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Using the Applied Element Method to simulate the dynamic response of full-scale URM houses tested to collapse or near-collapse conditions

Authors:

Abstract

In this work, the Applied Element Method (AEM) is employed to reproduce the dynamic response of three full-scale unreinforced masonry (URM) house specimens tested on a shake-table. Two of the test specimens correspond to a calcium-silicate terraced house typology (typical of construction in the Netherlands and other Northern European countries), whilst a third one corresponds to a clay masonry detached house (representative not only of Northern Europe construction typologies, but also of houses found in other regions of the world, such as Australia and New Zealand). The test specimens were subjected to dynamic inputs of increasing intensity, both for reasons of shake-table control as well as for monitoring of progressive damage/limit states evolution. For two of the specimens, near collapse conditions were reached during their testing, whilst for the third an explicit structural collapse was obtained.
USING THE APPLIED ELEMENT METHOD TO SIMULATE THE
DYNAMIC RESPONSE OF FULL-SCALE URM HOUSES TESTED TO
COLLAPSE OR NEAR-COLLAPSE CONDITIONS
Daniele MALOMO
1
, Rui PINHO1,2, Andrea PENNA1,3
ABSTRACT
In this work, the Applied Element Method (AEM) is employed to reproduce the dynamic response of three full-scale
unreinforced masonry (URM) house specimens tested on a shake-table. Two of the test specimens correspond to a calcium-
silicate terraced house typology (typical of construction in the Netherlands and other Northern European countries), whilst a
third one corresponds to a clay masonry detached house (representative not only of Northern Europe construction typologies,
but also of houses found in other regions of the world, such as Australia and New Zealand). The test specimens were subjected
to dynamic inputs of increasing intensity, both for reasons of shake-table control as well as for monitoring of progressive
damage/limit states evolution. For two of the specimens, near collapse conditions were reached during their testing, whilst for
the third an explicit structural collapse was obtained.
Keywords: applied element method; discrete elements modelling; unreinforced masonry; shake-table testing
1. INTRODUCTION
The construction culture and practice in the until recently non-seismic Groningen region, now subjected
to induced seismicity due to natural gas extraction, is understandably and naturally distinct from what
is typically found in areas of the world that have a long history of damaging earthquakes. As such,
neither experimental data nor verified numerical models for the characterisation of the seismic response
of these types of structures were available in the literature, the reason for which an extensive research
programme aimed at addressing such knowledge gap was deployed, under the sponsorship of the
Nederlandse Aardolie Maatschappij BV (NAM).
Such research programme featured a number of workstreams, described in van Elk et al. (2018),
including laboratory testing of a number of unreinforced masonry (URM) and reinforced concrete (RC)
full-scale test specimens. Of particular relevance to the work described herein is the shake-table testing
of two calcium-silicate terraced house specimens, as well as of a clay masonry detached house. For each
of these full-scale tests, a number of teams, each of which using different modelling approaches, were
invited to carry out, first, blind-predictions of the tests results, and then calibrated “post-dictions” (e.g.
Arup et al. 2015, 2017); such numerical validation endeavour lent confidence and reassurance to the
process through which the analytical fragility functions for the Groningen region was developed
(Crowley et al. 2017, Crowley and Pinho, 2017), since it was based on detailed nonlinear dynamic
analyses of representative buildings (Arup 2017, Mosayk 2017a).
In this paper, the employment of the Applied Element Method (Meguro and Tagel-Din, 2000, 2001,
2002) in such cross-modelling validation exercise is described, showing how this relatively recent
addition to the discrete elements methods family has the capability of producing reliable estimation of
the response of URM buildings subjected to earthquake loading.
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, 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 involve 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).


(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,  is composed of the brick
stiffnesses knb and ksb only (Equation 2), whereas for the interfaces,  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
 
 
(2)
(3)
The above parameters, representing the brick-mortar interaction, take 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. The 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.
2.3. Employed software tool
The Extreme Loading for Structures (ELS) is a commercial structural analysis software tool developed
by ASI (2017) and was employed to carry out the nonlinear dynamic analyses described in this paper.
3. MODELLING SHAKE-TABLE TESTING OF THREE FULL-SCALE URM BUILDINGS
3.1. Two-storey URM terraced house (EUC-BUILD1)
This specimen was built and tested on the shake-table of Eucentre (Pavia, Italy), and consisted of a full-
scale two-storey building (Figure 3) with a timber roof and RC slabs, 5.82 m long, 5.46 m wide and 7.76
m tall, for a total mass of 56.4 t. The walls, supported by a steel-concrete composite foundation,
consisted of two unreinforced masonry leaves; an air gap of 80 mm was left between them, as usually
seen in common practice, whilst steel ties with a diameter of 3.1 mm and a length of 200 mm were
inserted in the mortar layers during construction, ensuring the connection between the two masonry
leaves. The two gables in the transverse façades (East and West) supported a 43° pitched timber roof.
The inner loadbearing leaf was made of calcium silicate (CS) bricks whereas the external leaf was a clay
brick (CL) veneer without any loadbearing function. The inner CS masonry was continuous along the
entire perimeter of the house, while the outer clay brick leaf was not present in the South façade. It is
noteworthy that the slab was not directly supported by the CS longitudinal walls; the gap between the
slab and the inner CS longitudinal walls was filled with mortar after the removal of the temporary
supports and the attainment of the slab’s deflection resulting in almost no vertical load being transmitted
to the longitudinal walls under static conditions. Further information on this specimen, including
construction details and material properties can be found in Graziotti et al. (2015, 2017).
4
Figure 3. EUC-BUILD1: shake-table test specimen and corresponding damage pattern at end of testing on both
outer-leaf clay walls and inner-leaf calcium-silicate walls (Graziotti et al. 2015, 2017)
The specimen was subjected to incremental dynamic testing, i.e. a series of shake-table runs under input
motions of increasing intensity up to near-collapse of the structure. Two different ground motions, herein
named EQ1 and EQ2, were employed in these tests (again, refer to Graziotti et al. 2015, 2017 for further
details), with the building sustaining shaking of peak ground acceleration (PGA) of 0.14g (EQ1@150%)
with no visible damage, and reaching instead a near-collapse state under the EQ2@200 test run,
exhibiting the damage pattern shown in Figure 3.
Table 1 summarises the most relevant modelling assumptions made when developing EUC-BUILD1’s
AEM numerical model. Particularly noteworthy is perhaps the issue of the connections between wall
elements; three different geometries for such connections were studied, with a 45° wall-to-wall interface
joint (see Figure 4c) being found to be that leading to best results. Interested readers are referred to the
report by Mosayk (2017b) for further details on this and all other modelling issues, including the
calibration of constitutive relationship employed to model ties, nails and anchors.
Table 1. EUC-BUILD1: main modelling assumptions
Structural component/detail
Corresponding modelling assumption
Masonry discretisation
Rigid units and dimensionless mortar layers assembly
Boundary conditions
Structure connected through a mortar interface to a fixed slab
Roof diaphragm
Nailed connection between planks and beams modelled as equivalent
spring interfaces characterised by an elastic-perfectly-plastic behaviour
Wall ties
Elastic-perfectly-plastic link elements
First floor slab-front/back inner
leaves connection
Mortar interface
Second floor slab-front/back
inner leaves connection
Weak mortar interface (since the gap between the slab and the wall was
filled after the temporary supports removal, i.e. after RC slab deflection)
Timber beam-front/back outer
leaves connection
Weak mortar interface (since the gap between the slab and the wall was
filled after the temporary supports removal, i.e. after RC slab deflection)
First and second floor slab and
end/party walls connection
Mortar interface
Connection between roof girders
and end/party walls
Mortar interface plus elastic-perfectly plastic L-steel anchors
Wall-to-wall connection
45° connections between adjacent walls (Figure 4c)
5
(a)
(b)
(c)
Figure 4 AEM: different types of wall-to-wall connections that may be adopted
In Figure 5(a), the maximum horizontal drifts at the attic floor level recorded for each test run are plotted
against the latter PGA values, and compared with their corresponding numerical counterparts. In Figure
5(b), on the other hand, the experimental and numerical base shear vs. attic displacement hysteretic
curves are compared. Finally, in Figure 6, the numerical deformed shape at instant of peak response
displacement is shown.
(a)
(b)
Figure 5. EUC-BUILD1: (a) PGA-Drift envelope of incremental dynamic tests/analyses, (b) experimental vs.
numerical hysteretic plots (grey is experimental and black is numerical)
Figure 6. EUC-BUILD1: deformed shape of AEM model at instant of peak deformation (magnified x5)
3.2. One-storey URM terraced house (LNEC-BUILD1)
This specimen, built and tested on the shake-table of LNEC (Lisbon, Portugal), is a full-scale one-storey
building with a timber roof and RC slab, corresponding to the second floor and roof of the EUC-BUILD1
EQ1@50
EQ1@100
EQ1@150
EQ2@100
EQ2@125
EQ2@150
EQ2@200
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-1 -0.5 0 0.5 1
PGA [g]
Attic floor drift ratio [%]
Experimental Numerical
-200
-150
-100
-50
0
50
100
150
200
-60 -40 -20 0 20 40 60
Total base shear [kN]
Attic floor horizontal displacement [mm]
Experimental Numerical
6
(considered in Section 3.1 above); it was thus 5.82 m long, 5.46 m wide and 4.93 m tall, for a total mass
of 31 t. The seismic input introduced at the base of LNEC-BUILD1 specimen corresponded to the floor
accelerations that had been recorded during the EUC-BUILD1 test, with the exception of the final test
run, which corresponded to levels of acceleration that had not been reached during such first experiment,
and which led to the collapse of the structure (Figure 7). Further details on the specimen and its response
can be found in Tomassetti et al. (2017).
Figure 7. LNEC-BUILD1: damaged specimen at end of testing (Tomassetti et al., 2017)
Table 2 summarises the most relevant modelling assumptions made when developing LNEC-BUILD1’s
AEM numerical model. It is also noted that, as in the case of EUC-BUILD1, in order to decrease the
computational burden, the bricks were assumed to be rigid and the number of springs was reduced,
which effectively implies that mechanisms that involve the deformability of bricks, such as crushing of
masonry due to the splitting of the unit, could not be taken into account (this may result in a lower
prediction of energy dissipation).
Further, it is equally herein highlighted that the gravity contribution of the roof tiles was modelled
through a system of lumped masses shared amongst the elements of the mesh, again with the aim at
reducing the calculation steps, resulting in a potentially slightly altered acceleration demand at the roof
structure. Interested readers are referred to the report by Mosayk (2017c) for further details on the
development of the model.
Table 2. LNEC-BUILD1: main modelling assumptions
Structural component/detail
Corresponding modelling assumption
Masonry discretisation
Rigid units and dimensionless mortar layers assembly
Boundary condition
Structure connected through a mortar interfaces to a fixed slab
Roof diaphragm
Nailed connection between planks and beams modelled as equivalent
spring interfaces characterised by an elastic-perfectly-plastic behaviour
Wall ties
Elastic-perfectly-plastic beam elements
Attic floor slab and front/back
inner leaves connection
Mortar interface (active after the static/gravity loading stage)
Timber beam and front/back outer
leaves connection
Mortar interface (active after the static/gravity loading stage)
Attic floor slab and end/party
walls connection
Mortar interface
Connection between roof girders
and end/party walls
Mortar interface plus elastic-perfectly plastic L-steel anchors
7
In Figure 8(a), the maximum horizontal drifts at the attic floor level recorded for each test run are plotted
against the latter PGA values, and compared with their corresponding numerical counterparts. In Figure
8(b), on the other hand, the experimental and numerical base shear vs. attic displacement hysteretic
curves are compared. Whilst it can be seen from the latter plot that the AEM model was not able to
adequately reproduce the final wider cycles of vibration (it is worth noting that the in-plane energy
dissipation of the last cycle of both CS and CL longitudinal walls has been underestimated by the model),
Figure 9 shows that nonetheless the collapse mode of the specimen (shown in Figure 7 above) was fully
captured by the model (at the very same base level intensity as during the test).
(a)
(b)
Figure 8. LNEC-BUILD1: (a) PGA-Drift envelope of incremental dynamic tests/analyses, (b) experimental vs.
numerical hysteretic plots (grey is experimental and black is numerical)
Figure 9. LNEC-BUILD1: specimen collapse mode as reproduced by AEM model
3.3. URM detached house (EUC-BUILD2)
This specimen was built and tested on the shake-table of Eucentre (Pavia, Italy), and consisted of a full
scale building featuring construction details typical of Dutch terraced houses built before the 1940s,
including the so-called Dutch cross brickwork bond. It is therefore a two-storey double-wythe clay
masonry building with timber floor diaphragm and timber roof. The roof is comprised of roof trusses
that span perpendicular to the direction of motion. The timber roof boards support ceramic tiling.
Dimensions of the structure are 5.8 m in the North-South direction (i.e., shaking direction) and 5.3 m in
the east-west direction, while the building height is 6.2 m. Further, the specimen was designed to include
large asymmetrical openings on all sides and a re-entrant corner (see Figure 10), causing a discontinuity
in one of the perimeter walls with the intention to magnify torsional effects under uniaxial seismic
excitation. Further details can be found in Graziotti et al. (2016).
EQ1@150
EQ2@100
EQ2@150
EQ2@200
EQ2@300
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-6 -3 0 3 6
PGA [g]
Attic floor drift ratio [%]
Experimental Numerical
-200
-150
-100
-50
0
50
100
150
200
-200 -100 0 100 200
Total base shear [kN]
Attic floor horizontal displacement [mm]
Experimental Numerical
8
Figure 10. EUC-BUILD2: shake-table test specimen and corresponding damage pattern at end of testing
(Graziotti et al., 2016)
Similarly to the previous two tests, the specimen was subjected to incremental dynamic testing with
input motions representative of induced seismicity scenarios for the Groningen region (see Graziotti et
al. 2016). The building suffered only minor damage under the input motion with PGA of 0.23 g and
reached its near-collapse state for a PGA value of 0.68 g (with the damage pattern shown in Figure 10).
Table 3 summarises the most relevant modelling assumptions made when developing EUC-BUILD2’s
AEM numerical model, from where it can be gathered that a roof modelling strategy different from that
employed in the previous models was herein adopted; rather that modelling each plank separately,
accounting both for nails slip, rigid rotation, flexural and shear deformation of the plank elements, the
roof of EUC-BUILD2 was instead modelled by means of an equivalent membrane element (Brignola et
al., 2008) that intrinsically attempts to account for the abovementioned roof response components.
It is also noted that, for modelling simplicity, and given that it appeared to have negligible influence on
the analyses’ results, the Dutch cross brickwork modelled was not explicitly modelled. Finally,
interested readers are referred to the report by Mosayk (2017b) for further details.
Table 3. EUC-BUILD2: main modelling assumptions
Input
Modelling assumption
Masonry discretisation
Rigid units and dimensionless mortar layers assembly
Boundary condition
Structure connected through a mortar interfaces to a fixed slab
Roof diaphragm
Equivalent membrane elements
First-floor diaphragm/wall
connection
Mortar interface
Timber beam/wall connection
Mortar interface
Connection between roof
girders and wooden diaphragm
Nailed connection between membrane and beams modelled as equivalent
spring interfaces characterised by an elastic-perfectly-plastic behaviour
Wall-to-wall connection
45° connections between adjacent walls (Figure 4c)
Double-leaf brickwork
The influence of cross brick arrangement was not accounted (i.e. no
perpendicular bricks to the bed joints were introduced)
In Figure 11(a), the maximum horizontal drifts at the attic floor level recorded for each test run are
plotted against the latter PGA values, and compared with their corresponding numerical counterparts.
In Figure 11(b), on the other hand, the experimental and numerical base shear vs. attic displacement
hysteretic curves are compared. In Figure 12, instead, the numerical deformed shape and damage pattern
at instant of peak response displacement are shown.
9
(a)
(b)
Figure 11. EUC-BUILD2: (a) PGA-Drift envelope of incremental dynamic tests/analyses, (b) experimental vs.
numerical hysteretic plots (grey is experimental and black is numerical)
Figure 12. EUC-BUILD2: deformed shape and damage pattern of AEM model at instant of peak deformation
(magnified x2)
4. CLOSING REMARKS
Three different full-scale URM house specimens subjected to earthquake loading were modelled using
the Applied Element Method (AEM). This exercise confirmed the capability of the latter in analysing
masonry structures under seismic excitation, independently of construction details and masonry material
types.
For what concerns specimen EUC-BUILD1, the numerical results can be deemed as representative of
the actual experimentally observed behaviour of the specimen. Indeed, the overall response was
adequately captured, as also confirmed by comparing the numerical crack patterns of the last cycles with
their experimental counterparts.
With regards to specimen LNEC-BUILD1, this endeavour also confirmed the capability of the employed
modelling approach in adequately capturing the seismic response of URM buildings, given that the
model did reproduce the overall structural response and the collapse of the specimen.
The numerical simulation of EUC-BUILD2 was slightly more challenging, due to the complexity of the
roof structure. Indeed, the dynamic behaviour of the roof was well reproduced by the model only in the
EQ1@100
EQ1@150
EQ2@100
EQ2@150
EQ2@200
EQ2@250
EQ2@300
EQ2@400
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-1 -0.5 0 0.5 1
PGA [g]
Attic floor drift ratio [%]
Experimental Numerical
-200
-150
-100
-50
0
50
100
150
200
-30 -10 10 30
Total base shear [kN]
Attic floor horizontal displacement [mm]
Experimental Numerical
10
very last stages, thus leading to a numerical response that is stiffer than the experimental one.
It is important to note that the vast majority of modelling properties adopted for the development of the
post-test models coincided with their experimental counterparts, without the need for any significant
adjustments to be introduced. This is further reassuring for when this modelling approach is employed
in contexts where no test data is available.
Notwithstanding the above, this study also showed that further improvements are warranted, with a view
to try to better capture the energy dissipation of some of the specimens, together with a better numerical
reproduction of the response of the roof structures. Avenues worth exploring include:
- the possibility of adjusting, in the numerical model, the parameters that control degradation of
cohesion and tensile strength (currently this is not possible, in the tool employed for these
analyses);
- the feasibility of calibrating the equivalent viscous damping (currently this is not possible, in
the tool employed for these analyses);
- meshing the bricks (so far modelled as rigid units), so that the energy dissipation associated to
their deformation (in particular of CS bricks), cracking, splitting and crushing may be taken into
account;
- better modelling the connections between wooden elements (e.g. between beam/beam and
beam/plank), particularly if specific experimental data can be obtained.
5. 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) and at the Portuguese Civil
Engineering National Laboratory (LNEC, Lisbon, Portugal) 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 software - Extreme Loading for Structures.
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... When using equivalent frame models that do not capture the out-of-plane behaviour, other types of analyses (i.e. rigid body limit analysis of collapse mechanisms 27 or discrete element modelling 28,29,30 ) have to also be performed. This necessarily assumes, however, that the in-plane and out-of-plane responses are not coupled. ...
Article
The seismic performance of unreinforced masonry buildings is commonly assessed using equivalent frame modelling. Its computational efficiency allows for a large number of analyses to be conducted, which are often required to account for epistemic and aleatoric uncertainties. To obtain a full description of the building response, in‐plane and out‐of‐plane failure modes need to be considered, though previous elements for equivalent frame models of unreinforced masonry buildings only account for the in‐plane response. This paper presents the formulation of a three‐dimensional macroelement for modelling the dynamic in‐plane and out‐of‐plane behaviour of masonry panels, which extends the approach of a previously developed macroelement to simulate the in‐plane response. The proposed three‐node, three‐dimensional macroelement is implemented in the software OpenSees and describes the main features of the in‐plane and out‐of‐plane behaviour of a masonry wall, including second‐order geometrical effects and a coupled shear/flexural response. It also allows for the use of complex material models. The proposed element is used to simulate experimental results for in‐plane shear‐compression tests and out‐of‐plane free vibration tests of masonry panels. The implemented element, as well as the example models, is openly shared through the repository https://github.com/eesd-epfl/OpenSees/wiki.
... Calvi et al. 2018;Salem and Helmy 2014) or blocky (e.g. Karbassi and Lestuzzi 2012;Malomo et al. 2018c) highly nonlinear systems. ...
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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.
... The explicit representation of complete structural collapse, and corresponding formation of debris, is still an open challenge in numerical modelling. However, recent applications [36][37][38][39] have shown that the Applied Element Method (AEM) does appear to be able to capture adequately the progressive failure of both masonry, steel and RC structures. Originally developed by Meguro and Tagel-Din [40][41][42] to simulate controlled structural demolition and the impact of blast events, it is based on the mechanical interaction between rigid bodies connected to each other by zero-thickness interface spring layers, in which the material properties of the system are lumped. ...
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On 14 August 2018 at 11:35 AM, a relevant portion (about 243 m) of the viaduct over the Polcevera river in Genoa collapsed, killing 43 people. The bridge was designed in the early 1960s by Riccardo Morandi, a well-known Italian engineer, and opened to the public in 1967. The collapsed part of the bridge essentially comprised an individual self-standing structure spanning 171 m and two simply-supported connecting Gerber beam systems, each spanning 36 m from the self-standing structure to the adjacent portions of the bridge. This paper aims to reminisce the complete story of the bridge, from the Italian construction boom in the 1960s to some of the issues that soon arose thereafter: the strengthening intervention in the 1990s, the subsequent structural monitoring and, finally, the strengthening project never brought to fruition. Potential reasons for the collapse are discussed, together with some of the possible inadequacies of the bridge, its maintenance and loading history based on critical reflection, comparison with specific features of bridge construction practice today and results obtained using numerical models with different levels of refinement. Since the entire matter (specifically the debris) was considered classified by the investigating magistrate in the immediate aftermath of the bridge collapse, this work is based entirely on publicly available material.
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A new approach to the analysis of the stress-strain state of adhesive joints and the transverse strength of layered composites is proposed. It consists in a combined use of finite-element and contact layer methods. Based on this approach, the problem of the long-term strength in normal separation of two adhesively bonded disks glued together by an epoxy resin, which was previously considered by R. A. Turusov, is solved. The nonlinear Maxwell–Gurevich equation is used as the law of adhesion creep. The model constructed by R. A. Turusov does not take into account the shear creep strains of contact layer and is based on the hypothesis of linear distribution of shear stresses across the thickness of adhesive layer and substrate. It was found that these simplifications lead to overestimated tangential stresses. By analyzing the creep law with time tending to infinity, the long-term elastic modulus and Poisson ratio of the adhesive are derived and the reliability of their values is confirmed.
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.
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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.
Article
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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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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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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 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.
Typology modelling: Analysis results in support of fragility functions -2017 batch results
  • Arup
Arup (2017). Typology modelling: Analysis results in support of fragility functions -2017 batch results. Report n. 229746_031.0_REP2005. Available from http://www.nam.nl/feiten-en-cijfers/onderzoeksrapporten.html.
LNEC-BUILD1: Modelling predictions and analysis cross validation
  • T U Arup
  • Delft
Arup, TU Delft, Eucentre and Arcadis, 2015. EUC-BUILD2: Modelling predictions and analysis cross validation, Report n. 229746_031.0_REP1009. Available from URL: http://www.nam.nl/feiten-en-
Extreme Loading for Structures v5
  • Asi
ASI (2017). Extreme Loading for Structures v5. Applied Science International LLC, Durham (NC), USA.