 0.14 224.06
3.00 0.30 1.000 0.29 88.33 0.13 150.53 0.26 158.96 0.12 188.19
UNDEX-10 1.50 0.15 1.010 0.52 269.37 0.47 348.02 0.32 279.81 0.47 308.83
UNDEX-6 1.99 0.20 1.015 0.34 202.00 0.31 310.63 0.18 239.11 0.30 267.78
UNDEX-9 2.48 0.25 1.024 0.42 123.56 0.28 216.17 0.16 170.14 0.28 187.47
UNDEX-3 2.98 0.30 1.025 0.27 103.75 0.17 207.44 0.08 156.47 0.16 174.66
UNDEX-4 2.98 0.30 1.023 0.22 140.25 0.17 204.27 0.09 155.04 − −
Tab.6  Peak strains Sm and corresponding accumulated shock impulse Ia
Fig.12  The relationship between the peak strains Sm and the accumulated shock impulse Ia. (a) 4-2-x; (b) 4-2-y; (c) 4-3-x; (d) 4-3-y.
1 J G Kirkwood, H A Bethe. Basic Propagation Theory. OSRD, 1942, 588–595
2 R H Cole. Underwater Explosions. New Jersey: Princeton University Press, 1948
3 A H Keil. The Response of Ships to Underwater Explosions. Washington D.C.: David Taylor Model Basin, 1961
4 W D Reid. The Response of Surface Ships to Underwater Explosions. Defence Science and Technology Organization Canberra, 1996
5 Q K Jin, G Y Ding. A finite element analysis of ship sections subjected to underwater explosion. International Journal of Impact Engineering, 2011, 38(7): 558–566
https://doi.org/10.1016/j.ijimpeng.2010.11.005
6 T Rabczuk, R Gracie, J H Song, T Belytschko. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71
7 N Vu-Bac, T Lahmer, X Y Zhuang, T Nguyen-Thoi, T Rabczuk. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31
https://doi.org/10.1016/j.advengsoft.2016.06.005
8 Y W Kwon, R E Cunningham. Comparison of USA-DYNA finite element models for a stiffened shell subject to underwater shock. Computers & Structures, 1998, 66(1): 127–144
https://doi.org/10.1016/S0045-7949(97)00049-7
9 S W Gong, K Y Lam. Transient response of floating composite ship section subjected to underwater shock. Composite Structures, 1999, 46(1): 65–71
https://doi.org/10.1016/S0263-8223(99)00046-X
10 A M Zhang, W X Zhou, S P Wang, L H Feng. Dynamic response of the non-contact underwater explosions on naval equipment. Marine Structures, 2011, 24(4): 396–411
https://doi.org/10.1016/j.marstruc.2011.05.005
11 A Schiffer, V L Tagarielli. The dynamic response of composite plates to underwater blast: Theoretical and numerical modelling. International Journal of Impact Engineering, 2014, 70: 1–13
https://doi.org/10.1016/j.ijimpeng.2014.03.002
12 Y S Shin. Ship shock modeling and simulation for far-field underwater explosion. Computers & Structures, 2004, 82(23–26): 2211–2219
https://doi.org/10.1016/j.compstruc.2004.03.075
13 J LeBlanc, A Shukla. Dynamic response and damage evolution in composite materials subjected to underwater explosive loading: An experimental and computational study. Composite Structures, 2010, 92(10): 2421–2430
https://doi.org/10.1016/j.compstruct.2010.02.017
14 J LeBlanc, A Shukla. Dynamic response of curved composite panels to underwater explosive loading: Experimental and computational comparisons. Composite Structures, 2011, 93(11): 3072–3081
https://doi.org/10.1016/j.compstruct.2011.04.017
15 Y W Kwon, P K Fox. Underwater shock response of a cylinder subjected to a side-on explosion. Computers & Structures, 1993, 48(4): 637–646
https://doi.org/10.1016/0045-7949(93)90257-E
16 K Cichocki. Effects of underwater blast loading on structures with protective elements. International Journal of Impact Engineering, 1999, 22(6): 609–617
https://doi.org/10.1016/S0734-743X(99)00012-3
17 Z Zong, Y Zhao, H T Li. A numerical study of whole ship structural damage resulting from close-in underwater explosion shock. Marine Structures, 2013, 31: 24–43
https://doi.org/10.1016/j.marstruc.2013.01.004
18 H Arora, P Del Linz, J P Dear. Damage and deformation in composite sandwich panels exposed to multiple and single explosive blasts. International Journal of Impact Engineering, 2017, 104: 95–106
https://doi.org/10.1016/j.ijimpeng.2017.01.017
19 T Rabczuk, T Belytschko. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799
https://doi.org/10.1016/j.cma.2006.06.020
20 T Rabczuk, P M A Areias, T Belytschko. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548
https://doi.org/10.1002/nme.2013
21 T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
https://doi.org/10.1016/j.cma.2010.03.031
22 K M Hamdia, M Silani, X Y Zhuang, P F He, T Rabczuk. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227
https://doi.org/10.1007/s10704-017-0210-6
23 K M Hamdia, H Ghasemi, X Y Zhuang, N Alajlan, T Rabczuk. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Computer Methods in Applied Mechanics and Engineering, 2018, 337: 95–109
https://doi.org/10.1016/j.cma.2018.03.016
24 A De, T F Zimmie. Centrifuge modeling of surface blast effects on underground structures. Geotechnical Testing Journal, 2007, 30(5): 427–431
25 C F Hung, B J Lin, J J Hwang-Fuu, P Y Hsu. Dynamic response of cylindrical shell structures subjected to underwater explosion. Ocean Engineering, 2009, 36(8): 564–577
https://doi.org/10.1016/j.oceaneng.2009.02.001
26 J Li, J L Rong. Experimental and numerical investigation of the dynamic response of structures subjected to underwater explosion. European Journal of Mechanics-B/Fluids, 2012, 32: 59–69
https://doi.org/10.1016/j.euromechflu.2011.09.009
27 K Ramajeyathilagam, C P Vendhan, V B Rao. Non-linear transient dynamic response of rectangular plates under shock loading. International Journal of Impact Engineering, 2000, 24(10): 999–1015
https://doi.org/10.1016/S0734-743X(00)00018-X
28 K Ramajeyathilagam, C P Vendhan. Deformation and rupture of thin rectangular plates subjected to underwater shock. International Journal of Impact Engineering, 2004, 30(6): 699–719
https://doi.org/10.1016/j.ijimpeng.2003.01.001
29 R Rajendran, K Narasimhan. Linear elastic shock response of plane plates subjected to underwater explosion. International Journal of Impact Engineering, 2001, 25(5): 493–506
https://doi.org/10.1016/S0734-743X(00)00056-7
30 C F Hung, P Y Hsu, J J Hwang-Fuu. Elastic shock response of an air-backed plate to underwater explosion. International Journal of Impact Engineering, 2005, 31(2): 151–168
https://doi.org/10.1016/j.ijimpeng.2003.10.039
31 B L Kutter, L M O’Leary, P Y Thompson, R Lather. Gravity-scaled tests on blast-induced soil-structure interaction. Journal of Geotechnical Engineering, 1988, 114(4): 431–447
https://doi.org/10.1061/(ASCE)0733-9410(1988)114:4(431)
32 G Plizzari, F Waggoner, V E Saouma. Centrifuge modeling and analysis of concrete gravity dams. Journal of Structural Engineering, 1995, 121(10): 1471–1479
https://doi.org/10.1061/(ASCE)0733-9445(1995)121:10(1471)
33 H G Snay. The scaling of underwater explosion phenomena. White Oak, MD: Naval Ordnance Lab,1962
34 J Hu, Z Y Chen, X D Zhang, Y Q Wei, X Q Liang, J H Liang, G W Ma, Q S Wang, Y Long. Underwater explosion in centrifuge part I: Validation and calibration of scaling laws. Science China. Technological Sciences, 2017, 60(11): 1638–1657
https://doi.org/10.1007/s11431-017-9083-0
35 W Vanadit-Ellis, L K Davis. Physical modeling of concrete gravity dam vulnerability to explosions. In: Waterside Security Conference (WSS). Carrara, 2010: 1–11
36 G Song, Z Y Chen, Y Long, M S Zhong, J Y Wu. Experimental and numerical investigation of the centrifugal model for underwater explosion shock wave and bubble pulsation. Ocean Engineering, 2017, 142: 523–531
https://doi.org/10.1016/j.oceaneng.2017.04.035
37 Y Long, H Y Zhou, X Q Liang, G Song, Z Y Chen, J Hu, Q S Wang, X D Zhang, J H Liang, Z J Huang. Underwater explosion in centrifuge Part II: Dynamic responses of defensive steel plate. Science China. Technological Sciences, 2017, 60(12): 1941–1957
https://doi.org/10.1007/s11431-017-9107-2
38 B V Zamyshlyaev, Y S Yakovlev. Dynamic Loads in Underwater Explosion. Naval Intelligence Support Center Washington D. C. Translation Div, 1973
39 Z H Zhang, Y Wang, L J Zhang, J H Yuan, H F Zhao. Similarity research of anomalous dynamic response of ship girder subjected to near field underwater explosion. Applied Mathematics and Mechanics, 2011, 32(12): 1491–1504
https://doi.org/10.1007/s10483-011-1518-9
40 Z Zong, Y J Zhao, L Zou. Numerical Computation for Structural Damages of Underwater Explosion. Beijing: Science Press, 2014 (in Chinese)
41 X L Yao, A M Zhang, W J Xu. Application of coupled acoustic-structural analysis to warship underwater explosion. Journal of Harbin Engineering University, 2005, 26(6): 707–712 (in Chinese)
42 Y G Xu, Z Zong, H T Li. Numerical analysis of structure response due to the combined effects of underwater explosion shock wave and bubble pulse. Chinese Journal of Ship Research, 2011, 6(3): 8–11 (in Chinese)
43 D M Russell. Error measures for comparing transient data: Part I: development of a comprehensive error measure. In: Proceedings of the 68th Shock and Vibration Symposium. Hunt Valley, MD, 1997, 175–184
44 A S Lee, B O Kim, Y C Kim. A finite element transient response analysis method of a rotor-bearing system to base shock excitations using the state-space Newmark scheme and comparisons with experiments. Journal of Sound and Vibration, 2006, 297(3–5): 595–615
https://doi.org/10.1016/j.jsv.2006.04.028
[1] Jianling HOU, Weibing XU, Yanjiang CHEN, Kaida ZHANG, Hang SUN, Yan LI. Typical diseases of a long-span concrete-filled steel tubular arch bridge and their effects on vehicle-induced dynamic response[J]. Front. Struct. Civ. Eng., 2020, 14(4): 867-887.
[2] Tian ZHANG, He XIA, Weiwei GUO. Analysis on running safety of train on the bridge considering sudden change of wind load caused by wind barriers[J]. Front. Struct. Civ. Eng., 2018, 12(4): 558-567.
[3] Pengfei LIU, Dawei WANG, Frédéric OTTO, Markus OESER. Application of semi-analytical finite element method to analyze the bearing capacity of asphalt pavements under moving loads[J]. Front. Struct. Civ. Eng., 2018, 12(2): 215-221.
[4] Mehmet Bar?? Can üLKER. Modeling of dynamic response of poroelastic soil layers under wave loading[J]. Front Struc Civil Eng, 2014, 8(1): 1-18.
[5] Linjia BAI, Yunfeng ZHANG. Collapse fragility assessment of steel roof framings with force limiting devices under transient wind loading[J]. Front Struc Civil Eng, 2012, 6(3): 199-209.
[6] Xuexing CAO, Yunlong HE, Kun XIONG, . Confining pressure effect on dynamic response of high rockfill dam[J]. Front. Struct. Civ. Eng., 2010, 4(1): 116-126.
[7] Hanlong LIU, Xuanming DING. Propagation characteristics of transient waves in low-strain integrity testing on cast-in-situ concrete thin-wall pipe piles[J]. Front Arch Civil Eng Chin, 2009, 3(2): 180-186.
[8] He XIA, Yushu DENG, Yongwei ZOU, Guido DE ROECK, Geert DEGRANDE. Dynamic analysis of rail transit elevated bridge with ladder track[J]. Front Arch Civil Eng Chin, 2009, 3(1): 2-8.
[9] LI Liang, DU Xiuli, LI Liyun, ZHAO Chenggang. Explicit finite element method for calculation and analysis to the elasto-plastic dynamic response of fluid-saturated porous media[J]. Front. Struct. Civ. Eng., 2007, 1(4): 436-442.
[10] GUO Weiwei, XIA He, XU You-lin. Dynamic response of a long span suspension bridge and running safety of a train under wind action[J]. Front. Struct. Civ. Eng., 2007, 1(1): 71-79.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed