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Finite element modeling of mechanical responses of concrete pavement with partial depth repair
Construction and Building Materials 240 (2020) 117960
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Finite element modeling of mechanical responses of concrete pavement with partial depth repair Jiaqi Chen a,b, Hao Wang b,⇑, Pengyu Xie b a b
Department of Civil Engineering, Central South University, Changsha, Hunan 410075, China Department of Civil and Environmental Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA
h i g h l i g h t s Investigate mechanical responses of concrete pavement with partial depth repair. Calculate tensile stresses for different combinations of patch material, location, and depth. Recommend selection of appropriate material for partial depth repair.
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Article history: Received 20 July 2019 Received in revised form 22 December 2019 Accepted 24 December 2019
Keywords: Partial depth repair Concrete pavement Patch material Elastic modulus Tensile stress
a b s t r a c t Partial depth repair (PDR) is usually used to repair surface distresses of concrete pavement. The mechanical property of patch material was mainly considered when selection the patch material. However, the stress state in the patch material or surrounding concrete varies depending on patch location and depth. This study aims to evaluate mechanical responses of PDR patch in concrete pavement under moving traffic loading using finite element modeling. The FE model was first validated using field test results reported in the literature. Totally seven different patching materials, three different patching locations, and two different patching depths were considered in the analysis. The critical tensile stresses in the patch and the surrounding concrete under moving tire loading were analyzed for each case. The analysis results show that for PDR patch in the middle of concrete slab, the maximum tensile stress in the thicker PDR patches is greater than that in the thinner ones. For PDR patch in the corner of concrete slab, the tensile stress can be found not only at the bottom of slab and patches, but also at the surface of slab and patches. When low modulus patch material is used, the tensile stress at the bottom of slab with the thinner PDR patch is smaller. On the other hand, the tensile stress at the bottom of slab with thicker PDR patch is smaller when high modulus patch material is used. Based on analysis results, recommendations for selection of patching material were made for repairing concrete pavement at different locations. The study findings can help select appropriate material for PDR of concrete pavement for different patch locations and depths. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Spalling and top-down cracking are surface distresses in Portland Cement Concrete (PCC) pavements that impair pavement performance and driving safety. In order to reduce the impact of concrete pavement repair on traffic, the rapid and effective repair of concrete distresses is desired, especially for the road with heavy traffic. Due to the advantages of shorter lane closure and less construction cost, partial depth repair (PDR) is usually used to rehabil⇑ Corresponding author. E-mail address: [email protected] (H. Wang). https://doi.org/10.1016/j.conbuildmat.2019.117960 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
itate surface distresses of concrete pavement, by removing small areas of the deteriorated concrete and replacing it with suitable repair material [1,2]. However, previous studies have found that the service life of concrete pavement with PDR could vary significantly [3,4]. Although the performance of PDR could be affected by construction technology, the effectiveness of PDR depends largely on mechanical properties of repair materials, as well as the compatibility between concrete substrate and the repair material [5]. The properties of patching material, such as compressive strength, flexural strength, freeze-thaw durability, shrinkage, coefficient of thermal expansion, bond strength, and so on, should be comprehensively evaluated before the application of PDR [6,7].
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A number of experimental studies have been conducted to characterize mechanical properties of various patching materials with different mix designs. The mechanical properties of different patching materials are compared, so that the proper material can be selected based on the desired properties of patching material and the repair type [8–11]. Although laboratory test is the most commonly used method for selecting patching material, the mechanical stress state experienced by patch material in concrete pavement is usually different from that in the laboratory experiment. Previous researches have monitored the performance of concrete pavement with PDR for years after repair. It was found that the effectiveness of different patching materials varied based on the observed pavement condition rating [12–15]. Since the pavement condition rating is generally based on visual inspection, the failure of PDR in relation to the mechanical stress and strain experienced in the pavement is still unclear. Three-dimensional (3-D) finite element (FE) model is an effective method to study pavement responses under traffic loading [16–20]. Few researches have been focused on mechanical responses of concrete pavement with PDR in the past. One previous study used simplified static load to investigate the maximum stress in the PDR patch of concrete pavement [21]. However, in the real traffic condition, the mechanical responses of concrete pavement with the PDR patch under moving load is more complicated due to the interaction between patch material and concrete substrate. The stress and strain distributions inside the PDR patch and the surrounding pavement may be different. The effects of patch material, location, and depth on mechanical responses remain unknown. Therefore, a comprehensive study is needed to identify the failure mechanism of PDR and concrete substrate and help select the better performing patch material. 2. Objective and scope The primary objective of this study is to evaluate mechanical responses of PDR patch in concrete pavement under moving traffic loading based on finite element modeling. The tensile stress was selected as critical response for evaluating fatigue cracking potential in the PDR patch and the surrounding concrete. Various patching materials, locations, and depths were considered in the analysis. Based on analysis results, recommendations for patching material selection were made for repairing concrete pavement distresses at different locations.
3. Development of 3-D FE model 3.1. Model dimensions and meshes A three-dimensional (3-D) finite element (FE) model was developed to simulate pavement responses under moving tire loading. Fig. 1 illustrates the schematic diagram of 3-D FE model. The 3-D pavement model was consisted of two slabs with four parts, namely, concrete slab, base layer, subgrade, and dowel bars at the transverse joint. The length of the pavement model was 6 m along the traffic direction. The width of concrete slab, base, and subgrade was 3.64 m, 4.88 m, and 6 m, respectively. The thickness of concrete slab, base, and subgrade was 0.202 m, 0.15 m, and 3 m, respectively. The diameter and length of dowel bars used in the model were 3.8 cm and 45.7 cm, respectively, and the spacing between dowel bars was 30 cm. The model parameters are based on concrete pavement structures analyzed in the literature [22]. The moving traffic loading used in the FE model was represented by one single truck axle with dual-tire assembly at each side. The axle weight was 72 kN, which was selected as a typical value in the load axle spectrum of trucks and is smaller than the maximum allowable single axle weight in most states. Thus the load applied on each dual-tire assembly was 36 kN. The tire inflation pressure was 724 kPa that is typical for truck tires. One possible location of loading path is shown in Fig. 1. The location of loading path in the transverse direction can be changed to induce critical loading at the center and edge of concrete slab, but the axle width (distance between two dual tire assemblies) was kept as 1.826 m. The tire loading was applied on pavement surface considering the non-uniform distribution of vertical contact stresses at each tire rib in the contact area. The contact area of each tire was assumed as rectangle with 215 mm and 180 mm in the transverse and longitudinal directions. The non-uniform distribution of vertical tire contact stresses was shown in Fig. 2(a). The moving load was simulated using a continuous moving load approach, in which both tire contact stress and contact area changed at each time step, as shown in Fig. 2(b). The simulated speed was 8 km/h. More details on moving load and tire contact stresses can be found in the authors’ previous work [23,24]. In the FE model, the pavement structure including the slab, base and subgrade was meshed with eight-node brick elements and structured meshing technique. The dowel bars were meshed with
Fig. 1. Schematic diagram of 3-D FE model: (a) global view; (b) local view with dowel bars at the joint.
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Fig. 2. Simulation of tire loading: (a) non-uniform distribution of tire contact stresses; (b) continuously moving load approach.
eight-node brick elements and advancing front sweep meshing technique. The meshes were refined around the loading area along the wheel path. The element size was controlled fine enough in the pavement loading area in order to accurately simulate pavement responses. The relatively coarse meshes were used far from the loading area to reduce computational time. The friction interface was usually used to describe the interaction between pavement layers (concrete slab base layer, and subgrade) and the interface between dowel bars and the surrounding material [18,25,26]. In this study, the value of friction coefficient was set to be 1.0 between pavement layers; while the friction coefficient of 0.3 was used for the interface between dowel bars and the surrounding concrete considering the smoother surface of steel bar.
simulated with the model, and the results were compared with the measured data reported in the previous literature [18]. For the purpose of validation, the model dimensions, material properties were kept the same with those used in the FWD test. A circular pulse load of 0.7 MPa was applied to the edge of concrete slab at a distance of 0.09 m away from the joint [27]. The deflections at different locations were calculated with the 3-D FE model and compared with the measured data, as shown in Fig. 5. It can be seen that the deflection profile predicted with the FE model is generally consistent with the measurements. The relative differences between the predicted and measured deflections range from 0.1% to 9.7%, with an average value of 3.9%. In general, the accuracy of the presented FE model is acceptable. 4. Results and analysis
3.2. Locations of patch repair 4.1. Pavement responses around middle patch Three different locations for PDR patch were considered in the FE modeling, including the middle patches, the corner patches, and the edge patches, as shown in Fig. 3. For each location, two different patch depths were considered, namely, 1/3 and 1/2 depth of the slab. The patch area simulated in this study is the same, with 240-mm length in the traffic direction, and 552-mm width in the direction perpendicular to the traffic direction. For all cases, dual tires at one side of axle were assumed to travel above the PDR patches. The elastic modulus, Poisson’s ratio, and density of concrete, dowel bar, base layer, and subgrade used in the FE model are shown in Table 1. These are the inputs of material properties used in the finite element model, which were kept constant in the analysis. Since the mechanical properties of different patching materials may vary significantly, totally seven patching materials with different elastic modulus values were considered based on laboratory testing results [5]. The elastic modulus of patching material, which are labelled as P1–P7, were shown in Fig. 4. The patching materials include three sets of polymer concrete (P1, P2, and P3), three sets of magnesium polyphosphate (P4, P6, and P7), and one set of hydraulic cement (P5). Since the formulation for each patching material was different from each other, the elastic modulus of the above patching materials differs significantly. The interface between the PDR patches and the surround concrete slab was assumed as frictional interface with friction coefficient of 1.0. 3.3. Model validation In order to validate the 3-D FE model for jointed plain concrete pavement (JPCP), a falling weight deflectometer (FWD) test was
The middle patches were modeled in the middle area of concrete slab, under one of the loading path shown in Fig. 3(a). When the moving tire travels over the PDR patches, the stress in the PDR patches and concrete slab was calculated. Figs. 6 and 7 show the distributions of longitudinal stress in the PDR patches and the surrounding concrete, respectively, for the pavement repaired with 1/3-depth repair. The longitudinal stress was extracted from the locations under the center of tire, close to the vertical interface between the surrounding concrete and the PDR patch. Fig. 6(a) shows the longitudinal stress in the PDR patches before the tire loading stepping on the patches, when the front edge of the tire is at the interface of the PDR patches and the slab. At this time compressive stress and tensile stress could be found at the surface and bottom of patch, respectively. The similar trend could be found when the center of the tire loading is right on the interface between the PDR patch and the slab, as shown in Fig. 6(b). It should be noted that, when the tire loading is stepping on the PDR patch, the longitudinal stress at the patch bottom gradually turns from tensile to compressive. And as shown in Fig. 6(c), when the tire loading is completely on the PDR patch, the longitudinal stress in the PDR patch through the depth is compressive and no tensile stress is observed. This is mainly because the PDR patches only exist at the top 1/3 part of concrete slab, which is usually the compressive zone in the tire loading. Fig. 7 shows the variation of longitudinal stress in concrete slab, from the time when the tire loading is totally on the surrounding concrete, to the time when the tire loading is completely on the PDR patches. It can be seen that during this process, the longitudinal stress in concrete slab is compressive at the surface and tensile
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Fig. 3. Schematic diagram of PDR locations: (a) middle patches; (b) corner patches; (c) edge patches with respect to loading paths.
Table 1 Material properties used in the FE model.
Density (kg/m3) Elastic modulus (GPa) Poisson’s ratio
Concrete Slab
Dowel bar
Base Layer
Subgrade
2400 28 0.2
7830 210 0.3
2100 2.9 0.3
2040 0.14 0.35
Fig. 5. Comparison of deflections from FE model and measured data under FWD test.
Fig. 4. Elastic modulus of patching materials used in the FE model (5).
at the bottom, respectively. The maximum tensile and compressive stress was observed when the center of tire loading was right on the interface between the PDR patch and the surrounding concrete. For the pavement repaired with 1/3-depth PDR patches, the stress changing point was observed at the depth of the patch bottom, which was 67 mm for 1/3-depth patch. This is caused by the difference in the properties of concrete and patching materials.
Figs. 6 and 7 also show that with different patching material, the stress distributions in the patches and the surrounding concrete could vary significantly. Fig. 8 shows the effect of elastic modulus of patching material on maximum tensile stresses in concrete slab and in the patch, respectively. It can be seen that when using patching material with higher elastic modulus, the tensile stress in the concrete slab decreases but the tensile stress in the patch increases. However, the tensile stress in the patch is smaller than that in concrete slab. Therefore, for PDR in the middle of concrete slab, patching material with relative large elastic modulus and tensile strength is recommended. On the other hand, the max-
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Fig. 6. Longitudinal stress in the PDR patches with 1/3-depth repair: (a) tire front edge on the interface; (b) tire center on the interface; and (c) tire back edge on the interface.
imum tensile stress in the 1/2-depth PDR patches is greater than that in the 1/3-depth PDR patches. This indicates that the thicker PDR patch has fewer fatigue life if the same patch material is used. Thus, the thicker PDF patch requires the patching material to have the higher tensile strength to reach the same performance. 4.2. Pavement responses around corner patch The corner patches were modeled at the corner of concrete slab, next to the joint, as shown in Fig. 3(b). When the moving load travelled on the patches, the stress in the patches and concrete slab was calculated. Figs. 9 and 10 show the distributions of longitudinal stress in the patches and the surrounding concrete, respectively, for the pavement repaired with 1/3-depth repair. The longitudinal stress was extracted from the locations under the center of tire, close to the vertical interface between the surrounding concrete and the patch. Fig. 9(a) shows the longitudinal stress in the PDR patches when the tire loading is right on the interface between the patches and the surrounding concrete. At this time compressive stress and tensile stress could be found at the patch surface and bottom, respectively. When the tire loading was moving from the concrete slab to the patches, and finally to the other slab, the stress in the slab kept
changing. As shown in Fig. 9(c), when the tire loading is totally moved to the other slab, stress at patch surface changed from compressive to tensile, and stress at patch bottom changed from tensile to compressive. In fact, this change happens first when the patching material with lower elastic modulus is used. As shown in Fig. 9 (b), when the tire loading moved to the center of the patches, for pavement using lower modulus PDR material, the stress at patch surface has already changed from compressive to tensile. Fig. 10 shows the variation of longitudinal stress in concrete slab, when the tire loading moves from the surrounding concrete to the patch and finally the other slab. Similar with the stress in the patches, when the tire loading and the patch is at the same side of the joint, the stress at the surface of concrete slab is compressive, and gradually changes to tensile through the depth. When the tire loading moved to the other slab, the stress at the surface of concrete slab changed from compressive to tensile, and the stress at the bottom of concrete slab changed from tensile to compressive. For the pavement with 1/3-depth patches, the stress changing point was observed at the depth of the patch bottom, which was 67 mm for 1/3 depth patches. Figs. 9 and 10 also show that with different patching material, the stress distributions in the patches and the surrounding concrete could vary a lot. Based on the above analysis, when the tire
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Fig. 7. Longitudinal stress in the slab with 1/3-depth repair (a) tire front edge on the interface; (b) tire center on the interface; and (c) tire back edge on the interface.
Fig. 8. Variation of longitudinal stress with elastic modulus of patching material (a) in concrete slab; (b) in the patch.
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Fig. 9. Longitudinal stress in the PDR patches with 1/3-depth repair: (a) tire center on the interface; (b) tire on patch center; and (c) tire on adjoining slab.
loading was passing the corner PDR patches, the tensile stress could be found not only at the bottom of slab and patches, but also at the surface of slab and patches. Therefore, the tensile stress at these locations was further analyzed. Fig. 11 shows the effect of elastic modulus of patching material on maximum tensile stress at surface and bottom of concrete slab. It can be seen that when using patching material with higher elastic modulus, the tensile stress at the surface of slab increases, while the tensile stress at the bottom of slab decreases. The tensile stress at the surface of concrete slab with 1/3-depth PDR is smaller than that with 1/2-depth PDR. When the patching material with the smaller elastic modulus is used, the tensile stress at the bottom of slab with 1/3-depth PDR is smaller than that with 1/2-depth PDR. However, when patching material with the greater elastic modulus is used, the tensile stress at bottom of concrete slab with 1/3-depth PDR is greater than that with 1/2-depth PDR. This indicates that the patching material with smaller elastic modulus is more suitable for the PDR with smaller depth. Fig. 12 shows the effect of elastic modulus of patching material on maximum tensile stress at surface and bottom of the patch. It can be seen that when using the patching material with the greater elastic modulus, the induced tensile stress at the surface and bottom of patch both increase. Moreover, the maximum tensile stress in the 1/2-depth PDR patches is larger than that in the 1/3-depth PDR patches. Therefore, patching material with low tensile strength is more suitable for PDR patch with smaller depth.
In order to reduce the critical tensile stress at bottom of slab, patching material with higher elastic modulus should be used, but this can induce the greater tensile stress in the patch. Therefore, for the patch in the corner of concrete slab, patching material with moderate elastic modulus and adequate tensile strength is recommended. 4.3. Pavement responses around edge patch The edge patches were modeled at the longitudinal edge of concrete slab, about 0.7 m from the joint, as shown in Fig. 3(c). The reason for simulating this condition is that when the moving load passes the joint, the stress at pavement surface is usually tensile at this location. Figs. 13 and 14 show the distributions of longitudinal stress in the PDR patches and the surrounding pavement slab, respectively, for the pavement repaired with 1/3-depth repair. The longitudinal stress was extracted from the locations under the center of tire, close to the vertical interface between surrounding concrete and the patch. Fig. 13(a)–(c) shows longitudinal stress in the 1/3-depth PDR patch, during the process when the tire loading travelled on the transverse joint 0.7 m away from the patch. In Fig. 13(a), the tire loading is totally on the same slab with the patch right before the joint, with its front edge on the joint. It can be seen that the longitudinal stress through the depth of patch is tensile. In Fig. 13(b), the center of tire loading is right on the center of joint,
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Fig. 10. Longitudinal stress in the slab with 1/3-depth repair: (a) tire center on the interface; (b) tire on patch center; (c) tire on adjoining slab.
Fig. 11. Variation of tensile stress with elastic modulus of patching material at the (a) surface; and (b) bottom of concrete slab near corner patch.
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Fig. 12. Variation of tensile stress with patching material elastic modulus at the (a) surface; and (b) bottom of corner patch.
Fig. 13. Longitudinal stress in the PDR patches with 1/3-depth repair: (a) tire front edge on the joint; (b) tire center on the joint; and (c) tire back edge on the joint.
with half tire on the same slab with the patch, and another half tire on the other slab. It can be seen that the longitudinal stress through the depth of patch is also tensile. In Fig. 13(c), when the
tire loading is totally on the other slab with the tire back edge on the joint, tensile stress was observed though the depth of the patch. It can be also seen from Fig. 13, when the tire loading was
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Fig. 14. Longitudinal stress in the slab with 1/3-depth repair: (a) tire front edge on the joint; (b) tire center on the joint; and (c) tire back edge on the joint.
Fig. 15. Variation of longitudinal stress with elastic modulus of patching material (a) at the surface of concrete slab near edge patch; and (b) at the surface of patch.
moving through the joint, the tensile at the surface of patch decreased, while the tensile stress at the bottom of patch increased. The tensile stress at the surface of patch is always greater than that at the bottom of patch
Fig. 14 shows longitudinal stress in the pavement slab, when the tire loading moves over the transverse joint with 0.7-m away from the patch. It can be seen that during this process, for the pavement with 1/3-depth patches, the longitudinal stress at the pave-
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ment slab surface is tensile, and gradually turns to be compressive with the growing of the depth. The stress changing point was observed at the depth of patch bottom, which was 67 mm for 1/3-depth patches. Fig. 15 shows the effect of patching material elastic modulus on the maximum tensile stress in concrete slab and in the patch. It can be seen that when using patching material with higher elastic modulus, the tensile stress in concrete slab and in the patch both increases. On the other hand, the maximum tensile stress in the 1/2-depth patches is slightly greater than that in the 1/3-depth patches. Therefore, in order to avoid high tensile stress, patching material with small elastic modulus and adequate strength is recommended for PDR at slab edges. 5. Conclusions This study aimed to investigate mechanical response of concrete pavement with PDR under traffic landing through 3-D FE models. The influences of patching material, location, and depth on critical tensile stresses were analyzed. The effect of patch depth on tensile stress is dependent on path location and elastic modulus of patch material. For PDR patch in the middle of concrete slab, the maximum tensile stress in the thicker patch is greater than that in the thinner patch. For the patch in the corner of concrete slab, the tensile stress was found not only at the bottom of slab and patches, but also at the surface of slab and patches. When low modulus patch material is used, the tensile stress at the bottom of slab with the thinner PDR is smaller; while the tensile stress at the bottom of slab with the thicker PDR is smaller when high modulus patch material is used. The critical stress location varies depending on the elastic modulus of patch material and path location. When patching material with low modulus is used in the middle and corner part of concrete slab, the tensile stress at the bottom of slab is critical. When patching material with high modulus is used in the edge and corner of concrete slab, the tensile stress at the surface of slab is critical. Based on the calculated critical tensile stresses at different combinations of patch material, location, and depth, the selectin of patch material for PDR of concrete slab was recommended. For the patch in the middle of concrete slab, patching material with relative high modulus and tensile strength is recommended. For PDR patch in the corner of concrete slab, patching material with moderate modulus and tensile strength is recommended. For PDR patch at the edge of concrete slab, patching material with small elastic modulus and adequate tensile strength can be used. The analysis findings can help select appropriate material for PDR of concrete pavement for different patch locations and depths. CRediT authorship contribution statement Jiaqi Chen: Methodology, Writing - original draft. Hao Wang: Conceptualization, Supervision, Writing - review & editing. Pengyu Xie: Investigation. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to acknowledge the financial support provided by China Postdoctoral Science Foundation and the Center
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Finite element modeling of mechanical responses of concrete pavement with partial depth repair Jiaqi Chen a,b, Hao Wang b,⇑, Pengyu Xie b a b
Department of Civil Engineering, Central South University, Changsha, Hunan 410075, China Department of Civil and Environmental Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA
h i g h l i g h t s Investigate mechanical responses of concrete pavement with partial depth repair. Calculate tensile stresses for different combinations of patch material, location, and depth. Recommend selection of appropriate material for partial depth repair.
a r t i c l e
i n f o
Article history: Received 20 July 2019 Received in revised form 22 December 2019 Accepted 24 December 2019
Keywords: Partial depth repair Concrete pavement Patch material Elastic modulus Tensile stress
a b s t r a c t Partial depth repair (PDR) is usually used to repair surface distresses of concrete pavement. The mechanical property of patch material was mainly considered when selection the patch material. However, the stress state in the patch material or surrounding concrete varies depending on patch location and depth. This study aims to evaluate mechanical responses of PDR patch in concrete pavement under moving traffic loading using finite element modeling. The FE model was first validated using field test results reported in the literature. Totally seven different patching materials, three different patching locations, and two different patching depths were considered in the analysis. The critical tensile stresses in the patch and the surrounding concrete under moving tire loading were analyzed for each case. The analysis results show that for PDR patch in the middle of concrete slab, the maximum tensile stress in the thicker PDR patches is greater than that in the thinner ones. For PDR patch in the corner of concrete slab, the tensile stress can be found not only at the bottom of slab and patches, but also at the surface of slab and patches. When low modulus patch material is used, the tensile stress at the bottom of slab with the thinner PDR patch is smaller. On the other hand, the tensile stress at the bottom of slab with thicker PDR patch is smaller when high modulus patch material is used. Based on analysis results, recommendations for selection of patching material were made for repairing concrete pavement at different locations. The study findings can help select appropriate material for PDR of concrete pavement for different patch locations and depths. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Spalling and top-down cracking are surface distresses in Portland Cement Concrete (PCC) pavements that impair pavement performance and driving safety. In order to reduce the impact of concrete pavement repair on traffic, the rapid and effective repair of concrete distresses is desired, especially for the road with heavy traffic. Due to the advantages of shorter lane closure and less construction cost, partial depth repair (PDR) is usually used to rehabil⇑ Corresponding author. E-mail address: [email protected] (H. Wang). https://doi.org/10.1016/j.conbuildmat.2019.117960 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
itate surface distresses of concrete pavement, by removing small areas of the deteriorated concrete and replacing it with suitable repair material [1,2]. However, previous studies have found that the service life of concrete pavement with PDR could vary significantly [3,4]. Although the performance of PDR could be affected by construction technology, the effectiveness of PDR depends largely on mechanical properties of repair materials, as well as the compatibility between concrete substrate and the repair material [5]. The properties of patching material, such as compressive strength, flexural strength, freeze-thaw durability, shrinkage, coefficient of thermal expansion, bond strength, and so on, should be comprehensively evaluated before the application of PDR [6,7].
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A number of experimental studies have been conducted to characterize mechanical properties of various patching materials with different mix designs. The mechanical properties of different patching materials are compared, so that the proper material can be selected based on the desired properties of patching material and the repair type [8–11]. Although laboratory test is the most commonly used method for selecting patching material, the mechanical stress state experienced by patch material in concrete pavement is usually different from that in the laboratory experiment. Previous researches have monitored the performance of concrete pavement with PDR for years after repair. It was found that the effectiveness of different patching materials varied based on the observed pavement condition rating [12–15]. Since the pavement condition rating is generally based on visual inspection, the failure of PDR in relation to the mechanical stress and strain experienced in the pavement is still unclear. Three-dimensional (3-D) finite element (FE) model is an effective method to study pavement responses under traffic loading [16–20]. Few researches have been focused on mechanical responses of concrete pavement with PDR in the past. One previous study used simplified static load to investigate the maximum stress in the PDR patch of concrete pavement [21]. However, in the real traffic condition, the mechanical responses of concrete pavement with the PDR patch under moving load is more complicated due to the interaction between patch material and concrete substrate. The stress and strain distributions inside the PDR patch and the surrounding pavement may be different. The effects of patch material, location, and depth on mechanical responses remain unknown. Therefore, a comprehensive study is needed to identify the failure mechanism of PDR and concrete substrate and help select the better performing patch material. 2. Objective and scope The primary objective of this study is to evaluate mechanical responses of PDR patch in concrete pavement under moving traffic loading based on finite element modeling. The tensile stress was selected as critical response for evaluating fatigue cracking potential in the PDR patch and the surrounding concrete. Various patching materials, locations, and depths were considered in the analysis. Based on analysis results, recommendations for patching material selection were made for repairing concrete pavement distresses at different locations.
3. Development of 3-D FE model 3.1. Model dimensions and meshes A three-dimensional (3-D) finite element (FE) model was developed to simulate pavement responses under moving tire loading. Fig. 1 illustrates the schematic diagram of 3-D FE model. The 3-D pavement model was consisted of two slabs with four parts, namely, concrete slab, base layer, subgrade, and dowel bars at the transverse joint. The length of the pavement model was 6 m along the traffic direction. The width of concrete slab, base, and subgrade was 3.64 m, 4.88 m, and 6 m, respectively. The thickness of concrete slab, base, and subgrade was 0.202 m, 0.15 m, and 3 m, respectively. The diameter and length of dowel bars used in the model were 3.8 cm and 45.7 cm, respectively, and the spacing between dowel bars was 30 cm. The model parameters are based on concrete pavement structures analyzed in the literature [22]. The moving traffic loading used in the FE model was represented by one single truck axle with dual-tire assembly at each side. The axle weight was 72 kN, which was selected as a typical value in the load axle spectrum of trucks and is smaller than the maximum allowable single axle weight in most states. Thus the load applied on each dual-tire assembly was 36 kN. The tire inflation pressure was 724 kPa that is typical for truck tires. One possible location of loading path is shown in Fig. 1. The location of loading path in the transverse direction can be changed to induce critical loading at the center and edge of concrete slab, but the axle width (distance between two dual tire assemblies) was kept as 1.826 m. The tire loading was applied on pavement surface considering the non-uniform distribution of vertical contact stresses at each tire rib in the contact area. The contact area of each tire was assumed as rectangle with 215 mm and 180 mm in the transverse and longitudinal directions. The non-uniform distribution of vertical tire contact stresses was shown in Fig. 2(a). The moving load was simulated using a continuous moving load approach, in which both tire contact stress and contact area changed at each time step, as shown in Fig. 2(b). The simulated speed was 8 km/h. More details on moving load and tire contact stresses can be found in the authors’ previous work [23,24]. In the FE model, the pavement structure including the slab, base and subgrade was meshed with eight-node brick elements and structured meshing technique. The dowel bars were meshed with
Fig. 1. Schematic diagram of 3-D FE model: (a) global view; (b) local view with dowel bars at the joint.
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Fig. 2. Simulation of tire loading: (a) non-uniform distribution of tire contact stresses; (b) continuously moving load approach.
eight-node brick elements and advancing front sweep meshing technique. The meshes were refined around the loading area along the wheel path. The element size was controlled fine enough in the pavement loading area in order to accurately simulate pavement responses. The relatively coarse meshes were used far from the loading area to reduce computational time. The friction interface was usually used to describe the interaction between pavement layers (concrete slab base layer, and subgrade) and the interface between dowel bars and the surrounding material [18,25,26]. In this study, the value of friction coefficient was set to be 1.0 between pavement layers; while the friction coefficient of 0.3 was used for the interface between dowel bars and the surrounding concrete considering the smoother surface of steel bar.
simulated with the model, and the results were compared with the measured data reported in the previous literature [18]. For the purpose of validation, the model dimensions, material properties were kept the same with those used in the FWD test. A circular pulse load of 0.7 MPa was applied to the edge of concrete slab at a distance of 0.09 m away from the joint [27]. The deflections at different locations were calculated with the 3-D FE model and compared with the measured data, as shown in Fig. 5. It can be seen that the deflection profile predicted with the FE model is generally consistent with the measurements. The relative differences between the predicted and measured deflections range from 0.1% to 9.7%, with an average value of 3.9%. In general, the accuracy of the presented FE model is acceptable. 4. Results and analysis
3.2. Locations of patch repair 4.1. Pavement responses around middle patch Three different locations for PDR patch were considered in the FE modeling, including the middle patches, the corner patches, and the edge patches, as shown in Fig. 3. For each location, two different patch depths were considered, namely, 1/3 and 1/2 depth of the slab. The patch area simulated in this study is the same, with 240-mm length in the traffic direction, and 552-mm width in the direction perpendicular to the traffic direction. For all cases, dual tires at one side of axle were assumed to travel above the PDR patches. The elastic modulus, Poisson’s ratio, and density of concrete, dowel bar, base layer, and subgrade used in the FE model are shown in Table 1. These are the inputs of material properties used in the finite element model, which were kept constant in the analysis. Since the mechanical properties of different patching materials may vary significantly, totally seven patching materials with different elastic modulus values were considered based on laboratory testing results [5]. The elastic modulus of patching material, which are labelled as P1–P7, were shown in Fig. 4. The patching materials include three sets of polymer concrete (P1, P2, and P3), three sets of magnesium polyphosphate (P4, P6, and P7), and one set of hydraulic cement (P5). Since the formulation for each patching material was different from each other, the elastic modulus of the above patching materials differs significantly. The interface between the PDR patches and the surround concrete slab was assumed as frictional interface with friction coefficient of 1.0. 3.3. Model validation In order to validate the 3-D FE model for jointed plain concrete pavement (JPCP), a falling weight deflectometer (FWD) test was
The middle patches were modeled in the middle area of concrete slab, under one of the loading path shown in Fig. 3(a). When the moving tire travels over the PDR patches, the stress in the PDR patches and concrete slab was calculated. Figs. 6 and 7 show the distributions of longitudinal stress in the PDR patches and the surrounding concrete, respectively, for the pavement repaired with 1/3-depth repair. The longitudinal stress was extracted from the locations under the center of tire, close to the vertical interface between the surrounding concrete and the PDR patch. Fig. 6(a) shows the longitudinal stress in the PDR patches before the tire loading stepping on the patches, when the front edge of the tire is at the interface of the PDR patches and the slab. At this time compressive stress and tensile stress could be found at the surface and bottom of patch, respectively. The similar trend could be found when the center of the tire loading is right on the interface between the PDR patch and the slab, as shown in Fig. 6(b). It should be noted that, when the tire loading is stepping on the PDR patch, the longitudinal stress at the patch bottom gradually turns from tensile to compressive. And as shown in Fig. 6(c), when the tire loading is completely on the PDR patch, the longitudinal stress in the PDR patch through the depth is compressive and no tensile stress is observed. This is mainly because the PDR patches only exist at the top 1/3 part of concrete slab, which is usually the compressive zone in the tire loading. Fig. 7 shows the variation of longitudinal stress in concrete slab, from the time when the tire loading is totally on the surrounding concrete, to the time when the tire loading is completely on the PDR patches. It can be seen that during this process, the longitudinal stress in concrete slab is compressive at the surface and tensile
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Fig. 3. Schematic diagram of PDR locations: (a) middle patches; (b) corner patches; (c) edge patches with respect to loading paths.
Table 1 Material properties used in the FE model.
Density (kg/m3) Elastic modulus (GPa) Poisson’s ratio
Concrete Slab
Dowel bar
Base Layer
Subgrade
2400 28 0.2
7830 210 0.3
2100 2.9 0.3
2040 0.14 0.35
Fig. 5. Comparison of deflections from FE model and measured data under FWD test.
Fig. 4. Elastic modulus of patching materials used in the FE model (5).
at the bottom, respectively. The maximum tensile and compressive stress was observed when the center of tire loading was right on the interface between the PDR patch and the surrounding concrete. For the pavement repaired with 1/3-depth PDR patches, the stress changing point was observed at the depth of the patch bottom, which was 67 mm for 1/3-depth patch. This is caused by the difference in the properties of concrete and patching materials.
Figs. 6 and 7 also show that with different patching material, the stress distributions in the patches and the surrounding concrete could vary significantly. Fig. 8 shows the effect of elastic modulus of patching material on maximum tensile stresses in concrete slab and in the patch, respectively. It can be seen that when using patching material with higher elastic modulus, the tensile stress in the concrete slab decreases but the tensile stress in the patch increases. However, the tensile stress in the patch is smaller than that in concrete slab. Therefore, for PDR in the middle of concrete slab, patching material with relative large elastic modulus and tensile strength is recommended. On the other hand, the max-
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Fig. 6. Longitudinal stress in the PDR patches with 1/3-depth repair: (a) tire front edge on the interface; (b) tire center on the interface; and (c) tire back edge on the interface.
imum tensile stress in the 1/2-depth PDR patches is greater than that in the 1/3-depth PDR patches. This indicates that the thicker PDR patch has fewer fatigue life if the same patch material is used. Thus, the thicker PDF patch requires the patching material to have the higher tensile strength to reach the same performance. 4.2. Pavement responses around corner patch The corner patches were modeled at the corner of concrete slab, next to the joint, as shown in Fig. 3(b). When the moving load travelled on the patches, the stress in the patches and concrete slab was calculated. Figs. 9 and 10 show the distributions of longitudinal stress in the patches and the surrounding concrete, respectively, for the pavement repaired with 1/3-depth repair. The longitudinal stress was extracted from the locations under the center of tire, close to the vertical interface between the surrounding concrete and the patch. Fig. 9(a) shows the longitudinal stress in the PDR patches when the tire loading is right on the interface between the patches and the surrounding concrete. At this time compressive stress and tensile stress could be found at the patch surface and bottom, respectively. When the tire loading was moving from the concrete slab to the patches, and finally to the other slab, the stress in the slab kept
changing. As shown in Fig. 9(c), when the tire loading is totally moved to the other slab, stress at patch surface changed from compressive to tensile, and stress at patch bottom changed from tensile to compressive. In fact, this change happens first when the patching material with lower elastic modulus is used. As shown in Fig. 9 (b), when the tire loading moved to the center of the patches, for pavement using lower modulus PDR material, the stress at patch surface has already changed from compressive to tensile. Fig. 10 shows the variation of longitudinal stress in concrete slab, when the tire loading moves from the surrounding concrete to the patch and finally the other slab. Similar with the stress in the patches, when the tire loading and the patch is at the same side of the joint, the stress at the surface of concrete slab is compressive, and gradually changes to tensile through the depth. When the tire loading moved to the other slab, the stress at the surface of concrete slab changed from compressive to tensile, and the stress at the bottom of concrete slab changed from tensile to compressive. For the pavement with 1/3-depth patches, the stress changing point was observed at the depth of the patch bottom, which was 67 mm for 1/3 depth patches. Figs. 9 and 10 also show that with different patching material, the stress distributions in the patches and the surrounding concrete could vary a lot. Based on the above analysis, when the tire
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Fig. 7. Longitudinal stress in the slab with 1/3-depth repair (a) tire front edge on the interface; (b) tire center on the interface; and (c) tire back edge on the interface.
Fig. 8. Variation of longitudinal stress with elastic modulus of patching material (a) in concrete slab; (b) in the patch.
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Fig. 9. Longitudinal stress in the PDR patches with 1/3-depth repair: (a) tire center on the interface; (b) tire on patch center; and (c) tire on adjoining slab.
loading was passing the corner PDR patches, the tensile stress could be found not only at the bottom of slab and patches, but also at the surface of slab and patches. Therefore, the tensile stress at these locations was further analyzed. Fig. 11 shows the effect of elastic modulus of patching material on maximum tensile stress at surface and bottom of concrete slab. It can be seen that when using patching material with higher elastic modulus, the tensile stress at the surface of slab increases, while the tensile stress at the bottom of slab decreases. The tensile stress at the surface of concrete slab with 1/3-depth PDR is smaller than that with 1/2-depth PDR. When the patching material with the smaller elastic modulus is used, the tensile stress at the bottom of slab with 1/3-depth PDR is smaller than that with 1/2-depth PDR. However, when patching material with the greater elastic modulus is used, the tensile stress at bottom of concrete slab with 1/3-depth PDR is greater than that with 1/2-depth PDR. This indicates that the patching material with smaller elastic modulus is more suitable for the PDR with smaller depth. Fig. 12 shows the effect of elastic modulus of patching material on maximum tensile stress at surface and bottom of the patch. It can be seen that when using the patching material with the greater elastic modulus, the induced tensile stress at the surface and bottom of patch both increase. Moreover, the maximum tensile stress in the 1/2-depth PDR patches is larger than that in the 1/3-depth PDR patches. Therefore, patching material with low tensile strength is more suitable for PDR patch with smaller depth.
In order to reduce the critical tensile stress at bottom of slab, patching material with higher elastic modulus should be used, but this can induce the greater tensile stress in the patch. Therefore, for the patch in the corner of concrete slab, patching material with moderate elastic modulus and adequate tensile strength is recommended. 4.3. Pavement responses around edge patch The edge patches were modeled at the longitudinal edge of concrete slab, about 0.7 m from the joint, as shown in Fig. 3(c). The reason for simulating this condition is that when the moving load passes the joint, the stress at pavement surface is usually tensile at this location. Figs. 13 and 14 show the distributions of longitudinal stress in the PDR patches and the surrounding pavement slab, respectively, for the pavement repaired with 1/3-depth repair. The longitudinal stress was extracted from the locations under the center of tire, close to the vertical interface between surrounding concrete and the patch. Fig. 13(a)–(c) shows longitudinal stress in the 1/3-depth PDR patch, during the process when the tire loading travelled on the transverse joint 0.7 m away from the patch. In Fig. 13(a), the tire loading is totally on the same slab with the patch right before the joint, with its front edge on the joint. It can be seen that the longitudinal stress through the depth of patch is tensile. In Fig. 13(b), the center of tire loading is right on the center of joint,
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Fig. 10. Longitudinal stress in the slab with 1/3-depth repair: (a) tire center on the interface; (b) tire on patch center; (c) tire on adjoining slab.
Fig. 11. Variation of tensile stress with elastic modulus of patching material at the (a) surface; and (b) bottom of concrete slab near corner patch.
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Fig. 12. Variation of tensile stress with patching material elastic modulus at the (a) surface; and (b) bottom of corner patch.
Fig. 13. Longitudinal stress in the PDR patches with 1/3-depth repair: (a) tire front edge on the joint; (b) tire center on the joint; and (c) tire back edge on the joint.
with half tire on the same slab with the patch, and another half tire on the other slab. It can be seen that the longitudinal stress through the depth of patch is also tensile. In Fig. 13(c), when the
tire loading is totally on the other slab with the tire back edge on the joint, tensile stress was observed though the depth of the patch. It can be also seen from Fig. 13, when the tire loading was
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Fig. 14. Longitudinal stress in the slab with 1/3-depth repair: (a) tire front edge on the joint; (b) tire center on the joint; and (c) tire back edge on the joint.
Fig. 15. Variation of longitudinal stress with elastic modulus of patching material (a) at the surface of concrete slab near edge patch; and (b) at the surface of patch.
moving through the joint, the tensile at the surface of patch decreased, while the tensile stress at the bottom of patch increased. The tensile stress at the surface of patch is always greater than that at the bottom of patch
Fig. 14 shows longitudinal stress in the pavement slab, when the tire loading moves over the transverse joint with 0.7-m away from the patch. It can be seen that during this process, for the pavement with 1/3-depth patches, the longitudinal stress at the pave-
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ment slab surface is tensile, and gradually turns to be compressive with the growing of the depth. The stress changing point was observed at the depth of patch bottom, which was 67 mm for 1/3-depth patches. Fig. 15 shows the effect of patching material elastic modulus on the maximum tensile stress in concrete slab and in the patch. It can be seen that when using patching material with higher elastic modulus, the tensile stress in concrete slab and in the patch both increases. On the other hand, the maximum tensile stress in the 1/2-depth patches is slightly greater than that in the 1/3-depth patches. Therefore, in order to avoid high tensile stress, patching material with small elastic modulus and adequate strength is recommended for PDR at slab edges. 5. Conclusions This study aimed to investigate mechanical response of concrete pavement with PDR under traffic landing through 3-D FE models. The influences of patching material, location, and depth on critical tensile stresses were analyzed. The effect of patch depth on tensile stress is dependent on path location and elastic modulus of patch material. For PDR patch in the middle of concrete slab, the maximum tensile stress in the thicker patch is greater than that in the thinner patch. For the patch in the corner of concrete slab, the tensile stress was found not only at the bottom of slab and patches, but also at the surface of slab and patches. When low modulus patch material is used, the tensile stress at the bottom of slab with the thinner PDR is smaller; while the tensile stress at the bottom of slab with the thicker PDR is smaller when high modulus patch material is used. The critical stress location varies depending on the elastic modulus of patch material and path location. When patching material with low modulus is used in the middle and corner part of concrete slab, the tensile stress at the bottom of slab is critical. When patching material with high modulus is used in the edge and corner of concrete slab, the tensile stress at the surface of slab is critical. Based on the calculated critical tensile stresses at different combinations of patch material, location, and depth, the selectin of patch material for PDR of concrete slab was recommended. For the patch in the middle of concrete slab, patching material with relative high modulus and tensile strength is recommended. For PDR patch in the corner of concrete slab, patching material with moderate modulus and tensile strength is recommended. For PDR patch at the edge of concrete slab, patching material with small elastic modulus and adequate tensile strength can be used. The analysis findings can help select appropriate material for PDR of concrete pavement for different patch locations and depths. CRediT authorship contribution statement Jiaqi Chen: Methodology, Writing - original draft. Hao Wang: Conceptualization, Supervision, Writing - review & editing. Pengyu Xie: Investigation. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to acknowledge the financial support provided by China Postdoctoral Science Foundation and the Center
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