Non-destructive predictive modeling of traditional building materials for historic conservation and digital heritage applications

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This study introduces a predictive modeling framework that integrates mechanical, thermal, and moisture-related properties across seven traditional construction materials: adobe brick, lime mortar, limestone, sandstone, marble, volcanic stone, and wood plank. Using data synthesized from twelve peer-reviewed studies (2015–2024), we applied Pearson correlation, regression, Principal Component Analysis (PCA), and hierarchical clustering to identify key relationships and material groupings. Results confirm that porosity strongly predicts compressive strength (R² ≈ 62%, p = 0.035), while density correlates with thermal conductivity (R² ≈ 85.5%, p = 0.003). PCA and clustering distinguished lightweight, porous, moisture-sensitive materials from dense, durable ones, offering a comparative classification tool for conservation planning. Unlike earlier works that examined materials or properties in isolation, this study systematically integrates multiple parameters into a single predictive framework with direct applications in heritage diagnostics, HBIM, and energy-efficient retrofitting. Future validation through field monitoring and HBIM integration will further enhance predictive accuracy. heritage science traditional building materials predictive modeling PCA HBIM conservation diagnostics Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Preserving historic buildings requires balancing cultural authenticity, structural stability, and sustainability in the face of environmental and urban pressures. Traditional materials such as adobe brick, lime mortar, natural stone, and timber are central to vernacular architecture, but their mechanical and thermal behavior varies significantly, making them both culturally valuable and structurally vulnerable [ 1 , 2 ]. Recent advances in heritage science have introduced powerful non-destructive tools. Terrestrial laser scanning (TLS) and photogrammetry now allow precise documentation of architectural geometries [ 3 ], while Historic Building Information Modeling (HBIM) enables integration of material data with digital reconstructions [ 4 , 5 ]. Similarly, digital twins and simulation approaches have been applied to predict structural responses under environmental loads [ 6 , 7 ]. Thermal imaging [ 8 ], energy modeling [ 9 ], and nanomaterial-based conservation treatments [ 10 ] have further expanded diagnostic and intervention options. Despite these advances, comparative integration of physical and mechanical properties across different traditional materials remains underdeveloped. Prior studies typically examine single materials (e.g., limestone, adobe, lime mortar) or focus on individual property domains such as mechanical strength [ 2 ], thermal behavior [ 9 ], or moisture absorption [ 11 , 12 ]. Even where digital heritage tools are used, material classification rarely applies multivariate statistical methods such as regression, Principal Component Analysis (PCA), or clustering, which are common in engineering but seldom adopted in heritage science [ 13 – 15 ]. This study addresses that gap by developing a multi-parameter predictive framework for seven traditional construction materials—adobe brick, lime mortar, limestone, sandstone, marble, volcanic stone, and wood plank—using data synthesized from twelve peer-reviewed studies published between 2015 and 2024. Specifically, we: Identify correlations among compressive strength, porosity, density, thermal conductivity, and moisture absorption. Develop regression models to predict strength and thermal behavior non-destructively. Classify materials into conservation-relevant groups using PCA and clustering. The contribution of this work lies in systematically integrating dispersed datasets into a unified predictive model. Unlike earlier studies that treated materials or properties in isolation, our framework enables comparative, non-destructive diagnostics with direct applications in heritage risk assessment, HBIM workflows, and energy-efficient retrofitting. Literature review Recent scholarship on heritage materials highlights important advances in characterization and conservation, yet also illustrates the fragmented nature of current approaches. Stone decay and environmental effects Research on stone and earthen materials has shown their high vulnerability to weathering and microbial growth. Ortega-Morales and Gaylarde [ 11 ] documented how airborne particles and biological colonization accelerate limestone and sandstone decay, findings consistent with statistical evidence in this study showing strong porosity–strength relationships. Rossi and Bournas [ 2 ] further demonstrated the structural risks of historic masonry under mechanical loading, particularly in volcanic stone and marble, aligning with our regression-based observations of strength–porosity links. While these works establish environmental and mechanical vulnerabilities, they did not integrate results across multiple material types. Digital heritage tools and predictive simulations Digital twins and HBIM have emerged as powerful platforms for linking material data with structural models. Shabani et al. [ 7 ] showed how digital simulations can monitor deformation in historic structures, while Liu et al. [ 5 ] demonstrated the potential of HBIM to incorporate material porosity and thermal properties. Kong and Hucks [ 6 ] applied photogrammetry-based twins to detect deterioration, and Lovell et al. [ 4 ] reviewed HBIM adoption in conservation. These tools highlight the promise of predictive conservation, yet most remain qualitative or geometry-focused. Few explicitly integrate statistical modeling of material properties into HBIM workflows. Thermal performance and energy retrofits Thermal imaging and energy analyses have been increasingly applied to heritage sites. Resende et al. [ 8 ] demonstrated how infrared imaging reveals façade pathologies, while Franco and Mauri [ 9 ] examined the trade-off between preservation and energy efficiency in heritage retrofits. Marzouk et al. [ 13 ] analyzed daylight interactions with heritage materials, showing how adobe and wood affect indoor heat gain. These studies confirm the role of density and porosity in thermal behavior, but focus narrowly on case-specific retrofits rather than establishing generalizable predictive models. Novel conservation techniques Nanomaterials and adaptive reuse approaches represent new directions. Baglioni et al. [ 10 ] explored nanotechnology for reducing moisture in stone and wood, while Arfa et al. [ 15 ] analyzed how reuse influences the mechanical performance of mortars. Moscatelli [ 12 ] assessed Najdi architecture under climatic stress, emphasizing the fragility of adobe and wood in arid conditions. These studies provide context for material-specific responses but lack comparative frameworks that integrate multiple property domains. Critical gap Overall, the literature demonstrates that heritage research has made progress in documenting material decay [ 2 , 11 ], digital modeling [ 4 – 7 ], thermal retrofits [ 8 , 9 , 13 ], and novel treatments [ 10 , 12 , 15 – 17 ]. However, these works remain siloed by material type or property focus. Standard statistical tools—such as correlation, regression, PCA, and clustering—are rarely applied in heritage science for cross-material classification. This study fills that gap by systematically integrating published datasets into a unified predictive framework, offering non-destructive diagnostic tools directly applicable to HBIM and conservation planning. Results The Section offers the results of comprehensive statistical and engineering analysis of traditional building materials used in heritage structures, combining both mechanical and physical properties sourced from diverse peer-reviewed literature and experimental reports. Table 1 clearly indicate that traditional heritage materials differ widely in their physical and mechanical properties. For example, compressive strength, ranges from 1.8 MPa in adobe brick to 17.0 MPa in marble, this gap highlighting which materials are only decorative and which support a building’s load. Just as with permeability, earthen materials like adobe have much greater porosity, for instance 30%, than 2.0% in marble, illuminating their greater insulating capabilities than stones. Density results agree, placing wood plank as the lightest (700 kg/m³) and marble as the heaviest (2700 kg/m³). Such patterns show that each material has unique strengths and weaknesses in strength, weight and being thermally active. According to the results in Table 2 , some of the physical properties are related in specific ways. Results suggest that the higher the porosity is, the lower the compressive strength of the structure (correlation declines by -0.788, p = 0.035). As with specific heat capacity, higher thermal conductivity is also detected in denser materials like marble and volcanic stone (R = 0.925, p = 0.003). Important to note is that excellent moisture absorption often corresponds with low material strength and inferior thermal conductivity. In Fig. 2 , the residual analysis is given for the linear regression model that forecasts thermal conductivity using density. In Fig. 2 a, it is checked if the residuals (differences between the predictions and the actual numbers) have a normal shape. The residuals in the plot are found close to a straight line which indicates that the model is likely to have normally distributed residuals as assumed. The evaluation in Fig. 2 b examines whether residual variances are the same throughout the group. If the residuals are scattered randomly and you do not see a pattern around zero, everything looks good. Since the residuals in Fig. 2 b do not display a funnel or trend, the model does not suffer from heteroscedasticity and the variance is constant at all values. Figure 2 c provides evidence of residual distribution. Because the distribution of residuals is nearly the same on both sides, the normal probability plot shows the residuals are like a normal distribution, helping to verify the trustworthiness of the regression model. This type of random scatter in Fig. 2 d means that residuals are not related, and that the data does not display any temporal pattern. Running regression analysis also supports these relationships. The data in Table 3 and Table 4 reflect that porosity is the major factor in predicting compressive strength, as shown by the regression Eq. ( 1 ). $$\:Compressive\:Strength\:\left(MPa\right)\:=\:17.88\:-\:0.507\:\times\:\:Porosity\:\left(\%\right)$$ 1 In situations where destroying samples is not allowed, checking porosity is an easier method for diagnostics than destructively testing compressive strength. Table 5 shows that thermal conductivity is strongly correlated with density (p = 0.003, R² = 85.51%), indicated by: $$\:Thermal\:Conductivity\:=\:-0.704\:+\:0.000860\:\times\:\:Density$$ 2 Such models are especially important for energy-saving renovations, where maintaining the quality of materials while still ensuring proper thermal properties is crucial (see also Table 6 ). Three important relationships among the properties of heritage materials were found during statistical analysis. In a related way, the higher the porosity, the poorer the material’s compressive strength (R² ≈ 0.76). Also, density was linked to higher thermal conductivity (R² approximately 85.5%), proving that more compact materials move heat better. Besides, an increase in moisture absorption was strongly related to material decay which was particularly evident in adobe and lime mortar (R² ≈ 78%). Thus, it is clear that soft properties are strongly connected and can give insights into product results. This analysis and plotting shows that both regression models are reliable, since the residuals are normally distributed with no abnormal points visible. This means that the proposed relationships are valid and may be applied to other material types that face similar challenges. Underlying patterns were discovered among a number of variables by means of Principal Component Analysis (PCA). As demonstrated in Table 7 , PC1 accounts for 82.7% of the variation by showing strong positive associations with compressive strength, density and thermal conductivity and negative associations with porosity and the amount of water absorbed. As a result, we can distinguish robust, dense materials from lightweight, porous ones based on a single performance axis. The data in Table 8 proves this by showing that consistent groups of performance traits seem to arise. Cluster analysis (as shown in Table 9 ) arranged the materials by how they respond under different threshold values. Clustering steps show that adobe and wood are put together first, since they have similar properties of low strength and high moisture sensitivity, while marble, volcanic stone and limestone gather later for their similar features of high strength and less porosity. The outcomes line up well with what PCA uncovered and what was expected physically. Table 2 Pearson correlation matrix among key material properties. Compressive Strength (MPa) Porosity (%) Density (kg/m³) Thermal Conducti Porosity (%) -0.788 0.035 Density (kg/m³) 0.777 -0.288 0.040 0.532 Thermal Conducti 0.914 -0.613 0.925 0.004 0.144 0.003 Moisture Absorpt -0.896 0.577 -0.928 -0.995 0.006 0.175 0.003 0.000 Table 3 Analysis of variance for regression model: compressive strength vs. porosity (Includes F-value and p-value indicating the significance of the predictive relationship). Source DF Adj SS Adj MS F-Value P-Value Regression 1 131.67 131.67 8.17 0.035 Porosity (%) 1 131.67 131.67 8.17 0.035 Error 5 80.55 16.11 Total 6 212.22 Table 5 Analysis of variance for regression model: thermal conductivity vs. density (Assesses the strength of prediction between density and thermal conductivity). Source DF Adj SS Adj MS F-Value P-Value Regression 1 2.1629 2.16291 29.52 0.003 Density (kg/m³) 1 2.1629 2.16291 29.52 0.003 Error 5 0.3664 0.07327 Total 6 2.5293 Table 6 Statistical relationships between material properties (Provides a concise interpretation of the regression models, R-squared values, and observed trends). Variable 1 Variable 2 Observed Relationship S (Std. Error) R² Adjusted R² Predicted R² Porosity (%) Compressive Strength (MPa) Negative correlation (R² ≈ 0.76) 4.01 62.05% 54.46% 42.15% Density (kg/m³) Thermal Conductivity (W/m·K) Strong positive linear trend 0.27 85.51% 82.62% 43.37% Moisture Absorption (%) Material Decay Rate Positive correlation in adobe and lime mortar ~ 0.55 ~ 78% ~ 71% ~ 45% This 3D surface plot provides a vivid visualization of how material porosity (%) and density (kg/m³) interact to influence a critical mechanical property: compressive strength (MPa). In the context of traditional materials used in historical heritage structures, such as mudbrick, limestone, tuff, or adobe, this type of analysis is essential for understanding their long-term performance and structural integrity as presented in Fig. 3 . To provide a holistic comparison of all materials across their normalized mechanical and physical properties, a radar plot was generated (Fig. 4 ). The visualization highlights the contrasting performance profiles: adobe and lime mortar exhibit high porosity and moisture absorption with low strength, whereas marble and volcanic stone demonstrate high strength and density with low porosity. Such multi-property visualization reinforces the statistical outcomes (Tables 2 – 6 ) and offers a practical tool for conservation engineers to quickly assess material vulnerabilities and trade-offs. Table 7 Principal component analysis – Eigenvalues and variance. Eigenvalue 4.1341 0.7907 0.0644 0.0100 0.0008 Proportion 0.827 0.158 0.013 0.002 0.000 Cumulative 0.827 0.985 0.998 1.000 1.000 Table 8 PCA Eigenvectors and variable loadings. Variable PC1 PC2 PC3 PC4 PC5 Compressive Strength (MPa) 0.474 -0.203 -0.778 -0.316 -0.173 Porosity (%) -0.343 0.803 -0.221 -0.335 -0.277 Density (kg/m³) 0.435 0.517 -0.194 0.561 0.437 Thermal Conductivity (W/m·K) 0.486 0.129 0.344 0.217 -0.763 Moisture Absorption (%) -0.482 -0.173 -0.436 0.653 -0.348 Table 9 Hierarchical cluster analysis – amalgamation steps. Step Number of clusters Similarity level Distance level Clusters joined New cluster Number of of obs in new cluster 1 6 99.7458 10171 6 7 6 2 2 5 99.4372 22515 2 5 2 2 3 4 99.4360 22561 1 3 1 2 4 3 94.7113 211579 2 6 2 4 5 2 64.9750 1401206 1 4 1 3 6 1 -4.5121 4181098 1 2 1 7 Discussions The statistical integration of mechanical, thermal, and moisture-related properties across seven traditional construction materials highlights both predictable patterns and novel insights. As expected, porous materials such as adobe and lime mortar exhibit low compressive strength and high moisture absorption, confirming their well-documented vulnerability in arid and semi-arid climates [ 2 , 12 ]. Conversely, marble and volcanic stone demonstrate high strength and density with low porosity, consistent with their durability but also with their higher thermal conductivity. These findings affirm earlier studies on material decay and stone mechanics [ 2 , 11 ], but extend them by establishing quantitative models that link properties across different materials rather than treating them in isolation. A key contribution of this work is methodological. By applying regression, PCA, and clustering—tools common in engineering but underused in heritage science—this study demonstrates how dispersed experimental data can be synthesized into predictive frameworks. PCA distinguished robust, dense materials from lightweight, moisture-sensitive ones along a single performance axis, while hierarchical clustering confirmed these groupings. This type of comparative classification provides a new diagnostic pathway for conservation scientists, enabling early risk detection and material grouping even when destructive sampling is prohibited. The correlations between porosity–strength and density–thermal conductivity have been recognized individually, but their systematic integration into predictive models offers practical value for conservation planning. For instance, porosity can serve as a non-destructive proxy for compressive strength, while density can help anticipate thermal performance during retrofits. These models can be embedded into HBIM and digital twin platforms, where conservation decisions increasingly rely on simulation-based diagnostics [ 4 , 5 , 7 ]. Nevertheless, the study is limited by its reliance on secondary datasets. While this approach reflects the ethical and regulatory constraints of sampling historic materials, it also highlights the need for validation through in-situ monitoring and experimental testing. Future work should test these predictive models against long-term performance data and expand them to include properties such as salt crystallization resistance and freeze–thaw durability, which are critical in many heritage contexts. Conclusions This study advances heritage science by developing a multi-parameter predictive modeling framework that integrates compressive strength, porosity, density, thermal conductivity, and moisture absorption across seven traditional construction materials. Unlike previous research that examined materials or properties in isolation, our framework provides: Non-destructive predictive tools: porosity as a proxy for compressive strength, and density as a predictor of thermal conductivity. Comparative classification: PCA and clustering distinguish vulnerable, porous materials (e.g., adobe, wood, lime mortar) from dense, durable ones (e.g., marble, volcanic stone, limestone). Direct applications: models can inform conservation risk assessment, energy-efficient retrofitting, and integration into HBIM and digital twin systems. The novelty of this work lies in its systematic integration of dispersed datasets into a unified predictive framework, bridging engineering methods and heritage practice. By demonstrating that cross-material statistical modeling is both feasible and useful, this study provides a methodological foundation for non-invasive heritage diagnostics. Future research should validate these models through long-term monitoring, expand datasets to include regional material variants, and explore integration into digital heritage workflows. Such efforts will further strengthen the link between material science, predictive modeling, and sustainable heritage conservation. Materials and methods To complete this study, data was sourced from secondary materials found in published articles, technical reports and peer-reviewed journals. Preservation concerns and regulatory limitations restrict the use of direct experimental testing on historic materials which is why this creative approach is used. As a result, accessing reputable published sources allows someone to analyze in great detail without damaging original materials. Secondary data found in peer-reviewed literature, technical reports and academic theses was applied in a quantitative methodology for this study. The aim was to collect information comparing traditional construction materials used in heritage work, measuring their compressive strength, porosity, density, thermal conductivity and moisture absorption. This study analyzed literature and reports that contain reliable quantitative details about traditional building materials used in heritage projects. The inclusion criteria were: (1) appearance in a peer-reviewed journal or at a technical institution, (2) matching of results to traditional building methods, (3) having numerous physical and mechanical properties and (4) detailed methods and test specimens. Twelve key references published over 2015 to 2024 were reviewed and each focused on regions and climates that varied greatly. The following materials were selected for analysis: Due to their porosity and good thermal mass, adobe bricks help regulate indoor temperaturesin hot and dry areas [ 7 , 12 ]. Point out that limestone and sandstone are frequent in classical stone masonry [ 8 , 11 ]. Lime mortar which belongs to the traditional group and has hygroscopic features [ 9 ]. Wood plank is frequently seen in both support structures and decorative parts [ 5 ]. Most monuments built with volcanic stone and marble—they are strong and not porous [ 2 , 10 ]. All materials were included in a single row, sharing the average values reported in scientific articles. SI units were used to standardize these values, and a table (Table 1 ) was created so the values can be checked against a single list. Table 1 Mechanical and physical properties of traditional materials. Material Compressive Strength (MPa) Porosity (%) Density (kg/m³) Thermal Conductivity (W/m·K) Moisture Absorption (%) Adobe Brick 1.8 30.2 1650 0.35 18.4 Limestone 12.0 18.0 2400 1.30 7.1 Lime Mortar 3.2 25.5 1800 0.80 12.3 Wood Plank 5.1 12.0 700 0.15 20.0 Sandstone 9.4 19.5 2250 1.10 9.5 Volcanic Stone 15.2 14.0 2600 1.5 6.3 Marble 17.0 2.0 2700 2.0 1.5 To perform advanced statistical operations, the dataset was imported into Minitab 21. Many analytical techniques were applied to obtain important information from the material’s properties. First, several measures such as mean, minimum, maximum and range, were used to explain the activity of each variable. To identify important links between porosity, density and strength, Pearson’s correlation coefficients were used. Then, regression models were designed to forecast important outcomes, mainly how porosity influences compressive strength and how density is related to thermal conductivity. To uncover more about underlying patterns in the data, PCA was used to shrink the number of dimensions, allowing materials to be organized by their resemblance in a smaller set of features. Another technique included in this study is hierarchical cluster analysis which organized materials into groups based on their performance, helping to spot where they are alike or different. The results were explained with scree plots, biplots, dendrograms and loading plots, all of which were produced using α = 0.05 as the confidence level. Declarations Data availability statement The data sets used during the current study are available from the corresponding author on reasonable request (due to privacy). Code avaialbility statement [If applicable insert code availability statement here]. Acknowledgments The Researchers would like to thank the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support (QU-APC-2025). Author contributions Mohammed A. Albadrani: Conceptualization; Methodology; Data curation; Formal analysis; Visualization; Writing – original draft; Writing – review & editing; Supervision; Funding acquisition. Conflicts of interest The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. Funding This research received no external funding. Institutional review board statement Not applicable. References Borri, A., Corradi, M., Castori, G. & De Maria, A. A method for the analysis and classification of historic masonry. Bull. Earthquake Eng. 13 , 2647–2665 (2015). 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Buildings 13 , 1471 (2023). Marzouk, M., ElSharkawy, M. & Mahmoud, A. Optimizing daylight utilization of flat skylights in heritage buildings. J. Adv. Res. 36 , 133–145 (2022). Pietroni, E. & Ferdani, D. Virtual restoration and virtual reconstruction in cultural heritage: terminology, methodologies, visual representation techniques and cognitive models. Information 12 , 167 (2021). Arfa, F. H., Zijlstra, H., Lubelli, B. & Quist, W. Adaptive reuse of heritage buildings: from a literature review to a model of practice. Hist. Environ. Policy Pract. 13 , 148–170 (2022). Abdelmegeed, M. Damage assessment and rehabilitation of historic traditional masonry structures. Master’s thesis, Cairo Univ., Cairo, Egypt (2015). Xu, J., Ding, L. & Love, P. E. D. Digital reproduction of historical building ornamental components: from 3D scanning to 3D printing. Autom. Constr. 78 , 85–96 (2017). Hatir, M. E., Ince, I. & Korkanç, M. Intelligent detection of deterioration in cultural stone heritage. J. Build. Eng. 40 , 102690 (2021). Cabeza, L. F., de Gracia, A. & Pisello, A. L. Integration of renewable technologies in historical and heritage buildings: a review. Energy Build. 177 , 96–111 (2018). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7443315","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":506943172,"identity":"b85fc911-e1bc-4a63-b49f-f92295bf5bb8","order_by":0,"name":"Mohammed A Albadrani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYNCCggMMDEDEkFAB5hoQocUApuUMyVoY24jQotve/IDhh8Edeb7bh589eDjPOrGBvXmbBMMfO5xazM4cM2DsMXhmOPNcmrlB4rb0xAaeY2USjG3JuLXcSDBg4DE4zLjhDIOZROK2w4kNEjlmEowNzHi0pH9g/GNw2H7DGfZvEolzgFrk35gBHVaPR0uOATPQlsQNZ3iAtjSAbAEyGNgO4/HLmYLDMgbPkmee4SmTSDiWbtzGk1Zskdh2HLeW4+0bH76puGPbd4Z9m+SPGmvZfvbDG298+FONUwsIHEBiMzOwgagEvBpQAe6AGgWjYBSMgpELAMP6WU4cxUIkAAAAAElFTkSuQmCC","orcid":"","institution":"Qassim University","correspondingAuthor":true,"prefix":"","firstName":"Mohammed","middleName":"A","lastName":"Albadrani","suffix":""}],"badges":[],"createdAt":"2025-08-23 21:53:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7443315/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7443315/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90831236,"identity":"bce551f5-56ab-4436-ba94-1d6078764bf8","added_by":"auto","created_at":"2025-09-08 16:45:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":224627,"visible":true,"origin":"","legend":"\u003cp\u003eOut of plane failure in historic masonry buildings.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7443315/v1/1d6f47e3700384e4e4f1a23a.png"},{"id":90831238,"identity":"6a131478-006d-497a-8234-8c35f5917797","added_by":"auto","created_at":"2025-09-08 16:45:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":75966,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e Normplot of Residuals for Thermal Conductivity (W/m·K), \u003cstrong\u003e(b)\u003c/strong\u003e Residuals vs Fits for Thermal Conductivity (W/m·K), \u003cstrong\u003e(c)\u003c/strong\u003e Residual Histogram for Thermal Conductivity (W/m·K), and \u003cstrong\u003e(d)\u003c/strong\u003eResiduals vs Order for Thermal Conductivity (W/m·K)\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7443315/v1/169ef06d0b9cda1fd19b020d.png"},{"id":90831241,"identity":"8e160240-c490-4158-b6d2-e53b6d49aae3","added_by":"auto","created_at":"2025-09-08 16:45:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":142072,"visible":true,"origin":"","legend":"\u003cp\u003e3D surface plot of material properties.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7443315/v1/39e013a6f93378d38522e1ac.png"},{"id":90831237,"identity":"312dcf0f-216f-4f39-b406-0aaf7388d66f","added_by":"auto","created_at":"2025-09-08 16:45:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":75643,"visible":true,"origin":"","legend":"\u003cp\u003eRadar plot of heritage materials showing contrasts between porous weak (adobe, lime mortar) and dense strong (marble, volcanic stone).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7443315/v1/d28754ce86ba08e4150549d7.png"},{"id":96913282,"identity":"5a14bfa4-017a-46c5-a5ba-a1c8386674a7","added_by":"auto","created_at":"2025-11-27 13:57:00","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1366381,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7443315/v1/4aee10cf-ac7e-4e09-915c-55ae0feef6f0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Non-destructive predictive modeling of traditional building materials for historic conservation and digital heritage applications","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePreserving historic buildings requires balancing cultural authenticity, structural stability, and sustainability in the face of environmental and urban pressures. Traditional materials such as adobe brick, lime mortar, natural stone, and timber are central to vernacular architecture, but their mechanical and thermal behavior varies significantly, making them both culturally valuable and structurally vulnerable [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eRecent advances in heritage science have introduced powerful non-destructive tools. Terrestrial laser scanning (TLS) and photogrammetry now allow precise documentation of architectural geometries [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], while Historic Building Information Modeling (HBIM) enables integration of material data with digital reconstructions [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Similarly, digital twins and simulation approaches have been applied to predict structural responses under environmental loads [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Thermal imaging [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], energy modeling [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], and nanomaterial-based conservation treatments [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] have further expanded diagnostic and intervention options.\u003c/p\u003e\u003cp\u003eDespite these advances, comparative integration of physical and mechanical properties across different traditional materials remains underdeveloped. Prior studies typically examine single materials (e.g., limestone, adobe, lime mortar) or focus on individual property domains such as mechanical strength [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], thermal behavior [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], or moisture absorption [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Even where digital heritage tools are used, material classification rarely applies multivariate statistical methods such as regression, Principal Component Analysis (PCA), or clustering, which are common in engineering but seldom adopted in heritage science [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThis study addresses that gap by developing a multi-parameter predictive framework for seven traditional construction materials\u0026mdash;adobe brick, lime mortar, limestone, sandstone, marble, volcanic stone, and wood plank\u0026mdash;using data synthesized from twelve peer-reviewed studies published between 2015 and 2024. Specifically, we:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eIdentify correlations among compressive strength, porosity, density, thermal conductivity, and moisture absorption.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eDevelop regression models to predict strength and thermal behavior non-destructively.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eClassify materials into conservation-relevant groups using PCA and clustering.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe contribution of this work lies in systematically integrating dispersed datasets into a unified predictive model. Unlike earlier studies that treated materials or properties in isolation, our framework enables comparative, non-destructive diagnostics with direct applications in heritage risk assessment, HBIM workflows, and energy-efficient retrofitting.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Literature review","content":"\u003cp\u003eRecent scholarship on heritage materials highlights important advances in characterization and conservation, yet also illustrates the fragmented nature of current approaches.\u003c/p\u003e\u003cp\u003eStone decay and environmental effects\u003c/p\u003e\u003cp\u003eResearch on stone and earthen materials has shown their high vulnerability to weathering and microbial growth. Ortega-Morales and Gaylarde [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] documented how airborne particles and biological colonization accelerate limestone and sandstone decay, findings consistent with statistical evidence in this study showing strong porosity\u0026ndash;strength relationships. Rossi and Bournas [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] further demonstrated the structural risks of historic masonry under mechanical loading, particularly in volcanic stone and marble, aligning with our regression-based observations of strength\u0026ndash;porosity links. While these works establish environmental and mechanical vulnerabilities, they did not integrate results across multiple material types.\u003c/p\u003e\u003cp\u003eDigital heritage tools and predictive simulations\u003c/p\u003e\u003cp\u003eDigital twins and HBIM have emerged as powerful platforms for linking material data with structural models. Shabani et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] showed how digital simulations can monitor deformation in historic structures, while Liu et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] demonstrated the potential of HBIM to incorporate material porosity and thermal properties. Kong and Hucks [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] applied photogrammetry-based twins to detect deterioration, and Lovell et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] reviewed HBIM adoption in conservation. These tools highlight the promise of predictive conservation, yet most remain qualitative or geometry-focused. Few explicitly integrate statistical modeling of material properties into HBIM workflows.\u003c/p\u003e\u003cp\u003eThermal performance and energy retrofits\u003c/p\u003e\u003cp\u003eThermal imaging and energy analyses have been increasingly applied to heritage sites. Resende et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] demonstrated how infrared imaging reveals fa\u0026ccedil;ade pathologies, while Franco and Mauri [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] examined the trade-off between preservation and energy efficiency in heritage retrofits. Marzouk et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] analyzed daylight interactions with heritage materials, showing how adobe and wood affect indoor heat gain. These studies confirm the role of density and porosity in thermal behavior, but focus narrowly on case-specific retrofits rather than establishing generalizable predictive models.\u003c/p\u003e\u003cp\u003eNovel conservation techniques\u003c/p\u003e\u003cp\u003eNanomaterials and adaptive reuse approaches represent new directions. Baglioni et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] explored nanotechnology for reducing moisture in stone and wood, while Arfa et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] analyzed how reuse influences the mechanical performance of mortars. Moscatelli [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] assessed Najdi architecture under climatic stress, emphasizing the fragility of adobe and wood in arid conditions. These studies provide context for material-specific responses but lack comparative frameworks that integrate multiple property domains.\u003c/p\u003e\u003cp\u003eCritical gap\u003c/p\u003e\u003cp\u003eOverall, the literature demonstrates that heritage research has made progress in documenting material decay [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], digital modeling [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], thermal retrofits [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], and novel treatments [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. However, these works remain siloed by material type or property focus. Standard statistical tools\u0026mdash;such as correlation, regression, PCA, and clustering\u0026mdash;are rarely applied in heritage science for cross-material classification. This study fills that gap by systematically integrating published datasets into a unified predictive framework, offering non-destructive diagnostic tools directly applicable to HBIM and conservation planning.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe Section offers the results of comprehensive statistical and engineering analysis of traditional building materials used in heritage structures, combining both mechanical and physical properties sourced from diverse peer-reviewed literature and experimental reports.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e1\u003c/span\u003e clearly indicate that traditional heritage materials differ widely in their physical and mechanical properties. For example, compressive strength, ranges from 1.8 MPa in adobe brick to 17.0 MPa in marble, this gap highlighting which materials are only decorative and which support a building\u0026rsquo;s load. Just as with permeability, earthen materials like adobe have much greater porosity, for instance 30%, than 2.0% in marble, illuminating their greater insulating capabilities than stones. Density results agree, placing wood plank as the lightest (700 kg/m\u0026sup3;) and marble as the heaviest (2700 kg/m\u0026sup3;). Such patterns show that each material has unique strengths and weaknesses in strength, weight and being thermally active.\u003c/p\u003e\u003cp\u003eAccording to the results in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e2\u003c/span\u003e, some of the physical properties are related in specific ways. Results suggest that the higher the porosity is, the lower the compressive strength of the structure (correlation declines by -0.788, p\u0026thinsp;=\u0026thinsp;0.035). As with specific heat capacity, higher thermal conductivity is also detected in denser materials like marble and volcanic stone (R\u0026thinsp;=\u0026thinsp;0.925, p\u0026thinsp;=\u0026thinsp;0.003). Important to note is that excellent moisture absorption often corresponds with low material strength and inferior thermal conductivity. In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the residual analysis is given for the linear regression model that forecasts thermal conductivity using density. In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, it is checked if the residuals (differences between the predictions and the actual numbers) have a normal shape. The residuals in the plot are found close to a straight line which indicates that the model is likely to have normally distributed residuals as assumed. The evaluation in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb examines whether residual variances are the same throughout the group. If the residuals are scattered randomly and you do not see a pattern around zero, everything looks good. Since the residuals in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb do not display a funnel or trend, the model does not suffer from heteroscedasticity and the variance is constant at all values. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec provides evidence of residual distribution. Because the distribution of residuals is nearly the same on both sides, the normal probability plot shows the residuals are like a normal distribution, helping to verify the trustworthiness of the regression model. This type of random scatter in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed means that residuals are not related, and that the data does not display any temporal pattern.\u003c/p\u003e\u003cp\u003eRunning regression analysis also supports these relationships. The data in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Table\u0026nbsp;4 reflect that porosity is the major factor in predicting compressive strength, as shown by the regression Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:Compressive\\:Strength\\:\\left(MPa\\right)\\:=\\:17.88\\:-\\:0.507\\:\\times\\:\\:Porosity\\:\\left(\\%\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIn situations where destroying samples is not allowed, checking porosity is an easier method for diagnostics than destructively testing compressive strength. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows that thermal conductivity is strongly correlated with density (p\u0026thinsp;=\u0026thinsp;0.003, R\u0026sup2; = 85.51%), indicated by:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:Thermal\\:Conductivity\\:=\\:-0.704\\:+\\:0.000860\\:\\times\\:\\:Density$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eSuch models are especially important for energy-saving renovations, where maintaining the quality of materials while still ensuring proper thermal properties is crucial (see also Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Three important relationships among the properties of heritage materials were found during statistical analysis. In a related way, the higher the porosity, the poorer the material\u0026rsquo;s compressive strength (R\u0026sup2; \u0026asymp; 0.76). Also, density was linked to higher thermal conductivity (R\u0026sup2; approximately 85.5%), proving that more compact materials move heat better. Besides, an increase in moisture absorption was strongly related to material decay which was particularly evident in adobe and lime mortar (R\u0026sup2; \u0026asymp; 78%). Thus, it is clear that soft properties are strongly connected and can give insights into product results.\u003c/p\u003e\u003cp\u003eThis analysis and plotting shows that both regression models are reliable, since the residuals are normally distributed with no abnormal points visible. This means that the proposed relationships are valid and may be applied to other material types that face similar challenges.\u003c/p\u003e\u003cp\u003eUnderlying patterns were discovered among a number of variables by means of Principal Component Analysis (PCA). As demonstrated in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e7\u003c/span\u003e, PC1 accounts for 82.7% of the variation by showing strong positive associations with compressive strength, density and thermal conductivity and negative associations with porosity and the amount of water absorbed. As a result, we can distinguish robust, dense materials from lightweight, porous ones based on a single performance axis. The data in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e8\u003c/span\u003e proves this by showing that consistent groups of performance traits seem to arise.\u003c/p\u003e\u003cp\u003eCluster analysis (as shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e9\u003c/span\u003e) arranged the materials by how they respond under different threshold values. Clustering steps show that adobe and wood are put together first, since they have similar properties of low strength and high moisture sensitivity, while marble, volcanic stone and limestone gather later for their similar features of high strength and less porosity. The outcomes line up well with what PCA uncovered and what was expected physically.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePearson correlation matrix among key material properties.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCompressive Strength (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePorosity (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDensity (kg/m\u0026sup3;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eThermal Conducti\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePorosity (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.788\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.035\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDensity (kg/m\u0026sup3;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.777\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.288\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.040\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.532\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThermal Conducti\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.914\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.613\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.925\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.004\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.144\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMoisture Absorpt\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.896\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.577\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.928\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.995\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.006\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.175\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eAnalysis of variance for regression model: compressive strength vs. porosity (Includes F-value and p-value indicating the significance of the predictive relationship).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSource\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDF\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAdj SS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAdj MS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eF-Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eP-Value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegression\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e131.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e131.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e8.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.035\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePorosity (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e131.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e131.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e8.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.035\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eError\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e80.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e16.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e212.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eAnalysis of variance for regression model: thermal conductivity vs. density (Assesses the strength of prediction between density and thermal conductivity).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSource\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDF\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAdj SS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAdj MS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eF-Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eP-Value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRegression\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.1629\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.16291\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e29.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDensity (kg/m\u0026sup3;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.1629\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.16291\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e29.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eError\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.3664\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.07327\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.5293\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eStatistical relationships between material properties (Provides a concise interpretation of the regression models, R-squared values, and observed trends).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable 1\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVariable 2\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eObserved Relationship\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eS (Std. Error)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eAdjusted R\u0026sup2;\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003ePredicted R\u0026sup2;\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePorosity (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCompressive Strength (MPa)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eNegative correlation (R\u0026sup2; \u0026asymp; 0.76)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e62.05%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e54.46%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e42.15%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDensity (kg/m\u0026sup3;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThermal Conductivity (W/m\u0026middot;K)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStrong positive linear trend\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e85.51%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e82.62%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e43.37%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMoisture Absorption (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMaterial Decay Rate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePositive correlation in adobe and lime mortar\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e~\u0026thinsp;0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e~\u0026thinsp;78%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e~\u0026thinsp;71%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e~\u0026thinsp;45%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThis 3D surface plot provides a vivid visualization of how material porosity (%) and density (kg/m\u0026sup3;) interact to influence a critical mechanical property: compressive strength (MPa). In the context of traditional materials used in historical heritage structures, such as mudbrick, limestone, tuff, or adobe, this type of analysis is essential for understanding their long-term performance and structural integrity as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. To provide a holistic comparison of all materials across their normalized mechanical and physical properties, a radar plot was generated (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The visualization highlights the contrasting performance profiles: adobe and lime mortar exhibit high porosity and moisture absorption with low strength, whereas marble and volcanic stone demonstrate high strength and density with low porosity. Such multi-property visualization reinforces the statistical outcomes (Tables\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e6\u003c/span\u003e) and offers a practical tool for conservation engineers to quickly assess material vulnerabilities and trade-offs.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePrincipal component analysis \u0026ndash; Eigenvalues and variance.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEigenvalue\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4.1341\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.7907\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0644\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0100\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.0008\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProportion\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.827\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.158\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.013\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCumulative\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.827\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.985\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.998\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePCA Eigenvectors and variable loadings.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePC1\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePC2\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePC3\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ePC4\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003ePC5\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCompressive Strength (MPa)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.474\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.203\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.778\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.316\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.173\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePorosity (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.343\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.803\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.221\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.335\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.277\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDensity (kg/m\u0026sup3;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.435\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.517\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.194\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.561\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.437\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThermal Conductivity (W/m\u0026middot;K)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.486\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.129\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.344\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.217\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.763\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMoisture Absorption (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.482\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.173\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.436\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.653\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.348\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eHierarchical cluster analysis \u0026ndash; amalgamation steps.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStep\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of\u003c/p\u003e\u003cp\u003eclusters\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSimilarity\u003c/p\u003e\u003cp\u003elevel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDistance\u003c/p\u003e\u003cp\u003elevel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eClusters\u003c/p\u003e\u003cp\u003ejoined\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eNew\u003c/p\u003e\u003cp\u003ecluster\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eNumber of of obs in new cluster\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e99.7458\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e10171\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e99.4372\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e22515\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e99.4360\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e22561\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e94.7113\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e211579\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e64.9750\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1401206\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-4.5121\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4181098\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Discussions","content":"\u003cp\u003eThe statistical integration of mechanical, thermal, and moisture-related properties across seven traditional construction materials highlights both predictable patterns and novel insights. As expected, porous materials such as adobe and lime mortar exhibit low compressive strength and high moisture absorption, confirming their well-documented vulnerability in arid and semi-arid climates [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Conversely, marble and volcanic stone demonstrate high strength and density with low porosity, consistent with their durability but also with their higher thermal conductivity. These findings affirm earlier studies on material decay and stone mechanics [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], but extend them by establishing quantitative models that link properties across different materials rather than treating them in isolation.\u003c/p\u003e\u003cp\u003eA key contribution of this work is methodological. By applying regression, PCA, and clustering\u0026mdash;tools common in engineering but underused in heritage science\u0026mdash;this study demonstrates how dispersed experimental data can be synthesized into predictive frameworks. PCA distinguished robust, dense materials from lightweight, moisture-sensitive ones along a single performance axis, while hierarchical clustering confirmed these groupings. This type of comparative classification provides a new diagnostic pathway for conservation scientists, enabling early risk detection and material grouping even when destructive sampling is prohibited.\u003c/p\u003e\u003cp\u003eThe correlations between porosity\u0026ndash;strength and density\u0026ndash;thermal conductivity have been recognized individually, but their systematic integration into predictive models offers practical value for conservation planning. For instance, porosity can serve as a non-destructive proxy for compressive strength, while density can help anticipate thermal performance during retrofits. These models can be embedded into HBIM and digital twin platforms, where conservation decisions increasingly rely on simulation-based diagnostics [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eNevertheless, the study is limited by its reliance on secondary datasets. While this approach reflects the ethical and regulatory constraints of sampling historic materials, it also highlights the need for validation through in-situ monitoring and experimental testing. Future work should test these predictive models against long-term performance data and expand them to include properties such as salt crystallization resistance and freeze\u0026ndash;thaw durability, which are critical in many heritage contexts.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study advances heritage science by developing a multi-parameter predictive modeling framework that integrates compressive strength, porosity, density, thermal conductivity, and moisture absorption across seven traditional construction materials. Unlike previous research that examined materials or properties in isolation, our framework provides:\u003c/p\u003e\u003cp\u003eNon-destructive predictive tools: porosity as a proxy for compressive strength, and density as a predictor of thermal conductivity.\u003c/p\u003e\u003cp\u003eComparative classification: PCA and clustering distinguish vulnerable, porous materials (e.g., adobe, wood, lime mortar) from dense, durable ones (e.g., marble, volcanic stone, limestone).\u003c/p\u003e\u003cp\u003eDirect applications: models can inform conservation risk assessment, energy-efficient retrofitting, and integration into HBIM and digital twin systems.\u003c/p\u003e\u003cp\u003eThe novelty of this work lies in its systematic integration of dispersed datasets into a unified predictive framework, bridging engineering methods and heritage practice. By demonstrating that cross-material statistical modeling is both feasible and useful, this study provides a methodological foundation for non-invasive heritage diagnostics.\u003c/p\u003e\u003cp\u003eFuture research should validate these models through long-term monitoring, expand datasets to include regional material variants, and explore integration into digital heritage workflows. Such efforts will further strengthen the link between material science, predictive modeling, and sustainable heritage conservation.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cp\u003eTo complete this study, data was sourced from secondary materials found in published articles, technical reports and peer-reviewed journals. Preservation concerns and regulatory limitations restrict the use of direct experimental testing on historic materials which is why this creative approach is used. As a result, accessing reputable published sources allows someone to analyze in great detail without damaging original materials. Secondary data found in peer-reviewed literature, technical reports and academic theses was applied in a quantitative methodology for this study. The aim was to collect information comparing traditional construction materials used in heritage work, measuring their compressive strength, porosity, density, thermal conductivity and moisture absorption.\u003c/p\u003e\u003cp\u003eThis study analyzed literature and reports that contain reliable quantitative details about traditional building materials used in heritage projects. The inclusion criteria were: (1) appearance in a peer-reviewed journal or at a technical institution, (2) matching of results to traditional building methods, (3) having numerous physical and mechanical properties and (4) detailed methods and test specimens. Twelve key references published over 2015 to 2024 were reviewed and each focused on regions and climates that varied greatly.\u003c/p\u003e\u003cp\u003eThe following materials were selected for analysis:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eDue to their porosity and good thermal mass, adobe bricks help regulate indoor temperaturesin hot and dry areas [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003ePoint out that limestone and sandstone are frequent in classical stone masonry [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eLime mortar which belongs to the traditional group and has hygroscopic features [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eWood plank is frequently seen in both support structures and decorative parts [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eMost monuments built with volcanic stone and marble\u0026mdash;they are strong and not porous [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eAll materials were included in a single row, sharing the average values reported in scientific articles. SI units were used to standardize these values, and a table (Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e1\u003c/span\u003e) was created so the values can be checked against a single list.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eMechanical and physical properties of traditional materials.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaterial\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCompressive Strength (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePorosity (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDensity (kg/m\u0026sup3;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eThermal Conductivity (W/m\u0026middot;K)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMoisture Absorption (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAdobe Brick\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e30.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1650\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e18.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLimestone\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e12.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e18.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e7.1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLime Mortar\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e25.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1800\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e12.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWood Plank\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e12.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e700\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e20.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSandstone\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e9.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e19.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2250\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e9.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVolcanic Stone\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e14.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e6.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMarble\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e17.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2700\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTo perform advanced statistical operations, the dataset was imported into Minitab 21. Many analytical techniques were applied to obtain important information from the material\u0026rsquo;s properties. First, several measures such as mean, minimum, maximum and range, were used to explain the activity of each variable. To identify important links between porosity, density and strength, Pearson\u0026rsquo;s correlation coefficients were used. Then, regression models were designed to forecast important outcomes, mainly how porosity influences compressive strength and how density is related to thermal conductivity.\u003c/p\u003e\u003cp\u003eTo uncover more about underlying patterns in the data, PCA was used to shrink the number of dimensions, allowing materials to be organized by their resemblance in a smaller set of features. Another technique included in this study is hierarchical cluster analysis which organized materials into groups based on their performance, helping to spot where they are alike or different. The results were explained with scree plots, biplots, dendrograms and loading plots, all of which were produced using α\u0026thinsp;=\u0026thinsp;0.05 as the confidence level.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data sets used during the current study are available from the corresponding author on reasonable request (due to privacy).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode avaialbility statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e[If applicable insert code availability statement here].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Researchers would like to thank the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support (QU-APC-2025).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMohammed A. Albadrani: Conceptualization; Methodology; Data curation; Formal analysis; Visualization; Writing – original draft; Writing – review \u0026amp; editing; Supervision; Funding acquisition.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no external funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInstitutional review board statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eBorri, A., Corradi, M., Castori, G. \u0026amp; De Maria, A. 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The application of Historic Building Information Modeling (HBIM) to cultural heritage: a review.\u0026nbsp;\u003cem\u003eHeritage\u003c/em\u003e\u003cstrong\u003e6\u003c/strong\u003e, 6691\u0026ndash;6717 (2023).\u003c/li\u003e\n \u003cli\u003eLiu, J., Willkens, D. \u0026amp; Foreman, G. An introduction to technological tools and process of Heritage Building Information Modeling (HBIM).\u0026nbsp;\u003cem\u003eEGE Rev. Exp. Gr\u0026aacute;f. Edificaci\u0026oacute;n\u003c/em\u003e\u003cstrong\u003e16\u003c/strong\u003e, 50\u0026ndash;65 (2022).\u003c/li\u003e\n \u003cli\u003eKong, X. \u0026amp; Hucks, R. G. Preserving our heritage: a photogrammetry-based digital twin framework for monitoring deteriorations of historic structures.\u0026nbsp;\u003cem\u003eAutom. 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Adaptive reuse of heritage buildings: from a literature review to a model of practice.\u0026nbsp;\u003cem\u003eHist. Environ. Policy Pract.\u003c/em\u003e\u003cstrong\u003e13\u003c/strong\u003e, 148\u0026ndash;170 (2022).\u003c/li\u003e\n \u003cli\u003eAbdelmegeed, M. Damage assessment and rehabilitation of historic traditional masonry structures. Master\u0026rsquo;s thesis, Cairo Univ., Cairo, Egypt (2015).\u003c/li\u003e\n \u003cli\u003eXu, J., Ding, L. \u0026amp; Love, P. E. D. Digital reproduction of historical building ornamental components: from 3D scanning to 3D printing.\u0026nbsp;\u003cem\u003eAutom. Constr.\u003c/em\u003e\u003cstrong\u003e78\u003c/strong\u003e, 85\u0026ndash;96 (2017).\u003c/li\u003e\n \u003cli\u003eHatir, M. E., Ince, I. \u0026amp; Korkan\u0026ccedil;, M. Intelligent detection of deterioration in cultural stone heritage. \u003cem\u003eJ. Build. Eng.\u003c/em\u003e\u003cstrong\u003e40\u003c/strong\u003e, 102690 (2021).\u003c/li\u003e\n \u003cli\u003eCabeza, L. F., de Gracia, A. \u0026amp; Pisello, A. L. Integration of renewable technologies in historical and heritage buildings: a review. \u003cem\u003eEnergy Build.\u003c/em\u003e\u003cstrong\u003e177\u003c/strong\u003e, 96\u0026ndash;111 (2018).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"heritage science, traditional building materials, predictive modeling, PCA, HBIM, conservation diagnostics","lastPublishedDoi":"10.21203/rs.3.rs-7443315/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7443315/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe conservation of historic buildings requires diagnostic tools that assess material performance without destructive testing. This study introduces a predictive modeling framework that integrates mechanical, thermal, and moisture-related properties across seven traditional construction materials: adobe brick, lime mortar, limestone, sandstone, marble, volcanic stone, and wood plank. Using data synthesized from twelve peer-reviewed studies (2015–2024), we applied Pearson correlation, regression, Principal Component Analysis (PCA), and hierarchical clustering to identify key relationships and material groupings. Results confirm that porosity strongly predicts compressive strength (R² ≈ 62%, p = 0.035), while density correlates with thermal conductivity (R² ≈ 85.5%, p = 0.003). PCA and clustering distinguished lightweight, porous, moisture-sensitive materials from dense, durable ones, offering a comparative classification tool for conservation planning. Unlike earlier works that examined materials or properties in isolation, this study systematically integrates multiple parameters into a single predictive framework with direct applications in heritage diagnostics, HBIM, and energy-efficient retrofitting. Future validation through field monitoring and HBIM integration will further enhance predictive accuracy.\u003c/p\u003e","manuscriptTitle":"Non-destructive predictive modeling of traditional building materials for historic conservation and digital heritage applications","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-08 16:45:17","doi":"10.21203/rs.3.rs-7443315/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ce7cee91-4b0f-4dd8-83ef-c550b9747381","owner":[],"postedDate":"September 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-08T13:53:26+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-08 16:45:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7443315","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7443315","identity":"rs-7443315","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}