Seismic fragilities of non-ductile reinforced concrete frames with consideration of soil structure interaction

Soil Dynamics and Earthquake Engineering 40 (2012) 78–86

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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn

Seismic fragilities of non-ductile reinforced concrete frames with consideration of soil structure interaction P. Rajeev a, S. Tesfamariam b,n a b

Dept. of Civil Engineering, Faculty of Engineering, Monash University, Clayton Campus, Vic 3800, Australia School of Engineering, The University of British Columbia, Okanagan, 3333 University Way, Kelowna, BC, Canada V1V 1V7

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 January 2011 Received in revised form 12 May 2011 Accepted 26 April 2012 Available online 29 May 2012

Seismic fragilities of buildings are often developed without consideration of soil-structure interaction (SSI), where base of the building is assumed to be fixed. This study highlights effect of SSI and uncertainty in soil properties such as friction angle, cohesion, density, shear modulus and Poisson’s ratio and foundation parameters on seismic fragilities of non-ductile reinforced concrete frames resting in dense silty sand. Three-, five-, and nine-storey three-bay moment resisting reinforced concrete frames resting on isolated shallow foundation are studied and the numerical models for SSI are developed in OpenSees. Three sets of 10 ground motions, with mean spectrum of 100, 500, and 1000 yr return period hazard level (matching EC-8 design spectrum), are used for the nonlinear time history analyses. An optimized Latin Hyper Cube sampling technique is used to draw the sample of soil properties and foundation parameters. The fragilities are developed for the fixed base model and SSI models. However, the fragilities that incorporate the soil parameter and foundation uncertainties are only slightly different from those based solely on the uncertainty in seismic demand from earthquake ground motion, suggesting that fragilities that are developed under the assumption that all soil and foundation parameters at their median (or mean) values are sufficient for the purpose of earthquake damage or loose estimation of structures resting on dense silty sand. But the consideration of the SSI effect has the significant influence on the fragilities compare to the fixed base model. The structural parameter uncertainty and foundation modeling uncertainty are not considered in the study. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Soil-structure interaction Uncertainty Optimized Latin Hyper cube Fragility curves

1. Introduction Fragility theory is a generalized branch of structural reliability that is used to asses vulnerability of a structure subject to external perturbation. Seismic fragilities of buildings are often developed without consideration of soil-structure interaction (SSI). Response of structures subject to earthquake induced ground shaking, however, introduces demand in shear and moment at the foundation system, which can induce foundation displacements and rotations [14]. Ignoring foundation deformations in such cases results in undermining dynamic properties of the building (e.g. fundamental mode period, damping ratio, etc.) (e.g., Refs. [48,43]). Incorporation of SSI on seismic response of structures is often done by modifying fixed-base building period and damping ratio for the effects of foundation compliance [19,47,48]. SSI is an important issue, especially for stiff and large structures constructed on a

n

Corresponding author. Tel.: þ1 250 807 8185. E-mail addresses: [email protected] (P. Rajeev), [email protected] (S. Tesfamariam). 0267-7261/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.soildyn.2012.04.008

relatively soft ground (e.g. 44,30,29). The problem is even more pronounced when nonlinear behavior of the superstructure is considered. For example, structural yielding increases the flexibility of the system and thus, assists the beneficial role of SSI [10,46]. In contrast, it is also argued that the ductility demand may increase significantly due to the impact of foundation flexibility [15,26,49]. Myat [28] studied the seismic performance of strip foundation for low-rise buildings with shear wall and showed that the axial forces, shear forces and bending moments of the shear walls are considerably larger for SSI case than for the fixed base case. Dutta et al. [12] showed that the SSI can increase the seismic base shear of low-rise building frames. However, seismic response generally decreases due to the influence of SSI for medium to high rise buildings. The study also shows that this effect may strongly be influenced by the frequency content of the earthquake ground motion. There are few reported studies that showed insignificance of SSI when inelastic response of the superstructure is considered [3,41]. Moghaddasi et al. [27] showed that the SSI effects on the median seismic response of structures exhibiting nonlinear behavior are relatively small, and the amplification of structural displacements due to SSI effects is more significant for structures exhibiting nonlinear behavior.

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Different authors have studied stochastic models to quantify impact of SSI on seismic demand (e.g., Refs. [42,39,23,6,20,27]). Sa´eza et al. [42] have numerically modeled structural response variability by considering SSI and they showed that reduction in the structural response in comparison with fixed base model. Raychowdhury [39] studied the seismic response of stiff and flexible low-rise moment resisting steel frames considering variability in soil properties and model (linear and non-linear soil behviour). The author showed that, uncertainty in soil properties may result in significant response variability, especially if the foundation is heavily loaded and the structure is relatively stiff. Also, for elastic and nonlinear SSI models, variation of the soil properties showed, respectively, no significant and significant contribution on response of the structures. However, the study is limited to the parameter considered (i.e., soil type, ground motion, and structure). In Lutes et al. [23], SSI is studied in frequency domain considering the soil and structural uncertainty. The authors showed that non-negligible uncertainties in soil or the superstructure may lead to significant uncertainty about the spectral density of the structural response near the resonant frequencies of a model incorporating SSI. The problem is further compounded due to inherent uncertainties arising from structural, soil material properties, modeling of foundation elements, and magnitude of seismic loads [42,27]. Sa´eza et al. [42] concluded that the inelastic SSI could increase or decrease the seismic demand depending on the type of structure, the input motion characteristics and the dynamic soil characteristics. However, further investigations in this way will be needed in order to obtain more general conclusions for diverse structure and soil typologies. Moghaddasi et al. [27] reports that the amplification of structural displacement due to SSI effects is more significant for structures exhibiting nonlinear behavior. Considering all these somewhat contradictory findings, further studies are needed to rigorously evaluate the SSI effects on seismic demand of structures, with varying building height.

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In this study, the effect of soil parameter uncertainty coupled with foundation dimension variability on probabilistic seismic fragilities is investigated. Three-, five-, and nine-storey three-bay non-ductile reinforced concrete (RC) moment resisting frame buildings are selected in order to cover the low- to high-rise building. The foundation is modeled using Winkler-based approach developed in Ref. [16]. Hazard uncertainty is also considered by assuming an ensemble of 30 recorded ground motions at three different hazard levels (100, 500 and 1000 yr return period). The combined effects of the different uncertainties in seismic fragility are modeled using optimized Latin Hypercube sampling technique. Comparison in the response of fixed base and flexible base structure is presented. Finally, the fragility bounds are developed to provide a sense their accuracy.

2. Building design consideration Three-, Five-, and nine-storey three-bay RC frame structures are employed to illustrate the effects soil and foundation uncertainty in seismic fragilities assessment (Fig. 1). The building is designed for gravity loads and a nominal lateral load of 8% of its weight according to an ‘‘old’’ seismic code. The reinforcement details attempted to mirror the practices used in southern European countries in the 1950s; the columns were non-ductile, smooth reinforcing bars were used, and capacity design principles were not considered. The structure is assumed to be rested on isolated footings (Fig. 2a). The soil beneath the footings is considered dense silty sand.

3. Finite element modeling Finite element analysis of the frame and foundation is performed using OpenSees finite element analysis package [25]. Finite element modeling details of the RC frames and foundation are provided below.

Fig. 1. Building configuration, (a) 3-storey, (b) 5-storey, and (c) 9-storey.

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Fig. 2. Schematic diagram of (a) superstructure-foundation system, (b) BNWF model and corresponding springs, and (c) hysteretic behavior of BNWF model springs (adapted from [39]).

3.1. Reinforced concrete frames Beam and columns are modeled as nonlinear beam-column elements with hinges. P–D effect is considered. Tangent-stiffness proportional damping has been used, which are calibrated to yield a 5% equivalent viscous damping ratio on the first elastic mode. Concrete behavior is modeled by a uniaxial Kent–Scott– Park model (Concrete01) with degrading, linear, unloading/reloading stiffness according to the work of Karsan-Jirsa [22] without consideration of tensile strength. For the confined concrete, the strength and strain values have been increased according to the formulae developed by Mander et al. [24]. Steel behavior is represented by a uniaxial Giuffre–Menegotto–Pinto model (Steel02). 3.2. Foundation models Numerous studies have been conducted to model the behavior of structures supported on shallow foundations [9,31,14,1,32,34,16,8]. The Beam on Nonlinear Winkler Foundation (BNWF) approached is often used to model interaction between the shallow foundation and soil interface [40,37]. BNWF models can capture the rocking, sliding, and permanent settlement of the footing through the nonlinear and inelastic soil behavior. The nonlinearity is manifested from moment-rotation, shear-sliding, or axial-vertical displacement modes and also by development of gaps during cyclic loading. It also captures hysteretic energy dissipation through these modes and can account for radiational damping at the foundation base. Radiation

damping is accounted for through a dashpot placed within the farfield elastic component of each spring. The BNWF model has the capability to provide larger stiffness and finer vertical spring spacing at the end regions of the footing such that the rotational stiffness is accounted for. The limitations of the BNWF model are (1) vertical and lateral capacities of the foundation are not coupled, and (2) individual springs along the base of the footing are uncoupled. This means that the response of one spring will not be influenced by the responses of its neighboring springs. Despite this limitation, Raychowdhury and Hutchinson [40] have stated that the model shows good prediction of experimentally observed behavior of shallow foundation. The schematic diagram of shallow foundation and its BNWF model is given in Fig. 2a and b, respectively. The vertical and rotational behavior of the footing is controlled by vertical q–z springs spaced in specified intervals (le), and two lateral springs, p–x and t–x, intended to capture passive and sliding resistance of the footing, respectively (Fig. 2b). The constitutive relations for the q–z, p–x and t–x springs are represented by nonlinear backbone curves that have been calibrated against shallow foundation tests (Fig. 2c) [39]. In OpenSees framework, respectively, the models are named as QzSimple2, PxSimple1 and TxSimple1 material models [25,39,5]. The q–z captures the axial and rotational behavior of shallow foundation (has asymmetric hysteretic response); the p–x captures passive resistance (has pinched hysteretic behavior) and the t–x captures the frictional resistance at the base of the footing (has higher initial stiffness and broad hysteresis). These material models are constructed modifying the

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pile-calibrated backbone curves [4,5]. More details about the BNWF and corresponding governing equations can be found in Ref. [39], for brevity, they are not repeated here. The dynamic response of a shallow foundation is controlled by the input parameters of the soil properties and the dimension of the footing. It is evident that the cohesion, friction angle and unit weight control the strength of the nonlinear springs without affecting the initial spring stiffness and shear modulus, and Poisson’s ratio control the initial stiffness of a nonlinear spring with no effect on the ultimate force capacity. On the other hand the length, height and depth of foundation have the effect on both strength and stiffness. Distributed stiffness intensity along the length of the foundation is provided in the BNWF model. The ratio of end stiffness intensity to mid stiffness intensity is considered five, while the length of increased stiffness region is assumed to be 10% of the footing length based on the recommendations of Harden et al. [17]. The spacing between the vertical springs is assumed as 2% [38] and a nominal tension capacity (¼ 5% of ultimate capacity) is provided to the vertical q–z springs. u and s¼horizontal and vertical displacements, y ¼rotation, V and Q¼horizontal and vertical forces, and M¼moment. kin ¼initial elastic stiffness; z ¼instantaneous displacement

Table 1 Soil and foundation parameter uncertainty. Soil parameters uncertainty

Mean

Unit

CoV(%)

Cohesion (c) Friction angle (f) Unit weight (g) Shear modulus (G) Poisson’s ratio (u) Foundation ‘‘geometrical’’ uncertainty Length (L/B) Height (Hf) Depth (Df/B)

5 38 18 70 0.35 Minimum 1.0 300 0.50

kPa deg kN/m3 MPa – Unit – mm –

10 10 10 10 10 Maximum 2.00 700 1.50

Table 2 Fundamental period of fixed base and SSI model. Structure

Three storey Five storey Nine storey

Fundamental period, T1 (s) Fixed base model

SSI model

0.64 0.85 1.81

0.71 0.88 1.88

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qo ¼load at the yield point, Cr ¼parameter controlling the range qult, pult, tult ¼ultimate load capacity of the footing for q–z, p–x and t–x springs, respectively. z50 ¼displacement at which 50% of ultimate load is mobilized, zp0 ¼displacement at the yield point, zp ¼displacement at any point in the post-yield, and c and n ¼constitutive parameters controlling the shape of the post-yield portion. 4. Variability in soil properties and foundation dimension The soil uncertainty parameters (aleatoric uncertainty) considered are cohesion (c), friction angle (f), unit weight (g), shear modulus (G) and Poisson’s ratio. The foundation ‘‘geometrical’’ uncertainties considered are length to width ratio (L/B), thickness (Hf) and depth to width ratio (Df/B). The geometrical uncertainty is due to the different design methods and factor of safety considered in the design and construction phase. Table 1 shows the list and respective mean values and corresponding 10% coefficient of variation (CoV) of the input parameters (values of the soil parameters uncertainties provided in Table 1 are adapted from Ref. [39]). Although some studies have reported that a larger variation of the in situ CoV, the 10% CoV for different soil types including, sand, clay and silt seems to be reasonable [21]. The foundation ‘‘geometrical’’ uncertainty is modeled with uniform distribution defined by the minimum and the maximum values given in Table 1. The BNWF modeling uncertainty such as spring spacing and stiffness intensity ratio is not considered in this study. The fundamental period T1 of the fixed base and SSI model of the reference structures are computed and summarized in Table 2. The reference structure entails the soil properties and foundation parameters are set at their mean values. The period of the SSI model is elongated from the fixed base model due to flexibility of the foundation. The change in period is nearly 11% for three-storey and 4% for five- and nine-storey.

5. Earthquake ground motions In order to perform nonlinear time-history analyses for three frames, a suite of 30 recorded ground motion are selected as three groups of ten records from the European Strong Motion Data Base (ESD) maintained at Imperial College [2]. Each group matches a different target uniform hazard spectrum of average return periods of 100, 500, and 1000 yr, respectively as defined in EC-8. Fig. 3 shows the target uniform hazard spectrum and the average elastic 5% damped response spectra of ten records. The records have been selected from stiff to soft soil sites, free-field, including large and distant, large and close, moderate and close as well as intermediate earthquake records in an attempt to cover a

Fig. 3. Target and average demand spectra.

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demand about its median, which is conditioned upon the IM, the fragility can be written as 0 1 b ^ ÞC B lnðCÞlnðaUIM PðD 4 C9IMÞ ¼ 1F@qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA ð6Þ b2D9IM þ b2C þ b2M

Table 3 Median and logarithmic standard deviation of spectral acceleration at the fundamental period of the fix based and SSI model. Structure Return period (years)

Fixed base model

SSI model

Median in g

Logarithmic standard deviation

Median in g

Logarithmic standard deviation

Three storey

100 500 1000

0.35 0.82 1.11

0.44 0.32 0.39

0.34 0.85 1.10

0.49 0.36 0.39

Five storey

100 500 1000

0.30 0.82 1.15

0.55 0.38 0.32

0.27 0.80 1.06

0.56 0.37 0.33

Nine storey

100 500 1000

0.10 0.29 0.45

0.31 0.28 0.33

0.10 0.26 0.44

0.31 0.28 0.33

sufficiently representative range of distances and the expected range of magnitude in Europe. The magnitude (Mw) range from 5.5 to 7.9 and source-to-site distances (r) of 0 rr r97 km. Details about the records employed can be found in Ref. [35]. Table 3 shows the median and logarithmic standard deviation of spectral acceleration of records at the period of fixed base and SSI model. The differences between the fixed base and SSI median and logarithmic standard deviation of spectral acceleration are not significant. But the median spectral acceleration has changed significantly with increasing building height.

6. Seismic fragility modeling For seismic loading, the fragilities simply look at the probability that the seismic demand (D) placed on the structure is greater than the capacity (C) of the structure. This probability statement is conditioned on a chosen intensity measure (IM), which represents the level of seismic loading. The generic representation of this conditional probability is Fragility ¼ PðD 4 C9IMÞ

ð4Þ

One possibility to evaluate the fragility function given in Eq. (4) is by developing a probability distribution for the demand conditioned on the IM, also known as a probabilistic seismic demand model (PSDM), and convolving it with a distribution for the capacity. The demand on the structure is quantified using some chosen metric(s) (e.g. inter storey drift, ductility). Cornell ^ et al. [11] suggested that the estimate for the median demand (D) can be represented by a power model as ^ ¼ aIM b D

where C^ is the median structural capacity, associated with the limit state, bC and bM denote the aleatoric uncertainty in capacity (C) and epistemic uncertainty in modeling, respectively [7]. For simplicity, maximum interstorey drift ðymax Þ is selected as demand parameter. The capacities are defined by the maximum interstorey drift that correspond to three widely used performance levels, immediate occupancy (IO), life safety (LS), and collapse prevention (CP). The IO level is described by the limit below which the structure can be occupied safely without significant repair, and is defined by the value of ymax at which the frame enters the inelastic range. The LS level occurs at deformation level at which significant damage has been sustained, but at which a substantial margin remains against incipient collapse. Because this limit is hard to quantify in terms of interstorey drift or other structural response parameters, the intermediate level is identified as the interstorey drift, ymax, at which significant structural damage (SD) has occurred. The CP level is defined by the point of incipient collapse of the frame due to either severe degradation in strength of members and connections or significant P–D effects resulting from excessive lateral deformations. Table 4 presents the medians of ymax associated with these limit states according to FEMA 356. Finally, the capacity and modeling uncertainty (bC and bM) is assumed be 0.20 for all the performance levels. The seismic IM used is the spectral acceleration at the fundamental period of the frame, Sa(T1), for 5% damping, which is a more efficient parameter to characterize earthquake intensity for building frames of moderate height [36,45]. The fragility curves for different performance levels of the fixed base structure and SSI model are given in Fig. 4. The influence of SSI on fragility is high for three- and nine-storey frame than the five-storey frame. The change in median spectral acceleration from fixed base to flexible base is around 15%, 2% and 11% for three-, five-, and nine-storey frame, respectively.

ð5Þ

where a and b are regression coefficients. The non-linear dynamic analyses can be used to build the PSDM. One procedure, also known as the ‘‘Cloud Analysis’’ [18], is a convenient choice (though not the most accurate). An advantage of this method is that it is based on the ground motions as they are recorded and does not require scaling. The procedure consists of applying a suite of ground motion records (in the order of 10–30 records) to the structure and to calculate the demand D. Then, by performing a simple linear regression of the logarithm of D against the logarithm of IM, one can obtain the PSDM parameters a and b. Furthermore, the distribution of the demand about its median is often assumed to follow a two parameter lognormal probability distribution. Thus, after estimating the dispersion (bD9IM) of the

6.1. Response variability using optimized Latin hypercube sampling The seismic fragilities are affected by the uncertainties associated in soil properties and foundation parameters (as shown in Table 1). Derivation of the uncertainty in the fragility curves can be derived using computationally intensive Monte Carlo simulation with random sampling [7]. The uncertainty in the fragilities can be efficiently quantified using optimized Latin hypercube sampling (OLHS) [33]. OLHS provides a stratified sampling scheme rather than the purely random sampling, as it provides more efficient means of covering the probability space. For a unit hypercube of dimension n (number of uncertain parameter) that contains Ns (number of simulation) data points, there are Ns subcubes each thatffi has 1/Ns volume. Thus the side length of each subpffiffiffiffiffiffiffiffiffiffi cube is n 1=Ns , which is selected as the minimal inter-point distance. In this study, 8 number of uncertain parameter (n) Table 4 Parameters used for estimating capacity. Parameter

Limit state

Interstorey drift limit (%)

C^ ð%Þ

IO LS CP

1 2 4

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83

Fig. 4. Compression of fragilities fixed based and SSI models.

Fig. 5. Distribution of uncertain parameters R-value after sampling using OLHS.

Fig. 6. Seismic demand database for three-, five- and nine-storey frames.

(Table 1), and 60 number of simulation (Ns) is considered. The OLHS is sampled from Ns  n matrix of independent random numbers RA[0,1]. Fig. 5, for example, illustrates optimized distribution of R-values of uncertain parameters (n1  n2), (n1  n3), and (n1 n4). Each element of uncertain parameters x is then mapped according to xij ¼ F 1 x ðRij Þ F 1 x

ð8Þ

where is the inverse CDF for parameter j. Each row of x contains different set of sampled parameters, from which statistical sample of soil and foundation parameters are obtained and the sample frames are created. For each random frame generated using OLHS, nonlinear dynamic analyses were carried out for using the 30 ground motion records, and corresponding PSDM are developed, for three-, five-, and nine-storey frames (i.e., total

number of analysis per frame is 1800). The seismic demand database is generated and shown in Fig. 6.

7. Results and discussion The PSDMs incorporate the uncertainties in soil and foundation parameters (Table 1) in addition to consideration of uncertainty in ground motion. Subsequently, the fragilities are derived using these demand models along with the capacity parameters summarized in Table 4. However, to quantify epistemic uncertainty associated with the sampling process, 30 samples each are re-sampled 1000 times from Fig. 6 using bootstrapping method [13] and corresponding fragility curves are generated. Results of the fragility curves are summarized in Figs. 7–9, respectively, for three-, five- and nine-storey. Figs. 7–9 show the

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Fig. 7. 16th and 84th percentile fragility bounds on the optimized Latin hypercube sampled frames and SSI median valued and fixed based frame fragilities for three storey frame.

Fig. 8. 16th and 84th percentile fragility bounds on the optimized Latin hypercube sampled frames and SSI median valued and fixed based frame fragilities for five storey frame.

16th and 84th percentile bounds on the fragility curves along with the median value of SSI and fixed base model Fig. 4. Table 5 presents the parameters of lognormal distributions that model these frailties: _ the median S C ðgÞ and logarithmic standard deviation x, where the differences in the medians for the same limit states depict the epistemic uncertainty due to the sampling process. Fig. 7 and Table 5 show that fragility of the median valued SSI is bounded between the 16th and 84th percentile. Whereas, the fixed based model is very close to the 16th percentile fragility for all the limit state. It can also be noted that uncertainty in the fragility

Fig. 9. 16th and 84th percentile fragility bounds on the optimized Latin hypercube sampled frames and SSI median valued and fixed based frame fragilities for nine storey frame.

function is less in the IO and LS limit state compare to CP limit state. The uncertainty in the fragility of CP is significantly less in the lower probabilities that at the higher probabilities. This may be due to the fact that most of the 1800 data are not exceeding the capacity. Thus, the fragility function is relatively well constrained by the demand data at low cumulative probabilities. Fig. 8 and Table 5 show that fragility of the median valued SSI and the fixed base model approximately are closer to the median value and bounded between the 16th and 84th percentile. It is also noted that uncertainty in the fragility function is increasing with the limit states. Again, the uncertainty in the fragility of CP is significantly less in the lower probabilities that at the higher probabilities. Fig. 9 and Table 5 show that fragility of the median valued SSI is bounded between the 16th and 84th percentile. Whereas, the fixed base model, for IO and LS performance level, it is closer to the 16th percentile. However, for the CP performance level, lower portion of the fragility curve follows the 16th percentile curve, and approach the median value in the upper portion. In all cases, however, the SSI median valued frame model fragilities are enclosed by the lower and upper bound fragility curves. Hence, the contribution of the soil and foundation parameter uncertainties is relatively small in comparison with the uncertainty from the ground motion. The record-to-record variability is sufficient to develop the seismic fragilities for SSI model. But, the comparison of the bounds and the fixed base model indicates fragilities for the five storey frame is positioned lower within the bounds and three and nine story frame are position slightly outside the 16th percentile bound in some part and inside in the other part. The overall change in the median spectral acceleration of fixed base and SSI model is nearly 40%, 16%, and 25% for three-, five-, and nine-storey frame, respectively. It shows the influence of SSI on the seismic fragilities.

8. Conclusion The influence of SSI effects and soil properties and foundation parameter uncertainty on the seismic fragilities of non-ductile RC

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85

Table 5 Fragility parameters. Structure

Fragility parameters

_ S C ðgÞ

x

IO

LS

CP

IO

LS

CP

Three storey

84% percentile SSI median valued model Fixed base model 16% percentile

0.223 0.260 0.302 0.308

0.430 0.489 0.537 0.552

0.838 0.921 0.957 0.987

0.453 0.461 0.410 0.428

0.465 0.461 0.410 0.419

0.471 0.461 0.410 0.413

Five storey

84% percentile SSI median valued model Fixed base model 16% percentile

0.258 0.296 0.302 0.335

0.503 0.564 0.575 0.626

0.987 1.08 1.09 1.16

0.453 0.457 0.449 0.433

0.466 0.457 0.449 0.423

0.476 0.457 0.449 0.415

Nine storey

84% percentile SSI median valued model Fixed base model 16% percentile

0.074 0.089 0.100 0.108

0.151 0.180 0.200 0.207

0.312 0.365 0.401 0.400

0.493 0.503 0.483 0.467

0.505 0.504 0.483 0.460

0.514 0.504 0.483 0.453

frames was investigated at various levels of earthquake hazard level and performance levels. Three-, five- and nine-storey buildings supported by shallow foundation on dense silty sand are considered in this study. The foundation is modeled as BNWF using vertical and horizontal springs. Optimized Latin-hypercubesampling technique is used randomize the soil and foundation parameters. Structural parameter uncertainty, different types of foundation modeling and different soil type are not considered in this study. Within this limitation, the analysis results show that the uncertainty in ground motion dominated the overall uncertainty in structural response of SSI model. This finding supports the view that the fragilities developed using median (or mean) values of the soil properties and foundation parameters may be sufficient for the earthquake damage and loose estimation of nonductile gravity load designed RC frames. But, the fragilities derived from the fixed base model may differ from the SSI model depending on the nature of the structure. It should be highlighted that this study does not consider the different types of foundation modeling and soil type. Thus, the conclusion is limited within the context of the foundation type considered and needs further study to investigate different foundation models.

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