Longitudinal Road Profile Model Generation Based on Measurement Data Using Mathematical Approach

Transcription

1 Longtudnl Rod Profle Model Generton Bsed on Mesurement Dt Usng Mthemtcl Approch Rosnwt Buhrl'", Muhmd Rzwn Zulkrnn2'b, Munzlh Md Rohn nd Nurul Frhh Sulong3'" 1'3 Smrt Drvng Reserch Centre (SDRC),Fcut[ of Cvl nd Envronmentl Engneerng, UnverstTun Hussen Onn Mlys, 86400, Johor, Mlys 2 Fculty of cvlnd Envro"*"$X,r::r1l""::ff,$',:"rstrun Hussen onn Mtys, 'tqs'{]q' :1j-:'.-..,L-.--'., -.?'l?-,;-=r.-c.f:#r.ldljllg.-l:.1,::":j!.-:,.-l.:.ll::.'-=',,1, "ej1j,.r efl g :; 1l';ry, Keynrords: wlkng profler, rod scnner, nterntonl roughness ndex, rod profles Abstrct. Ths study ws conducted to produce rod profle model bsed on vertcl dsplcement dt from nstrument wlkng profler nd rod scnner tht could be mplemented n long term pvement performnce model for predctng the dynmc lodng of the vehcles tyre. Rod profles dt ws suppled by KRAM Engneerng, Mlys. A vertcl dstnce dt from two rods, pproxmtely 0.8 km of new federl rod nd 5 km of stte rod were obtned. The nterntonl Roughness ndex (1R) ws used to clssf types of rod bsed on the R clssfcton. The R for ech smple of rod profle ws computed usng softwre nmed ProVl nd FOOTWORKs. Rod profle genertng process ws followed the theory Dodds nd Robson nd lso Hrdy nd Cebon. The process ws performed usng MATLAB softwre. After genertng rod profles, the clbrton between reference nd generted rod profles ws performed by clcultng the corelton coeffrcent vlue. The correlton coeffcent vlue rnges between -0.7 to -l nd 0.7 to s consdered to hve smlrty ech other. As results, for federl nd stte rod, severl models of rod profles were generted for ech smple dt. n concluson, ll the rod profles generted wll be ble to be used s n herntve rod profle n long term pvement performnce nlyss. ntroducton A new pvement desgn method, Mechnstc-Emprcl Pvement Desgn Gude (MEPDG) hs been used n severl countres.the concept tht used n ths gude s bout r:m,lyzng the pvement performnce from the strt to the end of ts lfe bsed on the mechncl propertes towrd evlutng the structurl desgn of the pvement or nmed Whole lfe Pvement Performnce Model. n more specfc, Whole lfe Pvement Perfornrnce Model s pplcble for desgn pvement by predctng the performnce of the pvement due to envronmentl nd vehcle effect n mechnclly. Knowng tht by usng ths model, rod profle s suffcent nput to determne the effect of vehcle dynmc lod to the response n the pvement. Theoretclly, the ncresed of pvement surfce roughness wll ncresed the dynmc lod. Ths wll ncrese the response (.e. stress/strn) n the pvement nd thence, the erler flure of pvement wll be experenced. Therefore, ths study wll concentrte to produce sutble model of rod profle tht cn be used n the Whole lfepvement Performnce Model whch wll be smultng the overll performnce of the pvement. Towrd developng MEPDG for Mlys, by usng the Whole lfe Pvement Performnce Model, model of rod profle bsed on lldlys's rod s desred Althougll ths knd of rod profle hs yet not been developed. Thereforg the m of ths study re to generte rod profle model from

2 rod profle dt mesured by nstrument wlkng profler nd rd scnner for new pved federl nd stte rod. Lterture Revew Two-dmensonl rndom profles my be generted by pplyng set of rndom phse ngles, unformly dstrbuted between 0 nd?-n to seres of coeffcents derved from the desred drect spectrl densty. The correspondng seres of spot heghts, (refer Eq.l) t regulr ntervls long the trck s obtned by tkng the nverse Dscrete Fourer Trnsform (DFT) of the spectrl coeffcents. Most expermentl mesurements of rndom processes re crred out dgtlly. Typcl smples re mesured t seres of regulrly spced tmes. The tme seres nlyss s used to determne the spectrl estmtes of the orgnl functon by nlysng the dscrete tme seres obtned by smplng fnte length of smple functon nd employng Fourer trnsform. The dscrete vlue of the seres s crred out by usng n nverse Fourer trnsform [l]. u, :f,1s*<'*t\ k: o,1, 2,3,...(N -r) (1) Where, S* s the trget spectrl densty, N s the totl number of wves used to generte the rod surfce nd & s set of ndependent rndom phse ngles unformly dstrbuted between 0 to 2n. The spectrl densty of the profle heght s used to chrcterse the mpltude nd wvelength of rods where the rod s consdered homogeneous, sotropc rndom process wth Gussn dstrbuton. An dequte descrpton of rod profle spectr re referred to Dodds nd Robson [2] nd Hrdy nd Cebon [3], tht roughness coeffrcent correlted wth the 1R1. Methodologr The reserch methodology begns wth the dt cquston from KRAM Engneerng. A totl of four smples of Herl rod profle dt were obtned usng wlkng profler nd one smple of 6 km of stte rod profle dt ws obtned from rod scnner mesurement. For Federl rod, profle or vertcl dstnce dt hs been clssfed s FT23, FT21, FT25, FT26 long 200 m ech. Ech smple rod profle dt were plotted by usng FOOTWORKs softwre. Next, the generton of R conducted by usng FOOTWORKs softwre n whch the.r/ genertng set for the 200 m. For ths study four smples of rod profles meet the crter of the R for new pvement whch s rnges between 1.5mlkm nd 3.5m/km. For stte rod, vertcl dstnce dt ws ctegores nto severl secton nd ech secton conssts of 300 rn Fve models wth lrl rnges between zm/l<f nd 4mkm were obtned by usng PToVAL softwre. Mthemtcl pproch s fst fourer trnsform nd power spectrl densty bsed on the study by Dodds nd Rob,soq lso Hrdy nd Cebon hs been used n the process of genertng rod profle model t1l-t21. The generton process of rod profle model s crred out n MATLAB softwre where the progrm tht s the sme softwre used n Buhr et. l. []. n the process, the Eq. 1 ws used. The process lso used ncluded the generton of sequence numbers tht pproxmtes the propertes of unform rndom seed numbers for genertng set of ndependent rndom phse ngle, 6s unforrnly dstrbuted between O nd 2n. Then the followng step s clbrton. The clbrton s process to check whether the rod profles model generted re cceptble n terms of fetures nd chrcterstcs of sptl smlrty by usng sttstcl methods The men, vrnc, covrnce computed n MATLAB softwre to obtn

3 the correlton coeffcent of ech model generted. The correlton coeffcents wthln the rnges from -0.7 to -l nd A.7 b shows the rod profles generted re pprochng nd/or duplctng the mesured rod profle. Results nd lscussons Federl Rostl For federl rod, the Rl vlues for ech smple of rod profle dt re gven n Tble l. The R1 vlue ws generted by usng FOOTWORKS for rod long 200 m ech. From the results, t shows tht four dt smples re n the rnge between 1.5 m / km nd 3.5 m / km nd t belongs n clss of new pvement bsed oflrtl clss clssfcton. Tble : R vlue for ech smple dt Number Smple 1R(m/km) FT z FT J FT FT After gettng N fr ech smple dt of rod profle,the rod profle generton process ws conducted by frndrng seed number tht cn generted new model of rod profle. Four models were selected for ech smple of rod profle. Fg. 1 nd Fg. 2 shows the generted rod profle model nd the profle of the wlkng profler nstrument. Ths fourth model represents the best profle for ech smple of rod profle dt. Fg. l shows the rod profle generton for smple dt F'f X, the seed number tht hs been used to generte ths profle s 27. The correlton coeffrcent vlue for ths generted profle s Menwhle, Fg. lb shows the generted profle for smple FT24 wth seed number 93. The correlton coeffcent for ths rod profle model s whch s the hghest vlue of correlton coeffcent for smple FT24. ' -:- " c'."*"';"',.'.. _ '!{.f.d Prorl. Er d :lo3s t "rt l.c-..-g!*.--:?-1;--ft-.s*-.?!; () j 1 Fgure 1: () rod profle generton for seed number 27 for smple FT23 (b) rod profle generton for seed number 93 for smple FTl24 (b) Fg. 2 shows the rod profle generted bsed on smple dt FT25, the seed number used to generte ths profle s 57. The correlton coeffrcent vlue gettng for ths rod profle s n

4 Fg. 2b, t shows the rod profle generted bsed on smple FT26 usng seed number 80. The correlton coeffcent for the rod profle generted s A comprson between ll models of rod profles generted ws exmned to determne the rod profle model tht hs correlton coeffrcent close to -l or 1. The closest vlue s defned s close to or hs smlrty wth the reference rod profle. Tble 2 summrzes the correlton coeffcents for ech rod profles tht were generted. PROFL :2' r--'* ;--:,:J]l-:j:jT:,:::t:; *- -"" Gfn.rltd P.ot'rc erofdc { -tt.rurcd l z = d -- :,-''' t ",..*--"' j { 40 o 80 loo DtS 1ANCE n t4c () FnoFtLe 126 '-- ' ' l C6n.rrl& PBtlt. j t-:::::_$:::-"l:gg:!g =^ v ' ; *-f -*6t****fo- (b) Fgure 2: () rod profle generted usng seed number 57 (bsed on smple FTl25) (b) rod profle generted usng seed number 80 (bsed on smple FT126) Bsed on ll models of the rod profles tht were generted, t s found tht the thrd model generted bsed on smple dt FT24 gves the hghest correlton coeffrcent vlue compre to others, tht s Ths rod profle profle s consdered the closest or smlr to the orgnl rod profle bsed on wlkng profler mesurement dt s tr,vng the best correlton coeffcent vlue pproches the vlue 1.

5 Tble 2 : Comprson of the correlton coeffcents vlue for ll models of rod profle Smple Dt Model frf full<ffl Seed Number Correlton Coeffcent FT J FT FT l J l 0.75s0 t J M FT J Stte Rod Tble 3 shows the R vlue for 5 models nd ech R vlue ws generted usng PToVAL softwre. A 1000 seed number hve been obtned for ech model but seed number rnges from to -l nd 0.7 to s cceptble to the next process. Two exmples wth the srnllest Rl dfferences re chosen to represent the best profle for ech model s shown on the followng fgures nd the Tble 4 shown the comprson between ech model. Tble 3: R vlue for ech model Model R (m/km) Dstnce (m) ) 2.t Tble 4: Comprson between generted nd mesured profle for ech model R Dff (%\ Model Seed Correlton Correlton Generted Mesured Fgure Number Coeffcent Dfferences Profle 1R Profle R Fgure l38r t r Fgure J Fgure Fgure r t98l FgureT

6 From the resuh, the blue lne s representng s mesured profle nd the green lne s representng s generted profle. The R for ech profle generted s dfferent nd t s depend on the chrcterstcs of the profle. t s lso depend on the strtng dstnce for ech secton but the dfference between R s less thn 5olo. rt : r''.4*,_/ *q, '**-j.-s-! -r 1\. E_r:t - Fgure 3: Model 1 wth seed number 46 (left) nd 183 (rght) "' l ---;;;4j.t t-j- V,,1' -!/!-' tt'*- -r -r t-.vrtl".,{ *...,^ -n ' t*n'/ ng,rr;;, ulodel2 wth seed numhr 173 (left) t z.gtto "f "f "l "l/ tr lt "l'/ "t t.- "l "t,-. /\ j '- /'t Fgure 5: Model3 wth seed nurnber 225 (left) nd247 (rght)

7 : ": {: ;' /rr"t"-,*\*. :,f "r', : '":-;;";r - --:-ft:fl tt-';;;:; lrr:r::.-r:*.'* : $, l ",; l :l Fgure 7: Model 5 wth seed number 627 (left) nd744 (rght) Concluson For federl rod, bsed on eoh reference rod profle, there re severl models of rod profle were selected. AlthougtL only four models were chosen tht gves the hghest correlton coefcent mong ll rod profle models for ech reference rod profle. From ll rod profle models tht generted, the model bsed on smple FT24 tht produced usng the seed number 93 hs the hghest correlton coeffcent between ll rod profle models. The vlue s For stte rod, ll the models lso pss 5 percent of dfferences between the generted nd mesured. However, the ffth model wth seed number 627 h:rs the smllest vlue n R dfferences, 0.9 percent. Thus, the generted profle s consdered s the closest nd smlr to the orgnl rod profle. Aclmowledgement The uthors wsh to thnk the KUMPULAN KRAM SDN. BHD. for the rod scnner nd wheel trckng dt suppled nd n prtculq ther stff who sssted the reserch. Also thnks to the Unverst Tun Hussen Onn Mlys for fundng ths reserch. References [1] Cebon. D. Hndbook of Vehcle ntercton, Tylor &Frncs Group, 2006, pp [2] Dodds, C. J. nd Robson, J. D., The descrpton of rod surfce roughness, J. Sound nd vbrton, (1 873), 3l(2):pp [3] Hrdy, M. S. A, Ceboq D., mportnce of speed nd frequency n flexble pvement respolrse, J. Eng. Mech. ASCE, 120(3), (1994), pp [4] Buhr, R., Puteh S., Dmge Equvlent of the flexble pvement Vrton wth Lod Appled Appled Mechncs nd lvterls Vols , (2013), pp