Mathematical Prediction of the Structural Substance of Asphalt Pavements as a Prerequisite for Economical Maintenance

Jörg Patzak*

*Professor of Traffic Route Engineering at Beuth University of Applied Sciences Berlin, Germany

*Corresponding author: Jörg Patzak, Professor of Traffic Route Engineering at Beuth University of Applied Sciences Berlin, Germany, E-mail: Joerg.Patzak@beuth-hochschule.de

Citation: Jörg P (2021) Mathematical Prediction of the Structural Substance of Asphalt Pavements as a Prerequisite for Economical Maintenance. J Civil Engg ID 2(1):23-29.

Received Date: June 23, 2020; Accepted Date: December 07, 2020 Published Date: April 02, 2021

Abstract

Since the introduction of the guidelines for mathematical dimensioning of foundations of traffic surfaces with a course asphalt surface (RDO Asphalt) [1] in 2009 in Germany, it is possible to determine the layer thicknesses of pavements individually based on a computational dimensioning process. In the opposite case, the structural substance of existing asphalt pavements can be predicted and valuated by calculation (RSO Asphalt, draft 2016) [2]. The aim is to calculate the structural substance expressed by the remaining service life of an asphalt pavement, with the focus of the asphalt base. The knowledge of the remaining service life of an asphalt pavement is the crucial basis for sustainable and economical maintenance. The planning of an economical service life can be realized only then, if the service life of the remaining asphalt layers is adjusted to the renewed layers. The basis for the application of this method is the knowledge of the existing pavement structure and the performance parameters of all asphalt materials in the existing pavement. That means in detail the master curves and the fatigue function. Additional to that, the traffic load and the climate conditions are the main input factors.

This new method and the application in practice in combination with a new developed software solution called Analysing and Design Tool for Pavements (ADtoPave) especially developed for pavement engineering are introduced in this paper.

1. Introduction

Compared to the conventional empirically dimensioning method according to the RStO [4], the guidelines for mathematical dimensioning of foundations of traffic surfaces with a course asphalt surface (RDO Asphalt) [1] in 2009, brought an essential step to a sustainable and economical maintenance. In the traffic forecast 2030, the government primarily focuses on the maintenance with 69 % of the available financial resources. Therefore, it is absolute necessary to evaluate the structural substance of pavement in advance of maintenance decisions.

The basis for this is a process that enables the evaluation of the structural substance of asphalt pavements in field (RSO Asphalt, draft 2016) [2]. It is important to point out that this process does not focus on surface features but on the internal condition of the pavement. Exactly that is the foundation of an economical service life which can be realized only then, if the service life of the remaining asphalt layers is adjusted to the renewed layers.

2. Valuation of the structural substance of asphalt pavements

2.1 Basics of this method

The application of this method based mainly on the following four work packages, which will be explained later in this paper.

  1. Determining of homogeneous road sections, called structural homogeneous sections.
  2. Extraction of drill cores in the structural homogeneous sections.
  3. Material testing to determine the performance parameters of all asphalt materials in the existing pavement.
  4. Evaluation of the structural substance with the deterministic procedure or with the probabilistic procedure.

2.2 Structural homogeneous sections

The pavement to be investigated has to be divided in section, with a homogeneous character. Homogeneous at this point means no changes in the kind of construction, the same traffic and climate conditions and the same age of the asphalt layers for instance.

2.3 Extraction of drill cores

The extraction of drill cores takes place in all defined structural sections distributed throughout the whole section, if possible in the right-hand wheel path. The aim is to achieve a representative sample. That is essential for mathematically consideration of the variation of the material parameters and the variation of the layer thicknesses in the calculation.

2.4 Determination of the performance parameters

The determination of the performance parameters in laboratory takes place at specimen prepared from drill cores. For all in the pavement existing asphalt layers the following tests has to be carrying out.

  • stiffness (bituminous mixtures – test methods for hot mix asphalt EN 12697 Part 26) with IT-CY according to the German guidelines TP Asphalt-StB, part 26) [6]
  • And additionally, for the asphalt base course

  • resistance to fatigue (bituminous mixtures – test methods for hot mix asphalt EN 12697 Part 24) with IT-CY according to the German guidelines TP Asphalt-StB, Part 24) [5]
  • The last test is the

  • determination of the interlayer bond between the asphaltlayers on drill cores according to the German guidelines (TP Asphalt- StB, Part 80) [9]

2.5 Evaluation of the structural substance

For the evaluation of the structural substance two different procedures are possible. By using the first way i.e. the deterministic procedure, the structural substance will be calculated based on average values of all essential needed parameters. If the probabilistic procedure is chosen, the variability of the parameters (stochastically modelled) will be considerate. The result is the probability of default of the investigated section. It is also possible to predicates the probability of default so that the remained years to reach the defined probability can be calculated. The main differences between these procedures are shown in the following steps.

3. Examples

Specific example at this point is a structurally homogeneous section of a federal road with a length of approximately 1200 m.

For the calculation of the structural substance a new software called Analysing and Design Tool for Pavements (ADtoPave) [3] especially developed for pavement engineering was used (figure 1). This makes it possible starting from test interpretation to data management up to structural analyses and evaluation of the structural substance edit everything as a one stop. The work processes are considerably accelerated and the usability is excellent.

Figure 1: Analysing and Design Tool for Pavements (ADtoPave) [3]

In the investigated section, the following construction layers were found:

  • asphalt surface course, average thickness of 4 cm
  • asphalt binder course, average thickness of 5 cm
  • asphalt base course, average thickness of 13 cm
  • stabilization of the sub base, average thickness of 15 cm

The thickness of the construction layers was evaluated in advance by measurements by georadar and additionally by drill cores. Furthermore, the laboratory investigation shows that the asphalt surface course could be identified as a stone mastic asphalt (grading 11 mm), the asphalt binder course as a asphalt concrete (grading 16mm) and the asphalt base course as a asphalt concrete too (grading 32 mm).

3.1 Traffic load

Based on the present traffic census (year 2015) an average number of daily axle transitions for heavy load of 4856 were determined. The found layer thicknesses in field appropriate the expected thicknesses according to the German guidelines.

3.2 Extraction of drill cores

The extraction of drill cores in the structural homogeneous section was done as a so-called section sampling. That means the drill cores are not extracted in one place of the investigated section but uniformly distributed over the investigated section.

In the structural section with a length of nearly 1200 m 21 drill cores had to be extracted in general for all required laboratory tests.

In detail the following number of drill cores was used for the performed material tests (vgl. Pkt. 2.4):

  • 13 drill cores for determining the resistance to fatigue
  • 5 drill cores for determining the stiffness
  • 3 drill cores for determining the interlayer bond

3.3 Material testing - determine the performance parameters

Master-curve

On the basis of bituminous mixtures – test methods for hot mix asphalt EN 12697 Part 26 with IT-CY and according to the German guideline’s TP Asphalt-StB, Teil 26 [6] equation 1 is used as the master-curve function.

|E*|=|E *| + |E *| + |E *| 1+ e ( z 1 * x * + z 0 )             (1)             MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qadaabbaqaaiaahweaaiaawEa7amaaeiaabaGaaiOkaaGaayjcSdGa eyypa0ZaaqqaaeaacaWHfbaacaGLhWoadaabcaqaaiaacQcaaiaawI a7amaaBaaaleaacqGHsislcqGHEisPaeqaaOGaey4kaSYaaSaaaeaa daabbaqaaiaahweaaiaawEa7amaaeiaabaGaaiOkaaGaayjcSdWaaS baaSqaaiabgUcaRiabg6HiLcqabaGccqGHsisldaabbaqaaiaahwea aiaawEa7amaaeiaabaGaaiOkaaGaayjcSdWaaSbaaSqaaiabgkHiTi abg6HiLcqabaaakeaacaWHXaGaey4kaSIaaCyzamaaCaaaleqabaGa aiikaiaahQhadaWgaaadbaGaaCymaaqabaWccaGGQaGaaCiEamaaCa aameqabaGaaiOkaaaaliabgUcaRiaahQhadaWgaaadbaGaaCimaaqa baWcdaahaaadbeqaaiabgkHiTaaaliaacMcaaaGccaGGGcaaaiaacc kacaGGGcGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii aiaabccacaqGOaGaaeymaiaabMcacaGGGcGaaiiOaiaacckacaGGGc GaaiiOaiaacckacaGGGcGaaiiOaiaacckacaGGGcGaaiiOaiaaccka aaa@7824@

with

|E*| absolute valueof the complex young’s modulus (stiffness) [MPa]

|E*|+∞ limit of stiffness at low temperatures and/or high frequencies [MPa]

|E*|-∞ limit of stiffness at high temperatures and/or low frequencies [MPa]

x* any value on the abscissa at the master curve, determined with the temperature-frequency-equivalence [Hz]

, material parameters of the master-curve [-]

T0 reference temperature [°C]

Φ material Parameter [-]

Table 1 shows exemplarily the material parameter of the master-curve of the tested asphalt surface course.

Table 1: Parameters of the master curve of the asphalt surface course

E-∞

E+∞

z1

z0

T0

Φ

[N/mm²]

[N/mm²]

[-]

[-]

[°C]

[-]

0

23277

-0,751602

1,998533

20

22377

Figure 2 shows the master curve of the asphalt surface course including the measured values.

Figure 2: Master curve of the asphalt surface course

For better understanding shows Figure 3 the absolute value of the complex young’s modulus only depending on the temperature (constant frequency of 10 HZ) of all tested asphalt materials in the investigated section.

Figure 3: : Absolute value of the complex young’s modulus depending on temperature of all tested asphalts

Resistance to fatigue

The function for the description of the fatigue of asphalt is another essential base for dimensioning und the assessment of the structural substance. Equation 2 shows the mathematical function.

N zul =k n el,Anfn         (2)    MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWHobWaaSbaaSqaaiaahQhacaWH1bGaaCiBaaqabaGccqGH9aqp caWHRbGaeyOiGCRaeyicI48aaWbaaSqabeaacaWGUbaaaOWaaSbaaS qaaiaahwgacaWHSbGaaiilaiaahgeacaWHUbGaaCOzaiaah6gaaeqa aOGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGOaGaaeOmaiaabMcacaGGGcGaaiiOaiaacckaaaa@5146@

with

εel,Anf… elastic stain (initial stain) [‰]

Nzul… bearable load cycles

k, n… material parameter [-]

Table 2 shows the material parameters of the fatigue function.

Table2: Parameters of the fatigue function for the asphalt base course

k

[-]

n

[-]

8,888921

-2,676168

Figure 4 shows the function including the values of the material tests on the example of the asphalt base course.

Figure 4: Fatigue function of the asphalt base course

Interlayer bond

The investigation of the interlayer bond was carried out with the shear test according to the German guidelines (TP Asphalt-StB, Part 80) [9]. The test has to performed for all interlayer bonds, i.e. the asphalt surface course and asphalt binder course as well as asphalt binder course and asphalt base course. The test results show that the limits of the requirements were fulfilled, so that in the calculation a full impact of the interlayer bond was assumed.

3.4 Evaluation of the structural substance using the deterministic procedure

3.4.1 Pavement construction

In the deterministic procedure the layer thicknesses are considered as average values of all measurements. The values based on measurements with the georadar and include the asphalt layers and the stabilization.

As a safety factor the thickness of the asphalt base course must be mathematically considered as a the 10-percentile value (p=0,1; α=95%). Figure 5 shows the used model of the pavement construction

Figure 5: Model of the investigated pavement construction

3.4.2 Traffic load and climate conditions

In rare cases detailed axle loads are known. So, it is possible on the one hand to determine theses necessary information even before the tests of the structural substance started or well-known axle load distribution are used on the other hand. In the concrete example a standard axle load distribution (Figure 6) for federal highways was used, because the investigated road is the connection of two highways with a high percentage of heavy load traffic.

Figure 6: Used axle load distribution [1]

Either for dimensioning as well as evaluation of the structural substance, characteristic temperature profiles for asphalt pavements can be used (RSO Asphalt, draft 2016) [2]. The frequencies of these temperatures are depending on climate zones. For the whole country of Germany 4 different climate zone are defined. Alternatively, and very easy for the usability is, the coordinate of the position of the section can be entered directly in the software ADtoPave and the climate zone is chosen automatically.

3.4.3 Material parameter

The used material parameters for the procedure are descripted in Pkt. 3.3.

3.4.4 Results

Figure 7 shows the result of the calculation by using the deterministic procedure with a remaining service life of the section of nearly 15 years. The ordinate represented the state of fatigue. State of fatigue describes the ongoing process of fatigue of the asphalt base course layer. The calculation of the damage accumulation depending on time follows the well-known “miner´s rule”. If the state of fatigue reaches 100 %, it must be assumed that the base course layer isn’t able to bear the applied stresses in future. This information is essential for the decision of the kind of maintenance. Important is, that the layers which will be renewed are adjusted to the service life of the remaining asphalt base course layer.

Figure 7: Remained service life of the asphalt base course layer until 100 % state of fatigue are reached

3.5 Evaluation of the structural substance using the probabilistic procedure

3.5.1 Pavement construction

Fundamental difference by using the probabilistic procedure is the consideration of the variation of the relevant input values. Every pavement construction subjected to fluctuations of the layer thicknesses. Figure 8 shows as an example the measured total thickness, i.e. the thickness of all three asphalt layers together.

Figure 8: Total asphalt layer thickness, measured with georadar (blue -measured values; red - average value)

If it is worked only with average values, for instance with the average value of the total thickness, the impact of thinner or bigger thicknesses will be neglected. Therefore, the variability of the layer thickness is modeled stochastically in order to be able to carry out a discretization with classes of thickness and associated class probability. In the concrete example 5 classes were defined (figure 9). Class 3 represented the average value of the total layer thickness with 225 mm (figure 10) Classes 1 and 2 representing classes below, classes 4 and 5 above the average value.

Figure 9: Classes of layer thickness with associated probability

Figure 10: Model of the investigated pavement construction

3.5.2 Traffic load and climate conditions

Traffic load and climate conditions are considerate in the same way explained under point 3.4.2.

3.5.3 Material parameter

Just like the layer thicknesses, material parameters are also subject to fluctuations. It is recognizable that the measured stiffness values (stochastic sample) placed above and below the regression function (average function) in Figure 2 (Pkt. 3.3).

Discretization is also used for stochastic description of the material variation in order to be able to create classes with assigned class probabilities. Three classes were determined for the discretization of the stiffness in the example so that consequently three master-curve functions represented theses classes. Figure 11 shows the master-curves in linearized form.

Figure 11: Linearized master-curves for the three defined classes

For better understanding, Figure 12 shows the stiffness modulus depending on temperature on the example of the asphalt surface course, based on the three class functions in figure 11. This has to be done additionally for the asphalt binder layer and the asphalt base course layer too.

Analogous to the consideration of the variability of the stiffness modulus, the variability of the fatigue of the asphalt base course is to be treated. The separate presentation is dispensed with at this point.

Figure 12: Absolute value of the complex young’s modulus depending of temperature for the three defined classes

3.5.4 Results

The number of possible combinations of the input and comparison parameters (number of virtual sub-sections in one structural homogeneous section) results from the number of classes selected in the context of the discretization. In the present example the following classes for the existing three asphalt layers were selected:

Master-Curve: 3 classes for each asphalt layer)

Fatigue function: 7 classes (asphalt base course)

Layer thickness: 5 classes (thickness in total)

Based on this assumption 945 combinations (3 x 3 x 3 x 7 x 5) can be determined. The decisive factor at this point is that these combinations only results from construction and material variations. For each of these virtual subsections resulting from the explained combinations, the damage of the impacts from traffic load and climate must be calculated to be able to calculate the total amount of the damage accumulation. The sum of the frequency of occurrence of all virtual subsectors with a total damage > 1 corresponds to the failure probability of the investigated sector, i.e. the structurally homogeneous section. In the result of the discussed example a failure probability of 20 % will be reached after 9 years (figure 13), i.e. a fifth of the asphalt base course in the investigates section isn’t able to remain the impact of traffic load and climate after 9 years (starting from the point of analysis).

Figure 13: Remained service life of the asphalt base course layer until 20 % failure probability are reached

If a lesser failure probability is chosen for the investigated section, the predictable remaining service life is consequently shortened. Figure 14 shows this fact with an assumed 10% failure probability, with a predictable remaining service life of only 5 years. The authorities can influence the determination of the routespecifically defined failure probability, for example with regard to the priority of the route or financial resources. Currently failure probabilities between 10% and 20% depending on the road class are recommended.

Figure 14: Remained service life of the asphalt base course layer until 10 % failure probability are reached

3.6 Conclusions

The assessment of the structural substance according to the RSO asphalt, draft 2016 is used to calculated the remaining service life of asphalt base layers. This is the basis for the decision whether existing asphalt pavement can be retained or a reconstruction should be sought. With regard to the decision-making basis, the calculation results are more reliable when the probabilistic procedure is used. Using this procedure, the remaining service life could be assessed between 5 and 9 years with a failure probability of 10% respectively of 20%.In other words, after 5 years or 9 years of further impact of traffic load and climate influence, 10% respectively 20% of the investigated structural homogeneous section is to be regarded as failed, which is an essential statement for the maintenance strategy

3.7 References

  1. Richtlinien für die Dimensionierung des Oberbaus von Verkehrsflächen mit Asphaltdeckschicht. RDO Asphalt. FGSV 2009. 

  2. Richtlinien zur Bewertung der strukturellen Substanz des Oberbaus von Verkehrsflächen mit Asphaltdeckschicht. RSO Asphalt, Entwurf. FGSV 2016.

  3. Analysing and Design Tool for Pavements (AD-toPave), IDAV GmbH, Schnorrstraße 70, 01069 Dres-den

  4. Richtlinien für die Standardisierung des Oberbaus von Verkehrsflächen. RStO. FGSV 2012.

  5. Technische Prüfvorschriften für Asphalt, Teil 24 Spaltzug-Schwellversuch – Beständigkeit gegen Ermüdung. TP Asphalt-StB, Teil 24. FGSV 2018.

  6. Technische Prüfvorschriften für Asphalt, Teil 26 Spaltzug-Schwellversuch – Bestimmung der Steifigkeit. TP Asphalt-StB, Teil 26. FGSV 2018.

  7. Technische Prüfvorschriften für Verkehrsflächenbefestigungen – Betonbauweisen, Teil 3.1.05. TP B-StB, Teil 3.1.05. FGSV 2016.

  8. Technische Prüfvorschriften für Asphalt, Teil 27 Probenahme. TP Asphalt-StB, Teil 27. FGSV 2016.

  9. Technische Prüfvorschriften für Asphalt, Teil 80 Abscherversuch. TP Asphalt-StB, Teil 80. FGSV 2007.

  10. Technische Prüfvorschriften für Boden und Fels im Straßenbau. Teil E1 Prüfung auf statistischer Grundlage – Stichprobenprüfpläne. TP BF-StB E 1. FGSV 1993.

  11. Zusätzliche Technische Vertragsbedingungen und Richtlinien für den Bau von Verkehrsflächenbefestigungen aus Asphalt. ZTV Asphalt-StB. FGSV 2007. Fassung 2013.