INTERNATIONAL SOCIETY FOR

SOIL MECHANICS AND

GEOTECHNICAL ENGINEERING

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D is c u s s io n le a d e r ’s re p o r t

R a p p o rt d e I’a n im a te u r

T R E V O R L .L .O R R , T r in i ty C o l le g e , D u b lin U n ive rs ity , Ire la n d

SYNOPSI S: The di scuss i on sessi on on pr obabi l i s t i c appr oaches i n geot echni cal engi neer i ng concent r at ed on r ecent r esear ch i nt o t he use of pr obabi l i s t i c appr oaches and on t he appl i cat i on of t hese appr oaches i n pr act i ce. The Gener al Repor t er out l i ned how pr obabi l i s t i c appr oaches may be used as a ' desi gn t ool and gave some exampl es. However , he poi nt ed out t hat t her e i s ver y l i t t l e i nf or mat i on about t he st at i s t i cal nat ur e of soi l par amet er s and t hi s i s a di sadvant age when usi ng a pr obabi l i s t i c appr oach i n pr act i ce. The i nvi t ed speaker s spoke f r om a r esear ch backgr ound but showed how t he r esul t s of t hei r wor k on pr obabi l i s t i c appr oaches wer e bei ng appl i ed i n pr act i ce, f or exampl e, i n t he case of cost ef f ect i ve si t e i nvest i gat i ons and i n f oundat i on desi gn agai nst di f f er ent i al set t l ement . The cont r i but or s t o t he gener al di scuss i on pr ov i ded f ur t her exampl es t o show wher e pr obabi l i s t i c appr oaches had been used successf ul l y t o sol ve geot echni cal desi gn pr obl ems. The conc l us i on t hat t he Di scussi on Leader dr ew f r om t he di scuss i on was t hat t he use of pr obabi l i s t i c appr oaches i n geot echni cal engi neer i ng had i ncr eased s i gni f i cant l y over t he past f ew year s and t hat t hese appr oaches wer e pr ovi ng t o be ver y usef ul f or t aki ng account of par amet er var i abi l i t y , opt i mi z i ng des i gn and assess i ng r i sk and r el i abi l i t y.

REVI EW OF SESSI ON

The di scuss i on sessi on was chai r ed by Pr of essor S. Fr ydman f r om I sr ael and t he Di scuss i on Leader was Dr . T. Or r f r om I r el and. The sessi on began wi t h t he pr esent at i on by t he Gener al Repor t er , Dr . A. Het t l er f r om t he FGR, of hi s r epor t on pr obabi l i s t i c appr oaches whi ch was pr epar ed wi t h t he ass i s t ance of hi s Co- r epor t er , Mr . E. Schwi ng. I n or der t o obt ai n an i nt er nat i onal per spect i ve on t he subj ect , t he Chai r man and Di scuss i on Leader i nvi t ed t he f ol l owi ng peopl e t o make shor t cont r i but i ons out l i ni ng some r ecent devel opment s i n t hi s ar ea:

Pr of essor E. E. Al onso ( Spai n)Pr of essor W. H. Tang ( USA)

Fol l owi ng t he pr epar ed pr esent at i ons by t he Gener al Repor t er and t he i nvi t ed speaker s, t her e was a gener al di scuss i on whi ch i ncl uded cont r i but i ons f r om t he f ol l owi ng peopl e:

Pr of essor G. Gudehus Dr . W. Hachi ch Dr . F. Oboni Pr of essor M. Pacheco Mr . E. Schwi ng Mr . J . Wei j er s

( FRG)( Br az i 1)( Swi t zer l and) ( Br az i l )( FRG)( Ne t her l ands)

I n or der t o f ocus t he gener al di scussi on, t he Di scussi on Leader , af t er consul t at i on wi t h t he Chai r man and t he i nvi t ed speaker s, pr oposed t hat t he cont r i but or s t o t he gener al di scuss i on shoul d addr ess t he f ol l owi ng t opi cs:

- The use of pr obabi l i s t i c appr oaches;When ar e t hey appr opr i at e ?What ar e t hei r advant ages and l i mi t at i ons ?

- The pr obabi l i t y of f ai l ur e;What val ues ar e appr opr i at e ?How r eal i s t i c ar e cal cul at ed val ues ?

- Pr obabi l i s t i c based desi gn;What char act er i s t i c val ues shoul d be used ?What par t i al f act or s ?

Most of t he speaker s addr essed t he f i r st t opi c and many exampl es wer e gi ven wher e st at i s t i cs and pr obabi l i s t i c appr oaches have been used successf ul l y t o f i nd sol ut i ons f or pr act i cal geot echni cal pr obl ems. The des i gn pr obl ems gi ven i ncl uded soi l var i abi l i t y , pi pi ng, sl ope st abi l i t y and opt i mi zat i on. The speaker s al so poi nt ed out some of t he advant ages and l i mi t at i ons of t hese appr oaches. Thi s r esul t ed i n a l i vel y and st i mul at i ng di scussi on.

The gener al r epor t , t he i nvi t ed cont r i but i ons, t he gener al di scuss i on and t he paper s submi t t ed t o t he sessi on al l ser ved t o demonst r at ed t hat , s i nce t he l ast I nt er nat i onal Conf er ence i n San Fr anci sco i n 1985, t he use of pr obabi l i s t i c appr oaches has i ncr eased s i gni f i cant l y i n geot echni cal engi neer i ng, par t i cul ar l y amongst des i gn engi neer s. I n some des i gn of f i ces t hese appr oaches ar e now used on a r egul ar basi s. One speaker r emar ked t hat , al t hough s t at i s t i cal l y based met hods ar e pr omi s i ng i n pr i nci pl e, i t wi l l t ake many year s of t eachi ng and l ear ni ng bef or e t hey ar e wi del y adopt ed and accept ed by al l t he peopl e i nvol ved i n an engi neer i ng pr oj ec t .

The paper s t o t he sessi on c l ear l y demonst r at ed t hat t he f i r st or der second moment met hod was t he most popul ar pr obabi l i s t i c f or mul at i on. The Gener al Repor t er i n hi s pr esent at i on showed how t hi s met hod i s used i n pr act i ce and how t he st at i s t i cal val ues f or t he geot echni cal par amet er s may be det er mi ned. For exampl e, he poi nt ed out t hat most geot echni cal dat a i s best r epr esent ed by a l og- nor mal di st r i but i on. He al so dr ew at t ent i on t o t he scar c i t y of i nf or mat i on about t he s t at i s t i cal nat ur e of

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par amet er val ues and t o t he f act t hat some of t he i nf or mat i on, such as t hat about aut ocor r el at i on l engt hs, appear ed t o be cont r adi ct or y. Thus t her e i s a gr eat need f or f ur t her r esear ch i n t hi s ar ea.

Some of t he advant ages of pr obabi l i s t i c appr oaches whi ch wer e poi nt ed out dur i ng t he di scuss i on and whi ch have l ed t o t hei r i ncr eased use ar e

- t hey pr ovi de a r at i onal way of account i ng f or par amet er var i abi l i t y,

- t hey al l ow r i sk and r el i abi l i t y t o be assessed. Thi s i s becomi ng mor e i mpor t ant wi t h t he i ncr easi ng cost and compl ex i t y of moder n st r uct ur es and wher e t her e i s l esB mar gi n f or er r or ,

- t hey enabl e opt i mi zat i on i n desi gn,- t hey may be used f or qual i t y cont r ol ,- t hey ar e usef ul i n new des i gn s i t uat i ons wher e

t her e i s no body of exper i ence upon whi ch t o base desi gn or choose f act or s of saf et y.

Anot her appl i cat i on of pr obabi l i s t i c appr oaches, whi ch was mor e t he concer n of t he di scuss i on sessi on on codes and st andar ds, i s t hat t hey f or m t he basi s f or t he new l i mi t st at e des i gn codes such as Eur ocode 7.

2 GENERAL REPORT

2. 1 Openi ng r emar ks

Dr . A. Het t l er , t he Gener al Repor t er , not ed i n hi s openi ng r emar ks he not ed t hat 16 paper s on pr obabi l i s t i c appr oaches had been pr esent ed t o t hi s sessi on f r om count r i es al l over t he wor l d. As pr obabi l i t y i s such a br oad t opi c, t hese paper s cover a wi de r ange of t opi cs, r angi ng f r om t he des i gn of bor ed pi l es by Oboni ( 1989) t o an assessment of t he geol ogi cal condi t i ons al ong t he l i ne of t he Channel t unnel by Magnan ( 1989) . Rat her t han sayi ng a f ew wor ds about each of t hese paper s, Dr . Het t l er made a pr esent at i on based on hi s own wor k and exper i ences usi ng pr obabi l i s t i c appr oaches and t ook exampl es f r om t he paper s t o i l l ust r at e hi s poi nt s .

2. 2 Pr obabi l i t y Theor y

To i l l ust r at e t he use of pr obabi l i t y t heor y i n geot echni cal desi gn, Dr . Het t l er showed a sl i de of a Bavar i an cast l e bui l t about 100 year s ago wi t h beaut i f ul , ol d st yl e wal l s. He had been abl e t o i nspect behi nd t hese wal l s and had been as t oni shed t o di scover t hat t he ol d wal l s wer e suppor t ed by moder n st eel beams and conceal ed moder n t echnol ogy such as el ect r i c i t y. He dr ew an anal ogy bet ween t hi s cast l e and moder n soi l mechani cs by l i keni ng t he beaut i f ul ol d wal l s t o c l assi cal t heor i es and t he conceal ed moder n component s t o pr obabi l i t y t heor y whi ch gi ves a r at i onal basi s f or saf et y cal cul at i ons.

2. 3 Nat ur al Var i abi l i t y

The pr obl em of t he nat ur al var i abi l i t y ( scat t er i ng) i n t he pr oper t i es and t hi cknesses of soi l s and r ocks was cons i der ed by Dr . Het t l er and was t he subj ect of t he paper by Bl anchi n et a l . ( 1989) . Because t he t hi cknesses of soi l st r at a var y and because t he pr oper t i es

wi t hi n each st r at um var y, i t i s of t en ver y di f f i cul t t o pr edi ct set t l ement as shown i n t he paper by Tsuchi da and Ono ( 1989) . They cal cul at ed t he set t l ement usi ng a pr obabi l i s t i c appr oach, t aki ng account of t he cor r el at i on of t he geot echni cal pr oper t i es i n each l ayer , and obt ai ned good agr eement bet ween t he cal cul at ed and measur ed set t l ement s. However , Dr . Het t l er wonder ed what woul d have been t he r esul t i f t he set t l ement s had been cal cul at ed usi ng a convent i onal anal ysi s.

The weat her i ng of r ocks, such as mar l and mudst one, pr oduces soi l s wi t h var yi ng t hi cknesses and pr oper t i es. Thi s var i abi l i t y wi l l need t o be t aken i nt o account i f , f or exampl e, soi l nai l i ng i s used t o s t abi l i ze such weat her ed soi l sl opes. The pr obl em of assessi ng t he nat ur al var i abi l i t y of soi l pr oper t i es was exami ned by cons i der i ng t he r esul t s of penet r at i on t est s on a si t e usi ng di f f er ent s i zed cones. Al t hough t he t r end was t he same, t he measur ed var i abi l i t y depended on t he si ze of t he cone, wi t h t he l ar ger cone r ecor di ng a smal l er var i abi l i t y .

2. . 4 I nduced Var i abi l i t y

Var i abi l i t y or uncer t ai nt y i s al so i nt r oduced i nt o geot echni cal desi gn by t he const r uct i on equi pment used. An exampl e was gi ven by Dr . Het t l er wher e hydr aul i c equi pment i s used t o i nser t and r emove a pi l e casi ng. I f t he casi ng becomes i ncl i ned and has t o be r eadj ust ed, t hi s wi l l al t er t he st r ess st at e ar ound t he pi l e and cause var i abi l i t y i n t he ski n f r i ct i on. Anot her exampl e gi ven of i nduced var i abi l i t y i s t hat due t o t he gr ab, i n t he case of bor ed pi l es, di s t ur bi ng t he gr ound beneat h t he pi l e t oe and causi ng var i abi l i t y i n t he end r esi st ance. Thi s di s t ur bance was demonst r at ed by cons i der i ng t he l oad- set t l ement cur ves f or bor ed pi l es whi ch i ni t i al l y show some per t ur bat i ons due t o di s t ur bance but , as t he set t l ement i ncr eases, t hese per t ubat i ons di sappear .

An exampl e was gi ven wher e a bor ed pi l e had been shaf t gr out ed t o i ncr ease t he ski n f r i ct i on and t hus r educe set t l ement . Af t er excavat i on i t was f ound t hat t he t hi ckness of t he gr out ar ound t he pi l e var i ed due t o var i at i on i n t he gr adi ng and per meabi l i t y of t he soi l . A s i mi l ar s i t uat i on occur s when st abi l i s i ng a sl ope usi ng shot cr et e. The t hi ckness and s t i f f ness of t he concr et e l ayer wi l l be var i abl e and wi l l depend on bot h t he r oughness of t he gr ound sur f ace and on t he wor kmanshi p. Anot her s i t uat i on wher e var i abi l i t y occur s due t o const r uct i on i s i n t he case of a cas t - i n- s i t u concr et e pi l e. I n t hi s case t he cr oss sect i on of t he pi l e i s not const ant but var i es due t o t he l at er al gr ound st i f f ness changi ng wi t h dept h and due t o t he const r uct i on met hod, as was demonst r at ed by an exampl e of an excavat ed pi l e.

2. 5 Desi gn Met hods

Dr . Het t l er next cons i der ed t he basi c quest i on of how t o car r y out a geot echni cal desi gn. I n geot echni cal desi gn t he des i gner i s f aced wi t h a gr eat di ver s i t y of par amet er val ues and t hus l i mi t s have t o be det er mi ned f or t he par amet er s so t hat t he desi gn i s saf e and economi c. A t r adi t i onal met hod t o det er mi ne t he desi gn l oad f or a pi l e i s t o di v i de t he ul t i mat e pi l e l oad obt ai ned f r om cone penet r at i on t est r esul t s by a

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saf et y f act or of t wo. Dr . Het t l er poi nt ed out t hat t hi s met hod i s ver y ar bi t r ar y and st at ed t hat t he use of s t at i s t i cs of f er ed a r at i onal and easy met hod t o cal cul at e t he saf e desi gn l oad.

2. 6 Pr obabi l i s t i c met hods

The most i mpor t ant pr obabi l i s t i c met hod used i n geot echni cal des i gn i s t he f i r st or der second moment ( FOSM) or l evel I I met hod. Thi s met hod i s based on t he mean val ue, coef f i c i ent of var i at i on and dens i t y f unct i on. Al t hough onl y an appr ox i mat e met hod, Dr . Het t l er cons i der ed t hi s met hod t o be suf f i c i ent l y accur at e. Er r or s ar i se f r om uncer t ai nt y about t he par amet er s and t her ef or e f ut ur e wor k needs t o be car r i ed out t o i nvest i gat e t he par amet er s. Dr . Het t l er not ed t hat , because t hi s met hod has become popul ar , t her e ar e a number of cont r i but i ons t o t he Conf er ence whi ch use t hi s met hod t o sol ve geot echni cal desi gn pr obl ems and, as exampl es, he ment i oned t he paper s by Gassi er and Gudehus ( 1989) , de Quel er i j ( 1989) , Cal l e et al . ( 1989) , Lacasse and Goul oi s ( 1989) and Knoesen ( 1989) . Wi t h r egar d t o t he paper by Pet acci a and Tancr edi ( 1989) , wher e a pr obabi l i s t i c met hod i s used t o l ocat e t he cr i t i cal s l i p sur f ace i n a s l ope s t abi l i t y anal ysi s, Dr . Het t l er quest i oned i f i t woul d not have been eas i er t o f i nd t he cr i t i cal s l i p sur f ace det er mi ni st i cf l y and t hen use t he FOSM met hod t o cal cul at e t he pr obabi l i t y of f ai l ur e. Dr . Het t l er not ed t hat t he FOSM met hod i s not t he onl y pr obabi l i s t i c appr oach t hat may be used but t hat t he Mont e Car l o met hod may al so be used, as i n t he cont r i but i on by Yakov l ev & Shkol a ( 1989) .

2. 7 St at i s t i cal nat ur e of par amet er s

Dr . Het t l er pr esent ed dat a f r om a ser i es of pi l e l oadi ng t est s whi ch showed t hat t he pi l e poi nt r es i s t ance was best r epr esent ed by a l og- nor mal di st r i but i on. A nor mal di s t r i but i on was l ess accur at e. Bout wel l and Hedges ( 1989) , who measur ed t he per meabi l i t y of undi s t r i but ed sampl es of wast e r et ent i on l i ner s, f ound t hat t he measur ed per meabi l i t y al so had a l og- nor mal and not a nor mal di st r i but i on, whi ch makes much mor e sense. I n t he paper by Gar zoni o ( 1989) , t he var i abi l i t y of var i ous geot echni cal par amet er s was i nvest i gat ed and Dr . Het t l er concl uded, agai n, t hat t he par amet er s ar e best r epr esent ed by l og- nor mal di s t r i but i ons. I n t he cont ext of t he s t at i s t i cal nat ur e of mat er i al pr oper t i es, Dr . Het t l er r ef er r ed t o t he paper by Maschwi t z and Cunze ( 1989) wher e t he use of s t at i st i cal met hods t o ensur e qual i t y cont r ol i n f oundat i on engi neer i ng i s descr i bed.

Dr . Het t l er cons i der ed t he val ue of t he coef f i c i ent of var i at i on. I n pr act i ce, f r om a st at i s t i cal poi nt of vi ew, t he amount of dat a avai l abl e t o assess t he coef f i c i ent of var i at i on i s ver y l i mi t ed and hence pr agmat i c assumpt i ons ar e necessar y. I t has been assumed t hat t he coef f i c i ent i s appr ox i mat el y const ant and i s i ndependent of t he mean val ue of a par amet er . Dr . Het t l er pr esent ed t he r esul t s of a ser i es of pi l e l oadi ng t est s wher e i t was obser ved t hat , f or set t l ement s of 3, 6 and 9mm, t he coef f i c i ent s of var i at i on of t he pi l e l oads wer e i ndependent of t he mean val ue and had a const ant val ue of about 20%. I t i s known t hat t he coef f i c i ent of var i at i on depends on t he sampl e

si ze. Thi s i s demonst r at ed by Schwi ng and Het t l er ( 1989) i n t hei r paper on t he pul l - out t est s on soi l nai l s wi t h di f f er ent l engt hs. Dr . Het t l er t hen ment i oned t he wi de r ange of aut ocor r el at i on l engt hs quot ed bot h i n t he l i t er at ur e and i n t he cont r i but i ons by Tsuchi da and Ono ( 1989) and Bol l e et a l . ( 1989) . These ser ve t o i l l ust r at e t he pr esent l ack of knowl edge about t hi s subj ect .

I t f ol l ows f r om t he c l ass i cal t heor y of smal l sampl es t hat var i at i on i n t he mean val ue has much l ess i nf l uence on t he des i gn l oads t han t he var i at i on i n t he coef f i c i ent of var i at i on. For t hi s r eason, a smal l number of sampl es i s of t en suf f i c i ent i n pr act i ce t o det er mi ne t he mean, or el se i t may be det er mi ned i ndi r ect l y f r om i ndex t es t s .

2. 8 Pr act i cal Appl i cat i on

As a pr act i cal exampl e, Dr . Het t l er out l i ned how t he pr obabi l i s t i c appr oach may be used t o est i mat e t he des i gn l oads f or pi l es. I f t her e has onl y been one pi l e l oad t est , t hen i t i s not possi bl e t o use c l ass i cal s t at i s t i cal met hods t o cal cul at e t he des i gn pi l e l oad. I n pr act i ce i t i s of t en necessar y t o i nt r oduce exper i ence i nt o t he st at i s t i cal f or mul ae, f or exampl e by usi ng a Bayes i an appr oach or a maxi mum l i kehood met hod as out l i ned i n t he cont r i but i on by Ledesma et a l . ( 1989) . The Bayes i an appr oach i s a ver y usef ul met hod. Usi ng t hi s appr oach and t aki ng i nt o account t he assumpt i ons al r eady ment i oned r egar di ng t he st at i s t i cal nat ur e of soi l par amet er s, Dr . Het t l er sai d i t i s possi bl e t o expl ai n t he val ues of t he saf et y f act or s whi ch ar e used i n pr act i ce.

I n concl usi on, Dr . Het t l er poi nt ed out t hat t he best pr obabi l i s t i c des i gn wi l l not guar ant ee saf et y i f a par t i cul ar f ai l ur e mechani sm has been over l ooked. As an exampl e, he r ef er r ed t o a pi t wher e pi l es wer e bei ng i nst al l ed. As l ong as t he sun shone t he sl opes of t he pi t r emai ned st abl e but , af t er a f ew days of heavy r ai n, a l andsl i de occur r ed.

3 I NVI TED PRESENTATI ONS

3. 1 Rel i abi l i t y and Geol ogi cal Anomal y

Pr of essor W. Tang, t he f i r st i nvi t ed speaker , addr essed t he pr obl em of unsat i s f act or y geot echni cal per f or mance due t o t he pr esence of unexpect ed geol ogi cal anomal y wi t hi n a supposedl y wel l - def i ned soi l st r at um. For i nst ance, sof t soi l pocket s coul d cause excess i ve or uneven set t l ement or t hey coul d i ni t i at e pr ogr ess i ve f ai l ur e of sl opes. To i ncl ude t he ef f ect of possi bl e pr esence of geol ogi cal anomal y on geot echni cal per f or mance, t wo t ypes of uncer t ai nt y ar e encount er ed. Fi r st , t he occur r ence of t he anomal y i s not known, nor i t s si ze, l ocat i on and soi l pr oper t i es. Secondl y, even i f a speci f i c anomal y can be assumed at a par t i cul ar si t e, f oundat i on per f or mance may not be accur at el y pr edi c t ed due t o uncer t ai nt i es i n bot h t he desi gn model and i t s par amet er s. A pr ocedur e, t her ef or e, i s needed t o pr oper l y model and anal yse t hese t wo t ypes of uncer t ai nt i es and t o combi ne t hem ef f i c i ent l y i n assess i ng t he r el i abi l i t y of geot echni cal per f or mance.

Engi neer s may dr aw upon t hei r pr of essi onal exper i ences and knowl edge of t he r egi onal

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geol ogy i n assess i ng t he chance of geol ogi cal anomal y occur r i ng at a gi ven si t e, as wel l as some pr el i mi nar y est i mat es on i t schar act er i s t i cs i f i t i ndeed exi st s. Si t e expl or at i on dat a, such as bor i ng l ogs, pr ovi de f ur t her ev i dences t o subst ant i at e or modi f y t he engi neer s1 pr i or est i mat es. Pr of essor Tang appl i es t he Bayes i an met hodol ogy t o synt hesi se t he r espect i ve sour ces of i nf or mat i on i n assessi ng t he anomal y st at i st i cs, such as occur r ence pr obabi l i t y and si ze di s t r i but i on, at t he gi ven si t e. I n pr i nc i pl e a f ul l scal e Mont e Car l o s i mul at i on pr ocedur e can be per f or med t o i ncor por at e t he anomal y uncer t ai nt i es i nt o t he f oundat i on per f or mance r el i abi l i t y cal cul at i on. However t hi s pr ocedur e can easi l y become comput at i onal l y i nf easi bl e f or any r eal i st i c pr obl em. Mor eover , r ecent advance i n geot echni cal anal yses, such as f i ni t e el ement pr ocedur es, of t en r equi r e ext ensi ve comput at i on t hemsel ves. For pr act i cal pur poses such st at e- of - t he ar t met hods cannot be ef f i c i ent l y used i n conj uct i on wi t h Mont e Car l o s i mul at i on pr ocedur es. A pr omi s i ng appr oach t o al l ev i at e t hi s pr obl em i s t o f i r st est abl i sh per f or mance i ndi cat or s numer i cal l y as f unct i ons of anomal y si ze, l ocat i on and pr oper t y t hr ough sens i t i v i t y and r egr essi onal anal ysi s. Per f or mancer el i abi l i t y can be det er mi ned subsequent l y usi ng t he Advanced Fi r st Or der Second Moment ( AFOSM) met hod by i ncor por at i ng appr opr i at e st at i st i cs of anomal y, as wel l as t hose of ot her desi gn var i abl es. For s i mpl er cases wher e geot echni cal per f or mance i s gover ned sol el y by t he spat i al aver age soi l pr oper t y, anal yt i cal expr essi ons of t he r espect i ve r el i abi l i t i es coul d be der i ved based on r andom f i el d model s of anomal y occur r ence and soi l pr oper t i es. Pr of essor Tang sai d t hat t he met hods devel oped above have been demonst r at ed i n a f oundat i on set t l ement pr obl em and pr ogr essi ve f ai l ur e of a sl ope.

An ef f i c i ent pr ocedur e f or es t i mat i ng t he r el i abi l i t y of geot echni cal per f or mance i nvol v i ng geol ogi cal anomal i es has been f or mul at ed. The pr ocedur e ut i l i zes geol ogi cal i nf or mat i on, engi neer i ng exper i ence and j udgement as wel l as st at e- of - t he- ar t geot echni cal anal ys i s and r el i abi l i t ymet hodol ogi es. When new st at i s t i cs on anomal y become avai l abl e, f or exampl e t hr ough addi t i onal si t e expl or at i on, updat i ng of r el i abi l i t y est i mat es woul d i nvol ve onl y s i mpl e cal cul at i on. Mor eover , s i nce t he per f or mance r el i abi l i t y can now be r el at ed t o t he ef f or t spent i n si t e char act er i zat i ons, det er mi nat i on of cost - ef f ect i ve soi l expl or at i on pr ogr ammes coul d al so be f aci l i t at ed.

3. 2 Ef f ect of r andom soi l het er ogenei t y on soi l - s t r uct ur e i nt er act i on

Pr of essor Al onso, t he second i nvi t ed speaker , addr essed t he pr obl em of t he ef f ect of r andom soi l het er ogenei t y on soi 1- s t r uct ur ei nt er act i on. He poi nt ed out t hat t he spat i al cor r el at i on of soi l pr oper t i es i s a key concept when f or mul at i ng r el i abi l i t y pr obl ems i n soi l mechani cs and f oundat i on engi neer i ng i n t he pr esence of soi l het er ogenei t y. When t he obser ved het er ogenei t y i s l umped i nt o t he not i on of " scat t er i ng" t hr ough t he adopt i on of r andom var i abl es f or t he model par amet er s, a conser vat i ve r esul t i s usual l y obt ai ned. Conser vat i ve her e means t hat t he comput ed saf et y l evel i s cons i der abl y smal l er t han t hat

gener al l y obser ved i n pr act i ce by i ndi r ect or appr ox i mat e pr ocedur es. Thi s i s t he si t uat i on, f or i nst ance, i n t he case of s t abi l i t y pr obl ems.

However , Pr of essor Al onso poi nt ed out t hat t her e ar e ot her k i nds of pr obl ems f or whi ch t he r andom var i abl e appr oach may l ead t o t he opposi t e r esul t and an unconser vat i ve r esul t i s der i ved f r om t he anal ysi s. Such s i t uat i ons may ar i se i n soi l - s t r uc t ur e i nt er act i on pr obl ems. These comment s wer e i l l ust r at ed by means of a pr obabi l i s t i c anal ys i s of t he behav i our of a r el at i vel y s i mpl e pr obl em cons i s t i ng of a uni f or ml y l oaded f i ni t e beam r est i ng on soi l whose def or mat i on ( r eact i on) modul i ar e descr i bed by means of a one- di mensi onal r andom f unct i on. The f ol l owi ng desi gn var i abl es wer e consi der ed: bendi ng moment , shear f or ce, t ot al and di f f er ent i al set t l ement and cont act pr ess ur e.

The mechani cal pr obl em was f or mul at ed by pl ac i ng t he beam on a Yemochki n- Davi dov f oundat i on. Two soi l " l ayer s" wer e cons i der ed i n t hi s appr oach: a sur f ace l ayer of spr i ngs whi ch t r ansmi t t he l oad r ecei ved f r om t he beam t o a second l ayer whi ch i s an el ast i c hal f - space. Spat i al r andomness was at t r i but ed onl y t o t he f i r st l ayer and t he di scr et e set of spr i ng r eact i on modul i wer e comput ed f r om t he or i gi nal r andom f unct i on descr i bi ng t he spat i al var i at i on of soi l modul us by means of t he appr opr i at e aver agi ng t echni que.

Compat i bi l i t y of ver t i cal def or mat i ons and ver t i cal f or ce equi l i br i um pr ovi de t he necessar y equat i ons t o sol ve t he pr obl em. Wi t hi n t he f r amewor k of a second or der t heor y, expl i c i t expr essi ons wer e der i ved f or t he expect ed val ue and var i ance of t he desi gn var i abl es. These r esul t s wer e appl i ed t o a par t i cul ar case i n or der t o di scuss t he behav i our of t he beam.

The i nf l uence of cor r el at i on di s t ance on t he t ot al set t l ement var i ance i s shown i n Fi gur e 1. The cor r el at i on di s t ance i s r epr esent ed by t he par amet er a ( uni t s: m“ l ) wher e l / OC i s a measur e of t he cor r el at i on di st ance. I n t hi s case i t can be obser ved t hat t he l ar ger t he cor r el at i on di st ance, t he l ar ger t he var i ance of t he t ot al set t l ement . I n t he l i mi t when a = 0 ( i . e. hor i zont al cor r el at i on of t he pr oper t i es i s st r ong) one get s t he same r esul t as one woul d obt ai n by a r andom var i abl e r epr esent at i on of t he soi l modul i . I f Ct i s i ncr eased, a " r api d" osc i l l at i on of soi l modul i i s expect ed and t he aver agi ng ef f ect i nduced by t he beam st i f f ness l eads t o a pr ogr ess i ve r educt i on i n t he set t l ement var i ance. An opposi t e t r end i s obser ved when t he var i ance of cont act pr essur e i s r epr esent ed as a f unct i on of a as shown i n Fi gur e 2.

The bendi ng moment di f f er s f r om bot h t he set t l ement and t he cont act pr essur e as a maxi mum var i ance i s f ound at some i nt er medi at e val ue of Ot as shown i n Fi gur e 3. The comput ed l ow var i ance of t he bendi ng moment f or l ar ge cor r el at i on di s t ances i s expl ai ned by t he smal l var i ance of t he cont act pr essur es when a i s smal l . On t he ot her hand, t he " r api dl y" var yi ng cont act pr essur es f or l ar ge val ues of a ar e aver aged i n t he pr ocess of moment comput at i on and t he r esul t i s, agai n, a l ow var i ance of t he moment .

A summar y of t hese r esul t s, i n qual i t at i ve t er ms, i s gi ven i n Tabl e 1 whi ch shows t he t ype of cor r el at i on s t r uct ur e ( smal l , hi gh or some i nt er medi at e val ue of Ct) whi ch l eads t o t he wor st s i t uat i on, i . e. maxi mum var i ance of t he

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A V E R A G IN G

E F F E C T

( B E A M S T IF F N E S S )

Fi gu r e 1: I n f l uenc e of c o r r e l a t i o n d i s t a n c e on

t o t a l s e t t l e me n t v ar i anc e.

R A N D O M

V A R IA B L E

A P P R O A C H

Fi gu r e 3: I n f l uenc e of c o r r e l a t i o n d i s t anc e on

momen t v ar i anc e.

Tabl e 1: I nf l uence of cor r el at i on di s t ance on t he var i ance of desi gn var i abl es i n soi l - s t r uct ur e i nt er act i on pr obl ems.

Des i gnVar i ab l e

Set t l ement Cont ac tPr es s ur e

Bendi ng MomentDi f f er ent i a lSet t l ement

Cr i t i c a l

Co r ­

r e l a t i onSt r uc t ur e

SMALL a

soi l

pr oper t i eshi ghl yc or r e l a t ed

LARGE a

s oi l

pr oper t i esweak l yc or r e l a t ed

I NTERMEDI ATE (X

c r i t i c a l O

c ont r o l l ed by a c har ac t er i s t i c beam l engt h

var i abl e consi der ed. Not e t hat t he maxi mum var i ance of t he di f f er ent i al set t l ement , as wel l as t hat of t he bendi ng moment , i s comput ed f or some i nt er medi at e val ue of t he cor r el at i on di st ance, whi ch i s r el at ed t o t he beam st i f f nes s .

Pr of essor Al onso conc l uded by sayi ng t hat hi s anal ys i s showed t hat a s i mpl i f i ed descr i pt i on of t he soi l pr oper t i es i n t er ms of r andom var i abl es may l ead t o a conser vat i ve or unconser vat i ve r esul t , i n t er ms of t he comput ed var i ance of t he comput ed var i ance of t he desi gn var i abl es. The si mpl i f i ed anal ys i s per f or med has i ndi cat ed t hat no gener al t r ends can be gi ven. As a consequence, t he pr oper cons i der at i on of t he cor r el at i on di s t ance of soi l def or mat i on pr oper t i es becomes a necessar y f eat ur e of t he mobi l i zat i on of soi 1- s t r uct ur e i nt er act i on pr obl ems when soi l het er ogenei t y i s of pr i mar y c onc er n.

S M A L L V A R IA N C E

O F C O N T A C T

P R E S S U R E

5 6 m A V E R A G IN G

E F F E C T O F

" R A P ID L Y " V A R Y IN G

C O N T A C T P R E S S U R E S

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□ X

O X

o X

x z 3 4 5 6 m

Fi gu r e 2: I n f l uenc e of c o r r e l a t i o n d i s t a n c e on

c o n t ac t p r es s u r e v ar i anc e.

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4 GENERAL DI SCUSSI ON

Pr of essor G. Gudehus began t he gener al di scuss i on by cons i der i ng t he advant ages of pr obabi l i s t i c appr oaches f or t he di f f er ent peopl e i nvol ved i n an engi neer i ng pr oj ect and t he at t i t udes of t hese peopl e t owar ds t he use of st at i st i cs. He expl ai ned t hat , by al l owi ng a mor e r at i onal assessment of t he uncer t ai nt i es i nvol ved i n desi gn, t hese appr oaches coul d be of benef i t t o t he cl i ent , t he si t e i nvest i gat or , t he desi gn engi neer , t he cont r act or , t he super v i s i ng engi neer , t he i nsur ance manager and t he l awyer . However , he al so poi nt ed out a l i mi t at i on i n t hat i t may t ake many year s of t eachi ng and l ear ni ng bef or e al l t hese peopl e wi l l accept a pr obabi l i s t i c desi gn.

Mr . J. Wei j er s descr i bed t he use of a pr obabi l i s t i c appr oach t o desi gn agai nst pi pi ng i n sandy soi l beneat h an i mper meabl e c l ay di ke due t o di f f er ent i al wat er head acr oss t he di ke. Thi s appr oach i s based on a r ecent l y devel oped model f or t he pi pi ng phenomenon and det ai l s ar e gi ven i n t he paper by Cal l e et a l . ( 1989) . The desi gn s i t uat i on i s shown on t he l ef t i n Fi gur e4 whi l e, on t he r i ght , a gr aphi calr epr esent at i on of t he devel opment of t he pi pe wi t h i ncr ease i n wat er head i s gi ven. As t he di f f er ence i n wat er head i s i ncr eased t he pi pe l engt h i ncr eases unt i l , at a cr i t i cal head di f f er ence, no st abl e pi pe i s f or med and er osi on beneat h t he di ke wi l l cont i nue unt i l col l apse of t he di ke occur s.

Fi gur e 4: Geomet r y and st abl e sl i t ( pi pe) l engt h ver sus di f f er ent i al wat er head.

The model f or t he st abl e pi pe l engt h depends on a number of par amet er s whose i n si t u val ues ar e subj ect t o cons i der abl e var i at i ons and hence uncer t ai nt i es. A pr obabi l i s t i c appr oach, based on mean val ues and st andar d dev i at i ons f or t he par amet er s, has been used t o t ake account of t hese uncer t ai nt i es. As t hi s appr oach i s t oo compl i cat ed f or nor mal engi neer i ng pr act i ce, t he r esul t s of such anal yses have been t r ansl at ed i nt o par t i al saf et y f act or s f or t he l oad f or use i n nor mal desi gn si t uat i ons. The val ues of t hese f act or s can be der i ved usi ng a pr obabi l i s t i c anal ysi s of some pi l ot cases and assumi ng some t ar get pr obabi l i t y of f ai l ur e. I n t hi s appr oach t he par t i al f act or s ar e used t o der i ve des i gn par amet er val ues f r om char act er i s t i c val ues r epr esent i ng t he l ower or hi gher quant i l es ( e. g. 5%) of t he par amet r i c di st r i but i on. Tar get

pr obabi l i t i es of f ai l ur e of 2. 10" 5 and 2. 10- 6 per year have been used f or l evees and sea di kes i n t he Net her l ands.

Pr of essor Gudehus quest i oned t he appl i cabi l i t y

of t he so- cal l ed l i mi t st at e met hod t o pi pi ng, whi ch i s a pat h dependent s t ochast i c pr ocess. He al so sai d t hat i t was not j us t i f i abl e t o mul t i pl y a di f f er ence i n wat er l evel by a par t i al f act or , but sai d t hat addi t i ve f act or s wer e r equi r ed i nst ead. Mr . Wei j er s r ef ut ed t hese agr eement s. He sai d t hat t he phenomenon of pi pi ng has been obser ved al ong t he Dut ch and Ger man r i ver s and s t udi ed i n l abor at or y exper i ment s and i t has been f ound t hat , af t er an i ni t i al er os i on of sand, a st abl e pi pe l engt h i s f or med f or a par t i cul ar di f f er ent i al wat er l evel . He r ef er r ed t o a t heor et i cal model devel oped t o descr i be t hi s phenomenon whi ch al so shows t hat a st abl e pi pe l engt h can exi st beneat h a di ke wi t hi n a cer t ai n r ange of di f f er ent i al wat er l evel s. Thus, he concl uded, t he phenomenon of pi pi ng i s not pr edomi nant l y s t ochas t i c .

Wi t h r egar d t o t he use of par t i al f act or s, Mr . Wei j er s sai d t hat , i n t he Net her l ands, t he r i ver and pol der l evel s have been r ecor ded over a per i od of mor e t han 100 year s wi t h t he r esul t t hat t he st at i st i cal di s t r i but i on of t he wat er l evel i s wel l known and hence a par t i cul ar char ac t er i s t i c val ue can be chosen. Si nce bot h t he l oad and t he mat er i al st r engt h ar e r andom var i abl es, char act er i s t i c val ues can be assessed and t he FOSM met hod used t o det er mi ne t he par t i al saf et y f act or s r equi r ed t o achi eve a desi gn wi t h a suf f i c i ent l y smal l pr obabi l i t y of f ai l ur e.

Pr of essor M. Pacheco addr essed t he pr obabi l i s t i c anal ys i s of t he s t abi l i t y of s l opes wher e i t i s common pr act i ce t o r est r i c t t he anal ys i s t o t he f i xed cr i t i cal sl i p sur f ace est i mat ed f r om a det er mi ni s t i c anal ysi s. He poi nt ed out t hat t he l ocat i on of t he sl i p sur f ace depends on t he shear st r engt h par amet er s and, as t hese ar e r andom, t he l ocat i on of t he s l i p sur f ace i s al so r andom. He al so ment i oned t hat r andom f l uct uat i ons i n gr ound wat er l evel can be i ncl uded i n pr obabi l i s t i c s l ope st abi l i t y anal yses. I n r espondi ng t o t hi s pr esent at i on, Pr of essor Gudehus cont ended t hat , as t he det er mi ni s t i c mechani sm f or sl ope f ai l ur e i s not yet suf f i c i ent l y c l ar i f i ed and as t he s l i p zone i s scal e and hi s t or y dependent , a uni que l i mi t st at e equat i on cannot gener al l y exi st . Al so i r r educi bl e act i ons, such as c l i mat e and human i nf l uences, cannot r easonabl y be cor r ect ed by saf et y f act or s.

Dr . F. Oboni , i n hi s di scussi on, expl ai ned t hat t he ext ens i ve use of pr obi l i s t i c appr oaches i n a geost r uct ur al desi gn of f i ce such as hi s was ext r emel y usef ul f or t he f ol l owi ng r easons:

- i t enabl es t he i ncor por at i on of new i nf or mat i on acqui r ed on si t e so as t o updat e t he desi gn, t her eby opt i mi z i ng t he use of t he avai l abl e i nf or mat i on

- i t expl i cat es t he i nt er pr et at i on of t he new dat a and f ur ni shes a concept ual l y c l ear appr oach t o t he saf et y of t he des i gned s t r uct ur es

- i t enabl es t he devel opment of monet ar y r i sk eval uat i ons .

However , he al so poi nt ed out t hat engi neer s who use t hese appr oaches shoul d t ake car e t o f ul l y under st and t he r esul t s and t o pr esent t hem t o t hei r c l i ent s i n compl et el y under s t andabl e l anguage. I t shoul d be not ed t hat cl i ent s' i nt er est s ar e f ocussed on t he f i nal gl obal

2920

per f or mance at t he ser vi ce l evel r at her t han on saf et y i ndi cat or s such as r el i abi l i t y i ndex, pr obabi l i t y of f ai l ur e and t r ansi t i on pr obabi l i t y . He sai d t hat hi s c ompany ’ s exper i ence was t hat c l i ent s ar e sensi t i ve t o concept s such as monet ar y r i sk t o whi ch t hey can r el at e by t hei r exper i ences i n ot her br anches of busi ness. Consequent l y hi s company has i mpl ement ed a pol i cy of pr esent i ng c l i ent s wi t h t er ms and concept s t hey can under st and. He r ecommended t hat al l engi neer s shoul d adher e t o such a pol i cy so as t o i mpr ove t he popul ar per cept i on of t he pr of essi on.

Dr . W. Hachi ch, i n hi s cont r i but i on, addr essed t he quest i on of t he r eal i sm of pr obabi l i s t i c cal cul at i ons. I n t hi s cont ext he st r essed i mpor t ance of t aki ng spat i al cor r el at i on i nt o account i n pr obabi l i s t i c anal yses, par t i cul ar l y i n FOSM anal yses wher e pr obabi l i t y densi t y f unct i ons ar e not gener al l y r equi r ed. I f aut ocor r el at i on f unct i ons ar e not t aken i nt o account , t he second moment met ht >d l eads t o unr eal i s t i c r esul t s whi ch ar e gener al l y conser vat i ve, but , as shown by Pr of essor Al onso, may somet i mes be unconser vat i ve t oo.

Consi der i ng t he l ack of s t at i st i cal dat a f or soi l par amet er s, Dr . Hachi ch suggest ed t hat , r at her t han def i ne saf et y by a pr obabi l i t y of f ai l ur e, whi ch i s not al ways needed, i t woul d be mor e sensi bl e t o use t he bet a val ue t o expr ess saf et y as t hi s val ue i s mor e r eal i s t i c as i t r ef l ect s t he uncer t ai nt i es i n t he var i abl es i nvol ved. Ref er r i ng t o t he cont r i but i on by Pr of essor Pacheco, he sai d out t hat t he par amet er s def i ni ng t he l ocat i on of a sl i p sur f ace shoul d not be t r eat ed as r andom var i abl es .

Mr . E. Schwi ng, t he Co- r epor t er , descr i bed a s i t uat i on wher e he used t he FOSM met hod t o i nvest i gat e t he s t abi l i t y of a gr avi t y r et ai ni ng wal l . Taki ng account of t he var i abi l i t y of t he soi l par amet er s and usi ng r eal i s t i c coef f i c i ent s of var i at i on, t he pr obabi l i t y of f ai l ur e of t he wal l , due t o bear i ng capac i t y f ai l ur e of t he soi l under an i ncl i ned and an eccent r i c l oad, was cal cul at ed t o be about 20%. As t he wal l had al r eady par t l y f ai l ed, t hi s anal yt i cal val ue agr ees wel l wi t h t he act ual pr obabi l i t y of f ai l ur e. He expl ai ned t hat t he FOSM met hod coul d be used t o der i ve par t i al saf et y f act or s f or al l t he i ndependent var i abl es and t hat t hese f act or s l ead t o a uni f or m l evel of saf et y. Uni f or m l evel s of saf et y wi l l not be achi eved i f gl obal f act or s of saf et y ar e used. He concl uded, t her ef or e, t hat a r el i abl e assessment of t he saf et y of a st r uct ur e can onl y be achi eved usi ng par t i al saf et y f ac t or s .

Cal l e E. O. F. , Best H. , Sel l mei j er J. B. & Wei j er s J. ( 1989) . Pr obabi l i s t i c anal ys i s of pi pi ng under neat h wat er r et ai ni ng st r uct ur es. Pr oc. 12t h I CSMFE, 2, 819- 822.

Gar zoni o C. A. Var i abi l i t y of t he geot echni cal pr oper t i es of pi i o- pl ei s t ocene cl ays ( Ancona, I t al y) . Pr oc. 12t h I CSMFE, 2, 823- 827.

Gassi er G. & Gudehus G. ( 1989) Anchor ed wal l s Model t est s and s t at i s t i cal desi gn. Pr oc. 12t h I CSMFE, 2, 829- 832.

Knoesen J. S. ( 1989) Pr obabi l i s t i c saf et y eval uat i on of ear t h dams. Pr oc. 12t h I CSMFE,2, 837- 843.

Lacasse S. & Goul oi s A. ( 1989) . Rel i abi l i t y anal ys i s of axi al pi l e capaci t y. Pr oc. 12t h I CSMFE, 2, 845- 848.

Ledesma A. , Gens A. & Al onso E. E. ( 1989) . Pr obabi l i s t i c backanal ys i s usi ng a maxi mum l i kel i hood appr oach. Pr oc. 12t h I CSMFE, 2, 849- 852.

Magnan J. - P. ( 1989) . Var i abi l i t e des pr opr i et es des sol s et di mens i onnement des ouvr ages. Pr oc. 12t h I CSMFE, 2, 853- 854

Maschwi t z G. & Cunze G. ( 1989) . Det er mi nat i on of s i gni f i cant mat er i al par amet er s f or qual i t y cont r ol of new t echni ques i n geot echni cal engi neer i ng usi ng st at i st i cal met hods. Pr oc. 12t h I CSMFE, 2, 865- 868.

Oboni F. ( 1989) . Pr obabi l i s t i c model s f or ax i al l y l oaded bor ed shaf t s. Pr oc. 12t h I CSMFE, 2, 859- 864.

Pet t ac i a A. & Tancr edi G. ( 1989) . Compar i son among cr i t i cal sur f ace sear ch di r ect met hods i n s l ope st abi l i t y anal ysi s. Pr oc. 12t h I CSMFE, 2, 865- 868.

de Quel er i j L. ( 1989) . Pr obabi l i s t i c saf et y anal ys i s of anchor ed sheet pi l i ngB. Pr oc. 12t h I CSMFE, 2, 869- 872.

Schwi ng E. & Het t l er A. ( 1989) . Scat t er of nai l f or ces i n soi l nai l i ng. Pr oc. 12t h I CSMFE,3, 1253- 1255.

Tsuchi da T. & Ono K. ( 1989) . Eval uat i on of di f f er ent i al set t l ement s i n t he ai r por t . Pr oc. 12t h I CSMFE, 2, 873- 876.

Yakovl ev P. I . & Shkol a A. V. ( 1989) . Bear i ng capac i t y of doubl e l ayer base, i t s pr obabi l i t y est i mat i on. Pr oc. 12t h I CSMFE,2, 877- 880.

REFERENCES

Bl anchi n R. , Chi l es J. P. , Mar gr on P. & Pi r aud J. ( 1989) . Tunnel sous l a Manche - Cal cul de l a coupe geol ogi que par i nt er pol at i on geost at i que ent r e sondages et pr of i l s s i smi ques. Pr oc. 12t h I CSMFE, 2, 809- 810.

Bol l e A. , Bonnecher e F. & Cr emer J. - M. ( 1989) . Pr obabi l i s t i c appr oach of t he set t l ement of an ar ch br i dge. Pr oc. 12t h I CSMFE, 2, 811- 814.

Bout wel l G. 8l Hedges C. ( 1989) . Eval uat i on of wast e- r et ent i on l i ner s by mul t i var i at e st at i st i cs. Pr oc. 12t h I CSMFE, 2, 815- 818.

2921

P a n e lis t c o n trib u tio n

C o n trib u tio n d e p a n e lis t

W .H .T A N G , U n iv e rs i ty o f Il lin o is , U rb a n a -C h a m p a ig n , III., U S A

Unsat i sf act or y geot echni cal per f or mance mi ght of t en be t r aced back t o t he pr esence of unexpect ed geol ogi cal mat er i al wi t hi n a supposedl y wel l - def i ned soi l st r at um. For I nst ance, sof t soi l pocket s coul d cause excessi ve and uneven set t l ement , t hey coul d al so I ni t i at e pr ogr essi ve f ai l ur e of sl opes. To I ncl ude t he ef f ect of possi bl e pr esence of geol ogi cal anomal y on geot echni cal per f or mance, t wo t ypes of uncer t ai nt i es ar e encount er ed. Fi r st , t he occur r ence of t he anomal y i s not known, nor ar e i t s si ze, l ocat i on and soi l pr oper t i es. Secondl y, even i f a speci f i c anomal y conf i gur at i on can be assumed at a gi ven si t e, f oundat i on per f or mance may not be accur at el y pr edi ct ed due t o unavoi dabl e uncer t ai nt i es I n bot h t he desi gn model and i t s par amet er s. A pr ocedur e i s, t her ef or e, needed t o pr oper l y model and anal yze t hese t wo t ypes of uncer t ai nt i es, and t o combi ne t hem ef f i ci ent l y i n assessi ng t he r el i abi l i t y of geot echni cal per f or mance.

Engi neer s may dr aw upon t hei r pr of essi onal exper i ences and knowl edge of t he r egi onal geol ogy I n assessi ng t he chance of geol ogi cal anomal y occur r i ng at a gi ven si t e, as wel l as some pr el i mi nar y est i mat es on i t s char act er i st i cs i f I t I ndeed exi st s. Si t e expl or at i on dat a, such as bor i ng l ogs pr ovi des f ur t her evi dences t o subst ant i at e or modi f y t he engi neer s' pr i or est i mat es. Bayesi an met hodol ogy can be appl i ed t o synt hesi ze t he r espect i ve sour ces of i nf or mat i on i n assessi ng t he anomal y st at i st i cs, such as occur r ence pr obabi l i t y, l ocat i on and si ze di st r i but i on, at t he gi ven si t e. I n pr i nci pl e, a f ul l scal e Mont e Car l o si mul at i on pr ocedur e can be per f or med t o I ncor por at e t he anomal y uncer t ai nt i es i nt o t he f oundat i on per f or mance r el i abi l i t y cal cul at i on. However , t hi s pr ocedur e can easi l y become comput at i onal l y i nf easi bl e f or any r eal i st i c pr obl em. Mor eover , r ecent advances i n geot echni cal anal yses, such as f i ni t e el ement pr ocedur es, of t en r equi r e ext ensi ve comput at i on t hemsel ves. For pr act i cal pur poses, such st at e- of - t he- ar t met hods may not be ef f i ci ent l y used i n conj unct i on wi t h t he Mont e Car l o si mul at i on pr ocedur es. Ue have devel oped sever al met hods t o al l evi at e t hi s pr obl em. A pr omi si ng appr oach i s t o f i r st est abl i sh per f or mance i ndi cat or s numer i cal l y as f unct i ons of anomal y si ze, l ocat i on, and pr oper t y t hr ough sensi t i vi t y and r egr essi onal anal ysi s. Per f or mance r el i abi l i t y can be det er mi ned subsequent l y usi ng t he Advanced Fi r st Or der Second Moment ( AFOSM) met hod by i ncor por at i ng appr opr i at e st at i st i cs of anomal y, as wel l as t hose of ot her desi gn var i abl es. For si mpl er cases wher e geot echni cal per f or mance i s gover ned sol el y by t he spat i al aver age soi l pr oper t y, anal yt i cal expr essi ons of t he r espect i ve r el i abi l i t i es coul d be der i ved based on r andom f i el d model s of anomal y occur r ence and soi l pr oper t i es. pi e met hods devel oped above have been demonst r at ed i n a f oundat i on set t l ement pr obl em and pr ogr essi ve f ai l ur e of sl ope.

I n shor t , we have f or mul at ed an ef f i ci ent pr ocedur e f or est i mat i ng r el i abi l i t y of geot echni cal per f or mance i nvol vi ng geol ogi cal anomal i es. The pr ocedur e ut i l i zes geol ogi cal i nf or mat i on, engi neer i ng exper i ence and j udf t aent as wel l as st at e- of - t he- ar t geot echni cal anal ysi s and r el i abi l i t y met hodol ogi es. When new st at i st i cs on anomal y

become avai l abl e, f or exampl e, t hr ough addi t i onal si t e expl or at i on, updat i ng of pr evi ous r el i abi l i t y est i mat es woul d I nvol ve onl y si mpl e cal cul at i on. Mor eover , si nce t he per f or mance r el i abi l i t y can be r el at ed t o t he ef f or t spent i n si t e char act er i zat i ons, det er mi nat i on of cost - ef f ect i ve soi l expl or at i on pr ogr am coul d al so be f aci l i t at ed.

Resear ch on t he r el i abi l i t y of geot echni cal syst ems consi der i ng geol ogi c anomal y has been car r i ed out f or sever al year s at t he Uni ver si t y of I l l i noi s. Publ i cat i on t hus f ar I ncl udes t he f ol l owi ng:

Tang. W. H. & Quek. S. T. ( 1906) St at i st i cal Model of Boul der Si ze and Fr act i on, Jour nal of Geot echni cal Engi neer i ng, ASCE, 112, 1, 79- 90.

Tang, W. H. ( 1987) Updat i ng Anomal y St at i st i cs - Si ngl e Anomal y Case, Jour nal of St r uct ur al Saf et y, El sevi er Sci ence Publ i sher s, 4/ 2: 1, 151- 163.

Tang. W. H. & Hal i m, I . ( 1988) Updat i ng Anomal y St at i st i cs - Mul t i pl e Anomal y Pi eces, Jour nal of Engi neer i ng Mechani cs, ASCE, June, 1091- 1096.

Tang, W. H. ,Hal i m, I . & Gi l ber t , R. B. ( 1988) Rel i abi l i t y of Geot echni cal Syst ems Consi der i ng Geol ogi cal Anomal y, Pr oceedi ngs, ASCE Conf er ence on Pr obabi l i st i c Met hods, VPI , May, 136-139.

Kwee. A. Pr edi ct i ng t he Set t l ement of a Foot i ng Syst em Usi ng t he Mont e Car l o Si mul at i on Met hod, Techni cal Repor t , Dept , of Ci vi l Engi neer i ng, U. of I l l i noi s, Ur bana, IL.

Tang. W. H. , Si dl , I . & Gi l ber t , R. B. ( 1989) Aver age Pr oper t y i n a Random Two- St at e Medi um, Jour nal of Engi neer i ng Mechani cs, ASCE, Januar y, 131- 144.

Tang. W. H. & Gi l ber t , R. B. ( 1988) Two- St at e Random Fi el d Model , Pr oceedi ngs, Symposi um on St ochast i c St r uct ur al Dynami cs, Ur bana, I L, Oct ober , 107- 127; al so t o appear i n Jour nal of St r uct ur al Saf et y.

Gi l ber t , R. B. & Tang, W. H. ( 1989) Pr ogr essi ve Fai l ur e Pr obabi l i t y of Soi l Sl opes Cont ai ni ng Geol ogi cal Anomal i es, Pr oceedi ngs, I COSSAR.

Tang. W. H. & Hal i m, I . ( 1989) Rel i abi l i t y of Raf t Foundat i on Set t l ement Consi der i ng Geol ogi cal Anomal y, i n Comput at i onal Mechani cs of Pr obabi l i st i c and Rel i abi l i t y Anal ysi s, ed. by W. K. Li u and T. Bel yt schko, El mepr ess I nt er nat i onal , 560- 583.

Hal i m, I . & Tang. W. H. ( 1990) Anomal y St at i st i cs: Locat i on and Si ze, ( i n Pr ess)

Kohno. S. ; Ang, A. H- S. & Tang. W. H. Rel i abi l i t y of Tunnel l i ng Syst em, ( i n Pr ess)

2922

Discussion

G.GUDEHUS, Institute ot Soil Mechanics & Rock Mechanics,

University of Karlsruhe, Germany

Comment on Paquec o' s paper

Fi r st , t he saf et y f act or shoul d not be t r eat ed as a r andom var i abl e. I t i s r at her a subst i t ut e f or t he r andomness of t he r espect i ve basi c var i abl e.

Second, t he det er mi ni s t i c mechani sm i s not yet suf f i c i ent l y cl ar i f i ed. The l ocal i zat i on of t he gr owi ng nar r ow sl i p zone i s scal e and hi s t or y dependent so t hat a uni que l i mi t st at e equat i on cannot gener al l y exi st .

Thi r d, i r r educi bl e act i ons ( f r om cl i mat e, hu ­man i nf l uence et c. ) cannot r easonabl y be cor ­r ect ed by saf et y f act or s.

Gener al Comment

The at t i t ude t owar ds s t at i s t i cal desi gn i s t ypi cal l y di f f er ent f or di f f er ent peopl e i n­vol ved i n an engi neer i ng pr oj ect :

The owner wi l l scar cel y r eal i ze an i mmedi at e benef i t . He wi l l even be af r ai d of hi gher ex ­penses f or mor e compl i cat ed i nvest i gat i on and desi gn. However , t he S concept can act ual l y hel p hi m t o make a r at i onal sel ect i on of saf e­t y measur es wi t h an adequat e di s t r i but i on of wei ght s .

The soi l i nvest i gat or i s not s i mpl y encour aged t o make mor e l abor abor y and f i el d t est s. He can be encour aged and even f or ced t o pr ovi de r at i on­al ar gument s f or t he sel ect i on of t est s and f or hi s j udgement ( Bayes ' concept ) .

The desi gn engi neer i s enabl ed t o obt ai n a mor e r at i onal di s t r i but i on of bear i ng s t r uc t ur ­al el ement s. Thus, he can st r eaml i ne hi s i nt ui ­t i on t owar ds a saf e opt i mum.

The comput er spec i al i s t can wor k wi t h a mor e r eal i s t i c spect r um of par amet er s. He shoul d al so r eal i ze t he r el at i ve wei ght of hi s cont r i ­but i on, whi ch i s most l y r at her moder at e.

The cont r act or can hope f or a f ai r compet i ­t i on i f di f f er ent t ender s ar e j udged by means of a mor e obj ect i ve saf et y est i mat i on. He wi l l al so appr ec i at e a st r engt heni ng of s t at i st i cal qual i t y assur ance i n geot echni cal engi neer i ng.

The super v i s i on engi neer has a chance t o eval ­uat e hi s obser vat i ons wi t hi n t he f r ame of r a­t i onal dec i s i on t heor y.

The i nsur ance manager i s enabl ed t o make a

mor e r at i onal es t i mat i on of i nsur ance pr emi um, and he can make use of r i sk management wi t h a pr obabi l i s t i c backgr ound.

Lawyer s coul d get mor e pr ec i se def i ni t i ons of such not i ons as " ver y pr obabl e" or " pr edi c t ­abl e" .Al t oget her , t he st at i s t i cal concept i s pr i nc i ­pal l y pr omi si ng. However , i t wi l l t ake many year s of t eachi ng and l ear ni ng unt i l al l t hese peopl e wi l l r eal l y t ake up t he message.

Comment on Wei er s' paper

As t he r ef er ence wat er l evel i s al ways ar bi ­t r ar y, a l evel di f f er ence cannot j ust i f i abl y be mul t i pl i ed by a par t i al saf et y f act or . I n­st ead, addi t i ve l evel cor r ect i ons ar e r equi r ed.

Concer ni ng t he mechani sm of pi pi ng, one has al so t o r eal i ze t hat t he so- cal l ed l i mi t st at e equat i on does not gener al l y exi st . Pi pi ng i s a st ochast i c pr ocess whi ch i s pat h dependent .

2923

D is c u s s io n : P o in t e s t im a te s f o r t h e r a n d o m lo c a t io n o f

th e c r i t ic a l f a i lu r e s u r f a c e in s lo p e s ta b i l i t y a n a ly s is

D is c u s s io n : P o in ts d ’e s t im a t io n p o u r I’e m p la c e m e n t

a r b i t r a i r e d e la s u p e r f ic ie c r i t iq u e d e g l i s s e m e n t d a n s

I 'a n a ly s e d e s t a b i l i t e d e s p e n te s

M . P A C H E C O , U n i v e r s i t y o f t h e S t a t e o f R io d e J a n e i r o , U E R J , B r a z i l

I t i s common pr act i ce t o r un pr obabi l i st i c anal - ys i s of sl opes by st ar t i ng f r om t he l ocat i on a

’’cr i t i cal " f ai l ur e sur f ace whi ch i s f r equent l y det er mi ned on a convent i onal det er mi ni st i c ba­

si s. Once t hi s cr i t i cal sur f ace i s l ocat ed, t he shear i ng st r engt h par amet er s ar e assumed as r an­

dom var i abl es and t he pr obabi l i st i c anal ysi s i s t hen car r i ed out consi der i ng t hat t he r esi st ant

f or ces act on t hat f i xed, pr edet er mi ned sur f ace. As i t i s wi del y known i n Soi l Mechani cs, t he l o­

cat i on of t he so- cal l ed cr i t i cal sur f ace i s st r ongl y dependent upon t he adequat e sel ect i on

of t he st r engt h par amet er s. Ther ef or e, i f t hese par amet er s ar e assumed as r andom var i abl es, i t

i s concept ual l y i ncor r ect t o assume a f i xed sur ­

f ace as a st ar t poi nt t o t he pr obabi 1i st i c anal ­ysi s. I n t hi s di scussi on, i t i s shown t hat t he

Poi nt Est i mat e t echni que, as concei ved by Rosen-

bl uet h, appear s t o be an adequat e t ool t o t he pr obab i 1 i st i c ana 1 ys i s of si opes . I ri t h i s pr oce­dur e, sever al " cr i t f cal " sur f aces ar e i ncl uded

i n t he* anal ysi s, as opposed t o t he usual pr oce­dur e wher e onl y one sur f ace i s eval uat ed.

The scope of t hi s di scussi on i s l i mi t ed t o t he cases of convent i onal ci r cul ar met hods of anal y ­

si s. I n spi t e of t he r emar kabl e i mpr ovement i n

t he ana I yt i c a1 t echni ques f or sI ope st ab i 1i t y , t he r esul t s of such met hods shoul d be i nt er ­

pr et ed i n pr act i ce as an appr ox i mat i on of what

act ual l y happens i n t he f i el d. Thi s appr oxi ma­t i on i s not onl y due t o t he r andom nat ur e of

so i 1 , but al so due t o er r or s i nher ent t o t he

met hod i t sel f . Some sour ces of er r or ar e t he as ­sumpt i on of pl ane st r ess ( negl ect i ng t he ef f ect

of t he i nt er medi at e pr i nci pal st r esses) , t he i n­abi l i t y t o i ncl ude t he por e pr essur e component pr oduced by t he shear i ng st r esses, t he shape of

t he assumed sl i p sur f ace, non- homogenei t y, ani sot r opy, mi cr o- di scont i nui t i es, among ot her s. Ext ensi ve r esear ch per f or med on f ul l y i nst r u­ment ed and t hor oughl y i nvest i gat ed t r i al embank ­

ment s at t he Feder al Uni ver si t y of Ri o de

Janei r o i ndi cat e t hat i n gener al i t i s ver y di f f i cul t t o pr edi ct si mul t aneousl y t he condi ­t i on o f f ai l ur e (SF =1. 0) and t he l ocat i on of t he

cr i t i cal sur f ace by t he usual det er mi ni st i c pr o­

cedur es, consi der i ng di f f er ent t ypes of i nt er ­pr et at i on of t he st r engt h par amet er s. One possi ­

bl e way t o appr oach t hi s pr obl em i s t o assume

t he st r engt h par amet er s as r andom var i abl es and det er mi ne a r ange wer e t he cr i t i cal sur f ace i s expect ed t o f al 1.

The var i abi l i t y of t he st r engt h par amet er s The l ong t er m st abi l i t y anal ysi s of a 3 0 year - ol d homogeneous ear t h dam ( wi t h st abi l i t y wo b - 1 ems due t o t he unf or eseen sat ur at i on of " t he

downst r eam sl ope) i nvest i gat ed r ecent l y by t he

aut hor wi l l be pr esent ed t o i I l ust r at e t hi s di s ­

cussi on. The r esul t s of many CD t r i axi al conven­

t i onal t est s per f or med on t he compact ed r esi dual

cl ay wer e i nt er pr et ed i n t he p- q st r ess space by means of a l i near r egr essi on anal ysi s, t hus en­

abl i ng t o est i mat e t he uncer t ai nt y of t he shear st r engt h par amet er s a and y , i n addi t i on t o t he

cor r espondi ng mean val ues. Usi ng Tayl or Ser i es

expansi on, t he r esul t s of t he I i near r egr essi on wer e mapped i nt o t he g ' - z st r ess space l eadj ng

t o t he var i ances V[ c] =414. 15; V[ t g0] =6. 76x10 wi t h t he mean val ues " c=77. 5 ; t g0- 0. 48 ( cohesi on i n kPa) .

Pr obab i I i st i c ana l ysi s by po i nt est i mat es

I f , f or si mpl i ci t y, t he 2- poi nt est i mat e pr oce­

dur e pr oposed by Rosenbl uet h i s used wi t h 2 r an­dom var i abl es ( c and 0) , t he uncer t ai nt y of t he

var i abl es SF ( saf et y f act or ) , x and y

( coor di nat es of t he cent er of t he ’’ cr i t i cal "

sur f ace) , and R ( r adi us of t he cor r espondi ng ci r cl e) can, be est i mat ed by aver agi ng t he r e­

sul t s of 2 =4 det er mi ni st i c ana l ysi s, each one wi t h st r engt h par amet er s det er mi ned as I i near

combi nat i ons of t he mean val ue pl us or mi nus one st andar d devi at i on ( al l assumed as st at i st i caI I y

i ndependent r andom var i abl es) , as f ol l ows:

F S x(rrt) y (rn) R( m)++ 1 . 65 72. 50 92 . 50 87. 50+- 1 . 58 72. 50 102. 50 97. 50- + 1 . 28 72. 50 90. 00 83. 00- - 1. 21 75. 00 90. 00 83. 00

1 st mom 1 . 43 73. 12 93. 75 87. 75

( HS) 2 (Y) ( R)++ 2. 72 8556. 25 7656. 25+ - 2. 50 10506. 25 9506. 25- + 1 . 64 8100. 00 6889. 00— 1 . 46 8100. 00 6889. 00

2nd mom 2. 08 8815. 62 7735. 12

I t i s seen t hat t he anal ysi s i s not sensi t i ve t o t he coor di nat e x. The var i abi l i t y of SF, y, and R can be expr essed as:

mean st . dev . c . o. V.FS 1 . 43 0. 19 13%

y 93. 75 rn 5. 15 m 5%R 87. 75 m 5. 92 m 77.

nor ma 1 1og- nor ma 1 bet a (*P[ FS«1 nj 0. 012 6. 0041 0. 01 ?■P[ FSX<1 i ] 0 . U 4 1 0. 027 0. 040

_p[ FS£1 5.1 0. 644 0. 665 0. 629( *) upper bound- 5 st . dev.

The r andom l ocat i on of t he cr i t i cal sur f ace was

r epr esent ed by a bet a di st r i but i on bounded by t he mean val ue pl us or mi nus 5 st andar d dev f a-

t i ons . The cor r espondi ng 95% conf i dence I i m i t s ar e:

bounds 957. conf 1 i m i t s1 ower upper 1ower ] upper

y 68. 00 119. 50 86. 10 101. 60R 58. 15 117. 35 7 7. 70 98. 00

Th i s pr ocedur e may become par t i c u1a r 1y he Ip f uI

i n t he case of mul t i - l ayer ed syst ems wer e t he

2924

fat lure mechanism may be controlled by more than

one layer. It is clear that this type of intei—

preii*i‘ion cannot be accompl ished by the u^ual

procedure wt-re the probabilistic ana I ys i s is

control led only by the most unfavorable surface

searched in the deUerministic procedure. The

po i nt-est imate technique can also be used to

model the uncertainty c*f the position of the wa­

ter levei and the correspond Ing mobilization of

pore pressures. This will not be presented due

to length limitations.

REFERENCE

Rosenblueth, E. (1975). Point Estimates for

Probability Moments. National Academy of

Sc i ences, U .5.A .. Vo I. 72» No. 10, 3812-3814.

2925

D is c u s s io n

WALDEMAR HACHICH, INTERACT, University of Sao Paulo, Brazil

whet her we shoul d al ways r equi r e pr obabi l i t i es of f ai l ur e ( do we al ways need t hem?) or shoul d we be cont ent ed — and mor e r eal i st i c - - wi t h bet a val ues.

Dr . Pacheco' s r emar ks on t he r andomness of t he act ual f ai l ur e sur f ace i n an embankment seem t o suggest t hat t he l ocat i on i t sel f of t he cr i t i cal f ai l ur e sur f ace shoul d be anal yzed pr obabi l i s t i cal l y. However , a pr oper r andom f i el d descr i pt i on of t he pr oper t i es of t he embankment and i t s f oundat i on does al r eady account f or al l pr obabi l i s t i c aspect s r el at ed t o t he l ocat i on of t he cr i t i cal sur f ace, pr ovi ded t he model i s adequat e f r om a geol ogi cal - geot echni cal vi ewpoi nt .

Some paper s pr esent ed t o t hi s Sessi on do not t ake spat i al cor r el at i on i nt o account . I t may be t hat cor r el at i on i s somet i mes i gnor ed on gr ounds of conser vat i sm. Not so! Dr . Al onso pr esent ed a case I n whi ch l ack of cor r el at i on i nf or mat i on may l ead t o an unconser vat i ve pr obabi l i s t i c des i gn.

Dr . Or r st ar t ed t hi s di scussi on by pr ompt i ng us t o comment on t he r eal i sm of our pr obabi l i s t i c pr edi ct i ons. I bel i eve i t i s appr opr i at e, i n t hi s cont ext , t o st r ess Dr . Al onso' s poi nt t hat t he cor r el at i on st r uct ur e i s essent i al i f we want t o achi eve any r eal i sm.

I n t hi s r espect , i t i s unf or t unat e t hat Dr . Het t l er , i n hi s ot her wi se excel l ent gener al r epor t , has emphasi zed " mean, coef f i c i ent of var i at i on, and densi t y f unct i on" as t he t hr ee essent i al pi eces of i nf or mat i on f or f i r s t - or der second- moment anal ysi s.

As a mat t er of f act , one of t he advant ages of f i r s t - or der second- moment anal ysi s i s pr eci sel y t he f act t hat one can der i ve moment s of t he dependent var i abl e f r om moment s of t he I ndependent var i abl es, wi t hout knowl edge of pr obabi l i t y densi t y f unct i ons. Onl y i f a pr obabi l i t y st at ement about t he dependent var i abl e i s sought , ar e we r equi r ed t o assume a pr obabi l i t y densi t y f unct i on, and t hen j ust f or t he dependent var i abl e. I t I s of t en possi bl e t o make an assumpt i on about t he pr obabi l i s t i c behavi or of t he dependent var i abl e on t he basi s of s i mi l ar i t i es bet ween t he mechani cs of t he physi cal phenomenon and some mat hemat i cal r ul e gener at i ng a p. d. f . ( e. g. by i nvoki ng t he cent r al l i mi t t heor em) , even when t he p. d. f . of each i ndependent var i abl e i s not known.

On t he ot her hand, as pr ev i ousl y di scussed, knowl edge of t he aut ocor r el at i on f unct i on of t he f i el d I s of par amount i mpor t ance f or f i r st - or der second- moment anal ysi s, si nce ot her wi se t he second- moment descr i pt i on of t he var i abl es woul d be i ncompl et e, l eadi ng t o unr eal i s t i c r esul t s - - whi ch ar e gener al l y conser vat i ve ( somet i mes t oo conser vat i ve! ) but , as we have l ear ned t oday, may be unconser vat i ve t oo.

Fi r s t - or der second- moment anal ys i s has t he advant age of easi ng t he r equi r ement s of pr obabi l i s t i c descr i pt i on, r equi r i ng onl y second- moment i nf or mat i on unl ess expl i ci t pr obabi l i t y s t at ement s ar e r equi r ed. For saf et y eval uat i ons a bet a val ue - - number of st andar d devi at i ons bet ween wor k i ng and f ai l ur e condi t i ons - - I s al r eady a l ot mor e meani ngf ul t han a f act or of saf et y ( or even par t i al saf et y f act or s) , si nce bet a val ues do r ef l ect t he uncer t ai nt i es i n t he var i abl es i nvol ved, wr t i l e r et ai ni ng an over al l measur e of saf et y. I t her ef or e submi t t o t hi s audi ence t he quest i on

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