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Discrete Element models
for the seismic assessment
of unreinforced masonry structures
Daniele Malomo – University of California, Berkeley, USA
Matthew DeJong – University of California, Berkeley, USA
Andrea Penna – University of Pavia, Italy
Rui Pinho – University of Pavia, Italy
Problem overview
SIMPLIFIED
Suitable for IP-governed responses
Reduced computational cost
Simplified damage representation
1/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Numerical modeling of URM systems still represents an open challenge
� Wide variety of computational strategies developed so far
� Simplified and continuum-based models widely used by both practitioners and researchers
OOP modes often neglected
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Problem overview
1/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Numerical modeling of URM systems still represents an open challenge
� Wide variety of computational strategies developed so far
� Simplified and continuum-based models widely used by both practitioners and researchers
CONTINUUM
Homogenisation procedures
Mesh sensitive
Difficult interpretation of
damage prediction
Modelling of collisions
among units challenging
DE models for masonry structures
2/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Originally conceived for solving soil and rock mechanics problems
� Damage propagation explicitly represented
� Suitable for collapse analysis
� IP-OOP interaction accounted
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DE models for masonry structures
2/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Originally conceived for solving soil and rock mechanics problems
� Damage propagation explicitly represented
� Suitable for collapse analysis
� IP-OOP interaction accounted
� Each unit (rigid or deformable) is modeled separately
� Zero-thickness equivalent interface spring layers
� Simplified micro-modeling approach
DE models for masonry structures
2/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� DE analysis are typically very time-consuming
� Long and difficult calibration process
� Complex and ad-hoc modeling strategies
� Failure in compression is challenging using rigid block models
� Use of deformable blocks further increase analysis time
� Use of DE models presently confined to the simulation of local
problems and reduced-scale structures
5 months!
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Research objectives
3/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Development of modeling strategies for optimizing the use of DE micro-models
� Use DEM for dynamic and collapse analysis of large-scale URM buildings
� Use of DEM for calibrating simplified models
� Investigate the influence of construction techniques on the response of URM structures
� Development of a FDEM macro-element model for simulating IP-OOP interaction
� To improve and validate effective DE models, accurately calibrated against experimental
results, for the seismic assessment of URM structures at both local and global scales
� Development of modeling strategies for optimizing the use of DE micro-models
1. Use DEM for dynamic and collapse analysis of large-scale URM buildings
2. Use of DEM for calibrating simplified models
� Investigate the influence of construction techniques on the response of URM structures
3. Development of a FDEM macro-element model for simulating IP-OOP interaction
Research objectives
3/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� To improve and validate effective DE models, accurately calibrated against experimental
results, for the seismic assessment of URM structures at both local and global scales
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1. Collapse analysis using DE models (Applied Element Method - AEM)
4/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
D.Malomo, A. Penna, R. Pinho
� Three full-scale URM building prototypes tested in 2016-2018 at Eucentre (Pavia, Italy)
� Meant to represent typical Dutch URM terraced houses
� Subjected to ground motions of increasing intensity up to either near or complete collapse
Plan view and photo of the specimen (Correia et al. 2018) Screenshot of AEM model
LNEC-BUILD2
Experimental Numerical
Attic-roof prototype with flexible roof
1. Collapse analysis using DE models (Applied Element Method - AEM)
4/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
D.Malomo, A. Penna, R. Pinho
� Three full-scale URM building prototypes tested in 2016-2018 at Eucentre (Pavia, Italy)
� Meant to represent typical Dutch URM terraced houses
� Subjected to ground motions of increasing intensity up to either near or complete collapse
Plan view and photo of the specimen (Tomassetti et al. 2018) Screenshot of AEM model
LNEC-BUILD1
Experimental Numerical
Single-storey cavity-wall prototype with both flexible (roof ) and rigid (1st floor) diaphragms
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1. Collapse analysis using DE models (Applied Element Method - AEM)
4/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Three full-scale URM building prototypes tested in 2016-2018 at Eucentre (Pavia, Italy)
� Meant to represent typical Dutch URM terraced houses
� Subjected to ground motions of increasing intensity up to either near or complete collapse
Plan view and photo of the specimen (Graziotti et al. 2017) Screenshot of AEM model
Experimental Numerical
EUC-BUILD1Two-storey cavity-wall prototype with both flexible (roof and 2nd floor) and rigid (1st floor) diaphragms
D.Malomo, A. Penna, R. Pinho
1. Collapse analysis using DE models (Applied Element Method - AEM)
5/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� The influence of several constructive details was duly accounted for numerically
� Simplified roof modeling strategies employed
� Roof system nonlinearity lumped into plank-to-joist interface joints
Constructive details of terraced house test specimen and numerical idealisations
D.Malomo, A. Penna, R. Pinho
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1. Collapse analysis using DE models (Applied Element Method - AEM)
6/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Experimental vs numerical shake-table response of LNEC-BUILD2
� Base-shear [kN] vs ridge displacement [mm]
Experimental vs numerical hysteretic response and crack patterns of LNEC-BUILD2
D.Malomo, A. Penna, R. Pinho
1. Collapse analysis using DE models (Applied Element Method - AEM)
7/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Experimental vs numerical shake-table response of LNEC-BUILD1
� Base-shear [kN] vs 1st floor displacement [mm]
Experimental vs numerical hysteretic response and damage propagation of LNEC-BUILD1
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1. Collapse analysis using DE models (Applied Element Method - AEM)
7/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Experimental vs numerical shake-table response of LNEC-BUILD1
� After FEQ2-300%, due to the intensive rocking response of longitudinal piers, the RC slab
experienced a vertical displacement, inducing OOP collapse of CS party wall
� The model captured explicitly such response
Numerical prediction of the vertical displacement of the RC slab up to OOP collapse (FEQ2-300%)
D.Malomo, A. Penna, R. Pinho
1. Collapse analysis using DE models (Applied Element Method - AEM)
7/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Experimental vs numerical shake-table response of LNEC-BUILD1
� After FEQ2-300%, due to the intensive rocking response of longitudinal piers, the RC slab
experienced a vertical displacement, inducing OOP collapse of CS party wall
� The model captured explicitly such response
Predicted progressive OOP damage of LNEC-BUILD1 due to the 1st floor slab uplift
D.Malomo, A. Penna, R. Pinho
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1. Collapse analysis using DE models (Applied Element Method - AEM)
8/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Experimental vs numerical shake-table response of EUC-BUILD1
� Base-shear [kN] vs 1st floor displacement [mm]
Experimental vs numerical hysteretic response and damage propagation of EUC-BUILD1
D.Malomo, A. Penna, R. Pinho
1. Collapse analysis using DE models (Applied Element Method - AEM)
9/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Use of simplified assumptions greatly decreased computational time
� AEM models captured accurately the hysteretic response of the tested specimens
� Crack patterns adequately reproduced up to the end of each tests
� Activation of collapse mechanisms well represented
� In some cases, the models marginally underestimated displacement capacity (e.g. LNEC-
BUILD1) and dissipated energy (e.g. LNEC-BUILD2)
Final remarks:
Malomo, D., Pinho, R., and Penna, A. (2019). “Applied Element modelling of the dynamic response of a full-scale clay brick
masonry specimen with flexible diaphragms” International Journal of Architectural Heritage
Related publications:
Malomo D., Pinho R., Penna A. (2019). “Simulating the shake-table response of URM cavity-wall structures tested to collapse or
near-collapse conditions.” Earthquake Spectra
D.Malomo, A. Penna, R. Pinho
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2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)
10/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
D.Malomo, M.J. DeJong, A. Penna
� The EFM idealisation of URM systems with irregular opening layouts is challenging
� The identification the definition of the effective wall height and the definition of rigid and
deformable regions becomes non-unique and may lead to epistemic modeling errors
� Lacking consistency in literature regarding the experimental assessment of the influence
of irregular distribution of openings in the case of URM structures
� Equivalent-frame models (EFM) widely used for simulating IP-governed response
� Acceptable compromise between accuracy and computational expense
2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)
10/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
D.Malomo, M.J. DeJong, A. Penna, R. Pinho
� Typically-employed EFM idealizations based on either geometrical considerations or
simplified analysis outcomes (e.g. linear elastic FEM analysis)
� LIN (30°-limited
effective height
accounting for the
presence of a rigid
lintels)
� AVG (average
effective height)
� MIN (minimum
effective height)
� LIM (30°-limited
effective height)
respectively.
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2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)
11/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� EFM results using LIN, AVG, MIN, LIM idealization schemes were compared to each other
� Outcomes from DEM models were taken as term of comparison for assessing the reliability
of the various EFM discretization methods
� Determining the influence of EFM discretization on the predicted monotonic IP response
� A number of two-storey URM façades characterized by different opening layouts were
considered
D.Malomo, M.J. DeJong, A. Penna
2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)
12/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� EFM models, despite the relatively low compression level, predicted shear failure at the
second floor, where only minor damage was detected using the DEM
� The latter aspect might be related to the modeling of spandrel elements (no damage)
D.Malomo, M.J. DeJong, A. Penna
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2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)
13/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Base shear and initial lateral stiffness normalized with respect to the maximum DEM values
� With reference to the maximum base shear, only minor differences were predicted, with
respect to DEM outcomes, employing a MIN-based EFM mesh
� In terms of residual lateral strength, a good agreement was found between DEM and MIN
models, while the use of LIM, AVG and LIN discretisation schemes often led to more
conservative results (up to approximately -15%)
D.Malomo, M.J. DeJong, A. Penna
2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)
13/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Base shear and initial lateral stiffness normalized with respect to the maximum DEM values
� Opposite trend found here, better agreement was obtained using LIM and AVG idealisations
� MIN discretization tends to overestimate significantly (up to x2.5) the predicted lateral stiffness
� As for the base shear, major differences found along negative direction of loading
D.Malomo, M.J. DeJong, A. Penna
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14/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� Parametric study performed for assessing the influence of irregular openings distribution on
EFM results, DEM outcomes taken as a reference
� Among the tested idealization schemes, best results in terms of both maximum and residual
base shear obtained using MIN
� The use of LIM might lead to an underestimation of lateral capacity
� With reference to the predicted initial lateral stiffness, best agreement found using LIM and
AVG idealisations, while the employment of MIN provided unconservative results
Final remarks:
Related publications:
Morandini C., Caserini M., Malomo D., Penna A., DeJong M.J. (2019). “Equivalent-frame models idealisation of laterally-loaded
URM façades with irregular opening distributions” In Proceedings of the XVIII Anidis Conference, Ascoli Piceno, Italy.
Malomo D., DeJong M.J., Penna A. (2019). “Distinct Element modelling of the in-plane cyclic response of URM piers subjected to
shear-compression” Earthquake Engineering and Structural Dynamics.
2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)
D.Malomo, M.J. DeJong, A. Penna
15/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
D.Malomo, M.J. DeJong
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� A new FDEM macro-element model developed in a DEM framework
� Aimed at combining DEM accuracy with macro-element efficiency
� Final goal simulating IP-OOP governed responses in a reasonable timeframe
� Assembly of FE deformable blocks (wall element)
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15/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� A new FDEM macro-element model developed in a DEM framework
� Aimed at combining DEM accuracy with macro-element efficiency
� Final goal simulating IP-OOP governed responses in a reasonable timeframe
� Assembly of FE deformable blocks (wall element) connected by nonlinear springs
� Crushing phenomena accounted
by FE blocks
� Flexural and shear mechanisms
accounted by spring layers
D.Malomo, M.J. DeJong
15/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� A new FDEM macro-element model developed in a DEM framework
� Aimed at combining DEM accuracy with macro-element efficiency
� Final goal simulating IP-OOP governed responses in a reasonable timeframe
� Assembly of FE deformable blocks (wall element) connected by nonlinear springs
� Crushing phenomena accounted
by FE blocks
� Flexural and shear mechanisms
accounted by spring layers
D.Malomo, M.J. DeJong
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16/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� Assembly of FE deformable blocks (wall element) connected by nonlinear springs
� Discretization based on experimentally-observed damage of URM elements
� Accounts for both IP and OOP failure modes
D.Malomo, M.J. DeJong
16/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� Assembly of FE deformable blocks (wall element) connected by nonlinear springs
� Discretization based on experimentally-observed damage of URM elements
� Accounts for both IP and OOP failure modes
DIAGONAL
VERTICAL
HORIZONTAL
�̅� μ cos 𝛼 sin 𝛼cos 𝛼 𝜇sin 𝛼𝑐̅ c cos 𝛼cos 𝛼 𝜇sin 𝛼𝑓 𝑓cos 𝛼
μ and c from triplet test
ft from bond wrench test
D.Malomo, M.J. DeJong
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17/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� Assembly of FE deformable blocks (wall element) connected by nonlinear springs
� Discretization based on experimentally-observed damage of URM elements
� Accounts for both IP and OOP failure modes
� Concept extended to building scale
D.Malomo, M.J. DeJong
17/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� Assembly of FE deformable blocks (wall element) connected by nonlinear springs
� Discretization based on experimentally-observed damage of URM elements
� Accounts for both IP and OOP failure modes
� Concept extended to building scale
� Discretization changes as a function of the aspect ratio
D.Malomo, M.J. DeJong
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17/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� Assembly of FE deformable blocks (wall element) connected by nonlinear springs
� Discretization based on experimentally-observed damage of URM elements
� Accounts for both IP and OOP failure modes
� Concept extended to building scale
� Discretization changes as a function of the aspect ratio
� Enabling the representation of IP-OOP failure modes
D.Malomo, M.J. DeJong
18/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� Validation process: IP-loaded wall components and full-scale façades
Num. damage Exp. damage
NUM
EXP
D.Malomo, M.J. DeJong
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19/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
� Validation process: IP-loaded wall components and full-scale façades
-200
-175
-150
-125
-100
-75
-50
-25
0
25
50
75
100
125
150
175
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Ho
riz
on
tal
force [
kN
]
Horizontal top displ. [mm]
NUM
EXP
Num. damage Exp. damage
NUM
EXP
D.Malomo, M.J. DeJong
20/20DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� IP response adequately captured
� Reduced computational time
� Explicit representation of damage
� Possibility of accounting for IP/OOP modes
� Future developments include:
� OOP and IP/OOP validation
� Building-scale dynamic analysis
� Collapse analysis
Final remarks and future developments:
3. A new FDEM macro-element for the IP-OOP analysis of URM structures
D.Malomo, M.J. DeJong
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DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� DEM to overcome the limitations of simplified and continuum-based models
� DE models can be used at multiple levels and scales
� Micro-modeling strategies useful for calibrating simple models
� It is possible to reduce computational time using simplified assumptions
� FDEM-macro models represent a valid alternative for the modeling of IP modes, and their
use for representing IP-OOP interaction seems promising
� Using the proposed modeling strategies, DEM might be also use by practitioners
Closing remarks
DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
� DEM to overcome the limitations of simplified and continuum-based models
� DE models can be used at multiple levels and scales
� Micro-modeling strategies useful for calibrating simple models
� It is possible to reduce computational time using simplified assumptions
� FDEM-macro models represent a valid alternative for the modeling of IP modes, and their
use for representing IP-OOP interaction seems promising
� Using the proposed modeling strategies, DEM might be also use by practitioners
� FDEM-macro modeling of IP/OOP interaction
� Pounding phenomena among adjacent structures using FDEM-macro (SERA PROJECT)
� Collapse analysis using FDEM-macro and modeling of debris coverage
Closing remarks
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DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF
UNREINFORCED MASONRY STRUCTURES
THANK YOU
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