Finite Element Performance Based Evaluation of Seismically
Retrofitted Masonry Buildings– Study case
A. DOGARIU & D. DUBINA
“Politehnica” University of Timisoara
ROMANIA
[email protected], [email protected]
Abstract: Using advanced Finite Element Method, a building designed at the beginning of the XX century has
been evaluated and consolidated applying a strengthening solution based on metallic sheathing. On this,
purpose a Performance Based Seismic Assessment (PBSA) procedure was applied using an equivalent FE
model. This model, experimentally and numerical calibrated, to simulate the nonlinear behavior of masonry
shear walls strengthened with metal sheathing is applied by ABAQUS code, in order to establish the
acceptance criteria, performance levels and building performance.
Key-Words: Advanced FE models, FE Performance Based Assessment, retrofitting techniques;
1 Introduction Advanced Finite Element Analysis is used to
evaluate the seismic performance of a masonry
building retrofitted with ductile steel plates. Because
the building masonry walls sheathed of steel plates
[5] [7] [9] is a complex composite structure, the FE
numerical model used to evaluate its performance
must be able to replicate the real behavior of
characteristic component of the system i.e. masonry
specific layout, connection behavior, etc. This very
detailed model, showed in [8] [17], is almost
impossible to be applied in case of global analysis;
even in case of use advanced tools supplementary
simplifications must be made. The idea to find an
equivalent material to replicate the behavior of the
retrofitted model arisen [16]. This simplification
must be carefully analyzed and argued.
The advantages of such a model is the possibility
to applies the nonlinear analysis and to characterize
the global behavior of the building in term of drift
ratios, which gives the possibility to use the FEMA
356 [3] criteria for validation and performance
levels’ characterization.
2 Description of the study case It is presented the general description of a masonry
building, located in Toscana region, Italy, designed
according only to geometrical considerations (Fig.
1&2); this building was selected as reference
benchmark structure for the performance analyses of
the steel intervention techniques in the frame of
STEELRETRO Project (RFSR-CT-2007-00050)
[13]. An intensity of 0.24g of PGA and type B soil
has been considered.
The reference building respect all the main fea-
tures of traditional masonry building, ground floor
plus two floors, symmetrical in plan and elevation
with small and well positioned openings, with an
almost cubical shape of 15m width, long and height.
The bearing wall thickness varies from 350 mm to
650 mm and is made from stone masonry.
The material mechanical properties adopted for
the structural modelling of the masonry benchmark
are drawn by literature [14]. The walls are built by
stone masonry with the following mechanical
characteristics: mean compressive strength fm = 1.5
MPa, Elastic Modulus Em = 1500 MPa and mean
unit weight w = 21 kN/m3.
In order to apply the steel sheathing retrofitting to
the vertical elements, it was considered the
necessary measures to provide the rigid diaphragm
effect of floors and roof, the integrity of the wall
junctions have been already done.
Fig. 1 Horizontal plan of the first floor
Proceedings of the 3rd WSEAS Int. Conference on FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS
ISSN: 1790-2769 264 ISBN: 978-960-474-180-9
Fig. 2 Transversal section of the building
2.1 Reinforced areas of the building The building façade was reinforced with steel pates
on the entire height of the building as shown in Fig.
3a, and all the internal transversal shear walls from
the ground floor. Other possible location of
sheathing on external façade would be at the corners
of the entire ground floor (Fig. 3b)
a) b)
Fig. 3 Steel plates location: a - between the openings
(middle model); b – at the corners (corner model)
Beside structural aspects, selection of intervention
solution must consider the costs and time, and the
aesthetically reasons. The possibility to maintain
using the building even partially during intervention
is also very important.
The applied techniques attempt to be minimal
one and avoid affecting internal walls to not disturb
the occupancy of the building.
3 Performance based evaluation 3.1 Nonlinear model and specific acceptance
criteria A proper application of PBSA needs for a reliable
nonlinear analysis FE model to perform advanced
displacement control analysis.
The ABAQUS finite element model applied in
this study was calibrated on the basis of
experimental tests and is present in detail in [8] [17].
A homogeneous macro-model using 3D Shell
Deformable finite elements (a 4-node doubly curved
thin shell, reduced integration, hourglass control,
finite membrane strains) with a Concrete Damage
Plasticity material model [4] has been choose for
numerical simulation to obtain a good balance
between the computational time effort and accuracy
of the results.
PBSA considers the entire building as an
assembly of its individual components. The building
performance level is defined in relation with its
element performance. The evaluation of building
performance must concentrate on how component
properties change as result of damage. The response
of components is controlled by force – deformation
properties (e.g. cracking point) [1] [2].
Some elements exhibit ductile modes of post-
elastic behavior, maintaining strength even with
large displacement. Others are brittle and lose
strength abruptly after small inelastic displacement
or strain. The behavior of masonry wall depends on
its strength in flexure relative to that in shear.
Cracks and other signs of damage must be
interpreted in the context of the behavior mode of
each specific component.
A complete evaluation must take into account the
cracks width, location, orientation, and their number
and distribution pattern. In a simple manner cracks
width is commonly used to determine the damage
level or performance of the wall. The performance
acceptance criteria were established on the retrofit-
ted wall panel model in terms of plastic strain at cer-
tain performance level. A quicker assessment of the
overall performance can be based shear stress. The
reinforced panel F.E. model fails due compressive
load by crushing of masonry. If the unreinforced
model fails at a level of an approximate 0.15% of
plastic strain, in terms of tensile strain in shear
diagonal strip the retrofitted models allows for
reaching more than 3.5% strain before collapse pre-
vention level and failure (Fig. 4) [6] [7] [8] [17].
The global behavior curves (see Fig. 4) come to
sustain, ones again, the possibility to enhance de-
formation of the masonry wall and prove suitability
to apply the performance levels presented in Fig. 5,
showing the benefit of applied reinforcing.
For establish the behavior of the retrofitted
elements, a parametrical study has been performed
using the complex F.E. model described in [17]. In
this study, a “numerical experimental procedure”
was applied (Fig. 6) aiming to observe the effect of
the retrofitting solution in case of an old masonry of
varying mechanical characteristics presented above
Proceedings of the 3rd WSEAS Int. Conference on FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS
ISSN: 1790-2769 265 ISBN: 978-960-474-180-9
(§2) expressed in terms wall thickness ranking from
350 to 600 mm.
Fig. 4 Element behavior curves of unreinforced and
reinforced FE model and maximum plastic strain
level at failure
Experimental tests on retrofitted wall specimens
have concluded this technique improves the
behavior in the range of Life Safety – Collapse
Prevention, accompanying by a ductile increase in
strength (Fig. 5) [5] [7].
Fig. 5 Benefit of the reinforcing from the
performance levels point of view
If the virgin masonry elements have a brittle
failure due to the small tension resistance, the
retrofitted elements exhibits an ductile failure mode.
These observations allow using an equivalent
material model for masonry, removing the tension
softening (Fig. 7) from the constitutive law, to
obtain the same global behavior as in case of
specimens “numerically tested” retrofitted
specimens (Fig. 6).
This observation simplifies a lot the numerical
effort, by a simple change in the original material
parameters in order to replicate the beneficial effect
of reinforcing i.e. possibility to maintain the
capacity of wall at large displacement. The
numerical results may be observed in Fig. 8 [7].
Fig. 6 Numerical results for unreinforced and
retrofitted masonry walls
Tension behaviour for equivalent material
Tension softening for URM
Tensile stress (MPa)
Displacement (mm)6543210
0.02
0.04
0.06
0.08
0.10
0.12
Fig. 7 Material constitutive law in tension (tension
softening – unreinforced model)
Fig. 8 Comparative numerical results for calibrated
models and equivalent material models
Such a procedure may be applied with success in
case of global analysis of real façades and for differ-
ent building typologies, making the analysis easy
and quick. The retrofitted model, described in detail
in [17], reached at CP level 2.5% ultimate maximum
plastic strain and -0.7% ultimate minimum plastic
strain. In case of equivalent model, at the same
displacement of 10 mm, corresponding to a 1/150
drift, it was recorded 1.5% ultimate maximum
plastic strain and -0.07% ultimate minimum plastic
strain. These values will be used in the further
evaluation as reference acceptance criteria. So by an
advanced FE model can be numerically establish the
Proceedings of the 3rd WSEAS Int. Conference on FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS
ISSN: 1790-2769 266 ISBN: 978-960-474-180-9
failure criteria that will be used for PBSA of this
type of retrofitted technique.
3.2 Numerical analysis of the existing
building Using ABAQUS code a complete 3D model of the
building has been built.
Some simplifications regarding to the fixed base
and rigid diaphragm behavior of the floors have
been used. The model is build of shell elements and
a material model of Concrete Damage Plasticity was
applied. The horizontal load was introduced quasi-
statically, performing an explicit analysis, as force
concentrated in the mass centre of the floors respect-
ing a triangular shape, according to the first eigen
vibration mode. The results of pushover analysis are
presented in terms of base shear force – top dis-
placement (see Fig. 9).
0.0E+00
1.5E+06
3.0E+06
4.5E+06
0 2 4 6 8 10
Displacement (mm)
Load (N)
Bilinear behavior Z direction
Behavior curve X direction
Behavior curve Z direction
Bilinear behavior X direction
Fig. 9 Global behavior of the unreinforced building
and the approximate elasto-plastic force –
displacement relationship
Usually, after reaching the point of maximum
force, then masonry building behave fragile showing
an instable behavior and losing much of the strength
at small displacement.
3.3 Performance analysis and evaluation To establish the seismic response of both initial and
retrofitted structure (middle and corner), a
displacement based procedure was used [11]. This
procedure, N2, is recommended by the EN 1998
[10] P100-3/2005 [15]. The target displacement for
the single degree of freedom model (SDOF),
6.77mm, has been determined at the intersection of
capacity curve and inelastic spectrum, considering a
constant ductility of 1.5 (Fig. 10).
The damage level and evidence of the attainment of
the performance criteria at 9.77 mm target dis-
placement for unreinforced model in terms of plastic
strain (the cracks with) is plotted in Fig. 11.
Fig. 10 N2 demand spectra and capacity diagram for
the unreinforced and reinforced numerical model
a)
Fig. 11 Unreinforced model plastic strain which
exceed the collapse prevention level value
One remarks in case of unreinforced model at the
level of ground floor, all the diagonal cracks formed
in between the openings and have exceeded the CP
value of plastic strain (0.15%); consequently give a
soft storey collapse mechanism mode occurred.
At the attainment of 9.77 mm target displacement
(of MDOF) the retrofitted model, similar with the
unreinforced building, the level of reference plastic
strain is exceeded in the unreinforced walls (Fig.
12), but not in the reinforced ones (Fig. 13). Even if
in the adjacent unreinforced walls the failure
occurred, the reinforced walls are able to preserve
the global safety of the building, by maintaining the
same level of strength (Fig. 14). In Fig. 15 is
presented the global curves for the two reinforced
models. Because of the almost same reinforced area
of the building the global results are similar.
The retrofitted building subjected to a seismic
motion of PGA up to 0.16g behaves in elastic range
and fulfils the IO performance level; for PGA be-
tween 0.16-0.44g the LS performance level is at-
tained. At a displacement larger than 30 mm the
building reach CP level. Using the recurrence
formulas for PGA given in Romanian Code P100-3
[15], even calibrated for Vrancea earthquake, a
Proceedings of the 3rd WSEAS Int. Conference on FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS
ISSN: 1790-2769 267 ISBN: 978-960-474-180-9
matrix may be build showing the performance
objective possible to achieve by retrofitted building
(see Table 1).
a)
b)
Fig. 12 Retrofitted model behavior plastic strain in
un-reinforced elements (a) middle model (b) corner
model;
a)
b)
Fig. 13 Plastic strain in retrofitted elements (a)
middle model (b) corner model;
Fig. 14 Comparative global behavior of the
unreinforced and retrofitted building
Table 1 Performance Objective
PL/IMR 30 y 50 y 100 y 225 y 475 y 975 y
PGA 0.072g 0.168g 0.24g 0.288g 0.36g 0.48g
IO x
LS x x x x
CP x
Such a matrix can be calibrated for other type of
seismic motion, too.
However, to validate the equivalent material
simplifications made in this case for global analysis
it is needed to extract the areas of important plastic
strains concentration and to perform, using the
advanced numerical model [17], a new local
analysis of, respecting the geometry and boundary
condition.
0
1000000
2000000
3000000
4000000
0 5 10 15 20 25 30 35 40
Displacement (mm)
Load (N)
Middle
Corners
Fig. 15 The behavior curves for the two retrofitting
possibilities
4 Concluding remarks The present paper proposed a “numerical experi-
mentation” procedure to analyses and evaluate the
behavior of the masonry structures retrofitted by
metallic plates on base of performance criteria.
In the first step of the procedure, a stable a robust
FE Model able to replicate the experimental ob-
Proceedings of the 3rd WSEAS Int. Conference on FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS
ISSN: 1790-2769 268 ISBN: 978-960-474-180-9
served failure mode and global behavior was build
[17].
In second step, numerical simulations of wall
panel unreinforced and reinforced masonry
considering the real mechanical characteristic was
done; the main advantages and benefits of the
strengthening solution and acceptance criteria for
the retrofitted elements have been obtained.
In the third step, equivalent materials that repli-
cate the numerical results need to be determined.
This approach allows for performing global analysis
on real façade or entire buildings and asses the dam-
age at a certain seismic demand using a non-linear
evaluation method, based on the acceptance criteria
previously established.
In the fourth step, the validation, the most critical
areas of the building must be selected to verify the
local behavior introducing relevant continuity con-
ditions and using the calibrated model in step one.
The retrofitting solution has showed a god behav-
ior being able to preserve the initial capacity simul-
taneous by allowing for considerable ultimate dis-
placement of approximate 0.7% drift ratio, which
corresponds to collapse prevention level of the
building.
Acknowledgments
This experimental work was carried out in the
CEMSIG Laboratory and Laboratory of Department
of Civil Engineering from the “Politehnica”
University of Timisoara.
The applied strengthening technique of masonry was
developed within PROHITECH (FP6 INCO-CT-
2004-509119/2004).
The masonry structure have been proposed and
analyzed as benchmark building in the frame of
RFSR-CT-2007-00050 STEELRETRO.
References:
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Proceedings of the 3rd WSEAS Int. Conference on FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS
ISSN: 1790-2769 269 ISBN: 978-960-474-180-9