Suggested t-z and q-z functions for load-movement responsef

Transcription

1 40 Rtio (Exponent = % Fnction (.5 times 0 Hypeolic ( = 0 % SHAFT SHEAR (% of lt ULT Zhng = / = 50 % Exponentil (e = % (stin-softening RELATIVE MOVEMENT BETWEEN PILE AND SOIL ELEMENT (mm Sggested t-z nd q-z fnctions fo lod-movement esponsef Fellenis, B.H., 03. Simplified non-line ppoch fo single pile settlement nlysis. Discssion. Cndin Geotechnicl Jonl, 50(

2 Discssion on Zhng Q.Q. nd Zhng, Z.M., 0. Simplified non-line ppoch fo single pile settlement nlysis. Cndin Geotechnicl Jonl, 49( y Bengt H. Fellenis, D.Tech., P.Eng. Cndin Geotechnicl Jonl, 50( The thos hve poposed n inteesting t-z fnction fo se in modeling stin-softening pile shft esponse of pile sjected to sttic loding test. A t-z fnction descies the eltion etween the mont of stess (o lod necessy to genete movement of soil element (o pile hed in sttic loding test. The thos fnction fits in well with existing fnctions: the Rtio Fnction, the 80-% Fnction, the Hypeolic Fnction, nd the Exponentil Fnction, smmized elow. The Rtio Fnction is defined y Eq. D. Eq. D = ltimte esistnce = movement vile = movement moilized t = n exponent nging fom smll vle thogh nity The 80-% Fnction is defined y Eqs. D thogh Dc. Eq. D Eq. D C C C Eq. Dc C = ltimte esistnce δ = movement t ltimte esistnce, C = C = the slope of the stight line in the δ/q vess movement (δ digm odinte intecept of the stight line in the δ/ vess movement (δ digm The Hypeolic Fnction is defined y Eq. D3. Eq. D3 C C C = / (lso the slope of the line in /δ vs. movement (δ digm, C = odinte intecept = ltimte esistnce The Exponentil Fnction is defined y Eq. D4. Eq. D4 ( e = coefficient e = se of the ntl log. (.78 The thos fnction, hee clled the Zhng Fnction, cn e ewitten s shown in Eqs. D5 thogh D5e. Eq. D5 Eq. 5 ( c ( 4( c

3 Fellenis, B.H., 03. Discssion on Zhng nd Zhng (0 Cn. Geotechnicl J. 50( Eq. D5c Eq. D5d Eq. D5e Eq. D5f c c 4 c SHAFT SHEAR (% of lt δ ULT Rtio (Exponent = 0.5 Zhng = / = 50 % 80 % Fnction (.5 times Hypeolic ( = 0 % Exponentil (e = % (stin-softening = ltimte esistnce = esistnce t infinite movement = movement moilized t = independent coefficient nd c = dependent coefficients The t-z fnctions cn e employed to fit clclted stess-movement ecod to the esponse mesed in sttic loding test. It is est chieved y fist estlishing fom the mesed cve the ltimte esistnce,, nd the movement fo this esistnce, δ, employing sitle definitions nd jdgment. As ech of the five t-z cves ely on single dditionl pmete, simple til-nd-eo ppoch will chieve the est fit etween the clclted nd mesed cves. Fitting y the 80-% nd Hypeolic fnctions cn e speeded p y detemining the espective C nd C pmetes fom line egession ove sitly selected nge of mesed -δ vles. The five fnctions e illstted in Fige D compising lod-movement cves clclted fo n ssmed ltimte esistnce,, of 00 %, occing t movement, δ, of 4 mm. The 80-% fnction is lwys stin-softening fte the ltimte esistnce. The fige shows tht the Zhng fnction fo stin-softening to 50 % of t lge movement is pcticlly eql to the cve clclted y the 80-% fnction. Howeve, the Zhng fnction llows fo the post-pek softening to tke diffeent shpes, whees the 80-% fnction hs fixed shpe (once the vles of nd δ e selected. 0 Fig. D RELATIVE MOVEMENT BETWEEN PILE AND SOIL ELEMENT (mm Compiltion of t-z cves fo common = 00 % nd = 4 mm The independent coefficient, contols the degee of stin-softening fte the pek (00 % she esistnce is moilized. It cn nge fom fo no stin-softening, thogh fo loss of ll (00 % of she esistnce t lge ( infinite movement. Fo = 4 mm, "" = coesponds to 50-% edction t lge ( infinite movement nd = eslts in 00 % edction. In n ctl cse, diffeent soil lyes will hve diffeent stess-movement cves. Some will e stin-softening, s in the thos cse, othe lyes will e stin-hdening. While the fige shows the cves fo common point, nd δ, the cves cn e mde to e qite diffeent efoe nd fte the common point. Theefoe, it is lwys possile to fit one o moe of the fnctions to given mesed stess-movement cve. The definition of the 80-% fnction is the eqiement tht the stess-movement cve mst lso go thogh point tht hs stess eql to 80 % of the chosen ltimte esistnce,, developing t movement tht is eql to 5 % of. Ths, the fnction cn e sed to model lso the stess-movement fo cse whee n ltimte esistnce,, is ssmed to occ pio to pek esistnce, if the pek vle nd its movement e ssmed to e.5 nd 4δ, espectively.

4 Fellenis, B.H., 03. Discssion on Zhng nd Zhng (0 Cn. Geotechnicl J. 50( The thos lso poposed tht the pile toe stessmovement (o lod-movement shold e modeled y i-line cve. This ecognizes tht pile toe does not show file mode, t the esistnce lwys inceses with movement. Howeve, nmeos fll-scle sttic loding tests with mesements of toe stess vess toe movement hve shown tht the pile toe esponse is lwys cved fo oth the initil potion nd the lge movement potion, nd the pile toe q-z esponse is slly simil to the Rtio fnction. Fige D shows typicl Rtio fnction stess-movement cve fom stt to lge movement (50 mm nd i-line eltion fitted to the esponse with the kink t 5-mm movement. Fige D3 shows the sme ecods plotted with the mximm movement edced to 5 mm. The stess scle is the sme s in Fige D. While the ssmed i-line esponse cold e djsted to esonle fit etween the stt nd p to the 5- mm movement with kink t ot movement of 5 o 0 mm, the new set wold not fit the esponse eyond 5-mm. To fit eyond 5 mm wold eqie tht the i-line ppoch e chnged to ti-line. And if the fit wold e to the nge fom the stt to 5 mm (the thos toe movement efeence, s well s to sevel nges eyond 5 mm, mlti-line ppoch wold e necessy. Indeed, the i-line ppoch is n nnecessy simplifiction, ecse s the Rtio fnction (which est epesents the pile toe esponse cn jst s esily s the i-line esponse e coded into compte softwe fo nlysis of the esponse. The infomtion pesented fo the thos pmetic stdy of n 800 mm dimete, 0 m long pile in soil with nifom shft esistnce of 50 KP does not inclde the toe esistnce. Howeve, the 50 KP nit shft esistnce vle eslts in totl shft esistnce of,500 KN nd, s the thos Figes 7 nd 8 show finl esistnce of 8,000 KN t ot 30 mm pile hed movement, the pile toe esistnce t the pplied lod of 8,000 KN wold e 5,500 KN. This toe esistnce is stted to hve developed t the mximm pile hed movement of ot 30 mm. As the pile compession fo the 8,000 KN pile hed lod is ot 5 mm, the pile toe movement t the 8,000 KN lod is ot 5 mm. Howeve, toe esistnce of 5,500 KN moilized t sch smll toe Fig. D Toe stess-movement y i-line modeling nd y the Rtio method to 50 mm Fig. D3 Toe stess-movement y i-line modeling nd y the Rtio method to 5 mm movement does not coelte well to shft esistnce of only 50 KP immeditely ove the pile toe (pesmly the soils ove nd elow the pile toe e simil. It is not likely tht the shft esistnce wold e constnt with depth, howeve. It wold nomlly e smlle ne the gond sfce nd lge t depth nd, ths, coelte ette to the toe esistnce. The thos ssmption of constnt shft esistnce is n dditionl nnecessy simplifiction. The shft esistnce fo 0 m long pile in homogenos soil, whethe it is snd o cly wold e esponding in ccodnce to the effective stess. An effective stess nlysis employing constnt vle of effective stess et-coefficient wold hve een moe elistic ssmption thn the thos ssmption of constnt nit shft esistnce. The,500 KN totl shft esistnce coeltes to et-coefficient of ot 0.5, lge vle in most non-esidl soils. When the eslts fom sttic loding test ppe to show lod distition nsweing to constnt nit shft esistnce, this is often conseqence of esidl

5 Fellenis, B.H., 03. Discssion on Zhng nd Zhng (0 Cn. Geotechnicl J. 50( lod in the pile. Piles, lso oed piles, e slly ffected y locked-in lod ( esidl lod, which needs to e consideed in evey evltion of test eslts. I elize tht the pmetic stdy is not n ctl cse nd sed to demonstte the vestility of the thos compte pogm. Howeve, insmch s the ppe pesents conclsions petining to engineeing pctice, moe el cse wold in my opinion hve seved ette fo demonstting the eslts of the thos methods nd nlyses.