IGC. 50 th. 50 th INDIAN GEOTECHNICAL CONFERENCE SEISMIC ACTIVE EARTH PRESSURE ON RETAINING WALL CONSIDERING SOIL AMPLIFICATION

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1 INDIAN GEOTECHNICAL CONFERENCE SEISMIC ACTIVE EARTH PRESSURE ON RETAINING WALL CONSIDERING SOIL AMPLIFICATION Obaidur Raaman 1 and Priati Raycowdury 2 ABSTRACT Te quet for te realitic etimation of eimic eart preure on retaining wall a been purued for everal decade by variou geotecnical eartquake engineer. Over te year variou reearcer ave developed everal metod like peudo-tatic, peudo-dynamic, dynamic etc. to etimate te eart preure on retaining wall due to eartquake. Generally, te eimic acceleration witin te backfill i non-uniform, it amplifie a it approace ground urface. Preent tudy incorporate te effect of backfill amplification and explain it effect on eimic active eart preure beind a vertical cantilever retaining wall. Te limit equilibrium metod wit a planar failure urface beind te retaining wall a been conidered to compute te active eart preure and for implicity only te orizontal eimic acceleration a been conidered. Ti tudy explore te effect of ear wave velocity, damping ration of oil on eimic active preure uing peudo-dynamic approac. Te effect of eimic acceleration, oil friction angle, wall friction angle on eimic active eart preure coefficient a alo been tudied. Te preent tudy ow tat te previou peudo-dynamic metod fail to etimate te proper value of eimic active eart preure coefficient near te natural frequency of te backfill wic can be oberved in te Figure given below. Te eimic active eart preure coefficient decre ignificantly wen oil friction angle incre but tere i little influence of wall friction angle eimic active eart preure coefficient. Te damping ratio of te backfill oil play an important role on eimic active eart preure coefficient. Te active preure ditribution i greatly under etimated if oil amplification i neglected alo a damping ratio decre eimic preure on te wall incre quite ignificantly. Comparion of reult ow tat maximum value of normalized eimic active eart preure incre up to 27%, 47.3% and 1 Raaman, Civil Engineering, Former M. Tec Student IIT Kanpur, India, obaidur.ju@gmail.com 2 Raycowdury, Civil Engineering, Aitant Profeor, IIT Kanpur, India,, priati@iitk.ac.in

2 Obaidur Raaman & Priati Raycowdury 81.82% for damping ratio 1%, 2% and 3% repectively. So for a afe deign of retaining wall te effect of damping ratio of te backfill oil mut be conidered. Figure: Comparion of active eart preure coefficient wit Steedman & Zeng (199) Keyword: Seimic active eart preure, oil amplification, damping ratio, natural frequency

3 INDIAN GEOTECHNICAL CONFERENCE SEISMIC ACTIVE EARTH PRESSURE ON RETAINING WALL CONSIDERING SOIL AMPLIFICATION Obaidur Raaman, Former M. Tec Student, IIT Kanpur, Priati Raycowdury, Aitant Profeor, IIT Kanpur, ABSTRACT: Generally, te eimic acceleration witin te backfill i non-uniform, it amplifie a it approace ground urface. Preent tudy incorporate te effect of backfill amplification and explain it effect on eimic active eart preure beind a retaining wall. Te limit equilibrium metod wit planar failure urface a been conidered to compute te active eart preure on te retaining wall and for implicity only te orizontal eimic acceleration a been conidered. Ti tudy explore te effect of ear wave velocity, damping ration of oil, eimic acceleration, oil friction angle and wall friction angle on eimic active eart preure coefficient and it ditribution along te eigt of te wall, uing peudo-dynamic approac. Te preent tudy ow tat te previou peudo-dynamic metod fail to etimate te proper value of eimic active eart preure coefficient near te natural frequency of te backfill alo te damping ratio of te backfill oil a an important role on eimic active eart preure coefficient. INTRODUCTION Till date, te mot popular and widely ued metod for te analyi of eimic preure on retaining wall a been te peudo-tatic metod bd on te equation preented by Okabe [1] and Mononobe and Matuo [2] recognized a te Mononobe-Okabe (M-O) metod. Ti metod calculate peudo-tatic eart preure, wic i baically an extenion of Coloumb 1776 claical limit equilibrium teory applied to a oil wedge wit conideration of tatic force to reflect te inertial effect of eartquake loading on te oil backfill. However, ti metod a ome baic ortcoming. For example, it aume tat te magnitude and p of acceleration i uniform trougout te backfill. To overcome ti drawback, Steedman and Zeng [3] propoed a imple peudo-dynamic metod to account for te influence of p cange and amplification effect in te dry backfill beind a vertical retaining wall ubjected only to orizontal acceleration. Te ear wave wa aumed to travel vertically witout reflection on te backfill urface. Ti metod wa extended by Coudury and Nimbalkar [5] by including vertical acceleration. Ten, uing te peudo-dynamic teory, Go [6] derived a teoretical olution of eart preure beind a rigid cantilever retaining wall wit non-vertical backface. After tat a new peudo-dynamic metod wa propoed by Coudury and Katdare [7] in wic te effect of Rayleig wave wa alo incorporated. Te eimic acceleration witin te backfill i not uniform and ti may influence te eimic preure on te retaining wall ignificantly. However, ti apect a not invetigated properly. Moreover, te above mentioned tudie did not take into account ome oter apect tat migt influence te overall beavior of te ytem i.e. te damping, te natural frequencie of te ytem, and te amplification effect witin te backfill. Uing peudo-dynamic approac and conidering amplification of ear wave in te backfill; effect of different parameter uc a oil friction angle, wall friction angle, orizontal acceleration, ear wave velocity and damping ratio of oil on eimic active preure coefficient and eimic active eart preure ditribution

4 Obaidur Raaman & Priati Raycowdury along te eigt of te wall ave been focued in ti tudy. Te limit equilibrium metod wit a planar failure urface beind te retaining wall a been conidered to compute te active eart preure on te retaining wall. Te reult are compared wit Steedman and Zeng [3]. DEFINITION OF THE PROBLEM A rigid vertical cantilever retaining wall of eigt H, founded on rigid bedrock wit a dry, coeionle, orizontal backfill i conidered for analyi a own in Figure 1. A planar failure urface at an angle wit te orizontal a been conidered. Te active eart trut make an angle wit te normal to te wall face. Te b of te wall i ubjected to a armonic orizontal eimic acceleration of amplitude kg were g i acceleration due to gravity. Te objective i to determine te active eart preure coefficient and ditribution of active eart preure over te eigt of te wall per unit lengt of wall. Figure 1 Failure mecanim and force acting on oil wedge in active c METHOD OF ANALYSIS Te peudo-dynamic analyi, wic incorporate a finite ear wave velocity, a been developed by taking into account te amplification of te acceleration in te backfill and tu bot p and magnitude of te acceleration vary. Te ear wave velocity can be expreed a G V (1) were G i te ear modulu of te oil and ρ i te denity of oil. Te analyi include a period of lateral aking [4] 2 4H T V (2) were ω i angular frequency. If te rigid bedrock i ubjected to orizontal armonic acceleration generally te magnitude of te acceleration i amplified wile approacing to te overlaying oil urface. Te repone of any oil layer i evaluated from a known bedrock repone in term of tranfer function. Te tranfer function i defined a te ratio of diplacement amplitude of any two point in te oil layer. For an iotropic, linear elatic oil overlying rigid bedrock te tranfer function [4] i given by A f 1 w (3) H co( ) V It i very clear from te above equation tat wen H / V approace /2 n te tranfer function produce an unrealitic and unbounded amplification. For ti reaon te beavior of te backfill oil i aumed a vico-elatic in nature wic give more realitic reult. Te tranfer function for vertically propagating onedimenional ear wave in a vico-elatic medium [4] i A ( w) f 1 2 H H co D V V 2 (4) were D i damping ratio of te backfill oil. If te b i ubjected to inuoidal orizontal acceleration of amplitude, ten te acceleration at dept z below te top of te wall and time t can be expreed a - H z z, t in t V (5)

5 INDIAN GEOTECHNICAL CONFERENCE If te oil amplification i accounted for, te acceleration at te top of te backfill become A ( w), were A ( w ) i te f amplification function. Now te acceleration at dept z and time t can be expreed a, z, t 1 H z ( Af ( w) 1) H z in t H V f (6) Te ma of te tin element of te oil wedge of tickne dz at dept z from te oil urface a own in Figure 1 i m z H z dz (7) g tan were, i unit weigt of te backfill oil and i angle of failure plane wit orizontal. Terefore, te weigt of te wole wedge i 2 1 H W (8) 2 tan Te total orizontal inertia force acting on te wall can be expreed a zh, Q t m z z t dz (9) z And conequently, Q () t can be written a Q t TV k 2 Hco TV 2 in int 4 tan TV k( Af ( w) 1) H H co TV in TV (co t co ) 4 H tan (1) H were, t V Te eimic force Q act on wall from rigt to left and vice vera, te critical combination of te load to find te maximum eimic eart preure a been own in Figure 1. Te total active trut, P can be obtained by reolving te force on te wedge conidering te tatic force equilibrium. P can tu be expreed a follow P Win Q co( ) co( ) (11) were i friction angle of te backfill oil, i friction angle between oil and wall and W i total weigt of te oil wedge. Te eimic active eart preure coefficient can ten be defined a K 2P 2 (12) H Subtituting Q in Equation (11) and ten P in Equation (12) it can be oberved tat K i a function of dimenionle expreion H / TV, t / T and failure angle. Te function H / TV i te ratio of time taken for a wave to travel te full eigt of te backfill to te period of lateral aking of te eartquake. According to Steedman and Zeng [3] for dominant eartquake period in te range econd, H / TV i alo in te range To get te maximum value of K, Equation (12) i optimized wit repect to t / T and. Te value of t / T a been varied from to1 and te value of a been varied from to 9 during optimization. RESULTS AND DISCUSSIONS Variation of Seimic Active Eart Preure Coefficient Te variation of eimic active eart preure coefficient for different value of H / TV a been own in Figure 2 uing te preent approac a well a uing te metod propoed by Steedman and Zeng [3] wit amplification factor

6 Obaidur Raaman & Priati Raycowdury 1 and 2. Te magnitude of eimic acceleration ( k ), earing reitance angle of te backfill ( ), friction angle between wall and backfill ( ) and oil damping ( D ) are taken a.2, 33, 16 and.5 repectively to be conitent wit Steedman and Zeng [3]. It i oberved tat te eimic active eart preure coefficient propoed by Steedman & Zeng [3] decre monotonically wit increaing value of H / TV for bot te amplification factor. However, te preent tudy ow two ditinct peak for two different value of H / TV. Tere i a arp incre in te value of K wen H / TV i.25. After reacing firt peak, te curve decre monotonically and ten incre again at H / TV =.75 to reac te econd peak but te econd peak value i muc lower tan previou one. It can be undertood tat te peak correpond to te firt and econd natural frequency of te backfill. Terefore it i obviou tat te previou peudo-dynamic metod ignificantly underetimate te eimic active eart preure coefficient near te natural frequency of te backfill. Figure 2 Comparion of active eart preure coefficient wit Steedman & Zeng [3] for different value of H / TV for k.2, 33, 16 and D 5% Effect of Damping Ratio In Figure 3 te cange of eimic active eart preure coefficient wit repect to H / TV a been own for tree different value of damping ratio. It i clear from Figure 3 tat a damping ratio incre, K at te natural frequencie decre ignificantly. In c of D 3%, te peak value at econd natural frequency almot vanie and te curve ow almot a decreaing trend after te firt apex. Te damping ratio of oil incre mean diipation of energy incre o te peak value of K alo decre. Effect of Horizontal Seimic Acceleration Coefficient and Soil Friction Angle Te combined effect of eimic acceleration coefficient ( k ) and friction angle ( ) of te backfill on eimic active eart preure coefficient ( K ) a been own in Figure 4. It i oberved tat K incre wit increaing k, a expected. For 3, wen k cange from.1 to.2 ten K incre by 4%. Similarly for 5, K incre by 46.17% wen k cange from.3 to.4. It alo demontrate tat te magnitude of K i ignificantly affected by oil friction angle. For example, wit k.2, wen te value cange from 4 to 5, K decre from.412 to.294 i.e. K decre by almot 4%. A te decre, oil become ofter o K i found to incre wit even iger rate. Ti indicate tat eartquake input and oil ear trengt parameter play important role for etimating K and proper care ould be taken to caracterize teir input parameter. Effect of Wall Friction Angle Wall-oil friction angle a an influence on tatic coefficient of eart preure. Terefore a parametric tudy a been done to invetigate it effect on K. Figure 5 preent te variation of eimic active eart preure coefficient for different value of /. It i oberved tat te nature of curve i not monotonic and te effect of

7 INDIAN GEOTECHNICAL CONFERENCE Figure 3 Te variation of active eart preure coefficient for different value of H / TV and damping ratio for 33, 16 and k.2 Figure 5 (a) Variation of eimic active eart preure coefficient wit / for different, H / TV.3, k.2 and D 1% Figure 4 Seimic active eart preure coefficient wit different k and for H / TV.3, /2and D 2% Figure 5 (b) Variation of eimic active eart preure coefficient wit / for different, H / TV.3, k.2 and D 2%

8 Obaidur Raaman & Priati Raycowdury wall friction angle on K i negligible a compared to oter parameter uc a oil friction angle. K become maximum at and te maximum value of K decre rapidly wen damping ratio of oil incre from 1% to 2%. For example, for 2 te cange in maximum value of K i decred to.92 from 1.78 wen D cange to 2% from 1%. Seimic Active Eart Preure Ditribution Te effect of different parameter like damping ratio, oil friction angle, wall-oil friction angle on normalized eimic active eart preure a been dicued in ti ection. A te damping ratio a ignificant effect on eimic active eart preure coefficient o it will alo affect te eimic preure ditribution. Figure 6 illutrate te effect of damping ratio on active oil preure ditribution wit typical value of 33, 16, H / TV.3and k.2. It i noticed tat a damping ratio incre normalized active eart trut decre. At z/ H.9, wen damping ratio incre from 5% to 1% te active preure on te wall decre by 13.8% and eimic preure get reduced by 13% wen damping ratio incre from 1% to 2%. Terefore it i important to ave a clear idea of te dynamic propertie of te backfill oil wile deigning a retaining wall in a eimic zone. Te variation of p / H along dept for different a been own in Figure 7. In te upper portion at z/ H.1, wen incre from to /2 normalized eimic active eart preure decre by 2% and for te incre in from /2 to te magnitude of p / H decre by 37.82%. In te middle portion at z/ H.5, wen incre from to /2 normalized eimic active eart preure decre by 4.14% and for te incre in from /2 to te magnitude of p / H decre by 14.85%. In te lower portion at z/ H.9, wen incre from to /2 normalized eimic active eart preure decre by 3.17% and for te incre in from /2 to te magnitude of p / H decre by 13.38%. Wit incre in, p / H varie more nonlinearly o te nature of Figure 6 Variation of eimic active eart preure ditribution wit z/ H and damping ratio for H / TV.3, 33, 16 and k.2 Figure 7 Variation of eimic active eart preure ditribution wit z/ H and wall-oil friction angle for H / TV.3, 33, D 1% and k.2

9 INDIAN GEOTECHNICAL CONFERENCE Figure 8 Variation of eimic active eart preure ditribution wit z/ H and oil friction angle for H / TV.3, D 2%, /2and k.2 curve cange in upper part of te wall. In Figure 8 te variation of p / H for H / TV.3, D 2%, /2and k.2 a been own. It can be een tat te normalized eimic active eart preure decre a oil friction angle incre. Te maximum value of p / H decre by 43.37% wen cange from 2 to 3 and it decre by 27.62% wen cange from 3 to 4 repectively. COMPARISON Te influence of oil amplification on active preure ditribution can not be ignored. Figure 9 compare te reult of preure ditribution wit Steedman and Zeng [3] wit aving te value of oter parameter are H / TV.3, 33, 16 and k.2. Ti figure decribe clearly ow te oil preure incre wen backfill oil amplification and oil damping i taken into conideration. Te incre in active preure in upper part i le wile in lower part i very ig. Ti penomenon i clear in Figure 1 wic diplay te deviation of normalized eimic Figure 9 Comparion of preure ditribution wit Steedman & Zeng [3] for H / TV.3, 33, 16, D 1% and k.2 Figure 1 Deviation of normalized preure ditribution in percentage from Steedman and Zeng [3] along te eigt of wall for different damping ratio and H / TV.3, 33, 16 and k.2

10 Obaidur Raaman & Priati Raycowdury active preure ditribution from te reult obtained by Steedman and Zeng [3] witout conidering te amplification. It i oberved tat maximum value of p / H incre up to 27%, 47.3% and 81.82% for D 3%, D 2% and D 1% repectively. So for a afe deign of retaining wall te effect of damping ratio of te backfill oil mut be conidered. CONCLUSION Te traditional peudo-tatic metod for etimating eimic preure on retaining wall do not take care of p cange in eimic acceleration wit dept, werea te conventional peudo-dynamic metod do not conider te non-uniform cange in magnitude in eimic acceleration. Te preent tudy introduce a tranfer function to take care of te oil amplification. In ti way, variation of magnitude a well a p of eimic acceleration wit dept i accounted for te analyi of a vertical cantilever retaining wall. Te key finding are preented below. a) Te preent tudy ow tat te conventional peudo-dynamic metod do not properly etimate te eimic active eart preure coefficient near te natural frequency of te backfill. Te active preure ditribution i ignificantly under-etimated if te oil amplification i neglected. b) Te preent tudy indicate tat damping ratio of te backfill oil play an important role on eimic active eart preure coefficient and ditribution of eimic active eart preure. Wen damping ratio incre from 1% to 2% te normalized eimic active preure at upper ection of te wall decre almot by 1.% and te magnitude of p / H get reduced by 13% wen damping ratio incre from 2% to 3%. At middle egment wen damping ratio incre from 1% to 2% te value of p / H decre by 15% and it get reduced by 3% wen damping ratio incre from 2% to 3%. At te bottom, wen damping ratio incre from 1% to 2% te value of p / H decre by 13% and it get reduced by 1% wen damping ratio incre from 2% to 3%. c) Te eimic active eart preure coefficient decre ignificantly wen oil friction angle incre. An incre of from 2 to 3, te value of K decre from to.868 tat i by 61.45% and K decre by 31.57% wen incre from 3 to 4 However, wall friction angle doe not affect K ignificantly. Alo te maximum value of p / H decre by 93.37% wen cange from 2 to 3 and p / H decre by 27.62% wen cange from 3 to 4. REFERENCES 1. Okabe, S. (1926). General Teory of Eart Preure. Journal of te Japanee Society of Civil Engineer, 1 (12). 2. Mononobe N. and Matuo H. (1929). On te determination of eartquake preure during eartquake. In Proc.of World Engineering Congre. Tokyo, Japan, pp Steedman, R., & Zeng, X. (199). Te influence of p on te calculation of peudo-tatic eartpreure on retaining wall. Geotecnique, 4 (1), Kramer, S. (1996). Geotecnical eartquake engineering. Upper Saddle : Prentice Hall. 5. Coudury, D., & Nimbalkar, S. (26). Peudo-dynamic approac of eimic active eart preure beind retaining wall. Geotec Geol Eng, 24 (5), Go, P. (28). Seimic active eart preure beind a non-vertical retaining wall uing. Can Geotec J, 45 (1), Coudury D., Katdare AD. (213). New approac to determine eimic paive reitance on retaining wall conidering eimic wave. Int J Geomec ASCE 13(6):

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