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2 CHAPTER 2 RESEARCH APPROACH 2.1 INTRODUCTION The first rigid pavements, constructed of Portland cement concrete (PCC), were placed directly on the subgrade (Ahlvin, 1991; Fitch, 1996). Base layers were later introduced to avoid pumping as the subgrade eroded, not to provide structural support (Gage, 1932). Thus, early models of slab response treated the pavement as a slab on grade and discounted the base layer entirely (Westergaard, 1926). In this representation, important factors to pavement behavior are the elastic modulus of the PCC slab, the thickness of the PCC slab, and the modulus of subgrade reaction, or k-value. With an increase use of the base courses, the concept of increasing (or âbumpingâ) the k- value to account for the structural contribution of the base layer was introduced. This concept adjusts the k-value based on the thickness of the base and stiffness of the base material. This concept was incorporated into the Portland Cement Association (PCA) design procedure (Packard, 1984) and AASHTO-93 design procedure (AASHTO, 1993), up until recently the most widely used design procedures for rigid pavements. This approach leads to a composite k- value that accounts for both subgrade and base, and for certain base materials (such as chemically stabilized bases) the approach leads to extremely high k-values. Table 1 presents an example of k-values recommended by the PCA design procedure. These high composite k-values may not represent actual behavior, particularly when the pavement is subjected to thermal loads. Table 1. Design moduli of subgrade reaction for pavements with untreated and treated base layers [from Packard (1984)] Subgrade k-value, pci Untreated subbase k-value, pci Cement-treated subbase k-value, pci 4 in 6 in 9 in 12 in 4 in 6 in 8 in 10 in 50 65 75 85 110 170 230 310 390 100 130 140 160 190 280 400 520 640 200 220 230 270 320 470 640 830 In addition, research beginning with Goldbeck (1924) addressed the idea that friction between the slab and the base layer may affect the slab response. This field of pavement research is extensive, and includes push-off testing, erosion testing, brush testing, etc. of various base materials or combinations of slab and base materials. The result of these tests is typically a parameter quantifying some level of friction or erosion. While this parameter may be included in models for joint behavior (opening/closing and faulting) in JPCP (Darter, 1977) and crack spacing in CRCP (Ma and McCullogh, 1975; McCullogh et al, 1977), this parameter is ignored by structural modeling parameters that use the composite k-value. Structural models considered the effect of friction on the bending of a slab on a base layer. Traditionally they considered two conditions: âfully bondedâ (wherein displacements in the layers near the interface are identical) or âfully unbondedâ (wherein vertical displacements at the interface are identical and horizontal displacements in the layers are independent across the interface) (Tabatabaie et al, 1979; Ioannides et al, 1992; Khazanovich, 1994). In these models, the bond condition, the base layer thickness, and the base elastic modulus all contribute to the overall flexural stiffness and response of the pavement system to loading. This representation of the pavement behavior allows for an understanding of its response to wheel loads, however it
3 does not adequately represent the behavior of the pavement between these bond condition extremes. The characterization of slab-base-foundation interaction extends beyond friction, bond, and vertical support; it includes the concept of built-in curl, a concept proposed by Eisenmann and Leykauf (1990). Built-in curl refers to a stress-free state induced by a thermal gradient through a concrete pavement, and it can have significant effects on the slab shape and slab-base contact conditions under loading. While theoretically supported, field studies have illustrated that built-in curl is difficult to quantify as a property of a given pavement (Yu et al, 1998; Rao, 2005). The AASHTO M-E procedure for rigid pavement design and analysis, in determining the slab response to wheel and thermal loads, utilizes all of the modeling features characterizing slab-base interaction that are discussed above: a composite k-value, a binary bond condition, and the built-in curl concept (AASHTO, 2008). In spite of these features to characterize the slab-base interface, it has important limitations. For example, AASHTO M-E does not consider gradual changes in bond or built-in curl over the pavement service life and the influence of these changes on pavement performance. The omission of these factors from consideration could lead to an under designed or over designed pavement structure. The research approach is thus designed to (a) characterize slab-base interaction, (b) identify the factors that influence the interaction between the slab and base layer, (c) evaluate models for slab-base interaction and pavement performance, and (d) develop an improved mechanistic-empirical model that considers slab-base interaction in the design and analysis of concrete pavements. 2.2 ASSESSMENT OF SLAB-BASE INTERACTION STUDIES This section summarizes available (1) studies on and (2) state-of-the-art evaluation methods for the characterization of slab-base interaction. Popular laboratory tests to characterize the interaction of the slab and base in terms of erosion or friction were reviewed along with the studies of full-scale pavement data that inferred slab-base interaction behavior (such as bonding or built-in curl) to explain observed pavement behavior. 2.2.1 Laboratory studies on slab-base interaction Laboratory studies have used various tests to examine the friction between the slab and base to estimate the horizontal opening and closing of joints due to thermal contraction and crack formation in Continuously Reinforced Concrete Pavements. One popular friction test is the push- off test, which involves the controlled displacement and measurement of a slab across a base. The historical extent of push-off testing can be appreciated through Wimsatt and McCullough (1989) or Lee (2000), the latter of which summarizes 68 different push-off tests. The final goal of these studies is to examine friction parameters relative to various conditions, most notably the influence of base material on friction at the slab-base interface, as in Wimsatt et al. (1987) or Tarr et al (1999). However, more recent laboratory tests of friction that use cyclical, push-off loading show that the slab-base interface degrades to a near-frictionless state within a few load cycle applications (Figure 1). These studies imply that the long-term behavior is effectively frictionless (Suh et al, 2004; Li et al, 2013).
Figure Erosion r base laye reviewed test, jettin performe cylinder of the rot test for er standard 1996). In original s A (2009). U directly t confinem resistanc interactio 2.2.2 O Data from Term Pav full-scale interactio 1. Effective esistance of r below con to assess th g test, brus d by placing filled with w ational test osion is the load or pres erosion test pecimen an more recen nlike many o a specime ent. The tria e to degrada n for structu bservation accelerate ement Prog pavement b n is made d loss of bond base materi crete pavem e erodibility h test, and S a sample te ater. (Bhatt device that c brush test, w sure applied s, erosion is d the eroded t variant on erosion test n of stabilize xial test, lik tion in a gen ral and pav s of slab-ba d pavement ram (LTPP) ehavior. Th ifficult by th slab-base et al is an imp ent may lea of base/sub outh Africa st specimen i et al, 1996 an evaluate hich acros to specimen quantifies b specimen a brush/erosio s, the triaxia d base mate e other eros eral sense; h ement perfo se interacti testing prog were consu e use of full e need to is 4 interface af al, (2013)] ortant perfor d to pumpin base materi erosion test in a relativ ). The jettin non-cohesiv s all variants of base ma y calculatin fter testing. n tests is th l test uses a rial in contr ion tests, is owever it d rmance mod on using ful rams using h lted to addr -scale pavem olate behavi ter less tha mance-relat g, loss of su als included . A rotation ely stationar g erosion te e soils. (PIA can be desc terial (Dem g the differe e triaxial tes concrete sp olled loadin valuable wh oes not read eling. l-scale pave eavy-vehic ess the effec ent data to or related to n two load ed property pport, and f the rotation al shear dev y position w st device is RC, 1987) ribed as a b psey, 1982; nce in the w t described ecimen (ins g under tria en evaluatin ily characte ment data le simulator t of slab-ba investigate slab-base in cycles [from . Erosion of aulting. The al shear dev ice test is ithin a rotat a modificati . One comm rush under a Bhatti et al, eight of the by Jung et a tead of a bru xial g base rize slab-ba s and the Lo se interactio slab-base teraction fr Li the tests ice ing on on l sh) se ng- n on om
5 behavior due to temperature response, loading, creep effects, existing damage, etc. That is, the analyses lack a control against which slab-base interaction may be identified. Some of the studies reviewed controlled pavement design and loading in such a way as to allow observations on behavior according to base type. In accelerated pavement testing of jointed plain concrete sections in California, Rao and Roesler (2005) observed that slabs on unbound bases had generally higher permanent deformations over those with stabilized bases. Cervantes and Roesler (2009) later observed in accelerated testing of jointed plain concrete pavements that slabs on unbound bases failed earlier than those on bound bases. Similarly, using data from instrumented pavements at the Denver International Airport, Rufino et al (2004) observed seasonal effects contributing to changes in slab-base contact; these effects led to slabs with unbonded or partially bonded interfaces responding similarly to fully bonded slabs. Furthermore, Rufino et al (2004) observed that slab-base interaction is a combination of slab-base contact and friction, and that full friction/fully bonded interfaces are not required to produce slab responses similar to that of a fully bonded interface. Many full-scale pavement studies reviewed addressed the need to characterize the PCC slab foundation contact condition in the absence of external axle and temperature loading. . While the classical Westergaard theory assumes that in the absence of external loading, the slab remains flat and in full contact with the foundation. The slab geometry, or slab shape, indirectly refers to built-in curl. Characterizing built-in curl through pavement testing has been proposed by measuring gaps in downward curled slabs (Dong et al, 1998), estimation using slab responses from FWD or HWD loading (Rao, 2005), or surface profile data (Yu and Khazanovich, 2001). The parameter remains difficult to estimate using full-scale data; ideally built-in curl represents the temperature differential present at the time the concrete slab hardens after placement (Yu et al, 1998). It has been hypothesized that pavement profilometer data can be used to examine the effect of pavement features (including slab-base interaction) on slab curvature (Byrum, 2000). The estimation of slab curvature, or profile, may provide insight on the slab built-in curl and/or slab foundation support conditions. Thus, methods to use profilometer data to characterize slab- base interface behavior are of interest. Methods to estimate slab profile from profilometer data include the end-slope method (Byrum 2000; Byrum 2009) and curve-fit methods (Chang et al, 2008). Karamihas and Senn (2012) introduced the pseudo-strain gradient approach, a refinement of the curve-fit method, to account for the curvature of a slab profile (and for a section in a gross average). The methods reviewed each require significant conditioning and/or selection of the profilometer data prior to analysis. Furthermore, the analysis requires additional nuance and effort, such as imposing joint locations upon the data to later fit slab deflection profile curves to the conditioned profile data. Given the importance of assessing slab contact conditions and possibly built-in curl in characterizing slab-base interaction, the research approach included the development of an automated analysis method for in-situ profile data to quantify slab profile in JPCP sections. 2.3 EFFECT OF SLAB-BASE INTERACTION ON IN-FIELD PAVEMENT PERFORMANCE A review of available literature and analysis of available data was conducted to identify in-situ pavement features related to slab-base interaction that affected pavement performance. This
6 analysis focused on (a) the effect of base type on pavement performance and (b) the effect of base type on structured responses. 2.3.1 Effect of base type on pavement performance Khazanovich et al (1997) analyzed data from LTPP test sections to identify design and construction features that lead to good and bad performance in rigid pavements. This study considered the effect of both base type and elastic modulus on performance. It was observed that. JPCP with stabilized bases had significantly lower IRI when compared against pavements with unbound bases. On the other hand, JPCP sections with granular bases and asphalt stabilized bases were observed to have a significantly lower percentage of cracked sections than JPCP sections with cement-treated or lean concrete bases. A more direct evaluation of the effect of the base layer on pavement performance was conducted using performance data from the LTPP Special Pavement Study (SPS-2). The SPS-2 experiment examines the effect of important pavement properties on the long-term performance on full-scale JPCP sections located in 12 states. Properties isolated for study include: ï· 8â or 11â slab thickness; ï· unbound aggregate base (AGG), lean concrete base (LCB), or permeable stabilized asphalt base (PSAB) materials; ï· 14-day concrete flexural strength values of 550 psi or 900 psi; ï· presence or lack of drainage; ï· climate region: dry-freeze, dry-no freeze, wet-freeze, and wet-no freeze; and ï· 12â or 14â lane widths. Regular monitoring of the SPS-2 sections provides response and performance data for pavement research. This research expanded the summary of LTPP Special Pavement Study (SPS) JPCP sections initiated in Jiang and Darter (2005) using the January 2014 standard release of LTPP performance data (FHWA, 2014). Based on the analysis of performance data from 196 pavement sections in the SPS-2 experiment, it was observed that sections using asphalt-treated bases outperformed sections using other base types in every regard (faulting, transverse/longitudinal cracking, and IRI). It was also observed that sections using cement-treated bases showed significantly higher transverse and longitudinal cracking than sections using other base types (Figure 2, where âAGGâ refers to aggregate bases, âLCBâ refers to cement-treated bases, and âPATBâ refers to asphalt stabilized bases). This analysis confirms the observations of the made by the earlier study by Khazanovich et al. (1997). At the same time, the performance of pavements with cement-treated bases in the SPS-2 experiment contradicts the expectation of Table 1, where bumping a composite k-value is expected to yield improved performance. This supports the idea that slab-base interaction is complex, as performance is not necessarily improved by base stabilization.
Figure 2.3.2 B The defle structura program, sections u calculatio LTPP da values fro stabilized these sec subgrade 1993 des A deflection designate conducte from the calculate layer. Th the seaso T (2001) co assume in edge, the discussed locations 2. (a) Trans ase layer ef ction respon l capacity, m deflection t sing Falling n of layer m tabase collec m 331 pave bases, only tions, the co reaction is n ign procedu comprehen s was cond d for the Se d more frequ SMP, Khaz d subgrade k is variation nal behavior he research nsidered int terior (or ce exclusive u a differenc (Rufino et a (a) verse crack fect on pav se of the pa aterial prop esting is con Weight De aterial prop ted between ment sectio a small per ntribution o ot as signif res. sive evaluat ucted by Kh asonal Mon ently, abou anovich et a -value, but was pronoun to bond at methodolog erior load F nter) loaded se of interio e in the bina l, 2004), the ing and (b) ement defle vement to a erties, and s ducted peri flectometer erties for rig 1989 and 1 ns showed t centage of th f the base la icant as it is ion of the co azanovich e itoring Prog t 12 to 14 ti l (2001) obs also in the b ced in secti the slab-bas y accounted WD data on basins. Giv r-loaded bas ry bonded/u se studies d 7 longitudin type ctions n applied lo easonal vari odically at G (FWD). Kh id pavemen 997. An an hat although e sections e yer toward a assumed by mbined effe t al (2001) f ram (SMP). mes per yea erved season ackcalculate ons using ce e interface d for the fact ly, as conve en the com ins may not nbonded ch id not exam al cracking ad is an imp ations of the eneral Pave azanovich e ts using the alysis of the a significan xhibited ve n increase i the PCA (P ct of the ba or sections In the LTPP r. Using a la al variation d flexural s ment-treate uring the tim that studies ntional back plex slab-ba be appropri aracterizatio ine effects d (b) in SPS-2 s ortant indic pavement. ment Study t al. (2001) deflection b reported ba t portion of ry high k-va n the effecti acker, 1984 se layer and of the LTPP SMP, FWD rge database not only in tiffness of th d base. This e of FWD such as Kha calculation se interactio ate. While o n at the cen ue to locati ections by b ator of the In the LTPP (GPS) and conducted b asins from ckcalculated the section lues. Thus, ve coefficie ) and AASH climate on experiment testing is of FWD da the back e construct study attrib testing. zanovich et methods n at the slab ther studies ter and edge on on a larg ase SPS ack the k- s had for nt of TO the ta ed uted al e
8 scale. Thus, the research in this study included the development of a back calculation procedure using edge- or center-loaded data, as backcalculated layer properties at both locations may reveal factors that impact both slab-base interaction and the likelihood of pavement distress. 2.4 EVALUATION OF MODELS FOR SLAB-BASE INTERACTION AND PAVEMENT PERFORMANCE Two types of models were considered: pavement performance models that account for slab-base interaction and mechanical models of the friction between the slab and base layer. The performance models use parameters and coefficients that relate to one or more of the friction models reviewed. Only the AASHTO M-E performance models were considered in this study. 2.4.1 Mechanical models for slab-base bending The interaction of the slab and base in bending is described in pavement response and distress models using friction modeling. Available friction models were identified and reviewed. A summary is provided in Table 2. Table 2. Assessment of available friction models Model type Ease of implementation Computationally efficient? Extent of interaction Bonded interface Easy (Currently used in AASHTO M-E) Yes Displacements across interface assumed equal Unbonded, no separation Easy (Currently used in AASHTO M-E) Yes Slip can occur, i.e. horizontal displacements across interface are not equal Unbonded with separation Difficult (Used indirectly in AASHTO M-E though reduction of unit weight of base layer) Yes Slip and separation can occur, i.e. horizontal and vertical displacements across interface are not equal Modified Coulomb friction Requires development No Intermediate between full bond and full slip with separation between layers Simplified friction Included in ISLAB2005, can be included in AASHTO M-E Yes, with modifications to AASHTO M-E discussed below Intermediate between full bond and full slip, no separation between layers The bonded interface model assumes that vertical deflections and horizontal displacements are the same across the slab-base interface. Modeling the two layers as individual plates requires that the composite, two-layer system have one neutral plane. In this model, any cross-section normal to the neutral plane before deformation remains normal to the neutral plane after deformation (Ioannides et al, 1992). The unbonded interface without separation model assumes that, at the slab-base interface, vertical deflections in the layers are the same and shear stresses in both layers are equal to zero. In this model the layers can independently displace horizontally. The multi-layer plate model for this condition requires that the layers have their own neutral planes, located at the mid-depth of each layer (Ioannides et al, 1992). The unbonded model becomes more complex when separation between the plates (or layers) is allowed; in this case, vertical deflections in the layers at the interface can be different, however shear stresses across the interface must be equal to zero. A form of this model, first developed by Totsky, is implemented in the rigid pavement analysis
9 program, ISLAB2005 (Khazanovich and Ioannides, 1994). ISLAB2005 models pavement responses using finite element analysis. For the Totsky model for the behavior of unbonded layers with separation, ISLAB2005 uses independent plate elements for the slab and base layer. Due to the introduction of fictitious springs between plate elements to model behavior, the unbonded with separation model is more computationally demanding than the bonded and unbonded-without-separation models. The Coulomb model assumes that in the multi-layer plate model, the contact surfaces do not slide over each other if the shear stress magnitude is less than the coefficient of friction multiplied by the pressure stress between the two surfaces. In modeling interfacial behavior, sometimes a shear stress limit is prescribed such that, regardless of the normal pressure stress, sliding will occur if the magnitude of the shear stress reaches this value (Ozer et al, 2008). Of the models for slab-base interaction reviewed, the Coulomb model is the most rigorous yet also the most computationally demanding, given that it represents a nonlinear contact problem between the layers. The use of the Coulomb or Modified Coulomb model for individual problems would require the use of three-dimensional finite element modeling. The simplified friction model, like the bonded and unbonded-without-separation models, assumes that the vertical displacements of the slab and base layers at the interface are the same. It also assumes that horizontal displacements at the interface are proportional to the horizontal shear stresses at the interface. (In this arrangement, horizontal shear stresses are conventionally attributed to friction.) In a multi-layer plate model, the location of the neutral plane in each layer depends on the degree of friction between the layers: ï· If the friction is very low, then the neutral plane of each layer is located near its mid- depth location, as in the unbonded interface model. ï· If friction is very high, then the model behaves similar to the bonded interface model, wherein the location of the neutral plane for the layers is the neutral plane for the composite system. Thus, the simplified friction model is an intermediate model between the bonded and unbonded interface models that are currently implemented in the AASHTO-ME procedure. The simplified friction model is a popular layer interaction model for various pavement applications. It is implemented in ISLAB2005 (Gotlif and Khazanovich, 2002) for the analysis of rigid pavements, and it has also been utilized by layered elastic programs such as BISAR, JULEA, LEAF, and MnLayer (De Jong et al. 1979; Uzan 1994; Hayhoe 2002; Khazanovich and Wang 2007). Given its popularity and the ease with which it can be adopted to research needs, the research approach adopted the simplified friction model to represent slab-base interaction in the developed models for pavement performance. 2.4.2 AASHTO M-E procedure and slab-base interaction The AASHTO M-E procedure was evaluated to identify characterization of the slab-base interaction in the AASHTO methodology, and its effect on predicted pavement performance. The composite k-value of the foundation support; initial contact conditions between the slab and foundation (built-in curl, or the permanent curl/warp effective temperature difference); and pavement performance modeling are discussed below.
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Figure 126.96.36.199 D As discu distress p there are Three pe model fo model fo Transver framewo cracking where CR and FD i where where n i type, load (respectiv 5. Sensitivit istress mode ssed, both E rediction ac features rela rformance m r JPCP proje r JPCP proje se cracking rk, it was ne model, whic Ü¥Ü´ àµ is percent s total bottom Ü¨Ü¦ s the applie level, equi ely); and N y of LTPP ling for JPC -to-k and sla ross all JPC ting to slab odels consi cts, the crac cts. and loss of f cessary to fu h is express Ü¥à¬µ Ü¥à¬¶ àµ Ü¥à¬· â slabs transve -up and to àµà·Ýà¯,à¯,à¯,à¯ à¯Ü°,à¯,à¯,à¯ d number of valent temp is the allow Project 04- par P and CRC b support in P and CRCP -base interac der specific k spacing m riction. To c lly understa ed as Ü¨Ü¦à®¼à°° rsely crack p-down fatig ,à¯ ,à¯¡,à¯¢ ,à¯ ,à¯¡,à¯¢ load applic erature diffe able numbe 12 0213 to slab ameter ïT P projects fluence stru projects. W tion that are effects of sl odel for CR onsider slab nd the form ed, C1 throu ue is calcul ations; indic rence, traffi r of load app support co ctural mode ithin the di specific to ab-base inte CP projects -base effect of the AAS gh C4 are g ated accord es i through c offset, and lications su nditions an ling and con stress predic a given dist raction: the , and the tra s within the HTO M-E J lobal calibra ing to Miner o refer to a hourly truc ch that d built-in c sequently tion models ress model. joint faultin nsverse crac AASHTO M PCP transv tion constan âs hypothes ge, month, a k traffic url , g king -E erse 1 ts, is, 2 xle
13 logàµ« à¯Ü°,à¯,à¯,à¯,à¯ ,à¯¡àµ¯ àµ Ü¥à¯ â á Ü¯Ü´à¯ßªà¯,à¯,à¯,à¯,à¯ ,à¯¡á à®¼à³ àµ Ü£à¬· 3 where Ü¯Ü´à¯ is the PCC modulus of rupture at age i in psi; ßªà¯,à¯,à¯,à¯,à¯ ,à¯¡ is the critical stress for associated indices in psi; and Ca and Cb are calibration constants (AASHTO, 2008). The A3 term is misstated in the documentation for the AASHTO M-E procedure as being equivalent to zero (AASHTO, 2008). Through investigations of this model described in following subsections, it was determined that this term has a value of 0.4371 (ARA, 2004). An analysis of Equations 2 and 3 shows that fatigue damage in JPCP depends on the number of axle load applications and the magnitude of stresses in the concrete slab those loads induce in a combination with temperature curling. The Enhanced Integrated Climatic Model (EICM) predicts the hourly pavement temperature profiles at 11 evenly spaced nodes throughout the slab thickness. The thermal profile is considered alongside differential shrinkage and built-in curling. For each combination of axle loading, axle location, and temperature profile, the following conceptual procedure is followed: 1. Parameters (thickness, radius of relative stiffness, and unit weight) are computed for the equivalent single layer slab that has the same flexural stiffness as the PCC slab and base system. These equivalent-slab parameters depend on the properties of the slab and base (thickness, modulus of elasticity, and unit weight) and the interface condition between the layers (bonded or unbonded). 2. The temperature distribution through the thickness of the PCC layer is split into three components: the constant strain causing component, the linear (bending) strain causing component, and the nonlinear strain (self-equilibrating stress) causing component (Khazanovich, 1994). 3. Using rapid solutions, bending stress in the equivalent slab is calculated. 4. Using a closed-from relationship, bending stresses at the top and bottom of the slab are determined. 5. Self-equilibrating stresses at the top and bottom of the PCC slab are calculated. 6. Total stresses at the top and bottom PCC surfaces are computed by adding bending and self-equilibrating stresses. Steps 1, 2, and 4 are affected by base properties. The effect of the base layer on AASHTO M-E predicted cracking performance was investigated using the LTPP SPS-2 and GPS-3 projects used for the calibration of the AASHTO M-E procedure (Sachs et al, 2014). The investigation used the AASHTO default values of -10ï°F for ïT instead of the non-default values assumed in the AASHTO M-E calibration database. Figure 6 compares the predicted JPCP transverse cracking with LTPP observed cracking by project base type; Figure 6 also presents linear regression statistics for each subset of projects by base type.
Figure 6 For granu in the mo trend pre have line This indi character permanen It (bonded procedur cracking unbonded friction (L F to the LO M-E uses damage a AASHTO this way, (outside o paramete A bonded c . Effect of lar bases, th del. A high sent in the d ar regression cates a lack ization of sl t curl/warp is also impo or unbonded e uses one o in JPCP pro (with no se OF) conce or a given m F paramete the structur nd consequ M-E uses base layer a f built-in cu r. ASHTO rec onditions sh default slab e slope of t R-squared v ata. Regress model slop of fit and m ab foundatio effective tem rtant to not ), as represe f two structu jects: the re paration) in pt. onth of the r. If LOF is al response ently crackin the response nd slab-bas rl, discusse ommended ould be assu support (ï and predi he regressio alue of 0.84 ions for cem es significa odel bias. T n support in perature d e that Steps nted by the ral respons sponse of th terface. The pavement se greater than of a system g. Howeve of a fully u e interaction d above) are in the MEPD med (i.e., L 14 T = -10ï°F) cted perform n line is nea 84 indicates ent-treated ntly less tha herefore, the the AASH ifference, es 1, 2, and 4 a loss of frict es to determ e system wi parameter c rvice life, to the age of th with a fully r, if LOF is nbonded sla contributio characteriz G Manual OF is greate on AASTH ance r a value of that the mo and permea n one, along re is a need TO M-E stru pecially for re affected b ion paramet ine levels of th a bonded ontrolling t predict cra e pavemen bonded slab less than the b to predict ns to JPCP c ed using the of Practice r than the s O M-E resp 1, indicating del describe ble asphalt-t with low R to consider ctural mod stabilized b y the interf er. The AAS damage an slab-base in his concept cking AASH t in months, -base interf pavement a damage and racking per loss of frict (AASHTO, ervice life) f onse mode a lack of b s 84% of th reated base -squared va the els through t ases. ace conditio HTO M-E d consequen terface or fu is the loss o TO M-E lo than AASH ace to calcu ge, then cracking. I formance ion (LOF) 2008) that f or all projec ling ias e s lues. he n tly lly f oks TO late n ully ts
15 except those using cement-treated bases (CTB). In addition, AASHTO recommended that CTB projects be fully unbonded for the entire service life (i.e., LOF = 0). Thus, according to the MEPDG Manual of Practice, slab-base interaction in the AASHTO M-E procedure should be limited to two cases: (A) fully bonded, non-CTB projects or (B) CTB projects with frictionless slab-base interfaces. Intermediate cases, where full bond is lost after a certain number of months, are not recommended. These recommendations are similar to those developed by the Arizona DOT in its local calibration of the AASHTO M-E procedure (Darter et al, 2014). To examine the influence of bond and related parameters on transverse cracking, five JPCP projects with 15-foot joint spacing, a service life of 10 years, and traffic volume of 25000 AADTT were considered: 1. 6-inch JPC over a 4-inch cement stabilized base course with base modulus of elasticity Ebase = 10,000 psi and loss of friction LOF = 0 months (i.e., unbonded over the service life) 2. 6-inch JPC over a 4-inch cement stabilized base course with Ebase = 10,000 psi and LOF = 120 months (i.e., fully bonded over the service life) 3. 6-inch JPC over a 4-inch cement stabilized base course with base modulus of elasticity Ebase = 4,000,000 psi and loss of friction LOF = 0 months (i.e., unbonded over the service life) 4. 6-inch JPC over a 4-inch cement stabilized base course with Ebase = 4,000,000 psi and LOF = 60 months (i.e., unbonded for half of the service life, fully bonded otherwise) 5. 6-inch JPC over a 4-inch cement stabilized base course with Ebase = 4,000,000 psi and LOF = 120 months (i.e., fully bonded over the service life) These unrealistically high and low elastic properties of the cement stabilized base layer were selected intentionally to highlight the influence of the base layer and interface properties on the predicted cracking. Additional project settings were assumed to eliminate the influence of climate and shrinkage, thus the five projects are subject to identical loads and vary only in base layer stiffness and slab-base interaction (bonding, controlled here through LOF). The cracking results from these four cases are shown in Figure 7. When the base is less stiff, as in Figure 7a, the influence of bond is negligible and the predictions are nearly identical. When the base is very stiff, as in Figure 7b, bond controls predicted cracking performance.
(a) Figure The case to unders structura structura loading. to be iden 4-inch JP engineeri The pred Figure 8 The crack interface expectati calculatio performa Projects w 7. AASHTO with a stiff tand slab-ba lly equivalen l equivalenc For this com tical; the pr C system ha ng expectat icted crackin . Cracking ing perform model for th ons. Thus, th n procedure nce, the stud ith Ebase = 1 M-E crac base layer a se interactio t to the 6-in y implies th parison usin ojects use c ve identical ion is that st g performa performan ance in bot e slab-base is study rec . Given AA y investigat 0,000 psi king predic and lo nd full bond n in AASH ch JPC on 4 at the system g AASHTO ustom clima temperatur ructurally eq nce of these ce of struct M-E h Figure 7 a interface le onsidered th SHTO reco ed (1) altern 16 (b) P tions for fo ss of frictio (âBonded, TO M-E. Co -inch base b s respond i M-E, prop te files so th e gradients t uivalent sy two using A urally equiv procedure nd Figure 8 ads to predic e slab-base mmendation ative mode rojects wh ur projects n Ebase = 4M nsider a 10 onded, very dentically un erties in the at the 10-in hrough the p stems perfor ASHTO M alent JPCP suggest that ted crackin interface m s and the di ls for slab-b ere Ebase = 4 with varied â) can be fu -inch JPC pr stiff base p der wheel a slab and ba ch JPC syst avement sy m identicall -E is shown projects i the AASHT g that does n odeling in th scussed exa ase interacti ,000,000 p base stiffn rther examin oject that is roject, wher nd thermal se were sele em and the 6 stem. The y in crackin in Figure 8 n the AASH O M-E bon ot conform e JPCP stre mple of crac on in the si ess ed e cted -on- g. . TO ded to ss king
17 existing AASHTO M-E framework and (2) incorporating these models into JPCP transverse cracking predictions. Joint faulting, erodibility, and base LTE. The AASHTO M-E JPCP faulting has a complex form (AASHTO, 2008), expressed in Equations 4 through 10 below: Ü¨Ü½ÝÝÝà¯ àµà·âÜ¨Ü½ÝÝÝà¯ à¯ à¯àà¬µ 4 âÜ¨Ü½ÝÝÝà¯ àµ Ü¥à¬·à¬¸ â Ü¦Ü§à¯ â áºÜ¨Ü£Ü·Ü®Ü¶Ü¯Ü£ à¯Üºà¬¿à¬µ àµ Ü¨Ü½ÝÝÝà¯à¬¿à¬µá»à¬¶ 5 Ü¨Ü£Ü·Ü®Ü¶Ü¯Ü£Üºà¯ àµ Ü¨Ü£Ü·Ü®Ü¶Ü¯Ü£Üºà¬´ àµ Ü¥à¬» â Ü¥à¬¹à¬º â à·Ü¦Ü§à¯ à¯ à¯àà¬µ 6 Ü¨Ü£Ü·Ü®Ü¶Ü¯Ü£Üºà¬´ àµ Ü¥à¬µà¬¶ â Ü¥à¬¹à¬º â ßà¯à¯¨à¯¥à¯ â Ü®ÝÝ àµ¬ à¬¶Ü²à¬´à¬´ â Ü¹ÝÝÜ¦Ü½ÝÝÝà¯¦ àµ° à®¼à°² 7 Ü¥à¬¹à¬º àµ Ü®ÝÝáº1 àµ Ü¥à¬¹ â 5à®¾à¯à¯à®½á»à®¼à°² 8 Ü¥à¬µà¬¶ àµ Ü¥à¬µ àµ Ü¥à¬¶âÜ¨Ü´à°° 9 Ü¥à¬·à¬¸ àµ Ü¥à¬· àµ Ü¥à¬¸âÜ¨Ü´à°° 10 where Ü¨Ü½ÝÝÝà¯ ï® Mean joint faulting at the end of month m, inches âÜ¨Ü½ÝÝÝà¯ ï® Incremental change (monthly) in mean transverse joint faulting during month i, inches Ü¨Ü£Ü·Ü®Ü¶Ü¯Ü£ à¯Üº ï® Maximum mean transverse joint faulting for month i, inches Ü¨Ü£Ü·Ü®Ü¶Ü¯Ü£Üºà¬´ ï® Initial maximum mean transverse joint faulting, inches Ü§Ü´Ü±Ü¦ ï® Base/subbase erodibility factor Ü¦Ü§à¯ ï® Differential density of energy of subgrade deformation accumulated during month i Ü¨Ü´ ï® Base freezing index defined as percentage of time the top base temperature is below freezing (32Â°F) temperature à¬¶Ü²à¬´à¬´ ï® Percent subgrade material passing #200 sieve Ü¹ÝÝÜ¦Ü½ÝÝ ï® Average annual number of wet days (greater than 0.1 inch rainfall) Ýà¯¦ ï® Overburden on subgrade, pounds ßà¯à¯¨à¯¥à¯ ï® Maximum mean monthly slab corner upward deflection PCC due to temperature curling and moisture warping Ü¥à¬µ. . . Ü¥à¬» ï® Global calibration constants The AASHTO M-E joint faulting model accounts for the effect of base layer on the faulting prediction through the erodibility factor and the differential energy parameter. The increment of differential energy, DEi, for month i, is defined as Ü¦Ü§à¯ àµ Ý2 áºÝà¯ àµ Ýà¯à¯ á»áº Ýà¯ àµ Ýà¯à¯ á» 11 where k is the modulus of subgrade reaction and wL and wUL are the respective deflections at the corner of a loaded and unloaded slab. The PCC slab corner deflections depend on the base
propertie slab expe (2) the co between joint load T investiga M-E proc observed subset of Figure In genera the mode for each r for granu model wa Punchout per mile associate s (thickness riences the ncrete slab the slab and transfer eff he effect of ted using th edure (Sach faulting by projects by 9. AASTHO l, the slope l toward ove egression in lar sections. rranted a re s and crack at a given ag d load repet Ü²Ü± and stiffnes largest relati is often lifte the base in iciency used the base lay e LTPP SPS s et al, 2014 project base base type. M-E fault LTP of the regres r prediction dicate that t In general, consideratio spacing. Ac e are a func itions), expr àµ Ü¥31 àµ Ü¥4 â Ü¨ s) and the lo ve displacem d from the b the model is in the AAS er on AASH -2 and GPS ). Figure 9 type; Figur ing predict P calibratio sion lines fo of faulting he model pr the lack of f n of the effe cording to t tion of the c essed as Ü¦à®¼à¬¹ 18 ad transfer ent with re ase due to c assumed to HTO M-E a TO M-E pr -3 projects u compares th e 9 also pres ed perform n sections b r each base by 20 to 30 esents, at be it and mode ct of the ba he AASHTO umulative f efficiency o spect to the urling and w be unbonde nalysis dep edicted fault sed for the c e predicted j ents linear r ance relativ y base typ type show t percent. Lik st, 59% of t l bias presen se layer on f punchout m atigue dama f the joint. A base layer n arping, the d. On the ot ends on the ing perform alibration o oint faultin egression st e to observ e he presence ewise, the R he trend pre t in the JPC aulting perf odel, the t ge at the giv s (1) the PC ear the join interface her hand, th base proper ance was f the AASH g with LTPP atistics for e ed faulting of slight bi -squared te sent in the d P faulting ormance. otal punchou en age (and C t and e ties. TO ach for as in sts ata ts 12
19 where PO is punchouts per mile, C3 through C5 are global calibration constants, and FD is total fatigue damage determined using Minerâs hypothesis Ü¨Ü¦ àµà·Ýà¯,à¯ à¯Ü°,à¯ 13 where n is the applied number of load applications; indices i and j refer to age and load level, respectively; and à¯Ü°,à¯ is the allowable number of load repetitions at age i and load magnitude j such that logàµ« à¯Ü°,à¯àµ¯ àµ Ü¥à¯ â áÜ¯Ü´à¯ßªà¯,à¯ á à®¼à³ àµ 1 14 to determine N given Ü¯Ü´à¯ the slab modulus of rupture at age i in psi; ßªà¯,à¯, the critical stress at time increment i due to load magnitude j in psi; and calibration constants Ca and Cb (AASHTO, 2008). The stress calculation procedure in AASHTO-ME for CRCP pavement assumes presence of a void and the edge of the CRCP panel, therefore the interface between the PCC layer and the base is assumed to be unbonded. However, the critical stress ßªà¯,à¯ is further dependent on both the CRCP mean crack spacing model and CRCP crack width model, which are expressed as Ü®à´¤ àµ à¯§Ý àµ Ü¤à¯à¯¨à¯¥à¯ßªà¬´ àµ¬1 àµ 2Ü¦à¯¦à¯§à¯à¯à¯Ýà¯à®¼à®¼ àµ° Ý 2 àµ Ü·à¯ à¯¦Ü²à¯§à¯à¯à¯Ü¿à¬µÝà¯ 15 Ü¿Ý àµ Ü¯Ü£ÜºàµÜ®à´¤ â Ü¥à¯ â àµ¬ßà¯¦à¯à¯¥ àµ ßà¯à®¼à®¼ß à°Ü¶ àµ Ü¿à¬¶ßªà¯ à¯¢à¯¡à¯Ü§à¯à®¼à®¼ àµ°àµ± 16 where Ü®à´¤ ï® Mean crack spacing based on design crack distribution, inches à¯§Ý ï® Concrete indirect tensile strength, psi Ý ï® Base friction coefficient Ü·à¯ ï® Peak bond stress, psi à¯¦Ü²à¯§à¯à¯à¯ ï® Percent longitudinal steel Ýà¯ ï® Reinforcing steel bar diameter, inches Ü¿à¬µ ï® First bond stress coefficient ßªà¯à¯¡à¯© ï® Tensile stress in the PCC due to environmental curling, psi Ýà¯à®¼à®¼ ï® Slab thickness, inches Ü¦à¯¦à¯§à¯à¯à¯ ï® Depth to steel layer, inches ßªà¬´ ï® Westergaardâs nominal stress factor based on PCC modulus, Poissonâs ratio, and unrestrained curling and warping strain Ü¤à¯à¯¨à¯¥à¯ ï® Bradburyâs curling/warping stress coefficient
An analy Thus this punchout In was inve procedur punchout presents Figure A challen generally Ü¿Ý ßà¯¦à¯à¯¥ ßà¯à®¼à®¼ Î à°Ü¶ Ü¿à¬¶ ßªà¯ à¯¢à¯¡à¯ Ü§à¯à®¼à®¼ Ü¥à¯ sis of Equat study re-ev predictions addition, th stigated usin e (Sachs et a s by project linear regres 10. AASTH ge of the G fail in punc ï® Averag ï® Unrestr ï® PCC co ï® Drop in temper ï® Second ï® Maxim ï® PCC el ï® Local c ion 5 shows aluated both . e general ef g the LTPP l, 2014). Fig base type g sion statistic O M-E pre c PS-5 calibra houts; of th e crack wid ained concr efficient of PCC tempe ature at the d bond stress um longitud astic modulu alibration c that the cra this parame fect of the b GPS-5 proj ure 10 com iven 355 ob s for each s dicted pun alibration s tion dataset e 355 total o 20 th at the dep ete drying s thermal exp rature from epth of the coefficient inal tensile s, psi onstant (CC ck spacing d ter and its i ase layer on ects used fo pares the pr servations fr ubset of pro chouts relat ections by b is that CRC bservations th of the ste hrinkage at ansion, /ï°F the concret steel for con stress in PC = 1 for the g epends on t nfluence on AASHTO r the calibra edicted pun om 103 GP jects by bas ive to obse ase type P sections in , only 65 of el, mils steel depth, e âzero-stre struction m C at steel le lobal calibr he base frict the AASHT M-E predict tion of the A chouts with S-5 sections e type. rved punch the LTPP those observ microstrain ssâ onth, ï°F vel, psi ation) ion coeffici O M-E ed punchou ASHTO M LTPP obser . Figure 10 outs for LT database do ations reco ent. ts -E ved also PP not rd
non-zero AASHTO ability of Whereas improve address i 2.5 R The follo using pav character and analy 2.5.1 C Characte edge- and 188.8.131.52 B As discu accounte of subgra to the po interactio conventio into slab for other developm FWD bas base type Figure The deve procedur Westerga punchouts p M-E calib the model t previous ca model fitnes ssues with la ESEARCH wing subsec ement data ized slab-ba sis. haracteriza rization of s center-load ase layer an ssed above, d for the eff de reaction. ssibility that n may vary nal FWD b behavior an locations (m ent of a pro ins and com s. 11. Meshes loped modif e for rigid p ardâs solutio er mile. Fur ration datab o capture pu libration eff s, consideri ck of fit and METHODO tions descri and (b) deve se interactio tion of slab lab-base inte ing as well d composite many pavem ect of base l Studies suc slab behavi with contac ack calculat d possibly s ost notably cedure to ba paring the b (a) and load l deve ied back ca avements (K n for an inf thermore, o ase, 31 of th nchout beha orts have lim ng the effect model bias LOGY be the meth lop alternat n for the AA -base inter raction in th profilomete k-value ent design p ayer on pave h as Khazan or may vary t conditions ion methods lab-base inte the slab edg ckcalculate ackcalculat ocations for loped back lculation pro hazanovich inite slab on 21 f the 65 non ose observa vior is com ited the cal of the base . odology (A) ive perform SHTO M-E action is project w r data collec rocedures, ment perfor ovich et al ( based on lo at a location , which use raction, no e). Thus, th layer prope ed k-values (a) center- calculation cedure exte et al., 2001 a Winkler -zero punch tions origina promised, a ibration to s layer on pu to characte ance predict procedure as evaluate ted in the L including A mance thro 2001) and R cation. In a (e.g., edge interior FW similar back e research a rties from b from the adj and edge-l procedure nds the LTP ). The Best F foundation, out observa te from 3 se s shown in F ubsets of th nchout pred rize slab-bas ion models for rigid pa d using FWD TPP databas ASHTO M- ugh adjustin ufino et al curled slab, versus inter D data only calculation pproach inc oth edge- an acent sectio (b) oading sim P Best Fit b it procedur loaded by a tions in the ctions. Thu igure 10. e GPS-5 dat iction may a e interactio to account f vement desi basins for e. E, have g the coeffi (2004) point slab-base ior). While , provide ins method exi luded the d center-loa ns with diff ulations in t ack calculat e is based o uniform s the a to lso n or gn cient ed ight sts ded erent he ion n
22 pressure distributed over a circular area. This solution relates the deflections of FWD sensors with the applied FWD load and pavement system properties as follows: ÝáºÝà¯á» àµ ÝÝ à¯Ý á Ü½ â , Ýà¯ âá 17 where ÝáºÝà¯á» is the deflection of sensor i, k is the modulus of subgrade reaction; p is the applied pressure; and à¯Ý is a non-dimensional function relating ri, the distance from the center of loaded area to sensor i, and a, the radius of a FWD load plate, given â, the radius of relative stiffness of the pavement. The back calculation of layer properties given FWD basins at the slab edge is a more complex problem than the interior method. Back calculation procedures using edge basins must consider the influence of the shoulder joint, thus interior assumptions are invalid. As a result, the developed back calculation procedure for edge basins uses ISLAB2005 finite element simulations to generate a database of deflection basins for center- and edge-loaded slabs (Figure 11). Using the similarity procedure utilized in the development of rapid solutions under the NCHRP 1-37A study (Khazanovich et al., 2001; ARA, 2004), the deflections of the pavement system shown in figure 8 can be presented in the following form: ÝáºÝà¯á» àµ ÝÝ à¯Ý á Ü½ â , Ýà¯ â , Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá â¡ Ý Ý à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá» 18 where LTEx and LTEy are load transfer efficiency values for the longitudinal (shoulder) and transverse joints, respectively. The Best Fit method requires finding a set of a radius of relative stiffness and coefficient of subgrade reaction that minimize the discrepancy between the measured deflections Wi and computed deflections. If the error function is defined as Ü§ÝÝÝÝáºâ, Ýá» àµà·áÝÝ à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá» àµ à¯Ü¹á à¬¶à¯¡ à¯àà¬µ 19 then the radius of relative stiffness that minimizes the error function can be obtained by solving the following equations (Khazanovich et al 2001): â à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá» ß² à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá»ß²âà¯¡à¯àà¬µ â áº à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá»á»à¬¶à¯¡à¯àà¬µ àµ â à¯Ü¹ ß² à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá»ß²âà¯¡à¯àà¬µ â à¯Ü¹ à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá»à¯¡à¯àà¬µ 20 and the corresponding subgrade k-value can be computed form the following relationship: Ý àµ Ýâ Ü½à¯áº à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá»àµ¯ à¬¶à¯¡à¯àà¬´ â Ü½à¯à¯¡à¯àà¬´ à¯Ü¹ à¯Ýáºâ, Ü®Ü¶Ü§Ý, Ü®Ü¶Ü§Ýá» 21 Two factorials of ISLAB2005 runs (one for edge loading case and another for an interior loading case) were performed for a wide range of radii of relative stiffness (from 20 inches to 60 inches) and joints load transfer efficiencies (from 10% to 90%). The obtained deflection basins were
23 used to develop rapid solutions for functions fi for FWD sensor locations at 0, 8, 12, 18, 36, and 60 inches from the center of the FWD plate. Those rapid solutions were used to develop an efficient procedure for back calculation of layer properties given FWD basins collected at the slab edge and slab interior using Equations 20 and 21. The developed back calculation procedure was applied to a database of 289,816 individual FWD tests from 208 individual JPCP pavement projects throughout North America, as reported in the LTPP database for SPS-2 and GPS-3 experiments. Backcalculated layer properties were then used to evaluate the effect of base type on backcalculated k-value. The analysis considered LTPP projects with multiple years of FWD data for loading at edge and center locations and multiple observation dates to investigate the effect of the base layer on the backcalculated coefficient of subgrade reaction at the slab edge. This investigation was used to re-evaluate the calculation of the composite k-value in the AASHTO M-E procedure. 184.108.40.206 Effect of slab-base interaction on flexural stiffness As discussed above, the simplified friction model was selected as an alternative to the fully bonded and unbonded interface models currently implemented in the AASHTO M-E procedure. However, to implement this model into performance models for the AASHTO M-E framework, the model is reconsidered. A two-layered model with simplified friction at the interface can be considered through structurally equivalent single layer systems, developed according to the transformed section concept (Ioannides et al, 1992). This concept was originally developed to illustrate the effect of bond in the fully bonded and fully unbonded conditions. The equivalent single layer thickness for a fully unbonded slab, Ýà¯à¯à¯à¯ , and a fully bonded slab, Ýà¯à¯à¯à®» , is described by Equations 22 and 23, where h1 and h2 are the slab and base layer thicknesses, respectively, and E1 and E2 are the slab and base layer Youngâs moduli, respectively. Ýà¯à¯à¯à¯ àµ à¶¨Ýà¬µà¬· àµ Ü§à¬¶Ü§à¬µ Ýà¬¶ à¬·à°¯ 22 Ýà¯à¯à¯à®» àµ à¶¨Ýà¬µà¬· àµ Ü§à¬¶Ü§à¬µ Ýà¬¶ à¬· àµ 12 áÝà¬µ àµ¬Ý àµ Ýà¬µ2 àµ° à¬¶ àµ Ýà¬¶ Ü§à¬¶Ü§à¬µ àµ¬Ýà¬µ àµ Ý àµ Ýà¬¶ 2 àµ° à¬¶ áà°¯ 23 Figure 12 uses an example from Khazanovich and Gotlif (2002) illustrating this concept with an original 2-layer system (9 inches of PCC over 6 inches of lean concrete base material), which corresponds to an effective single layer slab of 9.22 inches if an unbonded interface is assumed and 11.82 inches if a bonded interface is assumed.
24 Figure 12. Transformed section concept (from Khazanovich and Gotlif 2002) While the transformed sections concept is implemented in the AASHTO M-E procedure, its implementation in AASHTO M-E only accounts for fully bonded or fully unbonded interfaces. Khazanovich and Gotlif (2002) generalized the Transformed Section concept for the case of a simplified friction interface. This generalization introduced a coefficient of friction Î for interlayer friction; for small values of Î, the equivalent unbonded thickness shown in Figure 12 is modeled, whereas for large values of Î, the system behaves structurally as a slab with the equivalent bonded thickness. Due to high stiffness of the PCC layer, the FWD deflection basin does not permit back calculation of individual elastic properties of the slab and base layers (E1 and E2). An additional input parameter is needed. Khazanovich et al. (2001) introduced the slab-to-base ratio parameter, Î², describing the ratio of the elastic moduli of the slab and base layers, respectively (i.e., Î²=E1/E2). An alternative approach was proposed to consider back calculation results from multiple days of testing for the same location. From back calculation of each FWD deflection basin, the backcalculated flexural stiffness of the composite system was found using the following relationship Ü¦à¯à¯à¯ àµ âà¬¸Ý 24 where â and k the (the radius of relative stiffness and modulus of subgrade reaction, respectively) are properties that can be determined from back calculation. The analysis assumes that a fully bonded interface can be associated with the maximum value of Deff, whereas a full-slip interface can be associated with the minimum value of Deff. From these two conditions, the elastic moduli of the individual layers, E1 and E2, were determined and the moduli ratio Î² was computed. The calculation of Î* for tests associated with intermediate values of Deff follows a procedure set forth in Khazanovich and Gotlif (2002). As implemented in the corresponding program, it is an iterative procedure for the coefficient of friction, Î. The iteration is governed by the percent error between the estimated effective flexural stiffness, Dest, and the effective flexural stiffness, Deff (Equation 24), where Dest can be expressed as Ü¦à¯à¯¦à¯§ àµ Ü¦à¬µ àµ Ü¦à¬¶ 25 and D1 and D2 are Original slab thickness = 9.2 in LCB Equivalent plate unbonded interface Equivalent plate bonded interface thickness = 6 in PCC thickness = 9 in thickness = 11.82 in
25 Ü¦à¯ àµ Ü§à¯3áº1 àµ ß¤à¬¶á» áºÝà¯ à¬· àµ 3Ýà¯à¬¶Ü¾à¯ àµ 3Ýà¯Ü¾à¯à¬¶á» 26 for layers Ý àµ 1,2, where hi is layer thickness, Ei is layer modulus, and Î¼ is the Poisson ratio (assumed to be equal for the two layers), and where parameters b1 and b2 are defined as Ü¾à¬µ àµ 0.5Ü§à¬¶ âÝà¬¶à¬¶ àµ Ýà¬µÎ Î àµ Ü§à¬¶â àµ Î Î á Îáº0.5Ü§à¬µâÝà¬µà¬¶ àµ Ýà¬µÎá» àµ áºÜ§à¬µâÝà¬µ àµ Îá»áºàµ0.5Ü§à¬¶âÝà¬¶à¬¶ àµ Ýà¬µÎá» Ü§à¬µâÜ§à¬¶âÝà¬µÝà¬¶ àµ Ü§à¬µâÝà¬µÎ àµ Ü§à¬¶âÝà¬¶Î á 27 Ü¾à¬¶ àµ Î áº0.5Ü§à¬µâÝà¬µà¬¶ àµ Ýà¬µÎá» àµ áºÜ§à¬µâÝà¬µ àµ Îá»áºàµ0.5Ü§à¬¶âÝà¬¶à¬¶ àµ Ýà¬µÎá» Ü§à¬µâÜ§à¬¶âÝà¬µÝà¬¶ àµ Ü§à¬µâÝà¬µÎ àµ Ü§à¬¶âÝà¬¶Î 28 and the star notation on E1 and E2 denote Ü§à¯â àµ Ü§à¯1 àµ ß¤à¬¶ 29 The value of Î associated with the minimal error àµ¬à®½à³à³à³à¬¿à®½à³à³à³à®½à³à³à³ àµ° for a given test (applied iteratively) is thus the inferred coefficient of friction. This parameter is nondimensionalized as Îâ àµ ÎÜ§à¬µÝà¬µ àµ Ü§à¬¶Ýà¬¶ 30 In this study, this back calculation procedure was applied for analysis of the FWD data reported for the LTPP SPS-2 section to investigate variation of the apparent friction condition over time. The adoption of simplified friction for slab-interface modeling also allows for the consideration of thermal loading effects at intermediate levels of friction at the interface. Currently the thermal analysis in the AASHTO M-E procedure is valid only for the bond/no bond model. Thus, the analysis utilized backcalculated properties for the LTPP sections reviewed for the base type k-value study to calculate composite slab-base interaction parameters over the observed service lives. This information can be used to develop models to characterize slab-base interaction in pavement response and distress prediction. 220.127.116.11 Built-in curl As discussed above, the temperature gradient present during slab placement leads to a permanently deformed slab profile (Yu et al, 1998). The extent of curl in the slab naturally affects the support conditions for the slab under loading, which in turn affects the slab response and the likelihood of pavement distress. While the reviewed literature discussed methods to estimate slab curling profile, these methods did not lend themselves to large sets of data, and thus did not suit this comprehensive study of slab-base interaction. Thus, the research approach included the development of an analysis method to quickly estimate slab curl from profilometer data with no prior conditioning of the raw data. The developed method is based on the empirical mode decomposition (EMD) process, which was used by similar efforts to review LTPP profilometer data (Franta, 2012). The EMD method decomposes a profilometer signal into successive wavelengths, one of which may correspond to slab curl. The decomposition uses the Hilbert-Huang Transform (HHT) in a manner similar to
Adu-Gya decompo the origin the sum o recombin The deve given sec A decompo within th using inf distance passes in spacing, Figure cu Thus, the informati This shap built-in c interest w and for e entire du 2.5.2 D The AAS performa concrete modifica mfi et al. (2 sition of dat al signal, y( f its intrinsi ed with the ÝáºÝá» loped EMD tion and ob s implied by sition, a seri e larger sign ormation on between loc Figure 13a; and they rep 13. (a) Raw rling from shape of th on on long- e can be ass url. To quan as compute ach section, ration of obs evelopment HTO M-E J nce predicti layer â base tions. 010) and At a from a pro x), and the d c mode func residue, wo àµà· à¯Ü¿áºÝá» àµ à¯¡ à¯àà¬µ method wa servation da Equation 3 es of intrins al: in this an the joint sp al maxima). these IMFs resent upwa (a) profilome three passe e curling pro wave profile ociated with tify this dist d for each a an average ervations w of alternat PCP transv on models w interaction. toh-Okine e filometer pa ecomposed tions, cj(x), uld allow on Ýà¯¡áºÝá» s applied dir te. An exam 1, the origin ic mode fun alysis, the I acing given Figure 13b have period rd curled sl ter data an s of profilo file, shown variation a a distortion ortion, the s nalyzed curl of standard d as determin ive models erse crackin ere reconsi This section 26 t al. (2006). ss, where th signal, resp or IMFs, an e to recover ectly to the ple of raw p al profilom ctions. Cert MF relating the periodic illustrates IM icity that ro abs. d (b) EMD meter on M in Figure 13 nd short-wa of the slab tandard dev ing profile. eviations fo ed. for paveme g and joint f dered in this provides a Equation 31 e left- and r ectively. He d residue, r the origina raw profilom rofile data i eter signal th ain IMFs ca to slab curl ity of the IM Fs decomp ughly corres -decompose arch 30, 19 b, is extrac ve texture w profile caus iation of the The study e r the first y nt perform aulting as w study to im n overview illustrates t ight-hand s re the decom n(x). Thus, th l signal. eter data fo s shown in F us contains n represent p ing profile w F (that is, t osed from t ponds with (b) d signal re 94 on LTPP ted by filter ithin the pro ed by curlin amplitude valuated all ear, the last ance ell as CRCP prove accou of the perfor he ides represen posed sign e IMFs, if r passes on igure 13a. , through hysical fea as identifie he average he original the section j sembling sl 37-0201 ing out filometer d g, including of the IMF o SPS-2 secti year, and fo punchouts nting for mance mod t al is 31 a tures d oint ab ata. f ons, r the el
27 18.104.22.168 Transverse cracking The modified JPCP transverse cracking prediction model to account for slab-base interaction considers all of the inputs in a manner that is nearly identical to the AASHTO M-E procedure. The modified AASHTO M-E damage calculation and performance prediction process closely follows the AASHTO procedure with additional steps to account for the gradual deterioration of the slab-base interaction coefficient Î. The modified procedure for JPCP transverse cracking involved revisions to (a) thermal linearization, (b) stress analysis and damage calculation, and (c) cracking prediction (outputs). Table 3 summarizes the difference in the two models in regards to the estimation of the structural response and damage calculation, where Ï is the critical stress, MR is the modulus of rupture (i.e. the strength criteria), n is the applied load repetitions, and N is the allowable number of load repetitions given changes to the input wheel load, climate, and new slab-base interface parameter. In addition, ï* is the dimensionalized slab-base interface parameter from Equation 30 in Section 2.3.3; P is the load level applied incrementally for a given load type; load type is the axle type (single, tandem, and tridem for bottom-up cracking; short, medium, and long wheelbase for top-down cracking); traffic wander is the load location in the wheel path; ïTL is the linear temperature difference through the equivalent slab; TNL is the nonlinear top or bottom surface temperature; and TNLï±a is the nonlinear surface temperature at characteristic length, a, away from the top or bottom surface of the slab. The use of an exclamation point in Table 3 indicates partial or qualified sensitivity of the response/damage calculation to the input parameter. The slab-base interface influences the structural response calculation of Ï in the original AASHTO model only in terms of loss of friction; furthermore, the nonlinear top and bottom surface temperatures used in the original AASHTO model are exact only for 18-kip loads (ARA, 2004). Table 3. Consideration of relevant items in the original and modified JPCP transverse cracking procedures Original NCRHP 1-37A Procedure Modified Procedure Ï MR n N Ï MR n N Slab-base interface (ï*) ï¡ ï¼ ï¼ P ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ Load type ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ Traffic wander ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ ïTL ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ ï¼ TNL ï¡ ï¡ ï¡ ï¼ ï¼ ï¼ ï¼ TNLï±a ï¼ ï¼ ï¼ ï¼ - handled directly, ï¡ - handled indirectly with limitations Modifications to the stress calculation procedure. The effective thickness heff accounts for the slab-base interaction coefficient Î (i.e. the possibility of partial bond). The procedure results in identical effective slab thicknesses at friction extremes for fully unbonded and fully bonded cases under the original AASHTO M-E JPCP transverse cracking model.
28 Ýà¯à¯à¯ àµ à¶¨12 áº1 àµ ß¤à¬¶á»Ü¦à¯à¯à¯ Ü§à¯à®¼à®¼ à°¯ 32 where Î¼ is the Poisson ratio for the PCC and base layers, EPCC is the PCC elastic modulus, and Deff is the effective flexural stiffness, which is identical to the parameter Dest expressed in Equation 25. Thus, the radius of relative stiffness, â, uses the modified effective thickness heff that considers Î and is â àµ à¶© Ü§à¯à®¼à®¼àµ«Ýà¯à¯à¯àµ¯ à¬· 12Ý á1 àµ àµ«ß¤à¯à¯à¯àµ¯à¬¶á à°° 33 where k is the coefficient of subgrade reaction. Likewise, the effective unit weight of the equivalent slab, Î³eff, now accounts for partial bond at the interface through the slab-base interaction coefficient Î. ßà¯à¯à¯ àµ Ýà¯à®¼à®¼Ýà¯à¯à¯ ßà¯à®¼à®¼ àµ Ýà¯à¯à¯¦à¯ Ýà¯à¯à¯ ßà¯à¯à¯¦à¯ â á Ýà¯à¯à¯ àµ Ýà¯¨à¯¡à¯ Ýà¯à¯¢à¯¡à¯ àµ Ýà¯à¯à¯á 34 where hunb is the effective thickness of the equivalent system when the slab and base are fully unbonded; hbond is the effective thickness of the equivalent system when the slab and base are fully bonded; and Î³PCC and Î³base are the unit weights of the slab and base, respectively. The effective thermal gradient ÎTeff through the equivalent slab accounts for the slab-base interaction coefficient Î (i.e. the possibility of partial bond) Î à¯ Ü¶ àµ 12 áº1 àµ ß¤à¬¶á» Ü§à¬µÝà¯à¯à¯à¬¶ áàµà¶± Ü§à¬µ 1 àµ ß¤à¬¶ ßà¬µáº à¬µÜ¶áºÝà¬µá» àµ à¬´Ü¶á»Ýà¬µ dzà¬µ à¯à°à¬¿à¯à° à¬¿à¯à° àµ ßà¬µÜ§à¬µÝà¬µáº0.5Ýà¬µ àµ Ü¾à¬µá» àµ ßà¬¶Ü§à¬¶Ýà¬¶áº0.5Ýà¬¶ àµ Ü¾à¬¶á»á 35 where parameters b1 and b2 (described in Equations 27 and 28) depend on the properties of the layers. More detail on the modifications to the process that approximates of temperature distributions through the slab can be found in the subsection below. The total linear temperature difference in the equivalent slab, determined as the sum of the permanent and transient temperatures (ÎTL and ÎTp, respectively), is Î à¯Ü¶à¯à¯ àµ Î à¯ Ü¶ àµ ß à¯£Ü¶ 36 The following sub-steps are used to calculate the bending stress in the effective slab. First, Korenevâs non-dimensional thermal gradient, ï¦, is calculated to consider the radius of relative stiffness (â), effective thermal gradient (ÎTeff), effective thickness (heff), and the effective unit weight of the equivalent slab (Î³eff). The modified non-dimensional thermal gradient will then also be influenced by the partial bond through the slab-base interaction coefficient Î
29 ß¶ àµ 2ßà¯à®¼à®¼áº1 àµ ß¤à¯à®¼à®¼á»â à¬¶ Ýà¯à¯à¯à¬¶ Ý ßà¯à¯à¯ Î à¯Ü¶à¯à¯ 37 where hPCC is the PCC slab thickness, ï¡PCC is the PCC coefficient of thermal expansion, and all others are as above. The next sub-step is to compute the adjusted Load-to-Pavement-Weight ratio (i.e., the normalized load). The adjusted load/pavement weight ratio q* accounts for the presence of partial bond at the slab-base interface through the use of the equivalent slab effective thickness (heff) and the effective unit weight of the equivalent slab (Î³eff). Ýâ àµ Ü²ßà¯à¯à¯Ýà¯à¯à¯ 38 where P is the axle weight and all others are as above. The final sub-step to calculate bending stresses is to compute the stresses in the equivalent structure. Using the respective AASHTO M- E neural networks for JPCP projects, the modified procedure computes stresses or deflections in the equivalent structure that have the same radius of relative stiffness, crack spacing, Korenevâs non-dimensional temperature gradient, traffic offset, normalized load ratio, and joint load transfer efficiency. Following the procedure described in ARA (2004), compute stresses at the top and bottom of the slab according to Equation 39. ßªà¯à¯à¯áºß¦á» àµ Ýà¬µßà¬¶âà¬¶ à¬¶ Ýà¬¶ßà¬µâà¬µà¬¶ ßªà¯à¯áºß¦á» 39 While the final sub-step is not modified from its original state, it now accounts for Î given that all previous steps in the structural response and damage calculation have created a normalized equivalent structure that accounts for partial bond through the slab-base interaction coefficient Î. The next step in the modified stress calculation is to determine thermal stresses in the equivalent structure. The nonlinear temperature stress, ÏNL, is defined as ßªà¯à¯ áºÝá» àµ Ü§à¬µßà¬µ1 àµ ß¤ áºÜ¶áºÝá» àµ à¬´Ü¶à¬µá» 40 where T01 is the slab reference temperature and the nonlinear temperature distribution is TN(z) TN(z) is expressed as a function of position, z, through the layer thickness à¯Ü¶áºÝá» àµ Ü¶áºÝá» àµ à¯Ü¶à¬µ àµ à¯ Ü¶à¬µáºÝá» àµ 2 à¬´Ü¶à¬µ 41 and where TL1 is the linear strain temperature through the layer and TC1 is a constant strain temperature through the layer, as expressed below à®¼Ü¶à¬µ àµ à¬´Ü¶à¬µ àµ áºÜ§à¬¶ âÝà¬¶ àµ Îá»áºßà¬µÜ§à¬µÝà¬µáº à¯Ü¶à¬µ àµ à¬´Ü¶à¬µá»á» àµ Îáºßà¬¶Ü§à¬¶Ýà¬¶áº à¯Ü¶à¬¶ àµ à¬´Ü¶à¬¶á»á» Îà¬¶ àµ áºÜ§à¬µâÝà¬µ àµ Îá»áºÜ§à¬¶âÝà¬¶ àµ Îá» 42
Finally, g determin slab-base accounts calculate where Ïef neutral ax nonlinear the analy interface Revised t computat distributi distributi procedur combinat T loads as a nonlinear in this pr critical lo standard at the mi left. For load with on the rig Figure 1 T linear tem frequency iven stresse ed. Not only interaction for the effec d stress at th ßªà¬µ àµ f is determin is; heff and thermal dis sis would as location) in hermal line ion of critic on, axle load on through t e converts th ions of traff he AASHTO function of gradients w ocess is to c cations for axle loading d-slab edge, top-down d a medium w ht. 4. Critical he second st perature gr distributio s due to wh is the modi contributes ts of tempe e interface, 2áºÝ àµ Ü¾à¬µá» Ýà¯à¯à¯ ed from the b1 are as abo tribution thr sume a valu Equations 4 arization pro al stresses in , axle weig he system f ose hourly ic and temp M-E linea both linear ith those du ompute the linear tempe . For bottom where it wi amage accum heel base i load and st crac ep in the lin adients, in in n (without n eel loading a fied process to PCC slab rature and m Ï1, as follow ßªà¯à¯à¯ àµ ßªà¯à¯ AASHTO M ve, and ÏNL ough the pa e of h1 for z 0 and 41. cedure. The the pavem ht, and axle or every hou predictions i erature (kno rization proc and nonline e to linear g monthly PC rature gradi -up damag ll produce th ulation, a s placed at t ress locatio king (at rig earization p crements o onlinear tem 30 nd tempera compatible flexural stif oisture curl s -E neural n is the self-e vement. For (correspond procedure d ent system f position. Ho r of the pav nto monthly wn as the th ess elimina ar temperatu radients (AR C stresses fr ents, ÎTL, no e accumulat e maximum 12-kip single he critical lo ns for botto ht) [from A rocess invol f 2Â°F, which perature str ture, the stre with the ori fness, but it /warp. The etworks; z quilibrating the stress c ing to the b escribed ab or any comb wever, EIC ement life. T distribution ermal linear tes the need re gradient A, 2004; Y equency dis nlinear tem ion, an 18-k stress, as sh axle load a ading locat m-up crack RA (2004)] ves finding produces th esses) that i ss in the ori ginal proced is also com procedure w is the distan stress assoc alculation o ottom of the ove allows ination of te M predicts t he original s of probab ization proc to compute s by equatin u et al, 200 tribution in perature gra ip single ax own in Fig nd a 34-kip ion, as show ing (at left the frequenc e PCC bend s the same a ginal structu ure in how patible in ho ill result in ce from the iated with th f Equation 4 slab, i.e. th for the mperature he temperat AASHTO M ility of ess). the number g stresses du 4). The firs the pavemen dients, TNL, le load is pl ure 14 on th tandem axle n in Figure ) and top-d y distributio ing stress s the stress re si w it the 43 e 3, e ure -E of e to t step t at and aced e 14 own n of
31 distribution from the previous step. The temperature frequency distribution for each month, which is developed only for the standard load and wheel offset conditions, is used in the fatigue analysis for all axle loads and offsets conditions. This process drastically reduces the amount of computing required to estimate stresses. The thermal linearization process in the original model assumes that the stress due to the interaction between nonlinear temperature and traffic is constant for all traffic loads. The new cracking model reconsiders the thermal linearization process significantly and computes stresses not only at the top and bottom of the slab, but also at a specified distance from the surfaces. The modified approach involves computing the linear temperature difference in the equivalent slab, the corresponding nonlinear temperature at the PCC surface (top if the temperature difference is negative, bottom if it is positive), and the nonlinear temperature at a specified distance from that surface. These combinations of factors are computed for each hour of the day to create frequency distribution tables. The allocation of combinations per hour for each day is conducted in a manner resembling the tributary area method (used in most contexts for boundary conditions in statics problems). The frequency distribution of linear temperature gradients in the modified method is in increments of 2Â°F; the frequency distribution of nonlinear temperature gradients is in increments of 0.25Â°F. The frequency tables that result from this methodology are very large. To illustrate the concept, Table 4 and Table 5 present thermal gradients according to the revised method.Table 4 presents the probability of different combinations of ïTL and TNL in the pavement system for the first two hours of any day (12-1 AM and 1-2 AM) in the first month (January). For the sake of illustration, let us consider the likelihood of ïTL = -22ï°F and TNL= -2ï°F (at the top surface) in both hours of a January day. Table 4 highlights the probabilities of that combination of thermal characteristics in the first two hours of that day (the values being 0.0435 and 0.0734, respectively). The new thermal linearization process determines the likelihood of TNLï±a within a specific combination of ïTL and TNL. Thus, Table 5 illustrates the probabilities of TNLï±a taking on different values for the specific case when ïTL = -22ï°F and TNL= -2ï°F in the first two hours of a January day. Also, in Table 4, all probabilities associated with Hour 1 in the lookup table sum to a value of 1; the same is true for all probabilities associated with Hour 2. Table 5 shows that the expressed probabilities for each value of TNLï±a sum to the probability associated with the ïTL = - 22ï°F and TNL= -2ï°F for the hour indicated in Table 4.
32 Table 4. Example of frequency distribution of probability of a given combination of ïTL and TNL for a given hour of a specific calendar month MonthÂ HourÂ ïTLÂ ProbabilityÂ ofÂ givenÂ valueÂ ofÂ TNLÂ 2Â 1.75Â 1.5Â 1.25 1 0.75 0.5 0.25 0 â0.25Â â0.5 â0.75 â1 â1.25 â1.5 â1.75 â2Â 1Â 1Â 0Â 0Â 0Â 0Â 0Â 0 0 0 0 0 0Â 0 0 0 0 0 0 0Â 1Â 1Â â2Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â4Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â6Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â8Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â10Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0002Â 0.0003Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â12Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0012Â 0.0025Â 0.0009Â 0.0002Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â14Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0076Â 0.0353Â 0.0078Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â16Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0116Â 0.1458Â 0.1052Â 0.0033Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â18Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0054Â 0.1304Â 0.2457Â 0.0136Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â20Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0241Â 0.1377Â 0.0322Â 0.0004Â 0Â 0Â 0Â 0Â 1Â 1Â â22Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0056Â 0.0435Â 0.0227Â 0.0008Â 0Â 0Â 0Â 0Â 1Â 1Â â24Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 5Eâ05Â 0.0062Â 0.009Â 0.0002Â 0Â 0Â 0Â 0Â 1Â 1Â â26Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0001Â 0.0004Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â28Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 1Â â30Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â2Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â4Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â6Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â8Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â10Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â12Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 3Eâ05Â 0.0029Â 0.0014Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â14Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 8Eâ05Â 0.0093Â 0.0282Â 0.0027Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â16Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0218Â 0.1439Â 0.0395Â 0.0005Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â18Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0053Â 0.176Â 0.201Â 0.0056Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â20Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Eâ06Â 0.0601Â 0.1628Â 0.0125Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â22Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.0127Â 0.0734Â 0.0176Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â24Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.001Â 0.0107Â 0.005Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â26Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0.001Â 0.0015Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â28Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 1Â 2Â â30Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â 0Â Table 5. Example of frequency distribution of total frequencies from Table 4 with respect to TNLï±a Month Hour ïTL FrequencyÂ (fromÂ ïTLv.Â TNLÂ table)Â ProbabilityÂ ofÂ givenÂ valueÂ ofÂ TNLï±aÂ (whenÂ ïTL=â22,Â TNL=â0.5)Â â1 â0.75 â0.5 â0.25 0 0.25 0.5 0.75 1 1Â 1Â â22Â 0.043464Â 0 0.0008 0.0268 0.0159 0 0 0 0 0 1Â 2Â â22Â 0.073352Â 0 0.001 0.0418 0.0306 1Eâ05 0 0 0 0
33 Modifications to the damage calculation in the modified JPCP transverse cracking prediction model. This step involves the calculation of accumulated top-down and bottom-up damage in the slab given the structure response (i.e. critical stress calculation) according to Minerâs hypothesis, where Ü¨Ü¦ àµà·Ýà¯,à¯,à¯,à¯,à¯ ,à¯¡,à¯¢ à¯Ü°,à¯,à¯,à¯,à¯ ,à¯¡,à¯¢ 44 where n is the applied number of load applications; indices i through o refer to age (i), month (j), axle type (k), load level (l), equivalent temperature difference (m), traffic offset (n), and hourly truck traffic (o) (respectively); and N is the allowable number of load applications such that logàµ« à¯Ü°,à¯,à¯,à¯,à¯ ,à¯¡àµ¯ àµ Ü¥à¬µ â áßà¯ßà®¼Ü¯Ü´à¯ßªà¯,à¯,à¯,à¯,à¯ ,à¯¡á à®¼à°® àµ Ü£à¬· 45 where Ü¯Ü´à¯ is the PCC modulus of rupture at age i in psi; ßªà¯,à¯,à¯,à¯,à¯ ,à¯¡ is the applied critical stress for associated indices in psi; Ca and Cb are calibration constants (AASHTO, 2008); Î²S is an adjustment factor for the deviation from the pure bending stress state; Î²C is a strength adjustment factor for curing conditions; and A3 has a value of 0.4371. If Î²C and Î²S are equivalent to 1, then the model reduces to the AASHTO M-E fatigue damage model, expressed in Equation 3. Strength adjustment for deviation from pure bending stress state. Modulus of rupture is designed to assess flexural strength. But because of nonlinear temperature stresses, the stress distribution throughout the slab can deviate from a linear state. This nonlinearity can either increase or decrease damage. Thus, estimation of the damage from the maximum stress is not a reliable process. The AASHTO M-E fatigue damage model indirectly accounts for the phenomenon by reducing the maximum stress at the PCC surface. Instead of adding the entire nonlinear temperature stress, the AASHTO procedure accounts for only 40% of surface nonlinear temperature stress. In this study, an alternative damage criteria is proposed. The criteria hypothesis is that if a stress distribution near the slab surface (S1) deviates from a pure bending stress state, then the damage from this distribution (S1) is equal to the damage of a bending stress distribution (S2) that produces the same energy of elastic deformation as the original stress distributions (S1). We now consider a stress state in a beam under bending with a constant moment. In this configuration, the stress, ßª, at any point of the beam is ßªáºÝá» àµ 2ÝÝ ßªà¯ 46 where Ý is the thickness of the beam, Ý is the distance from the neutral axis, and the stress at the surface is ßªà¯ àµ ßªáºÝ àµ à¯à¬¶á», which is assumed to be tensile (i.e. positive). The energy of elastic deformation of a representative cube with side Ü½ is equal to
34 Ü¹ àµ Ü½ à¬¶ 2Ü§à¶± 2Ý Ý ßªà¯dz à¯ à¬¶ à¯ à¬¶à¬¿à¯ àµ Ü½ à¬·ßªà¯à¬¶ 2Ü§ àµ¤1 àµ 2 Ü½ Ý àµ 4 3 á Ü½ Ýá à¬¶ àµ¨ 47 Consider a case when the stress varies linearly through depth Ý within a characteristic length Ü½, but the manner of variation in stress is not proportional to Ý. This may happen when a beam is subjected to bending and a nonlinear temperature distribution. Let ßªà¬´ be the stress at the surface and ßªà¬µ àµ ßª áÝ àµ à¯à¬¶ àµ Ü½á. The expression for the energy of elastic deformation in Equation 47 becomes Ü¹ àµ Ü½à¬· ßªà¬´ à¬¶ 6Ü§ á1 àµ ßªà¬µ ßªà¬´ àµ àµ¬ ßªà¬µ ßªà¬´àµ° à¬¶ á 48 Equating the two expressions for the energy of elastic deformation above â Equations 47 and 48 â one can find the maximum bending stress ßªà¯ that produces the same energy as the distribution expressed in Equation 47. Thus, the criteria for failure becomes ßªà¯ àµ ßªà¬´Î²à 49 where ßà¯ àµ à¶¨1 àµ ßªà¬µßªà¬´ àµ á ßªà¬µ ßªà¬´ á à¬¶ à¶§3 àµ 6Ü½Ý àµ 4 á Ü½ Ýá à¬¶ 50 Recall that the allowable number of load repetitions for the bending distribution is determined from Equation 45. Therefore substituting equation for Ï0 into Equation 45, we have Ü¥à¬µ áÜ¯à¯ßªà¬´ßà¯ á à®¼à°® àµ 0.4371 àµ Ü¥à¬µ áßà¯Ü¯à¯ßªà¬´ á à®¼à°® àµ 0.4371 51 If ßªà¬´ and ßªà¬µ are linearly related to the distance to neutral axis â i.e. they describe a pure bending stress state near the surface â then Î²S is equivalent to 1. If ßªà¬µdeviates from pure bending in a manner that increases the slope between ßªà¬´ and ßªà¬µ, then Î²S is greater than 1 â that is, the apparent strength is higher. Alternatively, when the slope between ßªà¬´ and ßªà¬µ is decreased and the stress state is closer to uniform tension, then Î²S is less than 1 and the apparent strength is lower. Strength adjustment for curing condition. Wood (1992) found that air-cured specimens exhibited 70% lower compressive strength than corresponding moist-cured specimens. Since the curing condition of the bottom surface of the PCC layer is closer to moist-curing conditions while top
35 surface curing conditions resembles air-curing conditions, it is reasonable to expect that there will exist a difference in the flexural strength of the two surfaces of the slab. This phenomenon was incorporated into the original development of the AASHTO M-E procedure through the use of a strength adjustment factor (ARA, 2004). This factor is still present in the intermediate files to the AASHTO M-E JPCP transverse cracking model, including the most recent implementation (Pavement M-E 2.1.24); however, this factor is not used in the most recent cracking models (i.e., the factor is effectively set to a value of 1). In the modified procedure, the strength adjustment factor, Î²C, provides the ability to set different strengths for the two surfaces. This factor has been set to have a default value of 0.95 and can be changed by the user. Transverse cracking prediction in the modified model (outputs). This step is unmodified from the original procedure and uses the sinusoidal relationship Ü¥Ü´ àµ 11 àµ Ü¥à¬· â Ü¨Ü¦à®¼à°° 52 to predict transverse cracking CR in the JPCP project, where Ci are global calibration constants described elsewhere (ARA, 2004; AASHTO, 2008). Once top-down and bottom-up damage are estimated, transverse cracking is computed by damage type using Equation 52 and the total combined cracking, CRTotal, is the sum of the bottom-up cracking, CRBottom-up, and top-down cracking, CRTop-down, as follows Ü¥Ü´à¯à¯¢à¯§à¯à¯ àµ Ü¥Ü´à®»à¯¢à¯§à¯§à¯¢à¯ à¬¿à¯¨à¯£ àµ Ü¥Ü´à¯à¯¢à¯£à¬¿à¯à¯¢à¯ªà¯¡ àµ Ü¥Ü´à®»à¯¢à¯§à¯§à¯¢à¯ à¬¿à¯¨à¯£ â Ü¥Ü´à¯à¯¢à¯£à¬¿à¯à¯¢à¯ªà¯¡ 53 The modified cracking model was calibrated using performance data from the LTPP SPS-2 and GPS-3 projects used for the calibration of the AASHTO M-E procedure (Sachs et al, 2014). 22.214.171.124 Joint faulting In order to assess the influence on slab-base interaction on joint behavior in the AASHTO M-E procedure, it is necessary to recreate the underlying structural and performance models to ensure that the modeled behavior is understood. The research approach of this study was to evaluate slab-base interaction parameters in the AASHTO M-E framework in terms of joint performance and to develop model modifications and/or new values for these parameters, where justified. The JPCP joint faulting model requires the prediction of deflections at the loaded and unloaded sides of a joint. However, as the slab near the joint experiences greater relative horizontal moments at the corner and edge, the AASHTO M-E assumes that the interface between the slab and the base is unbonded. Slab-base interaction and base layer contributions to faulting are accounted for indirectly in the AASHTO M-E procedure. The investigation focused on two features present in the joint faulting model that relate to slab-base interaction: base material erodibility (EROD) and base material load transfer efficiency (LTEbase). Base erodibility. EROD is easily classified by pavement engineers using the PIARC system (AASHTO, 2008). EROD has an index rating between 1 and 5, where 1 indicates âExtremely Resistantâ to base erosion and 5 indicates âVery Erodibleâ base material. To examine the JPCP faulting model sensitivity to EROD, the AASHTO JPCP calibration projects were simulated with
the full c are summ EROD. I total faul Figure It can be individua Moreove sensitivit predicted recomme Developm faulting m not docum team recr goal bein the origin AASHTO results in comparis inches). A Figure 16 omplement arized in Fi n the AASH ting for proj 15. Predict observed in l sections, i r, the modif y of predicte and measur ndations for ent of a joi odel has so ented and/ eated the ge g to create a al AASHTO M-E proje an identical on produced compariso . of erodibility gure 15. As TO calibrat ects with ER (a) ed perform CTB and Figure 15 th t has a mino ication of th d faulting t ed faulting. base erodib nt faulting m me docume or publically neral AASH faulting mo M-E joint ct folder int format. Th results that n of the dev indices. Th shown, the ion projects, OD =1 and ance vs. me (b) PSAB f at although r effect on th e EROD fac o EROD fac Based on th ility were n odel for th ntation, spe available ( TO M-E fa del that use faulting mo ermediate in e recreated m were nearly eloped mod 36 e results of JPCP faultin there is an EROD =5. asured per or all five e the EROD e predicted tor from the tor would o ese observa ot modified e AASHTO cific details ARA, 2004; ulting mode s identical i del. In other put files (e. odel was c identical (i el and the o these simul g model is 11% averag formance f rodibility in index may a faulting for default valu nly increase tions, the cu in this study M-E framew of modifica AASHTO, l framework nputs and pr words, the g., faultgene onsidered to .e. differenc riginal AAS ations for st relatively in e percent di (b) or LTPP se dices ffect faultin the majorit e for the se a discrepan rrent AASH . ork. While tions made a 2008). Thu from first p oduces iden developed m ralinput.txt, be complet es did not e HTO model abilized bas sensitivity t fference betw ctions with g prediction y of the sect ctions show cy between TO M-E the JPCP jo fter 2003 ar s, the researc rinciples, th tical output odel reads ) and produ e when this xceed 0.000 is illustrate es o een (a) for ions. ing the int e h e s to the ces 1 d in
Figure 1 Base load slab-base paramete paramete (LTEtotal) where LT LTEdowel interlock investiga documen that the o ï· ï· ï· Although assigned recreation climates type.) U using SP M-E cali 6. Compari AA transfer eff interaction r is load tran r can affect of the syste LTEà²à Ebase is the b is the LTE d in the slab. tion to recre tation (ARA riginal mod Granular Asphalt-tr Cement-tr the AASHT Ü®Ü¶Ü§à¯à¯à¯¦à¯ valu that both L when the ba sing the rec S-2 and GPS brations. Un son of pred SHTO M-E iciency. Du parameter a sfer efficien the faulting m, as expres à²ààª àµ 100 â àµ¬1 ase LTE (w ue to the us From the AA ate the origi , 2004) and el assumes t base: 20% eated base: eated base: O M-E doc es of 40% (A CB and CT se is 32ï°F o reated mode -3 LTPP pr doweled sec icted faulti model for ring the recr ffecting join cy for a giv prediction, a sed by Equ àµ áº1 àµ Ü®Ü¶Ü§à¯à¯100 here this va e of dowelin SHTO M- nal AASHT in the recre he following 30% 40% umentation RA, 2004; B were assig r less, the ba l, the sensiti ojects with n tions only w 37 ng from the LTPP GPS eation of th t performan en base typ s the base L ation 54. à¯¦à¯á» â áº1 àµ áº1 àµ lue is assum g, and LTEP E document O M-E join ation of the values for suggests tha AASHTO, ned values se LTE is a vity of joint o dowels th ere conside unmodifie -3 and SPS e AASHTO ce was reve e (ARA, 200 TE contribu Ü®Ü¶Ü§à¯à®¼à®¼ 100 á» â áº1 ed to be 90% CC is the LT ation (ARA t faulting mo original AA Ü®Ü¶Ü§à¯à¯à¯¦à¯: t only lean 2008), it wa of 40%. (No ssumed to b faulting to at were incl red to more d, recreated -2 projects faulting mo aled for stud 4; AASHT tes to the to àµ áº1 àµ Ü®Ü¶Ü§à¯10 if the base E associate , 2004) and del, In the A SHTO mod concrete bas s found in th te that for m e 90% regar base LTE w uded in pre accurately model and del, another y. This O, 2008). Th tal LTE à¯¢à¯ªà¯à¯ 0 á»àµ° is frozen), d with aggre from this ASHTO el, it was fou es (LCB) w e model onths and dless of bas as investiga vious AASH gauge the the is 54 gate nd ere e ted TO
sensitivit assumed squared e where Fa Figure 17 different Fig One can faulting i values fo support, adjustme T granular 1 2 3 y of model p for each bas rror, SSE, b ÜµÜµÜ§ àµ ultobs is the illustrates t by base type ure 17. Sen observe in F s quite sensi r the base L a decision w nts to ïT. he first step base. The pr . Recre . Recor projec . Apply betwe erformance e type, and etween the o à·áºÜ¨Ü½ÝÝÝà¯¢à¯ à¯¡ à¯àà¬µ observed fau he sensitivit s. sitivity of j igure 17 tha tive to the a TE were con as made to m in modifyin ocess to det ate and run t d the differe t at all ages an iterative en observed to base LTE the model se bserved and à¯¦ àµ Ü¨Ü½ÝÝÝà¯à¯à¯à¯á» lting and F y of SSE fo oint faultin calibr t the overall ssumed base sidered in t odify the A g the faultin ermine the c he calibratio ntial energy associated w solver to de and predict 38 . For the st nsitivity wa predicted f à¬¶ aultcalc is the r undowled g to Base L ation projec discrepancy load transf his study. In ASHTO fa g model wa alibration c n project us within the i ith LTPP o termine mo ed faulting a udy, a range s considere aulting, exp predicted f projects to c TE in undo ts between th er efficiency addition, g ulting mode s to re-calib oefficients w ing the alte ntermediate bservations del coefficie cross all ca of values o d in terms o ressed as aulting for e hanges in b weled AAS e predicted . Therefore iven the imp l included in rate it for se as: rnative fault project file ; and nts that min libration pro f base LTE f the sum of ach observa ase LTE for HTO M-E and measur , recommen ortance of s ternal ctions with ing model; s for a given imize the er jects. were 55 tion. ed ded lab ror
39 After the model was re-calibrated for granular bases, the sensitivity of joint faulting to base LTE and ïT was investigated for sections with CTB and PATB bases. The combinations of these parameters resulting in the least discrepancy between the predicted and observed joint faulting were recommended as new default parameters. 126.96.36.199 Punchouts The AASHTO M-E procedure models CRCP distress performance in terms of punchouts, which in turn affects smoothness (ARA, 2004; AASHTO, 2008). The AASHTO M-E punchout model itself is dependent on the crack width and crack spacing models. Although the model predicts crack spacing distribution, only panels with narrow crack spacing (2-foot width) are considered in the punchout prediction. These panels result from secondary cracking of the larger panel, and therefore are free to slide. Because of this, the CRCP punchout structural model assumes a fully unbonded interface between the base and PCC panel. However, the interaction between the base and the CRCP slab is accounted for through the use of the slab-base friction parameter, f, in the crack spacing model (ARA, 2004; AASHTO, 2008). According to AASHTO (2008), the pavement designer should assign Ý a value according to base type and the guidelines in Table 6. Table 6. AASHTO recommendations for base friction coefficient in CRCP project design [reproduced from AASHTO (2008)] Subbase/Base Type Friction Coefficient (low â mean â high) Fine grained soil 0.5 â 1.1 â 2 Sand 0.5 â 0.8 â 1 Aggregate 0.5 â 2.5 â 4.0 Lime-stabilized clay 3 â 4.1 â 5.3 ATB 2.5 â 7.5 â 15 CTB 3.5 â 8.9 â 13 Soil cement 6.0 â 7.9 â 23 LCB 3.0 â 8.5 â 20 The performance of 18 LTPP GPS-5 projects with unbound bases from the AASHTO M-E calibration database (Sachs et al., 2014) were simulated for f values of 0.25, 1, and 2. The resulting calculated damage ratios (Equation 13) were extracted from the intermediate AASHTO M-E output files and summarized in Figure 18. It can be observed that the punchout damage is very sensitive to an assumed value of the base friction parameter. Since for stabilized bases, AASHTO recommends a wide range for this parameter, these recommendations were re- evaluated in this study.
Figu The first base. The 1 2 3 After the stabilized and 24). punchout of discrep 2.5.3 Im The alter framewo alternativ through d implemen requires m T companio intermed according faulting m re 18. Sensi step in mod process to . Recre . Recor given . Apply betwe model was bases was For each bas s was quant ancy were plementat native mode rk to simplif e CRCP pun irect modif tation of th ore effort, o implemen n to the AA iate AASHT to the alter odels were tivity of GP ifying the pu determine th ate and run t d the fatigue project at al an iterative en observed re-calibrated simulated us e type and f ified and the recommende ion of alter ls were dev y their incor chout mode ication of th e alternative as the mode t the alterna SHTO M-E O M-E proj native mode coded into S-5 aggreg nchout mod e calibratio he LTPP GP damage wi l ages assoc solver to de and predict for granula ing 14 valu riction valu values of th d. native mod eloped to be poration int l can be im e default par JPCP crack ls have been tive models software an ect files to s ls develope standalone F 40 ate base pr el was to re n coefficient S-5 project thin the AA iated with L termine mo ed punchout r bases, per es of f (0.25 e, the discre e friction p els for the A completely o the AASH plemented in ameters of t ing and fau modified i into practice d projects. imulate the d in this stud ORTRAN p ojects to ba -calibrate it s was: within AAS SHTO M-E TPP observ del coefficie s per mile. formance of , 1, 2, 4, 6, 8 pancy betwe arameters re ASHTO M compatible TO M-E pr the curren he current m lting models n this study. , software w This compan performanc y. The alter rograms. T se friction p for sections HTO M-E; intermediat ations; and nts that min CRCP sect , 10, 12, 14 en predicte sulting in th -E procedu with the AA ocedure and t AASHTO odel. Howe into AASH as develop ion softwar e of AASHT native JPCP hese progra arameter, f with granul e files for a imize the er ions with , 16, 18, 20, d and measu e least amo re SHTO M-E software. T M-E softwa ver, the TO M-E ed that acts e uses O M-E proj cracking a ms accept th ar ror 22, red unt he re as a ects nd e
41 same input files and produce identical output files to those of the original AASHTO M-E JPCP cracking and faulting performance prediction programs. To simplify the use of the alternative JPCP transverse cracking model, the companion software was developed using Java and built to run alongside the AASHTO M-E software on Windows operating systems. The software interfaces with the FORTRAN-coded alternative models, which are Windows executable files. The companion software provides a graphical-user interface (GUI) that simplifies the process of (1) providing slab-base interaction parameters and (2) applying the alternative models to an AASHTO M-E project.