EXPERIMENTAL RESULTS ON EARTH PRESSURES ON RIGID WALL UNDER SEISMIC CONDITION

Transcription

1 3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada Augut -6, 24 Paper No. 88 EXPERIMENTAL RESULTS ON EARTH PRESSURES ON RIGID WALL UNDER SEISMIC CONDITION Agatino Simone Lo Grao, Michele Maugeri 2 and Erneto Motta 3 SUMMARY Thi paper contain the experimental reult of a erie of haking table tet of a model of gravity retaining wall, with the purpoe to invetigate the ditribution of dynamic earth preure in dry coheionle backfill and the effect of the oil-wall friction on the ditribution of preure. All the tet were conducted at the Univerity of Catania haking table. The model were intrumented to meaure diplacement, acceleration and dynamic preure. The reult of the experimental program how that the dynamic earth preure ditribution i influenced by the wall movement mode and the point of application of the active thrut i alway near the top of the wall. The reduction of the wall friction produce an increment of dynamic preure, influencing the failure mode of the oil-wall ytem. All the recorded preure how a non linear ditribution with depth. INTRODUCTION The evaluation of the dynamic earth preure i an important apect in the retaining tructure deign. Recent earthquake how that the preure ditribution depend on the wall movement and on the acceleration level; the magnitude of the total lateral earth preure and the point of application of the total thrut are not univocally determinate and thee value often differ from olution. The method i baed on three aumption: the wall ha already deformed outward ufficiently to generate the minimum active earth preure; a planar failure urface were formed when lateral oil deformation become large enough to fully mobilize the hear trength of the oil; the oil wedge formed i conidered a a rigid body o that the acceleration maintaining contant hi value with depth and amplification effect i not oberved. Thi theory, however, cannot take into account the effect of oil deformation and the conequent degradation of internal friction angle to reidual tate that occur in a dene oil during an earthquake. PhD Doctor Dept. of Civil and Environmental Engineering Univerity of Catania, Italy, imone.lograo@ticalinet.it 2 Full Profeor in Geotechnical Engineering, Dept. of Civil and Environmental Engineering Univerity of Catania, Italy, mmaugeri@dica.unict.it 3 Profeor in Geotechnical Engineering, Dept. of Civil and Environmental Engineering Univerity of Catania, Italy, emotta@dica.unict.it

2 Many author have tudied the ditribution of the tatic and dynamic earth preure, with variou olution, yet there i not enough experimental analyi to validate thee theorie and epecially in evaluating the effect of the oil-wall friction angle on dynamic earth preure. Prakah (98) reported a coure tudy conducted by Nandakumaran [6] on rigid wall, meter high, with different wall movement, howing that the ditribution of preure i non linear with depth and the maximum value i reached at 65% of wall height from the top of the wall. Sherif, Ihibahi and Lee (982) [] conducted a erie of tet on the Wahington Univerity haking table. The quai-tatic and dynamic tet howed that the preure ditribution wa dependent on the oil-wall friction angle and that the critical value of the wall diplacement i: S=H(7-,3ϕ)-4 where H i the height of the wall an ϕ i the value of internal friction angle. The tet how that the value of dynamic preure i increaed of 3% repect the theoretical prediction and the point of application of total active thrut can be aumed to 5H from the bae of the wall. The ditribution of the dynamic preure i influenced by the wall movement a hown in the tet conducted by Sherif & Fang (984) [9] where the wall i contrained to rotate about the top. In thee tet wa oberved an increment of the preure near the top of the wall due to arching tre effect of the oil and the point of application of total thrut correponding to the value of 5H from the bae of the wall. Thee reult compare well with thoe computed previouly by Scott (973), Matuo and Ohara (96) [4] and Wood (973) a well a by Fang and Ihibahi, (986) [] and Ihibahi and Fang (987) [2]. Recent theoretical approache have been developed to determine a more careful method of prediction of the total earth preure under eimic condition baed on a kinematical approach (Soubra and Macuh, 2) [], or conidering the effect of train localization (Zhang and Li, 2) [6], or conidering the lateral deformation of the oil between the active and paive tate of tre, including the tate at ret (Zhang, Shamoto and Tokimatu, 998a, Zhang, Shamoto and Tokimatu, 998b, Zhang, Shamoto and Tokimatu, 998c) [3] [4] [5]. Thi paper give an experimental confirmation to the theoretical approache howing that the ditribution of earth preure under eimic condition i non-linear. The point of application of the total thrut i trongly dependent by the wall movement during the motion and the ditribution i alo influenced by the oil-wall friction angle. The reult of the tet compare well with thoe computed uing the peudodynamic approach imilar to the method of Steedman and Zeng, (99) [2] where the inuoidal acceleration along the wall i given by H z u& &( z, t) = k genω t h V where V i the hear wave velocity, ω i the pulation of the lateral haking, H i the height of the wall and z the current height. The final expreion of the ditribution of the lateral preure can be expreed a: which i clearly non linear. p AE co( α φ) k γz h = enω co( δ α φ ) tanα t z V en( α φ) γz co( δ α φ ) tanα EXPERIMENTAL PROCEDURE The haking table of the laboratory of the Univerity of Catania conit in a teel frame and a teel plate bolted on the frame. It i 2 m long, m wide and 8mm thick and i upported by four roller contrained to move on rail, in order to retrict the motion only to one direction. The tet box i m long, m wide and m. The motion i provided to the table by a loading unit coniting of a hydraulic ytem whoe capacity i to tranfer a tatic load of 3 dan and a dynamic load equal to dan when the acceleration value i equal to 2g. The ytem i able to tranfer a maximum diplacement equal to ±25mm. The ide of the tet box are in gla with the purpoe to oberve

3 the model deformation and the failure urface during the tet. The thickne of the gla ide wa choen equal to mm in order to enure a plane-train deformation.the wall ued in the tet i a model micro concrete gravity retaining wall of height H=3. In order to avoid friction between the wall and the gla ide of the tet box, the wall wa made 5mm horter than the box width and the wall end were equipped with flexible platic flag to prevent and paing through the lateral gap. The oil ued in all tet i a dry ilica and from the Sicily eat coat which characteritic are D 6 /D = 2.47, D 5 = 2mm, maximum and minimum unit weight γ max =8.27KN/m3 and γ min =5.4 KN/m3 repectively, and peak value of the hear trength angle ϕ = 37 obtained at the ame relative denity ued in the tet a a reult of a erie of direct hear tet. The backfill were prepared by dry pluviation in the tet box, in which the depoition height wa maintained contant repect the backfill, obtaining a final relative denity Dr 75%. In each tet the model wa intrumented with two accelerometer and two LVDT diplacement tranducer with the purpoe to record acceleration and diplacement at the top and at the bae. A further accelerometer wa placed into the backfill, outide the failure wedge, to meaure the oil acceleration. Five preure tranducer were fixed on the internal face of the wall; the tranducer were provided of a circular contact area of of diameter, to record the value of preure at an interval of 6 along the depth. In figure i hown the experimental device. A data acquiition ytem and oftware for data proceing were employed to record and analyze data obtained during dynamic teting. To oberve the formation of the failure urface through the gla ide of the tet box, vertical black and marcher were introduced into the backfill. Diplacement Tranducer Preure Tranducer Accelerometer Dimenion in mm Figure : Poition of meaure intrument RESULTS General The oil-wall ytem were ubjected to a inuoidal input acceleration whoe amplitude wa trongly increaed with time until to a maximum value wherea the frequency wa maintained contant. A certain number of model were invetigated; in thi paper four tet are reported. The label TH indicate the model in which the oil-wall friction angle wa not reduced and the label TG indicate the model in which the oil-wall friction angle wa trongly reduced introducing a thin gla heet that wa glued on the internal face of the wall. The frequency of the input motion wa fixed to the value of 6Hz, while two different value of the amplitude, equal to 2,5mm and 3,mm, were ued. Thee amplitude value are able to tranfer to the ytem a maximum acceleration of 7g and 3g repectively. Diplacement and dynamic preure analyi Time-hitorie of diplacement and rotation for the tet named TH4 and TG2 (f=6hz, =2.5mm) are hown in figure 2. For the tet TH4, the accumulation of permanent diplacement wa gradual, but a large vibration wa poible to be oberved at the top of the wall from the beginning of the haking tet. Thi vibration increae when the wall and the table acceleration are negative, that i, directed backward. The rotation

4 of the ytem how different wall movement mode during the ame tet. It i poible to ditinguih a firt tage (until 3 ec.) in which the top of the wall, accumulate permanent diplacement and rotation, maintaining large vibration. degree Rotazione Rotation Spotamento Top diplacement Teta degree Rotazione Rotation Spotamento Top diplacement teta Spotamento Bae diplacement piede 5 3 Spotamento Bae diplacement Piede Figure 2: wall diplacement and ytem rotation for the tet TH4 (on the left) and TG2 (on the right) In a econd tage (after 3 ec), in which, i reached the threhold acceleration value, a udden increae of the permanent wall bae diplacement wa oberved. At thi phae of the motion correponded an abrupt change in the rate of rotation which invert hi coure. Thee two ditinct mode of ytem rotation produced different ditribution of dynamic preure, generating, during the econd tage, paive phenomena between the wall and the backfill near the top. In figure 3 i hown a detail of the recorded data at the intant of the tranlational failure. The notation PTh5 and PTh2, in figure 3, repreent the data of the preure tranducer at 5 and 2 of depth repectively. Figure 3 alo how the ditribution of the total dynamic preure at the two different tage of collape of the oil-wall ytem. 3. Cella PTh5 H5 Traduttore Top diplacement in teta Traduttore Bae diplacement al piede.5. σ [ ] σ [] Cella PTh2 H2 f=6hz, =2.5mm - Amax=2g Figure 3: wall diplacement and preure for the tet TH4 (on the left) and the ditribution of the dynamic preure for the tet TH4 for the two different wall movement mode (on the right) The recorded preure were compared with thoe computed with the and Coulomb theorie, auming a linear ditribution. From the data recorded for the tet TG2 can be oberved that the accumulation of permanent diplacement wa achieved without large vibration at the top of the wall from the beginning of the haking tet. The increae in the wall vibration i evident when the limit equilibrium at the bae i reached and an evident tranlation of the wall appear. Thi different behaviour could be attributed to the reduction of the oil-wall friction angle value. Alo in thi tet the ytem how different wall movement mode.

5 Comparing the two tet, it can be oberved that the final permanent diplacement value are approximately the ame, but the tet TG2 hown a notable reduction of rotation both at the firt tage and at the end of the haking tet. The reduction of the oil-wall friction angle and the conequently reduction of the top wall ocillation, produced a ditribution of the dynamic preure, that i characterized by a trong value of the preure recorded near the top of the wall, even when the limit equilibrium wa reached, due to the udden increae of permanent diplacement at the bae, with the conequent action of the paive effect between the wall and the backfill. Figure 4 how the time-hitory of the preure tranducer. The notation PTh have the ame previou ene of figure Cella PTh9 H9 Cella PTh5 H5 Cel PTh2 la H2 Cel pth27 la H27 f=6hz, =2.5mm - Amax=g 5 2 Figure 4: time-hitorie of the preure tranducer of the tet TG2 Figure 5 how the ditribution of the total dynamic preure at the collape of the ytem. Similar reult were obtained for the tet in which the hape of inuoidal input i different and the acceleration level wa increaed linearly until the end of the tet. σ [] Figure 5: ditribution of the dynamic preure for the tet TG2 The two tet reported in thi paper, labeled TH8 and TG4, how the ame behaviour of the tet previouly decribed. Two different tage of rotation correponding to two different ditribution of dynamic preure are evidenced: a marked ocillation of the top of the wall for the ytem without reduction of the oil-wall friction and an evident udden increae of permanent diplacement at the bae, with the paive effect for the ytem with low oil-wall friction.

6 Comparing the final value of permanent diplacement and rotation, it i poible to oberve that the final value of diplacement i the ame for both tet but a reveral of the final rotation wa recorded for the tet with the lower oil-wall friction angle. Thee reult are plotted in fig.6. The ditribution of dynamic preure are plotted in figure 7. degree degree Rotazione Rotation Top diplacement Rotazione Rotation Spotamento Top diplacement Teta Spotamento Bae Diplacemente Piede -.5 Spotamento Bae diplacement Piede Cella TPh9 H9 Cella TPh5 H5 Cella TPh2 H2 Cella TPh27 H27 Fae Stage "A" (a) f=6hz, =3mm - Amax=5g Fae Stage "B" (c) (d) Figure 6: a) wall diplacement and ytem rotation tet TH8; (b) wall diplacement and ytem rotation tet TG4; (c) time-hitory of dynamic preure tet TH8; (d) time-hitory of dynamic preure tet TG Cella TPh9 H9 Cella TPh5 H5 Cella TPh2 H2 Cella TPh27 H27 Fae Stage "A" (b) f=6hz, =3mm - Amax=8 5 Fae Stage "B". σ [] 2 7 σ [] σ [] 2 3 σ [] (a) (b) (c) (d) Figure 7: (a) ditribution of dynamic preure at tage A tet TH8; (b) ditribution of dynamic preure at tage B tet TH8; (c) ditribution of dynamic preure at tage A tet TG4; (d) ditribution of dynamic preure at tage B tet TG4 Bae motion amplification analyi The accelerometric data how a imilar behaviour for all ytem teted: before the threhold acceleration i reached, the wall acceleration i imilar to the acceleration in the backfill; when input acceleration i

7 grater than the threhold acceleration, a cutoff for the wall i clearly evident, indicating that a relative diplacement ha developed in the ytem and a erie of amplification phenomena appear. Figure 8 how the input, top and bae acceleration, and relative diplacement time-hitory for the tet TH4, wherea in figure 9 the peak acceleration progre are reported. The parabolic line repreent the envelope of the peak of input acceleration. It i apparent that permanent diplacement build up in the outward direction when the table i moving backward. After 3 econd, when the input acceleration i equal to 2g the wall bae how a reduction of the acceleration up to 5g, wherea the wall top acceleration, at the ame time, howed amplification phenomena when the input acceleration wa g at.8 ec. Thi behaviour i more evident for the acceleration in the backward direction. When the wall bae acceleration hown a reduction, a failure urface wa clearly formed and oberved through the gla ide of the tet box. At the maximum value of input acceleration wa recorded an amplification of the wall top acceleration of about 5% and a reduction of wall bae acceleration of about 3%. a/g a/g Top diplacement. 5 2 Bae diplacement Input acceleration Top acceleration Bae acceleration Input acceleration Figure 8: input and wall top acceleration compared with wall top and bae diplacement (on the left); input and wall bae acceleration compared with wall top and bae diplacement (on the right) Acceleration (a/g) Acceleration (a/g) Backfill_acceleration Wall top_ acceleration Wall bae acceleration Time () -. Backfill acceleration Wall top acceleration Wall bae acceleration Time () Figure 9: time-hitorie of peak acceleration when ytem wa direct outward(on the left); time-hitorie of peak acceleration when ytem wa direct backward (on the right) Moreover with the amplification phenomena recorded i aociated a difference of phae between the accelerometric record of the input and of the top of the wall, a hown in the previou fig.8a.thi phae change in lateral acceleration play an important role on the ditribution of the dynamic increment of the earth preure. Thee reult compare well with thoe meaured by Steedman and Zeng (99) by centrifuge tet. In figure the acceleration and diplacement time-hitory a well a the peak acceleration progre for the tet TG2 are reported. For the ame tet, after about 3 econd, when the input acceleration i equal to 2g the wall bae how a reduction of the acceleration until 2g,

8 wherea the wall top acceleration howed amplification phenomena when the input acceleration wa 5g at 2 ec. Thi behaviour i again evident for the acceleration in the backward direction. At the maximum value of input acceleration wa recorded a very trong amplification of the wall top acceleration of about % and a reduction of wall bae acceleration, imilar to the TH4 tet, of about 3%. Alo for thi tet, the amplification phenomena recorded are aociated to a different of phae between the accelerometric record of input and of wall top. Similar reult were obtained for the tet TH8 and TG4. a/g. 5 8 Backfill acceleration Top acceleration a/g Diplacem ent Diplacement Bae acceleration Backfill acceleration (a) (b) - - Acceleration (a/g). Backfill acceleration Wall top acceleration Wall Bae acceleration Time () (c) (d) Figure (a) input and wall top acceleration compared with wall top and bae diplacement; (b) input and wall bae acceleration compared with wall top and bae diplacement; (c) time-hitorie of peak acceleration when ytem wa direct outward; (d) time-hitorie of peak acceleration when ytem wa direct backward Failure urface analyi For all tet a clear failure urface wa oberved. In figure the ytem TH4 before and after the development of the failure urface i reported. It i clear the effectivene of black and marker evidencing the failure urface. An evident concavity wa detected in the failure urface a remarked by the red curve. For thi tet the angle formed by the failure urface with the horizontal wa approximately aumed equal to 55. The rotational behaviour decribed previouly, i emphaized by the large inclination of the black and marker placed inide the failure wedge, wherea the failure urface i well evidenced due to the large permanent diplacement of the wall. The average value of the vertical marker rotation i equal to 5 direct clockwie. When the oil-wall friction wa reduced, in the tet TG2, a different failure mode of the ytem wa oberved and a different failure wedge formed at the end of the tet (figure 2). For thi tet, i clear that the failure urface i a plane, a proved by the red line, with the angle formed repect the horizontal equal to 6. The rotational behaviour i emphaized by the large inclination of the black and marker placed both inide the failure wedge and both epecially outide the Acceleration (a/g) Backfill acceleration wall top acceleration wall bae acceleration Time ()

9 failure wedge. The average value of the vertical marker rotation i equal to 9 direct clockwie. For the tet TH8 and TG4 imilar reult were oberved and it had been reported in figure 3. (a) (b) Figure : The ytem named TH4: (a) before and (b) after the formation of the failure urface Figure 2: The ytem named TG2 after the formation of the failure urface (a) (b) Figure 3: The ytem named TH8 (a) and TG4 (b) after the formation of the failure urface. DISCUSSION Analyzing the previou data can be underlined that a reduction of oil-wall friction angle produce a very large increment of acceleration level at the wall top. With thi behaviour two different type of diplacement are aociated: a recoverable and an irrecoverable that occur for each cycle of input load; the firt, defined a elatic diplacement can be calculated and hi effect on acceleration level can be expreed by the follow equation:

10 2 2 2 ( xt ) xt & ' w = = t t t where i the diplacement impoed by the input motion and xt i the relative diplacement between the oil-table ytem and the top wall. The tet conducted have hown that, the elatic diplacement of the wall top i depending by the value of oil-wall friction angle, epecially in the initial tage of the motion, and that hi value ha a ignificant influence on dynamic preure. Diplacement analyi how that two different wall movement mode occur during the ame tet. In a firt tage a reduction of the preure cell TPh3 and TPh9, becaue of the initial rotation and to a trong increment of the dynamic earth preure near the bae wa oberved, with the maximum value recorded at the load cell TPh2. Thee different value of preure are due to the different value of relative permanent diplacement recorded at wall top and bae. Thi firt tage i generated by the inertial force that occur near the top of the wall due to the failure wedge hape. Wherea the acceleration level wa increaing together to the permanent rotation at the top of the wall, the threhold acceleration wa reached and a bae diplacement wa clearly evident. At thi tage the preure change and the ytem involved in a rotation about the top mode. The preure meaured by cell TPh3 and TPh9 began to build up with mall rotation angle. A oil arching developed in the backfill and a new dynamic preure ditribution appeared, totally different from the previou one. Thi difference reult in a higher point of application of the total thrut. When the oil-wall friction wa reduced the oil arching effect maintained contant ince low level of acceleration, and the preure ditribution wa trongly influenced. The paive phenomena oberved during the tet near the top, where large vibration were recorded, are due to different mode of vibration for the wall and the backfill, epecially when the oil degradation and the effect of train localization and pot-peak reduction in hear reitance occur in the backfill oil generating a reduction in the natural frequency of the oil-tructure ytem. The tet performed how that a trong reduction of oil-wall friction produce a ditribution of total dynamic preure with a point of application placed near the top of the wall and with a value that differ from the prediction. Thi apect i evident alo during the tet without reduction of oil-wall friction angle, where the recorded value of preure at the two failure tage are alway higher than thoe etimated by Mononobe-Okabe formula. When the acceleration level wa increaed and the failure of the ytem wa due to a rotational about top mode, the oil wedge formed tend to puh up the wall, becaue a change for an upward hear force wa occur. The failure urface hape how the concavity toward the backfill. When the oil-wall friction angle wa reduced a imilar behaviour did not appear and a plane failure urface formed with a maller failure wedge. The previou dicuion how that a low value of oil-wall friction angle produce a trong increment of the acceleration amplification near the top of the wall, generating a non-linear preure ditribution with an higher point of application. The oil-wall friction reduction produce a reduction of the amplification of wall top acceleration. Moreover for all the tet conducted, it wa oberved that the reduction of oil-wall friction produce large deformation alo into the backfill outide the failure wedge. CONCLUSIONS The following concluion could be made baed on the experimental reult obtained and dicued in thi paper: The dynamic preure ditribution i trongly influenced by the wall movement mode and two different tage were oberved during the ame tet; An elatic diplacement i exerted by the wall during the initial tage of the motion producing a ort of reduction in the acceleration amplification; a reduction of oil-wall friction angle produce a large increment of acceleration level at the wall top; for rotation about bae mode, that occur during the firt tage, the dynamic earth preure ditribution i non-linear with depth and the point of application i near the bae of the wall;

11 For rotation about top, during the econd tage, the dynamic preure ditribution i non linear with depth, arching oil tre wa deduced acting near the top of the wall and higher point of application of the reultant i reached; a trong reduction of oil-wall friction angle produce a ditribution of total dynamic preure with a point of application placed near the top of the wall and with a value that differ from the prediction; Failure wedge hape i influenced by oil-wall friction angle deducing a change in the inertia force; All the experimental value of dynamic preure meaured, are higher repect to the theoretical value of the active earth equation given by Mononobe & Okabe. Thi indicate a paive tate due to relative diplacement of oil-wall ytem, epecially near the top of the wall.. REFERENCES. V. S. Fang, I. Ihibahi, Earth Preure with Variou Wall Movement, Journal of Geotechnical Engineering, ASCE, Vol. 2, N. 3, Ihibahi, V. S. Fang Dynamic Earth Preure with Different Wall Movement Mode, Soil and Foundation, Vol. - 27, N. 4, A. S. Lo Grao, dynamic analyi of the earth preure ditribution on a gravity retaining wall by haking table tet, Ph.D. Diertation, Geotechnical Engineering, Univerity of Catania, Italy, December H. Matuo, S. Ohara, Lateral Earth Preure and Stability of Quay Wall during Earthquake, Proc. 2nd World Conference on Earthquake Engineering, Tokyo, Japan, N. Mononobe, R. Matuo, On the Determination of Earth Preure during Earthquake, Paper No. 388, Proc. of World Engineering Congre, Vol. 9, P. Nandakumaran, V. H. Johi, and dynamic Active Earth Preure behind Retaining Wall, Bulletin of the Indian Society of Earthquake Technology, Vol,, N. 3, September P. Nandakumaran, V. S. Praad, Determination of Dynamic Paive Preure of and, Proc., 7th World Conference on Earthquake Engineering, Itanbul, Turkey, S. Okabe, General Theory of Earth Preure, Journal of Japanee Society of Civil Engineer, Vol. 2, N., M. A. Sherif, Y. S. Fang, Dynamic Earth Preure on Wall Rotating About Top, Soil and Foundation, Vol. 24, N.4m M. A. Sherif, I. Ihibahi, C. D. Lee, Earth Preure againt Rigid Retaining Wall, Journal of Geotechnical Engineering, ASCE, Vol. 8, A. H. Soubra, B. Macuh, Seimic Active and Paive Earth Preure on Rigid Retaining Structure by a Kinematical Approach, 4th International Conference on Recent Advance in Geotechnical Earthquake engineering and Soil Dynamic and Sympoium in Honour of Profeor W.D. Liam Finn, San Diego California, March R. S. Steedman, X. Zeng, The Influence of Phae on the Calculation of Peudo-tatic Earth Preure on a Retaining Wall, Geotechnique, 4, n., J. M. Zhang, Y. Shamoto, K. Tokimatu, Earth Preure on Rigid Wall During Earthquake, Geotechnical Earthquake Engineering and Soil Dynamic III, ASCE J. M. Zhang, Y. Shamoto, K. Tokimatu, Seimic Earth Preure theory for Retaining Wall Under Any Lateral Diplacement, Soil and Foundation, Vol.38, N.2, J. M. Zhang, Y. Shamoto, K. Tokimatu, Evaluation of Earth Preure Under Any Lateral Deformation, Soil and Foundation, Vol.38, N., J. M. Zhang, D. Li Seimic Active Earth Preure Conidering Effect of Strain Localization, 4th International Conference on Recent Advance in Geotechnical Earthquake engineering and Soil Dynamic and Sympoium in honor of Profeor W.D. Liam Finn, San Diego California, March 2.