finite element performance based evaluation of seismically ... · finite element performance based...

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


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


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


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-


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:

[1] Applied Technology Council (ATC), Evaluation

of Earthquake damaged concrete and masonry

wall buildings-FEMA-307, 1998;

[2] Applied Technology Council (ATC), Repair of

earthquake damaged concrete and masonry wall

buildings FEMA-308, 1998;

[3] Applied Technology Council (ATC),

Prestandard and commentary for seismic

rehabilitation of buildings. FEMA-356, 2000;

[4] ABAQUS Version 6.6 Documentation, 2006;

[5] Dogariu A., Stratan A., Dubina D., Gyorgy-

Nagy T., Daescu C., Stoian V., Strengthening of

masonry walls by innovative metal based

techniques COST 26, pp. 201-210, ISBN 978-

80-01-03583-2, 2007;

[6] Dogariu A., Dubina D. & Campitiello F., De

Matteis G., FEM Modeling Masonry Shear Walls

strengthened with metal sheathing - datasheet

no. 2-21 - COST 26, 2008;

[7] Dogariu A. Seismic retroffiting techniques based

on metallic materials of RC and/or masonry

building, PhD Thesis, ISBN 978-973-625-849-7;

2009;

[8] Dogariu A., Dubina D. & Campitiello F.,

DeMatteis G. Experimental based calibration of

a FE Model for Numerical Analysis of Masonry

Shear Panels strengthened by Metal Sheathing

PROHITECH09, pg. 1133-1138, ISBN 978-0-

415-55803-7, 2009;

[9] Dubina D., Dogariu A., Stratan A., Stoian V.,

Nagy-Gyorgy T., Dan D., Daescu C. Masonry

wall strengthening with innovative metal based

techniques –ICSCS07, Manchester – pp. 1071-

1077 – ISBN 978-0-415-45141-3; 2007;

[10] EN1998 - Design of structures for earthquake

resistance, 2005,

[11] Fajfar P., EERI M., A Nonlinear Analysis

Method for Performance Based Seismic Design,

Earth. Spectra, Vol.16, No.3, pp.573-592, 2000;

[12] FIB, Seismic assessment and retrofit of

reinforced concrete buildings – no. 24, 2003;

[13] Nardini L., Braconi A., Osta A. & Salvatore

W., RFCS STEELRETRO report –Definition of

the masonry benchmark building for the

execution of comparative performance analyses

between steel intervention techniques, 2008;

[14] O.P.C.M. 3431/2005 – Technical Italian

Standards for Design, Seismic Assessment and

Retrofitting of Buildings, 2005;

[15] P100-3/2005. Seismic design code – Part 3:

Rules for evaluation and retrofitting of buildings

(in Romanian), 2005;

[16] Dogariu A., Dubina D Performance Based

Seismic Evaluation of a Non-Seismic Masonry

Building of Metal Sheathed Walls –Part I: PBSE

and intervention strategy & Part II: Study case

PROHITECH09, pp. 1009-1014, 1015-1020,

ISBN 978-0-415-55803-7, 2009;

[17] Dogariu A., Dubina D. & Campitiello F.,

DeMatteis G. Experimental based calibration of

a FE Model for Numerical Analysis of Masonry

Shear Panels strengthened by Metal Sheathing,

the 3rd WSEAS Intern. Conf. F-and-B’10, 2010;


ISSN: 1790-2769 269 ISBN: 978-960-474-180-9

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