SETTLEMENT PREDICTION OF PILE-SUPPORTED STRUCTURES IN LIQUEFIABLE SOILS DURING EARTHQUAKE

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1 SETTLEMENT PREDICTION OF PILE-SUPPORTED STRUCTURES IN LIQUEFIABLE SOILS DURING EARTHQUAKE Chandra Dev Raman 1, Subhamoy Bhattacharya 2 and A Blakeborough 3 1 Research Scholar, Department of Engneerng Scence,Unversty of Oxford, UK 2 Unversty Lecturer, Department of Cvl Engneerng, Unversty of Brstol, UK 3 Professor, Department of Engneerng Scence,Unversty of Oxford, UK Emal: chandra.raman@eng.ox.ac.uk, S.Bhattacharya@brstol.ac.uk, tony.blakeborough@eng.ox.ac.uk ABSTRACT : It s observed from the past earthquakes that the ple foundatons n lquefable sol are very susceptble to damage or falure. Often, the structures n lquefed sol experence excessve tltng and/or settlement. Though, the falure s often attrbuted to lateral spreadng of the ground, however detaled study of some case hstores shows that the settlement of ple foundaton could be a potental falure mode that can cause tltng of the structure. The settlement of a ple when loaded axally s consdered to be of three parts: (a) Axal compresson of ple; (b) Slp between sol-ple nterface; (c) Settlement of the sol mass as a whole. Ths present addresses the ssue of settlement of ple-supported structures due to the loss of ple capacty n lquefed sol. A smple mathematcal model that can be mplemented n an EXCEL type program has been proposed for characterzng the above phenomenon. The method uses envelopes of unt load transfer curve that descrbes the axal load transfer mechansm of the ple foundaton n lquefed sol. KEYWORDS: Settlement predcton, Axal load transfer, Lquefacton, Ple foundaton 1. INTRODUCTION Ple foundatons are commonly used to transfer axal loads from a superstructure to the ground n cases where: (a) the structural loads are very hgh; (b) where the surface sol or sols at shallow depths cannot carry the mposed loads. Also, ples are used to support structures n areas of sesmc rsk especally where the sols can lquefy due to the sesmc shakng. Followng a moderate to strong earthquake n lquefable areas, t has been observed that pled foundaton suffer tltng along wth settlement. Fgure 1(a & c) shows two such cases. In each of the cases, the ples supportng the buldng ether passed through lquefable sols or were founded on lquefable sols. Ths paper nvestgates some aspects of the vertcal settlement of the pled foundaton when the sol surroundng the ple lquefes. (a) (b) (c) (d) Fgure 1 (a) Tltng of Customs Tower House followng the 2001 Bhuj EQ, Dash et al (2008); (b) Schematc dagram of falure of 1(a); (c) Tltng of Ple-supported buldng followng the 1995 Kobe EQ, Bhattacharya (2006); (d) Schematc dagram of falure of 1(c)

2 2. PROBLEM DEFINITION Often n practce, engneers need to desgn a pled foundaton where the sol profle s layered and one of the layers may lquefy. Fgure 2 shows typcal ste condtons to be encountered at ste. Table 1 lsts some case hstores where such condtons have been encountered. Case I Case II Case III Case IV Non-lquefed crust Lquefed sol Non-lquefed base layer Sol flow Fgure 2 Dfferent feld condtons of sol-ple nteracton Durng sesmc shakng, loose to medum dense sol lquefes. As the result of lquefacton, the effectve stress n the lquefed sol zone reduces to a near zero value. Therefore, the shaft resstance of the ple n lquefable layer also becomes zero. The ple has to therefore transfer the axal load to deeper layers below the lquefable zone whch may result n ple head settlement often termed as axal load transfer mechansm. If the ple head dsplacement s more than the allowable lmt for the structure, then the structure may fal by Servceablty Lmt State. For Case I and Case II n fgure 2, due to the loss of shaft resstance n the lquefed layer, the ple wll settle but the catastrophc collapse or falure may be avoded f the ple s suffcently embedded n the non-lquefable layer below the lquefable layer. In these cases, bucklng of slender ples and bendng due to lateral loads may form plastc hnges n the ple, Bhattacharya (2003). On the other hand, for Case III and Case IV, where the ple rests on lquefable sol deposts, settlement or tltng of the structure s nevtable. Structural falures such as plastc hnges etc., are most unlkely notced n these stuatons. Table 1 Classfcaton of case hstores accordng to dfferent cases as shown n fgure 2 Cases n fgure 2 Case I Case II Case III Case IV Examples Ple supported buldng n Fgure 1(c), near to Quay wall. More detals of buldng 1(c) can be found n Bhattacharya (2006). Here the non-lquefed crust above lquefable sol s about 2m. Ths case s typcally encountered n brdge per ples (Showa brdge ples). Detals compled n Bhattacharya (2003). Pled foundatons for Saseka Hosptal, Ishzue Prmary School, Irfune Prmary School and East Polce Staton. Detals of performance of these foundatons durng the 1964 Ngata Earthquake can be found n Hdeak (1966). Buldng n Fgure 1(a). Customs Tower House n Kandla Port followng the 2001 Bhuj Earthquake. Detals can be found n Dash et al (2008). The am of ths paper s therefore the followng: 1. Develop a smple framework to predct the ple head settlement based on the varous mechansms that control the overall settlement. 2. Valdate the smple frame work through the analyss of a feld case record.

3 3. A SIMPLE FRAMEWORK TO PREDICT SETTLEMENT 3.1 Physcal understandng behnd the framework Fgure 3 shows a smple schematc dagram of a ple-supported buldng n two stages: (a) before earthquake; (b) at full lquefacton. (a) (b) Fgure 3 (a) Schematc representaton of a ple-supported structure. The sol s replaced by t-z and q-z sprngs; (b) Idealzed sngle ple Before earthquake, the axal load s shared between the shaft resstance and the end-bearng resstance (pont resstance). One of the practcal ways to analyse the settlement of an axally loaded ple s to consder the sol as a sprng. The resstve capacty of the sprng vares wth the amount of deflecton.e. the relatve movement between the ple and the sol for shaft resstance and the settlement of the ple tp for end-bearng resstance. The resstance rses to a maxmum value whch s then mantaned for any further dsplacement. In other words, the maxmum resstance s moblsed. The maxmum value of ths resstance can be obtaned from the sol propertes and s drectly proportonal to the effectve stress of the sol. Conventonally, the shaft resstance s denoted by t-z sprng and the end-bearng resstance s denoted by q-z sprngs (Vjayvergya, 1977). The natures of the sprngs are shown n fgure 4. Fgure 4 Load-movement and load transfer characterstcs of an axally loaded ple In loose saturated sandy sol, as the shakng contnues the pore pressure wll rse and the sol may start to lquefy. The ple wll then start to lose ts shaft resstance n the lquefed layer and shed axal loads down the ple. As a result, the sprngs n the lquefed zone cease to act as shown n fgure 3. If the bearng capacty at s exceeded, settlement falure may occur.

4 3.2 Mathematcal formulaton behnd the framework Fgure 5 shows the ple and t s dvded nto N elements. In the model, s a general element havng a length of dx. The value of F represents a proporton of the maxmum resstve force moblzed defned by the deflecton of the element u. F = f s A s = β f s max A s (1) In the above equaton f s max A s represents the maxmum shaft resstance for the ple element. Also, the change s axal load can be expresses as follows: dp = π. D. f s = F dx (2) The settlement of the ple element can be expressed by eqn. 3 where EA s the axal stffness of the ple. du P = ε x = dx ( EA) P (3) Combnng eqns. 2 and 3, we arrve at eqn d u πd = f 2 s dx ( EA) P (4) Fgure 5 An element of a ple wth sprng Equatons 3 and 4 are approxmated to form the bass for a computatonal method of calculatng the deflectons n the ple. du du dx D f dx. π 1 s( ) = dx ( EA) P (5)

5 Therefore, we obtan that the du P dp = dx ( EA) P ( EA) P ( P dp) = ( EA) P ( P + dp) dx ( EA) u u 1 + dx u = u P (6) (7) (8) deflecton = deflecton ple compresson The other equatons are: u = u ( P F ) ( EA) P dx (9) P = P F (10) 3.3 Algorthm for mplementaton of the above n a spreadsheet The above equatons can be easly mplemented n a spreadsheet type program to compute the loads and dsplacement of the ple. The steps are: 1. Calculate the ple head load P 0 actng at node 0 n fgure Choose an ncremental length, dx. 3. For each element, calculate the ultmate shaft resstance and pont bearng for N th element. By addng all the resstances, fnd the ultmate capacty of the ple and compare wth P Assume an ntal ple head deflecton. 5. Use Eqn.1 to fnd the value of ultmate shaft resstance force F (or dp) n the top element. The value of factor β can be found usng fgure Use computatonal Eqns. 9 and 10 to calculate the deflecton and the load on the next element. 7. Repeat steps 5 and 6 for every element down the ple. 8. Usng Eqn.1 and a value of β from fgure 4 fnd the fnal resstve force under the base of the ple. 9. Use Eqn.10 to fnd the load that would be on the top of an element below ths pont, should one exst. 10. Now return to step 4 and carry out an teratve procedure usng steps 4 to 10 untl the resultng load n step 9 s zero. Equlbrum requres that the sum of the loads carred by the sol (modelled as sprngs) must equal the appled load. When ths s true the load resultng from step 9 must be zero as there are no further sprngs below the base. The ple head deflecton that results n ths equlbrum s the deflecton predcted for the load appled n step STUDY OF A CASE STUDY: TILTING OF SAISEIKAI HOSPITAL BUILDING 4.1 Damage to the buldng Durng the 1964 Ngata Earthquake (magntude, M w = 7.6) many renforced concrete buldngs supported on ple foundatons experenced tlt or subsdence. The maxmum ground acceleraton at the ste s reported as 0.14g (Fukuoka, 1966). The subsol condton n Ngata cty s mostly sandy (Yorhko, 1966). The nvestgated Saseka hosptal buldng s a three-stored renforced concrete structure. The ples supportng the hosptal are of made of concrete, 7.2m n length and 0.18m n dameter. The allowable bearng capacty was 60kN per ple. The tp of ple s placed 8.4m below ground level. The buldng subsded m and tlted about 5.6 towards east drecton n the short span.

6 (a) (b) Fgure 5 (a) Schematc dagram of Saseka hosptal buldng along wth sol profle; (b) Factor of Safety aganst lquefacton of the Saseka hosptal buldng ste 4.2 Sol profle at the Saseka hosptal buldng ste The sol profle at the ste conssts of slty sand to about 5m depth and then medum dense sand tll 20m depth. The Ngata cty straddles very nearer to Shnano rver at ts mouth and t nfluences the depth of water table and ts locaton s assumed of about 1.5m below ground level. The dry unt weght of the sol s assumed as 16kN/m 3 and also the saturated unt weght of the sol as 17kN/m 3. The Standard Penetraton Test (SPT) N value can be seen n fgure 5. The overall observed settlement of the ple s a combnaton of the settlement of the sol mass as a whole, axal compresson of ple and slp between sol-ple nterfaces due to loss of shaft resstance owng to lquefacton. It s therefore requred to dentfy the lquefacton potental of the ste before performng the predcton of ple foundaton settlement. 4.3 Evaluaton of lquefacton potental at the ste Idrss and Boulanger (2004) have developed a sem-emprcal approach for lquefacton assessment, whch s an extenson of Seed and Idrss (1970) work. The factor of safety aganst lquefacton for the ste s shown n fgure 5(b). The analyss suggests that the sol lquefed to about 10m. Therefore, the foundaton was fully embedded n lquefable sol.e. Case III n fgure Computaton of ple head settlement based on the smplfed framework Based on the framework dscussed n secton 3, t has been estmated that the ultmate load of the ple s about 80kN. Therefore, the strength of sol s adequate to carry the allowable load on the ple under servce condton. But n case of sesmc condton, the sol sprngs along the shaft and end bearng area weakens. Hence, to predct the behavour of ple n bearng ts allowable load under ths sesmc case, the sol sprngs along the ple s reduced accordngly. Here a factor s ntroduced asα, called as sol strength reducton factor. It s done by reducng the shaft and bearng resstance of the sol n lquefable area to 20%, 40%, 60%, 80%, 90%, 95%, 99% and fnally 100%. Fgure 6 and table 2 shows the results of the analyss.

7 Ple Head Dsplacement n m α = 0 α = 0.20 α = 0.40 α = 0.60 α = 0.80 α = 0.90 α = 0.95 α = Ultmate Axal Load Bearng Capacty n kn Fgure 6 Predcted ple head settlement of Saseka hosptal buldng for both servce and sesmc condton (α = 0, denotes the servce condton) α = 1.00 Table 2 Results of ple head settlement Case hstory/ Comments Saseka Hosptal Buldng (case III) / Ple tp at lquefed area Sol profle 0 5m : slty sand 5m 20m : medum sand Ple length, dameter and allowable load under each ple 7.2m, 0.18m and 60kN Thckness of lquefed layer 8m (6.5m ple embedded) Estmated ple head settlement Servce condton 0.003m Sesmc condton of varous % shaft and base resstance n lquefacton area 0.003m (90%) 0.010m (80%) Infnty - Snk/tlt (70%) 4.5 Estmaton of ground settlement One of the case hstores, Saseka hosptal buldng that falls under Case III s consdered for lquefacton-nduced ground settlement estmaton whch s calculated usng two methods proposed by Tokmatsu et. al (1987) and Ishhara et. al (1992). The result of ths analyss s shown n table 3. Table 3 Post lquefacton ground settlement Case Hstory Saseka Hosptal Buldng, 1964 Ngata EQ Ple Length Ground Settlement Sol Depth Consdered Method 1 Method 2 Tokmatsu et al (1987) (Ishhara 1992) 7.2m 20m 0.368m 0.430m

8 5. DISCUSSION AND CONCLUSIONS The analyss of the case study showed that when the reducton n sol strength s about 30%, the ple wll lose t bearng capacty and wll tlt or snk. The case falls under Case III n fgure 2. The ground wll settle by 400mm The predcton of lquefacton depth shows that the ple rests on lquefed layer tself, hence the settlement or tltng falure, see table 2. The ple tp rests on lquefed area and structural falure n the ple s unlkely. One of the lmtatons of ths method s that dynamc effects are gnored. A smplfed approach of quantfyng the settlement of a ple due to loss of effectve stress owng to lquefacton has been dscussed. The method s based on axal load transfer (t-z, q-z) curves extensvely used n offshore engneerng practce (API, 2000). An example s consdered to demonstrate the applcaton of the method. REFERENCES API (2000). 2A-WSD:Recommended practce for plannng, desgnng and constructng fxed offshore platforms workng stress desgn. Amercan Petroleum Insttute Recommended Practce, Bhattacharya, S. (2003). Ple nstablty durng earthquake lquefacton. PhD thess, Unversty of Cambrdge, UK. Bhattacharya, S. (2006). Safety assessment of exstng pled foundaton n lquefable sols aganst bucklng nstablty. ISET Journal of Earthquake Technology, 43:4, Dash, S.R., Govndaraju, L. and Bhattacharya, S. (2008). A case study of damages of the Kandla port and customs offce tower supported on a mat-ple foundaton n lquefed sols under the 2001 Bhuj earthquake. Sol Dynamcs and Earthquake Engneerng, do: /j.soldyn (Artcle n Press) Hdeak, K. (1966). Damage to renforced concrete buldngs n Ngata cty wth specal reference to foundaton engneerng. Sols and Foundatons, 6:2, Idrss, I.M. and Boulanger, R.W. (2004). Sem-emprcal procedures for evaluatng lquefacton potental durng earthquakes. Proceedngs of the 11th Internatonal conference on sol dynamcs and earthquake engneerng, 1, Ishhara, K. and Yoshmne, M. (1992). Evaluaton of settlements n sand deposts followng lquefacton durng earthquakes, Sols and Foundatons, 32:1, Fukuoka, M (1966). Damage to cvl engneerng structures, Sols and Foundatons, 6:2, Seed, H.B. and Idrss, I.M. (1970). Smplfed procedure for evaluatng sol lquefacton potental. Journal of Sol Mechancs and Foundaton Engneerng, ASCE, 97:9, Tokmatsu, K. and Seed, H.B. (1987). Evaluaton of settlements n sand due to earthquake shakng. Journal of Geotechncal Engneerng, ASCE, 23(4), Vjayvergya, V.N. (1977). Load-movement characterstcs of ples. Conference report, Long Beach, Calforna Yorhko, O. (1966). Ngata earthquakes, 1964 buldng damage and sol condton. Sols and Foundatons, 6:2,