Integrating Experimental Analysis and Gradient Boosting for the Durability Assessment of Lime-Based Mortar in Acidic Environment

Abstract

This paper presents a comprehensive study of the mechanical properties of lime-based mortar in an acidic environment, employing both experimental analysis and machine learning to model techniques. Despite the extensive use of lime-based mortar in construction, particularly for the strengthening of structures as externally bonded materials, its behavior under acidic conditions remains poorly understood in the literature. This study aims to address this gap by investigating the mechanical performance of lime-based mortar under prolonged exposure to acidic environments, laying the groundwork for further research in this critical area. In the experimental phase, a commercial hydraulic lime-based mortar was subjected to varying environmental conditions, including acidic solution immersion with a pH of 3.0, distilled water immersion, and dry storage. Subsequently, the specimens were tested under flexure following exposure durations of 1000, 3000, and 5000 h. In the modeling phase, the extreme gradient boosting (XGBoost) algorithm was deployed to predict the mechanical properties of the lime-based mortar by 1000, 3000, and 5000 h of exposure. Using the experimental data, the machine learning models were trained to capture the complex relationships between the stress-displacement curve (as the output) and various environmental and mechanical properties, including density, corrosion, moisture, and exposure duration (as input features). The predictive models demonstrated remarkable accuracy and generalization (using a 4-fold cross-validation approach) capabilities (R² = 0.984 and RMSE = 0.116, for testing dataset), offering a reliable tool for estimating the mortar’s behavior over extended periods in an acidic environment. The comparative analysis demonstrated that mortar samples exposed to an acidic environment reached peak values at 3000 h of exposure, followed by a decrease in the mechanical properties with prolonged acidic exposure. In contrast, specimens exposed to distilled water and dry conditions exhibited an earlier onset of strength increase, indicating different material responses under varying environmental conditions.

1. Introduction

Masonry structures, comprising mortar and masonry units, remain prevalent in developing countries and hold significant historical value across Europe, particularly in cultural heritage sites [1,2]. Preserving these structures is vital, given their architectural significance. This preservation mainly be categorized into either resistance against loadings or aging. Aging processes are inevitable and may affect the structural stability of masonry buildings due to material degradation, anthropic modifications, and climate and environmental changes [3]. Developing reliable inspection and testing programs along with proper modeling is essential to predict the need for intervention [4]. Moreover, recent innovative strengthening techniques, like textile-reinforced mortar (TRM), are gaining attention as alternatives to traditional methods [5,6]. TRM offers advantages in compatibility with masonry substrates, high-temperature resistance, and vapor permeability, making it particularly suitable for historic building restoration alongside natural lime mortar matrices, ensuring compatibility with monumental structures [7]. Despite the good performance of this strengthening technique against loading, their durability performance is still a matter of concern, requiring further investigation. The durability of these composites is generally dependent on the durability performance of each component, particularly the inorganic matrix (mortar) [8,9].

Over time, different types of mortars have been selected for various purposes, driven by technological advancements and application-specific requirements. The historical transition from lime-based mortars to Portland cement in the 19th century marked a significant shift in construction practices [10]. While Portland cement offers advantages such as higher strength, quicker hardening, and ease of use, its widespread adoption in historical building restoration has led to notable drawbacks, including incompatibility with historic masonry, accelerated deterioration, and a high content of soluble salts [11,12]. Cement-based mortars, with their lower permeability and excessively high compressive strength, can cause stress concentrations and damage to ancient structures, undermining their long-term durability. In contrast, lime-based mortars offer unique benefits that align better with the preservation and strengthening of historic masonry. Their flexibility, permeability, and lower thermal expansion coefficients enable them to accommodate slight movements and mitigate stress on the masonry substrate [13,14]. Additionally, lime-based mortars facilitate moisture regulation, reducing the risk of salt crystallization and associated damage. These characteristics make lime mortars particularly suitable for rendering, pointing, and other repair works in historic buildings, where maintaining structural integrity and authenticity is paramount [10,15]. The renewed interest in lime-based mortars on restoration projects reflects an understanding of their compatibility with historical materials and their ability to preserve heritage structures over time [11,16]. While cement-based mortars remain advantageous in modern applications requiring strength and rapid setting, their limitations in restoration contexts underscore the need for careful material selection.

However, a critical aspect of lime-based mortars that warrants further investigation is their durability, particularly in challenging environments [17]. Research into the mechanical behavior and compositional changes of lime-based mortars exposed to different environments has been conducted, emphasizing the need for a deeper understanding of their long-term performance [8]. The durability of lime-based mortars is essential for ensuring the longevity and sustainability of masonry structures in historical and cultural heritage sites. Therefore, ongoing efforts to evaluate the durability of lime-based mortars are crucial for informing restoration practices and preserving architectural heritage for future generations [18].

Masonry structures and architectural heritage are significantly threatened by harsh environmental conditions [19], with acid deposition from atmospheric pollution being a major and widespread cause of decay, endangering historical heritage [19]. The heightened concentration of acid rain contributes to the dissolution of masonry materials, leading to the formation of harmful salts and consequent deterioration in mechanical properties, ultimately diminishing the structural service life [20,21,22]. The degradation patterns and rates of cultural heritage are intricately linked to various factors, including material composition, preservation conditions, and microenvironmental changes. Temperature fluctuations and acid rain exacerbate the dissolution and weathering processes of masonry relics, particularly those composed of carbonate rock materials [23]. The impact of acid deposition on the weathering of carbonate stone has long been acknowledged, with recent decades witnessing a global escalation in the prevalence of acid deposition and its deleterious effects, highlighting the urgency of addressing this pervasive issue [20,23,24]. Despite the importance of this issue, there exist very limited studies, either experimental or modeling, that survey the aging effect and more specifically prediction of the acidic environments on the mechanical performance of lime mortars [25,26,27]. This highlights the need for a better understanding of this phenomenon.

While traditional preservation techniques remain essential, innovative machine-learning strategies are being explored as complementary tools to support experimental investigations and analysis. Machine learning can assist in identifying patterns, analyzing large datasets, and predicting short-term material behavior under specific conditions, such as degradation in acidic environments [28,29,30]. However, it is important to recognize that machine learning alone cannot address long-term challenges, such as understanding the full lifecycle performance of materials or their long-term behavior under varying environmental conditions. Experimental testing remains indispensable for validating predictions, ensuring accuracy, and advancing the development of sustainable construction materials. By integrating machine learning with experimental research, a more comprehensive understanding of material properties and performance can be achieved, offering valuable insights for restoration and preservation practices [31,32,33].

By leveraging the power of advanced analytics and predictive modeling, researchers have begun to unravel the complexities of material degradation, offering new tools for the preservation of cultural heritage. In recent years, the utilization of machine learning (ML) algorithms has been prominently extended towards predicting the mechanical characteristics of mortar in structural components [34,35,36,37]. Studies have employed adaptive boosting and bagging machine learning models to predict the improved durability and flexural strength of different types of mortar composites including biochar-cement and marble cement, demonstrating the development of high-precision prediction models for sustainable construction materials [38,39,40]. Analyzing the shapely additive explanations plot (SHAP) of the gradient boosting model revealed that the compressive strength of the recycled waste slurry micro powder (RSP) mortar has a negative correlation with the RSP replacement rate [41]. Another study found that the aramid fiber-reinforced polymer (AFRP) wrap’s tensile strength has a critical role in enhancing the structural integrity and performance of confined concrete [42]. Moreover, ensemble learning models, particularly Random Forest, were employed to predict the elastic modulus of fly ash incorporated recycled coarse aggregate (FARAC), identifying sand, cement, natural, and recycled aggregate as the most important input features [43].

Therefore, this paper aims to assess the evolution of mechanical properties of mortars in acidic environments utilizing an experimental dataset and machine learning. This objective is motivated by the fact that the impact of acidic conditions on the mechanical behavior of masonry is not yet fully understood. This evaluation encompasses the flexural test of mortar being analyzed using a fine-tuned Extreme Gradient Boosting (XGBoost) algorithm, to predict the strength of the utilized lime-based mortar. This method enhances the existing comprehension of the critical mechanical factors influencing lime-based mortar’s strength in various acidic environments over time. Moreover, this innovative methodology is designed to yield insights that enhance sustainable preservation and strengthen resilience against atmospheric pollution challenges.

2. Materials and Methods

The research undertaken in this study encompassed two primary components. Firstly, a series of mechanical tests were conducted on lime-based mortar specimens subjected to varying testing ages and exposure conditions. Secondly, a data-driven machine learning modeling approach was employed to predict the stress-displacement behavior of a commercially available lime-based mortar. The model considered aging parameters in acidic environments, with different exposure times, to provide insights into the mechanical performance of the mortar over time. This section provides a comprehensive exposition of the experimental campaign, detailing the materials utilized, the methodology employed for specimen preparation, the conducted testing procedures, and an elucidation of the modeling methodology. Figure 1 outlines the experimental program and machine learning methodology used to predict the stress values of lime-based mortar under different curing conditions. The framework begins with the research direction, guiding the experimental program’s design, which encompasses the following curing conditions: dry condition, water immersion, and acidic solution immersion. Each of these conditions is tested at multiple exposure times (0 h, 1000 h, 3000 h, and 5000 h) to understand the material’s behavior over time. The experimental data obtained from flexural tests is randomly divided into training and testing datasets, with 70% allocated for training (20,000 observations) and 30% for testing (8500 observations). During the fitting process, the model is trained and evaluated on the training data to optimize the model’s hyperparameters. Once the desired model’s performance on the training data is obtained, the model is evaluated on the testing data to ensure its generalizability and robustness.

This study identifies the most important features affecting stress-displacement curve prediction in the utilized lime-based mortar. The following sections of the paper discuss the experimental testing procedure, as well as machine learning methods to enhance the predictive capabilities for material behavior analysis using an integrated approach. This methodology underscores the importance of combining robust experimental data with advanced computational techniques to achieve reliable and accurate predictions.

The experimental campaign focused on aging specimens fully immersed in a sulfuric acid solution with a pH of 3.0, following methods established in previous research on TRM composites [8]. A solid-to-solution ratio of ¼ was maintained constant. For the dry condition, specimens were stored under controlled laboratory conditions (20 ± 5 °C, 65 ± 10% RH). For the water immersion condition, specimens were placed in a tank full of distilled water. Temperature regulation at 20 °C was ensured using a temperature regulator for both acidic and distilled water tanks, with water pumps facilitating uniform circulation. Solution replacement occurred after 1000 and 3000 h to minimize material leaching, while pH variations were corrected twice weekly by adding additional acid to maintain solution density.

2.1. Mechanical Tests

A commercially available hydraulic lime-based mortar, namely Planitop HDM Restauro by Mapei, reinforced with short fibers, utilized in prior research [5], was employed in this study. Flexural tests were conducted on the mortar under three different ages and three exposure environments. It is noteworthy that exposure was started after an initial curing period (90 days), aligning with methodologies established in previous studies [5,6].

Figure 2 depicts the flexural strength samples and also the test setup performed in this investigation. Notably, the surfaces of the mortar samples were rectified at the end of the initial curing process to achieve a uniform surface roughness consistent with other surfaces and ensure uniform boundaries. For specimens exposed to dry conditions, testing was conducted under ambient conditions, while immersed specimens underwent evaluation under saturated-surface-dry (SSD) conditions. The testing procedure for SSD conditions involved removing samples from water 15 min before testing and carefully wiping off any excess surface moisture.

Flexural tests were conducted on specimens measuring 40 × 40 × 160 mm³, following the EN 1015-11 [44] standard. A hydraulic actuator with a 25 kN capacity was employed for flexural testing, with specimens subjected to displacement control at a rate of 0.005 mm/s. The notation assigned to each specimen follows a structured format: S_M_T_R, where “S” denotes the type of test conducted, which is flexural (denoted by F); “M” indicates the aging medium (e.g., “DC” for dry condition, “WI” for water immersion, and “AC” for acidic solution immersion); “T” represents the exposure duration (e.g., 0, 1000, 3000, 5000, denoting the exposure time in hours); and “R” signifies the specimen number. Each test type was conducted with six specimens. For example, specimen F_AC_1000_2 corresponds to a specimen tested under flexure after exposure to acidic solution for 1000 h, and it is the second specimen within the series. A comprehensive overview of all specimen groups is provided in

Table 1. Test Scheme Specifications.

Specimen’s Name	Aging Medium	Exposure Time
F_DC_0 F_DC_1000 F_DC_3000 F_DC_5000	Dry condition	0 h 1000 h 3000 h 5000 h
F_WI_0 F_WI_1000 F_WI_3000 F_WI_5000	Distilled water	0 h 1000 h 3000 h 5000 h
F_WI_0 F_AC_1000 F_AC_3000 F_AC_5000	Acidic solution	0 h 1000 h 3000 h 5000 h

.

2.2. Machine Learning Model: eXtreme Gradient Boosting

One of the most popular and effective machine learning techniques for regression problems is XGBoost, which stands for eXtreme Gradient Boosting. XGBoost is an ensemble method that combines multiple weak learners, usually decision trees, into a strong learner that can make accurate predictions on complex data sets. XGBoost uses a gradient-boosting framework that iteratively updates the weights of the learners based on the residuals of the previous predictions, minimizing a predefined loss function. XGBoost has several advantages over mathematical regression methods, such as its scalability, robustness, and interpretability [45,46]. The symbolic mathematical formulation of XGBoost and its decision-making process is presented in the following paragraphs. XGBoost has an objective function, which combines a loss function that measures the difference between the predicted and actual values, and a regularization term to control the complexity of the model [47]. The objective function reads:

$$\Phi \left(\Theta \right)=\underset{Loss}{\underbrace{\sum _{i=1}^n\mathcal{L}\left(y_i,{\widehat{y}}_i\right)}}+\underset{Regularization}{\underbrace{\sum _{k=1}^K\Omega \left(f_k\right)}}$$

(1)

where:

• $\mathsf{\Phi }\left(\mathsf{\Theta }\right)$ is the overall objective function.
• $\mathcal{L}\left(y_i,{\widehat{y}}_i\right)$ is the loss function, often mean squared error for regression tasks.
• $\Omega \left(f_k\right)$ is the regularization term for the k^th tree.
• $y_i$ is the actual value for the i^th input.
• ${\widehat{y}}_i$ is the predicted value for the i^th input.
• n is the number of inputs.
• K is the total number of trees.
• $f_k$ represents the k^th tree.

The loss function measures the difference between predicted and actual values, presented in Equation (2):

$$\mathcal{L}\left(y_i,{\widehat{y}}_i\right)={\displaystyle \frac{1}{n}}\sum _{i=1}^n(y_i-{\widehat{y}}_i{)}^2$$

(2)

The regularization term $\Omega \left(f_k\right)$ is used to penalize the complexity of the model and can be expressed as:

$$\Omega \left(f_k\right)=\mathsf{{\rm Y}}\mathsf{{\rm T}}+{\displaystyle \frac{1}{2}} \lambda \sum _{j=1}^T{\omega }_j^2$$

(3)

where:

• $\mathsf{{\rm Y}}$ is the parameter that controls the complexity of the tree.
• $\mathsf{{\rm T}}$ is the number of leaves in the tree.
• $\lambda$ is the parameter that controls the regularization of the leaf weights.
• ${\omega }_j$ is the weight of the jth leaf.

The XGBoost algorithm, illustrated in Figure 3, is an advanced implementation of gradient boosting that enhances performance and speed. This ensemble learning method involves constructing a sequence of decision trees, each aiming to correct the errors of its predecessor by focusing on the residuals. Initially, the data from the database is fed into the first decision tree, $Tree (X,{\theta }_1)$. Within the XGBoost algorithm, the residuals of decision trees, which are the differences between predicted and actual values, are computed and used as input for all subsequent trees. For instance, the function $f_1(X,{\theta }_1)$ represents the output of the first decision tree, and its residuals are then fed into the next decision tree. This process of calculating residuals and feeding them into subsequent trees continues iteratively through the ensemble up to the $\left(n-1\right)-$ th tree, $f_{n-1}(X,{\theta }_{n-1})$. This iterative process ensures that each tree in the sequence improves upon the predictions of its predecessors such that each one learns to correct the errors made by the previous trees. After all the decision trees are culminated, a cumulative sum integrates the contributions of all trees, effectively capturing the complexities in the data. In Figure 3, the white, red, yellow, and green nodes represent different stages of data processing within each decision tree. The white nodes typically represent the root nodes where the initial decision splits occur. The yellow nodes indicate the intermediate decision points where the chosen splits are made, guiding the flow of data based on specific criteria, while the red nodes represent the paths that were not selected at each decision point within the tree. Finally, the green nodes signify the leaf nodes where final predictions or residuals are computed.

One of the challenges of using machine learning models is to understand how the model makes predictions and what features are important for the model. A common way to measure feature importance is to use the number of times a feature is used to split a node in a tree or the total reduction in the loss function due to splitting on a feature. However, these methods do not account for the interaction effects between features or the impact of a feature on the prediction for a specific instance. To address these limitations, a novel method called SHAP (SHapley Additive exPlanations) was proposed by Lundberg and Lee [48], which provides a unified framework to explain the output of any machine learning model. SHAP values are based on the concept of Shapley values from cooperative game theory, which measures the contribution of each player to the outcome of a game. The SHAP values interpretation for this study would be to measure the contribution of features to the prediction of a model, and the direction and magnitude of their effects, as well as the interactions and nonlinearities among them. A summary of the experimental database prepared for the machine learning model, as well as the histogram for each variable, is brought in

Table 2. Summary of the experimental database prepared for the machine learning model.

Statistic	Output	Input
	Stress [MPa]	Displacement [mm]	Density [gr/cm3]	Aging Environment [pH]	Moisture [%]	Time [h]
count	12,901	12,901	12,901	12,901	12,901	12,901
mean	1.94	0.36	1.70	7.78	81.03	3075.58
std	1.93	0.27	0.06	2.78	19.98	1713.23
min	0.00	0.00	1.57	3.5	60	0
25%	0.32	0.14	1.66	3.5	60	1000
50%	1.34	0.29	1.69	8.5	100	3000
75%	3.23	0.52	1.74	10	100	5000
max	14.46	1.40	1.8	10	100	5000

and Figure 4.

3. Results and Discussion

The following sections present and discuss the results of both the experimental and machine learning analyses. Initially, data was collected from the experimental process, as detailed in the materials and methods section.

3.1. Mechanical Tests

The flexural strength tests provided valuable insights into the behavior of lime-based mortars subjected to various environmental conditions and exposure durations. The stress versus displacement response, as shown in Figure 5, highlights the bell-shaped curve typical of flexural tests. This curve generally comprises an initial elastic region, a peak corresponding to the maximum load capacity, and a post-peak region where the load gradually decreases. The width and shape of the curve, as well as the post-peak behavior, depend on the exposure conditions. For instance, lime-based mortars tend to exhibit wider bell-shaped curves due to their ductile properties, while exposure to harsh environmental conditions can alter this behavior significantly [26].

According to the Figure 6, under dry curing conditions, the flexural strength showed a continuous increase up to 5000 h. This improvement is likely due to ongoing hydration and limited carbonation, which enhanced the material’s structural integrity over time. For specimens exposed to water immersion (WI), an initial drop in load capacity was observed at 1000 h, likely due to saturation and the lubrication of short fibers within the mortar matrix. However, subsequent strength gains were recorded, suggesting that the prolonged hydration effect eventually outweighed the initial weakening. Specimens exposed to acidic conditions displayed a peak in flexural strength at 3000 h before reaching a plateau. The enhanced strength observed in acidic environments can be attributed to ongoing hydration and carbonation processes, which contributed to improved mechanical performance up to this point. Beyond 3000 h, however, the acidic exposure may have limited further strength development due to chemical interactions that could destabilize the mortar matrix.

The inclusion of short fibers in the mortar played a critical role in enhancing flexural strength across all conditions. These fibers effectively bridged cracks improved overall toughness, and reduced crack width during loading. Such mechanisms were particularly evident in the post-peak behavior, where the presence of fibers mitigated the rapid loss of load-bearing capacity [49]. As illustrated in Figure 5, the stress-displacement curves for different groups reveal varied mechanical responses based on exposure time and environmental conditions. Mortar samples exposed to distilled water demonstrated higher strength values compared to those in dry conditions. This can be attributed to continuous hydration and carbonation, particularly within the interfacial transition zone (ITZ), which contributed to the improved mechanical properties [8,15,50]. The contrasting behaviors depicted in Figure 5 underscore the significant influence of environmental conditions on the flexural performance of lime-based mortars, highlighting the need for tailored approaches in restoration and repair applications.

3.2. Machine Learning

following the process of the experimental results data, they fed into the machine learning model for further analysis. As shown in Figure 7a, the analysis of the model’s performance across different cross-validation folds reveals that the 4-fold cross-validation provided the highest R² score. However, while 10-fold cross-validation yields a marginally higher accuracy, it requires more computational resources. The decision to use 4-fold cross-validation was made to balance accuracy and efficiency, ensuring robust performance with fewer computational demands. As illustrated in Figure 7b, Bayesian optimization identified an optimal learning rate of 0.01729, achieved at iteration 9 of, resulting in the highest R² scores for both training and validation sets. This indicates the best generalization performance for the model.

Additionally, detailed results of the stress-displacement diagram’s prediction are provided, emphasizing the quantified effects of various explanatory variables. The experimental results involve mechanical tests conducted on the mortar samples, as described in the previous section and brought into by previous research, portraying each sample’s outcome. Moreover, the machine learning results discussion encompasses comparative plots of actual versus predicted values for both training and testing datasets, along with kernel density estimation (KDE) plots to assess the distributions of actual-vs-predicted values visually. The close correspondence between the KDE plots of actual and predicted values indicates robust predictive performance. Additionally, SHAP plots are employed to identify the most significant input features and their respective impacts on the output. To validate the prediction accuracy multiple mathematical metrics were employed and evaluated. Primarily, the coefficient of determination (R²) measures the proportion of variance in the dependent variable that is predictable from the independent variables (Equation (4)). Mean Absolute Error (MAE) represents the average absolute difference between observed and predicted values, highlighting the average magnitude of errors in the predictions (Equation (5)). Root Mean Square Error (RMSE) assesses the magnitude of prediction errors, offering a measure of the model’s predictive accuracy by evaluating the square root of the average squared differences (Equation (6)). Together, these metrics provide a comprehensive assessment of the model’s performance, capturing various aspects of prediction accuracy and error magnitude.

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^n(y_i-{\widehat{y}}_i{)}^2}{\sum _{i=1}^n(y_i-{\overline{y}}_i{)}^2}}$$

(4)

$$\mathit{MAE}={\displaystyle \frac{1}{n}}\sum _{i=1}^n|y_i-{\widehat{y}}_i|$$

(5)

$$\mathit{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n(y_i-{\widehat{y}}_i{)}^2}$$

(6)

where:

• $y_i$ denotes actual values,
• ${\widehat{y}}_i$ represents predicted values,
• ${\overline{y}}_i$ is the mean of actual values, and
• n is the number of observations.

As discussed in the methodology section, the XGBoost model is an optimized gradient-boosting algorithm that iteratively refines its predictions by building an ensemble of decision trees.

Table 3. Hyperparameter tuning results of Bayesian optimization methods for the XGBoost model.

Hyperparameters	Bayesian
Maximum Depth	9
No. of Estimators	1500
Subsample	0.60
Min Child Weight	8
Learning Rate	0.0173
Gamma	0.0
Colsample-bytree	0.85
Cross Validation	4
No. of Iteration	50
Total fits	200
Training time	4 min

summarizes the hyperparameter tuning results for the XGBoost model using three different methods: Randomized Search, Grid Search, and Bayesian Optimization. The table shows that the Bayesian Optimization method achieved a maximum depth of 12,950 estimators, a subsample of 0.60, and a learning rate of 0.0124, among other settings. This method used 10-fold cross-validation over 50 iterations, resulting in a total of 500 fits and a training time of 4 min. In comparison, Randomized Search and Grid Search used different parameter values and required more total fits and training time to optimize the model. Bayesian Optimization provided the best results for fine-tuning the model and is used for the results discussion.

The results presented in

Table 4. Comparing performance metrics of machine learning models on training and testing datasets for stress prediction.

Dataset	MSE	MAE	RMSE	R2
Training	0.011	0.042	0.105	0.984
Testing	0.014	0.050	0.116	0.980

confirm that the XGBoost model performs exceptionally well in both training and testing phases. For the training dataset, the model achieves a MSE of 0.011, MAE of 0.042, RMSE of 0.105, and an R² score of 0.984, indicating a high level of accuracy and minimal error. Similarly, in the testing dataset, the model maintains strong performance with an MSE of 0.014, MAE of 0.050, RMSE of 0.116, and an R² score of 0.980. These metrics demonstrate that the model generalizes well to unseen data, maintaining low error rates and high explanatory power. The consistency between training and testing results underscores the model’s reliability for predicting stress values in various time intervals.

Figure 8 presents a comparative performance analysis of the XGBoost model. The KDE plots for the training (a) and testing (b) datasets reveal a close alignment between the distributions of predicted and actual values, indicating the model’s accuracy in stress prediction. The scatterplots of actual vs. predicted values for training (c) and testing (d) datasets display a strong linear relationship, with the most points closely aligned along the line of perfect fit (diagonal line). The comparison of scatter plots (a and b) suggests that the model is performing remarkably well in terms of predicting stress values based on the selected set of input features. The consistency across training and testing datasets suggests the model’s robustness and reliability, demonstrating its effective generalization from training to unseen data.

Figure 9 illustrates the most important input features for predicting stress values of mortar, highlighting their impact on the model’s output. Each point on the plot corresponds to a SHAP value for a particular instance, with the color indicating the feature value (red for high values and blue for low values). The “Displacement (mm)” feature has the most significant impact on stress prediction, showing a wide range of SHAP values. It’s important to note that to predict stress using the algorithm, a notional displacement, based on the observed displacement range, is used as the input, with stress then predicted accordingly. This underscores that variations in displacement greatly influence the predicted stress, consistent with experimental findings, where displacement is the most critical parameter in the flexural test. “Density” and “Time” also make substantial contributions, highlighting their importance in the model’s predictions. While “Corrosion (pH)” and “Moisture (%)” have relatively smaller, yet noteworthy, negative and positive correlations with stress, they still play crucial roles. Overall, the plot provides insights into how each feature influences the model’s output, shedding light on the factors driving stress predictions in the mortar samples.

3.3. Discussion

The variation of the flexural strength across different aging media, as determined from the experiments, is shown in Figure 6, while Figure 10 illustrates the corresponding values predicted by the model. Figure 10 illustrates the flexural strength of specimens under zero exposure, 1000-h exposure, 3000-h exposure, and 5000-h exposure across three different environments: DC, WI, and AC. Figure 5 shows a significant variation in flexural strength depending on the aging medium and exposure duration. For instance, the flexural strength of specimens under zero exposure starts at 4.54 MPa for DC, with notable increases or decreases observed at subsequent exposure durations. Specifically, the strength in the DC environment shows a peak at 5000 h with a value of 6.78 MPa, while the WI environment shows a decline over time, indicating the influence of water on material degradation. Conversely, the AC environment maintains a more stable flexural strength over time. The experimental results highlight the importance of environmental factors on the evolution of material properties, which the gradient boosting model aims to predict and interpret with high accuracy. By comparing the experimental data with the model predictions, there would be a better understanding of the reliability and applicability of machine learning in predicting material behavior under various conditions.

Figure 5 and Figure 11 present the actual and predicted stress-displacement curves for specimens subjected to DC, WI, and AC environments after zero and 1000 h of exposure. These graphs provide a detailed comparison of the behavior of different specimens under varying conditions. Additionally, the area under the curve for each diagram was calculated, and the ratio of the predicted values’ area to the tested values’ area was measured. These ratios ranged from 0.957 to 1.007, with a CoV of 2, further highlighting the accuracy of the model. Subsequently, a XGBoost model was trained and evaluated based on the experimental data, enabling a comparison of the model’s robustness and interpretability against different environmental conditions provided by the experimental results.

In Figure 5a, the stress values for the F_0 condition demonstrate a rapid increase after approximately 0.15 mm of displacement, reaching a peak stress of around 6.0 MPa. This behavior is indicative of the material’s initial stiffness and subsequent yielding. The corresponding graph in Figure 11a shows the predicted stress values following a similar trend. The predicted values closely align with the actual data, peaking around the same displacement range, with a rough margin of error of ±0.05 mm in displacement and ±0.2 MPa in maximum stress. This close alignment validates the accuracy of the XGBoost model in capturing the material’s mechanical response under this condition.

As for the F_WI_1000 condition, Figure 5b illustrates the actual stress values, which initially increase sharply, peaking at approximately 6.5 MPa near 0.75 mm of displacement. In Figure 11b the predicted values also show a steep rise, albeit with slight deviations. The margin of displacement error is around ±0.05 mm, and the maximum stress difference is about ±0.3 MPa. Despite these minor discrepancies, the model successfully captures the overall trend, indicating its robustness in predicting stress-displacement behavior of specimens under water immersion after 1000 h.

For the F_DC_1000 condition depicted in Figure 5c, the actual stress values rise steadily, reaching a peak around 4.0 MPa at 0.75 mm of displacement. Figure 11c shows the predicted stress values with a similar trend, with the model accurately reflecting the material’s behavior after exposure to distilled conditions for 1000 h. The estimated margin of error for displacement is ±0.1 mm, and for maximum stress, it is about ±0.3 MPa. This consistency further demonstrates the model’s predictive reliability across varied conditions.

Finally, the F_AC_1000 condition in Figure 5d shows a more gradual increase in stress, peaking at around 4.5 MPa near 0.6 mm of displacement. The predicted stress values in Figure 11d mirror this pattern, with the XGBoost model effectively capturing the slower rate of stress increase associated with acidic exposure after 1000 h. The rough margin of error for displacement here is ±0.05 mm, with a maximum stress difference of approximately ±0.2 MPa. The model’s prediction accuracy under this condition highlights its ability to adapt to different environmental stressors and predict material degradation over time. These estimated margins of error indicate the model’s overall effectiveness in predicting the stress-displacement curves across different exposure conditions. Indeed, the XGBoost model effectively captures the overall behavior of the material under prolonged acidic exposure, reflecting its capability for predicting the mechanical behavior of lime-based mortars under various environmental conditions.

Figure 12 illustrates the comparison between the experimental results and the machine learning predicted flexural stress for different environments (DC, WI and AC) over time intervals of 1000, 3000, and 5000 h. The actual average flexural stress values are represented by solid lines, while the predicted values are shown with dashed lines. The experimental results encompass the mechanical test outcomes for mortar samples subjected to various aging durations and conditions.

For all environments, there is a noticeable trend where the predicted values closely follow the actual values, although the XGBoost results slightly underpredict the actual stress values. The experimental results show that DC samples exhibit the highest flexural stress, followed by acidic and distilled samples. This pattern is similarly predicted by the machine learning model, demonstrating its reliability and robustness. The average predicted values for all environments closely align with the average actual values at different hour-marks, showcasing the generalizability of the model’s predictive performance under varying environmental conditions. The model achieved an R² of 0.984 and an RMSE of 0.116 for the testing dataset using a 4-fold cross-validation approach, indicating excellent accuracy and consistency in capturing the complex relationships between input features (e.g., density, corrosion, moisture, and exposure duration) and the stress-displacement behavior of lime-based mortar. These metrics provide a standard measure of the model’s error, allowing for direct comparison with other studies in the literature. While the model demonstrates robust predictive capabilities, slight increases in deviations are observed at higher time points, particularly under acidic exposure conditions. This suggests potential areas for refinement, such as incorporating more data points or leveraging additional machine learning techniques to further enhance the model’s accuracy and reliability. Overall, the results underline the strength of the XGBoost model in delivering reliable predictions and its potential as a valuable tool for assessing material performance in adverse environmental conditions.

4. Conclusions

This study integrates experimental analysis and machine learning modeling to investigate the mechanical behavior and durability of lime-based mortar under acidic environmental conditions. The findings contribute valuable insights for engineering applications, particularly in the conservation of historic structures and the development of durable construction materials. The following conclusions are drawn:

• A commercial hydraulic lime-based mortar was exposed to three conditions—acidic solution (pH 3.0), distilled water immersion, and dry storage, and tested after 1000, 3000, and 5000 h. Dry storage samples exhibited the highest flexural stress, followed by acidic and distilled water environments. The flexural strength of acidic specimens peaked at 3000 h but declined with prolonged exposure, while specimens in distilled water and dry conditions demonstrated earlier strength gains due to ongoing hydration and carbonation.
• The eXtreme Gradient Boosting (XGBoost) algorithm accurately predicted the mechanical behavior of lime-based mortar under varying exposure conditions. Using stress-displacement as the output and environmental and material properties as inputs, the model achieved excellent predictive performance, with R²= 0.984 and RMSE = 0.116 for the testing dataset. Minor discrepancies in acidic environment predictions were noted but did not significantly impact the model’s overall reliability.
• Combining experimental results with machine learning provides a robust tool for predicting the behavior of lime-based mortars in adverse environments. This approach enhances the assessment of durability and offers a predictive framework for optimizing material selection and restoration strategies.
• Future studies should investigate the behavior of lime-based mortars under varying levels of acidity to better understand the influence of acid concentration on mechanical performance and durability. This could expand the applicability of lime-based mortars to different industrial and urban environments with varying acidic exposures.
• Given the use of lime-based mortars in Textile Reinforced Mortar (TRM) systems for structural strengthening, these findings can be directly applied to assess the durability and mechanical performance of TRM composites under acidic environmental conditions. This insight is valuable for the design and implementation of TRM systems in restoration projects involving challenging environmental conditions.