Foundation design reliability issues

Transcription

1 GEO.MCM.0001.SUB.1 Foundaton desgn relablty ssues K. McManus Overvew The New Zealand Buldng Code through Verfcaton Method VM4 permts the use of very low factors of safety for the desgn of buldng foundatons under certan earthquake load cases (as low as FS = 1.1). The use of such low factors of safety for vertcally loaded foundatons s questoned because t mples a hgh probablty of foundaton falure durng the desgn earthquake. Even where the desgner may wsh to lmt forces wthn the structure and perhaps encourage system dampng by permttng sol yeldng, the results are lkely to be unpredctable because of the uncertanty n predctng foundaton performance and varablty n performance among ndvdual foundaton elements. The desred structural behavour pattern may not develop, wth unntended consequences such as excessve ductlty demands on some parts of the structure. Excessve foundaton deformatons may develop prematurely resultng n sgnfcant damage, even for lesser earthquakes. Background The procedure for desgnng buldng foundatons n NZ may be descrbed as a Load and Resstance Factor Desgn procedure (LRFD). In ths procedure, the uncertanty and varablty n the loads and desgn actons on foundaton elements are consdered separately from the uncertanty and varablty n the resstance of the foundatons, accordng to the desgn nequalty: In whch; Q R (1) = load factor for load type (e.g. 1.2 for dead loads, 1.7 for lve loads, 1.0 for EQ loads, for the ultmate lmt state n NZS 1170) Q = nomnal value of load type = resstance factor for component of resstance R = nomnal value of computed resstance for component The above nequalty must be satsfed for several lmt states whch are defned n relevant codes. For strength lmt states (e.g. the ultmate lmt state n NZS 1170, or ULS) load and resstance factors are chosen to provde a hgh level of relablty that the foundaton wll have suffcent strength to prevent collapse. For servce lmt states (e.g. the servceablty lmt state n NZS 1170), generally checkng for excessve deformatons, load and resstance factors are often taken to be at or near 1.0 reflectng a phlosophy that a lower level of relablty can be accepted for servceablty ssues not nvolvng safety. (It should be noted that for the case where the load factor and the resstance factor are both taken as 1.0, the probablty of exceedance s nomnally 50 percent)

2 GEO.MCM.0001.SUB.2 In some jursdctons, extreme event lmt states are also consdered (e.g. maxmum consdered earthquake or MCE) but not n NZS A lower level of relablty s often accepted for extreme events. Fgure 1 llustrates how the desgn nequalty of Equaton (1) operates: Both the nomnal loads (Q m ) and the nomnal resstance (R m ) have a certan nherent varablty llustrated as bell shaped dstrbuton curves. Generally, the varablty n foundaton resstance wll be much greater than for the loads, and so the bell s shown to be fatter. The probablty of falure (.e. load beng greater than resstance) may be computed as the area of overlap of the two bell curves, shown shaded. To mantan the probablty of falure at a low level t s necessary to ensure that the nomnal resstance s larger than the nomnal loads (R m >Q m ) by applyng load factors greater than 1 and resstance factors less than 1. The approprate values of these factors depends on the shape (wdth) of the respectve bell curves and the desred level of relablty. Hstory of geotechncal resstance factors n NZ Pror to the adopton of the LRFD desgn procedure wth NZS 4203 n 1976, the varablty and uncertanty n both the load and resstance sdes of the desgn equaton were lumped together as a sngle factor of safety (FS) beng the rato of nomnal resstance over nomnal load (FS = R m /Q m ). Tradtonally, for foundatons, the mnmum factor of safety was taken to be 3 for statc loads and 2 for sesmc loads (e.g. NZS 1900 of 1965), based largely on precedent. Wth the ntroducton of LRFD wth NZS 4203:1976, t was ntended to mantan the overall factor of safety for foundatons at smlar levels as prevously but there was a new complcaton of a load factor that vared from 1.0 to 1.7. Strength reducton factors were not gven n NZS 4203:1976 as these were ntended to be provded n the respectve materal codes as they were updated. For foundaton desgn, NZS 4203:1976 recommended (n the commentary) that pendng revson of NZS4205 [Code of Practce for Foundaton Desgn] a factor of safety of 1.8 should be appled (equvalent to a strength reducton factor of = 0.56) n addton to the load factors for all load combnatons, ncludng those wth sesmc actons. Capacty desgn was n ts nfancy at the tme of the ntroducton of NZS4203 and the code suggested that for certan ductle structure types where desgn loadngs on the foundaton system are determned by the yeld capacty of other parts of the structure, a factor of safety of 1.1 for sol pressures s suggested, pendng revson of the foundaton code, because at ths extreme condton partal yeldng of the subsol mght not be sgnfcantly damagng and t provdes an addtonal energy dsspatng mechansm. (.e. a strength reducton factor of = 0.9). Effectvely, ths recommendaton reduced the tradtonal all-up factor of safety for foundatons wth sesmc loadng from 2.0 down to 1.1 for buldngs desgned usng capacty desgn - wth sesmc load levels already reduced because of allowance for ductlty - and from 2.0 down to 1.8 for other buldngs. Capacty desgn consderatons The ntroducton of such a low factor of safety for the foundatons of capacty desgned buldngs s surprsng gven the contemporary publshed vews of the man proponent of capacty desgn, Professor Tom Paulay (Bnney & Paulay, 1980). Dscussng the desgn of foundatons for shear wall structures, Bnney and Paulay recommended that for ductle shear wall structures the foundatons must be capable of transmttng the largest feasble actons to the supportng sol, otherwse the ntended response of the superstructure cannot eventuate. Further, that: Bearng areas of footngs, ples, or cassons should be such that neglgble

3 GEO.MCM.0001.SUB.3 nelastc deformatons, f any, are developed n the supportng sol under actons correspondng to overstrength of the superstructure. The wrters of NZS4203:1976 seemed to agree by stpulatng that foundaton systems shall be desgned to preclude foundaton falure, or uplft of an entre foundaton element, at loadngs correspondng to yeldng of the earthquake energy dsspatng elements, takng concurrency effects nto account where applcable. Fulflment of ths code requrement would requre a much hgher factor of safety than the value of 1.1 suggested n the code commentary. Bnney and Paulay acknowledged that n some cases, the dmensons and locatons of shear walls wthn a buldng mght be such that the overturnng moments would be dffcult or mpossble to resst at the foundatons. They recommended that rockng (.e. uplft of the foundaton) mght be permssble but that desgn should be by specal study ncludng dynamc analyses and that bearng areas wthn the foundaton structure be so proportoned as to protect the sol aganst excessve plastc deformatons that would be dffcult to predct, and whch mght result n premature msalgnment of the otherwse undamaged shear wall or the entre buldng. To provde the mpled level of foundaton performance, relably, requres the use of much hgher factors of safety (or lower strength reducton factors n LRFD desgn). Current code Snce 1976, the loadng code has been revsed three tmes and the prevous references to foundaton desgn have been removed. Instead, Verfcaton Method VM4 was ntroduced to the Buldng Code documents to provde gudance on foundaton desgn ncludng the strength reducton factors to be appled. The earler relance on tradtonal factors of safety (e.g. FS = 3 for foundaton desgn) has been replaced by a more ratonal approach that accounts for specfc causes of uncertanty and varablty n the computaton of foundaton resstance ncludng the thoroughness of the ste nvestgaton, the way n whch sol propertes are assessed, the desgn procedure used, the extent of on-ste verfcaton by load testng, and the degree of constructon control. In VM4 strength reducton factors range from 0.40 to 0.65 dependng on the method of computng the foundaton capacty and the desgners qualtatve assessment of the above sources of uncertanty, for all load combnatons not nvolvng earthquake over-strength. Typcally, n practce, values range from 0.45 to 0.5 for shallow foundatons and from 0.5 to 0.65 for ple foundatons. Values hgher than 0.65 may be used where statc load testng of foundatons s carred out up to 0.85 where a sgnfcant percentage of the foundatons are load tested statcally to falure at sutable stes. However, for load combnatons ncludng earthquake over-strength, the strength reducton factor s between 0.8 and 0.9 rrespectve of the desgn methodology and not requrng statc load testng. The use of such hgh values s napproprate n most cases gven the hgh level of uncertanty and varablty n foundaton behavour and the requrement, dentfed by Bnney and Paulay, for relable foundaton performance n the event of over-strength beng developed n capacty desgned structures.

4 GEO.MCM.0001.SUB.4 The meanng of the words n VM4 ncludng earthquake over-strength may not be well understood by some engneers, especally those unfamlar wth capacty desgn, and the hgh values of strength reducton factor may be beng routnely appled to all load combnatons wth sesmc actons. Snce the ntroducton of VM4, there have been further developments n assessng sutable strength reducton factors for geotechncal desgn. For example, the Australan plng code AS has ntroduced a much more thorough rsk based approach where ndvdual rsk factors are assessed ncludng geologcal complexty of the ste, extent of ground nvestgaton, amount and qualty of ground data, experence n smlar condtons, method of assessng sol propertes, desgn methodology, n-stu testng and testng durng ple nstallaton, level of constructon control, level of performance montorng after constructon, and the level of redundancy n the foundaton system. Resultng strength reducton factors range from 0.40 for hgh rsk, low redundancy cases to 0.76 for low rsk, hgh redundancy cases. Recommendatons The use of very hgh strength reducton factors (as hgh as 0.9 equvalent to FS = 1.1) for capacty desgned structures s napproprate. Many foundatons so desgned wll receve overstrength loads durng earthquakes exceedng ther capacty and leadng to excessve plastc deformaton. The hgh varablty of sol propertes and foundaton performance ensures that the overall behavour of the structure wll be unpredctable and, most lkely, undesrable. Premature falure of some foundatons s lkely. I recommend that for the case of the ultmate lmt state of NZS1170, the selecton of strength reducton factors for foundaton desgn n all cases be based on a rsk assessment procedure such as that used n AS The objectve beng to ensure relable foundaton performance under all load combnatons. There seems to be no bass for treatng capacty desgned buldngs as a specal case where unrelable foundaton performance s acceptable. The present provson appears to have arsen from a hstorcal msunderstandng. K. McManus October 2011

5 GEO.MCM.0001.SUB.5 Fgure 1. Idealsed probablty dstrbutons of load and resstance on a foundaton [Source: O Nell and Reese, 1999] References: Bnney, J.R. and Paulay, T. (1980). Foundatons for Shear Wall Structures, Bulletn of the N.Z. Natonal Soc. of Earthquake Eng., Vol.13. No. 2 June O Nell, M. W. and Reese, L. C. (1999). Drlled Shafts: Constructon Procedures and Desgn Methods, FHWA-IF , U.S. Department of Transportaton, Federal Hghway Admnstraton, Washngton, D.C. Standards Assocaton of New Zealand (1976) Code of Practce for General Structural Desgn and Desgn Loadngs for Buldngs, NZS 4203:1976, Wellngton, New Zealand.