Contribution to the modelling of
interfaces in masonry
constructions (2006)
Fazia Fouchal
Supervisor: Frédéric LEBON
CNRS
Laboratoire de
Mécanique et d Acoustique –
Marseille France
a
Groupe de Mécanique,
Matériaux Et Structures
URCA - Reims - France
b
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1
Context of study
Loading out of plane
Hoceima ; Earthquake
Maroc 2004
Loading in plan
Algiers Earthquake
Algeria 2003
2
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Context of study
Observation
Modelling
Schematization
Experimentation
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3
Context of study
In addition to the vertical and horizontal LOADS
….
Masonry constructions are sensitive to :
Fatigue, stiffness degradation, climatic
environment (moisture, temperature , soil, …)
Discontinuities
INTERFACES
DAMAGE
4
FAILURE
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I. INTRODUCTION
II. EXPERIMENTAL STUDY
III. NUMERICAL STUDY
IV. CONCLUSIONS
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State of the art
1. Masonry constructions modelling
2. Interface behavior modelling
3. RCCM model
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State of the art
1.  Masonry constructions modeling
o  global Approach
Local behavior
modelling of each
components (blocks, mortar joints and / or
interface)
Blocs (rigide ou
déformable)
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Interfaces
blocs/blocs
Interfaces blocs/
mortar
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Mortar
Blocs
State of the art
a) Depth knowledge of the various components
(experimentally).
b) Consideration of the anelastic phenomena
(damage, cracking, ...)
§  Mortar joints: nonlinear behavior [Page 78,
Luciano
& al 98,Casalo 04, Formica & al
96]
§  Blocs: [Del peiro 89]
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§  Interfaces: nonlinear behavior [Stankowski
& al 93, Lofti & al 94, Gambarotta & al 97,
Oliviera & al 04]
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o  Homogenization Approach
State of the art
Modelling the average behavior of
masonry structure
a) substitute the several
materials of masonry by
equivalent material.
b) change the physical
parameters of the
problem
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State of the art
Medium made with a
periodic cells
A fiber-reinforced
composite material
?
10
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Old
masonry
State of the art
2. Interface behavior modelling
Brique
Joint de mortier
e=épaisseur de joint de mortier
Brique-brique
=joint de mortier
mortier/brique
Interphase (faible épaisseur)
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Interface
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State of the art
• Brittle behavior
Page [78] considers elastic brick and mortar
joint is modeling by interface elements with
(elasto-plastic) non-linear behavior with a
brittle fracture criterion.
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State of the art
• Quasi-brittle fracture
* Modèle d interface (interphase?) élastoplastique avec adoucissement
-Lofti et al [94] pour tous les
constituants
-Lourenço [96] briques parfaitement
élastiques
* Gambarotta et al [97] Modèle volumique
d interphase prenant en compte
l endommagement du joint du mortier.
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Experimental study
• Characterization of the masonry materials
Quantitative results:
§  Bricks (210*100*50 mm3)
Ef≈ 9438.5 MPa; Eh≈ 6058.8 MPa; ν ≈ 0.135
f: full, h: hollow
§  Mortar (10mm)
E ≈ 8200 MPa; ν ≈ 0.3
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Experimental study
Fc
Fc
Fn
Fn
Essai sur les couplets [Pluijm, 99]
Essai sur les triplets [NF EN 772-1]
Fn
Fc
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Fn
Fn
Fc
Fn
Essai sur un assemblage de
briques [Lourenço et al, 04]
Fn
Essai sur un assemblage de
briques [Gabor, 02]
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Experimental study
•  The masonry interface behaviour
1.
Shear test on coplets of full / hollow bricks (Device N°1)
Full bricks
Hollow bricks
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Experimental study
2.
Shear test on triplets of full/hollow bricks (Device N°2)
Full bricks
Hollow bricks
Full brick case
Hollow brick case
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Experimental study
•  Summary
Similar behaviour under shear test between the
couplet and triplet.
1.
2.
Elastic domain: very rigid behaviour
Post pick domain:
§  Brittle behaviour for a full brick specimen
§  Softening behaviour and sliding motion
between the ajdacent bricks of a hollow
bricks specimen.
Arbitrary distribution of Mortar’s spikes
Dispersion of the results.
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Experimental study
Difference about the stress limit for the
full brick case
Shear stress at the rupture = 2.6 MPa
Test N°2
Shear stress at the rupture =1.6 MPa
Shear stress at the rupture =2.3 MPa
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Experimental study
Difference about the stress limit for the
hollow brick case
Shear stress at the rupture =1.6 MPa
Shear stress at the rupture =1.45 MPa
Test N°2
Shear stress at the rupture =1.2 MPa
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First Conclusion
§  No linear behaviour of masonry under shearing test.
§  Choice of basic cell have no influence on local scale of
masoneries.
§  Rupture / decohesion modes analysis confirms
hetetogeneity
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Numerical study
Interface model
RCCM is coupling adhesion model for unilateral contact and
friction, (Raous – Cangémi – Cocu - Monerie)
§  Unilateral contact conditions
§  Friction and adhesion
§  Evolution of the adhesion intensity
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Numerical study
variables : δN , δ T , b, CN, CT
q  Model parameters :
CN , CT : normal and tangentiel
stiffnesses of the interface
μ : friction coef
b :Viscosity parameter
w : Dupré’s energy
p =1
h(β) : given
q  Contact
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Numerical study
Shear test on triplets of full bricks
F = 53 kN
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Numerical study
Shear test on triplets of full bricks
1
4
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Numerical study
Shear test on triplets of full bricks
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Numerical study
Shear test on triplets of full bricks
2
3
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Numerical study
Shear test on triplets of full bricks
Matériau cohésif
Adh1
Cn1 et Ct1
adh2
Cn2 et Ct2
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adh1: adhérence interface mortier-mortier
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adh2: adhérence interface brique-mortier
Numerical study
Shear test on triplets of full bricks
2
3
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Numerical study
Shear test on triplets of full bricks
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Numerical study
Shear test on triplets of hollow bricks
adh1
adh1: adhérence interface brique-mortier
adh2:
adhérence interface mortier-mortier (picots)
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Numerical study
Shear test on triplets of hollow bricks
2
3
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Numerical study
Shear test on triplets of hollow bricks
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Numerical study
Shear test on doublets of full /
hollow bricks
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Numerical study
Shear test on doublets of full bricks
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Numerical study
Shear test on doublets of hollow
bricks
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Numerical study
A small wall
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Numerical study
A small wall
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Numerical study
RILEM TEST
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Numerical study
RILEM TEST
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Numerical study
•  Summary
1.  RCCM interface model is able to be
used to modeling
behavior of
masonry at local scale. (qualitatively
and quantitatively)
2.  High number of parameters
3.  LMGC90 code is able to be used to
calculate masonry structures.
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Experimentally
CONCLUSIONS
1.  Full brick have a brittle behavior with a very
stiff elastic domain
2. Hollow brick have softening behavior with a
very stiff elastic domain.
Numerically:
1.  Taking into account the damage of interfaces in
masonry structures.
2.  Ability to model the rupture at the interface
(brick-mortar) and at the mortar joint.
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