Modelling masonry structures using discrete element method

GEOMECHANICS ● HYDROGEOLOGY ● MICROSEISMICS MINING ● CIVIL ● ENERGY ● MATERIALS●
●GEOMECHANICS ● HYDROGEOLOGY ● MICROSEISMICS MINING ● CIVIL ● ENERGY ● MATERIALS●
●
Discrete Element Modelling
of Masonry Structures
26/03/2020
Dr Vasilis Sarhosis
Associate Professor in Structural Engineering, University of Leeds
Chair of the Scientific Committee on the Analysis and Restoration of Structures of Architectural Heritage in UK
V.Sarhosis@leeds.ac.uk

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Aim: Undertake multi-disciplinary research to quantify
degradation and understand long term behaviour of
ageing masonry infrastructure and provide detailed and
accurate data that will better inform maintenance
programmes and asset management decisions.
Applications
1. Compressive strength prediction in masonry
prisms
2. Soil-structure interaction in masonry arch
bridges
3. Stochastic strength prediction of masonry
wall panels with openings
4. Analysis of complex in geometry masonry
structure - Spiral stairscases
5. Future trends
Aim of my research and overview of the webinar

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Mechanical behavior of masonry
• Masonry is a composite material consisting of masonry units bonded
together with or without mortar
• Although it is very easy to construct, its mechanical behaviour is
very complex
• Masonry is a brittle, heterogenic and anisotropic material.
• The need to predict the in-service and load carrying capacity has led
to the development of computational strategies characterised by
different letters of complexity
Detailed Simplified
Micro-modelling
Macro-modelling
Transverse section of a typical Gothic cathedral, Amiens,
France (1220-1288)

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Failure mechanisms in low bond strength masonry
Diagonal
cracking
Diagonal cracking in Lambton Castle, UK Diagonal and flexural cracking above a window opening
(Bersche-Rolt Ltd)

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Modelling masonry structures using DEM
Lemos 2011
Bui et al. 2016
• DEM developed by Cundall to
model sliding rock masses in which
fracture occurs at the interface
• More recently the approach used
with success to model masonry
structures
Sliding between rock masses
Çaktı et al. 2016

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GEOMECHANICS ● HYDROGEOLOGY ● MICROSEISMICS MINING ● CIVIL ● ENERGY●
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MASONRY IN COMPRESSION
Beyer & Dazio 2012

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• Masonry structures are often subjected to compressive loads
Masonry in compression
Source: CIRIA C656 - Masonry arch bridges: condition,
appraisal and remedial treatment.

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• When mortar is weaker than the strength of the bricks
Masonry in compression
Thaickavil & Thomas (2018)
(a) (b)
(c) (d)
Hendry (1998)

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• Numerical models should allow a reliable estimation of the masonry
compressive strength and failure pattern
Computational modelling of the compressive strength of
masonry prisms
Abu-Bakre & Chen (2016) Vindhyashree et al. (20014)
Macro Micro
Modelling of masonry
Limitations
• Mechanical behavior of masonry is
represented in a phenomenological
manner
• The quasi-brittle behavior of
masonry under compression is not
simulated.

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• Current approaches for modelling masonry structures
using DEM
Discrete Element Modelling of Masonry Structures
Lemos (2007)
Foti et al. (2018)
Bui, Sarhosis et al. (2018)
Sarhosis et al.(2014)
Limitations
• Since, mortar is reprezented
as zero thickness interface
• Cracking in masonry units
can not be simulated

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• Representation of masonry units and mortar joints by
inner-particles
Proposed computational approach for modelling the
discrete nature of masonry
Masonry
unit
Masonry
unit
Mortar
Perpend or head jointUnit (brick, block)
2. Mortar-to-mortar
interface
Inner mortar
particles
1. Masonry unit-to-
masonry unit interface
Deformable blocks
Zone elements
Inner-block or
Voronoi element
Triangular zones in inner block
particles
Inner brick particles
3. Masonry unit-to-mortar
interface
Rigid blocks

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Mechanical representation at the interface
Contact representation
• Inner- blocks are connected together by point contacts
• At each contact point there are two springs which can
transfer a normal and shear force
Δσn = JKn ΔUn
Δτs = JKs Δus
At the joint contact:
• If tensile strength exceeded (σn < - T), then σn = 0
• In shear direction, the shear strength is limited by a
combination of cohesive (C) and frictional strength (φ)
|τs| ≤ C + σn tan φ = τmax
Contact
point
σ (Normal stress)
Un
(Normal
displacement)
fs
JKn JKs
τ (Shear stress)
Us
(Shear
displacement)
τu
τres
Inner-block or
Voronoi
element

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Development of the computational model
• A numerical model has been developed to represent
the compressive strength test of a masonry prism
carried out in the laboratory by Oliveira (2003)*
• The masonry prism composed of five bricks
• Bricks dimensions: 290 mm × 130 mm × 50 mm.
• Joints were all made of cement mortar and
thickness equal to 10 mm.
• The prism placed between two steel platens
• Subjected to an axial control displacement until
failure
• Ex = Ey = 4.1 Gpa
• Poisson’s ratio 0.2
• Compressive strength 27.5 MPa
*Oliveira DV. Experimental and numerical analysis of blocky
masonry structures under cyclic loading, PhD thesis, University of
Minho, Portugal, 2003.

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Development of the proposed computational model
Geometry of the prism Triangular zones in the brick
and mortar Inner particles
Size of brick
voronoi: 10 mm
Size of mortar
voronoi: 3 mm
Rigid blocks
Deformable
blocks with
triangular zones
Sarhosis & Lemos (2018)
Computers & Structures

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Experimental vs Numerical Results
Crack developed
at the brick and
mortar
Brittle behaviour
of masonry
Experimental behaviour of masonry prisms
Vertical splitting of
cracks in bricks at the
middle of the masonry
prism
Numerical behaviour of masonry prisms
Sarhosis & Lemos
(2018) Computers &
Structures

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Behaviour of masonry in shear and direct tension
Shear strength test
• Vertical precompression σ = 1 N/mm2
Direction of shear
Direct tensile strength
(Abdou et al., 2006) (Abdou et al., 2006)
Sarhosis & Lemos
(2018) Computers &
Structures

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A NUMERICAL APPROACH TO MODEL SOIL-STRUCTURE
INTERACTION IN MASONRY ARCH BRIDGES

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Development of the Computational Model
The Prestwood Bridge
Field testing of Prestwood Bridge (Page, 1993)
• An attempt has been made to simulate
the in-service condition, load carrying
capacity, and failure mode of the
Prestwood bridge
• Prestwood bridge is a single ring,
brickwork masonry arch bridge located
in Staffordshire
• Span 6.5 m; Rise 1.44 m; Width 3.8 m
• The inner-backfill particles were
simulated as elasto-plastic material
while their interaction with each other
was controlled by Mohr-Coulomb law.
Sarhosis, Forgács, Lemos
(2019) Computers &
Structures

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An alternative approach to represent soil
in masonry arch bridges
Geometric model of the Prestwood bridge in UDEC – Soil
represented by 10 mm inner particles
• The discontinuous nature of backfill or
soil was represented by a series of
irregular in shape particles of
polygonal/Voronoi shape.
• Such fictitious irregular deformable
particles, here named “inner-backfill
particles”
• Inner-backfill particles were connected
together by zero thickness interfaces.
• Interfaces can be viewed as the location
where mechanical interaction between
“inner-backfill particles” takes place and
could be potential fracture slip lines.
(2019) Computers &
Structures

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Development of the Computational Model – The
Prestwood Bridge
0
50
100
150
200
250
0.00 0.25 0.50 0.75 1.00 1.25 1.50
Load[kN]
Vertical displacement at quarter span [cm]
Experimental
Voronoi size = 30cm
Voronoi size = 20cm
Voronoi size = 10cm
UDEC simulation of masonry arch
bridge subjected to direct point
load at quarter span
• The size of Voronoi elements varied from
5, 10, 20 and 30 cm.
• Good agreement between the experimental
and the numerical results
• The Voronoi model has the advantage of
naturally modelling crack initiation and
propagation as real discontinuity.
• Further research is required to develop
methodologies used for the calibration of the
interface material properties
(2019) Computers &
Structures

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STOCHASTIC STRENGTH PREDICTION
OF MASONRY STRUCTURES

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Material variability in masonry constructions
Material variability in masonry
• Masonry unit characteristics
• Mortar joint characteristics
• Brick-mortar bond characteristics
• Curing process
• Quality of masonry work
• Deterioration caused by weathering

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Stochastic strength prediction of masonry structures
Variation of joint friction angle in the masonry wall panel
Dimensions of the masonry wall panel constructed in the laboratory
Masonry wall panel developed in UDEC
Typical masonry wall panel constructed in the laboratory
Application of
the load
Sarhosis et al. 2020
RILEM Technical Letters

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• Point #1
• Point #2
• Point #3
 Sub-point #1
 Sub-point #2
 Sub-point #3
Stochastic strength prediction of masonry structures
(failure mode 1)
(failure mode 2)
(failure mode 3)
(failure mode 4)
(failure mode 5)
Numerical modelling results
Failure mode observed in the
experiment
Experimental (in red) against numerical (in grey) load
displacement curves

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Sensitivity of the ultimate load on the material paramters
Sensitivity of the ultimate load on the strength parametersSensitivity of the ultimate load on the elastic material
parameters

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SELF SUPPORTUNG SPIRAL STAIRCASES

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Self-supporting spiral staircases
Equilibrium Solution!

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Numerical modelling of helical staircases
1 Helix (44 stairs) 2 Helices (88 stairs) 3 Helices (132 stairs)
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
0 2 4 6 8 10 12 14 16Numberofsteps
Normal Pressure (MPa)

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FUTURE TRENDS https://research.ncl.ac.uk/heritageconservation/outputs/

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Recent trends (Cloud2DEM)
Numerical modelling of rubble masonry
http://eprints.whiterose.ac.uk/144607/7/ispr
s-archives-XLII-2-W7-17-2017.pdf

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Recent trends (Cloud2DEM)
Numerical modelling of rubble masonry
Cloud2FEM Cloud2DEM
Southwest tower of Caerphilly castle: a) Historic drawing (AD 1773); and b,c) photos
of the tower in its present condition
(a) (b) (c)
D’Altri et al. 2019

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Peer-reviewed International Journals
• Sarhosis V, Forgcas T, Lemos JV (2020). Spatial variability of material properties in
numerical models: A methodological approach or a way forward for the analysis of masonry
structure. RILEM Technical Letters, 40, pp. 122-129. doi: 10.21809/rilemtechlett.2019.100.
• Sarhosis V, Forgcas T, Lemos JV (2019). A discrete approach for modelling backfill material
in masonry arch bridges. Computers and Structures, 224, 106-118.
• Tavafi E., Mohebkhah A., Sarhosis V. (2019). Seismic behavior of the cube of Zoroaster
tower using the discrete element method. International Journal of Architectural Heritage,
55-72.
• Sarhosis V., Baraldi D., Lemos JV., Milani G. (2019) Dynamic behaviour of ancient
freestanding multi-drum and monolithic columns subjected to horizontal and vertical
excitations. Soil Dynamics and Earthquake Engineering 120, 39-57.
Publications
• Sarhosis V, Dais D, Smyrou E, Bal IE. (2019). Evaluation of modelling strategies for
estimating cumulative damage on Groningen masonry buildings due to recursive
induced earthquakes. Bulletin of Earthquake Engineering, 1-22
• Bui T.T., Limam A., Sarhosis V. (2019). Discrete element modelling of masonry wall
panels subjected to in-plane and out-of-plane loading. European Journal of Civil
Engineering, 34-49.
• Sarhosis V., Lemos J.V. (2018). Detailed micro-modelling of masonry using the discrete
element method. Computers and Structures, 206, 66-81.
• Forgács T., Sarhosis V., Bagi K., (2018). Influence of construction method on the load
bearing capacity of skew masonry arches. Engineering Structures, 168, 612-627.
• D’Altri A.M, Milani G., de Miranda S., Castellazzi G., Sarhosis V. (2018). Stability
Analysis of Leaning Historic Masonry Structures. Automation in Construction. 92(1),
199-213.
• Forgács T., Sarhosis V., Bagi K., (2017). Minimum thickness of semi-circular skewed
masonry arches. Engineering Structures, 140, 317–336.
• Sarhosis V., Asteris P., Wang T., Hu W., Han Y. (2016). On the stability of ancient
colonnades under static and dynamic conditions, Bulletin of Earthquake Engineering,
1-22, DOI 10.1007/s10518-016-9881-z.
• Sarhosis V., De Santis S., De Felice G. (2016). A review of experimental investigations
and assessment methods for masonry arch bridges. Journal of Structure and
Infrastructure Engineering, 1, 1-26.
• Sarhosis V., Garrity S.W., Sheng Y. (2015). Influence of the brick-mortar interface on
the mechanical response of low bond strength masonry lintels, Engineering
Structures, 88, 1-11.
• Sarhosis V., Sheng Y. (2014). Identification of material parameters for low bond
strength masonry, Engineering Structures, 60, 100-110.
• Giamundo V., Sarhosis V., Lignola G.P., Sheng Y., Manfredi G. (2014). Evaluation of
different computational modelling strategies for modelling low strength masonry,
Engineering Structures, 73, 160-169. DOI: 10.1016/j.engstruct.2014.05.007
• Sarhosis V., Oliveira D.V., Lemos J.V., Lourenco P. (2014). The effect of the angle of
skew on the mechanical behaviour of arches, Mechanics Research Communications,
61, 53-49.
Books
• Sarhosis V., Bagi K., Lemos J.V., Milani G. (Eds) (2016).
Computational Modelling of Masonry Structures Using the
Discrete Element Method, IGI Global.
DOI: 10.4018/978-1-5225-0231-9
Book Sections
• Sarhosis V., Lemos J.V., Bagi K. (2019). Discrete element
modelling of the non-linear static and dynamic response of
masonry structures. In Milani G. & Ghiassieds B. eds.
Numerical Modelling of Masonry and Historical Structures.
Elsevier.
• Sarhosis V., Oliveira D.V., Lourenco P.B. (2016). On the
mechanical behaviour of masonry structures. In: Sarhosis V.,
Lemos J.V., Bagi K., Milani G. eds. Computational Modelling
of Masonry Structures Using the DEM. IGI Global.

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I would like to thank:
• Prof Jose Lemos – National Technical University of Lisbon (LNEC)
• Prof Gabriele Milani – Politecnico di Milano, Italy
• Prof Katalin Bagi - University of Technology and Economics, Budapest
• Prof Jon Mills – Newcastle University, UK
• Prof Santiago Huerta - Universidad Politécnica de Madrid, Spain
• Dr Belén Riveiro – Vigo University, Spain
• Dr Tan Trung BUI – INSA Lyon, France
• Dr Wen Xiao – Newcastle University, UK
• Dr Oriel Prizeman – Cardiff Universiyt
• Dr Amin Mohebkhah - Malayer University, Iran
• Dr Antonio Maria D’Altri – Bologna University, Italy
• Dr Gabriel Stockdale – Politecnico di Milano
• Mr Tamas Forgacs - University of Technology and Economics, Budapest
• Mr Nicko Kassotakis – Newcastle University, UK
Acknowledgement
Financial support is greatly
acknowledged

●GEOMECHANICS ● HYDROGEOLOGY ● MICROSEISMICS MINING ● CIVIL ● ENERGY ● MATERIALS●
●
Thank you for your attention
For questions and comments please send an email to
V.Sarhosis@leeds.ac.uk

Modelling masonry structures using discrete element method

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