A Network-Level Methodology for Evaluating the Hydraulic Quality Index of Road Pavement Surfaces

Abstract

Traffic loads and environmental factors cause various forms of distress on road pavements (cracks, depressions, potholes, ruts, etc.). Depressions and ruts produce localized variations of longitudinal and cross slopes, which are very hazardous for drivers, especially during rain. In such conditions, these defects alter the surface water path, creating abnormal water accumulations and significant water film depths to induce aquaplaning risk. In current practice, in preliminary analysis phases and at the network scale, the control of road surfaces is carried out with expeditious techniques and with synthetic indicators, e.g., pavement condition index (PCI), through which a quality judgment related to the detected distresses on the pavement surface, is given. In truth, the detection of specific defects (ruts and depressions) should also include further analyses to evaluate the hydraulic efficiency of the carriageway related to their severity. Therefore, in this paper, a synthetic indicator called Hydraulic Condition Index (HCI) is proposed for evaluating the hydraulic quality of road pavement surfaces. This index is related to the hydrologic conditions of the site, the pavement characteristics, and the defects that can alter the flow of water on the carriageway, determining and increasing the risk of aquaplaning. The methodological framework is discussed by means of some numerical applications developed for different road typologies according to their functional classification. The final aim is to provide road agencies with another solution to evaluate road quality and ensure safer roads for users. The methodological framework for evaluating the HCI may be adopted by the road agencies for the network-scale priority ranking of road segments maintenance needs also involving safety traffic conditions.

1. Introduction

The deformations and irregularities of the road surface, localised and widespread, are very hazardous defects for drivers’ safety. With time, depending on their severity and density, the carriageway can undergo significant changes of its 3D conformation with consequential effects on the vehicle–road interaction, especially in critical environmental conditions.

During rain, the longitudinal and transversal irregularities, beyond modifying the drainage path of the surface water, form potentially dangerous puddles that can cause high risks for drivers and even aquaplaning [1,2]. The phenomenon of aquaplaning occurs when the water film depth (WFD) is such that the wheels lose contact with the pavement; thus, the vehicle “floats” with a complete loss of control. Aquaplaning is a very complex phenomenon and depends on numerous variables, e.g., length of flooded sections, speed, road surface texture, pressure and condition of tires, wheel loads, etc. [3,4]. When aquaplaning occurs, the accident risk becomes very high, and the consequences for drivers can be severe. The critical aquaplaning speed is a fundamental index for road safety evaluation and is strongly associated with the drainage capacity of the pavement [4]. Of course, porous pavements may ensure benefits in terms of surface water drainage [5] when properly designed, but they require appropriate and frequent maintenance activities to guarantee their draining properties [6].

According to Lee et al. [7], the influencing factors for this phenomenon can also be grouped into four macro categories: (1) roadway and pavement parameters, (2) environmental factors, (3) driving factors, and (4) vehicle factors, as shown in

Table 1. Classification of factors influencing aquaplaning according to Lee et al. [7].

(1) Roadway and Pavement Parameters	(2) Environmental Factors	(3) Driving Factors	(4) Vehicle Factors
- Surface type - Ruth depth - Permeability surface - Micro and macro texture - Cross-slope - Longitudinal grade - Pavement width - Roadway bends - Depressions	- Rainfall intensity and duration - Temperatures	- Speed - Acceleration or braking - Steering maneuvers	- Tire tread design - Tire tread wear - Tire pressure - Vehicle or axle weight

:

Given the importance of the phenomenon, there are numerous models in the literature to predict the speed of aquaplaning and the depth of the water film based on both empirical relationships and analytical studies [8,9,10]. Some of the most commonly used relationships to evaluate WFD and aquaplaning initiation speed are shown below in

Table 2. Main experimental reports in the literature on the evaluation of the initiation speed of aquaplaning.

Author	Formula
Gallaway et al. [11]	${\mathrm{V}}_{\mathrm{P}}={\mathrm{SD}}^{0.04}{\ast \mathrm{p}}^{0.3}\ast {\left(\mathrm{TD}+1\right)}^{0.06}\ast \mathrm{A}$	(1)
Agrawal et al. [12]	${\mathrm{V}}_{\mathrm{P}}=33.7+5.28{\ast \mathrm{WFD}}^{-0.5}$	(2)
Agrawal et al. [12]	${\mathrm{V}}_{\mathrm{P}}=26.04{\ast \mathrm{WFD}}^{-0.259}$	(3)
NASA-modified equation [13]	${\mathrm{V}}_{\mathrm{P}}=10.35{\ast \mathrm{p}}^{0.5}$	(4)
Gengebach [14]	${\mathrm{V}}_{\mathrm{P}}=508\ast {\left(\frac{\mathrm{Q}}{\mathrm{B}}{\ast \mathrm{WFD}\ast \mathrm{C}}_{\mathrm{H}}\right)}^{0.5}$	(5)

Legend of the above equations: ${\mathrm{V}}_{\mathrm{P}}$—start speed of aquaplaning, SD—spin down, P—inflation pressure, TD—depth of the tire tread grooves, A—maximum$\left\{[(\frac{10.409}{{\mathrm{WFD}}^{0.06}}+3.507)];[(\frac{28.952}{{\mathrm{WFD}}^{0.06}}-7.817){\ast \mathrm{TXD}}^{0.14}]\right\}$, TXD—texture depth, Q—wheel load, B—length of the tire contact patch, ${\mathrm{C}}_{\mathrm{H}}$—coefficient of lift of the tire.

and

Table 3. Main literature models for the evaluation of the water film depth.

Empirical Models	Formula
RLL method [15]	$\mathrm{WFD}=0.046\ast \frac{{\left(\mathrm{L}\ast \mathrm{In}\right)}^{0.5}}{{\mathrm{S}}^{0.2}}$	(6)
Equation Modified New Zealand [9]	$\mathrm{WFD}=\frac{0.0502{\ast \mathrm{L}}^{0.3168}{\ast \mathrm{In}}^{0.2712}}{{\mathrm{S}}^{0.3}}-\mathrm{TXD}$	(7)
PAVDRN model [16]	$\mathrm{WFD}=\frac{0.00372{\ast \mathrm{L}}^{0.519}{\ast \mathrm{In}}^{0.562}{\ast \mathrm{TXD}}^{0.125}}{{\mathrm{S}}^{0.364}}-\mathrm{TXD}$	(8)
Gallaway [11]	$\mathrm{WFD}=0.01485\ast \frac{{\mathrm{L}}^{0.43}{\ast \mathrm{In}}^{0.59}{\ast \mathrm{TXD}}^{0.11}}{{\mathrm{S}}^{0.42}}-\mathrm{TXD}$	(9)
Analytical Models	Formula
PAVDRN model [16]	$\mathrm{WFD}=\frac{\mathrm{n}\ast \mathrm{L}\ast \mathrm{In}}{36.1{\ast \mathrm{S}}^{0.5}}-\mathrm{TXD}$	(10)

Legend of the above equations: WFD—water film depth, L—length of the drainage path, In—intensity of rain, S—slope of the drainage path, TXD—texture depth, N—Manning coefficient.

.

The above equations were verified and compared by Huebner et al. [17] to study the effects of dynamic aquaplaning in relation to the numerous involved variables, looking for the exact moment when aquaplaning begins. More recent studies have shown how the speed of aquaplaning is also closely linked to some uncertain factors, such as the driver’s driving behaviour, lighting levels, environmental conditions, and visibility during rain events. Furthermore, the availability of state-of-the-art equipment and technologies is leading to the definition of critical aquaplaning thresholds and increasingly reliable predictive methodologies [18].

From the previous equations, however, it can be seen that WFD also depends on pavement surface conditions (such as roughness and texture), the geometry of the road, and the meteorological conditions [3,19]. Therefore, these factors must also be properly estimated and assessed in order to evaluate WFD on the pavement surface [4]. The conditions generally depend on five factors: rainfall intensity, texture, pavement structure, cross slope, and longitudinal slope [20,21].

In particular, Luo et al. [21] carried out a sensitivity analysis on some of the surface WFD prediction methods, such as the Gallaway’s method, the modified New Zealand method, the empirical PAVDRN method, and the analytical PAVDRN method. Their results show that the Gallaway’s model, followed by the analytical PAVDRN model, is the most sensitive to variations in rainfall intensity and cross slope; on the sensitivity in detecting variations in texture depth, there are no obvious distinctions. The analytical PAVDRN is the most sensitive method for detecting the variations in the longitudinal slope. Furthermore, Ong et al. [22] have developed a finite element model describing the aquaplaning phenomenon as the conditions of the microtextures of the road pavement and variations in tire pressure. They demonstrated how microtextures of the order of 0.2 ÷ 0.5 mm increase the triggering speed of aquaplaning up to 20%, reducing the likelihood of accidents.

Important results have been obtained by Ong et al. [23] that reconstructed the trigger conditions of the phenomenon under different scenarios and for specific boundary conditions, using 3D finite element models. They based their model on solid mechanics and fluid dynamics, verifying the reduction in skid resistance on wet pavement as vehicle speed increases. These authors also provided important considerations on the dependence of the aquaplaning speed on the WFD, as the conditions of the inflation pressures and loads on the wheel. In another study, Ong et al. [24] instead focused on the influence of the tire tread grooves on the aquaplaning conditions. They developed an analytical approach to evaluate the tire slipping process in wet conditions as a function of two different types of tread grooves (transverse and longitudinal) for a fixed conditions side dish.

Later, Gunaratne et al. [18] used the graphs derived by Ong et al. [24] to develop a revised version of the models existing in the literature to determine the aquaplaning speed and WFD. The authors showed that the speed reduction in rainy weather depends not only on the intensity of the precipitation but also on the instantaneous traffic volume and that the critical WFD varies according to the different geometric conditions of the road, such as straight sections, superelevation, and transition sections.

Fwa et al. [25] presented an analytical study aiming to quantitatively characterise the influence of different tread patterns and groove depths on the behaviour of vehicles under aquaplaning conditions. Cerezo et al. [3] proposed a simplified approach for the assessment of critical aquaplaning conditions, taking into account the variation of the characteristics of the infrastructure, the depth of the water film, the load transfer between the rear and front wheels of the vehicle, the resistance to skidding and the intensity of the rain. Chu et al. [26] proposed a theoretical finite element simulation model to quantitatively characterise the influence of different tread patterns and groove depths on the aquaplaning phenomenon. In their studies, Luo et al. [27] and Luo et al. [21] have defined a new model on the basis of both empirical and analytical methods, trying to overcome some of the limitations of the already existing methods; they simulated the dynamics of runoff formation on the pavement surface and calculated the water film by combining the rain factors with the permeability of the material, the texture, and the geometry of the road. Luo et al. [28], based on previous studies, simulated the flow dynamics even in the presence of grooves using high-resolution 3D point clouds in order to verify the accumulation of water within the furrows and ensure the use of effective corrective measures to reduce the potential risk of aquaplaning and minimise the accident rate. Alber et al. [29] proposed a modular hydromechanical approach to evaluate the short- and long-term surface drainage behaviour of flexible pavements, consisting of three phases: experimental materials testing, finite element modelling of long-term structural deformation, and modelling of surface drainage.

From these models, it can be deduced that they mainly concern detailed analyses, which can be conducted only if precise and timely data on the conditions of the pavement, as well as specific rainfall data, are available. In fact, from the literature review, it is evident that there are no quick methods that can qualitatively (and also quantitatively) define the conditions in which a road pavement—with specific distresses—is found during rainy events, which is useful for preliminary analyses at a network level.

Considering the effects of distresses on road safety, the presence of depressions on the road surface is closely linked to the driving safety of users, although there is no clear and defined relationship between the depth of ruts and road accidents [30]. The depressions interrupt the natural flow path of the water, generating situations of potential danger for users, which are difficult to predict. Since the beginning of the 1970s, several researchers have conducted experimental tests to verify the depression depth that could cause the phenomenon of aquaplaning and, therefore, loss of slip resistance. Barksdale [31] and later Lister et al. [32] have discovered, through load tests on flexible pavements, that in the grooves with a depth of about 0.5 inches (12.7 mm), the accumulation of water is sufficient to cause the vehicles to lose resistance at speeds above 50 km/h. Balmer et al. [33] showed how the aquaplaning phenomenon could occur when the transverse slopes are less than 2.5%, and the depression depth is ≤0.61 cm; moreover, adequate values of the transversal slopes and sufficiently large values of the longitudinal slopes avoid excessive stagnation of water with possible triggering of aquaplaning. On the basis of these assumptions, the authors define an admissible limit depth of the depression to avoid stagnation of water, considering a minimum transversal slope useful to favour a good drainage capacity equal to 0.5% and with a width of the depression equal to 60 cm.

Sousa et al. [34] claimed that for groove depths exceeding 0.2 inches (5.1 mm), aquaplaning is a real threat to users. Hicks et al. [35] have adopted the following three levels of gravity for the ruts based on the aquaplaning phenomenon:

-

Low gravity: The depression depth is less than 6 mm. Problems with aquaplaning and accidents in the wet are unlikely;

-

Moderate gravity: The depression depth is between 7 and 12 mm. An inadequate cross slope can cause aquaplaning and accidents in rainy weather;

-

High gravity: The depression depth is greater than 13 mm. The likelihood of aquaplaning and accidents in the wet is very high.

Fwa et al. [30] instead defined an analytical procedure to assess the severity of the depression on the basis of the analysis of the braking distance, establishing five critical depth thresholds between 5 mm and 25 mm. Yan et al. [1] studied the influence of the variation of lateral slopes on the depth of the water-filled valley and how the slopes affect the aquaplaning phenomenon. The Unified Facilities Criteria (UFC) of the United States Department of Defense [36] defined, in the presence of ruts, three different levels of risk as a function of their depth, as shown in

Table 4. Severity levels for pavements with rutting according to the UFC, 2001.

Severity	All Pavement Sections
Low	≤1/4 to 1/2 inch (≤6.4 to 12.7 mm)
Medium	>1/2 inch ≤ 1 inch (>12.7 mm ≤ 25.4 mm)
High	>1 inch (>25.4 mm)

.

It is noted that despite the common understanding by researchers that aquaplaning and the loss of slip resistance during rainy events should form the basis for the classification of the severity of depression and consequently for better management of road maintenance, there are no specific quantitative guidelines useful for establishing thresholds to assign the severity levels of ruts in relation to the aquaplaning phenomenon [30].

From the presented literature, it is evident that there is a lack of a quick and simplified methodology that takes into account distress characteristics with hydraulic hazard conditions for road maintenance purposes. In this regard, in this paper, a methodology is proposed for evaluating the hydraulic priority class of road pavement surfaces, considering degradation and hydraulic conditions, useful for network-scale analyses [37,38]. For this aim, this paper proposes a synthetic indicator, called Hydraulic Condition Index (HCI), of the defects that can alter the flow of water on the carriageway and create the risk of aquaplaning, considering the hydrological features of the area and the geometric characteristics of the platform. This index may be helpful to road agencies in the road maintenance planning phases to identify the most urgent interventions with regard to safety conditions.

2. Proposed Methodology

During rain, irregularities on the pavement surface can cause critical water accumulations and paddles, compromising the friction conditions of the pavement and increasing the probability of accidents. This may lead to considerable increases in the risk of aquaplaning, leading to an overestimation of the phenomenon trigger speed [39,40].

The authors aim to define a synthetic and simplified approach for the preliminary management phases of the road maintenance processes, to perform a qualitative evaluation of the hydraulic conditions of road pavements with depressions and ruts. The objective is to support road administrators with a preliminary estimation and selection of the hydraulic classes of road segments useful in determining the investigation and analysis priority rankings of maintenance needs at a network level in the first phase of analyses [37].

In this regard, a synthetic indicator, named Hydraulic Condition Index (HCI), was proposed. This index, presented in Equation (11), was defined by combining two parameters:

-

Hydraulic coefficient (CH), depending on the geometric characteristics of the pavement, on the intensity of rain and, thus, on the return period, and the texture characteristics, described in terms of TXD;

-

Physical coefficient (CP), related to the severity of irregularities and their extension with respect to the area of the analysis.

$$\mathrm{HCI}=100-\left(\mathrm{CH}·\mathrm{CP}\right)$$

(11)

The HCI has to be evaluated for each homogeneous hydraulic segment, i.e., for each portion of the road pavement with constant values of slope and grade, with homogeneous texture features, determining a closed system in terms of water runoff. The area of the homogeneous hydraulic segment is indicated with A_h.

In detail, for the i-th segment, the hydraulic coefficient CH_i is given in Equation (12), in which:

-

V_pi is the aquaplaning speed for a fixed return period T_x (as a function of slope, s, and drainage path, L);

-

V_l is the legal speed, depending on the maximum allowable speed for the selected road during rain;

-

TXD_i is the measured texture depth on the selected segment;

-

TXD_ref is a fixed value of the texture depth, assumed as a reference for the considered network;

-

k is a numerical coefficient calibrated as a function of the road classification and its relevance.

$${\mathrm{CH}}_{\mathrm{i}}=\frac{{\mathrm{V}}_{\mathrm{l}}}{{\mathrm{V}}_{\mathrm{pi}}}{\left(\frac{{\mathrm{TXD}}_{\mathrm{ref}}}{{\mathrm{TXD}}_{\mathrm{i}}}\right)}^{\mathrm{k}}$$

(12)

The equations for WFD and V_p calculations can be derived from literature, for example, considering those defined by Gallaway (Equations (1) and (9)).

The physical coefficient CP_i of the i-th segment (Equation (13)) was defined to take into account the pavement distresses.

$${\mathrm{CP}}_{\mathrm{i}}={{\displaystyle \sum }}_{\mathrm{j}}{\mathrm{w}}_{\mathrm{ji}}{\ast \mathrm{d}}_{\mathrm{ji}}={{\displaystyle \sum }}_{\mathrm{j}}\frac{{\mathrm{RD}}_{\mathrm{ji}}}{{\mathrm{RD}}_{\max }}\frac{{\mathrm{A}}_{\mathrm{ji}}}{{\mathrm{A}}_{\mathrm{ref}}}$$

(13)

In Equation (13), w_ji and d_ji represent respectively some weights obtained from the ratio of the j-th rut (or depression) depth RDji to the maximum allowable depth for the selected road type (RD_max) and the extension of the j-th rut (A_ji) to the reference area of the road segment (A_ref). A_ref should be evaluated according also to the number of lanes (nl) and the traffic flow directions (fd)—single or both directions. In the case of single-direction flow, A_ref is equal to A_hi divided by nl. In the case of the flow in both directions, A_ref is equal to A_hi.

For the values of RD_max, reference can be made, for example, to the values listed in Table 4, by defining appropriate thresholds for each road functional class.

The overall procedural scheme for calculating the HCI of a generic road segment is shown in Figure 1.

The proposed procedure is highly dependent on the information relating to the geometry of the road platform and the alignment, as well as on the characteristics of the eventual distresses (typology, extension, and severity) [41,42], resulting from condition surveys of the pavements, nowadays available with modern high-performance survey systems [21,27,43,44]. This information must, however, be contextualised to the selected road segments, considering, for example, the choice of homogeneous sections associated with the type of road, as well as the evaluation of the hydraulic conditions of the site. For this, some general criteria useful for calculating the HCI have been defined and provided in the following, even for performing some numerical examples presented in Section 3.

One of the most delicate aspects of data processing is the choice of sections with homogeneous hydraulic characteristics (Ah_i, relative to the geometrical configuration, the pavement typology, and the surface drainage systems. In this regard, a subdivision criterion should be associated with the planimetric and altimetric configuration of the road by separating both the different geometric elements of the horizontal alignment (straights and curves) and the different grades in the road profile. Therefore, as anticipated, complete and reliable knowledge of 3D road geometry is strongly recommended and may be obtained through modern mobile mapping systems. The identification of the homogeneous sections and their succession is required for the identification of the hydraulic parameter of each section and the related boundary conditions involved in the WFD and V_p equations.

For the evaluation of the hydraulic coefficients, and therefore of the WFD, it is necessary to establish some basic hydraulic parameters, such as the return period (T_x) and the intensity of rain (In). In this regard, the rainfall intensity–duration–frequency curves can help the analysts in forecasting rainfall during specific rain durations, relying on historical local rainfall data. These curves may be used to estimate, in a synthetic way, for a fixed location, a fixed return period, and a given duration of rain, the information relating to the maximum rainfall. It is obvious that, consequently, the selection of the homogeneous sections also has to take into account the hydrological homogeneity of the different areas.

The functional classification of the selected road is also strategic for performing correct analysis. The reference values for TXD and the k parameter may be properly tuned by the road agencies for enhancing the model sensitivity and fitting the index to the expected attention class criteria for ranking purposes at the network level, according to the aim of the proposed indicator. A reference value for TXD could be assumed equal to 1.0 mm, considering an acceptable texture depth for average maintained asphalt roads. The k parameter may vary in a range optimised by the road agency according to the network features. In the following numerical example, it was tuned for each specific road category to give relevance to the expected maintenance quality of each road functional class; the higher the functional classification of the road, the higher the influence of the texture amplifier parameter. For further deepening this preliminary evaluation, a sensitivity analysis for the k parameter was performed.

The last step of the procedure regards the analysis of the surface distresses that may influence the proper runoff drainage and, thus, the overall safety. Moreover, the traditional formulations are generally defined for standard scenarios, with no distresses. Then, in this procedure, the CP values were specifically defined and involved. In particular, precautionarily, neglecting the effects of distresses (such as cracks) that may reduce WFD values may be convenient. On the contrary, the analysis should take into account distresses (such as ruts and depressions) that may represent anomalous water accumulation areas and are critical for safety.

In this regard, for example, in literature, there are specific depth ranges to refer to for assessing the level of severity of the damage related to the type of road. These ranges may be used to fix the maximum allowable depth of the irregularities (RD_max), considering different threshold reference values for different road categories.

3. Numerical Applications and Discussions

In order to preliminary test the procedure, some numerical simulations based on different scenarios were performed. All the simulations were performed by using some original spreadsheets specifically developed for the numerical experiments. In detail, the various scenarios regarding to the different road types, road platforms, and pavement conditions were developed. Consequently, the adopted variables are listed in the following:

• Road typology: A—motorway (autostrada), C—secondary highway (extraurbana secondaria), and F—local rural road (locale), classified according to the Italian Standards (MIT, 2001) [45];
• Density and severity of ruts and depressions (low, medium, and high);
• TXD (fine, medium, and coarse).

According to the road typology, the following variables were fixed (beyond TXD_ref, which was fixed at 1.0 mm for all cases):

-

k = 1.7 (road type A), k = 1.5 (C), and k = 1.3 (F);

-

RD_max = 12 mm (A), 15 mm (C), and 20 mm (F);

-

Speed limit during rain, V_l = 110 km/h (A), V_l = 70 km/h (C), and V_l = 50 km/h (F).

For all the road types, the following geometrical and structural parameters were fixed:

• Traditional asphalt pavements;
• Length of the homogeneous hydraulic segment, L_s (125 m);
• Width of the hydraulic carriageway, w (varying with the road section);
• Grade (2.1%);
• Slope (2.5%).

To perform the calculation of the critical aquaplaning speed, through Gallaway’s Equation, the following parameters related to the conditions of a reference vehicle were assumed (fixing SD at 10%):

• Tire pressure (180 kPa);
• tread depth (0.5 mm).

Finally, considering hydrological conditions, the analysis was performed using real historical rainfall data related to a basin in northeaster Sicily, Italy, for a return period equal to 10 years. From the rainfall analysis (Figure 2), the following parameters of the intensity–duration–frequency curve were determined to calculate rainfall as a function of rain duration: a = 50.39, n = 0.22. In the following examples, concerning rain duration, it was fixed equal to 10 min.

In

Table 5. Input data for the numerical analysis.

ID	Road Type	w (m)	Ls (m)	s	g	S	A [m2]	L [m]	Tx [y]	tc [h]	h [mm]	TXD [mm]	Vleg [km/h]	RDmax [mm]
1	F	9	125	0.025	0.021	0.033	1125	11.75	10	0.167	28.44	0.40	50	20
2	F	9	125	0.025	0.021	0.033	1125	11.75	10	0.167	28.44	0.80	50	20
3	F	9	125	0.025	0.021	0.033	1125	11.75	10	0.167	28.44	1.20	50	20
4	C	9.5	125	0.025	0.021	0.033	1187.5	12.41	10	0.167	28.44	0.40	70	15
5	C	9.5	125	0.025	0.021	0.033	1187.5	12.41	10	0.167	28.44	0.80	70	15
6	C	9.5	125	0.025	0.021	0.033	1187.5	12.41	10	0.167	28.44	1.20	70	15
7	A	11.2	125	0.025	0.021	0.033	1400	14.63	10	0.167	28.44	0.40	110	12
8	A	11.2	125	0.025	0.021	0.033	1400	14.63	10	0.167	28.44	0.80	110	12
9	A	11.2	125	0.025	0.021	0.033	1400	14.63	10	0.167	28.44	1.20	110	12

, input data used for performing the numerical elaborations are reported.

In

Table 6. Results of the numerical analysis.

Road Type	ID′	k	TXD [mm]	WFD [mm]	Vp [km/h]	Vl [km/h]	CH	CP	HCI
F	1L	1.3	0.4	3.4	80.7	50	2.04	10.00	80
	1M	1.3	0.4	3.4	80.7	50	2.04	20.00	59
	1H	1.3	0.4	3.4	80.7	50	2.04	30.00	39
	2L	1.3	0.8	3.3	81.2	50	0.82	10.00	92
	2M	1.3	0.8	3.3	81.2	50	0.82	20.00	84
	2H	1.3	0.8	3.3	81.2	50	0.82	30.00	75
	3L	1.3	1.2	3.1	86.4	50	0.46	10.00	95
	3M	1.3	1.2	3.1	86.4	50	0.46	20.00	91
	3H	1.3	1.2	3.1	86.4	50	0.46	30.00	86
C	4L	1.5	0.4	3.5	80.6	70	3.43	10.00	66
	4M	1.5	0.4	3.5	80.6	70	3.43	20.00	31
	4H	1.5	0.4	3.5	80.6	70	3.43	30.00	0
	5L	1.5	0.8	3.4	81.0	70	1.21	10.00	88
	5M	1.5	0.8	3.4	81.0	70	1.21	20.00	76
	5H	1.5	0.8	3.4	81.0	70	1.21	30.00	64
	6L	1.5	1.2	3.2	86.2	70	0.62	10.00	94
	6M	1.5	1.2	3.2	86.2	70	0.62	20.00	88
	6H	1.5	1.2	3.2	86.2	70	0.62	30.00	81
A	7L	1.7	0.4	3.8	80.3	110	6.50	10.00	35
	7M	1.7	0.4	3.8	80.3	110	6.50	20.00	0
	7H	1.7	0.4	3.8	80.3	110	6.50	30.00	0
	8L	1.7	0.8	3.7	80.5	110	2.00	10.00	80
	8M	1.7	0.8	3.7	80.5	110	2.00	20.00	60
	8H	1.7	0.8	3.7	80.5	110	2.00	30.00	40
	9L	1.7	1.2	3.5	85.5	110	0.94	10.00	91
	9M	1.7	1.2	3.5	85.5	110	0.94	20.00	81
	9H	1.7	1.2	3.5	85.5	110	0.94	30.00	72

, the results of the performed analyses for the various considered scenarios are listed. In particular, for each of the nine cases described in Table 5, the values of CH and HCI were calculated, considering three specific possible distress conditions of the road surface, i.e., CP (L—Low, M—Medium, and H—High). In detail, for the different conditions, the numerical calculations were performed considering CP values equal to 10, 20, and 30.

In Figure 3, the HCI values obtained for the 27 considered cases are shown, classified for the different surface distress categories (CP). In Figure 4, the HCI trends as a function of the CP are provided.

From the analysis of the results, as expected, it appears that the surface texture plays a fundamental role in the phenomenon and consistently significantly influences CH and CP values and, thus, HCI. Indeed, as evidenced in both Figure 3 and Figure 4, in conditions of poor macrotexture, the hydraulic quality indicator assumes remarkably low values in all the degradation conditions and for all the considered road classes. In particular, this difference is sharper also owing to the different functional classifications of the considered roads. For example, hierarchically more important road type A, despite the lower distress level caused by the different exercise conditions and the higher speed values admitted in wet conditions, shows greater hydraulic critical levels for all the assumed TXD values.

As anticipated, in order to understand the effect of k on the proposed indicator, a preliminary sensitivity analysis was performed (Figure 5). In this numerical investigation, for the road class A and the same TXD values of ID’ 7, 8, and 9 (Table 6), the HCI was calculated for the following values of k: 1.3, 1.5, and 1.7. As expected, the lower the ratio of TXD to TXD_ref, the stronger the k effect. When TXD < TXD_ref, higher k values heavily penalise the HCI; however, for TXD > TXD_ref, the lower the k value, the lower the HCI. This graph shows the effects and influence of the proposed indicator of the k parameter, and it is possible to infer that selecting a higher k value for the main road classes is preferable in order to maximise the effects of inadequate conditions on maintenance planning management.

As shown in the previous graphs (Figure 3, Figure 4 and Figure 5), the HCI may, then, represent further useful information to classify the efficiency of the road surface, not only related to the eventual distress but also considering the possible problems resulting from them in particularly critical conditions, as well as during rain and on wet surfaces. Although this proposal fits into a context of first-level analysis of road conditions at the network level for defining a hydraulic priority class for the different arcs, the structure of the proposed index may even represent a pilot indicator for traffic safety. The definition of appropriate threshold values, chosen according to the exercise and traffic conditions, will allow road authorities to identify the most critical segments on which to urgently perform detailed analyses for an effective space and time optimization of the eventually necessary maintenance interventions.

As an example, in Figure 6, different hydraulic critical zones for road classes A (a) and F (b) are depicted based on the same assumptions previously described. The different colour tones from bottom to top represent decreasing values of hydraulic alert, defined in line with proper thresholds that the road administrators may fix for maintenance targets and goals. In this example, the red area represents the zone below the safety threshold, while the green one denotes the zone where there is no urgent need for maintenance interventions. The intermediate area represents the range in which to plan detailed analyses through high-performance survey systems and maintenance activities.

A further helpful element to calibrate the alert and intervention thresholds could refer to a more complex risk analysis, taking into account even the levels of service that the considered road has to guarantee in the use phases. In future developments of this research, these aspects will be properly analysed, aiming to propose a comprehensive methodological framework for network-scale hydraulic risk analyses by defining hazards, vulnerabilities, and exposure factors for distressed road segments in wet conditions.

Finally, the authors believe that thanks to the modern 3D survey techniques and the quality and precision of their acquired data, this methodology may for sure find wide applications in building information modelling (BIM) frameworks, with clear advantages for road authorities in the maintenance management of transport infrastructures. From different studies, numerous operative advantages have already been raised, particularly related to the quick and user-friendly visualization and querying of information, to data interoperability, and, thus, to correct management of the maintenance strategies [37,46] in optimised digitalised environments, both in technical and economic terms.

4. Conclusions

In this paper, a synthetic indicator called Hydraulic Condition Index (HCI) was proposed to analyse the hydraulic quality of road pavement surfaces in wet conditions and in the presence of surface distresses, determining critical accumulations of water on the pavement. This proposal integrates other existing quality indicators that are actually limited only to the physical features of the distresses, neglecting any relationship with exercise conditions and the consequent risks. These issues become very relevant in critical scenarios, such as during rain, when some distress features (such as ruts and depressions) may lead to high water film depths, which is very dangerous for the aquaplaning risk. To bypass this limitation, the presented methodology represents a numerical support tool to road agencies for the preliminary analyses at network level, for identifying the hydraulic quality of the road pavement surfaces.

Some preliminary numerical applications presented in the paper proved the effectiveness and the eventual advantages of the procedure in view of a maintenance management scheduling that also involves the hydraulic quality of the pavements.

The proposed index and the consequent analytical applications may be helpful for road agencies in the maintenance planning phases to identify the most urgent needs with regard to safety conditions in optimised management environments at the network level. In future research, the numerical application will be widened by integrating the methodology with a hydraulic risk analysis and including additional traffic and exercise conditions of the considered infrastructure for more comprehensive elaborations.