Analytical Solution for Estimating Sliding Displacement of Rigid Barriers Subjected to Boulder Impact
Publication: Journal of Engineering Mechanics
Volume 145, Issue 3
Abstract
Rigid barriers are commonly used as defense measures in hilly areas to contain falling boulders and landslide debris, and the sliding displacement of these barriers is a key design consideration when space is limited. A new displacement-based model in the form of a closed-form solution is introduced in this paper to estimate the amount of sliding displacement that a barrier undergoes following a boulder impact. The model was derived based on the principles of energy and momentum conservation, and the derivations were presented. Laboratory tests were conducted to validate the analytical model, and the results consistently matched the analytical results for different impact velocities. Finite-element modeling was subsequently carried out on a real-scale barrier in Hong Kong to verify the scale-independent nature of the model. A parametric study was also carried out to investigate the effect of basal friction on the sliding behavior of the barrier. The results revealed that the effect of friction diminishes with increasing barrier:boulder mass ratio.
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Acknowledgments
Financial support from the Australian Research Council (ARC) Discovery Project DP170101858, New Approach for Design of Barriers for Impact, is gratefully acknowledged. This paper is published with the permission of the Head of the Geotechnical Engineering Office and the Director of Civil Engineering and Development, the Government of the Hong Kong Special Administrative Region (SAR). Julian S. H. Kwan is grateful for the financial support from the theme-based research Grant No. T22-603/15-N provided by the Research Grants Council of the Government of the Hong Kong SAR, China.
References
Ali, M., J. Sun, N. Lam, L. Zhang, and E. Gad. 2014. “Simple hand calculation method for estimating deflection generated by the low velocity impact of a solid object.” Aust. J. Struct. Eng. 15 (3): 243–259.
Austroads. 2013. Standardised bridge barrier design. Sydney, Australia: Austroads.
Bala, S., and J. Day. 2006. General guidelines for crash analysis in LS-DYNA. Troy, MI: Livermore Software Technology Corporation.
Barton, N., and V. Choubey. 1977. “The shear strength of rock joints in theory and practice.” Rock Mech. 10 (1–2): 1–54. https://doi.org/10.1007/BF01261801.
BSI (British Standard Institute). 2008. Eurocode 1—Actions on structures—Part 1-7: General actions—Accidental actions. London: European Committee for Standardization.
Donnelly, C. R., and S. J. Rigbey. 2007. “The assessment of sliding resistance beneath concrete structures.” In Proc., Canadian Dam Association Conf. Toronto: Canadian Dam Association.
Fujikake, K., B. Li, and S. Soeun. 2009. “Impact response of reinforced concrete beam and its analytical evaluation.” J. Struct. Eng. 135 (8): 938–950. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000039.
GEO (Geotechnical Engineering Office). 2017. Guide to retaining wall design (Geoguide 1) (Continuously updated e-version released on 29 August 2017), 245. Hong Kong: Geotechnical Engineering Office, Civil Engineering and Development Dept., Government of the Hong Kong Special Administrative Region.
Hallquist, J.O. 2006. LS-DYNA theory manual. Livermore, CA: Livermore Software Technology Corporation.
Hummeltenberg, A., B. Beckmann, T. Weber, and M. Curbach. 2011. “Investigation of concrete slabs under impact load.” Appl. Mech. Mater. 82: 398–403. https://doi.org/10.4028/www.scientific.net/AMM.82.398.
Johnston, I. W., and T. S. K. Lam. 1989. “Shear behavior of regular triangular concrete/rock joints—Analysis.” J. Geotech. Eng. 115 (5): 711–727. https://doi.org/10.1061/(ASCE)0733-9410(1989)115:5(711).
Kennedy, R. 1976. “A review of procedures for the analysis and design of concrete structures to resist missile impact effects.” Nucl. Eng. Des. 37 (2): 183–203. https://doi.org/10.1016/0029-5493(76)90015-7.
Kishi, N., and H. Mikami. 2012. “Empirical formulas for designing reinforced concrete beams under impact loading.” ACI Struct. J. 109 (4): 509–519.
Kwan, J. S. H. 2012. Supplementary technical guidance on design of rigid debris-resisting barriers. Hong Kong: Geotechnical Engineering Office, Government of the Hong Kong Special Administrative Region.
Kwan, J., R. Koo, and C. W. W. Ng. 2015. “Landslide mobility analysis for design of multiple debris-resisting barriers.” Can. Geotech. J. 52 (9): 1345–1359. https://doi.org/10.1139/cgj-2014-0152.
Lam, N. T. K., A. C. Y. Yong, C. Lam, J. S. H. Kwan, J. S. Perera, M. M. Disfani, and E. Gad. 2018. “Displacement-based approach for the assessment of overturning stability of rectangular rigid barriers subjected to point impact.” J. Eng. Mech. 144 (2): 04017161. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001383.
Li, Q., S. Reid, H. Wen, and A. Telford. 2005. “Local impact effects of hard missiles on concrete targets.” Int. J. Impact Eng. 32 (1): 224–284. https://doi.org/10.1016/j.ijimpeng.2005.04.005.
Mougin, J. P., P. Perrotin, M. Mommessin, J. Tonnelo, and A. Agbossou. 2005. “Rock fall impact on reinforced concrete slab: An experimental approach.” Int. J. Impact Eng. 31 (2): 169–183. https://doi.org/10.1016/j.ijimpeng.2003.11.005.
Ng, C. W. W., C. E. Choi, A. Y. Su, J. S. H. Kwan, and C. Lam. 2016. “Large-scale successive boulder impacts on a rigid barrier shielded by gabions.” Can. Geotech. J. 53 (10): 1688–1699. https://doi.org/10.1139/cgj-2016-0073.
Ng, C. W. W., Y. Su, C. E. Choi, D. Song, C. Lam, J. S. H. Kwan, R. Chen, and H. Liu. 2018. “Comparison of cushion mechanisms between cellular glass and gabions subjected to successive boulder impacts.” J. Geotech. Geoenviron. Eng. 144 (9): 04018058. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001922.
O’Connor, C., and P. Shaw. 2002. Bridge loads: An international perspective. Boca Raton, FL: CRC Press.
Pathirana, M., N. Lam, S. Perera, L. Zhang, D. Ruan, and E. Gad. 2017a. “Damage modelling of aluminium panels impacted by windborne debris.” J. Wind Eng. Ind. Aerodyn. 165: 1–12. https://doi.org/10.1016/j.jweia.2017.02.014.
Pathirana, M., N. Lam, S. Perera, L. Zhang, D. Ruan, and E. Gad. 2017b. “Risks of failure of annealed glass panels subject to point contact actions.” Int. J. Solids Struct. 129: 177–194. https://doi.org/10.1016/j.ijsolstr.2017.09.001.
Perera, S., N. Lam, M. Pathirana, L. Zhang, D. Ruan, and E. Gad. 2016. “Deterministic solutions for contact force generated by impact of windborne debris.” Int. J. Impact Eng. 91: 126–141. https://doi.org/10.1016/j.ijimpeng.2016.01.002.
Perera, S., N. Lam, M. Pathirana, L. Zhang, D. Ruan, and E. Gad. 2017. “Use of static tests for predicting damage to cladding panels caused by storm debris.” J. Build. Eng. 12: 109–117. https://doi.org/10.1016/j.jobe.2017.05.012.
Santos, P. M. D., and E. N. B. S. Júlio. 2012. “A state-of-the-art review on shear-friction.” Eng. Struct. 45: 435–448. https://doi.org/10.1016/j.engstruct.2012.06.036.
Sun, J., N. Lam, L. Zhang, D. Ruan, and E. Gad. 2015. “Contact forces generated by hailstone impact.” Int. J. Impact Eng. 84: 145–158. https://doi.org/10.1016/j.ijimpeng.2015.05.015.
Tachibana, S., H. Masuya, and S. Nakamura. 2010. “Performance based design of reinforced concrete beams under impact.” Nat. Hazards Earth Syst. Sci. 10 (6): 1069–1078. https://doi.org/10.5194/nhess-10-1069-2010.
Wu, M., Z. Chen, and C. Zhang. 2015. “Determining the impact behavior of concrete beams through experimental testing and meso-scale simulation: I. Drop-weight tests.” Eng. Fract. Mech. 135: 94–112. https://doi.org/10.1016/j.engfracmech.2014.12.019.
Yang, Y., N. T. K. Lam, and L. Zhang. 2012. “Evaluation of simplified methods of estimating beam responses to impact.” Int. J. Struct. Stab. Dyn. 12 (3): 1250016-1250011–1250016-1250024. https://doi.org/10.1142/S0219455412500162.
Yankelevsky, D. Z. 1997. “Local response of concrete slabs to low velocity missile impact.” Int. J. Impact Eng. 19 (4): 331–343. https://doi.org/10.1016/S0734-743X(96)00041-3.
Zhan, T., Z. Wang, and J. Ning. 2015. “Failure behaviors of reinforced concrete beams subjected to high impact loading.” Eng. Fail. Anal. 56: 233–243. https://doi.org/10.1016/j.engfailanal.2015.02.006.
Zineddin, M., and T. Krauthammer. 2007. “Dynamic response and behavior of reinforced concrete slabs under impact loading.” Int. J. Impact Eng. 34 (9): 1517–1534. https://doi.org/10.1016/j.ijimpeng.2006.10.012.
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©2019 American Society of Civil Engineers.
History
Received: Apr 21, 2018
Accepted: Sep 4, 2018
Published online: Jan 8, 2019
Published in print: Mar 1, 2019
Discussion open until: Jun 8, 2019
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