1、GEOTECHNICAL SPECIAL PUBLICATION NO. 80 ANAlYSIS AND DESIGN OF RETAINING STRUCTURES AGAINST EARTHQUAK y r-, - f. t ! X I I / He c- , x,+nHanH / c x, -2 ) k.fx,+nHenH H 1 . a I j_. c x,+% HB J T I .4;. c.h at I I tlljll f i.1 k. x,+% He J nH e j , e l I I I L-:-_-lxl -c.te c.,x, “k.e 6 EDITBJ BY SHAM
2、SHER PRAKASH GEOTECHNICAL SPECIAL PUBLICATION NO. 80 ANAlYSIS AND DESIGN OF RETAINING STRUCTURES AGAINST EARTHQUAKES Proceedngs of seal sponsored by the Soli Dynamics Committee of The Geo-lnslltute of the American SOciety or Civil Engineers In conJunction With the ASCE Nallonal Convenllon . In W8shl
3、ngton, DC November 1 D-14, 1998 EDITED BY SHAMSHER PRAKASH Published by scr AmertCIIn soelty S of Civil EnglnHrs 345 East 47th Street New York, New York 1 0017-2398 Abstract: This proceedings, Analysis and Design of Retaining Structures against Earthquakes, contains both invited and contributed pape
4、rs, which focus on the questions of 1) dynamic earth pressures on fixed and movable rigid and flexible walls; 2) displacements in translation and rotation of walls under earthquakes; 3) behavior offi!Js an.d abutments during earthquake; and 4) centrifuge tests on walls. Both analytical and experimen
5、tal data have been presented on possible behavior of retaining structures under seismic loading. A study of this volume and other published literature shows considerable effort is being devoted to determination of realistic dynamic pressures, displacement in translation and rotation of retaining str
6、uctures and behavior of fills for abutments. Since a synthesis of these studies is not currently available, there are no unified and generally acceptable solutions to the above questions. However, the discussions and presentations of the papers during the session does highlight the need for such sol
7、utions and more definite descriptions of unsolved problems. Library of Congress Cataloging-in-Publication Data Analysis and design of retaining structures against earthquakes : proceedings of sessions sponsored by the Soil Dynamics Committee of the ASCE Geotechnical Engineering Division in conjuncti
8、on with the ASCE Convention in Washington, D.C., November 10-14, 1996 I edited by Shamsher Prakash. p. em. - (Geotechnical special publication ; no. 60) Includes bibliographical references and indexes. ISBN 0-7844-0206-X I. Retaining walls-Design and construction-Congresses. 2. Earthquake resistant
9、design- Congresses. 3. Structural analysis (Engineering)-Congresses. I. Prakash, Shamsher. II. American Society of Civil Engineers. Geotechnical Engineering Division. Soil Dynamics Committee. IH. ASCE National Convention (1996 : Washington, D.C.) IV. Series. TA77.A53 1996 96-44715 624.164-dc20 CIP T
10、he Society is not responsible for any statements made or opinions expressed in its publications. Photocopies. Authorization to photocopy material for internal or personal use under circumstances not falling within the fair use provisions of the Copyright Act is granted by ASCE to libraries and other
11、 users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service, provided that the base fee of $4.00 per article plus $.25 per page is paid directly to CCC, 222 Rosewood, Drive, Danvers, MA 01923. The identification for ASCE Books is 0-7844-0206-X/96/$4.00 + $.25 per copy
12、. Requests for special permission or bulk copying should be addressed to Permissions GEOTECHNICAL AND CONSTRUCTION CONSIDERATIONS PREFACE Retaining structure may be subjected to seismi c loads and experience either deformations and/or increased earth pressures. These structures may be either rigid-m
13、asonry free-s tanding retaining wall s for highways, sections of wing walls for hydraulic structures, and abutments of bridges. Flexible retaining structures are most often reinforced earth sections. Rigid structures have been designed for dynamic earth pressures most of the time. A sol u tion for d
14、isplacements of rigid retaining walls was obtained by our Research Group at the University of Roorkee (India) in I 974 for the first time. Subsequently for the last two de cades, their displacements were analyzed and designs based on permissibl e displacements were attempted. We have not reached a s
15、tage where acceptable analytical tools and design procedures for such structures are available. Studies on such structures during earthquakes is difficult because earthquakes cannot be made to order! Therefore, recourse is made to alter nate studies, e.g. on centrifuge and, shake table models, and a
16、nalytical studies and their com parison with performance records. Thus this session is organized with the objective to identify the state of practice in analysis and design of retaining structures under dynamic loads and address the unsolved issues. The papers were, therefore, invited from authors b
17、oth within and outside the USA. There are 5 contributions from the US and 3 from overseas. This session was held at the ASCE Fall Convention in Washington DC on November 12, 1996 and was sponsored by the Soil Dy nanJics Committee of the Geotechnical Engineering Division of ASCE. It is the current pr
18、actice of the Geotechni cal Engineering Division that each paper pub lished in a Geotechni cal Special Publication (GSP) be reviewed for its content and quality. These special technical publications are intended to reinforce the programs presented at con vention sessions or specialty conferences and
19、 to contain papers that are timely and may be controversial to some extent. Because of the need to have the GSP avail abl e at the conven tion, time available for reviews is generally not as long and reviews may not be as compre hensive as those given to papers submitted to the Journal of the Divisi
20、on. Still we had orga nized our review process in a timely manner. At least 2-positive reviews were obtained for each paper accepted for publication and discussion. In fact one paper will be published in the Journal based on our review process but was presented at this session. Thus there is hardly
21、any difference in the purpose and technical status of contributions to this geotechnical special publication as compared to those in the Journal. In accordance with ASCE policy, all papers published in this vol ume are e ligible for dis cussion in the Journal of the Geotechnical Engineering Division
22、 and are eligible for ASCE awards. Reviews of papers published in this volume were conducted by the Soil Dynamics Committee of the Geotechnical Engineering Division. The following committee members or cooperating persons from the general membership reviewed these papers: T. Crespell ani Ahmed W.M. E
23、lgamal Steve Kramer Jeen-Shang Lin Rowland Richards, Jr. Raj Siddharthan A.S. Veletsos v Panos Dakoulas W.D. Liam Finn Sanjeev Kumar Farrokh Nadim Glenn J. Rix Cetin Soydemir Mishac Yegian Personal thanks go to Panos Dakoulas, Chairman of the Soil Dynamics Committee, for his help and support in orga
24、nizing this session. I also want to thank all the experts who gave both the time and effort in reviewing the papers. Last but not least, thanks are due to all the authors who kindly accepted the invitation to contribute to this volume and to the session in Washing ton D.C. August 28, 1996 vi Shamshe
25、r Prakash, F. ASCE Professor of Civil Engineering University of Missouri-Rolla Rolla, Missouri Session Organizer and Editor CONTENTS Seismic Pressures against Rigid Walls G. Wu and W.D . Liam Finn . . . . . I Dynamic Response of Cantilever Retaining Wa:lls A.S. Veletsos and A.H. Younan . . : 19 On S
26、eismic Displacements of Rigid Retaining Walls Y. Wu and Sharnshet Prakash 21 Rotation of Large Gravity Walls on Rigid Foundations Under Seismic Loading R.S. Steedman and X. Zeng . . 38 In-Situ Dynamic Response of Cantilever Walls Sreenivas Alampalli and Ahmed W.M. Elgarnal . 57 Seismic Analysis and
27、Model Studies of Bridge Abutments K.L. Fishman and R. Richards, Jr . 77 Earthquake-Induced Ground Settlements of Bridge Abutment Fills Raj V. Siddharthan and Mahmoud El-Gamal . . 100 Earthquake Destructiveness Potential Factor and Permanent Displacements of Gravity Retaining Walls T. Crespellani, C.
28、 Madiai and G. Vannucchi . . . 124 Subject Index . . 135 Author Index . . . , . . . . . 136 vii SEISMIC PRESSURES AGAINST RIGID WALLS Guoxi Wul and W.D. Liam Finn2 ABSTRACT Simplified linear elastic analytical solutions are presented for the seismic pressures against rigid walls which agree closely
29、with the exact solutions presented by Wood (1973). The finite element method is used to extend the analyses to nonhomogeneous elastic materials and to nonlinear soils. The finite element analyses give almost exact solutions for the elastic cases. Some practical guidelines are given for estimating th
30、e dynamic pressures for use in practice. INTRODUCTION Seismic pressures against retaining walls are usually determined using the Mononobe-Okabe method (Mononobe and Matsuo, 1929; Okabe, 1924). This method is based on the assumption that a wedge of soil bounded by the wall and the shear failure plane
31、 in the backfill moves as a rigid body under the peak vertical and horizontal ground accelerations or designated fractions thereof. Most commonly only horizontal inertia forces are included. The Mononobe-Okabe method is based on the assumption that the wall can displace enough to permit a failure pl
32、ane. Rigid walls, such as deep basement walls, do not satisfy the displacement criteria for shear plane development, and therefore the Mononobe-Okabe approach cannot be used. Matsuo and Ohara (1960) formulated an elastic solution to the seismic pressures against a rigid wall, but did not present any
33、 numerical values. Wood (1973) developed an exact analytical plane strain solution assuming elastic response of a uniform backfill. The solution is quite complicated and is usually applied approximately. Significant errors in estimating 1 AGRA Earth Finn et a!., 1994). The model is applicable to bot
34、h finite and semi-infinite backfills. An analytical solution is presented for a uniform elastic backfill and a finite element solution for nonhomogeneous elastic and nonlinear backfills. The elastic analytical solutions are validated by comparison with the exact solutions by Wood (1973). Comparisons
35、 with the other approximate elastic solutions show that the modified shear beam model of Arias (1981) gives results closer to the Wood (1973) solution over all ranges of significant variables (Wu, 1994; Finn et al., 1994). Veletsos eta!. (1995) also adopted the simple Arias (1981) shear model in the
36、ir analyses of rigid walls with backfills of finite length rather than the model with a more exact expression for shear stress used by Veletsos and Younan (1994). FORMULATION OF ANALYSIS Figure 1(a) shows the geometry of the plane strain problem and associated boundary conditions. A uniform elastic
37、soil layer is confined by two vertical rigid walls and a rigid base. The soil layer has a total length of 2L and height of H. When subjected to horizontal seismic body forces, the soil layer in the system generates an antisymmetric field of horizontal normal stresses, cr, with cr, = 0 at x = L. Ther
38、efore, the original wall-soil problem can be reduced to the system in Fig. 1(b) for all subsequent analyses. The ground acceleration is input at the base of the wall-soil system. Although the problem involves two displacement components, horizontal and vertical components u and v, only the horizonta
39、l displacements u have been taken into account in the analysis in order to simplify the solution of the problem. It will be shown that this simplification does not induce a significant error in the solution and that reliable estimates of the dynamic earth thrust can be obtained. H SEISMIC PRESSURES
40、AGAINST RIGID WALLS Y (a) u=O liu/liv-0 homogeneous elastic soil (plane strain) u=O .(X.X.X. and (b) equivalent problem by using anti symmetric condition. Initially, the soil is assumed to be homogeneous, isotropic and elastic, with a shear modulus G, Poissons ratio v, and mass density p. The equati
41、ons of dyilamic force equilibrium for the backfill in the horizontal and vertical directions are written as (1) (2) 3 4 RETAINING STRUCTURES ANALYSIS AND DESIGN where ax and cry are the normal stresses in the X and Y directions and txy is the shear stress in the X-Y plane. The displacements in the X
42、 and Y directions are u and v, respectively. For two-dimensional plane strain conditions, the stress components are related to the displacements by 2G au av a =- (1-v)-+v- 1- 2v ax fly (3) 2G av au a =- (1-v)-+v-Y 1-2v By ax (4) t = o(au + Bv) xy By ax (5) Since only the horizontal displacements u a
43、re taken into account in the analysis, only the equation of dynamic force equilibrium in the horizontal direction, Eq. (1), is used. Considering various forms of approximation to the problem, the governing equation of the undamped free vibration of the backfill in the horizontal direction can be wri
44、tten as and the normal stress ax is given by au (j = AG -x ,. ax (6) where pis the mass density of the soil backfill, tis time, and 8 and 13 are functions of Poissons ratio v (Wu, 1994). The precise expressions for e and p depend on the approximations used to model the wall-soil system. Three cases
45、are examined and their corresponding expressions for 8 and 13 are given below. SEISMIC PRESSURES AGAJNST RIGID WALLS Proposed Modified Shear Beam Model In the poposed model, the shear stresses are modelled using the shear beam analogy. Therefore, shear stress “txy is given by au = G -xy Oy The norma
46、l stress cr., after assuming cry= 0 in the backfill, is found to be cr =_2_ Gau X 1-V ax Comparison with Eq. (7) gives =-2-1- v (8) (9) (10) Substituting Eq. (8) and Eq. (9) into Eq. (1) and comparing with Eq. (6), one finds, 2 8 : -1- v (11) 5 The values of 8 and may be derived in a similar manner
47、for other assumptions. Values are given below for two other models; cry = 0 which was adopted by Veletsos and Younan (1994) and v = 0. v=O Model In this case 8 = = 2(1 - v) 1- 2v Qy=OModel In this case, (12) 6 RETAIN1NG STRUCTURES ANALYSIS AND DESIGN 2 - v 8=-1- v 2 13=-1- v (13) (14) The dynamic re
48、sponse of the wall-soil system for these three cases can be represented by the saine equation, Eq. (6), using appropriate values for 8. Therefore, the general derivation of dynamic solutions proceeds from Eq. (6). SOLUTIONS FOR LlNEAR ELASTIC CASE: UNIFORM BACKFILL The equation of motion for free vi
49、bration of the system is (6 his) This equation may be solved by the separation of variables technique. Assume that the displacement solution has the form, For the given boundary conditions, the solution reduces to (16) in which the mode shapes cl.,.,(x,y) are given by (17) b = (2n - l)1t . n 2H n = 1,2, . (18) and (2m -1)7t am = 2L ; m = l,2, . (19) SEISMIC PRESSURES AGAINST RIGID WALLS 7 The natural frequencies of the system are given by (20) The frequency of the first mode is given by (21) Whe
