Sensitivity and accuracy of the pile wave equation - vulcanhammer ...

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"I'DYNAMIC-.by GEORGE E. RAMEY* and ALAN P. HUDGlNS5 .WAVE EQUATION proameans of evaluating pile capacityis mathematically well-foundedG, and+ably qrovides the most realistic mathe--'!'Ca ""':I available for depictingictual behavlob. of the hammer-pile-soil!,stem. Numerical '.teoration of this equa-$r,, .with tile aid of . digital compiller,12pmrs 10 be trle most t,7ional arraivl;calfiesearchers at Texas A R. M Universityscje~t:luf~ed a cornl~ute: program which??sns of evaluating pile ~.,,~~i~~, -rl,isa numerical solui!url of tht wave.s been accomplished by sev,l inves- equation as outlined by Smith. Their proaat or^'.^.^."." and excellent corre.,.,ions gram increments time (in steps of At)Idween predicted and measured failwe until all movement of the pile tip due to:5ds have been observed.the simulated single hammer blow hasA computer program solution of the1. ,-ye .. osuation was utilised in the investi-?ion beirl~ n',-qed to adjudge (j) tileinsitivity of proorart, -JPrleiated P-n:lrtes to the program input so11 1\2r2.-,Hers, and (ii) the acc~~ro-y of the pro-;am in predictino r,ile capacity.iave equation-computerCevelopment of the pile wave equationrulted from a consideration of the inler-'rl forces and motion of a segment of a:sly suspended prismatic bar that was-l!ect to an impact at one end. For the.!ss of a pile, the equation was modified(cons~der external resistance to the seg-.:IT motion offered by the soil. Smith';.:averted the resulting partial differential'iudiion to a finite difference equation-id outlined a numerical procedure for3 solution. His procedure accomplishedlepproximate solution of the real system? determining the displacement of each63ment of the idealised system over a';t time interval (e.g , 1/4 000 second).i :,? algor~tlim begins at the impact of thej'7mer and the time ,is incremented inintervals until the pile tip stops1 !vine. The invcrre of rhe displzcenm~of thc pile tip due to one hammer blowis the number of blows per foot thatwould be required during driving todevelop the assumed pile static capacity.The interested reader is referred toSmith's article for .a detailed descriptionof his solution procedure.ceased and prints the resultinppr~-'~-"""~ JS1DEset of thi: pilo tip. Ttlr r,.JQa" repeats'its series of calcul.,:~ns :or as many input, ;, -.,-.,. ,tes as desired, and hencecan bu uscJ to generate pile P-n curves.lllcsc cltrves, in turn, can be used topredict p~lc capaciiy fu~ ony given blowcount value. Fig. 1 provides a generalisedpictorial summary of the fundamentals ofthe computer progrsmme. This programmewas slightly modified by the authors tofacilitate I/O, and used in this investigation.Since the description of the computerprogram is well documentedf its discussio~ihere will be brief and limited tothosc items specifically considered in thisinvcstirjntion.Proc~rani input data fall into the generalcategories of:1. P~le characteristics and pile capacitydesired,2. Hammer characteristics, and3. Soil properties and pile soil interactions.(d) Poini snd side soii damping coefficients.This infomazion is inpu: in ~hti programunder the follow in^. variable nemes(and definirio~s).PERCNT -Toe .percenraoe of pile capacitythat IS developed by pointbeerinq,QPOIIdT - OUP..~ Or u~rrrnz~e sfratn ofrrie - sori ar -me - oiie tip,QSI.DE -Quake or himace strain ofcne soil atma me sides,JPOINT - Gemnino cocr;lc!i.n? of the soila: ;F5e piie TIC. e&- Damping coeiftcienr of the soilaiong .!f.e sician. .Because of the potenrialiy - iaroe variationof .the values oi ihese pararne:ers,an abbreviated study we5 performed toadjudge ihe sensitivity of tne programthese parameiers.Sensitivity and evaluation of wave .equation piie-soii interactionparametersUse was made of previous publ~shedre~vigs-.~ which ind~cates linear relationshipsbetween QSlDE and QPOINT andbetween JSlDE and JPOINT, or morespeciiically,QSlDE = QPOINT ... (7)JSIDE = 1/3* JPOINT ,"These relationships were assumed to bevalid and Thereby reduced he investigationof evaluating the sensitivity of theprogram generated P-n curves to theItems (I) and (2) can normally be readily parameters, PERCNT, QPOINT, and'determined from the pile properties andJPOINT.hammcr manufacturers' literature. How-An abbreviated investigation was perever,the input data required for itemformed whereby each parameter was(3), are not so readily determined. The varied over .its full realistic range whilespecific information required for this is:holding the other two parametem constant.(a) Dislribution of static capacity between Since the ,purpose of the study was top~in; t.l%?rinc rnr; sitir frict~pnadjudoe he sensirivifv of the proormii t?j ~-~i~tt?~n!-, o: :ads- :rtc:~qfi ~ lc~r~c pvle .snIu~~cio 10 ii'e pilc-sc.il .inierarxion nara-. -...: > ,..... . % L,,,' 1 ,, ,., , , I , .,;:r3$;.',-?., r:if- ;>~..;I?-!JI?. r.,;le (;~xP cort~toeredLli..a,l. L I . ~ ~ ~ ~ [:5r - , ,.(,-'I tt;:,., ;-I, -?rill. r,. l,,, :n,! ;-: It,? pot,>:. % rr,o,r,-+,. ,A,~.>I-V E i r ~ i r C~ L ~ . :\.lI~l~l~-., v . . ~ t)o~ ci,*rqat;.~ crtrc~al. Tnr cnsc of ;'. klibh",,6:ir. i.;vrt!, rtie slnc:. (C~rr;.ic!15.24m srcel U6p 2% x 254 x 63nglm- -.- - --7driven 73.72m inro a relatively uniformsand with 2 Vulcan 05 hammer was utilisedfor the investigation.Separate P-n curves were generatedfor each of the .three parameter variationsand ~hese are shown in Figs. 2, 3 and 4.In ,each case, large variations ,in the soilparameters caused much smaller variationsin predicted pile capacities, indicating thedampened effect of the soil parameters.This is desirable and means that errors-in estimating these parameters will leadto errors .of much smaller magn~tude inpredicted pile capacity. For example, lookingat Fig. 2, one can see that a 200%error in estimating PERCNT leads to onlya 13% error in the predicted pile capacityfor a blow count of 30.Results from several representative field_'I. A .-. . . -

-----bC-'TABLE I. VALUES OF WAVE EQUATIONItPELGRAM SOlL PARAMETERS FORcoA".~y~sa~ CF WAVE EQUATION AND D y ~TWO COI\~lMON ALABAMA SOlL-- ---.. . )\:'ON !'QEDICTED CAPACITIES-. -. .- ----SETTINGS Pile Soil bl~,~st~r+~j ,:?,+- -- type t./ps$ ~3p.2c,t\, , , , CN MEN t. . HICS tra tihad sand . - .. -.. .-Parameter Sand and clay withS. QSs

-'TABLE Ill. COMPAHISON OF WAVE EQCI.-IONAND DYNAMl~- Pl,red ~ . ~ w ~ : J ~ c : SPIIIII$!.~ I I1kclcr~r~wit-doeri,~r>rsII,,I,! "I one (11 ti):. ~~-~-.~l-?!c.,: J-,: .I:, lp!; in?: tfl~ or~i?l+-. hc~:le: tlxh~t?(\td Th~s s~uoy Noas conaucwd unoe- rr..; :i. For each of 1ile.z~ cases. a wtvb. uv rite steel H p~irrs iz oue 10 vilr~ancesofof AlabanljA-.