SEISMIC VULNERABILITY OF MASONRY INFILLED REINFORCED CONCRETE FRAMES Marin Grubišić a, Vladimir Sigmund b a
b
Ph.D. Student, Full Professor, Faculty of Civil Engineering, J.J. Strossmayer University of Osijek, Crkvena 21, 31000 Osijek, Croatia,
[email protected]
1. Abstract This study assesses the seismic vulnerability of ductile reinforced concrete frames with masonry infill walls, utilizing nonlinear dynamic analysis of building models. The evaluation is based on structures designed and detailed according to Eurocodes. The research quantifies the effect of presence and configuration of masonry infill walls on the seismic collapse risk using Incremental Dynamic Analysis within the performance-based framework. Seismic vulnerability assessment indicated that of the configurations considered (bare, partiallyinfilled and fully-infilled frames), the fullyinfilled frame had the lowest collapse risk and the bare frame is found to be the most vulnerable to earthquake-induced collapse.
2. Introduction Reinforced concrete frame buildings with masonry infill walls are widely constructed for commercial, industrial and multi-family residential uses in seismic prone regions in Southern Europe. A masonry infill wall panel typically consist of clay brick or concrete block walls and is constructed after the reinforced concrete frame has been finished.
Figure 1. Mechanisms of response and seismic loads transmission for moment resisting bare frame and masonry infilled frame.
These panels are generally not considered in the design process and are treated as architectural (non-structural) components. Their presence increases structural strength and stiffness, but at the same time diminishes ductility and introduces brittle failure
mechanisms associated with the wall failure and wall-frame interaction.
Figure 2. Schematic depiction of the use of inelastic analysis procedures to estimate forces and deformations for given seismic ground motions [ATC-55, FEMA 440, 2005].
The study presented in this paper compares seismic vulnerability of reinforced-concrete frame structures with- and without infill. An incremental nonlinear dynamic analysis of the model planar reinforced-concrete frames exposed to a set of recorded ground motions was performed in order to evaluate their seismic vulnerability.
3. Model Buildings Model structures used for the analysis were based on a 7-storey reinforced concrete middle frame of the regular low-rise "Tsukuba" building with different infill configurations as presented in Figure 3.
Model (1)
Model (2)
Model (3)
Figure 3. Middle frame models of the "Tsukuba" building with different infill configurations [Grubišić, M., Sigmund V., 2011].
Reinforced concrete frame elements were designed according to the EC8 and were the same in all three models (1) bare frame; (2) middle bay is full-height infilled with masonry
and (3) all three bays are fully-infilled with masonry. Bay spans were 6m, 5m and 6m and story heights were 3,75m in the first- and 3m in all other stories. Slabs were 18cm thick, columns were 50/50cm and beams were 30/50cm. Slab contribution is modelled by modelling the beams as T–sections. The materials used were C30/37, f ck =30 MPa concrete, and B500B, f yk =500 MPa reinforcing bars. The reinforcedconcrete frames were designed for standard vertical and seismic loads with a g =0,3g as required by Eurocodes.
compressive strength). The width of the masonry infill was 25cm and the thickness of mortar joints was 1cm. These properties represented a medium strength masonry infill as is commonly used. The masonry compressive strength was f m =3,5 MPa and its Young’s modulus was E m =2000 MPa.
4. Nonlinear Models Dealing with the vulnerability assessment of reinforced concrete frame structure, with- and without infill walls, both simplicity and reliability were targeted as fundamental properties of the numerical model. The regularity of building in terms of mass and stiffness in plan and elevation enables a 2D analysis to be used when assessing its seismic response and in this study, the building was modelled as 2D planar frame with lumped masses. Seismic risk of the models was evaluated by probabilistic analysis that takes into account the randomness in seismic excitations and evaluates the probability of crossing a certain critical state (Performance State). An Incremental Dynamic Analysis (IDA) of the nonlinear analytical models was performed using the SeismoStruct ver. 5.2.2. software.
Figure 4. Plan view and middle frame extracted and later set as 2D models of the "Tsukuba" building [Grubišić, M., Sigmund V., 2011].
For dynamic analysis masses were concentrated at the nodes. The weight of structural members was included, but without masonry infill to maintain the same total mass and observe the impact of masonry infill to the seismic vulnerability of structure.
Reinforced-concrete frame elements were modelled as inelastic displacement-based fiber elements and infill walls were modelled as inelastic infill panel element [Kalman Šipoš, T., Sigmund, V., 2010]. At low levels of lateral force, frame and infill wall act in a fully composite fashion. As the lateral force level increases, the frame attempts to deform in a flexural mode while the infill attempts to deform in a shear mode.
Figure 5. Typical slab-beam T-sections of reinforced concrete frame, in the middle and at the support, and the corresponding column cross section.
Masonry material properties for walls were based on data from the experiments of medium strength hollow bricks and mortar type “O” (1:1:5 ratios of cement, lime and sand, with relatively low
Figure 6. Nonlinear analysis model for RC frame building with masonry infill walls [Grubišić, M., Sigmund V., 2011].
Result is a frame and infill separation at the corners of tension diagonal and diagonal compression with the effective width lower than that of the full panel.
Nonlinear hysteresis steel model proposed by Menegotto-Pinto (1973) was used for the longitudinal reinforcement (Figure 9a) and concrete was modelled by Mander (1988) concrete model (Figure 9b).
a)
b)
Figure 9 a, b. General characteristics for nonlinear cyclic behaviour of a) steel [Menegotto-Pinto, 1973] and b) confined concrete [Mander, J.B., 1988]
Figure 7 a, b. Masonry panel elements containing nonlinear truss and shear mechanism [SeismoSoft, 2002].
Modal and inelastic time history analyses of the infilled-frame structures should be based on the structural stiffness after separation. Stiffness properties of the infill were obtained using the equations equation adopted in FEMA guidelines. 1
E ⋅ t ⋅ sin 2θ 4 λ1 = m inf 4 ⋅ Ec ⋅ I col ⋅ hinf a= 0,175 ⋅ ( λ1 ⋅ hcol )
−0,4
h θ tg −1 ⋅ inf = Linf
⋅ rinf
Bazzuro and Cornell (1994) suggested use of five to seven input ground motions for representing the hazard in an uncoupled analysis, but Dymiotis (1999) stated that three ground motions were sufficient if appropriate records and scaling were made. Since greatest uncertainties lie in ground motion records we used a set of ten ground motion records as shown in Figure 10 represented by the response spectra. They all belong to ground motions with magnitudes of 6.3–7.7 (Kobe, Loma Prieta, NorthRidge, Imperial Valley, Kocaeli, Chi Chi, Emeryville, Friuli, Corralitos and one Artificial) that effectively represented the scenario earthquakes.
(1)
(2) (3)
The nonlinear model for masonry was used as proposed by Crisafulli (1997). The stressstrain relation of the hysteric model is shown Figure 8. Figure 10. Inelastic 5% damped response spectra of ten ground motion records, matched with EC8 target spectrum type 1, soil C and PGA 0,3; compared with the mean spectrum [Grubišić, M., Sigmund V., 2011].
The set of normalised earthquake records was individually applied to structural models. Records were scaled in an increasing intensity (Incremental Dynamic Analysis, IDA) until the structural failure occurred. Structural behaviour Figure 8. General characteristics for nonlinear cyclic axial behaviour of masonry [Crisafulli 1997].
was evaluated based on the recorded Interstorey Drift Ratio (IDR or θ max ). The IDA curves were generated in a way of matching the points of the maximum peak interstorey drift ratio, θ max , with the corresponding ground motion intensity level measured by 5% damped first-mode spectral acceleration S a (T 1 ,5%). It is important to emphasize that the Inter-storey Drift Ratio is associated to structural damage level defined as damage measure, DM, and Spectral acceleration is associated to intensity measure, IM. The nonlinear analysis was repeated for each incremental increase in the motion’s intensity until numerical non-convergence was encountered (indicating global dynamic instability, Figure 11).
5. Seismic Vulnerability Assessment Different analytical methods for deriving a vulnerability relationship for masonry infilled reinforced concrete buildings are existing. We used a method of deriving vulnerability curve functions (expressed as lognormal functions) by estimating them directly from the seismic response by Incremental Dynamic Analysis that represent cumulative probability of reaching or exceeding predefined structural (or non-structural) limit states. In other words, statistical analysis used here was done by simply empirical account of how many timehistory records will collapse the building or reach limit state at the certain spectral acceleration. Vulnerability curves for civil engineering structures play an important role in seismic vulnerability and hazard assessment, which are essential for purposes of response planning. These curves take into account the variability and uncertainty associated with capacity curve properties, limit states and ground shaking. The vulnerability curves, later termed as fragility curves thus provide a graphical representation of the seismic vulnerability of the building structure in statistical terms.
Figure 11. Relationship between IDA curves and the features of a typical force-displacement capacity boundary [ATC-55, FEMA 440A, 2005].
Various studies [ATC-55, FEMA 440A, 2005] have shown that nonlinear dynamic response is directly influenced by features of force-displacement capacity boundary (Figure 11). They both have the same initial linear stiffness for low levels of ground motion intensity and the area of softening is associated with regions of negative post-elastic stiffness until a collapse occurs. Four limit states: Slight, Moderate, Extensive and Complete could be defined on every IDA curve and summarized to produce the probability of reaching a specified limit state for the IM level. The final results are presented in a format that could be integrated with a conventional hazard (vulnerability curve) in order to calculate the annual rates of exceeding a certain limit state for a certain demand. Definition of the limit states is the most significant for constructing the vulnerability curves.
Figure 12. Example of fragility function showing intensity measure value with corresponding failure probability.
Discrete limit state probabilities that consider a level of structural damage were used as inputs for calculation and assessment of the seismic vulnerability. Conditional probability of being in, or exceeding, a particular limit state, given the spectral acceleration as intensity measure, IM, is defined by equation: ln IM − µ P ( LS | IM ) = Φ ⋅ σ
(4)
where Φ denotes the standard normal cumulative distribution function (Laplace integral, generally built-in function in spreadsheet), μ is the mean or expectation, and σ is standard deviation.
6. Results and discussion Model buildings had following first natural periods: T 1 =0.439s for Model 1, T 1 =0.195s for Model 2 and T 1 =0.151s for Model 3. The addition of infill walls produced a significant increase in the system’s stiffness. The influence of masonry infill walls on the structural capacity is obvious on the results of adaptive static pushover curves. Addition of infill walls in the reinforced-concrete frame brought an increase in initial stiffness, strength, and energy dissipation, provided that the frame is properly designed for avoidance of shear failure.
Model 1
a)
Model 2
b)
Model 3
c)
Figure 14 a, b, c. IDA results for 7-storey Models 1, 2 and 3 subjected to 10 earthquake records. [Grubišić, M., Sigmund V., 2011].
Figure 13. Static adaptive pushover curves of all three Models [Grubišić, M., Sigmund V., 2011].
Figure 13 shows that Model 2 has up to 80% (and Model 3 up to 285%) greater ultimate load capacity in regard to Model 1. After the diagonal compressive strut load capacity was reached the base shear capacity came down to that of a pure frame system. The IDA curves shown in Figures 14 a, b, c were not additionally smoothed and were left as original as possible to represent the behaviour of individual models under increasing ground motion acceleration. Due to variability of earthquake records a statistical treatment of multi-record IDA output is essential in order to summarize the results and use them in a predictive mode, as in Performance Based Earthquake Engineering (PBEE) context. Seismic vulnerability curves, created from the IDA, provide useful tools for evaluation of seismic structural behaviour and vulnerability.
Fragility curves became flatter as the limit state shifted from slight to complete because of the nature of statistical distribution of response data. Variability of Inter-storey drift at high ground motion intensity levels was more pronounced than at low intensity levels. The vertical distance between two adjacent fragility curves represents the probability or the structure being within lower of the two performance limit states under consideration following the design seismic event. Further, a steep rise in the fragility curve implies that the seismic vulnerability of the structure is highly sensitive to changes in the seismic demand. On the other hand, a more level or flat rise in the fragility curve represents superior seismic performance. The steep shape of the slight, moderate or extensive limit state curve was due to infill panels that dominated the response. This continued until the panels reached their deformation capacity. Afterwards the response was dictated by the bare frame system.
Model 1
a)
Model 2
b)
Model 3
c)
Figure 15 a, b, c. Fragility curves for 7-storey Models 1, 2 and 3 as assessment of the probability of reaching each limit state [Grubišić, M., Sigmund V., 2011].
The obtained fragility curves for all three models, as shown in Figures 15 a, b, c, predict the probability of reaching a certain performance level as a function of the ground motion intensity expressed by its spectral acceleration, for a particular structure. Performance levels were defined according to the IDR (Inter-story Drift Ratio %) as: Serviceability limit state (SLS) at IDR
