Jankowski 2007

Assessment of Damage Due to Earthquake-Induced Pounding

Between the Main Building and the Stairway Tower

Robert Jankowski1,a 1Faculty of Civil and Environmental Engineering, Gdańsk University of Technology,

ul. Narutowicza 11/12, 80-952 Gdańsk, Poland

aemail: [email protected]

Keywords: Damage assessment, structural pounding, earthquakes, damage model.

Abstract. The reports after earthquakes indicate that earthquake-induced pounding between

insufficiently separated structures, or their parts, may cause substantial damage or even lead to

structural collapse. One of the most spectacular example of pounding-involved destruction resulted

from interactions between the Olive View Hospital main building and one of its independently

standing stairway towers during the San Fernando earthquake of 1971. The aim of the present paper

is to assess the range and intensity of damage caused by collisions between these reinforced

concrete structures based on the results of a detailed 3D non-linear FEM analysis of pounding-

involved response. In the study, reinforced concrete has been modelled as layered material with

rebar elements embedded into concrete. The non-linear material behaviour, including stiffness

degradation of concrete due to damage under cyclic loading, has been incorporated in the numerical

model. The results of the study show that pounding may lead to the significant increase of the range

and intensity of damage at the base of the stairway tower, as a lighter structure, as well as may cause

substantial damage at the points of contact. On the other hand, the intensity of damage induced in

the heavier main building has been found to be nearly unaffected by structural interactions.

Introduction

Interactions between insufficiently separated buildings, or bridge segments, have been repeatedly

observed during earthquakes. This phenomenon, usually referred as the earthquake-induced

structural pounding, may result in substantial damage or even contribute to structural collapse [1].

The main factor recognised as a reason for interactions between buildings is usually the difference

in the natural vibration periods of adjacent structures resulting in their out-of-phase vibrations. On

the other hand, in the case of longer bridge structures, it is often the seismic wave propagation effect

(see [2]), that is a dominant factor leading to pounding of superstructure segments.

Earthquake-induced structural pounding has been recently intensively studied applying various

models of structures and using different models of collisions. The fundamental study on pounding

between buildings in series modelled by single-degree-of-freedom systems and using a linear

viscoelastic model of collisions has been conducted by Anagnostopoulos [3]. Jankowski et al. [4]

applied a similar approach to study interactions between superstructure segments in bridges. Further

analyses were carried out applying discrete multi-degree-of-freedom structural models [5] or using

simple linear FEM models [6]. In order to simulate impact force during collisions more realistically,

a non-linear elastic model following the Hertz law of contact has been adopted by a number of

researchers (see, for example, [7]). The more accurate non-linear viscoelastic pounding force model

has been also proposed and applied in the analysis [8,9]. In the case of these studies, however,

simple single-degree-of-freedom systems were used to model structural behaviour.

In spite of the fact that the research on earthquake-induced structural pounding has been recently

much advanced, the studies were often conducted on much simplified, one-dimensional structural

models, including linear simulation of structural response not allowing for modelling of any damage

during earthquake. Therefore, the aim of the present paper is to conduct a detailed 3D non-linear

FEM analysis of pounding-involved response of two structures with different dynamic properties

Key Engineering Materials Vol. 347 (2007) pp. 339-344online at http://www.scientific.net© (2007) Trans Tech Publications, Switzerland

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(mass, stiffness) in order to assess the range and intensity of damage caused by collisions. The

analysis concerns the case of pounding between the Olive View Hospital main building and one of

its independently standing stairway towers (tower C), which was observed during the San Fernando

earthquake of 1971 (see [10,11]).

Numerical model of colliding structures

Structural members of the Olive View Hospital main building as well as the stairway tower C were

constructed out of cast-in-place reinforced concrete. Modelling of this material is extremely

difficult, mainly due to highly non-linear behaviour of concrete and consideration of steel

reinforcement supplementing the composite system. In this study, reinforced concrete has been

modelled as layered material with rebar elements embedded into concrete. This approach allows us

to use two different constitutive laws for concrete and steel assuming that the strain compatibility

between both is maintained. Concrete itself is a structural material with dramatically lower strength

in tension than in compression, which shows highly non-linear stress-strain behaviour. It also

experience stiffness and strength degradation due to damage under large load reversals during cyclic

loading [12]. The assumed in the numerical model relation between stresses and strains under

uniaxial cyclic loading of concrete is shown schematically in Fig. 1.

εt

σcr

εcr

σcu

σcy

εcyεcu

0.2

εc

strain

stress

εcu4

σcu

Es

EEc

Et

Fig. 1. Stiffness degradation damage Fig. 2. FEM model of interacting stairway

model of concrete under cyclic loading tower and main building

Tensile loading of concrete leads to the formulation and propagation of cracks. Due to tension

softening, the material softens until there is no stress across the crack (decreasing branch in the

tensile stress-strain diagram of Fig. 1). The progressive tensile cracking leads to the degradation of

elastic stiffness due to damage. In the model considered, this degradation is expressed by the

formula defining the effective Young’s modulus as [13]:

( )cr s t cr

t

t

EE

σ ε ε

ε

− −= . (1)

where σ cr εcr are the critical cracking stress and strain, respectively, sE is a tension-softening

modulus and tε is a strain on the envelope curve at unloading (see Fig. 1). When the loading of

concrete is reversed for compression during cyclic loading, the crack closes and full compressive

stress-carrying capacity is assumed. After the compressive stress exceeds the elasticity limit, defined

by the yield stress, cyσ , the material hardens with a gradually decreasing slope of the stress-strain

curve until the ultimate compressive strength, cuσ , is exhausted (see Fig. 1). After passing this

Damage Assessment of Structures VII340

point, the stress-strain relation exhibits a downward slope, which is considered to be linear in the

model (see [14]) as shown in Fig. 1. Finally, the material loses its integrity and all load-carrying

capacity is lost. This point, referred to as crushing, is assumed to be reached at a strain of 4 cuε and a

corresponding stress of 0.2 cuσ [14]. The stiffness degradation in compression due to damage is

observed with increasing number of cycles beyond the peak stress, cuσ . In the model considered,

this degradation is expressed by the formula defining the effective Young’s modulus as [14]:

(3.8 0.8 )

3 (0.87 0.145 )

cu cu cc

c cu c

Eσ ε ε

ε ε ε

−=

−. (2)

Based on the tests conducted on concrete samples taken from the buildings of the Olive View

Hospital after the San Fernando earthquake (see [10,11] for details), the following values have been

determined and applied in the numerical analysis: 21.24 GPaE = , 35.85MPacuσ = , =σ cy

11.95MPa , =3.59 MPacrσ , 7.08 GPasE = (for all concrete, except for the ground and first storey

columns of the main building), 24.41GPaE = , 48.26 MPacuσ = , 16.09 MPacyσ = , σ =cr

4.83MPa , 8.14 GPasE = (for the ground and first storey columns of the main building).

A non-linear (elastoplastic) strain-hardening model has been used to simulate the behaviour of

reinforcing steel under cyclic loading. Based on the tests conducted on reinforcement samples taken

from the buildings of the Olive View Hospital after the San Fernando earthquake (see [10,11] for

details), the following values have been determined and applied in the numerical analysis:

200.64 GPaE = , 362.66 MPatyσ = , 548.13MPatuσ = (for all reinforcing steel, except for vertical

column reinforcement of the main building), 196.78 GPaE = , 494.35MPatyσ = , σ =tu

775.66 MPa (for vertical column reinforcement of the main building), where E, tyσ , tuσ are the

Young’s modulus, yield stress and ultimate tensile strength of steel, respectively. The detailed non-

linear tensile stress-strain relation for steel, used in the numerical model, corresponds to the

diagram, which has been obtained from the tests (see [10]).

The FEM MSC.Marc software has been employed for the purposes of the analysis of pounding-

involved response of structures under earthquake excitation. In the case of the main building,

similarly as in the analysis conduced by Mahin et al. [11], a model of isolated portion of the

structure (wing C model) has been considered in the study. All structural members, i.e. columns,

walls and slabs, of the main building and stairway tower have been modelled by four-node

quadrilateral shell elements with multiple integration points through the thickness. The details of

geometric properties have been specified according to the descriptions given in [10,11]. Pounding

between the stairway tower and the main building has been controlled by gap-friction elements

placed between the structures. These elements work in the way that, when contact is detected, the

gap is closed in the longitudinal direction and friction forces are imposed in the transverse and

vertical directions. The separation gap of 0.1016 m (4 inches) has been left between the structures

(see [10]). In the analysis, the friction coefficient of 0.5 has been applied. The FEM model of

interacting structures consisting of 11610 multi-layer shell elements is shown in Fig. 2.

Response analysis

The detailed 3D non-linear FEM analysis has been carried out using the model of interacting

structures from Fig. 2 in order to assess the range and intensity of damage caused by collisions. The

scaled N16°W, N74°E and UD components of the San Fernando earthquake of 1971 recorded at the

Pacoima Dam station (see [11] for details), have been applied along the longitudinal, transverse and

vertical direction, respectively. The pounding-involved structural response has been determined by

the use of the time-stepping Newmark method with the standard parameters: 0.5γ = and 0.25β = .

Key Engineering Materials Vol. 347 341

The use of FEM with the non-linear model of material behaviour allows us to precisely identify

places in the structures, where earthquake-induced damage occurs. According to the material model

incorporated, damage in the steel reinforcement takes place when the stress value exceeds the

yielding level in tension or compression (see [15]). On the other hand, damage of concrete is

considered, when the stress value exceeds the cracking level in tension or the yielding level in

compression [15]. The intensity of damage has been assessed by observing the levels of cracking

and plastic strains as well as by calculating the Park and Ang damage indexes (see [16] for details).

An example of damage to the points of contact between the stairway tower and the main

building, obtained as the result of the FEM analysis, is shown in Fig. 3. In particular, Fig. 3(a)

presents the plastic strains in concrete and Fig. 3(b) shows the plastic strains in the steel

reinforcement. It can be seen from the figure that it is only the stairway tower, which enters the

inelastic range in the vicinity of contact point as the result of collisions between structures. On the

other hand, Fig. 3 indicates that the stress values in the main building are not high enough to exceed

the yielding level (no plastic strains occur).

Damage at the base of the stairway tower for the pounding-involved response is shown in Fig. 4.

In particular, Fig. 4(a) presents the cracking strains in concrete, whereas Fig. 4(b) shows the plastic

strains in the steel reinforcement. The damage index (see [16]) for the pounding-involved response

of the structure has been calculated as equal to 1.16. In order to assess the influence of collisions on

the overall damage induced in the structure during earthquake, the corresponding results obtained

for the independent vibration response (assuming large separation gap between structures

preventing contacts) are also shown in Fig. 5. It can be seen from this second figure that the

allowable stress limits are exceeded in a number of places due to intensive ground motion excitation

alone (the damage index for the independent vibration response of the structure has been calculated

as equal to 0.83). The comparison between Fig. 4 and 5, as well as between the corresponding

damage indexes, indicates that structural pounding leads to the substantial increase of the range and

intensity of damage in the stairway tower.

Finally, an example of damage to the columns of the main building is presented in Fig. 6. The

figure shows the cracking strains in concrete (Fig. 6a) and the plastic strains in the steel

reinforcement (Fig. 6b) for the pounding-involved response (nearly identical results have been

obtained for the independent vibration response). It can be seen from the figure that the columns of

the structure experience substantial inelastic behaviour, especially at the bases. In the case of this

structure, however, the induced damage is mainly the effect of intensive ground motion excitation

and is nearly unaffected by collisions between structures (the damage indexes equal to 0.72 have

been calculated for both pounding-involved and independent vibration responses).

Conclusions

The range and intensity of damage caused by the earthquake-induced pounding between two

reinforced concrete structures (the main building and the stairway tower) have been assessed in this

paper. The investigation has been conducted based on the results of a detailed 3D non-linear

analysis of pounding-involved response of the structures under earthquake excitation.

The results of the study show that pounding may lead to the significant increase of the range and

intensity of damage at the base of the lighter stairway tower. It may also cause substantial damage at

the points of contact of this structure. On the other hand, the intensity of damage induced in the

heavier main building has been found to be mainly the effect of intensive ground motion excitation,

nearly unaffected by structural interactions. These results clearly indicate, that in the process of

design of pounding-prone buildings (for which collisions can not be prevented), a special attention

should be paid to the weaker (lighter) structure, for which structural interactions can be catastrophic.


a) plastic strains in concrete b) plastic strains in steel reinforcement

Fig. 3. Damage to the points of contact

a) cracking strains in concrete b) plastic strains in steel reinforcement

Fig. 4. Damage at the base of the stairway tower for pounding-involved response

(deformation factor: 50)


Fig. 5. Damage at the base of the stairway tower for independent vibration response


Key Engineering Materials Vol. 347 343


Fig. 6. Damage to the columns of the main building for pounding-involved response


Acknowledgments

The research was supported by the Ministry of Science and Higher Education of Poland through a

research project financed in the years 2006-2007 from the resources for science (contract no.

3004/T02/2006/31). This support is greatly acknowledged. Numerical calculations were carried out

at the Academic Computer Centre (TASK) in Gdańsk.

References

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[11] S.A. Mahin, V.V. Bertero, A.K. Chopra and R.G. Collins: EERC Report No. 76-22 (Earthquake

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[12] J. Lee and G.L. Fenves: J. of Engineering Mechanics Vol. 124 (1998), p 892.

[13] H.M. Farag and P. Leach: Int. J. for Numerical Methods in Engineering Vol. 12 (1996), p 2111.

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[15] M. Jirásek and Z.P. Bažant: Inelastic Analysis of Structures (John Wiley & Sons, UK 2002).

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Jankowski 2007