Behavior of dowels in concrete pavements
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Concrete structural elements such as wall sections, bridge abutments and slabs on grade rely on dowels to transfer loads across the joints. As the joint width becomes wider, or if the joint is formed, the effect of aggregate interlock to transfer load is reduced and the loads are transferred by dowels. The dowels can be circular or elliptical shaped and are more commonly made of steel or Fiber Reinforced Polymer (FRP). This research project considered steel dowels with either a circular or an elliptical shape used in a highway or airport pavement. The following linear-elastic analysis, however, can be used for FRP dowels and for other doweled structural elements.
Dowels are spaced along transverse joints in a highway or airport pavement. The dowel's main purpose is to transfer shear load across the joint which separates adjacent concrete slabs. Dowels are approximately eighteen inches (457 mm) long, placed at mid-height of the pavement thickness, positioned parallel to the pavement surface, and embedded symmetrically about the transverse joint centerline. The transverse joint was assumed to open, and its width is dependent on the combination of concrete shrinkage and slab contraction due to colder temperatures.
Wheel loads from a single axle, positioned along the open transverse joint, apply a shear load to each effective dowel along the joint. Effective dowels are those dowels included in the distribution of the wheel loads. The shear load causes the dowels to bear against the concrete and causes the dowels to deflect within the concrete. These deflections are directly related to the bearing stress between the embedded dowel and the concrete (or contact bearing stress). The maximum bearing stress corresponds to the maximum deflection which occurs at the transverse joint face. If the maximum bearing stress does not exceed some portion of the elastic-limit stress for concrete, the deformed concrete around the deflected dowel will rebound to its original or reference state. Repetitive loading, however, may not allow the deformed concrete around the dowel to rebound to its original state before another set of wheel loads crosses the transverse joint. In this repetitive load case, permanent concrete deformation would be present.
A need exists to reduce the bearing stress around dowels for maximum axle loading, as well as, repetitive axle loading. Therefore, a comparison was made between circular- and elliptical-shaped dowels with equivalent flexural rigidity. This dowel comparison showed that, for a given load, the elliptical shape with a wider cross section had reduced deflections within the concrete and, reduced bearing stress between the dowel and the concrete. Also, the deflections of the dowel within the concrete at the transverse joint face, for the circular and elliptical shapes, compare favorably with measured deflections found through experimental methods.
Two published analytical foundation models for a beam on elastic foundation were used to determine the deflections of the embedded dowel within the concrete. The first foundation model is referred to as the one-parameter (or Winkler) model, and the second foundation model is referred to as the two-parameter model. The deflections along the dowel were found using each model's respective assumed displaced shape (general solution to the differential equation). The first model's general solution, based on the embedded length of the dowel, was divided into separate theories used for analyzing the dowel. The second model's general solution was simplified due to a slight modification.
The contribution of this research project was to simplify beam on elastic foundation theory through matrix formulation and apply these improved analysis methods to dowels embedded in concrete pavements joints. One of these simplifications allows for the analysis of any dowel embedment length greater than about nine inches (229 mm). Dividing the dowel into smaller elements is not required in the solution.
The analytical foundation models represented the concrete with linear-elastic springs. The spring stiffness for each model is given by elastic constants or parameters. Each model predicts slightly different deflection behavior for the embedded dowel based on these parameters. The first model assumes the springs act independently to support the dowel; whereas, the second model assumes interaction between adjacent springs. Modifications were made to the first model to include the effect of pavement thickness which allowed for comparison of both models.
The theoretical bearing stress between the dowel and the concrete was determined based on the fourth derivative of the assumed displaced shape for a particular model. Therefore, the bearing stresses along the dowel-concrete interface are directly related to the corresponding deflections along the dowel within the concrete. The maximum theoretical bearing stress at the transverse joint face was compared to experimental bearing stress. The experimental bearing stress was calculated from the measured deflection of the dowel at the transverse joint face. The maximum bearing stress was limited to some portion of the elastic-limit stress for the concrete medium.
For a given concrete depth below the dowel, as the load on the dowel is increased, the deflections along the dowel within the concrete and the bearing stresses along the dowel-concrete interface will increase. The analyses using the foundation models (described previously) showed, however, that as the medium depth below the dowel was reduced the dowel deflections within the concrete decreased. A decrease in deflection could be explained by the reduction in cumulative compression over the smaller depth. In addition, the analyses by these models showed that as the concrete medium depth below the dowel decreased the contact bearing stress increased. To verify the deflection behavior of dowels embedded in concrete, experimental testing was undertaken for various size steel dowels having either a circular or an elliptical shape.
Three laboratory test methods were modeled using the stiffness method of structural analysis. Two elemental shear test methods and a cantilever test method were modeled. The elemental shear test methods investigated a single dowel that was embedded in concrete on either side of an open transverse joint and subjected to shear loading. The models, based on the assembled stiffness matrix, were used to determine the deflections along the dowel within the concrete and to verify elastic constants for a particular foundation model.
Additional analysis of the elemental shear test specimens allowed for the inclusion of an elastic medium under a portion of the test specimen to model soil-pavement interaction. This analysis was referred to as the three-parameter model which defines a layered system. In this system, the embedded dowel and surrounding concrete are idealized as beams, connected together with springs and the concrete beam is further supported by an elastic medium.