A Review of PCN Determination of Airport Pavements Using FWD/HWD Test

Airport pavements are widely constructed as airport runways, taxiways, and aprons. The airport traffic should be considered during the design stage of airport pavements before the construction. To protect airport pavements from negligent overload, a pavement strength rating system and an aircraft load classification system are adopted. Under the rating systems developed by the International Civil Aviation Organization (ICAO), Aircraft Classification Number (ACN) and Pavement Classification Number (PCN) are calculated to assess the aircraft loads and the load-carrying capacity of the airport pavements for unrestricted operations. With the increase in the air transport demand, increasing attention on the continuous evaluation of airport pavement conditions is introduced to airports across the globe. The load-carrying capacity can be evaluated to assess airport pavement conditions by calculating the value of PCN continuously during the service cycle of pavements. The value of PCN can be estimated by testing the response of stationary dynamic loads, adopting a Falling Weight Deflectometer (FWD) or a Heavy Weight Deflectometer (HWD) device that simulates the stress generated by aircraft movements. By evaluating the PCN continuously in Airport Pavement Management System (APMS), cyclic determinations of the load-carrying capacity can be conducted to support the maintenance and rehabilitation (M&R) decision-makers. This review summarizes the methodology for determining the PCN and the tests conducted for evaluating the strength of airport pavement presented in the published literature. Further, the review highlights the benefits of determining PCNs by adopting the FWD or HWD field data with more precise results through mechanistic procedures.


Background
The airports are generally divided into two areas: airside and landside [1]. Airside consists of all controlled access zones, such as runways, taxiways, aprons, aircraft service areas, and air control facilities. After that, the airport's landside includes public access areas such as the part of passenger terminal before security check, parking lots, and other public service facilities [2]. The landing and take-offs of aircraft are taken place by the runways that are usually connected with the apron by the taxiways. An apron provides a place for aircraft parking, refuelling, and the operations of loading and unloading with passengers, luggage, and cargo [3]. According to the recommendation from both the International Civil Aviation Organization (ICAO) and the Federal Aviation Administration (FAA), the runways should be arranged to ensure that no obstacles affect landing and take-offs, and the aircraft can land at least 95% of the time with acceptable crosswind components [4].
Flexible airport pavement and rigid airport pavement can generally be two categories of airport pavement. To provide an alternative solution for extending the service life of rigid pavements, there may be composite pavements with a flexible layer over a rigid layer constructed using Portland cement concrete (PCC) [3]. Similar to the road pavement, flexible airport pavement commonly consists of four layers-surface layer, base layer, subbase layer, and subgrade layer. Therefore, flexible airport pavement can be considered multi-layer composite pavement [5]. A thin layer of dense-graded hot-mix asphalt (HMA) ranged from 50 to 60 mm thickness is generally designed as the surface layer of flexible airport pavement, however, a thicker HMA surface layer was also suggested referring to the US standard to overcome increasing aircraft load [6]. The maintenance operation of the airport asphalt surface such as resurfacing may be applied within the expectancy life of around 20 years [7]. Crushed rock or gravel is usually applied for unbound base or subbase courses of around 150 mm. Cement, lime, or asphalt can also be employed to stabilize base or subbase materials [8]. For rigid airport pavement, the thickness of a concrete layer is constructed on the base layer within the range from 225 to 450 mm [5].
The design methods of road and airport pavements are developed using mechanistic methods such as layered elastic method and finite element modeling. Based on the relationship between transportation repetitions and the strains observed by the actual performance of full-scale pavements under full-scale loading, the pavement life can be estimated to meet the requirements of airport design [9].
For the considerations of pavement design procedures, the magnitude of the load and the number of load repetitions on the pavement structure are the major differences between airport and road pavements. A much higher magnitude of tire pressure and a much lower load repetition during a pavement life cycle are considered for airport pavements. For example, a gross weight of up to 750,000 pounds is supported by only two six-wheel main landing gears of the Boeing B-777-ER with resulted in high tire pressure. To prevent high tire pressure, a total of 20-wheel main gear assembly including two six-wheel body gears in addition to two four-wheel wing gears were designed for Airbus A380 with a gross weight of 1.3 million pounds. However, the complex gear loads provided by these new aircraft models generate different structural responses from the older generations of airplanes and requirements of pavement design due to the potential premature failure of the pavement structure [10,11].
Owing to the hard loading of heavy aircraft or accidental conditions such as high-velocity objects or terrorist attacks, airport pavement may be subjected to multi-levels of impact loading [5]. Generally, the structural deterioration of airport pavement is caused by deflection, cracking, surface depression, rutting, potholes, and the exponential reduction of the dynamic stiffness with the age of the pavement under repetitive loading [12,13]. After that the extra contact pressure can be induced on the runway pavement by the high speed and heavy aircraft during the take-off or landing processes [7]. The maintenance of pavement during the arrival and departure of aircraft is difficult and could cause an increase of the service cost [14]. Therefore, it is important to understand the relevant factors to be considered in the airport pavement management system (APMS).

Transition from ACN-PCN to ACR-PCR
As described in ICAO Annex 14 Aerodromes, Volume I-Aerodrome Design and Operations, ICAO introduced the method as a standard to identify the bearing strength of airport pavements in 1981 [15]. International Civil Aviation Organization (ICAO) requires member states to report aerodrome-related aeronautical data, including pavement strength. The standardized ICAO method is recommended to report airport runway, taxiway, and apron pavement strength. The standardized method, known as the Aircraft Classification Number-Pavement Classification Number (ACN-PCN) method, has been developed and adopted as an international standard and has facilitated the exchange of pavement strength rating information [16].
As a new classification system developed by ICAO for airport pavement strength, the Aircraft Classification Rating-Pavement Classification Rating (ACR-PCR) pavement strength rating system has not yet been implemented by member states but is planned to be conducted before November 2024 [17]. As introduced by CASA [17], until the system is applied the aerodrome operator in Australia is still needed to publish the PCN in accordance with the Part 139 MOS [18].
The ACN-PCN system uses simple mathematics to evaluate the relative pavement damage based on subgrade deflection, which was applied as the indicator of pavement damage and the pavement analysis systems in the late 1970s and early 1980s [17]. With the development in pavement thickness design software, more sophisticated layered elastic, and finite element mathematics have been adopted to promote the accuracy of pavement design. The difference between the promoted sophistication of software applied for pavement design and the ACN-PCN pavement strength rating has caused anomalies, where aircraft which were considered in the pavement design of new design software are found to exceed the estimated pavement structural capacity in the ACN-PCN system [17]. To deal with these anomalies, the ACR-PCR system has been promoted by ICAO to introduce 1 3 the same mathematical models in the determination of relative aircraft damage of the new aircraft pavement strength rating system, as adopted for airport pavement thickness design. Further, as researched by CASA [17], the ratio between ACR and ACN ranges in value from 7.7 to 12.0. The around 10 times ACR values were designed by ICAO to avoid confusion during the transition from the ACN-PCN system to the ACR-PCR system.
The new airport strength rating system ACR-PCR has been approved by ICAO in 2019 [17]. The implementation by all member states must be performed between July 2020 and November 2024. For the complicated basis for selecting a PCR that cannot be replicated from the basis of the current PCN value, professional assistance might be needed to determine a reasonable PCR value. Therefore, before the approval of the ACR-PCR system in member states, the ACN-PCN system is still effective for airport pavement strength rating. The method to determine the ACN-PCN value is critical to be studied for the successful transition from the ACN-PCN system to the ACR-PCR system.

Article Structure of Literature Review
This paper intends to summarize the findings from the published literature related to the methods for evaluating structural strength, calculating Pavement Classification Number (PCN), and designing maintenance and rehabilitation (M&R) policy of airport pavements. Further, this paper focuses on pavement structural analysis and evaluation of the airport pavement strength. To avoid confusion, this paper does not mainly address airport pavement design methods. This paper has five sections. Section 1 introduces the background of strength rating systems of airport pavements. Section 2 introduces the methods to back calculate the measures from FWD and HWD tests. Section 3 focuses on the determination process for PCN based on the evaluated pavement structural properties after the basic theory of PCN calculation methods is reviewed. Section 4 describes the procedures using the results of the evaluation of pavement structural conditions for the design of maintenance and rehabilitation (M&R) policy and Sect. 5 ends the paper by summarizing the findings.

Back Calculation Methods Used for FWD and HWD Tests
With the increasing demand for air transportation in airports around the world, the overall and continuous assessment of runways and taxiways pavement conditions has attracted greater attention from the airport owners. However, this need is often limited by the finite budget and the assurance of the normal airport operation. The improvement of new optimized tools, which could be easily applied to assess the pavement conditions subjected to aircraft loads without extreme costs, has become a critical objective of airport owners. The gathered data by in situ tests and often collected without comparable conditions, such as the temperature of the asphalt surface and moisture content of subgrades, can be used to estimate structural conditions of airport pavements for the conduction on budgeting, planning, programming, and prioritization of Airport Pavement Management System (APMS) and the selection about the appropriate actions of Maintenance and Rehabilitation (M&R) [14,19]. The load-carrying capacity is the most important indicator adopted to assess airport pavement conditions using the in situ tests to estimate the structural response of stationary dynamic loads [6]. To evaluate the structural capacity of pavement, the deflectometer devices, such as the Falling Weight Deflectometer (FWD) and the Heavy Weight Deflectometer (HWD), have been widely employed to simulate the impact on pavement structures induced by an aircraft moving at moderate speed because these tests are nondestructive and rapid to execute for cyclic investigations [19]. The FWD test has been widely used to test the material properties of road and airport pavements [3]. The drop load generally ranges from 7 to 150 kN for the standard FWD, whereas a HWD is a FWD that has higher drop loads up to 250 kN [1,3]. Because higher loads are required to test an airport pavement's structural capacity to handle heavy aircraft, the HWD test has been primarily applied to test airport pavements [1]. The measured deflection basin generated by the applied stationary dynamic load in the tested pavement can then be analyzed by deflection basin parameters or back calculation analysis that normally assumes linear elastic theory. The deflection basin of pavement can reflect an overall response of the pavement structural layers to a dynamic load [20]. The measured pavement deflections and back calculated results are important inputs to several assessment methods of pavement conditions, such as structural capacity indicator tools and the methods used to estimate the remaining life of pavements. The measure basin shape, which is related to pavement structural characteristics including layer stiffnesses, layer thicknesses, and subgrade mechanical properties, can be primarily analyzed using the deflection basin parameters [21].
Falling weight deflectometer (FWD) and heavy weight deflectometer (HWD) data are widely processed through back calculation programs for calculating layer modulus of airport pavements. The process for computing the modulus values of pavement layer materials from deflection data and layer thickness is defined as back calculation. These back calculated moduli are adopted in critical applications including pavement design, strength rating, and overlay thickness design [22]. However, though several back calculation programs are presently available, it is not determined that the programs compute consistent and accurate results. Inconsistent and inaccurate back calculation results can induce a crucial influence on the overlay and rehabilitation design of airport pavements as layer modulus being the inputs for the design process [23]. For most back calculation programs, an initial value of modulus, known as seed modulus, is essential to initiate simulations. It means that the outputs vary with the original selection of seed modulus [22]. After that the final outputs could be different from the laboratory-measured value of modulus, depending on the accuracy of error minimization algorithms applied in a specific software [23].
Researchers have performed comparative studies of back calculation software, which is based on different calculation methods, such as linear elastic theory and finite element method. Ameri et al. [24] conducted a comparative study on four software, such as Dynamic Back calculation with System Identification (DBSID) and static load analysis software including MODULUS 6.0, ELMOD 5.0, and EVERCALC 5.0. Regarding static analysis, the surface deflection at each offset is assumed to be a function of the elastic modulus at a particular depth. By comparing the back calculated subgrade modulus to the measured subgrade modulus that was derived from California Bearing Ratio (CBR) and soil properties, MODULUS 6.0 was selected to be the most appropriate software with higher back calculation accuracy of subgrade modulus [24]. A spline semi-analytical method, which considers flexible pavement as a multilayered viscoelastic system, was developed by Ji et al. [25] to estimate pavement response and system identification approach to back calculate modulus. The analysis result of this method was compared to the results from two back calculation software including DYNABACK-F and MICHBACK in good agreement, which were a dynamic analysis software and a static back-calculation software launched by the Michigan Department of Transportation and the University of Michigan Transportation Research Institute respectively [25].
Mahoney et al. [26] pointed out the reasons for variations in the back calculated moduli from the different programs was due to the varied number of deflections needed for each software, variations in calculation procedures differences in seed moduli and modulus limits, variations in deflection basin convergence subroutines of minimization algorithms and the admissible tolerance in matching the computed and measured deflection basin, and the ability to solve nonlinear material response. In addition, the differences in stress states and load pulse duration between the FWD test and the laboratory tests should be the main reason for the deviation between back calculated FWD modulus and the laboratory modulus. Uddin and McCullough [27] applied a methodology to determine seed moduli according to the measured deflections and radial distances of the geophones. In order to predict effective moduli from the deflection basins, the selfiterative procedures, which included appropriate structural response model, elimination of guessing the seed moduli, modification of the back calculated modulus for nonlinear behavior of granular layers and subgrade soils, temperature correction for asphalt concrete layers, and the effect of an underlying rock layer in the analysis, were suggested by Uddin and McCullough [27].
The back calculation process using the layered elastic (LE) analysis method is shown in Fig. 1. Typically, the back calculation procedure needs inputs including the number of layers, layer thicknesses, Poisson's ratio of each layer, the temperature of the asphalt layer, and the presence of rigid layer underneath the subgrade. The initially assumed layer modulus called seed modulus is also required before the analysis [23]. After that the surface deflections at each radial offset of geophone locations are determined by the LE theory using the seed modulus and defined layer geometry [26]. After the comparison between the calculated deflections and the field measured deflections, the estimation cycle is repeated by changing the seed moduli each time, until the difference between the computed and measured deflections are within a customized tolerance or limit value [23]. Khazanovich and Wang [28] reported the following assumptions of back calculation associated with multilayer elastostatics analysis: all layers are linear elastic, all layers are infinite in the horizontal direction, and the surface load is uniformly distributed over a circular area. The effect of the rigid or stiff layer is critical on the static back calculation of layer moduli whenever the depth is shallow [29]. It means that the rigid layer has slight or no influence on the back calculation results when the depth is over 12 m. Theoretically, the thickness of the subgrade is finite and can be estimated by deducting the total thickness of the surface and base from the depth to the rigid layer [23]. Referring to the FAA advisory circular guideline AC 150/5370-11B [30], the Poisson's ratio of surface, base, and subgrade are recommended to be 0.35, 0.4, and 0.5, respectively.
In summary, the mechanical models used for the back calculation of both flexible and rigid pavements can generally be categorized as layered elastic analysis and finite element analysis. The layered elastic analysis has been adopted in the majority of the existing back calculation software that uses the mechanical analysis to match the measured deflection basin of both flexible and rigid pavements. To improve the accuracy of the mechanical analysis of the rigid pavement (that generates discontinuous mechanical response due to slabs), the finite element method has been applied by researchers into the back calculation process of rigid airport pavement [31]. However, long computation time and complex mechanical parameters have significantly affected the efficiencies of the finite element analysis in back calculating a large volume of field data [32]. Before the effective improvement for the efficiency of the finite element analysis, the layered elastic analysis is still a rational method to back calculate rigid pavement deflections. In addition, with the development of advanced nondestructive tests and the improved analysis methods of pavement structural properties, the airport pavement structural evaluation methods have become more important.

Methodology of Using FWD and HWD for Calculation of Airport Pavement Classification Number
To operate a safer and efficient air transport system for any country, it is critical to evaluate the pavement condition of airport runways, taxiways, and apron areas. As a result of an increase of aircraft traffic on airports where airport owners cannot afford to close the airport pavements for in situ destructive pavement evaluation activities, nondestructive tests such as falling weight deflectometer (FWD) and heavy weight deflectometer (HWD) are conducted popularly in the past few decades to evaluate the airport pavement strength [33]. The pavement classification number (PCN) of every airport which provides commercial airline operations is requested by the International Civil Aviation Organization (ICAO) to be published in its aeronautical information publication. The PCN number is determined as a number illustrating the bearing strength of pavement for unrestricted operations. Meanwhile, each airline should provide the aircraft classification number (ACN) corresponding to each type of aircraft it uses [34]. Based on the method applied in the Aerodrome Design Manual [35], the aircraft manufacturers developed charts for determining the ACN value by inputting the aircraft gross weight and subgrade category. If an aircraft's ACN is less than the airport pavement's PCN, the aircraft are allowed to land with its maximum landing weight. Elsewise, the aircraft should be operated under a restricted weight [33]. The empirical (U) method and the technical (T) method can be used to estimate the PCN. Typically, the technical method, which can be conducted according to the pavement material properties estimated by analyzing FWD or HWD field data or laboratory testing data, can express the pavement structural bearing capacity and PCN values more precisely than the applying the empirical method [33,34,36].

Review of Pavement Classification Number Methods
This section reviews and evaluates the current U and T methods applied to determine the PCN value of airport pavements and discusses the T method, which integrates the procedure of evaluating the pavement material properties and the procedure of evaluating the pavement PCN. According to the ICAO design method, the Aircraft Classification Number (ACN) and Pavement Classification Number (PCN) were developed as an airport pavement resistance rating system, ACN-PCN. Based on the characteristics of aircraft and pavement without restriction, the pavement resistance can be specified when the structure of airport pavements can support an aircraft with a maximum allowable load and maximum tire pressure [37]. The method of ICAO was created to describe the resistance of the pavements for the aircraft having a mass over 5700 kg. Typically, the Pavement Classification Number must be equal to or greater than the Aircraft Classification Number. It means that the load induced by the aircraft should be theoretically limited to equal to or less than the designed pavement resistance. As illustrated in Table 1, the following elements in the ACN-PCN method are presented: • The pavement classification number (PCN); • Pavement type for ACN-PCN determination (rigid or flexible); • Subgrade strength category (4 categories); • The maximum allowable tire pressure category or the maximum allowable tire pressure value (4 categories); • The evaluation method used (technical or empirical).
For example, a rigid pavement, which is designed to rest on a medium strength subgrade with a technically assessed PCN of 80 and no tire pressure limitation, would be classified simply by ICAO [37] with the reported information of PCN 80/R/B/W/T. As a result, the ACN-PCN rating system developed by ICAO is the standard applied in the civil aviation area.
Moreover, the methods used for determining PCN based on empirical and technical calculation processes, are reviewed as follows. The empirical method was first introduced by ICAO in 1983, whereas the technical methods were developed by various institutes, including Boeing and CROW based on, respectively, practical considerations.

Empirical Method
The empirical (U) method selects the highest ACN value of the aircraft in the fleet mix as the PCN value [35]. If the runway is allocated this ACN value, it may be needed to regulate this value downward, based on the predicted distress condition of the pavement, to ensure normal airport operations [34]. The general policy, which is conducted to solve one or more aircraft have ACNs exceed the lowered PCN, is restricting the allowable gross weight for those aircraft [33].

Technical Methods
The technical (T) method is dependent on the estimation of the pavement response to aircraft loading. Two different methods of T methods, the Boeing method and the cumulative damage method, are discussed next. Based on the development of the theories used to the elastic behavior of pavement structure shown the relationship between load and deflection, analyzing that deflection could obtain the capacity of a pavement's ability to support aircraft load [35]. Nevertheless, the pavement bearing strength is not merely dependent on an allowable load, but the repetitions use level for the loading. It is necessary to evaluate pavement bearing strength in terms of some predicted loading level or the allowable repetitions use level [34]. To accomplish this, a model between loading and repetitions to induce failure should be developed for a particular runway, taxiway, or apron [35].

Boeing Method
In 1998, Boeing developed a T method that applies the design method of the Portland Cement Association (PCA) and the design concepts proposed by FAA as the foundation of airport pavement analysis [38]. The PCN evaluation process of flexible pavements is similar to that of rigid pavement with different design charts [34]. The PCN calculation procedures for rigid pavements are proposed as follows: 1. Estimate the traffic volume corresponding to traffic cycles for each aircraft that has been operated or is planned to be operated in the airport along with the pavement design life. 2. Identify the critical aircraft as the design aircraft of the aircraft fleet mix. Using the PCA design method, the aircraft needing the greatest pavement thickness is defined as the critical aircraft. 3. According to the conversion factors and the transmission equation described in FAA [16,39], calculate the equivalent traffic cycles based on gear type and load magnitude. 4. Transform the accumulated equivalent traffic cycles of the identified critical aircraft in the fleet mix to load repetitions as illustrated in Eq. (1). where, TC = accumulated equivalent traffic cycles; LR = load repetitions; P/LR = pass-to-load repetition ratio; P/TC = pass-to-traffic cycles ratio. This ratio depends on the taxiway type connected with the runway and obtaining fuel at the airport or not [16]. 5. Determine the pavement characteristics, such as the concrete slab thickness, the concrete modulus of rupture, and the modulus of the subgrade, k. 6. Transform load repetitions to stress ratio using Eq. (2).
The working concrete tensile stress is calculated by multiplying the concrete modulus of rupture by stress ratio [34].
where, SR = stress ratio of concrete; LR = load repetitions. 7. Using the determined allowable working concrete tensile stress, slab thickness, and subgrade modulus, the maximum allowable gross weight of the critical aircraft can be calculated by using the PCA chart. If the calculated gross weight is less than the operational gross weight of the critical aircraft, then the PCN of this pavement may be equal to the ACN of the critical aircraft at that operational gross weight, but with a decreased pavement life. 8. As illustrated in Table 1, select the ACN-PCN subgrade code based on the subgrade modulus (k value). 9. According to ICAO [35] or the websites of aircraft manufacturers, the ACN of the critical aircraft under the allowable gross weight and standard subgrade code can be determined and assigned as the numerical PCN. 10. As shown in Table 1, determine the tire pressure code based on the highest tire pressure in the fleet mix. Generally, code W is assigned to rigid pavements that can support high tire pressure.
After the reviewing of the general pavement community, the Boeing method was promoted by the FAA who consulted much of Boeing's PCN method [34]. Applying a similar method as discussed above, FAA launched AC 150/5335-5C in 2014 to discuss the ACN-PCN method for reporting airport pavement strength. The determination process of PCN numerical values was developed to apply design charts that needed determining two parameters, subgrade strength category and allowable gross weight [16]. For airport pavements, the design charts for different landing gear types, such as single, dual, and dual tandem landing gear, are provided in the Boeing or FAA methods [34].

Cumulative Damage Method
One PCN estimation method similar to the Boeing method was described in the CROW report [40]. CROW is the Dutch acronym for Information and Technology Centre for Transport and Infrastructure who applied the fatigue models in the design method and PCN estimation method for airport pavements [34]. The recommended calculation procedures are proposed as follows: The determination process of flexible pavement PCN value is similar to the discussed methods of rigid pavements. This determination process can be conducted by using the finite element analysis for rigid pavements and layered elastic analysis for flexible pavements [33]. Normally, the U method is the most convenient method used to determine the PCN value and could be performed without any field tests or laboratory tests [34]. To overcome the shortage of applying the U method, the actual damage of pavement structure under aircraft loading is evaluated in more complex T methods. The discussed T methods perform the designed PCN procedures after determining the material properties, including concrete modulus of rupture and subgrade reaction value, k. Different from the Boeing method, the cumulative damage method involves the failure models that related loading and repetitions through laboratory experiments [33]. The field tests, such as FWD, HWD, and the plate loading test, can be performed to determine the relationship between the load and deflections. Generally, the Boeing method is regarded as the simplest T method to be performed among these two T methods after the determination of material properties [34].
To discuss the method to calculate PCN based on the test results of the FWD/HWD test, a representative example is reviewed to describe the PCN calculation process of airport pavement. As illustrated in Fig. 2, Chou et al. [34] proposed a modified T method based on the Boeing method and in situ HWD test that was executed to evaluate the pavement structural strength of an in-use runway. The measured deflection basins obtained from HWD tests at the tested slab centers were analyzed to evaluate the overall structural strength and back calculated elastic moduli of each layer for the following PCN determination process. The determination process of PCN based on the FWD/HWD test developed by Chou et al. [34] was typical to present the theory of the PCN calculation method based on the modified T methods with back calculated layer moduli. Further, it is difficult to conduct the back calculation process and the PCN determination process in the case of the pavement comprised of several pavement sections with varied layer properties, such as layer thicknesses or subgrade conditions. A method developed by Chou et al. [34] to deal with this difficulty is also reviewed.

Example of Determination of PCN Value Based on HWD Test for Rigid Airport Pavement
The example for determining PCN values of rigid airport pavement based on the HWD test was conducted by Chou et al. [34] to provide standardized procedures for PCN determination of rigid airport pavement with PCC slabs. The PCN determination method developed by Chou et al. [34] is representative and critical in the available published information to explain the theory of PCN calculation with the in situ HWD test data and PCN calculation results.
Because the design charts of Portland Cement Association (PCA) applied in the PCN determination process were mainly used to design the thickness of PCC slabs, the PCN determination process of Chou et al. [34] should be modified with the analysis procedure of flexible pavement structures to be used for flexible airport pavement.
To determine the layer thicknesses and seed moduli of structural layers for the back calculation process, the measured HWD deflection basins along the tested runway should be classified into different groups with similar test results to ensure a reasonable analysis of structural properties can be obtained. The identification of uniform properties of a homogeneous subsection, which has the same layer thicknesses, similar overall structural conditions, and similar subgrade strength, is critical after obtaining the raw HWD test results [30]. As stated in Eqs. (3,4), the normalized deflection of plate load, d 1n and impulse stiffness modulus (ISM) were calculated by using raw HWD deflection data to divide the entire runway into some structural homogeneous subsections. The overall pavement structural strength can be detected by using the normalized deflection data, d 1n [30]. Meanwhile, the value of ISM also reveals the overall pavement structural strength, but the meaning of ISM contrasts with that of d 1n . It means that higher normalized deflection data of plate load represents poor structural strength, while higher ISM values mean stronger structural strength. As for the determination process of the homogeneous subsections, the overall structural condition indicated by d 1n , ISM, and the slab depth were applied to identify the starting point and ending point of each subsection [34]. As stated in Table 2, based on the analysis about d 1n , ISM, and the slab depth, the tested runway was separated into six homogeneous subsections with the varied overall structural strength and different slab thicknesses including 41 cm at both ends of the runway and 38 cm at the middle of the runway [34]. Subsection 1 and subsection 6 were identified due to their 41 cm slab depth, whereas subsections 2-5 were constructed with 38 cm slab depth. Further, subsections 2 and 4 were found with higher overall structural strength than subsections 3 and 5 due to the low d 1n and high ISM. where, ISM = impulse and dynamic stiffness modulus, kN/ micron; L applied = applied load, kN; d 1 = measured deflection of plate load, micron.
Moreover, the back calculation program was executed to estimate the scatter of concrete elastic modulus and subgrade k. After that, a statistical method was suggested by FAA to determine the representative concrete elastic modulus and subgrade k for each homogeneous subsection. According to the suggestion of FAA, if the coefficients of variation, C v of concrete elastic modulus and subgrade k were less than 20% for each subsection, the mean values (4) ISM = L applied ∕d 1 of these moduli can be accepted for HWD-based pavement properties [30]. As recommended in FAA [30], if the value of C v exceeds 20% for each subsection, the values of concrete elastic modulus and subgrade k should be chosen as a value less than 85% of all calculated values for further calculation of the PCN value. As illustrated in Table 2, the back calculated concrete elastic modulus and subgrade k of each tested subsection were summarized for further PCN calculation.
After the determination of representative concrete elastic modulus and subgrade k for each subsection, the annual traffic by the traffic data for each aircraft during the pavement design life was evaluated as stated in Table 3. As illustrated in Table 3 and Eq. (1), the value of TC/LR varied with the type of aircraft, meanwhile, the value of P/ TC was equal to 1, because the type of taxiway connected to the tested runway was parallel with most aircraft fueled in this airport [34]. After that, using Eqs. (1,2), the load repetition and stress ratio of each aircraft was calculated to obtain the working concrete tensile stress by multiplying the stress ratio by the modulus of rupture ( M rup ) of Portland cement concrete (PCC), which was converted from the back calculated PCC elastic modulus by using Eq. (5) [39]. Finally, as illustrated in Table 3, the required PCC slab depth would be determined by inputting the values of M rup , subgrade k, and working concrete tensile stress into the PCA design chart of each type of aircraft. As presented in Table 3, the B777-300 needs the largest PCC slab thickness and was determined as the critical aircraft used to calculate the value of PCN for each subsection. The ACN codes of the fleet mix were also shown in Table 3. The number, the second code, and the third code referred to the ACN value, rigid pavement, and subgrade category, respectively. The B777-300 also corresponded to the aircraft with the largest ACN value [34].  where, M rup = PCC modulus of rupture, MPa; E pcc = back calculated PCC elastic modulus, MPa. As presented in Table 3, through the calculation process described in FAA [16,39], the accumulated equivalent traffic cycles of critical aircraft were calculated as 33,385 from every aircraft shown in Table 3 [34]. Next, accumulated equivalent traffic cycles of the critical aircraft, PCC slab elastic modulus, subgrade k, PCC slab depth, and predicted pavement life were used to determine the allowable gross weight and the corresponding ACN value of the critical aircraft, which could be set as the PCN value of the pavement subsection under a specific pavement life [16]. As reported in FAA [16], the value of PCN is a dynamic value depending on the expected pavement life under certain annual departures. Based on that, the remaining pavement life of the tested runway was predicted by Chou et al. [34] as 1, 3, 5, 10, and 20 years to investigate the relationship between pavement life and the ACN value of critical aircraft. The ACN values of the critical aircraft B777-300 or the PCN value for each subsection at the individual estimated remaining life of the runway were calculated as shown in Table 3. For instance, the PCN codes for Subsection 1, which were set as RCWT with subgrade category C, would vary from 54 to 76 when the estimated pavement life decreased from 20 years to 1 year. According to the back calculated subgrade k, the subgrade of Subsections 1, 2, and 4 was categorized to C, meanwhile, the subgrade of Subsections 3, 4, and 6 belong to Category D. The PCN value of Subsection 2 was highest among the three subsections having subgrade of category C due to the highest surface elastic modulus and subgrade k, even if its slab thickness was smaller. When comparing with that the PCN value of Subsection 6 was largest due to its larger slab thickness and surface elastic moduli, and that of Subsection 4 is smallest due to its low surface elastic modulus [34].
Chou et al. [34] concluded that the pavement life of the tested runway was 5 years with sufficient strength capacity and the PCN value for current aircraft volume (marked in Table 4). To report the PCN value and the subgrade category of the entire runway including more than one homogeneous subsection with various lengths due to the nature of pavement maintenance and rehabilitation history, the representative PCN value for the entire tested runway was estimated by adopting the length of each subsection as a weight factor to achieve 85% reliability and avoid critically conservative estimation. As presented in Fig. 3, the PCN of six subsections were reordered from the smallest value 50 at Subsection 4 to the highest value 75 at Subsection 2 before plotting the PCN values with the cumulative length percentage of sections. The PCN value 55 was then determined by Chou et al. [34] as the representative PCN value for the entire runway with the cumulated 15% of the pavement length, as shown in Fig. 3. Similarly, the subgrade category D was selected by Chou et al. [34] to represent the PCN subgrade category of the entire runway. In summary, the PCN value of 55 RDWT was assigned by Chou et al. [34] for the entire runway with an estimated 5-year pavement remaining life.
In comparison with the reviewed T methods, this modified method developed by Chou et al. [34] considered the in situ measured pavement properties, such as the nonuniform slab thickness, varied PCC slab elastic modulus, and different subgrade k along the tested runway. It was noteworthy to correlate the allowable ACN load or the PCN value with the pavement life in their research. If small remaining life of the runway was predicted, the pavement with the certain bearing strength could be assigned a high PCN value corresponding to a larger allowable gross weight of fleet mix, meanwhile, a low PCN value also could be estimated corresponding to a larger design life [16,34]. To balance the expected damage on pavements and the restriction on the aircraft operation, the airport owner should set the predicted design life of the runway and the corresponding PCN value, based on not only a technical analysis but a decision of an operation policy [34].

Concluding Remarks
The concept of pavement classification number (PCN) developed by ICAO is described in this section to discuss the evaluation process of airport pavement structural conditions using the PCN number.  Table 3. The subgrade category with higher subgrade k corresponds with a higher ACN value of the same aircraft and a higher PCN value estimated [16]. Therefore, the PCN values corresponding to different subgrade categories could not be summarized to obtain the representative PCN value of the entire runway without a unified subgrade category of each subsection [33,34]. Many relevant published information examined the airport pavement structural capacity based on the back calculated material properties. However, only limited published information has provided the full details of their examples. As such, this paper will only review the published information with full details of the reported examples. These full details of the published examples with the PCN calculation procedures can be adopted by other researchers to carry out similar back calculation for determining the PCN of tested airport pavements. Moreover, as airport pavement management moves further away from traditionally empirical management, the methodology of adopting nondestructive tests for airport pavement maintenance and rehabilitation (M&R) has become increasingly important. The studies conducted by Bandara et al. [33] and Mascio and Moretti [41] are also reviewed in this paper as examples to discuss the methodology of applying nondestructive tests for the airport pavement M&R works which were based on the examined pavement structural capacity indicated by the calculated PCN values.

Examples of Development of Airport Pavement Maintenance and Rehabilitation Based on HWD Tests
In the civil aviation industry, the requirement for the increasing of service quality and safety is essential to provide an efficient transport system [41]. As for the airport pavement system, to ensure the required level of service, to avoid the risk of accidents, and to maximize the benefits generated from pavement services, a pavement management policy is critical to obtain certification by the national aviation authorities [33,41]. The FWD or HWD test can effectively indicate structural strength properties for the airport owner to develop the policy of airport pavement maintenance and rehabilitation (M&R). Also, the FWD or HWD deflections and deflection indexes, such as d 1n and ISM referred to Eqs. (3,4), can be used to analyze the pavement condition directly as supplementary data.
The example for determining PCN values of composite pavement based on the HWD test was performed by Bandara et al. [33] to discuss standardized procedures for PCN determination of the rigid airport pavement with asphalt overlay. The PCN determination process described by Chou et al. [34] is typical in the available published information to explain the theory of PCN calculation with the in situ HWD test data and PCN calculation results. Because the PCN calculation process of composite pavement structure considers the distress condition of both AC and PCC materials, the PCN calculation method described by Bandara et al. [33] should be modified with the analysis procedure of only AC or PCC surface course in the cumulative damage method. Further, Mascio and Moretti [41] provided a more recent discussion about the application of in situ HWD tests for the ACN and PCN calculations of flexible airport pavement. The calculation results of ACN and PCN values of each HWD test point were also studied in this research to guide the policy of airport pavement maintenance and rehabilitation (M&R). However, the back calculation results and the PCN calculation procedures were not discussed in this research.
As for the method of applying HWD tests for airport pavement maintenance and rehabilitation, one pavement maintenance policy was made based on a series of HWD testing, which was conducted by Lima Airport Partners at the Jorge Chavez International Airport in Lima, Peru [33]. A representative process, which was applied to determine the sections of pavement needed to be maintained to achieve the required PCN (larger than ACN in the service life of pavement), was described by Bandara et al. [33] based on a maintenance project of airport pavement. The research completed by Bandara et al. [33] is reviewed as an example to discuss the analysis process that is used to develop the policy of airport pavement maintenance and rehabilitation based on the methods of the layer moduli back calculation and the PCN determination. Meanwhile, the PCN calculation process described by Bandara et al. [33] is based on the cumulative damage method, which is different from the modified Boeing method applied by Chou et al. [34]. The calculation process of PCN using the cumulative damage method is also reviewed.
Based on the predicted aircraft traffic, the structural condition and remaining life of various pavement areas of this airport were evaluated and represented as a PCN value for each pavement area. This airport had one runway (Runway 15-33), which was constructed in early 1960 by using rigid pavements with 7.5 × 7.5 meter PCC slab around 300 mm of the thickness. After that, a thin asphalt overlay over a reinforcing glass grid had been applied to rehabilitate the Runway 15-33. In this example, the structure of the Runway 15-33 should be considered as a composite pavement structure with the asphalt overlaying above the rigid pavement. Three load levels, including 180 kN, 230 kN, and 270 kN, were used to load each test location through a circular plate with a 225 mm radius. The deflection basin under HWD loading was back calculated using software ELMOD 5 before the prediction process of the PCN value and remaining life of this runway [33].

Evaluation of Pavement Layer Moduli Involved in the Example Composed of a Composite Runway Structure at the Jorge Chavez International Airport
Based on the back calculated moduli of pavement layers for each HWD test point, the remaining life and the overlay thickness required to strengthen the pavement up to its expected design life could be calculated by using ELMOD 5 [33]. The seasonal adjustments also can be considered to investigate the influence of various material moduli on the pavement life and overlay design. For example, the lower rainy season subgrade modulus could cause concentrated damage on the pavement structure because accelerated permanent deflection in the subgrade layer could be generated [6]. As shown in Fig. 4, the representative pavement layer moduli, including E1, E2, and E3 for the back calculated elastic moduli of the PCC slab, the AC layer, and the subgrade respectively, were plotted along with the test points. Before the computation of pavement remaining life and overlay requirements, the back calculated layer moduli should be modified to represent the material properties of each season along the design period [33]. As for flexible pavements, asphalt moduli can be evaluated as a function of temperature, meanwhile, the moduli of unbound layers, such as base, subbase, and subgrade layers, can be evaluated as a function of the season of the year containing spring thaw or wet period [30]. Next, based on the calculated critical stresses and strains, the cumulative damage on pavement layers, induced during each season by aircraft loading, should be computed by Miner's law associated with pre-defined failure models (fatigue or rutting) [39]. After that the expected remaining life of the pavement and the overlay thickness designed using a defined overlay material can be predicted based on the failure models and predicted aircraft volume for a required design period [33,39]. Typically, according to the analysis about the pavement design and prediction of pavement remaining life, there are two main types of pavement deterioration models are involved in the cracking of bound layers and permanent deformation of unbound layers [6,39]. Bound layers, which may be the materials composed of aggregates bonded together by binders including asphalt or Portland Cement, generally generate tensile stresses at the bottom of material layers under aircraft loading. Unbound layers consist of compacted aggregates or soils hold together through inter-particle friction or cohesion (silt and clay). Because the tensile stresses cannot be generated in unbound layers, the main stress existing in these layers should be compression stresses [6].

Pavement serviceability and damage criteria
involved in PCN determination procedure of the example composed of a composite runway structure at the Jorge Chavez International Airport As discussed for the determination methods of PCN, the cumulative damage method, which applies the pavement serviceability and failure criteria to estimate the remaining service life and PCN of airport pavements (based on the obtained pavement layer properties tested by nondestructive tests), has been adopted in several software programs for indicating the pavement structural strength and guiding the design of airport pavement maintenance and rehabilitation [40,42]. The use of the pavement serviceability and damage criteria in the process associated with estimating the pavement structural condition, evaluating the PCN of FWD or HWD test points, and predicting the remaining service life of pavements is a converse process adopted for the airport pavement design [4]. The theory that adopts pavement serviceability and damage criteria to analyze the pavement structure is reviewed. Moreover, as a result of the discussed stress patterns of bound and unbound materials, the typical deterioration mode for bound layers is fatigue cracking, which depends on the magnitude of the repeated tensile stresses or strains at the bottom of the bound layers [6]. Detailly, the repeated tensile strain in asphalt concrete was reported by Horonjeff et al. [4] to significantly affect the cracking in asphalt concrete of flexible pavements. After that, the cracking in PCC slab or cement stabilized layers of rigid pavements is critically controlled by the repeated tensile stresses. Because the failure pattern of unbound layers is generally rutting or poor ride quality (roughness), the typical deterioration mode for unbound layers is permanent deformation under repeated vertical loading. Therefore, the repeated vertical compressive stresses or strains at the top of the subgrade layer are widely used as the damage criteria of unbound layers [33].

Pavement Serviceability and Damage Criteria of Rigid Pavement
Moreover, to understand the process for determining the remaining life of used pavements and required overlay thicknesses for the designed pavement life, the main pavement damage criteria with the corresponding equations and parameters are reviewed as follows. As shown in Eq. (6), a fatigue failure criterion was developed by Portland Cement Association (PCA) to describe the relationship between the permissible tensile stress at the bottom of the PCC slab and the loading repetitions to cracking failure [43].
where: σ PCC = permissible tensile stress at the bottom of PCC slab, MPa; N = number of aircraft loading repetitions to failure; E = elastic modulus of PCC slab, MPa.

Pavement Serviceability and Damage Criteria of Flexible Pavement
As far as the failure criteria associated with the asphalt layer of flexible pavements, Eqs. (7,8) were developed by the U.S. Army Corps of Engineers and French LCPC respectively to describe the relationship between the permissible horizontal tensile strain at the bottom of the asphalt layer and the loading repetitions to cracking failure [36,42,44].
where: ε = permissible horizontal tensile strain at the bottom of the asphalt layer; N = number of aircraft loading repetitions to failure; E = elastic modulus of asphalt, MPa.
where: ε = permissible horizontal tensile strain at the bottom of the asphalt layer; N = number of aircraft loading repetitions to failure. Furthermore, as illustrated in Eqs. (9,10), the permissible vertical compressive stress and permissible vertical compressive strain at the top of the subgrade were investigated by Kirk [45] and PIARC [46] respectively to correlate the failure condition of the subgrade layer to loading repetitions.
where: σ zz = permissible vertical compressive stress at the top of the subgrade; N = number of aircraft loading repetitions to failure; E = elastic modulus of unbound materials, MPa; c = 1 for E > 160MPa ; c = 1.16 for E < 160MPa.
where: ε zz = permissible elastic vertical compressive strain at the top of the subgrade; N = number of aircraft loading repetitions.

PCN Estimation and Design of Maintenance Policy Involved in the Example Composed of a Composite Runway Structure at the Jorge Chavez International Airport
Before calculating the remaining life of the airport pavements based on back calculated moduli, the seasonal moduli for each pavement material at each season should be predicted based on defined models and records of asphalt concrete temperatures or wet periods [42]. Bandara et al. [33] assumed that the modulus of the subgrade was constant during the design period. As shown in Fig. 5, the seasonal moduli, which were evaluated for the assumed twelve seasons per year with average monthly temperatures recorded in Lima, Peru, were plotted by Bandara et al. [33] for the AC pavement layer along the HWD test line of the runway. According to the aircraft types and the number of operations during the design period provided by Lima Airport Partners, the tensile stress at the bottom of the PCC slab induced by each aircraft type was calculated by layered Elastic analysis, as illustrated in Fig. 6 [33]. For example, as shown in Fig. 6, the calculated tensile stress at the bottom of the PCC slab induced by MD-11 aircraft load in Season 10 was calculated by Bandara et al. [33] along with the HWD test points. Next, applying Miner's law, the pavement damage, generated during each season, by each load, was summarized based on the determined pavement damage criteria discussed from Eq. (6) to Eq. (10). The predicted seasonal modulus of the AC layer during the design period shown in Fig. 5 was used to correct the calculation of the tensile stress at the bottom of the PCC slab and the cumulative damage of pavement during each season. Finally, the expected remaining life of the pavement was calculated by comparing the allowable loading repetitions and required loading repetitions [39]. If the expected remaining life of the pavement is less than the required pavement life, the overlay should be designed. Furthermore, similar to the PCN calculation process proposed by Chou et al. [34], Bandara et al. [33]  calculated the PCN value for each HWD test point at slab centers after the determination of critical aircraft. Different from the method reported by Chou et al. [34] and FAA [16], Bandara et al. [33] applied the software ELMOD 5 to directly select the aircraft having the highest ACN value as the critical aircraft. After that, using the method described in FAA [16,39], the fleet mix in Lima Airport was converted to the number of equivalent coverages by critical aircraft during the assumed design life of 20 years. Comparing to the PCN evaluation process of rigid pavements, the modulus of the overlaid AC layer for each season was considered in the PCN evaluation process through computing the pavement response [33]. As for the pavement type required to present PCN codes of the composite pavement structure (refer to Table 1), the pavement type of a composite pavement should be determined as the type which most precisely reflects the structural behavior of the pavement [16]. As recommended in FAA [16], the rigid pavement with the asphalt overlay can be considered as a flexible pavement when the overlay reaches 75% to 100% of the rigid pavement thickness. Therefore, the pavement type and the PCN code of the composite pavement studied by Bandara et al. [33] are rigid pavement and "R" respectively.
Moreover, the PCN value is calculated in ELMOD 5 by the definition of the ACN value, which was two times the derived single wheel load (thousand kilograms) corresponding to the damage criteria for the PCC slab or subgrade, at the determined number of load repetitions [16,33]. Generally, the vertical compressive stress or strain at the top of the subgrade is the damage criteria for flexible pavements, while the tensile stress at the bottom of the PCC slab is the criterion for rigid pavements [39]. As shown in Fig. 7, the calculated ACN-PCN values along the runway of Lima Airport were plotted by Bandara et al. [33] to investigate the relationship between the calculated PCN value or the ACN value of critical aircraft as well as the tested pavement properties. The fluctuation of estimated PCN values coincided well with the trend of the back calculated modulus of the PCC slab, while the trend of estimated ACN values related well to the variation of the back calculated modulus of subgrade [33]. After that, the sections, such as 250-750 m, 1200-1650 m, 1950-2050 m, 2400-2500 m, and 2950-3250 m, might need to be overlaid to achieve the requirement of predicted traffic volume in 20 years.

PCN estimation and Development of Maintenance Policy Involved in the Example Composed of a Flexible Airport Pavement Structure at an Airport in Italy
Safe and regular aircraft operations should be satisfied by airport pavements that are necessary to be monitored for the surface conditions and implemented expensive maintenance and rehabilitation (M&R) works during the service life of pavements. To further discuss the application of PCN estimation in the design of maintenance policy, a more recent example, which was conducted by Mascio and Moretti [41] related to design procedures of the M&R works of an Italian airport with a flexible airport pavement system, is reviewed. The HWD tests were applied in this example as a monitoring method of pavement conditions to determine the priorities for intervention, to plan, and to allocate resources through M&R procedures. Further, the PCN number derived from HWD tests conducted at each pavement section was used as the indicator of the structural capacity of pavements. The investigated pavement sections of the airport in Italy included a runway, a parallel taxiway, and five exit taxiways. Measurements of structural capacity, transversal and longitudinal evenness, skid resistance, and pavement distress in terms of Pavement Condition Index (PCI) were conducted comprehensively in this example to identify the required M&R works. Particularly, the Pavement Condition Index (PCI) was tested by laser scanning data and visual investigations to detect superficial distresses [4]. The PCI value, which is rated based on a numerical scale from 100 (perfect condition) to 0 (failed pavement), is a synthetic parameter to estimate both structural and functional performance of a pavement [4]. Based on these measures, the required structural and functional M&R works were designed for the greater parts of the runway and the parallel taxiway, and two exit taxiways to solve the revealed structural and functional distresses of each pavement section [41]. These investigation methods helped this M&R project to minimize the impact on the traffic with the reduced closure period to 15 consecutive days.
The frequency of pavement inspections in the investigated airport was arranged at 36-48-month frequency and 60-month frequency for functional conditions (transversal and longitudinal evenness, skid resistance, and PCI) and structural capacity (HWD and PCN) respectively [41]. According to the specifications in ICAO [37] and FAA [16], the ACN and PCN values of each HWD test point were calculated and compared by Mascio and Moretti [41]. If the value of ACN is less than the value of PCN at one HWD test point, the structural capacity of the related pavement section could not support the required aircraft operations during the service life of the pavement. Nondestructive deflectometer tests were conducted to measure data about the existing pavements and the subgrade bearing capacity [30]. Similar to the PCN determination process of Chou et al. [34] and Bandara et al. [33], the back calculation of data obtained from HWD tests was carried out to calculate the elastic moduli and the Poisson's ratio of the tested pavement layers and the subgrade [41]. Given the fleet mix of aircraft, both a fatigue and rutting analysis has been conducted in the cumulative damage method. It means that the PCN calculation method used by Mascio and Moretti [41] was the same as the method described by Bandara et al. [33]. The cumulative damage method can be not only used for composite pavement structures but also used for flexible pavement structures. According to the specifications in FAA [39], the fatigue failure criterion developed by the Asphalt Institute for bitumen-bound materials and the rutting failure criterion developed by Shell for unbound material were adopted by Mascio and Moretti [41] for the analysis of the asphalt surface and the subgrade. The PCN value was derived from the highest single wheel load (SWL) that induces pavement failure after 10,000 coverages. The design traffic volume and the design service life of the pavement were 65,000 yearly movements and 20 years. However, the profile of the tested pavement structure and the computation details of back calculation and PCN determination were not provided by Mascio and Moretti [41]. Mascio and Moretti [41] provided only the calculation results of ACN and PCN values to determine the critical alignments or sections (ACN > PCN) at the tested pavement. The most critical alignments were at 3 m to the left and right of the centerline of both the runway and the parallel taxiway. The critical conditions did not be found at the unloaded alignments (e.g. 6 m to the left and right of the centerline of both the runway and the parallel taxiway). To statistically interpret the results of ACN/PCN in each pavement section, the reference PCN derived from the 15th percentile of the subgrade bearing capacity was calculated to avoid determining as representative a PCN value that reflects localized structural deficiencies [41]. The most critical condition was at the taxiway with representative PCN and ACN of 48 and 50. Based on the structural conditions derived from the PCN determination and other measures, the required M&R works were identified with more than 100,000 m 2 of the runway and 40,000 m 2 of the parallel taxiway in this research.

Concluding Remarks
The pavement serviceability and damage criteria for both flexible and rigid pavements are reviewed in this section, where the theory for detecting the pavement sections needed to be maintained to achieve the required service life is presented. Generally, the damage criterion of rigid pavement is based on the tensile stress at the bottom of the PCC slab, whereas the criteria of flexible pavement are based on the tensile strain at the bottom of the asphalt layer and the compressive stress (or strain) at the top of the subgrade layer. Also, a case study conducted by Bandara et al. [33] is reviewed as an example to discuss the calculation procedure of PCN and the determination process of the weak sections of one runway constructed with a composite pavement structure, which had been overlaid by asphalt concrete (AC) on the existing rigid pavement structure with PCC slabs. The calculation process of the PCN of this example used the cumulative damage method developed by CROW to consider the damage situation of the AC layer using the seasonal moduli of AC. Meanwhile, the tensile stress at the bottom of the PCC slab was also evaluated in this example to consider the aircraft loading response of this composite structure. Further, Mascio and Moretti [41] also applied the cumulative damage method to estimate the cumulative damage factors at the asphalt surface and the subgrade in the PCN calculation procedures. In summary, the cumulative damage method developed by CROW can provide the evaluation of pavement structural evaluation and PCN calculation in a technical calculation process, which combines the back calculation process using the mechanical analysis and the prediction of the pavement damage influenced by the seasonal temperature variation. As indicated by the study of Mascio and Moretti [41], with the development of the techniques used in the airport pavement management, the evaluation methods and the prediction models of airport pavement structural conditions would relate to more in situ test methods, such as skid resistance and pavement condition index (PCI) in the future.
Furthermore, this paper focuses on the application of pavement structural analysis and PCN determination on the guidance to the required maintenance and rehabilitation (M&R) works. The methods of determination of PCN values of tested airport pavement based on FWD and HWD tests are reviewed in this article to discuss the procedures for identifying the critical pavement sections needed structural M&R works. To avoid confusion, this paper does not address the conduction of M&R works for airport pavements.

Conclusions
The evaluations of pavement strength and condition to elaborate planned maintenance or rehabilitation activities are critical to protecting pavement assets and safe aircraft operations in an airport. Destructive or nondestructive tests can be applied in situ for airport pavement evaluations. The combination of comprehensive nondestructive tests and limited destructive tests is employed extensively, because of its fast test process and reduced damage to the structure of in-service pavements. With the advancements in nondestructive testing technology and back calculation methods, the advantages of applying the nondestructive tests have benefitted airport pavement engineers in managing their pavement maintenance and rehabilitation (M&R) activities.
This research focuses on providing an overview of the nondestructive tests (FWD and HWD), the back calculation methods, and the evaluation process of pavement remaining life and PCN of pavement structures. The Layered Elastic (LE) analysis is reviewed for the applications of these methods in back calculation analysis and pavement strength evaluations. Before commencing the back calculation, the deflection basin parameters are analyzed to divide the pavement into some homogeneous subsections and preliminary evaluations of pavement conditions. As a reverse process of the design of airport pavements, the determination of the pavement remaining life and the PCN value of airport pavements is based on the layer moduli back calculated from HWD tests. In addition, the seasonal layer moduli of pavement layers should be assessed based on environmental conditions along the design period. Next, the pavement response under each aircraft loading can be calculated to determine the cumulative damage factors of the respective aircraft. Subsequently, the ACN of critical aircraft or the PCN value of pavements can be derived from the equivalent single wheel load or the allowable gross weight of the critical aircraft corresponding to the damage criterion at the equivalent number of load repetitions. Finally, the cumulative pavement damage can be summed for each load and each season using Miner's law to estimate the predicted pavement remaining life and design the required overlay thickness for pavement sections when the pavement remaining life is less than the design period.
Because the very high aircraft gross weight consumes the pavement life, the determination of the PCN value of airport pavements is not only a technical issue but also a strategic policy of the airport management. A suitable PCN value should be calculated for the objective of avoiding unexpected early damage of pavements or to restrict aircraft operations. In short, the technical determination methods of PCN provide the opportunity to combine the back calculated pavement properties into the structural evaluation of airport pavement. In addition, the application of the FWD or HWD test for the development of the maintenance policy has been widely conducted in airport pavement management. Future policy of maintenance and rehabilitation (M&R) works shall be largely based on pavement modeling, which can be used for evaluation and predicting airport pavement structural conditions from comprehensive field testing and pavement condition index (PCI) assessment.