Pavement Infrastructures Footprint: The Impact of Pavement Properties on Vehicle Fuel Consumption. A. Louhghalam & M. Akbarian & F.-J. Ulm Massachusetts Institute of Technology Cambridge, Massachusetts, United States ABSTRACT: A novel mechanistic model based on an infinite beam on elastic foundation is developed to quantify the impact of pavement structural and material properties on pavement deflection and consequently on vehicle fuel consumption. The model can also account for the effect of temperature and vehicle speed on fuel consumption. A simplified expression for evaluating the energy dissipation for practical purposes is proposed and used to investigate the impact of various pavement design systems on fuel consumption. GPS (General Pave- ment Studies) sections from the FHWA’s Long Term Pavement Performance program (FHWA 2011) are used for this study. These sections consist of asphalt concrete (AC), portland cement concrete (PCC) and composite pavements. The model quantifies the impact of temperature and vehicle speed on the fuel consumption and confirms that those impacts are negligible for PCC and significant for AC pavements due to their viscoelasticity. 1 INTRODUCTION on pavement type, but they fail to establish a link be- tween structural and material properties of the pave- Road transportation accounts for 27% of all green- ment and vehicle fuel consumption due to pavement house gas (GHG) emissions in the United States (EPA deflection and there is high uncertainty and variabil- 2012). Hence there is growing interest in development ity within the suggested values. Another restriction of of rigorous mechanistic models for assessing pave- the empirical approach is the measurement precision ment sustainability performance in order to reduce required for determining the relatively small change carbon footprint of the roadway network. One way to in fuel consumption. While the cumulative fuel con- achieve this, is to use Pavement-Vehicle Interaction sumption difference between pavement types can be (PVI) to determine the major contributors to rolling large when measured over the pavement’s service life, resistance and quantify their impact on the environ- the impact for a single vehicle is quite small. Mea- mental footprint of the transportation system. Pave- surements at this scale, thus will be highly influenced ment texture, roughness and deflection are the rele- by external factors affecting both the vehicle and the vant factors contributing to the rolling resistance. The pavement properties and small changes in testing con- dissipated energy and thus fuel consumption due to ditions can affect fuel consumption on the same order the deflection-induced pavement-vehicle interaction as any pavement-type effects. In addition to the above (PVI) depends on the pavement material and struc- reasons the empirical values are not useful for the life tural properties whereas roughness-induced PVI de- cycle assessment of the pavements where a quantita- pends primarily on vehicle characteristics (Zaabar & tive model is necessary to relate the pavement condi- Chatti 2010). Hence the excess fuel consumption due tion to the carbon footprint of the pavement system. to pavement deflection, which is related to pavement In this paper we propose a mechanistic model for properties, is studied herein. deflection-induced PVI that quantifies the impact of Various empirical investigations have examined the pavement material and structure on vehicle fuel con- dependence of pavement type on deflection-induced sumption. In addition, the model also accounts for PVI (Zaniewski et al. (1982) De Graff (1999), Tay- the effect of temperature and vehicle speed on fuel lor et al. (2000), Taylor (2002), Taylor and Pat- consumption by considering pavement viscoelastic- ten (2006), Ardekani and Sumitsawan (2010) and ity. Although the impact of temperature and vehi- VEROAD (2002)). The results of these empirical cle speed is small for PCC pavements, to develop a studies, summarized in Figure 1, suggest the depen- method that can be used for comparative studies in the dence of deflection-induced vehicle fuel consumption roadway network, the model must account for these effects to represent other types of pavements (e.g, vis- dynamics (see for example Coussy 1995 and Ulm & coelastic AC pavements). Coussy 2002 ): The outline of the paper is as follows: the under- dΨ lying theory of the mechanistic model is described = δW 0 (1) in Section 2. In Section 3, the mechanistic model D − dt ≥ is used to evaluate the fuel consumption throughout with: the United States roadway network and effect of var- Z du ious pavement design systems from the Long Term δW = T dS (2) S dt Pavement Performance program’s General Pavement · Studies (GPS) sections (FHWA (2011)) is studied. the external power supplied to the system, Ψ the The designs include two types of asphalt concrete (Helmholtz) free energy and u = wez the beam de- (AC) pavements; two types of composite pavements; flection. The total (Lagrangian) derivative− d=dt in the and three types of Portland cement concrete (PCC) above for any function f of time and space subjected pavement designs. Finally, Section 4 summarizes the to velocity field V reads as: findings of this study. df @f = + V f (3) dt @t · r 2 THEORETICAL ANALYSIS with representing the gradient vector. In the above movingr coordinate system and under steady-state Consider a pavement structure subjected to a load condition (where @f=@t = 0) one can show that the which moves with the constant speed c. To maintain change in free energy is zero (Louhghalam et al. this speed, the energy dissipated due to the viscoelas- 2013a) and the dissipation rate for an infinite beam ticity of the beam is compensated by the extra power on elastic foundation can be obtained as: provided by the vehicle, leading to excess fuel con- Z @w sumption. = δW = c p dS 0 (4) D − S @X ≥ If the traction on the beam is approximately sub- 2.1 Dissipated energy stituted by the resultant concentrated load P = R pdS the dissipation rate can be simplified as = One way to calculate the dissipated energy, i.e. the S cbP dw=dX with b the width of the beam. ForD the amount of energy which is not recoverable and is lost elastic− case where there is no dissipation, the slope in heat form, is through calculation of viscoelastic is zero at pavement-tire contact point, confirming that stresses and strains in the viscoelastic layer, in a fixed the maximum displacement occurs exactly below the coordinate system x, as the load (tire) passes the pave- tire. Furthermore the non-negativity of the dissipation ment, using computational methods such as finite el- rate requires that dw=dX 0 which indicates that the ement analysis (Pouget et al. (2011)), and integration tire is on an upward slope≤ as shown in Figure 2 (b) over the entire pavement block. To minimize the ef- (Flugge¨ 1967). fect of boundary conditions the pavement block must The above analysis indicates that for evaluating the be sufficiently large. In another approach used herein, dissipated energy one only needs to find the displace- the displacement field is calculated in a coordinate ment profile at the tire-pavement contact surface in system X which moves with the tire at a constant the moving coordinate system. speed c, i.e. X = x ct where t is the time variable. In presence of damping,− due to the viscoelasticity of the material, the deflection profile becomes asymmetrical 2.2 Viscoelastic beam on elastic foundation and the maximum deflection moves behind the load. Let h be the thickness of the infinite viscoelastic beam Therefore the wheel is always on an uphill slope, re- and k be the Winkler modulus of the elastic founda- sulting in excess rolling resistance (Flugge¨ 1967). Us- tion. The viscoelasticity of the beam is modeled us- ing the second law of thermodynamics, in (Louhgha- ing the Maxwell model with stiffness E and viscosity lam et al. 2013a) the authors proved theoretically that η (see the inset of Figure 2(a)) for which the consti- the two approaches described above are strictly equiv- tutive equation is σ + τσ_ = τE_, where τ = ηE is alent and the only difference between the two is the the relaxation time of the viscoelastic material that reference frame. The first approach uses a fixed co- varies with temperature, leading to temperature de- ordinate system attached to the pavement while the pendent mechanical properties for viscoelastic mate- latter considers a moving reference frame attached to rial. The time-temperature superposition principle is the tire-pavement contact surface. used to establish this temperature dependance and to Let the pavement structure be an infinite viscoelas- find the relaxation time of the material at any given tic beam on an elastic foundation subjected to a dis- temperature T from the relaxation time measured at a tributed load T = pez moving at a constant speed reference temperature T : c in x-direction (see− Figure 2). The dissipation rate ref can be evaluated from the second law of thermo- τ(T ) = aT τ(Tref ) (5) D × 5 4 3 2 1 0 Excess fuel consumption (Ltr/100Km) -1 (90) (100) (60) (80) (100) (60) (100) (60) (60) (100) (60) Speed (Km/h) NPC 1999 NRC I De Graaff De Graaff 1982 (cars) 2010 (cars) 2010 (cars) Taylor et. al Taylor 2006 (cars) 1982 (trucks) 2000 (truck) 2006 (truck) 2010 (truck) 2000 (truck) 2002 (truck) Zaniewski et. al Zaniewski et. al 2006 (full truck) Taylor and Patten Taylor and Patten Taylor and Patten Taylor Taylor and Patten Taylor Zaabar and Chatti Zaabar and Chatti Taylor 2002 (truck) Taylor Taylor 2002