discrete element models for the ... - the masonry society€¦ · 1. collapse analysis using de...

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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



� 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



� 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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� 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 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



� 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



� 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)



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








Plan view and photo of the specimen (Tomassetti et al. 2018) Screenshot of AEM model

LNEC-BUILD1


Single-storey cavity-wall prototype with both flexible (roof ) and rigid (1st floor) diaphragms

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Plan view and photo of the specimen (Graziotti et al. 2017) Screenshot of AEM model


EUC-BUILD1Two-storey cavity-wall prototype with both flexible (roof and 2nd floor) and rigid (1st floor) diaphragms





� 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


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� 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






� Base-shear [kN] vs 1st floor displacement [mm]

Experimental vs numerical hysteretic response and damage propagation of LNEC-BUILD1

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� 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%)






� 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


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� 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





� 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


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2. Use of DEM for calibrating simplified models (Distinct Element Method - DEM)



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




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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� 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





� 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)


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� 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%)





� 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


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� 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.





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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� 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









� Crushing phenomena accounted

by FE blocks

� Flexural and shear mechanisms

accounted by spring layers


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� 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


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� Concept extended to building scale









� Discretization changes as a function of the aspect ratio


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� Discretization changes as a function of the aspect ratio

� Enabling the representation of IP-OOP failure modes





� Validation process: IP-loaded wall components and full-scale façades

Num. damage Exp. damage

NUM

EXP


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� 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




� 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:



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DISCRETE ELEMENT MODELS FOR THE SEISMIC ASSESSMENT OF


� 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



� 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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THANK YOU

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