Dynamic constitutive model of coral sand under blast loading
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摘要: 以珊瑚砂为主要覆盖域的岛礁在面临动力灾变时，确定岛礁工程抵抗极端冲击荷载的阈值至关重要，珊瑚砂的动态本构关系是防护工程设计的关键要素。本文中，根据SHPB实验和静态压缩实验的结果，提出了一种基于应变率强化规律确定珊瑚砂物态方程的方法，并确定了珊瑚砂动态本构模型的参数。分别基于流体弹塑性模型和Perzyna黏塑性帽盖模型，结合LS-DYNA有限元程序，通过对侵彻和爆炸的数值计算，验证了模型的适用性。基于建立的模型，对不同相对密实度的珊瑚砂开展了侵彻和爆炸数值计算，结果表明，密实度对爆炸波的衰减影响较大、对侵彻深度的影响较小。
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关键词:
- 珊瑚砂 /
- 动态本构 /
- LS-DYNA有限元程序 /
- 侵彻 /
- 爆炸
Abstract: Coral sand is widely distributed in the large area of reefs and lagoons in the South China Sea. During the construction of various projects on islands and reefs, the coral sand is extensively used as a local material resource. It is very important to determine the threshold of the reef engineering to resist extreme impact loads when the islands and reefs covered with coral sand was suffered from dynamic disasters such as penetration and explosion. The coral sand dynamic constitutive model is a key component for protection engineering design when engineering calculations are required. Based on the results of SHPB experiment and static compression experiment of coral sand from the previous works, a method was proposed to determine the equation of state of coral sand based on the law of strain rate strengthening effect by comparing the static compression curves and the dynamic compression curves. It has been proved that the average pressure of the compression curve can reach more than 100 MPa by using this fitting method.The parameters of the dynamic constitutive model of coral sand were determined through the processing of a lot of experiment results. Based on the hydrodynamic elasto-plastic model and the Perzyna viscoplastic cap model, combined with the LS-DYNA finite element program, the applicability of the dynamic constitutive models was verified by contrasting the numerical calculations and experimental results of the coral sand suffered from the projectile penetration and the blasting of explosive. According to the established model, numerical calculations of penetration and explosion in coral sand with different compactness levels were carried out using the hydrodynamic elasto-plastic model. The results show that the compactness levels of coral sand have a greater influence on the attenuation of the blasting wave and less on the penetration depth. This is because the poorly graded original coral sand has a smaller measurement difference between the maximum and minimum dry densities.-
Key words:
- coral sand /
- dynamic constitutive /
- LS-DYNA finite element program /
- penetration /
- explosion
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图 1 确定屈服参数的摩尔圆
Figure 1. Mohr’s circle geometry used to determine yield surface parameters
图 3 在不同相对密实度下平均压力与体应变的关系
Figure 3. Average pressure-volumetric strain curves under different compactness levels
图 6 侵彻计算模型网格划分（靶体为部分显示）
Figure 6. Finite element mesh of calculated model (target is partially displayed)
图 8 不同入射速度时速度与深度的关系
Figure 8. Velocity versus penetration depth at different initial velocities
图 9 珊瑚砂在不同时刻的压力场和弹丸产生的磨蚀区
Figure 9. Pressure fields of coral sand at diffident times and scratch area of projectile
图 10 不同压实密度时速度与深度的关系
Figure 10. Velocity versus penetration depth under different compactness levels
图 11 峰值压力的衰减
Figure 11. Calculated and experiment results of peak pressure attenuation
图 14 不同相对密度时爆炸峰值压力与比例距离的关系
Figure 14. Peak pressure versus scaled distance under different compactness levels
表 1 当
Dr=0.30 时珊瑚砂的5#材料模型参数Table 1. Parameters of 5# constitutive model for coral sand when
Dr=0.30 ρ/（g·cm−3） G/MPa Ku/MPa a0/kPa2 a1/kPa a2 1.178 107.7 647.3 84.77 16.23 0.777 ln（V/V0） 0 0.02 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 p/MPa 0 2.3 5.8 8.5 11.7 15.83 21.03 36.43 62.23 105.09 
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表 2 当
Dr=0.60 时珊瑚砂的5#材料模型参数Table 2. Parameters of 5# constitutive model for coral sand when
Dr=0.60 ρ/（g·cm−3） G/MPa Ku/MPa a0/kPa2 a1/kPa a2 1.219 125.2 698.7 84.77 16.23 0.777 ln（V/V0） 0 0.02 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 p/MPa 0 3.0 7.5 10.4 14.0 18.9 25.6 45.0 77.2 132.3
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表 3 当
Dr=0.90 时珊瑚砂的5#材料模型参数Table 3. Parameters of 5# constitutive model for coral sand when
Dr=0.90 ρ/（g·cm−3） G/MPa Ku/MPa a0/kPa2 a1/kPa a2 1.260 158.9 717.2 84.77 16.23 0.777 ln（V/V0） 0 0.02 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 p/MPa 0 3.66 8.43 10.87 14.51 19.56 26.48 46.89 82.18 141.09
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表 4 当
Dr=0.30 时珊瑚砂Perzyna黏塑性帽盖模型参数Table 4. Perzyna viscoplastic cap model parameters of coral sand when
Dr=0.30 K/MPa G/MPa α/kPa β/MPa−1 γ/kPa θ T/kPa 125.2 101.1 32.5 2.207 165 0.416 1.2 W D/GPa−1 R X0/kPa η/μs−1 f0/GPa N 0.365 5.58 5.15 10 0.02 120 1.0
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[1] 任辉启, 黄魁, 朱大明, 等. 南沙群岛珊瑚礁工程地质研究综述 [J]. 防护工程, 2015, 37(1): 63–78.REN H Q, HUANG K, ZHU D M, et al. Review of engineering geology of coral reef in Nansha Islands [J]. Protective Engineering, 2015, 37(1): 63–78. [2] 王建平, 马林建. 岛礁工程长期安全保障理论与技术研究进展 [J]. 防护工程, 2019, 41(3): 70–78.WANG J P, MA L J. Research progress of long-term safety theory and technology for reef engineering [J]. Protective Engineering, 2019, 41(3): 70–78. [3] 孙吉主, 汪稔. 钙质砂的耦合变形机制与本构关系探讨 [J]. 岩石力学与工程学报, 2002, 21(8): 1262–1266. DOI: 10.3321/j.issn:1000-6915.2002.08.030.SUN J Z, WANG R. Study on coupling deformation mechanism and constitutive relation for calcareous sand [J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21(8): 1262–1266. DOI: 10.3321/j.issn:1000-6915.2002.08.030. [4] 谷建晓, 杨钧岩, 王勇, 等. 基于南水模型的钙质砂应力-应变关系模拟 [J]. 岩土力学, 2019, 40(12): 4597–4606. DOI: 10.16285/j.rsm.2018.2087.GU J X, YANG J Y, WANG Y, et al. Simulation of carbonate sand with triaxial tests data based on modified model of south water double yield surface [J]. Rock and Soil Mechanics, 2019, 40(12): 4597–4606. DOI: 10.16285/j.rsm.2018.2087. [5] 曹梦, 叶剑红. 中国南海钙质砂蠕变-应力-时间四参数数学模型 [J]. 岩土力学, 2019, 40(5): 1771–1777. DOI: 10.16285/j.rsm.2018.1267.CAO M, YE J H. Creep-stress-time four parameters mathematical model of calcareous sand in South China Sea [J]. Rock and Soil Mechanics, 2019, 40(5): 1771–1777. DOI: 10.16285/j.rsm.2018.1267. [6] LV Y R, LIU J G, XIONG Z M. One-dimensional dynamic compressive behavior of dry calcareous sand at high strain rates [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2019, 11(1): 192–201. DOI: 10.1016/j.jrmge.2018.04.013. [7] LV Y R, WANG Y, ZUO D J. Effects of particle size on dynamic constitutive relation and energy absorption of calcareous sand [J]. Powder Technology, 2019, 356: 21–30. DOI: 10.1016/j.powtec.2019.07.088. [8] XIAO Y, LIU H, XIAO P, et al. Fractal crushing of carbonate sands under impact loading [J]. Géotechnique Letters, 2016, 6(3): 199–204. DOI: 10.1680/jgele.16.00056. [9] LV Y R, LI X, WANG Y. Particle breakage of calcareous sand at high strain rates [J]. Powder Technology, 2020, 336: 776–787. DOI: 10.1016/j.powtec.2020.02.062. [10] 徐学勇. 饱和钙质砂爆炸响应动力特性研究[D]. 武汉: 中国科学院武汉岩土力学研究所, 2009. [11] 曾惠泉, 杨秀敏, 焦云鹏, 等. 触地爆炸流体弹塑性模型数值计算 [J]. 爆炸与冲击, 1982, 2(2): 45–54.ZENG H Q, YANG X M, JIAO Y P, et al. The hydrodynamic elasto-plastic model calculation of the contact-burst ground shock [J]. Explosion and Shock Waves, 1982, 2(2): 45–54. [12] 温垚珂, 徐诚, 陈爱军. 高应变率下弹道明胶的本构模型研究 [J]. 兵工学报, 2014, 35(1): 128–133. DOI: 10.3969/j.issn.1000-1093.2014.01.019.WEN Y K, XU C, CHEN A J. Study of constitutive model of ballistic gelatin at high strain rate [J]. Acta Armamentarii, 2014, 35(1): 128–133. DOI: 10.3969/j.issn.1000-1093.2014.01.019. [13] TONG X L, TUAN C Y. Viscoplastic cap model for soils under high strain rate loading [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133(2): 206–214. DOI: 10.1061/(ASCE)1090-0241(2007)133:2(206). [14] 丁育青. 非饱和黏土动态力学特性及其本构关系研究[D]. 长沙: 国防科学技术大学, 2013. [15] Livermore Software Technology Corporation. LS-DYNA keyword user’s manual: volume II: material models: version 971 R6.0. 0 [Z]. Livermore Software Technology Corporation, 2012. [16] WANG J. Simulation of landmine explosion using LS-DYNA3D software: benchmark work of simulation of explosion in soil and air [R]. Australia: Weapons Systems Division Aeronautical and Maritime Research Laboratory, 2001. [17] FASANELLA E L, LYLE K H, JACKSON K E. Developing soil models for dynamic impact simulations[C] // Proceedings of the American Helicopter Society 65th Annual Forum. Grapevine, TX, 2009: 27–29. [18] 王志鹏, 李海超, 周双涛, 等. 黄土中爆炸空腔体积规律的数值模拟 [J]. 爆破, 2016, 33(4): 73–77, 126. DOI: 10.3963/j.issn.1001-487X.2016.04.013.WANG Z P, LI H C, ZHOU S T, et al. Numerical simulation of cavity volume rule of explosion in loess [J]. Blasting, 2016, 33(4): 73–77, 126. DOI: 10.3963/j.issn.1001-487X.2016.04.013. [19] 马林. 钙质土的剪切特性试验研究 [J]. 岩土力学, 2016, 37(S1): 309–316. DOI: 10.16285/j.rsm.2016.S1.041.MA L. Experimental study of shear characteristics of calcareous gravelly soil [J]. Rock and Soil Mechanics, 2016, 37(S1): 309–316. DOI: 10.16285/j.rsm.2016.S1.041. [20] 王亚松, 马林建, 李增, 等. 钙质砂强度与变形机制研究 [J]. 防护工程, 2018, 40(4): 31–35.WANG Y S, MA L J, LI Z, et al. Investigation on the deformation mechanism of calcareous sand [J]. Protective Engineering, 2018, 40(4): 31–35. [21] WRIGHT A. Tyre/soil interaction modelling within a virtual proving ground environment[D]. Cranfield: Cranfield University, 2012. [22] 文祝, 邱艳宇, 紫民, 等. 钙质砂的准一维应变压缩试验研究 [J]. 爆炸与冲击, 2019, 39(3): 033101. DOI: 10.11883/bzycj-2018-0015.WEN Z, QIU Y Y, ZI M, et al. Experimental study on quasi-one-dimensional strain compression of calcareous sand [J]. Explosion and Shock Waves, 2019, 39(3): 033101. DOI: 10.11883/bzycj-2018-0015. [23] 董凯, 任辉启, 阮文俊, 等. 珊瑚砂应变率效应研究 [J]. 爆炸与冲击, 2020, 40(9): 093102. DOI: 10.11883/bzycj-2019-0432.DONG K, REN H Q, RUAN W J, et al. Study on strain rate effect of coral sand [J]. Explosion and Shock Waves, 2020, 40(9): 093102. DOI: 10.11883/bzycj-2019-0432. [24] 席道瑛, 徐松林. 岩石物理与本构理论[M]. 合肥: 中国科学技术大学出版社, 2016. [25] 苗伟伟, 邱艳宇, 程怡豪, 等. 钙质砂侵彻试验与理论研究 [J]. 振动与冲击, 2019, 38(17): 232–237. DOI: 10.13465/j.cnki.jvs.2019.17.032.MIAO W W, QIU Y Y, CHENG Y H, et al. Penetration tests of calcareous sand and theoretical study [J]. Journal of Vibration and Shock, 2019, 38(17): 232–237. DOI: 10.13465/j.cnki.jvs.2019.17.032. [26] SHI C C, WANG M Y, ZHANG K L, et al. Semi-analytical model for rigid and erosive long rods penetration into sand with consideration of compressibility [J]. International Journal of Impact Engineering, 2015, 83: 1–10. DOI: 10.1016/j.ijimpeng.2015.04.007. [27] OMIDVAR M, MALIOCHE J D, BLESS S, et al. Phenomenology of rapid projectile penetration into granular soils [J]. International Journal of Impact Engineering, 2015, 85: 146–160. DOI: 10.1016/j.ijimpeng.2015.06.002. [28] 苗伟伟, 程怡豪, 文祝, 等. 不同头部形状弹体侵彻石英砂的试验研究 [J]. 防护工程, 2017, 39(5): 6–12.MIAO W W, CHENG Y H, WEN Z, et al. Experimental study on the penetration into silica sand by projectiles with different nose shape [J]. Protective Engineering, 2017, 39(5): 6–12. [29] 赵章泳, 邱艳宇, 王明洋, 等. 非饱和钙质砂中平面爆炸波传播试验研究 [J]. 防护工程, 2017, 39(3): 22–28.ZHAO Z Y, QIU Y Y, WANG M Y, et al. Experimental study on plane explosive wave propagation in unsaturated calcareous sand [J]. Protective Engineering, 2017, 39(3): 22–28. [30] 于潇, 陈力, 方秦. 一种量测松散介质对应力波衰减效应的实验方法及其在珊瑚砂中的应用 [J]. 工程力学, 2019, 36(1): 44–52; 69. DOI: 10.6052/j.issn.1000-4750.2017.11.0867.YU X, CHEN L, FANG Q. A testing method on the attenuation of stress waves in loose porous media and its application to coral sand [J]. Engineering Mechanics, 2019, 36(1): 44–52; 69. DOI: 10.6052/j.issn.1000-4750.2017.11.0867. [31] YU X, CHEN L, FANG Q, et al. Determination of attenuation effects of coral sand on the propagation of impact-induced stress wave [J]. International Journal of Impact Engineering, 2019, 125: 63–82. DOI: 10.1016/j.ijimpeng.2018.11.004. [32] 王礼立, 董新龙. 聊聊动态塑性和黏塑性 [J]. 爆炸与冲击, 2020, 40(3): 031101. DOI: 10.11883/bzycj-2020-0024.WANG L L, DONG X L. Talk about dynamic plasticity and viscoplasticity [J]. Explosion and Shock Waves, 2020, 40(3): 031101. DOI: 10.11883/bzycj-2020-0024. [33] 崔溦, 宋慧芳, 张社荣, 等. 爆炸荷载作用下土中爆坑形成的数值模拟 [J]. 岩土力学, 2011, 32(8): 2523–2528. DOI: 10.3969/j.issn.1000-7598.2011.08.045.CUI W, SONG H F, ZHANG S R, et al. Numerical simulation of craters produced by explosion in soil [J]. Rock and Soil Mechanics, 2011, 32(8): 2523–2528. DOI: 10.3969/j.issn.1000-7598.2011.08.045. [34] ESMAEILI M, TAVAKOLI B. Finite element method simulation of explosive compaction in saturated loose sandy soils [J]. Soil Dynamics and Earthquake Engineering, 2019, 116: 446–459. DOI: 10.1016/j.soildyn.2018.09.048. -
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