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Evaluation of dynamic tensile strength of concrete using lattice-based simulations of spalling tests

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Abstract

The mechanical properties and failure modes of concrete are affected by strain rate. Therefore, various experimental methods have been used to quantify the strain-rate dependency of concrete properties, such as the spalling test by using a Hopkinson bar. In the test, pullback velocity at the free-end surface of the specimen is usually measured to evaluate the dynamic tensile strength of concrete, instead of directly measuring the critical stresses at the damaged location(s) due to experimental constraints. Herein, such indirect measurements of tensile strength are compared with direct determinations of tensile strength based on lattice models of the spalling tests. To represent rate-dependent material behavior, rheological units are introduced within the lattice elements. The parameters of the rheological units are calibrated through comparisons with experimental data. The calibrated values remain unchanged in subsequent simulations, which can be regarded as virtual spalling tests at various high strain rates of loading. The separation of viscous and inertial contributions to apparent tensile strength provides insights into the dependence of actual tensile strength on high strain rates. The simulation results indicate indirectly measured dynamic tensile strength, as commonly done in practice, is sufficiently close to directly measured strength.

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References

  • Amini M, Eastwood JW, Hockney RW (1987) Time integration in particle models. Comput Phys Commun 44:83–93

    Article  Google Scholar 

  • Asahina D, Ito K, Houseworth JE, Birkholzer JT, Bolander JE (2015) Simulating the Poisson effect in lattice models of elastic continua. Comput Geotech 70:60–67

    Article  Google Scholar 

  • Asahina D, Aoyagi K, Kim K, Birkholzer JT, Bolander JE (2017) Elastically-homogeneous lattice models of damage in geomaterials. Comput Geotech 81:195–206

    Article  Google Scholar 

  • Berton S, Bolander JE (2006) Crack band model of fracture in irregular lattices. Comput Methods Appl Mech Eng 195:7172–7181

    Article  Google Scholar 

  • Bischoff PH, Perry SH (1991) Compressive behavior of concrete at high strain rates. Mater Struct 24:426–450

    Article  Google Scholar 

  • Bolander JE, Saito S (1998) Fracture analyses using spring networks with random geometry. Eng Fract Mech 61:569–591

    Article  Google Scholar 

  • Bolander JE, Yoshitake K, Thomure J (1999) Stress analysis using elastically uniform Rigid-Body-Spring Networks, Journal of Structural Mechanics and Earthquake Engineering, Japan Society of Civil Engineers, No. 633/I-49:25-32

  • Brara A, Cambord F, Klepaczko JR, Mariotti C (2001) Experimental and numerical study of concrete at high strain rates in tension. Mech Mater 33:33–45

    Article  Google Scholar 

  • Cadoni E, Solomos G, Albertini C (2013) Concrete behavior in direct tension tests at high strain rates. Mag Concrete Res 65(11):660–672

    Article  Google Scholar 

  • Comité Euro-International du Béton (1990) CEB-FIP Model Code 1990. Redwood Books, Trowbridge, Wiltshire

  • Cotsovos DM, Pavlovic MN (2008) Numerical investigation of concrete subjected to high rates of uniaxial tensile loading. Int J Impact Eng 35:319–335

    Article  Google Scholar 

  • Curosu I, Mechtcherine V, Forni D, Cadoni E (2017) Performance of various strain-hardening cement-based composites (SHCC) subject to uniaxial impact tensile loading. Cem Concr Res 102:16–28

    Article  CAS  Google Scholar 

  • Cusatis G (2011) Strain-rate effects on concrete behavior. Int J Impact Eng 8:162–170

    Article  Google Scholar 

  • Cusatis G, Mencarelli A, Pelessone D, Baylot JT (2008) Lattice Discrete Particle Model for fracture dynamics and rate effect in concrete. In: Proceedings of \(18^{{\rm th}}\) analysis and computation specialty conference—structures congress 2008, ASCE, 315, pp 1–11

  • Cusatis G, Pelessone D, Mencarelli A (2011a) Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. I: Theory. Cem Concr Compos 33(9):881–890

    Article  CAS  Google Scholar 

  • Cusatis G, Mencarelli A, Pelessone D, Baylot JT (2011b) Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. II: Calibration and validation. Cem Concr Compos 33(9):391–905

    Google Scholar 

  • Daphalapurkar NP, Ramesh KT, Graham-Brady L, Molinary JF (2011) Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws. J Mech Phys Solids 59:297–319

    Article  Google Scholar 

  • Eliáš J (2016) Adaptive technique for discrete model of fracture. Int J Solids Struct 100–101:376–387

    Article  Google Scholar 

  • Eliáš J, Stang H (2012) Lattice modeling of aggregate interlocking in concrete. Int J Fract 175(1):1–11

    Article  Google Scholar 

  • Eliáš J, Vorechovsky M, Skocek J, Bazant ZP (2015) Stochastic discrete meso-scale simulations of concrete fracture: comparison to experimental data. Eng Fract Mech 135:1–16

    Article  Google Scholar 

  • Erzar B, Forquin P (2010) An experimental method to determine the tensile strength of concrete at high rates of strain. Exp Mech 50:941–955

    Article  Google Scholar 

  • Erzar B, Forquin P (2011) Experiments and mesoscopic modelling of dynamic testing of concrete. Mech Mater 43:505–527

    Article  Google Scholar 

  • Freund LB (1973) Crack propagation in an elastic solid subjected to general loading - III. Stress wave loading. J Mech Phys Solids 21:47–61

    Article  Google Scholar 

  • Gedik YH, Nakamura H, Yamamoto Y, Kunieda M (2011) Evaluation of three-dimensional effects in short deep beams using a rigid-body-spring-model. Cem Concr Compos 33(9):978–991

    Article  CAS  Google Scholar 

  • Hentz S, Donze FV, Daudeville L (2004) Discrete element modelling of concrete submitted to dynamic loading at high strain rates. Comput Struct 82:2509–2524

    Article  Google Scholar 

  • Hild F, Denoual C, Forquin P, Brajer X (2003) On the probabilistic-deterministic transition involved in a fragmentation process of brittle materials. Comput Struct 81:1241–1253

    Article  Google Scholar 

  • Hwang YK, Lim YM (2015) Rheological models for simulations of concrete under high-speed load. J Kor Soc Civil Eng 35:769–777 (In Korean)

    Google Scholar 

  • Hwang YK, Lim YM (2017) Validation of three-dimensional irregular lattice model for concrete failure mode simulations under impact loads. Eng Fract Mech 169:109–127

    Article  Google Scholar 

  • Hwang YK, Bolander JE, Lim YM (2016) Simulation of concrete tensile failure under high loading rates using three-dimensional irregular lattice models. Mech Mater 101:136–146

    Article  Google Scholar 

  • John R, Shah SP (1990) Mixed-mode fracture of concrete subjected to impact loading. J Struct Eng 116(3):585–602

    Article  Google Scholar 

  • Kang J, Bolander JE (2017) Event-based lattice modeling of strain-hardening cementitious composites. Int J Fract 206(2):245–261

    Article  CAS  Google Scholar 

  • Kim K, Lim YM (2011) Simulation of rate dependent fracture in concrete using an irregular lattice model. Cem Concr Compos 33(9):949–955

    Article  CAS  Google Scholar 

  • Kim D, Sirijaroonchai K, El-Tawil S, Naaman AE (2010) Numerical simulation of the split Hopkinson pressure bar test technique for concrete under compression. Int J Impact Eng 37:141–149

    Article  Google Scholar 

  • Kim K, Bolander JE, Lim YM (2013) Failure simulation of RC structures under highly dynamic conditions using random lattice models. Comput Struct 125:127–136

    Article  Google Scholar 

  • Kishi N, Mikami H, Matsuoka KG, Ando T (2002) Impact behavior of shear-failure-type RC beams without shear rebar. Int J Impact Eng 27:955–968

    Article  Google Scholar 

  • Klepaczko JR, Brara A (2001) An experimental method for dynamic tensile testing of concrete by spalling. Int J Impact Eng 25:387–409

    Article  Google Scholar 

  • Larcher M (2009) Development of discrete cracks in concrete loaded by shock waves. Int J Impact Eng 36:700–710

    Article  Google Scholar 

  • Le J-L, Eliáš J, Gorgogianni A, Vievering J, Květoň J (2018) Rate-dependent scaling of dynamic tensile strength of quasibrittle structures. J Appl Mech 85(2):1–12

    Article  CAS  Google Scholar 

  • Li QM, Meng H (2003) About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test. Int J Solids Struct 40:343–360

    Article  Google Scholar 

  • Malvar LJ, Ross CA (1998) Review of strain rate effects for concrete in tension. ACI Mater J 95(6):735–739

    CAS  Google Scholar 

  • Martys NS, Mountain RD (1999) Velocity Verlet algorithm for dissipative- particle-dynamics-based models of suspensions. Phys Rev E 59(3):3733–3736

    Article  CAS  Google Scholar 

  • McGuire W, Gallagher RH (1979) Matrix structural analysis. Wiley, New York

    Google Scholar 

  • Nagai K, Sato Y, Ueda T (2005) Mesoscopic simulation of failure of mortar and concrete by 3D RBSM. J Adv Concr Technol 3(3):385–402

    Article  Google Scholar 

  • Novikov SA, Divnov II, Ivanov AG (1966) The study of fracture of steel, aluminium and copper under explosive loading. Fizika Metallov i Metallovedeniye 21(4)

  • Ožbolt J, Sharma A, İrhan B, Sola E (2014) Tensile behavior of concrete under high loading rates. Int J Impact Eng 69:55–68

    Article  Google Scholar 

  • Park SW, Xia Q, Zhou M (2001) Dynamic behavior of concrete at high strain rates and pressures: II. Numerical simulation. Int J Impact Eng 25:887–910

    Article  Google Scholar 

  • Pedersen RR, Simone A, Sluys LJ (2008) An analysis of dynamic fracture in concrete with a continuum visco-elastic visco-plastic damage model. Eng Fract Mech 75:3782–3805

    Article  Google Scholar 

  • Reinhardt H, Weerheijm J (1991) Tensile fracture of concrete at high loading rates taking account of inertia and crack velocity effects. Int J Fract 51:31–42

    Article  CAS  Google Scholar 

  • Rossi P (1991) A physical phenomenon which can explain the mechanical behavior of concrete under high strain rates. Mater Sturct 24:422–424

    Article  CAS  Google Scholar 

  • Rossi P, van Mier JGM, Toutlemonde F, Le Maou F, Boulay C (1994) Effect of loading rate on the strength of concrete subjected to uniaxial tension. Mater Struct 27:260–264

    Article  CAS  Google Scholar 

  • Schuler H, Mayrhofer C, Thoma K (2006) Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates. Int J Impact Eng 32:1635–1650

    Article  Google Scholar 

  • Shah SP, Wang ML, Chung L (1987) Model concrete beam-column joints subjected to cyclic loading at two rates. Mater Struct 20:85–95

    Article  Google Scholar 

  • Smith J, Cusatis G, Pelessone D, Landis E, O’Daniel J, Baylot J (2014) Discrete modeling of ultra-high-performance concrete with application to projectile penetration. Int J Impact Eng 65:13–32

    Article  Google Scholar 

  • Weerheijm J, Van Doormaal JCAM (2007) Tensile failure of concrete at high loading rates: new test data on strength and fracture energy from instrumented spalling tests. Int J Impact Eng 34:609–626

    Article  Google Scholar 

  • Xu PB, Xu H, Wen HM (2016) 3D meso-mechanical modeling of concrete spall tests. Int J Impact Eng 97:46–56

    Article  Google Scholar 

  • Yip M, Li Z, Liao BS, Bolander JE (2006) Irregular lattice models of fracture of multiphase particulate materials. Int J Fract 140:113–124

    Article  CAS  Google Scholar 

  • Zhou W, Tang L, Liu X, Ma G, Chen M (2016) Mesoscopic simulation of the dynamic tensile behavior of concrete based on a rate-dependent cohesive model. Int J Impact Eng 95:165–175

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20194030202460) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1A2C1090426).

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Correspondence to Yun Mook Lim.

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Hwang, Y.K., Bolander, J.E. & Lim, Y.M. Evaluation of dynamic tensile strength of concrete using lattice-based simulations of spalling tests. Int J Fract 221, 191–209 (2020). https://doi.org/10.1007/s10704-020-00422-w

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