Settlement Analysis of Geosynthetic Reinforced Soil Retaining Walls at Foundation Level

Transcription

1 Settlement Analyi of Geoyntheti Reinfored Soil Retaining Wall at Foundation Level Halil Murat Algın Aoiate Profeor, Department of Civil Engineering, Faulty of Engineering, Harran Univerity, Omanbey Campu, 63000, Sanliurfa, Turkey ABSTRACT Thi paper preent the pratial loed-form olution for the ettlement analye of flexibly faed Geoyntheti Reinfored Soil (GRS wall at foundation level. The analytial olution are developed for elati ettlement and D ultimate primary onolidation ettlement analye. The preented expreion an be readily implemented into the limit equilibrium deign method urrently ued for GRS wall. Unlike the onventional ettlement alulation method ued in the urrent pratie, the preented expreion adequately take into aount the linear foundation preure aumed in the limit equilibrium deign proedure. The preented olution allow effiient and aurate predition of elati and ultimate primary onolidation ettlement of GRS wall. The preented formulae are baed on the theory of elatiity whih i widely ued in the pratial ettlement analyi of hallow foundation. The flexible linear foundation preure on the urfae of a ingle layer ytem i aumed in thi paper. The appliability of the olution on multi-layered ground i alo explained. The ommon aumption of linear plane train bearing preure at the foundation level of GRS wall i adopted for the olution and their appliability to the urrent limit equilibrium deign method i demontrated. KEYWORDS: GRS wall; elati ettlement; onolidation ettlement; angular ditortion; limit equilibrium method. INTRODUCTION Current deign pratie of GRS retaining wall with flexible faing i baed on the limit equilibrium method that involve atifying external and internal tabilitie in whih the required deign riteria and minimum afety fator are fulfilled. The limit equilibrium method i detailed in many peifiation and guideline (e.g. AASHTO, 00; BS8006, 995; Elia et al., 00; Holtz et al., 998; NCMA, 00; NCHRP, 006. External tability refer to the tability of the reinfored oil ma a a whole in relation to the oil adjaent to it. The internal tability of GRS wall require that the wall i uffiiently table againt failure within the reinfored oil ma

2 Vol. 5 [00], Bund. G 698 There are alo loal tability riteria, uh a for the onnetion of reinforement and faing unit, onidered in the deign. In the external tability, the entire reinfored zone that ontain bakfill oil, reinforement, and the faing unit i onidered to at a a monolith whoe main role i to reit the detabilizing ative earth preure exerted by the retained oil. The behaviour of GRS wall during and after ontrution exhibit ome omplexity and it i till a ubjet area of many new reearhe (e.g. Bilgin, 009; Lee et al., 008; MGown and Brown, 008; Reddy et al., 008; Skinner and Rowe, 005; Viwanadham and König, 009; Yang et al., 009. The external tability hek generally onidered in the deign are liding, overturning, bearing apaity and eentriity, deep-eated failure and ettlement. The foundation oil of GRS wall mut have uffiient bearing apaity to prevent failure and exeive ettlement. GRS wall having unaeptable differential ettlement and angular ditortion may reult loing the load bearing funtion and trutural tability. Signifiant ettlement an reult in vertial rak and ditre to the truture at the top of the reinfored fill. The limit equilibrium method aume the linear bearing preure at the foundation level, reulting from the lateral fore onidered in the wall deign uh a ative earth preure exerted by the retained oil. The eentriity i limited by many peifiation and guideline to avoid the tenion between the bae of wall and foundation oil, and the full ompreion ae i therefore onidered in the deign (e.g. AASHTO, 00; BS8006, 995; Elia et al., 00; Holtz et al., 998; NCMA, 00; NCHRP, 006. The linear ontat preure aumption at the foundation level i alo ued in the bearing preure hek in the external tability analyi (i.e. Meyerhof effetive area method i ued. The aumption of uniform or linear ontat preure at the foundation level i not tritly valid, but it i generally onidered uffiiently aurate for ordinary problem of deign. In fat, mot oil how evidene of ome plati behaviour, the reinfored oil generally have a finite tiffne and the ditribution of bearing preure within oil varie with time. The atual ditribution of bae preure within oil i depending on the type of oil and the tiffne of reinfored oil. Sine the behaviour of GRS wall involve many unertaintie regarding the ation of ground and the loading, the foundation preure ditribution rather than linear are uually not onidered in the preent-day limit equilibrium deign method and the linear ontat preure aumption in plane train ae i widely ued in many peifiation and guideline (e.g. AASHTO, 00; BS8006, 995; Elia et al., 00; Holtz et al., 998; NCMA, 00; NCHRP, 006. The behaviour of GRS wall ha reently been invetigated by National Cooperative Highway Reearh Program (NCHRP, 006 uing the full ale meaurement and numerial omputer analyi, the part of tudy wa ummaried by Wu et al. (006; the almot linear ontat preure in the foundation level i oberved in thi reearh. It wa tated that the meaured ontat preure wa the highet beneath the wall fae and dereaed almot linearly with the ditane from the wall fae (NCHRP, 006. The aumption of linear foundation preure i alo jutified by Yang et al. (009 by onduting full ale field meaurement. Some other reearher (MGown and Brown, 008; Reddy et al., 008; Skinner and Rowe, 005; Viwanadham and König, 009; Otani et al., 998; Yamaoka et al., 990 are alo agreed with the dih-haped ettlement profile and the linear ontat preure at the foundation level of GRS wall. Bilgin (009 invetigated the reinforement length uing the internal and external tability analye by auming the linear ontat preure at the foundation level. Holtz et al. (998 and NCHRP (006 tate that the tolerable angular ditortion at the foundation level of GRS wall i /00 for modular blok wall and /50 for wrapped fae wall. The limitation of tilt at the foundation level i given in order of magnitude one-tenth of % of the

3 Vol. 5 [00], Bund. G 699 height of wall or le (NCHRP, 006. Additionally, oil improvement at the foundation level i reommended if the alulated ettlement exeed the projet requirement (Holtz et al., 998. Although the neeity of the ettlement evaluation i emphaied by many peifiation and guideline (e.g. Holtz et al., 998; NCHRP, 006, the detail of ettlement analyi are not provided in thee doument. For intane, Holtz et al. (998 refer to the onventional ettlement analyi of hallow foundation ued in geotehnial and foundation engineering text book for performing the ettlement analyi of GRS wall. Similarly, NCHRP (006 refer to the well known text book and doument publihed by Terzaghi and Pek (967, Perloff (975 and Poulo (000 for the foundation ettlement analyi of GRS wall. However, the ettlement expreion in thee literature are for the uniform foundation preure ae. For that reaon, the ettlement analyi referred in the urrent literature annot diretly be ued ine the linear ontat preure i aumed at the foundation level of GRS wall in the deign proedure. FHWA (006 alo tate that the urrent deign method do not allow the deigner to etimate total and differential ettlement at the foundation level of GRS wall. Sine the pratial ettlement analyi i not provided by the peifiation and guideline (e.g. AASHTO, 00; BS8006, 995; Elia et al., 00; Holtz et al., 998; NCMA, 00; NCHRP, 006, the required ettlement hek annot be performed diretly on the bae of limit equilibrium method. Additionally, thi hortoming aue ome further tudie not performing the ettlement analyi in their reearhe. For intane, Bilgin (009 exluded the ettlement analyi hek in hi ueful tudy. Thi gap in knowledge ha brought about the need to develop the preented formulae for the ettlement analyi of GRS wall at the foundation level by onidering the linear foundation preure aumed in the deign proedure (e.g. Holtz et al., 998; NCHRP, 006. In thi paper the reently publihed elati ettlement olution by the author (Algin, 009a; Algin and Algin, 009 are evaluated to the plane train ae for the elati ettlement analyi of GRS wall. Similarly, the vertial tre expreion for the linear foundation preure (Algin, 000; Algin, 00 are evaluated to obtain the pratial average tre expreion whih are required in D ultimate primary onolidation ettlement analyi of GRS wall. Aordingly, the olution at the foundation level are thereby developed for GRS wall both for the elati ettlement and the ultimate primary onolidation ettlement analye. However, the preented olution have limited appliability for organi oil ine the eondary ompreion i uually the predominating ettlement omponent in organi oil. Therefore, the amount of organi material hould be very mall for the preented olution to be appliable. The preented olution are baed on the theory of elatiity whih i widely ued for the pratial ettlement analyi of hallow foundation. Although the linear elati oil model do not properly reflet the nonlinear repone of oil, it i onidered uffiiently aurate for ordinary problem of deign. The ommon aumption of linear bearing preure at the foundation level of GRS wall i adopted for the olution and their appliability to the urrent limit equilibrium deign method i demontrated. The appliability of the olution on multi-layered ground i alo explained. By uing the preented olution, the ettlement analye under GRS wall an wiftly be onduted and the reulting value an be ompared with the projet requirement. Aordingly, the deiion on oil improvement at foundation level an be made, uh a replaement, ompation, and tabilization of the oil or hanging the reinforement length. The preented olution are alo ueful for the onfrontation of reult obtained from the modern tehnique uh a the finite element method.

4 Vol. 5 [00], Bund. G 700 ELASTIC SETTLEMENTS UNDER GRS WALLS The pratial elati ettlement formulae for the flexibly faed GRS wall on and depoit are derived from the ettlement expreion reently developed by the author (Algin, 009a for the eentrially loaded hallow footing reting upon an elati ma. Thee olution are baed on the integration of train expreion with the Bouineq tre equation (Algin, 009a. The linearly ditributed ontat preure adopted by Algin (009a are generally aumed in pratie for retangular footing having one or two-way eentriitie (Barne, 000; Bowle, 996; Da, 999a; Da, 999b; Poulo and Davi, 974. The elati ettlement olution (Algin, 009a; Algin and Algin, 009 are baed on the linear ontat preure having full ompreion and the aumption of flexible foundation on the urfae of ingle layered oil ytem. In thee olution, the modulu of elatiity (E and Poion ratio ( μ for a given oil mut be known to alulate the elati ettlement of a foundation. Obtaining reliable value of elati parameter i ruial for the aurate etimation of ettlement. There i a great tendeny in pratie to ue the field tet reult to obtain the reaonable value of elati parameter when the reliable laboratory tet reult are not available. The empirial orrelation developed for the tandard penetration tet (SPT and one-penetration tet (CPT are widely ued in pratie to obtain the modulu of elatiity of oil (Bowle, 996; Da, 999a; Da, 999b. A omprehenive lit of thee orrelation i provided by Bowle (996. In many ae, a uggeted by D Appolonia et al. (97 the modulu of elatiity of aturated lay (undrained i orrelated with undrained hear trength ( u. Dunan and Buhignani (976 orrelated E / u with the overonolidation ratio (OCR and platiity index (PI of everal lay oil. In pratie, the approximate range of typial value i ommonly ued for Poion ratio (Bowle, 996; Da, 999a; Da, 999b or it may be etimated from the empirial orrelation (Bowle, 996; Da, 999b. Alternatively, Poion ratio an be etimated from the relationhip between the repreentative initial elati modulu and hear modulu whih i orrelated with mean effetive tre, OCR and PI a uggeted by Foye et al. (008. If there i tratifiation in the onidered oil depth, more than one et of elati parameter mut be obtained and the weighted average of elati parameter may be applied a uggeted by Bowle (996 or alternatively the approximation tehnique preented in thi paper may be ued in the elati ettlement omputation. Thi approximation tehnique may be adopted by dividing the oil depoit into multi-layered ytem in the ae where the elati modulu of a oil varie with depth. An illutration of a typial GRS wall, along with the fore ating on the wall ued for external tability analyi, i hown in Figure. The reulting linear preure onidered in the ettlement analyi i illutrated at the foundation level. If the reinfored oil foundation i aumed to be perfetly flexible, the wall truture undergoe the ettlement with tilt whih an have the dih-haped ettlement profile. The linear ontat preure at the foundation level i aumed in many pratial deign guide for GRS wall (e.g. AASHTO, 00; BS8006, 995; Elia et al., 00; Holtz et al., 998; NCMA, 00; NCHRP, 006 and dih-haped ettlement profile agree with the reult from numerial model onduted by many reearher (e.g. Alfaro et al., 997; Guler et al., 007; MGown and Brown, 008; Otani et al., 998; Reddy et al., 008; Skinner and Rowe, 005; Viwanadham and König, 009; Yamaoka et al., 990.

5 Vol. 5 [00], Bund. G 70 Figure : A typial GRS wall with the linear preure at the foundation level The aumption of perfet flexibility at the foundation level i not tritly valid, but it i onidered uffiiently aurate for the ordinary problem of deign. In fat, the tiffne of reinfored oil depend on the number of reinforement, the variation in reinforement length, the reinforement type et. (Alfaro et al., 997. Sine the dereae in vertial paing between the geoyntheti reinforement may reult an inreae in the rigidity of the reinfored bakfill (i.e. the reinforement at a a tiffener, the ettlement may be lightly redued by a dereae in vertial paing between the reinforement (Alfaro et al., 997. Thi rigidity effet may be introdued to the preented expreion in thi paper by a redution fator a it i ued in the ettlement analyi of retangular footing (Barne, 000; Bowle, 996; Da, 999a; Da, 999b; Poulo and Davi, 974. For example, a uggeted by Barne (000 the elati ettlement expreion of retangular footing may be ued with Fraer and Wardle (976 tiffne orretion fator and Burland (970 depth orretion fator. The depth fator indiate that the ettlement i redued when it i plaed at ome depth in the ground, depending on Poion ratio and the hape fator of footing. However, analytial tudie have hown that imply auming the urfae of elati medium at the level of loading and ignoring the oil above it give relatively good reult ompared with the olution inluding the depth fator. The tiffne orretion take aount of the foundation tiffne effet on elati ettlement. Therefore, the preented expreion an diretly be ued for the flexible foundation of GRS wall but they an be ued for le flexible foundation by introduing the relevant tiffne orretion. The foundation preure hown in Figure an be obtained by modifying the preure onfiguration introdued by Algin (009a, 009 to the plane train ae. Aordingly, the maximum elati ettlement under the eentriity point an be obtained a follow.

6 Vol. 5 [00], Bund. G 70 S Bqa ( + μ = ( I( e + μ I ( ( E E( e e Where, n = H B, t = q b q, a d = + t, d = + t, t = q q, ( ( b a = n + t + t + t, = ( d ( + 5t( + t, 3 = ( d (5 + t(5 + t, 4 = 96n( d + t d, 5 = 3n( + t, = 9n ( + t + d, = 9n ( + t + d, 6 7 I e = ( 36π ( + t ( ( Tan ( d / + Tan ( d / + ln( d + ln( ( ( d I( e = ( 44π ( + t ( ( Tan + ln( d + ln( d d 3 40 d t( t( n ( + tln( ( d / + Tan ( d / + n ( + tln( 5 + t ln( d d ln( d d (3 By uing the imilar notation, the elati ettlement expreion under any point of the linear foundation preure (Figure i evaluated and thi expreion i then integrated over the foundation width and divided by the width of foundation to obtain the average ettlement under the preure blok. Similar tehnique i ued by Janbu et al. (956 to develop an average elati ettlement equation for a uniform foundation preure on aturated lay oil ( μ = 0. 5 (Da, 999a. The average ettlement an be ued if an approximate olution i required. The reulting expreion for the average elati ettlement under the linear foundation preure i provided a follow. S Where, n = H B, I B( q a + qb ( + μ = ( I (4 E E ( av av = ( 4π ( n((μ ( Cot n + nln( + n + n( μ ln( n ( + n ( μ ln( n (5 av + The term I ( e, I ( e and I av (ee Eq.,3 and 5 are the influene fator for the elati ettlement expreion. Thee fator are the funtion of dimenionle parameter of n ( = H B and t (= q b qa, and they an therefore be repreented in a graphial form a hown in Figure.

7 Vol. 5 [00], Bund. G 703 Figure : Influene fator for the elati ettlement expreion (ee Eq., 4 AVERAGE VERTICAL STRESS AND THE CONSOLIDATION SETTLEMENT ANALYSIS By uing the experimentally determined reompreion (C r and ompreion (C indexe, the ultimate primary onolidation ettlement i ommonly determined by uing the expreion related with the overonolidation ratio (OCR (Bowle, 996; Da, 999a; Da, 999b. In thee expreion the average preure inreae i required within the onolidated oil layer. The average preure expreion preented in thi paper may be more ueful for the onidered oil layer where the oeffiient of volume ompreibility ( m v i aumed be ontant at leat in ertain depth. Thi i a ommon ae for many primary onolidation ettlement analye (uh a one penetration tet (CPT and Dilatometer baed analye. For example, in pratie, in the CPT baed ompreibility aement of oil, the D ontrained modulu ( M = / mv i aumed to be ontant within the ertain depth of CPT-baed oil profile data. M an be determined mainly in term of the one tip reitane, overburden tre and/or the oil type (Sanglerat, 97; Kulhawy and Mayne, 990; Maheh and Vikah, 995. Thi aumption may be more reaonable for tiff, overonolidated oil in whih the loading inrement doe not aue the preonolidation preure to be exeeded. In order to alulate the average preure within the depth (in whih M i of ontant value a ommerial omputer oftware with advaned modelling i normally required uh a Fla 3D, Plaxi et. The auray of the reult depend on the auray of model, element type and ize et. The diret ue of point-tre olution at the middle of oil layer however may provide inaurate reult and an be quite mileading when it i ompared with the omputer-baed reult (Algin, 009b. Wherea the average tre olution preented for the linear foundation preure of GRS wall implify thi omputation and an diretly be ued with an aeptable auray. The average tre required in D onolidation ettlement analyi of GRS wall ha brought about the need to develop an analytial olution whih an diretly be ued in the ettlement analyi. The average preure inreae in a oil layer i generally required for an aurate etimation of the onolidation ettlement reulting from a foundation preure (Da, 999a; Da, 999b. The urrent pratie of etimating the average preure inreae in a oil

8 Vol. 5 [00], Bund. G 704 layer under GRS wall uually employ the numerial proe (i.e. the ub-layer method uing the mid-depth tree baed on the well-known point-tre expreion or diret ue of mid-depth tre in a oil layer. In pratie, the point-tre expreion are generally ued to obtain the middepth tre in a oil layer. The point-tre that i the vertial tre at a point in a depth of a oil tratum i uually determined by the integration of Bouineq equation over the loaded urfae area (Bowle, 996; Da, 999a; Da, 999b; Poulo and Davi, 974. Many point-tre olution adopted in pratie are available for hallow foundation (Bowle, 996; Da, 999a; Da, 999b; Poulo and Davi, 974. The limitation and the perentage error enountered in the diret ue of mid-depth tree are preented by Algin (009b with the onfrontation of the reult from the exat analytial olution for hallow foundation. The ublayer method however involve replaing the moothly varying tre ditribution within a oil by a tairae-like ditribution whih aume a ontant tre (uually mid-depth tre over eah ublayer. Sine the diret ue of mid-depth tree in a oil layer oaionally provide invalid reult, the ublayer method i ued in pratie intead of diret mid-depth tre approah to obtain the realiti tree. Uually in the ub-layer method, the mid-depth tree are ued in eah ublayer a an average tre. Although the ub-layer method redue the error, the reliability of ublayer method ignifiantly depend on the thikne of ublayer onidered (Bowle, 996; Algin, 009b. Sine the oeffiient of volume ompreibility ( m v i uually aumed a ontant over a peifi oil layer epeially in the ettlement analyi baed on the CPT tet reult, the diret average tre expreion an avoid the neeity of onidering the ompreible oil layer a a erie of ublayer unlike the ublayer method ued in the onolidation ettlement analyi. More pratial and reliable ettlement analyi an therefore be undertaken by uing the diret average tre expreion for the peifi oil layer in whih m i aumed ontant. Although there are ome hart (Griffith, 984; Brown, 004 and the analytial olution of average tre (Algin, 009b for a uniform foundation preure are exit, the analytial olution of average tre for the linear foundation preure hown in Figure are not mentioned in the urrent literature. The required expreion for the average tre under the linear foundation preure hown in Figure an be obtained from the point-tre equation previouly developed by Algin (00. Sine the foundation preure hown in Figure an be obtained by modifying the linear retangular preure onfiguration to the plane train ae, the point-tre expreion for the eentriity point (Figure an be obtained a follow. σ = q I (6 z( e a z( e Where, f = z B, t = q b q, a f = + f, t = ( + t, t = + t, t3 = + t, t 4 = + t + t, t 5 = 9 ft, t = ft +, t = ft +, 6 5 t 7 5 t3 I z ( e ( t7 = (6π t ( t t t t + t t t + t ( Sin ( t t + Sin ( t (7 The term z(e I (ee Eq. 7 i the influene fator for the point-tre expreion whih an be repreented in a graphial form hown in Figure 3(a. v

9 Vol. 5 [00], Bund. G 705 Figure 3: Influene fator for the point-tre olution given in Eq. (6 and for the average tre olution given in Eq. (9 If a ingle layer oil ytem i onidered, the average tre under the linear foundation preure hown in Figure an now be obtained by the following integration of point-tre expreion (Eq. 6 over the depth of interet (H. H σ = σ dz (8 av H 0 z H indiate the depth between the loading plane and the plane in depth H. The above integration ha been olved and the reulting average tre expreion i preented a follow. σ = q I (9 av( e a av( e Where, n = H B, t = q b q, a t = ( + t, t = + t, t3 = + t, t 4 = + t + t, 3 e = 9n ( + t + ( + t, e = 9n ( + t + ( + t, e 3 = 6nt 4 ( + t, e 4 = 4 + t + 5t + 5t, 3 e 5 = 5 + 5t + t + 4t, I = /(8n π t ( e ( Sin ( t e + Sin ( t e + e ln( e ( + t + e ln( e ( (0 av ( e ( t Therefore, the average tre under the loaded area hown in Figure an be obtained a a funtion of average influene fator ( I av over the depth of interet (H. The influene fator for the average tre expreion given by Eq.(0 depend on the dimenionle parameter of n ( = H B and t (= q b qa, and an be repreented in a graphial form a hown in Figure 3(b. For a ingle layered oil ytem, the required onolidation ettlement equation an then be expreed a follow. S = m H σ ( C( e v av( e

10 Vol. 5 [00], Bund. G 706 THE USE OF SOLUTIONS FOR MULTI-LAYERED GROUNDS A uggeted by ome of the method ued in the elati ettlement analyi of hallow foundation (uh a the train influene fator diagram method developed by Shmertmann and Hartman (978, the approximate variation of the one penetration reitane or tandard penetration number in the oil profile an be aumed to be ontant within a peifi depth of the laified oil. By uing thi ommon aumption, the approximate variation of the modulu of elatiity with depth an be evaluated. Several invetigator have orrelated the value of the modulu of elatiity (E, with the field tandard penetration number (N F and the one penetration reitane (q (Bowle, 996; Da, 999a; Da, 999b. For example, Shmertmann and Hartman (978 uggeted that the equivalent modulu of elatiity for a layer of thikne ( Δ z i an be obtained by multiplying the average one tip reitane of the ith layer ( q i by 3.5 for trip loading on and and ilty and (E=3.5q. Although thi orrelation i generally onidered valid for pratial purpoe (Bowle, 996; Da, 999a; Da, 999b, ome reearher (Sargand et al. 003 ugget that the ratio of E /q for overonolidated and an be in the range of 3-6 time larger than thoe for normally onolidated and. Bowle (996 ugget the orrelation of E =(-4q for and and ilty and, and E =(3-8q for lay layer. Some reearher (Lee and Salgado, 00; Lee et al., 008 have reently orrelated the ratio of E /q with relative denity of eah ublayer, ettlement and footing width. Thi orrelation an alo be ued with the ettlement expreion preented in thi paper. Many reearher developed expreion for the ontant ontrained modulu (M in the ertain depth of CPT-baed oil profile data (e.g. Sanglerat, 97; Kulhawy and Mayne, 990; Maheh and Vikah, 995. Aordingly, by uing the uitable expreion for the ontrained modulu the oeffiient of volume ompreibility ( m v for the peifi oil layer an be determined in term of the one tip reitane, overburden tre and/or the oil type. If there i tratifiation in the onidered oil depth, more than one et of oil parameter mut be obtained and the uperpoition tehnique hown in Figure 4 an be ued in the ettlement analye in whih the oil depoit i divided into multi-layered ytem. Figure 4: Appliation of the preented expreion for multi-layered ground. The approah hown in Figure 4 take into aount the deformation experiened by every layer within the oil profile data. In thi uperpoition tehnique, the elati ettlement (Eq. and 4 and the onolidation ettlement (ee Eq. 9 and are alulated for eah onidered

11 Vol. 5 [00], Bund. G 707 oil layer. At firt, the oil parameter within the depth between the loading plane and the bottom of onidered oil layer are taken a the layer oil parameter, and then, the diarded upper layer having ame oil parameter a the onidered oil layer are ubtrated a illutrated in Figure 4. The alulation are repeated for all ubequent oil layer. Then, the reult are added to obtain the value of total ettlement. A imple preadheet program may be ued for thee alulation. Thi uperpoition tehnique wa originally preented by Butler (975 for the elati ettlement analyi of hallow foundation. Thi approximation i adopted in thi paper for the linear foundation preure of GRS wall to obtain not jut for the elati ettlement but alo the onolidation ettlement. Unlike the train influene fator diagram method developed for uniform loading by Shmertmann and Hartman (978, the propoed elati ettlement analyi preented in thi paper for the linear foundation preure take into aount the variation of Poion ratio by every layer within the oil profile data. Analytial tudie how that the variation of Poion ratio ha a ignifiant influene on the ettlement reult. Thi may be the reaon why the train influene fator diagram method often over predit the atual elati ettlement (Anderon et al., 007; Da et al., 009. The propoed elati ettlement analyi in thi paper alo avoid any ertain train influene fator diagram aumed by Shmertmann and Hartman (978, ine the exat elati olution are preented. NUMERICAL EXAMPLE Example: Figure 5 illutrate a GRS abutment with an integrated ill and a tall upper wall. NCHRP (006 provided the detailed deign olution of thi example baed on the limit equilibrium method. However, the alulation detail of ettlement analyi are not provided by NCHRP (006. It only refer to the well known text book for the foundation ettlement analyi of GRS wall, even though the referred ettlement analye annot diretly be ued due to the linear preure aumption made at the foundation level of GRS wall in the deign proedure. Only the reult of maximum foundation ettlement i provided by NCHRP (006 for thi example without explaining how it i obtained. The data given for thi example are provided in Figure 5 (NCHRP, 006. By auming a flexible behaviour at the foundation level it i required in thi paper to determine the ettlement under the point of eentriity (i.e. point e hown in Figure 5. Depending on the foundation ettlement, it i alo required to determine the maximum angular ditortion under the GRS wall illutrated in Figure 5.

12 Vol. 5 [00], Bund. G 708 Figure 5: A GRS abutment with an integrated ill and a tall upper wall onidered in Example (NCHRP, 006. Solution: A hown in Figure 5, ine the oil depoit i only a ingle layered medium and foundation, the preented ettlement equation (i.e. Eq.(, 4 an diretly be ued. The required influene fator in Eq.(, 3 and 5 an be obtained from Figure (ee the dahed line in Figure a and b a follow, n = H B = 6 7 = 0.86 and t = q b qa = = Thu, the influene fator from Figure (a are I ( e = 0. 3and I ( e = Hene, the maximum elati ettlement an be etimated from Eq. ( a, Bqa( + μ (7(347.8( SE( e = ( I( e + μ I( e = ((0.3 + (0.3(0.35 = 0.0m E 4400 Therefore, the maximum foundation ettlement i obtained a 0.0 m (0mm. Thi reult i idential with the maximum ettlement value provided by NCHRP (006. Additionally, the influene fator for the average elati ettlement i I av = (ee Eq.(5 and the dahed line in Figure (b. Thu, the average ettlement an be etimated from Eq.(4 a,

13 S Vol. 5 [00], Bund. G 709 B( q + qb ( + μ ( I E (7( ( = ( a E( av = av = 0.008m It hould be noted that the above maximum ettlement i baed on the foundation ettlement only and the additional abutment ettlement reommended by NCHRP (006 i S abutment = (.5%( H = (0.05(7.5 = 0.5m S total Thu, the total ettlement and the angular ditortion beome, = ( (0.5 = 0.5m Angular ditortion S total 0.5 = = Span length 4 Thi reult baed on the analytial olution preented in thi paper i idential with the reult provided by NCHRP (006. CONCLUSIONS The pratial loed-form olution and the reulting influene fator were preented for etimating the elati ettlement and D ultimate primary onolidation ettlement under the linear foundation preure aumed in the limit equilibrium deign approah urrently ued for GRS wall. The appliability of the olution on multi-layered ground wa alo explained. Numerial example wa provided to explain how the loed form olution an be ued in pratie. Paper demontrated that the preented expreion an be readily implemented into the limit equilibrium deign method urrently ued for GRS wall. In thi repet, it repreent a ignifiant tep forward in pratial ettlement analye of GRS wall at foundation level. REFERENCES. AASHTO, (00 Standard peifiation for highway bridge, 7th ed. Amerian Aoiation of State Highway and Tranportation Offiial, In., Wahington DC.. Abu-Farakh, M., (003 Evaluation of onolidation harateriti of oheive oil from piezoone penetration tet, LTRC projet No.00-3GT, Louiiana Tranportation Reearh Centre. 3. Alfaro, M.C., Hayahi, S., Miura, N., Bergado, D.T., (997 Deformation of reinfored oil-wall-embankment ytem on oft lay foundation, Soil and Foundation, 37:4, Algin, H.M., (000 Stree from linearly ditributed preure over retangular area, Int. Jrnl. for Numerial and Analytial Method in Geomehani, 4: Algin, H.M., (00 Vertial tre formula for preure over retangular area, Géotehnique, 5:8, 79-7.

14 Vol. 5 [00], Bund. G Algin, H.M., (009a Elati Settlement under Eentrially Loaded Retangular Surfae Footing on Sand Depoit, Journal of Geotehnial and Geoenvironmental Engineering, ASCE, 35:0, Algin, H.M., (009b Analytial olution of average preure inrement for primary onolidation ettlement omputation, Pro. nd Int. Conf. on New Development in Soil Mehani and Geotehnial Engineering, Near Eat Univerity, Nioia, North Cypru, Algin, H.M., Algin, Z., (009 Elati ettlement under linear urfae preure on retangular area, Int. Jrnl. for Numerial and Analytial Method in Geomehani, 33:8, Anderon, J.B., Townend, F.C., Rahelion, L., (007 Load teting and ettlement predition of hallow foundation, Journal of Geotehnial and Geoenvironmental Engineering, ASCE, 33:, Barne, G.E., (000 Soil mehani priniple and pratie, nd Edn., Palgrave Mamillan, New York.. Bilgin, Ö., (009 Failure mehanim governing reinforement length of geogrid reinfored oil retaining wall, Engineering Struture, 3:9, Bowle, J.E., (996 Foundation analyi and deign, 5th Edn, The MGraw-Hill Companie, New York. 3. Brown, R., (004 Pratial Foundation Engineering Handbook, MGraw-Hill, nd Ed., New York. 4. BS8006, (995 Code of pratie for trengthened/reinfored oil and other fill, Britih Standard Intitution, BSI, London. 5. Burland, J.B., (970 Diuion on eion A, Pro. Conf. on In-Situ Invetigation in Soil and Rok, Britih Geotehnial Soiety, London, Butler, F.G., (975 Heavily overonolidated lay. Settlement of Struture, Britih Geotehnial Soiety Sympoium, Penteh, London, D Appolonia, D.T., Poulo, H.G., Ladd, C.C., (97 Initial ettlement of truture on lay, J. Soil Meh. Found. Dev., ASCE, 97:0, Da, B.M., (999a Priniple of foundation engineering, 4th Edn., PWS Publihing, New York. 9. Da, B.M., (999b Shallow foundation: bearing apaity and ettlement, t Edn., CRC Pre LLC, Florida. 0. Da, B.M., Atalar, C., Shin, E.C., (009 Development in elati ettlement etimation proedure for hallow foundation on granular oil, Pro. nd Int. Conf. on New Development in Soil Mehani and Geotehnial Engineering, Near Eat Univerity, Nioia, North Cypru, Dunan, J.M., Buhignani, A.L., (976 An engineering manual for ettlement tudie, Department of Civil Engineering, Univerity of California, Berkeley.

15 Vol. 5 [00], Bund. G 7. Elia, V., Chritopher, B.R., Berg, R.R., (00 Mehanially tabilized earth wall and reinfored oil lope, deign and ontrution guideline, Publiation No. FHWA-NHI , Federal Highway Adminitration (FHWA, Wahington (DC. 3. FHWA, (006 Promoting geoyntheti ue on federal land highway projet, Central Federal Land Highway Diviion, Publiation No. FHWA-CFL/TD , 300 Wet Dakota Avenue Lakewood, CO Foye, K.C., Bau, P., Prezzi, M., (008 Immediate ettlement of hallow foundation bearing on lay, Int. J. Geomeh., ASCE, 8:5, Fraer, R.A., Wardle, I.J., (976 Numerial analyi of retangular raft on layered foundation, Geotehnique, 6:4, Griffith, D.V., (984 A hart for etimating the average vertial tre inreae in an elati foundation below a uniformly loaded retangular area, Canadian Geotehnial Journal, :4, Guler, E., Hamderi, M. Demirkan, M.M., (007 Numerial analyi of reinfored oilretaining wall truture with oheive and granular bakfill, Geoyntheti International, 4:6, Holtz, R.D., Critopher, B.R., Berg, R.R., (998 Geoyntheti Deign & Contrution Guideline, Publiation No: FHWA HI , National Highway Intitute Federal Highway Adminitration (FHWA, MLean, Virginia. 9. Janbu, N., Bjerrum, L., Kjaernli, B., (956 Veiledning ved loning av fundamentering oppgaver, Publiation No.6, Norwegian Geotehnial Intitute, pp Kulhawy, F.H., Mayne, P.H., (990 Manual on etimating oil propertie for foundation deign, Eletri Power Reearh Intitute, EPRI, Palo Alto, CA. 3. Lee, J., Eun, J. Prezzi, M., Salgado, R., (008 Strain influene diagram from ettlement etimation of both iolated and multiple footing in and, Journal of Geotehnial and Geoenvironmental Engineering, ASCE, 34:4, Lee, J.H., Salgado, R., (00 Etimation of footing ettlement in and, Int. J. Geomeh., ASCE, :, Maheh, D., Vikah, J., (995 State of art of CPT in India, International Sympoium on Cone Penetration Teting, Vol., pp.87-95, Linköping, Sweden. 34. MGown, A., Brown, S.F., (008 Appliation of reinfored oil for tranport infratruture, Pro. of the t Int. Conferene on Tranportation, Geotehni, Nottingham, UK., Advane in Tranportation Geotehni E. Elli, H.S. Yu, G. MDowell, A. Dawon, N. Thom (Ed, CRC Pre, Taylor & Frani Group, London, pp NCHRP, (006 Deign and ontrution guideline for geoyntheti-reinfored oil bridge abutment with a flexible faing, National Cooperative Highway Reearh Program, Report 556, Wahington D.C. 36. NCMA, (00 Deign manual for egmental retaining wall, National Conrete Maonry Aoiation. nd ed., Collin, editor. Herndon, VA. 37. Otani, J., Hirai, T., Ohiai, H., Shinowaki, S., (998 Evaluation of foundation upport for geoyntheti reinfored oil wall on loping ground, Sixth International Conferene

16 Vol. 5 [00], Bund. G 7 on Geoyntheti, Atlanta, USA, 5 9 Marh 998. Indutrial Fabri Aoiation International, pp Perloff, W.H., (975 Preure ditribution and ettlement, Chapter 4, Foundation Engineering Handbook (Winterkorn and Fang, editor Van Notrand Reinhold, New York, pp Poulo, H.G., (000 Foundation ettlement analyi pratie veru reearh, The Eighth Spener J. Buhanan Leture, Texa A&M Univerity. 40. Poulo, H.G., Davi, E.H., (974 Elati olution for oil and rok mehani, t Edn., John Wiley & Son, New York. 4. Reddy, G.V.N., Madhav, M.R., Reddy, E.S., (008 Peudo-tati eimi analyi of reinfored oil wall Effet of oblique diplaement, Geotextile and Geomembrane, 6:5, Sanglerat, G., (97 The penetrometer and oil exploration, Elevier, Amterdam, pp Sargand, S.M., Maada, T., Abdalla, B., (003 Evaluation of one penetration tetbaed ettlement predition method for hallow foundation on oheionle oil at highway bridge ontrution ite, Journal of Geotehnial and Geoenvironmental Engineering, ASCE, 9:0, Shmertmann, J.H., Hartman, J.P., (978 Improved train influene fator diagram, Journal of the Geotehnial Engineering Diviion, ASCE, Vol. 04, No. GT8, Skinner, G.D., Rowe, R.K., (005 Deign and behaviour of a geoyntheti reinfored retaining wall and bridge abutment on a yielding foundation, Geotextile and Geomembrane, 3:3, Terzaghi, K., Pek, R.B., (967 Soil mehani in engineering pratie, nd edition, John Wiley and Son, New York. 47. Viwanadham, B.V.S., König, D., (009 Centrifuge modelling of geotextile-reinfored lope ubjeted to differential ettlement, Geotextile and Geomembrane, 7:, Wu, J.T.H., Lee, K.Z.Z., Pham, T., (006 Allowable bearing preure of bridge ill on GRS abutment with flexible faing, Journal of Geotehnial and Geoenvironmental Engineering, ASCE, 3:7, Yamaoka, I., Nihigata, T., Yauda, K., Mondori, K., (990 Load tet and long term obervation of geotextile reinfored retaining wall, Fourth International Conferene on Geotextile, Geomembrane and Related Produt, Vol, The Hague, Netherland. pp Yang, G., Zhang, B., Lv, P., Zhou, Q., (009 Behaviour of geogrid reinfored oil retaining wall with onrete-rigid faing, Geotextile and Geomembrane, 7:5, ejge