Abstract
A comprehensive literature review has been carried out on existing models that characterize soil response under the impact of blast shock waves. Various models in the literature are reviewed and discussed in terms of their equations of state that account for the effect of high pressure, failure models that control the yield behaviour, and strength models that represent the effect of high strain-rates, along with a comparison of their advantages and limitations. Then, the application of different soil models to blast-induced liquefaction is elucidated and compared. Consequently, this review provides a comprehensive understanding of the fundamental and unique aspects of modelling soil response subjected to such transient impulsive loading on the grounds of increasing global interest in blast response of soils.
Similar content being viewed by others
References
Akiyoshi T, Fuchida K, Matsumoto H, Hyodo T, Fang HL (1993) Liquefaction analyses of sandy ground improved by sand compaction piles. Soil Dyn Earthq Eng 12:299–307
Al-Qasimi EMA, Charlie WA, Woeller DJ (2005) Canadian liquefaction experiment (CANLEX): blast–induced ground motion and pore pressure experiments. Geotech Test J 28(1):1–13
An J (2010). Soil behavior under blast loading. PhD thesis, University of Nebraska–Lincoln, Lincoln
An J, Tuan CY, Cheeseman BA, Gazonas GA (2011) Simulation of soil behavior under blast loading. Int J Geomech ASCE 11:323–334
Aráoz G, Luccioni B (2015) Modeling concrete like materials under severe dynamic pressures. Int J Impact Eng 76:139–154
Ashford SA, Rollins KM, Lane JD (2004) Blast-induced liquefaction for full-scale foundation testing. J Geotech Geoenviron Eng ASCE 8:798–806
Awad AA (1990). A numerical model for blast–induced liquefaction using displacements–pore pressure formulations. PhD thesis, Colorado State University, Fort Collins
Baron ML, Nelson I, Sandler I (1973) Influence of constitutive models on ground motion predictions. J Eng Mech Div 99:1181–1200
Biot MA (1956a) Theory of propagation of elastic waves in a fluid saturated porous solid. I. Low frequency range. J Acoust Soc Am 28(2):168–178
Biot MA (1956b) Theory of propagation of elastic waves in a fluid saturated porous solid. II. Higher-frequency range. J Acoust Soc Am 28(2):179–191
Biot MA (1962a) Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33(4):1482–1498
Biot MA (1962b) Generalized theory of acoustic propagation in porous dissipative media. J Acoust Soc Am 34(5):1254–1264
Bloom F (2006) Constitutive models for wave propagation in soil. Appl Mech Rev 59:146–175
Bolton JM, Durnford DS, Charlie WA (1994) One–dimensional shock and quasi–static liquefaction of silt and sand. J Geotech Eng, ASCE 120:1874–1888
Bretz TE (1990). Soil liquefaction resulting from blast-induced spherical stress waves. Final Rep. No. WL-TR-89-100, Weapons Laboratory, Air Force Systems Command
Busch CL, Aimone-martin CT, Tarefder RA (2016) Experimental evaluation and finite–element simulations of explosive airblast tests on clay soils. Int J Geomech ASCE 16:04015097
Cai M, Kaiser PK, Suorineni F, Su K (2007) A study on the dynamic behavior of the Meuse/Haute–Marne argillite. Phys Chem Earth 32:907–916
Casagrande A, Shannon WL (1948) Strength of soils under dynamic loads. Proc Am Soc Civ Eng 74(4):591–608
Charlie WA, Doehring DO (2007) Ground water table mounding, pore pressure, and liquefaction induced by explosions: engery-distance relations. Rev Geophys 45:1–9
Charlie WA, Doehring DO, Veyera GE, Hassen HA (1988). Blast induced liquefaction of soils: laboratory and field tests. Final Rep., USAF Office of Scientific Research, Bolling AFB, Washington, DC
Charlie W, Veyera GE, Durnford DS, Doehring DO (1996) Porewater pressure increases in soil and rock from underground chemical and nuclear explosions. Eng Geol 43(4):225–236
Charlie WA, Bretz TE, Schure LA, Doehring DO (2013) Blast–induced pore pressure and liquefaction of saturated sand. J Geotech Geoenviron Eng ASCE 139(8):1308–1319
Chen WF, Baladi GY (1985) Soil plasticity: theory and implementation. Elsevier, Amsterdam
DiMaggio FL, Sandler IS (1971) Material models for granular soils. J Eng Mech Div 97:935–950
Dolarevic S, Ibrahimbegovic A (2007) A modified three–surface elasto–plastic cap model and its numerical implementation. Comput Struct 85:419–430
Dowding CH, Hryciw RD (1986) A laboratory study of blast densification of saturated sand. J Geotech Eng 112(2):187–199
Drake JL, Little CD (1983) Ground shock from penetrating conventional weapons. In: Proc symp on the interaction of non-nuclear munitions with structures, US Air Force Academy, Colorado Springs, pp 1–6
Duvaut G, Lions JL (1972) Les Inequations en Mechanique et en Physique. Dunos, Paris
Feldgun VR, Kochetkov AV, Karinski YS, Yankelevsky DZ (2008a) Internal blast loading in a buried lined tunnel. Int J Impact Eng 35(3):172–183
Feldgun VR, Kochetkov AV, Karinski YS, Yankelevsky DZ (2008b) Blast response of a lined cavity in a porous saturated soil. Int J Impact Eng 35(9):953–966
Feldgun VR, Karinski YS, Yankelevsky DZ (2011) Blast pressure distribution on a buried obstacle in a porous wet soil. Int J Prot Struct 2(1):45–70
Feldgun VR, Karinski YS, Yankelevsky DZ (2013) A coupled approach to simulate the explosion response of a buried structure in a soil-rock layered medium. Int J Prot Struct 4(3):231–292
Feldgun VR, Karinski YS, Yankelevsky DZ (2014) Riemann solver for irreversibly compressible three-phase porous media. Int J Numer Anal Methods Geomech 38:406–440
Fragaszy RJ, Voss ME (1981). Laboratory verification of blast–induced liquefaction mechanism. Final Report ADA109000, US Air Force Office of Scientific Research, Washington, DC
Fragaszy RJ, Voss ME (1986) Undrained compression behavior of sand. J Geotech Eng ASCE 112(3):334–347
Ghaboussi J, Kim KJ (1984) Quasistatic and dynamic analysis of saturated and partially saturated soils. In: Desai CS, Gallagher RH (eds) Mechanics of engineering materials. Wiley, Somerset, pp 277–296
Ghassemi A, Pak A, Shahir H (2010) Numerical study of the coupled hydro–mechanical effects in dynamic compaction of saturated granular soils. Comput Geotech 37:10–24
Grujicic M, Pandurangan B, Cheeseman BA (2006) The effect of degree of saturation of sand on detonation phenomena associated with shallow-buried and ground-laid mines. Shock Vib 13:41–61
Grujicic M, Pandurangan B, Cheeseman BA, Roy WN, Skaggs RR, Gupta R (2008a) Parameterization of the porous–material model for sand with various degrees of water saturation. Soil Dyn Earthq Eng 28:20–35
Grujicic M, Pandurangan B, Coutris N, Cheeseman BA, Roy WN, Skaggs RR (2008b) Computer-simulations based development of a high strain–rate, large–deformation, high-pressure material model for STANAG 4569 sandy gravel. Soil Dyn Earthq Eng 28:1045–1062
Grujicic M, Pandurangan B, Coutris N, Cheeseman BA, Roy WN, Skaggs RR (2009) Derivation and validation of a material model for clayey sand for use in landmine detonation computational analysis. Multidiscip Model Mater Struct 5:311–344
Grujicic M, Pandurangan B, Coutris N, Cheeseman BA, Roy WN, Skaggs RR (2010) Derivation, parameterization and validation of a sandy–clay material model for use in landmine detonation computational analyses. J Mater Eng Perform 19(3):434–450
Gu Q, Lee FH (2002) Ground response to dynamic compaction of dry sand. Géotechnique 52(7):481–493
Henrych J (1979) The dynamics of explosion and its use. Elsevier, New York
Higgins W, Chakraborty T, Basu D (2013) A high strain-rate constitutive model for sand and its application in finite-element analysis of tunnels subjected to blast. Int J Numer Anal Methods Geomech 37(15):2590–2610
Ivanov PL (1967) Compaction of noncohesive soils by explosions. US Department of the Interior, Bureau of Reclamation and Natrual Science Foundation, Washington, DC
Jackson JG, Rohani B, Ehrgot JQ (1980) Loading rate effects on compressibility of sand. J Geotech Eng Div 106(8):839–852
Karinski YS, Feldgun VR, Yankelevsky DZ (2009a) Explosion-induced dynamic soil–structure interaction analysis with the coupled Godunov-variational difference approach. Int J Numer Methods Eng 77:824–851
Karinski YS, Feldgun VR, Yankelevsky DZ (2009b) Effect of soil locking on the cylindrical shock wave’s peak pressure attenuation. J Eng Mech ASCE 135(10):1166–1180
Katona MG (1984) Evaluation of viscoplastic cap model. J Geotech Eng ASCE 110(8):1106–1125
Khoei AR, Mohammadnejad T (2011) Numerical modeling of multiphase fluid flow in deforming porous media: a comparison between two- and three-phase models for seismic analysis of earth and rockfill dams. Comput Geotech 38:142–166
Khoei AR, Azami AR, Haeri SM (2004) Implementation of plasticity based models in dynamic analysis of earth and rockfill dams: a comparison of Pastor–Zienkiewicz and cap models. Comput Geotech 31(5):384–409
Kim KJ, Blouin SE (1996) Response of saturated porous nonlinear materials to dynamic loadings. Final Report ADA148528, US Air Force Office of Scientific Research, Washington, DC, 1984
Krajcinovic D (1996) Damage mechanics. Elsevier, New York
Kumar R, Choudhury D, Bhargava K (2014) Prediction of blast-induced vibration parameters for soil sites. Int J Geomech 14(3):341–349
Laine P, Sandvik A (2001). Derivation of mechanical properties for sand. In: Proceedings of the 4th Asia–Pacific conference on shock and impact loads on structures, Singapore, pp 361–368
Lee WY (2006) Numerical modeling of blast induced liquefaction. PhD thesis, Brigham Young University, Provo
Leong EC, Anand S, Cheong HK, Lim CH (2007) Reexamination of peak stress and scaled distance due to ground shock. Int J Impact Eng 34(9):1487–1499
Lewis BA (2004) Manual for LS–DYNA soil material model 147. Federal highway administration. Publication No. FHWA–HRT–095, McLean
Li X, Zienkiewicz OC (1992) Multiphase flow in deforming porous media and finite element solutions. Comput Struct 45:211–227
Li X, Thomas HR, Fan Y (1999) Finite element method and constitutive modeling and computation for unsaturated soils. Comput Methods Appl Mech Eng 169:135–159
Livermore Software Technology Corporation (LSTC) (2007) LS–DYNA Keyword user’s manual, Version 971, Livermore
Loukidis D (2006). Advanced constitutive modeling of sands and applications to foundation engineering. PhD thesis, Purdue University, West Lafayette
Lu G, Fall M (2016) A coupled chemo-viscoplastic cap model for simulating the behaviour of hydrating cemented tailings backfill under blast loading. Int J Numer Anal Methods Geomech 40:1123–1149
Lu G, Fall M (2017) Modelling blast wave propagation in a subsurface geotechnical structure made of an evolutive porous material. Mech Mater 108:21–39
Lu Y, Wang Z, Chong K (2005) A comparative study of buried structure in soil subjected to blast load using 2D and 3D numerical simulations. Soil Dyn Earthq Eng 25:275–288
Lundborg N (1968) Strength of rock-like materials. Int J Rock Mech Min Sci 5:427–454
Lyakhov GM (1974) Fundamentals of the dynamics of detonation waves in soils and rock. Nedra, Moscow
Lyakhov GM, Okhitin VN (1977a) Nonstationary plane waves in media with bulk viscosity. J Appl Mech Tech Phys 18(5):693–700
Lyakhov GM, Okhitin VN (1977b) Plane waves in nonlinear viscous multicomponent media. J Appl Mech Tech Phys 18(2):241–248
Manzari MT, Dafalias YF (1997) A critical state two-surface plasticity model for sands. Géotechnique 47(2):255–272
Merkle DH, Dass WC (1985) Fundamental properties of soils for complex dynamic loadings. Final Report ADA164206, US Air Force Office of Scientific Research. Washington, DC
Murray YD (2007) Users manual for LS–DYNA concrete material model 159. Report FHWA–HRT–05–062, Federal Highway Administration, McLean
Murray YD, Lewis BA (1995) Numerical simulation of damage in concrete. Report DNA–TR–94–190, Defense Nuclear Agency, Alexandria
Nelson I, Baladi GY (1977) Outrunning ground shock computed with different models. J Eng Mech Div 103(3):377–393
Nelson I, Baron ML, Sandler I (1971) Mathematical models for geological materials for wave-propagation studies. Report DASA2672, Defense Nuclease Agency, Washington, DC
Omidvar M, Iskander M, Bless S (2012) Stress–strain behavior of sand at high strain rates. Int J Impact Eng 49:192–213
Perzyna P (1966) Fundamental problems in viscoplasticity. Adv Appl Mech 9:243–377
Prapaharan S, Chameau JL, Holtz RD (1989) Effect of strain rate on undrained strength derived from pressuremeter tests. Geotechnique 39(4):615–624
Puebla H, Byrne PM, Phillips R (1997) Analysis of CANLEX liquefaction embankments: prototype and centrifuge models. Can Geotech J 34:641–657
Sandler IS, Rubin D (1979) An algorithm and a modular subroutine for the cap model. Int J Numer Anal Methods Geomech 3:173–186
Sandler IS, DiMaggio FL, Baladi GY (1976) Generalized cap model for geological materials. J Geotech Eng Div 102:683–699
Schapermeier E (1978) Liquefaction produced by compressional waves. In: Proc int. workshop on blast–induced liquefaction, Dames and Moore/US Air Force Maidenhead, UK, pp 57–64
Schrefler BA, Scotta R (2001) A fully coupled dynamic model for two-phase fluid flow in deformable porous media. Comput Methods Appl Mech Eng 190:3223–3246
Schwer LE (1994) Viscoplastic augmentation of the smooth cap model. Nucl Eng Des 150:215–223
Schwer LE, Murray YD (1994) A three-invariant smooth cap model with mixed hardening. Int J Numer Anal Methods Geomech 18:657–688
Semblat JF, Luong MP, Gary G (1999) 3d-Hopkinson bar: new experiments for dynamic testing on soils. Soils Found 39(1):1–10
Simo JC, Wu JW, Pister KS, Taylor RL (1986) Assessment of cap model: consistency return algorithms and rate-dependent extension. J Eng Mech, ASCE 114(2):191–218
Simo JC, Kennedy JG, Govindjee S (1988) Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms. Int J Numer Methods Eng 26:2161–2185
Taiebat M, Dafalias YF (2008) SANISAND: simple anisotropic sand plasticity model. Int J Numer Anal Methods Geomech 32(8):915–948
Tong X, Tuan CY (2007) Viscoplastic cap model for soils under high strain rate loading. J Geotech Geoenviron Eng ASCE 133(2):206–214
Tu Z, Lu Y (2009) Evaluation of typical concrete material models used in hydrocodes for high dynamic response simulations. Int J Impact Eng 36(1):132–146
Veyera GE, Charlie WA (1990) Laboratory study of compressional liquefaction. J Geotech Eng 116:790–804
Veyera GE, Charlie WA, Hubert ME (2002) One–dimensional shock-induced pore pressure response in saturated carbonate sand. Geotech Test J 25(3):277–288
Wang Z, Lu Y (2003) Numerical analysis on dynamic deformation mechanism of soils under blast loading. Soil Dyn Earthq Eng 23:705–714
Wang Z, Hao H, Lu Y (2004a) A three-phase soil model for simulating stress wave propagation due to blast loading. Int J Numer Anal Methods Geomech 28:33–56
Wang Z, Lu Y, Hao H (2004b) Numerical investigation of effects of water saturation on blast wave propagation in soil mass. J Eng Mech ASCE 130(5):551–561
Wang Z, Lu Y, Bai C (2008) Numerical analysis of blast-induced liquefaction of soil. Comput Geotech 5:196–209
Wang ZL, Konietzky H, Huang RY (2009) Elastic–plastic–hydrodynamic analysis of crater blasting in steel fiber reinforced concrete. Theor Appl Fract Mech 52:111–116
Wang Z, Lu Y, Bai C (2011) Numerical simulation of explosion-induced soil liquefaction and its effect on surface structures. Finite Elem Anal Des 47(9):1079–1090
Whitman RV (1970) The response of soils to dynamic loading. Final Report AD708625, US Army Engineer Waterways Experiment Station, Vicksburg
Xu TH, Zhang LM (2015) Numerical implementation of a bounding surface plasticity model for sand under high strain-rate loadings in LS–DYNA. Comput Geotech 66:203–218
Yamamuro JA, Lade PV (1993) Effects of strain rate on instability of granular soils. Geotech Test J 16(3):304–313
Yankelevsky DZ, Feldgun VR, Karinski YS (2008) Underground explosion of a cylindrical charge near a buried wall. Int J Impact Eng 35(8):905–919
Zhang HW, Sanavia L, Schre BA (2001) Numerical analysis of dynamic strain localisation in initially water saturated dense sand with a modified generalised plasticity model. Comput Struct 79:441–459
Zienkiewicz OC, Shiomi T (1984) Dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerical solution. Int J Numer Anal Methods Geomech 8:71–96
Zienkiewicz OC, Chan AHC, Pastor M, Paul DK, Shiomi T (1990a) Static and dynamic behavior of soils: a rational approach to quantitative solution, I. Fully saturated problems. Proc R Soc Lond 429:285–309
Zienkiewicz OC, Xie YM, Schrefler BA, Ledesma A, Bicanic N (1990b) 1990b. Static and dynamic behavior of soils: a rational approach to quantitative solution, II. Semi-saturated problems. Proc R Soc Lond 429:311–321
Zukas JA (2004) Introduction to hydrocodes. Elsevier, Kidlington
Acknowledgements
Gongda Lu is grateful to the China Scholarship Council (CSC) for providing a scholarship for his study in Canada. The authors would like to thank the University of Ottawa and the National Natural Sciences and Engineering Research Council of Canada (NSERC) for supporting this project.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, G., Fall, M. State-of-the-Art Modelling of Soil Behaviour Under Blast Loading. Geotech Geol Eng 36, 3331–3355 (2018). https://doi.org/10.1007/s10706-018-0560-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10706-018-0560-5