92 ■ Transportation Research Record 1853Paper No. 03-2223

The features and concepts underlying EverFE2.2, a freely availablethree-dimensional finite element program for the analysis of jointedplain concrete pavements, are detailed. The functionality of EverFE hasbeen greatly extended since its original release: multiple tied slab orshoulder units can be modeled, dowel misalignment or mislocation canbe specified per dowel, nonlinear thermal or shrinkage gradients can betreated, and nonlinear horizontal shear stress transfer between the slabsand base can be simulated. Improvements have been made to the userinterface, including easier load creation, user-specified mesh refinement,and expanded visualization capabilities. These new features are detailed,and the concepts behind the implementation of EverFE2.2 are explained.In addition, the results of two parametric studies are reported. The firststudy considers the effects of dowel locking and slab–base shear transferand demonstrates that these factors can significantly affect the stressesin slabs subjected to both uniform shrinkage and thermal gradients. Thesecond study examines transverse joint mislocation and dowel loosenesson joint load transfer. As expected, joint load transfer is greatly reducedby dowel looseness. However, while transverse joint mislocation can sig-nificantly reduce peak dowel shears, it has relatively little effect on totalload transferred across the joint for the models considered.

The use of three-dimensional finite element (FE) methods for ana-lyzing rigid pavements subjected to mechanical and environmentalloadings has grown significantly in the last decade. The increased useof three-dimensional FE analysis has given pavement researchersand designers a better understanding of critical aspects of pavementresponse that cannot be captured with analytical solutions, such asjoint load transfer (1, 2), the effect of slab support on stresses (3),and pavement response under dynamic loads (4, 5).

However, many aspects of rigid pavement behavior have not beenthoroughly studied with three-dimensional FE analysis. This can beattributed to several factors, including the complexity of concretepavement structures (especially joint load transfer mechanisms),the need to consider both environmental and mechanical load effects,the difficulty of model generation and result interpretation, and therelatively long solution times required for large three-dimensional FEanalyses. These factors become especially challenging for the analystwhen general-purpose FE programs are used. To circumvent theseissues, three-dimensional FE analysis packages have been developed

specifically for analyzing rigid pavements (6, 7). EverFE1.02, whichwas first made available in 1998 (7), addressed these difficultiesthrough the use of an interactive graphical user interface for easy modeldefinition and visualization of results, specialized techniques for mod-eling both dowel and aggregate interlock joint load transfer (2, 8), andfast iterative solution strategies for inclusion of inequality constraintsfor modeling slab–base separation and material nonlinearity (9).

Recently, EverFE2.2 has been developed, which retains the orig-inal capabilities of EverFE1.02 while incorporating the followingfeatures that substantially extend its usefulness:

• The ability to model tied adjacent slabs and shoulders. Multi-ple slab or shoulder systems can be modeled, and transverse tie barsare explicitly incorporated.

• Extended dowel modeling capabilities. Dowel–slab interactioncan be captured via either the specification of dowel looseness orsprings sandwiched between the dowels and slabs, and the effect ofdowel misalignment or mislocation can be simulated.

• Modeling of nonlinear thermal gradients. Bilinear or trilinearthermal gradients through the pavement thickness can be specified.

• Simulation of slab–base interaction. Separation of the base andslab under tension is handled via inequality constraints, and interme-diate degrees of horizontal slab–base shear transfer can be captured.

• Expanded postprocessing capabilities. In addition to visualizingslab stresses and displacements—as well as retrieving precise stressand displacement values at specific coordinates—the user can viewshears and moments in individual dowels.

• Expanded library of axle loads. Loads ranging from single wheelsto dual-wheel, tandem axles can be quickly created, positioned, anddeleted, as shown in Figure 1a.

This manuscript details the features of EverFE2.2 and the con-cepts underlying implementation, with a primary focus on model-ing of the dowels and ties, treatment of nonlinear thermal gradients,and simulation of slab–base interaction. The results of parametricstudies that consider the effects of dowel locking, slab–base sheartransfer, and transverse joint mislocation on pavement response arereported to illustrate the flexibility and modeling capabilities ofEverFE2.2.

FEATURES OF EverFE2.2

EverFE2.2 employs several element types to discretize concretepavement systems that have from one to nine slab or shoulderunits. Up to three elastic base layers can be specified below the slab,and the subgrade is idealized as either a tensionless or a tension-

Three-Dimensional Finite Element Analysis of Jointed Plain ConcretePavement with EverFE2.2

William G. Davids, Zongmu Wang, George Turkiyyah, Joe P. Mahoney, and David Bush

W. G. Davids and Z. Wang, Department of Civil and Environmental Engineering,University of Maine, 5711 Boardman Hall, Orono, ME 04469-5711. G. Turkiyyah and J. P. Mahoney, Department of Civil and Environmental Engineering, University of Washington, Box 352700, Seattle, WA 98195-2700.D. Bush, Dynatest Consulting, Inc., 165 South Chestnut Street, Ventura, CA 93001.

supporting dense liquid foundation. Twenty-noded quadratic hexa-hedral elements are used to discretize the slabs and elastic baselayers (10), and the dense liquid foundation is incorporated vianumerically integrated, eight-noded quadratic elements that aremeshed with the bottommost layer of solid elements. Linear or non-linear aggregate interlock joint load transfer as well as dowel loadtransfer can be modeled at transverse joints. Load transfer across

Davids et al. Paper No. 03-2223 93

longitudinal joints via transverse tie bars can also be modeled. Fig-ure 1b is a screen shot of the EverFE2.2 meshing panel, showingmany of the basic elements. (The user can selectively refine thenumber of elements used to discretize the slabs and base or subgradelayers.) The remainder of this section highlights significant fea-tures that are new to EverFE2.2; detailed discussions of the basiccomponents, including the nonlinear aggregate interlock modeling

(a)

(b)

FIGURE 1 Model generation with EverFE2.2: (a) axle and thermal load specification, (b) typical model illustrating discretization and element types.

capabilities, are available in Davids and Mahoney (2), Davids (8),and Davids and Turkiyyah (11).

Dowel and Transverse Tie-Bar Modeling

EverFE2.2 models dowels and transverse tie bars explicitly withembedded flexural finite elements (8, 11), which has the advan-tage of allowing the dowels and tie bars to be precisely locatedirrespective of the slab mesh lines, as shown in Figure 1b. Thisembedded element formulation also permits significant savings incomputation time by allowing a range of load transfer efficienciesto be simulated without requiring a highly refined mesh at thejoints. Dowel–slab interaction can be captured either by specify-ing a length and magnitude of gap between the dowels and theslabs or by specifying dowel support moduli in the dowel localcoordinates, which translate into springs sandwiched between thedowels and slabs (Figure 2a). The latter approach was not avail-able in EverFE1.02, and it permits varying degrees of dowel–slabinteraction to be modeled while avoiding the contact nonlinearityinherent in the modeling of dowel looseness. However, thisapproach is a simplification of a complex phenomenon (8). Thelocalized stresses in the concrete surrounding the dowels may notbe accurately predicted when the embedded element formulationis used. Tie–slab interaction is captured via user-specified tie-barsupport moduli in the tie-bar local coordinates.

Once the dowels have been located within the model, the user canspecify four misalignment or mislocation parameters (∆x, ∆z, α, β)that shift an individual dowel along the x- and z-axes and define itsangular misalignment in the horizontal and vertical planes (see Fig-ure 2b and 2c). The dowel support moduli coincide with the localdowel coordinate axes (q, r, s), which are rotated from the global (x, y, z) axes by the angles α and β. The meshing algorithm preciselylocates individual flexural elements within the mesh of solid elementsby first solving for the intersection of each dowel with solid elementfaces and then subdividing each dowel into at least 20 individualquadratic embedded flexural elements.

94 Paper No. 03-2223 Transportation Research Record 1853

Nonlinear Thermal Gradients

Previous studies noted that thermal gradients through the depth of concrete pavements are often nonlinear (12, 13). EverFE2.2allows the consideration of this important effect by the specifi-cation of a bilinear or trilinear approximation to a nonlinear gra-dient, which is easily defined in the loading panel (Figure 1a).The temperature changes are converted to equivalent element pre-strains via the slab coefficient of thermal expansion, and thesestrains are numerically integrated over the element volume togenerate equivalent nodal forces (10). The 20-noded quadraticelement employed by EverFE2.2 can accurately capture strainsthat vary linearly over its volume. This implies that multiple ele-ments through the pavement thickness should be used to accu-rately model bilinear or trilinear thermal gradients. The effect ofuniform or nonuniform shrinkage strains can be simulated throughtheir conversion to equivalent temperature changes for input toEverFE2.2.

Simulation of Slab–Base Interaction

Modeling interaction of the slab and base is crucial for accuratelypredicting pavement response to axle loads near joints and ther-mal or shrinkage gradients. EverFE2.2 allows the specification ofeither perfect bond between the slab and base (no slip and no sep-aration) or free separation of the slab and base under tension. Inboth cases, the slab and base do not share nodes, and constraintsare used to satisfy the required contact conditions (Figure 3). Thesolution algorithm relies on a perturbed Lagrangian formulationand a constraint updating scheme based on the current normalstress between the slab and base.

Shear transfer between the slab and base can be important whenanalyzing pavements subject to uniform thermal expansion or con-traction or shrinkage strains. Rasmussen and Rozycki (14) over-viewed the factors governing slab–base shear transfer, noting thatboth friction and interlock between the slab and base play a role.

Elevation

x∆x

y

α

Original position

Misalignedposition

x

zz∆

Original position

Misaligned position

β

qr

qs

(a)

Slab

Dowel-slab springs

C.L.

Gap between dowel and slab

Plan View

(b)

FIGURE 2 (a) Dowel–slab interaction and (b) dowel misalignment parameters.

In addition, a bilinear, elastic-plastic shear transfer model was cal-ibrated on the basis of push tests of slabs on various bases. The studyconcluded that the effect of slab–base shear transfer should be in-corporated in three-dimensional analyses of pavement systems. Astudy by Zhang and Li (15) focused on developing a one-dimensionalanalytical model for predicting shrinkage-induced stresses in con-crete pavements that accounts for slab–base shear transfer. Likethe model developed by Rasmussen and Rozycki, that model ulti-mately relied on a bilinear, elastic-plastic shear transfer model.Zhang and Li concluded that the type of supporting base—and thusthe degree to which it restrains slab shrinkage—significantly affectsslab stresses.

To capture slab–base shear transfer, EverFE2.2 employs a 16-noded, zero-thickness quadratic interface element that is meshedbetween the slab and the base (Figure 3). The element constitutiverelationship is based on that given by Rasmussen and Rozycki (14)and Zhang and Li (15). The bilinear constitutive relationship, defin-ing the relationship between the shear stress (τ) and the relative slipbetween the slab and base is shown in Figure 3. This relationship ischaracterized by an initial distributed stiffness kSB (MPa/mm) andslip displacement δ0. (While kSB has the same units as the well-known modulus of subgrade reaction, kSB is a distributed stiffnessin the horizontal direction, and the shear stresses developed at theslab–base interface depend on the relative horizontal displace-ments between the slab and the base layer.) This constitutive rela-tionship is assumed to apply independently in both the x and ydirections if the slab and base remain in contact, which implies thata compressive normal stress exists at the slab–base interface. Thatthere will be little or no shear transfer when slab–base separationoccurs is accommodated by setting the interface stiffness and shearstress to zero whenever δz > 0. Modeling this loss of shear trans-fer with loss of slab–base contact is important, especially whenthermal gradients are simulated. The interface element stiffnessmatrix and nodal force vector are computed numerically via 3 × 3Gauss point integration.

For very large values of kSB, this model approaches Coulomb fric-tion with a very large friction coefficient, and for very small valuesof kSB, it is equivalent to a frictionless interface. An advantage ofthis modeling scheme is that the symmetry of the system stiffnessequations is maintained, which allows the use of the existing,highly efficient preconditioned conjugate-gradient solver. Ideal-izing slab–base interaction with conventional Coulomb frictionwould destroy this symmetry, requiring the use of more complex(and likely less efficient) solution techniques.

Davids et al. Paper No. 03-2223 95

EFFECT OF DOWEL LOCKING AND SLAB–BASESHEAR TRANSFER ON THERMAL STRESSES

The potential detrimental effects of dowel locking—where the dow-els become effectively bonded to the slabs—on pavement response tothermal loads are well recognized. Dowel locking is commonly attrib-uted to dowel misalignment, which can cause flexure of the dowelsand large frictional forces to develop at locations of dowel–slab con-tact, or corrosion of the dowels, which can result in bond betweenthe dowels and slabs. In addition, one study suggested that frictionbetween properly aligned dowels and slabs can provide significantaxial restraint and increased stresses in slabs that are simultaneouslysubjected to a uniform temperature change and a negative thermalgradient (1). Other studies (14, 15) also concluded that shear trans-fer at the slab–base interface can significantly affect slab stresses.Here, EverFE2.2 is used to simulate the effect of dowel locking ona rigid pavement system subjected to a variety of thermal and self-weight loadings. The degree of slab–base interaction also is variedto study the effect of this important parameter on response.

Model Description

A three-slab system was modeled to capture the effect of the re-straint provided by adjacent slabs. The 250-mm-thick slabs were4,600 mm long and 3,600 mm wide, with a modulus of elasticity Eof 28,000 MPa, a Poisson ratio ν of 0.20, a coefficient of thermalexpansion of 1.1 × 10−5 per °C, and a density of 2,400 kg/m3. Theslabs were founded on a 150-mm-thick asphalt-treated base with Eof 3,500 MPa, ν of 0.20, and density of 2,000 kg/m3. The dense liq-uid foundation was assumed to have a modulus of subgrade reactionof 0.03 MPa/mm. Each transverse joint had 11 dowels 32 mm indiameter and 450 mm long, spaced at 300 mm on center. The FEmesh, shown in Figure 4, had 3,024 solid elements. The center slabwas meshed with 18 × 18 elements in plan, and the outer slabs weremeshed more coarsely, as they are of secondary interest.

The analyses considered dowels that were both locked and un-bonded (free slip). In all cases, the locked and unbonded dowelswere assumed to have no looseness (i.e., they provided maximumvertical joint load transfer). No tensile bond stresses were allowedbetween the slab and the base, but three levels of slab–base sheartransfer were considered in the analyses to capture the effect of thisimportant parameter. The low degree of slab–base interaction corre-sponded to a slab–base interface shear stiffness kSB of 0.0001 MPa/mm,which is the minimum value used by EverFE2.2; this value might

Base elementInterfaceelements transfershear stress

Slab element

Pairs of nodes vertically constrainedif compression at interface

δx or δy

δz

τ

δx or δy

kSB

δo

τo z

o

(b)

(a)

FIGURE 3 Modeling of (a) slab–base interaction and (b) interface shear transfer.

96 Paper No. 03-2223 Transportation Research Record 1853

Parametric Study Results and Significance

Table 1 shows the maximum principal stresses predicted in the cen-ter slab for all parameter combinations and loadings. These stressesoccurred at either the top center or the bottom center of the middleslab. Note that when there is full bond between the dowels and slabs,the model may predict higher tensile stresses around the dowels;however, these stresses are not reliable because of insufficient meshrefinement at the joints. Figure 5 shows a colormap of principalstresses and the deformed shape of the system under DL − ∆T − Tassuming high slab–base shear transfer.

When an intermediate level of slab–base shear transfer isassumed, dowel locking increases stresses due to a uniform shrink-age load (DL − T ) by 35%. When high slab–base shear transferexists, dowel locking has a much less marked effect for this load

FIGURE 4 Finite element mesh used in parametric study on dowel locking.

(a)

(b)

Degree of Slab-Base Interaction

Dowel Type Load Case Low Intermediate High

DL – T 0 0.159 (B) 0.594 (B) DL + ∆ T 0.871 (B) 0.886 (B) 0.945 (B)

DL + ∆T – T 0.870 (B) 0.973 (B) 1.18 (B) DL – ∆T 0.689 (T) 0.705 (T) 0.815 (T)

Locked

DL – ∆T – T 0.688 (T) 0.818 (T) 0.991 (T) DL – T 0 0.118 (B) 0.591 (B)

DL + ∆ T 0.871 (B) 0.880 (B) 0.938 (B) DL + ∆T – T 0.872 (B) 0.906 (B) 1.51 (B)

DL – ∆T 0.689 (T) 0.703 (T) 0.785 (T)

Free Slip

DL – ∆T – T 0.689 (T) 0.669 (T) 0.547 (T)

*All values in MPa; letter in parentheses indicates either top (T) or bottom (B) of slab.

TABLE 1 Maximum Principal Stresses Caused by TemperatureCurling or Shrinkage or Both

FIGURE 5 (a) Tensile stresses on top of slabs and (b) displaced shape (scale factor �500) (DL � �T � T, high slab–base shear transfer).

be expected when a bond-breaker such as polyethylene sheeting isplaced on the base before the slab pour. (Note that kSB cannot betaken as zero because the slabs would be horizontally unrestrained,giving an unstable model.) The intermediate slab–base shear trans-fer parameters were kSB = 0.035 MPa/mm and δ0 = 0.60 mm, whichcorrespond to an asphalt-treated base (15). The high slab–base sheartransfer parameters of kSB = 0.416 MPa/mm and δ0 = 0.25 mm werereported by Zhang and Li for a hot-mix asphalt concrete base (15).

Five load cases were considered:

• A uniform temperature change of −10°C (DL − T );• A positive thermal gradient of 0.032°C/mm (DL + ∆T);• A negative thermal gradient of −0.032°C/mm (DL − ∆T);• A positive thermal gradient of 0.032°C/mm plus a uniform

temperature drop of −10°C (DL + ∆T − T ); and• A negative thermal gradient of −0.032°C/mm plus a uniform

temperature change of −10°C (DL − ∆T − T ).

The term DL refers to model self-weight. The uniform temperaturechange is equivalent to a uniform slab shrinkage of 110 µ�.

case because of the significant reduction in overall slab shortening.Dowel locking increases stresses for the DL − ∆T − T load case forboth intermediate slab–base shear transfer (16% increase) and highslab–base shear transfer (81% increase). However, stress increasescaused by dowel locking are only 7% for the DL + ∆T − T load casewith intermediate slab–base shear transfer (although the overallstresses are higher than for DL + ∆T − T ). This difference can beattributed to the fact that under DL + ∆T − T, the bottom of the slabis shrinking under a net temperature change of −14°C. This causesshear stresses at the slab–base interface that are concentrated nearthe edges of the slab and act away from the slab center, which tendsto increase tensile stresses in the bottom of the slab significantlymore than dowel locking alone. In contrast, under DL − ∆T − T, thenet temperature change at the bottom of the slab is only −6°C, andthe resulting shear stresses, which are concentrated near the centerof the slab, tend to reduce the peak tensile stress that occurs at the topof the slab. Further, the ends of the slab are not in contact with thebase because of slab liftoff (see Figure 5). As a result, the increase intensile stress arising from the restraining effect of the dowels is morepronounced.

A counterintuitive result is the 28% decrease in slab stressescaused by dowel locking under DL + ∆T − T with a high degree ofslab–base shear transfer. This can be explained by the fact that dowellocking tends to prevent contraction of the bottom of the slab, reduc-ing the relative displacements between the slab and base and thus theshear at the slab–base interface near the transverse joints. In fact, themaximum relative x-direction displacement between the central slaband the base predicted by EverFE, which occurs at the slab ends, is0.078 mm when dowel locking exists, giving τ = 0.032 MPa. In con-trast, when there is no dowel locking, the x-direction relative dis-placements at the slab ends are 0.25 mm, implying that the peakvalue of τ = τ0 = 0.104 MPa. As discussed, this reduction in slabstress with dowel locking was not observed for the intermediatedegree of slab–base interaction, where the reduced stiffness kSB ofthe slab–base interface allows a relative x-direction displacement of0.208 mm when the dowels are locked and 0.308 mm when the dow-els are unbonded. These values result in relatively low slab–baseinterface shear stresses of 0.0073 MPa and 0.011 MPa, respectively.This explanation was further verified by running of simulations inwhich the effect of the degree of bond between the dowels and slabson slab stress was simulated by varying the dowel–slab axial re-straint modulus. Figure 6 shows the results of these analyses formodels with both high and intermediate degrees of slab–base sheartransfer subjected to DL + ∆T − T. Note the increase in slab stresseswith increasing dowel–slab restraint modulus for the case of inter-mediate slab–base shear transfer. Conversely, slab stresses decreasewith increasing dowel–slab restraint modulus, assuming a highdegree of slab–base shear transfer. For both degrees of slab–baseshear transfer, the limiting stresses given in Table 1 bound the resultsshown in Figure 6.

Increasing slab–base shear transfer tends to increase slab stressessignificantly for most loadings. As expected, when kSB = 0.0001 MPa/mm, there are no slab stresses for the DL − T load case, as shrink-age is effectively unrestrained; however, significant tensile stressesare observed for DL − T loading with intermediate slab–base sheartransfer for both locked and unlocked dowels. The effect of increas-ing slab–base shear transfer is also dramatic for the model withlocked dowels subjected to DL −∆T − T, where slab stresses increase44% as slab–base shear transfer increases from low to high. Onlythe DL − ∆T − T loading with unbonded dowels shows a decreasein slab stresses with increasing slab–base shear transfer. This de-

Davids et al. Paper No. 03-2223 97

crease results from the increased shear stresses between the slaband the base under uniform temperature shrinkage that tend toreduce the peak tensile stress at the top of the slab.

In general, the results of the simulations indicate that there is acomplex interaction among dowel locking, slab–base interaction,and thermal loading. The need for three-dimensional analysis(instead of one- or two-dimensional) when simulating both ther-mal gradients and shrinkage is evident: even under uniform shrink-age, the slab–base shear stresses acting at the bottom of the slabresult in slab–base separation and a nonuniform distribution ofstresses over the slab thickness because of the eccentricity of theshear stress respective to the center of gravity of the slab. How-ever, creep of both slab and base, which is not considered byEverFE2.2, will mitigate these stress increases.

EFFECT OF TRANSVERSE JOINT LOCATION ONJOINT LOAD TRANSFER

Poor construction can lead to effective misalignment or mislocationof dowels at transverse contraction joints (16 ). While dowel mis-alignment or mislocation is suspected to decrease load transfer (16),this topic has not been extensively studied either experimentally ornumerically. Here, the effect of transverse joint location is examinedby using the dowel mislocation–misalignment feature of EverFE2.2.

Model Description

The FE model used in this parametric study has the same slab dimen-sions and material properties assumed in the previous parametricstudy. However, only two slabs are modeled, because the focus is jointload transfer, and the slab–base shear transfer parameters were fixedat kSB = 0.035 MPa/mm and δ0 = 0.60 mm. The only load case con-sidered is an 80-kN dual-wheel axle located at the joint and centeredtransversely on the left-hand slab combined with a negative thermalgradient of −0.032°C/mm. Each slab was discretized with 18 ×18 ele-ments in plan, and the slab and base each had two elements throughtheir thickness.

0 200 400 600 800 1000 1200 1400 1600 1800 20000.9

1

1.1

1.2

1.3

1.4

1.5

1.6

Dowel Axial Restraint Modulus (MPa)

Max

imum

Prin

cipa

l Stre

ss (M

Pa)

Intermediate Slab-Base Shear High Slab-Base Shear

FIGURE 6 Variation in peak slab stress caused by dowel axialrestraint (DL � �T � T ).

Two primary parameters are considered in the analyses: dowelmislocation (simulated through specification of ∆x, as shown in Fig-ure 2a) and dowel looseness. Values of ∆x ranged from −100 mm to100 mm, where ∆x = 0 corresponds to a perfectly located sawed joint;note that a negative value of ∆x corresponds to a joint sawed too farto the right (i.e., more of the dowel is located in the loaded slab thanin the unloaded slab). Dowel looseness was simulated by explicitlymodeling gaps of 0 to 0.2 mm between the dowels and slabs, whichcan have significant effects on joint load transfer (8, 17, 18). Thegaps were assumed to vary parabolically along the embedded por-tions of each dowel, with no gap at the dowel start or end and withthe maximum gap at the joint. To ensure sufficient potential pointsof nodal contact between the dowels and slabs, 24 three-nodedflexural elements were used to discretize each dowel.

Parametric Study Results and Significance

Figure 7 shows the variation in peak dowel shear and total sheartransferred across the joint with gap for ∆x = −100 mm, 0 mm, and100 mm. The peak dowel shear occurs at the third dowel in from thepavement edge, which is centered between two wheels on one sideof the axle. As expected, both peak and total shear decrease rapidlywith increasing dowel looseness; when ∆x = 0, total shear trans-ferred across the joint decreases by 73% as the gap increases from0 mm to 0.2 mm. In addition, the effect of transverse joint locationon peak dowel shear is pronounced for intermediate values of dowellooseness (0.05 to 0.10 mm). However, joint location has a smalleffect on total load transferred across the joint. This can be explainedby the equalization of shear between dowels that grows both withincreasing gaps and with increasing ∆x. Figure 8 shows the varia-tion in dowel shear across the joint for selected values of dowellooseness and ∆x, highlighting this equalization of dowel shear.

98 Paper No. 03-2223 Transportation Research Record 1853

However, while this equalization of dowel shear can be expected tolead to lower peak dowel–slab bearing stresses, it cannot be con-cluded from this that dowel mislocation is beneficial. This equal-ization of dowel shear implies less effective dowel load transfer andhigher slab stresses caused by edge loading. In fact, as dowel loose-ness increases from 0 to 0.2 mm with no joint mislocation, the joint-displacement load transfer computed between the two wheels oneach side of the axle decreases from 99% to 45%, and the peak ten-sile stress on the slab bottom under the wheel load increases from0.401 to 0.522 MPa.

The results of the analyses indicate that fairly small shifts in jointlocation can have a large effect on peak dowel shears. Further,dowel looseness has a large effect on joint load transfer. However,total shear transferred across the joint remains relatively constantwith joint location, even at shifts in joint location approaching halfthe embedded length of the dowel. The results of this study cannotbe considered conclusive, because only a single load case, systemgeometry, and set of material properties were considered. Further,dowel mislocation may produce high, localized stresses in the con-crete surrounding the dowels that the models employed here cannotcapture. However, the need for three-dimensional analysis withwhich to simulate these effects is evident.

SUMMARY AND CONCLUSIONS

This paper highlighted the features of the program EverFE2.2, whichwas developed specifically for the three-dimensional FE analysis ofjointed plain concrete pavements. EverFE2.2 allows the modeling ofone to nine slab–shoulder units with tied adjacent slabs and shouldersand the rigorous treatment of joint load transfer via dowels, aggregateinterlock, and transverse tie bars. Dowel misalignment or mislocationcan be specified per dowel. In addition, nonlinear thermal and shrink-age gradients can be treated, and slab–base interaction—includingseparation and horizontal shear stress transfer between the slab andbase—can be incorporated in the analyses. The interactive, user-friendly interface of EverFE2.2 eases model generation and resultinterpretation through simple creation or deletion of a variety of axle

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

2

4

6

8

10

Magnitude of Gap (mm)

Pea

k D

owel

She

ar (

kN)

∆x = -100 mm ∆x = 0 ∆x = 100 mm

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

10

20

30

40

Magnitude of Gap (mm)

Tot

al S

hear

(kN

)

∆x = -100 mm ∆x = 0 ∆x = 100 mm

(a)

(b)

-1500 -1000 -500 0 500 1000 1500 0

1

2

3

4

5

6

7

8

9

10

Dow

el S

hear

(kN

)

Dowel Location Across Joint (mm)

Gap = 0 mm, ∆x = 0 Gap = 0.10 mm, ∆x = 0 Gap = 0.10 mm, ∆x = 100 mm Gap = 0.10 mm, ∆x = -100 mm

FIGURE 7 Variation in dowel shear with joint location and dowellooseness: (a) peak dowel shear and (b) total shear transferredacross joint.

FIGURE 8 Variation in dowel shear across joint with �x(gap fixed at 0.10 mm).

types, automatic mesh generation, and efficient visualization of slabstresses and displaced shapes. The use of specialized solvers targetedto the model geometry and mechanics allows solutions to be obtainedrapidly on modern desktop machines.

Two parametric studies were completed that illustrated the fea-tures of EverFE2.2. These studies examined the effect of dowellocking and slab–base shear transfer on pavement stresses due tothermal gradients and uniform slab shrinkage, as well as the effectof dowel misalignment and looseness on pavement response. Fromthese studies, the following conclusions can be drawn:

• Slab stresses can be highly affected by shear transfer betweenthe slab and base. In turn, the degree of slab–base shear depends onbase type and the particular environmental loading (combination oftemperature gradient and uniform shrinkage) considered in an analy-sis. The complex interaction between the effect of slab–base sheartransfer and dowel locking is best captured with three-dimensionalFE analysis.

• Dowel locking can have an effect on pavement stresses. Theeffect of dowel locking on stresses caused by shrinkage and by combined shrinkage and thermal gradients is significant for the range of slab–base shear transfer values considered here. Theeffect of dowel locking was most pronounced for a combined neg-ative thermal gradient and shrinkage, producing an increase inpeak tensile stress of 81% when there is a high degree of slab–baseshear transfer.

• Mislocation of transverse doweled joints can affect joint loadtransfer. When moderate degrees of dowel looseness exist (0.05 to0.10 mm), peak dowel shears can be reduced significantly by jointmislocation. However, because of equalization of dowel shears, thetotal load transferred across the joint remains relatively constanteven with a mislocation of the transverse joint approaching half theembedded length of the dowel.

• Dowel looseness has a large effect on joint load transfer. Para-bolically varying gaps around the dowels as small as 0.20 mm canreduce joint load transfer by as much as 73% under a combined80-kN axle load and negative thermal gradient.

These parametric studies have not fully explored the features ofEverFE2.2, and it is expected to be a valuable tool for a wide rangeof problems in the forensic analysis of pavements as well as pave-ment design. EverFE2.2 is freely available, and documentation anddetails for obtaining EverFE2.2 can be found at cae4.ce.washington.edu/everfe/.

ACKNOWLEDGMENTS

EverFE2.2 was developed with financial support from the Wash-ington and California Departments of Transportation. The authorsthank Linda Pierce of the Washington State Department of Trans-portation and John Harvey of the University of California at Davisfor their valuable advice and input during the development ofEverFE2.2.

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Publication of this paper sponsored by Committee on Rigid Pavement Design.