INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE

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1 13 th World Confrnc on Earthquak Enginring Vancouvr, B.C., Canada August 1-6, 2004 Papr No INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE Omar PINEDA 1, Mario ORDAZ 2 SUMMARY Th main objctiv of this papr is to analyz th influnc of ground subsidnc, typical in th Vally of Mxico, in th obsrvd damag to Mxico City s primary watr systm during th 1985 Michoacan arthquak. According to th obsrvd damag, it is blivd that sismic wav propagation was th main caus for th failurs. Howvr, th accumulatd subsidnc in th Vally of Mxico could hav incrasd th dstructiv action of th arthquak. W analyz damag data to th primary watr systm during th 1985 arthquak and try to xplain thm using two variabls: pak ground vlocity a paramtr rlatd to th arthquak and accumulatd ground subsidnc a paramtr rlatd only to th ground. Th main conclusion of this papr is that ground subsidnc, along with pak ground vlocity, ar bttr prdictors of damag than pak ground vlocity alon, which clarly indicats that ground subsidnc is an important vulnrability factor. Finally, according to th rsults, th sismic damag to burid piplin watr systms could b incrasd by th ffct of ground subsidnc. This ffct was idntifid only for wak ground motions. For strong ground motion, it was not possibl to quantify th ffct of ground subsidnc. INTRODUCTION Aftr th occurrnc of th 1985 Michoacan arthquak, it is blivd that th main caus for th failurs in th Mxico City s Watr Systm (MCWS) was th sismic wav propagation. Howvr, th ground subsidnc could hav incrasd th damag (Ayala [1]). In ordr to analyz th piplin failurs du to th influnc of sismic wav propagation, th damag has bn associatd to pak ground acclration (PGA) and pak ground vlocity (PGV). Thortically, PGV 1 Rsarch Assistant, Instituto d Ingniría UNAM, Distrito Fdral, México. Phon (52) xt opindap@iingn.unam.mx 2 Profssor, Instituto d Ingniría UNAM, Distrito Fdral, México. Phon (52) xt mors@pumas.iingn.unam.mx

is bttr rlatd to burid piplin sismic damag. Pinda [2] dmonstratd that PGV has bttr corrlation with damag than PGA, for th obsrvd damag in th MCWS aftr th occurrnc of th 1985 Michoacan arthquak.

2 is bttr rlatd to burid piplin sismic damag. Pinda [2] dmonstratd that PGV has bttr corrlation with damag than PGA, for th obsrvd damag in th MCWS aftr th occurrnc of th 1985 Michoacan arthquak. Som authors hav proposd svral damag functions in ordr to stimat th damag in th watr systm, using PGV as a sismic paramtr (O Rourk [3] and Pinda [4]); howvr, thr is not a function which includs th ffct of ground subsidnc and taks into considration th piplin diamtr. This papr intnds to propos damag functions considring two variabls: pak ground vlocity PGV, which is a paramtr rlatd to th arthquak, and ground subsidnc, a paramtr rlatd only to th ground. Ths functions wr associatd to 3 important piplin diamtrs in th systm. DAMAGE FUNCTIONS USING PEAK GROUND VELOCITY AND SUBSIDENCE AS PARAMETERS Figur 1 shows th spatial distribution of th man annual ground subsidnc valus for Mxico City btwn 1983 and 1992 (DGCOH [5]). In th sam pictur th Mxico City s watr systm and th obsrvd damag sits aftr th occurrnc of th 1985 arthquak ar shown. Figur 1. Man Annual Ground Subsidnc Map ( ), Mxico City s Primary Watr Systm and Rpair Sits aftr th Occurrnc of th 1985 Earthquak It is considrd that th ground subsidnc has influnc in th burid piplins damag bcaus th joints could b partially affctd; and, as a consqunc, a highr numbr of failurs du to ground motion could b xpctd than th numbr xpctd without th influnc of ground subsidnc. Figur 2 shows th stimatd pak ground vlocity map for th 1985 Michoacan arthquak (Pinda [2]). Thr, th dashd zon, which includs th wll-known transition and lak zons, is composd mainly by

clay sdimnts which produc dynamic amplification of sismic wavs. For this rason th PGV lvls in th dashd zon ar highr than th PGV valus in th hill zon (locatd outsid of th dashd rgion). Figur 2.

3 clay sdimnts which produc dynamic amplification of sismic wavs. For this rason th PGV lvls in th dashd zon ar highr than th PGV valus in th hill zon (locatd outsid of th dashd rgion). Figur 2. Pak Ground Vlocity Map for th 1985 Earthquak Comparing th spatial distributions of ground subsidnc (fig. 1) and PGV (fig. 2) it is important to notic that thr is a clos rlation btwn ths two factors. This is a problm in th damag stimation, bcaus a function which uss corrlatd paramtrs could produc ambiguous rsults. Howvr, th piplin damag is not ncssarily rlatd to th absolut ground subsidnc valus; w bliv damag is bttr corrlatd with th rlativ ground subsidnc in th dirction of ach piplin sgmnt. In othr words, th important paramtr is th dflction angl γ of th pip sgmnt causd by th ground subsidnc, which can b stimatd with quation 1. H f H i γ = (1) L Whr Hi and Hf ar th ground subsidnc valus associatd to th initial and final nd of ach sgmnt pip with lngth L. γ is th man annual dflction angl, causd by th rlativ ground subsidnc in th sgmnts. Sinc th authors do not hav rliabl information about th ag of ach piplin sgmnt, ag has bn considrd uniform for th whol watr systm.

4 In ordr to gt bttr rsults in this study, th watr systm was dividd in pip sgmnts with lngth qual to 50 m or lss. Rlation Btwn γ and th obsrvd damag In ordr to gt a bttr apprciation of th influnc of γ in th obsrvd damag, damag indx valus wr calculatd taking into considration th rlativ ground subsidnc as a uniqu paramtr. Ths valus ar shown in figur 3. By omitting othr paramtrs (.g. PGV) it was possibl to vrify that, as a gnral tndncy, th damag indx incrass as γ dos, for most valus of γ. Howvr, for γ largr than E-04 thr is a discontinuity, which could b xplaind by th scarc piplin lngth associatd to ths lvls of γ. For this rason, ths data points wr discardd in furthr analyss. Figur 3. Damag indxs associatd to diffrnt rlativ subsidnc valus Damag functions using γ and PGV as paramtrs Hr, w dtrmin damag functions that rlat D with PGV and γ. Sinc D is a sort of damag dnsity paramtr, thr is not a uniqu way of rlating damag with γ and PGV, bcaus th procdur to calculat th damag data points is th following: 1) divid th watr systm in zons associatd to intrvals of γ and PGV; 2) count th numbr of rpairs; 3) masur th piplin lngth in that zon; and 4) calculat th avrag damag D in th zon as th ratio btwn th numbr of obsrvd rpairs and th piplin lngth. This avrag damag, thn, would b rlatd with th PGV and γ valus associatd to th zon. W discardd th data points with damag indx qual to zro. Following th procdur dscribd, th damag functions, for piplins with 3 diffrnt diamtrs (figurs 4, 5 and 6), wr calculatd. Piplins with 20 and 48 wr slctd bcaus thy hav th gratst lngth proportion in th watr systm (23.22% and 53.57%, rspctivly). Th damag function for D = 32, although associatd to a small piplin lngth (only 3.77% of th total lngth), shows th ffct of ground subsidnc. In viw of th procdur to calculat th man damag indxs D, it is difficult to rduc disprsion, and as a consqunc, to adjust quations. Equations 2 to 10 ar proposd in ordr to stimat th numbr of piplin rpairs taking into considration th ffct of ground subsidnc and th ground motion intnsity (masurd as PGV), for 3 diffrnt piplin diamtrs.

5 Figur 4. Damag Function for Piplins with D = 20 Damag functions for piplins with D = 20 ar: For γ = (fig 4, 1) For γ = (fig 4, 2) PGV D = (2) PGV D = (3) Figur 5. Damag Function to Piplins with D = 32

6 Damag functions for piplins with D = 32 ar: For γ = (fig 5, 1) For γ = (fig 5, 2) D = D = (5) PGV (4) PGV Most of th 20 and 32 piplins ar mad of stl, concrt and asbstos cmnt. Figur 6. Damag Function to Piplins with D = 48 Damag functions for piplins with D = 48, which ar mainly mad of prstrssd concrt, ar: For γ = (fig 6,1) For γ = (fig 6,2) For γ = (fig 6,3) For γ = (fig 6,4) For γ = (fig 6,5) PGV D = (6) PGV D = (7) PGV D = (8) PGV D = (9) PGV D = (10) QUANTIFYING THE EFFECT OF RELATIVE SUBSIDENCE IN THE SEISMIC DAMAGE Th objctiv of th following rsults is to quantify th ffct of ground subsidnc in th piplin sismic damag. This was possibl bcaus som of th failurs obsrvd aftr th 1985 arthquak wr rlatd to γ valus qual to zro. Thn, sismic wav propagation must hav bn th only caus of failurs. D valus associatd to γ = 0, wr calculatd and compard to othr data points usd to calculat a damag function (Pinda [4]) which considrs only th ffct of ground motion, masurd with PGV (figur 7 and quation 11), but includs implicitly th ffct of ground subsidnc.

7 Study Zon Figur 7. Damag Function to MCWS, Proposd by Pinda [4] D( 5.35 V < 95) = nˆ( V; , ) (11) In quation 11, nˆ is th cumulativ normal function, dfind by quation 12; and V is th pak ground vlocity in cm/s. V 1 2πσ [ ] 2 (1/ 2) ( v µ ) / σ nˆ ( V ; µ, σ) = dv (12) D was calculatd dividing th PGV map in zons of qual PGV intrvals (9 PGV intrvals wr usd), and stimating th ratio btwn th numbr of rpairs and th piplin lngth. For th purpos of this study, w slctd, from figur 7, only th data points associatd to PGV smallr than 20 cm/s (fig 10, cas 1), bcaus th availabl damag data points associatd to sits with γ = 0 ar only found in this PGV intrval (fig 8, cas 2). In figur 8 th ffct of ground subsidnc on damag indx D is vidnt. Cas 1 includs data points from figur 7, in which th ffct of ground subsidnc is implicitly accountd for; cas 2 includs only data points associatd to sits without rlativ ground subsidnc.

8 Figur 8. Damag indxs With and Without th Rlativ Subsidnc Effct. (For PGV < 20cm/s) CONCLUSIONS W analyzd th ffct of ground subsidnc in th sismic damag to Mxico City s Primary Watr Systm during th 1985 Michoacan arthquak. Using pak ground vlocity and rlativ ground subsidnc as paramtrs, thr damag functions, for pip diamtrs of 20, 32 and 48, wr dtrmind. Ths functions stimat th damag indx, masurd as th numbr of xpctd rpairs pr unit lngth, for diffrnt lvls of ground motion and diffrnt rlativ ground subsidnc lvls. It was found that th damag indx D incrass with th ground motion intnsity, and, additionally, with th rlativ ground subsidnc γ. In othr words, th ffct of γ incrass D for a spcific ground motion intnsity, which indicats that γ is an important paramtr in th stimation of sismic damag to th watr systm studid and othrs systms locatd in sits affctd by ground subsidnc. Finally, w compard damag indxs considring two cass: Cas 1 includs data points in which th ffct of ground subsidnc is implicitly accountd for; cas 2 includs only data points associatd to sits without rlativ ground subsidnc. It was found that, for PGV valus lss that 20 cm/s, th ffct of ground subsidnc could hav incrasd th sismic damag to th watr systm, during th 1985 arthquak; for PGV valus highr than 20 cm/s, this ffct was not analyzd, bcaus nough damag data wr not availabl. REFERENCES 1. Ayala G, O Rourk M. Effcts of th 1985 Michoacan arthquak on watr systms and othr burid liflins in Mxico. Tchnical Rport NCEER , Multidisciplinary Cntr for Earthquak Enginring Rsarch. Nw York, 1989.

9 2. Pinda O. Estimación d daño sísmico n la rd primaria d distribución d agua potabl dl Distrito Fdral. Postgraduat thsis, División d Estudios d Posgrado d la Facultad d Ingniría, Univrsidad Nacional Autónoma d México. Mxico, O Rourk M, Ayala G. Piplin Damag to Wav Propagation, Journal of Gotchnical Enginring, ASCE, Vol. 119, No Pinda O, Ordaz M Sismic vulnrability function for high-diamtr burid piplins: Mxico City s primary watr systm cas, 2003 ASCE Intrnational Confrnc on Piplin Enginring and Construction, Amrican Socity of Civil Enginrs. Baltimor, USA. 5. DGCOH Plan mastro d agua potabl , Dircción Gnral d Construcción y Opración Hidráulica. México, 1996.

4.2 Design of Sections for Flexure

4.2 Design of Sections for Flexure 4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt