cc2013: analysis, modelling and design of masonry structures
DESCRIPTION
CC2013: Analysis, Modelling and Design of Masonry Structures. Mesoscale Modelling of Masonry Structures Accounting for Brick-Mortar Interaction. Francisco B. Xavier, Lorenzo Macorini, Bassam A. Izzuddin. Project Funding. Department of Civil & Environmental Engineering, Imperial College London. - PowerPoint PPT PresentationTRANSCRIPT
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CC2013: Analysis, Modelling and Design of Masonry Structures
Francisco B. Xavier, Lorenzo Macorini, Bassam A. Izzuddin Project Funding
Mesoscale Modelling of Masonry Structures Accounting for Brick-Mortar Interaction
Department of Civil & Environmental Engineering, Imperial College London
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Outline
Introduction
- Standard Mesoscacle Modelling
- Importance of Brick-Mortar Interaction
Enhanced Meoscale Modelling
- Interface FE Formulation
Verification Examples under Uniaxial Compression
- Elastic Analysis of Single Prism
- Crack Initiation on Masonry Wall
Closure
- Ongoing Work
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Numerical Analysis of Masonry Panels
Brick Unit
Bed Joint
Head Joint
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Numerical Analysis of Masonry Panels
a) Micro-Model
b) Simplified Micro-Model – Mesoscale Model
c) Homogenised Macro-Model
Increasing
Computational Expense
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Mesoscale Modelling
20-Noded Solid Element
Elastic Material
16-Noded Interface Element
Material Nonlinearity, Mix-Mode Cohesive Cracking, Crushing, Damage
• Brick Units
• Brick-Mortar Interfaces
• “Brick-Brick” Interfaces
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Brick Mortar Interaction Leading to Unit Cracking
Mesoscale Modelling - Drawback
e.g.: Masonry Prism – Uniform CompressionTension
Compressionassuming Eb > Em
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Mesoscale Modelling - Drawback
Brick Mortar Interaction Leading to Unit Cracking
e.g.: Masonry Prism – Uniform Compression
assuming Eb > Em
However, with standard interface modelling there is no coupling between in-plane and normal deformations:
0 0
0 0
0 0
z z z
x x x
y y y
k
k
k
z
2 2x y Tension & Shear
“Crushing” Failure Surface
No Lateral Tension Develops in the Units
Approximate Solution at Interface Material Level
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Enhanced Mesoscale Modelling
a) Micro-Model
b) Simplified Micro-Model – Mesoscale Model
Brick-Mortar Interaction
- Typically Captured with Refined Micro-Models
Modified Interface Element Kinematics
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Enhanced Mesoscale Modelling
Considering interface finite elements representing an actual volume, in which one of the dimensions is considerable smaller than the other two – in this case the mortar joint thickness h
It is possible to introduce triaxial stresses and deformations into a zero-thickness interface, while maintaining its capabilities for cohesive crack modelling
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Enhanced Mesoscale Modelling
1( , , ) ( ) ( )
2
zu x y z u u u u
h
• Assuming displacements inside the mortar layer as linear function of top and bottom surfaces:
• A representative average strain vector is obtained as:
2 2
2 2
1 1( , , )
h h
avh h
dz Lu x y z dzh h
• Introducing a further simplification with regards to shear strain definition in the x-z and z-y planes:
' '; yxxz yz
uu
z z
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Enhanced Mesoscale Modelling
1( , , ) ( ) ( )
2
zu x y z u u u u
h
• Assuming displacements inside the mortar layer as linear function of top and bottom surfaces:
• A representative average strain vector is obtained as:
2 2
2 2
1 1( , , )
h h
avh h
dz Lu x y z dzh h
• Assemble matrix L as:
0 0 0
0 0 0
0 0 0 0 0
T
x z y
Ly z x
z
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Enhanced Mesoscale Modelling
The strain vector for the enhanced interface element yields:
'
'
( )1
2
( )1
2
( ) ( )1 1
2 2
x x
y y
x
y z z
z
xz x x
yz
y yxy av
y y x x
u u
x
u u
y
u u
h
u u
h
u u
h
u u u u
x y
1z
x
y
h
Typical Interface displacement discontinuities uniformly smeared over the height of the mortar layer
Average of top and bottom surface engineering strain
Considering the conjugate stress vector:
T
av x y z xz yz xy
The local elastic constitutive relationship is:
av avD
with:
(1 ) 0 0 0
(1 ) 0 0 0
(1 ) 0 0 0
0 0 0 0 0
0 0 0 0 0
(1 2 )0 0 0 0 0
2
x
y
A v Av Av
Av A v Av
Av Av A vD G
G
vA
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Enhanced Mesoscale Modelling
(1 ) 0 0 0
(1 ) 0 0 0
(1 ) 0 0 0
0 0 0 0 0
0 0 0 0 0
(1 2 )0 0 0 0 0
2
x
y
A v Av Av
Av A v Av
Av Av A vD G
G
vA
3D Constitutive matrix:
(1 )(1 2 )
EA
v v
Coupling between interface opening and normal strains at mid-surface
Interface stiffness to sliding
In-plane shear stiffness at mid-surface
Directly obtained with shear test
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Enhanced Mesoscale Modelling
Co-rotational Framework
• Large Displacements
Out-of-Plane Response under Extreme Loading
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Enhanced Mesoscale Modelling
Comparison between full continuum and enhanced interface elastic response at detailed level
Masonry prism under uniform compression
• 10 mm thick mortar joints• 250x120x55 mm3 units• Eb>Em
Mortar joints detailed with solid FE
Mortar joints lumped into zero-thickness enhanced interfaces
Symmetry Boundary Conditions
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Enhanced Mesoscale Modelling
Full Continuum With Interfaces
• Lateral Tensile Stresses in Brick Units
• Lateral Stresses in Mortar Joint
Good Match especially in the region where tensile cracks are expected to develop
Continuum Mortar Joint Interface Mortar Joint
Z
X
Similar Pattern in Z-Y PlaneImportance of 3D Modelling
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Enhanced Mesoscale Modelling
Full Continuum
Detailed with Interfaces
Symmetry Boundary Conditions
Brick-Brick Interface
Standard Formulation
Brick-Mortar Interface
Enhanced Formulation
Mesoscale a)
Brick-Brick InterfaceBrick-Mortar
Interface
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Enhanced Mesoscale Modelling
Full Continuum
Detailed with Interfaces
Mesoscale b) Mesoscale c)
Lateral tensile Stresses in the Brick Units
Mesoscale a)
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Enhanced Mesoscale Modelling
Comparison in terms of global stiffness
Response obtained with standard interfaces
No lateral stresses
Full Continuu
m
Detailed w/
interfaces
Mesoscale a)
Mesoscale b)
Mesoscale c)
DOFs 27951 23535 1440 2880 10560
Computational Cost
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Enhanced Mesoscale Modelling
Unreinforced Masonry Wall – Uniaxial Compression test
• Head and Bed mortar joints 10 mm thick
Symmetry Boundary Conditions
Mesoscale a) Mesoscale b)
• Mesocale Model a) – 1 solid element along the height of brick units
• Mesocale Model b) – 2 solid elements along the height of brick units • Head Mortar Joints Modelled with standard
interfaces
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Enhanced Mesoscale Modelling
Experimental
0 2 4 6 8 10 12 140
1
2
3
4
5
6
7
8
9
10
11
12
Vertical Strain (x103)
Com
pres
sive
Str
ess
(MP
a)
Enhanced Mesoscacle Elastic
Brick Cracking Activated
Onset of cracking recorded experimentally
Initiation of cohesive cracking in theMesoscale model
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Closure
Further Improvements on the enhanced interface element:
• Adapt previous cohesive model (Macorini & Izzuddin, 2011) to accommodate new stress components in the new interface, i.e., allow mix-mode fracture (Tension & Shear) in brick-mortar interfaces (bed joints)
• Introduce failure surface at interface level, accounting for triaxial stress state in order to capture the actual failure of confined mortar material
• Non-linear response of masonry prisms by the knowledge of individual components properties, as opposed to composite properties dependent on the prism characteristics
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Closure
• Despite mechanically sound, full potential of this enhanced mesoscale modelling strategy is only achieved if realistic material properties for both mortar and brick units are available
• Current published research underlines mortar material properties when part of a masonry assemblage or taken from single specimen to be markedly different
• There is the need to establish procedures to assess the actual mortar material properties, thus enabling the composite behaviour o masonry panels to be characterized by its individual constituents properties
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Thank You!
Questions?