A Comparison of Numerical and Analytical Methods in Dynamic Analysis of Embankment Dams (Case Study Balarud Embankment dam)

Document Type : Research Paper



     Due to accuray of numerical methods and constitutive equations, a comparison of these methods with the classical methods of dynamic analysis of earthfill dams seems necessary. The results of Seed-Makdisi, Sarma and Ambrasys-Sarma analysis of a homogenous dam are compared with those of Quake/W and Slope/W softwares. A code is developed for calculating permanent displacements based on Newmark double integration method. The results of linear and equivalent linear models show that, due to unrealistic linear assumption of the behaviour of the material, the calculated accelerations are high and the analytical methods are overdesign. This is due to realistic constitutive models. Also, in homogenous dam, as the assumed critical wedge in analytical methods is different from that calculated in numerical analyses, the critical acceleration estimated is different too (0.45g in Ambrasys-Sarma method compared to 0.26g in equivalent linear model for a wedge of 0.6h depth). This shows that realistic models must be utilized. In the developed code first the average aceleration of assumed wedge is calculated using acceleration calculated with finite element codes utilizing modern constitutive models and consequently the permanent displacements are calculated. The results show that the current methods are overestimating. Also, the assumed critical wedges are unrealestic and pass through the dam core. While the critical wedges pass through downstream shell. The permanent displacement of a wedge with 0.6h depth is estimated to be 3 cm compared to zero in Sarma method. The developed code was used for dynamic analysis of Balarud earthfill dams.


1-       داودی، م.،  هنردوست، ح. و ک. جعفری. (1392).  بررسی رفتار دینامیکی سد های خاکی کوتاه و بلندتحت اثر زلزله های حوزه دور و حوزه نزدیک. هفتمین کنگره ملی مهندسی عمران زاهدان.
2-    Ambraseys, N. N. and S.K. Sarma, 1967. The response of earth dams to strong earthquakes. Geo-Technique, 7: 18l-213.
3-    Bandini, V., Biondi, G, Cascone, E. and S. Rampello, 2015. A GLE-based model for seismic displacement analysis of slopes including strength degradation and geometry rearrangement. Soil Dynamics and Earthquake Engineering, 71:128–142.
4-    Daghigh, Y.1993. Numerical simulation of dynamics behavior of and earth dam during seismic loading. Thesis Presented to Delf University of Technology Netherland In Partial Fulfillment of The Requirement for the Degree of Doctor in Technical sciences.
5-    Day, R.W. 2002. Geotechnical earthquake engineering handbook. McGraw-Hill.
6-    Dong, W.X., Xu, W.J., Yu, Y.Z. and H. Lv, 2013. Numerical analysis of earthquake response of an ultra-high earth-rockfill dam.  Natural Hazards and Earth System Sciences, 1(12): 2319–2351.
7-    Finn, W.D.L., Yogendrakumar, M., Yosida, N., and H. Yoshida. 1986. Tara-3: A program for nonlinear static and dynamic effective stress analysis. Soil Dynamics Group, University of British Columbia, Vancouver, B.C., Canada.
8-    Goodman, R.E. and H.B, Seed, 1966. Earthquake-induced displacements in sand embankments. Journal of the Soil Mechanics and Foundations Division, 90(SM2): 125-146.
9-    Han, Y. Hart. and  R. 2006. Application of a simple hysteretic damping formulation in dynamic continuum simulations. Proceedings of the Fourth International FLAC Symposium on Numerical Modeling in Geomechanics, Madrid, Spain. Paper No. 04-02. R. Hart and P. Varona, Eds.
10- Hsieh, S.U. and C.T. Lee, 2011. Empirical estimation of the Newmark displacement from the Aria intensity and critical acceleration. Engineering Geology, 122 (1-2): 34–42.
11- Hynes-Griffin, M.E. and A.G. Franklin 1984. Rationalizing the seismic coefficient method. Miscelaneous Paper. GL-84-13, Vicksburg, Miss, USA: US Army Corps of Engineers Waterways Experiment Station.
12- Jibson, R.W. 2011. Methods for assessing the stability of slopes during earthquakes: A retrospective, Engineering Geology. 122(1-2):43-50.
13- Jinto, H. and R. Davidson. 2010. Earthquake –induced displacements of Earth dams and Embankments. Australian Geomechanics Journal, 45(3): 65-84.
14- Makdisi, F. I. and H. B. Seed, 1978. Simplified procedure for estimating dam and embankment earthquake-induced deformations. Journal of Geotechnical Engineering, ASCE, 104, (GT7), 849- 867.
15- Matsumoto, N. 2002. Evaluation of permanent displacement in seismic analysis of fill dams. In Proc third US-Japan Workshop on Advanced Research on Earthquake Engineering for Dams, San Diego, 22-23 June.
16- Mononobe, N., Takata, A., and M. Matsumura, 1936.Seismic stability of the earth dam. Proceedings of 2nd  Congress on Large Dams, Washington DC, (4), pp. 1435-1442.
17- Newmark, N.M. 1965. Effects of earthquakes on dams and embankments.Geotechnique,15(2):139-160
18- Rampello, S., Cascone, E., and N. Grosso, 2009.  Evaluation of the seismic response of a homogeneous earth dam. Soil Dynamics and Earthquake Engineering, 29(5):782–798.
19- Sarma, S. K. 1973. Stability analysis of embankments and slopes. Géotechnique, 23(3):423-433.
20- Sarma, S. K. 1975. Seismic stability of earth dams and embankments. Géotechnique, 25 (4): 743.761.
21-   Sarma, S. K. 1979. Response and stability of earth dams during strong earthquakes. Misc. paper GL-79-13. Geotechnical Laboratory, U.S. Army Engineer Waterways Experiment Station, P.O. Box, 631, Vicksburg, Mississippi, 39180.
22- Sarma, S. K. and M. V. Bhave,1974. Critical acceleration versus static factor of safety in stability analysis of earth dams and embankments. Geotechnique, 24(4): 661-665.
23- Seed, H.B. 1966.  A method for earthquake resistant design of earth dams. Journal of the Soil Mechanics and Foundations Division, ASCE, 92(1):13–41.
24- Seed, H. B. 1980. Lessons from the performance of earth dams during earthquakes. Design of Dams to Resist Earthquake, Institution of Civil Engineers, London, pp. 251-258.n
25- Skermer, N.A.1973. Finite element analysis of El infiernilo dam. Canadian Geotechnical Journal, 10(2):129-144.
26- Swaisgood, J. R. 2003. Embankment dam deformations caused by earthquakes.  7th Pacific Conference on Earthquake Engineering, 13-15 February, University of Canterbury Christchurch, New Zealand, paper 014.
27- Terzaghi, K. 1950. Mechanisms of landslides. Engineering Geology, (Berkley) Volume, Geological Society of America, New York, NY, USA.
28- Wang, Z.L., Makdisi, F.I. and J. Egan, 2006. Practical applications of a nonlinear approach to analysis of earthquake-induced liquefaction and deformation of earth structures. Soil Dynamics and Earthquake Engineering, 26(4):231–252.
Volume 40, Issue 2
September 2017
Pages 265-281
  • Receive Date: 31 January 2016
  • Revise Date: 25 September 2017
  • Accept Date: 12 June 2016
  • First Publish Date: 23 August 2017