Predicting the Mechanical Behavior of Cold Asphalt Mixtures Using Optimized Artificial Neural Networks

The growing global trend toward sustainable infrastructure has cranked up the interest in alternative techniques to Hot Mix Asphalt (HMA) production. One alternative in particular are the new cold asphalt mixes (CAMs). They’re a carbon lightweight alternative to HMA because they’re produced and used at room temperature, leading to significantly reduced energy consumption and Greenhouse Gas Emissions (GHGs) because production energy moves from the tier 5 stovetop to near zero with CAMs, because of lowered emissions carbon dioxide emissions and the lack of required active ingredient persistence it’s a great, new, trending approach to infrastructure [1]. Accessibility for CAMs use perseveres in terms of use in inaccessible or underdeveloped areas globally and is suitable for temporary, low traffic pavements, like caravan sites and patching of highways [2, 3].

In comparison to conventional HMA, cold-applied mixtures (CAMs) report inferior mechanical performances, especially during the early stages after their application. This includes a range of material properties such as indirect tensile strength (ITS), flow, rutting resistance, and moisture susceptibility. These limitations are mainly due to its low initial cohesion made worse by prolonged curing periods, which are the primary reasons for its poor properties. To overcome this drawback, the utilization of additives within CAM compositions has emerged as a popular method respondents have tested to enhance the mechanical behavior of these mixtures.

Various types of polymers, cement, natural and synthetic fibers, waxes, and even recycled materials such as polyethylene terephthalate (PET) bottles, rubber, and fly ash, have been used as modifying agents to improve the mechanical properties and durability of cold mixes. In general, the addition of these modifiers influences and changes the internal structure of the asphalt matrix and the interaction between the binder and the aggregate, thereby enhancing the mechanical properties such as strength, stiffness, adhesion, and durability of the mixtures, towards environmental factors [4]. Despite the significant potential of these additives’ effects on the mechanical properties of cold mixtures, predicting the mechanical behavior of modified cold mixes remains complex. This is due to the largely nonlinear and interdependent relationships between a range of mixture parameters, including the type and amount of the additive, the characteristics of the binder used, the curing period, and environmental factors (namely the environmental temperature which significantly affects the curing process of cold mixes).

To respond to the intricacy, current studies have inclined towards data based models, which Artificial Neural Networks (ANNs) are newly found to have great capacities [5, 6]. ANNs imitate the behaviour of the organic neural system and are notable for its ability to depict the most complicated patterns and associations through large multidimensional databases without needing specific mathematical formulas [7, 8]. ANNs mainly consist of neurons and synaptic weights, and these qualities provide the flexibility and resilience necessary to model civil engineering materials, which are difficult to analyse with traditional linear mathematical models.

ANN applications in the field of construction and pavement engineering have grown at staggeringly rates in last few years. A few examples include the forecast of compressive strength of concrete, modeling of asphalt binder viscosity with changing temperature, and long-term behavior of pavement under traffic loading constraints. According to the researches done by Uwanuakwa et al. [9]. ANN has ability to predict the mix proportion of self-compacting concrete by the help of slump flow and compressive strength which was helped by the_help_word multi-output ANN. Similarly, Mugume [10] utilized ANN integrated with multi scale modelling to predict the strength of fly ash enhanced mortar, and the prediction answer was found to be highly correlated with the experimental result.

Aiming at proposing an ANN forecast model for ITS of CAMs which were modified with different common industry additives and exposed to many premature aging conditions, this paper applied the ANNs method to establish the theoretical model under a selection of comprehensively designed and statistically perfect model serial production test data. The accuracy of the model was evaluated based on statistical performance measures and sensitivity analysis, while also use the performance of the model to identify the most prominent factors in the model. Finally, this research focus on providing practical applications for engineers, as a flexible and reliable estimating tool, to optimize the mix design of the cold asphalt and better achieve the requirements of road engineering design, considering economical and spatial distribution issues to apply more sustainable and performance based flexible pavement systems.

The ANN was developed using a structured dataset where the dependent variable was the post-curing ITS, and the independent variables are shown in Table 1. These inputs encompass design parameters of the CMA, such as emulsion content, sludge ash content, curing period, and additive types.

To ensure robust evaluation, the dataset was partitioned into three subsets:

Training set (86%) – used for weight optimization;

Testing set (9%) – monitored during training to avoid overfitting;

Validation set (5%) – used for final model performance assessment.

The training process was halted once the error on the testing set began to increase, a standard practice to mitigate overfitting and ensure generalizability.

Table 1. Definition of variables used in the ANN model for CMA

The development of the linear model structure did facilitate the ability to identify which variables were most influential to the mechanical performance of CMA. Based off the initial results, it was discovered that ITB and SSA had the most significant influence on the ITS, and ATB and MS did in the MBV. The critical level of interaction that was found in the CMA formulation was between ATB and MC.

The performance of the ANN was analyzed for different data division ratios, with results summarized in Table 2. The optimal split was determined as 86% training, 9% testing, and 5% validation, which yielded the highest correlation coefficient of 96.3% and the lowest testing error of 2.9%. This configuration was found to provide the best generalization capability of the model. The dataset, consisting of 163 mix designs, was partitioned using integrated random and striped sampling techniques, with the striped division yielding superior performance.

Table 2. Effect of data division ratios on ANN performance for CMA

Table 3. Effect of data division ratios on ANN performance for CMA

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Figure 1. Effect of data division ratios on ANN performance

In order to get optimal performance, particular in computation, and to avoid overfitting a sensitivity analysis was carried out to discover the effect ratio of each input variable. Finally, there were five inputs found in the ANN model out of the seven at first. Pretesting experiments such as curing time, water content, gradation type and additive type percentage indicated the most influence on the output predictions while emulsion content, and moisture condition showed the very low effect and they were deleted.

The process of modeling is able to show the promising of machine learning tools in attempting to predict key mechanical outcomes of sustainable CMA. The research shows that use inclusive of machine learning techniques in predications important mechanical characteristics of interest his globally appears its capacity to reduce the volumes of physical testing required as well to as accelerate material design cycle what been sought for. The significance of the physical of the primary variables: curing time, moisture content, gradation type, type of additive, percentage of additive etc. reflects the main physical mechanisms for the performance of CMAs. The curing time means moisture evaporation and binder setting, in this sense, it has directly dominance on stiffness and cohesion. The moisture content means the method to provide workability; excess of water gives down to a down of strength because pore pressure or incomplete bonding etc. The gradation type gives us internal structure, which means how much percentage of aggregate could take load and how the load would be distributed etc. The additive type and its dosage changes binder-aggregate adhesion and viscoelasticity, etc. On the contrary, emulsion content and initial moisture condition are less significant because of low weightage which means little differentiation, or other significant variables would be less affect under lower variation of laboratory test conditions in Table 3 and Figure 1.

Table 4 presents the productive units of the ANN model with diverse hidden nodes. The best prediction accuracy is achieved at having 3 hidden neurons (testing error of 2.9% and correlation coefficient of 96.3%), the test set with the highest correlation coefficient and lowest error rate was chosen because it is the highest set and provides greater reliability of the results because it was trained on more elements., which represents better generalization and stability than that of the others. And also, ANN model with the architecture of 7:3:1, as shown in Figure 2, provides the mapping of non-linear relationships of the cold asphalt mix parameters and mechanical performance. The hyperbolic tangent (tanh) activation function with 0.4 learning rate and 0.9 momentum coefficient is applied in Hidden Layer nodes which leads to faster convergence and improved error backpropagation.

The seventh model architecture, as seen in Figure 2, simple and shorten dependent on the result of relative importance became contains six input nodes, three hidden nodes and a single output node which is capable of accurately predicting the mechanical behaviour of cold-laid asphalt mixtures modified with eco-friendly industrial by-products such as sludge ash.

Table 4. Effect of hidden neurons on ANN prediction accuracy for ITS in CMA

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Figure 2. Neural network for CMA

The objective of this study was to develop a feed-forward ANN model for predicting key mechanical properties of cold asphalt mixtures incorporated with industrial additives such as WSA. The developed ANN architecture adopted a hyperbolic tangent (tansig) as activation function at the hidden layer and a linear activation function (purelin) at the output node, given the prior modeling techniques reported by Cui-hong [40] and Al Nageim et al. [17] for asphalt materials.

The mathematical form of the ANN model is given by:

$y=\sum_{j=1}^n\left(w_j *\left(\tanh \left(\sum_{i=1}^3\left(w_{j i} \cdot x_i\right)+\beta_j\right)\right)\right)+\beta$            (2)

where,

y: is the predicted output,

$x_i$: are the normalized input variables (such as aggregate gradation, binder content, curing time),

Wji: denotes the weight between input neuron i and hidden node j,

βj: is the bias associated with the hidden neuron j,

Wj: is the weight between the hidden node jjj and the output node,

β: represents the bias at the output layer,

n: is the number of hidden neurons.

To assess the accuracy of prediction of the developed ANN model for CAMs with WSA, different structures of network were checked. Out of the various structures tested, it was found that the perfect architecture having 8 input neurons, three neurons in hidden layer and single output neuron gave better performance in term of high correlation coefficient (r = 0.963) and low testing error (2.9%). The prediction capability of the configuration of such network was found quite good for the indirect tensile stiffness modulus in terms of the high consistency between the ANN estimations and laboratory evaluation of CMA specimens. This confirms the high performance ability of the ANN model in capturing the nonlinear interaction of the input parameters with the asphalt mixture behavior, which can be an effective decision support tool for optimal CMA design.

The optimized ANN model of 5:3:1 structure has exhibited a strong predictive accuracy with the R-Square value of 96.3% and the low testing error of 2.9% for estimating the indirect tensile strength of the cold asphalt mixes.

Curing time and water content were identified as the most influential factors on mechanical performance, while emulsion content and moisture condition had minimal impact.

A dataset of 163 mix designs ensured robust training, validation, and testing, enabling generalizable predictions across various cold mix asphalt formulations.

The sensitivity analysis confirmed sludge ash content and additive type as key modifiers influencing the mechanical behavior of CAMs.

This ANN model provides a reliable, data-driven tool for optimizing sustainable cold asphalt mixtures, reducing reliance on extensive laboratory testing.

The ANN model can be integrated with on-site construction data, enabling parameter adjustments such as curing duration or emulsion rate to suit varying temperature and moisture conditions in field applications.

The model supports stepwise mix optimization by predicting ITS under adjusted aggregate gradations and moisture contents, providing a practical decision-making tool for engineers.