The Impact of Pavement Structural Response on Vehicle Fuel ...

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The Impact of Pavement Structural Response on Vehicle Fuel Consumption

Erdem Coleri1; and John T. Harvey, Affiliate M. ASCE2

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ABSTRACT

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In this study, vehicle energy consumption induced by the viscous behavior of asphalt

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pavement materials was calculated by using 3D viscoelastic finite element (FE) modeling.

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Five pavement structures with conventional, rubber, and polymer-modified asphalt overlay

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mixes with old asphalt, cracked concrete, and cement treated base (CTB) underlying layers

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were modeled to evaluate the impact of structure type on calculated excess fuel consumption

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(EFC). A fully loaded 18 wheel tractor-trailer was simulated. EFC was defined as the fuel

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consumption beyond what occurs for an ideal pavement with no energy consumed due to

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structural response. A total of 234 FE models for a full factorial design were developed to

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simulate the impacts of three speed levels (8, 52, 105 kph), two subgrade stiffnesses (50 and

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200 MPa), and nine temperatures (0oC to 80oC at 10oC intervals) on calculated EFC. Results

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show that the greatest EFC is primarily observed at pavement temperatures higher than 40oC.

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For an average truck highway speed of 97 kph, average pavement temperatures for three

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cities in California (Daggett, Sacramento, and San Francisco) result in excess fuel

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consumptions ranging from 0.1% to 0.35% for the structures analyzed in this study. Although

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this level of EFC appears to be much less than typical roughness related EFC, models for

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EFC due to structural response can aid in decision-making processes, particularly where 1

Assistant Professor, School of Civil and Construction Engineering, Oregon State University, 101 Kearney Hall, Corvallis, OR, USA, 97331, Tel: (541) 737-0944, Email: [email protected]. 2

Professor, University of California Pavement Research Center, Department of Civil and Environmental Engineering, University of California, Davis, One Shields Avenue, Davis, CA, 95616, Tel: (530) 754-6409, [email protected].

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models show it to be greatest. Polymer-modified overlays were observed to have the highest

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EFC when compared with other structures. Having a concrete layer or a CTB layer under the

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asphalt overlay rather than having an aged asphalt layer did not create any significant

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reduction in EFC. Subgrade stiffness was also not observed to be a significant factor

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affecting EFC.

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Key words: excess fuel consumption; viscoelasticity; energy dissipation; pavement; asphalt;

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finite element modeling.

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INTRODUCTION

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Pavements can influence the fuel efficiency and greenhouse gas (GHG) emissions of vehicles

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through three mechanisms, which together can be called the pavement-related rolling

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resistance (Coleri et al. 2015). These three mechanisms are: i) roughness: consumption of

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energy through the working of shock absorbers, drive train components, and deformation of

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tire sidewalls related to pavement roughness; ii) texture: consumption of energy through

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viscoelastic working of the tire rubber in the tire/pavement contact patch as it passes over

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positive macrotexture of the pavement surface; and iii) asymmetrical and viscoelastic

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deformation: Consumption of energy in the pavement itself through asymmetrical (due to

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any dissipation mechanisms within pavement such as damage and dissipation between

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layers) and viscoelastic deformation of pavement materials.

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A number of models have been developed for energy dissipation by the deflection

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mechanism, including models developed by the Massachusetts Institute of Technology

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(Louhghalam et al. 2013; Louhghalam et al. 2014), the University of Lyons National School

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of Public Works of the State (Pouget et al. 2011), the Swedish National Road and Transport

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Research Institute (VTI) (Jonsson and Hultqvist 2009) and Michigan State University. There

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is active research in the development of these models, and several general approaches are

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being used by model developers. The MIT model has been used to characterize the Virginia

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DOT pavement network albeit with very simplified structure, climate and load information

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(Akbarian et al. 2014). Kim et al. (2016) also developed a new method for estimating the

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energy dissipation in the tire and the suspension of vehicles traversing rough non-deformable

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pavements. Shakiba et al. (2016) also developed a mechanics based model for predicting

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structure-induced rolling resistance. The effects of tire contact stresses, viscoelastic

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properties, speed, and temperature were evaluated. None of these models has been

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empirically calibrated yet. Empirical calibration in the field is difficult because most of the

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response occurs at hotter temperatures limiting the time available, and measurements can

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only be done on nearly windless days.

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consistent pavement structures where traffic flow allows for relatively slow constant

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operation are also needed. A model calibration study is currently collecting calibration data

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in California.

Long, straight, flat sections of roadway with

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Models are needed for the use stage of life cycle assessment (LCA) studies for pavement that

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include the effects of pavements on vehicle fuel use (Van Dam et al. 2015). Models for

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calculating the GHG emissions from pavement rehabilitation and maintenance, materials

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production and construction, and the resulting changes in pavement roughness and

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macrotexture, have been developed by the University of California Pavement Research

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Center (UCPRC) and implemented in LCA procedures that are being used to analyze

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Caltrans practices for potential use in network and project-level decision-making (Wang et

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al. 2012; Wang et al. 2014). Models considering roughness and texture developed by Chatti

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and Zaabar (2012) adapted by Wang et al. (2012 and 2014) have also been used by others for

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similar purposes such as Dass and Mukherjee (2011) and Ozer et al. (2017).

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Models for the roughness mechanism (1st mechanism stated above) are well established and

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have been empirically validated and calibrated. Chatti and Zaabar (2012) concluded that a 1

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m/km (63.4 in./mi) decrease in pavement roughness results in a 3% decrease in the fuel

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consumption for passenger cars at highway speeds, which translates into an annual fuel

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savings of $24 billion in the U.S. For heavy trucks, this decrease is about 1% at a normal

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highway speed of 96 km/h and about 2% at low speed at a speed of 56 km/h. This paper

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focuses on the quantification of energy consumption due to viscoelastic deformation of

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pavement materials (3rd mechanism stated above) using finite element (FE) modeling. The

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significance of viscoelastic deformation related fuel consumption when compared to

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roughness related consumption is investigated. The impacts of temperature, vehicle speed,

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pavement structure, and material type on viscoelastic deformation related fuel consumption

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were investigated.

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OBJECTIVES AND SCOPE

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The major goals of this study are as follows:

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

Compare the pavement structural response related EFC for different pavement

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structures with conventional dense graded, rubberized and polymer modified

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overlays.

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

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graded asphalt concrete (DGAC), and cement treated base) on EFC. 

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

Develop a method to simplify the thermal gradient simulation in asphalt pavements to facilitate the use of thermal gradients in network level applications.

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Evaluate the effects of temperature and speed on EFC for different pavement material types.

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Determine the impact of underlying bounded materials (cracked concrete, old dense

Determine the accuracy of calculated total vehicle EFC determined by calculating the EFC from one tire and multiplying it by the number of tires on a vehicle.



Using the climate data for three cities in California, determine the approximate

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contribution of structural response related fuel consumption to total fuel consumption

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of a fully loaded 18 wheel semi-tractor trailer.

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GENERAL PROCEDURE FOR MODEL DEVELOPMENT

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Materials and Testing

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Four asphalt mixes were tested in this study to develop viscoelastic FE models: i) New

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DGAC: a dense graded mixture with PG 64-16 binder with a nominal maximum aggregate

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size (NMAS) of 19mm, 5.2% binder content, 4% air-void content, 15.5% voids in mineral

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aggregate (VMA), and 74.9% voids filled with asphalt (VFA); ii) Rubberized Hot-Mix

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Asphalt (RHMA): a gap-graded rubberized asphalt mix with PG 64-16 binder with an

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NMAS of 12.5mm, 7.5% binder content, 4% air-void content, 18.7% VMA, and 78.8%

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VFA; iii) Polymer-Modified (PM): a dense graded polymer modified mixture with PG 64-

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28 binder with an NMAS of 25mm, 6.0% binder content, 4.3% air-void content, 17.6%

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VMA, and 74.9 VFA; iv) Aged DGAC: a highly field aged dense graded mixture with PG

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64-16 binder with an NMAS of 19mm. After mixing, all mixtures [except the Aged DGAC

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(field mix)] were subjected to short-term oven-aging at 135°C for four hours (AI 2001).

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Dynamic modulus (compressive stiffness) of these four asphalt mixes were determined by

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conducting experiments with two replicates of each mix at four temperatures (4, 21, 38,

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55oC) for a frequency sequence of 25, 10, 5, 1, 0.5, 0.1 Hz. Master curves developed for a

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reference temperature of 21 oC are shown in Figure 1. It can be observed that Aged DGAC

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mix has a significantly higher dynamic modulus than all other mixes. PM mix has the lowest

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dynamic modulus values for all loading frequencies.

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Model Details

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A viscoelastic finite element (FE) model was developed to calculate the dissipated energy

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under different conditions. Energy dissipation due to damping in the subgrade and all other

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layers other than those that are asphalt-bound was not simulated in the model. In the

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developed viscoelastic FE model, only the linear behavior was considered (small strain

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domain). The possible impacts of pavement distresses (fatigue, permanent deformations, and

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cracks) were not taken into account. The material constituting the base is considered isotropic

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linear elastic.

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The temperature dependency of the asphalt mix was defined by using the Williams-Landel-

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Ferry (WLF) equation, given as follows (Ferry 1980):

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log( aT ) 

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where

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 C1 T  Tref 

C 2  T  Tref 

(1)

aT = the time-temperature shift factor, C1 and C2 = regression coefficients,

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Tref = the reference temperature, and

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T = test temperature.

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To optimize the regression coefficients C1 and C2, the shear modulus data were first fitted to

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a sigmoid function, in the form of:

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log G    

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where

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

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

1  exp    log 

(2)

= regression coefficients, and reduced time.

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Shift factors were calculated by fitting the measured modulus to the sigmoidal function (Eqn.

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2). One shift factor was calculated at each test temperature while the shift factor for the

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reference temperature (21oC) is set at zero. A MatlabTM code was developed to optimize the

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regression coefficients and shift factors for all temperatures. Regression coefficients

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C1 and C2 were calculated by simply fitting the WLF equation to the calculated shift factors.

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C1 for New DGAC, PM, and RHMA mixes were calculated to be 36.7, 17.2, and 16.6,

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respectively. C2 for New DGAC, PM, and RHMA mixes were calculated to be 300.8, 149.1,

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and 131.9, respectively.

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The generalized Maxwell-type viscoelastic model (Prony series) was used in this study to

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simulate the time dependency. The model consists of two basic units, a linear elastic spring

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and a linear viscous dash-pot. Various combinations of these spring and dashpot units define

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the type of viscoelastic behavior. The implementation procedure developed by Pouget et al.

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(2011) was used to simulate the effects of truck loads, vehicle speed, and temperature on

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dissipated energy.

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AbaqusTM software was used for model development.

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represented by a 3.5 m long and 2 m wide slab. The finite-element mesh consists of Lagrange

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brick elements with a second-order interpolation function. The mesh was refined under the

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wheel path. International Roughness Index (IRI) and macrotexture are not simulated in the

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model. Therefore, the effects of vehicle suspension dynamics on the wheel load were not

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simulated.

The pavement structure was

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The bottom side of the model is clamped. The symmetry condition in the transversal

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direction imposes a boundary condition on one side. To ensure the continuity of this slab

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with the rest of pavement, only vertical displacement was allowed for other lateral sides

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(Pouget et al. 2011). Perfect bonding was assumed between different pavement layers.

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In order to simulate moving wheel loading in the viscoelastic FE model, the trapezoidal

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impulsive loading method (quasi-static) was used (Yoo et al. 2006). Only one vehicle was

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simulated in this study, a fully loaded (maximum gross vehicle weight in many states), 18

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wheel class 9 truck. The tire is assumed to have a square contact area (175 by 175 mm) and

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the distribution of load on the tire is assumed to be constant. Tire pressure of the truck was

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assumed to be 670 kPa. For a class 9 truck with 18 tires (one single steering axle and two

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dual-tandem axles), the simulated total loaded truck weight adds up to be 37.7 tons.

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The dissipated energy per time w(t) was integrated on a d long slice of the asphalt layer,

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located in the center of the 3.5 m long structure. The dissipated energy for a truck (Wtruck)

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with Z dual wheels, covering a distance of X can be calculated using the following equation

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(Pouget et al. 2011):

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Wtruck 

 wt   dt  xd  Z

(3)

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Where w(t) is calculated using the following equation in which E is the phase angle, 0z is

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the stress curve for the loading time while 0z is the strain for the same loading time for a unit

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volume dV. Unit volume is the volume of each Lagrange brick element in the center of the

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3.5 m long structure with a d long slice (Pouget et al. 2011):

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

 E   0z   0z  dV

w(t)       sin 

(4)

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Sensitivity Analysis

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Sensitivity analyses were conducted to evaluate the effects of several factors on calculated

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deflection basin and excess fuel consumption (EFC). The model developed for the project

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was revised and improved according to the findings of the sensitivity analysis. The factors

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considered for the sensitivity analyses were i) Temperature gradient and ii) Number of tires.

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Temperature Gradient Effect

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In this section, the impact of using an average temperature for the complete asphalt layer

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rather than simulating the temperature gradients is investigated. Using an average

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temperature for the complete asphalt layer creates a significant reduction in model run times.

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Asphalt layer temperature distributions for a summer day were simulated using a random air

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and surface temperature for Sacramento and the software Enhanced Integrated Climatic

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Model (EICM) (Zapata and Houston 2008). The distribution of temperatures along the

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asphalt depth at different times of the day are given in Figure 2. The asphalt layer in the FE

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model was divided into 10 layers (Figure 3a) and the temperatures given in Figure 2 were

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assigned to the layers.

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EFC outputs were determined for all six hours of the day used for the analysis. These results

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were assumed to be the ground truth outputs simulating the effect of temperature gradients on

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EFC. In addition, four finite element models were developed by using only one temperature

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for the complete asphalt layer. Temperatures at the surface (0 mm depth), at 75mm depth

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(one third depth), at 125mm depth, and at 175mm depth were used for the analysis (Figure

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2). Figure 3(b) shows the distribution of EFC at different times of the selected day for five

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different cases with: i) actual temperature gradient simulated (ground truth); ii) surface

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temperatures; iii) temperature at one third depth (75 mm); iv) temperature at 125mm depth;

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and v) temperature at 175mm depth.

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It can be observed from Figure 3(b) that simulations conducted with the temperature at one

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third depth (75mm) provides EFC values that are almost identical to the case with the actual

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temperature gradient. To check the validity of this conclusion for sections with thinner

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asphalt layers, a model with the same material properties and with a thinner (175mm thick)

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asphalt layer was developed. A temperature profile for an air temperature of 26.6oC and a

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surface temperature of 31.8 oC at 10am was developed using the EICM software. The model

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had seven sublayers for the asphalt layer to be able to input the thermal gradient.

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Results showed that the excess fuel consumption for the model with seven sublayers in the

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asphalt layer was almost identical to the section with one asphalt layer using the one-third

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depth temperature (EFC7sublayers=1.44ml/km; EFCone-third

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suggested that there is no need to simulate temperature gradients in the simulations for the

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sections considered in this study. These results suggest that for the calculation of annual fuel

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use (network level application), pavement temperatures at one third depth can be used to

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simulate the effect of temperature gradients throughout the pavement depth. This assumption

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can create a significant reduction in model development and run times. Model runtime is

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longer since additional calculations are required at the boundaries between additional layers.

temp=1.43ml/km).

These results

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The validity of this assumption for predicting vertical strain ( was also investigated.

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Calculated vertical strain for a surface volume element in the middle of the model structure

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for the section with seven sublayers was determined to be almost identical to the section with

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one asphalt layer using the one-third depth temperature (7sublayers=152.8; one-third

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temp=147.4).

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Number of Tires

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The effect of number of tires used for the finite element modeling was investigated. The

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objective was to determine minimum number of tires that will provide total dissipated energy

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that is close to the dissipated energy calculated from a four-tire model. The objective was to

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reduce model runtime by reducing the number of tires. Figure 4 shows the displacement field

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for the finite element models with: i) one tire; ii) two tires; and iii) four tires (one side of

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dual-tandem axle). Figure 5(a) shows the change in calculated dissipated energy with

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temperature for models with one, two, and four tires. The increase in dissipated energy with

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increasing number of tires can be observed. However, when the dissipated energy values in

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Figure 5(a) are divided by the number of tires, all three curves overlap (Figure 5b). This

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result suggests that total vehicle dissipated energy and EFC can be accurately calculated by

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modeling one tire and multiplying the output by the number of tires on the vehicle.

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MODEL DEVELOPMENT

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Several FE models were developed to evaluate the impacts of temperature, vehicle speed,

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subgrade stiffness, mix types, and structural properties on pavement structural response

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related EFC. Figure 6 shows the structures for which models were developed. For structures

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1 through 4, models for a full factorial design were developed to simulate the impacts of

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three speed levels (8, 52, 105 kph), two subgrade stiffnesses (50 and 200 MPa), and nine

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temperatures (0oC to 80oC at 10oC intervals). Structure 5 was used to evaluate the impact of

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having a cement treated base (CTB) layer under the asphalt layer rather than having an old

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DGAC layer. For this reason, in order to reduce the number of model simulations, models for

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structure 5 were only developed for a speed level of 52 kph. Table 1 presents the factorial

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developed for model simulations. In this study, a total of 234 models were developed (Table

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1).

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Structures 1 through 5 were selected to simulate typical structures in California. Structures 1

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through 3 were used to simulate the impact of rubber-modified and polymer-modified asphalt

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mix use on EFC. Structure 4 was used to evaluate the impact of using an asphalt overlay to

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rehabilitate cracked concrete structures in California. Cracked concrete and CTB layers were

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simulated as elastic layers with stiffnesses 25,000 and 4,300 MPa, respectively. Aggregate

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base (AB) and subgrade (SG) layers were also assumed to be elastic layers. All asphalt layers

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were assumed to be linear viscoelastic materials. Boundary conditions and truck loads used

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for modeling were discussed in the “Model details” section.

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RESULTS

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Stress, strain, and phase angle were integrated over time to calculate dissipated energy in the

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pavement (Eqn.3 and Eqn.4). Calculated dissipated energy values were converted to energy

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required to make the vehicle move. Finally, EFC for all temperatures, structures, subgrade

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stiffnesses, and speeds were calculated by dividing the calculated dissipated energy (MJ/km)

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by the calorific value of the fuel (MJ/L) (Eqn. 5). The calorific value of diesel for trucks is

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assumed to be 40 MJ/L (Coleri et al. 2015). Since the engine efficiency of trucks are

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generally around 40 percent, 16MJ/L (40x0.40) is used as the final calorific value of diesel

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for trucks (Chatti and Zaabar 2012; Coleri et al. 2015). By using a 40 L/100km (400 ml/km)

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fuel consumption rate for a 40-ton truck (Sharpe and Muncrief 2015), percent EFC is

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calculated using Eqn. 6.

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excess fuel consumption (

ml ) km

Wtruck  MJ  Fuel calorific    L 

 1000

(5)

excess fuel consumption (ml / km)  100 400 ml / km

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excess fuel consumption (%) 

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Results are shown in Figures 7 through 11 for all structures. In general, much higher EFC can

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be observed at pavement temperatures higher than 40oC. For some cases, EFC starts to

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decrease at very high temperatures (Figure 7 and 10). This reduction is a result of change in

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asphalt behavior from viscoelastic to elastic at very high temperatures (Pouget et al. 2011).

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Although 40oC and higher pavement temperatures are commonly observed on roadways on

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summer days, pavement temperature distributions for different climate regions need to be

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combined with the EFC curves obtained in this study to determine the importance of

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structural response on fuel consumption. The annual pavement temperature distributions at

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one-third depth for Daggett, Sacramento, and San Francisco in California were calculated by

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using the weather station data and the Enhanced Integrated Climate Model (EICM).

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Distributions for a year are shown in Figure 12. These distributions were used to find

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temperature averages for a year and simulations for the entire distributions were not

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conducted. The average one-third depth pavement temperatures for Daggett, Sacramento, and

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San Francisco are 26.4oC, 24.5oC, and 20.3oC, respectively. For an average truck highway

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speed of 97 kph in California, these average pavement temperatures result in average excess

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fuel consumptions ranging from 0.1% to 0.35% across all 5 structures and three locations.

(6)

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Although the level of EFC found in this study is smaller than typical calculations of

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roughness related EFC, which is most likely approximately independent of EFC from

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structural response, it can be considered in the decision-making process, and will have

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greater significance where there are heavy vehicles traveling at slow speeds in hotter climates

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(Harvey et al. 2015).

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Simulations using this model and models from the Massachusetts Institute of Technology

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(Louhghalam et al. 2013) and Michigan State University have been used to estimate annual

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EFC due to structural response as is described in Harvey et al. (2015). These simulations

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included the joint distributions across representative days in each month of hourly annual

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pavement temperatures, actual typical hourly urban and rural speed distributions for different

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types of vehicles, and hourly distributions of car and truck wheel loads based on weigh-in-

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motion distributions.

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Table 3 also presents the EFC for different speeds and structure types for the average one-

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third depth pavement temperatures for Daggett, Sacramento, and San Francisco. It can be

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observed that the section with PM mix has the largest EFC while the section with RHMA

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mix has the second largest values. Structure 2 with the polymer-modified overlay has the

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highest EFC when compared with other structures (Figure 8-Table 3). This is a result of the

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low stiffness of the polymer-modified mix (Figure 1). Calculated EFC for Structure 1 (New

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DGAC on old DGAC) and Structure 3 (RHMA) were observed to be close (Figures 7 and 9 –

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Table 3). Although the differences in EFC between Structure 1 and Structures 4 (New DGAC

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on cracked concrete) (Figure 10) and 5 (New DGAC on CTB) (Figure 11) were not

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significant, EFC for Structure 1 was observed to be higher than the EFC for Structures 4 and

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5. This result suggests that having a concrete layer or a CTB layer under the asphalt overlay

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rather than having an aged asphalt layer does not create any significant reduction in EFC, and

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that most of the energy dissipation is near the surface in the asphalt layer.

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The analysis of variance (ANOVA) approach was used to quantify the impact of pavement

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temperature, speed, structure type, and subgrade stiffness on calculated EFC. The results of

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the ANOVA are given in Table 2. Independent variables with p-values larger than 0.05 can

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be regarded as insignificant variables. It can be observed that subgrade stiffness does not

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have any significant effect on EFC with a p-value of 0.82 (significantly larger than 0.05). On

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the other hand, temperature, speed, and structure type appeared to be important factors

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affecting EFC. F values given in Table 2 suggested that temperature is the major factor

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controlling EFC. While speed is also a significant parameter, its effect on EFC is

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significantly lower than the influence of temperature.

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SUMMARY OF FINDINGS AND CONCLUSIONS

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In this study, vehicle energy consumption induced by the viscous behavior of asphalt

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pavement materials was calculated by using 3D viscoelastic FE modeling. Five pavement

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structures with conventional, rubber, and polymer-modified asphalt overlay mixes with

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underlying old asphalt, cracked concrete, and CTB layers were modeled to evaluate the

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impact of structure type on calculated excess fuel consumption (EFC). A total of 234 FE

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models for a full factorial design were developed to simulate the impacts of three speed

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levels (8, 52, 105 kph), two subgrade stiffnesses (50 and 200 MPa), and nine temperatures

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(0oC to 80oC at 10oC intervals) on calculated EFC.

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Results of this study can be summarized as follows: 

For the structures analyzed in this study, there is no need to simulate temperature

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gradients in the simulations. For the calculation of average annual EFC (network

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level application), pavement temperatures at one third depth can be used to simulate

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the effect of temperature gradients throughout the pavement depth. This assumption

397

can create a significant reduction in model run times.

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

Total vehicle dissipated energy and EFC can be accurately calculated by modeling

399 400

one tire and multiplying the output by the number of tires on the vehicle. 

The greatest EFC can be observed at pavement temperatures higher than 40oC. For

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the fully loaded truck simulated in this study and an average truck highway speed of

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97 kph, average pavement temperatures for three cities in California (Daggett,

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Sacramento, and San Francisco) result in EFCs ranging from 0.1% to 0.35% for the

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structures analyzed in this study. Although this level of EFC appears to be much less

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than the roughness related EFC (1-3%) (Chatti and Zaabar 2012), which is most

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likely approximately independent of EFC from structural response, EFC from

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structural response can be considered in the decision-making process, and will have

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greater significance where there are heavy vehicles traveling at slow speeds in hotter

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climates (Harvey et al. 2015).

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

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Polymer-modified overlays showed the highest EFC when compared with other structures.



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Having a concrete layer or a CTB layer under the asphalt overlay rather than having an aged asphalt layer did not create any significant reduction in EFC.

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

Subgrade stiffness was not observed to be a significant factor affecting EFC.

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

Temperature, speed, and structure type were determined to be important factors

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affecting EFC. Temperature was observed to be the major factor controlling EFC.

417

While speed is also a significant parameter, its effect on EFC is significantly lower

418

than the influence of temperature.

419 420

In this study, average annual temperatures for three different cities in California were used to

421

provide a first estimate of the average percentage contribution of pavement structural

422

response on EFC. These results have been used with hourly temperature and traffic data to

423

calculate the percentage contributions for different cities. The impact of subgrade damping

424

and layer densities on EFC should also be investigated by using a dynamic model. The

425

impact of subgrade thickness and bedrock location should also be evaluated. The interaction

426

of roughness-induced dynamic loading should be considered.

427 428

The EFCs predicted in this study do not provide an absolute value associated with a

429

particular pavement, and these results are as-yet uncalibrated with field data. However,

430

results will provide important information about the impacts of speed, temperature, material

431

type, and structure configuration on pavement structural response related EFCs. This study

432

also points out the level of significance of pavement structural response on vehicle fuel

433

economy. Models should be calibrated by using field measurements.

434 435

ACKNOWLEDGMENTS

436

This paper describes research activities that were requested and sponsored by the California

437

Department of Transportation (Caltrans), Division of Research and Innovation. Caltrans

438

sponsorship is gratefully acknowledged. The contents of this paper reflect the views of the

439

authors and do not reflect the official views or policies of the State of California or the

440

Federal Highway Administration. The advice regarding model development elements of Dr.

441

Shmuel Weissman of Symplectic Engineering Corporation is appreciated.

442 443 444 445 446 447

448 449 450

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451

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529

LIST OF TABLES Table 1 Factorial Design for FE Models Table 2 ANOVA Results Identifying the Effects of Speed, Temperature, and Subgrade Stiffness on Excess Fuel Consumption Table 3 Excess Fuel Consumptions for Average Temperatures and Different Speeds (for 200MPa subgrade stiffness)

Table 1 Factorial Design for FE Models Structures

Temp. (oC)

Speed (kph)

STR#1 STR#2 STR#3 STR#4 STR#5

0, 10, 20,…,80 0, 10, 20,…,80 0, 10, 20,…,80 0, 10, 20,…,80 0, 10, 20,…,80

8, 52, 105 8, 52, 105 8, 52, 105 8, 52, 105 52

EAB (MPa) 250 250 250 250 250

ESG (MPa) 50, 200 50, 200 50, 200 50, 200 50, 200

Number of models 54 54 54 54 18

NOTE: Temp. = Temperature; EAB = Aggregate base stiffness; ESG = Subgrade stiffness.

Table 2 ANOVA Results Identifying the Effects of Speed, Temperature, and Subgrade Stiffness on Excess Fuel Consumption Variable Temp. Speed Str Esg Temp:Speed Temp:Str Temp:Esg Speed:Str Speed:Esg Str:Esg

Df 1 1 4 1 1 4 1 3 1 4

SS 1616.6 112.7 147.3 0.29 119.9 162.8 0.02 64.6 0.00 0.09

F value 303.9 21.2 6.9 0.05 22.5 7.7 0.00 4.04 0.00 0.00

p-value 0.00000 0.00000 0.00003 0.81558 0.00000 0.00000 0.94824 0.00795 0.99840 0.99996

NOTE: Temp. = Temperature; Str = Structure; Esg = Subgrade stiffness; Df = degrees of freedom; SS = sum of squares.

Table 3 Excess Fuel Consumptions for Average Temperatures and Different Speeds (for 200MPa subgrade stiffness) City Daggett Sacramento San Francisco Daggett Sacramento San Francisco Daggett Sacramento San Francisco

Average Temp.(oC) 26.4 24.5 20.3 26.4 24.5 20.3 26.4 24.5 20.3

Speed (kph) 8 8 8 52 52 52 105 105 105

EFC STR1(%) 0.38 0.33 0.23 0.21 0.19 0.13 0.17 0.14 0.09

EFC STR2(%) 0.94 0.80 0.50 0.44 0.39 0.26 0.35 0.30 0.18

EFC STR3(%) 0.56 0.48 0.30 0.29 0.26 0.20 0.23 0.20 0.15

NOTE: Temp. = Temperature; Str = Structure; EFC=Excess fuel consumption.

EFC STR4(%) 0.19 0.16 0.09 0.09 0.07 0.05 0.07 0.06 0.03

EFC STR5(%) 0.13 0.12 0.08 -

LIST OF FIGURES Figure 1 Dynamic modulus master curves for all asphalt mixes. Figure 2 Asphalt layer temperature distributions for a summer day in Sacramento, California. Figure 3 Simulation of temperature gradient in the asphalt layer (a) Asphalt layer divided into 10 segments to simulate the effect of temperature gradient (b) Calculated excess fuel consumption for the case with temperature gradients and temperatures at different depths. Figure 4 Displacement field for the finite element models with: a) one tire b) two tires; c) four tires (one side of dual-tandem axle). Figure 5 Change in calculated dissipated energy with temperature for models with one, two, and four tires (a) total dissipated energy (b) total dissipated energy normalized by the number of tires. Figure 6 Cross sections of structures used for FE modeling. Figure 7 The impact of speed, temperature, and subgrade stiffness on fuel consumption excess - Structure 1: New DGAC on old DGAC. Figure 8 The impact of speed, temperature, and subgrade stiffness on fuel consumption excess - Structure 2: PM on old DGAC. Figure 9 The impact of speed, temperature, and subgrade stiffness on fuel consumption excess - Structure 3: RHMA on old DGAC. Figure 10 The impact of speed, temperature, and subgrade stiffness on fuel consumption excess - Structure 4: New DGAC on cracked concrete. Figure 11 The impact of temperature and subgrade stiffness on fuel consumption excess Structure 5: New DGAC on CTB. Figure 12 Cumulative distributions of pavement temperatures at one-third depth for Daggett, Sacramento, and San Francisco in California.

Temperature (C) 20

25

30

35

40

45

50

0 mm

0 50

Depth (mm)

75 mm 100

125 mm 150 0:00

200 250 300

4:00 8:00 12:00 16:00 20:00

175 mm

Excess fuel consumption (ml/km)

5 4.5 4 3.5 3 2.5 2 With gradient 0 mm 75mm

1.5 1

125mm 175mm

0.5 0 0.00

4.00

8.00

12.00

16.00

Time of day

20.00

24.00

3.0 One tire two tires

2.5

four tires

Energy (mJ)

Car

2.0 1.5 1.0 0.5 0.0 0

20

40

60

80

100

Temperature (C)

Energy/Number of Tires (mJ)

0.8 One tire two tires

0.7

four tires

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

10

20

30

40

50

Temperature (C)

60

70

80

90

100 mm

New DGAC

100 mm

PM

150 mm

Old DGAC

150 mm

Old DGAC

200 mm

EAB = 250 MPa

AB

ESG = 50 and 200 MPa

SG

200 mm

EAB = 250 MPa

AB


SG

100 mm

RHMA

100 mm

150 mm

Old DGAC

200 mm

EPCC = 25,000 MPa

200 mm

EAB = 250 MPa

AB


SG

200 mm

EAB = 250 MPa

AB


SG

100 mm

New DGAC

150 mm

ECTB = 4,300 MPa

200 mm

EAB = 250 MPa

AB


SG

CTB

New DGAC Cracked PCC

Fuel consumption excess (%)

14

Speed=8kph & Esg=50MPa

12

Speed=8kph & Esg=200MPa Speed=52kph & Esg=50MPa

10


8


6 4 2 0 0

20

40 60 Temperature (C)

80

100

14 Fuel consumption excess (%)


28.3% at 80oC


12


10


8


6 4 2 0 0

20


80

100

14 Fuel consumption excess (%)


12


10


8


6 4 2 0 0

20


80

100


14


12


10


8


6 4 2 0 0

20


80

100


14 Speed=52kph & Esg=50MPa

12 Speed=52kph & Esg=200MPa

10 8 6 4 2 0 0

20


80

100

1.0 Daggett

Cumulative distribution

0.9

Sacramento

0.8

San Francisco

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

-10

0

10

20

30

40

50

Pavement temperatures at one third depth (C)

60

70