DYNAMIC MODEL TESTS ON L-SHAPED GRAVITY RETAINING WALLS

Transcription

1 DYNAMIC MODEL TESTS ON L-SHAPED GRAVITY RETAINING WALLS Erneto CASCONE 1, Simone LO GRASSO 2 And Michele MAUGERI 3 SUMMARY Seimic deign of retaining wall i traditionally baed on the Mononobe-Okabe method of analyi. Thi method i an extenion of the claical wedge theory in which both vertical and horizontal inertia force are introduced in order to take into account the effect of earthquake haking on the thrut acting on the wall. In recent year a number of theoretical analye have been preented to predict the eimic behaviour of gravity retaining wall. Although all thee tudie provided intereting reult, there i the need of experimental evidence and documented real cae. In thi paper ome haking table tet performed on a L-haped gravity wall retaining dry and are decribed and the experimental reult are preented with the aim to provide, though qualitatively, an inight into ome important apect of the dynamic behaviour of retaining tructure reting on rigid foundation oil. Two different ytem have been taken into conideration, namely, a wall retaining a horizontal backfill and a wall retaining an inclined backfill. During tet, both acceleration and wall diplacement were meaured. Through the tranparent ide of the tet box it wa poible to oberve the development of the failure urface and to meaure the angle formed by uch urface to the horizontal axi. INTRODUCTION Seimic deign of earth retaining wall i conventionally carried out by mean of the Mononobe-Okabe theory, which i an extenion of the claical olution due to Coulomb and Rankine for the evaluation of the earth preure in tatic condition. According to the peudotatic Mononobe-Okabe theory, the effect of earthquake haking on the lateral earth preure acting againt the wall can be modelled by imply introducing in the limit equilibrium equation of the oil failure wedge, the inertia force developing in the oil becaue of a eimic acceleration aumed contant. Although it i generally agreed that wall reting above the water table and retaining dry oil, if properly deigned according to Mononobe-Okabe theory, did not experience evere damage in pat earthquake [Whitman 1991], in recent year eimic failure and damage of earth retaining wall have been documented. In fact, Tateyama et al. [1995], for example, reported on damage and failure of traditional gravity and cantilever retaining wall occurred during the 1995 Kobe earthquake. In order to take into account the accumulation of permanent diplacement in the eimic deign of retaining wall extenive tudie have been carried out in the lat 20 year. Thoe tudie were mainly devoted to the prediction of permanent diplacement by either the formulation of empirical relationhip baed on numerical analyi [Richard and Elm 1979, Zarrabi 1979, Whitman and Liao 1984, Crepellani et al 1996] or the modelling of Faculty of Engineering, Univerity of Catania, Italy. Tel Faculty of Engineering, Univerity of Catania, Italy. Tel Faculty of Engineering, Univerity of Catania, Italy mmaugeri@ifa.ing.unict.it

2 dynamic oil-tructure interaction [Nadim and Whitman 1983, Siddharthan and Norri 1991, Cacone et al. 1994, Prakah et al. 1995, Caltabiano et al. 1999a]. Experimental tudie have been performed a well, uing either haking table or centrifuge facilitie. Effort were addreed to the experimental evaluation of lateral oil preure ditribution [Sherif et al. 1982, Ihibahi and Fang 1987] and to the obervation of wall diplacement [Bolton and Steedman 1984, Al-Homoud and Whitman 1995, Cacone and Maugeri 1995, Oldecop et al. 1996]. In thi paper the reult of ome haking table tet are reported. The tet were carried out on two different ytem: a wall retaining a horizontal oil backfill and a wall retaining a loping oil backfill. The wall choen for the tet preent an L-haped cro ection and reit againt driving tatic and dynamic force by mean of it own weight and of the weight of the oil reting on the foundation lab. TESTING PROCEDURE The haking table available at the laboratory of the Univerity of Catania wa decribed by Cacone and Maugeri [1995] and i hown in Fig.1. The table conit of a teel frame and a teel plate bolted on the frame, it i 2 m long, 1m wide and 80 mm thick and i upported by four roller contrained to move on rail, in order to retrict the motion only to one direction. The motion i provided to the table by a loading unit coniting of an electric trhee-phae ynchronou engine with a teel dik mounted on the engine haft. The poition of the dik i adjutable allowing to produce different eccentricitie in the range 1-10 mm. The motion i tranferred from the engine to the table by mean of a ball-bearing placed on the edge of the table. The contact between the dik and the bearing i maintained by a pring fixed on a contrat beam and kept compreed throughout the dynamic teting. A tet box 0.9 m long, 0.7 m wide and 0.4 m deep i fixed to the table. The ide of the box are made of tranparent gla and allow the obervation of the model during the tet. The thickne of the gla ide wa choen equal to 10 mm in order to reproduce a plane-train condition. Studie related to tatic tet on model of retaining tructure report omewhat contrating opinion [Arthur and Rucoe 1965, Rowe 1970, Branby and Smith 1975] about the lateral friction between the oil and the ide which may affect the formation of the failure urface in the backfill. In order to minimize thi effect, the gla ide were treated with a chemical olution. In order to provide adequate friction between the oil and the tet box a heet of cardboard, previouly roughened by glueing and on it, wa fixed on the bae of the box. The wall ued in the tet i a microconcrete retaining wall of height H=cm 25 coniting of a vertical tem 3 cm thick and a horizontal lab 10.5 cm wide and 2.5 cm thick. In order to avoid friction between the wall and the gla ide of the 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 and ued in the tet i uniform (D 60 /D 10 = 1.60) with mall (D 50 = 0.3 mm) ub-angular grain, maximum and minimum unit weight γ max = 16.8 KN/m 3 and γ min = 14.5 KN/m 3, repectively, and peak value of the angle of hear trenght ϕ = 35. Dry ilica and wa pluviated in the tet box from a contant height of 70 cm, at a relative denity D R = 85%. The effect of relative denity on the angle of hear trenght for thi and, wa hown to be negligible [Lo Grao 1999]. In each 7tet the wall wa intrumented with two Figure 1: Experimental et-up 2

3 accelerometer and two LVDT diplacement tranducer to record both acceleration and diplacement at the top and at the bae; two accelerometer were placed in the backfill: one at a depth of 22 cm and the other almot at the backfill urface; one additional accelerometer wa fixed on the table to record the input motion. A data acquiition ytem and a oftware for data proceing were employed to record and analyze data obtained during dynamic teting. In order to detect the formation of the failure urface in the backfill, vertical black and marker were introduced in the model. TEST RESULTS AND DISCUSSION The oil-wall ytem were ubjected to an input acceleration lowly increaing with time. In fact, the table diplacement wa adjuted at 4 mm and both table frequency and acceleration were varied until a failure urface wa clearly ditinguihed through the gla ide of the tet box. Figure 2 how a ketch of the wall retaining a horizontal oil backfill after the development of a clear failure urface. It i eay to oberve that the oil reting on the wall foundation lab moved together with the wall and that the failure urface originate at the heel of the wall and can be approximated to a plane, inclined of 47 with repect to the horizontal. The time-hitorie of acceleration and diplacement of thi oil-wall ytem are hown in Fig.3. In particular, Fig. 3a how the input acceleration and wall top and bae diplacement for the lat 30 econd of the tet. In the initial 100 econd the accumulation of permanent diplacement wa negligible, while the input motion frequency wa varying from 2.9 to 6.8 Hz and the table maximum acceleration wa conequently increaing from 0.08g to 0.36g. Diplacement tarted to build up in the interval from 104 ec to 119 ec, at a frequency of about 7 Hz and table maximum acceleration g. Finally, a further increae of the frequency up to 7,3 Hz brought the table maximum acceleration up to 0.49g, producing a udden accumulation of permanent diplacement. Diplacement reached 0.95 cm at the bae of the wall and 1.20 cm at the top of the wall, howing a light permanent rotation. Only at thi tage the formation of the failure urface wa oberved through the gla ide of the tet box and the haking table wa topped. In Fig.3b the table acceleration and the wall top acceleration and diplacement time-hitorie are plotted for a hort interval. It i poible to oberve that top diplacement have large ocillation and increae when the wall and the table acceleration are negative, that i, directed backward. Likewie, in Fig.3c the table acceleration and the wall bae acceleration and diplacement time-hitorie are plotted for the ame hort interval. It i apparent that permanent diplacement build up in the outward direction when the table i moving backward. The diplacement build-up follow a tepwie pattern alternating phae of relative motion, in which the wall move relatively to the table, and phae of abolute motion, in which the wall move together with the table. In agreement with other experimental reult [Richard and Elm 1990], in any cycle of motion the wall acceleration become le than the input acceleration and i almot contant, producing a ort of plateau. Fig.3d how the comparion between the acceleration of the table and the acceleration recorded at the urface of the backfill. A light amplification can be oberved for negative acceleration howing the tendency of the ytem to rotate in the lat econd of excitation. Finally, Fig.3e how the comparion Figure 2: ketch of the wall retaining a horizontal oil backfill after the development of a clear failure urface 3

4 0,25-0,25 - A 1,25 0,75 0,25-0, , , input bae diplacement tranducer top diplacement tranducer 0,60 0,30-0,30-0,60 B , ,3 1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,60 0,30-0,30-0,60 input acceleration input + wall top acceleration o wall bae acceleration wall top diplacement wall bae diplacement C , ,3 1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,60 D 1,30 E 0,30 1,10 0,90-0,30 0,70-0, , input acceleration backfill acceleration , wall top diplacement wall bae diplacement Figure 3: Wall with horizontal oil backfill: time-hitorie of acceleration and diplacement. 4

5 between the wall top and bae diplacement. Top diplacement preent large amplitude ocillation due to the top of the wall moving back and forth during haking. Bae diplacement preent ocillation a well, due to the fact that the accelerometer i placed at a certain height (3 cm) from the bae of the wall. The final permanent rotation i quite mall and i due to the and introducing underneath the wall heel during wall rocking. Figure 4 how photograph of the wall retaining a loping oil backfill before the tet (Fig 4a) and after the formation of the failure urface in the backfill (Fig.4b) The angle of the loping backfill i β = 15. Alo in thi cae, a expected, the oil reting on the wall foundation lab moved together with the wall, while the failure urface inclined of about 46 how a mall concavity. Finally Fig.4c how the ytem after further diplacement which brought the oil-wall ytem to a condition of collape. It i poible to ee different failure urface. In general, for tranlational diplacement, the failure urface developing after the firt one are internal to the firt failure wedge [Caltabiano et al. 1999a]. In thi cae it i poible to explain the econd failure urface, external to the previou wedge, a a conequence of a lope failure mechanim due to the fact that the wall, after having uffered large diplacement, i not capable to retain the backfill. Time-hitorie of recorded acceleration and diplacement are plotted in fig.5. Mot of the feature oberved in the tet of the wall retaining a horizontal backfill can be recognized, even with more evidence in the reult of thi tet: wall top negative acceleration larger (in value) than input acceleration at failure indicating ome rotation of the top of the wall (Fig.5b); wall bae poitive acceleration maller than input acceleration at failure howing a typical plateau (Fig.5c); no appreciable amplification i oberved in the backfill (Fig.5d); almot no appreciable permanent rotation i accumulated, in fact the final wall top and bae diplacement are 1.82 cm and 1.76 cm repectively. Alo thi tet wa topped when the failure urface wa detected through the gla ide of the tet box. Comparing the reult of the two tet it i poible to conclude that both the ytem conidered in the experimental programme exhibit a baically tranlational failure mode. Thi mechanim can be partly attributed to the rigid foundation condition and to the abence of any embedment in front of the wall. In fact ome rotation might have been expected if the wall wa reting on a compliant oil and/or preented even a mall embedment creating a retrain to liding. For the cae of wall with horizontal backfill, diplacement tarted when the maximum table acceleration became a high a 0.25g, while the failure urface appeared for a maximum table acceleration equal to 0.49g. For the cae of wall with loping backfill, diplacement tarted when the maximum table acceleration reached 0.1g and the failure urface appeared for a maximum table acceleration a high a 0.32g. Thee marked difference are obviouly due to the different boundary condition: the loping backfill exert a larger thrut and involve larger inertia force with maller acceleration. Critical acceleration and failure urface angle computed for the two ytem uing the relationhip propoed by Caltabiano et al. [1999a and b] reulted: Wall with horizonthal backfill a cr = 0.21g α = 48.6 Wall with loping backfill a cr = 0.11g α = 46.0 CONCLUDING REMARKS Shaking table tet on two different oil-wall ytem were carried out and the following concluion were drawn: The behaviour of L-haped wall reting on rigid foundation under dynamic loading i baically tranlational; The oil ma partecipating to the ytem motion i the ma reting on the wall foundation lab and the ma of the failure wedge; Acceleration required to produce wall diplacement are higher for the cae of horizontal backfill and compare well with thoe computed according to the theoretical model by Caltabiano et al. [1999a and b]; The failure urface angle meaured experimentally compare well with thoe computed according to the theoretical model by Caltabiano et al. [1999a and b]; The ytem with loping backfill at large diplacement, exhibit a lope failure mechanim. REFERENCES [1] Al-Homoud A.S., Whitman R.V., 1994 Comparion Between the Prediction and Reult from Dynamic Centrifuge Tet on Tilting Gravity Wall". Soil Dynamic and Earthquake Engineering, Vol 14, [2] Bolton M.D., Steedman R.S., "Modelling the Seimic Reitance of Retaining Structure", Proc 1 th International Conference on SMFE, San Francico, CA, USA, [3] Al-Homoud A.S., Whitman R.V., 1994 Comparion Between the Prediction and Reult from Dynamic Centrifuge Tet on Tilting Gravity Wall". Soil Dynamic and Earthquake Engineering, Vol 14, [4] Bolton M.D., Steedman R.S., "Modelling the Seimic Reitance of Retaining Structure", Proc 1 th International Conference on SMFE, San Francico, CA, USA,

6 A B C Figure 4: Wall with loping backfill: A) at ret; B) after the formation of the failure urface; C) at collape. 6

7 0,4 A 2,00 0,3 0,2 0,1 0,0-0,1-0,2 - -0,3-0,4-2, input bae diplacement tranducer top diplacement tranducer 0,4 0,3 0,2 0,1 0,0-0,1-0,2-0,3-0,4 B 2,00 1,50 0,4 0,3 0,2 0,1 0,0-0,1-0,2-0,3-0,4 C 2,00 1,50 29,0 29,5 30,0 29,0 29,5 30,0 input acceleration input o wall top acceleration o wall bae acceleration wall top diplacement wall bae diplacement 0,4 0,3 0,2 0,1 0,0-0,1-0,2-0,3-0,4 D 2,00 1,50 E 29,0 29,5 input acceleration 30,0 backfill acceleration 29,0 29,5 wall top diplacement 30,0 wall bae diplacement Figure 5: Wall with loping backfill: time-hitorie of acceleration and diplacement. 7

8 [5] Caltabiano S., Cacone E., Maugeri M., 1999a. "Sliding Repone of Rigid Retaining Wall". Proc. International Conference on Earthquake Engineering, Libon, [6] Caltabiano S., Cacone E., Maugeri M., 1999b. "Seimic Stability of Retaining Wall with Surcharge". Proc. IX International Conference on Soil Dynamic and Earthquake Engineering, Bergen, Augut [7] Cacone E., Maugeri M., Motta E., 1994."Ripota Simica dei Muri di Sotegno a Gravità". Rivita Italiana di Geotecnica, Vol. XXVII, N.4, [8] Cacone E., Maugeri M., "Shaking Table Tet of Gravity Retaining Wall". Proc. 7 th International Conference on Soil Dynamic and Earthquake Engineering, Chania, Greece, [9] Crepellani T., Madiai C., Vannucchi G., "Earthquake detructivene potential factor and permanent diplacement of gravity retaining wall". Seion on Analyi and Deign of Retaining Structure Againt Earthquake, ASCE Annual Convention, Wahington DC. [10] Ihibahi I., Fang Y.S.. "Dynamic Earth Preure with Different Wall Movement Mode". Soil and Foundation, Vol.27, N.4, [11] Lo Grao A. S., "Effect of a urcharge on the dynamic behaviour of retaining wall by haking table tet". Diploma Thei, Univerity of Catania, Italy, in Italian, unpublihed: pp.350. [12] Nadim F., Whitman R.V.,1983 "Seimically Induced Movement of Retaining Wall". Journal of the Geotechnical Engineering Diviion, ASCE, Vol.109, N.7, July [13] Oldecop L., Zabala F., Almazan J.L., 1996 "Shaking Table Tet on Small Prototype of Soil Retaining Wall", Proc., 11 th World Conference on Earthquake Engineering, paper N. 1094, [14] Richard R., Elm D.G., 1979 "Seimic behaviour of gravity retaining wall", Journal of Geotechnical Engineering Diviion, ASCE, 1979, Vol.105(4), [15] Richard R., Elm D.G., "Seimic Deign of Retaining Wall". Proceeding of the Conference on Deign and Performance of Earth Retaining Structure, Ithaca, USA, ASCE Geo-Special Publ. 25, 1990, [16] Sherif M.A., Ihibahi I., Lee C.D., "Earth Preure againt Rigid Retaining Wall". Journal of Geotechnical Engineering, ASCE, Vol.108, [17] Siddharthan R., Norri G.M., "On the Seimic Diplacement Repone of Rigid Retaining Wall". Soil and Foundation, Vol31, N.2, [18] Tateyama M., Tatuoka F., Koeki J., Horii K., "Damage to Soil Retaining Wall for Railway Embankment during the Great Hanhin-Awaji Earthquake". Proc., It International Conference on Earthquake Geotechnical Engineering, Tokio, Japan, [19] Whitman R.V., "Seimic Deign of Earth Retaining Structure". Proc., 2 nd International Conference on Recent Advance in Geotechnical Earthquake Engineering and Soil Dynamic, St. Loui, Miouri, [20] Whitman R.V., Liao S., "Seimic Deign of Gravity Retaining Wall". Proc., 8th World Conference on Earthquake Engineering, San Francoco, Vol3, Zarrabi-Kahani K., "Sliding of Gravity Retaining Wall during Earthquake Vertical Acceleration and Changing Inclination of Failure Surface". M.S. Thei, Dept. Of Civil Engineering MIT, Cambridge, USA,