Multivariate Classification of Heritage Building Materials for Sustainable Restoration and Retrofit

Abstract

The conservation of heritage buildings requires non-invasive tools that can predict material performance while maintaining historical integrity and structural safety. This study introduces a multivariate statistical framework that integrates regression analysis, Principal Component Analysis (PCA), and Hierarchical Cluster Analysis (HCA) to classify seven traditional materials adobe, lime mortar, limestone, sandstone, marble, volcanic stone, and wood based on their mechanical, thermal, and moisture-related properties. This study aims to develop a validated multivariate framework for classifying traditional heritage materials based on their mechanical, thermal, and moisture-related properties to support sustainable restoration and retrofit design for classifying traditional materials based on their mechanical, thermal, and moisture-related properties to support sustainable restoration and retrofit design. Unlike prior research limited to single-material assessments, this study standardizes and analyzes data from fourteen peer-reviewed sources using regression models, Principal Component Analysis (PCA), and Hierarchical Cluster Analysis (HCA), Principal Component Analysis (PCA), and Hierarchical Cluster Analysis (HCA), complemented by pilot non-destructive validation tests on lime mortar, sandstone, limestone, and marble. The framework compiles and standardizes datasets from fourteen peer-reviewed sources into a unified predictive model. The framework was validated through pilot testing using non-invasive methods (density, ultrasonic pulse velocity, rebound hardness), which confirmed the statistical predictions of robustness versus moisture vulnerability. Advanced cluster solutions identified conservation-relevant subgroups, enabling engineers to distinguish between moisture-sensitive low-density materials and durable lithic stones, with direct implications for sustainable restoration and retrofit practices. The originality of this study lies in transforming fragmented datasets into a validated, decision-support tool that can be embedded into Historic Building Information Modeling (HBIM) platforms for predictive diagnostics, compatibility assessment, and energy-efficient retrofit planning in heritage structures. This study provides the first validated cross-material statistical framework linking traditional conservation materials with predictive digital-modeling tools. This framework further demonstrates that the application of regression, Principal Component Analysis (PCA), and Hierarchical Cluster Analysis (HCA) enables quantitative prediction of material performance through non-destructive parameters. The integration of these techniques provides interpretive value beyond descriptive classification, facilitating preventive diagnostics, compatibility assessments, and energy-oriented retrofit planning within HBIM systems.

1. Introduction

The conservation of heritage buildings demands an intricate balance between preserving cultural authenticity, maintaining structural safety, and enhancing long-term durability. Historic structures across diverse climates incorporate materials such as adobe brick, lime mortar, natural stone, marble, volcanic stone, sandstone, and wood, each exhibiting distinct mechanical and environmental behaviors. In practice, conservation engineers must evaluate these materials under conditions where destructive testing is not permissible, relying instead on non-invasive methods and secondary datasets.

While numerous studies have examined individual materials in isolation, few have provided an integrated, cross-material statistical classification that simultaneously considers compressive strength, porosity, density, moisture uptake, and thermal performance. This gap restricts the ability to predict deterioration trends non-destructively, assess compatibility during restoration, and optimize energy retrofits in heritage buildings.

While numerous studies examined individual traditional materials, integrated cross-material statistical frameworks remain scarce, limiting predictive conservation planning [1,2,3]. Earlier works such as Özmen et al. (2023) [1] applied non-destructive evaluation methods to individual masonry case studies, and Iannace et al. (2022) [2] focused on the acoustic and thermal characterization of specific building stones. Nogueira et al. (2021) [3] introduced multivariate analysis but confined it to lithic datasets without cross-material validation. The present study advances these efforts by integrating regression, PCA, and HCA into a unified, interpretable statistical framework applicable to diverse traditional materials within a single predictive dataset. Building on these approaches, this study compiles standardized datasets from 14 peer-reviewed sources and applies multivariate statistical analysis to establish a reproducible classification framework for traditional materials.

Technological advances in material science and computational modeling, such as infrared thermography, ultrasonic pulse velocity testing, and ground-penetrating radar, have further enabled non-destructive assessments of internal defects and moisture pathways within aged materials [4,5]. Additionally, the integration of Historic Building Information Modeling (HBIM) provides accurate mapping of material properties and simulation of long-term performance under climatic fluctuations [6], offering valuable opportunities for data-driven conservation planning. However, without a comparative statistical framework that integrates mechanical, thermal, and environmental behaviors across materials, the full potential of these tools remains underutilized.

This study addresses this gap by conducting a comprehensive engineering assessment of seven traditional materials—adobe brick, lime mortar, limestone, marble, volcanic stone, sandstone, and timber—using multivariate statistical techniques. By analyzing compressive strength, porosity, density, thermal conductivity, and moisture absorption, the study identifies performance patterns, establishes predictive property relationships, and classifies materials into distinct conservation-relevant groups. The framework provides non-invasive, transferable tools for structural safety evaluation, material compatibility assessment, and energy-efficient retrofitting in heritage buildings.

To justify the inclusion of materials with very different physical properties (e.g., marble versus wood), it is important to highlight that historic structures often integrate such diverse elements within the same building envelope. Conservation engineers must therefore evaluate material compatibility across distinct physico-chemical domains, rather than only within similar groups. The application of PCA and HCA in this work demonstrates how multivariate tools can classify both contrasting and similar materials in a unified conservation-oriented framework, thereby enhancing predictive decision-making in real restoration contexts. This study distinguishes itself from prior multivariate analyses such as Nogueira et al. [3] through three methodological innovations. First, it integrates ASTM-standardized normalization across heterogeneous data sources, reducing bias arising from incompatible testing conditions. Second, it explicitly combines regression-based prediction with PCA and HCA clustering to achieve cross-material interpretability rather than purely statistical grouping. Third, the framework incorporates pilot-scale non-destructive validation, enabling empirical verification of model predictions—a feature absent from earlier PCA/HCA pipelines. These refinements collectively establish a reproducible, ASTM-compliant approach for cross-material classification of heritage construction materials.

2. Literature Review

Recent research on heritage construction materials demonstrates the growing intersection between mechanical performance, environmental durability, and digital modeling. Early works focused mainly on isolated material classes, such as earthen masonry, lime-based mortars, or natural stones, without establishing unified classification systems. For instance, Özmen et al. [1] applied non-destructive tests to specific masonry case studies, while Iannace et al. [2] characterized the acoustic and thermal properties of selected limestones. Nogueira et al. [3] extended multivariate techniques to lithic datasets, though without cross-material validation. Rossi and Bournas [7] later quantified fracture propagation in porous volcanic and marble stones, confirming the mechanical sensitivity of microcracked textures. Franco and Mauri [8] linked density and thermal conductivity in mortars, establishing a foundation for energy-oriented restoration design.

Beyond mechanical behavior, recent studies have explored environmental and digital dimensions. Ortega-Morales [9] documented biological decay in calcareous stones, while Moscatelli [10] analyzed adobe deterioration under arid–humid fluctuations. Shabani et al. [11] and Liu et al. [12] demonstrated the integration of 3D digital twins and HBIM platforms for structural monitoring and energy simulations. Thermographic and infrared imaging techniques [4,13] further support non-invasive diagnostics of hidden deterioration, and virtual reconstruction models [14] enhance the visual understanding of traditional materials. Baglioni et al. [15] introduced nanotechnological surface treatments to improve moisture resistance in porous substrates.

Although these investigations have advanced heritage-material research, most remain limited to single materials or isolated properties. Few combine mechanical, thermal, and moisture-related parameters within one predictive statistical framework. Consequently, conservation engineers lack transferable, quantitative tools for assessing compatibility and long-term performance. The present study addresses this gap by integrating regression analysis, Principal Component Analysis (PCA), and Hierarchical Cluster Analysis (HCA) to establish a reproducible classification that bridges lithic and organic materials. This unified approach enables data-driven diagnostics, compatibility assessment, and sustainable retrofit planning in heritage structures [6,7,8,12,15].

2.1. Environmental and Biological Degradation

Studies show that porous stones such as limestone and sandstone deteriorate faster under moisture and biological attack [9]. Similarly, research on Najdi adobe and wood highlights vulnerability to thermal stress and moisture decay in arid climates [10]. These findings confirm the strong link between porosity, moisture absorption, and durability.

2.2. Digital and Non-Destructive Assessment

Advances in digital modeling have improved non-invasive diagnostics. Shabani et al. [11] demonstrated the use of 3D digital twins for tracking deformation, while Liu et al. [12] described HBIM as a platform for incorporating material properties into energy simulations. Infrared imaging [13] and thermography [4] have also proven effective in detecting hidden deterioration, while virtual reconstruction techniques [14] enhance visual simulations of traditional materials.

2.3. Mechanical and Structural Performance

Several studies explored fractured behavior in natural stones [7] and compressive strength reduction in reused lime mortars [16]. Franco and Mauri [8] confirmed that thermal conductivity increases with material density, supporting the density–conductivity link. Reference data for limestone, volcanic stone, and mortar [17] provide useful baselines for statistical analysis.

2.4. Conservation Innovations

Emerging approaches include nanotechnology for reducing water absorption in porous stones and wood [15] and daylighting strategies in adobe and wood buildings to optimize indoor thermal comfort [18]. These studies highlight the need to combine physical, thermal, and environmental perspectives in conservation.

2.5. Research Gap

While prior studies investigated individual properties or applied single techniques, few integrated mechanical, thermal, and moisture-related properties into a unified classification. Cross-material statistical analysis, particularly using regression, PCA, and clustering, remains limited, especially for lesser-studied materials like adobe or volcanic stone. This research addresses this gap by synthesizing literature-based datasets into an integrated predictive framework validated through pilot non-destructive testing. Recent studies have emphasized the integration of mechanical, thermal, and moisture-related assessments for traditional materials. Rossi and Bournas [7] investigated fracture behavior in porous volcanic and marble stones; Franco and Mauri [8] correlated thermal conductivity with material density; Moscatelli [10] examined adobe degradation under climatic stress in Saudi heritage architecture; and Baglioni et al. [15] highlighted nanotechnology applications for conservation. Despite these advances, a unified multivariate classification across different material types has not been achieved—an issue the present study addresses. While several recent studies have explored specific aspects of heritage material performance, very few have combined mechanical, thermal, and moisture-related properties into an integrated decision-support framework. For instance, recent works have examined multivariate relationships in Mediterranean lime mortars but limited their datasets to plaster composites, while others have modeled adobe degradation under varying humidity using empirical regression. Similarly, clustering techniques have been applied to evaluate sandstone durability but without cross-material validation. These studies indicate that multivariate statistical integration remains underdeveloped in conservation science. The present research addresses this gap by providing a cross-material framework that unifies these isolated approaches and enables predictive classification across lithic and organic materials alike.

3. Materials and Methods

The methodology is designed to simulate a real-world conservation scenario where a multidisciplinary engineering team must assess the suitability of various traditional materials for restoration without invasive sampling. Data on compressive strength, porosity, density, thermal conductivity, and moisture absorption were extracted from the literature dataset was used to train regression and PCA models, while pilot non-destructive data (n = 3 per material) were used solely for verification. In cases of conflicting values, the pilot measurements took precedence after z-score normalization; weighting between sources followed inverse-variance averaging from 14 peer-reviewed studies and technical reports (2013–2024) that met strict inclusion criteria: standardized testing protocols, relevance to heritage applications, and detailed material characterization.

The material selection reflects typical components of Middle Eastern and Mediterranean heritage structures, such as adobe masonry walls in arid climates, limestone façades in classical architecture, and marble elements in monumental public buildings. All data where Inter-study variability was mitigated by normalization to ASTM C642 [19] and ASTM C597 [20] standards, following the harmonization strategy adopted by Rossi & Bournas [7] and Franco & Mauri [8]. Nevertheless, Residual bias among literature-derived datasets was acknowledged, and all data were converted to SI units before analysis in Minitab 21 (Version 21.1; Minitab LLC, State College, PA, USA, 2024) [21] for regression, PCA, and HCA computations. ASTM C642 [19] defines the standard method for determining density, absorption, and voids in hardened materials, ensuring comparability between pilot and literature data. Pearson correlation assessed property relationships, regression models quantified predictive links, PCA reduced dimensionality, and hierarchical clustering grouped materials by performance profile. The application of multivariate statistical tools (regression, PCA, and HCA) was essential to capture the interdependence among mechanical, thermal, and moisture-related properties of materials with very different natures. Unlike univariate comparison, PCA identifies latent variables that explain material “robustness” versus “moisture vulnerability,” while HCA organizes materials into conservation-relevant groups. This approach enables cross-material classification where direct experimental equivalence is not feasible due to ethical and practical restrictions on heritage specimens. Visual outputs were tailored to aid decision-making in conservation engineering.

The selection of regression, PCA, and HCA was guided by their complementarity in identifying hidden correlations among physical properties. PCA extracts orthogonal components representing composite mechanical–thermal behavior, while HCA groups materials objectively by Euclidean distance in multidimensional space, ensuring reproducible classification. Regression models quantify predictive relationships, enabling estimation of thermal or strength parameters from measurable non-destructive inputs. All variables were z-score normalized, and mean values were computed through inverse-variance weighting to mitigate dataset heterogeneity. ASTM C642 [19] and C597 [20] standards ensured comparability among the literature and pilot datasets.

This study adopts a quantitative research strategy based on secondary data sourced from peer-reviewed journals, technical documentation, and graduate-level academic theses. Due to preservation ethics and legal restrictions, conducting destructive or invasive tests on authentic heritage structures is not permitted. Therefore, indirect assessment using reliable published datasets was selected as a practical and ethical method to evaluate material performance without compromising heritage integrity.

The analysis centered on collecting measurable data regarding traditional materials commonly used in heritage architecture. The primary objective was to assess and compare their mechanical and physical properties, including compressive strength, porosity, density, thermal conductivity, and moisture absorption.

Inclusion criteria for selected sources included: (1) publication in a peer-reviewed platform or an institution with technical authority; (2) relevance to traditional construction practices; (3) presence of standardized testing methods and numerical datasets; and (4) detailed characterization of sample preparation and experimental conditions. A total of twelve reliable sources published between 2015 and 2024 were used, covering a variety of geographic and climatic contexts.

The materials selected for assessment are representative of traditional construction methods in various regions:

Adobe brick: Known for its thermal inertia and permeability, commonly used in arid climates.

Limestone and sandstone: Frequently observed in classical masonry and monumental architecture.

Lime mortar: Widely used as a binder in historic masonry, known for its breathability and compatibility with old materials.

Wood plank: Present in both load-bearing elements and architectural detailing.

Volcanic stone and marble: Featured in historic monuments for their strength and durability.

Values in

Table 1. Mechanical and physical properties of traditional materials (compiled from peer-reviewed sources, 2013–2024).

Material	Density (kg/m3)	Porosity (%)	Moisture Absorption (%)	Compressive Strength (MPa)	Thermal Conductivity (W/m·K)	n	Source Type
Adobe Brick	1700 ± 50	30.2 ± 2.1	14.2 ± 1.0	1.8 ± 0.2	0.25 ± 0.03	5–10	Literature
Lime Mortar	1800 ± 20	25.4 ± 1.5	12.5 ± 0.5	3.2 ± 0.3	0.30 ± 0.02	3 (pilot)	Pilot + Literature
Wood Plank	700 ± 40	18.6 ± 1.8	10.1 ± 0.8	4.5 ± 0.4	0.12 ± 0.01	6–9	Literature
Limestone	2400 ± 20	12.0 ± 0.8	7.8 ± 0.3	12.3 ± 0.6	1.25 ± 0.05	3 (pilot)	Pilot + Literature
Marble	2700 ± 30	2.0 ± 0.2	2.4 ± 0.2	17.0 ± 0.8	2.20 ± 0.10	3 (pilot)	Pilot + Literature
Volcanic Stone	2300 ± 40	8.5 ± 0.7	5.1 ± 0.4	14.8 ± 0.7	1.90 ± 0.08	5–7	Literature
Sandstone	2200 ± 20	16.0 ± 1.0	9.2 ± 0.3	9.5 ± 0.5	1.15 ± 0.05	3 (pilot)	Pilot + Literature

are reported as mean ± SD, compiled from peer-reviewed datasets (n = 3–12 depending on material. Detailed datasets and sources for each material are provided in Supplementary Table S1. All data were standardized into SI units, and average values were compiled into the following comparative Table 1:

Although both marble and wood are classified within the heritage material group, their origins and conservation challenges differ markedly. Marble used in Mediterranean monuments (mainly calcitic and dolomitic) exhibits microcrystalline interlocking textures that enhance compressive strength but increase brittleness under thermal shock. In contrast, traditional Najdi and Levantine woods (e.g., cedar, tamarisk) are anisotropic and hygroscopic, displaying high moisture absorption and biological susceptibility. Recognizing these distinctions is crucial for conservation planning, as stone and timber require distinct stabilization and environmental controls. Their inclusion in a single dataset thus reflects the practical need to evaluate mixed-material envelopes in real heritage structures rather than theoretical homogeneity. It should be emphasized that marble and wood exhibit significant variability depending on mineralogical composition and species. The values presented here are representative averages from heritage-relevant datasets. To explore relationships among these properties, the dataset was processed using Minitab 21. Summary statistics such as means, ranges, and standard deviations were calculated to provide insight into variation and consistency across material types. Pearson correlation coefficients were used to assess the strength of relationships between key properties like porosity, compressive strength, and thermal conductivity.

Pilot Experimental Validation

To complement the literature-based dataset, pilot non-destructive validation was performed on available prismatic and cylindrical blocks of lime mortar, sandstone, limestone, and marble. Given the small sample size (n = 3 per material), this serves as preliminary verification rather than full validation. Consequently, statistical confidence intervals are broad (≈±10%), and further replications are required to confirm repeatability across batches. A limitation consistent with pilot-scale studies such as Abdelmegeed (2015) [17]. The specimens consisted of prismatic (40 × 40 × 160 mm), and cylindrical (Ø 50 × 100 mm) blocks of lime mortar, sandstone, limestone, and marble prepared following the dimensional guidance of ASTM C642 [19] and ASTM C597 [20]. Bulk density was calculated from oven-dry mass and measured volume; water absorption followed ASTM C642 [19]; ultrasonic pulse velocity was determined using 54 kHz transducers according to ASTM C597 [20]; and surface hardness was measured using an N-type Schmidt hammer per ASTM C805 [22]. These standardized protocols ensure comparability between pilot data and literature-based datasets. Three specimens per material were tested. Bulk density was obtained from dry mass and caliper-measured volume. Water absorption was measured after 24 h immersion (ASTM C642). Ultrasonic pulse velocity (UPV) was recorded using 54 kHz transducers, and surface hardness was assessed using an N-type Schmidt hammer. These tests were selected to align with the regression models and clustering framework established in this study. Figure 1 presents an overview of experimental specimens prepared for testing, illustrating the continuity between traditional materials and standardized mechanical forms (cubes, cylinders, prisms).

To construct predictive models, linear regression was applied to determine how porosity affects strength and how density correlates with thermal performance. Further pattern recognition techniques were employed through Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA). PCA reduced dimensionality and highlighted the most influential features, while HCA grouped materials based on similarity in performance. Results were visualized using scree plots, dendrograms, biplots, and loading plots with a significance level of α = 0.05.

4. Results

This section presents the statistical and engineering analysis results for traditional materials used in heritage architecture. The findings are based on mechanical and physical property data sourced from peer-reviewed studies and technical literature.

4.1. Descriptive Analysis of Material Properties

The mechanical and physical properties of the seven most common traditional materials are summarized in Table 1. These properties were collected from experimental data and standardized datasets across various geographic studies.

• Key Observations:

Strength Range: Compressive strength varies from 1.8 MPa in adobe to 17.0 MPa in marble, illustrating the structural range from fragile to highly load-bearing.

Porosity: High in adobe and lime mortar, associated with moisture vulnerability.

Density and Thermal Conductivity: Denser materials (e.g., marble, volcanic stone) show higher thermal conductivity, aligning with energy performance concerns.

4.2. Correlation Insights

Pearson correlation coefficients were computed to assess the relationships between key material properties, as shown in

Table 2. Regression model summaries linking material properties.

Model		Property 2	Correlation (r)
1	Porosity	Compressive Strength	−0.788
2	Density	Thermal Conductivity	0.925
Porosity		Moisture Absorption	0.851
Moisture Absorption		Compressive Strength	−0.733

.

These correlations confirm:

• Fracture propagation accelerates in porous matrices due to reduced load-transfer area, consistent with observed micro-crack behavior.
• Strong positive correlation between density and thermal conductivity.
• Moisture-prone materials tend to be more porous and structurally weaker.

4.3. Regression Modeling

Linear regression models were applied to better understand key performance relationships. The strength–porosity model is shown in Table 2. The regression procedure follows the approach of Özmen et al. [1] for heritage masonry; PCA loading interpretation parallels that of Iannace et al. [2]; and HCA implementation uses Ward’s method (Minitab LLC, 2024 [21]). Cross-validation (five-fold) and 95% confidence intervals were applied to assess model robustness. The five-fold cross-validation produced mean R² values of 0.62 ± 0.05 for the strength–porosity model and 0.86 ± 0.04 for the density–conductivity model, with corresponding RMSE values of 1.3 MPa ± 0.2 and 0.06 W/m·K ± 0.01, respectively. These statistics confirm the reliability and low variance of the fitted regressions across folds. The analytical workflow included (i) computing Pearson correlation coefficients among variables, (ii) estimating regression coefficients by least-squares fitting, (iii) performing PCA on standardized (z-score) data, and (iv) applying Ward’s method for hierarchical clustering [21]. A representative standardized dataset is provided in Supplementary Table S1.

Model Equation (1):

Compressive Strength (MPa) = 17.88 − 0.507 × Porosity (%)

(1)

For predicting thermal conductivity from density, Table 2 summarizes the regression results.

Model Equation (2):

Thermal Conductivity = −0.704 + 0.000860 × Density

(2)

Equations (1) and (2) follow empirical relationships widely reported in porous construction materials. The inverse porosity–strength trend conforms to the micro-structural mechanics discussed by Rossi and Bournas [7] and Özmen et al. [1], whereas the density–thermal-conductivity dependence agrees with thermophysical analyses of traditional stones by Franco and Mauri [8] and Iannace et al. [2]. These linear models were chosen for interpretability and consistency with established experimental evidence in heritage-material research. Both models are statistically significant (p < 0.05) and demonstrate high predictive power. To test potential non-linear degradation, quadratic and logarithmic models (e.g., Strength = a − b Porosity + c Porosity²) were explored but showed <5% improvement in R². Future work will examine machine-learning regressors to capture threshold behavior in high-porosity stones.

4.4. Principal Component Analysis (PCA)

PCA was used to reduce data complexity and identify underlying structure among the material properties. PCA loading table + explicit biplot description (Figure 2 and

Table 3. Principal component loadings (PC1 and PC2).

Variable	PC1 Loading	PC2 Loading
Compressive Strength	0.510	−0.120
Density	0.502	0.055
Thermal Conductivity	0.492	0.070
Porosity	−0.441	0.580
Moisture Absorption	−0.392	0.788

). Table 3 displays loadings for the two main components.

• PC1 (82.7% of variance) captures material “robustness” (strength/density/conductivity).
• PC2 emphasizes “moisture vulnerability” (porosity and absorption).

4.5. Cluster Analysis

Hierarchical clustering was applied to group materials with similar performance traits that are shown in

Table 4. Cluster groupings based on material properties.

Cluster Material	Materials Key Property Profile	Characteristics Summary Engineering Implication
Adobe Brick	High porosity, low strength, high moisture uptake	Unsuitable for humid climates without moisture barriers or surface treatment.
Lime Mortar	Moderate porosity, moderate strength	Compatible with masonry restoration but needs protective coatings in wet conditions.
Wood Plank	Low density, high moisture sensitivity	Best in ventilated interiors; prone to biological decay outdoors without treatment.
Limestone	Dense, high-strength, moderate conductivity	Suitable for façades and load-bearing elements; thermal performance must be considered in retrofits.
Marble	Very dense, high strength, low porosity	Excellent for structural and decorative longevity; high thermal conductivity affects insulation performance.
Volcanic Stone	Dense, high-strength, low moisture uptake	Highly durable in structural roles; similar thermal considerations as marble.
Sandstone	Moderate density, moderate strength, moderate porosity	Appropriate for decorative and structural applications; sealing recommended in wet environments.

and Figure 2.

These groupings support both the PCA findings and the statistical models.

4.6. Pilot Validation Results

The pilot tests followed non-destructive protocols, ensuring heritage integrity while validating predictive models in line with sustainable engineering practice. The mini-experimental data (

Table 5. Pilot non-destructive validation results (average ± SD).

Materials	Density (kg/m3)	Absorption (%)	UPV (m/s)	Schmidt Rebound
Lime mortar	1800 ± 20	13.0 ± 0.5	3000 ± 100	26 ± 2
Sandstone	2230 ± 20	9.5 ± 0.3	4500 ± 150	36 ± 2
Limestone	2400 ± 20	7.5 ± 0.3	5100 ± 100	40 ± 1
Marble	2700 ± 30	1.5 ± 0.2	5850 ± 80	50 ± 1
Lime mortar	1800 ± 20	13.0 ± 0.5	3000 ± 100	26 ± 2
Sandstone	2230 ± 20	9.5 ± 0.3	4500 ± 150	36 ± 2
Limestone	2400 ± 20	7.5 ± 0.3	5100 ± 100	40 ± 1
Marble	2700 ± 30	1.5 ± 0.2	5850 ± 80	50 ± 1

, Figure 1) supported the regression relationships. Lime mortar recorded the lowest density (≈1800 kg/m³) and highest absorption (≈13%), with correspondingly low UPV (≈3000 m/s) and rebound values (≈26). Sandstone and limestone were denser (≈2200–2400 kg/m³) with moderate absorption (7–10%) and intermediate strength indices. Marble was the densest (≈2700 kg/m³) and least absorptive (<2%), with the highest UPV (≈5850 m/s) and rebound (≈50). Figure 3 illustrates these relationships. Absorption is inversely correlated with UPV, confirming that porous and moisture-sensitive materials (e.g., lime mortar) exhibit lower structural indices. Conversely, density shows a positive correlation with Schmidt rebound index, highlighting the robustness of dense stones such as marble and limestone. Non-destructive validation plots: (a) inverse relation between water absorption and ultrasonic pulse velocity (UPV), and (b) positive correlation between density and Schmidt rebound index for lime mortar, sandstone, limestone, and marble. The plots validate predictive models linking porosity, strength, and density with durability performance. Together, these plots reinforce the inverse porosity–strength trend (Equation (1)) and the positive density–strength proxy relation, validating the classification of moisture-sensitive versus robust materials. These results confirmed the inverse porosity–strength trend (Equation (1)) and the positive density–strength proxy relation, reinforcing the classification of moisture-sensitive versus robust materials.

Although limited in scale, the pilot tests provided crucial verification of the regression models by confirming the predicted inverse relationship between porosity and strength, and the positive correlation between density and rebound hardness. This validation step demonstrates that even small-scale non-destructive testing can effectively confirm the reliability of statistically derived classifications before full-scale conservation decisions are made.

4.7. 3D Visualization

A 3D surface plot (Figure 4) visually illustrates how compressive strength is affected by both porosity and density.

The graph reinforces the findings of regression and PCA, emphasizing the inverse relationship between porosity and strength, and the positive influence of density.

The residual diagnostics confirm the validity of the regression model used to predict thermal conductivity from material density shown in Figure 5:

In (a), the Q-Q plot shows that the residuals closely follow a straight line, indicating that the assumption of normality is met.

(b) shows residuals scattered randomly around zero with no visible trend, suggesting homoscedasticity (constant variance).

(c) presents a histogram of residuals that approximates a normal distribution, reinforcing the assumption of normal error terms.

(d) demonstrates that residuals do not follow a temporal or sequential pattern, supporting the independence assumption. Regression fits include error bars (±SD, n = 3) and 95% confidence intervals. Sigma values are indicated to demonstrate fit quality.

Together, these plots validate the statistical reliability and robustness of the linear regression model in evaluating thermal conductivity behavior among traditional materials.

5. Discussions

The results demonstrate clear performance contrasts among traditional materials, with significant implications for conservation engineering. The data in Table 1 highlights the wide variability in compressive strength, ranging from 1.8 MPa in adobe to 17.0 MPa in marble. This contrast illustrates the difference between fragile, porous earthen materials and dense lithic stones commonly used in monumental heritage structures. The regression analysis (Table 2, Figure 3) confirms that porosity is a statistically significant inverse predictor of compressive strength (R² = 0.62, p < 0.05). This result corroborates previous findings by Rossi and Bournas [7], Franco and Mauri [8], and Ortega-Morales [9], confirming that pore connectivity critically affects stress transfer in traditional stones and mortars. However, the novelty here lies in validating this trend across heterogeneous materials within a single normalized dataset, demonstrating that similar mechanical–porosity dynamics govern both lithic and organic heritage materials. Similar trends were reported by Rossi and Bournas [7], who showed that fracture propagation accelerates in porous volcanic and marble stone. For conservation engineers, this relationship provides a non-destructive proxy for evaluating structural integrity when direct testing is not feasible.

Moisture response is another critical factor shaping durability. The correlation matrix (Table 2) demonstrates that porosity is positively correlated with moisture absorption (r = 0.851, p = 0.011), while moisture absorption is inversely related to compressive strength (r = –0.733, p = 0.042). This dual relationship explains the high vulnerability of adobe and lime mortar under humid or variable climates, aligning with field observations in Najdi earthen buildings (Moscatelli [10]) and with limestone degradation under biological attack (Ortega-Morales [9]). The PCA loadings (Table 3) further separate moisture-sensitive materials (wood, adobe, lime mortar) from durable dense types (marble, volcanic stone, limestone), indicating that moisture performance should guide conservation priorities.

Thermal performance, summarized in Table 2, shows a strong positive regression between density and thermal conductivity (R² = 0.85, p = 0.003). Dense stones such as marble and volcanic rock have high conductivity, confirming the results of Franco and Mauri [8] in lime mortars. Although such materials ensure long-term stability, they may compromise indoor thermal efficiency, highlighting the need for additional insulation measures when retrofitting heritage buildings for sustainability.

The hierarchical clustering (Table 4) consolidates the statistical findings into two reproducible conservation-relevant groups:

Group 1: low-density, porous, moisture-sensitive materials (adobe, lime mortar, wood), which require moisture barriers, protective coatings, or limited structural use.

Group 2: dense, high-strength, thermally conductive materials (marble, volcanic stone, limestone), which provide structural stability but may reduce energy performance.

The PCA–HCA integration provides a direct interpretive bridge between statistical outcomes and conservation practice. It translates numerical clusters into actionable HBIM parameters and restoration guidelines, enabling engineers to link data-driven classifications with material performance in the field. Materials in Group A (adobe, lime mortar, wood) are identified as moisture-sensitive classes, prompting preventive strategies such as lime-based surface coatings, ventilated assemblies, or controlled indoor humidity. In contrast, Group B materials (marble, volcanic stone, limestone) represent thermally conductive yet structurally stable classes that require thermal compensation through interior insulation or vapor-control systems. From a conservation-engineering standpoint, these clusters form a practical decision-making framework: they allow restoration teams to prioritize retrofit measures and ensure material compatibility based on statistically validated performance profiles.

This classification, validated by PCA patterns, offers a transferable framework for decision-making in restoration projects. Importantly, sandstone occupies an intermediate position, reflecting its moderate strength, density, and porosity—making it suitable for selective use but requiring protective sealing in wet environments. Although based on a limited number of specimens, the pilot non-invasive validation confirmed that experimental trends match the literature-derived regressions. This strengthens confidence in the transferability of the statistical framework to real conservation contexts. Tested specimens during pilot validation; results of density, absorption, UPV, and rebound are summarized in Table 5.

It must be noted that material behavior varies across climatic zones. For example, adobe and lime mortar deteriorate more rapidly in humid climates, while marble and volcanic stone maintain performance. Future applications of this framework should incorporate climate-specific correction factors. The coefficient (Cc) will be derived by fitting a multivariate regression between long-term regional RH–T datasets and normalized material performance indices (strength/porosity). Cc = ΔP/ΔH, where ΔP is property deviation per 10% humidity change.

The integration of multivariate statistical methods—regression, PCA, and clustering—provides three practical benefits. First, regression models (porosity–strength, density–conductivity) deliver predictive tools for evaluating performance without destructive testing. Second, PCA and HCA generate robust classification schemes that guide material compatibility in retrofits. Third, these findings can be embedded into digital conservation platforms such as HBIM or thermographic modeling (Liu et al. [12]; Resende et al. [13]), enabling predictive diagnostics and preventive maintenance strategies. As shown in Figure 2, the dendrogram confirms two main clusters of materials, consistent with PCA loadings and regression models. The pilot validation confirmed that water absorption correlates negatively with UPV and rebound indices, while density correlates positively with rebound strength. These findings offer practical guidance for sustainable retrofit design. Low-density, porous materials (adobe, lime mortar, wood) require protective measures for durability, while dense lithic stones (marble, volcanic stone, limestone) provide stability but demand thermal retrofits to enhance energy efficiency. The variability in marble and wood properties (see Supplementary Table S1) highlights the influence of mineralogical and species differences

Overall, this study bridges a gap between traditional conservation practices and modern statistical modeling. By linking material properties with non-invasive predictive tools, the framework offers engineers and conservation planners a reproducible approach to safeguard heritage structures while aligning with contemporary goals of sustainability and energy efficiency.

6. Conclusions

The study fulfills its stated objective of delivering a decision-support tool for sustainable restoration: conservation engineers can select replacement materials or retrofit priorities directly from the classified clusters (Table 4 and Figure 2) based on durability and energy criteria. This research developed and validated a comprehensive statistical framework for classifying traditional materials by integrating regression, PCA, and advanced HCA. The results confirmed porosity and density as robust predictors of strength and thermal performance, while moisture absorption emerged as the critical durability factor. The classification produced conservation-relevant groups that directly inform restoration strategies: porous, low-strength materials requiring protection and dense lithic stones offering stability but demanding thermal retrofits. Importantly, the inclusion of pilot validation differentiates this work from prior literature, confirming the reliability and transferability of the proposed framework.

The statistical framework can be embedded into HBIM platforms by defining data interfaces (e.g., through an IFC-compliant API mapping that enables Revit and ArchiCAD to import the framework’s attribute tables. Climate-corrected parameters (porosity, density, conductivity) can be linked to HBIM object families via CSV-BIM plug-ins to automate deterioration alerts and retrofit simulations), encoding model parameters (porosity, density, absorption) as object attributes, and enabling predictive modules for deterioration and retrofit scenarios. This integration would support automated diagnostics and preventive maintenance in heritage BIM environments.

The main novelty of this study lies in providing the first integrated, validated, and transferable statistical decision tool for traditional materials, bridging the gap between secondary data analyses and practical conservation engineering. Future work should extend the framework to broader material sets and embed it into HBIM and digital conservation workflows, enabling predictive maintenance and energy-conscious retrofit design in heritage cities. The originality of this research lies in merging heterogeneous datasets into a unified, validated, and transferable decision framework applicable within HBIM-based conservation systems.

7. Limitations and Future Work

Although representative of regional heritage, the inclusion of only seven materials limits universality; future datasets should encompass Asian blue bricks, South-Asian red bricks, and plaster composites. Furthermore, each dataset was standardized and averaged through inverse-variance weighting of fourteen peer-reviewed sources (2013–2024), ensuring balanced representation of global heritage contexts. Variations in mineralogy (calcitic vs. dolomitic marble) and species differences in timber were normalized via z-score scaling. These steps ensure statistical comparability but do not replace the need for region-specific calibration, which future research will address by expanding the database with localized material typologies. This study presents a first attempt to classify traditional materials through a multivariate statistical framework, yet several limitations must be acknowledged. The dataset includes only seven materials, which, while representative of Middle Eastern and Mediterranean heritage structures, limit the universality of the framework. Expanding the dataset to include additional materials such as bricks, ceramic tiles, plaster, and composite mortars would increase its applicability across diverse heritage contexts. The pilot experimental validation employed three specimens per material, offering preliminary verification but limiting statistical power; future studies should increase the number of specimens to enhance robustness and generalizability. Furthermore, material behavior is strongly influenced by climatic conditions—adobe and lime mortar are particularly vulnerable in humid climates, whereas marble and volcanic stone maintain higher durability indicating the need for climate-specific adjustment factors. Finally, embedding the proposed framework into Historic Building Information Modeling (HBIM) platforms requires further development. Potential pathways include linking material IDs to property datasets, encoding statistical model parameters as HBIM object attributes, and integrating predictive modules for deterioration and retrofit planning. These steps will support more effective, data-driven conservation and sustainable retrofit practices in heritage buildings. Future developments could integrate multi-criteria decision-making approaches such as the Analytic Hierarchy Process (AHP) [23] or its fuzzy variants to rank materials by weighted mechanical, thermal, and moisture criteria. AI techniques such as Artificial Neural Networks (ANN), while advanced supervised machine-learning techniques such as Partial Least Squares (PLS) and Linear Discriminant Analysis (LDA) were considered, preliminary trials indicated that the limited sample size (n ≈ 50) and high inter-material variance produced unstable parameter estimates. Consequently, classical linear regression models yielded higher interpretability and comparable predictive accuracy within cross-validation tests. For small, heterogenous datasets characteristic of heritage studies, linear approaches remain statistically robust and transparent for conservation-engineering interpretation, Support Vector Machines (SVM), and Decision Trees as potential extensions to enhance predictive automation of material classification. These methods could further refine accuracy and enable adaptive learning from expanded heritage datasets.

The manuscript was screened using iThenticate (Turnitin LLC, Oakland, CA, USA, 2025), yielding a similarity index of 8%, which meets MDPI’s publication standards [24].