PCA Thickness Design Method

Transcription

1 PCA Thckness Desgn Method (Slde 2) The PCA thckness desgn method s a mechanstc-emprcal desgn method n that t reles heavly on mechanstc analyss of the stresses and deflectons n concrete pavements along wth emprcal relatonshps to determne the pavement lfe as a functon of those stresses and deflectons. The PCA thckness desgn method consders two types of falure: 1. Fatgue falure due to tensle stress repettons n the slab 2. Eroson falure due to repeated deflecton of the slab nto the foundaton A fnte-element analyss of the deflectons and stresses at the jonts, corners, and edges of slabs revealed two thngs: 1. Edge loads produce the worst stresses n the pavement 2. Corner loads produce the worst deflectons n the pavement As a result, fatgue falure s analyzed based on the flexural stresses produced by edge loads and eroson falure s analyzed based on the deflectons produced by corner loads. (Slde 3) Both the fatgue and eroson analyses use Mner s cumulatve damage hypothess. The stresses or deflectons produced by a gven vehcle class or axle load class are used to predct the number of passages needed to fal the pavement. Wth that, we can calculate the pavement lfe consumed by all the vehcles or axles n that class: d n N The total pavement lfe consumed by the vehcle mx s found by summng over all of the vehcle or axle load classes: D d The goal s to determne the slab thckness for whch the pavement lfe consumed by the desgn traffc s exactly equal to 1.0 (pavement lfe). Fatgue Falure Fatgue analyss s based on wheel loads appled near the edge of the slab mdway between the transverse jonts. Ths s the worst loadng condton from the standpont of flexure, especally f there s no shoulder or an asphalt shoulder because the wheel loads have to be supported by half as much slab as n the nteror of the pavement. n N 1

2 As the contact patch moves nto the slab nteror, edge stresses drop off rapdly. So you can t just assume all of the trucks are at the pavement edge or well away from the pavement edge. You have to take wander nto account. By law, trucks can t be more than 8½ feet wde. Most hghway lanes are 12 feet wde, so a truck centered n the lane s drvng nearly 2 feet from the edge of the pavement. In other words, only a few trucks actually approach the edge of the pavement. Ths s especally true when the shoulder s unpaved, because drvers want to ensure they don t nadvertently run off the slab. Studes have shown that as much as 6% of trucks encroach on the pavement edge f the shoulders are paved but less than ½% encroaches on the pavement edge f the shoulders are unpaved. If 100% of the trucks travel exactly at the edge of the pavement, exstng mechanstc formulas for the edge stresses could be used drectly to estmate the number of repettons to falure, N. As more and more trucks move away from the edge, the number of repettons to falure ncreases because the edge stresses aren t as severe as when the trucks are exactly at the pavement edge. Usng fnte element analyses, PCA researchers calculated the average fatgue consumpton as a functon of the percentage of trucks at the edge of the pavement. They then equated ths average to an equvalent edge stress. In other words, what unversal edge stress would produce the same amount of fatgue consumpton as the mx of edge stresses produced by the wanderng trucks? It turned out that f you calculate fatgue lfe usng 89.4% of the edge stress produced by a truck runnng exactly at the edge of the pavement, you ll get the same fatgue lfe as s produced by a mx of trucks, 6% of whch are runnng exactly at the edge. (Slde 4) Ths 89.4% edge stress factor s bult nto the PCA fatgue lfe equatons, whch have the general form of log where s the flexural stress n the slab and Sc s the modulus of rupture of the concrete. If the flexural stress s less than 45% of the modulus of rupture, the pavement wll last ndefntely. If the flexural stress s more than 55% of the modulus of rupture, the pavement lfe s gven by log Between 45% and 55%, the pavement lfe s gven by. log For each axle load class, you wll need to calculate a flexural stress rato and a pavement lfe, then determne what percentage of the pavement lfe s consumed by the axles n that load class. 2

3 Eroson Falure Eroson falure takes nto account such thngs as pumpng, the creaton of vods beneath the pavement corners, and jont faultng. These are all related more to the deflecton of the slab than they are the stresses n the slab. (Slde 5) Actually, deflecton alone turned out to be a poor predctor of pavement lfe. A better predctor was the rate of work done on the foundaton by the deflectng slab. The rate of work s proportonal to the contact pressure and deflecton and nversely proportonal to the radus of the deflecton basn (the more concentrated the load, the faster the load s appled and released as a wheel rolls over the pavement). The actual equaton used s P p 0.73 hk where p s the contact pressure, h s the slab thckness, and k s the modulus of subgrade reacton, whch relates p to the slab deflecton and s used here as a surrogate for deflecton. Note that the radus of the deflecton basn s related to the radus of relatve stffness, whch s related to the thckness of the slab and the modulus of subgrade reacton. That s how h gets n the equaton. The resultng fatgue equaton (whch s emprcal) s gven by 2 C P log N where C1 = 1.0 for slabs on untreated subbases and C1 = 0.9 for slabs on stablzed subbases. Dstance from the pavement edge s just as mportant n eroson analyss as fatgue analyss. In ths case, though, t depends on whether or not there s shoulder support. Shoulder support comes from tyng the traffc lane nto a concrete shoulder usng te bars. (Slde 6) If there s an asphalt or gravel shoulder (or no shoulder at all) there s no support for the outsde edge of the traffc lane. In that case, the corner loads produced by the 6% of trucks rdng rght aganst the edge are crtcal and the eroson damage s calculated as D eroson 0.06n N In other words, frst calculate how long the pavement wll last f all the trucks are runnng at the pavement edge, then multply by 6% to account for the fact that only 6% are runnng at the edge. If there s a concrete shoulder, corner deflecton s not sgnfcantly affected by the placement of the wheel loads (at that pont, all of the wheel loads are nteror to the ted pavement system) so the corner loads produced by the 94% of trucks that don t encroach on the shoulder are the most mportant: 0.94n D eroson N 3

4 Snce the deflectons are much smaller when the slab s supported by a shoulder, the N values wll not be the same as those calculated when there s no shoulder support. Curlng Stresses The PCA desgn method purposefully gnores stresses due to curlng and/or warpng (the latter results from a temperature dfferental through the slab, the latter from a mosture dfferental). Wth regard to warpng, the thnkng s that most slabs are wetter on the bottom than on the top, so the slabs wll want to curl upward but can t. Ths nduces tensle stresses n the top of the slab and compressve stresses n the bottom of the slab. The compressve stresses n the bottom of the slab wll offset some of the tensle stresses due to wheel loadng (as n prestressed concrete) so t s conservatve to gnore warpng stresses. Wth regard to curlng, the bottom of the slab s warmer than the top more hours per day than the reverse, so most of the day (except n the mddle of the afternoon) the slab wll want to curl up, whch nduces compressve stresses n the bottom of the slab that also offset some of the tensle stresses due to wheel loadng. Durng the afternoon, the tensle curlng stresses wll be somewhat offset by the compressve warpng stresses, reducng the need to consder them n the analyss. Thckness Desgn Procedure (Slde 7) Only four desgn parameters are needed n the PCA desgn procedure: 1. the modulus of rupture of the concrete 2. the modulus of subgrade reacton of the slab foundaton 3. the desgn traffc volume 4. the axle load spectrum The modulus of rupture s just the average 28-day modulus of rupture obtaned from thrd-pont loadng of concrete beams. To account for varablty n concrete strength, the desgn charts were calculated usng a modulus of rupture 15% lower than the average, based on the observaton that concrete strengths have a coeffcent of varablty of 15% f qualty control on the job ste s adequate. So they actually use the mean mnus one standard devaton. To account for strength gan over tme, the desgn charts were also calculated usng a modulus of rupture that rses over tme, albet at a steadly decreasng rate. The modulus of subgrade reacton for the subgrade sol could be obtaned from plate load tests, but more often t s found through correlatons wth the CBR because the CBR test s much less expensve than the plate load test. Snce we typcally only determne the pavement thckness to the nearest ½, we really don t need any more accuracy than that. (Slde 8) If the pavement system wll ncorporate a subbase, the k-values have to be adjusted to nclude the stffenng effect of the subbase. The PCA desgn gude ncludes tables for estmatng the composte modulus of the subgrade and subbase. One table s used for untreated subbases 4

5 and the other for cement-treated subbases. The values n those tables were found usng a twolayer Burmster analyss of the plate load test (much as we dd n an earler homework problem). NOTE: In concrete pavements, we usually refer to the layer between the slab and subgrade as a subbase rather than a base because base mples a structural layer. Instead, the subbase s usually there to provde dranage, prevent pumpng, or help mtgate frost heave, not provde structural support to the pavement. Unlke flexble pavement analyss, seasonal varatons n subgrade modulus are not consdered n the PCA method because the AASHO Road Test results suggest that the requred slab thckness does not change apprecably f seasonal changes are ncluded. In parts of the country where freeze/thaw s a problem, the mproved support durng the wnter freeze makes up for the degraded support durng the bref sprng thaw. In the rest of the country, the subgrade modul may rse durng the dry seasons and fall durng the wet seasons, but the changes are far less than experenced durng freezng and thawng. (Slde 9) The desgn traffc volume can be estmated n much the same way as t s for asphalt pavements. You want to know how many trucks wll use the desgn lane over the chosen desgn perod. The equaton s smlar but not dentcal to the Asphalt Insttute and AASHTO formulas: 365 In the PCA method, only trucks wth 6 tres or more are used for desgn purposes, so your truck factor should nclude only vehcles n FHWA Class 3 and above. (Slde 10) Recall that the Asphalt Insttute method uses the growth factor G n 1 r 1 to convert the ntal ADT (or ADTT) nto a total traffc volume over the entre desgn perod. Ths s perfectly vald and there s no reason you can t use ths for rgd pavements, too. (Slde 11) The PCA manual suggests a somewhat smpler alternatve. Smply calculate the traffc volume halfway through the desgn perod (relatve to the startng traffc volume): r 1 2 G r Y and use that as the average traffc volume over the entre desgn lfe. So ths G converts the startng traffc volume nto the desgn year traffc volume. You stll have to multply by the desgn lfe Y to get the total traffc over the entre desgn perod. 5

6 (Slde 12) The lane dstrbuton factor (L) can be determned from ths graph. The y-axs s the one-way ADT n the desgn year (whch, as we sad above, s smply halfway through the desgn perod). (Sldes 13-14) The prmary dfference between the traffc analyses we performed earler and the traffc analyss used n the PCA method s that we don t multply the desgn lane traffc volume by a truck factor to convert everythng to ESALs. Instead, we use the axle load spectra (for both sngle and tandem axles) drectly. (Slde 15) The general desgn procedure s as follows: 1. Choose a tral slab thckness. 2. For each axle load beng consdered, determne the number of repettons to falure for a slab of that thckness. Ths s done twce: once for fatgue falure and once for eroson falure. 3. Dvde the actual number of load repettons n each load class by the number of repettons to falure to get a damage factor for each load class. These represent the amount of pavement lfe consumed by the vehcles n each class based on ether the fatgue or eroson crteron. 4. Sum the damage factors over all the load classes to get the total pavement lfe consumed by the projected traffc mx for both fatgue and eroson. If ether result s greater than 1.0 (lfe), we need to ncrease the slab thckness by ½ and redo the calculatons. If both results are less than 1.0, we could reduce the slab thckness by ½ and repeat the calculatons to see f we can save some money. Desgn Nomographs To keep you from havng to do a lot of number crunchng, the PCA desgn manual uses a seres of tables and nomographs to compute the allowable number of load repettons N for each axle load class n your hstogram. We ll start by lookng at the fatgue analyss. In general, the number of repettons to falure, N, s a functon of the stress rato, whch s the rato of the edge stress to the modulus of rupture of the concrete: e S c In an elastc analyss, the edge stress s drectly proportonal to the wheel load: 3P e 2 h P f a, k, h, If you can calculate the edge stress for one wheel load, you can determne the edge stress for any other wheel load usng a drect proporton. Twce the wheel load, twce the stress. 6

7 The slab thckness (h) and the modulus of subgrade reacton (k) determne the radus of relatve stffness, so f you know h and k and make some smplfyng assumptons about the contact radus a you can calculate the value of the functon f akhl,,,, whch s just the edge stress per pound of wheel load. That s exactly what s been done n the PCA manual. (Slde 16) These tables provde the edge stress produced by an 18,000-lb sngle axle load and a 36,000-lb tandem axle load for select combnatons of h and k. The table on the left s used when there are no ted concrete shoulders to support the edge of the pavement and the table on the rght s used when there s shoulder support. For example, the edge stress produced by an 18-kp sngle axle load appled to an 8" concrete pavement wth ted shoulders supported by a foundaton wth a 200 ps/n modulus of subgrade reacton s 197 ps and the edge stress produced by a 36-kp tandem axle load s 168 ps. The edge stress values from those tables are dvded by the modulus of rupture of the concrete to produce a correspondng edge stress rato for both sngle-axle and tandem-axle loads: e S c Because the edge stresses are drectly proportonal to the wheel loads, ths stress rato s used as a multplcaton factor to convert the axle loads for each load class nto an edge stress rato that can then be used to calculate the expected pavement lfe under that axle load. (Slde 17) The PCA manual recommends that you frst multply the axle loads n each load class by a load safety factor that vares based on the user costs that would be ncurred f the road has to be shut down for mantenance. For roads and streets wth low truck traffc volumes, they recommend LSF = 1.0. For hghways and arterals wth moderate truck traffc, the recommend LSF = 1.1. For nterstate hghways, they recommend LSF = 1.2 and suggest that a load safety factor as hgh as 1.3 mght be approprate for premum facltes (say urban nterstates wth lots of commuter traffc n addton to trucks). (Slde 18) Ths nomograph s used to convert the factored sngle and tandem axle loads nto an expected fatgue lfe for the pavement. A lne drawn from the factored axle load on the left scale through the approprate stress rato on the mddle scale wll ntersect the rght scale at the correct fatgue lfe. Another set of tables and nomographs do the same thng based on the eroson falure crteron. In ths case, t s slghtly more complcated because the amount of eroson damage depends on the presence or absence of ted shoulders and the presence or absence of dowels. As a result, there 7

8 are four tables nstead of two. There are also separate nomographs for pavements wth and wthout shoulders. Other than that, though, the procedure s the same. (Slde 19) These tables provde an eroson factor produced by ether an 18-kp sngle axle load or a 36-kp tandem axle load for select combnatons of h and k for pavements wth ted concrete shoulders. Ths eroson factor s used n another nomograph (Slde 20) that converts the factored axle loads nto an expected number of repettons to falure due to eroson. (Slde 21) These tables are for pavements wthout ted concrete shoulders (.e., wth asphalt or gravel shoulders or no shoulder at all). They go wth ths nomograph (Slde 22) that converts the factored axle loads nto an expected number of repettons to falure due to eroson. (Slde 23) The best way to llustrate all of ths s wth an example. (Slde 24) We re gong to desgn a concrete pavement for a 4-lane rural nterstate hghway wth average daly traffc of 12,900 vehcles, of whch 19% are trucks. The traffc s expected to grow by 4% per year over the 20-year desgn lfe of the pavement. (Slde 25) The traffc volume halfway through the 20-year desgn perod (relatve to the startng traffc volume) s gven by: Y say 1.5 G r (Slde 26) So the one-way ADT halfway through the 20-year desgn perod wll be ADT (D) (G) = 12,900 (0.5) (1.5) = 9675 (Slde 27) Based on a one-way ADT of 9675 and two lanes n each drecton ths graph gves a lane dstrbuton factor of 0.81, so the number of trucks n the desgn lane over the 20-year lfe of the pavement wll be (Slde 28) V 365ADTTDLGY 36512, mllon (Slde 29) We ll assume that the pavement wll be supported by a 4-nch-thck granular subbase on a clay subgrade wth a 100-ps/n modulus of subgrade reacton. The pavement wll be a JPCP wth dowel bars and asphalt shoulders. The modulus of rupture of the concrete s assumed to be 650 ps. Note that ths s the only concrete property needed for the PCA desgn method. (Slde 30) These tables can be used to estmate the composte modulus of subgrade reacton of the foundaton materal. The combnaton of a 4-nch-thck granular (.e., untreated) subbase and a subgrade wth a 100-ps/n modulus of subgrade reacton produces a composte k of 130 ps/n. (Slde 31) We ll assume that ths hstogram gves the antcpated number of sngle axle loads n each of 10 dfferent load classes over the 20-year lfe of the pavement. Wegh staton data can be used to determne the mx of axle loads (say, per 1000 trucks) and those results scaled up to the 10.8 mllon trucks we antcpate over the lfe of ths pavement. 8

9 (Slde 32) Smlarly, ths hstogram gves the antcpated number of tandem axle loads over the lfe of the pavement. (Slde 33) Here s the upper half of the worksheet we ll use to determne the requred thckness of the slab. The upper half s used for the sngle axle loads and the lower half (Slde 34) s used for the tandem axle loads. (Slde 35) We ll start by assumng a 9.5-nch concrete pavement. We ve already been told that t wll be a doweled pavement wth no ted concrete shoulders. The composte modulus of subgrade reacton of the subbase and subgrade was found to be 130 ps/n and the modulus of rupture of the concrete was gven as 650 ps. (Slde 36) Snce ths s an nterstate hghway, we ll use a load safety factor of 1.2. Ths s also flled n at the top of the sheet (Slde 37). (Slde 38) We ll do the fatgue analyss frst. For an assumed slab thckness of 9.5 nches wth no concrete shoulders and a subbase-subgrade modulus of 130 ps/n, we nterpolate an equvalent edge stress of 206 ps for sngle axles. (Slde 39) Dvdng the 206 ps sngle-axle stress by the modulus of rupture of the concrete, we get a sngle-axle stress rato factor of 206 / 650 = Now we can start enterng the axle load classes from the hstograms. We start wth the hghest load for reasons that wll become apparent n just a mnute. The hghest sngle axle load s 30 kps. Applyng a 1.2 factor of safety ncreases that to 36 kps. From the earler hstogram, the number of axle loads expected n that class s (Slde 40) To determne the fatgue lfe of ths pavement under a 36-kp sngle axle load, we draw a lne from 36 on the sngle-axle sde of the axle load scale, through on the stress rato scale, producng a fatgue lfe of 27,000 load repettons. (Slde 41) If we re gong to apply 6310 axle loads to a pavement that can wthstand 27,000 load repettons before falng, we re consumng 6310 / 27,000 = = 23.4% of the pavement s lfe wth the axles n ths load class. (Slde 42) We can repeat the same procedure for the 28-kp load class, the 26-kp load class, and so on. Note that as the axle loads go down, the fatgue lfe goes up. (Slde 43) Eventually we ll get to an axle load class for whch the projected fatgue lfe s off the scale. At ths pont, we call the fatgue lfe nfnte and stop. (That s why we start wth the hghest load class and work our way down; you ll almost always acheve an nfnte fatgue lfe before you get to the lowest axle load classes.) 9

10 (Slde 44) Fnally, we sum up the percentages of pavement lfe consumed by the axles n each of the load classes. In ths case, all of the sngle axles traversng ths pavement over the next 20 years wll consume 61% of the pavement s lfe. (Slde 45) Now we turn our attenton to the tandem axle and repeat the same procedure. (Slde 46) For an assumed slab thckness of 9.5 nches wth no concrete shoulders and a subbasesubgrade modulus of 130 ps/n, we nterpolate an equvalent edge stress of 192 ps for tandem axles. (Slde 47) Dvdng the 192 ps sngle-axle stress by the modulus of rupture of the concrete, we get a tandem-axle stress rato factor of 192 / 650 = The hghest tandem axle load s 52 kps. Applyng a 1.2 factor of safety ncreases that to 62.4 kps. From the earler hstogram, the number of axle loads expected n that class s 21,320. (Slde 48) To determne the fatgue lfe of ths pavement under a 62.4-kp tandem axle load, we draw a lne from 62.4 on the tandem-axle sde of the axle load scale, through on the stress rato scale, producng a fatgue lfe of 1.1 mllon load repettons. (Slde 49) If we re gong to apply 21,320 axle loads to a pavement that can wthstand 1.1 mllon load repettons before falng, we re consumng 21,320 / 1,100,000 = = 1.9% of the pavement s lfe wth the axles n ths load class. (Slde 50) We can repeat the same procedure for the 48-kp load class. Applyng the load safety factor, we ll enter the hstogram (Slde 51) wth a tandem axle load of 57.6 kps. Drawng a lne through the stress factor of 0.295, we get a projected fatgue lfe off the scale, so we re done. (Slde 52) Addng the tandem axle results to those of the sngle axles, we fnd that we ll consume 62.9% of ths pavement s lfe wth the traffc loads we ve assumed over the next 20 years. (Slde 53) So far, ths would seem to be a successful, albet somewhat conservatve, desgn. But we re only halfway done because we also have to perform the eroson analyss. (Slde 54) For an assumed slab thckness of 9.5 nches wth dowels but no concrete shoulders and a subbase-subgrade modulus of 130 ps/n, we nterpolate an eroson factor of 2.59 for sngle axles. (Slde 55) We ve already entered all of the sngle-axle data nto the worksheet, so all we have to do s determne the allowable repettons n each load class from an eroson perspectve. (Slde 56) Enterng the nomograph wth a factored sngle-axle load of 36 kps and drawng a lne through an eroson factor of 2.29, we get a pavement lfe of 1.5 mllon. 10

11 (Slde 57) That means our hghest sngle-axle load only consumes 0.4% of the pavement s eroson lfe. (Slde 58) If we repeat that for all of the other sngle-axle loads (ncludng for some lghter load classes not used n the fatgue analyss) we fnd that the sngle-axle loads wll consume only 6.1% of the pavement s eroson lfe. (Slde 59) Turnng our attenton to the tandem axles, we need to frst come up wth an eroson factor to use n the nomographs. (Slde 60) For an assumed slab thckness of 9.5 nches wth dowels but no concrete shoulders and a subbase-subgrade modulus of 130 ps/n, we nterpolate an eroson factor of (Slde 61) Our frst tandem-axle load class s 52 kps (whch s 62.4 kps wth the safety factor). (Slde 62) Startng at a tandem-axle load of 62.4 kps and drawng a lne through an eroson factor of 2.79, we get a pavement lfe of 920,000 (f we have really good eyes!). (Slde 63) So our hghest tandem-axle load consumes 2.3% of the pavement s eroson lfe. (Slde 64) If we repeat that for all of the other tandem-axle loads (ncludng for some lghter load classes not used n the fatgue analyss) we fnd that all of the axle loads combned consume 38.9% of the pavement s eroson lfe. So ths stll seems to be a successful, albet somewhat conservatve, desgn. It would be worth t to repeat all of these calculatons for a 9-nch slab thckness to see f we could save some money. If ether the fatgue or eroson lfe consumed exceeds 100%, the slab s too thn and we ll specfy a 9.5-nch slab thckness and we re done. 11