Citation :

M S Sunil Kumar, G Ravi, S Raviraj, "Reliability and Structural Performance Assessment of Solid Concrete Block Masonry Prisms using Compressive Strength Modelling and Monte Carlo Simulations," International Journal of Civil Engineering, vol. 13, no. 7, pp. 117-127, 2026. Crossref, https://doi.org/10.14445/23488352/IJCE-V13I7P107

Abstract

Solid concrete block masonry is widely used in construction, but its performance is affected by variability in material properties, workmanship, and block quality. Traditional deterministic design methods often fail to capture these uncertainties, potentially leading to unsafe designs. This research proposes a reliability approach to assess masonry prism compressive strength through the integration of predictive modelling and probabilistic analysis. The objective is to perform a reliability analysis of masonry prisms and determine the Probability of failure. Five cement-sand mortar ratios (1:3 to 1:7) were experimentally evaluated, and Multiple Linear Regression (MLR) models were developed to estimate prism strength as a function of block and mortar strengths. The developed regression equations were incorporated into a Monte Carlo simulation framework with 40,000 iterations to evaluate the Probability of failure and reliability index for a typical residential building configuration. Results indicate that the 1:3 mortar mix provides superior structural performance, yielding a probability of failure (𝑃𝑓) of 0.0479 and a reliability index (𝛽) of 1.66, satisfying the adopted target reliability criterion. Floor optimization analysis further revealed that the structure can safely support up to 14 floors while maintaining the adopted Probability of failure limit of 5%. The findings highlight the significant influence of material variability on masonry reliability and demonstrate the effectiveness of probabilistic methods for realistic safety assessment and performance-based masonry design.

Keywords

Masonry reliability, Monte Carlo simulation, Probability of failure, Reliability index, Solid concrete blocks, Structural safety, Multiple linear regression.

References

1. Ismail Bello et al., “Complete Stress-Strain Analysis of Masonry Prisms under Compressive Loading-Unloading Cycles through Digital Image Correlation,” Engineering Structures, vol. 298, pp. 1-31, 2024.
   [CrossRef] [Google Scholar] [Publisher Link]
2. Thuany E. S. de Lima et al., “Influence of the Mortar Bedding in Compressive Strength of Masonry Wallets made of Brazilian Concrete Blocks,” International Journal of Civil Engineering, vol. 22, pp.1945-1959, 2024.
   [CrossRef] [Google Scholar] [Publisher Link]
3. Siddharth B. Baeen et al., “Effect of Thin Reinforcement in Bed-Joint on the Compressive and Shear Strength of Brick and Block Masonry- An Experimental Investigation,” Journal of Building Pathology and Rehabilitation, vol. 10, 2025.
   [CrossRef] [Google Scholar] [Publisher Link]
4. Ali Abasi, Bennett Banting, and Ayan Sadhu, “Towards Design of Temporary Bracing for Early-Age Unreinforced Masonry Walls Against Out-of-plane Loading,” Engineering Structures, vol. 345, pp. 1-13, 2025.
   [CrossRef] [Google Scholar] [Publisher Link]
5. Lewis J. Gooch, Mark G. Stewart, and Mark J. Masia, “Model Accuracy for the Prediction of Unreinforced Clay Brick Masonry Shear Wall Resistance,” Bulletin of Earthquake Engineering, vol. 24, pp.1-29, 2025.
   [CrossRef] [Google Scholar] [Publisher Link]
6. Navaratnarajah Sathiparan, “Predicting Compressive Strength of Grouted Masonry using Machine Learning Models with Feature Importance Analysis,” Materials Today Communications, vol. 41, 2024.
   [CrossRef] [Google Scholar] [Publisher Link]
7. Francesco P. A. Portioli, and Paulo B. Lourenço, “Nonlinear Static Analysis of Masonry Structures with Mortar Joints and Cracking units by Optimization-based Rigid Block Models,” Earthquake Engineering & Structural Dynamics, vol. 53, no. 13, pp. 3963-3982, 2024.
   [CrossRef] [Google Scholar] [Publisher Link]
8. Davi Fagundes Leal, Jorge Munaiar Neto, and Cristian Maluk, “Thermal Behavior of Dry-Cast Concrete Blocks Masonry Walls at Elevated Temperatures,” Journal of Building Engineering, vol. 89, 2024.
   [CrossRef] [Google Scholar] [Publisher Link]
9. Gustavo Henrique Nalon et al., “Self-Sensing Concrete Masonry Structures with Intrinsic Abilities of Strain Monitoring and Damage Detection,” Structures, vol. 59, 2024.
   [CrossRef] [Google Scholar] [Publisher Link]
10. Abrahem A. Ali Blash et al., “Evaluating the Behaviour of Axially Loaded Hollow Concrete Block Masonry Walls with Small-Size Openings: Various Opening Positions and their Influence on Experimental Results,” Engineering Structures, vol. 301, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
11. Julian Thamboo, Mathavanayakam Sathurshan, and Tatheer Zahra, “Reliable Unit Strength Correlations to Predict the Compressive Strength of Grouted Concrete Masonry,” Materials and Structures, vol. 57, pp. 1-19, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
12. Maria Concetta Oddo, Panagiotis G. Asteris, and Liborio Cavaleri, “Monte Carlo Analysis of Masonry Structures under Tsunami Action: Reliability of Lognormal Fragility Curves and Overall Uncertainty Prediction,” Structures, vol. 63, pp. 1-15, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
13. Tingwei Shi et al., “Influences of Random Imperfection Distribution on the Compressive Properties of Interlocking Block Wall,” Structures, vol. 56, pp. 1-19, 2023.
    [CrossRef] [Google Scholar] [Publisher Link]
14. Luis C.M. da Silva, Gabriele Milani, and Paulo B. Lourenço, “Probabilistic-based Discrete Model for the Seismic Fragility Assessment of Masonry Structures,” Structures, vol. 52, pp. 506-523, 2023.
    [CrossRef] [Google Scholar] [Publisher Link]
15. Hae-Chang Cho et al., “Structural Safety Inspection of Reinforced Concrete Structures Considering Failure Probabilities of Structural Members,” International Journal of Concrete Structures and Materials, vol. 17, pp. 1-17, 2023.
    [CrossRef] [Google Scholar] [Publisher Link]
16. Mauricio Guamán-Naranjo, José Poveda-Hinojosa, and Ana Gabriela Haro-Báez, “Probabilistic Loss Assessment for the Typology of Non-Ductile Reinforced Concrete Structures with Flat Slabs, Embedded Beams, and Unreinforced Infill Masonry,” Buildings, vol. 14, no. 10, pp. 1-17, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
17. Mahmoud Zaki Abdelrahman, and Khaled Galal, “Experimental Investigation of In-plane Shear and Compressive Behaviour of Dry-Stacked Interlocking Concrete Masonry,” Construction and Building Materials, vol. 505, pp. 1-17, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
18. R. Ranganathan, Structural Reliability Analsis and Design, Jaico Publishing House, pp. 1-456, 1998.
    [Google Scholar] [Publisher Link]
19. S. R. Balasubramanian et al., “Experimental Determination of Statistical Parameters Associated with Uniaxial Compression Behaviour of Brick Masonry,” Current science, vol. 109, no. 11, pp. 2094-2102, 2015.
    [CrossRef] [Google Scholar] [Publisher Link]
20. Dae-Kyung Kim, and Woo-Young Lim, “Correlation between Brick-and-mortar Material Properties and Brick Masonry Prism Compressive Strength and Elastic Modulus,” Journal of Building Engineering, vol. 111, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
21. Deepa A. Joshi, and R. K. Jain, “Evaluation of Compressive Strength and Basic Compressive Stress of Clay Brick Unreinforced Masonry by Prism Test,” International Journal of Science and Research (IJSR), vol. 4, no. 5, pp. 913-916, 2015.
    [Google Scholar] [Publisher Link]
22. Fei Zhu et al., “Compressive behavior of Fully Grouted Concrete Bond Beam Block Masonry Prisms,” Materials, vol. 18, no. 11, pp. 1-16, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
23. C. Freeda         Christy, D. Tensing, and R. Mercy Shanthi, “Experimental Study on Axial Compressive Strength and Elastic Modulus of the Clay and Fly Ash Brick Masonry,” Journal of Civil Engineering and Construction Technology, vol. 4, no. 4, pp. 134-141, 2013.
    [Google Scholar] [Publisher Link]
24. Julio Garzón-Roca, Creu Obrer Marco, and Jose M. Adam, “Compressive Strength of Masonry made of Clay Bricks and Cement Mortar: Estimation based on Neural Networks and Fuzzy Logic,” Engineering Structures, vol. 48, pp. 21-27, 2013.
    [CrossRef] [Google Scholar] [Publisher Link]
25. Ronald Lumantarna         , David T. Biggs, and Jason M. Ingham, “Uniaxial Compressive Strength and Stiffness of Field-Extracted and Laboratory-Constructed Masonry Prisms,” Journal of Materials in Civil Engineering, vol. 26, no. 4, pp. 1-41, 2012.
    [CrossRef] [Google Scholar] [Publisher Link]
26. Mehar Babu Ravula, and Kolluru V. L. Subramaniam, “Experimental Investigation of Compressive Failure in Masonry Brick Assemblages made with Soft Brick,” Materials and Structures, vol. 50, 2017.
    [CrossRef] [Google Scholar] [Publisher Link]
27. S.B. Singh, and Pankaj Munjal, “Bond Strength and Compressive Stress-Strain Characteristics of Brick Masonry,” Journal of Building Engineering, vol. 9, pp.10-16, 2017.
    [CrossRef] [Google Scholar] [Publisher Link]
28. Nassif Nazeer Thaickavil, and Job Thomas, “Behaviour and Strength Assessment of Masonry Prisms,” Case Studies in Construction Materials, vol. 8, pp. 23-38, 2018.
    [CrossRef] [Google Scholar] [Publisher Link]
29. K. S. Gumaste et al., “Strength and Elasticity of Brick Masonry Prisms and Wallettes under Compression,” Materials and Structures, vol. 40, pp. 241-253, 2007.
    [CrossRef] [Google Scholar] [Publisher Link]
30. Hemant B. Kaushik, Durgesh C. Rai, and Sudhir K. Jain, “Stress-Strain Characteristics of Clay Brick Masonry under Uniaxial Compression,” Journal of Materials in Civil Engineering, vol. 19, no. 9, pp.728-739, 2007.
    [CrossRef] [Google Scholar] [Publisher Link]
31. Gihad Mohamad, Paulo B. Lourenço, and Humberto R. Roman, “Mechanics of Hollow Concrete Block Masonry Prisms under Compression: Review and Prospects,” Cement and Concrete Composites, vol. 29, no. 3, pp. 181-192, 2007.
    [CrossRef] [Google Scholar] [Publisher Link]
32. K. S. Jagadish, S. Raghunath, and K. S. Nanjunda Rao, “Behaviour of Masonry Structures during the Bhuj Earthquake of January 2001,” Journal of Earth System Science, vol. 112, pp. 431-440, 2003.
    [CrossRef] [Google Scholar] [Publisher Link]
33. Jahangir Bakhteri, Ahmad Mahir Makhtar, and Shamala Sambasivam, “Finite Element Modelling of Structural Clay Brick Masonry Subjected to Axial Compression,” Journal of Technology, vol. 41, pp.57-68, 2004.
    [CrossRef] [Google Scholar] [Publisher Link]
34. Mangala Keshava, K.V. Vijayendra, and S. Raghunath, “Strength Efficiency of Commonly used Block Work Masonry,” International Journal of Earth Sciences and Engineering, vol. 3, no. 4, pp. 586-598, 2010.
    [Google Scholar]
35. Md Monjur Hossain, Sk Sekender Ali, and M. Azadur Rahman, “Properties of Masonry Constituents,” Journal of Civil Engineering, vol. 25, no. 2, pp.135-155, 1997.
    [Google Scholar]
36. Hemant B. Kaushik, Durgesh C. Rai, and Sudhir K. Jain, “Uniaxial Compressive Stress–strain Model for Clay Brick Masonry,” Current Science, vol. 92, no. 4, pp. 497-501, 2007.
    [Google Scholar] [Publisher Link]
37. Navaratnarajah Sathiparan, and Pratheeba Jeyananthan, “Comparative Analysis of Machine Learning Models and Standard Codes for Predicting Compressive Strength in Hollow Block Masonry,” Journal of Umm Al-Qura University for Engineering and Architecture, vol. 16, pp. 1806-1838, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
38. Sreedhara B. Marulasiddappa et al., “Strength Assessment of Structural Masonry Walls: Analysis based on Machine Learning Approaches,” HBRC Journal, vol. 20, no. 1, pp. 505-524, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
39. Lanh Si Ho, and Quan Tran, “Evaluation and Estimation of Compressive Strength of Concrete Masonry Prism using Gradient Boosting Algorithm,” Plos one, vol. 19, no. 3, pp. 1-23, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
40. Abdulelah Al-Ahdal, Belal AbdelRahman, and Khaled Galal, “Compressive, Shear, and Tensile Behaviours of Concrete Masonry: Experimental and Numerical Study,” Construction and Building Materials, vol. 458, pp. 1-23, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
41. Md Mohsin M. Dafedar et al., “Evaluation of the Engineering Properties and Sustainability of Solid Masonry Blocks Produced with Recycled Concrete Aggregates,” Innovative Infrastructure Solutions, vol. 9, no. 11, pp. 1-19, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
42. Mohamed Y. Zorainy et al., “Stress-Strain Behavior of Masonry Boundary Element Prisms under Axial Compression,” Structures, vol. 80, pp. 1-15, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
43. Priyanka Singh et al., “Development of Performance-based Models for Green Concrete using Multiple Linear Regression and Artificial Neural Network,” International Journal on Interactive Design and Manufacturing (IJIDeM), vol. 18, no. 5, pp. 2945-2956, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
44. IS: 383, Specification for Coarse and Fine Aggregates from Natural Sources for Concrete, Bureau of Indian Standards, pp. 1-24, 1970.
    [Google Scholar] [Publisher Link]
45. IS: 1905, Code of Practice for Structural use of Unreinforced Masonry, Bureau of Indian Standards, pp. 1-30, 1987.
    [Publisher Link]
46. IS: 2185-1, Concrete Masonry Units, Part 1: Hollow and Solid Concrete Blocks, Bureau of Indian Standards, pp. 1-17, 2005.
    [Publisher Link]
47. IS: 2250, Code of Practice for Preparation and use of Masonry Mortars, Bureau of Indian Standards, pp. 1-36, 1981.
    [Google Scholar] [Publisher Link]
48. IS: 4031 (Part 6), Methods of Physical Tests for Hydraulic Cement Part 6: Determination of Compressive Strength of Hydraulic Masonry Cement, (First revision), Bureau of Indian Standards, 1988.
    [Publisher Link]
49. IS: 5512, “Specification for Flow Table for use in Tests of Hydraulic Cements and Pozzolanic Materials,” Bureau of Indian Standards, pp. 1-17, 1983.
    [Google Scholar] [Publisher Link]