The interdisciplinary role of dilatancy in the unifying approach for the interpretation of direct shear tests of masonry


In a general sense, the mechanism of dilatancy is the volume change observed in a body when it is subjected to shear displacements. The term “dilatancy” was originally introduced by Osborne Reynolds (1885) to denote a particular type of behaviour exhibited by a collection of particles in contact with one another. Since then, this concept has taken a key role in development of rock mechanics and geotechnical engineering (e.g. critical state soil mechanics) with important practical significances in earthquake engineering (e.g. liquefaction, fault rupture propagation).

Dilatancy is a distinctive feature of granular materials but the contribution of this phenomenon in defining the shear strength has been recognized also for concrete (i.e. aggregate interlock). Although this mechanism has already been observed for masonry by various researchers, it has received comparatively little attention in this field. This aspect is particularly important when refined numerical models are used. When brick units, mortar joints and unit-mortar interfaces are explicitly modelled (i.e. micro-modelling) the mortar joints generally require the definition of the parameters related to dilatancy. Since experimental investigations focused on the characterization of this phenomenon are rather limited for masonry, the mechanical parameters related to dilatancy are generally assumed in an arbitrary way. This problem has proved to be relevant in the definition of the unifying approach for the interpretation of the direct hear tests of masonry specimens.

In Europe, the triplet test has been adopted as the standard laboratory procedure for the characterization of the initial shear strength under zero compressive load. Alternatively, an equivalent in-situ test can be used for the same purpose but for existing structures only; this test is called the ‘shove’ test. Unfortunately, significant differences have been observed when the strength parameters determined through laboratory-simulated shove tests are compared with those obtained via triplet tests. So far, research has attributed these discrepancies to the difficulty of estimating the compressive stress that act on the mortar joints under investigation of the shove test. To be specific, the actual compressive stress induced by the flat-jacks on the tested bed joints has been seen to be influenced by the removal of the adjacent units. As a resolve, many opt to estimate the compressive stress acting on the mortar joints in the shove test. In addition, the dilatancy normally experienced along the bed joint during the shear failure process has also been postulated to generate, under certain boundary conditions, a local increase of the normal compression stress. This way, estimation becomes difficult and therefore, the problem ought to be understood so as to overcome this shortcoming. Consequently, this has prompted much research.

Recently, in a multidisciplinary research collaboration Dr. Guido Andreotti from the European Centre for Training and Research in Earthquake Engineering – EUCENTRE in collaboration with Dr. Francesco Graziotti and Prof. Guido Magenes at University of Pavia developed a numerical tool that would be implemented in Abaqus so as to derive reliable values for the compressive shear test. Additionally, they focused in their study on normal dilatancy as it has been previously seen to influence the compressive stress of the mortar joints. Their work is currently published in the research journal, Engineering Structures.

In brief, the research method employed entailed the application of a detailed micro-modelling approach to develop a numerical model capable of accurately simulating the triplet test and the shove test. To actualize this model, the researchers used units and mortar joints with continuum elements and cohesive interface elements, with zero thickness, for the unit-mortar interfaces. Lastly, modifications were implemented on the standard constitutive laws available for continuum elements within the general-purpose software as they were not adequate to model accurately the mechanism of dilatancy.

The authors observed that using their modified model, experimental results of several triplet tests and shove tests were reproduced numerically. The researchers noted that the calibration of the dilatancy angle controlled the expansion of the masonry samples. Moreover, a good agreement between the experimental tests and the numerical simulations was observed, and served as the first encouraging result as regards the reliability of the proposed model. Further, it was shown that the dilatancy angle controlled the expansion of the masonry samples and increased the shear strength of the mortar joints with two different mechanisms: (a) increase in mobilized friction; (b) local increase of normal stress in mortar joints.

In summary, the study presented a novel numerical approach implemented in Abaqus with the sole purpose of interpreting the phenomena involved in the failure of a mortar bed joint. They realized that method they had advanced allowed the quantification of the amount of shear strength and compressive stress generated by the mechanism of dilatancy. Altogether, utilization of the numerical technique presented in this article has potential to be further exploited through additional parametric analysis and numeric-experimental comparison to develop a sufficiently general reference for an update of the criteria for the execution and interpretation of the shove test, which is commonly used for in-situ evaluation of bed joint shear strength.

According to the authors of the paper: The dilatancy mechanism (expansion due to shearing) has a key role in unifying the interpretation of the direct shear test of different disciplines.

 interdisciplinary role of dilatancy in unifying approach for interpretation of direct shear tests of masonry - Advances in Engineering

About the author

Dr. Guido Andreotti received a B.Sc. in Natural Science (2003), a B.Sc. in Civil Engineering (2010) and a M.Sc. in Civil Engineering (2013) at University of Pavia (Pavia, Italy). He worked as a consultant in the field of Civil Engineering before undertaking a Ph.D. in Earthquake Engineering and Engineering Seismology at UME School (Pavia, Italy). He was visiting researcher at University of California, Berkeley (USA) and at University of Canterbury (New Zealand). He also collaborated with the EUCENTRE foundation ( Now he is a postdoc researcher at University of Pavia.

His main research interests are: (a) numerical modelling of dynamic soil-structure interaction, (b) assessment of seismic risk and damage of geotechnical structures, (c) ground response analysis, (d) constitutive modelling and (e) micro-detailed modelling of masonry.

About the author

Dr. Francesco Graziotti is Assistant Professor of Structural Engineering at the Department of Civil Engineering and Architecture (DICAr) at the University of Pavia, Italy. He received his PhD in Earthquake Engineering and Engineering Seismology from the UME School (ROSE programme, IUSS) of Pavia and his MSc degree in Structural Engineering from the University of California, San Diego.

Since 2014, he collaborates with the EUCENTRE foundation as team leader for a full-scale static and shake-table testing campaign as part of the framework of a project to evaluate the seismic vulnerability of unreinforced structures subjected to induced seismicity.

His research primarily focuses on characterising the non-linear global and local behaviour of masonry structures via numerical models in addition to large-scale laboratory tests investigating the seismic vulnerability of masonry structures.

About the author

Prof. Guido Magenes is Full Professor of Structural Engineering at the University of Pavia, Department of Civil Engineering and Architecture (DICAr). He is also collaborating with the EUCENTRE Foundation (European Centre for Training and Research in Earthquake Engineering).

Guido Magenes has over 28 years research experience in the area of seismic analysis, design and assessment of structures, including extensive experimental activity. He has authored or co-authored over 200 scientific papers in the field of structural engineering, with emphasis on masonry and reinforced concrete structures subjected to seismic and nonseismic loading.

His main research interest is the structural behaviour of masonry and reinforced concrete constructions and the relevant strategies and techniques of repair/rehabilitation/strengthening, with particular reference to seismic engineering.


G. Andreotti, F. Graziotti, G. Magenes. Detailed micro-modelling of the direct shear tests of brick masonry specimens: The role of dilatancy. Engineering Structures, volume 168 (2018) page 929–949.

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