Optimal Seismic Intensity Measures for Slopes at Various Heights Under Vertical and Horizontal Ground Motions

Abstract

Identifying the optimal intensity measures (IMs) of ground motion is a critical step in the seismic fragility analysis of slopes using probabilistic seismic demand models. In this study, we investigated various IMs of earthquake ground motions, considering both vertical and horizontal components that can trigger landslides, through numerical simulations. A set of 19 IMs was examined for three heights of slopes. The optimal IMs were assessed using the maximum permanent displacement as an engineering demand parameter. The findings reveal that acceleration-related parameters specifically sustained maximum acceleration (SMA) and root-mean-square of acceleration, and velocity-related parameters namely sustained maximum velocity (SMV) and peak ground velocity, are the most effective IMs for slopes subjected to both vertical and horizontal ground motions. For slopes subjected exclusively to horizontal ground motion, SMA is recommended as the optimal IM for lower-height slopes, while SMV is more suitable for the taller slope. In contrast, for models subjected to combined horizontal and vertical ground motions, SMA is consistently identified as the optimal IM for slope across all heights. Notably, the study concludes that peak ground acceleration, a commonly used parameter in seismic analysis, is unsuitable for the considered slopes.

Keywords

Ground motion components / Intensity measures / PSDMs / Seismic fragility / Slopes

References

[1] Alielahi H, Moghadam MR. Fragility curves evaluation for broken-back block quay walls. Journal of Earthquake Engineering, 2016, 21(1): 1-22

[2] Arias A. A measure of earthquake intensity. Seismic Design for Nuclear Power Plants, 1970, 1970: 438-483

[3] Baker JW. Efficient analytical fragility function fitting using dynamic structural analysis. Earthquake Spectra, 2015, 31(1): 579-599

[4] Bentley 2022. PLAXIS 2D tutorial manual connect edition V22. Exton, PA: Bentley.

[5] Bentley 2024. PLAXIS 2D-material-models connect edition V24. Exton, PA: Bentley.

[6] Che W, Chang P, Wang W. Optimal intensity measures for probabilistic seismic stability assessment of large open-pit mine slopes under different mining depths. Shock and Vibration, 2023

[7] Cornell CA, Jalayer F, Hamburger RO, Foutch DA. Probabilistic basis for 2000 SAC Federal Emergency Management Agency steel moment frame guidelines. Journal of Structural Engineering, 2002, 128(4): 526-533

[8] Crowley H, Pinho R, Bommer JJ. A probabilistic displacement-based vulnerability assessment procedure for earthquake loss estimation. Bulletin of Earthquake Engineering, 2004, 2: 173-219

[9] Cundall, P., H. Hansteen, S. Lacasse, and P. Selnes. 1980. NESSI: Soil structure interaction program for dynamic and statistic problems. Report 51508-9. Oslo, Norway: Norwegian Geotechnical Institute.

[10] Deierlein, G.G., A.B. Liel, C.B. Haselton, and C.A. Kircher. 2008. ATC 63 methodology for evaluating seismic collapse safety of archetype buildings. In Structures Congress 2008, ed. D. Anderson, C. Ventura, D. Harvey, and M. Hoit. Reston, VA: American Society of Civil Engineers.

[11] EU (European Union). 2004. Eurocode8. Design of structures for earthquake resistance. Brussels, Belgium: The EU.

[12] Fotopoulou SD, Pitilakis KD. Predictive relationships for seismically induced slope displacements using numerical analysis results. Bulletin of Earthquake Engineering, 2015, 13(11): 3207-3238

[13] Hariri-Ardebili MA, Saouma VE. Probabilistic seismic demand model and optimal intensity measure for concrete dams. Structural Safety, 2016, 59: 67-85

[14] Housner, G. 1975. Measures of severity of earthquake ground shaking. In Proceedings of the U.S. National Conference on Earthquake Engineering, 18–20 June 1975, Ann Arbor, Michigan, USA.

[15] Hu, H., and Y. Bao. 2024. Seismic fragility functions for earthquake-induced landslide risk assessment using identified optimal earthquake intensity measures. CATENA 234: Article 107589.

[16] Hu, H., Y. Huang, and Z. Chen. 2019. Seismic fragility functions for slope stability analysis with multiple vulnerability states. Environmental Earth Sciences 78(24): Article 690.

[17] Irslan Khalid, M., D. Park, J. Fei, V.-Q. Nguyen, D.-D. Nguyen, and X. Chen. 2023. Selection of efficient earthquake intensity measures for evaluating seismic fragility of concrete face rockfill dam. Computers and Geotechnics 163: Article 105721.

[18] Khalid, M.I., J. Fei, D.-h. Lee, D. Park, and X. Chen. 2024. Probabilistic assessment of seismic performance of slopes considering the sensitivity of sliding surface to input motion. Soil Dynamics and Earthquake Engineering 182: Article 108737.

[19] Kim JM, Sitar N. Probabilistic evaluation of seismically induced permanent deformation of slopes. Soil Dynamics and Earthquake Engineering, 2013, 44: 67-77

[20] Kim, C., H.D. Nguyen, M. Shin, and J.M. LaFave. 2025. Fragility analysis of APR-1400 nuclear containment structures under internal pressure. Nuclear Engineering and Design 433: Article 113864.

[21] Kramer SL. Geotechnical earthquake engineering, 1996, Upper Saddle River, NJ, Prentice-Hall Inc

[22] Kumar, S., S.S. Choudhary, and A. Burman. 2023. The effect of slope height and angle on the safety factor and modes of failure of 3D slopes analysis using limit equilibrium method. Beni-Suef University Journal of Basic and Applied Sciences 12(1): Article 84.

[23] Kurama YC, Farrow KT. Ground motion scaling methods for different site conditions and structure characteristics. Earthquake Engineering & Structural Dynamics, 2003, 32(15): 2425-2450

[24] Kwok, J.P.S., Y.M.A. Hashash, N. Matasovic, R. Pyke, Z. Wang, and Z. Yang. 2007. Use of exact solutions of wave propagation problems to guide implementation of nonlinear seismic ground response analysis procedures. Journal of Geotechnical and Geoenvironmental Engineering 133(11): Article 1385.

[25] Latha GM, Garaga A. Seismic stability analysis of a Himalayan rock slope. Rock Mechanics and Rock Engineering, 2010, 43(6): 831-843

[26] Lysmer, J., and R.L. Kuhlemeyer. 1969. Finite dynamic model for infinite media. Department of Civil Engineering, University of California, Berkeley, CA, USA.

[27] Mackie, K., and B. Stojadinović. 2001. Probabilistic seismic demand model for California highway bridges. Journal of Bridge Engineering 6(6): Article 468.

[28] Malhotra PK. Response of buildings to near-field pulse-like ground motions. Earthquake Engineering & Structural Dynamics, 1999, 28(11): 1309-1326

[29] Maruyama Y, Yamazaki F, Mizuno K, Tsuchiya Y, Yogai H. Fragility curves for expressway embankments based on damage datasets after recent earthquakes in Japan. Soil Dynamics and Earthquake Engineering, 2010, 30(11): 1158-1167

[30] McCartney, J.S., H. Yu, E. Ntambakwa, B. Mendes, and I. Tomac. 2020. Comparison of 1-D seismic site response analysis tools for layered liquefiable deposits at an offshore windfarm site. E3S Web of Conferences 205: Article 12005.

[31] Meko, L., Y.C. Chemeda, and B. Meko. 2023. Road cut slope stability analysis for static and dynamic (pseudo-static analysis) loading conditions. Open Geosciences 15: Article 20220561.

[32] Murthy TN, Patil GR. Effect of vertical ground motion on reinforced concrete structures. Mechanical and Civil Engineering, 2015, 12: 33-39

[33] Nguyen, H.D., N.D. Dao, and M. Shin. 2021. Prediction of seismic drift responses of planar steel moment frames using artificial neural network and extreme gradient boosting. Engineering Structures 242: Article 112518.

[34] Nguyen, H.D., C. Kim, Y.-J. Lee, and M. Shin. 2024. Incorporation of machine learning into multiple stripe seismic fragility analysis of reinforced concrete wall structures. Journal of Building Engineering 97: Article 110772.

[35] Nguyen, H.D., Y.-J. Lee, J.M. LaFave, and M. Shin. 2023. Seismic fragility analysis of steel moment frames using machine learning models. Engineering Applications of Artificial Intelligence 126: Article 106976.

[36] Nguyen, H.D., M. Shin, and J.M. LaFave. 2023. Optimal intensity measures for probabilistic seismic demand models of steel moment frames. Journal of Building Engineering 65: Article 105629.

[37] Nguyen, H.D., M. Shin, and M. Torbol. 2020. Reliability assessment of a planar steel frame subjected to earthquakes in case of an implicit limit-state function. Journal of Building Engineering 32: Article 101782.

[38] NIBS (National Institute of Building Sciences) and FEMA (Federal Emergency Management Agency). 2003. HAZUS-MH MR4 technical manual. Washington, DC: NIBS and FEMA.

[39] Nuttli, O.W. 1979. The relation of sustained maximum ground acceleration and velocity to earthquake intensity and magnitude. Vicksburg, MI: U.S. Army Engineer Waterways Experiment Station.

[40] Özmen, B.O. 2019. Modelling the variability in seismically induced slope displacements due to ground motion selection. https://etd.lib.metu.edu.tr/upload/12623183/index.pdf. Accessed 22 Jul 2020.

[41] Padgett JE, DesRoches R. Methodology for the development of analytical fragility curves for retrofitted bridges. Earthquake Engineering & Structural Dynamics, 2008, 37(8): 1157-1174

[42] Padgett JE, Nielson BG, DesRoches R. Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios. Earthquake Engineering & Structural Dynamics, 2007, 37(5): 711-725

[43] Park, Y.-J., A.H.-S. Ang, and Y.K. Wen. 1985. Seismic damage analysis of reinforced concrete buildings. Journal of Structural Engineering Ill(4): Article 705.

[44] Pushpa K, Prasad SK, Nanjundaswamy P. Critical analysis of slope stability analysis methods. International Journal of Engineering Research & Technology (IJERT), 2016, 5(7): 128-136

[45] Rathje EM, Saygili G. Probabilistic assessment of earthquake-induced sliding displacements of natural slopes. Bulletin of the New Zealand Society for Earthquake Engineering, 2009, 42(1): 18-27

[46] Reed JW, Kassawara RP. A criterion for determining exceedance of the operating basis earthquake. Nuclear Engineering and Design, 1990, 123(2): 387-396

[47] Riddell R, Garcia JE. Hysteretic energy spectrum and damage control. Earthquake Engineering & Structural Dynamics, 2001, 30(12): 1791-1816

[48] Saygili G, Rathje EM. Empirical predictive models for earthquake-induced sliding displacements of slopes. Geotechnical and Geoenvironmental Egineering, 2008, 134: 790-803

[49] Saygili G, Rathje EM. Probabilistically based seismic landslide hazard maps: An application in Southern California. Engineering Geology, 2009, 109(3–4): 183-194

[50] Shome N, Cornell CA, Bazzurro P, Carballo JE. Earthquakes, records, and nonlinear responses. Earthquake Spectra, 1998, 14(3): 469-500

[51] Stokoe, II, K.H., M.B. Darendeli, R.B. Gilbert, F.-Y. Menq, and W.K. Choi. 2001. Development of a new family of normalized modulus reduction and material damping curves. https://apps.peer.berkeley.edu/lifelines/Workshop304/pdf/Stokoe_PlenaryPaper.pdf. Accessed 20 Nov 2020.

[52] Thun J, Roehm LH, Scott GA, Wilson JA. Earthquake ground motions for design and analysis of dams. Geotechnical Special Publication, 1988, 20: 463-481

[53] Tidke AR, Adhikary S. Optimal intensity measure selection and probabilistic seismic demand models for dam-reservoir-layered foundation system. Structures, 2022, 37: 318-337

[54] Tothong P, Luco N. Probabilistic seismic demand analysis using advanced ground motion intensity measures. Earthquake Engineering & Structural Dynamics, 2007, 36(13): 1837-1860

[55] Tran DTP, Cho Y, Seo H, Kim B. Seismic fragility assessments of fill slopes in South Korea using finite element simulations. Geomechanic and Engineering, 2023, 34: 341-380

[56] Travasarou, Th., and J.D. Bray. 2003. Optimal ground motion intensity measures for assessment of seismic slope displacements. In Proceedings of the 2003 Pacific Conference on Earthquake Engineering, 13–15 February 2003, University of Canterbury, Christchurch, New Zealand.

[57] Trifunac MD, Brady AG. On the correlation of seismic intensity scales with the peaks of recorded strong ground motion. Bulletin of Seimological Society of America, 1975, 65: 139-162

[58] Tsompanakis Y, Lagaros ND, Psarropoulos PN, Georgopoulos EC. Probabilistic seismic slope stability assessment of geostructures. Structure and Infrastructure Engineering, 2010, 6(1–2): 179-191

[59] Wang, H., M. Jia, Y. Yao, X. Chen, and Z. Zhang. 2023. Influence of the vertical component of Yangbi ground motion on the dynamic response of RC frame and brick-concrete structure. Buildings 13(1): Article 147.

[60] Wen, Y.K., B.R. Ellingwood, and J. Bracci. 2004. Vulnerability function framework for consequence-based engineering. https://www.researchgate.net/publication/32962749_Vulnerability_Function_Framework_for_Consequence-Based_Engineering. Accessed 1 Jan 2022.

[61] Wibowo, H., and S. Sritharan. 2022. Effects of vertical ground acceleration on the seismic moment demand of bridge superstructure connections. Engineering Structures 253: Article 113820.

[62] Wu XZ. Development of fragility functions for slope instability analysis. Landslides, 2014, 12(1): 165-175

[63] Xiao, Y., Y. Zhang, X. Cheng, and C. Xiang. 2024. Dynamic response and seismic vulnerability assessment of the near-fault steep slope. Soil Dynamics and Earthquake Engineering 183: Article 108794.

[64] Zhang YB, Chen G, Wu J, Zheng L, Zhuang X. Numerical simulation of seismic slope stability analysis based on tension-shear failure mechanism. Geotechnical Engineering, 2012, 43(2): 18-28

[65] Zhang, C., M. Zhao, Z. Zhong, and X. Du. 2022. Optimum intensity measures for probabilistic seismic demand model of subway stations with different burial depths. Soil Dynamics and Earthquake Engineering 154: Article 107138.

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