Revised Faulting Model to Account for Dowel Looseness and Corrosion in Long-Life Pavements

Abstract

The current AASHTOWare Pavement Mechanistic-Empirical Design faulting model framework has several limitations, which prohibit the consideration of alternative dowels commonly used in long-life pavements. Users cannot account for key design parameters, such as dowel stiffness, which is a critical need given the increased use of alternative dowel bars. Also, the effect of corrosion is not integrated into the model. Lastly, because of a lack of available faulting data from doweled pavements, the calibration alone is unable to account for the effect of loss of dowel performance resulting from corrosion. This study presents a revised faulting model framework which incorporates key design, loading, and environmental parameters. First, a comprehensive dowel damage model was developed based on an accelerated dowel loading test. The damage model incorporates critical parameters such as dowel stiffness which, before this work, could not be directly considered. Second, a novel corrosion model informed by a laboratory analysis is incorporated to account for the reduction of dowel diameter caused by corrosion. Lastly, the concept of “equivalent dowel diameter” was introduced into the faulting model. The faulting model was calibrated using faulting data from a national database of in-service pavements. A series of model adequacy checks was conducted to demonstrate that the model does not exhibit bias and to illustrate the effect of key parameters on predicted faulting. The improved faulting model framework is the first comprehensive model able to account for damage accumulation resulting from both vehicle loads and corrosion for the range of dowel bars currently on the market.

Keywords

faulting dowel bars performance prediction calibration pavement ME

Introduction

“Faulting” is distress that can develop in jointed plain concrete pavements (JPCPs) and is defined as the difference in elevation between the approach and leave slabs ( 1 ). Dowels are commonly used to mitigate the development of faulting and thus extend the design life of concrete pavements. The long-term performance of doweled joints is known to decrease primarily through two fundamental mechanisms: damage to the concrete surrounding the dowel and corrosion of the dowel. The first mechanism is caused by high bearing stresses which form between the dowel and the surrounding concrete when the pavement is subjected to vehicle loading. Over time, repeated loading can cause the development of damage to the concrete directly adjacent to the dowel, resulting in looseness of the dowel. Static load test results indicate that looseness is a function of the magnitude of the applied load, dowel diameter, and concrete stiffness ( 2 – 4 ). Subsequent studies identified that repeated load applications cause an increase in looseness over time, thereby decreasing the performance of the dowel ( 5 , 6 ). The second mechanism of dowel damage is corrosion of the dowel. Green epoxy-coated (EC) carbon steel dowels have been the industry standard for decades. While the green epoxy-coating provides some degree of corrosion protection, it has been shown that long-term exposure to deicing salts and moisture can lead to corrosion development ( 7 – 9 ). Corrosion reduces the cross-sectional area of the dowel, introducing looseness to the doweled joint and lowering the effective stiffness of the dowel. Many U.S. state agencies have begun to adopt the use of alternative dowel bars to mitigate the effect of corrosion. These alternative dowel bars are often produced with non-corrosive or corrosion-resistant materials and coatings, including fiber-reinforced polymer (FRP), stainless steel, or zinc-based galvanization ( 10 ). The effect of corrosion varies as a function of dowel type and level of exposure to corrosive agents, which must be accounted for in the design process.

While it is known that long-term dowel performance decreases because of vehicle loading and corrosion, the current faulting prediction framework in the AASHTOWare Pavement Mechanistic-Empirical Design (Pavement ME) procedure has several limitations in the way loss of dowel performance is accounted for. The following section details the current faulting model framework and the limitations to how this framework currently accounts for loss of dowel performance.

Current Faulting Model Framework

Faulting is calculated in Pavement ME using a monthly incremental approach ( 1 ). The cumulative faulting is determined by summing the total faulting from the previous months with the incremental change in faulting in the given month. Equations 1–4 are used to calculate the iterative change in faulting for a given structure.

\begin{matrix} {FMAX}_{0} = (C_{1} + C_{2} \times {FR}^{0.25}) \times δ_{curl} \\ \times {[Log (1 + C_{5} \times 5^{EROD}) \times Log (\frac{P_{200} \times WetDays}{p_{s}})]}^{C_{6}} \end{matrix}

(1)

\begin{matrix} {FMAX}_{i} = {FMAX}_{i - 1} + C_{7} \times {DE}_{i} \\ \times {[Log (1 + C_{5} \times 5^{EROD})]}^{C_{6}} \end{matrix}

(2)

\begin{matrix} Δ {Fault}_{i} = (C_{3} + C_{4} \times {FR}^{0.25}) \\ \times {({FMAX}_{i - 1} - {Fault}_{i - 1})}^{2} \times {DE}_{i} \end{matrix}

(3)

{Fault}_{i} = {Fault}_{i - 1} + Δ {Fault}_{i}

(4)

where

${FMAX}_{0}$ = the initial maximum mean transverse joint faulting (in.),

FR = the base freezing index (FI) (defined as the percentage of the time that the top of the base is below freezing [<32^oF]),

$δ_{curl}$ = the maximum mean monthly Portland cement concrete (PCC) upward slab corner deflection caused by temperature curling and moisture warping,

EROD = the base/subbase erodibility index (integer between 1 and 5),

$P_{200}$ = the percent of the subgrade soil passing No. 200 sieve (%),

WetDays = the average number of annual wet days (>0.1 in. of rainfall),

$p_{s}$ = the overburden on subgrade (lb),

${FMAX}_{i}$ = the maximum mean transverse joint faulting for month i (in.),

${FMAX}_{i - 1}$ = the maximum mean transverse joint faulting for month i−1 (in.),

${DE}_{i}$ = the DE density of subgrade accumulated during month i,

$Δ {Fault}_{i}$ = the incremental monthly change in mean transverse joint faulting during month i (in.),

${Fault}_{i - 1}$ = the mean joint faulting at the beginning of month i (in.), and

$C_{1} \dots C_{7}$ = calibration coefficients.

The differential energy (DE) concept is used to calculate damage accumulation by relating the density of the subgrade deformation to slab deflections. The DE concept was based on the deformation energy applied by Larralde to develop a pumping model in concrete pavements ( 11 ). DE is calculated for a given month using Equation 5:

{DE}_{m} = \sum_{A = 1}^{3} \sum_{i = 1}^{N_{A}} \frac{1}{2} n_{i, A} k_{m} (δ_{L, i, A}^{2} - δ_{U, i, A}^{2})

(5)

where

${DE}_{m}$ = the DE density of subgrade deformation accumulated for month m,

$n_{i, A}$ = the number of axle load applications for current month and load group i,

$k_{m}$ = the modulus of subgrade reaction for month m (pounds per square inch [psi]/in.),

$δ_{L, i, A}$ = the corner deflections of the loaded slab caused by axle loading (mils), and

$δ_{L, i, A}$ = the corner deflections of the unloaded slab caused by axle loading (mils).

Artificial neural networks are used to calculate the corner deflections under loading for various axle and temperature loading conditions ( 1 , 12 ).

The performance of the joint is accounted for using load transfer efficiency (LTE), defined in Equation 6. The overall joint LTE is a function of contributions from the dowels, aggregate interlock, and base and is calculated using Equation 7.

LTE = \frac{δ_{U L}}{δ_{L}} \times 100 %

(6)

\begin{matrix} {LTE}_{joint} = 100 \\ [1 - (1 - \frac{{LTE}_{Dowel}}{100}) (1 - \frac{{LTE}_{Agg}}{100}) (1 - \frac{{LTE}_{Base}}{100})] \end{matrix}

(7)

where

$LTE$ = load transfer efficiency (%),

$δ_{UL}$ = the deflection of the unloaded face of the joint (mils),

$δ_{L}$ = the deflection of the loaded face of the joint (mils),

${LTE}_{joint}$ = the overall joint LTE (%),

${LTE}_{Dowel}$ = the joint LTE if dowels are the only mechanism of load transfer (%),

${LTE}_{Agg}$ = the load transferred through aggregate interlock (%), and

${LTE}_{Base}$ = the load transferred through the base (%).

The contribution of dowels to LTE is determined using the nondimensional dowel stiffness, $J_{d}$ , calculated in Equations 8–12. The nondimensional stiffness of doweled joints was developed by Ioannides and Korovesis and adopted into the current faulting framework ( 1 , 13 ).

J_{d} = J_{d}^{*} + (J_{0} - J_{d}^{*}) \exp (- {DAM}_{dowels})

(8)

J_{0} = \frac{152.8 A_{d}}{h_{PCC}}

(9)

J_{d}^{*} = {\begin{matrix} 118 & if \frac{A_{d}}{h_{PCC}} > 0.656 \\ 210.0845 \frac{A_{d}}{h_{PCC}} - 19.8 & if 0.009615 \leq \frac{A_{d}}{h_{PCC}} \leq 0.656 \\ 0.4 & if \frac{A_{d}}{h_{PCC}} < 0.09615 \end{matrix}

(10)

{Δ DOWDAM}_{i} = C_{8} \frac{F}{{df}_{c}^{*}}

(11)

F = J_{d} (δ_{L} - δ_{UL}) \times DowelSpace

(12)

where

$J_{d}$ = the nondimensional dowel stiffness,

$J_{d}^{*}$ = the critical nondimensional dowel stiffness,

$J_{0}$ = the initial nondimensional dowel stiffness,

${DAM}_{dowels}$ = the damage parameter for dowels,

$A_{d}$ = the cross-sectional area of the dowel (in.),

$h_{PCC}$ = the PCC thickness (in.),

${Δ DOWDAM}_{i}$ = the increase in dowel damage from an individual load application,

$C_{8}$ = a calibration coefficient specific to doweled joints,

F = effective shear force (lb),

d = the diameter of the dowel (in.),

$f_{c}^{*}$ = the compressive strength of the concrete (psi),

$δ_{L}$ = corner deflections of the loaded slabs (mils),

$δ_{UL}$ = corner deflections of the unloaded slabs (mils), and

DowelSpace = the dowel spacing (in.).

There are several limitations to the current faulting framework that adversely affect performance prediction of doweled pavements.

Firstly, the availability of faulting performance data for doweled pavements is limited. The calibration constants $C_{1}$ – $C_{7}$ were, therefore, calibrated primarily using data for in-service undoweled sections for both the doweled and undoweled pavements. As a result, faulting prediction is controlled by performance data obtained from undoweled sections. The calibration constant $C_{8}$ was included specifically to scale the predicted faulting for doweled pavements; however, this constant cannot be decoupled from the DE model developed for both doweled and undoweled pavements ( 14 ).

Secondly, the damage parameter, ${Δ DOWDAM}_{i}$ , only directly accounts for the applied load, concrete strength, and dowel diameter. The material and shape of the dowel are not directly accounted for in the model; therefore, it is not possible to directly consider alternative dowel designs. Alternative dowels include non-metallic dowels (e.g., FRP dowels) and dowels with non-standard shapes (e.g., tubular, elliptical, or plate dowels). Moreover, alternative dowel bars are not accounted for in the calibration database. This also prohibits the model from directly accounting for the loss of dowel performance because of corrosion. To date, there has not been a component of the model developed to directly account for the development of dowel corrosion and the resultant loss of dowel performance. Critical factors which affect corrosion development (e.g., degree of exposure and coating type) are, therefore, excluded in the faulting model. As a result, pavement engineers and managers are unable to evaluate the potential benefits of alternative dowels with higher resistance to corrosion to justify the increase costs that can be associated to the use of alternative dowels.

Lastly, there are limitations to the equations used to calculate the initial and critical nondimensional dowel stiffness, $J_{0}$ and $J_{d}^{*}$ , shown in Equations 9 and 10. These equations are a function of the ratio of the area of the dowel, $A_{d}$ , and the thickness of the slab, $h_{PCC}$ . In the current framework, a negative value for $J_{d}^{*}$ can be calculated if the ratio $A_{d}$ / $h_{PCC}$ is less than 0.094. There is no physical meaning for a negative nondimensional dowel stiffness and, thus, the model should be adjusted to ensure this is not feasible ( 14 ). Moreover, increasing pavement thickness while fixing all other parameters causes a decrease in the $J_{d}^{*}$ value. Counterintuitively, this would lead to an increase in predicted faulting when increasing the thickness of the pavement, which does not align with conventional understanding of pavement performance. Changes have been made in subsequent performance prediction models for unbonded overlays (UBOL-ME) and bonded concrete overlays of asphalt (BCOA-ME) to account for some of these ( 15 , 16 ). To date, these changes have not been incorporated into the Pavement ME faulting model framework. These limitations affect not only the predicted faulting but also the predicted International Roughness Index (IRI) for a given pavement structure. The IRI model accounts for the effect of faulting on ride quality by considering the cumulative faulting for a given section. Therefore, limitations to the faulting model must be addressed to improve both the faulting and IRI models in the current pavement design tool.

In this study, a series of revisions to the faulting model framework are presented to account for the effect of corrosion and damage caused by vehicle loads. First, the dowel damage was revised to incorporate a comprehensive dowel damage model informed by an accelerated dowel laboratory study. This revised model addresses limitations to the existing faulting model framework and can account directly for key dowel design and loading parameters. Second, a novel corrosion model was developed based on the results from an accelerated corrosion study. The revisions presented in this section contain the first model, which directly accounts for the loss of dowel cross-sectional area caused by corrosion development. Several additional refinements to the faulting model framework are then presented. The revised model was calibrated using faulting data from in-service JPCPs, and a series of model validation checks are presented. The resulting model is shown to sufficiently account for key design, loading, and corrosion parameters, which affect the long-term dowel performance. Critically, alternative dowel materials and designs can be directly accounted for in this revised model, which is a significant advancement given the increased use of these dowels in newly constructed pavements.

Faulting Model Revisions

Revised Damage Model

The first revision to the faulting model framework consists of a novel dowel damage model that accounts for the loss of dowel performance caused by repeated vehicle loads. The objective of this revision was to incorporate key design and loading parameters, such as dowel stiffness, dowel diameter, applied load magnitude, and number of applied loads. These revisions will enable alternative dowels, such as FRP and tubular dowels, to be considered in the model, whereas the existing faulting model framework is unable to do so.

The revised damage model was developed based on the results from a small-scale accelerated load test conducted at the University of Pittsburgh ( 17 ). The purpose of the test was to rapidly quantify damage accumulation in doweled beam specimens caused by repeated vehicle loading. The damage parameter developed in the laboratory test, referred to as “beam deflection energy” (DE_Beam), is adopted as the damage parameter in the revised faulting damage model presented in this study. The training dataset consists of DE_Beam values obtained from the accelerated loading test for 45 specimens. The analysis of the experimental results demonstrated that the parameters significant for DE_Beam include dowel diameter, applied load, dowel bending stiffness, and number of load cycles. The load transferred through the dowel is determined based on the load applied in the laboratory. This is calculated assuming that 10% of the load is transferred through the simulated base layer, which is consistent with the current design procedure ( 18 ). Half of the remaining load is assumed to transfer through the dowel, which is equal to 45% of the applied load.

Stiffness is accounted for using the dowel constant, β, developed by Friberg, which is calculated using Equations 13 and 14 ( 2 ):

β =^{4} \sqrt{\frac{K \times d}{4 \times E_{dowel} \times I}}

(13)

K = \frac{E_{PCC}}{h_{PCC}}

(14)

where

β = a dowel constant ( ${in .}^{- 1}$ ),

$K$ = the modulus of dowel reaction (psi/in.),

d = the diameter of the dowel (in.),

E = the modulus of elasticity of the dowel (psi),

I = the moment of inertia of the dowel ( ${in .}^{4}$ ),

$E_{PCC}$ = the elastic modulus of the dowel (psi), and

$h_{PCC}$ = the slab thickness.

The concrete elastic modulus for each specimen was measured before testing. For each specimen, ${DE}_{Beam}$ is calculated at 49 discrete times throughout the loading test, which results in a total of 2,205 data points. The database of calculated ${DE}_{beam}$ for each specimen was used to develop a predictive dowel damage model using multiple linear regression. The resulting ${DE}_{Beam}$ prediction model is shown in Equation 15:

\begin{matrix} D E_{Beam} = α_{1} \times \log (x + 1) + α_{2} \times \log (x + 1) \\ \times \frac{\log (Load)}{β} + α_{3} \times \frac{\log (x + 1)}{β} \end{matrix}

(15)

where

$D E_{Beam}$ = the beam deflection basin,

x = the number of applied loads,

Load = the magnitude of the load transferred through the dowel (lb),

β = the dowel constant ( ${in .}^{- 1})$ ,

$α_{1}$ = coefficient equal to 592.8,

$α_{2}$ = coefficient equal to 353.3, and

$α_{3}$ = coefficient equal to −1,256.5.

The adjusted R² is equal to 0.82, and the root mean square error is equal to 192. The measured versus predicted $D E_{beam}$ is shown in Figure 1.

Figure 1.

Measured versus predicted beam deflection energy (DE_Beam) values.

The DE_Beam prediction equation shown in Equation 15 was adopted into the faulting model framework to predict the cumulative dowel damage (DOWDAM). It was observed that the original equation predicts negative values for DE_Beam for low loads transferred through the dowel. This occurred because the training data did not include low load values, since the lowest applied laboratory load is equal to 2,000 lb, or 900 lb transferred through the dowel. To remedy this, a stepwise form of the function was developed to ensure a continuous and positive prediction of DOWDAM for all loads. The modified DOWDAM equation is shown in Equation 16:

\begin{matrix} DOWDAM = \\ {\begin{matrix} C 8 \times \sum [α_{1} \times \log (x_{i} + 1) + α_{2} \times \log (x_{i} + 1) \times \frac{\log (Loa d_{i})}{β} + α_{3} \times \frac{\log (x_{i} + 1)}{β}] & if Loa d_{i} \geq 900 \\ C 8 \times \frac{Loa d_{i}}{900} \times [α_{1} \times \log (x_{i} + 1) + α_{2} \times \log (x_{i} + 1) \times \frac{\log (900)}{β} + α_{3} \times \frac{\log (x_{i} + 1)}{β}] & if Loa d_{i} < 900 \end{matrix}} \end{matrix}

(16)

where

$DOWDAM$ = the cumulative dowel damage,

$x_{i}$ = the number of applied loads at the ith load magnitude,

Load _i = the magnitude of load transferred through the dowel at the ith load magnitude (lb),

β = the dowel constant ( ${in .}^{-})$ ,

$α_{1}$ , $α_{2}$ , and $α_{3}$ = coefficients determined through laboratory testing, and

C₈ = the calibration coefficient specific to doweled pavements.

Calibration of C₈ is discussed in greater detail in the subsequent sections.

Corrosion Model

The second revision made to the faulting model is the direct consideration of the reduction in dowel diameter caused by corrosion development. In the current faulting model framework, dowel diameter is a constant value over the life of the pavement, which does not account for the effect of corrosion development. The rate at which corrosion occurs is a function of the exposure conditions as well as the corrodibility of the material. To address this limitation, the findings from an accelerated dowel corrosion test were used to develop a framework for the corrosion model ( 19 ). The accelerated corrosion study evaluated a range of dowel bars currently on the market by subjecting doweled specimens to an accelerated corrosion program. Corrosion development was evaluated at frequent intervals to quantify the development of corrosion on the surface of the dowels and the potential for loss of dowel performance. The results from this corrosion study show that a reduction in dowel diameter occurs as a function of initial diameter, amount of chloride exposure, coating type, and dowel material. Therefore, the faulting model was revised to account for a monthly reduction in dowel diameter caused by corrosion. The effective dowel diameter equation is presented in Equation 17:

\begin{matrix} d_{i} = d_{0} \times \frac{1}{{(mont h_{i} - CL)}^{\frac{WetDays}{365} \times C_{EXP} \times C_{Coating}}} \end{matrix}

(17)

where

$d_{i}$ = the monthly dowel diameter (in.),

$d_{0}$ = the initial dowel diameter (in.),

${month}_{i}$ = the current month,

CL = the typical coating life (months) (included to account for the delayed development of corrosion achieved through use of coatings),

WetDays = the average number of wet days per year,

$C_{EXP}$ = the severity of the corrosion exposure, and

$C_{Coating}$ = the resistance of the bar to corrosion development.

The exposure condition is quantified using the WetDays and FI parameters. WetDays is included to account for the climatic effect of precipitation that carries chlorides into the joint. The exposure parameter is introduced to capture the range of exposure conditions throughout various regions. Corrosion potential is greatest where high quantities of deicing salts enter the joint, which occurs in regions with frequent snowfall events and frequent freeze-thaw cycles. Corrosion potential is lower in regions with mild winters with little freezing, or in regions with hard winters in which the pavement structure remains below freezing and, thus, deicing salts are not carried into joints. The exposure parameter is determined as a function of FI, which is calculated by comparing the average annual cumulative difference in mean daily temperature to 32°F. The magnitude of FI is used to establish $C_{EXP}$ using Table 1. Note that, at extreme FI values, the magnitude of $C_{EXP}$ becomes asymptotic. This is because of the potential for extended durations of freezing and fewer freeze-thaw cycles, thus fewer opportunities for deicing salts carried by melted snow to penetrate the joint and corrode the dowel before being removed off the roadway surface during snow plowing. The FI is a output parameter calculated in Pavement ME as it is incorporated into the IRI prediction model, which will assist with the incorporation of this revised faulting prediction framework into Pavement ME ( 20 ).

Table 1.

The Severity of the Corrosion Exposure ( $C_{EXP}$ ) Corresponding to the Freezing Index (FI) at the Pavement Location

FI (°F day)	$C_{EXP}$
<100	0
100–400	0.15
400–600	0.2
600–1,000	0.25
>1,000	0.25

The susceptibility of the dowel to corrosion is quantified using the CL and $C_{Coating}$ parameters, which characterize the delay in initiation of corrosion (CL) as well as the rate of corrosion development after initiation ( $C_{Coating}$ ). From the accelerated corrosion study, it was observed that corrosion development was delayed as a function of coating type.

The following types of dowel were considered in the accelerated corrosion study: green EC carbon steel, purple EC carbon steel, green EC zinc-based galvanized tubular steel, purple EC zinc-based galvanized tubular steel, FRP, zinc-clad tubular, and stainless-steel tubular. The CL parameter is informed using field performance data as well as the results of the accelerated corrosion study ( 21 ). For standard, EC carbon steel dowels it is assumed that CL is equal to 240 months (20 years). Corrosion initiation was delayed for galvanized dowels; therefore, CL for galvanized dowels is equal to 600 months (50 years) ( 19 ). The rate of corrosion is characterized using $C_{Coating}$ , which is determined as a function of the type and diameter of dowel being evaluated. Larger-diameter dowels have greater surface area in the open joint exposed to chlorides; therefore, $C_{coating}$ is calculated using Equation 18:

C_{coating} = α \times (π \times d) \times jw

(18)

where

$C_{coating}$ = the coating parameter used in Equation 17,

α = selected based on the dowel coating or material,

d = the outer dowel diameter (in.), and

jw = the joint width (in.).

The sections included in the calibration dataset were all constructed with the standard, solid-steel EC dowels. For standard EC carbon steel dowels, α is equal to 0.15. The results from the accelerated corrosion study were used to estimate the α values for alternative dowel materials. Dowels which do not exhibit corrosion, such as FRP or stainless-steel dowels, are assumed to have an α equal to 0 because no corrosion was observed in the laboratory investigation. This would negate the effect of corrosion in the model, and the only loss of dowel performance would be the result damage in the concrete around the dowel caused by bearing stresses calculated through the DOWDAM portion of the framework. Galvanized dowels exhibited minor corrosion development in the laboratory investigation and varied as a function of epoxy-coating type; therefore, α for galvanized dowels is estimated to be 0.075 for green EC galvanized dowels and 0.01 for purple EC galvanized dowels. The joint width is determined incrementally throughout the life of the pavement life using Equation 19:

jw = (α \times Δ T + ϵ) \times L

(19)

where

jw = joint width (in.),

α = the coefficient of thermal expansion of concrete (°F⁻¹),

$Δ T$ = the change in temperature of the pavement (°F),

ϵ = the drying shrinkage of the concrete, and

L = the slab length (in.).

Equivalent Dowel Diameter

Two final adjustments were made to the faulting model framework to better account for faulting development for the range of dowel bars currently available on the market.

First, the layer in which pumping occurs was changed from the subgrade to the uppermost unbound layer. In the current Pavement ME framework, the percent fines (P200) used in the faulting model is a function of the subgrade material. However, it is likely that the mobilized fines would be located directly below the stabilized layers in the pavement structure. Therefore, the P200 in the revised model is selected based on the uppermost unbound layer in the pavement structure. To prevent excessively low P200 values from being used in the model, a lower limit threshold of 20% is adopted.

Second, the revised faulting model introduces the concept of equivalent dowel diameter, $d_{eq}$ , which allows for alternative dowel bars to be considered. As previously described, the current faulting model framework only accounts for the outer diameter of the dowel and therefore assumes the dowel is a green EC solid steel bar. To enable evaluation of alternative dowels, such as FRP or tubular dowels, the concept of equivalent dowel diameter was incorporated into the model. The inner and outer diameter, stiffness, and transverse spacing of a given dowel are used to calculate the diameter of a solid steel dowel at 12 in. transverse spacing that would generate the same level of bearing stresses under loading. Equivalent dowel diameter is calculated using Equation 20:

d_{eq} = {\frac{12}{DowelSpace}}^{7} \sqrt{\frac{d_{o}^{4} \times E_{dowel} \times (d_{o}^{4} - d_{i}^{4})}{E_{steel} \times d_{o}}}

(20)

where

$d_{eq}$ = the equivalent dowel diameter (in.),

$DowelSpace$ = the transverse spacing between bars (in.),

$d_{o}$ = the dowel outer diameter (in.),

$d_{i}$ = the dowel inner diameter (in.) (for solid dowel, $d_{i}$ equals 0),

$E_{dowel}$ = the dowel elastic modulus (psi), and

$E_{steel}$ = the elastic modulus of steel (defined as 29 x 10⁶ psi).

The calculated $d_{eq}$ for a range of standard and alternative dowels available on the market is shown in Table 2.

Table 2.

Equivalent Dowel Diameter for Commonly Used Dowel Bars

Dowel	Dowel spacing (in.)	Outer diameter (in.)	Inner diameter (in.)	Elastic modulus (psi)	Equivalent diameter (in.)
1 in. solid steel	12	1	0.0	29,000,000	1.00
1.25 in. solid FRP	12	1.25	0.0	5,500,000*	0.99
1.5 in. solid FRP	12	1.5	0.0	5,500,000*	1.18
1.25 in. solid steel	12	1.25	0.0	29,000,000	1.25
1.375 in. tubular steel	12	1.375	1.135	29,000,000	1.26
1.625 in. tubular steel	12	1.625	1.385	29,000,000	1.46
1.5 in. solid steel	12	1.5	0.0	29,000,000	1.50
1.9 in. tubular steel	12	1.9	1.6	29,000,000	1.72

Note: FRP = fiber-reinforced polymer; psi = pounds per square inch.

Can vary between 4 and 8 million psi depending on the manufacturer, but is commonly 5–6 million psi.

Faulting Model Recalibration

Calibration Database

The database used to calibrate the JPCP faulting model consists of faulting data used for the completion of the NCHRP Project 01-51. A subsequent recalibration of the faulting model was performed using the same calibration database ( 22 ). The database consists of 120 sections from 26 states, 1 province of Canada, and 6 sections at the Minnesota Road Research Facility. The number of sections and datapoints obtained from each region are shown in Table 3, and a map of the calibration site locations is shown in Figure 2. The database consisted of 644 datapoints, of which 380 were from doweled pavements sections. There are two limitations to the doweled pavement database. First, very few datapoints were collected when the pavement age was greater than 20 years. The average age of these sections was 7.9 years at the time of data collection, which is too early in the design life to typically see significant faulting. The second limitation is that this database only represents doweled pavements constructed with EC carbon steel dowel bars. Therefore, the effect of alternative dowels, such as FRP or tubular dowels, is not directly captured through calibration alone. Faulting was predicted for each section in the calibration database using Pavement ME version 2.6 ( 23 ). Climate data was sourced from the Long-Term Pavement Performance database, which is generated from MERRA data sets ( 24 ).

Table 3.

Calibration Database Geographical Details

Location	Number of sections	Number of calibration datapoints
Alabama	1	3
Florida	2	6
Georgia	4	23
Idaho	1	8
Indiana	4	11
Iowa	3	10
Kentucky	1	4
Michigan	8	50
Mississippi	1	14
Nebraska	2	5
Nevada	2	7
New Mexico	1	19
North Carolina	11	76
North Dakota	2	9
Ohio	5	24
Arizona	10	79
Oklahoma	2	10
Pennsylvania	1	6
South Carolina	1	1
South Dakota	3	14
Texas	1	9
Utah	3	14
Arkansas	9	57
Washington	10	62
Wisconsin	10	24
California	4	23
Colorado	8	50
Quebec	4	21
Minnesota Road Research Facility	6	5

Figure 2.

Map identifying sections included in calibration database.

Model Calibration

Calibration of the faulting model involves iteratively adjusting the calibration coefficients C₁–C₇ in Equations 1–3 and C₈ in Equation 16 to minimize the error between the predicted and actual faulting values. Error is calculated using Equation 21. The following calibration process was adopted. The monthly DE values were placed in a macro driven excel spreadsheet developed to calibrate the faulting model. Several calibration parameters were fixed, while the other parameters were varied. The combination of the parameters varied; those which yielded the lowest error were identified. These parameters remain fixed, while the parameters that were previously fixed were varied to find the new combination of parameters that yield the lowest error. The entire process was repeated until the lowest error was achieved. This method does not necessarily guarantee the lowest global error; however, it does provide reasonable results. Throughout the process, both the error and model bias are minimized to ensure sufficient model performance. The error between the predicted and measured faulting was minimized using the following function:

\begin{matrix} ERROR (C_{1}, C_{2}, C_{3}, C_{4}, C_{5}, C_{6}, C_{7}, C_{8}) = \\ \sum_{i = 1}^{N} {({FaultPredicted}_{i} - FaultMeasure d_{i})}^{2} \end{matrix}

(21)

where

ERROR = the error function (in.),

C₁–C₈ = the calibration coefficients,

${FaultPredicted}_{i}$ = the predicted faulting for the ith observation in the dataset (in.), and

${FaultMeasured}_{i}$ = the measured faulting for the ith observation in the dataset (in.).

The final model performance and coefficients determined through this calibration process are presented in Figure 3 and Table 4, respectively.

Figure 3.

Predicted versus measured faulting.

Table 4.

Jointed Plain Concrete Pavement Transverse Joint Faulting Calibration Coefficients

Calibration coefficient	Pavement ME model (original) ( 18 )	Pavement ME model (Task 327.7) ( 25 )	Pitt model
C ₁	1.29	0.595	0.55
C ₂	1.1	1.636	1.27
C ₃	0.001725	0.00217	0.0015
C ₄	0.0008	0.00444	0.0022
C ₅	250	250	230
C ₆	0.4	0.47	0.67
C ₇	1.2	7.3	10.6
C ₈	400	400	100

Note: Pavement ME = AASHTOWare Pavement Mechanistic-Empirical Design.

Model Adequacy Checks

Model adequacy checks were performed to ensure bias was eliminated from the model. The procedure developed by Mallela et. al was adopted for this analysis ( 26 ). The results from the null and alternative hypothesis tests outlined in Table 5 are shown in Table 6. A significance level of 0.05 was assumed for all hypothesis testing. It is concluded that the null hypothesis is not rejected for each of the three hypotheses. Therefore, it is concluded that the model does not exhibit bias and is acceptable.

Table 5.

Null and Alternative Hypothesis Tested for Jointed Plain Concrete Pavement Faulting

Hypothesis 1	Null hypothesis H_o: Linear regression model intercept = 0
	Alternative hypothesis H_a: Linear regression model intercept ≠ 0
Hypothesis 2	Null hypothesis H_o: Linear regression model slope = 1.0
	Alternative hypothesis H_a: Linear regression model slope ≠ 1.0
Hypothesis 3	Null hypothesis H_o: Mean predicted faulting = Mean measured faulting
	Alternative hypothesis H_a: Mean predicted faulting ≠ Mean measured faulting

Table 6.

Results from Transverse Joint Faulting Model Hypothesis Testing

Hypothesis testing and T-test
Test type	Value	95% confidence interval	P-value
Hypothesis 1: Intercept = 0	0.0006	(0.0013, 0.0025)	0.639
Hypothesis 2: Slope = 1	0.947	(0.89, 1.01)	0.638
Paired t-test	na	na	0.632

Note: na = not applicable.

Faulting Reliability Model

The faulting reliability model was determined using the same method adopted for Pavement ME ( 27 ). The reliability model is shown in Equation 22 and Figure 4. The R² of the reliability model is equal to 0.99.

Stdev (Fault) = 0.00594 + 0.0766 \times (Faul t^{0.318})

(22)

where

Stdev(Fault) = the faulting standard deviation (in.), and

Fault = the average transverse joint faulting (in.).

Figure 4.

Faulting standard deviation versus predicted faulting used to fit faulting standard deviation model.

Sensitivity Analysis

A sensitivity analysis of the predicted faulting is presented to evaluate the response of the model to key design, loading, and climatic parameters. A baseline structure was used for the sensitivity analysis with the key parameters shown in Table 7. All parameters remained fixed with one parameter varied at a time to evaluate the effect of the parameter on predicted faulting. The sensitivity plots are shown in Figures 5 –17.

Table 7.

Baseline Structure Examined in the Sensitivity Analysis

Parameter	Value
PCC thickness	10 in.
PCC 28-day MOR	600 psi
PCC CTE	5.0 x 10⁶/°F
Slab width	12 ft
Joint spacing	15 ft
Dowel bar	1.25 in. diameter, solid epoxy-coated steel
Shoulder type	Hot mix asphalt
Base type	6 in. granular
EROD	4
P200 of base	8.7%
Subgrade	A-4
Climate	Wet-freeze (Pittsburgh)
One-way annual average daily truck traffic	3,000
Linear growth rate	0%
Built-in gradient	−10°F
Reliability	50%

Note: CTE = coefficient of thermal expansion; EROD = the base/subbase erodibility index (integer between 1 and 5); MOR = modulus of rupture; PCC = Portland cement concrete; psi = pounds per square inch.

Figure 5.

Effect of Portland cement concrete thickness on predicted faulting for 1.25 in. diameter epoxy-coated dowel.

Figure 6.

Effect of Portland cement concrete thickness on predicted faulting for 1.5 in. diameter epoxy-coated dowel.

Figure 7.

Effect of joint spacing on predicted faulting.

Figure 8.

Effect of one-way annual average daily truck traffic on predicted faulting for 1.25 in. diameter epoxy-coated steel dowels.

Figure 9.

Effect of one-way annual average daily truck traffic on predicted faulting for 1.5 in. diameter epoxy-coated steel dowels.

Figure 10.

Effect of climate on predicted faulting.

Figure 11.

Effect of the resistance of the bar to corrosion development ( $C_{coating}$ ) on predicted faulting.

Figure 12.

Effect of the average number of wet days per year (WetDays) on predicted faulting.

Figure 13.

Effect of freezing index on predicted faulting.

Figure 14.

Effect of dowel diameter on predicted faulting.

Figure 15.

Effect of dowel diameter on predicted faulting for long-life fiber-reinforced concrete alternative and epoxy-coated steel dowels.

Figure 16.

Effect of dowel diameter on predicted faulting for long-life tubular alternative and epoxy-coated steel dowels.

Figure 17.

Effect of reliability on predicted faulting.

The effect of PCC thickness on predicted faulting is shown in Figures 5 and 6 for 1.25 and 1.5 in. solid EC dowels Increasing PCC thickness decreases the ratio of dowel cross-sectional area to slab thickness, thereby reducing the non-dimensional dowel stiffness and increasing predicted faulting. Faulting is not sensitive to thickness with small variations in pavement thickness; however, there is a significant increase in predicted faulting for 1.25 in. EC dowels when the pavement thickness is 12 in. If the pavement thickness is 10 in. or greater, then a 1.5 in. dowel is typically used; therefore, this sensitivity is reasonable.

The effect of joint spacing on predicted faulting is shown in Figure 7. Increasing joint spacing results in an increase in the DE predicted from the structural response model. This results in an increase in the predicted faulting.

The effect of traffic volume on predicted faulting is shown in Figures 8 and 9 for 1.25 and 1.5 in. solid EC steel dowels, respectively. The one-way AADTT volume is varied for each case. It should be noted that the one-way AADTT indicated in the legend was further reduced when predicting faulting by multiplying by a lane distribution factor. The portion of trucks in the design lane was assumed to be 95%. An increase in traffic is shown to cause an increase in predicted faulting because of the increase in DE calculated with the structural response model. The revised dowel damage model accounts for the loss of dowel performance caused by vehicle loads. Therefore, greater traffic volumes result in greater loss of dowel performance over time.

The effect of climate on predicted faulting is shown in Figure 10. The predicted faulting is lowest for Arizona because of the high temperatures, lack of freeze-thaw cycles, and dry climate. The predicted faulting for Atlanta, GA, is slightly higher because of the higher amount of precipitation present, which increases the mobility of fines and, therefore, the potential for the development of faulting. Faulting for Pittsburgh, Chicago, and Madison are similar because of their climates having similar precipitation and freeze-thaw cycles. The increase in faulting after 20 years can be seen for these regions. This is because of the effect of the corrosion model, which accounts for loss of dowel performance at the end of the life of the dowel coating.

The rate at which the corrosion model affects predicted faulting is a function of the $C_{coating}$ factor, WetDays, and FI. As shown in Figure 11, increasing $C_{coating}$ results in an increase in the predicted faulting. This parameter is calculated using Equation 18 and varies as a function of coating type and dowel diameter. Use of more corrosion-resistant coatings, such as zinc-based galvanization, results in a lower $C_{coating}$ than standard epoxy-coatings. This parameter could, therefore, be used to account for the difference in quality between similar types of coating, as improved materials science may further improve the corrosion resistance of existing coating types. The effect of corrosion is also a function of the climatic parameters WetDays and FI. This is shown in Figures 12 and 13. An increase WetDays not only increases the mobility of fines and, therefore, the potential for the development of faulting, but also helps to mobilize deicing salts into the transverse joint, thus accelerating corrosion development on the metallic dowel. The FI accounts for the amount of snowfall that is likely to occur. An increase in FI results in greater amounts of deicing salts being applied, thus increasing the effect of corrosion on predicted faulting. However, it was observed in the calibration dataset that the effect of FI on predicted faulting became asymptotic. It is hypothesized that at a certain threshold of FI there are fewer freeze-thaw cycles that allow for deicing salts to mobilize into the joint. Therefore, an upper limit on the effect of FI is applied.

The effect of dowel bar diameter and design on predicted faulting is shown in Figures 14 –16. EC solid steel, FRP, EC galvanized tubular dowels, and stainless-steel tubular dowels were considered. First, increasing dowel diameter for solid steel EC dowels is shown to reduce the predicted faulting. This is consistent with knowledge of pavement design. Novel to pavement performance modeling is the ability to account for long-life alternative dowel bars, as shown in Figures 15 and 16. Predicted faulting is calculated for FRP dowels using the concept of equivalent dowel diameter. As shown in Figure 15, this enables 1.25 and 1.5 in. FRP dowels to be used. It can be seen that 1.5 in. FRP dowels have a similar performance as 1.25 in. EC dowels for the first 20 years of the design life because of similar dowel stiffness values. However, FRP dowels do not corrode; therefore, the long-life performance of this dowel is superior to the EC dowel. It should be noted that the baseline pavement structure is located in a wet-freeze climate (Pittsburgh, PA), which results in high faulting development for the undoweled pavement structure. The predicted faulting for standard EC steel and green EC galvanized tubular dowels is shown in Figure 16. It can be seen that dowels with similar equivalent diameters have similar predicted faulting for the first 20 years of the design life. Once the coating life of the EC steel dowel is reached, however, the predicted faulting increases at a greater rate than the more corrosion-resistant EC galvanized dowel. The larger-diameter stainless-steel dowel is observed to have the lowest predicted faulting because of the higher equivalent dowel diameter and ability to resist corrosion. These results indicate that alternative dowels can be considered for long-life paving projects, which was not previously possible.

The final factor that is considered is the effect of reliability on predicted faulting. Five levels are examined, from 50% (control) to 99%. As a higher level of reliability is selected, a greater magnitude of faulting is predicted, as shown in Figure 17.

Conclusions

The performance of dowel bars in concrete pavements can decrease because of damage accumulation from repeated vehicle applications and corrosion development on the dowel. The current faulting model framework in Pavement ME has several limitations, which prohibit an accurate estimation of long-term dowel performance for the full range of dowels currently available on the market. First, the dowel damage model does not fully consider the range of parameters which have been shown to affect dowel stiffness. Second, corrosion is not directly accounted for in the model. A significant by-product of these limitations is the inability to directly consider alternative dowels, such as FRP or tubular dowels, in the current faulting model framework. Given the increase in the use of these dowels in long-life paving projects, there is a critical need to revise the faulting model framework to enable pavement engineers to evaluate the full range of dowel options.

This paper presents a revised faulting model which directly accounts for loss of dowel performance caused by repeated vehicle loads and corrosion. Results from an accelerated dowel loading test were used to develop a comprehensive dowel damage model based on the concept of beam deflection energy, ${DE}_{Beam}$ . The revised dowel damage model accounts for critical factors which previously were not directly considered in the faulting model framework, such as dowel stiffness. To account for the effect of corrosion on dowel performance, a novel corrosion model was developed which calculates a reduction in dowel diameter each month based on the exposure conditions and the susceptibility of the dowel material to corrosion. This model was informed by an accelerated corrosion study in which a range of dowel bars that are currently on the market were tested, including EC carbon steel, EC zinc-based galvanized tubular steel, zinc clad tubular steel, FRP, and stainless-steel tubular dowels. Lastly, the concept of equivalent dowel diameter, $d_{eq}$ , was incorporated into the model to enable the direct consideration of alternative dowels that have a stiffness that varies significantly from the industry-standard solid carbon steel dowel. A calibration was conducted using a national database of faulting performance data from in-service pavements. A sensitivity analysis was then conducted to ensure that the calibrated faulting model does not exhibit bias. Faulting was predicted while critical design, environmental, and loading parameters were individually varied to evaluate the effect of each parameter. The results from the sensitivity analysis demonstrate that the revised faulting model is robust.

The model presented in this paper is the first faulting prediction model to directly consider key design parameters which, to date, have been excluded, thus enabling dowels of all designs to be evaluated. First, the revised damage model was designed to directly consider the effect of alternative dowels on loss of dowel performance from vehicle loads. Second, corrosion is included as a mechanism which contributes to the loss of dowel performance. This model is the first which accounts for the corrosion resistance of non-metallic and corrosion-resistant dowels, which have seen increased use in recent years. Pavement designers are now able to consider the long-life performance for a range of dowel bar designs.

Footnotes

Acknowledgements

The authors would like to thank Tom Bryan and David Giehll at Bryan Materials Group, Katey Doman at TyeBar, Karl Zilske at CMC Rebar and Paving Solutions, Brad Zuan at Master Dowel, and Chris Schenk at O-Dowel for supplying materials used during the laboratory studies. The authors would also like to thank Megan Darnell for her assistance in calibrating the faulting model.

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: C. Donnelly, L. Khazanovich, J. Vandenbossche; data collection: C. Donnelly, J. Vandenbossche; analysis and interpretation of results: C. Donnelly, L. Khazanovich, J. Vandenbossche; draft manuscript preparation: C. Donnelly, J. Vandenbossche. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Funding for this project was provided by the Pennsylvania Department of Transportation and the IRISE Consortium.

ORCID iDs

Charles A. Donnelly

Lev Khazanovich

Julie M. Vandenbossche

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