Incorporating Slab/Underlying Layer Interaction into the Concrete Pavement Analysis Procedures (2017)

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42 CHAPTER 3 FINDINGS AND APPLICATIONS This chapter describes the results of analysis of full-scale pavement data and the use of developed tools to further analyze pavement data to characterize slab-base interaction. Influential factors in pavement performance models are discussed. The developed alternative distress models for the AASHTO M-E procedure to account for slab-base interaction are also detailed. The distress modeling effort includes revised parameters for slab-base bonding, built-in curl, and contribution of stabilized bases to load transfer efficiency transverse joints. 3.1 CHARACTERIZATION OF SLAB-BASE INTERACTION This study identified influential factors in slab-base interaction that also contributed measurably to pavement performance. These factors were then more closely examined to characterize slab- base interaction for the purposes of performance model development. The following subsections describe the findings for the major factors identified in this study: base layer material; partial bond; and slab foundation support (or built-in curl). 3.1.1 Base layer effect on the composite k-value The developed back calculation procedure was applied to 289,816 individual FWD basins (from center- and edge- loading) from 4,572 locations (stations) along 208 individual LTPP SPS-2 and GPS-3 sections. The results were used to investigate the effect of the base layer on the back calculated coefficient of subgrade reaction at both the interior and edge locations. This investigation was used to evaluate the composite k-value currently used by the AASHTO M-E procedure. The analysis of the results of back calculation indicated that significant variability existed within section (from location to location), between times of testing, and between sections. Furthermore, it was found that not all of the observed behavior (and variation in this behavior) could be attributed entirely to the interaction of the slab and base layer. Some factors affecting deflection basins include slab curl/warp and subgrade support. To separate the effect of slab-base interaction from other effects, such as PCC thickness variation, seasonal effects, etc., average backcalculated parameters for the same states (locations) with similar designs but different bases were compared. In addition, the study of base layer effects on system properties focused only on sections with 12-foot lane width. For each state in the SPS-2 study, the average of the interior and edge effective moduli of elasticity (Eeff) and k- values were determined and normalized to the average value for sections with unbound aggregate bases. These ratios of either are reported in Table 7 for Eeff and k. For interior loading, an average k-value ratio for sections is approximately 1.2 for both the LCB and PATB base types. For edge loading, those ratios are 1.4 for LCB and 1.3 for PATB. To evaluate this effect, two AASHTO M-E simulations were performed for an 8-inch PCC pavement located in Phoenix, AZ. The slab was placed over a 6-inch LCB layer in one simulation and over a 6-inch aggregate layer in the other. The E-to-k procedure in AASHTO M- E calculated k-values of 190 and 160 psi/in, respectively, for the projects. The ratio of these values is approximately 1.2, which suggests that the AASHTO M-E correctly captures the observed trend.

43 Table 7. Backcalculated subgrade k-values for LCB and PSAB base type (normalized to AGG base parameters) for center and edge locations STATE PCC THICK- NESS (in) LANE WIDTH (ft) Interior location Edge location LCB/AGG PATB/AGG LCB/AGG PATB/AGG AZ 8 12 1.75 1.84 1.44 1.16 11 12 1.71 1.16 2.15 0.72 AR 8 12 1.61 0.56 1.98 0.55 11 12 0.86 1.37 0.78 1.13 CA 8 12 1.10 1.53 0.69 1.10 11 12 0.85 1.55 0.66 1.60 CO 8 12 1.05 1.57 1.00 1.10 11 12 0.67 0.76 0.95 1.07 DE 8 12 1.06 0.97 1.40 1.40 11 12 0.98 1.25 1.39 1.58 IA 8 12 1.10 0.93 1.37 1.02 11 12 1.15 1.53 1.03 1.45 KS 8 12 1.17 0.94 1.35 1.03 11 12 1.50 1.16 1.48 0.92 MI 8 12 2.05 1.26 3.06 1.57 11 12 1.55 1.45 2.23 2.48 NV 8 12 1.34 0.63 1.27 1.46 11 12 0.82 0.95 0.59 0.92 NC 8 12 0.64 1.10 0.67 1.28 11 12 1.50 1.90 0.76 1.65 ND 8 12 1.22 1.74 1.35 1.35 11 12 1.73 1.19 1.77 1.22 OH 8 12 0.94 1.03 2.90 2.04 11 12 0.82 1.02 1.42 1.35 WA 8 12 1.10 0.73 1.42 1.44 11 12 1.06 0.72 1.24 1.23 WI 8 12 1.13 1.19 1.25 1.19 11 12 0.91 0.92 1.13 1.14 Average 1.19 1.18 1.38 1.29 3.1.2 Effective flexural stiffness under partially bonded slab-base interface The review of data collected from experimental JPCP and CRCP full-scale test sections in Minnesota (Minnesota Road Research Facility data), California (Rao and Roesler, 2005; Kohler and Roesler, 2006), Florida (Tia et al., 2007), and Illinois (Cervantes and Roesler, 2009) found that efforts to characterize the extent of bond at the slab-base interface from strain gauge (or similar experimental data) were overshadowed by other factors in the pavement system, such as PCC damage, environmental effects (warp/curl), etc. In this project, an attempt to evaluate a degree of composite bending behavior of the PCC slab and the base using the FWD deflection data was made. A procedure was developed to back calculate coefficients of friction from FWD tests at both edge and interior locations. The back calculation of each deflection basin, for a given date, time, and location, results in the subgrade k-value and the radius of relative stiffness. From these parameters, an effective flexural stiffness, Deff, can be obtained using Equation 24. The minimal non-dimensional coefficient of variation Λ* was assigned to the full-slip state and the maximum coefficient of variation was assigned to

44 the full-bond state on a section-by-section basis. For a full-slip interface Λ∗ ൌ 0.0001, and for a fully bonded interface ߉∗ ൌ 100. To evaluate this approach, the backcalculated slab-to-base moduli ratio, β, was compared with the corresponding moduli ratio, β0, recommended by the LTPP back calculation procedure for rigid pavements (Khazanovich et al, 1997). Table 8 presents the backcalculated moduli ratio for several locations of the SPS-2 experiment. FWD tests were performed at both the slab edge (J3) and interior (J1). Table 8. Comparison of backcalculated slab-to-base moduli ratio with recommendations from Khazanovich et al (1997) STATE CODE ID LOCN J1 or J3 # of TESTS MIN DEFF (lb in) MAX DEFF (lb in) H1 (in) H2 (in) β0 β 4 217 69.2 1 48 5.39E+08 1.10E+09 8.1 6.1 2 5.44 4 217 133.5 1 48 4.16E+08 1.21E+09 8.1 6.1 2 2.328 4 219 37.2 1 72 1.13E+09 2.28E+09 10.8 6.2 2 3.43 4 221 54.3 1 36 5.02E+08 7.40E+08 8.1 4.2 15 6.897 4 222 5.5 1 72 3.92E+08 9.03E+08 8.6 3.9 15 1.634 4 7614 3.4 1 36 6.00E+08 9.89E+08 9.7 5.2 5 5.141 4 7614 12.5 1 36 8.34E+08 1.33E+09 9.7 5.2 5 5.719 4 7614 135.6 1 36 7.14E+08 1.03E+09 9.7 5.2 5 7.752 26 222 124.1 1 36 3.93E+08 4.97E+08 8.3 4.2 15 12.306 26 222 147.5 1 36 3.38E+08 4.14E+08 8.3 4.2 15 14.601 28 3019 97.2 1 60 5.36E+08 7.62E+08 9.4 5.4 10 9.376 28 3019 103.3 1 60 4.48E+08 6.51E+08 9.4 5.4 10 8.64 28 3019 134.1 1 72 4.46E+08 6.25E+08 9.4 5.4 10 9.927 32 7084 145.4 1 36 4.82E+08 6.05E+08 11 5 10 10.817 4 217 69.2 3 48 5.29E+08 1.54E+09 8.1 6.1 2 2.325 4 217 133.5 3 48 4.18E+08 8.13E+08 8.1 6.1 2 6.099 4 219 37.2 3 72 4.90E+08 3.02E+09 10.8 6.2 2 1.001 4 221 54.3 3 36 6.78E+08 1.08E+09 8.1 4.2 15 5.366 4 222 5.5 3 100 3.59E+08 6.36E+08 8.6 3.9 15 3.166 4 7614 3.4 3 48 9.60E+08 1.34E+09 9.7 5.2 5 8.847 4 7614 12.5 3 36 1.10E+09 1.39E+09 9.7 5.2 5 13.63 4 7614 135.6 3 36 6.33E+08 1.03E+09 9.7 5.2 5 5.312 26 222 124.4 3 36 2.66E+08 5.05E+08 8.3 4.2 15 3.162 26 222 147.5 3 36 2.18E+08 3.39E+08 8.3 4.2 15 5.548 28 3019 97.2 3 60 4.49E+08 1.01E+09 9.4 5.4 10 2.589 28 3019 103.3 3 60 2.92E+08 4.32E+08 9.4 5.4 10 8.12 28 3019 134.1 3 72 2.94E+08 5.43E+08 9.4 5.4 10 4.247 32 7084 146 3 36 5.93E+08 9.04E+08 11 5 10 4.956 One can observe that for the majority of the locations the backcalculated ratios, β, are in line with β0, the LTPP recommendations. Also, for some locations the ratios were either significantly higher or lower than expected. At the same time, the backcalculated moduli ratios from the edge and interior testing were not necessarily the same. The latter can be explained by variations in the layer thicknesses in the transverse direction. The evolution of the backcalculated normalized apparent friction coefficients was also evaluated. Figure 19a presents the results of backcalculation for one of the edge loading locations of LTPP section 8-3032. One can observe that the apparent friction degrades from the

very high in betwee friction c Figur Figure 19 location a transition A similar these disc bond betw affect the pavemen T was appl conclude for slab-b the hypot behavior reliably d However character interactio can be re H a simplif laborator degrades the PCC due to ch slab-base value in Au n. At the sa oefficients f e 19. (a) We b shows a d nd section. from a very trend was o repancies: ( een the con back calcul t section, as he develope ied to FWD d that due to ase interfac hesis that th of a PCC sl etermine th , the (A) edg istics from b n for structu asonably ex owever, as t ied partial fr y study cond due to large slab/base fri anges in tem interface de gust 1998 t me time, Fig rom the sam (a) ll-behaved ifferent patt Although th high to a v bserved for A) if the tes crete and b ation results proposed in d procedure basins from variability e modeling e partial bon ab/base syst e partial fric e back calc ackcalculat ral models plained. he develope iction deteri ucted by Li relative dis ction deterio perature. T teriorates o o a very low ure 19a sho e test day, b and (b) err LTPP ern when ex e backcalcu ery low valu many other ting was no ase layer ma , (C) variab Rufino et a for inferrin all GPS-3 a in the FWD from the dat d model pr em, the reso tion parame ulation proc ed layer pro if these meth d alternativ oration mod et al. (2013 placements ration is ma he model as n a yearly b 45 value in Oc ws variabili ut different atic inferre Section 3-30 amining the lated non-di e, the degra locations. T t performed y not exist; ility in the i l (2004). g a coefficie nd SPS-2 se basin data, abase. Whil ovides a rea lution of the ter and deve edure and (B perties have ods are app e cracking m el was prop ) indicated t between the inly caused sumes that asis accordin tober of 20 ty in the bac FWD drops d friction p 23 interior lay mension fri dation does here can be immediatel (B) environ nterface pro nt of friction ctions in th it was not p e the back c sonable estim back calcu lop apparen ) method fo the potentia lied to relia odel suppo osed in this hat friction slab and th by longitud the non-dim g to the fol 10, with inte kcalculated and load le (b) erformance er propertie ction exhibi not occur c several exp y after const mental cond perties vary for slab-ba e LTPP data ossible to re alculation re ate of the lation is not t friction de r inferring l to charact ble data in w rts the partia study. As th at the slab-b e base, it wa inal movem ensional fric lowing equa rmediate va normalized vels. over time s at the sam ts a smooth hronologica lanations fo ruction, the itions could along the se interactio base. It was liably infer Λ sults suppo in-service sufficient to gradation m friction erize slab-ba hich variati l bond conc e results of ase interfac s assumed t ents in the s tion, Λ*, fo tion: lues in e lly. r full n * rt odel. se on ept, the e hat lab r the

46 Λ௝ାଵ∗ ൌ Λ௝∗ ∙ ݁ି ∑ ൬ ೎்,೘ೌೣି்೎,೘೔೙஼೑ ൰೔ Λଵ∗ ൌ ܮ∗ ܧ௉஼஼݄௉஼஼ܧ௉஼஼݄௉஼஼ ൅ ܧ௕௔௦௘݄௕௔௦௘ 56 where Tc,max and Tc,min are the maximum and minimum constant strain temperatures in the concrete slab for the month, i, respectively, Cf is a friction degradation parameter, index j denotes age in years, and ܮ∗ is the initial non-dimensional friction factor. The simplified friction deterioration model was implemented in the alternative cracking model developed in this study and described below. It requires the user to provide the initial friction (non-dimensional friction factor) and the friction degradation parameter for the slab-base interface, and monthly values of * thereafter are calculated according to Equation 56. The recommended values of Cf and ܮ∗ parameters have been determined during the calibration of the JPCP cracking model. Alternatively, the user may directly input monthly values of *. 3.1.3 Built-in curl analysis The developed EMD tool was applied to SPS-2 JPCP sections with six years or more of profilometer observations. This accounted for 5207 observations between 1992 and 2012 for 110 SPS-2 sections. The curling profiles (i.e. IMFs corresponding to the joint spacing) were extracted and standard deviations of the amplitude of these profiles were calculated. A higher standard deviation indicates more pronounced slab curling. Table 9 shows average standard deviations of the curling profiles for each combination of PCC slab thickness, base type, and lane width. It is observed that cement stabilized bases had the largest variance in slab curling profile of all base types. In the exception (sections with 8” slabs and 12-foot lane widths), the variance in average slab curling profiles of sections using aggregate bases was only slightly higher than those with LCB. This result confirms the observation that rigid support from cement stabilized bases increases the possibility of separation at the slab-base interface. Table 9. Average slab curling profile standard deviation (in inches) by base type, slab width, and slab thickness Base Type 12-foot lane width 14-foot lane width 8” slab 11” slab 8” slab 11” slab AGG 0.026 0.022 0.021 0.022 LCB 0.025 0.025 0.025 0.025 PSAB 0.021 0.021 0.019 0.020 In addition, a relationship between slab curling profile and pavement performance was investigated. In pavements with aggregate bases, the severity of slab curl was strongly correlated in 12-foot wide sections with an increase in roughness over the pavement life (shown in Figure 20). Likewise, statistically significant but less strong correlations were observed between curl and increased roughness for (A) sections with 8-inch slabs and (B) sections located in wet-freeze climates for both 12-foot and 14-foot lane widths.

Figure 2 Although sense, clo for desig extracted profiles a contribut materials irregular slabs clo Figure This anal limited to 0. Effect of the standar se examina n purposes i from the pr re close, the e to varianc , or environ slab profile se to early fo 21. Slab pr ysis suggest a single pa (a) slab profile d deviation tion of the p s challengin ofiles measu y vary cons e in slab cur ment. In add within a pro rmed joints ofiles given s that built- rameter/valu on increas and (b) 14 can reflect th rofilometer g. Figure 21 red on the s iderably wit ling profile, ition, post-c ject. For ins may exhibi EMD analy in curl mode e. Findings 47 e in IRI by -foot lane w e magnitud data by sect presents co ame day for hin a given including c onstruction tance, if the t higher curl sis of two p 37-0201 ling for pav to support t base type f idths e of slab cu ion suggests mparison of the same se project. The onstruction conditions m joint forma ing. rofilomete ement perfo his claim in (b) or sections rling/warpin that quanti two curling ction. Altho re are many conditions, p ay also con tion is not s r passes on rmance mod clude: with (a) 12- g in a gener fying slab pr profiles ugh the cur factors that aving and b tribute to imultaneous LTPP Sect els cannot b foot al ofile ling may ase , ion e

48  Sensitivity studies of the AASHTO M-E models determined that modifications to T can result in improved model predictions relative to observed performance for the AASHTO M-E calibration projects (Section 2.4).  The EMD analysis discussed above indicates that the slab profiles of in-situ pavements vary by base material. Furthermore, the analysis found high variance in slab profile within a given project.  Theories of slab behavior discussed in the literature review treat built-in curl as a property that depends on the paving conditions and varies throughout the service life (Eisenmann and Leykauf, 1990). In addition, built-in curl depends on the time of concrete placement, i.e., morning versus afternoon (Springenschmid and Fleischer, 2001). Thus, it is proposed to modify the built-in curl factor in pavement performance modeling by dividing the default AASHTO parameter into two different built-in curl temperature gradients for day-time and night-time conditions (Tbot and Ttop, respectively). Furthermore, it is proposed that the developed model for built-in curl consider relative differences in thickness and stiffness in the slab and base layers; this model thus ensures that projects with stiffer bases will have more exaggerated levels of built-in curl. The following representation for T is proposed (and implemented in the alternative modeling for transverse cracking): ∆ܶ ൌ Δ ௜ܶ௡௣௨௧ േ ܣ ൬1 െ ܧݔ݌ሺെܤ ܧ௕௔௦௘ ݄௕௔௦௘ܧ௉஼஼ ݄௉஼஼ ൅ ܧ௕௔௦௘݄௕௔௦௘ሻ൰ 57 where Tinput is the user-assigned value of the built-in curl (taken from an AASHTO general input file), EPCC is the elastic modulus of the concrete slab, hPCC is the thickness of the slab, Ebase is the elastic modulus of the base layer, hbase is the thickness of the base layer, and A and B are calibration factors to determine the extreme to which Tinput is bifurcated into two values. Once the calculation for T is conducted, it is split into (A) a more positive component to simulate slab-base interaction during day-time loading, or Tday, and (B) a more negative component to simulate the slab-base interaction during night-time loading, or Tnight. Finally, should it be desired, the use of the original AASHTO T value, Tinput, can be forced by setting the factor A equivalent to zero. 3.2 ALTERNATIVE PERFORMANCE MODELS TO ACCOUNT FOR SLAB-BASE INTERACTION The research study resulted in performance models for the AASHTO M-E procedure to be modified to improve its ability to account for the effects of slab-base interaction in pavement design and analysis. The alternative performance models for the JPCP joint faulting and CRCP punchout models represent relatively minor modifications of the existing AASHTO M-E models. The JPCP transverse cracking model was substantially revised.

49 3.2.1 Transverse cracking model To improve consideration of the interaction between the concrete slab and underlying layer in JPCP transverse cracking prediction, an alternative JPCP transverse cracking prediction procedure was proposed. The main steps of the proposed procedure are the same as the AASHTO M-E transverse cracking production and include the following: 1. Assemble a trial design for a specific site conditions such as traffic, climate, and foundation—define layer arrangement, PCC and other paving material properties, and design and construction features. 2. Process input to obtain monthly values of traffic, material, and climatic inputs needed in the design evaluations for the entire design period. 3. Compute structural responses (stresses and deflections) using finite element based rapid solution models for each axle type and load and for each damage calculation increment throughout the design period. 4. Calculate accumulated damage at each month of the entire design period. 5. Predict bottom-up and top-down cracking. 6. Predict total transverse cracking. The developed cracking model significantly differs from the AASHTO M-E model in the way how the structural responses and fatigue damage are computed, but it requires the same inputs as the AASHTO M-E cracking model:  PCC strength and modulus data for each month of the analysis period;  average daily number of single, tandem, tridem, and quad axles in each axle weight category for each month of the analysis period;  temperature information at 11 evenly spaced nodes in the PCC layer for every hour of the available climatic data are converted by the model into a distribution of linear temperature gradient frequency;  average monthly relative humidity, which is considered for each calendar month; and  average base layer moduli values, used to determine a monthly average effective subgrade modulus of reaction (k-value), based on the input subgrade resilient modulus by month. In addition to the inputs required by the currently AASTHTO M-E procedure, the alternative cracking model requires to provide the following inputs:  Non-dimensional friction, *, for the slab-base interface for each month. It can be done either directly or by selecting the simplified friction deterioration model described by Equation 56 and providing its parameters.  Parameters for the modified built-in curling model (Equation 57) enabling an assignment of different values of the built-in curling for the top and bottom PCC surfaces.  A ratio of the concrete flexural strengths at the top and bottom PCC surfaces to account for the difference in concrete curing conditions.  Characteristic length, a, in Equations 47 and 50, to account for the effect of nonlinear stress distribution throughout slab thickness on the apparent strength.

The mod AASHTO model wa 95% of th Equation assumed A used to d friction a coefficien conducte calibrated cracking resulted i in Figure by base t Figur Figure 22 bias for a types, the 0.9371, r the perfo ified JPCP t M-E calib s assumed f e bottom su 45 is equal to be equal n initial cali etermine the nd friction d ts of 0.211 d using sect by minimi model coeff n values of 22 are the l ype. e 22. Modi observatio shows that ll three base linear regre espectively. rmance of P ransverse cr ration datab or all sectio rface streng to 0.95) and to 2.5 inche bration was model coef egradation p and -2.336 f ions with sta zing the disc icients deter 6F and 20 ines of linea fied JPCP t ns by proje the modifie types. The ssion is a st Figure 22 a SAB projec acking mod ase (Sachs e ns. The top th (i.e., stren the charact s. conducted i ficients of E arameters e or C3 and C bilized base repancy bet mined from F for the cal r regression ransverse c ct base type d, calibrated figure also s rong fit to th lso shows th ts than previ 50 el was calibr t al., 2014). PCC surface gth adjustm eristic length n which onl quation 1. T qual to 0.1 4, respective s, and the b ween the ob calibration ibration par s with intere racking mo using deve model pred hows that fo e data, with at, while the ously, the R ated using t The default strength w ent factor f , a, of Equa y sections w he calibrati and 300, res ly. A secon uilt-in curlin served and of the sectio ameters A an sts set to ze del predict loped calib ictions fit th r cement-tr R-squared model exh -squared va he LTPP pr partial bond as assumed or curing co tions 47 an ith granular on resulted pectively, a dary calibra g model of predicted cr ns with gra d B, respec ro for each g ions compa ration coef e observed eated and gr values of 0. ibits less bia lue is 0.021 ojects in the deterioratio to be equal nditions, βC d 50 was bases were in the initial nd calibratio tion was the Equation 57 acking using nular bases. tively. Inclu roup of pro red to LTP ficients data with lit anular base 8029 and s in predict 7. For proje n to , in n n was the This ded jects P tle ing cts

with asph PSAB se 3.2.1.1 C The mod interactio inch JPC used the have iden the defau file). Sim becomes AASHTO when the case, whi 0% crack (a) L Figure The addi uses cust identical structura down dam alt-treated b ctions and th omparison w ified model n in the AA over a 4-inc custom therm tical temper lt slab-base ulations for more prono M-E proce base is very le the presen ed slabs as ess stiff ba 23. Influenc tional 10-inc om climate temperature lly identical age. As a r ases, some e performan ith AASHT was applied SHTO M-E h cement st al files so ature gradie interaction b these projec unced as the dure. Howe stiff and th ce of the bo in the AASH se (Ebase = 1 e of base st perform h JPC proje files so that gradients th projects are esult, their c of the “scatt ce of those O M-E trans to the proje procedure i abilized bas that the 10-i nts through ehavior ass ts illustrate stiffness of ver, the mod e slab-base nd reduces TO M-E m 0,000 psi) iffness on s ance in the ct was also the 10-inch rough the p subjected to racking per 51 er” can be a sections, wh verse crack cts created f n the introdu e and 10-in nch JPC sys the paveme umed by the that in the m the base inc ified mode interaction i cracking in odel (shown (b) V ensitivity to modified c simulated us JPC system avement sys identical w formance, sh ttributed to ich exhibit ing perform or the discu ction of Se JCP on a gra tem and the nt system. I modified m odified mo reases. Thi l differs from s bonded (sh the system, in Figure 7 ery stiff ba loss of fric racking mo ing the mod and the 6-on tem. As not heel and the own in Fig the small sa ed very little ance model ssion of slab ction 2.2 for nular base. 6-on-4-inch n addition, t odel (in the del, the effe s behavior re the AASH own in Figu a full bond b). se (Ebase = 4 tion in pred del ified model -4-inch JPC ed previous rmal loads ure 24, shou mple size of cracking. -base analysis of These proje JPC system he projects u “friction.tx ct of bond sembles the TO M-E m re 23b). In does not res ,000,000 ps icted crack . The projec system hav ly, the two to induce top ld be identi a 6- cts sed t” odel this ult in i) ing t e - cal.

Figure 2 The crack procedur model re in structu 3.2.1.2 S A factori The simu the factor performa O the initia simulatio initial fri underesti the predi 4. Crackin ing perform e is shown i solves the is ral modelin ensitivity an al of simula lations utili ial focused nce in terms ne subset of l slab-base f ns. The figu ction and too mated, but, cted perform g performa ance of the n Figure 8. A sues with (A g. alysis for ke tions using t ze the interm on new or m of slab-bas the factoria riction facto re shows th high initia for medium ance is clos nce of struc crac se structural compariso ) projects f y parameter he alternativ ediate proje odified inpu e interaction l isolated th r, ܮ∗, in Equ at, for param l friction), p values of in e to the tren 52 turally equ king model ly identical n of Figure eaturing stif s in the mod e model wa ct files prod t parameter . e sensitivity ation 56. F eters assum redicted crac itial friction d observed ivalent JPC systems und 24 and Figu f, bonded ba ified JPCP s conducted uced by Pa s that are in of the dama igure 25 pro ing bond or king is eith with subseq in the field. P projects er the AAS re 8 shows t ses and (B) transverse c for LTPP p vement ME tended to im ge and crac vides the re no bond co er overestim uent frictio in the mod HTO M-E hat the mod self-consist racking mo roject 04-02 2.1.24. Ove prove mode king results sults of thos nditions (too ated or n deteriorati ified ified ency del 19. rall, l to e low on,

Figure 2 Another discussed the streng stresses o develope length is modified 5. Perform subset of the in Section th criteria i nly, corresp d strength cr selected to b strength cri ance of LTP factorial ex 2.2.1.5. Figu mplemented onding to le iteria for th e equal to d terion signif P section 0 = -10, amined the re 26 prese in the origi vels of the c e modified m ouble the m icantly influ 53 4-0219 with A = 6, a = 2 new strengt nts a compar nal AASHT haracteristi odel descri aximum agg ences the ex different .5) h criteria for ison of the O M-E proc c length a ap bed above, regate size. tent of the p levels of ini the fatigue cracking per edure (base proaching 0 where the ch The figure redicted cra tial friction damage mo formance u d on maxim ) and the aracteristic shows that t cking. (T del, sing um he

Figure Another the modi effects on Figu 26. Perfor length sensitivity a fied built-in the damag re 27. Perfo coefficient mance of L , a, used in nalysis was curl parame e and cracki rmance of A for built TPP section strength cr performed t ter are cons ng results. LTPP sectio -in curl par 54 04-0219 w iterion (T o investigate idered. Figu n 04-0219 ameter, T ith differen = -10, A = the model re 27 shows with differe (T = -10, t values of 4, *=0.00 behavior wh that A has s nt values o *=0.001, a characteris 1) en changes ignificant f calibratio = 2.5) tic to n

55 The influence of the calibration parameter A in Figure 27 allows for a more direct modification of built-in curl by the user to adjust A to account for the stiffness of the base material relative to that of the slab. In this way, Equation 57 can then help assess the effects of slab-base interaction on transverse cracking. 3.2.2 Joint faulting model As discussed in Section 2.5.2.2, the basis of the alternative faulting model is a reproduction of the AASHTO M-E faulting model that behaves identically to the original (Figure 16). The first step in modifying the reproduced faulting model was to obtain model behavior for an unrestrained slab on a granular base. This was done through a calibration of the alternative model using the 206 observations in the AASHTO M-E calibration database for LTPP GPS-3 or SPS-2 sections with granular bases (ARA, 2004; AASHTO, 2008; Sachs et al, 2014). Projects with bound bases were not considered in the calibration. The process to determine the calibration coefficients given the AASHTO M-E calibration database was: 1. Recreate and run the AASHTO M-E calibration project using the alternative faulting model; 2. Record the differential energy within the intermediate project files for a given project at all ages associated with LTPP observations; and 3. Apply an iterative solver to determine model coefficients that minimize the error between observed and predicted faulting across all calibration projects. By minimizing the error between observed and predicted faulting using an iterative solver, new global calibration coefficients were obtained for the alternative model, presented in Table 10. Table 10. Global calibration coefficients for alternative JPCP faulting model Coefficient Value C1 0.27806 C2 1.63799 C3 0.00624 C4 0.001 C5 299.853 C6 0.3968 C7 8.69371 The effect of assumed base LTE and T was investigated using all 121 SPS-2 and GPS-3 LTPP projects included in previous AASHTO M-E calibrations. Simulations were conducted using the recreated, calibrated JPCP joint faulting model and the AASHTO M-E calibration sections with varied values of base LTE and T: six levels of T (-8F, -10F, -12F, -14F, -16F, and -18F) and nine values of base LTE (10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%). Figure 28 illustrates the sensitivity of LTPP calibration projects with cement-treated and asphalt-treated bases, respectively, to changes in base LTE and T for different base types. As in Section 2.5, model sensitivity by base type is expressed in terms of the sum of squared error, SSE, between observed faulting, Faultobs, and predicted faulting, Faultcalc, for all observations, in square inches.

Each figu 28a show the magn these par Figure calibrat To impro values sh type (SSE relatively should be modified     ܵܵܧ ൌ re identifies s that the C itude of the ameters. 28. Sensitiv ion projects ve the fitne ould (1) imp is an adequ low variab minimal). W as follows: The defau obtain the assumed. The defau obtain the assumed. The defau The modi treated ba ෍ሺܨܽݑ݈ݐ௢௕ ௡ ௝ୀଵ the variabi TB projects y-axis). Fig (a) ity of joint f with (a) ce ss of the mo rove the fit ate measur ility in SSE ith these c lt base LTE minimum S lt base LTE minimum S lt base LTE fied model w ses to accou ௦ െ ܨܽݑ݈ݐ௖௔௟௖ሻ lity in SSE f are the mos ure 28b show aulting to B ment-treat dified mode ness of the m e of model f across all T onsideration for asphalt- SE for PSA for granula SE for gran for cement- ill assume nt for the la 56 ଶ or each assu t sensitive to s that PSA ase LTE v ed bases an l, any poten odel for the itness by ba values (i.e s, the recre treated base B projects. r bases rema ular project treated base a value of -1 rge variabili med value o changes in B projects a aried value d (b) partia tial changes AASHTO se type) and ., the “sprea ated JPCP jo s was increa The AASHT ined unchan s. The AASH s was reduc 4F for T ty in SSE by f base LTE both base L re relatively (b) s of T for lly stabilize to the defau calibration p (2) be asso d” for the se int faulting sed from 30 O default  ged and equ TO defaul ed from 40% for projects T. and T. Fig TE and T insensitive AASHTO M d asphalt b lt base LTE rojects by b ciated with a lected base model was % to 40% t T value wa al to 20% t t T value w to 30%. with cemen 58 ure (note to -E ases ase LTE o s o as t-

Figure Figure 29 near pari granular respectiv This is du calibratio projects w T illustrate F faulting m   As descri alternativ differenc 29. Modifi L shows that ty that is pre bases, this li ely. For sect e mainly to n database a ith other ba he effect of d using LTP igure 30 com odel for tw Section 32 joint spac Section 5 joint spac bed by Figu e model gen e between th ed JPCP fa TPP obser the modifie sent in the o near regress ions with P (A) the rela nd (B) the l se types. the modifica P projects fr pares the A o GPS-3 sec -3010, a 9.7 ing and no d 5-6354, a 9.6 ing and no d re 29 and sh erally captu e two mode ulting mod vations in A d, calibrated bserved dat ion fits the SAB, the fit tively small ack of faulti tions to the om the AAS ASHTO M tions: -inch slab o owels with -inch slab o owels with own in Figu res observe ls is more s 57 el predictio ASHTO c faulting mo a for all bas data, with R is relatively sample of P ng of the ca faulting mo HTO M-E -E faulting m n a 5.6-inch 1500 AADT n a 3.2-inch 483 AADTT re 30a, for d behavior. ubtle and sp ns by proje alibration d del predicti e types. In a -squared va weak, as th SAB projec libration pro del for AAS calibration d odel and th cement-tre T in Nevad asphalt-tre in Wiscon granular and For paveme ecific to the ct base type atabase ons capture ddition, for lues of 0.639 e R-squared ts in the AA jects with P HTO M-E p atabase. e developed ated base w a, and ated base w sin. CTB base nts with PSA particulars compared a linear tren CTB and 1 and 0.629 value is 0.1 SHTO M-E SAB relativ rojects can alternative ith 14.5 foot ith 14.5 foot types the B, howeve of a project. to d 8, 424. e to be r, the

Figure 3.2.3 P To obtain (Equation calibratio The fatig outs was -3.630 fo A was cond CRCP pu were assu 12, 14, 1 was expr and predi The resul simulatio That is, a M-E cali 30. Compa alternative unchout mo alternative 12), perfor ns (Sachs et ue damage w minimized f r C3, C4, and factorial of ucted for th nchout mod med. Those 6, 18, 20, 22 essed in term cted puncho ܵܵܧ ൌ ts of error a n of all calib ll projects b bration datab (a) rison of fau model for L del calibration mance of 18 al, 2014) w as screened or 62 obser C5, respect Pavement M e 124 GPS-5 el calibratio values, ass , and 24. Th s of the sum uts, POcalc, ෍ሺܱܲ௢௕௦ െ ௡ ௝ୀଵ nalysis are s ration secti y base type ase. lting perfor TPP sectio coefficients LTPP GPS ith granular and the dis vations. Th ively. E 2.1.24 ru projects w n (Sachs et umed for ea e discrepan of squared for all obser ܱܲ௖௔௟௖ሻଶ hown by ba ons with CT assume an i 58 mance betw ns with (a) C3, C4, and -5 projects u bases was s crepancy be is process yi ns with the ith stabilized al, 2014). Fo ch of the 12 cy between error, SSE, vations. se type in T B or PSAB dentical valu een the cu CTB and (b C5 for the C sed in the A imulated us tween the p elded value modified pu bases used urteen addi 4 projects, w the measure between ob able 11. Eac base types w e of f for th (b) rrent AASH ) PSAB ba RCP punch ASHTO M ing Paveme redicted and s of 29.68, 8 nchout mod in the AAS tional base ere 0.25, 1, d and observ served punc h row repre ith an assu e sections in TO M-E a se types out model -E model nt ME 2.1.2 observed p .66, and el coefficie HTO M-E friction valu 2, 4, 6, 8, 1 ed punchou houts, POob sents the med value o the AASH nd 4. unch nts es 0, ts s, 59 f f. TO

59 Table 11. Statistics for CTB and PSAB calibration sections from the LTPP GPS-5 experiment f Sum of Squared Error CTB PSAB 0.25 27500 51343 1 20799 36932 2 12431 29036 4 3955 11968 6 2560 7189 8 3486 5579 10 4857 12029 12 4941 12178 14 4942 12178 16 4942 12178 18 4942 12178 20 4942 12179 22 4942 12180 24 4942 12180 The sum of the squared difference between the observed and predicted cracking values was used to assess the recommended value of f by base type for the guidelines for the AASHTO M-E procedures. On this basis, the values of f associated with a “best fit” for the CTB and PSAB sections are respectively 6 and 8. Figure 31 presents a comparison of the punchout model predictions with the observed punchouts when the projects with CTB base type have ݂ ൌ 6 and projects with PSAB base type have ݂ ൌ 8. As can be seen, the calibration using granular sections makes the modified model less conservative than previous calibrations of the AASHTO M-E CRCP punchout model (Sachs et al, 2014). Moreover, the goodness of fit of the alternative model for stabilized sections is comparable with the original model.

The effec illustrate compares sections:   Figure 31 t of the mod d using LTP the AASH Section 2 reinforcem Section 2 reinforcem . Predicted ifications to P projects fr TO M-E pun 8-5803, a 7.9 ent and wit 8-5805, a 8. ent and wit CRCP pun the puncho om the AAS chout mode -inch slab o h 571 AAD 1-inch slab o h 1154 AAD 60 chouts com ut model fo HTO M-E l and the m n a 6.4-inch TT in Missi n a 4.1-inch TT in Miss pared to L r AASHTO calibration d odified punc cement-tre ssippi, and asphalt-tre issippi. TPP observ M-E projec atabase. Fig hout model ated base w ated base w ation ts can be ure 32 for two GP ith 0.61% ith 0.59% S-5

Figure 3 3.3 IM PROCED The impl developm section. 3.3.1 A The trans transvers inputs req prior to tr performs required AASHTO           As the al the AASH 2. Compar alternative PLEMENT URE ementation ent of rudim lternative J verse crack e cracking m uired by AA ansverse cr the transver inputs (traff M-E proje GeneralIn SeasonPa SingleAx TandemA TridemAx QuadAxle _HourlyT ThermalP PCCModu Friction.tx ternative cra TO M-E c (a) ison of pun model for L ATION OF of the altern entary soft PCP transv ing analysis odel requir SHTO M- acking analy se cracking ic, materials ct files. Tho put.txt ttern.txt leOutput.csv xleOutput.c leOutput.cs Output.csv rafficPerc.tx CC.dat lus.txt t cking mode racking mod chout perfo TPP sectio ALTERNA ative transve ware. The m erse crack was implem es numerous E. In the AA sis and repo prediction. properties, se project f sv v t l uses the sa el, the user 61 rmance bet ns with (a) TIVE MOD rse crackin ain features ing model ented into a inputs, the SHTO M-E rted in the t The alternat temperature iles are: me rapid so must provid ween the c CTB and (b ELS FOR T g and joint f of this softw FORTRAN majority of software, t emporary fi ive model a information lutions for c e the locatio (b) urrent AAS ) PSAB ba HE AASH aulting mod are are pre program. T which are id hese inputs les read by t nalysis prog , etc.) from ritical stress n of the AA HTO M-E se types TO M-E els required sented in th he alternati entical to th are processe he program ram reads th the interme calculation SHTO M-E and is ve e d that e diate s as

62 neural network files. Information on these files is provided in the AASHTO M-E documentation (ARA, 2004). This arrangement offers two advantages: (1) it eliminates the need to replicate the AASHTO M-E input processing and (2) it ensures that the developed alternative procedure is compatible with the AASHTO M-E procedure. The new cracking model can be directed to an existing AASHTO M-E project folder and it will use the intermediate project files in a manner identical to the AASHTO M-E cracking model. To account for slab-base interaction, the user must also include a new input file titled “friction.txt.” This file (referred to as the friction input file) should be located in the project directory. The intent of this file is to provide access to the new features in the alternative model, including the inferred slab-base interaction parameter (Λ*) by pavement age (in months). In the absence of the friction input file, the default program behavior for the new cracking model is to use the previous AASHTO conventions for slab-base interaction (i.e. the “loss of friction” month parameter and the direct input built-in curl parameter). The friction input file provides important input parameters for the alternative transverse cracking model. The alternative model input parameters include:  Information on the friction at the slab-base interface, either: - Initial non-dimensional slab-base friction factor, L*, and friction degradation parameter, Cf, or - Non-dimensional slab-base friction coefficients, *, for all months in the project design life.  The characteristic length to be used in the new energy of elastic deformation strength criteria, a. This value has the unit of inches and is typically considered relative to coarse aggregate size.  The coefficient A3 that is used in the calculation of damage according to the fatigue equation in the modified M-E model (Equation 3). For the AASHTO M-E procedure, A3 has a value of 0.4371.  The calibration coefficients A and B for Equation 57, the new representation of built- in curl. The output of the alternative cracking model is stored in a comma-separated file 151_JPCP_Cracking.csv that has the same format as the corresponding MEPDG cracking output file JPCP_Cracking.csv. 3.3.2 Alternative JPCP joint faulting model The modified JPCP joint faulting has only relatively minor modifications from the AASHTO M- E faulting model. It does not use any additional input information and uses the same rapid solutions for corner deflections calculations as the AASHTO M-E faulting model. The new faulting model program can be directed to an existing AASHTO M-E project folder; it will use the intermediate project files in a manner identical to the AASHTO M-E cracking model. The output of the program is a comma-separated file (“151_JPCP_Faulting2.csv”) with identical formatting of the output file (“JPCP_Faulting2.csv”) from the AASHTO M-E faulting program.

3.3.3 C The alter generated perform t and fault faulting a T AASHTO FORTRA software slab-base project. T Step One model, th program “C:\NCH created d input fiel Figur Step Two existing A selected. ompanion t native crack in form of he AASHT ing models. nalysis usin he companio M-E softw N-coded al provides a g interaction he followin : Run comp e user may executable i RP_1_51\”) uring install ds indicated e 33. User : Select exi ASHTO M To do so, m o the AASH ing and faul the AASHT O M-E analy The compan g the alterna n software are on Win ternative mo raphical-use parameters g steps illus anion progra run the com s located in . This execu ation. The p in red. interface fo sting AASH -E design p ouse-click t TO M-E s ting models O M-E proj sis using th ion softwar tive models was develop dows operat dels, which r interface ( and (2) appl trate the use m. To prov panion softw the directory table can al rogram GU r alternativ TO M-E pro roject to be he button “S 63 oftware require mat ect. The eas e AASHTO e may then b . ed using Ja ing system. are Window GUI) that s ying the alte of the comp ide addition are within selected du so be run us I is shown in e models (r inputs) ject. Upon re-run using elect Projec erial, climat iest way to M-E softwa e used to p va and built The softwar s executabl implifies the rnative mod anion softw al inputs to a Windows ring the ins ing the Win Figure 33, ed number opening the the alternat t Directory, e, traffic an generate tho re with the erform the c to run along e interfaces e files. The process of els to an AA are: the alternati operating en tallation pro dows deskto with user se s added to i interface pr ive models ” labeled in d other data se files is to current crac racking and side the with the companion (1) providin SHTO M-E ve cracking vironment. cess (e.g. p shortcut lections and ndicate use ogram, first needs to be Figure 33 a king g The r the s

Number AASHTO directory Figure 3 O navigator shown in Step Thre alternativ input the numbers       1, in red. Up M-E proje of projects 4. Selecting nce the AA , the user sh Figure 33. e: Specify p e models re following in in red in Fig Character (2) Strength r condition The built- described The transv and 7, res If default parameter If the user then the “ using the value file non-dime headerles on clicking ct directory located at “D an existing SHTO M-E ould press “ arameters f quire additio to the interf ure 33: istic length eduction fac s, non-dimen in curl calib by Equation erse crackin pectively) interface de s 9 and 10 s has monthl User-provid file explorer in which the nsional frict s and will re “Select Proj . In Figure 3 :\NCHRP AASHTO altern design proje Select Fold or the altern nal inputs t ace program a, in inches, tor for the t sional, desc ration factor 57 (4 and 5 g model co terioration m hould be pro y interface f ed” box sho . User-prov first colum ion paramet ad each line 64 ect Director 4, the projec 1-51 Examp project dir ative mode ct folder ha er” to autom ative JPCP t o account fo , where the for the stren op PCC surf ribed by Eq s A, in degr , respective efficients C odel (Equa vided. riction data uld be ticke ided monthl n is the mon er. The com as the data y,” the user t “4_0217” les.” ectory in th ls s been selec atically retu ransverse c r slab-base numbers to gth criteria ace to accou uation 45 (3 ees Fahrenh ly) 3 and C4, de tion 56) beh for the serv d and month y data shoul th index an panion tool for the corre is prompted has been se e interface ted in the W rn to the ori racking mod interaction. follow refe , described b nt for diffe ) eit, and B, n scribed by E avior is assu ice life unde ly data will d be a comm d the second will assume sponding m to select an lected from software fo indows ginal interfa el. The The user sho r to those y Equation rence in cur on-dimensi quation 52 med, then r considerat be later loc a-separated column is t the file is onth (thus L the r the ce uld 47 ing onal, (6 ion, ated he ine

Fig Step Fou required project. T red. If th has been text file w Step Five project, t by the alt in the fol 1 correspo number o ure 35. An r: Run comp above, the u o do so, mo e “User-pro selected the ith monthly Figure : Read outp he AASHTO ernative mo lowing outp nds to Mon f lines shoul example of anion tool f ser runs the use-click th vided” optio n the file ex non-dimen 36. Select ut files from M-E proje dels. The pe ut files: th 1, Line 2 d be equal t monthly n or indicated alternative m e button “Ru n for frictio plorer dialog sional fricti ing user-pr alternative ct directory rformance p 65 to Month 2 o the numbe on-dimensi project. Up odels for t n Analysis, n inputs of t window w on data shou ovided nond models. Aft will contain rediction re , and so on) r of months onal friction on specifyin he existing A ” labeled in he interface ill be opene ld be locate imentiona er running t new interm sults, cracki as shown in in the perfo paramete g the model ASHTO M Figure 33 a friction mo d and a com d, as shown l friction da he alternativ ediate and o ng and fault Figure 35. T rmance peri r input file inputs as -E design s Number 1 del paramet ma-separate in Figure 3 ta e models fo utput files u ing, are stor he od. 1, in ers d 6. r the sed ed

  These ou generated in the firs month fo complete shown in Figure 3 3.4 A This sect with the 0217, a J is an 8.1- AADTT service li F model fo interface fully bon predict su cracking “151_JPC Cracking “151_JPC model. tput files are and used b t line of the r every mon d, the rudim Figure 37. 7. Results o PPLICATIO ion illustrate current AAS PCP project inch slab on in Arizona. fe. igure 38a co r this section is fully unb ded interfac bstantial cr for the entir P_Cracking model and P_Faulting. similar to J y the existin comma-sep th of the pro entary softw However, it (a) f the altern N OF ALT s capabilitie HTO M-E c in Arizona a 6.1-inch c In this instan mpares the . In the AA onded at the e for the ent acking in th e performan .CSV”, the CSV”, the f PCP_Crack g AASHTO arated value ject design are will ope is more con ative faultin ERNATIVE s of the dev racking mo which exper ement-treat ce, the crac predicted cr SHTO M-E time of ope ire performa e first 10 yea ce period. 66 final output inal output f ing.CSV an M-E proce (CSV) file life. After t n these file venient to o g model op MODELS T eloped alter del by simu ienced high ed base with king trend w acking from simulations ning to traff nce period. rs. The bon for the mod or the modi d JPCP_Fau dures. Colum , and all othe he execution s using Win pen the file ened with O AASHT native crack lating perfor levels of ea 15-foot joi as observe the AASHT , three cases ic, loss of b None of the ded interfa ified JPCP T fied JPCP Jo lting.CSV - n referenc r lines indic of the mod dows Notep in MS Exce (b) (a) Notepad O M-E P ing model a mance of L rly cracking nt spacing a d for the firs O M-E and were consi ond after 12 se simulatio ce model pre ransverse int Faulting the output f es are indica ate distress els is ad program, l program. and (b) Ex ROJECTS nd compare TPP section . Section 4- nd 1608 ini t twelve yea the alternat dered: the 0 months, a ns was able dicted no iles, ted by as cel s it 4- 0217 tial rs of ive nd to

67 (a) (b) Figure 38. Cracking observations and predicted performance according to (a) AASHTO M-E and (b) alternative model for LTPP Section 4-0217 The alternative model with the default parameter was capable of capturing the effect of early cracking (Figure 38b). Since the stiffness of the base is comparable with the stiffness of the PCC slab, an increase of the absolute value of built-in curling using Equation 57 by the alternative cracking model for the top-down cracking analysis was substantial. This permitted to predict higher damage at early age than it was done by the AASHTO M-E model. An increase in the initial non-dimensional slab-base friction factor, L*, from the default value of 0.1 to 1000 lead to under-predicting cracking. LTPP project 4-0217 is used to illustrate the ability of the alternative model to account for user-defined monthly data describing the slab-base interface. The following cases for the non-dimensional friction parameter, Λ*, were considered:  Case A: A constant through the entire performance period value of 0.001  Case B: A constant through the entire performance period value of 1000  Case C: For the first 12 years, a constant value of 1000, and a constant value of 0.001 for the remaining time.  Case D: Equal to 10 in January and February; 0.1 in March, April, and May; 0.001 from June through September; and 1 in October, November, and December. This pattern was repeated for every year during the analysis period. The first case describes the fully unbonded interface condition during the performance period, the second case corresponds to the fully bonded interface condition, the third case shows the loss of friction after 120 months in the AASHTO M-E model, and the last case illustrates an ability of the software to handle non-monotonic changes in non-dimensional friction. Figure 39 presents the results if these analyses along with the performance prediction using the default model as well as the observed cracking of this section. It can be observed that the use of very low friction (case A) resulted in the highest predicted cracking. The use of very high friction (Case B) resulted in some predicted cracking. This is an improvement over the AASHTO M-E model with the bonded interface that predicted no cracking over the entire design life (see Figure 38a). Cases C and D resulted in intermediate cracking between the cases approaching fully unbonded and fully bonded cases A and B, respectively. Finally, the default model resulted in predicted cracking slightly lower than that from the unbonded case. 0 10 20 30 40 50 60 70 80 90 100 0 48 96 144 192 240 %  Sla bs  Cr ac ke d T ra ns ve rs el y Age (mo) AASHTO, unbonded AASHTO, LOF=120 AASHTO, bonded LTPP Observations 0 10 20 30 40 50 60 70 80 90 100 0 48 96 144 192 240 %  Sla bs  Cr ac ke d T ra ns ve rs el y Age (mo) LTPP Observations Alternative Model, L*=0.1 Alternative Model, L*=1000

Fig ure 39. LTPP 4-0217 performanc 68 e prediction given user-defined friction data