Numerical and experimental investigation on existing structures: two seminars

Advanced 3D Modelling and
Analysis of Masonry Structures
Dr Lorenzo Macorini
CSM Group, Department of Civil and Environmental Engineering
Imperial College London
Rome, 30 January 2018

Advanced 3D Modelling and Analysis of Masonry Structures
Lorenzo Macorini, CSM Group
Outline
• Modelling strategies for masonry
• The proposed mesoscale model for brick-masonry
• Nonlinear analysis of brick-masonry components
• Mesh tying for representing heterogeneous systems and
enhancing computational efficiency
• Mesoscale Partitioned Modelling
• Numerical examples
• Conclusions

Structural masonry
• Most structures built before the second half of the
19th century are masonry structures.
• At present masonry is mainly used for housing
developments, cladding and partition walls.
• Research on masonry is essential to:
- assess the behaviour of existing structures;
- develop effective strengthening measures;
- explore the response under extreme loading;
- investigate new construction products.

Masonry under extreme loading

Assessment of Masonry Bridges
Arch bonding patterns (McKibbins et al., 2006)
Backfill
Load test to collapse on an arch bridge at
Preston, Staffordshire (Page, 1987)

Modelling strategies for masonry structures
FE modelling Macro-modelling
Equivalent material approach
Micro-modelling
Two-material approach
Material model
Lourenço, 1996
Lourenço,
1996

Macroscale model
Equivalent material
approach
Mesoscale model
Two-material approach
Structural
scale
Mesoscale
scale
Microscale
scale
Scale of representation
Anisotropy
Chemical -
Environmental
actions
Massart, 2003

Macroscale
models
A.W. Page (1983), The strength of brick
masonry under biaxial tension‐compression,
Int. J. Masonry Constr., 3(1).
• Specific phenomenological nonlinear models should be used
• Damage induced anisotropy cannot be effectively represented
• Problematic identification of material parameters for existing
structures

Macroscale
models
structures
Initial
orthotropy and
periodicity
Damage-
induced
orthotropic
state
Damage-induced
non-orthotropic
state
Massart, 2003

structures
Macroscale
models

• Material behaviour is associated with the scale of constituents
• Masonry bond is explicitly taken into account
• Mesoscale models can represent damage induced anisotropy
Tests on brick and mortar
Material identification:
Mesoscale
models

Masonry nonlinear behaviour depends upon the composition, the in-
plane stacking mode and the through-thickness geometry
Through-thickness
geometry
In-plane stacking mode
3D mesoscale modelling for masonry

3D mesoscale modelling for masonry
Shieh-Beygi & Pietruszczak, Computer &
Structures 2008
Milani, Journal of Mechanical Sciences, 2008
• 3D mesoscale models are used mainly in static simulations
of small components, often neglecting large displacement
contribution
• High computational cost

The proposed 3D mesoscale model
Solid and interface elements account for large displacements, while only
interface elements represent cracks in mortar and bricks
Blocks are modelled using continuum elements, while mortar and brick-
mortar interfaces are modelled by means of nonlinear interface elements
(Lourenço & Rots, 1996)

2D nonlinear interface elements
A co-rotational approach is employed to allow for large
displacements
• The local co-rotational system
follows the element current deformed
configuration
• The effects of geometric
nonlinearity are established through
transformation between global and
local entities

2D nonlinear interface elements
Material model
Multi-surface
non-associated plasticity
Elastic response
0σ = k u
0
0
0
0 0
0 0
0 0
t
t
n
k
k
k
 
 
 
  
0kElastic
stiffness
Mortar joints
0
m
t
j
G
k
h
 0
m
n
j
E
k
h

   
2 22 2
1 tan tan 0x y tF C C           
   
2 22 2
2 tan tan 0x y cF D D           
2 2Q F
   
2 22 2
1 tan tan 0x y Q Q Q t QQ C C           
Yield functions F1 - F2
Plastic potentials Q1 - Q2

Mesoscale modelling of masonry walls
Vermeltfoort & Raijmakers, 1993
J4D J5D
Wpl1
pv=0.3 MPa
In-plane behaviour

Chee Liang, 1996
Wpl1Wpl1
Out-of-plane
behaviour

Bean Popehn et al., Engineering
Structures, 2008
Out-of-plane
behaviour

Earthquake tests
66% El Centro (ag=0.23g)
• Out-of-plane failure is governed by geometric instability
Griffith et al., JSE ASCE, 2004
Out-of-plane behaviour

Mesoscale modelling of masonry arches
Brick-masonry skew arch
Wang, 2004
Zhang, Macorini & Izzuddin, Engineering
Structures, 2016

Improved material description for NL interfaces
• Enhanced efficiency and robustness
• It describes the response under cyclic
loading
Plasticity damage formulation
Minga, Macorini & Izzuddin, Meccanica 2017
Cyclic behaviour in the
normal direction
Yield functions
 1 2 3    p p pK        I D 
Cyclic behaviour in the
tangential direction

Anthoine et al., 1995
Minga, Macorini & Izzuddin, Meccanica, 2017

Anthoine et al., 1995

Griffith et al., EESD, 2007

Mesoscale Partitioned Approach
Structural scale
Solid elements and 2D
nonlinear interfaces
The advanced 3D mesoscale model is combined with a partitioning
approach allowing for parallel computation (HPC)
• Partitioning approach with super-elements
• Parallel computing enhancing efficiency Jokhio & Izzuddin, 2015

Domain Partitioned Approach
Macorini & Izzuddin, AES, 2013

Communication between parent structure and partitions

0 20 40 60 80
Processing elements - n
0
4
8
12
16
20
Speed-up-S
m
P2
P4
P8
P16 P32
P64
m P2 P4 P8 P16 P32 P64
Parent
Structure
46080 23040 11530 5760 2880 1440 720
Partition - 384 756 1500 2232 3672 4996
Number of nodes for the parent structure and for each partition
m
i
Pi
T
S
T

• Elastic analysis of a large URM wall (48  48 20-noded solid elements)
Prescribed top vertical
displacements in 1 step
and top horizontal
displacements in 10 steps
uz
ux

0 20 40 60 80
Processing elements - n
0
4
8
12
16
20
Speed-up-S
m
P2
P4
P8
P16 P32
P64m
i
Pi
T
S
T

Monolitic model Model with super-elements
Accuracy of the method
• Elastic analysis of a large URM wall (48  48 20-noded solid elements)

Enhancements to improve efficiency
• Modelling with hierarchic partitioning (Jokhio, 2012)

• Modelling with partitions and master-slave coupling (Jokhio, 2012)

Elastic analysis of a large URM wall (48  48 20-noded solid elements)
Standard (flat) Partitioning
Approach
Enhanced Partitioning Approach
(hierarchic partitioning)
P-L1
P-L2

• Numerical performance – Speed-up
model
N.
processors
Parent
Struct.
DOFs
Part. L1
DOFs
Part. L2
DOFs S
m 1 142848 - - -
P4 5 2304 36864 - 4.60
P16 17 6912 9792 - 6.96
P64 65 16128 2736 - 3.24
P4 mslc 5 576 36864 - 3.73
P16 mslc 17 1728 9792 - 12.43
P64 mslc 65 4032 2736 - 116.39
P44 20 768 2304 9792 14.40
P416 69 768 2304 2736 28.65
P44 mslc 20 96 576 9792 17.63
P4x16 mslc 69 96 576 2736 205.50
Si= Tm/TSi
Tm = 13152 s
flat partitioning

0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70
Speed-upS
N. of processors
P‐L1 Si= Tm/TSi
Tm = 13152 s
Flat partitioning

model
N.
processo
rs
Parent
Struct.
DOFs
Part. L1
DOFs
Part. L2
DOFs S
m 1 142848 - - -
P4 5 2304 36864 - 4.60
P16 17 6912 9792 - 6.96
P64 65 16128 2736 - 3.24
P4 mslc 5 576 36864 - 3.73
P16 mslc 17 1728 9792 - 12.43
P64 mslc 65 4032 2736 - 116.39
P44 20 768 2304 9792 14.40
P416 69 768 2304 2736 28.65
P44 mslc 20 96 576 9792 17.63
P4x16 mslc 69 96 576 2736 205.50
Si= Tm/TSi
Tm = 13152 s
hierarchic
partitioning with
mixed-dimensional
coupling

Si= Tm/TSi
Tm = 13152 s

• Solution accuracy: partitioned vs. monolithic model
Normal stresses after the application of the vertical displacement

• Solution accuracy: partitioned vs. monolithic model
Normal stresses at the end of the analysis

162840 nodes – 62 partitions
Magenes et al., 1995
Minga, Macorini & Izzuddin, Meccanica 2017

Magenes et al., 1995
162840 nodes – 62 partitions

Modelling heterogeneous structures
Infilled frames
Elasto-plastic beam elements are used for modelling beams and columns of the frame,
while the detailed mesoscale description is utilised for URM panels
Macorini & Izzuddin, JSE ASCE, 2014

• Analysis of heterogeneous structures under extreme loading

• Analysis of heterogeneous structures under extreme loading
Blast pressure in time
Model validation under blast loading Macorini & Izzuddin, JSE ASCE, 2014

• BASIS PROJECT
Experimental tests on cavity wall specimens
under blast loading (INERIS, France)
Numerical modelling and nonlinear
analysis of cavity walls under blast loading
-20
70
160
0 1 2 3 4
mbar
Time (s)
Deflagration

Mesh tying for non-conforming interfaces
• Modelling heterogeneous masonry components and
structures (e.g. multi-leaf walls, masonry bridges)
• Enhancing computational efficiency (mesh optimisation
for non-uniform domains)
Minga, Macorini & Izzuddin, IJNME 2017
New mesh tying element Minga, Macorini & Izzuddin, IJNME 2017

Mesh tying for non-conforming interfaces
• Modelling heterogeneous masonry components and
structures (e.g. multi-leaf walls, masonry bridges etc)
• Enhancing computational efficiency (mesh optimisation
for non-uniform domains)

• Modelling arch bridges
Parent structure
corresponding to
partitioned boundary
Communication
partition-parent
structureBrick-masonry arch
Continuum domain
Backfill
15-noded elasto-plastic
elements
Mescale masonry model
Plastic model for backfill (Zhang, 2015)

• Interaction between arch and backfill
Mesh tying for non-conforming meshes at
backfill-arch interface
Mesoscale modelling of arch bridges

• Interaction between arch and backfill
Mesh tying for non-conforming
meshes at backfill-arch interface
Increased Speed-up

Melbourne & Gilbert, Structural Engineer, 1995

Mesoscale modelling of masonry buildings
• Mesoscale partitioned approach
(hierarchic partitioning)
• Mesh tying to connect
perpendicular walls and floor slabs
• Nonlinear dynamic simulations to
investigate the seismic response

Conclusions
• The proposed nonlinear FE description provides accurate response
predictions of masonry components subjected to different loading
conditions.
• The partitioning approach allows for computational efficiency and
enables the analysis of realistic structures using detailed 3D
modelling.
• The developed computational strategy can be used for high-fidelity
simulations to investigate failure modes of complex systems with
masonry and to calibrate more efficient representations for practical
assessment and design.
The proposed models for masonry have been implemented in ADAPTIC*, an advanced FE
code developed at Imperial College London for nonlinear simulations of structures
subjected to extreme loading.
* B.A. Izzuddin, Nonlinear dynamic analysis of framed structures, PhD. Imperial College
London (University of London), 1991.

References
• L. Macorini, B.A. Izzuddin, A non-linear interface element for 3D mesoscale analysis of brick-masonry
structures, International Journal for Numerical Methods in Engineering 85(2011) 1584-608.
• L. Macorini, B.A. Izzuddin, Nonlinear analysis of masonry structures using mesoscale partitioned
modelling, Advances in Engineering Software, 60 (2013), 58-69.
• L. Macorini, B.A. Izzuddin, Nonlinear Analysis of Unreinforced Masonry Walls under Blast Loading Using
Mesoscale Partitioned Modeling, Journal of Structural Engineering, 140, 8(2014).
• G.A. Jokhio, B.A. Izzuddin, A dual super-element domain decomposition approach for parallel nonlinear
finite element analysis. International Journal for Computational Methods in Engineering Science and
Mechanics 16(2015) 188-212.
• Y. Zhang, L. Macorini, B.A. Izzuddin, Mesoscale partitioned analysis of brick-masonry arches, Engineering
Structures, 124 (2016) 142–166.
• E. Minga, L. Macorini, B.A. Izzuddin. A 3D mesoscale damage-plasticity approach for masonry structures
under cyclic loading. Meccanica (2017). https://doi.org/10.1007/s11012-017-0793-z.
• E. Minga, L. Macorini, B.A. Izzuddin. Enhanced Mesoscale Partitioned Modelling of Heterogeneous
Masonry Structures. International Journal for Numerical Methods in Engineering (2017),
doi:10.1002/nme.5728.

Numerical and experimental investigation on existing structures: two seminars

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