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The Applied Element Method and the modelling of both in-plane and out-of-plane response of URM walls

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The Applied Element Method (AEM) is a relatively recent addition to the discrete elements methods family. Initially conceived to model blast events and concrete structures, its use in the modelling of masonry structures subjected to earthquake actions is steadily gaining popularity. In this study, it is shown that this modelling strategy can indeed be employed to accurately predict the response of unreinforced masonry (URM) walls subjected to both in-plane and out-of-plane loading. The numerical validation is carried out through comparison with the results obtained from an extensive experimental campaign involving cyclic and dynamic testing of calcium-silicate and clay brick walls, featuring varying material properties and boundary conditions. In as much as possible, use was not made of the experimental results of the wall specimens to calibrate the corresponding numerical models; in this manner the proposed modelling approach may readily be employed for the more customary situations where test results of the structures being modelled are not available.
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THE APPLIED ELEMENT METHOD AND THE MODELLING OF
BOTH IN-PLANE AND OUT-OF-PLANE RESPONSE OF URM WALLS
Daniele MALOMO
1
, Paolo COMINI1, Rui PINHO1,2, Andrea PENNA1,3
ABSTRACT
The Applied Element Method (AEM) is a relatively recent addition to the discrete elements methods family. Initially conceived
to model blast events and concrete structures, its use in the modelling of masonry structures subjected to earthquake actions is
steadily gaining popularity. In this study, it is shown that this modelling strategy can indeed be employed to accurately predict
the response of unreinforced masonry (URM) walls subjected to both in-plane and out-of-plane loading. The numerical
validation is carried out through comparison with the results obtained from an extensive experimental campaign involving
cyclic and dynamic testing of calcium-silicate and clay brick walls, featuring varying material properties and boundary
conditions. In as much as possible, use was not made of the experimental results of the wall specimens to calibrate the
corresponding numerical models; in this manner the proposed modelling approach may readily be employed for the more
customary situations where test results of the structures being modelled are not available.
Keywords: applied element method; discrete elements modelling; unreinforced masonry; in-plane; out-of-plane
1. INTRODUCTION
The Groningen region, in the north of the Netherlands, historically not prone to tectonic earthquakes,
has in recent years been subjected to seismic events induced by reservoir depletion due to gas extraction
(e.g. Bourne et al. 2015, van Elk et al. 2018). Construction in this region is dominated by the presence
of unreinforced masonry (URM) structures, featuring clay and calcium-silicate bearing walls, both of
which have thus now become the focus of experimental research endeavours aimed at assessing their
response to horizontal seismic loading (e.g. Graziotti et al. 2015, 2016, 2017a). The work described in
this paper concerns thus the examination and verification, through comparison with experimental data,
of a possible modelling strategy for the assessment of the in-plane and out-of-plane response of the
aforementioned URM walls. Use was made of the Applied Element Method (Meguro and Tagel-Din,
2000, 2001, 2002), with a view to assess how this relatively recent addition to the discrete elements
methods family may or may not feature the capability of producing reliable estimation of the seismic
response of this type of structural elements.
Four clay brick and three calcium-silicate URM piers subjected to in-plane cyclic shear-compression
testing, together with four calcium-silicate/clay masonry walls subjected to out-of-plane dynamic
loading, were considered. The structural analysis software tool Extreme Loading for Structures (ELS),
developed by ASI (2017), was employed to carry out the AEM modelling of this study.
This modelling endeavour is part of a larger modelling cross-validation exercise (e.g. Arup et al. 2015,
2017) aimed at lending confidence and reassurance to the process through which the analytical fragility
functions for the Groningen region were developed (Crowley et al. 2017, Crowley and Pinho, 2017),
and which was based on detailed nonlinear dynamic analyses of representative buildings (Arup 2017,
Mosayk 2017a).
1
Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy
2 Modelling and Structural Analysis Konsulting (MOSAYK), Piazza Castello 19, 27100 Pavia, Italy
3 European Centre for Training and Research in Earthquake Engineering (EUCENTRE), Via Ferrata 1, Pavia
2
2. THE APPLIED ELEMENT METHOD (AEM) AND THE MODELLING OF MASONRY
STRUCTURES
Due to space constraints, a literature review of available discrete element methods, and of how the AEM
compares and differs from them, could not be included here, but may nonetheless be found in Malomo
(2018) and Malomo et al. (2018).
2.1. Formulation Overview
According to the Applied Element Method (AEM) procedure a given structure is modelled through
discretisation in a virtual assembly of small rigid units, carrying only mass and damping of the system,
connected by springs (see Figure 1, below).
Figure 1. AEM: multi-scale discretisation of plane element and domain influence of a set of springs in 3-D space
The i-th plane unit is represented by a control point Gi, located in its geometrical centroid, and by a set
of contact points that are uniformly distributed along the element edges. Two adjacent units are assumed
to be connected at contact points by a pair of normal and shear springs (implemented with linear or
nonlinear constitutive laws). Given that each group of springs completely describes stresses and
deformations of a certain area 𝛿𝐴, the behaviour of the whole assembly is deformable.
Each unit is characterised by three degrees of freedom (u,v,φ), representing its rigid body motion.
Naturally, the total amount of degrees of freedom of a given model is 3n, where n represents the number
of units considered. Each normal, kn, and shear, ks, spring stiffness is quantified respectively using
Equation (1), which involves geometrical parameters, such as the length li and the thickness ti, modelling
values such as the distance d between two consequent springs, and the elastic material properties E
(Young’s modulus) and G (shear modulus).
𝑘=𝐸 𝑑 𝑡
𝑙 , 𝑘=𝐺 𝑑 𝑡
𝑙
(1)
2.2. Formulation for masonry structures
Within the framework of AEM modelling of URM structures, an arbitrary masonry segment is
composed of brick elements connected to each other by equivalent springs, in which the mechanical
properties of brick-mortar interfaces (see Figure 2) are lumped (i.e. no additional DOFs are assigned to
mortar layers). A given brick can be modelled as a rigid block or as an assembly of units; if it is desired
to model potential splitting or crushing of bricks, then the latter need necessarily to be discretised).
From a computational viewpoint, two different stiffness matrices are needed here: for the brick elements
assembly, since the springs connect elements of identical material, 𝐾 is composed of the brick
stiffnesses knb and ksb only (Equation 2), whereas for the interfaces, 𝐾 is made up inferring the
equivalent stiffnesses kni and ksi (which, as indicated in Figure 2 and Equation 3 are obtained assuming
the brick and mortar springs arranged in series at an arbitrary contact point).
3
Figure 2. AEM: discretisation of a masonry segment (
𝑘 =𝐸 𝑑 𝑡
𝑙, 𝑘 = 𝐺 𝑑 𝑡
𝑙
(2)
1
𝑘 =𝑙𝑡
𝐸 𝑑 𝑡+𝑡
𝐸 𝑑 𝑡, 1
𝑘 =𝑙𝑡
𝐺 𝑑 𝑡+𝑡
𝐺 𝑑 𝑡
The above parameters, as defined in Malomo et al. (2018), represent the brick-mortar interaction taking
into account both the brick and the mortar elastic properties. Naturally, in a post-cracked response stage,
the elastic parameters implemented are modified according to the material constitutive laws. AEM
employs these criteria changing the stiffness values at each loading step, taking into account the damage
evolution; when a given amount of springs has failed and their stiffness is set to zero, contact between
units is lost.
3. URM WALLS SUBJECTED TO IN-PLANE CYCLIC LOADING
3.1. Test specimens and test setup
Slender (Table 1) and squat (Table 2) full-scale wall specimens were tested in different experimental
configurations at the Eucentre laboratory (Pavia, Italy). The calcium-silicate (CS) piers were
characterised by a single leaf periodic arrangement (stretcher bond) of 212x103x71 mm3 CS brick units
and 10 mm thick mortar joints. The clay (CL) piers, on the other hand, featured 208x100x50 mm3 CL
brick units arranged in a so-called Dutch Cross bond, leading to 208 mm thick double-wythe walls. The
walls were founded on a reinforced concrete (RC) beam clamped to the lab strong floor with post-
tensioned steel bars, whereas the top RC beam, to which the loading was applied, was connected to the
masonry piers by means of a layer of self-levelling high strength shrinkage-controlled gypsum to prevent
sliding. The top lateral displacements were imposed by a horizontal servo-hydraulic actuator through a
steel beam rigidly connected to the RC top-beam. Two horizontal servo-hydraulic actuators assured the
boundary conditions, as well as the vertical compression. Furthermore, a restraining system was
introduced in order to prevent out-of-plane deflection of the loading beam. Full details on the test
specimens and test setup can be found in Graziotti et al. (2015, 2016).
Table 1. Characteristics of the slender wall specimens and their boundary conditions
EC-COMP2-1
EC-COMP2-2
EC-COMP2-3
EC-COMP1
OOP restraints
Material
Clay
Clay
Clay
Calcium-silicate
h [mm]
2710
2710
2710
2750
L [mm]
1200
1200
1200
4000
t [mm]
208
208
208
103
σv [MPa]
0.52
1.20
0.86
0.30
4
Boundary
Conditions
Double fixed
Double fixed
Double fixed
Double fixed
Table 2. Characteristics of the squat wall specimens and their boundary conditions
EC-COMP2-5
EC-COMP3
OOP restraints
Material
Clay
Calcium-
silicate
h [mm]
2710
2750
L [mm]
1200
4000
t [mm]
208
103
σv [MPa]
0.30
0.30
Boundary
Conditions
Double fixed
Cantilever
For each test, after imposing the vertical top compression σv, the horizontal loading history was applied
in a displacement-controlled procedure, typically featuring 15 to 20 cycles of incremental displacements
ranging from approximately 0.3 mm to 60 mm for the slender piers, and 0.1 to 10 mm for the squat
walls. The tests were stopped when the specimens lost their bearing capacity, exhibiting damage of the
type exemplificatively shown in Figure 3, and further discussed below.
Figure 3. Experimental damage evolution of specimen EC-COMP3 (Graziotti et al. 2015)
3.2. Numerical modelling
A brick mesh-based modelling approach, whereby one discrete element is assigned to each brick, was
initially employed, thus faithfully reproducing the experimental arrangement of the specimens’ brick
units. An additional discretisation was then also applied by subdividing the elements along their vertical
axis with a view to try to better capture the brick splitting phenomena that was observed during the tests
(the impact on the results of such refinement was however very mild). Each surface of a given rigid
element was connected to the adjacent one by means of 25 springs, as depicted in Figure 4 below.
The loading and foundation RC beams were explicitly modelled, assuming a linear elastic response of
their constituent material. As shown in Figure 4, in order to decrease the computational burden, a coarser
mesh was assigned to the RC beams; it is noted that the AEM, unlike other methods (such as the FEM),
does not need a mesh transition from large-size elements to small elements, since partial connectivity
between units is allowed.
Figure 4. AEM mesh discretisation approach
5
In a simplified micro-modelling approach, such as the AEM being employed here, each component of a masonry
element (i.e. bricks and mortar) needs to be described in terms of its mechanical properties. However,
experimental campaigns on masonry elements rarely involve tests that would allow one to obtain all necessary
material characterisation for brick and mortar separately. This lack of experimental data calls for a pre-
processing effort that makes use of empirical formulae available in the literature to obtain first estimates of the
aforementioned parameters. In addition, and as suggested by Mayorca and Meguro (2003), the elastic material
properties of mortar need to be subsequently calibrated into equivalent values (Emo,eq, Gmo,eq) that ensue an initial
lateral stiffness computed by the model for the URM walls that matches either an expected value for such
response parameter (herein termed as “theoretical initial lateral stiffness”, Kthe) or, if available, the
experimentally observed initial lateral stiffness, Kexp. This approach for defining the material properties of a
URM structure in a micro-modelling context is summarised in
Figure 5 and Figure 6, and discussed in detail in Mosayk (2017b) and Malomo et al. (2018).
Figure 5. Masonry mechanical properties typically available and of use in a micro-modelling approach
(flowchart A)
Figure 6. Calibration of equivalent values of E and G for the mortar in URM brick walls (flowchart B)
Due to space constraints, it is not possible to describe here the computation of the material parameters
for the six URM models considered in this study; interested readers may however find these in Mosayk
(2017b), as well as, for what concerns the calcium-silicate walls, in Malomo et al. (2018).
3.3. Numerical results
Following the same order in which the specimens were listed in Section 3.1 above, in what follows we
show first the results for the slender walls (Clay and CS specimens) and then those for the squat walls
(Clay and CS specimens), also comparing them with their experimental counterparts (for which a
detailed description of the observed lab response can be found in Graziotti et al. (2015, 2016). As can
be observed from Figure 7 to Figure 10, the numerical models are able to capture relatively well the
shear/displacement capacity of the test specimens, as well as their (rocking-governed) response mode
and corresponding crack pattern. On the other hand, however, and with the exception of specimen EC-
COMP2-1, the numerical models struggled to adequately reproduce the shape of the hysteretic curves
of the specimens (i.e. their energy dissipation), an issue that, even if not unusual in the modelling of
masonry walls subjected to rocking, does warrant further scrutiny in the future.
6
(a)
(b)
(c)
Figure 7. EC-COMP2-1: (a) hysteretic response comparison, (b) experimental crack pattern (c) numerical crack
pattern
(a)
(b)
(c)
Figure 8. EC-COMP2-2: (a) hysteretic response comparison, (b) experimental crack pattern (c) numerical crack
pattern
(a)
(b)
(c)
Figure 9. EC-COMP2-3: (a) hysteretic response comparison, (b) experimental crack pattern (c) numerical crack
pattern
Figure 10. EC-COMP1: (a) hysteretic response comparison, (b) experimental crack pattern (c) numerical crack
pattern
-90
-60
-30
0
30
60
90
-150 -100 -50 0 50 100 150
Base sher [kN]
Horizontal displacement [mm]
Experimental Numerical
-200
-150
-100
-50
0
50
100
150
200
-40 -20 0 20 40
Base sher [kN]
Horizontal displacement [mm]
Experimental Numerical
-150
-100
-50
0
50
100
150
-40 -20 0 20 40
Base sher [kN]
Horizontal displacement [mm]
Experimental Numerical
(a)
(b)
(c)
-40
-30
-20
-10
0
10
20
30
40
-80 -30 20 70
Base sher [kN]
Horizontal displacement [mm]
Experimental Numerical
7
(a)
(b)
(c)
Figure 11. EC-COMP2-5: (a) hysteretic response comparison, (b) experimental crack pattern (c) numerical crack
pattern
(a)
(b)
(c)
Figure 12. EC-COMP3: (a) hysteretic response comparison, (b) experimental crack pattern (c) numerical crack
pattern
Contrary to what happened with their slender counterparts, the squat wall AEM models did manage to
capture the energy dissipation of the test specimens adequately, in addition to their displacement/shear
capacity and failure mode. It is however worth noting that the perfect matching of the experimental
results, and in particular of the X-stepped crack patterns, did require a somewhat empirical adjustment
of the default values of so-called post-failure stiffness of the normal and shear springs, in order to
accentuate the development of the diagonal shear crack pattern.
4. URM WALLS SUBJECTED TO OUT-OF-PLANE DYNAMIC LOADING
4.1. Test specimens and test setup
Two different types of full-scale specimens were tested dynamically, in their out-of-plane direction, at
the Eucentre laboratory (Pavia, Italy). The first wall tested (i.e. EC-COMP4), consisted of a single leaf
wall made of CS brick masonry. The remaining specimens (i.e. EC-COMP5, EC-COMP6 and EC-
COMP7), instead, consisted of an inner CS brick masonry load-bearing panel with an outer veneer in
CL bricks; the distance between the two leaves was approximately 80 mm, as typical in construction
practice in the Dutch region, and 2 ties/m were used for EC-COMP5 and EC-COMP6, whilst 4 ties/m
were employed for EC-COMP7 specimen. This is summarised in Table 3.
Table 3. Construction and dimensional properties of the full-scale wall specimens
Specimen Name
Typology
l [m]
t [m]
h [m]
𝛔𝐯 [MPa]
ties/𝐦𝟐 [-]
EC-COMP4
Single leaf
1.438
0.102
2.754
0.3-0.1
-
EC-COMP5
CS inner wall
1.438
0.102
2.754
0.1
2
Clay outer wall
1.425
0.100
2.700
-
-200
-150
-100
-50
0
50
100
150
200
-50 0 50
Base sher [kN]
Horizontal displacement [mm]
Experimental Numerical
-90
-60
-30
0
30
60
90
-10 -5 0 5 10
Base sher [kN]
Horizontal displacement [mm]
Experimental Numerical
8
EC-COMP6
CS inner wall
1.438
0.102
2.754
0.3
2
Clay outer wall
1.425
0.100
2.700
-
EC-COMP7
CS inner wall
1.438
0.102
2.754
0.1
4
Clay outer wall
1.425
0.100
2.700
-
At the bottom of each wall, a reinforced concrete (RC) foundation was anchored to the shake-table with
screwed steel rods. Since the envisaged loading protocol consisted of a series of accelerograms imposed
simultaneously to both the RC foundation and the top of the piers, a rigid steel beam connected the CS
wall to a rigid steel frame anchored to the shake-table, assuring a negligible amplification in height of
the seismic input applied to the shake-table (see Figure 13a). Different types of ground motions were
selected, scaled, and incrementally imposed to the full-scale wall specimens until collapse of the
specimens (see Figure 13b and Figure 13c), as described in further detail in Graziotti et al. (2015, 2017b).
(a)
(b)
(c)
Figure 13. (a) Test-rig setup, (b) collapse of EC-COMP5 specimen, (c) typical failure of connectors (or ties) in
cavity wall specimens (from Graziotti et al. 2015, 2017b)
As reported in the dedicated report by Graziotti et al. (2015, 2017b), all the specimens have shown
rocking behaviour with the formation of horizontal cracks at the walls bottom, top and around mid-
height sections. For what concerns the force-displacement response of these specimens, such results will
be shown in the following sub-section, together with their numerical counterparts.
4.2. Numerical modelling
Four different numerical models were developed, and, with a view to reproduce faithfully the
experimental boundary conditions, the following modelling strategy was undertaken:
- According to the experimental layout, the calcium-silicate wall was rigidly connected by means of
L-shaped steel anchors to the top steel beam. Thus, a linear elastic interface (characterised by high
Young’s and shear moduli) was introduced in the same position avoiding spurious relative
displacements between the top beam and the calcium-silicate brick masonry panel. For the same
purpose, the abovementioned linear elastic interface was also employed at the interface between the
calcium-silicate pier and the foundation beam.
- As reported above, during the experiments a rigid steel frame was connected to the top steel beam of
calcium-silicate piers in order to assure negligible amplification in height of the shake-table
acceleration. With the current version of the employed AEM software program, a given seismic input
can be applied only to a fixed element or region of the model. Hence, since the top beam could not
be fully restrained (the vertical displacement had to be allowed), an alternative modelling approach
had to be developed, whereby all the calcium-silicate piers were connected by means of a horizontal
9
rigid link to a fixed linear elastic beam (see Figure 14a), where the same seismic input that is
introduced at the foundation level is also applied, thus simulating the acceleration-history
transmission to the top beam with negligible amplification that took place during the tests.
- The cantilevered clay panels, instead, were connected to the bottom slab only by means of the same
linear elastic interface employed for the calcium-silicate walls.
- The overburden pressure was imposed to the models through the top beam, characterised by a mass
identical to that of its experimental counterpart. Rigid links, connecting the two beams, were again
used here to apply the vertical stress; an initial pre-stress was assigned to the link elements
reproducing the experimental one. Further, and in order to reproduce the actual stiffness of the
springs employed during tests (connecting the steel top beam to the RC foundation), an equivalent
Young’s modulus was computed (assuming an average link section of 100 mm2) and subsequently
allotted to vertical link elements.
For what concerns the tiewall interfaces, which typically failed in the middle of the clay mortar bonds
(see Figure 13c):
- The idealisation depicted in Figure 14b has been adopted, whereby the contact between masonry and
ties occurs only through the transverse section of the ties (i.e. the ties’ length is equal to that of the
cavity). This is because the modelling of interpenetration phenomena between elements (such as the
pull-out) would imply a very high computational burden, given that, amongst other things, the
number of dynamic contacts would increase considerably.
- Consequently, the adhesion stresses mobilised throughout the embedded perimetral surface of the
ties (herein termed Aa) were in the AEM models replaced by equivalent stresses developed on the
transverse section of the ties (herein termed Ae), as depicted in Figure 14(c).
- Linear elastic connection between calcium-silicate walls and ties was employed, characterised by the
contact stiffness of calcium silicate-mortar materials, whilst the connection between clay walls and
ties (where tie failure typically occurred) was characterised by bilinear behaviour with post-peak
softening branch and residual tensile strength.
- Finally, it is noted that steel ties were thus modelled as 3D beam elements with bilinear behaviour,
with an ultimate tensile strength equal to the experimentally-recorded one, i.e. 4.3 kN.
For further details on the development and calibration of the AEM models, readers are referred to the
report by Mosayk (2017c).
Experimental
Numerical
Experimental
Numerical
(a)
(b)
(c)
Figure 14. (a) AEM model, (b) modelling idealization of connectors (or ties) in cavity wall specimens, and (c)
corresponding calibration of mechanical properties of link element
4.3. Numerical results
In this Section, the numerical results are compared with their experimental counterparts in a series of
plots where the thick grey line stands for the test observations, whilst a thin black line is instead
employed for the results obtained with the AEM models. More detailed experimental vs. numerical
comparisons can also be found in the report by Mosayk (2017c).
10
Out-of-plane one-way bending of masonry walls is a very brittle response mechanism, hence numerical
prediction of its hysteretic behaviour and collapse capacity is inevitably and unavoidably challenging.
Within such context, therefore, the comparisons depicted below can be considered as encouraging, with
the numerical models producing results that appear to be within the range of their experimental
counterparts.
(a)
(b)
(c)
Figure 15. EC-COMP4: (a) hysteretic curve, (b) CS experimental damage, (c) numerical mechanism
(a)
(b)
(c)
Figure 16. EC-COMP5: (a) CS hysteretic curve, (b) CS experimental damage, (c) numerical mechanism
(a)
(b)
(c)
Figure 17. EC-COMP6: (a) CS hysteretic curve, (b) CS experimental damage, (c) numerical mechanism
(a)
(b)
(c)
Figure 18. EC-COMP7: (a) CS hysteretic curve, (b) CS experimental damage, (c) numerical mechanism
-100 -50 0 50 100
-20
0
20
Horiz. disp. 1/2 CS height [mm]
Acc. 1/2 CL height [m/s2]
-10 -5 0 5 10
-10
-5
0
5
10
Horiz. disp. 1/2 CS height [mm]
Acc. 1/2 CL height [m/s2]
-150 -100 -50 0 50 100 150
-40
-20
0
20
40
Horiz. disp. 1/2 CS height [mm]
Acc. 1/2 CL height [m/s2]
-4 -2 0 2 4
-5
0
5
Horiz. disp. 1/2 CS height [mm]
Acc. 1/2 CL height [m/s2]
11
The positive impression on the numerical vs. experimental comparison reported above is further
confirmed by the comparisons shown in Table 4 below, where it can be observed that the AEM models
estimated values of collapse ground acceleration that feature differences with respect to the tests
observations in the range of 7-15%.
Table 4 Comparison between the experimental and the numerical collapse ground acceleration values
Specimen Name
Experimental Failure
PGA [g]
Numerical Failure
PGA [g]
EC-COMP4
0.85
0.96
EC-COMP5
0.65
0.60
EC-COMP6
1.17
0.97
EC-COMP7
0.72
0.66
5. CLOSING REMARKS
This modelling exercise confirmed the capability of AEM in adequately capturing the in-plane and out-
of-plane response of URM components, given that the models did reproduce adequately both the
shear/displacement capacity of the test specimens, as well as their failure modes. Of non-negligible
importance is also the fact that the material properties adopted for the numerical models required no
empirical tweaking, which is reassuring. Still, further improvements should be pursued in the future,
since the hysteretic response was not always well captured, as discussed in the body of the paper.
6. ACKNOWLEDGMENTS
The work described in this paper was carried out within the framework of the research programme on
hazard and risk of induced seismicity in the Groningen region, sponsored by the Nederlandse Aardolie
Maatschappij BV (NAM). The authors also acknowledge all those at the European Centre for Training
and Research in Earthquake Engineering (EUCENTRE, Pavia, Italy) that were involved in the testing
campaign referred to in this paper, as well as the technical support staff from Applied Science
International LLC (ASI), for the guidance on the use of the employed AEM.
7. REFERENCES
Arup (2017). Typology modelling: Analysis results in support of fragility functions - 2017 batch results. Available
from URL: http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html.
Arup, TU Delft, Eucentre and Arcadis, 2015. EUC-BUILD2: Modelling predictions and analysis cross validation.
Available from URL: http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html
Arup, TU Delft, Eucentre and Mosayk, 2017. LNEC-BUILD1: Modelling predictions and analysis cross
validation. Available from URL: http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html
ASI (2017). Extreme Loading for Structures v5. Applied Science International LLC, Durham (NC), USA.
Bourne SJ, Oates SJ, Bommer JJ, Dost B, van Elk J, Doornhof D (2015). A Monte Carlo method for probabilistic
hazard assessment of induced seismicity due to conventional natural gas production. Bulletin of the Seismological
Society of America 105, 1721-1738.
Crowley H, Pinho R (2017). Report on the v5 Fragility and Consequence Models for the Groningen Field.
Available from http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html
Crowley H, Polidoro B, Pinho R, van Elk J (2017). Framework for developing fragility and consequence models
for inside local personal risk. Earthquake Spectra 33, 1325-1345.
Graziotti F, Tomassetti U, Rossi A, Kallioras S, Mandirola M, Cenja E, Penna A, Magenes G (2015). Experimental
campaign on cavity wall systems representative of the Groningen building stock. Report n. EUC318/2015U,
European Centre for Training and Research in Earthquake Engineering (Eucentre), Pavia, Italy. Available from
URL: www.eucentre.it/nam-project
Graziotti F, Tomassetti U, Rossi A, Marchesi B, Kallioras S, Mandirola M, Fragomeli A, Mellia E, Peloso S,
Cuppari F, Guerrini G, Penna A, Magenes G (2016). Shaking table tests on a full-scale clay-brick masonry house
12
representative of the Groningen building stock and related characterization tests. Report n. EUC128/2016U,
Eucentre Foundation, Pavia, Italy. Available from URL: www.eucentre.it/nam-project
Graziotti F, Tomassetti U, Kallioras S, Penna A, Magenes G (2017a). Shaking table test on a full scale URM cavity
wall building. Bulletin of Earthquake Engineering 15, 5329-5364.
Graziotti F, Tomassetti U, Penna A, Magenes G (2017b). Out-of-plane shaking table tests on URM single leaf and
cavity walls.” Engineering Structures 125, 455-70.
Malomo D (2018). Scrutinising the applicability of the Applied Element Modelling in the modelling of URM
structures subjected to earthquake loading. PhD Thesis, University of Pavia, Italy.
Malomo D, Pinho R, Penna A (2018). Using the Applied Element Method for modelling calcium-silicate brick
masonry subjected to in-plane cyclic loading. Earthquake Engineering and Structural Dynamics, submitted for
publication.
Mayorca P, Meguro K (2003). Modeling masonry structures using the applied element method. Journal of the
Institute of Industrial Science of the University of Tokyo 55, 581-584.
Meguro K, Tagel-Din H (2000). Applied Element Method for structural analysis: Theory and application for linear
materials. JSCE International Journal of Structural Engineering and Earthquake Engineering 17, 2135.
Meguro K, Tagel-Din H (2001). Applied Element simulation of RC Structures under cyclic loading. ASCE Journal
of Structural Engineering 127, 1295-1305.
Meguro K, Tagel-Din H (2002). Applied Element Method used for large displacement structure analysis. Journal
of Natural Disaster Science 24, 65-82.
Mosayk (2017a). Nonlinear dynamic analysis of index buildings for v5 fragility and consequence models. Report
n. D8. Available from http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html
Mosayk (2017b). Using the Applied Element Method to model in-plane cyclic shear-compression testing of URM
walls. Report n. D4. Available from URL: http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html
Mosayk (2017c). Using the Applied Element Method to model the shake-table out-of-plane testing of full-scale
URM wall specimens subjected to one-way bending. Report n. D9. Available from URL:
http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html
van Elk J, Bourne SJ, Oates SJ, Bommer JJ, Pinho R, Crowley H (2018). A probabilistic model to evaluate options
for mitigating induced seismic risk, Earthquake Spectra, submitted for publication.
... This way of elements connectivity provides an extra edge to AEM as it can predict not only the initial cracking, peak behaviour and post-peak behaviour but also the separation of the elements that reach their maximum capacities (Meguro and Tagel-Din 1997). The springs are responsible for transferring load and modeling deformations between elements, while elements in AEM carries only mass and damping of the system (Malomo et al. 2018a(Malomo et al. , 2018b. Degrees of freedom in AEM are assigned to the centroid of rigid elements thus resulting in 6 degrees of freedom (three translational and three rotational), whereas in FEM degrees of freedom are assigned to the nodes, meaning 24 degrees of freedom per element. ...
... AEM has been successfully applied to predict the response of URM walls including both the in-plane and out-of-plane behaviour (Malomo et al. 2018a(Malomo et al. , 2018b. For in-plane response, four slender walls and two squat walls that had been subjected to cyclic loading in-plane loading were selected (Malomo et al. 2018a). ...
... AEM has been successfully applied to predict the response of URM walls including both the in-plane and out-of-plane behaviour (Malomo et al. 2018a(Malomo et al. , 2018b. For in-plane response, four slender walls and two squat walls that had been subjected to cyclic loading in-plane loading were selected (Malomo et al. 2018a). Out of the four slender walls, three were made of clay and one of calcium-silicate bricks. ...
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Masonry is a composite material consisted of units and mortar that have a non-linear behaviour. Therefore, its numerical modelling presents several challenges. Different modelling techniques are available for masonry material including Applied Element Method (AEM). This research was aimed at validating AEM numerical models against existing experimental data. The data represents typical Australian single-leaf unreinforced masonry walls loaded in the out-of-plane (OOP) direction. A total of eight tested walls from the related literature were analysed to study the modelling technique. The walls had different geometry, openings and overburden loads. Although the test data has previously been validated using different numerical tools, the employed AEM assisted in a more accurate prediction of the behaviour and crack patterns. From this study, it was concluded that AEM not only predicted the experimental results with good accuracy but it also predicted a realistic crack patterns that matched experimentally observed damages.
... Calvi et al. 2018;Salem et al. 2016), is based on the mechanical interaction among rigid units, carrying only mass and damping of the system, connected by linear or nonlinear springs. The AEM formulation for masonry, discussed and described in subsequent sections of this paper, has been already employed for investigating both in-plane and OOP responses of experimentallytested components (Guragain et al., 2006;Malomo et al., 2018aMalomo et al., , 2018b, as well as for the modeling of large-scale URM structures (Karbassi and Nollet, 2013;Malomo et al., 2019a). However, as far as the authors are aware of, validation of AEM simulation through comparison against shake-table collapse testing of full-scale URM building specimens with cavity-walls has not been addressed yet. ...
... A complete set of results for all ten walls modeled, including the corresponding hysteretic curves, can be found in Malomo et al. (2019c). Additional information on the AEM validation process conducted in the framework of the same testing campaign, on both in-plane and OOP loaded components, are also available in Malomo et al. (2018b) and Malomo (2019). ...
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The seismic performance of existing unreinforced masonry (URM) buildings is considerably affected by typology and level of effectiveness of both construction details and structural components, especially if not originally designed for resisting earthquakes. Within this framework, the use of advanced numerical approaches that are capable of duly accounting for such aspects might improve significantly the assessment of the global response of URM structures. In this article, the applied element method is thus employed for simulating the shake table response of a number of full-scale building specimens representative of cavity wall terraced house construction, used in a number of countries exposed to tectonic or induced seismicity, accounting explicitly for the influence of the presence of both rigid and flexible diaphragms, degree of connections among structural members, and interaction between in- and out-of-plane mechanisms. Although the models slightly underestimated the energy dissipation in some specific cycles prior to collapse, the predicted crack patterns, failure modes, and hysteretic behaviors have shown a good agreement with their experimental counterparts.
... Similarly, the OOP quasi-static response of reduced-scale URM samples was investigated successfully by e.g. Karbassi and Nollet (2013) and Sathiparan, Guragain, and Meguro (2005), as well as the OOP dynamic behaviour of URM panels subjected to both blast loading (Keys and Clubley 2017) and shake-table motions (Malomo et al. 2018a). The seismic performance of existing and monumental large-scale buildings were also assessed numerically using AEM (e.g Garofano and Lestuzzi 2016;Karbassi and Lestuzzi 2012), albeit in most of these cases no comparisons with experimental results were available. ...
Conference Paper
The terraced house building typology, which typically consists of low-rise unreinforced masonry (URM) constructions with cavity-walls, rigid floor diaphragms and timber roof, is largely widespread in a number of countries exposed to tectonic or induced seismicity. Experimental evidence has shown that the lack of seismic details, as well as the presence of large openings at the ground floor, makes these structures particularly vulnerable towards horizontal actions. Their assessment, given the large variability of construction techniques and masonry properties from one region to another, may benefit significantly from validated numerical models able to predict the global dynamic behaviour until up to complete collapse. In this paper, advanced discontinuum-based models developed within the framework of the Applied Element Method, are employed for replicating the shake-table response of a series of full-scale building prototype representative of cavity-wall terraced houses construction, tested up to collapse or near collapse conditions. A novel methodology for accounting explicitly for the influence of the presence of both rigid and flexible diaphragms, degree of connections among structural members and interaction between in-plane and out-of-plane mechanisms, is proposed. The introduction of specific simplified assumptions and empirical expressions, initially selected depending on the considered test and then extended to the general case, provided an acceptable representation of crack patterns, failure modes and hysteretic behaviours within a reasonable timeframe.
... Similarly, the OOP quasi-static response of reduced-scale URM samples was investigated successfully by e.g. Karbassi and Nollet (2013) and Sathiparan et al. (2005), as well as the OOP dynamic behaviour of URM panels subjected to both blast loading (Keys and Clubley 2017) and shake-table motions (Malomo et al. 2018a). The seismic performance of existing and monumental large-scale buildings were also assessed numerically using AEM (e.g Garofano and Lestuzzi 2016;Karbassi and Lestuzzi 2012), albeit in most of these cases no comparisons with experimental results were available. ...
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Structural design of unreinforced masonry buildings in The Netherlands, recently exposed to low-intensity ground motions induced by gas extraction, was not originally conceived for earthquake-resistance. Indeed, the presence of both large openings and flexible diaphragms, and the lack of any specific seismic consideration or detailing significantly increase their vulnerability towards horizontal loading. In this paper, the Applied Element Method (AEM), which explicitly represents the discrete nature of masonry, is used to simulate the shake-table response of a full-scale building specimen representative of a typical Dutch detached house made of unreinforced solid clay-brick masonry. Using this modelling strategy, the damage evolution, as well as both global failure mode and hysteretic behaviour, are described. The results show a good agreement with the experimentally-observed response, confirming the capabilities of the AEM in reproducing effectively the behaviour of masonry structures, whilst simultaneously keeping computational costs within acceptable limits for this type of detailed modelling.
... Other inputs were also applied in order to facilitate the calibration of analytical and numerical models (e.g. Tomassetti et al. 2018b;Malomo et al. 2018a) as, for example, a Ricker Wave Acceleration input, which consists of a particular acceleration pulse. Table 4 and Fig. 6 summarize the configurations of the specimens tested on the EUCEN-TRE shaking table in between 2015 and 2018. ...
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The reliability of a risk assessment procedure is strictly dependent on the adopted hazard, exposure, fragility and consequence models. This paper presents the methodology adopted to support the assessment of the seismic vulnerability of buildings in the Groningen province of the Netherlands by means of a comprehensive in situ and laboratory testing programme. The area, historically not prone to tectonic ground motions, experienced seismic events induced by gas extraction and subsequent reservoir depletion in the last decades. The peculiarity of the input ground motions, the distinctive features and a general lack of knowledge on the seismic response characteristics of the Dutch building stock, and the goal to also assess the collapse risk drove the design and execution of a comprehensive test campaign comprising in situ tests and full-scale shaking table tests of buildings. An overview of the whole campaign is presented, focusing on the merits and roles of the different experimental techniques. The main outcomes of the experimental tests are summarized and additional and wider research findings together with potential research avenues for future studies are also identified.
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The seismic assessment of typical unreinforced masonry buildings in The Netherlands, recently exposed to low-intensity ground motions induced by gas extraction, is becoming the focus of both experimental and numerical research. Their design, originally not conceived for earthquake-resistance, often features the presence of both large openings and flexible diaphragms, and the lack of any specific seismic consideration or detailing further increases the associated vulnerability towards horizontal loading. In this paper, the Applied Element Method, which explicitly represents the discrete nature of masonry, is used to simulate the shake-table response of a full-scale building specimen representative of a typical Dutch detached house made of unreinforced clay brick masonry. Using this modelling strategy, the damage evolution, as well as both global failure mode and hysteretic behavior, are described. The results have shown a good agreement with the experimentally-observed response, confirming the capabilities of the Applied Element Method in reproducing effectively the large-scale response of masonry structures, whilst simultaneously keeping computational costs within acceptable limits for this time of detailed modelling.
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Natural gas production in the Groningen field in the Netherlands is causing induced earthquakes that have raised concerns regarding the safety of the local population given that the exposed building stock (which is predominantly unreinforced masonry residential housing) has not been designed and constructed considering seismic loading. Significant effort has been invested to date in assessing the safety risk of these buildings within a probabilistic framework. This paper describes the efforts that have since been made to extend this framework for probabilistic damage assessment of the buildings, for slight non-structural, slight structural and moderate structural damage. Fragility functions for non-structural damage have been developed considering the observed damage from damage reports, rather than from damage claims due to a number of issues with the latter, as described herein. Structural damage has been estimated using analytical models that have been calibrated through extensive in situ data collection and experimental testing. The probabilistic damage assessment is presented in terms of F-N curves, which plot the annual frequency of exceedance against number of buildings reaching each damage state.
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Common responses to induced seismicity are based on control of the anthropogenic activity causing the earthquakes, such as fluid injection or withdrawal, in order to limit either the magnitudes of the events or the level of ground motion to within established thresholds. An alternative risk-mitigation option is seismic retrofitting of the more vulnerable buildings potentially exposed to the ground shaking to reduce the risk to acceptable levels. Optimal mitigation strategies may combine both production control and structural strengthening, for which a probabilistic risk model is required that can estimate the change in hazard caused by production or injection variations and the changes in fragility resulting from structural interventions. Such a risk model has been developed for the Groningen gas field in the Netherlands. The framework for this risk model to inform decision making regarding mitigation strategies can be adapted to other cases of anthropogenically induced seismicity.
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The response of calcium silicate unreinforced masonry construction to horizontal cyclic loading has recently become the focus of experimental and numerical research, given its extensive use in some areas of the world that are now exposed to induced earthquakes (eg, north of the Netherlands). To assess the seismic behaviour of such construction, a relatively wide range of modelling methodologies are available, amongst which the discrete elements approach, which takes into account the intrinsic heterogeneity of a brick‐mortar assembly, can probably be deemed as the most appropriate computational procedure. On the other hand, however, since discrete elements numerical methods are based on a discontinuum domain, often they are not able to model every stage of the structural response adequately, and because of the high computational burden required, the analysis scale should be chosen carefully. The applied element method is a relatively recent addition to the discrete elements family, with a high potential for overcoming the aforementioned limitations or difficulties. Initially conceived to model blast events and concrete structures, its use in the earthquake engineering field is, of late, increasing noticeably. In this paper, the use of the applied element method to model the in‐plane cyclic response of calcium silicate masonry walls is discussed and scrutinised, also through the comparison with experimental results of in‐plane cyclic shear‐compression tests on unreinforced masonry walls.
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This paper describes the ongoing experimental and analytical activities that are being carried out to develop fatality and consequence models for the estimation of ‘Inside Local Personal Risk’ (ILPR) of buildings within the Groningen field. ILPR is defined as the annual probability of fatality for a hypothetical person who is continuously present without protection inside a building. In order to be able to estimate this risk metric, a robust estimate of the probability of collapse of structural and non-structural elements within a building is needed, as these have been found to be the greatest drivers of fatality risk. To estimate the collapse potential of buildings in Groningen, structural numerical models of a number of representative case studies have been developed and calibrated through in situ and laboratory testing on materials, connections, structural components and even full-scale buildings. These numerical models are then subjected to increased levels of ground shaking to estimate the probability of collapse, and the associated consequences are estimated from the observed collapse mechanisms.
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For the estimation of "local personal risk," i.e., the annual probability of fatality for a hypothetical person continuously present in or near a building, an analyticalmethodology based on the probability of partial and complete collapse mechanisms (fragility models) and the probability of death given those collapse mechanisms (consequence models) for a building stock exposed to induced seismicity ground shaking is presented.
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A shaking table test on a two-storey full scale unreinforced masonry (URM) building was performed at the EUCENTRE laboratory within a comprehensive research programme on the seismic vulnerability of the existing Dutch URM structures. The building specimen was meant to represent the end-unit of a terraced house, built with cavity walls and without any particular seismic design or detailing. Cavity walls are usually composed of an inner loadbearing leaf and an outer leaf having aesthetic and weather-protection functions. In the tested specimen, the loadbearing masonry was composed of calcium silicate bricks, sustaining two reinforced concrete floors. A pitched timber roof was supported by two gable walls. The veneer was made of clay bricks connected to the inner masonry by means of metallic ties, as seen in common construction practice. An incremental dynamic test was carried out up to the near-collapse limit state of the specimen. The input motions were selected to be consistent with the characteristics of induced seismicity ground motions. The article describes the characteristics of the building and presents the results obtained during the material characterization and the shaking table tests, illustrating the response of the structure, the damage mechanism and its evolution during the experimental phases. All the processed data are freely available upon request (see http://www.eucentre.it/nam-project).
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Damage observations from recent seismic events have confirmed that the activation of out-of-plane local mechanisms is one of the major causes of structural collapse in unreinforced masonry buildings. Particularly vulnerable are cavity walls commonly used in residential building in regions such as Central and Northern Europe, Australia, New Zealand, China and several other countries. Usually, the inner leaf has a load-bearing function, carrying vertical loads transmitted by floors and roof while the outer leaf, having only aesthetic and insulation functions, is lightly loaded. The two leaves are typically connected by means of metallic ties. The high out-of-plane vulnerability, which may prevent the exploitation of the global capacity associated with the in-plane capacity of the structural walls, is mainly due to the high slenderness of the masonry leaves and the lack, or ineffectiveness, of ties between leaves. Often ties are too widely spaced and/or heavily degraded. Despite the complexity of the composite behaviour of such a construction typology, no dynamic tests on cavity walls are reported in current literature. For this reason, four out-of-plane shaking table tests were conducted on full-scale unreinforced masonry assemblies of three cavity wall panels with different tie distributions (inner calcium silicate brick wall and outer clay brick wall) and one single-leaf wall constructed using calcium silicate brick masonry. The experimental arrangement allowed the specimens to be tested under different input signals and loading conditions, inducing an out-of-plane one-way bending action in the walls. The research is aimed at understanding the seismic behaviour of cavity walls, their failure mechanisms and how they are affected by boundary conditions and degree of connection between the two leaves. The paper describes the main experimental results, including deformed shapes, damage patterns, force-displacement relationships, and the capacities in term of acceleration sustained by the specimens. Additionally, the energy dissipation involved in the mechanism has been investigated in terms of coefficient of restitution and damping ratio. All the processed data are freely available upon request (see http://www.eucentre.it/nam-project).
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A new method, Applied Element Method (AEM) for analysis of structures is introduced. The structure is modeled as an assembly of distinct elements made by dividing the structural elements virtually. These elements are connected by distributed springs in both normal and tangential directions. We introduce a new method by which the total behavior of structures can be accurately simulated with reasonable CPU time. This paper deals with the formulations used for linear elastic structures in small deformation range and for consideration of the effects of Poisson's ratio. Comparing with theoretical results, it is proved that the new method is an efficient tool to follow mechanical behavior of structures in elastic conditions.
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A Monte Carlo approach to probabilistic seismic-hazard analysis is developed for a case of induced seismicity associated with a compacting gas reservoir. The geomechanical foundation for the method is the work of Kostrov (1974) and McGarr (1976) linking total strain to summed seismic moment in an earthquake catalog. Our Monte Carlo method simulates future seismic hazard consistent with historical seismic and compaction datasets by sampling probability distributions for total seismic moment, event locations and magnitudes, and resulting ground motions. Ground motions are aggregated over an ensemble of simulated catalogs to give a probabilistic representation of the ground-motion hazard. This approach is particularly well suited to the specific nature of the time-dependent induced seismicity considered. We demonstrate the method by applying it to seismicity induced by reservoir compaction following gas production from the Groningen gas field. A new ground-motion prediction equation (GMPE) tailored to the Groningen field has been derived by calibrating an existing GMPE with local strong-motion data. For 2013–2023, we find a 2% chance of exceeding a peak ground acceleration of 0:57g and a 2% chance of exceeding a peak ground velocity of 22 cm/s above the area of maximum compaction. Disaggregation shows that earthquakes of Mw 4–5, at the shortest hypocentral distances of 3 km, and ground motions two standard deviations above the median make the largest contributions to this hazard. Uncertainty in the hazard is primarily due to uncertainty about the future fraction of induced strains that will be seismogenic and how ground motion and its variability will scale to larger magnitudes.
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A new extension for the applied-element method for structural analysis is introduced. In this method, the structure is modeled as an assembly of elements made by dividing the structure virtually. This paper first introduces the element formulation of the applied-element method. Next, the effects of the element size and arrangement are discussed, and finally, the accuracy of the proposed method in a nonlinear material case is verified by studying the behavior of RC structures under cyclic loading. For effects caused by the size and arrangement of the elements, it is shown that accurate results of stresses and strains can be obtained if elements of small size are used. As for failure behavior simulation of RC structures, the complicated behavior of cracks in structures subjected to cyclic loading, such as crack initiation and propagation, and opening and closure of cracks during the unloading process, can be simulated automatically and without any use of complicated techniques. No special knowledge about the crack location or direction of propagation is needed before the analysis. The calculated load-displacement relation and the failure load show reliable accuracy.