Davids et al. 3D FINITE ELEMENT ANALYSIS OF JOINTED PLAIN CONCRETE PAVEMENT WITH EverFE2.2 1 William G. Davids* and Zongmu Wang University of Maine Department of Civil and Environmental Engineering 5711 Boardman Hall Orono, ME 04469-5711 George Turkiyyah, Joe P. Mahoney, and David Bush University of Washington Department of Civil and Environmental Engineering Box 352700 Seattle, WA 98195-2700 *Author to whom all correspondence should be addressed: wdavids@umeciv.maine.edu Phone: (207) 581-2116 Fax: (207) 581-3888 Word count: 7,490 (text @ 5,240 words including Abstract and References + 1 table @ 250 words + 8 figures @ 250 words each) ABSTRACT The features and concepts underlying EverFE2.2, a freely available 3D finite element program for the analysis of jointed plain concrete pavements, are detailed. The functionality of EverFE has been greatly extended since its original release: multiple tied slab/shoulder units can be modeled, dowel misalignment and/or mislocation can be specified on a per-dowel basis, nonlinear thermal or shrinkage gradients can be treated, and nonlinear horizontal shear stress transfer between the slabs and base can be simulated. Improvements have also been made to the user interface, including easier load creation, user-specified mesh refinement, and expanded visualization capabilities. This manuscript details these new features and explains the concepts behind the implementation of EverFE2.2. In addition, the results of two parametric studies are reported. The first study considers the effects of dowel locking and slab-base shear transfer, and demonstrates that these factors can significantly affect the stresses in slabs subjected to both uniform shrinkage and thermal gradients. The second study examines transverse joint mislocation and dowel looseness on joint load transfer. As expected, joint load transfer is greatly reduced by dowel looseness. However, while transverse joint mislocation can significantly reduce peak dowel shears, it has relatively little effect on total load transferred across the joint for the models considered here. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 2 INTRODUCTION The use of three-dimensional (3D) finite element (FE) methods for analyzing rigid pavements subjected to mechanical and environmental loadings has grown significantly over the past decade. The increased use of 3D FE analysis has provided pavement researchers and designers with a better understanding of critical aspects of pavement response that cannot be captured with analytical solutions, such as joint load transfer (1, 2), the effect of slab support on stresses (3), and pavement response under dynamic loads (4, 5). However, there are many aspects of rigid pavement behavior that have not been thoroughly studied with 3D FE analysis. This can be attributed to several factors, including the complexity of concrete pavement 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 the relatively long solution times required for large 3D FE analyses. These factors become especially challenging for the analyst when general-purpose FE programs are used. To circumvent these issues, 3D FE analysis packages have been developed specifically for analyzing rigid pavements (6, 7). EverFE1.02, which was first made available in 1998 (7), addressed these difficulties through the use of an interactive graphical user interface allowing easy model definition and visualization of results, specialized techniques for modeling both dowel and aggregate interlock joint load transfer (2, 8), and fast iterative solution strategies that allow the inclusion of inequality constraints for modeling slab-base separation and material nonlinearity (9). Recently, EverFE2.2 has been developed, which retains the original capabilities of EverFE1.02 while incorporating the following features that substantially extend its usefulness: · The ability to model tied adjacent slabs and shoulders. Multi-slab-shoulder systems can be modeled, and transverse tie bars are explicitly incorporated. · Extended dowel modeling capabilities. Dowel-slab interaction can be captured via either the specification of dowel looseness or springs sandwiched between the dowels and slabs, and the effect of dowel misalignment/mislocation can be simulated. · Modeling of nonlinear thermal gradients. Bilinear or trilinear thermal gradients through the pavement thickness can be specified. · Simulation of slab-base interaction. Separation of the base and slab under tension is handled via inequality constraints, and intermediate degrees of horizontal slabbase shear transfer can be captured. · Expanded post-processing capabilities. In addition to visualizing slab stresses and displacements ­ as well as retrieving precise stress and displacement values at specific coordinates ­ the user can view shears and moments in individual dowels. · Expanded library of axle loads. Loads ranging from single wheels to dual-wheel, tandem axles can be quickly created, positioned and deleted as shown in Figure 1(a). This manuscript details the features of EverFE2.2 and the concepts underlying the implementation, with a primary focus on the modeling of the dowels and ties, treatment of nonlinear thermal gradients, and simulation of slab-base interaction. In addition, the results of parametric studies that consider the effects of dowel locking, slab-base shear transfer, and transverse joint mislocation on pavement response are reported to illustrate the flexibility and modeling cababilities of EverFE2.2. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 3 FEATURES OF EverFE2.2 EverFE2.2 employs several element types to discretize concrete pavement systems having from one to nine slab/shoulder units. Up to three elastic base layers can be specified below the slab, and the subgrade is idealized as either a tensionless or tension-supporting dense liquid foundation. Twenty-noded quadratic hexahedral elements are used to discretize the slabs and elastic base layers (10), and the dense liquid foundation is incorporated via numerically integrated, 8-noded quadratic elements that are meshed with the bottom-most layer of solid elements. Linear or nonlinear aggregate interlock joint load transfer as well as dowel load transfer can be modeled at transverse joints. Load transfer across longitudinal joints via transverse tie bars can also be modeled. Figure 1b is a screen shot of the EverFE2.2 meshing panel, showing many of the basic elements (the user can selectively refine the number of elements used to discretize the slabs and base/subgrade layers). The remainder of this section highlights significant features that are new to EverFE2.2; see (2, 8, 11) for detailed discussions of the basic components, including the nonlinear aggregate interlock modeling capabilities. Dowel and Transverse Tie Bar Modeling EverFE2.2 models dowels and transverse tie bars explicitly with embedded flexural finite elements (8, 11), which has the advantage of allowing the dowels and tie bars to be precisely located irrespective of the slab mesh lines as shown in Figure 1b. This embedded element formulation also permits significant savings in computation time by allowing a range of load transfer efficiencies to be simulated without requiring a highly refined mesh at the joint(s). Dowel-slab interaction can be captured either by specifying a length and magnitude of gap between the dowels and the slabs, or by specifying dowel support moduli in the dowel local coordinates, which translate into springs sandwiched between the dowels and slabs (Figure 2a). The latter approach was not available in EverFE1.02, and permits varying degrees of dowel-slab interaction to be modeled while avoiding the contact nonlinearity inherent in the modeling of dowel looseness. However, it must be noted that this approach is a simplification of a complex phenomenon (8). We also note that the localized stresses in the concrete surrounding the dowels may not be accurately predicted when using the embedded element formulation. Tie-slab interaction is captured via user-specified tie bar support moduli in the tie bar local coordinates. Once the dowels have been located within the model, the user can specify four PLVDOLJQPHQWPLVORFDWLRQ SDUDPHWHUV x z  WKDW VKLIW DQ LQGLYLGXDO GRZHO DORQJ WKH x- and z-axes and define its angular misalignment in the horizontal and vertical planes (see Figure 2b). The dowel support moduli coincide with the local dowel coordinate axes (q,r,s), which are rotated from the global (x,y,z D[HV E\ WKH DQJOHV DQG 7KH PHVKLQJ DOJRULWKP SUHFLVHO\ ORFDWHV individual flexural elements within the mesh of solid elements by first solving for the intersection of each dowel with solid element faces, and then subdividing each dowel into at least 20 individual quadratic embedded flexural elements. Nonlinear Thermal Gradients Prior studies have noted that thermal gradients through the depth of concrete pavements are often nonlinear (12, 13). EverFE2.2 allows the consideration of this important effect by the specification of a bilinear or trilinear approximation to a nonlinear gradient, 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 these strains are numerically integrated over the element volume to generate equivalent nodal forces (10). It is important to note that the 20-noded quadratic element employed by EverFE2.2 is capable of accurately capturing strains that vary linearly over its volume. This implies that multiple elements through the pavement thickness should be used to accurately model bi/trilinear thermal gradients. The effect of uniform or non-uniform shrinkage strains can be simulated through their conversion to equivalent temperature changes for input to EverFE2.2. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 4 Simulation of Slab-Base Interaction Modeling interaction of the slab and base is crucial to accurately predicting pavement response to axle loads near joints and thermal or shrinkage gradients. EverFE2.2 allows the specification of either perfect bond between the slab and base (no slip and no separation), or free separation of the slab and base under tension. In both cases, the slab and base do not share nodes, and constraints are used to satisfy the required contact conditions (Figure 3). The solution algorithm relies on a perturbed Lagrangian formulation and a constraint updating scheme based on the current normal stress between the slab and base. Shear transfer between the slab and base can be important when analyzing pavements subject to uniform thermal expansion/contraction or shrinkage strains. Rasmussen and Rozycki (14) recently overviewed the factors governing slab-base shear transfer, noting that both friction and interlock between the slab and base play a role. In addition, a bilinear, elastic-plastic shear transfer model was calibrated based on push tests of slabs on various bases. One conclusion of the their study was that the effect of slab-base shear transfer should be incorporated in 3D analyses of pavement systems. Another recent study by Zhang and Li (15) focused on developing a onedimensional analytical model for predicting shrinkage-induced stresses in concrete pavements that accounts for slab-base shear transfer (15). Like the model developed by Rasmussen and Rozycki, their model ultimately relied on a bilinear, elastic-plastic shear transfer model. Zhang and Li concluded that the type of supporting base ­ and thus the degree to which it restrains slab shrinkage ­ significantly affects slab stresses. To capture slab-base shear transfer, EverFE2.2 employs a 16-noded, zero-thickness quadratic interface element that is meshed between the slab and base (Figure 3). The element constitutive relationship is based on that given by Rasmussen and Rozycki (14) and Zhang and Li (15). The bilinear constitutive relationship is shown in Figure 3, and is characterized by an initial distributed stiffness kSB >03DPP@ DQG VOLS GLVSODFHPHQW o. (We note that while kSB has the same units as the well-known modulus of subgrade reaction, kSB is a distributed stiffness in the horizontal direction, and the shear stresses developed at the slab-base interface depend on the relative horizontal displacements between the slab and base layer.) This constitutive relationship is assumed to apply independently in both the x and y directions if the slab and base remain in contact, which implies a compressive normal stress exists at the slab-base interface. The fact that there will be little or no shear transfer when slab-base separation occurs is accommodated by VHWWLQJ WKH LQWHUIDFH VWLIIQHVV DQG VKHDU VWUHVV WR ]HUR ZKHQHYHU z > 0. Modeling this loss of shear transfer with loss of slab-base contact is important, especially when thermal gradients are simulated. The interface element stiffness matrix and nodal force vector are computed numerically via 3x3 Gauss point integration. For very large values of kSB, this model approaches Coulomb friction with a very large friction coefficient, and for very small values of kSB, it is equivalent to a frictionless interface. An advantage of this modeling scheme is that the symmetry of the system stiffness equations is maintained, which allows the use of the existing, highly efficient preconditioned conjugategradient solver. Idealizing slab-base interaction with conventional Coulomb friction would destroy this symmetry, requiring the use of more complex (and likely less efficient) solution techniques. EFFECT OF DOWEL LOCKING AND SLAB-BASE SHEAR TRANSFER ON THERMAL STRESSES The potential detrimental effects of dowel locking ­ where the dowels become effectively bonded to the slabs ­ on pavement response to thermal loads are well recognized. Dowel locking is commonly attributed to dowel misalignment, which can cause flexure of the dowels and large frictional forces to develop at locations of dowel-slab contact, or corrosion of the dowels, which can result in bond between the dowels and slabs. In addition, one study has suggested that friction between properly aligned dowels and slabs can provide significant axial restraint and increased TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 5 stresses in slabs that are simultaneously subjected to a uniform temperature change and a negative thermal gradient (1). Prior studies (14,15) have also concluded that shear transfer at the slab-base interface can significantly affect slab stresses. Here, we will use EverFE2.2 to simulate the effect of dowel locking on a rigid pavement system subjected to a variety of thermal and self-weight loadings. The degree of slab-base interaction will also be varied to study the effect of this important parameter on response. Model Description A three-slab system was modeled to capture the effect of the restraint provided by adjacent slabs. The 250 mm thick slabs were 4600 mm long and 3600 mm wide, with a modulus of elasticity, E, of 03D D 3RLVVRQ¶V UDWLR RI D FRHIILFLHQW RI WKHUPDO H[SDQVLRQ RI 1.1x10-5 per 0C, and a density of 2400 kg/m3. The slabs were founded on a 150 mm thick asphalt DQG D GHQVLW\ RI NJP3. The dense liquid treated base having E 03D foundation was assumed to have a modulus of subgrade reaction of 0.03 MPa/mm. Each transverse joint had eleven 32 mm diameter, 450 mm long dowels spaced at 300 mm on center. The finite element mesh is shown in Figure 4, and had 3024 solid elements. The center slab was meshed with 18x18 elements in plan, and the outer slabs were meshed more coarsely as they are of secondary interest. The analyses considered dowels that were both locked and unbonded (free slip). In all cases the locked and unbonded dowels were assumed to have no looseness (i.e. provided maximum vertical joint load transfer). No tensile bond stresses were allowed between the slab and base, but three levels of slab-base shear transfer were considered in the analyses to capture the effect of this important parameter. The "low" degree of slab-base interaction corresponded 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 be expected when a bond-breaker such as polyethylene sheeting is placed on the base prior to the slab pour. (We note that kSB cannot be taken as zero as the slabs would be horizontally unrestrained, giving an unstable model.) The "intermediate" slab-base shear transfer parameters were kSB = 0.035 MPaPP DQG o = 0.60 mm, which correspond to an asphalt-treated base (15). The "high" slab-base shear transfer parameters of kSB = 0.416 MPa/mm DQG o = 0.25 mm are reported in (15) for a hot-mix asphalt concrete base. Five load cases were considered: (1) a uniform temperature change of -10 0C (DL ­ T); (2) a positive thermal gradient of 0.032 0C/mm (DL T); (3) a negative thermal gradient of 0.032 0C/mm (DL ­ T); (4) a positive thermal gradient of 0.032 0C/mm plus a uniform temperature drop of -10 0C (DL T ­ T); (5) a negative thermal gradient of -0.032 0C/mm plus a uniform temperature change of -10 0C (DL ­ T ­ T). The term "DL" refers to model self-weight. 7KH XQLIRUP WHPSHUDWXUH FKDQJH LV HTXLYDOHQW WR D XQLIRUP VODE VKULQNDJH RI Parametric Study Results and Significance Table 1 shows the maximum principal stresses predicted in the center slab for all parameter combinations and loadings. These stresses occurred at either the top center or bottom center of the middle slab. We 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 mesh refinement at the joints. Figure 5 shows a colormap of principal stresses and the deformed shape of the system under DL ­ T ­ T assuming high slabbase shear transfer. When an intermediate level of slab-base shear transfer is assumed, dowel locking increases stresses due to a uniform shrinkage load (DL ­ T) by 35%. When high slab-base shear transfer exists, dowel locking has a much less marked effect for this load case due to the significant reduction in overall slab shortening. Dowel locking increases stresses for the DL ­ T ­ T load case for both intermediate slab-base shear transfer (16% increase) and high slab-base shear transfer (81% increase). However, stress increases due to dowel locking are only 7% for the TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 6 DL T ­ T load case with intermediate slab-base shear transfer (although the overall stresses are higher than for DL T ­ T). This difference can be attributed to the fact that under DL T ­ T, the bottom of the slab is shrinking under a net temperature change of ­14 0C. This causes shear stresses at the slab-base interface that are concentrated near the edges of the slab and act away from the slab center which tend to increase tensile stresses in the bottom of the slab significantly more than dowel locking alone. In contrast, under DL ­ T ­ T the net temperature change at the bottom of the slab is only ­6 0C, and the resulting shear stresses, which are concentrated near the center of the slab, tend to reduce the peak tensile stress which occurs at the top of the slab. Further, the ends of the slab are not in contact with the base due to slab lift-off (see Figure 5). As a result, the increase in tensile stress arising from the restraining effect of the dowels is more pronounced. One counter-intuitive result is the 28% decrease in slab stresses due to dowel locking under DL + T ­ T with a high degree of slab-base shear transfer. This can be explained by the fact that dowel locking tends to prevent contraction of the bottom of the slab, reducing the relative displacements between the slab and base and thus the shear at the slab-base interface near the transverse joints. In fact, the maximum relative x-direction displacement between the central slab and base predicted by EverFE, which occurs at the slab ends, is 0.078 mm when dowel 03D ,Q FRQWUDst, when there is no dowel locking, the x-direction ORFNLQJ H[LVWV JLYLQJ UHODWLYH GLVSODFHPHQWV DW WKH VODE HQGV DUH PP LPSO\LQJ WKDW WKH SHDN YDOXH RI 0= 0.104 MPa. As discussed above, this reduction in slab stress with dowel locking was not observed for the intermediate degree of slab-base interaction, where the reduced stiffness kSB of the slabbase interface allows a relative x-direction displacement of 0.208 mm when the dowels are locked and 0.308 mm when the dowels are unbonded. These values result in relatively low slab-base interface shear stresses of 0.0073 MPa and 0.011 MPa, respectively. This explanation was further verified by running simulations where the effect of the degree of bond between the dowels and slabs on slab stress was simulated by varying the dowel-slab axial restraint modulus. Figure 6 shows the results of these analyses for models with both high and intermediate degrees of slabbase shear transfer subjected to DL T ­ T. We note the increase in slab stresses with increasing dowel-slab restraint modulus for the case of intermediate slab-base shear transfer. Conversely, slab stresses decrease with increasing dowel-slab restraint modulus assuming a high degree of slab-base shear transfer. For both degrees of slab-base shear transfer, the limiting stresses given in Table 1 bound the results shown in Figure 6. Increasing slab-base shear transfer tends to increase slab stresses significantly for most loadings. As expected, when kSB = 0.0001 MPa/mm there are no slab stresses for the DL ­ T load case, as shrinkage is effectively unrestrained; however, significant tensile stresses are observed for DL ­ T loading with intermediate slab-base shear transfer for both locked and unlocked dowels. The effect of increasing slab-base shear transfer is also dramatic for the model with locked dowels subjected to DL ­ T ­ T, where slab stresses increase 44% as slab-base shear transfer increases from low to high. Only the DL ­ T ­ T loading with unbonded dowels shows a decrease in slab stresses with increasing slab-base shear transfer. This decrease results from the increased shear stresses between the slab and base under uniform temperature shrinkage that tend to reduce the peak tensile stress at the top of the slab. In general, the results of the simulations indicate that there is a complex interaction between dowel locking, slab-base interaction, and thermal loading. The need for 3D analysis (as opposed to 1D or 2D) when simulating both thermal gradients and shrinkage is evident: even under uniform shrinkage the slab-base shear stresses acting at the bottom of the slab result in slab-base separation and a non-uniform distribution of stresses over the slab thickness due to the eccentricity of the shear stress with respect to the center of gravity of the slab. However, it must be noted that creep of both the slab and base, which is not considered by EverFE2.2, will mitigate these stress increases. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 7 EFFECT OF TRANSVERSE JOINT LOCATION ON JOINT LOAD TRANSFER Poor construction can lead to effective misalignment or mislocation of dowels at transverse contraction joints; see (16) for a review of available literature on the topic of dowel bar misalignment/mislocation. While dowel misalignment/mislocation is suspected to decrease load transfer (16), this topic has not been extensively studied either experimentally or numerically. Here, we examine the effect of transverse joint location using the dowel mislocation/misalignment feature of EverFE2.2. Model Description The finite element model used in this parametric study has the same slab dimensions and material properties assumed in the previous parametric study. However, only two slabs are modeled as the focus is joint load transfer, and the slab-base shear transfer parameters were fixed at kSB 03DPP DQG 0 = 0.60 mm. The only load case considered is an 80-kN dual-wheel axle located at the joint and centered transversely on the left-hand slab combined with a negative thermal gradient of -0.032 0C/mm. Each slab was discretized with 18x18 elements in plan, and the slab and base each had 2 elements through their thickness. Two primary parameters are considered in the analyses: dowel mislocation (simulated through specification of x DV VKRZQ LQ )LJXUH D DQG GRZHO ORRVHQHVV 9DOXHV RI x ranged from ­ PP WR PP ZKHUH x = 0 corresponds to a perfectly located sawn joint; note that a QHJDWLYH YDOXH RI x corresponds to a joint sawn too far to the right (i.e. more of the dowel is located in the loaded slab than in the unloaded slab). Dowel looseness was simulated by explicitly modeling gaps between 0 mm to 0.2 mm between the dowels and slabs, which can have significant effects on joint load transfer (8, 17, 18). The gaps were assumed to vary parabolically along the embedded portions of each dowel, with no gap at the dowel start/end and the maximum gap at the joint. To ensure sufficient potential points of nodal contact between the dowels and slabs, 24 three-noded flexural elements were used to discretize each dowel. Parametric Study Results and Significance Figure 7 shows the variation in peak dowel shear and total shear transferred across the MRLQW ZLWK JDS IRU x = -100 mm, 0 mm, and 100 mm. The peak dowel shear occurs at the third dowel in from the pavement edge, which is centered between two wheels on one side of the axle. As expected, both peak and total shear decrease rapidly with increasing dowel looseness; when x = 0, total shear transferred across the joint decreases by 73% as the gap increases from 0 mm to 0.2 mm In addition, the effect of transverse joint location on peak dowel shear is pronounced for intermediate values of dowel looseness (0.05 ­ 0.10 mm). However, joint location has a small effect on total load transferred across the joint. This can be explained by the equalization of shear between dowels that grows both with increasing gapV DQG LQFUHDVLQJ x. Figure 8 shows the YDULDWLRQ LQ GRZHO VKHDU DFURVV WKH MRLQW IRU VHOHFWHG YDOXHV RI GRZHO ORRVHQHVV DQG x, highlighting this equalization of dowel shear. However, while this equalization of dowel shears can be expected to lead to lower peak dowel-slab bearing stresses, we cannot conclude from this that dowel mislocation is beneficial. This equalization of dowel shear implies less effective dowel load transfer and higher slab stresses due to edge loading. In fact, as dowel looseness increases from 0.0 mm to 0.2 mm with no joint mislocation, the joint displacement load transfer computed between the two wheels on each side of the axle decreases from 99% to 45%, and the peak tensile stress on the slab bottom under the wheel load increases from 0.401 MPa to 0.522 MPa. The results of the analyses indicate that fairly small shifts in joint location 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 constant with joint location, even at shifts in joint location approaching half the embedded length of the dowel. We emphasize that the results of this study cannot be considered conclusive, as only a single load case, system geometry, and set of material properties were considered. Further, dowel mislocation TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. may produce high, localized stresses in the concrete surrounding the dowels that the models employed here cannot capture. However, the need for 3D analysis to simulate these effects is evident. 8 SUMMARY AND CONCLUSIONS This manuscript has highlighted the features of the program EverFE2.2, which has been developed specifically for the 3D finite-element analysis of jointed plain concrete pavements. EverFE2.2 allows the modeling of one to nine slab/shoulder units with tied adjacent slabs and shoulders, and the rigorous treatment of joint load transfer via dowels, aggregate interlock, and transverse tie bars. Dowel misalignment and/or mislocation can be specified on a per-dowel basis. In addition, nonlinear thermal/shrinkage gradients can be treated, and slab-base interaction ­ including separation and horizontal shear stress transfer between the slab and base ­ can be incorporated in the analyses. The interactive, user-friendly interface of EverFE2.2 eases model generation and result interpretation through simple creation/deletion of a variety of axle types, automatic mesh generation, and efficient visualization of slab stresses and displaced shapes. The use of specialized solvers targeted to the model geometry and mechanics allows solutions to be obtained very rapidly on modern desktop machines. Two parametric studies were completed that illustrated the features of EverFE2.2. These studies examined the effect of dowel locking and slab-base shear transfer on pavement stresses due to thermal gradients and uniform slab shrinkage, as well as the effect of dowel misalignment and looseness on pavement response. Based on these studies, the following conclusions can be drawn: · Slab stresses can be highly affected by shear transfer between the slab and base. In turn, the degree of slab-base shear depends on base type and the particular environmental loading (combination of temperature gradient and uniform shrinkage) considered in an analysis. The complex interaction between the effect of slab-base shear transfer and dowel locking is best captured with 3D finite-element analysis. Dowel locking can have an effect on pavement stresses. The effect of dowel locking on stresses due to pure shrinkage and combined shrinkage and thermal gradients is significant for the range of slab-base shear transfer values considered here. The effect of dowel locking was most pronounced for a combined negative thermal gradient and shrinkage, producing an increase in peak tensile stress of 81% when there is a high degree of slab-base shear transfer. Mislocation of transverse doweled joints can affect joint load transfer. When moderate degrees of dowel looseness exist (0.05 ­ 0.10 mm), peak dowel shears can be reduced significantly by joint mislocation. However, due to equalization of dowel shears, the total load transferred across the joint remains relatively constant even with a mislocation of the transverse joint approaching half the embedded length of the dowel. Dowel looseness has a large effect on joint load transfer. Parabolically varying gaps around the dowels as small as 0.20 mm can reduce joint load transfer by a much as 73% under a combined 80 kN axle load and negative thermal gradient. · · · These parametric studies have not fully explored the features of EverFE2.2, and we expect it to be a valuable tool for a wide range of problems in the forensic analysis of pavements as well as pavement design. EverFE2.2 is freely available, and documentation and details for obtaining EverFE2.2 can be found at http://cae4.ce.washington.edu/everfe/. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 9 ACKNOWLEDGEMENTS EverFE2.2 was developed with financial support from the Washington and California State Departments of Transportation. The authors would particularly like to thank Ms. Linda Pierce of WSDOT and Dr. John Harvey of the University of California at Davis for their valuable advice and input during the development of EverFE2.2. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 10 REFERENCES 1. William, G.W. and Shoukry, S.N. 3D Finite Element Analysis of Temperature-Induced Stresses in Dowel Jointed Concrete Pavements. International Journal of Geomechanics, 1(3):291 ­ 308, 2001. 2. Davids, W. and J. Mahoney. Experimental Verification of Rigid Pavement Joint Load Transfer Modeling with EverFE. Transportation Research Record 1684, TRB, National Research Council, Washington, D.C., 1999, pp. 81 ­ 89. 3. Kuo, C., K. Hall, and M. Darter. 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Rasmussen, R.O. and Rozycki, D.K. Characterization and Modeling of Axial Slab-Support Restraint. Transportation Research Record 1778, TRB, National Research Council, Washington, D.C., 2001, pp. 26 ­ 32. 15. Zhang, J. and Li, V.C. Influence of Supporting Base Characteristics on Shrinkage-Induced Stresses in Concrete Pavements. Journal of Transportation Engineering, ASCE, 127(6);455 ­ 642, 2001. 16. Turner-Fairbank Highway Research Center. Guide to Developing Performance-Related Specifications. Federal Highway Administration Report Nos. FHWA-RD-98-155, -156, -171, Vol. III, Appendix C. http://www.tfhrc.gov/pavement/pccp/pavespec/ 17. Zaman, M. and Alvappillai, A. Contact-Element Model for Dynamic Analysis of Jointed Concrete Pavements. Journal of Transportation Engineering, ASCE, 121(5):425 ­ 433, 1995. 18. Guo, H., Larson, R.M. and Snyder, M.B. A Nonlinear Mechanistic Model for Dowel Looseness in PCC Pavements. Proceedings of the Fifth International Conference on Concrete Pavement Design and Rehabilitation, Purdue University, West Lafayette, Indiana, April 20-22, 1993. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 11 TABLE 1: Maximum Principal Stresses Due to Temperature Curling and/or Shrinkage* Degree of Slab-Base Interaction Dowel Type Load Case DL ­ T DL T DL T ­ T DL ­ T DL ­ T ­ T DL ­ T DL T DL T ­ T DL ­ T DL ­ T ­ T Low 0 0.871 (B) 0.870 (B) 0.689 (T) 0.688 (T) 0. 0.871 (B) 0.872 (B) 0.689 (T) 0.689 (T) Intermediate 0.159 (B) 0.886 (B) 0.973 (B) 0.705 (T) 0.773 (T) 0.118 (B) 0.880 (B) 0.906 (B) 0.703 (T) 0.669 (T) High 0.594 (B) 0.945 (B) 1.18 (B) 0.815 (T) 0.991 (T) 0.591 (B) 0.938 (B) 1.51 (B) 0.785 (T) 0.547 (T) Locked Free Slip *All values in MPa; letter in parentheses indicates either top (T) or bottom (B) of slab TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 12 (a) Axle and Thermal Load Specification Solid elements Dowels Ties Plan Elastic base layers ~Dense liquid foundation~ Elevation (b) Typical Model Illustrating Discretization and Element Types FIGURE 1: Model Generation with EverFE2.2. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 13 x y Original position Gap between dowel and slab Slab C.L. x z Original position Misaligned position x
r
q Plan View z
s
Dowel-slab springs Misaligned position Elevation (a) Dowel-Slab Interaction (b) Dowel Misalignment q FIGURE 2: Dowel-slab Interaction and Dowel Misalignment Parameters. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 14 Pairs of nodes vertically constrained if compression at interface Slab element
o z kSB x or y Interface constitutive relationship
o Interface Base element elements transfer shear stress x or y FIGURE 3: Slab-Base Interaction and Interface Shear Transfer. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 15 FIGURE 4: Finite Element Mesh Used in Parametric Study on Dowel Locking. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 16 (a) Tensile Stresses on Top of Slabs (b) Displaced Shape (Scale Factor = 500) FIGURE 5: Slab Stresses and Displacements (DL ­ T ­ T, High Slab-base Shear Transfer). TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 17 1.6 1.5 1.4 1.3 1.2 1.1 1 Intermediate Slab-Base Shear High Slab-Base Shear Maximum Principal Stress (MPa) 0.9 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Dowel Axial Restraint Modulus (MPa) FIGURE 6: Variation in Peak Slab Stress Due to Dowel Axial Restraint (DL + T ­ T). TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 18 Peak Dowel Shear Peak Dowel Shear (kN) 10 8 6 4 2 0 0 40 Total Shear (kN) 30 20 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Magnitude of Gap (mm) Total Shear Transferred Across Joint 0.18 0.2 x = -100 mm x=0 x = 100 mm x = -100 mm x=0 x = 100 mm 10
0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Magnitude of Gap (mm) 0.18 0.2 FIGURE 7: Variation in Dowel Shear with Joint Location and Dowel Looseness. TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal. Davids et al. 19 10 9 8 Dowel Shear (kN) 7
6 5 4 Gap = 0 mm, [ *DS PP [ *DS PP [ PP *DS PP O[ -100 mm 3
2 1 -500 0 500 1000 1500 Dowel Location Across Joint (mm) FIGURE 9DULDWLRQ LQ 'RZHO 6KHDU DFURVV -RLQW ZLWK x (Gap Fixed at 0.10 mm). 0 -1500 -1000 TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.