Design of bituminous pavements – a performance-related approach

Abstract

Pavement design in Austria is currently based on a catalogue of standard constructions distinguishing seven load classes and eight pavement types, which can be chosen depending on the traffic-related parameters AADT${}_i$ (annual average of the daily traffic for each vehicle type i) or AADTT (annual average of the overall daily truck traffic). This approach does not allow one to take performance-related material characteristics or detailed traffic load information into account. To resolve these limitations, a mechanistic approach for the design of bituminous pavements in Austria was developed. Thereby, design levels for the important parameters traffic load as well as hot mix asphalt stiffness and fatigue behaviour are introduced accounting for the level of detail of these variables. This approach ensures that necessary design reserves decrease with increasing experimental effort related to the parameter identification. Hence, this method provides modern, performance-based and economic pavement design.

Keywords:

• mechanistic pavement design
• hot mix asphalt
• performance-based characteristics

1. Introduction

The objective of pavement design is to develop pavement constructions in a way that stresses and strains within the constructions due to traffic and climatic conditions do not exceed certain limits, or – in other words – to design pavements, which are able to resist appearing loads during the intended life time. As failure due to fatigue is regarded as relevant for the determination of the thickness of the bituminous layers, several criteria exist to predict the technical life time on the basis of empirical observations of the fatigue behaviour in the laboratory or in full-scale tests. All these criteria have in common that relevant stresses or strains within the construction are considered, which appear, in general, either as tensile load at the bottom of the bituminous base course or as compressive load at the top of the subgrade. For bituminous layers, for example, single cracks emerging at the bottom of the base course and developing to the surface are regarded as relevant for the structural fatigue of the pavement. At the surface, these single cracks lead to so-called alligator cracking and, hence, decreasing bearing capacity of the pavement construction.

The Austrian pavement design catalogue, RVS 03.08.63 (FSV, 2016), is based on a mechanistic approach (see Figure 1). Generally, valid physical and mechanical principles describe the reaction of the pavement construction on external loads (e.g. traffic, climatic conditions) on the basis of semi-analytical models (Litzka, Molzer, & Blab, 1996; Molzer, Fußeis, Litzka, & Steierwald, 1995; Wistuba, 2003). The respective design process is illustrated in Figure 1.

Figure 1. Mechanistic approach of the Austrian design process for bituminous pavements (Litzka, Molzer, & Blab, 1996).

The quality and reliability of the result of the design process strongly depends on the accuracy of the determination of the input parameters and the quality of their consideration within the design method. In general, they can be distinguished into the following four categories:

• traffic loads,

• subgrade behaviour,

• climatic conditions, and

• material behaviour.

The traffic loads are based on detailed axle load and vehicle type distributions obtained in Austria between 1988 and 1990 (Molzer et al., 1995). Thereby, load equivalence factors for five vehicle types (truck with trailer, truck without trailer, bus, city bus, and articulated city bus) and two heavy vehicle collectives (characteristic for highways or other roads) are derived, which link the damage induced by one passage of the respective vehicle type or group with the damage induced by a standard axle with a load of 100 kN (equivalent standard axle load ESAL). Hence, only this standard axle has to be considered to determine the number of load cycles the pavement is able to resist considering parameters from traffic counting like AADT${}_i$ (annual average of the daily traffic for each vehicle type i) or AADTT (annual average of the overall daily heavy traffic).

The subgrade bearing capacity is strongly influenced by local climatic and hydrological conditions. Hence, four periods during one year with varying subgrade modulus representative for bearing capacities of soils in Austria are considered. While a peak in bearing capacity is reached in winter, when the soil is frozen, the subgrade modulus decreases during the spring-thaw period. Due to the climatic conditions in Austria, variations in temperature within the bituminous pavement layers occur leading to varying stiffness of hot mix asphalt (HMA). Hence, 12 representative temperature periods during one year – corresponding to the four subgrade bearing capacity periods – are introduced (Mais, 2003; Milkovics, 1984) providing nearly homogeneous climatic conditions during each period.

Besides the volumetric composition of HMA (type of aggregate, gradation, binder content, etc.), the viscoelastic properties of bitumen lead to temperature- and frequency-dependent stiffness behaviour. An effective dynamic modulus $S_{\mathrm{mix}}$ is defined by an elastic model asphalt layer exhibiting the same strain characteristics resulting from a specified stress state as a viscoelastic material enabling one to apply linear elastic multi-layer theory for the determination of resulting stresses and strains. The temperature dependency of this equivalent elastic stiffness of the model asphalt $S_{\mathrm{mix}}$ can be described, according to Shell (1978), as follows: (1) $S_{\mathrm{mix}}\left(T\right)=-2.079\times {10}^4\cdot T^4-2.065\times {10}^{-3}\cdot T^3+5.271\times {10}^2\cdot T^2-4.193\times {10}^2\cdot T+9218,$(1) with $S_{\mathrm{mix}}$ in MPa and the temperature T in ${}^{\circ }$C.

With these input parameters at hand, the resulting stresses and strains can be determined using linear elastic multi-layer analysis according to Burmister (1943). As stiffness and strength of HMA decrease with repeatedly occurring dynamic traffic loads, damages within the pavement accumulate until the first cracks appear at the bottom of the bituminous layer. This phenomenon is known as fatigue (Zhiming, Little, & Lytton., 2002; Bonnaure, Gravois, & Udron, 1980; Shell, 1978; Tayebali, Deacon, Coplantz, Harvey, & Monismith, 1994). Models can be used to relate the allowable number of loadings $N_{\mathrm{all}}$ the construction is able to resist to the stress due to traffic (Litzka et al., 1996): (2) $N_{\mathrm{all}}=k_1\left(T\right)\cdot {\left(\frac{S_{\mathrm{mix}}}{{\sigma }_e}\right)}^{k_2\left(T\right)}.$(2) Thereby, an equivalent one-dimensional stress state ${\sigma }_e$ is considered (Leon, 1934; Lorenzl, 1996), which is correlated to the three-dimensional stress state resulting from linear multi-layer analysis. The fatigue parameters $k_1$ and $k_2$ are defined in Litzka et al. (1996).

With the help of Equation (2(2) $N_{\mathrm{all}}=k_1\left(T\right)\cdot {\left(\frac{S_{\mathrm{mix}}}{{\sigma }_e}\right)}^{k_2\left(T\right)}.$(2) ), partial damages for the 12 temperature periods are determined, which can be weighed and accumulated according to the superposition principal (Miner's law) to estimate the technical life time. Applying this design approach, standard pavement constructions were derived and given in a catalogue in RVS 03.08.63 (FSV, 2016). Considering only traffic-related parameters such as AADT${}_i$ or AADTT, a standard construction can be chosen for seven load classes from eight pavement types accordingly.

2. New mechanistic pavement design

To meet the demand for a design method able to take into account the characteristics of modern HMA types, which are optimised in terms of performance-related material properties, a new mechanistic design method for bituminous pavements in Austria is introduced (Blab, Eberhardsteiner, Haselbauer, Marchart, & Hessmann, 2014).

Within this design process (according to the serviceability limit state), the number of load cycles the pavement is able to resist, $N_{\mathrm{res}}$ (resistance), is related to the expected number of passages during the design life, $N_{\mathrm{imp}}$ (impact), by (3) $\frac{N_{\mathrm{imp}}}{N_{\mathrm{res}}}\le 1.$(3) $N_{\mathrm{res}}$ is determined on the basis of general physical and mechanical principles, which describe the response of the pavement construction to load due to traffic and climatic conditions. Thereby, design levels for the input parameters (traffic load, mechanical HMA stiffness and fatigue behaviour) depending on the availability of traffic data or experimental results are introduced allowing for a more economic design as necessary design reserves may be reduced with increasing accuracy of the determination of the input parameters.

2.1. Determination of relevant traffic loads

Information about the volume and composition of heavy traffic is essential for reliable pavement design. Thus, four important parameters have to be distinguished:

• traffic volume of heavy goods vehicles (HGV),

• probability of the appearance of HGV types,

• distribution of HGV gross vehicle weights, and

• distribution of HGV axle loads.

In Austria, detailed information about the volume of heavy traffic on freeways is available from records gained in the course of automatic road toll stations. Other roads are monitored by frequently conducted traffic counting. While these data are obtained regularly, distributions of vehicle types, gross weights and axle loads are determined only sporadically and point-wise by analysing the results of weight-in-motion measurements, for example. Hence, three traffic design levels according to Figure 2 can be distinguished.

Figure 2. Traffic design levels for consideration of traffic load (Blab et al., 2014).

Traffic design level 1 implies that only HGV traffic volume data from road toll stations are available. Hence, characteristic distributions of vehicle types (see Blab et al., 2014), gross weight $G_j$ of vehicle type j (see, for example, Figure 3(a)) and axle loads $A{L}_{ij}$ of axle i of vehicle j (see, for example, Figure 3(b)), which are representative for the heavy traffic in Austria, are applied to estimate the traffic load to be considered in the design process with (4) $p_{G_j}=g_1\cdot N({\mu }_1,{\sigma }_1)+g_2\cdot N({\mu }_2,{\sigma }_2)$(4) and (5) $A{L}_{ij}={\beta }_i+{\alpha }_i\cdot G_j.$(5) Thereby, μ and σ represent mean value and standard deviation of a standard normal distribution N and $g_1$ and $g_2$ are weighing factors. These parameters, as well as ${\beta }_i$ and ${\alpha }_i$, have been derived from bridge weight-in-motion measurements as described in Blab et al. (2014).

Figure 3. Representative distributions of gross weight $G_j$ (a) and axle loads $A{l}_{ij}$ exemplarily shown for two-axle truck (b).

Besides information about the traffic volume, the actual distribution of HGV types within the considered road section is accessible from detailed traffic counting at traffic design level 2. Consequently, only characteristic distributions of gross weights and axle loads (according to Equations (4(4) $p_{G_j}=g_1\cdot N({\mu }_1,{\sigma }_1)+g_2\cdot N({\mu }_2,{\sigma }_2)$(4) ) and (5(5) $A{L}_{ij}={\beta }_i+{\alpha }_i\cdot G_j.$(5) )) have to be used.

As actual data of traffic volume, vehicle gross weight and axle load distributions from weight-in-motion measurements are available at traffic design level 3, traffic loads can be taken into account as realistic as possible and, therefore, design reserves can be reduced to a minimum, since no characteristic distributions have to be applied.

2.2. Consideration of HMA stiffness behaviour

Due to the fact that the stiffness behaviour of the pavement layers plays a crucial role when it comes to determine resulting stresses and strains in the pavement construction, the applied assumptions to determine HMA stiffness $S_{\mathrm{mix}}$ strongly influences the design result (Yoder & Witczak, 1975). So, HMA material design levels are introduced to be able to consider the stiffness behaviour of the bituminous mixture actually used. According to Figure 4, four levels can be distinguished, where the level of detail increases with increasing experimental effort.

Figure 4. Stiffness design level for consideration of HMA stiffness behaviour.

At stiffness design level 1, only the volumetric composition of the mixture (air void and binder content as well as density of binder and mixture) is available. In that case, a Hirsch-type material model (Christensen, Pellinen, & Bonaquist, 2003; Garcia & Thompson, 2007; Dongre, Myers, D'Angelo, Paugh, & Gudimettla, 2005) estimating the elastic modulus of HMA, $S_{\mathrm{mix}}$ (in MPa) by taking the voids in the mineral aggregate (VMA, in vol.%), and the voids filled with binder (VFB, in vol.%), as well as the binder stiffness $|G_{\mathrm{bit}}^{\ast }|\left(T\right)$ (in MPa) into account, of the form (6) $\begin{array}{rl}{S}_{\mathrm{mix}}\left(T\right)& =\frac{P_c}{145.04}\left[a\left(1-\frac{\mathrm{VMA}}{100}\right)+145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)\frac{\mathrm{VFB}\cdot \mathrm{VMA}}{10,000}\right]\\ & +\frac{(1-P_c)}{145.04}{\left[\frac{1-\frac{\mathrm{VMA}}{100}}{a}+\frac{\mathrm{VMA}}{\mathrm{VMA}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}\right]}^{-1}\end{array}$(6) with (7) $P_c=\frac{{\left(b+{\displaystyle \frac{\mathrm{VFB}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}{\mathrm{VMA}}}\right)}^c}{d+{\left({\displaystyle \frac{\mathrm{VFB}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}{\mathrm{VMA}}}\right)}^c},$(7) is derived, where a, b, c and d are model parameters depending on the type of bitumen and the assumed failure probability (as exemplarily shown for paving-grade bitumen in Table 1). The bitumen stiffness $|G_{\mathrm{bit}}^{\ast }|\left(T\right)$ is approximated by the characteristic temperature- and frequency-dependent mechanical behaviour of a model bitumen, which was derived from a huge experimental dataset (333 experimental results from unmodified bitumen and 1239 results from polymer-modified binders) obtained from dynamic shear rheometer (DSR) tests conducted in various laboratories in Austria and Germany. Based on the DSR data for a representative paving-grade bitumen (pen 50/70) and a polymer-modified bitumen (PmB 45/80-65), statistically verified correlations between temperature and complex stiffness modulus $|G_{\mathrm{bit}}^{\ast }|$ were derived distinguishing for the relevant frequencies of 8 Hz (see Figure 5). As only the volumetric composition of the HMA mixture actually used is considered, significant design reserves have to be ensured. Therefore, several levels of failure probability are introduced.

Table 1. Parameters a, b, c and d exemplarily shown for paving-grade bitumen.

Assumed failure probability (%)	a	b	c	d
68	5,894,168	162.84	0.85	21,625.89
85	5,041,315	310.19	0.92	41,376.03
90	4,025,792	747.43	1.07	151,858.30
95	3,918,366	687.25	1.05	135,252.80

Figure 5. Statistically verified correlations between temperature and complex stiffness modulus $|G_{\mathrm{bit}}^{\ast }|$ for paving-grade bitumens (solid line) and polymer-modified bitumens (dotted line).

If the stiffness behaviour of the actually used bitumen is available from DSR tests according to EN 14770 (CEN, 2012c), stiffness design level 2 can be applied. An experimental program respecting three test temperatures and seven test frequencies is required ensuring the ability to reliably characterise the mechanical behaviour of the binder within one working day (Blab et al., 2014). Thereby, the time–temperature-superposition principle for thermo-rheologically simple materials like bitumen is applied to derive a so-called master curve (Steinmann & Friedrich, 2005; Hofko, 2011). With the bitumen stiffness $|G_{\mathrm{bit}}^{\ast }|\left(T\right)$ and the volumetric composition at hand, the Hirsch-type model in Equations (6(6) $\begin{array}{rl}{S}_{\mathrm{mix}}\left(T\right)& =\frac{P_c}{145.04}\left[a\left(1-\frac{\mathrm{VMA}}{100}\right)+145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)\frac{\mathrm{VFB}\cdot \mathrm{VMA}}{10,000}\right]\\ & +\frac{(1-P_c)}{145.04}{\left[\frac{1-\frac{\mathrm{VMA}}{100}}{a}+\frac{\mathrm{VMA}}{\mathrm{VMA}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}\right]}^{-1}\end{array}$(6) ) and (7(7) $P_c=\frac{{\left(b+{\displaystyle \frac{\mathrm{VFB}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}{\mathrm{VMA}}}\right)}^c}{d+{\left({\displaystyle \frac{\mathrm{VFB}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}{\mathrm{VMA}}}\right)}^c},$(7) ) can be applied to estimate HMA elastic modulus.

Stiffness design level 3 implies that the minimum stiffness modulus $S_{\min }$ according to the European standard EN 13108-1 (CEN, 2007) is declared by the manufacturer in the course of initial type testing (according to EN 13108-20, CEN, 2009) of the used bituminous mixture. $S_{\min }$ is the result of four-point bending beam tests (4PBBT) according to EN 12697-26 (CEN, 2012b) conducted at 20${}^{\circ }$C and 8 Hz. $S_{\min }$ can be used to adjust the temperature-dependent results of the Hirsch-type model by adding ${\mathrm{KF}}_S$ to $S_{\mathrm{mix}}$ according to Equation (6(6) $\begin{array}{rl}{S}_{\mathrm{mix}}\left(T\right)& =\frac{P_c}{145.04}\left[a\left(1-\frac{\mathrm{VMA}}{100}\right)+145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)\frac{\mathrm{VFB}\cdot \mathrm{VMA}}{10,000}\right]\\ & +\frac{(1-P_c)}{145.04}{\left[\frac{1-\frac{\mathrm{VMA}}{100}}{a}+\frac{\mathrm{VMA}}{\mathrm{VMA}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}\right]}^{-1}\end{array}$(6) ). ${\mathrm{KF}}_S$ is of the form (8) ${\mathrm{KF}}_S=S_{B1}\cdot (S_{\min }-E_p(T={20}^{\circ }\mathrm{C}){)}^{1/S_{B2}},$(8) where $S_{B1}$ and $S_{B2}$ are bitumen-type-related parameters (distinguishing paving-grade bitumen and polymer-modified bitumen) and $E_p$ is the stiffness according to Equation (6(6) $\begin{array}{rl}{S}_{\mathrm{mix}}\left(T\right)& =\frac{P_c}{145.04}\left[a\left(1-\frac{\mathrm{VMA}}{100}\right)+145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)\frac{\mathrm{VFB}\cdot \mathrm{VMA}}{10,000}\right]\\ & +\frac{(1-P_c)}{145.04}{\left[\frac{1-\frac{\mathrm{VMA}}{100}}{a}+\frac{\mathrm{VMA}}{\mathrm{VMA}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}\right]}^{-1}\end{array}$(6) ) at 20${}^{\circ }$C considering the characteristic bitumen stiffness according to Figure 5.

Additionally, the temperature- and frequency-dependent stiffness behaviour of HMA can be characterised experimentally by four-point bending tests according to EN 12697-26 (CEN, 2012b) without using model assumptions at stiffness design level 4. Although large experimental effort is required, the HMA material behaviour can be described most realistically at this design level yielding the best economic design results.

2.3. Consideration of HMA fatigue behaviour

According to Blab et al. (2014), the fatigue behaviour of HMA can be described by (9) $N=\frac{k_1\left(T\right)}{F\left({\epsilon }_6\right)}\cdot {\left(\frac{S_{\mathrm{mix}}\left(T\right)}{{\sigma }_e}\right)}^{k_2\left(T\right)},$(9) where $S_{\mathrm{mix}}\left(T\right)$ denotes the temperature-dependent elastic modulus of the mixture (compare to Equation (6(6) $\begin{array}{rl}{S}_{\mathrm{mix}}\left(T\right)& =\frac{P_c}{145.04}\left[a\left(1-\frac{\mathrm{VMA}}{100}\right)+145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)\frac{\mathrm{VFB}\cdot \mathrm{VMA}}{10,000}\right]\\ & +\frac{(1-P_c)}{145.04}{\left[\frac{1-\frac{\mathrm{VMA}}{100}}{a}+\frac{\mathrm{VMA}}{\mathrm{VMA}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}\right]}^{-1}\end{array}$(6) )), ${\sigma }_e$ refers to an equivalent one-dimensional stress state according to Leon (1934) and Lorenzl (1996), $k_1\left(T\right)$ and $k_2\left(T\right)$ are fatigue parameters, and $F\left({\epsilon }_6\right)$ is a factor depending on the performance-based fatigue parameter ${\epsilon }_6$, which is defined as strain in [μm/m], at which a prismatic specimen is able to resist ${10}^6$ load cycles in a four-point bending fatigue test (4PBBT) at 20${}^{\circ }$C and 30 Hz according to EN 12697-24 (CEN, 2012a). Figure 6 shows the derivation of ${\epsilon }_6$ from fatigue tests on the HMA specimen (AC22 binder PmB45/80-65) on the basis of 4PBBT at three different strain levels.

Figure 6. Derivation of ${\epsilon }_6$ on the basis of four-point bending beam fatigue tests at 20${}^{\circ }$C and 30 Hz.

$k_1\left(T\right)$ and $k_2\left(T\right)$ are defined as (10) $\begin{array}{rl}{k}_1\left(T\right)& ={10}^{-(0.0077\cdot T^2-0.4859\cdot T+17.602)},\end{array}$(10) (11) $\begin{array}{rl}{k}_2\left(T\right)& =0.0015\cdot T^2-0.0875\cdot T+6.1803,\end{array}$(11) with T in ${}^{\circ }$C. According to Leon (1934) and Lorenzl (1996), the equivalent one-dimensional stress state ${\sigma }_e$ is defined by a boundary layer of the form of a parabola being tangent to the Mohr circles, which denotes failure. The geometry of this parabola – and, hence, the failure type – is determined by the relation c between compressive strength ${\sigma }_c$ and tensile strength ${\sigma }_t$, which for HMA is temperature dependent (Hagemann, 1980) and can be given as (12) $c=\frac{{\sigma }_c}{{\sigma }_t}={\left(\frac{72.6649-T}{32.8565}\right)}^{1.923}.$(12)

While shear fracture occurs for $1\le c<3$, cracks due to stresses exceeding the tensile strength emerge for $c\ge 3$. According to the boundary layer concept (Altenbach, 1993), the parabola can be applied to every Mohr circle enabling the transformation of a three-dimensional into an equivalent one-dimensional stress state through (13) ${\sigma }_e=\frac{c-1}{2c}\pm \sqrt{\frac{(c-1{)}^2}{4c^2}({\sigma }_1+{\sigma }_3{)}^2+\frac{1}{c}({\sigma }_1-{\sigma }_3{)}^2}$(13) for $1\le c<3$, and through (14) ${\sigma }_e=-\frac{{\sigma }_1+{\sigma }_3}{2(q_c-2)}\pm \sqrt{\frac{({\sigma }_1+{\sigma }_3{)}^2}{4(q_c-2{)}^2}-\frac{({\sigma }_1-{\sigma }_3{)}^2}{4q_c(q_c-2)}}$(14) for $c\ge 3$ with the principal normal stresses ${\sigma }_1$ and ${\sigma }_3$, as well as (15) $q_c=0.5(c+2-2\sqrt{c+1}).$(15) To determine $F\left({\epsilon }_6\right)$, two fatigue design levels can be distinguished (see Figure 7).

Figure 7. Fatigue design level for consideration of HMA fatigue behaviour.

In the Austrian standard RVS 08.97.06 (FSV, 2013), minimum requirements regarding the performance-based material behaviour are defined. For bituminous base courses, ${\epsilon }_6$ has to fulfil either ${\epsilon }_6\ge 130\mu$m/m or ${\epsilon }_6\ge 190\mu$m/m depending on the expected traffic load. At fatigue design level 1, $F\left({\epsilon }_6\right)$ can be determined from this minimum requirement according to (16) $F\left({\epsilon }_6\right)=E_B\cdot \frac{130}{{\epsilon }_6},$(16) with $E_B$ as a bitumen-type-related parameter (distinguishing paving-grade bitumen and polymer-modified bitumen).

At fatigue design level 2, ${\epsilon }_6$ is declared by the manufacturer in the course of initial type testing (according to EN 13108-20 CEN, 2009). Then, the factor $F\left({\epsilon }_6\right)$ can be determined by applying Equation (16(16) $F\left({\epsilon }_6\right)=E_B\cdot \frac{130}{{\epsilon }_6},$(16) ) as well.

2.4. Properties of subgrade and unbound layers

To consider temperature- and moisture-dependent changes in subgrade modulus, four periods with differing subgrade bearing capacities during one year are introduced (see Table 2).

Table 2. Temperature- and moisture-dependent subgrade modulus.

Period	Date	Subgrade modulus (MPa)
Winter	16.12–15.3	280
Spring (thawing)	16.3–15.5	70
Pre-summer	16.5–15.6	100
Summer/fall	16.6–15.12	140

Austrian standard RVS 08.15.01 (FSV, 2017) defines 10 quality classes (U1–U10) for unbound layers depending on the quality of the aggregates, the compaction level and the bearing capacity of the respective layer. Additionally, the deformation modulus of the layer depends on the thickness and the stiffness of the layer below. Hence, proportion factors are introduced to determine the modulus of the respective unbound layer (see Table 3).

Table 3. Proportion factors between modulus of upper and lower layers for a lower unbound layer thickness of 30 cm.

	Proportion factor
	$E_{\mathrm{upper}\mathrm{layer}}/E_{\mathrm{lower}\mathrm{layer}}$
Subgrade −
lower unbound layer (classes U6, U7)	2.80
Lower unbound layer (classes U6, U7) −
upper unbound layer (classes U2, U3, U4)	1.22
Lower unbound layer (classes U6, U7) −
upper unbound layer (classes U1)	2.08

2.5. Determination of $N_{\mathrm{res}}$ and $N_{\mathrm{imp}}$

Considering these input parameters, the linear elastic multi-layer analysis according to Burmister (1943) and the modified shear stress hypothesis according to Leon (1934) and Lorenzl (1996) are applied to determine resulting stresses and strains. Thereby, 12 temperature periods – providing nearly constant climatic conditions during each period (according to Figure 1) – are introduced.

Applying Equation (9(9) $N=\frac{k_1\left(T\right)}{F\left({\epsilon }_6\right)}\cdot {\left(\frac{S_{\mathrm{mix}}\left(T\right)}{{\sigma }_e}\right)}^{k_2\left(T\right)},$(9) ), the number of load cycles $N_{ijk}$ the pavement is able to resist can be determined for each axle i of each vehicle j and each temperature period k. While the corresponding damage $C_{ijk}$ yields (17) $C_{ijk}=\frac{1}{N_{ijk}},$(17) the average damage $C_{\mathrm{res}}$ is provided by (18) $C_{\mathrm{res}}=\sum _i\sum _j\sum _k{p}_j\cdot p_k\cdot C_{ijk},$(18) with $p_j$ as the appearance probability of vehicle j on the HGV traffic volume and $p_k$ as the relative duration of temperature period k during one year. Hence, the number of load cycles the pavement is able to resist, $N_{\mathrm{res}}$, reads as (19) $N_{\mathrm{res}}=\frac{1}{C_{\mathrm{res}}}.$(19) $N_{\mathrm{imp}}$ depends on the number of HGV vehicles expected to pass the pavement expressed as AADTT (annual average of the overall daily heavy traffic), a factor V related to the distribution of vehicles to several lanes, a factor S considering the loading distribution of vehicle tracks within one lane, the design life n in years and a growth factor z, yielding (20) $N_{\mathrm{imp}}=\mathrm{AADTT}\cdot V\cdot S\cdot 365\cdot n\cdot z,$(20) with (21) $z=\frac{q^n-1}{n(q-1)},$(21) where $q=1+p/100$, and p denotes the annual traffic growth rate in %.

3. Advantages of mechanistic pavement design

The advantages of the presented mechanistic-empirical design approach for bituminous pavements in Austria can be summarised as follows:

• As design levels are introduced regarding the traffic load, HMA stiffness behaviour and HMA fatigue behaviour, actual data for the road section can be taken into account. Hence, design reserves are minimised with increasing accuracy of the determination of the input parameters leading to more economic pavements.

• As advantages of modern, performance-based bituminous mix design can be introduced within the presented design approach by considering the mechanical material properties of the mixture, research and enhancement of HMA materials is supported and stimulated.

Comparing the results of the currently used pavement design according to RVS 03.08.63 (FSV, 2016) and the new mechanistic approach should illustrate these advantages. Thereby, a road section with a traffic volume of $\mathrm{AADTT}=2200$  HGVs/24 h is considered. The bituminous base course consists of asphalt concrete AC22 (VMA = 27.2 vol.$\mathrm{\%}$, VFB = 63.3 vol.$\mathrm{\%}$) with a polymer-modified binder (PmB 45/80-65), which fulfils the requirements for level E1 (${\epsilon }_6\ge 190\mu$m/m) according to Austrian standard RVS 08.97.06 (FSV, 2013). Four-point bending beam stiffness and fatigue tests conducted on this material deliver the performance-based parameters $S_{\min }=4500$ MPa (at 20${}^{\circ }$C) and ${\epsilon }_6=250\mu$m/m (at 20${}^{\circ }$C). The input parameters and exemplary combinations are summarised in Table 4.

Table 4. Input parameters for comparison of design results.

Design	Standard catalogue	Traffic load	HMA stiffness	HMA fatigue
1	Design acc. to	$\mathrm{AADTT}=2.200$ HGVs/24 h	–	–
	RVS 03.08.63
2	–	Design level 1	Design level 1	Design level 1
		($\mathrm{AADTT}=2.200$ HGVs/24 h)	(PmB, VMA, VFB)	(${\epsilon }_6\ge 190\mu$m/m)
3	–	Design level 1	Design level 3	Design level 1
		($\mathrm{AADTT}=2.200$ HGVs/24 h)	($S_{\min }=4.500$ MPa)	(${\epsilon }_6\ge 190\mu$m/m)
4	–	Design level 1	Design level 1	Design level 2
		($\mathrm{AADTT}=2.200$ HGVs/24 h)	(PmB, VMA, VFB)	(${\epsilon }_6=250\mu$m/m)

Assuming a design life of 20 years and an annual traffic growth of 3%, the actual design catalogue in RVS 03.08.63 results in a pavement construction consisting of a 30-cm-thick unbound lower base course, a 20-cm-thick unbound upper base course and a 23-cm-thick bituminous layer, independent of the used bituminous HMA material.

Using mechanistic-empirical pavement design, the traffic information given above allows for applying traffic design level 1, which provides representative distributions for the appearance of HGV types, the gross vehicle weights as well as the axles loads. As the volumetric composition of the HMA and the use of a polymer-modified binder are known, stiffness design level 1 is available and the Hirsch-type model in Equation (6(6) $\begin{array}{rl}{S}_{\mathrm{mix}}\left(T\right)& =\frac{P_c}{145.04}\left[a\left(1-\frac{\mathrm{VMA}}{100}\right)+145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)\frac{\mathrm{VFB}\cdot \mathrm{VMA}}{10,000}\right]\\ & +\frac{(1-P_c)}{145.04}{\left[\frac{1-\frac{\mathrm{VMA}}{100}}{a}+\frac{\mathrm{VMA}}{\mathrm{VMA}\cdot 145.04\cdot 3|G_{\mathrm{bit}}^{\ast }|\left(T\right)}\right]}^{-1}\end{array}$(6) ) predicts the temperature-dependent stiffness behaviour of the HMA considering a model bitumen. The used HMA fulfils the requirements for level E1 according to RVS 08.97.06, implying that fatigue design level 1 can be applied and $F\left({\epsilon }_6\right)$ can be determined according to Equation (16(16) $F\left({\epsilon }_6\right)=E_B\cdot \frac{130}{{\epsilon }_6},$(16) ). Considering these input parameters, the mechanistic-empirical approach predicts a design life of 20 years for the examined pavement construction.

Determining the performance-related material parameter $S_{\min }$ from four-point bending stiffness tests at 20${}^{\circ }$C allows one to apply stiffness design level 3. Hence, the stiffness predicted by the Hirsch-type model can be adjusted by the factor $F_S$ depending on $S_{\min }$ (see Table 4). Considering traffic design level 1 as well as fatigue design level 1, a design life of 23 years is estimated.

The characterisation of the fatigue behaviour in terms of ${\epsilon }_6$ (obtained from four-point bending fatigue tests) enables the application of fatigue design level 2 (see Table 4). Hence, $F\left({\epsilon }_6\right)$ can be determined by using Equation (16(16) $F\left({\epsilon }_6\right)=E_B\cdot \frac{130}{{\epsilon }_6},$(16) ). Taking traffic design level 1 and stiffness design level 1 into account, mechanistic pavement design results in design life of 24 years for the examined pavement construction.

The predicted design lives are compared in Figure 8. Applying the mechanistic approach based on performance-related HMA pavements according to European standards results in an increase of technical lifetime of up to 20% compared to the traditional design catalogue. The detailed characterisation of material properties leads to a more effective design and hence more economic pavement constructions.

Figure 8. Comparison of results of examined example.

4. Conclusion

The design of bituminous pavements in Austria is currently based on a catalogue of standard constructions distinguishing seven load classes and eight pavement types. These can be chosen depending on the traffic-related parameters AADT${}_i$ (annual average of the daily traffic for each vehicle type i) or AADTT (annual average of the overall daily heavy traffic). This approach does not allow one to take performance-related materiel characteristics or detailed traffic load information into account. To resolve these limitations, a mechanistic approach for the design of bituminous pavements in Austria was developed. Thereby, design levels for relevant parameters are introduced accounting for the level of detail of these variables.

Three design levels are distinguished for traffic loading. Depending on the availability of data regarding traffic volume of heavy goods vehicles (HGVs), probability of appearance of HGV types, distribution of HGV gross weights as well as distribution of HGV axle loads, representative distributions or measured data can be considered.

HMA stiffness behaviour can be determined according to one of four design levels. Besides the volumetric composition, the mechanical behaviour of a model bitumen (stiffness design level 1) as well as of the actually used bitumen obtained from DSR testing (stiffness design level 2) can be applied to a Hirsch-type material model, which was adapted to fit stiffness test results of asphalts types commonly used in Austria. Additionally, the stiffness behaviour can be determined using the performance-based material parameter $S_{\min }$ according to European standard EN 13108-1 (stiffness design level 3) or obtained experimentally by four-point bending beam test according to EN 12697-26 (stiffness design 4).

To take a performance-based description of the fatigue behaviour into account, a factor $F\left({\epsilon }_6\right)$ was introduced. The fatigue parameter ${\epsilon }_6$ is specified either from performance-based requirements according to European standard EN 13108-1 related to the bituminous base course (fatigue design level 1) or can be obtained in four-point bending tests according to EN 12697-24 (fatigue design level 2).

With increasing detail, also the experimental effort related to the identification increases but necessary design reserves decrease allowing for more economic constructions. Hence, this mechanistic-empirical design method allows for a modern, performance-based and economic design of bituminous pavements, and is expected to be released as a new Austrian standard RVS 03.08.68. Further developments could cover the simulation of the bonding conditions between single bituminous courses to deliver more realistic design results. This would require the implementation of structural models based on finite element methods including viscoelastic material models for bituminous courses to predict stresses due to traffic loads. Additionally, the presented approach delivers a useful framework for next-generation pavement design procedures, which not only consider fatigue as the only failure mechanism but are also capable to take thermal cracking and permanent deformation into account. This would allow for a separate design of bituminous surface, binder and base courses and, hence, the simulation of realistic life cycles including maintenance as a basis of reasonable life-cycle cost analysis.

Acknowledgements

The authors acknowledge the TU Wien University Library for financial support through its Open Access Funding Program.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors gratefully acknowledge financial support from the Austrian Research Promotion Agency (FFG; Österreichische Forschungsförderungsgesellschaft [835690]) through project “OBESTO – Implementation of performance-based behaviour characterization and life-cycle cost analysis into pavement design in Austria”.