Evaluation Methodology for Jointed Concrete Pavements

Transcription

1 Transportation Research Record Evalation Methodology for Jointed Concrete Pavements MOHAMMED A. OZBEKI, W. P. KILARESKI, and D. A. ANDERSON ABSTRACT Many Interstate and other major highays that ere constrcted ith jointed portland cement concrete pavements have reached their design life and conseqently are deteriorating significantly. Fe transportation agencies have an effective method for evalating the strctral adeqacy of transverse joints. Most pavement rehabilitation programs no nder ay are based on sbjective engineering jdgment. A more objective evalation procedre is presented. A nely developed finite element program, JSLAB, as sed in a parametric stdy to determine hich variables have the most significant effect on the performance of transverse joints. It as conclded that the variables that most significantly affect pavement deflections and stresses are the modls of sbgrade reaction and the modls of doel-concrete interaction. On the basis of this stdy, it as conclded that a rigid pavement system can be strctrally evalated if the modls of sbgrade reaction and the doel-concrete modls are knon. Charts ere developed to determine these modli and sbseqently to evalate in-service pavements. Many of the Interstate and other major highays in the United States ere constrcted ith jointed portland cement concrete (PCC) pavements. Althogh these pavements have provided good serviceability, the design life of many of them has been exceeded and they have deteriorated significantly. In most cases the predominant distress associated ith these pavements is the deterioration of the transverse joints rather than of the slab itself. Spalling, cracking, and falting are the most serios types of distress fond at the joints. Many transportation agencies do not have an effective method for evalating the strctral adeqacy of transverse joints. Most of the pavement rehabilitation programs no nder ay ere ndertaken on the basis of sbjective engineering jdgment. Typically an engineer ill "alk" a project to determine the type of repairs or rehabilitation needed. The engineer ill visally select the joints that shold be removed and the joints that shold remain in place. This type of evalation can lead to the removal of sond joints or the acceptance of joints that are deteriorated. Withot the proper evalation of each joint it is difficlt to select the appropriate rehabilitation procedre. Becase repair and rehabilitation of major highays across the nation are important from an economic as ell as an engineering point of vie, a more objective scheme mst be sed to evalate the condition of joints and their expected ftre performance. The prpose of ths paper is to discss the development of a methodology for evalating the strctral behavior of jointed concrete ith a nondestrctive testing device (NDT). A nely developed finite element compter program, JSLAB, as sed for the analysis of the rigid pavement joints. PCC EVALUATION REQUIREMENTS There are several repair or rehabilitation schemes available for PCC pavements. They inclde resealing of joints, partial concrete removal and patching, joint removal and replacement, sbsealing, overlays, and complete reconstrction. The selection of the rong rehabilitation scheme ill reslt in a loss of both time and money becase the repairs may not perform for the expected design period or becase a repair scheme may be selected that is not needed. Deterioration of the transverse joints contribtes most to the poor performance of PCC pavements; therefore, an effective evalation methodology mst address the condition of these joints. Spalling and cracking at joints is of concern to engineers; hoever, falting of the slabs is the largest contribtor to the loss of serviceability of a PCC pavement. This falting can be de to a loss of sbgrade spport (voids) or deterioration of the load transfer system, or both. An evalation methodology shold be able to distingish the varios cases of deterioration becase the rehabilitation scheme is different for each type of distress. For example, sbsealing is needed to correct a loss of sbgrade spport, hereas establishment of load transfer is reqired for a deteriorated load transfer system. FINITE ELEMENT MODEL Most jointed PCC pavements are analyed and designed by assming continos slabs that are infinite in length. Different types of joints ith varios load transfer systems ill affect, in different ays, the strctral response of jointed concrete pavements nder the applied load. Therefore, any strctral model sed for design or analysis shold consider the entire pavement strctre ith all its components, sch as joints, load transfer systems, sbbase spport, and loading configration. It shold also consider loss of sbgrade spport, nonniform slab thickness, and nonniform sbgrade modls. A nmber of finite element models have been developed for the analysis of concrete pavement systems. These may be divided into the folloing major classes: plane-strain models, three-dimensional models, and slab models. The most desirable model for concrete pavement analysis is probably the three-dimensional one in hich the geometry of the entire system can be taken into consideration. There are compter programs that employ three-dimensional finite element models, sch as the SAP program de-

2 2 Transportation Research Record 143 veloped by Wilson I!), bt the amont of inpt and the comptational costs reqired to se these programs make them impractical. The to-dimensional plane-strain representation of the concrete pavement system is rather simplistic. The pavement system is represented as a transverse slice of pavement ith a nit thickness. These models, becase of their simplifying assmptions, are not sited to the analysis of sch concrete paveme11l featres as joints, cracks, and load transfer devices. The slab models are based on the classical theory of. medim-thick plate spported by a Winkler fndation. Slab models have been developed by Tabatabaie and Barenberg (2), Hang and Wang (3,4), and Bhatia (_?.). Althogh a nmber of strctral models have been available for the analysis of concrete pavement systems, none of these contains all of the featres that are essential to adeqate representation of the pavement system. The finite element model sed in this stdy is called JSLAB. It as developed by Tayabji and Colley at the Constrction Technology Laboratory, a division of the Portland Cement Association. The JSLAB program has many practical featres and has the ability to allocate stiffness parameters to the load transfer device (LTD). Ths LTD stiffness allocation is not done at each set of nodes along a joint as is the case ith programs sch as ILLI-SLAB Cl> and the program developed by Hang and Wang (3,4). This featre is sefl for the analysis of- fointed slabs ith nonniformly spaced LTDs at joints. The specific capabilities of JSLAB are 1. Stresses and deflections in concrete pavement sections of p to nine slabs ith longitdinal and transverse joints can be determined; 2. A to-layer system, in hich the layers may be bonded or nbonded, can be analyed; 3. Load transfer can be modeled ith doels, aggregate interlock, or keys; 4. Concrete pavement slabs ith fll or partial sbgrade contact can be analyed, and the effect of thermal gradients on crling stresses can be analyed, both independently and in combination ith traffic loads; and 5. The effect of joints ith nonniformly spaced load transfer devices can be analyed. The JSLAB finite element model (6,7) is represented by an assemblage of sbdivided- or discrete bodies called finite elements. These elements are interconnected at specified locations that are called nodes or nodal points. Simple fnctions are chosen to approximate the distribtion of displacements over each finite element. These assmed fnctions are called displacement fnctions or shape fnctions and are sed to express continos displacements in terms of discrete nodal displacements. Relationships are then established beteen nodal displacement () and nodal forces (p) applied at the nodes sing the principle of virtal ork or some other variational principle. These element forcedisplacement relationships are expressed in the form of an element stiffness matrix (k), hich incorporates the material and geometric properties of the element, namely, here {} is element displacement and {p} is element applied force. The overall or global strctral stiffness matrix [K] for the entire system is formlated by sperimposing the individal element stiffness matrices sing element connectivity properties of the strc- (1) tre. The overall stiffness matrix is sed to assemble a set of simltaneos eqations of the form: [Kl Jf=M here [K] {U} IP} overall stiffness matrix, global displacement, and global applied forces. The soltion to Eqation 2 reslts in nodal displaceme11ls fr the entire system. JSLAB COMPUTER PROGRAM The JSLAB compter program as ritten in FORTRAN for a CDC compter. The program as modified for se on an IBM compter, to inclde graphic capabilities. The inpt to the program is 1. Geometry of the concrete slab, stabilied base or overlay, and load transfer system; 2. Elastic properties of the concrete slab, stabilied base or overlay, load transfer system, and sbgrade; and 3. Loading configration. The otpt given by the program is 1. Doel shear and moment at each node along the joint (for nondoeled joints this otpt is omitted); 2. Stresses in the concrete pavement, stabilied base, or overlay; 3. Deformations of the pavement system, hich consist of vertical deflection and rotation; and 4. Applied loads, hich consist of vertical components of applied load and moments abot the x- and y-axis, respectively, at each node. Becase JSLAB is a relatively ne program, a comparison as made of the reslts obtained from the program and those obtained from other soltions. Interior stresses and edge and corner deflections ere calclated sing JSLAB and Westergaard' s eqations (_!!) as follos: a=.275 (I+ v) (P/h 2 ) j4(log(q/b)] +!.69f t.= (1/6Y') (I+.4 v) (P/kQ 2 ) t. = (P/kQ 2 ) [I. I -.88 (a/q)] here (edge deflection) (corner deflection) a = maximm stress nder the load; 6 maximm deflection nder the load; P applied load; a radis of a circlar!jded area; b (l.ga 2 + H h), for a < l.724h; b a, for a> l.724h; k modls of sbgrade spport; i radis of relative stiffness of the pavement ith respect to sbgrade given by i 4[Eh'/12(1 - v 2 )K]; h thickness of the concrete slab; E modls of elasticity of the concrete slab; and v = Poisson's ratio of the concrete slab. A comparison of the stresses and deflections obtained from the JSLAB program and Westergaard's eqation is shon in Figre 1. The solid line in the figre represents Westergaard' s exact soltion, (2) (3) (4) (5)

3 Obeki et al Ui Cl. " 1 g ea I I- Q: 6 ::::> 4 (/) (/) Ii! 2 I- (/) H=IO MODULUS OF SUBGRADE REACTION, PC I FIGURE 1 Comparison of finite element soltions and Westergaard's eqation for interior loading. - I. 3 ft. FIGURE 2 Slab sed in finite element analysis. Interior Loading.I 5 loaded area for Westergaard' s soltion, therefore, as assmed to be a circle ith a diameter of 15 in. (38.1 cm), and a 15-in. (38.cm) sqare as selected to represent the loading condition in the finite element analysis. A single load of 5 kips (222 kn) as sed for the loading configrations. Figre 2 also shos the mesh of the finite element models sed in this comparison. The modls of elasticity and the Poisson's ratio of the concrete slab ere assmed to be 5 x 1 6 psi (34.5 GPa) and.15, respectively. The comparison as made for a slab thickness of 1 in. (25.4 cm) and five modli of sbgrade reaction: 5, 1, 2, 3, and 5 pci (13.6, 27.1, 54.3, 81.4, and N/cm'). The agreement beteen the reslts obtained ith JSLAB and those obtained ith Westergaard's eqation as qite good. In general the differences beteen the to soltions ere small as shon in Figre 1 for an interior load. Corner and edge loading cases also have the same reslts. PARAMETRIC STUDY OF PCC PAVEMENT PROPERTIES A parametric stdy as condcted to determine the inflence of selected design variables on the strctral response of a typical jointed pavement as constrcted in Pennsylvania. The responses, hich ere calclated sing JSLAB, ere the srface deflection of the loaded slab along the transverse joint, and the tensile bending stresses in the concrete nder the tire along the longitdinal x-axis. The inflence of the design variables on the efficiency of the transverse joint as also stdied. Joint efficiency as defined as the vertical deflection of Point B divided by the vertical deflection of Point A (Figre 3). The loading sed in the parametric stdy consisted of an 18-kip single-axle trck. (This as the trck configration sed at the Pennsylvania Transportation Research Facility.) The contact area of the tire as converted to a niformly loaded area ith a tire pressre of 8 psi (9). The folloing jointed pavemt system, hich is typical of pavements constrcted in Pennsylvania in the 196s, as sed as a reference in the parametric stdy: hile the small circles represent the finite element soltions. Becase Westergaard's exact soltions are for an infinite slab, a large 3-ft (9.14-m) sqare slab (Figre 2) as sed in the finite element analysis. Westergaard assmed that the load as distribted niformly over the area of a small circle. The Slab thickness 1 in. (25.4 cm) Concrete modls of elasticity= 4,5, psi (31. GPa) Modls of sbgrade reaction = 2 pci (54.2 N/cm') Poisson's ratio of concrete=.2 Telve niformly spaced doels Doel diameter = 1 1/4 in. (3.2 cm) Doel spacing = 12 in. (3.5 cm).1.::, 61.5ft 6J.5 fl. FIGURE 3 Loading configration sed in the parametric stdy.

4 4 Transportation Research Record 143 Modls of doel-concrete interaction = 2 million pci (542.8 kn/cm') Doel modls of elasticity = 29 million psi (199.8 GPa) Poisson's ratio of doel material (steel) =.3 Joint opening =.25 in. (6.4 mm) Slab length= 61.5 ft (18.7 m) In considering the effect of a particlar design variable, only one of the inpt vales as changed hile all other design variables ere kept constant. The reslts are discssed in the folloing sections. Doel Sie The doel diameters considered ere 3/4, 1, 1 1/4, and 1 1/2 in. (19, 25.4, 32, and 38 mm). As shon in Figres 4(a) and 4(c), doel diameter has no major inflence on corner deflection and joint efficiency. Hoever, larger doel sies increase the tensile bending stresses along the x-axis (longitdinal) in the vicinity of the joint, as shon in Figre 4(b). Hoever, it can be shon that larger doel sie de- i Es= 25,,; 29,, and 3,, Psi LI.14., <a_) , Es = 25,, Psi E =29,. and s 3PoPOO Psi Ul f-'".16 to: lb '=.75 in >= l.oin >= 1.25, 1.5 in (a).14.,_ "t Li: lb , I 2 144,, ,,./ -...,,.,,.,,......_.. _ '* "' (c) - - E 9 = 25,,; 29,, and 3,, Psi o 36 ro n M 96 1 DISTANCE ALONG THE TRANSVERSE JOINT, INCHES FIGURE 5 Effect of doel modls of elasticity on pavement response: (a) deflection at the joint nder the tires, (b) stresses along the x-axis nder the tires, and (c) percentage joint efficiency '? 9 i5..., (c) ----4>.75 in ----4> 1. in > 1.25 in ----4> l. 5 1n DISTANCE ALONG THE TRANSVERSE JOINT, INCHES FIGURE 4 Effect of doel diameter on pavement response: (a) deflection at the joint nder the tires, (b) stresses along the x axis nder the tires, and (c) percentage joint efficiency. creases the stresses along the y-axis (transverse), hich is the critical stress in this case. Doel Modls of Elasticity The doel modls of elasticity vales considered ere 25 x 1 6, 29 x 1 6, and 3 x 1 6 psi (172.25, 199.8, and 26.7 GPa). As shon in Figre 5, responses are essentially the same in all cases. Joint Width The joint idths considered ere.1,.2,.25, and.5 in. (2.5, 5.1, 6.4, and 12.3 mm). It as fond that corner deflections, tensile bending stresses, and joint efficiencies are the same in all for cases. Concrete Modls of Elasticity The concrete modls of elasticity vales considered ere 4 x 1 6, 4.5 x 1 6, and 5 x 1 6 psi (27.6, 31.,

5 Obeki et al. 5 and 41.4 GPa). The tensile stresses along the x-axis and the joint efficiency are relatively naffected by these changes in modls. As the modls increases, the deflection decreases slightly. Hoever, this decrease in deflection is not significant becase the variation is less than 5 percent. Modle of Sbgrade Reaction..:.18 O.Ol 7 I I G=2, Pei ---- G=5, Pei ---- G=l,, Pei ---- G=2,, Pei The modls of sbgrade reaction vales considered ere 1, 2, 3, and 5 pci (27.2, 54.2, 81.6, and N/cm') As shon in Figre 6, as the modls of sbgrade reaction increases, the corner deflection of the pavement slabs decreases significantly. This increase in sbgrade reaction does not significantly change the tensile bending stresses along the x-axis, as shon in Figre 6(b). Joint efficiencies do vary, hoever, as shon in Figre 6(c). ff].3- I U!-.'." o.o J.2 I I K=IOO Pei ---- K=2 Pei K=3 Pei ---- K=5Pei t; _J l!:; gi ) x <! x g <! a:: (a) o.o " I 2 I K= 1 Pei K=2 Pei K=3 Pei K=5 Pei (b) Ui n. x <! x (!) g <! a:: I- (j it J (a) I G=2, Pei G=5, Pei ---- G= 1,, Pei ---- G=2,, Pei II (b) I : , _ G=2, Pei ---- G=5, Pei ---- G= 1,, Pei ---- G=2,, Pei I 2 I 4 DISTANCE ALONG THE TRANSVERSE JOINT, INCHES FIGURE 7 Effect of modls of doel-concrete interaetion on pavement response: (a) deflection at the joint nder the tires, (b) stresses along the x-axis nder the tires, and (c) percentage joint efficiency. 144 >-" LL: l!:; J K=IOO Pei -- --K=2 Pei K=3 Pei 8 (c) -----K=5Pei DISTANCE ALONG THE TRANSVERSE JOINT, INCHES FIGURE 6 Effect of modls of sbgrade reaction on pavement response: (a) deflection at the joint nder the tires, (b) stresses along the x-axis nder the tires, and (c) percentage joint efficiency. Modls of Doel-Concrete Interaction The modls vales of doel-concrete interaction considered ere 2 x 1 5, 5 x 1 5, 1 x 1 5, and 2 x 1' pci (54.3, 135.7, 271.4, and kn/cm'). As shon in Figre 7, the effect of these changes in modls is significant for all of the strctral responses. It shold be noted that many researchers assme a vale of 1.5 x 1 6 pci (47.1 kn/cm') for the modls of doel-concrete interaction. In this analysis the modls vales covered a ide range. The significance of the change in modls ill be discssed in detail later. It as conclded that the variables that appreciably affect calclated pavement response are the modls of sbgrade reaction (k) and the modls of doel-concrete interaction (G) The inflence of these parameters on pavement behavior as stdied frther.

6 6 Transportation Research Record 143 SENSITIVITY ANALYSIS FOR MODULUS OF SUBGRADE REACTION AND MODULUS OF DOWEL-CONCRETE INTERACTION The parametric stdy shoed that a loss in the modls of sbgrade reaction (lo k) or a loss in the modls of doel-concrete interaction (lo G) can increase pavement deflections and stresses enogh to case deterioration and evental failre of the joint system. Therefore a sensitivity analysis as condcted to determine the effect of variations in k and G on the corner deflection of the pavement slab (the deflection at Point A shon in Figre 3) and joint efficiency (the deflection at Point B divided by the deflection at Point A). These responses ere chosen becase they are easily obtained ith an NDT device sch as the Road Rater, falling eight deflectometer, or Benkelman beam. Ths the theoretical analysis can be verified by field measrements. For the pavement system analyed, srface deflections and joint efficiencies ere compted by varying one modls (k or G) hile keeping the other constant. All other parameters and the loading configration ere kept the same as for the typical pavement section defined in the previos section. Figres 8 and 9 sho, respectively, the absolte deflection and the joint efficiency verss the modls of doel-concrete interaction (G) for for different modli of sbgrade reaction (k): 2, 3, 4, and 5 pci (54.4, 81.6, 18.8, and K=2 Pei ---- K=3 Pei -- - K=4 Pei K=5 Pei t5 _J.2 "- O.Ol5 I-.1 ::> _J (/) m <t , 5, 75,, MOD OF DOWEL/CONCRETE INTERACTION, PCI FIGURE 8 Variation of srface deflection at the joint 6 in. (15.24 cm) from the sholder ith the modls of doel-concrete interaction. 1 6 >" 6 it 4-6.., K=2 Pei ----K=3 Pei ----K=4 Pei ----K=5 Pei , 5, 75, 1,, MOD OF DOWEL/CONCRETE INTERACTION, PCI FIGURE 9 Variation of amont of load transfer across the joint for first doel from the sholder ith modls of doel-concrete interaction. N/cm'). As shon in these figres, for all practical cases in hich the pavement spport is in good condition, the change in pavement response becomes insignificant for vales of G greater than approximately 2, pci (54.3 kn/cm'). A pavement is considered to have a good spport condition hen k is greater than 2 pci (1). Hoever, the reo;pnse of the pavement changes appreciably for vales of G less than 2, pci (54.3 kn/cm'). Therefore the limiting criterion selected for the modls of doel-concrete interaction, for pavements ith good spport (k > 2 pci), as 2, pci (54.3 kn/cm'). It can also be seen in Figres 8 and 9 that the changes in pavement deflections and joint efficiencies become insignificant for vales of k greater than 2 pci (54.4 N/cm') as long as the load transfer is adeqate (G > 2, pci). Ths the limiting er i ter ion selected for the modls of sbgrade reaction as 2 pci (54.4 N/cm'). EVALUATION PROCEDURE From the sensitivity analysis it as conclded that a rigid pavement system can deteriorate if it loses its sbgrade spport (k < 2 pci) or if the doel bar loses its interaction ith the srronding concrete. Therefore the condition of the joints in a rigid pavement can be established only if both the modls of sbgrade reaction and the modls of doel-concrete interaction are knon. The ability to distingish beteen the loss of sbgrade spport and the loss of doel-concrete interaction is important in the selection of rehabilitation treatments. A loss of sbgrade spport can be repaired by sbsealing, bt a loss of doel-concrete interaction reqires the reestablishment of load transfer. The rong repair scheme astes money and ill not extend the serviceability of the pavement. Figres 1 and 11 ere developed from the reslts of the sensitivity analysis for the prpose of determining these modli and sbseqently evalating the condition of in-service joints. Althogh these figres can be combined, they have been separated for ease of explanation. For any given combination of joint efficiency and corner deflection there is a niqe vale of k and G, These vales, compted ith the JSLAB program, have been plotted in Figres 1 and 11 on isobars of k and G, respectively. Figre 1 shos the joint efficiency verss the srface deflection at Point A (shon in Figre 3) for seven different modli of sbgrade reaction (k): 1, 2, 3, 4, 5, 6, and 7 pci (27.2, 54.4, 81.6, 18.8, 135.5, 163.2, and 19.4 N/cm'). Similarly, Figre 11 shos the joint efficiency verss the corner deflection of the same Point A for eight different modli of doel-concrete interaction (G):.1 x 1 6, o.1s x 1", o.11s x lo,.2 x 1 6,.25 x 1 6, a.so x 1 6,.75 x 1 6, and 1. x 1 6 pci (27.14, 4.7, 47.5, 54.2, 67.85, 135.7, 23.55, and 47.1 kn/cm'). This rigre, hich is based on the same data shon in Figre 1, can be sed to determine hether the load transfer system (G) is adeqate. Figres 1 and 11 can be sed to estimate k and G, hoever, only if both the corner deflection and the efficiency of the joint have been measred. This evalation techniqe differs from that sed in most evalation programs, in hich only the relative deflection across the joint is measred. As a conseqence, the to parameters, the modls of sbgrade reaction and the modls of doel-concrete interaction, can be estimated from these figres for a particlar joint and then compared ith the limiting vales to determine hether the joint is strctrally adeqate.

7 Obeki et al ,: (.) 6!!:' (.) "- "- 4 f-..., 2 Good Sb rodo Poor SbQrode / G=2, Pei 18 K Single Axle Load..5, :35.4 SURFACE DEFLECTION, IN. FIGURE 1 Joint efficiency verss srface deflection for varios modls vales of shgrade reaction hile modls of doel-concrete interaction is varied..,: (.)!!:' (.) 1 K 7 Pcl \K 2 Pei G l,, I G 75, ' ' \- \ 5, 6 \ \ \ 6 Li: "- 4 f-..., 2 G lo, 18 K Single Axle Load SURFACE DEFLECTION, IN. FIGURE 11 Joint efficiency verss srface deflection for varios modls vales of doel-concrete interaction hile modls of shgrade reaction is varied. SUMMARY AND CONCLUSIONS The methodology otlined here can be sed to evalate the condition of the sbgrade spport and the load transfer devices in a jointed concrete pavement. The methodology makes se of deflection measrements taken at the slab corners nder an 18-kip (8-kN) single axle load. The absolte deflection and the relative deflection at the joint are reqired in order to predict the modls of sbgrade reaction (k) and the modls of doel-concrete interaction (G). A vale of k less than 2 pci indicates a poor sbgrade, and a vale of G less than 2, pci indicates a poor joint system. Separating the evalation of sbgrade spport and joint efficiency ill help determine hether sbsealing or joint replacement, or both, are reqired for the rehabilitation scheme. The folloing conclsions have been dran: 1. The JSLAB finite element program is a practical model of a jointed concrete pavement system. It can be sed to calclate the stresses and deflections in a pavement system nder realistic loading conditions. The model can be sed to analye joints that are doeled, keyed, or have an aggregate interlock. 2. The parametric stdy shoed that the variations in the modls of sbgrade reaction and the modls of doel-concrete interaction have the most significant effect on changes in stresses and deflections in a jointed pavement system. 3. When the modls of doel-concrete interaction is 2, pci (54.3 kn/cm') or less, the deflections of the pavement increase significantly and therefore the stresses in the pavement increase significantly. 4. The modls of sbgrade reaction and the modls of doel-concrete interaction can be predicted from deflection measrements at the corners of the pavement slab. To measrements are reqired: the absolte deflection of the loaded slab and the relative deflection on either side of the joint. ACKNOWLEDGMENT This paper is based on "Forth Cycle of Pavement Research at the Pennsylvania Transportation Research Facility," Research Project 82-11, sponsored by the Pennsylvania Department of Transportation in cooperation ith the Federal Highay Administration. REFERENCES 1. E.L. Wilson. Solid SAP, A Static Analysis Program for Three Dimensional Solid Strctres. SESM 769. Strctral Engineering Laboratory, University of California, Berkeley, A.M. Tabatabaie and E,J. Barenberg. Finite Element Analysis of Jointed or Cracked Concrete Pavements. In Transportation Research Record 671, TRB, National Research Concil, Washington, D.C., 1978, pp Y.H. Hang and S.T. Wang. Finite-Element Analysis of Concrete Slabs and Its Implication for Rigid Pavement Design. In Highay Research Record 466, HRB, National Research Concil, Washington, D.C., 1973, pp Y.H. Hang and S.T. Wang. Finite-Element Analysis of Rigid Pavements ith Partial Sbgrade Contact. In Highay Research Record 485, HRB, National Research Concil, Washington, D.C., 1974, pp A.S. Bhatia. Mathematical Modeling for Design of Pavements and Highay Systems. Ph.D. dissertation. Ohio State University, University Park, 1978.

8 8 Transportation Research Record R.D. Cook. Concepts and Applications of Finite Element Analysis. John Wiley and Sons, Inc., Ne York, J.S. Premieniecki. Theory of Matrix Strctral Analysis, McGra-Hill Book Company, Ne York, , H,M, Westergaard. Stresses in Concrete Pavements Compted by Theoretical Analysis. Pblic Roads, Vol. 7, No. 2, Load StrP.ssP.s at PnvP.mP.nt F:ngP.: A Snppl P.mP.nt tn Thickness Design for Concrete Pavements. Report 1S3P. Portland Cement Association, Skokie, Ill., M. I. Darter. Design of Zero-Maintenance Plain Jointed Concrete Pavement, Vol. 1: Development of Design Procedres. Report FHWA-RD FHWA, U.S. Department of Transportation', This stdy as sponsored by the Pennsylvania Department of Transportation and the Federal Highay Administration. The contents of this paper reflect the vies of the athors, ho are responsible for the facts and the accracy of th& data. Th& contents do not necessarily reflect the official vies or policies of the sponsors. Pblication of this paper sponsored by Committee on Rigid Pavements. Controlling Longitdinal Cracking in Concrete Pav em en ts CHHOTE L. SARAF and B. FRANK McCULLOUGH ABSTRACT The objective of the stdy reported in this paper as to investigate the development of longitdinal cracks in ide concrete pavements (to or more lanes in one direction) and to develop a model to estimate the depth of sa ct needed tn cnntrnl these cracks ithin t.he groove. The model developed ses the concepts of variability in the material properties of the concrete (tensile strength), pavement thickness (as constrcted in the field), and depth of sact groove. It as observed that estimates of longitdinal cracking have a reasonable match ith field observations. It as observed that the longitdinal cracking of concrete pavements (to or more lanes in one direction) as dependent on the type of aggregate sed in the concrete mix. To types of aggregates ere investigated. Uniformity of concrete mix strength (tensile) represented by standard deviation (tensile strength) affected the development of longitdinal cracks. A loer vale of standard deviation obtained for concrete mix sing lime rock aggregate in the mix as responsible for confining more cracks ithin the sa ct compared ith the mix sing river gravel aggregate. A sensitivity analysis of the model indicated that sbstantial redction in sa-ct depth can be achieved if the variability of concrete strength dring constrction can be redced. Wide concrete pavements (to or more lanes in one direction) ill develop longitdinal crackc de to shrinkage of concrete soon after it is pored. The repair of these cracks is difficlt and expensive, especially hen they are spalled. The presence of these cracks in pavement is nsightly. Therefore longitdinal joints at reasonable spacing (12 ft or one lane ide) are provided to encorage development of controlled cracks along these joints. Longitdinal joints are generally formed by ctting a groove in the green concrete ith a poer sa. Adeqate depth of sa ct mst be provided to ensre that the longitdinal cracks ill be confined ithin the groove. This provides an aesthetically acceptable reglar longitdinal joint in the pavement at a lo maintenance cost. The performance of any sa-ct joint depends on its depth. An inadeqate depth of sa ct may reslt in the development of longitdinal cracks aay from the groove. These cracks eventally ill spall and reqire expensive repair and maintenance. The objective of this stdy as to investigate the development of longitdinal cracks in concrete pavements and to develop a model to estimate the depth of sa ct needed to control these cracks ithin the groove. DEVELOPMENT OF LONGITUDINAL CRACKS ALONG THE SAW-CUT GROOVE Let s assme t hat a ide concret e pavement is constrcted ith a sa ct, as shon in Figre 1. Fr-