# 지진 시 산사면의 영구변위 추정식 개발

• Lee, Jong-Hoo (Dept. of Civil and Environmental Engineering, Hanyang Univ.) ;
• Park, Duhee (Dept. of Civil and Environmental Engineering, Hanyang Univ.) ;
• Ahn, Jae-Kwang (Dept. of Civil and Environmental Engineering, Hanyang Univ.) ;
• Park, Inn-Joon (Dept. of Civil Engineering, Hanseo Univ.)
• 이종후 (한양대학교 건설환경공학과) ;
• 박두희 (한양대학교 건설환경공학과) ;
• 안재광 (한양대학교 건설환경공학과) ;
• 박인준 (한서대학교 토목공학과)
• Received : 2015.03.11
• Accepted : 2015.04.13
• Published : 2015.04.30

#### Abstract

Empirical seismic displacement equations based on the Newmark sliding block method are widely used to develop seismic landslide hazard map. Most proposed equations have been developed for embankments and landfills, and do not consider the dynamic response of sliding block. Therefore, they cannot be applied to Korean mountain slopes composed of thin, uniform soil-layer underlain by an inclined bedrock parallel to the slope. In this paper, a series of two-dimensional dynamic nonlinear finite difference analyses were performed to estimate the permanent seismic slope displacement. The seismic displacement of mountain slopes was calculated using the Newmark method and the equivalent acceleration time history. The calculated seismic displacements of the mountain slopes were compared to a widely used empirical displacement model. We show that the displacement prediction is significantly enhanced if the slope is modeled as a flexible sliding mass and the amplification characteristics are accounted for. Regression equation, which uses PGA, PGV, Arias intensity of the ground motion and the fundamental period of soil layer, is shown to provide a reliable estimate of the sliding displacement. Furthermore, the empirical equation is shown to reliably predict the hazard category.

지진에 대한 사면 재해도 작성 시 일반적으로 Newmark 활동블록 이론에 기초한 변위 추정식이 사용된다. 하지만 기존에 제안된 추정식들은 활동면에서의 동적 응답을 고려하지 않고 제방, 흙댐, 매립지 등 비교적 완만한 경사의 지반구조물을 대상으로 제안되었으며 산사면과 같이 경사진 기반암에 토사층이 피복된 경우에는 적합하지 않다. 본 연구에서는 산사면의 지형적 특성을 모사한 2차원 비선형 동적해석을 수행하여 이의 동적 응답 특성을 분석하였다. 지진 시 산사면의 영구변위는 활동면에서 계산된 등가가속도를 Newmark 활동블록 방법에 적용하여 계산하였다. 이와 같이 계산된 영구변위는 본 연구에서 제안된 간편 변위 추정식과 비교하여 정확도를 평가하였다. 검토 결과, 산사면의 기하학적 증폭은 입력 지진의 세기와 주기, 토층의 고유주기에 영향을 크게 받으므로 이를 고려하지 않는 기존의 경험식은 영구변위를 정확하게 예측하지 못하는 것으로 나타났다. 변위 예측식의 정확도는 최대지반가속도, 최대지반속도, Arias 진도, 평균주기와 토층의 고유주기가 고려될 경우 현격하게 향상되는 것으로 분석되었으며 이를 기반으로 하여 새로운 변위추정식이 제시되었다. 나아가 본 연구에 제안된 변위추정식은 산사태 재해 위험도 예측에 적용되어 정확성이 검증되었다.

#### Acknowledgement

Grant : 지진시 사면붕괴 등 지반피해 예측기술 개발

Supported by : 소방방재청

#### References

1. Agency, F.E.M. (2003), "HAZUS-MH MR4 Technical Manual": FEMA Washington, DC.
2. Ambraseys, N. and Menu, J. (1988), "Earthquake Induced Ground Displacements", Earthquake engineering & structural dynamics, Vol.16, No.7, pp.985-1006. https://doi.org/10.1002/eqe.4290160704
3. Blake, T., Hollingworth, R., and Stewart, J. (2002), Recommended procedures for implementation of DMG special publication 117 guidelines for analyzing and mitigating landslide hazards in California, Southern California Earthquake Center, University of Southern California.
4. Bray, J.D. and Travasarou, T. (2007), "Simplified Procedure for Estimating Earthquake-induced Deviatoric Slope Displacements", Journal of geotechnical and geoenvironmental engineering, Vol.133, No.4, pp.381-392. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:4(381)
5. Bray, J.D. and Travasarou, T. (2009), "Pseudostatic Coefficient for Use in Simplified Seismic Slope Stability Evaluation", Journal of Geotechnical and Geoenvironmental Engineering, Vol.135, No.9, pp.1336-1340. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000012
6. Chopra, A.K. (1966), Earthquake effects on dams, University of California, Berkeley.
7. Darendeli, M.B. (2001), Development of a new family of normalized modulus reduction and material damping curves, University of Texas at Austin.
8. Dikmen, U. (2009), "Statistical Correlations of Shear Wave Velocity and Penetration Resistance for Soils", Journal of Geophysics and Engineering, Vol.6, No.1, pp.61. https://doi.org/10.1088/1742-2132/6/1/007
9. Franklin, A.G. and Chang, F.K. (1977), "Earthquake Resistance of Earth and Rock-fill Dams. Report 5: Permanent Displacements of Earth Embankments by Newark Sliding Block Analysis", Unknown, Vol.1.
10. Itasca Consulting Group, I. (2011), Fast Lagrange Analysis of Continua, Version 7.0.
11. Jibson, R.W. (1993), "Predicting Earthquake-induced Landslide Displacements Using Newmark's Sliding Block Analysis", Transportation Research Record, pp.9-9.
12. Jibson, R.W. (2007), "Regression Models for Estimating Coseismic Landslide Displacement", Engineering Geology, Vol.91, No.2, pp. 209-218. https://doi.org/10.1016/j.enggeo.2007.01.013
13. Jibson, R.W., Harp, E.L., and Michael, J.A. (2000), "A Method for Producing Digital Probabilistic Seismic Landslide Hazard Maps", Engineering Geology, Vol.58, No.3, pp.271-289. https://doi.org/10.1016/S0013-7952(00)00039-9
14. Jibson, R.W. and Keefer, D.K. (1993), "Analysis of the Seismic Origin of Landslides: Examples from the New Madrid Seismic Zone", Geological Society of America Bulletin, Vol.105, No.4, pp.521-536. https://doi.org/10.1130/0016-7606(1993)105<0521:AOTSOO>2.3.CO;2
15. Jibson, R.W. and Michael, J.A. (2009), Map Showing Seismic Landslide Hazards in Anchorage, Alaska, US Department of the Interior, US Geological Survey.
16. Kramer, S.L. (1996), Geotechnical earthquake engineering, Prentice Hall, Upper Saddle River, N.J.
17. Kuhlemeyer, R.L. and Lysmer, J. (1973), "Finite Element Method Accuracy for Wave Propagation Problems", Journal of Soil Mechanics & Foundations Div, Vol.99, No. Tech Rpt.
18. Kwok, A.O.L., Asce, M., Stewart, J.P., Hashash, Y.M.A., Matasovic, N., Pyke, R., Wang, Z., and Yang, Z. (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, Vol.133, pp.1385. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:11(1385)
19. Lysmer, J. and Kuhlemeyer, R. (1969), "Finite Element Model for Infinite Media", Journal of Engineering Mechanics Division. ASCE, Vol.95, pp.859-877.
20. Makdisi, F.I. and Seed, H.B. (1978), "Simplified Procedure for Estimating Dam and Embankment Earthquake-induced Deformations", Journal of the Geotechnical Engineering Division, Vol.104, No.GT7, pp.849-867.
21. MLTM (2009), "Design criteria of Slope".
22. Newmark, N.M. (1965), "Effect of Earthquakes on Dams and Embankments", Geotechnique, Vol.15, No.2, pp.139-160. https://doi.org/10.1680/geot.1965.15.2.139
23. Park, D., Lee, J. H., Ahn, J. K., Han, J. T., Lee, J., and Park, I. J. (2014), "Development of Prediction Method Considering Geometrical Amplification Characteristics of Slope I : Analysis About Amplification Characteristics of Mountain Slopes in Seoul", J. Korean Soc. Hazard Mitig., Vol.14, No.5, pp.1-8. https://doi.org/10.9798/KOSHAM.2014.14.5.1
24. Park, D., Shin, J. H., and Yun, S.U. (2010), "Seismic Analysis of Tunnel in Transverse Direction Part II: Evaluation of Seismic Tunnel Response via Dynamic Analysis", Journal of Korean Geotechnical Society, Vol.26, pp.71-85.
25. Parrish, J.G. (2008), Guidelines for Evaluating and Mitigating Seismic Hazards.
26. Peck, R. B., Hanson, W. E., and Thornburn, T.H. (1974), Foundation Engineering, Wiley, New York.
27. Rathje, E.M. and Antonakos, G. (2011), "A Unified Model for Predicting Earthquake-induced Sliding Displacements of Rigid and Flexible Slopes", Engineering Geology, Vol.122, No.1, pp.51-60. https://doi.org/10.1016/j.enggeo.2010.12.004

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