Skip to main content

Expansion of mortar joints in direct shear tests of masonry samples: implications on shear strength and experimental characterization of dilatancy


The expansion of masonry specimens during direct shear tests has been reported in several research studies. This phenomenon, known as dilatancy, is caused by the formation of cracking surfaces in mortar joints. In particular, when the cracking surface is not perfectly flat, the shear displacements tend to increase the volume of the sample. Experimental investigations focused on the characterization of this phenomenon are rather limited for masonry and the effects on shear strength have received little attention, with consequent issues for a correct interpretation of the results. The present article reports the results of an ongoing research on brick masonry aimed to characterize experimentally the dilatancy and to evaluate the role of this phenomenon in the interpretation of the direct shear test. If the expansion of the specimen is significantly restrained, the standard approaches used for the characterization of the mechanical parameters (as per EN 1052-3 and ASTM C1531) tend to overestimate the initial shear strength (fvo) and underestimate friction. Moreover, no indications are generally given to characterize dilatancy with experimental data. This aspect is particularly important for the micro-modelling of masonry because the constitutive models commonly used for mortar joints require this information. One of the objectives of the present article is to propose a simple model for a sound interpretation of the direct shear test of masonry samples taking into account the dilatancy. Several masonry samples composed of calcium silicate units and cement mortar joints have been subjected to triplet tests (EN 1052-3) and laboratory-simulated shove tests. First, a repeatable and objective methodology to measure and characterize the dilatancy is provided. Then, an extension of the standard methodology of the EN 1052-3 and ASTM C1531 that includes the contribution of this phenomenon is proposed. The novel formulation offers the possibility to characterize dilatancy with experimental data and the definition of mechanical parameters that are not biased by the presence of this phenomenon. The model presented in this article has proven to be consistent with the experimental data and it has been validated numerically in another recent research study.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. Andreotti G, Graziotti F, Magenes G (2018) Detailed micro-modelling of the direct shear tests of brick masonry specimens: the role of dilatancy. Eng Struct 168:929–949.

    Article  Google Scholar 

  2. Atkinson RH, Amadei BP, Saeb S, Sture S (1989) Response of masonry bed joints in direct shear. J Struct Eng ASCE 115(9):2276–2296

    Article  Google Scholar 

  3. Lourenço PB (1996) Computational strategies for masonry structures. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands

  4. Lourenço PB (1998) Experimental and numerical issues in the modelling of the mechanical behaviour of masonry. In: Roca P et al (eds) Structural analysis of historical constructions II. CIMNE, Barcelona, pp 57–91

    Google Scholar 

  5. Lourenço PB, Barros JO, Oliveira JT (2004) Shear testing of stack bonded masonry. Constr Build Mater 18:125–132

    Article  Google Scholar 

  6. Lourenço PB, Ramos LF (2004) Characterization of cyclic behaviour of dry masonry joints. J Struct Eng ASCE 130(5):779–786

    Article  Google Scholar 

  7. van der Pluijm R (1992) Material properties of masonry and its components under tension and shear. In: Proceedings of the 6th Canadian masonry symposium, Saskatoon, Canada, pp 675–686

  8. van der Pluijm R (1993) Shear behaviour of bed joints. In: Proceedings of 6th North American masonry conference, Philadelphia, pp 125–136

  9. van der Pluijm R (1998) Overview of deformation controlled combined tensile and shear tests. Technical report TUE/BC0/98.20, Eindhoven University of Technology

  10. van der Pluijm R (1999) Out-of-plane bending of masonry: behavior and strength. Ph.D. thesis, Eindhoven University of Technology, The Netherlands

  11. Rots JG (1991) Numerical simulation of cracking in structural masonry. Heron 36(2):49–63

    Google Scholar 

  12. Serpieri R, Albarella M, Sacco E (2017) A 3D microstructured cohesive–frictional interface model and its rational calibration for the analysis of masonry panels. Int J Solids Struct 122–123(2017):110–127

    Article  Google Scholar 

  13. Zijl GPAG (1999) Numerical formulation for masonry creep, shrinkage and cracking. Technical report, series 11—Engineering Mechanisms 01, Delft University of Technology

  14. Bazant ZP, Gambarova PG (1980) Rough crack models in reinforced concrete. J Struct Eng ASCE 106(4):819–842

    Google Scholar 

  15. Wong RCK, Ma SKY, Wong RHC, Chau KT (2007) Shear strength components of concrete under direct shearing. Cem Concr Res 37(2007):1248–1256

    Article  Google Scholar 

  16. Goodman RE (1976) Method of geological engineering in discontinuous rocks. West Publishing Company, New York, p 472

    Google Scholar 

  17. Patton FD (1966) Multiple modes of shear failure in rock. In: Proceedings, 1st congress of international society of rock mechanics, Lisbon, vol 1, pp 509–513

  18. Bolton MD (1986) The strength and dilatancy of sands. Geotechnique 36(1):65–78

    Article  Google Scholar 

  19. Taylor DW (1948) Fundamentals of soil mechanics. Wiley, New York

    Book  Google Scholar 

  20. EN (2007) European Standard EN 1015-11. Methods of test for mortar for masonry. Part 11—determination of flexural and compressive strength of hardened mortars. Comitee Europeen de Normalisation, Brussels

  21. ASTM (2016) C1531-16: standard test methods for in-situ measurement of masonry mortar joint shear strength index. ASTM International, West Conshohocken, PA.

  22. Calvi GM, Kingsley GR, Magenes G (1996) Testing of masonry structures for seismic assessment. Earthq Spectra 12(1):145–162.

    Article  Google Scholar 

  23. Noland JL, Atkinson RH, Kingsley GR, Schuller MP (1990) Nondestructive evaluation of masonry structures. Atkinson-Noland & Associates Report to the National Science Foundation

  24. Zijl GPAG (2004) Modeling masonry shear-compression: role of dilatancy highlighted. J Eng Mech 130(11):1289–1296

    Article  Google Scholar 

  25. Bolhassani M, Hamid AA, Lau ACW, Moon A (2015) Simplified micro modeling of partially grouted masonry assemblages. Constr Build Mater 83:159–173

    Article  Google Scholar 

  26. Gabor A, Ferrier E, Jacquelin E, Hamelin P (2006) Analysis and modelling of the in-plane shear behaviour of hollow brick masonry panels. Constr Build Mater 20:308–321

    Article  Google Scholar 

  27. Graziotti F, Guerrini G, Rossi A, Andreotti G, Magenes G (2018) Proposal for an improved procedure and interpretation of ASTM C1531 for the in situ determination of brick-masonry shear strength. In: Krogstad NV, McGinley WM (eds) Masonry 2018, ASTM STP1612. ASTM International, West Conshohocken, PA, 2018, pp 13–33.

  28. Eucentre (2015) Technical report: experimental campaign on cavity walls systems representative of the Groningen building stock. European Centre for Training and Research in Earthquake Engineering, Pavia, Italy, 337 p.

  29. Graziotti F, Rossi A, Mandirola M, Penna A, Magenes G (2016) Experimental characterization of calcium-silicate brick masonry for seismic assessment. In Proceedings of 16th international brick/block masonry conference, June 2016, Padova, Italy.

  30. Stupkiewicz S, Mróz Z (2001) Modelling of friction and dilatancy effects at brittle interfaces for monotonic and cyclic loading. J Theor Appl Mech 3(39):707–739

    MATH  Google Scholar 

  31. Binda L, Mirabella G, Tiraboschi C, Abbaneo S (1994) Measuring masonry material properties. In: Proceedings US–Italy workshop on guidelines for seismic evaluation and rehabilitation of unreinforced masonry buildings. State University of New York at Buffalo, NCEER-94-0021, pp 6-3/24

  32. Bandis S, Lumsden AC, Barton NR (1981) Experimental studies of scale effect on the shear behaviour of rock joints. Int J Rock Mech Min Sci Geomech Abstr 18:1–21

    Article  Google Scholar 

  33. Kutter HK, Weissbach G (1980) Der Einfluss von Verformungs- und Bela- stungsgeschichte auf den Scherwiderstand von Gesteinskluften unter Besonderer Berucksichtigung der Mylonitbildung. Final Report, DFG Research Project Ku 361/2/4

  34. Sun Z, Gerrard C, Stephanson O (1985) Rock joint compliance tests for compression and shear loads. Int J Rock Mech Min Sci Geomech Abstr 4:197–213

    Article  Google Scholar 

  35. Rahman A, Ueda T (2014) Experimental investigation and numerical modeling of peak shear stress of brick masonry mortar joint under compression. J Mater Civ Eng 26(9):04014061

    Article  Google Scholar 

  36. Wood DM (2004) Geotechnical Modelling. London: CRC Press.

    Book  Google Scholar 

  37. CEN (2005) European Standard EN 1992-2:2005 Eurocode 2: design of concrete structures. Comitee Europeen de Normalisation, Brussels

    Google Scholar 

  38. CEN (2007) European Standard EN 1052-1. Methods of test for masonry. Part 1—determination of compressive strength. Comitee Europeen de Normalisation, Brussels

    Google Scholar 

  39. CEN (2007) European Standard EN 1052-3:2002/A1 Amendment A1 to European Standard EN 1052-3:2002. Comitee Europeen de Normalisation, Brussels

    Google Scholar 

  40. CEN (2007) European Standard EN 1052-5. Methods of test for masonry. Part 5: determination of bond strength by the bond wrench method. Comitee Europeen de Normalisation, Brussels

    Google Scholar 

Download references


Special thanks are due to Prof. Carlo Lai for his suggestions. The work presented in this paper was partially supported by the financial contribution of the Italian Department of Civil Protection within the framework “RELUIS-DPC” which is greatly acknowledged by the authors. The performed laboratory tests were part of the ‘‘Study of the vulnerability of masonry buildings in Groningen” project at the EUCENTRE, undertaken within the framework of the research program for hazard and risk of induced seismicity in Groningen sponsored by the Nederlandse Aardolie Maatschappij BV. The authors would like to express their gratitude also to S. Girello, A. Rossi and P&P Consulting Engineers Group for the execution of the tests at DICAr laboratory of University of Pavia.

Author information

Authors and Affiliations


Corresponding author

Correspondence to G. Andreotti.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material: Appendix A (DOCX 7072 kb)

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Andreotti, G., Graziotti, F. & Magenes, G. Expansion of mortar joints in direct shear tests of masonry samples: implications on shear strength and experimental characterization of dilatancy. Mater Struct 52, 64 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: