Site response analyses using downhole arrays at various seismic hazard levels of Singapore

Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

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

Site response analyses using downhole arrays at various seismic hazard levels of Singapore Wenqi Du a,n, Tso-Chien Pan a,b a b

Institute of Catastrophe Risk Management, Nanyang Technological University, 50 Nanyang Avenue, Singapore School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore

art ic l e i nf o

a b s t r a c t

Article history: Received 2 April 2015 Received in revised form 20 August 2016 Accepted 24 August 2016

Local site conditions can significantly influence the characteristics of seismic ground motions. In this study, site response analyses using one-dimensional linear elastic (LE), equivalent-linear (EQL) and nonlinear (NL) approaches are performed at different seismic hazard levels of Singapore. Two seismic stations, namely, the KAP and BES stations located at soft soil sites, are selected from the national network of Singapore. Firstly, site response estimates using the LE, EQL (SHAKE04) and NL (DEEPSOIL) approaches are compared with the borehole recordings. Results show favorable matches between the predictions and the observations at the KAP site, while under-predictions are observed for all the three site effect approaches at the BES site. Secondly, the applicability of the LE, EQL and NL models is examined at different hazard levels of Singapore. It is found that for the hazard level at a return period of 475 years, the computed maximum strain (γmax) is 0.06% and then the EQL model can provide accurate site response predictions. However, for the hazard level at a return period of 2475 years, the calculated γmax is larger than 2%, resulting in notable differences in the predictions of different site response models. This study highlights the importance of site effects in seismic hazard analysis of Singapore. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Site response analysis Downhole arrays Equivalent-linear Nonlinear analysis Urban seismic hazard Singapore

1. Introduction Although Singapore is located in low-to-moderate seismicity regions, seismic risk should be an important concern due to its strong economy, dense population and numerous high-rise buildings. Nowadays there are more than five million residents in Singapore, and most of them live in middle or high-rise buildings. These high-rise buildings have frequently experienced shakings by far-field Sumatran earthquakes. One of the major sources of ground shakings felt in Singapore is the Great Sumatran fault (at a distance of about 400 km from Singapore). It has been identified as a 1,900-km long right-lateral strike-slip fault consisting of 20 major segments [1]. Several studies have shown that the Great Sumatran fault, which is well known to produce earthquakes larger than moment magnitude (Mw) 7, may potentially affect Singapore regions by some major earthquakes [2,3]. In the new seismic design code of Singapore [4], the bedrock peak ground acceleration (PGA) value is given as 0.0178 g for a return period of 475 years (10% probability in 50 years). Besides, based on the Southeast Asia PGA hazard maps by U.S. Geological Survey (USGS), the rock PGA value with 10% probability of exceedance in 50 years n

Corresponding author. E-mail address: [email protected] (W. Du).

http://dx.doi.org/10.1016/j.soildyn.2016.08.033 0267-7261/& 2016 Elsevier Ltd. All rights reserved.

is in the range of 0.04-0.06 g, while the rock PGA with 2% probability of exceedance in 50 years is about 0.15-0.2 g [5]. It should be noted that the rock PGA value provided from the USGS hazard map is slightly greater than that of the seismic design code of Singapore. Local site conditions play an important role in the characteristics of surface seismic waves. In general, soft soil sites tend to increase ground motion amplitudes compared to rock sites. The earthquakes of 1985 Michoacan event [6], 1989 Loma Prieta event [7] and 2010 Haiti event [8] have shown the significant influence of local site conditions. For instance, the Mexico City, although it was located 400 km away from the epicenter, suffered severe damages and human losses due to strong site amplifications. Therefore, in view of a similar situation compared with the Mexico City, more attentions should be drawn to the high-rise buildings built on soft clays or reclaimed lands of Singapore. The surface ground motions are usually estimated by one-dimensional linear elastic (LE), equivalent-linear (EQL) frequency domain analysis [9] or fully nonlinear (NL) time domain analyses [10]. Downhole seismometer arrays are commonly used to compare and validate site response analyses, e.g. [11–20]. For example, Kwok et al. [13] performed blind site response predictions at the Turkey Flat array site using ground motions from the 2004 Parkfield earthquake. Kottke [15] evaluated the performance of equivalent-linear and fully nonlinear analyses using borehole sites

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in California and Japan, and Kaklamanos et al. [16] compared the accuracy of linear and equivalent-linear method using 100 KiKNET arrays. These results show that the suitability of different methods is strongly associated with ground motion intensities, one-dimensional assumptions as well as maximum strain levels. The objective of this paper is to perform a comprehensive site response analysis using two seismic downhole arrays of Singapore. Two major issues are addressed in this study. First, the computed ground motions by various methodologies (LE, EQL and NL) at different depths are compared with the recorded data at each vertical array. The computations are based on two recent earthquake events: the September 30, 2009 event (Mw 7.6 and rupture distance 470 km) and the October 1, 2009 event (Mw 6.6 and rupture distance 460 km). These events can be regarded as frequently felt earthquakes in Singapore. Second, site response analyses using the three aforementioned methods (LE, EQL and NL) are performed at various earthquake intensity levels: (i), the seismic design level of Singapore with a bedrock PGA 0.0178 g (10% probability of exceedance in 50 years); (ii), one ground motion with PGA 0.04 g from the 1985 Mexico earthquake which can be regarded as a rare event of Singapore due to the similar fault mechanisms and rupture distances; (iii), the up-scaled Mexico time history with PGA as 0.15 g (2% probability of exceedance in 50 years in Singapore); and (iv), the up-scaled Mexico motions with a series of target PGA values (from 0.05 g to 0.2 g with interval as 0.01 g). To sum up, the presented paper plans to quantitatively evaluate the site amplifications of the two soft clay sites in Singapore, and further clarify the suitability of the LE, EQL and NL methods at different intensity levels. It is to be noted that through this study, the LE and EQL analyses are performed in the frequency domain by SHAKE04 [21], and the fully NL approach is implemented in the time domain by DEEPSOIL v5.1 software [22].

2. Geology and seismic stations of Singapore Recently, the Defence Science and Technology Agency [23] provided detailed geological formations of Singapore, as shown in

Fig. 1. The geology of Singapore can be broadly classified into five major formations i.e., Gombak Norite (GN), Bukit Timah Granite (BTG), Jurong Formation (JF), Old Alluvium (OA) and Kallang Formation (KF). In particular, KF is the youngest formation, and it is located most abundantly on the coastline of the island with larger area coverage at the southeast part. The KF category consists of marine and littoral sediments with silt and clay lenses. In addition, a large portion of Reclaimed Land (RL) has been extended outwards to coast. Based on ground types classification of Eurocode 8 [24], the dominant site classifications in Singapore are mainly ground types B, C, D and S1, and the corresponding values of shear wave velocity in the top 30 m (Vs30) are in the range of 360-800 m/ s, 180-360 m/s, 100-180 m/s and less than 100 m/s, respectively. Seven seismic stations were set up in 1996 by the Meteorological Services Singapore. They are located at Bukit Timah Dairy Farm (BTDF), Fruit Tree Center (FTC), Nanyang Technological University (NTU), Pulau Tekong (PTK), Saint John's Island (SJA), Beatty Secondary School (BES), and Katong Park (KAP). The distribution of these stations is shown in Fig. 2. The stations have successfully captured hundreds of ground motions till now. The recorded ground motions have been used for some research topics, such as the development of ground motion prediction equations ([25,26]). More information about the national network of seismic stations can be found by Pan and Lee [27]. Among these stations, the KAP and the BES sites are located mainly on soft soils, and therefore they are particularly valuable for site response study. More importantly, both the two stations were built associated with downhole arrays, making it easier to capture the ground motions at multiple depths. It is noted that only these two stations have drilled boreholes to install seismometers at various depths and to perform geotechnical investigations. At the KAP site, the soil profile mainly consists of very soft marine/organic clay layers (about 6.5-34 m), and stiff silty clay and silty sand layers below 34-m depth. The soil profile of the BES site mainly consists of soft organic/marine clay layers (3.5-21.5 m), a 5-m thick poorly-graded loose sand layer and highly/moderately weathered granite layers below 26.5-m depth. A suspension P-S velocity logging method was used to measure the seismic wave

Fig. 1. Geological map of Singapore [18].

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3. One-dimensional site response methodologies One-dimensional (1D) ground response analyses (upward propagation of seismic waves) have been the most fundamental method to estimate site effects. They are based on the following assumptions: all boundaries are horizontal; the soil and bedrock surface can extend infinitely in the horizontal direction; and the response is dominated by vertically propagating shear waves from the bedrock. As summarized by Kramer [10], the predicted ground responses by 1D analyses are reasonably in agreement with the recorded ground motions in many cases, and therefore they are widely used in engineering practice. Nonetheless, a number of recent studies (e.g., [18,28–30]) have shown that the 1D analyses poorly represented observed ground motions for some cases, in which the assumptions of 1D wave propagation are not acceptable. Fig. 2. Location of seismic stations in Singapore.

velocity profiles of these sites. Laboratory tests were performed to determine the unit weight profiles. The geologic profiles, shear wave velocity (Vs) profiles and the unit weight profiles at the KAP and BES sites are shown in Fig. 3, respectively. The measured Vs30 values for these two sites are about 130 m/s and 150 m/s respectively. Both the two sites can be classified as ground type D based on Eurocode 8 [24], and then significant site effects would be expected. It should be noted that both the KAP and BES sites are divided into 35 sublayers for the subsequent LE, EQL and NL analyses, with sublayer thickness ranging from 1 to 2 m. The purpose of such discretization is to make sure the natural frequency of each sublayer is greater than 25 Hz, so that seismic waves with frequency smaller than 25 Hz can be propagated through the soil profile in the time-domain NL analysis.

3.1. Linear and equivalent-linear site response methods The simplest linear site response approach assumes that the stress-strain relationship of soils is viscoelastic. The small-strain shear modulus Gmax ( Gmax = ρ⋅Vs2, where ρ is the density of soils and Vs is shear-wave velocity) and constant damping ratio ξ would be assigned at all strain levels. In this study, we performed the LE frequency-domain computations using SHAKE04. The input values of ρ and Vs have been measured for the two sites (as shown in Fig. 3), while the site-specific estimates of small-strain damping ratio ξ are unknown. A method introduced by Thompson et al. [30] is then used to estimate ξ. This method assumes that the ξ values of all soil layers at a given site are constant, and then a grid search method is used to determine the ξ value which can provide the best fit for the weak motions recorded at this site. Based on this approach, the best-fit ξ values are 1.60% and 1.82% at the KAP and BES sites, respectively. It is worth noting that the two specified ξ values are generally similar to the small-strain damping values obtained from empirical models (e.g., [31]).

Fig. 3. (a) The geologic profiles; (b) shear-wave velocity (Vs) and unit weight profiles for the KAP and the BES sites, respectively. The black arrows denote the depths of the installed seismometers.

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The LE method is only suitable for small strain deformations. At medium and large shear deformation levels, the nonlinear behavior of soil materials has to be well approximated, generally associated with an equivalent-linear or a fully nonlinear method. The equivalent-linear approach is performed in a frequency domain. In addition to the shear velocity and density profiles, modulus reduction curves (G/Gmax) and damping curves, i.e., [31,32] are required. An iterative process is necessary to determine straincompatible soil dynamic properties: at each step, an effective strain is adopted to define new values of shear modulus and damping ratios. The famous industry-standard SHAKE program is based on this equivalent-linear approach. Although the EQL model is the most widely used method due to its simplicity, robustness and computational efficiency, it also has some limitations. Specifically, the EQL method assumes that the strain-compatible soil properties remain constant during earthquake shakings, resulting in poor predictions of site effects at large strains [33]. In this study, the empirical modulus-reduction and damping models proposed by Vucetic and Dobry [31] are used in the EQL computations. The adopted models only require the mean effective confining pressure σm′ and plasticity index PI as input parameters. Some modulus reduction and damping curves used for several soil layers at the KAP site are illustrated in Fig. 4. 3.2. Nonlinear site response method Fully nonlinear approaches analyze the actual nonlinear response of soils using direct numerical integration in the time domain. By integrating the motion equation in small time steps, a nonlinear inelastic stress-strain relationship can be followed in small incrementally linear steps. Some cyclic backbone stressstrain models such as modified hyperbolic models are necessary to characterize the stress-strain behavior of soils. The nonlinear model used in DEEPSOIL software is the modified Kondner and Zelasko (MKZ) model [34], which can be described as:

τ=

Gmaxγ 1+β

α

() γ γr

(1)

where Gmax is the maximum shear modulus which can be computed by shear wave velocity and density; γ ¼ shear strain; τ ¼shear strength; γr ¼reference strain; and α , β are model parameters. The parameters α , β and γr can be determined by fitting the empirical modulus reduction and damping curves. In this study, the aforementioned modulus-reduction and damping models [31] are adopted as the target curves. A modulus reduction and damping fitting (MRDF) pressure-dependent procedure proposed by Phillips

and Hashash [35] is chosen herein to fit the target curves. Compared with the traditional fitting procedure based on the extended Masing hysteretic behavior, the MRDF procedure can better fit the empirical soil curves over a wide range of strains (especially at large strains). Except hysteretic damping, viscous damping is also necessary to prevent nearly zero damping at small strains. As suggested by Stewart et al. [14], the full Rayleigh damping formulations incorporating two target frequencies (site frequency fs and 5 × fs) are used in this study. For each soil layer, the target viscous damping ratio is specified using the aforementioned MRDF procedure, by fitting the target damping curves [31]. The NL model employs a sophisticated analysis in the time domain. Theoretically it should produce more accurate results of site responses. Nonetheless, many input parameters are needed in the NL analysis, inevitably bringing in more uncertainties for the predictions. Besides the DEEPSOIL code, there are also some other nonlinear site response programs such as D-MOD_2 [36] and SUMDES [37].

4. Site response analysis using bedrock recordings Two recent earthquakes, namely, the Padang earthquake of Sep 30, 2009 and the Sumatra earthquake of Oct 01, 2009, caused a few tremors of buildings in Singapore. The details of the two earthquakes are listed in Table 1. The seismic stations in Singapore successfully captured these acceleration time histories at different ground levels ( 50 m,  32 m and ground surface at the KAP site;  50 m,  17 m and ground surface at the BES site). Therefore, the ground motions recorded at different depths at the KAP and the BES stations are used to validate the accuracy of site response methods. The raw earthquake data are processed via several standard procedures, including the baseline correction, truncation and downsampling techniques, band-pass filter and tapered window methods [38]. The proper signal processing tasks are necessary to remove the high-frequency and low-frequency noises, as well as to reduce the computational time. Since the input motions are obtained from downhole recordings, a rigid boundary condition is then employed for all the LE, EQL and NL analyses in this section. Figs. 5 and 6 show the comparisons between the recorded response spectral accelerations (Sa) and the computed response spectra by the LE, EQL and NL methods for the Sep 30, 2009 and the Oct 01, 2009 events, respectively. The ground motions recorded at 50 m depth (base level) are used as bedrock input time histories. Two features can be observed by these figures. First, for the KAP site, the predicted response spectra at ground surface and 32-m depth are quite comparable with the recorded spectra, while

25

Damping Ratio(%)

Modulus Reduction G/Gmax

30

1 0.8 0.6 0.4 0.2 0 0.0001

EQL−Sand EQL−Clay PI=15 EQL−Clay PI=30 Linear 0.001

0.01

20

EQL−Sand EQL−Clay PI=15 EQL−Clay PI=30 Linear

15 10 5

0.1

Shear Strain (%)

1

10

0 0.0001

0.001

0.01

0.1

1

10

Shear Strain (%)

Fig. 4. Demonstrated examples of the equivalent-linear modulus reduction and damping curves from Vucetic and Dobry [21]. The curves representing linear approaches are also shown in these plots (for KAP site).

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Table 1 Detail information of the Sep 30, 2009 and the Oct 01, 2009 earthquakes. Year

Month Day Lat (°)

2009 09 2009 10

30 01

Long (°) Depth (km)

 0.725 99.856  2.508 101.484

81 15

Mw Azimuth (°) Distance (km) 7.6 6.6

61 30

490 500

for the BES site, the computed response spectra are generally smaller than the recorded surface spectra. This under-estimation of site amplifications at the BES site is consistent for the two events, possibly because the 1D site response mode is inappropriate (breakdown of the aforementioned assumptions), or the soil properties of the BES site are not accurately investigated. Second, the computed spectra obtained by the three methods are almost identical, which is not unexpected since at such low input motions (maximum PGA as 0.0011 g), the shear-strain relationship is almost linear. The observed surface amplification factors (AFs) and the computed AFs by the three methods for the Sep 30 2009 event are shown in Fig. 7. Again, the computed AFs at the BES site are generally smaller. Besides, the maximum AF occurs at each corresponding site period (Ts), approximately at 1 s and 0.8 s for the KAP and BES sites, respectively.

173

5. Site response analysis at different seismic hazard levels 5.1. The earthquake events at design hazard level (return period of 475 years) The Singapore Standard seismic design code [4] was approved in February, 2013. The reference bedrock peak ground acceleration (PGArock) is 0.0178 g for a return period 475 years. The design response spectrum on bedrock at 5% damping is shown in Fig. 8(a). To accurately account for the site effects at this hazard level, a suite of appropriate acceleration time histories should be selected to fit the target response spectrum. Typical methods consist of selecting and adjusting several previously recorded or simulated ground motions, so that the mean spectrum of these motions matches the target spectrum. In this study, a program called RspMatch is adopted, which implemented a recently proposed spectral matching algorithm based on wavelet functions [39]. The advantage of this method is that it is capable of modifying existing accelerations while preserving the non-stationary characteristics of the ground motions. Successfully, the RspMatch code can modify the original time histories so that the modified response spectrum curve is compatible with the target spectrum. Due to the fact that the local seismicity of Singapore is low and

Fig. 5. Response spectra for recorded ground motions and the computed surface spectra at different depths for the Sep 30, 2009 event at the (a) KAP site and (b) BES site, respectively. The linear elastic (LE), equivalent-linear (EQL) and nonlinear (NL) methods are used for computation.

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Fig. 6. Response spectra for recorded ground motions and the computed response spectra at different depths for the Oct 01, 2009 event at the (a) KAP site and (b) BES site, respectively. The LE, EQL and NL methods are used for computation.

8

6

10

Amplification Factor

Amplification Factor

7

12

Observed AF Computed by LE Computed by EQL Computed by NL

5 4 3 2

6 4 2

1 0 −2 10

8

Observed AF Computed by LE Computed by EQL Computed by NL

−1

0

10

10

Period (s)

(a)

1

10

0 −2 10

−1

0

10

10

1

10

Period (s)

(b)

Fig. 7. Comparison of the computed amplification factors (AFs) obtained by the LE, EQL and NL methods for the Sep 30, 2009 event. The observed AFs using the recorded surface spectra are also shown in each subplot.

W. Du, T.-C. Pan / Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

Target design spectrum Selected GMs

0.08 0.06 0.04 0.02 0 0.05

0.1

1

0.1

Spectral acceleration (g)

Spectral acceleration (g)

0.1

175

Target design spectrum Mean spectrum of selected GMs

0.08 0.06 0.04 0.02 0 0.05

10

0.1

1

Period (s)

10

Period (s)

(a)

(b)

Fig. 8. (a) 16 selected input ground motions to fit the target design spectrum of Singapore; (b) comparison between the mean spectrum of the selected ground motions and the target design spectrum.

all ground shakings in the last 50 years were originated from distant Sumatran earthquakes, a set of well representative ground motions should be selected. Eight ground motions from a catalog of over 50 local ground motions in Singapore are firstly selected. Table 2 shows the selected local earthquake events in this study, out of which five events belong to Sumatra subduction and three events belong to Sumatra strike-slip fault. All the selected ground motions were recorded at rock sites of Singapore. In order to get statistically reliable results, eight global ground motions with various site-source distances are also collected. These earthquakes occurred in US (2010 EI Mayor Cucapah earthquake), in Chile (2014 Iquique earthquake) and in Japan (2011 Tohoku earthquake). The ground motions are selected based on the following criterion: (1) the ground motion was recorded at rock site, generally with a far-source distance (larger than 150 km) from a large event (Mw 47.0); (2) the fault types of earthquakes should be strike-slip or subduction (consistent with the scenarios of Singapore). The time histories are obtained from the KiK-Net database [40] for the Tohoku earthquake and CESMD website [41] for other earthquakes. The detailed information of the selected global ground motions is summarized in Table 3. Totally 16 ground motions are selected and then modified to match the design spectrum, as shown in Fig. 8(a). Fig. 8 (b) presents the comparison between the mean ground motion spectrum and the design spectrum. The resulting selected motions can acceptably match the target spectrum, while slightly positive errors can be observed in the period range 0.2 to 1 s. The selected ground motions can be used for subsequent site response analyses. It is noted that most input motions used in this section can be classified as rock outcropping motions, and therefore an elastic

boundary condition is used for all the LE, EQL and NL analyses. Fig. 9(a), (b) and (c) show the computed surface response spectra at the KAP site by the LE, EQL and NL approaches, respectively. The corresponding mean surface response spectra are shown in Fig. 9(d). It can be seen that the LE method produces the largest surface spectra, with the mean surface PGA as 0.07 g and the mean peak Sa as 0.25 g. On the other hand, the EQL method generates quite consistent surface spectra compared with those obtained by the NL method. Thus, at the seismic design level of Singapore, it is expected that the surface PGA can reach about 0.05 g, and the mean peak Sa values (at the period range around 0.5 s) are approximately 0.18 g at soft soil sites. The mean amplification factor (AF) for PGA is about 2.86, which is slightly larger than the AF of PGA for ground type D provided in Singapore design code [4]. The maximum shear strain in soil profiles (γmax) can be regarded as a good indicator to choose appropriate site response methodologies. Recently, Kaklamanos et al. [16] studied several critical parameters affecting the accuracy of the LE and EQL methods using KiK-NET downhole arrays. It is concluded that, the linear site-response approach over-predicts the surface spectral accelerations at shear strains in the range of 0.01%-0.1%, and the EQL model can give acceptable site response predictions at periods ranging from 0.01 to 10 s if the γmax is smaller than 0.1%. Besides, Kim and Hashash [17] also performed 1D site response analyses using some downhole recordings from the 11 March 2011 earthquake. They concluded that negligible differences between the EQL and NL models can be observed if γmax is smaller than 0.3%. Fig. 10 shows the mean calculated maximum strains with respect to the borehole depth at the KAP site. For the EQL and NL analyses, the

Table 2 Local ground motions selected to fit the design spectra. No.

1 2 3 4 5 6 7 8

Event Date (dd/mm/yyyy)

10/10/1996 22/03/1997 20/08/1997 24/05/1998 18/09/1999 11/05/2004 10/04/2005 14/05/2005

Epicenter Lat (°)

Long (°)

3.43 0.57 4.32  6.54  4.03 0.41 1.92 0.42

97.78 99.83 96.43 104.78 103.3 97.82 96.48 98.24

Ssb: Sumatra Subduction fault; Sst: Sumatra Strike-Slip fault.

Depth (km)

Distance (km)

Magnitude (Mw)

Source

22.8 18.2 6.9 33 33 21 24 39

697 454 879 885 601 600 822 631

6.3 5.8 5.8 5.2 5.4 6.2 6.1 6.8

Sst Sst Sst Sst Sst Ssb Ssb Ssb

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W. Du, T.-C. Pan / Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

Table 3 Global ground motions selected to fit the design spectrum. No.

Earthquake name

Station name

Date (dd/mm/yyyy)

Magnitude

Fault mechanism

Hypocentral distance (km)

PGA (g)

1 2 3 4 5 6 7 8

EI Mayor Cucapah

3147 3148 LVC AKTH14 IBRH12 IWTH09 SITH08 TCGH14

04/04/2010

7.2

Strike-slip

01/04/2014 11/03/2011

8.2 9.0

Subduction Subduction

179 176 384.0 239.0 245.0 208.0 395.0 313.0

0.051 0.055 0.016 0.020 0.124 0.043 0.039 0.04

Spectral acceleration (g)

0.35 0.3

0.35

Surface spectra by the LE code Input motions

Spectral acceleration (g)

Iquique, Chile Tohoku, Japan

0.25 0.2 0.15 0.1 0.05 0 −2 10

−1

0

10

10

0.3 0.25 0.2 0.15 0.1 0.05 0 −2 10

1

10

Surface spectra by the EQL code Input motins

−1

Period (s)

0.35

Surface spectra by the NL code Input motions

Spectral acceleration (g)

Spectral acceleration (g)

1

10

(b)

0.35

0.25 0.2 0.15 0.1 0.05 0 −2 10

10

Period (s)

(a) 0.3

0

10

−1

0

10

10

1

10

Period (s)

(c)

0.3

Mean spectrum by LE Mean spectrum by EQL Mean spectrum by NL

0.25 0.2 0.15 0.1 0.05 0 −2 10

−1

0

10

10

1

10

Period (s)

(d)

Fig. 9. (a), (b), (c): Input motions and the surface response spectra for the KAP site obtained by the EL, EQL and NL methods respectively; (d) comparison of the mean surface spectra by the three methods.

calculated γmax in the soil profile are roughly 0.06% at about 20-m depth. Hence, although the bedrock PGA is only 0.0178 g, the LE method fails to capture the de-amplification of surface ground motion due to soil nonlinearity, and the EQL approach should be the most appropriate method for design earthquakes in Singapore. Similar observations can be found at the BES site. 5.2. The 1985 Mexico event as a rare event of Singapore An earthquake of Mw 8.1 occurred at the west coast of Mexico on Sep 19, 1985. The earthquake was a result of the Cocos plate subducting under the North American Plate and occurred along the Michoacán seismic gap [42]. The lake zone of the Mexico City suffered significant damages due to site effects during this earthquake. A Fourier amplification factor up to 50 in the frequency range

0.3-0.7 Hz was observed in soft clay area [43]. Fig. 11(a) shows an acceleration time history recorded in Mesa Vibradora C.U., Mexico City with a PGA value 0.04 g. The station located on rock conditions is about 400 km away from the epicentre. Due to the similar fault mechanisms, rupture distances and site conditions, this ground motion can be regarded as a rare event occurred in Singapore. Fig. 11(b), (c) show the computed surface spectra obtained by the LE, EQL and NL methods at the KAP and the BES sites, respectively. First, as expected, the LE approach unrealistically overpredicts the surface response spectra, especially at the fundamental site periods. Second, closely agreement can be observed between the EQL approach and the fully NL approach. The results reveal that, if Singapore suffered an earthquake comparable with the 1985 Mexico event, the estimated surface PGA at soft soil areas would be 0.1 g and the Sa at periods close to 1 s can be amplified

W. Du, T.-C. Pan / Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

30

susceptible under earthquake loadings. Fig. 12 shows the maximum shear strains at different depths for the Mexico earthquake. At each plot, the maximum strain profile by the NL method is generally similar to that computed by the EQL method. The calculated γmax are 0.18% and 0.22% at the KAP and the BES sites, respectively. It has been reported that the EQL approach generally underestimates surface ground response at shear strain larger than 0.4% [16]. Also, similar predictions between the surface spectra computed by the EQL and NL approaches were observed at γmax smaller than 0.3% [17]. The observations indicate that both the EQL and NL models can be used to perform site response analyses for this Mexico input event, if the 1D assumption is satisfied.

35

5.3. The up-scaled 1985 Mexico event (return period of 2475 years)

Max. Strain (%) 0.00 0

0.02

0.04

0.06

0.08

5 10 15

Depth (m)

177

LE Method

20

EQL Method

25

NL Method

40

It has been studied that the PGA with a 2% probability of exceedance in 50-year hazard level at firm rock conditions of Singapore is in the range of 0.15 to 0.2 g [5,44]. To estimate the site effects at this hazard level (return period 2475 years), the aforementioned Mexico ground motion is then up-scaled to PGA as 0.15 g. In Fig. 13, the predicted surface response spectra and the corresponding amplification factors obtained by the LE, EQL and NL approaches are compared at the KAP and BES sites, respectively. Unlike previous cases, substantial prediction differences can be seen between the EQL and NL models, and the surface spectra by the nonlinear method tend to have more fluctuations that those by the EQL method. This is expected, since large variability exists

45 50 Fig. 10. The calculated maximum shear strain profiles at the KAP site for the EQL and NL methods at the design earthquake level in Singapore (PGArock ¼ 0.0178 g).

up to 0.5 g. The corresponding amplification factors (AFs) with respect to periods are shown in Fig. 11(d). Since the maximum AF value occurs at about 1 s (near the site period Ts), structures in this region with similar fundamental periods would be the most

1

0.04

Spectral accelerations (g)

Acceleration (g)

0.03 0.02 0.01 0 −0.01 −0.02

0.8

Input Mexico GM Surface spectra by LE Surface spectra by EQL Surface spectra by NL

KAP site

0.6 0.4 0.2

−0.03 −0.04

0

10

20

30

40

50

0 −2 10

60

−1

(a)

Amplification Factor

Spectral accelerations (g)

5

BES site

Input Mexico GM Surface spectra by LE Surface spectra by EQL Surface spectra by NL

0.6 0.4 0.2

−1

0

10

1

10

(b)

1

0 −2 10

10

Period (s)

Time (sec)

0.8

0

10

10

1

10

KAP Site BES site 4

3

2

1 −2 10

−1

0

10

10

Period (s)

Period (s)

(c)

(d)

1

10

Fig. 11. (a) The acceleration-time history for the Mexico event; (b) comparison of response spectra at the KAP site for the EL, EQL and NL approaches; (c) comparison of response spectra at the BES site for the EL, EQL and NL approaches; (d) amplification factors versus periods by the EQL approach for the KAP and BES sites respectively.

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W. Du, T.-C. Pan / Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

Max. Strain (%)

Depth (m)

0.00 0

0.05

0.10

Max. Strain (%)

0.15

0.20

0.00 0

5

5

10

10

15

15

20

20

25

25

30

30

35

35 LE Method

40

EQL Method

45

NL Method

50

40 45 50

KAP Site

0.10

0.20

0.30

LE Method EQL Method NL Method BES Site

Fig. 12. The maximum shear strains versus depth for the Mexico event (PGArock ¼0.04 g) at the KAP and BES sites, respectively.

among different EQL and NL models at medium or strong shaking levels [13]. In general, the EQL amplification factors are larger than the NL amplification factors at short periods. The corresponding maximum strain profiles are shown in Fig. 14. Both the two sites produce very large strains (γmax larger than 2.0% for the EQL method and 3.5% for the NL model), making it difficult to accurately predict the surface seismic responses for both the two approaches. Specially, the γmax as 1% is usually regarded as the upper limit on the use of the EQL method in case of convergence problems [45]. Therefore, in such case it may be necessary to accurately capture the shear strength at large strains by employing several nonlinear models, or to perform a more sophisticated multi-dimensional analysis. To further explore the differences between the EQL and NL site response predictions at different intensity levels of shakings, the Mexico ground motion is then up-scaled to a series of target PGA values (0.05 g to 0.2 g with interval as 0.01 g). At each target PGA value, the EQL and NL site response analyses can be performed using the up-scaled ground motion as input. The relative difference of the computed surface spectra by the EQL and NL approaches can be quantified as: N

δSa =

(

)

∑i = 1 ln SaEQL(Ti ) − ln( SaNL(Ti ))

N

computed δSa versus the computed maximum strains γmax. It can be seen that if γmax is smaller than 0.25% (PGArock r0.05 g), δSa is generally negligible; while when γmax is larger than 0.5% (PGArock E0.09 g), δSa becomes more significant (larger than 10%). It is also tempting to separate the computed δSa for various spectral period ranges. Without loss of generality, the short-, moderate- and long-period ranges are defined as 0-0.2 s, 0.2-2 s and 2-10 s, respectively. The computed δSa values for the three period ranges for the KAP and BES sites are shown in Fig. 16. As the input PGA increases, the computed δSa at the short-period range becomes significantly larger, while the computed δSa at moderate periods remains almost constant. This is perhaps because that at large strain levels, the EQL method would usually filter out some high-frequency (short-period) components of ground motions, bringing in a notable discrepancy compared to the NL method. This drawback of the EQL method has been pointed out by several studies (e.g., [33,46]). Due to the variability in the surface response predictions at large strains by different methods, this is preliminary and further work is still needed.

6. Discussions and conclusions

× 100

(2)

where SaEQL(Ti ) and SaNL(Ti ) are the computed surface spectral acceleration at period Ti using the EQL and NL approaches, respectively; N is the number of discrete spectral periods. δSa represents the mean difference ratio of the computed surface spectra considering specific spectral periods. Fig. 15(a) shows the computed δSa for all periods (0.01-10 s) at the KAP and BES sites versus the target PGA values of the up-scaled motions. As expected, δSa increases as the input PGA value increases. Fig. 15(b) displays the

This paper presented a comprehensive study of site effects in Singapore. Two boreholes, namely, the KAP and BES sites are selected to perform the one-dimensional linear, equivalent-linear and fully nonlinear site-response analyses. Judging from this study, it is clear that site effects play a profound role in the seismic hazard of Singapore. The major findings in this study are listed as: 1. The computed surface ground motions by the LE, EQL and NL models are compared with the recorded surface spectra at the

W. Du, T.-C. Pan / Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

179

Spectral accelerations (g)

3.5 3 2.5

Up−scale ed Mexico GM Surface spectra s by LE Surface spectra s by EQL Surface spectra s by NL

2 1.5 1 0.5 0 −2 − 10

−1

0

10 0

10

1

10

Period (s)

AP Site (a) KA 3 2.5

10 Up−scaled d Mexico GM Surface sp pectra by LE Surface sp pectra by EQL Surface sp pectra by NL

Amplification Factor

Spectral accelerations (g)

3.5

2 1.5 1 0.5 0 −2 − 10

−1

0

10 0

10

1

10

8

LE Me ethod EQL Method M NL Me ethod

6 4 2 0 −2 10 0

Period (s)

−1

0

1 10

10

1

10

Period (s)

(b) BE ES Site Fig. 13. The calculated response spectra as well as the amplification factors (surface/input spectral accelerations) by the LE, EQL and NL approaches using the up-scaled Mexico event (PGArock ¼0.15 g) for (a) KAP site and (b) BES site, respectively. The PGA value of this scaled input motion is 0.15 g.

KAP and BES sites. The calculated response spectra match well with the recorded spectra at the KAP site, while they poorly reproduce the recorded surface ground motions at the BES site. All the LE, EQL and NL models systematically under-predict surface ground motions at this site, which is possibly due to the breakdown of the 1D assumption, or inaccurate measurements of soil properties at the BES site. As mentioned previously, some three-dimensional (3D) phenomena, such as 3D soil stratigraphy, basin effects, topographic effects, could significantly influence site response predictions even at weak ground shakings (e.g., [16,28,29]). Specifically, Zhang and Zhao [29] observed that at weak and moderate shakings, site amplifications obtained from 2D basin models are significantly larger than those from 1D models. Therefore, it seems necessary to perform some sophisticated 3D site effect models at the BES site in future. Besides, the uncertainty of soil property estimates (especially the Vs profile) would also affect site response predictions. Recently some inverse algorithms of ground motion downhole recordings have been proposed to estimate or adjust dynamic soil profiles, e.g., [47]. Considering substantially uncertainties of the measured soil profiles, such inverse techniques are also necessary for the BES site. 2. For frequently felt earthquakes in Singapore, both the LE, EQL and NL models can result in consistent site amplifications, due to the small shaking intensities (smaller than 0.005 g at rock sties). The induced maximum strain value is usually smaller than 0.01%, so the linear stress-strain relationship can generally

capture soil dynamic properties. Then the most widely used EQL approach is preferable due to its simplicity and robustness. 3. At the seismic design level of Singapore (return period 475 years), although the bedrock PGA is only assigned as 0.0178 g, the LE analysis over-predicts surface ground motions especially for periods smaller than 1 s. Based on the calculated surface spectra by the EQL and the NL analyses at the KAP site, it is expected that the surface PGA is 0.05 g and the peak Sa values is about 0.2 g. Based on the computed mean surface spectral curves shown in Fig. 9(d), more attention should be paid to structures with fundamental periods ranging from 0.4 to 1.2 s in this region. Besides, in view of higher-mode effects, the seismic performance of structures with higher-mode periods in the range of 0.1 to 0.4 s should also be well studied. Since the computed maximum strain is less than 0.1%, the EQL site response model is recommended. Based on the sites and ground motions considered in this study, it seems not necessary to perform nonlinear time-domain site-response analysis at the design earthquake level. 4. The time history recorded at Mesa Vibradora of the 1985 Mexico earthquake is used as the bedrock input ground motion. In this case, the estimated surface PGA would be nearly 0.1 g; and the peak Sa values are about 0.3 g and 0.4 g at approximately 1 s for the KAP and BES sites, respectively. If this motion is up-scaled to 0.15 g, which is the PGA value with 2% probability of exceedance in 50 years at the bedrock level, the estimated surface PGA would be about 0.3 g and significantly large strains (γmax larger

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W. Du, T.-C. Pan / Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

Max. Strain (%)

Max. Strain (%) 0.0

1.0

Depth (m)

0

2.0

3.0

4.0

0.0

0

5

5

10

10

15

15

20

20

25

25

30

30 LE Method

35

2.0

45

4.0

EQL Method

40

NL Method

3.0

LE Method

35

EQL Method

40

1.0

NL Method

45

50

50 KAP Site

BES Site

Fig. 14. The maximum shear strain profiles for the up-scaled Mexico event (PGArock ¼ 0.15 g) at the KAP and the BES sites, respectively.

than 2%) would be anticipated. At large strains, both the EQL and the NL approaches may not provide accurate predictions, especially at the high frequency range [48]. Therefore, for extremely important structures in this region with a performance-based seismic design [49], site effect analyses including some advanced nonlinear models or sophisticated multipledimensional models are recommended. Finally, a series of site response analyses are performed at intermediate shaking levels between 0.04 g and 0.2 g, by which the Mexico motion is upscaled to target PGA values. It shows that when γmax is larger than 0.5% (PGArock E0.09 g), the differences between the EQL

and NL predictions become more significant. In summary, the soft clay areas of Singapore, where includes dense population and infrastructures, can generally amplify spectral accelerations by amplification factors as 2-5 at various fundamental periods. The maximum amplification factor is generally associated with periods around 0.7 s-2 s, depending on the input ground motions. Due to the significant site effects, as well as the fact that many buildings in Singapore were designed according to the British Standards (BS) code with the requirement of notional horizontal load, the seismic risk should not be underestimated.

30 25

30

KAP Site BES Site

25 20

δ Sa (%)

δ Sa (%)

20 15

15

10

10

5

5

0 0.04

KAP Site BES Site

0.08

0.1

0.15 rock

PGA

(a)

(g)

0.2

0 −1 10

0

1

10

10

Maximum Strain γ

max

(%)

(b)

Fig. 15. (a) Relative differences of the computed surface spectra between the EQL and NL methods δSa versus the up-scaled target PGA values for the Mexico ground motion; and (b) δSa versus the computed maximum strains using the up-scaled Mexico motions.

W. Du, T.-C. Pan / Soil Dynamics and Earthquake Engineering 90 (2016) 169–182

40 35

40 Short−period (0−0.2 s) Moderate−period (0.2−2 s) Long−period (2−10 s)

35 30

25

δ Sa (%)

δ Sa (%)

30

20 15

20 15 10

5

5 0.08

0.1

0.15 rock

PGA

(g)

KAP Site

0.2

Short−period (0−0.2 s) Moderate−period (0.2−2 s) Long−period (2−10 s)

25

10

0 0.04

181

0 0.04

0.08

0.1

0.15 rock

PGA

0.2

(g)

BES Site

Fig. 16. The computed δSa for short-, moderate- and long-period ranges versus the up-scaled rock PGA values for the KAP and the BES sites, respectively.

This study might be hopefully beneficial to the seismic hazard analysis of some cities that are also located in low-to-moderate seismic regions and built on soft sediments, such as New York City and Shanghai.

Acknowledgments The authors acknowledge financial supports provided by the Ministry of Home Affairs and the Monetary Authority of Singapore for this work. The authors thank two anonymous reviewers for their helpful comments to improve this manuscript.

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