# Experimental Study of Dowel Bar Alternatives Based on Similarity Model Test

Authors: Chichun Hu; Jiexian Ma; Jianying Zhao; Zhen Leng; Denis Jelagin
Journal: Advances in Materials Science and Engineering
 (2017)

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## Abstract

In this study, a small-scaled accelerated loading test based on similarity theory and Accelerated Pavement Analyzer was developed to evaluate dowel bars with different materials and cross-sections. Jointed concrete specimen consisting of one dowel was designed as scaled model for the test, and each specimen was subjected to 864 thousand loading cycles. Deflections between jointed slabs were measured with dial indicators, and strains of the dowel bars were monitored with strain gauges. The load transfer efficiency, differential deflection, and dowel-concrete bearing stress for each case were calculated from these measurements. The test results indicated that the effect of the dowel modulus on load transfer efficiency can be characterized based on the similarity model test developed in the study. Moreover, round steel dowel was found to have similar performance to larger FRP dowel, and elliptical dowel can be preferentially considered in practice.


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## Body

## 1. Introduction

The performance of jointed concrete pavements is often closely related to the load transfer capacity of dowel bars at the pavement joints. Faulting is frequently seen in the pavement joints without dowel bars, because the load transfer provided by aggregate interlock alone is insufficient. Steel dowels are commonly used to enhance load transfer in the concrete pavements. However, the issue of high bearing stress and corrosion of steel dowel has a significant impact on their long-term performance [1]. There have been efforts to improve dowel durability through the use of alternate shapes (other than round) to further reduce dowel-concrete bearing stresses and to use alternative materials for improved corrosion resistance [2–8]. Among those alternative materials, fiber reinforced polymer (FRP) dowel bars have been given considerable attention because of their excellent corrosion resistance.Usually, the laboratory experiments of dowel bar include static and fatigue elemental shear, bending strength, accelerated loading test, pull-out, alkalinity aging, and chemical properties [9]. Due to the relative low cost and time consumption and relative high reliability, evaluation of joint performance and dowel alternatives using laboratory accelerated loading has been conducted in the past 20 years.Among those researchers, Buch and Zollinger conducted a laboratory study to evaluate the dowel looseness across a saw-cut joint using concrete specimens with dimension of 610 mm × 254 mm × 915 mm [10]. The fatigue load application system consisted of a pair of hydraulic rams that pulsated alternately on either side of the joint to produce loads of up to a maximum of 40 kN, which can closely simulate that of a truck tire loading a joint. The total duration of the load and unload cycle was 1.5 seconds, of which the rest period lasted for 0.98 seconds. Melhem and Sheffield studied the performance of FRP and steel dowels in jointed slabs using a pulse load system [11]. Both slabs, the one with steel dowels and the one with FRP dowels, were tested side-by-side such that load was applied simultaneously. The load was applied by each actuator in a sinusoidal-shape function, with the two functions 180 degrees out of phase. Using this setup a speed of 9000 applications per hour can be achieved which is 15 times faster than the rolling axles. Bian and Harvey utilized the second generation of the Minnesota Accelerated Loading Facility (MinneALF-2) to study two jointed test pavement specimens that incorporate two different dowels [12]. The MinneALF-2 simulates vehicle loads traveling across pavement joints by means of two hydraulic actuators. The loading pattern for each actuator is a combination of a sinusoidal impulse (90 degrees out of phase for two actuators) and a small preload. Khazanovich et al. evaluated FRP dowel bars spaced at different intervals as load transferring devices in Jointed Plain Concrete Pavement (JPCP) under HS25 static and fatigue loads [13]. Five different concrete specimens with dimensions of 30.48 by 30.48 by 304.8 cm were cast for tests. Pavement load was applied on one side of the joint using a 244.65-kN hydraulic actuator system through a controller. Vijay et al. performed Heavy Vehicle Simulator (HVS) tests of several types of dowels at Palmdale’s dowel bar retrofitted concrete pavement test sections [14]. Channelized, bidirectional loading was conducted on the wheel path over the center of the dowel group. The results showed that four epoxy-coated steel dowels per wheel path had much smaller joint vertical deflections than the alternatives (four FRP dowels, four hollow stainless steel dowels).As mentioned above, the pulse load system can significantly shorten duration of time while HVS can exactly replicate the rolling wheel effects. But both of them need specialized equipment, which limits the laboratory study and practical application of dowel alternatives. The object of this research is to develop a small-scale accelerated loading test to evaluate dowel alternatives. Therefore, a similarity model test combining the advantages of pulse load system and HVS was introduced; the corresponding test program was described, and dowel bars with different materials and cross-sections were evaluated.


## 2. Model Design

A JPCP consisting of slabs 26 cm thick and 4.2 m wide is considered in this paper. Elasticity modulusEc and Poisson’s ratio μc of PCC slab is 31 GPa and 0.15, respectively. An axle load consisting of two identical tires 1.8 m apart, each carrying 50 kN, is applied at the edge of the joint, 15 cm from the edge of the slab. The total shear load carried by dowel group is assumed to be 50 percent of the applied load, which means only 25 kN shear load will be transferred by dowels within the radius of effective length leff. As the mid-panel load is carried by more dowels than the edge load, the critical dowel is the edge dowel. Before calculation of the effective length of load distribution, the modulus of subgrade reaction should be determined first.


### 2.1. Foundation Support

Using accelerated loading test to evaluate joint performance, the following factors should be considered: dowels, aggregate interlock, and base/subgrade reaction [15]. However, since the emphasis of this research was to compare dowel bar alternatives, rubber bearing was used to simulate the foundation support of JPCP, which could eliminate the effect of accumulated deformation and erosion of the supporting base or subgrade material. The modulus test result of rubber bearing Erb is shown in Table 1.Table 1
Modulus test result of rubber bearing.
Sequence Force (kN) Displacement (mm) Strain Modulus (MPa) Preloading 45 1 90 0.14925 0.0074625 134.00 2 135 0.34425 0.0172125 116.19 3 180 0.55375 0.0276875 108.35 4 225 0.83725 0.0418625 95.55  Average 113.53In the similarity model test, the value of elastic modulus similarity constantCE is taken as 1. Hence, the elastic modulus of the subgrade is(1)Es=CEErb=Erb=113.53MPa.And the modulus of subgrade reactionk is computed by the most commonly used expression for the relationship between k and Es [17, 18]:(2)k=EsEc1/3Es1-μs2h=0.0801262MPa/mm,where h is the thickness of the concrete slab and μs is the Poisson ratio of the subgrade, which is 0.4.


### 2.2. Load Distribution

The radius of relative stiffnesslr of the pavement-foundation system is calculated as follows [19]:(3)lr=Ech312k1-μc24=87.3cm,where μc is the Poisson ratio of the concrete slab.Tabatabaie et al. modeled a doweled joint using finite element showing that an effective length of 1.0lr is more appropriate for today’s construction practices [20]. Considering scaled model in this research cannot exactly simulate the boundary condition of the pavement slab, the effective length of load distribution is taken as 0.9lr to reflect the weakened boundary condition:(4)leff=0.9lr=78.6cm.Hence, the shear force transferred by the critical dowel can be obtained, which is 13.47 kN. Detail of the load distribution of dowel bars is shown in Figure1.Figure 1
Load diagram at pavement joint.


### 2.3. Similarity Constant

In order to decrease the scale of concrete slab and make the accelerated loading test easier to perform in the lab, the prototype of the similarity model test is only part of the pavement slab. The value of length similarity constantCl is taken as 3.5, and the load similarity constant can be derived, as shown in Table 2. Parameters of prototype and scaled model are presented in Table 3.Table 2
Similarity constant.
Similarity constant Length C l = 3.5 Deflection C w = 3.5 Elastic modulus C E = 1 Strain C ε = 1 Applied load C F = C E   C l 2 = 12.25Table 3
Parameters of prototype and scaled model.
Prototype Scaled model Length of concrete slab (mm) 520 148.5 Width of concrete slab (mm) 437.5 125 Thickness of concrete slab (mm) 262.5 75 Joint width (mm) 10 2.9 Dowel length (mm) 450 129 Applied load (kN) 13.47 1.1


### 2.4. Dowel Bars

In the experiment, steel dowels and FRP dowels are considered, and the cross-sections of the dowel bars are round, elliptical, and square (see Table4 and Figure 2). Among them, ϕ 10 round steel bar, square steel bar (8.9 mm × 8.9 mm), and elliptical steel bar (major axis = 12.5 mm, minor axis = 8 mm) have the same cross-section area, so as to evaluate the optimal cross-section with respect to the same material consumption.Table 4
Material, cross-section, and size of dowels.
Material Cross-section Code Prototype size (mm) Scaled Model Dimensions (mm) Cross-section area (mm2) Steel Round Steel35 ϕ35 ϕ   10 80 Steel42 ϕ   42 ϕ   12 110 Steel56 ϕ   56 ϕ   16 200  FRP Round FRP35 ϕ   35 ϕ   10 80 FRP56 ϕ   56 ϕ   16 200  Steel Elliptical Major axis Elliptical35 43.8 12.5 80 Minor axis 28 8  Steel Square Square 35 31.2 × 31.2 8.9 × 8.9 80Figure 2
Dowel bars with different materials and shapes.A nonstandard third point bending test and a double shear test were performed to evaluate the bending capacity and shear strength of the scaled dowel bar. The test results are presented in Figures3 and 4. As can be seen in these figures, under the condition of the same material and cross-section area, the bending failure force of the square steel bar is the largest, followed by the elliptical steel bar, and the round steel bar is the lowest. As for shearing test, the shear strengths of steel bars with different cross-sections are very close, and the difference is no more than 7%. In addition, the comparison of the FRP dowel to the steel dowel with the same area shows that the shear strength of the FRP dowel is about 1/5 of the steel dowel while the bending capacity of the FRP dowel is about 1/3.Figure 3
Maximum bending load for different dowels.Figure 4
Shear strength for different dowels.Joint deflection, dowel-concrete bearing stress and maximum strain of different types of dowels were computed using Friberg’s bearing stress analysis [21], to evaluate the influence of materials and cross-sections on the behavior of dowel load transfer system, assuming that the shear force Pc carried by the critical dowel was 13.47 kN and the modulus of dowel support K0 was 407 MPa/mm. The results are presented in Table 5. As shown in Table 5, the elliptical dowel can reduce dowel-concrete bearing stress compared to the round steel bar of the same cross-section area, which is very important in controlling the development of dowel looseness [8]. Square dowel is expected to reduce joint deflection and bearing stress in this research. However, the theoretical calculation does not agree with the expectation.Table 5
Sensitivity analysis of dowels in the prototype (computed using Friberg’s bearing stress analysis).
Code Dowel modulus (GPa) Joint Deflection at joint face (mm) Bearing stress (MPa) M m a x (N⋅m) ε m a x (10−6) Steel35 210 0.0460 18.71 −243.9 −276 Steel42 210 0.0330 13.43 −272.7 −179 Steel56 210 0.0196 7.98 −327.1 −90 FRP35 40 0.0731 29.75 −177.6 −1055 FRP56 40 0.0308 12.52 −232.1 −337 Elliptical35 210 0.0442 17.99 −213.7 −302 Square35 210 0.0490 19.95 −253.2 −238


## 2.1. Foundation Support

Using accelerated loading test to evaluate joint performance, the following factors should be considered: dowels, aggregate interlock, and base/subgrade reaction [15]. However, since the emphasis of this research was to compare dowel bar alternatives, rubber bearing was used to simulate the foundation support of JPCP, which could eliminate the effect of accumulated deformation and erosion of the supporting base or subgrade material. The modulus test result of rubber bearing Erb is shown in Table 1.Table 1
Modulus test result of rubber bearing.
Sequence Force (kN) Displacement (mm) Strain Modulus (MPa) Preloading 45 1 90 0.14925 0.0074625 134.00 2 135 0.34425 0.0172125 116.19 3 180 0.55375 0.0276875 108.35 4 225 0.83725 0.0418625 95.55  Average 113.53In the similarity model test, the value of elastic modulus similarity constantCE is taken as 1. Hence, the elastic modulus of the subgrade is(1)Es=CEErb=Erb=113.53MPa.And the modulus of subgrade reactionk is computed by the most commonly used expression for the relationship between k and Es [17, 18]:(2)k=EsEc1/3Es1-μs2h=0.0801262MPa/mm,where h is the thickness of the concrete slab and μs is the Poisson ratio of the subgrade, which is 0.4.


## 2.2. Load Distribution

The radius of relative stiffnesslr of the pavement-foundation system is calculated as follows [19]:(3)lr=Ech312k1-μc24=87.3cm,where μc is the Poisson ratio of the concrete slab.Tabatabaie et al. modeled a doweled joint using finite element showing that an effective length of 1.0lr is more appropriate for today’s construction practices [20]. Considering scaled model in this research cannot exactly simulate the boundary condition of the pavement slab, the effective length of load distribution is taken as 0.9lr to reflect the weakened boundary condition:(4)leff=0.9lr=78.6cm.Hence, the shear force transferred by the critical dowel can be obtained, which is 13.47 kN. Detail of the load distribution of dowel bars is shown in Figure1.Figure 1
Load diagram at pavement joint.


## 2.3. Similarity Constant

In order to decrease the scale of concrete slab and make the accelerated loading test easier to perform in the lab, the prototype of the similarity model test is only part of the pavement slab. The value of length similarity constantCl is taken as 3.5, and the load similarity constant can be derived, as shown in Table 2. Parameters of prototype and scaled model are presented in Table 3.Table 2
Similarity constant.
Similarity constant Length C l = 3.5 Deflection C w = 3.5 Elastic modulus C E = 1 Strain C ε = 1 Applied load C F = C E   C l 2 = 12.25Table 3
Parameters of prototype and scaled model.
Prototype Scaled model Length of concrete slab (mm) 520 148.5 Width of concrete slab (mm) 437.5 125 Thickness of concrete slab (mm) 262.5 75 Joint width (mm) 10 2.9 Dowel length (mm) 450 129 Applied load (kN) 13.47 1.1


## 2.4. Dowel Bars

In the experiment, steel dowels and FRP dowels are considered, and the cross-sections of the dowel bars are round, elliptical, and square (see Table4 and Figure 2). Among them, ϕ 10 round steel bar, square steel bar (8.9 mm × 8.9 mm), and elliptical steel bar (major axis = 12.5 mm, minor axis = 8 mm) have the same cross-section area, so as to evaluate the optimal cross-section with respect to the same material consumption.Table 4
Material, cross-section, and size of dowels.
Material Cross-section Code Prototype size (mm) Scaled Model Dimensions (mm) Cross-section area (mm2) Steel Round Steel35 ϕ35 ϕ   10 80 Steel42 ϕ   42 ϕ   12 110 Steel56 ϕ   56 ϕ   16 200  FRP Round FRP35 ϕ   35 ϕ   10 80 FRP56 ϕ   56 ϕ   16 200  Steel Elliptical Major axis Elliptical35 43.8 12.5 80 Minor axis 28 8  Steel Square Square 35 31.2 × 31.2 8.9 × 8.9 80Figure 2
Dowel bars with different materials and shapes.A nonstandard third point bending test and a double shear test were performed to evaluate the bending capacity and shear strength of the scaled dowel bar. The test results are presented in Figures3 and 4. As can be seen in these figures, under the condition of the same material and cross-section area, the bending failure force of the square steel bar is the largest, followed by the elliptical steel bar, and the round steel bar is the lowest. As for shearing test, the shear strengths of steel bars with different cross-sections are very close, and the difference is no more than 7%. In addition, the comparison of the FRP dowel to the steel dowel with the same area shows that the shear strength of the FRP dowel is about 1/5 of the steel dowel while the bending capacity of the FRP dowel is about 1/3.Figure 3
Maximum bending load for different dowels.Figure 4
Shear strength for different dowels.Joint deflection, dowel-concrete bearing stress and maximum strain of different types of dowels were computed using Friberg’s bearing stress analysis [21], to evaluate the influence of materials and cross-sections on the behavior of dowel load transfer system, assuming that the shear force Pc carried by the critical dowel was 13.47 kN and the modulus of dowel support K0 was 407 MPa/mm. The results are presented in Table 5. As shown in Table 5, the elliptical dowel can reduce dowel-concrete bearing stress compared to the round steel bar of the same cross-section area, which is very important in controlling the development of dowel looseness [8]. Square dowel is expected to reduce joint deflection and bearing stress in this research. However, the theoretical calculation does not agree with the expectation.Table 5
Sensitivity analysis of dowels in the prototype (computed using Friberg’s bearing stress analysis).
Code Dowel modulus (GPa) Joint Deflection at joint face (mm) Bearing stress (MPa) M m a x (N⋅m) ε m a x (10−6) Steel35 210 0.0460 18.71 −243.9 −276 Steel42 210 0.0330 13.43 −272.7 −179 Steel56 210 0.0196 7.98 −327.1 −90 FRP35 40 0.0731 29.75 −177.6 −1055 FRP56 40 0.0308 12.52 −232.1 −337 Elliptical35 210 0.0442 17.99 −213.7 −302 Square35 210 0.0490 19.95 −253.2 −238


## 3. Model Manufacture

As shown in Figure5, the mold of the scaled model consists of expansion joint plate, support of dowel bar, removable ears, rubber bearing, and connecting steel bar. The connecting steel bar is used to simulate the boundary condition of the prototype. Before making specimen, vaseline was smeared in the inner wall of the formworks to prevent leaking.Figure 5
Placing concrete into the formwork.All the FRP dowels and steel dowels were instrumented with strain gauges to monitor strains on dowel bars. The strain gauges were located on the top and bottom of the dowel bars on both sides, at a distance of 1.2 cm from the centerline of the 13 cm long dowel bars (see Figure6). Strain gauges are temperature compensated by using the dummy gauge technique. A dummy gauge is wired into a Wheatstone bridge on an adjacent arm to the active gauge so that the temperature effects on the active and dummy gauges counteract each other.Figure 6
The strain location on the dowel bar.


## 4. Test Program

In the scaled model, Asphalt Pavement Analyzer (APA) is used to perform small-scaled accelerated loading test. The APA tracks a loaded aluminum wheel back and forth across a pressurized linear hose over a beam sample which can simulate the traffic load of actual pavement. In this study, test molds composed of ultrahigh molecular weight polyethylene in the original APA test were removed and the wheel was tracked across the specimen for 864,000 cycles using a 1113 ± 4.5 N load and a 200 MPa hose pressure. Specimens with a dimension of 75 mm × 125 mm × 300 mm were prepared and DH3817 dynamic strain acquisition system was used. Steel holding fixtures were applied to both ends of the specimens, which allowed no displacement in the horizontal direction.The procedure of accelerated loading test is as follows. (1) Preheat specimens preheated at the test temperature (30°C) in oven for 3 h. (2) Set the hose pressure and load cylinder pressure to the desired levels. (3) Stabilize the testing chamber temperature at the test temperature. (4) Secure the preheated beam samples in the APA and fix the dial indicators which are mounted on each side of joint near the edge of the slab. (5) Close the chamber doors and allow a minimum of 10 min for the temperature to stabilize. (6) Apply 25 cycles to seat the specimens before taking the initial measurements and adjust the hose pressure as needed during these 25 cycles. (7) Clear the gauge and take initial strain and defection readings. (8) Start the test and collect the data of dowel strain and slab deflections at every 48,000 load cycles, as shown in Figures7 and 8.Figure 7
Similarity model test.Figure 8
Data collection.


## 5. Results and Discussion

### 5.1. Load Transfer Efficiency

Load transfer efficiency (LTE) is defined as the ability of a joint or crack to transfer load from one side of the joint or crack to the other. The method used to calculate load transfer efficiency is shown in (5). A load transfer efficiency of 70 to 100 percent is typically considered adequate:(5)LTE=wULwL100%,where wUL is the deflection of unloaded slab and wL is the deflection of loaded slab.The LTE and the corresponding number of wheel cycles for each type of dowel bar in the prototype are presented in Figure9. As shown in Figure 9, the average LTE of FRP35 observed in the accelerated loading test is 87.7%, which is smaller than the average LTE of Steel35, 91%. After 864,000 cycles, the LTE of FRP35 decreased from 90.8% to 82.6%, while the LTE of Steel35 decreased from 94.8% to 87%, indicating that the use of FRP dowel has a significant impact on the performance of pavement joint. The main reason is that FRP dowel has much lower elastic modulus than steel dowel, typically about 20 percent, which results in significantly higher bearing stress and differential joint deflection [8].Figure 9
Load transfer efficiency on load cycles for different dowels.A comparison between FRP56 and Steel42 was also conducted. The average LTE of FRP56 and Steel42 are 93.4% and 93.1%, respectively, which means those two have very close load transfer performance. Larger FRP dowel is a feasible solution for the above-mentioned phenomenon. The laboratory accelerated loading test results of other researchers are summarized in Table6. Due to the difference in dowel diameter for different researchers, the effectiveness of the similarity model test cannot be verified directly. Nevertheless, the result of the theoretical calculation using Friberg’s bearing stress analysis does indicate that the similarity model test can characterize the effect of the difference in dowel modulus on load transfer efficiency.Table 6
Steel dowel and FRP dowel having the same performance.
Accelerated loading test Theoretical calculation using Friberg’s bearingstress analysis Melham and Sheffield pulse load system [11] Embacher et al. full-scale repeated load test [16] Similarity model test Diameter Steel 1 in(25.4 mm) 1.5 in(38.1 mm) 1.65 in(42 mm) 1.5 in(38.1 mm) 1.65 in(42 mm) FRP 1.5 in(38.1 mm) 2 in(50.8 mm) 2.2 in(56 mm) 1.91 in(48.5 mm) 2.13 in(54 mm)For the joints with Steel35, Steel42 and Steel56, the average LTE is 91%, 93.1%, and 96.6%, respectively. It indicates that the dowel diameter strongly influences the load transfer capability and it is very reasonable for Chinese specification to increase the dowel diameter. The results also show that the average LTE of Steel35, Elliptical35, and Square35 is 91.0%, 91.6%, and 92.6%, respectively.


### 5.2. Differential Deflection

As LTE does not take into account the magnitude of deflections, it is necessary to calculate differential deflection (DD=wL-wUL) for better understanding of LTE effectiveness [6]. Different magnitudes of differential deflection can result in the same LTE value since LTE is simply a ratio of the corner deflection of unloaded slab divided by that of loaded slab. The result of differential deflection for joints with different dowels, shown in Figure 10, revealed that combining differential deflection to interpret the effectiveness of load transfer system is necessary, especially for those having similar LTE. It can be also observed that the slope of differential deflection curve varied with material, shape, and size of dowel bar. The main reason for this is the difference in dowel-concrete bearing stress, which is responsible for the development of dowel looseness and subsequent joint deflections. In this research, elliptical dowel was used to reduce bearing stress by presenting a larger bearing surface while holding constant cross-sectional area. As expected, Elliptical35 was found to have slightly better long-term load transfer performance than Steel35, though Elliptical35 has lower bending stiffness than Steel35.Figure 10
Differential deflection on load cycles for different dowels.


### 5.3. Differential Energy

The differential energy (DE) is defined as the energy difference in the elastic subgrade deformation under the loaded slab and unloaded slab [22]. MEPDG faulting models are highly dependent on the magnitude of the differential energy density at the slab corner. As DE increases, the potential for pumping and faulting increases greatly as well [8]. The following equation can be used to calculate DE:(6)DE=k2wL2-wUL2,where k is modulus of subgrade reaction, wL is the corner deflection of loaded slab, and wUL is the corner deflection of unloaded slab.The ratio of differential elastic deformation energy to modulus of subgrade reaction,DE/k, was used by Buch et al. to eliminate the impact of modulus of subgrade reaction and focus on the slab deflections [23]. In this research, DE/k was adopted to evaluate the development of differential deflection more clearly. As shown in Figure 11, the value of DE/k increased sharply after a certain amount of load cycles. The slope of DE/k after 600,000 cycles is directly related to the material, shape, and size of dowel bar, which can be selected as an indicator for dowel performance.Figure 11
The ratio of differential energy to modulus of subgrade reaction.


### 5.4. Deformation of Dowel Bar

Concerning the deformation of dowel bar, the strain was plotted against load cycles. The result of Steel35 and FRP35 presented in Figures12 and 13 show that the strain of Steel35 is smaller than the strain of FRP35 under the same wheel load due to the difference in elastic modulus. Comparison of the average strains of Steel35, Steel42, and Steel56, which are 145, 105, and 60 με, respectively, indicated that dowel bar with large diameter can effectively reduce the internal stress.Figure 12
Strains of dowels at loaded sides.Figure 13
Strains of dowels at unloaded sides.


### 5.5. Bearing Stress

Based on Friberg’s bearing stress analysis, bearing stress can be back-calculated using the test results of deflection and strain according to the following equations:(7)σL=EdεL,ML=σLWz,Pc=-βMLe-βxLsin⁡βxL+βz/2sin⁡βxL+cos⁡βxL,δ=λPczAG,y0=DD-δ2,σb=K0y0,where σL is stress of dowel where strain gauge is located, Ed is dowel modulus, εL is measured strain, ML is section bending moment where strain gauge located, Wz is section modulus in bending, Pc is shear force carried by the critical dowel, β is relative stiffness of the dowel bar encased in concrete, xL is distance of strain gauge from joint face in the prototype, z is joint width, δ is shear deflection, λ is form factor, A is cross-sectional area of the dowel bar, G is shear modulus, y0 is joint deflection at joint face, DD is measured differential deflection, σb is bearing stress, and K0 is modulus of dowel support.The back-calculated bearing stress and the corresponding number of wheel cycles for steel dowel bar in the prototype are demonstrated in Figure14. As shown in the figure, the bearing stress after 864,000 load cycles for Steel35, Elliptical35, and Square35 are 0.378 MPa, 0.228 MPa, and 0.266 MPa, respectively. It is suggested that Square35 dowel is able to reduce joint deflection and bearing stress, compared to Steel35. More research, especially field evaluation, is needed to confirm this laboratory finding.Figure 14
Back-calculated bearing stress.


## 5.1. Load Transfer Efficiency

Load transfer efficiency (LTE) is defined as the ability of a joint or crack to transfer load from one side of the joint or crack to the other. The method used to calculate load transfer efficiency is shown in (5). A load transfer efficiency of 70 to 100 percent is typically considered adequate:(5)LTE=wULwL100%,where wUL is the deflection of unloaded slab and wL is the deflection of loaded slab.The LTE and the corresponding number of wheel cycles for each type of dowel bar in the prototype are presented in Figure9. As shown in Figure 9, the average LTE of FRP35 observed in the accelerated loading test is 87.7%, which is smaller than the average LTE of Steel35, 91%. After 864,000 cycles, the LTE of FRP35 decreased from 90.8% to 82.6%, while the LTE of Steel35 decreased from 94.8% to 87%, indicating that the use of FRP dowel has a significant impact on the performance of pavement joint. The main reason is that FRP dowel has much lower elastic modulus than steel dowel, typically about 20 percent, which results in significantly higher bearing stress and differential joint deflection [8].Figure 9
Load transfer efficiency on load cycles for different dowels.A comparison between FRP56 and Steel42 was also conducted. The average LTE of FRP56 and Steel42 are 93.4% and 93.1%, respectively, which means those two have very close load transfer performance. Larger FRP dowel is a feasible solution for the above-mentioned phenomenon. The laboratory accelerated loading test results of other researchers are summarized in Table6. Due to the difference in dowel diameter for different researchers, the effectiveness of the similarity model test cannot be verified directly. Nevertheless, the result of the theoretical calculation using Friberg’s bearing stress analysis does indicate that the similarity model test can characterize the effect of the difference in dowel modulus on load transfer efficiency.Table 6
Steel dowel and FRP dowel having the same performance.
Accelerated loading test Theoretical calculation using Friberg’s bearingstress analysis Melham and Sheffield pulse load system [11] Embacher et al. full-scale repeated load test [16] Similarity model test Diameter Steel 1 in(25.4 mm) 1.5 in(38.1 mm) 1.65 in(42 mm) 1.5 in(38.1 mm) 1.65 in(42 mm) FRP 1.5 in(38.1 mm) 2 in(50.8 mm) 2.2 in(56 mm) 1.91 in(48.5 mm) 2.13 in(54 mm)For the joints with Steel35, Steel42 and Steel56, the average LTE is 91%, 93.1%, and 96.6%, respectively. It indicates that the dowel diameter strongly influences the load transfer capability and it is very reasonable for Chinese specification to increase the dowel diameter. The results also show that the average LTE of Steel35, Elliptical35, and Square35 is 91.0%, 91.6%, and 92.6%, respectively.


## 5.2. Differential Deflection

As LTE does not take into account the magnitude of deflections, it is necessary to calculate differential deflection (DD=wL-wUL) for better understanding of LTE effectiveness [6]. Different magnitudes of differential deflection can result in the same LTE value since LTE is simply a ratio of the corner deflection of unloaded slab divided by that of loaded slab. The result of differential deflection for joints with different dowels, shown in Figure 10, revealed that combining differential deflection to interpret the effectiveness of load transfer system is necessary, especially for those having similar LTE. It can be also observed that the slope of differential deflection curve varied with material, shape, and size of dowel bar. The main reason for this is the difference in dowel-concrete bearing stress, which is responsible for the development of dowel looseness and subsequent joint deflections. In this research, elliptical dowel was used to reduce bearing stress by presenting a larger bearing surface while holding constant cross-sectional area. As expected, Elliptical35 was found to have slightly better long-term load transfer performance than Steel35, though Elliptical35 has lower bending stiffness than Steel35.Figure 10
Differential deflection on load cycles for different dowels.


## 5.3. Differential Energy

The differential energy (DE) is defined as the energy difference in the elastic subgrade deformation under the loaded slab and unloaded slab [22]. MEPDG faulting models are highly dependent on the magnitude of the differential energy density at the slab corner. As DE increases, the potential for pumping and faulting increases greatly as well [8]. The following equation can be used to calculate DE:(6)DE=k2wL2-wUL2,where k is modulus of subgrade reaction, wL is the corner deflection of loaded slab, and wUL is the corner deflection of unloaded slab.The ratio of differential elastic deformation energy to modulus of subgrade reaction,DE/k, was used by Buch et al. to eliminate the impact of modulus of subgrade reaction and focus on the slab deflections [23]. In this research, DE/k was adopted to evaluate the development of differential deflection more clearly. As shown in Figure 11, the value of DE/k increased sharply after a certain amount of load cycles. The slope of DE/k after 600,000 cycles is directly related to the material, shape, and size of dowel bar, which can be selected as an indicator for dowel performance.Figure 11
The ratio of differential energy to modulus of subgrade reaction.


## 5.4. Deformation of Dowel Bar

Concerning the deformation of dowel bar, the strain was plotted against load cycles. The result of Steel35 and FRP35 presented in Figures12 and 13 show that the strain of Steel35 is smaller than the strain of FRP35 under the same wheel load due to the difference in elastic modulus. Comparison of the average strains of Steel35, Steel42, and Steel56, which are 145, 105, and 60 με, respectively, indicated that dowel bar with large diameter can effectively reduce the internal stress.Figure 12
Strains of dowels at loaded sides.Figure 13
Strains of dowels at unloaded sides.


## 5.5. Bearing Stress

Based on Friberg’s bearing stress analysis, bearing stress can be back-calculated using the test results of deflection and strain according to the following equations:(7)σL=EdεL,ML=σLWz,Pc=-βMLe-βxLsin⁡βxL+βz/2sin⁡βxL+cos⁡βxL,δ=λPczAG,y0=DD-δ2,σb=K0y0,where σL is stress of dowel where strain gauge is located, Ed is dowel modulus, εL is measured strain, ML is section bending moment where strain gauge located, Wz is section modulus in bending, Pc is shear force carried by the critical dowel, β is relative stiffness of the dowel bar encased in concrete, xL is distance of strain gauge from joint face in the prototype, z is joint width, δ is shear deflection, λ is form factor, A is cross-sectional area of the dowel bar, G is shear modulus, y0 is joint deflection at joint face, DD is measured differential deflection, σb is bearing stress, and K0 is modulus of dowel support.The back-calculated bearing stress and the corresponding number of wheel cycles for steel dowel bar in the prototype are demonstrated in Figure14. As shown in the figure, the bearing stress after 864,000 load cycles for Steel35, Elliptical35, and Square35 are 0.378 MPa, 0.228 MPa, and 0.266 MPa, respectively. It is suggested that Square35 dowel is able to reduce joint deflection and bearing stress, compared to Steel35. More research, especially field evaluation, is needed to confirm this laboratory finding.Figure 14
Back-calculated bearing stress.


## 6. Conclusions

The aim of this study is to develop a small-scale accelerated loading test to evaluate dowel bar alternatives, combining the advantage of pulse load system and HVS. Thus, a similarity model was developed and the corresponding test program was described. Dowel bars with different materials and cross-sections were evaluated. The following conclusions can be obtained:(1)
The use of FRP dowel would lead to significantly lower LTE compared with the specimen using round steel dowel when cross-section areas were held constant. This was related to Young’s modulus of FRP material which was about 80 percent lower than that of carbon steel. In the test, FRP56 and Steel42 had very close load transfer efficiency, indicating that larger FRP dowel was required when FRP dowel was used to replace steel dowel in concrete pavement.(2)
A comparison between the behaviors of the test specimens containing round steel dowel revealed that as dowel diameter increases, both differential deflection and dowel-concrete bearing stress reduce significantly which directly affects the rate of development of joint faulting. Hence, it can be concluded that dowel diameter strongly influences the load transfer behavior and performance of pavement joint.(3)
Steel dowels with round, elliptical, and square cross-sections were also evaluated in this research. The results of LTE and differential deflection illustrated that Elliptical35 had slightly better long-term load transfer performance than Steel35. It can be inferred that with the continued increase of the loading cycles, the gap between the performance of two types of dowels would be more significant, considering the back-calculated bearing stress of Elliptical35 was nearly 40 percent lower than that of Steel35 after 864,000 loading cycles. In addition, square dowel was found to have outstanding load transfer capacity, even better than elliptical dowel. However, there were no relevant studies in the literature that can confirm this finding. Full-scaled accelerated loading test for square dowel should be conducted in the future.(4)
The similarity model test developed in this study is effective in characterizing the impact of dowel modulus and cross-section on load transfer capacity.



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*Source: 3981908-2017-02-15.xml*