In Bogotá, Colombia, extensive stretches of PCCP were built exclusively for bus rapid transit (BRT) that integrates the TransMilenio transportation system. Due to various factors, some CSs have experienced distresses and the repair of the PCCP consisted of replacing the CSs with continuous dense gradation AC with 19 mm nominal maximum aggregate size (NMAS). Therefore, during the repairs, sections of the PCCP were converted to ACP, i.e., ACP-PCCP transitions were constructed.

It is worth mentioning that the ACP-PCCP transitions were not constructed with methods such as transition slab, elastomeric concrete joint, or patching mix, instead, the pavement transitions consisted solely of the sudden change from AC to CS (direct ACP-PCCP transitions). Nevertheless, prematurely in some direct ACP-PCCP transitions, the AC began to experience cracking and material heaving, mainly under the tire path and near the joint, as well as differential displacement of the joints (Figure 1). Currently, the origin of the distresses has not been investigated and remains uncertain. Although the literature reports possible causes of distresses for ACP-PCCP transitions, these do not allow an understanding of the failure mechanisms of a direct ACP-PCCP transition. Therefore, this study aims to determine the mechanical responses of a direct ACP-PCCP transition under moving vehicular loading by dynamic FE analysis in order to identify failure mechanisms.

Figure 1. Figure 1. Distresses in direct ACP-PCCP transitions Source: Created by the author.

Problems related to the prediction of mechanical responses and failure mechanisms of pavements have been addressed by applying the FE method [5], however, the literature related to ACP -PCCP transitions is limited and that related to FE modeling is even more limited. Although there is a study that modeled an ACP-PCCP transition using a transition slab by determining deflections on the granular subbase and a possible failure mechanism [2], the FE modeling was simple and the results do not allow identifying possible failure mechanisms of a direct transition due to the constructional differences of the transitions (i.e., one uses transition slab and the other does not). However, the literature related to FE modeling of PCCP, and ACP is extensive and since the direct transitions in Bogota were initially a PCCP to which a CS was removed and an AC layer was added, it was convenient to know about FE modeling of PCCP and ACP.

The recommended and commonly used approach for modeling PCCP has been the three-dimensional since it allows a realistic representation of the geometry, discontinuities and embedded elements of the pavement, for instances, transverse joints, longitudinal joints, dowel slots and dowels [5]–[7]; studies have paid particular attention to the mechanical responses of transverse joints since the load-carrying capacity of CS near the edge is small, thus, fine meshing near the transverse joint has been necessary to accurately capture the responses, however, fine meshing is also used in the load application zones and required in the dowel due to its small size [8]–[10]; It should be mentioned that every study reviewed considered the frictional behavior between the different pavement layers using only COFs, although there are complex models to characterize the interface between materials [11], [12], studies indicate that the Coulomb-type friction model which receives a COF can be acceptable for modeling the friction between layers of materials [13], [14]; on the other hand, FE models have been subjected to uniformly distributed vertical tire-pavement contact pressures applied on rectangular, ellipsoidal or circular areas [8], [15], [16], however, field measurements and FE simulations indicate that the tire-pavement contact pressures are vertical and tangential with non-uniform distribution [17]–[19], although these pressures have been commonly applied in ACP models, improving the accuracy of pavement mechanical responses [14], [20], [21], their application should also be considered for PCCP models. The application of these pressures is usually performed on an almost realistic representation of the tire-pavement footprint that is composed of different rectangular shapes simulating the tire treads (pressures vary along the treads) [18], [19], [22]. Furthermore, although some studies introduce improvements in concrete properties using models such as concrete smeared cracking and concrete damaged plasticity to predict the inelastic and post-cracking behavior of concrete, their application may be limited due to laboratory tests (compression and uniaxial cyclic tension) to obtain the necessary parameters of the models [5], [23]–[25], in this sense, it would be advisable to apply these models in cases where the concrete strain exceeds the elastic range. In the studies reviewed, granular layers and subgrade are assumed to be isotropic linear elastic characterized only with a modulus of elasticity and Poisson's ratio [23], [26], although there are sophisticated models to characterize these materials, assuming them to be elastic can be acceptable considering the good experiences in the validation of PCCP FE models [24]–[27].

On the other hand, based on FE simulations and instrumented pavement measurements, the following recommendations for FE modeling of ACP can be made: the AC should incorporate viscoelastic properties since using elastic tends to underestimate the material responses [28]; as mentioned previously, a realistic state of tire-pavement contact pressures should be included due to their non-conservative effect on AC strains mainly near the surface [22], [29]; consider the movement of contact pressures in order to capture the full viscoelastic response of the AC [30]; granular layers and subgrade should be characterized as nonlinear and anisotropic since the mechanical responses of the ACP tend to be greater than those experienced with linear elastic properties [31]–[33]; the model meshing should be fine in the areas of load application and where there is interest in knowing accurately the mechanical responses, when moving away from these areas the meshing can increase in size, it is also recommended the use of infinite elements to prevent the reflection of stresses during a dynamic analysis and to simulate the semi-infinite vertical and horizontal extension of the subgrade [21], [34]. It is also worth mentioning that in the previous studies the three-dimensional approach is used to model ACP and the frictional behavior is characterized by the Coulomb-type friction model.

The model used was taken from the literature since it had the necessary details for its reproduction and had been previously validated. Originally the model was used to examine the mechanical responses of precast panel pavement repair joints under static aircraft loads [25]. The characteristics of the doweled PCCP model are summarized below:

- Geometry: Figure 2 presents the dimensions of the model including the thicknesses of each layer. The model also included 10 dowels of 558.8 mm in length and 25.4 mm in diameter and the dowel grout.

Table 1. Table 1. Materials properties

Materials	Modulus of elasticity (MPa)	Poisson's ratio	Density (kg/m3)
Unloaded CS (D1)	33 440	0.2	2 320
Loaded CS (D0)	33 440	0.2	2 320
Dowels	199 948	0.3	7 800
Dowel grout	22 063	0.2	1 840
Base	379	0.4	2 000
Flowable fill	276	0.2	1 910
Subgrade	145	0.4	1 840

Source: Created by the author.

Figure 2. Figure 2. Three-dimensional FE model of PCCP Source: Created by the author.

In order to validate the model and modeling techniques a heavy impact deflectometer (FWD) test was simulated, therefore, a uniform pressure of 3.2 MPa was applied for 20 ms over a 300 mm diameter contact area near the transverse joint (Figure 2). Model validation was performed by comparing the deflections and load transfer efficiency (LTE) of the FE model against the results from Westergaard's analytical edge deflection equations and FWD field measurements. It is worth mentioning that the simulation was performed with a 2-core Intel Celeron with 3.5 GHz and 6 Gb of RAM and the calculation time was approximately 4 hours. The validation is presented in Table 2, as well as the difference between the calculated deflection and the field measurement (error column). In this table, it is observed that the FE model deflections were close to the field measurements at both D0 and D1, moreover, the FE model deflections were more accurate than those calculated using the Westergaard equations. The LTE of the FE model was similar to that measured in the field (3.4 % higher) and to that calculated with the Westergaard equations (2.1 % lower).

Table 2.

Note: LTE = D₁ / D₀ *100

^a Based on [25]

Even though the FE model deflections were not accurate to the field measurements, the differences exhibited (16.6 % and 12.3 %) were acceptable considering the high variability of the field measurements, even in the literature, maximum differences of 15 % and 20 % have been accepted in pavement validations [28], [35]. Therefore, the FE model can acceptably predict the responses of a PCCP and can be used to create a direct ACP-PCCP transition.

The following modifications were made to the PCCP model to create the direct ACP-PCCP transition: D₁ and the dowels were removed; the flowable fill was extended along the model above the base layer; an AC layer was added, being assumed as linear viscoelastic; and due to the model and load symmetry, the symmetry boundary condition in the YZ plane was added to decrease the model size by half and reduce the computational demand, in this sense, the model consisted of 31 487 elements and 38 682 nodes and the computational time was approximately 3 hours. The properties of the other materials and characteristics of the model such as mesh size, layer thicknesses, friction between layers, and boundary conditions were retained (Figure 3). It is worth mentioning that some of the changes introduced were made to meet the thickness limits for CS or AC (200 mm to 280 mm) and flowable fill (30 mm to 500 mm) of the TransMilenio pavement [36].

Figure 3. Figure 3. Three-dimensional FE model of direct ACP-PCCP transition Source: Created by the author.

Figure 9 illustrates the effect on vertical displacement and LTE caused by varying the COF at the AC-concrete interface. The effect was measured by the FWD test. According to the results, COFs of 0.02 and 0.1 represented debonding of the AC-concrete interface since sliding was experienced at the joint between the AC and the CS causing vertical displacement in different directions. The CS (loaded) was displaced downward causing an uplift of the flowable fluid fill, and consequently, upward displacement of the AC (unloaded). Due to debonding of the interface LTE across the transition joint was not experienced (negative LTE). Furthermore, increasing the COF from 0.02 to 0.1 (increasing the bonding) caused the reduction of the vertical displacement in the AC and CS, however, this effect was negligible on the LTE since it remained negative. In this sense, COFs of 0.02 and 0.1 could represent a state of a very poor and poor bond of the AC-concrete interface, respectively.

Figure 9. Figure 9. LTE and vertical displacement from FWD testing Source: Created by the author.

On the other hand, COFs f 1.5 and 0.7 allowed load transfer across the joint. The LTE experienced was 82.2 % and 67.1 %, respectively. In this regard, increasing the AC-concrete interface bonding increases the LTE, but increasing the interface bonding increased the vertical displacement of the AC and the CS by approximately 11 %. However, when comparing the PCCP results against those of the direct ACP-PCCP transition, for the 1.5 COF, good agreement was observed in the LTE (0.9 % difference) and the vertical displacement of the loaded (6.8 % difference) and unloaded (7.8 % difference) slab. Therefore, COFs of 1.5 and 0.7 could represent a state of good and acceptable bonding of the AC-concrete interface, respectively. Since the COFs of 0.02 and 0.1 represented debonding of the AC-concrete interface, these were not used to simulate the moving vehicular loading at the direct ACP-PCCP transition, instead, only the CFs of 1.5 and 0.7 were used.

The vertical and longitudinal displacement was measured at the surface edge of the AC and CS, along the transition joint (X direction). The difference between the displacement of the AC and CS represents the differential displacement (DD). It is thought that DD can affect the performance of an ACP-PCCP transition [2], therefore, it was analyzed in this study.

Figure 10 illustrates the vertical DD, noting that for the COFs of 0.7 and 1.5, in the time instants when the tires were mainly supported on the AC (29.1 ms and 52.6 ms), the maximum vertical DD was experienced, On the contrary, when the tires were mainly supported on the CS (152.4 ms and 178.8 ms) the vertical DD was approximately 35 % lower than the maximum vertical DD. This could be caused mainly by the difference in stiffness between the AC and the concrete since the modulus of the concrete is high compared to the AC allowing for smaller displacements. As the tires advanced above the joint (78.99 ms to 131.79 ms) the tire-pavement contact pressure was progressively distributed in the CS leading to the progressive reduction of the vertical DD.

Figure 10. Figure 10. Vertical DD between AC and CS Source: Created by the author.

On the other hand, just below the tires, the highest vertical DD of the joint was experienced (at all time instants), since the vertical DD increased between 0.5 m and 1.1 m, the distance where it was located to the loading area. In addition, increasing the CA-concrete interface bond reduced the vertical DD by approximately 47 % at each time instant, therefore, increasing the interface bond may be conservative.

Figure 11 reveals that the difference in stiffness between the AC and the concrete also affects the longitudinal DD of the joint, since the maximum DD occurred at the instant when the tires were mainly supported on the AC (78.99 ms), in the following time instants (105.4 ms to 178.8 ms) the maximum longitudinal DD was reduced between 17 % to 61 % when the tires were mainly supported on the CS.

Figure 11. Figure 11. Longitudinal DD between AC and CS Source: Created by the author.

Even though longitudinal DD was about 0.5 % of the maximum vertical DD (almost negligible), the longitudinal DD may increase due to the cyclic vehicle traffic. On the other hand, increasing the AC-concrete interface bonding reduces longitudinal DD, though not significantly, since increasing the COF from 0.7 to 1.5 caused approximately a 9 % reduction of the longitudinal DD at each time instant. It is worth mentioning that the data in Figure 10 presented dispersion due to its low magnitude and the vertical scale used for visualization.

Figure 12 illustrates the longitudinal and transverse tensile strains at the bottom of the AC (ε_L and ε_T, respectively). These strains were analyzed since they are related to fatigue cracking [29]. In addition, they were also calculated for an ACP to contrast them against those of the direct ACP-PCCP transition. To model the ACP, the AC and CS in the direct ACP-PCCP transition were replaced by AC with the VEL properties in Table 3.

Figure 12. Figure 12. Tensile strains at the bottom of the AC Source: Created by the author.

According to Figure 12, the direct ACP-PCCP transition might not develop cracking at the bottom of the AC, or its development might be delayed since the maximum ε_L in the ACP (51με) was reduced to one-third in the direct ACP-PCCP transition (16.9 με). On the other hand, even though the maximum ε. (23.5 με) at the direct ACP-PCCP transition was about 2 times higher than that of the ACP (12.5 με), its magnitude was 50 % lower than the maximum ε_L at the ACP, therefore, the increase in ε_T was negligible. Furthermore, increasing the AC-concrete interface bonding might be conservative for fatigue cracking, since increasing the COF from 0.7 to 1.5 reduced the ε_L and ε_T by 6 % and 9 %, respectively. It is worth noting that the maximum tensile strains were experienced at 52.6 ms, when the tires were supported on the AC, near the edge of the joint (Figure 8).

The near-surface vertical shear strains are related to top-down cracking of the AC [29], therefore, the shear strains in the YZ and XZ planes were analyzed and compared against those experienced in an ACP. Figure 13a shows that the shear strain in the YZ plane (ε_YZ) is susceptible to the sudden change from AC to concrete since when compared to that of the ACP, the ε_YZ at the beginning of the simulation was up to 80 % lower, however, as the tires passed over the joint the strain progressively increased until it reached its maximum magnitude (-103 με). In this regard, the AC may experience premature near-surface cracking since the maximum ε_YZ was 2.7 times greater than the maximum experienced in the ACP (- 38με). The maximum ε_YZ happened when the tires were supported at the AC and mainly at the CS (152.4 ms). On the other hand, the effect caused by increasing the AC - concrete interface bonding was negligible, since increasing the COF increased the maximum ε_YZ by 1.1 %. At times between 29.1 ms and 105.4 ms, increasing the bonding reduced the ε_YZ between 11 % and 29 %.

Figure 13. Figure 13. (a) εYZ and (b) εXZ near-surface Source: Created by the author.

Figure 13b allows observing that the effect on the shear strain in the XZ plane (ε_XZ) caused by the sudden change from AC to concrete and the increased AC-concrete interface bonding was not significant since the maximum ε_XZ was 1.6 % lower than the maximum ε_XZ (61 με) in the ACP and increasing the COF reduced the ε_XZ by approximately 2 %. On the other hand, it is important to mention that the maximum ε_YZ and ε_XZ were exhibited just below the tires.

Figure 14 shows that up to 40 mm below the AC surface, the ε_YZ was 2.6 to 3 times higher than that of the ACP. At the direct ACP-PCCP transition and ACP, the ε_YZ gradually increased within the thickness until it reached its maximum magnitude at 40mm below the surface. The maximum ε_YZ was approximately 1.5 times greater than the surface ε_YZ. At depths greater than 40 mm the ε_YZ gradually decreased.

Figure 14. Figure 14. εYZ within the thickness of the AC at 152.4 ms Source: Created by the author.

Therefore, premature near-surface cracking may initiate in the upper 40 mm of the AC. On the other hand, the effect on the ε_YZ caused by increasing the AC-concrete interface bonding was not significant in the upper 40 mm of the AC since increasing the COF caused between 1.1 % and 1.8 % increase in the ε_YZ. Figure 15 shows that the effect on the near-surface ε_XZ that causes the sudden change from AC to concrete, and the increase AC-concrete interface bonding might be negligible since the maximum ε_XZ of the direct ACP-PCCP transition was similar to that of the ACP (difference of 1.3 %), furthermore, up to 40 mm below the surface the difference between the ε_XZ of the direct ACP-PCCP transition and that of ACP ranged between 1.3 % and 3.3 % and, increasing the COF caused a reduction of the ε_XZ between 0.2 % and 1.2 %. The ε_XZ decreased with increasing depth in the AC, even though at depths greater than 40 mm the ε_XZ was approximately 15 % greater than that of the ACP, this increase may be depreciable due to its low magnitude compared to the maximum ε_XZ.

Figure 15. Figure 15. εXZ within the thickness of the AC Source: Created by the author.

The contours of ε_YZ within the AC at 152.4 ms are illustrated in Figure 16. It is observed that the sudden change from AC to concrete is not conservative for the AC near the joint surface due to the relatively high ε_YZ experienced. In this regard, in the ACP the ε_YZ was rapidly reduced in the X direction, e.g., at 60 mm from the outer rib the ε_YZ decreased to - 1.3με (3.4 % of the maximum ε_YZ), on the contrary, at the transition joint at 60 mm from the outer rib, the ε_YZ decreased to - 65 με (63 % of the maximum ε_YZ), this strain was 1.7 times greater than the maximum ε_YZ of the ACP and, at distances greater than 60 mm the ε_YZ was not less than -61 με (1.6 times greater). Thus, premature near-surface cracking may also be developed along the joint.

Figure 16. Figure 16. Contours of εYZ in the AC (a) COF: 1.5 at 152.4 ms and (b) ACP at 52.6ms Source: Created by the author.

Figure 16 also illustrates that even near the joint the AC experiences relatively high ε_YZ, for instance, the maximum ε_YZ measured at 72 mm from the joint just below the tires was 1.6 times higher than the maximum ε_YZ in the ACP (Figure 17a). Even though the ε_YZ (37.6 με) at 122 mm from the joint was reduced, it was similar to the maximum ε_YZ in the ACP. Therefore, the AC may experience premature near-surface cracking to an extent of 122 mm from the transition joint mainly below the tires. Finally, it should be considered that poor compaction near the joint could also contribute to premature cracking of the AC.

Figure 17. Figure 17. Contours of εYZ in the AC at (a) 72mm and (b) 122mm from the transition joint at 152.4ms (COF:1.5) Source: Created by the author.

The vertical compressive strain on the subgrade top (ε_Z) was analyzed since it is related to rutting development. According to Figure 18, in the direct ACP-PCCP transition, premature rutting might occur since the maximum ε_Z was about 1.26 times higher than that of ACP. Even though later the maximum ε_Z decreased by about 5 %, at the end of the simulation, the ε_Z was 3.1 times higher than that of the ACP. On the other hand, the effect on the maximum ε_Z caused by increasing the AC-concrete interface bonding might be negligible since increasing the COF reduced the maximum ε_Z by approximately 2 %. Furthermore, when the tires were mainly supported on the CS, no variation of ε_Z was observed with increasing COF.

Figure 18. Figure 18. Compressive vertical strain on the subgrade top Source: Created by the author.

Longitudinal (σ_L) and transverse (σ_T) stresses were analyzed since cracking can develop when they exceed the tensile strength of the concrete. Figure 19a and Figure 19b illustrate σ_L and Figure 19c and Figure 19d illustrate σT where positive indicates tensile stress and negative indicates compressive stress. As expected, compressive stresses were experienced mainly at the CS surface below the tires, however, at depths greater than 60 mm from the surface, the σ_L and σ_T changed to tension.

Figure 19. Figure 19. Longitudinal stress contours (a) COF: 1.5 and (b) COF: 0.7, and transverse stresses (c) COF: 1.5 and (d) COF: 0.7 in the CS, at 152.4 ms (Stress in Pa) Source: Created by the author.

The maximum tensile σ_L and σ_T were around 0.27 MPa and 0.39 MPa, respectively. In this study the concrete had a tensile strength of 4.1 MPa [25], therefore, the simulated vehicular loading could not cause cracking of the concrete due to the wide difference between the concrete strength and the measured stresses. On the other hand, it was observed that increasing the AC-concrete interface bonding reduced the maximum tensile σ_L and σ_T by 3 % and 1.6 %, respectively, however, this effect might be negligible due to the low magnitude of the reduction.