Models for the assessment of seismic vulnerability of old

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Models for the assessment of seismic vulnerability of old masonry buildings. Case

study of a “placa” building.

Pedro Gil Vasques Pombo1

1M. Sc. Student, Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049-001 Lisbon, Portugal;

[email protected]

ABSTRACT: In this document the main methods for the assessment of the seismic vulnerability of old

masonry buildings are briefly referred. Then, a “placa” building was modeled in software 3Muri/TreMuri

and nonlinear static analyses were performed aiming to assess its seismic performance. Some values

were set to materials’ mechanical properties and it was called as the reference case. For these values,

the dynamic characteristics of the building were analyzed and its seismic behavior (the capacity curve

and the damage distribution of two selected walls) were assessed. A sensibility study about the

influence of material’s mechanical properties in the seismic performance was carried out, taking into

account some changes for the properties of three types of masonry materials that belong to the

building. The influence of flexural behavior of the wooden floors in the structural seismic performance

was assessed. Finally, a comparison between capacity curves analytically derived and those

suggested by HAZUS was carried out.

KEY-WORDS: Seismic vulnerability, capacity curves, non-linear static analysis, masonry buildings

1. INTRODUCTION

To mitigate and prevent losses caused by an earthquake, seismic risk assessment should be carried

out. To assess the seismic risk of the building stock of an urban centre like the one that exists in

Lisbon, methods that allows assessing seismic vulnerability plays an essential role. In old south

european cities, the building stock is filled with many old masonry buildings. Lisbon has the so-called

“placa” building, a type of old masonry buildings which was studied in this work.

2. METHODS FOR THE SEISMIC VULNERABILITY ASSESSEMENT

Some approaches aiming to gather the methods for the assessment of seismic vulnerability into

different groups has been developed. These approaches assemble methods that share the same

characteristics. A most important criterion of distinguishing these approaches for old masonry

buildings, is whether the methods based on post-earthquake damage observation and expert

judgment or the ones based in mechanical models. In this work one of the approaches was selected; it

is the one that is divided into three groups, as shown in figure 1: empirical, analytical and hybrid.

mailto:[email protected]

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Figure 1 – Different groups of methods for the seismic vulnerability assessment

Reference is made to the most important methods for the assessment of seismic vulnerability of old

masonry buildings: a capacity spectrum-based method, HAZUS (FEMA, 2013), a fully displacement-

based method, MeBaSe (Restrepo-Veléz, 2003), two collapse mechanism-based method, VULNUS

(Bernardini et al., 1990) and FaMIVE (D’Ayala and Speranza, 2002; D’Ayala, 2005) and an empirical

method proposed by Vicente (2008). From the above mentioned methods, capacity curves for

unreinforced masonry buildings (URM) suggested by HAZUS were chosen to perform a comparison

with capacity curves derived analytically using Tremuri (Lagomarsino et al., 2012), as shown in section

3.6.

3. BUILDING STUDY CASE

The building studied is a “placa” building (“Rabo de Bacalhau” type) built in Rua Actor Isidoro (Lisbon)

in 1940. It is a four stories high building with a total height of 12.3 m and with in-plane maximum

dimensions 14.5 m x 20.5 m.

3.1 MODELING

Using software 3Muri commercial version (S.T.A. DATA, s.r.l., release 5.0.4) it was possible to create

a simplified model of the whole building taking into account the non linear behavior of all elements of

the structure – Figures 2 and 3.

Figure 2 – 3Muri model of the building (front façade) Figure 3 - 3Muri model of the building (back view)

There are four types of masonry’s materials for bearing walls, as shown in the figure 4.

Figure 4 – Location of different type of masonry (adapted form Monteiro and Bento, 2012)

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Table 1 shows the values of the mechanical properties of the masonry materials for reference case.

These values were defined by Milosevic et al. (2014).

Table 1 – Mechanical and geometrical properties of masonry materials for the numerical model (adapted from Milosevic et al., 2014)

Mechanical and geometrical properties

Thickness (m)

Young Modulus, E

(GPa)

Shear Modulus,

(GPa)

Comp.

Strength, (MPa)

Shear Strength,

(MPa)

Specific

Weight, (kN/m

3)

Rubble Stone Masonry 0,70 2,00 0,58

(0,44) 3,2 0,065 21,0

Concrete Block Masonry 0,20 2,00 0,74

(0,56) 3,7 0,210 14,0

Solid Clay Brick Masonry

0,20 1,5

(1,13) 0,50

(0,38) 3,2 0,076 18,0

Hollow Clay Brick Masonry

0,10 1,20

(0,90) 0,40

(0,30) 2,4 0,060 12,0

Note: for parameters that have more than a value, the one which is used on the model is the one between brackets

The building has two types of floors (concrete slab and wooden floor) and there is a reinforced

concrete frame in the back. Table 2 depicts the values of loads considered in the model and Table 3

the concrete and steel classes adopted. More details of geometrical properties and modeling

techniques can be found in Pombo (2014).

3.2 DYNAMIC CHARACTERISTICS OF THE BUILDING FOR REFERENCE CASE

The building’s dynamic characteristics for the reference case were assessed (Table 4). The first mode

of vibration is the fundamental translational mode in X direction, the second mode is the torsional

mode and the third one is the fundamental translational mode in Y direction.

Table 4 – Dynamic characteristics of the building (reference case)

Mode of Vibration

1st

2nd

3rd

T (s) 0.34 0.46 0.243

f (Hz) 2.94 4.064 4.114

Mass X (%) 71.80 13.20 3.97E-05

Mass Y (%) 1.74E-05 7.64E-04 85.28

3.3 CAPACITY CURVES FOR REFERENCE CASE

Using TreMuri research version (Lagomarsino et al., 2012), non-linear analyses were carried out and

capacity curves were derived, for the reference case. Those capacity curves were shaped as bilinear

capacity curves, as shown in figure 5. The building has higher seismic resistance in Y direction rather

Reinforced Concrete

Concrete Class C16/20

Steel Class A235

Gravity loads G (Variable loads Q) (kN/m

2)

Concrete slab Wooden floor

Floors 1.3 (2.0) 3.0 (2.0)

Staircase 1.3 (4.0) 3.0 (4.5)

Roof 1.9 (0.4)

Balcony 3.0 (2.0)

Table 2 - Loads for modeling floors (adapted form Milosevic et al., 2014)

Table 3 –Concrete and steel classes

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than in X direction. Furthermore when applied a triangular load pattern (for both directions) the

building has a higher ductility.

Figure 5 – Bilinear capacity curves (SDOF) for reference case

3.4 PARAMETRIC STUDY

A parametric study was carried out aiming to analyze the influence of the mechanical properties

values of the material in the seismic performance. Besides the reference case, six other cases were

considered by changing the values of materials’ mechanical properties for three types of masonry. It

was considered two cases for each material, an upper bound and a lower bound.

Table 5 - Acronyms that allows the identification of each case considered

Case Acronym

Rubble Stone Masonry Upper Bound

RS_UB

Rubble Stone Masonry Lower Bound

RS_LB

Concrete Block Masonry Upper Bound

CB_UB

Concrete Block Masonry Lower Bound

CB_LB

Solid Clay Brick Masonry Upper Bound SCB_UB

Solid Clay Brick Masonry Lower Bound SCB_LB

Each case uses exactly the same values set for the reference case (table 1) for every masonry

materials except for the material in case. For those, the values set are depicted in table 6, 7 and 8.

The values for both upper and lower bound are the maximum and minimum values suggested in

Italian Code (NTC, 2008) respectively, for each material.

For example, for RS_UB case the values for materials’ mechanical properties are the same as those

set in the reference case except the values for rubble stone masonry, which uses the values set in the

left side of table 6.

Table 6 – Values for both upper and lower bound case for rubble stone masonry

RS_UB Case RS_LB Case

Material Young

Modulus, E (MPa)

Shear Modulus, G (MPa)

Comp. Strength, fm (N/cm

2)

Shear Strength,

τ0 (N/cm2)

Young Modulus, E (MPa)



2)

Shear Strength,

τ0 (N/cm2)

Rubble Stone Masonry

1980 660 380 7,4 1500 500 260 5,6

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Table 7 – Values for both upper and lower bound case for concrete block

CB_UB Case CB_LB Case

Material Young

Modulus, E (MPa)



2)

Shear Strength,

τ0 (N/cm2)




2)

Shear Strength,

τ0 (N/cm2)

Concrete Block Masonry

3520 880 440 24,0 2400 600 300 18,0

Table 8 – Values for both upper and lower bound case for concrete block

SCB_UB Case SCB_LB Case

Material Young

Modulus, E (MPa)



2)

Shear Strength,

τ0 (N/cm2)




2)

Shear Strength,

τ0 (N/cm2)

Solid Clay Brick Masonry

1800 600 400 9,2 1200 400 240 6,0

3.4.1 CAPACITY CURVES AND SEISMIC PERFORMANCE

Bilinear capacity curves were derived to each case and the seismic performance were assessed.

Figure 6 – Bilinear capacity curves (SDOF) for each cases for uniform load pattern X direction

In table 9, 10, 11 and 12 the highest variation of capacity curves’ parameters between each case and

the reference case are presented.

Table 9 – Highest variation for capacity curve properties between reference and the other cases (Uniform load pattern X direction)

T* (s) µ* Fy* (kN) De* (m) Du* (m) Seism Type 1

Seism Type 2

Value for Reference Case

0.40 2.15 1369.31 0.0091 0.0196 0.0297 0.0157

Case which varies the most

SCB_UB SCB_UB RS_UB SCB_UB CB_UB SCB_UB SCB_UB

Value 0.36 2.57 1423.98 0.0076 0.0186 0.0257 0.0141

Variation (%) 10.0 19.6 4.0 17.0 4.8 13.1 9.9

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Table 10 – Highest variation for capacity curve properties between reference and the other cases (Uniform load pattern Y direction)


Seism Type 2


0,26 2,05 2778,37 0,0075 0,0153 0,0127 0,0103


SCB_UB CB_UB SCB_LB SCB_UB CB_UB SCB_UB SCB_UB

Value 0.23 2.87 2651.60 0.0058 0.0182 0.0100 0.0084

Variation (%) 13.2 40.4 4.6 22.6 18.5 21.8 18.7

Table 11 – Highest variation for capacity curve properties between reference and the other cases (Triangular load pattern X direction)


Seism Type 2


0.47 2.23 1277.79 0.0118 0.0264 0.0372 0.0186


SCB_UB RS_LB SCB_UB SCB_LB RS_LB SCB_UB SCB_UB

Value 0.44 2.57 1394.11 0.0127 0.0291 0.0333 0.0172

Variation (%) 7.5 15.1 9.1 7.3 10.3 10.6 7.5

Table 12 – Highest variation for capacity curve properties between reference and the other cases (Triangular load pattern Y direction)


Seism Type 2


0.30 2.37 2611.92 0.0095 0.0224 0.0162 0.0119


SCB_UB SCB_UB SCB_LB SCB_UB SCB_U

B SCB_UB SCB_UB

Value 0.27 3.29 2501.71 0.0076 0.0249 0.0133 0.0106

Variation (%) 11.3 38.8 4.2 20.2 10.8 17.9 11.3

In tables 9, 10, 11 and 12, the results for those different cases does not change significantly from each

other, which means the building is not quite sensitive to those mechanical properties changes. The

highest variations between reference case and the other cases occur to uniform load pattern in Y

direction. Furthermore, for both load patterns applied in X direction, the ultimate limit state is not

verified for any case once the displacement related to performance point is higher than the ultimate

displacement.

3.4.2 DAMAGE PATTERN

The damage patterns were analyzed for two specific walls, the front façade wall for seismic load

pattern applied in X direction and in a gable wall for Y direction (see Tables 13 and 14). For the first

one, the damage pattern were analyzed just for the ultimate displacement (Du) while for the gable wall

the damage pattern were analyzed for both displacement related to the performance point (D) and

ultimate displacement (Du).

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Figure 7 - TreMuri's color scale for damage patterns

Table 13 – Example of damage patterns in front façade wall for ultimate displacement (uniform load in X direction)

Reference Case RS_UB RS_LB

Du

There is not a great difference of damage patterns between uniform and triangular load patterns for

ultimate displacement (Du). For uniform load pattern, front façade wall shows a “soft storey” failure at

ground level due to flexural and shear failure of piers (vertical elements) to ultimate displacement. On

the other three levels, while most of the piers are in flexural plastic phase (especially in the last level)

the lintel beams are in shear plastic phase. The lintel beams at ground level are non-reactive elements

once they reach tensile failure just for gravity loads. In general, for triangular load pattern there is an

increasing of flexural failure of piers and a non-reactive element rather than flexural failure behavior of

one pier located on the ground level.

BB_LS BB_LI TM_LS TM_LI

Du

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Table 14 – Example of damage pattern for reference, RS_UB and RS_LB Cases (triangular load)

Reference Case RS_UB RS_LB

D

Du

In most cases, for uniform load pattern the gable wall is just in flexural plastic phase at the ground

level and in a pier at the last storey, for the displacement related to performance point (D). For ultimate

displacement (Du) the largest pier at ground level is in a shear plastic phase while two piers (one at

the ground floor and the other at the last floor) are still in flexural plastic phase. For triangular load

pattern and displacement D the damage pattern of the gable wall is the same described for uniform

load pattern. In most of the cases, when considering the ultimate displacement (Du) for the triangular

load the damage patterns remains the same that was observed to the displacement (D) except for

CB_LB and for SCB_UB. In the first case, besides the damage pattern shown to the other cases

there’s another pier that reaches flexural plastic phase and there’s a changing to shear failure at the

largest pier of ground level rather than a flexural plastic phase. In the second one beyond the damage

pattern observed for most of the cases there’s a worsening in three other piers (two of them are in the

flexural plastic phase and the other reaches shear plastic phase).

3.5 RIGID FLOOR

For both load patterns (uniform and triangular) and for every case the displacement related to

performance point (D) in X direction is higher than ultimate displacement (Du), taking into account

earthquake type 1 by means of elastic response spectrum, as suggested in EC8 (CEN, 2004). It

means that the building does not verify ultimate limit state in X direction and hence does not verify

ultimate limit state globally. Aiming to overcome this problem a new case was set, the rigid floor case.

With this case study, the influence of flexural behavior of the wooden floors in the structural seismic

performance was assessed. To this end, Shear Modulus (G) was increased, aiming to model the floor

rigid in its own plan, and then capacity curves were derived. As it can be seen in figure 8, for both load

patterns (uniform and triangular) there are just slight differences between the reference case and rigid

floor case. In spite of a slight reduction of the displacement related to performance point, a slight

reduction of the ultimate displacement occurred as well and the ultimate limit state still does not verify.

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In fact, the results obtained to this new case show that this building is not very sensitive to the floor

behavior.

Figure 8 – Capacity curves (MDOF) for both Reference and Rigid floor cases in X direction

3.6 COMPARISON OF CAPACITY CURVES

Finally, a comparison between capacity curves analytically derived and those suggested by HAZUS

was carried out. As shown in figures 9, 10, 11 and 12, capacity curves suggested by HAZUS for

URMM fit better to the X direction (both uniform and triangular load) analytical derived capacity curves.

On the other hand, capacity curves suggested by HAZUS for URML are more appropriate to the Y

direction (both uniform and triangular load) analytical derived capacity curves. Also, this comparison

shows that Hazus methodology considers that Unreinforced Masonry Buildings has much more

ductility than analytically derived curves reveals to have for this type of old masonry building.

Figure 9 – Bilinear capacity curves X direction uniform load (SDOF)

Figure 10 – Bilinear capacity curves Y direction uniform load (SDOF)

Figure 11 – Bilinear capacity curves X direction triangular load (SDOF)

Figure 12 – Bilinear capacity curves Y direction triangular load (SDOF)

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4. CONCLUSIONS

The non-linear analyses performed show the building does not verify the ultimate state limit for

earthquake type 1 (as suggested by EC8) in X direction for any case study (neither for the first seven

cases nor for rigid floor case) and for both load pattern. It means the building is globally unsafe for

ultimate state limit.

The building shows neither much sensitive to the changing of the values of materials’ mechanical

properties nor for the case of rigid floor in place of wooden floor.

HAZUS method considers that URM buildings have much more ductility than the analytically derived

curves reveals to have. The capacity curves for the studied building analytically derived in X and Y

direction fit better to URMM and URML capacity curves suggested by HAZUS, respectively.

5. REFERENCES

Bernardini, A., Gori, R. and Modena, C. (1990). “An Application of Coupled Analytical Models and

Experiential Knowledge for Seismic Vulnerability Analyses of Masonry Buildings”, in: Engineering

Aspects of Earthquake Phenomena (ed. A. Koridze), Omega Scientific, Vol. 3, pp. 161-180, Oxon,

U.K.

CEN (2004). “Eurocode 8: Design of structures for earthquake resistance - Part 1: General rules,

seismic actions and rules for buildings”, European Committee for Standartization, Bruxels, Belgium.

D'Ayala, D. (2005). "Force and Displacement Based Vulnerability Assessment for Traditional

Buildings". Bulletin of Earthquake Engineering. Vol. 3, No. 3, pp. 235-265.

D'Ayala, D. e Speranza, E. (2002). "An integrated procedure for the assessment of seismic

vulnerability of historic buildings". em: 12th European Conference on Earthquake Engineering, paper

No. 561.

FEMA (2013). “HAZUS-MH 2.1 Technical Manual”, Federal Emergency Management Agency,

Washington, DC, U.S.A.

Lagomarsino, S., Penna, A., Galasco, A. e Cattari, S. (2012). TREMURI program: Seismic Analyses of

3D Masonry Buildings, Release 2.0. University of Genova, Italy.

Milosevic, J., Bento, R. e Cattari, S. (2014). “Seismic assessmnet of a “Placa” building in Lisbon”,

Second European Conference of Earthquake engineering and seismology, Istambul, Turkey.

Monteiro, M. and Bento, R. (2012). “Seismic Assessment of a ’Placa Building”, ICIST Report, DTC nº

20/2012.

NTC (Norme Tecniche per le Costruzioni) (2008). “Italian Technical Code. Decreto Ministeriale

14/1/2008 Official Bulletin No. 29 of February 2008”, (in Italian).

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Pombo, P. G. V. (2014). “Modelos para a avaliação de vulnerabilidade sísmica de edifícios antigos de

Alvenaria. Aplicação de um modelo a um edifício de “placa”.”, MSc. Dissertation, Instituto Superior

Técnico, University of Lisbon, Lisbon (in Portuguese).

Restrepo-Veléz, L.F. (2003). “A simplified Mechanics-Based Procedure for the Seismic Risk

Assessment of Unreinforced Masonry Buildings”, PhD Thesis, European School for Advanced Studies

in Reduction of Seismic Risk (Rose School), Pavia, Italy.

S.T.A. DATA (2012). 3Muri Program, Release 5.0.4 (www.3muri.com).

Vicente, R. (2008). “Estratégias e Metodologias para intervenções de reabilitação urbana – Avaliação

da vulnerabilidade e do risco sísmico do edificado da Baixa de Coimbra”, PhD Thesis, Universidade

de Aveiro, Portugal (in Portuguese).

http://www.3muri.com/

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Models for the assessment of seismic vulnerability of old