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Diagonal compressive strength of masonry samples—experimental and numerical approach

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Abstract

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.

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Abbreviations

A n :

Net area of masonry sample

B :

Height of the masonry sample

D :

Isotropic scalar degradation variable

d c :

Compressive damage variable

d max :

Maximum aggregate size

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

Initial (undamaged) elastic stiffness

d t :

Tensile damage variable

e :

Thickness of the mortar parallel joints

E 0 :

Modulus of elasticity

F :

Compression load

f l :

Tensile flexural strength

F max :

Maximum compression load

F max :

Maximum compression load

G p :

Potential plastic flow

g :

Full width of the mortar strips

G :

Shear modulus

G F :

Fracture energy

G Fo :

Base value of the fracture energy

H :

Length of the masonry sample

h s :

Depth of a sample

K c :

Ratio between the tensile and compressive stress invariants at initial yield

L :

Distance between measurement points of ∆v and ∆h

N :

Percentage of gross area of the unit that is solid

\( \bar{p} \) :

Effective hydrostatic pressure

\( \bar{q} \) :

Von Mises equivalent effective stress

R 2 :

Coefficient of determination

s c :

Weight factor to control the recovery of the compressive stiffness

s t :

Weight factor to control the recovery of the tensile stiffness

t :

Total thickness of the wall

α i , β i , γ i :

Adimensional parameters

γ:

Shear strain

γmax :

Shear strain for the τmax

∆h :

Horizontal extensions

∆v :

Vertical shortening

ε:

Total strain

εcu :

Strain for σcu or ultimate strain

εc,limit :

Limit compressive strain

εel :

Elastic strain

εc :

Compression strain

εmax :

Strain of masonry for the F max

εpl :

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

εt :

Tensile strain

ν :

Poisson coefficient

σ:

Cauchy stress

\( \bar{\sigma } \) :

Effective stress

σb0 :

Initial equi-biaxial compressive yield stress

σc :

Uniaxial compression stress

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

Compressive effective stresses

σc0 :

Initial uniaxial compressive yield stress

σcu :

Compressive strength (maximum compression stress)

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

Maximum principal effective stress (algebraic value)

σt :

Uniaxial tensile stress

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

Tensile effective stresses

σto :

Uniaxial tensile strength

τ:

Shear stress

τmax :

Shear strength or maximum shear stress

ψ:

Dilation angle

∈:

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

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Acknowledgments

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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Authors and Affiliations

  1. GEQUALTEC, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    Rui Sousa, Hipólito Sousa & João Guedes

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  1. Rui Sousa
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Correspondence to Rui Sousa.

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Sousa, R., Sousa, H. & Guedes, J. Diagonal compressive strength of masonry samples—experimental and numerical approach. Mater Struct 46, 765–786 (2013). https://doi.org/10.1617/s11527-012-9933-z

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