Response and Stability of Earth Dams During Strong Earthquakes: Final
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r - > U, (Um 'f y> ruTün 0 D itlt urr D I 1 § D 1 1 M ISCELLA N EO U S PAPER GL-79-13 RESPONSE AND STABILITY OF EARTH DAMS DURING STRONG EARTHQUAKES by S. K. Sarma Department of Civil Engineering Imperial College of Science and Technology, London, U. K. June 1979 Final Report Approved For Public Release; Distribution Unlimited Prepared for Office, Chief of Engineers, U. S. Army Washington, D. C. 20314 Under Grant Agreement No. DAERO-75-G-OIO Monitored by Geotechnical Laboratory U. S. Army Engineer Waterways Experiment Station P. O. Box 631, Vicksburg, Miss. 39180 i library NOV 2 3 1979 Bureau of Reclamation penver, Colorado Destroy this report when no longer needed. Do not return it to the originator. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. V BUREAU OF RECLAMATION DENVER LIBRARY /A 92067231 dr 92067231 Unni aggi -P-j SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER Miscellaneous Paper GL-79-^3 4. T IT L E (and Subtitle) 5. TYPE OF REPORT ft PERIOD COVERED ' RESPONSE AND STABILITY OF EARTH DAMS Final report DURING STRONG EARTHQUAKES 6. PERFORMING ORG. REPORT NUMBER 7. AUTHORfa; 8. CONTRACT OR GRANT NUMBERfs) S. K. Sarnia Grant Agreement Wo. D A E R O - 75 - G - 010 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA ft WORK UNIT NUMBERS Department of Civil Engineering Imperial Coll'ege of Science and Technology CWIS Work Unit 311*+*+ London, United Kingdom 11. CONTROLLING OFFICE NAME AND ADDRESS REPORT DATE June 1979 / Office, Chief of Engineers, U. S. Army 13. NUMBER OF PAGES Washington, D. C. 2031*+ 269 14. MONITORING AGENCY NAME ft ADDRESS^// different from Controlling Office) 15. S E C U R IT Y CLASS, (of thia report) U. S. Army Engineer Waterways Experiment Station Unclassified Geotechnical Laboratory 15«. D E C L ASSI FI C A T IO N / DO W NG RADING P. 0. Box 631, Vicksburg, Miss. 39180 SCHEDULE 16. DISTRIBUTION STATEMENT (of thie Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abatract mitered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverae aida if neceaaary and identify by block number) Earth dams Earthquake resistant structures Earthquakes Earthquake engineering Dam stability 20, A B S T R A C T fConCfisu« a m reverwm f t naceaeaty and identify by block number) This earth dam study considers the response of an earth dam resting on a layer underlain by a rigid base and subjected to a strong ground motion. The dam and the layer are assumed to be elastic, homogeneous, and of simple geo metric form. The properties of the dam and the layer may be different. Several combinations of the properties of the dam and the layer, as well as. several ratios of the height of the dam to the depth of the layer, are studied. (Continued) OD ,;s rw M73 EDITION OF f NOV 65 IS OBSOLETE __________ Unclassified__________ SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) Unni assi fi prl SECURITY CLASSIFICATION OF THIS PAGEfBTian Data Entered) 20. ABSTRACT (Continued). All of these are subjected to nine strong motion acceleration records, and their response is calculated. At the same time, seismic coefficients for various sizes of sliding wedges are computed. The results of individual cases and their envelopes are presented in the spectral form for design purposes. Methods of stability analysis for static and pseudostatic conditions are examined, and two new methods are presented. One of these methods is suitable for analyzing existing slip surfaces, and the other for quick compu tation of the critical acceleration for a given surface. Since pore water pressure developed in the dam during an earthquake is an important factor, a method of stability analysis is developed that takes the excess dynamic pore water pressure into account. The method is based on limit equilibrium principle. Pore water pressures are introduced in the form of dynamic parameter An . The result is obtained in the form of a critical acceleration required to cause failure as a function of the number of cycles of earthquake load. Also shown is the computation of displacements of sliding wedges when the earthquake load is greater than the critical acceleration. Then the study is concluded with an example of the analysis of the effects of the San Fernando earthquake of 9 February 1971 on the Lopez Dam in California. Unclassified SECURITY CLASSIFICATION OF THIS PAGEfWTien Data Entered) PREFACE The work reported herein was performed by Dr. S. K. Sarma, of the Department of Civil Engineering, Imperial College of Science and Technology, London, United Kingdom, under Grant Agreement No. DAER0-75-G-010, dated 6 November 197*+ • This grant was sponsored by the Civil Works Directorate, Office, Chief of Engineers, U. S. Army, under CWIS Work Unit 311*+*+» and administered by the U. S. Army Procurement Agency (Europe). The research was conducted during the period from November 197*+ to November 1976 under the direction of Drs. F. G. McLean, former Chief, and A. G. Franklin, Research Civil Engineer, Earthquake Engineering and Vibrations Division, Soils and Pavements Laboratory (now designated Geo technical Laboratory (GL)). General guidance was provided by Mr. J. P. Sale, Chief, and Mr. S. J. Johnson (retired), Special Assistant, GL. The research in this document was made possible through the support and sponsorship of the U. S. Government through its European Research Office. The various computer programs were developed on the CDC 6*+00 computer at Imperial College. Special acknowledgement is due to Professor N. N. Ambraseys for several discussions during the course of the project. Directors of the WES during the performance of this work and preparation of the report were COL G. H. Hilt, CE, and COL J. L. Cannon, CE. The Technical Director was Mr. F. R. Brown. 1 CONTENTS Page PREFACE ........................................................ 1 CONVERSION FACTORS, U. S. CUSTOMARY TO METRIC (Si) UNITS OF MEASUREMENT .................................................. 3 PART I: INTRODUCTION.......................................... 1+ Background .............................................. 4 Purpose .................................................. 5 PART II: INERTIA FORCES AND SEISMIC COEFFICIENTS IN EARTH DAMS . 6 Inertia Forces .......................................... 6 Seismic Coefficient ............................. 19 Discussions and Design Curves .................. 25 PART III: STABILITY ANALYSIS.............................. .. 3b Critical Acceleration of Slip Surfaces ................... 3^ Existing Methods of Stability Analysis ................... 35 New Methods of Stability Analysis ........................ 39 Stability of Slopes Under Earthquake Conditions with Dynamic Pore Pressure ............................ 1+7 PART IV: DISPLACEMENT CRITERION OF D E S I G N .................... 58 PART V: ANALYSIS OF THE LOPEZ D A M ............................ 66 Seismic Coefficients .................................... 66 Critical Accelerations .................................. 73 Displacements ............................................ 73 PART VI: CONCLUSIONS.......................................... 79 R E F E R E N C E S ...................... 80 APPENDIX A: SOLUTION OF THE GOVERNING EQUATIONS FOR A DAM-FOUNDATION SYSTEM ........................ A1 APPENDIX B: SEISMIC COEFFICIENTS .............................. B1 APPENDIX C: ROOTS OF THE EQUATION m tan (qa ) = J (a )/J, (a ) . Cl n o n 1 n APPENDIX D: ACCELERATION RECORDS OF FIVE EARTHQUAKES .......... D1 APPENDIX E: SEISMIC COEFFICIENTS AND POINT ACCELERATION SPECTRA .......................................... El APPENDIX F: ENVELOPE OF SEISMIC COEFFICIENTS AND POINT ACCELERATION SPECTRA .............................. FI APPENDIX G: NOTATION.................................. G1 2 CONVERSION FACTORS, U. S. CUSTOMARY TO METRIC (Si) UNITS OF MEASUREMENT U. S. customary units of measurement used in this report can he con verted to metric (Si) units as follows: Multiply JJL To Obtain inches 2 .5 1* centimetres feet 0.301+8 metres pounds (mass) per 16.018U6 kilograms per cubic cubic foot metre pounds (force) 1+. 1+1+8222 newtons pounds (force) per 689^.757 pascals square inch pounds (force) per U7•88026 pascals square foot feet per second 0.301+8 metres per second degrees (angle) 0.017U5379 radians 3 RESPONSE AND STABILITY OF EARTH DAMS DURING STRONG EARTHQUAKES PART I: INTRODUCTION Background 1. With the failure of the Lover San Fernando Dam during the San Fernando earthquake of 9 February 1971, the attention is directed towards the problem of rational design of earth and rockfill dams against strong earthquake ground motion. With the aid of a high-speed computer and a very sophisticated method of finite element analysis using the nonlinear properties of the materials at the time of failure and knowing the ground motion characteristics of the San Fernando earthquake, it is possible to back-analyze and give the cause of this failure, Seed et al. (1973). But for the designer, who has yet to fix a dam section, to satisfy himself about the soil properties obtained from laboratory tests and assume the ground motion characteristics of a future event, the use of the finite element method is not economical. Moreover, the results obtained by a sophisticated