1. Introduction
Moisture damage in asphalt mixtures is the degradation of the mixture’s mechanical properties due to the existence of water in the pavement, either as a liquid or vapor, which eventually leads to an adhesive failure between the bitumen and mineral aggregates and a cohesive failure within the bitumen that coats the aggregates [
1,
2]. Moisture damage is a critical phenomenon that alleviates the stiffness and load capacity of flexible pavements [
3] and causes a costly failure of the pavement structure [
4]. It also leads to the formation of various pavement distresses, such as stripping, raveling, shelling, and hydraulic scour [
1], and increases the severity of existing rutting, cracking, and potholes [
5]. Moreover, stripping is the most common distress induced by moisture damage, where a physical separation (adhesive failure) can result at the aggregate–bitumen interface due to the higher surface energy of water compared to the asphalt cement [
2,
6,
7,
8].
Many laboratory testing methods were used to evaluate and measure the moisture susceptibility of asphalt mixtures. Some of the tests include immersed wheel-tracking configurations such as the Hamburg wheel-tracking test and the Asphalt Pavement Analyzer device [
9,
10], while others evaluate moisture damage by calculating the ratio of strength or stiffness of water-conditioned compacted Hot-Mix Asphalt (HMA) samples to that of unconditioned samples [
4]. The latter includes several testing protocols such as the immersion–compression test, the resilient modulus test, the double-punch method, the tensile strength ratio (TSR) or modified Lottman (AASHTO T 283), the Retained Stability Index (RSI), and others [
11,
12,
13,
14]. Even though these testing procedures help compare the moisture susceptibility of different mixtures, they do not provide information about the proper characteristics of asphalt mixes. This refers to the fact that they do not consider the fundamental measurements of material properties that influence the mechanisms of moisture-induced damage in asphalt mixes [
8]. Also, adopting a single test from among these methods as an ideal procedure for characterizing the moisture sensitivity performance of mixes is impractical due to the wide variety of conditions, factors, and material properties that impact the moisture susceptibility of asphalt pavement [
9,
10,
11,
15].
Machine learning (ML)-based methods, which are subfields of artificial intelligence (AI) techniques, have been widely implemented in various engineering disciplines due to their powerful ability and high accuracy in analyzing and developing predictive models [
16,
17,
18,
19]. Artificial Neural Networks (ANNs) and Gene Expression Programming (GEP) are typical examples of methods that are successfully utilized for predicting the complex characteristics of asphalt mixtures [
16,
20,
21]. Many research works have predicted the moisture sensitivity of asphalt mixes using the TSR test [
22,
23,
24]. A recent study introduced by Dalhat and Osman [
25] utilized the ANN technique to solely study the influence of volumetric and aggregate properties of asphalt mixtures on their moisture resistance based on the Retained Stability Index (RSI). Although their study thoroughly presented the relationships between various mixtures’ properties and RSI values, it included some little-to-none influential variables on moisture-induced damage and direct mathematical equations for predicting the RSI values of asphalt mixtures.
The RSI test is a straightforward testing method that is still valid and is used by pavement agencies to evaluate the moisture sensitivity of asphaltic mixes. This study aims to develop an accurate model that provides a practical and direct mathematical equation for estimating the RSI value of asphalt mixes using a hybrid machine learning approach, including the ANN and GEP techniques. In addition, the model will only consider the most crucial factors that affect the moisture damage of asphalt mixes, including aggregate absorption property, asphalt content, air void percentage, and filler content. These factors are fundamentally imperative in the design procedure of asphalt mixes, which would promote a model for easy implementation by pavement engineers and local agencies. The model will be useful to improve the performance of asphalt mixes before their production by evaluating the water susceptibility of mixes without the need to perform the destructive RSI test, saving time, materials, and effort.
Moisture damage mechanisms and common influential factors
Moisture usually reaches asphalt mixes through different mechanisms, including surface water infiltration, capillary rise action, and water diffusion. Infiltration is considered the primary source of moisture in asphalt pavements [
3,
8], while diffusion is the most common mechanism of moisture transport where molecules move from a high to a low concentration region, and hence durability damage in asphalt pavements occurs [
26,
27]. Moisture damage, however, starts with the moisture transport mechanisms by which the moisture gets into the asphalt mixture’s structure. A process of change in conditions at the aggregate–binder interface then occurs, adversely affecting the integrity and capacity of asphalt mixes [
1]. Typically, six mechanisms contribute to moisture damage in asphalt mixes: asphalt film detachment and displacement, mastic dispersion and desorption, film microcracks, and spontaneous emulsification [
1,
28].
The fundamental causes of moisture damage in asphalt pavement have been vastly investigated. Some causes can be related to aggregate mineralogy and binder characteristics [
27,
29,
30], while others refer to environmental and traffic conditions, volumetric properties, and a construction process [
12,
31]. Lu and Harvey [
2] conducted an in-field investigation of asphalt pavement cores to determine the most influential parameters for moisture damage. They found that air void content, pavement structure, pavement age, and overall rainfall significantly influence moisture damage [
2]. High air void contents in an asphalt mix not only increase the tendency of mixes to moisture damage but also could result in early aging and low fatigue resistance [
7].
Ahmed et al. [
32] evaluated the durability of HMA at different air void contents ranging from 4% to 9%. The study showed a proportional relationship between the air void percentage and HMA permeability, which is the ability of a porous medium such as an asphalt mix to transmit water [
33]. However, vulnerable mixes to moisture damage have been achieved at air void contents beyond 6% [
32]. Invisible cracks, known as “checks”, with a length of 1–4 inches and 1–3 inches apart, are typically propagated while paving asphalt mixes in fields [
6]. These checks, however, increase the permeability of the mixes by connecting the entrapped air voids and making effective routes for surface water to infiltrate inside the pavement structure, which leads to less durable mixtures prone to moisture damage [
6,
7].
In addition, moisture damage is influenced by the internal composition of the mixes. Insufficient asphalt cement contents in HMA can provide a relatively thin asphalt film coating the aggregate particles, promoting cohesive damage within the mastic and/or adhesive damage at the aggregate–bitumen interface in the presence of water [
31,
33]. However, aggregates’ mineralogy is much more dominant in moisture damage than asphalt cement types [
27,
29,
31]. For instance, siliceous-type (acid) aggregates such as gravel and granite are more prone to moisture damage than high-carbonate (basic) aggregates like limestone [
1,
29]. The limestone aggregate is mainly composed of calcite, a moisture-resistant mineral, whereas the granite aggregate is composed of albite, quartz, and K-feldspar, which are sensitive to moisture damage [
30]. Therefore, selecting proper types of aggregate with good compatibility with asphalt cement is imperative for designing asphalt mixes that are less sensitive to moisture damage [
34]. Further, the moisture-absorption property of aggregates is an important factor that significantly influences moisture attack in asphalt mixes [
29,
30]. Aggregates with high affinity to water impose an adhesive failure at the aggregate–binder interface [
3]. This is because of the required short time for water diffusion in such porous aggregates [
27,
30]. Dalhat and Osman [
25] studied the influence of asphalt mixes’ volumetric and aggregate properties on the moisture susceptibility of different asphalt mixtures using the RSI. The major findings of their study indicate that increasing the air void contents and amount of friable materials in asphalt mixtures reduces the moisture resistance performance of the mixtures.
Another critical parameter significantly influencing moisture damage is the mineral filler percentage in asphalt mixes [
35,
36,
37]. Mineral fillers are the proportion of blended aggregates in asphalt mixtures that passes through sieve No. 200 (<0.075 mm) and is suspended in bitumen to form mastic [
13,
38]. Previous studies indicated that incorporating cementitious types of mineral fillers in asphalt mixes could improve the moisture resistance, stability, and deformation resistance of the mixes [
13,
15,
37,
38]. However, increasing the filler contents in asphalt mixes could result in moisture damage. Huang et al. [
36] studied asphalt mix performance by utilizing different types of filler materials at various contents ranging from 2% to 10%. Their results revealed that the moisture susceptibility of the mixes increases by increasing the filler contents due to the reduction in the asphalt binder content that forms the exact amount of mastic for lubricating the aggregate particles. Airey et al. [
4] and Sakanlou et al. [
39] also stressed that moisture damage could happen due to the loss in cohesive strength of the asphalt–filler mastic coating the asphalt mix’s particles.
Overall, previous studies indicated that the progression of moisture damage in asphalt mixes is attributed to numerous factors. The materials and volumetric properties of asphalt mixes, including moisture absorption of aggregates, asphalt cement content, air void content, and proportion of mineral filler in the mixes, can be the most influential parameters that significantly control the moisture damage of the mixtures.
5. Evaluation and Sensitivity of the Proposed Model
The proposed GEP model is evaluated statistically in this section to validate its accuracy in predicting the asphalt mixes’ RSI value. The statistical measurements R
2, MAE, and RMSE were determined for the training, testing, and all datasets, as shown in
Table 6. The low error values and high R
2 values of these datasets and their convergence together indicate the generalization and high level of accuracy of the model in predicting the RSI value. The model also results in an average ratio of “tested-to-predicted” RSI of (1.00) and a very low coefficient of variation of (0.841).
The model sensitivity in capturing the impact of the input parameters on the predicted RSI values was investigated through a parametric analysis. This type of analysis was found to be a valuable and reliable approach for validating the sensitivity of predictive models [
16,
17,
25,
45,
46,
47]. It is based on utilizing the proposed model to predict a dependent variable that corresponds to interchangeable datasets of the input variables. Thus, the GEP model is utilized to predict the RSI values after varying every input parameter in the model while keeping the other three variables constant at their mean values. This approach was repeated in sequence for all parameters, as shown in
Figure 8. The obtained trends prove the model’s sensitivity and efficiency in predicting the RSI while considering the impact of the input variables, as they confirm the network connection weight results (see
Figure 6), where the RSI values increase by increasing the AC values and decreasing the F, Ab, and Va values.
While the moisture sensitivity of the mixes decreases as the RSI value increases, these plots were elucidated following results from previously published research articles.
Figure 8a shows a negative relationship between the mineral filler content and the durability of the asphalt mixes. Previous studies found that incorporating mineral filler in asphalt mixes enhances stability by increasing the stiffness of the asphalt mixes [
36,
38]. However, increasing the filler content reduces the asphalt proportion in the same amount of mastic required for coating and lubricating the aggregate particles, resulting in a mixture prone to moisture damage [
36].
Figure 8b shows that the RSI values decrease as the moisture-absorption property of the aggregates in the mixtures increases. This can be referred to as the nature of absorptive (porous) aggregates with a high affinity to moisture, facilitating water diffusion into the aggregate–bitumen interface and increasing the severity of moisture damage [
27,
30]. It is worth stating that moisture diffusion transforms the moisture-imposed damage from a cohesive to an adhesive mode. The former mode prevails in the dry-conditioned samples where failure is formed within the bulk of asphalt coating aggregates, whereas the latter is dominant in the wet-conditioned samples where the failure is interfacial and mainly weakens the aggregate–bitumen bonds by water intrusion [
29,
30].
Figure 8c indicates that the durability of asphalt mixes with high RSI values increases significantly as AC% increases in the mixes. This can be explained by the provided thicker asphalt film that coats the aggregate particles and hence reduces the adverse effect of water on asphalt mixes [
31].
Figure 8d shows a concave downward relationship between the RSI values and Va%. This refers to the fact that increasing Va% in asphalt mixes increases their permeability and induces their moisture susceptibility through adhesive failure [
1,
2,
7]. In addition, increasing the permeability of asphalt concrete makes it a porous medium for water infiltration, which impairs the mixture’s strength [
32]. This observation aligns with previous RSI results obtained by Behiry [
12] and Dalhat et al. [
25].