Materials and Structures

, Volume 46, Issue 5, pp 765–786 | Cite as

Diagonal compressive strength of masonry samples—experimental and numerical approach

  • Rui Sousa
  • Hipólito Sousa
  • João Guedes
Original Article


Masonry is a structural material that presents a quite complex behaviour that depends on the mechanical and geometrical characteristics of the units, the mortar and the link between these two elements. In particular, the characterization of the shear behaviour of masonry elements involves proper experimental campaigns that make these analyses particularly expensive. The main objective of this paper is to present a case study on the characterization of the shear behaviour of masonry through a methodology that merges a small number of laboratory tests with computer simulations. The methodology is applied to a new masonry system that has recently been developed in Portugal, and involves a FEM numerical approach based on micro3D modelling of masonry samples using nonlinear behaviour models that are calibrated through a small number of laboratory tests. As a result, the characterization of the masonry shear behaviour trough this methodology allowed simulating, with reasonably accuracy, a large set of expensive laboratory tests using numerical tools calibrated with small experimental resources.


Masonry Lightweight concrete units Diagonal compression Laboratory tests Computer simulations Sensitivity analysis 

List of symbols


Net area of masonry sample


Height of the masonry sample


Isotropic scalar degradation variable


Compressive damage variable


Maximum aggregate size

\( D_{0}^{\text{el}} \)

Initial (undamaged) elastic stiffness


Tensile damage variable


Thickness of the mortar parallel joints


Modulus of elasticity


Compression load


Tensile flexural strength


Maximum compression load


Maximum compression load


Potential plastic flow


Full width of the mortar strips


Shear modulus


Fracture energy


Base value of the fracture energy


Length of the masonry sample


Depth of a sample


Ratio between the tensile and compressive stress invariants at initial yield


Distance between measurement points of ∆v and ∆h


Percentage of gross area of the unit that is solid

\( \bar{p} \)

Effective hydrostatic pressure

\( \bar{q} \)

Von Mises equivalent effective stress


Coefficient of determination


Weight factor to control the recovery of the compressive stiffness


Weight factor to control the recovery of the tensile stiffness


Total thickness of the wall

αi, βi, γi

Adimensional parameters


Shear strain


Shear strain for the τmax


Horizontal extensions


Vertical shortening


Total strain


Strain for σcu or ultimate strain


Limit compressive strain


Elastic strain


Compression strain


Strain of masonry for the F max


Plastic strain

\( \tilde{\varepsilon }^{\text{pl}} \)

Multi-axial equivalent plastic strain

\( \tilde{\varepsilon }_{\text{c}}^{\text{pl}} \)

Compressive equivalent plastic strain

\( \tilde{\varepsilon }_{\text{t}}^{\text{pl}} \)

Tensile plastic strain


Tensile strain


Poisson coefficient


Cauchy stress

\( \bar{\sigma } \)

Effective stress


Initial equi-biaxial compressive yield stress


Uniaxial compression stress

\( \bar{\sigma }_{\text{c}} \)

Compressive effective stresses


Initial uniaxial compressive yield stress


Compressive strength (maximum compression stress)

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\bar{\sigma }}_{\max } \)

Maximum principal effective stress (algebraic value)


Uniaxial tensile stress

\( \bar{\sigma }_{\text{t}} \)

Tensile effective stresses


Uniaxial tensile strength


Shear stress


Shear strength or maximum shear stress


Dilation angle

Parameter that defines the rate at which G p approaches the asymptote



The authors gratefully acknowledged ADI-Portuguese Innovation Agency and the Company Maxit-Portugal for the help provided in the OTMAPS research project.


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Copyright information

© RILEM 2012

Authors and Affiliations

  1. 1.GEQUALTEC, Faculty of EngineeringUniversity of PortoPortoPortugal

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