Indian Journal of Engineering & Materials Sciences Vol. 10, June 2003, pp. 193-201

Calibration of structural cracking models for asphalt pavements: HDM-4 case

Heman de Solminihac•*, Priscila Hidalgob, Mauricio Salgadoc & Anfbal Altamirad

•oepartment of Construction Engineering and Management, School of Engineering, Pontificia Universidad Cat61ica de Chile, Casilla 306, Vicuna Mackenna 4860, Santiago, Chile

bDICTUC S.A., Pontificia Universidad Cat61ica de Chile, Santiago, Chile

cDepartment of Civil Engineer, Pontificia Universidad Javeriana, Bogota D.C. , Colombia

dMountain Roads Engineering School, Universidad Nacional de San Juan, Argentina

Received I April 2002; accepted 16 March 2003

The HDM-4 (Highway Development Management) models used for pavement management activities must be adapted to specific conditions of the country or region where they are to be used by adjusting certain calibration factors. This work presents results obtained from the calibration of structural cracking models in HDM-4 version 1.1, and comparing the results from equivalent HOM-Ill models. The "windows" methodology is used to reconstruct the distress performance curve of a specific road category based on the observation of conditions of diverse roads with simi lar characteristics (such as traffic, pavement structural capacity and climatic conditions) but different ages. Also, recommendations are made for calibrating performance models, as well as for establishing calibration factors for asphalt pavement structural cracking models more appropriate for Chilean roads. Although the results of the HDM-111 and HDM-4 calibrated models have si milar values, the HDM-4 version 1.1 cracking models are recommended due to their operational advantages.

The World Bank has developed computational systems to support professionals involved in pavement management. These models, developed in the 70's, have been important tools for economic development of highways and their technical evaluation 1. Moreover, these systems incorporate performance models which must be calibrated according to specific conditions of the country or region where they are to be used.

The performance models for visible distress in asphalt pavements in the HDM-4 model 1

'3 correspond

to structural cracking, thermal cracking, ravelling, potholes and edge breaks. The structural cracks models are divided into two groups: all structural cracks (including narrow, 1-3 mm width cracks, and wide, 3 mm width cracks) and wide structural cracks. Structural cracks are produced mainly by the effects of fatigue and aging, and are typically manifested as alligator cracks or block cracks, although they can also be present in the form of longitudinal cracks in an early phase of deterioration and are usually located in the wheel path zone.

These models are adjusted to a particular region or country by varying the values of calibration factors

*Author for correspondence (email hsolmini @ing.puc.cl)

for each distress type, in order that the models may represent pavements' real performance as closely as possible. This increases predictive capability of both the models as well as the possibility of conducting an efficient highway management process.

The present studies are aimed at proposing performance model calibration recommendations and establishing the most suitable and adequate calibration factors for HDM-4 version 1.1 structural cracking models for asphalt pavements in Chile, according to specific characteristics of the road(s) to be evaluated4

. In addition, this work compares these results with those obtained in the HOM-III cracking models5

. The methodology presented here is suitable for calibrating the HDM-4 to local conditions.

Experimental Calibration methodology

In order to calibrate a pavement performance model, it is necessary to have a group of distress data that represents the real performance curve, preferably data covering a relatively long period of time. The calibration process consists of determining which adjustment factors (k;) achieve the best agreement between the model ' s predictions and the field data6

-8

.

Among the calibration methodologies employed in previous studies9

-11

, the "test sections" or "film"

194 INDIAN J. ENG. MATER. SCI., JUNE 2003

method and the "windows" method are known. The "windows" methodologi has been used here as it offers the possibility of both relying upon a broader inference space and of integrating data gathered in previous studies with new data. Moreover, this methodology permits section distress measurements to be made in a brief period of time, and consequently a greater number of sections and categories can be evaluated. This is a major advantage of the "windows" method, because the "test sections" calibration methodology makes it necessary to continue measuring data for each selected section for an extended period of time in order to obtain reliable predictive data. In a previous study 12

, this "windows" methodology was compared with more traditional methods (using "test sections", which had been followed up during several years) and the results were statistically comparable.

In terms of methodology application, the first step is to define homogeneous road sections according to their most representative variables (structure, traffic, geometry and climate). Each of these sections is then considered a "window" m the pavement' s performance curve, and together with other "windows" (or similar individual sections), they represent that particular pavement's performance 12

•

If sections in a chosen "window" have different ages, one may obtain the performance curves for different distress types. In the same model, these curves should present relatively similar trends over the years. Performance data obtained from observations may then be compared with data obtained through modelling. The methodology enables one to calibrate the different models through the use of k; 12

• For another group of sections or "windows" with different characteristics, the data should present different trends, which will in turn modify the obtained k; values when performing the calibration (Fig. 1).

Each group of sections or "windows" that is uniform with respect to its representative variables is called a "category". Each category that is present in the practical application of this methodology will

. k f 12 possess Its own ; actors .

Design of the experiment's factorial

The equations for the structural cracking models in HDM-4 are referred in five models 13

: (i) The initiation model of all structural cracking for original surfacing and unbound granular materials (/CAs), (ii) the

initiation model of all structural cracking for overlay or reseals (ICA0 ), (iii) the initiation model of wide structural cracking (/CW), (iv) the progression model of all structural cracking (dACA), and (v) the progression model of wide structural cracking (dACW).

The components of these models are shown in the Eqs (1)-(5) 11

:

ICA, =

Kcia [ CDS2a0 exp(a,SNP+~YE4/SNP2 )+CRT] (1)

l [ [a exp(a,SNP+ a,YE4 /SNP2

) ]] ) CDS2 MAX o - +CRT

MAX (1- PCRW I a,,O),a4 HSNEW

(2)

(3)

... (4)

dACW = Kcpw ( CRP I CDS)Zw

[ ( ZwaA8tw + SCW"' )' ta, - SCW J ... (5)

where, the variables are: a1 (Coefficients for structural cracking models), ACAa. ACWa (Area of all and wide structural cracking at the beginning of the analysis

Calibratton for pavements type "A"

--Calibrated Model

"WINDOWS" Methodolo

-- Calibrated Model

Fig. !-Evaluated calibration methodology

SOLMINrHAC eta/.: CALIBRATION OF STRUCTURAL CRACKING MODELS FOR ASPHALT PAVEMENTS 195

year, respectively), CDS (Construction defects indicator for bituminous surfacings), CRT (Crack retardation time due to maintenance), CRP (Retardation of cracking progression due to preventative treatment, CRP = l-O.l2CRD. dACA, dACW [Incremental change in area of all and wide structural cracking during the analysis year (% of total carriageway area), respectively] , 8 ta. 8 tw (Fraction of analysis year in which all and wide structural cracking progression applies, respectively}, HSNEW [Thickness of the most recent surfacing (mm)], ICA, ICW [Time of initiation of all and wide structural cracks (years), respectively], K cia. Kc;w [Calibration factor for initiation of all and wide structural cracking, respectively], K cpm Kpw [Calibration factor for progression of all and wide structural cracking, respectively], PCRW [Area of wide cracking before latest reseal or overlay (% of total carriageway area)], SCAa [MAX (ACAa. 100- ACAa); if ACAa>0,5 MAX (SCAa, 0,5)], SCWa [MAX (ACWa, 100 - ACWa); if ACWa>0,5 MAX (SCWa, 0,5)], SNP (Average annual adjusted structural number of the pavement), Y£4 [Annual number of equivalent standard axles (millions/lane)], and Za. Zw (l if ACAa<50; -1 otherwise, and 1 if ACWa<50; -1 otherwise, respectively).

From the analysis of the cracking performance model equations, it is evident that a pavement's evolution over time depends fundamentally on four global variables: traffic, pavement age (calculated from the date of construction or most recent rehabilitation), dominant climatic conditions and structural capacity. These variables help define the initiation as well as progression of distress that pavements may present, as well as the interaction amongst different manifestations of damage and wear.

First, a matrix is created to select a group of roads having sufficiently similar characteristics so that a certain degree of reliability is guaranteed. This matrix is a combination of the various levels of its variables (the four previously mentioned and a fifth variable that differentiates the original structures from those that are overlaid). It defines the different road categories that compose the experiment's factorial 14

•

An effort has been made to include the largest possible number of homogeneous road sections possessing the greatest possible difference in age in each category, in order to reconstitute performance curves with the highest level of representation over time.

Once, the independent study variables (or factors) were defined, the criteria that permitted the precise determination of how many levels each variable had to be subdivided into were defined. In this manner, three traffic levels (expressed in daily equivalent axles), three levels of structural capacity (as a function of deflection in mm), three climatic zones (north, center and south) and three pavement age levels (initial, middle and final) were identified. Finally , for the variable which defines structure type, two aspects were taken into account: the structure type (original or overlaid) and the type of surface layer (asphalt mix or surface treatment) . Table 1 displays the factorial defined in the investigations,

Test sections selection methodology

Once the experiment's factorial was defined, a road section selection procedure by category was established. This procedure had to make two criteria simultaneously compatible: (a) to have a sufficient number of sections for each cell in order to get a minimum quantity of distress data for an adequate calibration of the performance prediction models; and (b) to have, whenever possible, sufficiently small ranges to ensure the greatest similarity and homogeneity of the different pavement types characteristics and thus ensure greater reliability of the calibration.

To this end, a test section selection procedure was defined based on the methodology employed in road section selections in previous studies 11

• As part of the methodology employed in this study for road section selection, the levels for traffic and structural capacity (deflection) variables were defined, with the criterion of distributing the system's roads equitably for each level (three for each variable). Next, the average weighted values were calculated for each traffic and deflections level.

Table 1-Variables of factorial

Variables Levels Types of levels

Climate 3 North , Center, South

Traffic 3 High, Medium, Low

Structural capacity 3 High, Medium, Low

Age 3 Initial , Middle, Final

Structure type 2 Original (asphalt mix or surface treatment), overla~ed

196 INDIAN J. ENG. MATER. SCI., JUNE 2003

From a total of 141 sections located throughout Chile and analyzed in this study, 65 were new sections and 76 had been included in previous studies9

-11

• Finally, only 97 sections comprising old and new sections were used to carry out the model calibration, as the aim was to satisfy the two criteria mentioned above. The present investigations deal with a total of 14 categories of sections, 5 asphalt mixes and 9 double surface treatments.

Distress measurement methodology

The data collected in the new test sections had to be as reliable as that of previous projects. It was therefore necessary to establish a measurement methodology which would define aspects covering the number of samples to be measured, to the way in which field data from each section was to be gathered. To this end, diverse statistical analyses were conducted using the data base created from road distress information submitted by the Chilean National Highway and Road Services Head Office, and complemented with information available from existing projects.

The. main objective of the measurement methodology was to obtain a sufficient number of samples to estimate average distress with an acceptable margm of error and with optimal

performance in field measurement. By means of the established measurement procedure, each sample section was composed of two kilometers and a total of 616 meters per section were measured, which constituted an excellent sample, equivalent to 31 % of the total. Visual inspections of 65 new sections located throughout Chile were conducted and the National Highway Laboratory performed roughness and deflection measurements of these sections. These data collection activities covered a period of seven months.

Statistical calibration of calibration factors k;

The procedure proposed for the statistical calibration of asphalt pavement performance models reported here is based mainly on the determination of the factors which allow a better adjustment of simulated di stress curves to real performance data by minimizing the sum of the squares of the differences (SSD) between estimated and observed data3

•11

• The ideal adjustment consists of minimizing differences to achieve the most accurate and real performance over time 15

• Minimizing the SSD value helps reduce the estimated average error, allowing one to locate the calibration factor that ensures the best adjustment of the distress curve, and thus the calibration of the analyzed performance model 16

•

Table 2-Calculated categories calibration factors for HDM-4

Surface type Region Traffic Deflection Number of Structural cracking

sections K cia Kcpa Kciw* K cpw

North Low Medium 6 1.86 0.61 1.25 0.75 South Low Medium 8 wid wid wid wid Center Low High 12 0.71 0.45 1.44 0.27 South Low High 12 1.43 1.44 0.83 0.20 Center Medium High 9 1.17 0.71 0.80 0.40

Double asphalt treatments South Medium High 9 0.83 0.87 0.75 0.42 Center Low Medium 3 wid wid wid wid Center Medium Medium 4 wid wid wid wid South Medium Medium 4 1.29 1.16 0.82 0.58

Global calibration factor 1.22 0.87 0.98 0.44 Asphalt concrete original North Medium Low 3 1.40 1.88 0.88 0.76

South High Low 6 1.00 0.33 0.80 0.22 North High Medium 8 0.60 0.30 1.00 0.55

Asphalt concrete overlaid North High Low 7 0.60 0.30 1.00 0.54 South High Medium 6 wid wid wid wid

Global calibration factor 0.73 0.31 0.93 0.44

k cia All structural cracking initiation calibration factor kt.·iw* Wide structural cracking initiation calibration factor obtained for electronic formularies ; default factor should be used

(kciw = 1)

kcpu All structural cracking progression calibration factor kcpw Wide structural cracking progression calibration factor wid Without distress data for calibration; global calibration factors should be used

SOLMINIHAC eta/. : CALIBRATION OF STRUCTURAL CRACKING MODELS FOR ASPHALT PA YEMENTS 197

Results and Discussion

Analysis of calibration factors for each category Based on the calibration models previously

described, calibration factors for the various structural cracking models were obtained, applying the "windows" technique for each of the categories. The structural cracking models contemplated by HDM-4 are all structural cracking model s as well as wide structural cracking models.

A tendency analysis of the calibration factors as a function of the average values of the factorial variables (traffic, structural capacity and climate) was carried out, distinguishing between asphalt mixes and double surface treatments. Table 2 presents the cracking models' calibration factor values for each category as well as global average values for Chile, differentiating between surface treatments and asphalt mixes.

All structural cracking model

For double surface treatments, the structural cracking initiation adjustment factors (kc;a) presented values exceeding 1.0 for the most part, with an average of 1.22, unlike the progression factor values (kcpa), thus presenting values that were mostly inferior to 1.0 with an average of 0.87 . This implies that in Chile, cracks generally appear later than predicted by the non-calibrated original HDM-4 model , and progression is slower than predicted by the model.

In the case of original asphalt mixes, both the initiation factor as well as the progression of structural cracking produced values greater than 1.0 (1.4 and 1.88, respectively), which may imply that structural cracks begin later than indicated by the non-calibrated model, whereas their progression is quicker than predicted by the model. However, as there is only one category corresponding to this surface type, it cannot be interpreted as representative of the performance of all asphalt mixes pavements in Chile.

For those asphalt mixes corresponding to overlays, the initiation and progression factors for structural cracking do not exceed 1.0 (average values of kc;a=0.73 and kcpa=0.31, respectively). This means that in Chile, asphalt overlays begin to display cracking sooner than predicted by the original uncalibrated HDM-4 model; however, the progression of these cracks is slower than predicted by the original model.

Wide structural cracking model The wide structural cracking ImtiatiOn model

proposed by HDM-4 has a wide cracking initiation

factor. The model considers that wide cracks appear only when the area affected by narrow cracks surpasses 5%, which translates into an interval of 3-4 years between the appearance of the two types of cracking. However, what has been observed in reality is that wide structural cracking in Chile begins approximately one year after structural cracking has begun, which suggests that the initiation of wide cracking occurs with a minimum percentage of narrow cracks. For this reason, it was not possible to incorporate the initiation of wide cracking when it was observed at ages preceding those predicted by the present version of HDM-4 computer program. This would indicate that the model does not adequately represent real pavement performance in Chile. Therefore, the wide cracking initiation and progression phases were simulated separately, by programming the cracking model s on an electronic spreadsheet. These adjustments allowed for a more accurate prediction of the age of appearance of wide structural cracking, and to calibrate progression beginning with the year in which this type of distress was observed. This is illustrated in Fig. 2, which corresponds to a typical category in Chile. In thi s figure, the curve predicted by the HDM-4 model is the segmented line, while the continuous line indicates that the current research ' s adapted curve adjusts most closely to observed conditions.

The factors proposed in Table 2 were those obtained by programming the HDM-4 equations for this type of distress in an electronic spreadsheet, as in this way the pavement's performance drew closer to field observations. The proposed factors kciw are the uncalibrated model's predicted adjustment what was

100 ,------------------,

90

80 .. /

/

70 / .. 60

50 I 40

I 30

20 J. 10 /

0

0 2 4 6 8 10 12 14 16 18 20

AGE(YEARS)

· Curve predic1ed by HDM-4 model --Curve adap1ed to the observed conditions

4 Observed Da1as

Fig. 2-Curve predicted by HDM-4 model vs. curve calibrated to the observed conditions

I98 INDIAN J. ENG. MATER. SCI. , JUNE 2003

actually observed in the Chilean asphalt pavements with values that in general do not exceed I, and an average of 0.98 for double surface treatments and 0.92 for asphalt mixes (original and overlaid, respectively), which would imply that wide cracks are beginning to appear earlier than is indicated by the uncalibrated model. A precaution to be kept in mind is that the proposed factor kciw will only be valid if the HDM-4 model changed the wide cracking initiation moment when this moment varies; however, the HDM-4 program as such does not change the pavement's performance when different values of the factor kc;w are introduced, and therefore, it is recommended to use the default factor of I . The resulting values for the wide cracking progression factors (kcpw) were all less than I with an average value of 0.44 for double surface treatments and 0.52 for asphalt mixes (original and resurfaced), meaning that progression of this type of cracking in pavements in Chile is significantly slower than the original model predicts.

A significant correlation was found between the variables used in the analysis (traffic, structural capacity and climate) and the cracking model 's progression factor for all structural cracking in double surface treatments. Thi s factor's value increases as the climate's severity intensifies. Similarly, it was found that the asphalt mixes wide structural cracking progression factor increases as the pavement's structural capacity diminishes. Unfortunately, this significant correlation was not found in the other calibration factors obtained for the cracki ng models. Nevertheless, as the number of categories is relatively small, it cannot be stated that the explanatory variables have in fact a significant influence on these factors. It is therefore reasonable to use an average value for all cracking adjustment factors , independent of the traffic, structural capacity and climate variables for Chilean conditions. This means that the explanatory variables would be adequately incorporated into the HDM-4 equations that predict superficial distress, corroborating the model's soundness.

Verification of prediction quality

To verify prediction quality, observed vaiues for each one of the structural cracking models were compared to values predicted using the calibration factors. Comparisons were made at two levels: using the recommended calibration factor for each category

and employing the generalized average factor. To do so, the statistical indicators in Eqs (6) and (7) were used as comparison models 11

:

R2 = 1-(L( Yesti-Yobsi JL( Yobsi - Y m/)

AE = [L( Yesti- Yobsd2/(N-1 )]05

(6) (7)

where, AE represents average error (average difference between observed and predicted values), N is the number of observations, R2 the correlation coefficient, Yesti represents predicted values, Ym are the mean value of the observations, Yobsi the observed values.

The results obtained using each category's own factors show significant correlation values for the different models (R2 over 0 .5). The AE values for each distress type are within the limits applicable to such measurements . Fig. 3 compares the calibrated and

tOOr-----------------------------~~

~ 80

'0

{:l 60 '0

i" 0..

"' c >< 40 :;: u <(

20

0

·~ 60 '0 ., a: "' 60 ~ u .. 40 :;

~ ~ 20

~

0

R2 = 0.85

AE = 6.28%

(a)

20 40 60 80

All Cracking Observed (%)

t:. Double Treatment --- Equality Line ---All Cracks ·AE

R2 = 0.81 AE = 6.22%

20 40

• Asphalt Concrete • · • • · ·All Cracks + AE

(b)

60 80 Wide Structural Cracks Observed(%)

t:. Double Treatment ---Equality Line - - -Wide Cracks • AE

• Asphalt ConCfete · · • · • ·wide Cracks + AE

100

100

Fig. 3-Yerification of prediction quality for cracking models using calibration factor for each category

SOLMINIHAC et al.: CALIBRATION OF STRUCTURAL CRACKING MODELS FOR ASPHALT PAVEMENTS 199

100

R2 = 0.38 .·

80 AE = 12.65% .·

~ .· " "' ~60 I'! a. .· C> c: :g 40 :!!

.· (a)

0

<( .·· . 20

0

0 20 40 60 80 All Cracking Observed(%)

l!. Double Treatment • Asphalt Concrete --Equality Line

• · . · · All Cracks + AE - - -All Cracks • AE

100.---------------------------~--~

~ 80

il u 'g 60 ii: C> c: :g 40 :!! 0

"' ~ 20

R2 = 0.08

AE = 13.72%

(b)

-0 .. ~~~------~----~------~----~

100

0 20 40 60 80 100 Wide Cracking Observed(%)

l!. Double Treatment • Asphalt Concrete --Equality Line

· · · • · Wide Cracks + AE - - - Wtde Cracks - AE

Fig. 4-Verification of prediction quality for cracking models usi ng calibration generalized middle factor

observed values for all the structural cracking and wide structural cracking models, indicating the line of uniformity and an equidistant band of ±A E. The figure illustrates that the majority of results fall within this band with a clear tendency to move towards the center, which means that prediction is satisfactory in the majority of observations.

When performing the evaluation usmg the generalized average factors, lower correlation levels than the previous case were obtained, which was to be expected and also quite logical, since these average factors do not minimize the estimation errors in each category. However, AE does not increase considerably in relation to the resulting average error when usi ng the differentiated factors belonging to each road category. Fig. 4 compares the observed and predicted values using the generalized average factors

Table 3- Calculated calibration factors for HDM-III

Surface type Structural cracking

Double asphalt treatments

Asphalt concrete (original and overlayed)

1.10

0.61

0.86

0.56

Table 4-Average prediction errors using different types of calibration factors

Models HDM-III HDM-4

AEtc (%) A£18 (%) AEtc (%) A£18 (%)

All structural cracking

6.25 13.98 6.28 12.65

Wide structural 7.10 17.01 6.22 13.72

cracking

A£1c average error in distress prediction using factors for categories, in pur:entage of total carriageway area

AEr~ average error in distress prediction using global factors , in percentage of total carriageway area

for all structural cracking and wide structural cracking models.

Comparison of the calibration factors for HDM-4 and HDM-lll

The HDM-IIl cracking models factors, that is, the cracking initiation factor kc;. and the cracking progression factor kcp• which had been calibrated for Chilean conditions in previous studies 11

, were also recalibrated in this study. The average results obtained for the HDM-III cracking models are shown in Table 3.

A tendency is evident for both the HDM-4 and HDM-IIl crack initiation models to have calibration factors greater than 1.0, and for the crack progression models to have calibration factors less than 1.0. This indicates that the calibrated models in both HDM-4 and HDM-lll predict crack initiation and slower crack progression later than the uncalibrated models . It is also possible to observe a tendency for asphalt mixes, in which cracking initiation begins earlier than predicted by the uncalibrated models (kc; and kcia <1 ) and progression is slower than predicted by the model (k,P and kcpa <1). This tendency occurs mainly because the relationships of the HDM-4 models are derived from those in the HOM-III models, and generally they do not present substantial differences. However, it was noted that although there is no significant difference between the values observed for kc; for original and overlaid asphalt mixes in the HDM-III cracking initiation model , there is a considerable difference in the HDM-4 models.

200 INDIAN J. ENG. MATER. SCI., JUNE 2003

With respect to the prediction quality of all cracking HDM-4 and HOM-III models when using the calibration factors of each category, correlation levels are very similar, as is the average error of the estimation, as shown in Table 4. Calculations were done with the already calibrated initiation and progression models , both for original and overlaid asphalt concrete.

With the generalized average factors , the evaluation using the HOM-4 model showed a lower estimation error and a higher correlation coefficient which implies that this model's average calibration factors predict the observed reality of Chilean asphalt pavements more accurately. However, in the case of wide structural cracking models, when comparing correlation levels obtained with HOM-4 and HOM-III (if the HDM-4 model could consider the initiation factor for this distress type to represent Chilean pavement performance), a weaker correlation of the HOM-III model is noted due to the fact that it does not have its own calibration factors, unlike the HOM-4 model. This is a great advantage of the latter model. However, ievels of correlation and error in the HOM-III model are quite acceptable in this case. So, it may be deduced that the HDM-III all structural cracking model calibration factors are correctly predicting both the initiation and progression of wide cracking. In the case of generalized average factors, a greater difference is noted between the average error predicted by the HDM-4 and the HOM-Ill models, as the HDM-4 is more accurate in representing the observed reality of pavement cracking in Chile. Moreover, this difference is predictable since the HDM-III wide cracking model does not have its own adjustment factors.

Conclusions The "windows" methodology allows a more global

vision of pavement distress since it is not limited to the study of any one pavement in particular. Also, it allows the evaluation of a large number of sections in a short period of time thus amplifying the calibration's inference space.

Calibration factors (as shown in Table 2) are recommended for Chile so that if characteristics of the road to be evaluated are known, the factors of the category to which the road belongs can be used. In case the road to be evaluated does not belong to any of the categories analyzed, it is suggested that the global average value obtained for each of the cracking

calibration factors be used as it provides equally satisfactory results in distress estimation.

As the results of the HDM-4 cracking model adjustment factors are as satisfactory as their HOM-III equivalents, it is recommended to adopt the HOM-4 models in the near future, given the enormous advantages that thi s new HOM version offers. The change should involve the implementation and utilization of this tool in the various regional offices of the Chilean National Road Administration. However, more extensive studies of the relationships that determine the initiation of wide structural cracking are recommended as the available model does not adequately represent Chilean reality due to the impossibility of changing the initiation of wide cracking at the early stages of the appearance of this distress.

Finally, the continued study of HDM-4 models is recommended in order to validate results obtained in the present investigations, allowing expansion of the inference space of the sections considered for the study, so that the models may be adapted to a greater quantity of pavement categories.

Acknowledgements We are grateful to the National Road

Administration of the Ministry of Public Works of Chile, and to DICTUC of the Pontifical Catholic University of Chile, for the technical and economic support granted through the research project "Follow­up to the Calibration of Distress Models for Asphalt Pavements."

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SOLMINIHAC eta/.: CALIBRATION OF STRUCTURAL CRACKING MODELS FOR ASPHALT PAVEMENTS 201

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