The life cycle length of pavement with asphalt concrete material (ACM) surfacing is significantly influenced, in addition to transport loading and climatic conditions, by design method and rehabilitation timing. Appropriate overlay thickness calculation and estimation of optimal rehabilitation time are crucial to maximizing life cycle length and, concurrently, reducing road administration costs and road user costs. This article describes a comprehensive method of ACM rehabilitation design. For optimization of life cycle cost analysis (LCCA) based design, mathematical analytical solution in combination with experimental verification of physical, mechanical, and fatigue characteristics is utilized. Pavement performance, that is, functions mathematically describing pavement’s degradation characteristics of operational capability, is represented by longitudinal and transverse unevenness; these are used to describe relations between traffic loading and pavement’s bearing capacity on 1 : 1 scale. Optimizing of rehabilitation plan is carried out by making a cost benefit analysis (CBA) for several rehabilitation scenarios in which different rehabilitation timing produces different capital cost requirements and social benefits. Rehabilitation scenarios differ in technology, the design of which needs to be mathematically optimized, and timing of rehabilitation execution. This article includes a case study for the sake of illustration of practical results and verification of applicability of used methodology.
Design optimization calculation method for ACM pavements is a complex method using analyticalexperimental methods for calculating of overlay thickness and resulting life cycle extension, in addition to general deterministic pavement performance modelling and CBA. To calculate the required ACM overlay thickness, it is imperative to know the mathematical model and numerical solution of layered elastic halfspace [
Because of the application of complex rehabilitation methodology needs to be performed on particular pavement type, experimental road section was designed and constructed. The surfacing is composed of ACM prescribed by technical standards to ensure quality and match with real life pavements. The base course in a mechanically bound aggregate, subbase, is a compressed gravel layer; the earth works are simulated by a rubber layer on concrete with the equivalent modulus of well compressed subsoil. The pavement was designed according to the standard dimensioning methodology [
Pavement structure.
Pavement structure layers are designed from generic materials defined in national standards. Table
Material characteristics of pavement layers.
Layer  Complex modulus  Resistance  Poisson number  Layer thickness 

AC 11 O  10,891  3.2 MPa  0.33  40 mm 
AC 16 P  8,317  2.4 MPa  0.33  80 mm 
MBA, 31,5 GB  586  0.1 MPa  0.30  180 mm 
Gravel subbase, 31,5  365  0.07 MPa  0.30  200 mm 
Subgrade  100  —  0.35  — 
Calculation of pavement life cycle is possible only on the basis of pavement design method, that is, structural design, and overlay design method.
The calculation of required overlay thickness is based on the analyticalexperimental methods. Pavement construction including ACM surfacing is to be considered as a multilayer system on a flexible subsoil. Each layer, including overlay layers, is characterized by its thickness, modulus of elasticity, and Poisson numbers. The calculated stress
SV is structural value (utilization index),
The characteristics of the fatigue that are in the equation are the average size of deformation derived from stress lines derived after 10^{6} loading cycles in microstrain (
The results of research carried out in the ambit of fatigue characteristics are presented in Figure
Values of fatigue parameters for mix AC 11 O.
Parameter 





Fatigue parameters  −15.0754  −0.1927  86.77  0.7871 
Wöhler diagram.
The life cycle of ACM in the pavement construction can be expressed through (
Obviously, during the service life, as the surfacing wears down, elastic modulus of ACM layers diminishes which results in surfacing resiliency loss. Calculation of elastic modulus decrease can be based on experimental fatigue testing. The results for materials used in this case study were published in [
Elastic modulus, radial strain, and resiliency decrease in relation to traffic loading.

0  0.4 × 10^{6}  0.8 × 10^{6}  1.2 × 10^{6}  1.6 × 10^{6}  2.0 × 10^{6} 

AC 11 O (MPa)  10,891  5,998  5,759  5,620  5,521  5,445 
AC 16 P (MPa)  8,317  4,580  4,398  4,291  4,216  4,158 
Radial strain (MPa)  0.978132  0.634328  0.613133  0.600401  0.591348  0.584278 
Resiliency (MPa)  0.92400  0.769512  0.690040  0.643552  0.610568  0.584984 
The shape of calculated strain in relation to elastic modulus decrease and resiliency loss is shown in Figure
Relationship between stress in ACM depending on repeated loading and decrease of ACM strength resiliency depending on the fatigue trend function.
The calculation of capacity utilization coefficient Sv based on (
Increase of capacity utilization coefficient Sv.
The life cycle represents number of load repetitions acting on ACM layer up to the state of a failure. As stated in Section
In terms of overlay design method, the rehabilitation entails increase in elastic modulus of ACM surfacing and by adjusted thickness of the surfacing layer. In Figure
Radial strains prior to and after overlay.
Year  5  10  15  20  25  30  35  40 

ACM layer thickness increase (mm) 




—  —  —  — 
AC 11overlay E (MPa)  10891  10891  1089  1089  5445  5445  5445  5445 
AC 11 O E (MPa)  5945  5682  5551  5445  5354  5304  5248  5205 
AC 16 P E (MPa)  4540  4339  4239  4158  4088  4051  4008  3975 
Strain prior to rehabilitation (Mpa)  0,751838  0,664456  0,620544  0,584984  0,48615  0,4465  0,42012  0,40146 
Strain after rehabilitation (Mpa)  0,508571  0,464004  0,429907  0,40146  0,477312  0,428528  0,404145  0,382118 
Radial strains before and after rehabilitation.
The development of radial strains in the pavement construction is shown in Figure
Overlay designs and their timing and life cycle extension are shown in Figure
Overlay design and timing of four rehabilitation scenarios: Sv and life cycle relation.
In order to ascertain rehabilitation timing and identify prudent rehabilitation scenarios, pavement performance degradation should be taken into account. If the rehabilitation is performed too early, it is usually inefficient; delayed rehabilitation may lead to loss of pavement’s operational serviceability [
The general principle of APT is simulation of real life traffic loading on real life pavement. This traffic load is preferably the design axle load, for which the pavement is designed. In this case, it is 50 kN. The loading unit is driven along a leading rail; it is powered by an electromotor. Acceleration, deceleration, and top speed are adjustable within constraints of the pavement length. Radial strains at the bottom edge of surfacing arise as a combination of surfacing deflection under the loading unit and acceleration and deceleration forces on the tirepavement contact area. APT facility parameters are listed in Tables
APT facility dimensions.
Technical parameters  

Length  9,042 mm 
Width  5,178 mm 
Width with protective fence  6,000 mm 
Height  2,452 mm 
APT facility technical parameters.
Technical parameters  

Facility  Accelerated pavement testing facility 
Construction  Semimobile, linear 
Type  1050301 
Maximum velocity  2.22 m·s^{−1} 
Load  57.5 kN 
Max acceleration  2 m·s^{−2} 
Max deceleration  5 m·s^{−2} 
Location  Indoor 
Operational temperature  10–40°C 
Operational humidity  30–80% without condensation 
Engine power  45 kW 
Transition  CLP HC VG 320, MOBIL SHC GEAR 320 
Energy requirements  3 + N + PE, AC, 50 Hz, 230/400, V, TNS 
The loading unit runs the pavement section in both directions. In addition to weight of the loading unit itself, additional weight is loaded on the unit to reach the required 50 kN loading. Shape of acceleration curve, constant speed, and deceleration curve is set up before the loading session. If valid, the loading unit will be driven at the desired speed conditions. The speed conditions are mirrored for the opposite direction drive. The APT facility is shown in Figure
APT facility.
Unevenness was ascertained from cross sections of pavement surface. The surface was scanned by a handheld Lidar laser scanner, high density point mesh was created with accuracy of 40
Transversal unevenness on the experimental pavement section.
The results can be deterministically evaluated and described by either linear or polynomic equation; see (
Linear equation:
Polynomic 5thdegree equation:
The same approach as that for transversal unevenness was used for data collection and evaluation of longitudinal unevenness. The longitudinal unevenness is represented by International Roughness Index (IRI) with unit m·km^{−1} [
IRI was evaluated in accordance with Reference Quarter Car Simulation Model; the values lie within interval 3.3–6.81 m·km^{−1}; however, these values are somewhat skewed since they incorporate outermost pavement stretches where the loading unit is in a standstill. After we adjust the IRI by exclusion of these local extremes, the interval for the constant speed stretch of the pavement is much more prudent, 3.3–3.9 m·km^{−1}. The longitudinal unevenness can be seen in Figure
IRI evaluation.
Pavement performance model used for optimization of overlay design was a result of APT pavement performance described in this section and long term pavement performance monitoring of real pavement section in operation. The pavement performance model is a cubic polynomial function described by
Optimizing of decisionmaking process in rehabilitation planning is based on the LCCA principles. The gist of the optimization is to perform CBA for each rehabilitation scenario and subsequent calculation and comparison of optimization index of those scenarios.
CBA compares the cash flows of “do nothing” scenario and “do something” scenario. As a result, economic benefits gained through rehabilitation can be compared with financial costs for applied rehabilitation technologies. Combination of three economic indicators is used to evaluate the economic viability of each scenario; the indicators are the payback period, internal rate of return, and the net present value. Monetization of socioeconomic costs and benefits from pavements with rehabilitated ACM surfacing, respectively, are crucial for ascertainment of economic indicators. The benefits are related to difference in pavement quality in scenario without rehabilitation and scenario with rehabilitation. Benefits can be internal and external. In this case study, we used internal benefits which include road user operation costs and travel time costs as these can be monetized using World Bank’s endorsed method. The external benefits including environmental savings and macroeconomic implications are omitted as all available monetization methods were considered by road administration authorities as subjective, that is, not reliable.
Overall road user benefits based on proposed rehabilitation technology and its investment costs, road administrator’s costs, timing of rehabilitation, and discount rate can be calculated according to
RUB are road user benefits [
Pavement performance model described in previous sections enters the overlay optimization model in the calculation of road user benefits in the form of
Optimization index is basically a unitless number calculated as division of all life cycle costs and extension of the original life cycle span.
OI is optimization index,
RC are rehabilitation costs [
Optimization in this case study is based on a calculation of described overlay design, pavement performance models, CBA, and optimization index. The calculation of optimization index itself is shown in Table
Life cycle cost analysis and cost benefit analysis.
Variant  Variant scenario  Rehabilitation 5th year  Rehabilitation 10th year  Rehabilitation 15th year  Rehabilitation 20th year 

Rehabilitation action  —  Overlay 
Overlay 
Overlay 
Overlay 


Investment cost  0€  69,084€  99,788€  118,978€  136,249€ 


Maintenance cost  846,938€  858,066€  941,350€  1,162,456€  1,581,330€ 


Road agency cost  846,938€  927,150€  1,041,138€  1,281,434€  1,717,579€ 


Road user costs  
Vehicle operating cost  8,316,431€  9,995,382€  11,689,165€  13,594,956€  16,045,362€ 
Travel time cost  822,241€  973,891€  1,125,826€  1,290,801€  1,569,194€ 
Total road user cost  9,138,673€  10,969,273€  12,814,991€  14,885,757€  17,614,555€ 


Life cycle length  20  25  30  35  40 


CBA  
NPV  —  20,333€  26,739€  14,527€  1,438€ 
IRR  —  48.30%  155.10%  139.40%  99.50% 
PP  —  6  11  15  20 
Calculation of optimization index.
Scenario  Sum of all life cycle costs 
Extension of the life cycle 
Optimization index 

No rehabilitation  846,938  0  0 
Rehabilitation in year 5  927,150  25  37,086 
Rehabilitation in year 10  1,041,138  30  34,705 
Rehabilitation in year 15  1,281,434  35  36,612 
Rehabilitation in year 20  1,717,579  40  42,939 
Optimization index.
More diligent approach would call for the evaluation to be done in each year, not just in years 5, 10, 15, and 20. The result would be a refined curve of the same shape, with the possibility that the refinement could shift the optimal rehabilitation by a year or two. This is a question of due diligence of particular administrator and possibility of automating the calculation by Excel macro file or a software solution.
Sensitivity analysis shows the effect of input changes on the overall result of the optimization. In the analysis, one input parameter for the optimization is changed and the resulting aberrations in financial and economical parameters are presented. To evaluate elasticity of individual parameters, only one particular parameter can be tested at a time. Individual parameter is critical; that is, it has elasticity over 5%, if a change of 1% in the parameter causes a shift in the result of 5%. Elasticity analysis for this particular case study is shown in Table
roughness pavement performance model,
fatigue parameter change (
resiliency of critical layer.
Elasticity analysis.
Input  Original NPV  NPV for 1% input change  Difference in NPV  Elasticity 

Roughness pavement performance model  573,502.33  543,660.36  15,642.52  2.8% 
Fatigue parameter change ( 
573,502.33  553,047.83  6,255.05  1.12% 
Resiliency of critical layer  573,502.33  553,047.83  6,255.05  1.12% 
The analysis shows that neither of observed input parameters is critical by itself. However, their effects are synergetic and combination of flaws in these inputs can easily lead to unrealistic results. Therefore, the most precise definition of said inputs is required for optimization of overlay design and timing strategies.
The objective of this article was to elucidate on the methods for overlay design and creation of pavement performance model and decisionmaking method for identification of optimal rehabilitation time. This approach is very complex. However, it can be adopted on national level with some effort, provided that the national research can supply or substitute the experimental part. The presented case study shows that the combination of pavement structure design methods, experimental fatigue tests of ACM, experimental pavement testing, and/or long term pavement performance monitoring if combined with economic appraising of road user costs can be used to optimize overlay thickness and rehabilitation timing. Additional data is required, namely, traffic data and climatic data of given region. The critical point of similar methodologies is usually the creation of pavement performance models. APT data backed by long term performance monitoring as described in this article seems to be preferable when creating pavement performance models. Downside of this approach is that the test needs to be performed for particular pavement type, which can take time as the data may not be readily available. The pavement performance model can be then employed for all pavements with ACM surfacing within given traffic load class, as these are not expected to differ significantly. Sensitivity analysis evaluates input parameters presented in the article that are needed for the overlay optimization. It shows impact of input changes on the overall result of the overlay scenario results. Preliminary results from this case study prove in practice that this approach is a good way to refine the decisionmaking process of rehabilitation planning which leads to increase in socioeconomic benefits for the public and at the same time helps to decrease capital cost of road administration.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This paper is the result of the project implementation “Independent Research of Civil Engineering Construction for Increase in Construction Elements Effectiveness” (ITMS: 26220220112) supported by the Research & Development Operational Programme funded by the ERDF.