Bulletin of Earthquake Science and Engineering

Bulletin of Earthquake Science and Engineering

Numerical Study of the Core Compression Test Method to Investigate the Behavior of the Existing Masonry Structure by the Model Based on the Space Angular Decomposition Concept

Document Type : Research Article

Authors
Hamid Tavanaeifar 1
Amir Houshang Akhaveissy Akhaveissy 2
1 Ph.D. Graduate in Structural Engineering, Department of Civil Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran
2 Associate Professor, Department of Civil Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
10.48303/bese.2024.2024805.1152
Abstract
The structural assessment of existing masonry buildings often requires reliable estimation of their compressive strength. However, conventional experimental methods such as testing full-scale prisms or wallettes are highly invasive, time-consuming, costly, and impractical for in-situ evaluation of historic or existing structures. Alternative techniques like the flat-jack test provide only elastic-range data and fail to capture post-peak softening behavior or ultimate compressive capacity. In this context, core drilling emerges as a promising minimally invasive approach, enabling the extraction of small cylindrical samples (masonry cores) for laboratory testing while preserving the integrity of the parent structure. Despite its potential, the interpretation of core compression tests remains challenging due to complex stress states, size effects, and the heterogeneous nature of masonry materials. 
This study presents a comprehensive numerical investigation into the compressive behavior of masonry cores compared to standard prismatic specimens, using advanced finite element modeling. A three-dimensional continuous micro-modeling strategy is employed, explicitly representing both bricks and mortar without interface elements. Two sophisticated constitutive models are implemented and compared: (1) the widely used Concrete Damage Plasticity (CDP) model available in Abaqus, and (2) an enhanced Multi-Laminate Model (MLM) based on the angular decomposition of stress space. The MLM is specifically upgraded to account for biaxial tensile-compressive stress states in bricks and triaxial confinement effects in mortar key mechanisms governing masonry failure under compression. 
The MLM incorporates a fracture-energy-based softening law and separates stress into volumetric and deviatoric components, applying the latter to multiple micro-planes (66 in this study) to inherently capture the pronounced anisotropy and directional dependency of quasi-brittle materials after cracking. In contrast, the CDP model relies on isotropic damage and invariant-based yield surfaces, which may inadequately represent the true 3D stress interaction between masonry constituents.
Both models are rigorously calibrated using experimental data from the literature, particularly from compression tests on masonry prisms and cores conducted by Pelà et al. (2016). Calibration involves determining path-dependent parameters for triaxial compression and biaxial tension-compression states through single-element simulations with appropriate boundary conditions. The models are then validated against three benchmark cases: (i) a five-brick prism, (ii) a 150-mm diameter masonry core under axial compression, and (iii) a full-scale shear wall tested at Eindhoven University.
Results demonstrate that the enhanced MLM accurately predicts both the peak compressive strength and the failure mode including vertical splitting in bricks and hourglass-shaped crushing closely matching experimental observations. The model correctly estimates the lateral confining stress in mortar (≈0.65 MPa), aligning with theoretical expectations from Hilsdorf’s framework. In contrast, the CDP model significantly overestimates strength (by up to 86% in prisms and 36% in cores), primarily due to unrealistic confinement assumptions and inability to capture directional tensile failure in bricks. 
Furthermore, the MLM successfully reproduces the load–displacement response and crack patterns of the Eindhoven shear wall under combined vertical and lateral loading, confirming its robustness for practical structural analysis. This study confirms that core testing, when interpreted through advanced, physically consistent numerical models like the enhanced MLM, offers a viable, minimally destructive method for assessing the compressive behavior of existing masonry. The proposed approach provides deeper insight than laboratory tests alone delivering full-field stress and strain distributions and outperforms conventional modeling techniques in accuracy and physical fidelity. 
Keywords
Masonry Core
Micro Modeling
Dilatancy Effect
Model Based on Angular Space Decomposition
CDP Model

Subjects

Akhaveissy, A. H., & Desai, C. S. (2011). Unreinforced masonry walls: Nonlinear finite element analysis with a unified constitutive model. Archives of Computational Methods in Engineering, 18(4), 485-502. doi: 10.1007/ s11831-011-9062-0
Alam, S. Y., Zhu, R., & Loukili, A. (2020). A new way to analyse the size effect in quasi-brittle materials by scaling the heterogeneity size. Engineering Fracture Mechanics, 225, 106864. doi: 10.1016/j.engfracmech. 2019.106864
Anthoine, A. (1997). A homogenisation of periodic masonry: Plane stress, generalised plane strain or 3D modelling? Communications in Numerical Methods in Engineering, 13(5), 319-326. doi: 10.1002/(SICI)1099-0887(199705)13:5<319::AID-CNM71>3.0.CO;2-9
Aref, A. J., & Dolatshahi, K. M. (2013). A three-dimensional cyclic meso-scale numerical procedure    for simulation of unreinforced masonry structures. Computers & Structures, 120, 9-23. doi: 10.1016/j. compstruc.2013.01.012
ASTM International. (2009). Standard Test Method for Compressive Strength of Masonry Prisms (ASTM C1314-09). https://www.astm.org/standards/c1314
Bažant, Z. P., & Oh, B. H. (1983). Crack band theory for fracture of concrete. Materials and Structures, 16(3), 155-177.
Binda, L., & Tiraboschi, C. (1999). Flat-jack test: A slightly destructive technique for the diagnosis of brick and stone masonry structures. Restoration of Buildings and Monuments, 5(5), 449-472. doi: 10.1515/rbm-1999-0032
Benedetti, A., & Tarozzi, M. (2022). Compressive strength of heterogeneous masonry walls containing blends of brick types. Materials and Structures, 55-71. doi: 10.1617/s11527-022-01912-0
Červenka, J., Červenka, V., & Laserna, S. (2018). On crack band model in finite element analysis of concrete fracture in engineering practice. Engineering Fracture Mechanics, 197, 27-47. doi: 10.1016/j.engfracmech. 2018.04.010
D'Altri, A. M., de Miranda, S., Castellazzi, G., & Sarhosis, V. (2018). 3D detailed micro-model for the in-plane and out-of-plane numerical analysis of masonry panels. Computers & Structures, 206, 18-30. doi: 10.1016/j.compstruc.2018.06.007
Drucker, D. C. (1954). Coulomb friction, plasticity,   and limit loads. Journal of Applied Mechanics, 21(1), 71-74.
Drougkas, A., Roca, P., & Molins, C. (2015). Numerical prediction of the behavior, strength and elasticity of masonry in compression. Engineering Structures, 90, 15-28. doi: 10.1016/j.engstruct.2015. 02.011
European Committee for Standardization. (1995). *Eurocode 6: Design of Masonry Structures — Part 1-1: General Rules for Reinforced and Unreinforced Masonry Structures* (ENV 1996-1-1).
European Committee for Standardization. (1998). Methods of Test for masonry – Part 1: Determination of Compressive Strength (EN 1052-1:1998).
Galavi, V. (2007). A Multilaminate Model for Structured clay Incorporating Inherent Anisotropy and Strain Softening. Ph.D. Thesis, Graz University of Technology. (Heft 32)
Ghadrdan, M., Sadrnejad, S. A., & Shaghaghi, T. (2015). Numerical evaluation of geomaterials behavior upon multiplane damage model. Computers and Geotechnics, 68, 1-7. doi: 10.1016/j.compgeo.2015.03. 008
Hassanli, R. (2019). Effect of Dimensions on the Compressive Strength of Concrete Masonry Prisms. In Behavior of unbounded post-tensioned masonry walls, 100-115. Springer.
Hilsdorf, H. K. (1969). Investigation into the Failure Mechanism of Brick Masonry Loaded in Axial Compression. In Designing, Engineering and Constructing with Masonry Products, 37-60. Gulf Publishing.
Hilsdorf, H. K. (1972). Masonry materials and their physical properties. Proceedings of the International Conference on Planning and Design of Tall Buildings, Lehigh University, Bethlehem, PA, United States.
Jafari, S., Rots, J. G., & Esposito, R. (2019). Core testing method to assess nonlinear behavior of         brick masonry under compression: A comparative experimental study. Construction and Building Materials, 218, 193-205. doi: 10.1016/j.conbuildmat. 2019.04.188
Jirásek, M., & Bauer, M. (2012). Numerical aspects of the crack band approach. Computers & Structures, 110-111, 60-78. doi: 10.1016/j.compstruc.2012.06.006
Kaushik, H. B., Rai, D. C., & Jain, S. K. (2007). Stress-strain characteristics of clay brick masonry under uniaxial compression. Journal of Materials in Civil Engineering, 19(9), 728-739. doi: 10.1061/(ASCE) 0899-1561(2007)19:9(728)
Koocheki, K., & Pietruszczak, S. (2023). Numerical analysis of large masonry structures: Bridging meso and macro scales via artificial neural networks. Computers & Structures, 282, 107042. doi: 10.1016/j. compstruc.2023.107042
Lee, J., & Fenves, G. L. (1998). Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics, 124(8), 892-900. doi: 10.1061/ (ASCE)0733-9399(1998)124:8(892)
Lourenço, P. B., & Rots, J. G. (1997). Multisurface interface model for analysis of masonry structures. Journal of Engineering Mechanics, 123(7), 660-668. doi: 10.1061/(ASCE)0733-9399(1997)123:7(660)
Lourenço, P. B., Rots, J. G., & Blaauwendraad, J. (1998). Continuum model for masonry: Parameter estimation and validation. Journal of Structural Engineering, 124(6), 642-652. doi: 10.1061/(ASCE) 0733-9445(1998)124:6(642)
Macorini, L., & Izzuddin, B. (2011). A non-linear interface element for 3D mesoscale analysis of brick-masonry structures. International Journal for Numerical Methods in Engineering, 85(12), 1584-1608. doi: 10.1002/nme.3046
Massart, T. J., Peerlings, R. H. J., Geers, M. G. D., & Gottcheiner, S. (2005). Mesoscopic modeling of failure in brick masonry accounting for three-dimensional effects. Engineering Fracture Mechanics, 72(8), 1238-1253. doi: 10.1016/j.engfracmech.2004.10.002
McNary, S. W., & Abrams, D. P. (1985). Mechanics     of masonry in compression. Journal of Structural Engineering, 111(4), 857-870. doi: 10.1061/(ASCE) 0733-9445(1985)111:4(857)
Milani, G., Lourenço, P. B., & Tralli, A. (2007). 3D homogenized limit analysis of masonry buildings   under horizontal loads. Engineering Structures, 29(12), 3134-3148. doi: 10.1016/j.engstruct.2007.03.021
Molins Borrell, C. (1996). Characterization of the mechanical behaviour of masonry. In Structural Analysis of Historical Constructions (Conference Paper). CIMNE, Barcelona, Spain.
Motamedi, M. H., & Foster, C. D. (2015). An improved implicit numerical integration of a non-associated, three-invariant cap plasticity model with mixed isotropic–kinematic hardening for geomaterials. International Journal for Numerical and Analytical Methods in Geomechanics, 39(16), 1853-1883. doi: 10.1002/nag.2372
Naciri, K., Aalil, I., Chaaba, A., & Al-Mukhtar, M. (2021). Detailed micromodeling and multiscale modeling of masonry under confined shear and compressive loading. Practice Periodical on Structural Design and Construction, 26(1), Article 04020048.   doi: 10.1061/(ASCE)SC.1943-5576.0000538
Nie, Y., Sheikh, A., Griffith, M., & Visintin, P. (2022). A damage-plasticity based interface model for simulating in-plane/out-of-plane response of masonry structural panels. Computers & Structures, 271, 106721. doi: 10.1016/j.compstruc.2021.106721
Pelà, L., Aprile, A., & Roca, P. (2016). Compression test of masonry core samples extracted from existing brickwork. Construction and Building Materials, 119, 230-240. doi: 10.1016/j.conbuildmat.2016.05.057
Pelà, L., Roca, P., & Benedetti, A. (2016). Mechanical characterization of historical masonry by core drilling and testing of cylindrical samples. International Journal of Architectural Heritage, 10(2-3), 360-374. doi: 10.1080/15583058.2015.1077906
Peyman, F., & Sadrnejad, S. A. (2017). Analysis of concrete crack growth based on micro-plane model. Structural Concrete, 18(5), 1-16. doi: 10.1002/suco. 201600208
Pietruszczak, S., & Niu, X. (1992). A mathematical description of macroscopic behaviour of brick masonry. International Journal of Solids and Structures, 29(5), 531-546. doi: 10.1016/0020-7683(92) 90052-U
Pulatsu, B., Erdogmus, E., Lourenço, P. B., & Quey, R. (2019). Simulation of uniaxial tensile behavior of quasi-brittle materials using softening contact models in DEM. International Journal of Fracture, 217(1-2), 105-125. doi: 10.1007/s10704-019-00362-4
Sarhosis, V., & Lemos, J. V. (2018). Detailed micro-modelling approach for the structural analysis of masonry assemblages. Computers & Structures, 206, 66-81. doi: 10.1016/j.compstruc.2018.06.003
Segura, J., Pelà, L., & Roca, P. (2018). Monotonic and cyclic testing of clay brick and lime mortar masonry in compression. Construction and Building Materials, 193, 453-466. doi: 10.1016/j.conbuildmat.2018.10.198
Shieh-Beygi, B., & Pietruszczak, S. (2008). Numerical analysis of structural masonry: Mesoscale approach. Computers & Structures, 86(17-18), 1958-1973. doi: 10.1016/j.compstruc.2008.04.009
Shrestha, J. K., Bhandari, S., Pradhan, S., & Gautam, D. (2020). Simplified frame model for capacity assessment of masonry buildings. Soil Dynamics and Earthquake Engineering, 131, 106056. doi: 10.1016/j. soildyn.2020.106056
Tavanaeifar, H., & Akhaveissy, A. H. (2023). Splitting test on masonry cores and modeling of the confined mortar behavior based on fracture energy. Amirkabir Journal of Civil Engineering, 55(3), 555-582. doi: 10.22060/ceej.2023.21192.7647
Union Internationale des Chemins de fer. (1995). Recommendations for the Assessment of the Load Carrying Capacity of Existing Masonry and Mass-concrete Arch Bridges (UIC Code 778-3R)
Vermeltfoort, A. T., Martens, D. R. W., & van Zijl, G. P. A. G. (2007). Brick-mortar interface effects on masonry under compression. Canadian Journal of Civil Engineering, 34(12), 1475-1485. doi: 10.1139/L07-067
Vermeltfoort, A. T., Raijmakers, T., & Janssen, H. (1993). Shear tests on masonry walls. Heron, 38(1),      3-22.
Vorel, J., Marcon, M., Cusatis, G., Caner, F., Di Luzio, G., & Wan-Wendner, R. (2021). A comparison of the state of the art models for constitutive modelling of concrete. Computers & Structures, 244, 106426. doi: 10.1016/j.compstruc.2020.106426
Zahra, T., & Dhanasekar, M. (2016). Prediction of masonry compressive behaviour using a damage mechanics inspired modelling method. Construction and Building Materials, 109, 128-138. doi: 10.1016/j. conbuildmat.2016.01.048
Zhao, Y. G., Lin, S., Lu, Z. H., Saito, T., & He, L. (2018). Loading paths of confined concrete in circular concrete filled steel tube stub columns subjected to axial compression. Engineering Structures, 156, 21-31. doi: 10.1016/j.engstruct.2017.11.010

  • Receive Date 13 March 2024
  • Revise Date 16 September 2024
  • Accept Date 08 October 2024