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Seismic load estimates of distant subduction earthquakes affecting Singapore
Engineering Structures 31 (2009) 1230–1240
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Seismic load estimates of distant subduction earthquakes affecting Singapore N.T.K. Lam a,∗ , T. Balendra b , J.L. Wilson c , S. Venkatesan d a
Department of Civil and Environmental Engineering, University of Melbourne, Parville 3010, Australia
b
Department of Civil Engineering, National University Singapore, Singapore
c
Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, Australia
d
School of Architectural, Civil & Mechanical Engineering, Victoria University, Australia
article
info
Article history: Received 11 July 2007 Received in revised form 9 January 2009 Accepted 12 January 2009 Available online 8 February 2009 Keywords: Distant earthquakes Stochastic simulations Subduction earthquakes Sunda Arc Singapore Malaysia
a b s t r a c t This paper introduces the use of a simple stochastic model for predicting elastic response spectra of 5% damping for structures founded on rock sites in Singapore based on earthquake scenarios of moment magnitude Mw = 9 − 9.5 generated from the Sunda-Arc subduction source at a closest distance of 600 km. Structures founded directly on rock are predicted to be subject to low response spectral accelerations of up to 1.3% gravitational acceleration. The maximum velocity demand on a structure is estimated to be in the order of 50 mm/s. The drift demand on a structure is estimated to be generally low but can be up to some 80 mm on single-degree-of-freedom systems possessing a high natural period of 10 s. Evidence of significant drift demand amplification on flexible soil sites due to the phenomenon of resonance is also presented. The long period ground shaking, when amplified, can be potentially hazardous to certain vulnerable structures such as buildings with a soft-storey and precast beams resting on supports of limited width. The stochastic model was originally developed by the authors based on observations from the magnitude 8 event of 4 June 2000 generated by the Sunda Arc subduction source as reported in an earlier publication by Balendra and others in this journal in 2002. Response spectra simulated by the same model based on the same set of parameters were found to be very consistent with those recorded in Singapore from the M9.3 Aceh earthquake of 26 December 2004, the M8.6 Nias earthquake of 28 March 2005 and the M8.4 earthquake of 12 September 2007 in southern Sumatra. In summary, response spectra generated by these major events in recent times could be simulated by the same model. The scale of events observed on this subduction source and the exceptionally long distance of wave travel (to Singapore) considered in this study are of a unique category. Developing an attenuation model by regressing recorded data is not a viable approach given the scarcity of data recorded from such events and hence stochastic modelling was used. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Singapore and the adjoining Malay peninsula have a long history of experiencing seismic tremors generated mainly from major interplate sources at long distances. The two major active earthquake generating sources are namely (i) the Sumatran fault source which has a closest distance of 400–450 km from Singapore and (ii) the Sunda-Arc subduction source off-shore of Sumatra on the Indian Ocean side of the island. This study is concerned with earthquakes generated from this second source (refer [1]). The Sunda Arc seabed subduction trench has a closest distance of 600–650 km from Singapore. In the past eight years, five major earthquake events of magnitude ranging between 7.9 and 9.3 generated from this fault source, were widely felt across the whole
∗
Corresponding author. E-mail address: [email protected] (N.T.K. Lam).
0141-0296/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2009.01.018
region including Singapore and parts of Malaysia. The first event was the magnitude 7.9 (Mw = 7.9) earthquake of 4 June 2000 which occurred offshore of Benkulu in the southern part of Sumatra and was approximately 700 km from Singapore. The second event was the Aceh earthquake of 26th December 2004 (also known as the ‘‘Great Sumatran earthquake’’ which caused the ‘‘BoxingDay Tsunami’’). This second earthquake was of a phenomenal magnitude of Mw = 9.3 and was amongst the largest ever recorded in the region. Whilst the epicentre of the earthquake was about 900 km from Singapore, the centroid of the fault source was much further away in the northwesterly direction. Three events of magnitudes exceeding 7.9 have occurred since then as listed in Table 1. The map of Fig. 1a shows the approximate location for each of these events and basic seismological information can be found in Ref. [2]. Each of these major earthquake events caused significant damage to infrastructure in Sumatra and was widely felt as far as Singapore and parts of Malaysia which are within the
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Table 1 Major earthquake events incorporated into the study. Moment magnitude
Approximate site–source distance to Singapore (km)
Place located closest to epicentre
Time of event
7.9 9.3 8.6 8.4 7.9
700 1200 750 700 550
Bengkulu Aceh Nias Bengkulu Mentawi Strait
4 June 2000 26 December 2004 28 March 2005 12 September 2007 at around 1100 h 12 September 2007 close to mid-night
Fig. 1a. Location of major events generated by Sunda Arc subduction source surrounding Singapore.
intraplate region of Eurasia. Whilst no structural damage was reported in Singapore from these recent events there are concerns that a much more onerous earthquake scenario in terms of its impact on Singapore is possible. An example of such a projected scenario, which can be used as a basis for seismic demand and risk assessment purposes, is an earthquake of the size of the second (Aceh) earthquake event striking at a much closer distance of 600 km from Singapore. None of the events reported above has this onerous combination as illustrated in Fig. 1b which shows the magnitude-distance combinations for both the recorded and projected (design) earthquake scenarios. The design of a building’s lateral force resisting system in Singapore is governed by the Building Control Act which calls up the relevant British Standards for defining the design wind pressure and for the structural (steel or concrete) design of the members. The serviceability and ultimate limit states performance criteria of a building are based on these standards and there are no additional performance criteria that are specific to seismic actions. No regulatory documents contain provisions for seismic actions other than stipulating a nominal horizontal force which is equivalent to 1.5% of the dead load of the building on each floor (which is translated into a design acceleration of 0.015g). This provision is to provide a minimum level of robustness for the building and is not specifically for seismic protection (refer [3] for a detailed review). The characteristic long-period waves of distant earthquake could potentially cause damage to certain structures with long period properties. Precast beams of limited seating length at their
Fig. 1b. Magnitude–Distance combinations of recorded large magnitude earthquakes.
end supports could be at risk of collapse when subject to drift irrespective of the acceleration amplitude of the ground. Other examples of long-period sensitive structures are tall buildings with a soft-storey, large containers filled with liquid and bridges supported on flexible piers. The drift demand on these structures could be accentuated considerably by resonance behaviour on flexible (deep and soft) soil sites. The impact of long period ground shaking on certain structures can have serious consequences irrespective of the ground acceleration amplitude. Thus, seismic
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Table 2 Component factors and input parameters to Stochastic Model. Component factors
Definition of factor and recommended parameter values
Source Factor S (f , M )
S (f , M ) = Mo {(1 − ε)SA+ ε SB ); Mo is the seismic moment. SA = 1/[1 + f /fa ] SB = 1/[1 + f /fb ] Log fa = 2.41 − 0.533M Log fb = 1.43 − 0.188M Log ε = 2.52 − 0.637M
Scaling factor of the source C (ρ, β)
p C = 4πρβ 3 where Rp is the wave radiation factor, F the free surface amplification factor, V the factor partitioning energy in the two orthogonal directions [the product Rp FV can be been taken as 0.78], ρ the density of the rock at the depth of rupture was taken as 2.8 kg/m3 and β the SWV of the rock at the depth of rupture was taken as 3.7 km/s. The anelastic attenuation model, An (f), is defined by the following well known relationships:
Anelastic whole path attenuation factor An(f , R, Q )
Geometrical Attenuation factor G(R, D) Upper crustal amplification factor Va (f , Vs ) Upper crustal attenuation factor P (f )
R FV
−. π.f .R
An (f ) = e Q .β ; Q (f ) = Q0 .f n Q (f ) = 150f 0.56qas obtained by calibration in Balendra et al. (2002) [1] G (R, D) = 1R.5D 0
R 2.5D
where R0 is the reference distance and D is the crustal thickness. D = 30 km
in this area according to information reported in the Global Crustal Model : CRUST 2.0 (2001) [15]. The upper crustal amplification function could be inferred from the shear wave velocity profile using the quarter wave-length method of Boore and Joyner (1997). A shear wave velocity of 1500 m/s was assumed to simulate the conditions of granite intrusion in the region. P (f ) = e−π f κ where κ = 0.04 in view of the SWV conditions of the upper crust in the region.
Definitions of the arguments used in the table have been given in the text below Eq. (2).
hazard models based only on peak ground accelerations (eg. recent publication by Petersen et al. [4]) would not provide accurate predictions of the potential impact of earthquakes of this nature. It is preferable to express such seismic hazards in the form of a response spectrum which can be used for estimating the structural drift demand for any given natural period of vibration. There are global response spectral attenuation relationships developed for subduction earthquakes (refer Section 4.2). However, the scale of events observed on this subduction source and the exceptionally long distance of wave travel to Singapore considered in this study are of a unique category and not covered by any existing global attenuation relationship (refer Fig. 1b). Developing an attenuation model by regressing recorded data is not a viable approach given the scarcity of data recorded from such events. This paper is aimed at presenting to engineers a simple stochastic model that can be used for simulating the effects of large magnitude earthquake events striking Singapore from a long distance. Stochastic modelling is very suited to engineering applications by virtue of its simplicity since the need to simulate wave propagation has been circumvented. Elastic response spectra on rock sites for 5% damping have been estimated by the model in the period range of 0.1–10 s to address civil engineering structures commonly encountered in practice. Waveform properties of the earthquake which require more sophisticated tools to simulate are not of interest in this study. An important element of originality in the paper is the use of the stochastic model (which is commonly used for simulating small and medium magnitude intraplate earthquakes) to obtain reasonably accurate simulations from large magnitude long distance earthquake events on rock sites and also on flexible soil sites due to the phenomenon of resonance. This paper: (i) introduces the use of a stochastic model for simulating elastic response spectra for earthquake ground shaking on rock generated by large magnitude distant earthquakes (Section 2), (ii) presents the simulated response spectra and the inferred drift demand on simple models of structures for the projected earthquake scenarios on rock sites (Section 3), (iii) verifies the accuracy of the model by comparison with recordings from four major past events (Section 4.1), and with models proposed previously in the literature (Sections 4.2 and 4.3), and (iv) demonstrates the use of the developed response spectrum model for estimating the inter-storey drift demand in buildings and the displacement demand in small bridges found on rock or flexible soil sites (Section 5).
2. Overview of the stochastic model for simulating elastic response spectra Stochastic simulations are about synthesizing ground surface acceleration time-series: ag (t ). Ground accelerations of unit variance and uniform frequency content within a limited bandwidth as defined by Eq. (1) is first generated. ag (t ) = w(t )
n=N X
An sin[n(1ω)t + φn ]
(1)
n =1
where An are of identical values for all values of n in the specified range for ‘‘band-limited white-noise’’, φn are random phase-angles obtained from random-number generations, and w(t ) is a timedomain windowing function which guides the ground motion intensity to gradually develop and decay with time as in a real earthquake. The generated random time-series is then subject it to a frequency-domain filter: Ax (f ) as defined by Eq. (2) for modifying the frequency content to emulate the behaviour of a real earthquake. Ax (f ) = S (f , M ).C (ρ, β).An(f , R, Q ).G(R, D).Va (f , Vs ).P (f , κ) (2) where S (f , M ) is the source factor of the seismological model which defines the frequency content of body waves radiating from the source of the earthquake, C (ρ, β) is a scaling factor, An(f , R, Q ) is the anelastic whole path attenuation factor, G(R, D) is the geometrical attenuation factor, Va (f , Vs ) is the upper crustal amplification factor, and P (f , κ) is the upper crustal attenuation factor; f is natural frequency, M is moment magnitude, ρ and β is density and shear wave velocity respectively of the earth crust at the depth of the source, R is site–source distance, Q is quality factor, D is depth of crust measured to the Moho discontinuity, Vs is the depth dependent shear wave velocity of the crust and κ is the ‘‘kappa’’ parameter. Table 2 contains a listing of the definitions for each of the component factors shown in Eq. (2) and their associated input parameters. A detailed review of the stochastic simulation methodology and the seismological model can be found in Lam et al. [5]. Sample time-series and frequency series generated at each step of the simulation procedure can also be found in this reference.
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(a) Example simulated and recorded acceleration time-history (1) based on recordings of Aceh Earthquake of 16 December 2004 on GNS rock site in Singapore in East-South direction.
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(b) Example simulated and recorded acceleration time-history (2) based on recordings of Aceh Earthquake of 16 December 2004 on GNS rock site in Singapore in East-South direction.
(c) Velocity response spectra calculated from 18 random simulations. Fig. 2. Simulated time-histories and response spectra.
Stochastic models of the form defined by Eqs. (1) and (2) have been used for simulating ground motions in North America for over two decades. The authors have adapted the model to studying the attenuation behaviour of earthquakes in different parts of Australia. The stochastic simulations were undertaken by the programme GENQKE developed in-house by the authors [6]. In this study, the same model is used for simulating response spectra of distant earthquakes experienced in Singapore during the major events generated by the Sunda Arc subduction source as outlined earlier in the paper. Input parameters that are suitable for simulations in the region have been identified in an earlier publication by the authors [1] in which ground motions recorded from the first event at Singapore on 4 June 2000 were studied. This same set of parameters (which are listed in Table 2) have been used to simulate ground motions for comparison with the more recent distant major earthquake events recorded in Singapore. Simulations were for horizontal (and not vertical) motions not directionally specific on the horizontal plane, as the response spectrum model developed in the study is based on averages of all directions, which is consistent with most earthquake attenuation relationships including those developed by stochastic simulations. Some 18 accelerograms were generated by stochastic simulations for each earthquake scenario of interest. Elastic response spectra for 5% critical damping were calculated from each of the synthetic accelerograms. Two example accelerograms that were stochastically simulated for the distant earthquake scenario in Singapore consistent with the Aceh event of 2004 are presented in Fig. 2a and b. The recorded acceleration time trace is also shown in each figure for comparison with the simulated traces. The amplitude and average pulse widths in the simulated and recorded traces are generally consistent whilst every record has its own pulse arrival details. The duration of strong shaking in the recorded trace is clearly longer than those in the simulated traces. Thus, the simulations were intended only for representing the response behaviour of structures (and soil-sediments) assuming linear (or
quasi-linear) stress–strain behaviour. The assumption of the linear elastic behaviour of the structure was not unreasonable in view of the intensity of ground shaking that was considered in the study. A more thorough and objective comparison of the spectral contents in the recorded and simulated motions is presented in Section 4. The frequency (spectral) content calculated from each of the 18 random simulations on rock is also shown in Fig. 2c. The ‘‘upperlimit’’ (5% exceedance) of the simulated response spectra is about 1.2–1.3 times that of the ‘‘mean’’ response spectrum (ie. upperlimit is approximately 0.1 units above the mean on the log10 scale) in the period range of engineering interest. Similar margins have been observed with simulations undertaken in the study for other earthquake scenarios. It is shown that inter-event random variabilities of ground shaking on rock in large magnitude distant earthquake events is much lower than that of smaller magnitude near-source earthquakes (provided that the moment magnitude of the earthquake has been pre-determined). This is believed to be due to the robustness of the characteristic high period wave components in a distant earthquake which are well constrained by the seismic moment generated by the earthquake. Whilst interevent random variability of distant earthquakes on rock is much lower than that of near source earthquakes, the ground shaking in a distant earthquake can be very sensitive to site conditions, which is the main contributor to intra-event variability. In the remainder of the paper, only the mean of the simulations on rock is shown. 3. Simulated response spectra for projected earthquake scenarios Debating exactly what moment magnitude that Singapore should consider for the ‘‘worst’’ scenario earthquake is not within the scope of the paper. Predictions for the projected earthquake scenarios can be presented in deterministic terms given the simulation is specific to one source (the Sunda Arc subduction source offshore of Sumatra) and one site (Singapore bedrock).
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(a) Ensemble averaged simulated velocity response spectra.
(b) Acceleration response spectrum envelope.
Fig. 3. Response spectra for projected critical earthquake scenarios.
Given that the largest earthquake ever recorded on this subduction source was of Mw = 9.3, the projected earthquake scenarios are accordingly Mw = 9, 9.3 and 9.5 located on the part of the fault which is at a fixed (closest) distance of 600 km from Singapore. Response spectra were simulated using the stochastic methodology described in Section 2 and the input parameters to the model listed in Table 2. Seismic drift demand of the earthquake on rock sites was then inferred from the simulated response spectra. The outcome of this study is as applicable to Singapore as it is to neighbouring centres of population in the southern part of the adjoining peninsula of Malaysia. This case study is also intended to demonstrate the generic use of the modelling methodology for other regions around the world subject to potential threats from large magnitude distant earthquakes of a similar nature. The ensemble average response spectrum (5% critical damping) simulated for each of the projected scenarios is shown in Fig. 3a together with lines corresponding to constant response spectral acceleration values of 0.004g and 0.013g. The response spectral behaviour of structures with natural period less than 2.5 s could be characterised by these two acceleration limits. Structures possessing a natural period close to 2.5 s pertain to the upper limit whilst structures possessing a low natural period pertain to the lower limit. This dual limit effectively envelopes the simulated response spectra. The response spectrum of Fig. 3a can be used for calculating the elastic drift demand (1) on single-degree-of-freedom lumpedmass systems of 5% critical damping. A response spectral acceleration of 0.004g and 0.013g (as shown in Fig. 3a) can be translated into Eqs. (3a) and (3b) respectively for providing conservative estimates for drift demands in acceleration controlled conditions. Similarly, a maximum velocity demand in the order of 50 mm/s can be translated into Eq. (3c) for estimating drift demands in velocity controlled conditions.
1 (mm) = 0.004 × 9.81 × 1000 ×
for 0.5 s < T < 2.5 s
1 (mm) = 50 ×
T 2π
2
2π
for T ≤ 0.5 s
1 (mm) = 0.013 × 9.81 × 1000 ×
T
≈ T2 (3a)
T 2π
2
≈ 3.2T 2
= 8T for T ≥ 2.5 s
where 1 is in units of mm ; T is in units of seconds.
(3b) (3c)
From Eq. (3), 1 is predicted to be negligible for stiff structures with T ≤ 0.5 s; up to about 20 mm for intermediate structures with T ≤ 2.5 s, and is linearly proportional to T for T > 2.5 s. The value of 1 is predicted to be equal to 80 mm for flexible structures with T = 10 s. Whilst Fig. 3a–b and Eq. (3) are based on bedrock conditions, the drift demand can be amplified many times on flexible soil sites as demonstrated in Section 5. The response spectrum envelope in the usual acceleration (force-based) format as used in current codes of practices is also shown in Fig. 3b to facilitate engineering applications. Also shown in Fig. 3b is the response spectrum model stipulated by the 1997 edition of the Uniform Building Code, USA [7] which is still widely used in codes of practices in many countries worldwide even though it has been superseded in the USA itself by the International Building Code [8]. The response spectrum model of UBC for Class B (rock) sites has been normalised to a notional peak ground acceleration of 0.004g for direct comparison with the response spectrum developed in this study for distant earthquakes. Gross non-conservatism of the (conventional) UBC model in the high period range is demonstrated. Thus, large magnitude distant earthquakes can be potentially much more hazardous to high period structures than normal earthquakes of similar peak ground accelerations. The nominal provisions of 0.015g are shown to be conservative for rock sites but could become inadequate for flexible soil sites. 4. Comparison of simulations with recorded response spectra 4.1. Comparison with response spectra recorded from major events in the region In this section, the elastic response spectra of 5% critical damping simulated from the stochastic model are compared with those recorded from the Bukit Timah Dairy Farm (BTDF) station in Singapore. The station is of rock conditions and hence suited to recording motions for comparison with stochastic simulated motions for rock conditions. Such a comparison has already been undertaken by the authors for the June 2000 Bengkulu event in Ref. [1] and is reproduced herein in Fig. 4d. Similar comparisons have been made in this study for three other events. In undertaking the simulations for each of these events, only the moment magnitude and site–source distance would need to be specified given that the same set of seismological parameters (as listed in Table 2) was used in all the simulations. The second event of Mw = 9.3 (near Aceh) had an epicentral distance (defined at the location where rupture was initiated) of 900 km from Singapore but the geometric centroid of the area covered by the earthquake rupture was estimated to be some 1200 km away from Singapore as shown by the regional map of
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(a) Aceh Earthquake of 16 December 2004 — M9.3 at 1200 km.
(b) Nias Earthquake of 28 March 2005 — M8.6 at 750 km.
(c) Bengkulu Earthquake of 12 September 2007 — M8.4 at 700 km (only records in one direction is available).
(d) Bengkulu Earthquake of 4 June 2000 M7.9 at 700 km.
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Fig. 4. Comparison of simulated and recorded velocity response spectra.
Fig. 1. It is noted that the rupture propagated from the epicentre in the northerly direction for about a thousand kilometres. Response spectra recorded from the Aceh earthquake at the GSN (rock) station in the north–south (NS) and east–west (EW) directions are shown in Fig. 4a along with the ensemble average response spectrum of the stochastically simulated accelerograms. The simulations were conducted with and without incorporating the modifications of the seismic waves by the upper crust. It is shown in Fig. 4a that the effects of crustal modifications were minor but slightly more conservative predictions were obtained when factors representing their effects have been included in the modelling. However, individual troughs and peaks that were featured on the recorded response spectra (including the notable spectral peak at the 4 s period) could not be reproduced by stochastic simulations from the point–source model. The third event of Mw = 8.6 (near Nias) had a site–source distance of about 750 km. A similar level of consistencies between the recorded and simulated response spectra with this third event are shown in Fig. 4b. The slight spectral sags recorded in the 1–3 s period range was again a feature that could not be reproduced by stochastic simulations of a point–source model. The very different site–source distance of the Aceh and Nias events means that significant errors would have resulted if unrepresentative attenuation parameters had been assumed. The fourth event of Mw = 8.4 (near Bengkulu) was with an epicentral distance of about 700 km from Singapore. With this event, the rock motion was back-calculated using program SHAKE from motions recorded on a soil site where details of the subsoil are known. The consistent agreement between the response spectrum calculated from field measurements and that calculated from accelerograms generated by stochastic simulations has again been
demonstrated in Fig. 4c. All the major earthquake events involved in the evaluation of the stochastic model are summarised in Table 1. 4.2. Comparison with predictions by a global attenuation model Generalised empirical attenuation models for subduction earthquakes have been developed from data collected worldwide for earthquakes with Mw < 8.5 and a site–source distance of up to 300 km (e.g. [9–11]). The empirical model of Ref. [9] for interface subduction earthquakes was developed from an expanded database obtained by merging and building on the databases of Refs. [10,11] for global applications. It is noted that this generalised (global) model cannot be realistically extrapolated to predict the intensity of ground shaking of long distance earthquakes affecting Singapore which involve much longer distance of wave-travel. Nevertheless, they could be used to make comparisons with simulations from the proposed stochastic model at a modest distance of 100 km. Fig. 5a and b show the 1 s and 3 s response spectral velocities predicted by this global empirical model on rock based on a common value of R = 100 km (where R is the distance to the closest point on the ruptured fault surface, and is denoted as Dfault in Ref. [9]). Although a closer reference distance seems more appropriate for the comparison of the ‘‘source’’ spectral properties, the choice of 100 km as the reference distance was intended to circumvent complications arising from near-fault effects given that the aim of this study was to model long-distance earthquakes affecting Singapore which has a minimum distance of 600 km from the Sunda-Arc subduction zone. The 100 km distance was also chosen as the reference distance for revealing source properties because of the abundance of empirical data in that distance range.
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(a) Response spectral velocity at 1 s period.
(b) Response spectral velocity at 3 s period. Fig. 5. Comparison of predictions by stochastic model with global attenuation model.
A focal depth of h = 20 km was assumed when applying the global empirical model for comparison with predictions by the stochastic model proposed by the authors. This assumption is close to the h = 24 km adopted by Megawati et al. [12] in their simulation of subduction earthquakes in the Sunda Arc region. The Quality factors of ‘‘Q = 680’’ and ‘‘Q = 150’’ as shown in the legend of Fig. 5a and b refer to the assumed Quality factors of Q = 680 f 0.36 and 150 f 0.56 respectively. Conditions enveloped by these limits represent a wide range of crustal conditions. Yet, the simulated response spectral velocities (at the 1 s and 3 s periods) associated with these limits were very close which effectively demonstrates that anelastic attenuation had only a minor effects on the ground shaking at 100 km distance with very large magnitude earthquakes. A robust comparison of predictions by the stochastic and empirical models was then possible. Both Fig. 5a and b show notable differences between predictions by the stochastic simulations of the seismological model and the empirical model, when Mw < 7. Interestingly, predictions from the two models are shown to be in much better agreement when Mw > 7. No instrumented recordings of the Aceh nor Nias earthquakes were available at a 100 km distance from the fault source making it difficult to directly verify the accuracy of the stochastic source model at the upper end of the magnitude range shown in Fig. 5a–b. However, Modified Mercalli Intensities (MMI) ranging between VIII-IX were reported at Banda Aceh due to the immediate impact of the ground shaking generated by the Aceh earthquake. According to a USGS source cited by RMS [13]: ‘‘violent shaking caused the collapse of some mid-rise reinforced concrete structures’’.
Banda Aceh was some 250 km from the epicentre of the earthquake but the closest distance of the city to the ruptured fault was only about 100–150 km. Given that the city was not in alignment with the ruptured fault, the effects of directivity were not dominant. In conclusion, simulations of the response spectral parameters (for 1 s and 3 s periods) by the proposed stochastic model are shown to be consistent with empirical models for interface subduction earthquakes. 4.3. Comparison with predictions by regional specific attenuation models Prior to the great earthquake of Aceh, seismic hazard modelling of long-distance earthquakes affecting Singapore had been undertaken by the authors [1] and by others [14,12,15]. The elaborate response spectral attenuation relationship of Eq. (4a) for horizontal motions was developed specifically for the region by Megawati, Pan and Koketsu [12]. 2 Loge (YH ) = a0 + a1 Mw + a2 Mw + a3 loge (R) + a4 R + a5 h + εH
(4a) where YH represents ground motion parameters including Peak Ground Acceleration, Peak Ground Velocity and response spectral acceleration for natural periods ranging between 0.5 s and 20 s; R is the distance from station to the centre of the rupture plane in kilometres; h is focal depth in kilometres; εH is the standard error; and a0 − a5 are period dependant coefficients. Earthquake data used in supporting the relationship was recorded from earthquakes with site–source distances of between
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(a) Aceh earthquake scenario (M9.3 at 1200 km).
(b) Nias earthquake scenario (M8.6 at 750 km). Fig. 6. Estimates by models of Refs. [12,15] and this study with recorded results.
200 and 1500 km. The relationship has also been used in Ref. [12] to simulate a historical event of 1833 (Mw = 9) at a distance of 700 km. Thus, ground shaking in Singapore generated by the Aceh and Nias earthquakes were intended to be within the intended scope of the proposed attenuation relationship of Eq. (4a). It is noted however that at the time Eq. (4) was developed by Ref. [12], instrumented strong motion data collected from within the region was mostly restricted to small and moderate magnitude earthquakes of Mw ≤ 6.5. Thus, the accuracies of the proposed attenuation relationship as applied to large magnitude earthquakes could not be tested. The rupture occurred at the relatively shallow part of the subduction zone with focal depth ranging between 10–30 km. A mean value of 20 km was taken as the value of ‘‘h’’ for the purpose of Eq. (4). The seismological information of the event as quoted above was based on information of the event provided by the Risk Management Solution in their publication: RMS [13]. The velocity response spectra calculated from the recorded accelerograms are shown in Fig. 6a and b for comparison with estimates from Eq. (4a). The estimated response spectra were up to two orders of magnitude (100 times) higher than the recorded results in the natural period range of 0.5–3.0 s from the Aceh earthquake event, and in an order of magnitude (10 times) higher than the recordings from the (closer) Nias earthquake event. The shape of the response spectra based on stochastic simulations (as defined by Eq. (4a)) were also significantly different from the response spectra calculated from the recorded accelerograms.
A more recent paper by Pan, Megawati and Lim [15], published 2 years after the Aceh and Nias earthquakes (by similar authorship constituents of Ref. [12]), presents an alternative attenuation relationship and a different set of coefficients. The revised relationship is of the form represented below and is similar, but not identical, to that of Eq. (4a). Loge (YH ) = a0 + a1 (Mw − 6) + a2 (Mw − 6)2
+ a3 loge (R) + (a4 + a5 Mw )R + εH .
(4b)
Estimates from Eq. (4b), based on Ref. [15], are also shown in Fig. 6a and b for comparison. Clearly, the revised estimates calculated from Eq. (4b) are closer to results derived from the field instrumented records than the initial estimates calculated from Eq. (4a), but there are still significant modelling errors with the revised relationship. The proposed attenuation relationships as represented by Eqs. (4a) and (4b) (based on Refs. [12, 15] respectively) do not appear to be suitable for modelling ground motions generated by very large magnitude, and distant, earthquakes. 5. Estimation of drifts in buildings and bridges 5.1. Basics The estimation of drifts in buildings and bridges begin with the calculation of the predicted effective displacement (1eff ) which is defined herein as the maximum displacement experienced by
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(a) Dislodgement of bridge decking.
(b) Low and medium-rise building with a soft-storey.
(c) Medium-rise moment frame.
(d) 30-storeys high-rise building frame. Fig. 7. Drift demand on buildings and bridges.
a lumped mass single-degree-of-freedom system of linear elastic dynamic properties and 5% critical damping. The value of 1eff can be calculated from Eq. (5) which requires the response spectral value (RSV) at the designated natural period (T ) to be read off directly from the velocity response spectrum of Fig. 3a.
1eff (mm) = RSV .
T 2π
.
(5)
Alternatively, the value of 1eff could be calculated using Eqs. (3a)–(3c) if the structure is founded directly on rock. It is noted that the velocity response spectrum model presented in Fig. 3a and b were based on the ensemble mean of the stochastically simulated response spectra. As shown in Fig. 2c, a factor of 1.3 will have to be applied to the mean estimates to obtain the ‘‘upper limit’’ estimates for 5% exceedance.
In this section, the maximum drift demand for each structure shown schematically in Fig. 7a–d are calculated from the response spectrum model presented in the paper. Storey drifts are calculated initially for structures founded directly on rock, and very modest values are predicted. Storey drift predictions are then made for structures founded on a flexible soil site. The example site used in the illustrations was at the location where accelerograms were recorded on the soil surface during the Aceh and Nias earthquakes. The response spectra calculated from the recorded accelerograms were used as the basis of estimating the soil amplification factor. 5.2. Drift demands calculated for structures founded on rock The drift demand on a building with a soft-storey, and that on a bridge deck found directly on rock, can be related directly to the
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(a) Recorded from Aceh earthquake.
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(b) Recorded from Nias earthquake. Fig. 8. Response spectra recorded from example flexible soil site.
calculated 1eff value given that both structures can be modelled as lumped-mass single-degree-of-freedom systems (Fig. 7a and b). Note, this assumption is only valid for a bridge with lengths much shorter than the horizontal component of the quarter wave-length of the transmitted seismic waves in order that relative movement between individual bridge supports can be ignored. Low-rise building structures with a natural period less than 0.5 s are estimated to have negligible drift demands. If the building and bridge systems have a natural period of 0.8 s, the value of 1eff is estimated at around 2–2.5 mm (based on Eq. (3b)), with an upper limit estimate for 5% exceedance of around 1.31eff ∼ 3 mm. The column drift ratio at the ground floor level of the soft-storey building for design purposes is accordingly equal to 0.1% (assuming a span length of 3 m of the column). Thus, the drift demand of the building on rock sites is negligible, and elastic response could be expected with no damage. The maximum angle of drift on a medium-rise moment frame (Fig. 7c) can also be calculated readily once the value of 1eff is known. The roof displacement will be approximately 1.3 times the value of 1eff for a moment frame building since the deflected shape is dominated by shear actions. In other words, the effective height of the building as defined by Fig. 7c is approximately 0.75 times the total height of the building (H ). The average drift of the building is then the roof displacement divided by H (which is translated into 1eff /0.75H or 1.31eff /H). It can be shown that the maximum inter-storey drift is approximately 1.5 times the average drift. Thus, for a building with a natural period of 0.8 s (same as above), the maximum inter-storey drift for design purpose is 1.5 × 1.3 × (1.31eff )/H which is equal to 0.025% approximately if H = 24 m. The predicted drift demand on rock sites is also negligible. Allowances for higher mode effects may have to be taken into account when calculating the maximum angle of inter-storey drift for the 30-storey high-rise building structure of Fig. 7d. Dynamic modal analysis of the building model for the first two significant modes of vibration revealed a modal natural period of 2.7 s and 0.6 s. If the building is founded on rock the value of 1eff is accordingly predicted (from Eqs. (3c) and (3b)) at 22 mm and 1 mm respectively (the latter second mode can be neglected). Modal analysis of the building structure revealed a maximum inter-storey drift of 0.002% per unit mm of 1eff at the upper levels. Thus, the maximum inter-storey drift is 22 × 0.002% = 0.045% approximately. For design purposes, a factor of 1.3 is applied to obtain the upper limit of 5% exceedance of 0.06% storey drift. Again, the inter-storey drift demand of the building on rock sites is negligible.
5.3. Drift demands calculated for structures founded on soft soil Response spectra recorded on the soil surface of the example flexible soil site indicates a site natural period of 0.8 s (refer Fig. 8a and b) and indicative of a fairly soft (and deep) soil site. Considering the worst scenario where the natural period of the structure is close to the natural period of the site, an anomalously high soil amplification factor of about 10 has consistently been revealed in the response spectra calculated from accelerograms recorded on rock and soil sites in Singapore during the Aceh and Nias earthquake events. The amplification factor associated with the critical earthquake scenario of M9.3 at 600 km distance should have lower amplification values given that the site factor is expected to decrease with increasing intensity of ground shaking. In the absence of representative earthquake records, the amplification factors have to be evaluated by dynamic analysis of the sedimentary layers. In the interim, a conservative amplification factor of 10 is assumed in the following examples. Under these onerous soil conditions assumed, the 3 mm displacement of the bridge on rock (refer Section 5.2) would be increased to 30 mm which could further be increased by torsional movements. Even higher movement could occur at halving joints which connect two parts of the bridge experiencing out-of-phase motions resulting in maximum movements of up to around 50 mm. The drift demand on low-rise buildings with natural periods less than 0.5 s would not be significant even with the effects of soil amplification. The 0.1% storey drift on the ground floor of a 0.8 s period softstorey building (founded on rock) could be increased to 1.0%–2.0% if amplification by soil resonance [16,17] and dynamic torsion [18, 19] have been included. Some damage could be expected at such drift levels but collapse is not considered to be likely. The engineering significance of the projected distant earthquake scenario has been demonstrated for soft-storey buildings founded on an onerous soil site. Based on similar amplification factors, the maximum angle of inter-storey drifts of medium-rise buildings could be increased from 0.025% to 0.2%–0.3% by soil amplification and to about 0.5% if the effects of dynamic torsion has been included. The 0.06% maximum inter-storey drift at the upper levels of a 30-storeys high-rise building founded on rock could only be increased to 0.2%–0.3% maximum since the soil amplification at a natural period of 3 s would only be in the order of 2–3, and not 10 for a soil site with site period in the order of 0.8 s (based on the trend shown in Fig. 8a and b).
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The predictions of inter-storey drifts from this study is lower than that predicted by the important study by Kirke and Hao [20] in which a magnitude 9 event at a distance of 550 km from Singapore was considered. Nonetheless, results reported from both studies are of the same order of magnitude, and both studies predict a drift demand in buildings of between 1% and 2% in the worst case. The two studies are also in agreement that the inter-storey drift demand predicted for medium-rise and high-rise buildings are much higher than that for low-rise buildings, which is a feature unique to large magnitude distant earthquakes. Finally, it is noted that certain slender unreinforced masonry walls may be susceptible to out-of-plane failure by overturning when subject to low frequency excitations despite their apparent ‘‘stiff’’ and ‘‘brittle’’ properties in the uncracked state. Refer to recent research on the displacement modelling of the out-of-plane seismic performance of unreinforced masonry walls [21–24] and the overturning of free-standing objects in buildings [25–27]. 6. Conclusion A stochastic model is introduced in this paper for simulating elastic response spectra (of 5% critical damping) of large magnitude long distance earthquakes generated by the Sunda Arc subduction source. Response spectra simulated for the projected scenarios of M9-M9.5 on rock sites at a critical distance of 600 km infer an acceleration demand of approximately 1.3% gravitational acceleration and a maximum velocity demand of 50 mm/s. Response spectra of four recent major subduction events of magnitudes ranging between 7.9 and 9.3 on the Sunda Arc have been presented for comparison with those simulated by the stochastic model. Good agreement between the recorded and simulated response spectra have been shown for each comparison. Further comparisons were made with both a global attenuation model for subduction earthquakes to demonstrate agreement at a reference site–source distance of 100 km, and other previously proposed attenuation relationships. The drift demand on structures founded on rock is estimated to be generally low but could be up to some 80 mm for single-degreeof-freedom systems possessing a very high natural period of 10 s. Importantly, the drift demand could be amplified many times on flexible soil sites resulting in:
• Drift demands substantially less than 1% for low rise buildings. • Soft-storey drifts of up to around 1%–2%. • Inter-storey drift demands of less than 1% for medium and high rise buildings.
• Relative movements in the end supports of precast beams of up to 50 mm. The simulation methodology presented in this paper is not specific to Singapore and could be applied to other parts of the world where large magnitude distant earthquakes are of concern, however path modification factors (such as the Quality factor in particular) assumed in the simulations would need to be representative of the region. Acknowledgements Constructive feedbacks from Dr Jack Pappin of Ove Arup & Partners (Hong Kong Office) on the draft manuscript of the paper are gratefully acknowledged. The provision of recorded accelerograms by the Meteorological Service Singapore is gratefully acknowledged. Research collaboration with University of Hong Kong (particularly with Dr Hing-Ho Tsang) in related studies have contributed to the development of the research methodology
which was employed in this study. Advice given by Professor C.G. Koh of National University Singapore on matters related to building construction in Singapore is also acknowledged. References [1] Balendra T, Lam NTK, Wilson JL, Kong KH. Analysis of long-distance earthquake tremors and base shear demand for buildings in Singapore. J Eng Struct 2001; 24:99–108. [2] United States Geological Survey (USGS) Earthquake Hazard program website: http://neic.usgs.gov/neis/eq_depot. USGS National Earthquake Information Centre: World Data Centre for Seismology. [3] Brownjohn JMW. Lateral loading and response of a tall building in the nonsesimic doldrums. J Eng Struct 2005;21:1801–12. [4] Petersen MD, Dewey J, Hartzell S, Mueller C, Harmsen S, Frankel A, et al. Probabilistic seismic hazard analysis for Sumatra, Indonesia and across the southern Malaysian Peninsula. Tectonophysics 2004;390:141–58. [5] Lam NTK, Wilson JL, Hutchinson GL. Generation of synthetic earthquake accelerograms using seismological modeling: A review. J Earthq Eng 2000; 4(3):321–54. [6] Lam NTK. Program GENQKE users’ manual, Department of Civil & Environmental Engineering. University of Melbourne. First written in 1999 and latest edition in 2002. [7] Uniform Building Code (1997 edition), Council of Building Officials, California, USA. [8] International Building Code (2006 edition), International Code Council, California, USA. [9] Atkinson GM, Boore DM. Relations for subduction zone earthquakes and their application to Cascadia and other regions. Bull Seismological Soc America 2003;93(4):1703–29. [10] Crouse CB, Yogesh KV, Schell BA. Ground motions from subduction-zone earthquakes. Bull Seismological Soc America 1999;78:1–25. [11] Youngs RR, Chiou SJ, Silva WJ, Humphrey JR. Strong ground motion attenuation relationships for subduction zone earthquakes. Seismological Res Lett 1997; 68(1):58–73. [12] Megawati K, Pan TC, Koketsu K. Response spectral attenuation relationships for Sumatran-Subduction earthquakes and the seismic hazard implications to Singapore and Kuala Lumpur. Soil Dynam Earthq Eng 2005;25:11–25. [13] Risk Management Solutions (RMS). Managing tsunami risk in the aftermath of the 2004 Indian ocean earthquake & tsunami. 2006. Publication accessible on website: http://www.rms.com. [14] Megawati K, Pan TC. Prediction of the maximum credible ground motion in Singapore due to a great Sumatran subduction earthquake: The worst case scenario. Earthq Eng Struct Dynam 2002;31:1501–23. [15] Pan TC, Megawati K, Lim CL. Seismic shaking in Singapore due to past sumatran earthquakes. J Earthq Tsunami 2007;1:49–70. [16] Chandler AM, Lam NTK, Sheikh N. Response spectrum predictions for potential near-field and far-field earthquakes affecting Hong Kong: Soil sites. Soil Dynam Earthq Eng 2002;22:419–40. [17] Lam NTK, Wilson JL, Chandler AM. Seismic displacement response spectrum estimated from the frame analogy soil amplification model. J Eng Struct 2001; 23:1437–52. [18] Balendra T, Lam NTK, Perry MJ, Lumantarna E, Wilson JL. Simplified displacement demand prediction of tall asymmetric buildings subjected to long distance earthquakes. J Eng Struct 2005;27:335–48. Elsevier Science Publisher. [19] Lam NTK, Wilson JL, Hutchinson GL. Review of the torsional coupling of asymmetrical wall-frame buildings. J Eng Struct 1997;19(3):233–46. [20] Kirke A, Hao H. Estimation of failure probabilities of RC frame structures in Singapore to the simulated largest credible ground motion. J Eng Struct 2004; 26:139–50. [21] Lam NTK, Wilson JL, Hutchinson GL. The seismic resistance of unreinforced masonry cantilever walls in low seismicity areas. Bull New Zealand National Soc Earthq Eng 1995;28(3):179–95. [22] Doherty K, Griffith M, Lam NTK, Wilson JL. Displacement-Based Analysis for out-of-plane bending of seismically loaded unreinforced masonry walls. Earthq Eng Struct Dyn 2002;31(4):833–50. [23] Lam NTK, Griffith MC, Wilson JL, Doherty K. Time History Analysis of URM walls in out-of-plane flexure. J Eng Struct 2003;25(6):743–54. [24] Griffith MC, Lam NTK, Wilson JL, Doherty K. Experimental investigation of unreinforced brick masonry walls in flexure. J Amer Soc Civil Eng 2003;130(3): 423–32. J Struct Eng. [25] Al Abadi H, Lam NTK, Gad EF. A simple displacement based model for predicting seismically induced overturning. J Earthq Eng 2006;10(6):775–814. [26] Al Abadi H, Lam NTK, Gad EF, Chandler AM. Earthquake floor spectra for unrestrained building components. Internat J Struct Stability Dynam 2004; 4(3):361–77. [27] Franke D, Lam NTK, Gad EG, Chandler AM. Seismically induced overturning of objects and filtering effects of buildings. Internat J Seismology Earthq Eng 2005;7(2):95–108.
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Seismic load estimates of distant subduction earthquakes affecting Singapore N.T.K. Lam a,∗ , T. Balendra b , J.L. Wilson c , S. Venkatesan d a
Department of Civil and Environmental Engineering, University of Melbourne, Parville 3010, Australia
b
Department of Civil Engineering, National University Singapore, Singapore
c
Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, Australia
d
School of Architectural, Civil & Mechanical Engineering, Victoria University, Australia
article
info
Article history: Received 11 July 2007 Received in revised form 9 January 2009 Accepted 12 January 2009 Available online 8 February 2009 Keywords: Distant earthquakes Stochastic simulations Subduction earthquakes Sunda Arc Singapore Malaysia
a b s t r a c t This paper introduces the use of a simple stochastic model for predicting elastic response spectra of 5% damping for structures founded on rock sites in Singapore based on earthquake scenarios of moment magnitude Mw = 9 − 9.5 generated from the Sunda-Arc subduction source at a closest distance of 600 km. Structures founded directly on rock are predicted to be subject to low response spectral accelerations of up to 1.3% gravitational acceleration. The maximum velocity demand on a structure is estimated to be in the order of 50 mm/s. The drift demand on a structure is estimated to be generally low but can be up to some 80 mm on single-degree-of-freedom systems possessing a high natural period of 10 s. Evidence of significant drift demand amplification on flexible soil sites due to the phenomenon of resonance is also presented. The long period ground shaking, when amplified, can be potentially hazardous to certain vulnerable structures such as buildings with a soft-storey and precast beams resting on supports of limited width. The stochastic model was originally developed by the authors based on observations from the magnitude 8 event of 4 June 2000 generated by the Sunda Arc subduction source as reported in an earlier publication by Balendra and others in this journal in 2002. Response spectra simulated by the same model based on the same set of parameters were found to be very consistent with those recorded in Singapore from the M9.3 Aceh earthquake of 26 December 2004, the M8.6 Nias earthquake of 28 March 2005 and the M8.4 earthquake of 12 September 2007 in southern Sumatra. In summary, response spectra generated by these major events in recent times could be simulated by the same model. The scale of events observed on this subduction source and the exceptionally long distance of wave travel (to Singapore) considered in this study are of a unique category. Developing an attenuation model by regressing recorded data is not a viable approach given the scarcity of data recorded from such events and hence stochastic modelling was used. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Singapore and the adjoining Malay peninsula have a long history of experiencing seismic tremors generated mainly from major interplate sources at long distances. The two major active earthquake generating sources are namely (i) the Sumatran fault source which has a closest distance of 400–450 km from Singapore and (ii) the Sunda-Arc subduction source off-shore of Sumatra on the Indian Ocean side of the island. This study is concerned with earthquakes generated from this second source (refer [1]). The Sunda Arc seabed subduction trench has a closest distance of 600–650 km from Singapore. In the past eight years, five major earthquake events of magnitude ranging between 7.9 and 9.3 generated from this fault source, were widely felt across the whole
∗
Corresponding author. E-mail address: [email protected] (N.T.K. Lam).
0141-0296/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2009.01.018
region including Singapore and parts of Malaysia. The first event was the magnitude 7.9 (Mw = 7.9) earthquake of 4 June 2000 which occurred offshore of Benkulu in the southern part of Sumatra and was approximately 700 km from Singapore. The second event was the Aceh earthquake of 26th December 2004 (also known as the ‘‘Great Sumatran earthquake’’ which caused the ‘‘BoxingDay Tsunami’’). This second earthquake was of a phenomenal magnitude of Mw = 9.3 and was amongst the largest ever recorded in the region. Whilst the epicentre of the earthquake was about 900 km from Singapore, the centroid of the fault source was much further away in the northwesterly direction. Three events of magnitudes exceeding 7.9 have occurred since then as listed in Table 1. The map of Fig. 1a shows the approximate location for each of these events and basic seismological information can be found in Ref. [2]. Each of these major earthquake events caused significant damage to infrastructure in Sumatra and was widely felt as far as Singapore and parts of Malaysia which are within the
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Table 1 Major earthquake events incorporated into the study. Moment magnitude
Approximate site–source distance to Singapore (km)
Place located closest to epicentre
Time of event
7.9 9.3 8.6 8.4 7.9
700 1200 750 700 550
Bengkulu Aceh Nias Bengkulu Mentawi Strait
4 June 2000 26 December 2004 28 March 2005 12 September 2007 at around 1100 h 12 September 2007 close to mid-night
Fig. 1a. Location of major events generated by Sunda Arc subduction source surrounding Singapore.
intraplate region of Eurasia. Whilst no structural damage was reported in Singapore from these recent events there are concerns that a much more onerous earthquake scenario in terms of its impact on Singapore is possible. An example of such a projected scenario, which can be used as a basis for seismic demand and risk assessment purposes, is an earthquake of the size of the second (Aceh) earthquake event striking at a much closer distance of 600 km from Singapore. None of the events reported above has this onerous combination as illustrated in Fig. 1b which shows the magnitude-distance combinations for both the recorded and projected (design) earthquake scenarios. The design of a building’s lateral force resisting system in Singapore is governed by the Building Control Act which calls up the relevant British Standards for defining the design wind pressure and for the structural (steel or concrete) design of the members. The serviceability and ultimate limit states performance criteria of a building are based on these standards and there are no additional performance criteria that are specific to seismic actions. No regulatory documents contain provisions for seismic actions other than stipulating a nominal horizontal force which is equivalent to 1.5% of the dead load of the building on each floor (which is translated into a design acceleration of 0.015g). This provision is to provide a minimum level of robustness for the building and is not specifically for seismic protection (refer [3] for a detailed review). The characteristic long-period waves of distant earthquake could potentially cause damage to certain structures with long period properties. Precast beams of limited seating length at their
Fig. 1b. Magnitude–Distance combinations of recorded large magnitude earthquakes.
end supports could be at risk of collapse when subject to drift irrespective of the acceleration amplitude of the ground. Other examples of long-period sensitive structures are tall buildings with a soft-storey, large containers filled with liquid and bridges supported on flexible piers. The drift demand on these structures could be accentuated considerably by resonance behaviour on flexible (deep and soft) soil sites. The impact of long period ground shaking on certain structures can have serious consequences irrespective of the ground acceleration amplitude. Thus, seismic
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Table 2 Component factors and input parameters to Stochastic Model. Component factors
Definition of factor and recommended parameter values
Source Factor S (f , M )
S (f , M ) = Mo {(1 − ε)SA+ ε SB ); Mo is the seismic moment. SA = 1/[1 + f /fa ] SB = 1/[1 + f /fb ] Log fa = 2.41 − 0.533M Log fb = 1.43 − 0.188M Log ε = 2.52 − 0.637M
Scaling factor of the source C (ρ, β)
p C = 4πρβ 3 where Rp is the wave radiation factor, F the free surface amplification factor, V the factor partitioning energy in the two orthogonal directions [the product Rp FV can be been taken as 0.78], ρ the density of the rock at the depth of rupture was taken as 2.8 kg/m3 and β the SWV of the rock at the depth of rupture was taken as 3.7 km/s. The anelastic attenuation model, An (f), is defined by the following well known relationships:
Anelastic whole path attenuation factor An(f , R, Q )
Geometrical Attenuation factor G(R, D) Upper crustal amplification factor Va (f , Vs ) Upper crustal attenuation factor P (f )
R FV
−. π.f .R
An (f ) = e Q .β ; Q (f ) = Q0 .f n Q (f ) = 150f 0.56qas obtained by calibration in Balendra et al. (2002) [1] G (R, D) = 1R.5D 0
R 2.5D
where R0 is the reference distance and D is the crustal thickness. D = 30 km
in this area according to information reported in the Global Crustal Model : CRUST 2.0 (2001) [15]. The upper crustal amplification function could be inferred from the shear wave velocity profile using the quarter wave-length method of Boore and Joyner (1997). A shear wave velocity of 1500 m/s was assumed to simulate the conditions of granite intrusion in the region. P (f ) = e−π f κ where κ = 0.04 in view of the SWV conditions of the upper crust in the region.
Definitions of the arguments used in the table have been given in the text below Eq. (2).
hazard models based only on peak ground accelerations (eg. recent publication by Petersen et al. [4]) would not provide accurate predictions of the potential impact of earthquakes of this nature. It is preferable to express such seismic hazards in the form of a response spectrum which can be used for estimating the structural drift demand for any given natural period of vibration. There are global response spectral attenuation relationships developed for subduction earthquakes (refer Section 4.2). However, the scale of events observed on this subduction source and the exceptionally long distance of wave travel to Singapore considered in this study are of a unique category and not covered by any existing global attenuation relationship (refer Fig. 1b). Developing an attenuation model by regressing recorded data is not a viable approach given the scarcity of data recorded from such events. This paper is aimed at presenting to engineers a simple stochastic model that can be used for simulating the effects of large magnitude earthquake events striking Singapore from a long distance. Stochastic modelling is very suited to engineering applications by virtue of its simplicity since the need to simulate wave propagation has been circumvented. Elastic response spectra on rock sites for 5% damping have been estimated by the model in the period range of 0.1–10 s to address civil engineering structures commonly encountered in practice. Waveform properties of the earthquake which require more sophisticated tools to simulate are not of interest in this study. An important element of originality in the paper is the use of the stochastic model (which is commonly used for simulating small and medium magnitude intraplate earthquakes) to obtain reasonably accurate simulations from large magnitude long distance earthquake events on rock sites and also on flexible soil sites due to the phenomenon of resonance. This paper: (i) introduces the use of a stochastic model for simulating elastic response spectra for earthquake ground shaking on rock generated by large magnitude distant earthquakes (Section 2), (ii) presents the simulated response spectra and the inferred drift demand on simple models of structures for the projected earthquake scenarios on rock sites (Section 3), (iii) verifies the accuracy of the model by comparison with recordings from four major past events (Section 4.1), and with models proposed previously in the literature (Sections 4.2 and 4.3), and (iv) demonstrates the use of the developed response spectrum model for estimating the inter-storey drift demand in buildings and the displacement demand in small bridges found on rock or flexible soil sites (Section 5).
2. Overview of the stochastic model for simulating elastic response spectra Stochastic simulations are about synthesizing ground surface acceleration time-series: ag (t ). Ground accelerations of unit variance and uniform frequency content within a limited bandwidth as defined by Eq. (1) is first generated. ag (t ) = w(t )
n=N X
An sin[n(1ω)t + φn ]
(1)
n =1
where An are of identical values for all values of n in the specified range for ‘‘band-limited white-noise’’, φn are random phase-angles obtained from random-number generations, and w(t ) is a timedomain windowing function which guides the ground motion intensity to gradually develop and decay with time as in a real earthquake. The generated random time-series is then subject it to a frequency-domain filter: Ax (f ) as defined by Eq. (2) for modifying the frequency content to emulate the behaviour of a real earthquake. Ax (f ) = S (f , M ).C (ρ, β).An(f , R, Q ).G(R, D).Va (f , Vs ).P (f , κ) (2) where S (f , M ) is the source factor of the seismological model which defines the frequency content of body waves radiating from the source of the earthquake, C (ρ, β) is a scaling factor, An(f , R, Q ) is the anelastic whole path attenuation factor, G(R, D) is the geometrical attenuation factor, Va (f , Vs ) is the upper crustal amplification factor, and P (f , κ) is the upper crustal attenuation factor; f is natural frequency, M is moment magnitude, ρ and β is density and shear wave velocity respectively of the earth crust at the depth of the source, R is site–source distance, Q is quality factor, D is depth of crust measured to the Moho discontinuity, Vs is the depth dependent shear wave velocity of the crust and κ is the ‘‘kappa’’ parameter. Table 2 contains a listing of the definitions for each of the component factors shown in Eq. (2) and their associated input parameters. A detailed review of the stochastic simulation methodology and the seismological model can be found in Lam et al. [5]. Sample time-series and frequency series generated at each step of the simulation procedure can also be found in this reference.
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(a) Example simulated and recorded acceleration time-history (1) based on recordings of Aceh Earthquake of 16 December 2004 on GNS rock site in Singapore in East-South direction.
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(b) Example simulated and recorded acceleration time-history (2) based on recordings of Aceh Earthquake of 16 December 2004 on GNS rock site in Singapore in East-South direction.
(c) Velocity response spectra calculated from 18 random simulations. Fig. 2. Simulated time-histories and response spectra.
Stochastic models of the form defined by Eqs. (1) and (2) have been used for simulating ground motions in North America for over two decades. The authors have adapted the model to studying the attenuation behaviour of earthquakes in different parts of Australia. The stochastic simulations were undertaken by the programme GENQKE developed in-house by the authors [6]. In this study, the same model is used for simulating response spectra of distant earthquakes experienced in Singapore during the major events generated by the Sunda Arc subduction source as outlined earlier in the paper. Input parameters that are suitable for simulations in the region have been identified in an earlier publication by the authors [1] in which ground motions recorded from the first event at Singapore on 4 June 2000 were studied. This same set of parameters (which are listed in Table 2) have been used to simulate ground motions for comparison with the more recent distant major earthquake events recorded in Singapore. Simulations were for horizontal (and not vertical) motions not directionally specific on the horizontal plane, as the response spectrum model developed in the study is based on averages of all directions, which is consistent with most earthquake attenuation relationships including those developed by stochastic simulations. Some 18 accelerograms were generated by stochastic simulations for each earthquake scenario of interest. Elastic response spectra for 5% critical damping were calculated from each of the synthetic accelerograms. Two example accelerograms that were stochastically simulated for the distant earthquake scenario in Singapore consistent with the Aceh event of 2004 are presented in Fig. 2a and b. The recorded acceleration time trace is also shown in each figure for comparison with the simulated traces. The amplitude and average pulse widths in the simulated and recorded traces are generally consistent whilst every record has its own pulse arrival details. The duration of strong shaking in the recorded trace is clearly longer than those in the simulated traces. Thus, the simulations were intended only for representing the response behaviour of structures (and soil-sediments) assuming linear (or
quasi-linear) stress–strain behaviour. The assumption of the linear elastic behaviour of the structure was not unreasonable in view of the intensity of ground shaking that was considered in the study. A more thorough and objective comparison of the spectral contents in the recorded and simulated motions is presented in Section 4. The frequency (spectral) content calculated from each of the 18 random simulations on rock is also shown in Fig. 2c. The ‘‘upperlimit’’ (5% exceedance) of the simulated response spectra is about 1.2–1.3 times that of the ‘‘mean’’ response spectrum (ie. upperlimit is approximately 0.1 units above the mean on the log10 scale) in the period range of engineering interest. Similar margins have been observed with simulations undertaken in the study for other earthquake scenarios. It is shown that inter-event random variabilities of ground shaking on rock in large magnitude distant earthquake events is much lower than that of smaller magnitude near-source earthquakes (provided that the moment magnitude of the earthquake has been pre-determined). This is believed to be due to the robustness of the characteristic high period wave components in a distant earthquake which are well constrained by the seismic moment generated by the earthquake. Whilst interevent random variability of distant earthquakes on rock is much lower than that of near source earthquakes, the ground shaking in a distant earthquake can be very sensitive to site conditions, which is the main contributor to intra-event variability. In the remainder of the paper, only the mean of the simulations on rock is shown. 3. Simulated response spectra for projected earthquake scenarios Debating exactly what moment magnitude that Singapore should consider for the ‘‘worst’’ scenario earthquake is not within the scope of the paper. Predictions for the projected earthquake scenarios can be presented in deterministic terms given the simulation is specific to one source (the Sunda Arc subduction source offshore of Sumatra) and one site (Singapore bedrock).
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(a) Ensemble averaged simulated velocity response spectra.
(b) Acceleration response spectrum envelope.
Fig. 3. Response spectra for projected critical earthquake scenarios.
Given that the largest earthquake ever recorded on this subduction source was of Mw = 9.3, the projected earthquake scenarios are accordingly Mw = 9, 9.3 and 9.5 located on the part of the fault which is at a fixed (closest) distance of 600 km from Singapore. Response spectra were simulated using the stochastic methodology described in Section 2 and the input parameters to the model listed in Table 2. Seismic drift demand of the earthquake on rock sites was then inferred from the simulated response spectra. The outcome of this study is as applicable to Singapore as it is to neighbouring centres of population in the southern part of the adjoining peninsula of Malaysia. This case study is also intended to demonstrate the generic use of the modelling methodology for other regions around the world subject to potential threats from large magnitude distant earthquakes of a similar nature. The ensemble average response spectrum (5% critical damping) simulated for each of the projected scenarios is shown in Fig. 3a together with lines corresponding to constant response spectral acceleration values of 0.004g and 0.013g. The response spectral behaviour of structures with natural period less than 2.5 s could be characterised by these two acceleration limits. Structures possessing a natural period close to 2.5 s pertain to the upper limit whilst structures possessing a low natural period pertain to the lower limit. This dual limit effectively envelopes the simulated response spectra. The response spectrum of Fig. 3a can be used for calculating the elastic drift demand (1) on single-degree-of-freedom lumpedmass systems of 5% critical damping. A response spectral acceleration of 0.004g and 0.013g (as shown in Fig. 3a) can be translated into Eqs. (3a) and (3b) respectively for providing conservative estimates for drift demands in acceleration controlled conditions. Similarly, a maximum velocity demand in the order of 50 mm/s can be translated into Eq. (3c) for estimating drift demands in velocity controlled conditions.
1 (mm) = 0.004 × 9.81 × 1000 ×
for 0.5 s < T < 2.5 s
1 (mm) = 50 ×
T 2π
2
2π
for T ≤ 0.5 s
1 (mm) = 0.013 × 9.81 × 1000 ×
T
≈ T2 (3a)
T 2π
2
≈ 3.2T 2
= 8T for T ≥ 2.5 s
where 1 is in units of mm ; T is in units of seconds.
(3b) (3c)
From Eq. (3), 1 is predicted to be negligible for stiff structures with T ≤ 0.5 s; up to about 20 mm for intermediate structures with T ≤ 2.5 s, and is linearly proportional to T for T > 2.5 s. The value of 1 is predicted to be equal to 80 mm for flexible structures with T = 10 s. Whilst Fig. 3a–b and Eq. (3) are based on bedrock conditions, the drift demand can be amplified many times on flexible soil sites as demonstrated in Section 5. The response spectrum envelope in the usual acceleration (force-based) format as used in current codes of practices is also shown in Fig. 3b to facilitate engineering applications. Also shown in Fig. 3b is the response spectrum model stipulated by the 1997 edition of the Uniform Building Code, USA [7] which is still widely used in codes of practices in many countries worldwide even though it has been superseded in the USA itself by the International Building Code [8]. The response spectrum model of UBC for Class B (rock) sites has been normalised to a notional peak ground acceleration of 0.004g for direct comparison with the response spectrum developed in this study for distant earthquakes. Gross non-conservatism of the (conventional) UBC model in the high period range is demonstrated. Thus, large magnitude distant earthquakes can be potentially much more hazardous to high period structures than normal earthquakes of similar peak ground accelerations. The nominal provisions of 0.015g are shown to be conservative for rock sites but could become inadequate for flexible soil sites. 4. Comparison of simulations with recorded response spectra 4.1. Comparison with response spectra recorded from major events in the region In this section, the elastic response spectra of 5% critical damping simulated from the stochastic model are compared with those recorded from the Bukit Timah Dairy Farm (BTDF) station in Singapore. The station is of rock conditions and hence suited to recording motions for comparison with stochastic simulated motions for rock conditions. Such a comparison has already been undertaken by the authors for the June 2000 Bengkulu event in Ref. [1] and is reproduced herein in Fig. 4d. Similar comparisons have been made in this study for three other events. In undertaking the simulations for each of these events, only the moment magnitude and site–source distance would need to be specified given that the same set of seismological parameters (as listed in Table 2) was used in all the simulations. The second event of Mw = 9.3 (near Aceh) had an epicentral distance (defined at the location where rupture was initiated) of 900 km from Singapore but the geometric centroid of the area covered by the earthquake rupture was estimated to be some 1200 km away from Singapore as shown by the regional map of
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(a) Aceh Earthquake of 16 December 2004 — M9.3 at 1200 km.
(b) Nias Earthquake of 28 March 2005 — M8.6 at 750 km.
(c) Bengkulu Earthquake of 12 September 2007 — M8.4 at 700 km (only records in one direction is available).
(d) Bengkulu Earthquake of 4 June 2000 M7.9 at 700 km.
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Fig. 4. Comparison of simulated and recorded velocity response spectra.
Fig. 1. It is noted that the rupture propagated from the epicentre in the northerly direction for about a thousand kilometres. Response spectra recorded from the Aceh earthquake at the GSN (rock) station in the north–south (NS) and east–west (EW) directions are shown in Fig. 4a along with the ensemble average response spectrum of the stochastically simulated accelerograms. The simulations were conducted with and without incorporating the modifications of the seismic waves by the upper crust. It is shown in Fig. 4a that the effects of crustal modifications were minor but slightly more conservative predictions were obtained when factors representing their effects have been included in the modelling. However, individual troughs and peaks that were featured on the recorded response spectra (including the notable spectral peak at the 4 s period) could not be reproduced by stochastic simulations from the point–source model. The third event of Mw = 8.6 (near Nias) had a site–source distance of about 750 km. A similar level of consistencies between the recorded and simulated response spectra with this third event are shown in Fig. 4b. The slight spectral sags recorded in the 1–3 s period range was again a feature that could not be reproduced by stochastic simulations of a point–source model. The very different site–source distance of the Aceh and Nias events means that significant errors would have resulted if unrepresentative attenuation parameters had been assumed. The fourth event of Mw = 8.4 (near Bengkulu) was with an epicentral distance of about 700 km from Singapore. With this event, the rock motion was back-calculated using program SHAKE from motions recorded on a soil site where details of the subsoil are known. The consistent agreement between the response spectrum calculated from field measurements and that calculated from accelerograms generated by stochastic simulations has again been
demonstrated in Fig. 4c. All the major earthquake events involved in the evaluation of the stochastic model are summarised in Table 1. 4.2. Comparison with predictions by a global attenuation model Generalised empirical attenuation models for subduction earthquakes have been developed from data collected worldwide for earthquakes with Mw < 8.5 and a site–source distance of up to 300 km (e.g. [9–11]). The empirical model of Ref. [9] for interface subduction earthquakes was developed from an expanded database obtained by merging and building on the databases of Refs. [10,11] for global applications. It is noted that this generalised (global) model cannot be realistically extrapolated to predict the intensity of ground shaking of long distance earthquakes affecting Singapore which involve much longer distance of wave-travel. Nevertheless, they could be used to make comparisons with simulations from the proposed stochastic model at a modest distance of 100 km. Fig. 5a and b show the 1 s and 3 s response spectral velocities predicted by this global empirical model on rock based on a common value of R = 100 km (where R is the distance to the closest point on the ruptured fault surface, and is denoted as Dfault in Ref. [9]). Although a closer reference distance seems more appropriate for the comparison of the ‘‘source’’ spectral properties, the choice of 100 km as the reference distance was intended to circumvent complications arising from near-fault effects given that the aim of this study was to model long-distance earthquakes affecting Singapore which has a minimum distance of 600 km from the Sunda-Arc subduction zone. The 100 km distance was also chosen as the reference distance for revealing source properties because of the abundance of empirical data in that distance range.
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(a) Response spectral velocity at 1 s period.
(b) Response spectral velocity at 3 s period. Fig. 5. Comparison of predictions by stochastic model with global attenuation model.
A focal depth of h = 20 km was assumed when applying the global empirical model for comparison with predictions by the stochastic model proposed by the authors. This assumption is close to the h = 24 km adopted by Megawati et al. [12] in their simulation of subduction earthquakes in the Sunda Arc region. The Quality factors of ‘‘Q = 680’’ and ‘‘Q = 150’’ as shown in the legend of Fig. 5a and b refer to the assumed Quality factors of Q = 680 f 0.36 and 150 f 0.56 respectively. Conditions enveloped by these limits represent a wide range of crustal conditions. Yet, the simulated response spectral velocities (at the 1 s and 3 s periods) associated with these limits were very close which effectively demonstrates that anelastic attenuation had only a minor effects on the ground shaking at 100 km distance with very large magnitude earthquakes. A robust comparison of predictions by the stochastic and empirical models was then possible. Both Fig. 5a and b show notable differences between predictions by the stochastic simulations of the seismological model and the empirical model, when Mw < 7. Interestingly, predictions from the two models are shown to be in much better agreement when Mw > 7. No instrumented recordings of the Aceh nor Nias earthquakes were available at a 100 km distance from the fault source making it difficult to directly verify the accuracy of the stochastic source model at the upper end of the magnitude range shown in Fig. 5a–b. However, Modified Mercalli Intensities (MMI) ranging between VIII-IX were reported at Banda Aceh due to the immediate impact of the ground shaking generated by the Aceh earthquake. According to a USGS source cited by RMS [13]: ‘‘violent shaking caused the collapse of some mid-rise reinforced concrete structures’’.
Banda Aceh was some 250 km from the epicentre of the earthquake but the closest distance of the city to the ruptured fault was only about 100–150 km. Given that the city was not in alignment with the ruptured fault, the effects of directivity were not dominant. In conclusion, simulations of the response spectral parameters (for 1 s and 3 s periods) by the proposed stochastic model are shown to be consistent with empirical models for interface subduction earthquakes. 4.3. Comparison with predictions by regional specific attenuation models Prior to the great earthquake of Aceh, seismic hazard modelling of long-distance earthquakes affecting Singapore had been undertaken by the authors [1] and by others [14,12,15]. The elaborate response spectral attenuation relationship of Eq. (4a) for horizontal motions was developed specifically for the region by Megawati, Pan and Koketsu [12]. 2 Loge (YH ) = a0 + a1 Mw + a2 Mw + a3 loge (R) + a4 R + a5 h + εH
(4a) where YH represents ground motion parameters including Peak Ground Acceleration, Peak Ground Velocity and response spectral acceleration for natural periods ranging between 0.5 s and 20 s; R is the distance from station to the centre of the rupture plane in kilometres; h is focal depth in kilometres; εH is the standard error; and a0 − a5 are period dependant coefficients. Earthquake data used in supporting the relationship was recorded from earthquakes with site–source distances of between
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(a) Aceh earthquake scenario (M9.3 at 1200 km).
(b) Nias earthquake scenario (M8.6 at 750 km). Fig. 6. Estimates by models of Refs. [12,15] and this study with recorded results.
200 and 1500 km. The relationship has also been used in Ref. [12] to simulate a historical event of 1833 (Mw = 9) at a distance of 700 km. Thus, ground shaking in Singapore generated by the Aceh and Nias earthquakes were intended to be within the intended scope of the proposed attenuation relationship of Eq. (4a). It is noted however that at the time Eq. (4) was developed by Ref. [12], instrumented strong motion data collected from within the region was mostly restricted to small and moderate magnitude earthquakes of Mw ≤ 6.5. Thus, the accuracies of the proposed attenuation relationship as applied to large magnitude earthquakes could not be tested. The rupture occurred at the relatively shallow part of the subduction zone with focal depth ranging between 10–30 km. A mean value of 20 km was taken as the value of ‘‘h’’ for the purpose of Eq. (4). The seismological information of the event as quoted above was based on information of the event provided by the Risk Management Solution in their publication: RMS [13]. The velocity response spectra calculated from the recorded accelerograms are shown in Fig. 6a and b for comparison with estimates from Eq. (4a). The estimated response spectra were up to two orders of magnitude (100 times) higher than the recorded results in the natural period range of 0.5–3.0 s from the Aceh earthquake event, and in an order of magnitude (10 times) higher than the recordings from the (closer) Nias earthquake event. The shape of the response spectra based on stochastic simulations (as defined by Eq. (4a)) were also significantly different from the response spectra calculated from the recorded accelerograms.
A more recent paper by Pan, Megawati and Lim [15], published 2 years after the Aceh and Nias earthquakes (by similar authorship constituents of Ref. [12]), presents an alternative attenuation relationship and a different set of coefficients. The revised relationship is of the form represented below and is similar, but not identical, to that of Eq. (4a). Loge (YH ) = a0 + a1 (Mw − 6) + a2 (Mw − 6)2
+ a3 loge (R) + (a4 + a5 Mw )R + εH .
(4b)
Estimates from Eq. (4b), based on Ref. [15], are also shown in Fig. 6a and b for comparison. Clearly, the revised estimates calculated from Eq. (4b) are closer to results derived from the field instrumented records than the initial estimates calculated from Eq. (4a), but there are still significant modelling errors with the revised relationship. The proposed attenuation relationships as represented by Eqs. (4a) and (4b) (based on Refs. [12, 15] respectively) do not appear to be suitable for modelling ground motions generated by very large magnitude, and distant, earthquakes. 5. Estimation of drifts in buildings and bridges 5.1. Basics The estimation of drifts in buildings and bridges begin with the calculation of the predicted effective displacement (1eff ) which is defined herein as the maximum displacement experienced by
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(a) Dislodgement of bridge decking.
(b) Low and medium-rise building with a soft-storey.
(c) Medium-rise moment frame.
(d) 30-storeys high-rise building frame. Fig. 7. Drift demand on buildings and bridges.
a lumped mass single-degree-of-freedom system of linear elastic dynamic properties and 5% critical damping. The value of 1eff can be calculated from Eq. (5) which requires the response spectral value (RSV) at the designated natural period (T ) to be read off directly from the velocity response spectrum of Fig. 3a.
1eff (mm) = RSV .
T 2π
.
(5)
Alternatively, the value of 1eff could be calculated using Eqs. (3a)–(3c) if the structure is founded directly on rock. It is noted that the velocity response spectrum model presented in Fig. 3a and b were based on the ensemble mean of the stochastically simulated response spectra. As shown in Fig. 2c, a factor of 1.3 will have to be applied to the mean estimates to obtain the ‘‘upper limit’’ estimates for 5% exceedance.
In this section, the maximum drift demand for each structure shown schematically in Fig. 7a–d are calculated from the response spectrum model presented in the paper. Storey drifts are calculated initially for structures founded directly on rock, and very modest values are predicted. Storey drift predictions are then made for structures founded on a flexible soil site. The example site used in the illustrations was at the location where accelerograms were recorded on the soil surface during the Aceh and Nias earthquakes. The response spectra calculated from the recorded accelerograms were used as the basis of estimating the soil amplification factor. 5.2. Drift demands calculated for structures founded on rock The drift demand on a building with a soft-storey, and that on a bridge deck found directly on rock, can be related directly to the
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(a) Recorded from Aceh earthquake.
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(b) Recorded from Nias earthquake. Fig. 8. Response spectra recorded from example flexible soil site.
calculated 1eff value given that both structures can be modelled as lumped-mass single-degree-of-freedom systems (Fig. 7a and b). Note, this assumption is only valid for a bridge with lengths much shorter than the horizontal component of the quarter wave-length of the transmitted seismic waves in order that relative movement between individual bridge supports can be ignored. Low-rise building structures with a natural period less than 0.5 s are estimated to have negligible drift demands. If the building and bridge systems have a natural period of 0.8 s, the value of 1eff is estimated at around 2–2.5 mm (based on Eq. (3b)), with an upper limit estimate for 5% exceedance of around 1.31eff ∼ 3 mm. The column drift ratio at the ground floor level of the soft-storey building for design purposes is accordingly equal to 0.1% (assuming a span length of 3 m of the column). Thus, the drift demand of the building on rock sites is negligible, and elastic response could be expected with no damage. The maximum angle of drift on a medium-rise moment frame (Fig. 7c) can also be calculated readily once the value of 1eff is known. The roof displacement will be approximately 1.3 times the value of 1eff for a moment frame building since the deflected shape is dominated by shear actions. In other words, the effective height of the building as defined by Fig. 7c is approximately 0.75 times the total height of the building (H ). The average drift of the building is then the roof displacement divided by H (which is translated into 1eff /0.75H or 1.31eff /H). It can be shown that the maximum inter-storey drift is approximately 1.5 times the average drift. Thus, for a building with a natural period of 0.8 s (same as above), the maximum inter-storey drift for design purpose is 1.5 × 1.3 × (1.31eff )/H which is equal to 0.025% approximately if H = 24 m. The predicted drift demand on rock sites is also negligible. Allowances for higher mode effects may have to be taken into account when calculating the maximum angle of inter-storey drift for the 30-storey high-rise building structure of Fig. 7d. Dynamic modal analysis of the building model for the first two significant modes of vibration revealed a modal natural period of 2.7 s and 0.6 s. If the building is founded on rock the value of 1eff is accordingly predicted (from Eqs. (3c) and (3b)) at 22 mm and 1 mm respectively (the latter second mode can be neglected). Modal analysis of the building structure revealed a maximum inter-storey drift of 0.002% per unit mm of 1eff at the upper levels. Thus, the maximum inter-storey drift is 22 × 0.002% = 0.045% approximately. For design purposes, a factor of 1.3 is applied to obtain the upper limit of 5% exceedance of 0.06% storey drift. Again, the inter-storey drift demand of the building on rock sites is negligible.
5.3. Drift demands calculated for structures founded on soft soil Response spectra recorded on the soil surface of the example flexible soil site indicates a site natural period of 0.8 s (refer Fig. 8a and b) and indicative of a fairly soft (and deep) soil site. Considering the worst scenario where the natural period of the structure is close to the natural period of the site, an anomalously high soil amplification factor of about 10 has consistently been revealed in the response spectra calculated from accelerograms recorded on rock and soil sites in Singapore during the Aceh and Nias earthquake events. The amplification factor associated with the critical earthquake scenario of M9.3 at 600 km distance should have lower amplification values given that the site factor is expected to decrease with increasing intensity of ground shaking. In the absence of representative earthquake records, the amplification factors have to be evaluated by dynamic analysis of the sedimentary layers. In the interim, a conservative amplification factor of 10 is assumed in the following examples. Under these onerous soil conditions assumed, the 3 mm displacement of the bridge on rock (refer Section 5.2) would be increased to 30 mm which could further be increased by torsional movements. Even higher movement could occur at halving joints which connect two parts of the bridge experiencing out-of-phase motions resulting in maximum movements of up to around 50 mm. The drift demand on low-rise buildings with natural periods less than 0.5 s would not be significant even with the effects of soil amplification. The 0.1% storey drift on the ground floor of a 0.8 s period softstorey building (founded on rock) could be increased to 1.0%–2.0% if amplification by soil resonance [16,17] and dynamic torsion [18, 19] have been included. Some damage could be expected at such drift levels but collapse is not considered to be likely. The engineering significance of the projected distant earthquake scenario has been demonstrated for soft-storey buildings founded on an onerous soil site. Based on similar amplification factors, the maximum angle of inter-storey drifts of medium-rise buildings could be increased from 0.025% to 0.2%–0.3% by soil amplification and to about 0.5% if the effects of dynamic torsion has been included. The 0.06% maximum inter-storey drift at the upper levels of a 30-storeys high-rise building founded on rock could only be increased to 0.2%–0.3% maximum since the soil amplification at a natural period of 3 s would only be in the order of 2–3, and not 10 for a soil site with site period in the order of 0.8 s (based on the trend shown in Fig. 8a and b).
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The predictions of inter-storey drifts from this study is lower than that predicted by the important study by Kirke and Hao [20] in which a magnitude 9 event at a distance of 550 km from Singapore was considered. Nonetheless, results reported from both studies are of the same order of magnitude, and both studies predict a drift demand in buildings of between 1% and 2% in the worst case. The two studies are also in agreement that the inter-storey drift demand predicted for medium-rise and high-rise buildings are much higher than that for low-rise buildings, which is a feature unique to large magnitude distant earthquakes. Finally, it is noted that certain slender unreinforced masonry walls may be susceptible to out-of-plane failure by overturning when subject to low frequency excitations despite their apparent ‘‘stiff’’ and ‘‘brittle’’ properties in the uncracked state. Refer to recent research on the displacement modelling of the out-of-plane seismic performance of unreinforced masonry walls [21–24] and the overturning of free-standing objects in buildings [25–27]. 6. Conclusion A stochastic model is introduced in this paper for simulating elastic response spectra (of 5% critical damping) of large magnitude long distance earthquakes generated by the Sunda Arc subduction source. Response spectra simulated for the projected scenarios of M9-M9.5 on rock sites at a critical distance of 600 km infer an acceleration demand of approximately 1.3% gravitational acceleration and a maximum velocity demand of 50 mm/s. Response spectra of four recent major subduction events of magnitudes ranging between 7.9 and 9.3 on the Sunda Arc have been presented for comparison with those simulated by the stochastic model. Good agreement between the recorded and simulated response spectra have been shown for each comparison. Further comparisons were made with both a global attenuation model for subduction earthquakes to demonstrate agreement at a reference site–source distance of 100 km, and other previously proposed attenuation relationships. The drift demand on structures founded on rock is estimated to be generally low but could be up to some 80 mm for single-degreeof-freedom systems possessing a very high natural period of 10 s. Importantly, the drift demand could be amplified many times on flexible soil sites resulting in:
• Drift demands substantially less than 1% for low rise buildings. • Soft-storey drifts of up to around 1%–2%. • Inter-storey drift demands of less than 1% for medium and high rise buildings.
• Relative movements in the end supports of precast beams of up to 50 mm. The simulation methodology presented in this paper is not specific to Singapore and could be applied to other parts of the world where large magnitude distant earthquakes are of concern, however path modification factors (such as the Quality factor in particular) assumed in the simulations would need to be representative of the region. Acknowledgements Constructive feedbacks from Dr Jack Pappin of Ove Arup & Partners (Hong Kong Office) on the draft manuscript of the paper are gratefully acknowledged. The provision of recorded accelerograms by the Meteorological Service Singapore is gratefully acknowledged. Research collaboration with University of Hong Kong (particularly with Dr Hing-Ho Tsang) in related studies have contributed to the development of the research methodology
which was employed in this study. Advice given by Professor C.G. Koh of National University Singapore on matters related to building construction in Singapore is also acknowledged. References [1] Balendra T, Lam NTK, Wilson JL, Kong KH. Analysis of long-distance earthquake tremors and base shear demand for buildings in Singapore. J Eng Struct 2001; 24:99–108. [2] United States Geological Survey (USGS) Earthquake Hazard program website: http://neic.usgs.gov/neis/eq_depot. USGS National Earthquake Information Centre: World Data Centre for Seismology. [3] Brownjohn JMW. Lateral loading and response of a tall building in the nonsesimic doldrums. J Eng Struct 2005;21:1801–12. [4] Petersen MD, Dewey J, Hartzell S, Mueller C, Harmsen S, Frankel A, et al. Probabilistic seismic hazard analysis for Sumatra, Indonesia and across the southern Malaysian Peninsula. Tectonophysics 2004;390:141–58. [5] Lam NTK, Wilson JL, Hutchinson GL. Generation of synthetic earthquake accelerograms using seismological modeling: A review. J Earthq Eng 2000; 4(3):321–54. [6] Lam NTK. Program GENQKE users’ manual, Department of Civil & Environmental Engineering. University of Melbourne. First written in 1999 and latest edition in 2002. [7] Uniform Building Code (1997 edition), Council of Building Officials, California, USA. [8] International Building Code (2006 edition), International Code Council, California, USA. [9] Atkinson GM, Boore DM. Relations for subduction zone earthquakes and their application to Cascadia and other regions. Bull Seismological Soc America 2003;93(4):1703–29. [10] Crouse CB, Yogesh KV, Schell BA. Ground motions from subduction-zone earthquakes. Bull Seismological Soc America 1999;78:1–25. [11] Youngs RR, Chiou SJ, Silva WJ, Humphrey JR. Strong ground motion attenuation relationships for subduction zone earthquakes. Seismological Res Lett 1997; 68(1):58–73. [12] Megawati K, Pan TC, Koketsu K. Response spectral attenuation relationships for Sumatran-Subduction earthquakes and the seismic hazard implications to Singapore and Kuala Lumpur. Soil Dynam Earthq Eng 2005;25:11–25. [13] Risk Management Solutions (RMS). Managing tsunami risk in the aftermath of the 2004 Indian ocean earthquake & tsunami. 2006. Publication accessible on website: http://www.rms.com. [14] Megawati K, Pan TC. Prediction of the maximum credible ground motion in Singapore due to a great Sumatran subduction earthquake: The worst case scenario. Earthq Eng Struct Dynam 2002;31:1501–23. [15] Pan TC, Megawati K, Lim CL. Seismic shaking in Singapore due to past sumatran earthquakes. J Earthq Tsunami 2007;1:49–70. [16] Chandler AM, Lam NTK, Sheikh N. Response spectrum predictions for potential near-field and far-field earthquakes affecting Hong Kong: Soil sites. Soil Dynam Earthq Eng 2002;22:419–40. [17] Lam NTK, Wilson JL, Chandler AM. Seismic displacement response spectrum estimated from the frame analogy soil amplification model. J Eng Struct 2001; 23:1437–52. [18] Balendra T, Lam NTK, Perry MJ, Lumantarna E, Wilson JL. Simplified displacement demand prediction of tall asymmetric buildings subjected to long distance earthquakes. J Eng Struct 2005;27:335–48. Elsevier Science Publisher. [19] Lam NTK, Wilson JL, Hutchinson GL. Review of the torsional coupling of asymmetrical wall-frame buildings. J Eng Struct 1997;19(3):233–46. [20] Kirke A, Hao H. Estimation of failure probabilities of RC frame structures in Singapore to the simulated largest credible ground motion. J Eng Struct 2004; 26:139–50. [21] Lam NTK, Wilson JL, Hutchinson GL. The seismic resistance of unreinforced masonry cantilever walls in low seismicity areas. Bull New Zealand National Soc Earthq Eng 1995;28(3):179–95. [22] Doherty K, Griffith M, Lam NTK, Wilson JL. Displacement-Based Analysis for out-of-plane bending of seismically loaded unreinforced masonry walls. Earthq Eng Struct Dyn 2002;31(4):833–50. [23] Lam NTK, Griffith MC, Wilson JL, Doherty K. Time History Analysis of URM walls in out-of-plane flexure. J Eng Struct 2003;25(6):743–54. [24] Griffith MC, Lam NTK, Wilson JL, Doherty K. Experimental investigation of unreinforced brick masonry walls in flexure. J Amer Soc Civil Eng 2003;130(3): 423–32. J Struct Eng. [25] Al Abadi H, Lam NTK, Gad EF. A simple displacement based model for predicting seismically induced overturning. J Earthq Eng 2006;10(6):775–814. [26] Al Abadi H, Lam NTK, Gad EF, Chandler AM. Earthquake floor spectra for unrestrained building components. Internat J Struct Stability Dynam 2004; 4(3):361–77. [27] Franke D, Lam NTK, Gad EG, Chandler AM. Seismically induced overturning of objects and filtering effects of buildings. Internat J Seismology Earthq Eng 2005;7(2):95–108.