Sindhu Rudianto.pdf_ Wiratman Wangsadinata .Pdf_ Ellen M. Rathje - Makalah

DEVELOPMENT OF SITE-SPECIFIC VERTICAL RESPONSE SPECTRUM

Sindhu Rudianto

(1); Wiratman Wangsadinata

(2) and Ellen M. Rathje

(3)

(1) Principal – PT Geo-Optima, Jakarta. (2) President Director – PT Wiratman & Associates and Professor Emeritus

Tarumanagara University, Jakarta (3) Professor, University of Texas, Austin, USA

1 INTRODUCTION The new British Embassy Building in Jakarta will be a 4-story structure with a fundamental building period of less than 1 sec. Considering some structural elements will consist of long span cantilever beams and canopies that are sensitive to vertical ground motions, PT Wiratman & Associates was commissioned to provide a structural design that includes the development of site-specific response spectra for both horizontal and vertical directions. At the present time, there is some ambiguity in determining the vertical spectral accelerations that are mostly derived from the horizontal spectral. For instance, the Indonesian seismic code, SNI 03-1726-2002 [1] stipulates the nominal vertical seismic response factor for Jakarta is taken to as half of the peak ground surface acceleration factor, independent to the natural period of the structure. The nominal vertical seismic response is defined as the elastic vertical response spectrum divided by a seismic reduction factor R that is associated with the ductility of the structure. Newmark–Hall [2] specifies the vertical spectrum to be about 2/3 of the horizontal spectral acceleration for all periods. The US Nuclear Regulatory Commission, NRC [3], specifies the ratio of vertical to horizontal spectral acceleration (V/H ratio) as 1 for short period (< 0.3 sec.); 2/3 for long period (> 4 sec) and 2/3 to 1 for periods in between (0.3< t < 4 sec.). With recent increase in strong motion data, the variation of the V/H spectral ratios is predictable and dependent on the magnitude, distance and local soil conditions. Many attenuation models [4, 5, 6] have been developed recently to include the vertical and horizontal components of motion. This paper discusses a procedure to develop a site-specific horizontal and vertical response spectrum for the new British Embassy Building using a Probabilistic Seismic Hazard Analysis (PSHA) approach, where the regional seismicity and local site conditions are taken into account.

2 PROBABILISTIC SEISMIC HAZARD ANALYSIS (PSHA) For a typical 4-story structure, a Probabilistic Seismic Hazard Analysis (PSHA) was conducted to determine the 500-year ground motion (10% probability of being exceeded in 50 years) for the peak bedrock acceleration (t=0). This shaking level was used for scaling time histories and determining the controlling seismic events.

The seismic hazard in Jakarta is affected by subduction zone earthquakes (Megathrust and Benioff) and shallow crustal earthquakes (known faults and a background zone). The subduction source is a far-field event with M7.8 to 8.3 at distance 150 to 300 km away from Jakarta. The shallow crustal sources represent large known faults with M7.0 to 7.6 at distance 100-150 km and the background source (unknown faults) represents events with M5.5 to 6.5 at closer distance (radius 25 km). The seismic modeling, source parameters,

and attenuation models that are used in PSHA are discussed in detail by Rudianto, et al. [7]. The computed 500-year peak bedrock acceleration (PBA) is about 0.25 g, with the horizontal response spectrum on “rock” as shown below (Fig. 1) including the contribution from each source. The seismic hazard was de-aggregated to compute the fraction contribution of each source to the total hazard for PBA=0.25 g (Fig. 2), as well as to determine the controlling magnitude and distance for the 500 year return period. The deaggregation indicates the PBA is controlled by two different seismic sources; near-field background source (± 42% contribution) with M5.7 at mean distance 10 km; and far-field Benioff source (± 58% contribution) with M7.3 at mean distance 150 km.

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Figure 1 Design Response Spectral on “Rock” for 500 years Event

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Figure 2 Deaggregated Hazard for PBA of 0.25g (500 years event)

3 APPROACH At present time, there are no analytical tools available to calculate direct amplification of the vertical ground motions from the bedrock to ground surface, unlike those that have been developed for the horizontal ground motion. While vertical rock response spectra can be predicted from attenuation models and PSHA, it is difficult to perform vertical site response analysis because little data is available regarding the appropriate dynamic soil properties (i.e., constrained modulus, damping ratio in constrained compression, and the variation of these parameters with cyclic axial strain). Additionally, available computer software (e.g., SHAKE) that is used for horizontal site response analysis has not been validated for propagation of vertical waves (P-wave). For practical purpose, the vertical response spectrum is derived from the horizontal spectrum by multiplying a vertical to horizontal (V/H) ratio of spectral acceleration at different periods. The V/H spectral ratio is computed using the following approach:

a. Obtain the horizontal response spectrum on ”rock” from PSHA; b. Determine the dominant magnitude(s) and distance(s) from deaggregations; c. Compute the vertical and horizontal spectra using the derived magnitude(s) and

distance(s), and available attenuation models that include vertical and horizontal components;

d. Develop the ratio of vertical to horizontal spectra for the dominant events; e. Perform site-specific seismic site response analysis (SSRA) to establish the

design horizontal surface spectrum that includes local site effects;

f. Multiply the recommended V/H spectral ratio to the horizontal surface spectrum to obtain the vertical spectral accelerations at the surface.

4 SITE-SPECIFIC V/H SPECTRAL RATIO Attenuation models developed by Abrahamson & Silva [4]; Campbell [5] and Campbell & Bozorgnia [6] were used to compute the horizontal and vertical response spectra for two dominant events (M5.7 @ D= 10 km and M7.3 @ D=150 km) as shown below (Fig. 3 and 4). Although these attenuation models are not applicable to the M7.3 Benioff event, no subduction zone attenuation model includes vertical motions. Fig. 5 shows the computed V/H spectral ratios for the dominant events, including the recommended V/H curve. Knowing the limitation of the current attenuation models, it is prudent to verify the recommended V/H ratio from recorded motions, especially from background/crustal sources.

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Figure 3 Horizontal Response Spectra for M=5.7, D=10 km Dominant Event

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Figure 4 Vertical Response Spectra for M=7.3, D=150 km Dominant Event

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Figure 5 V/H Spectral Ratio for Dominant Events

Three ground motions, one each from the 1979 Imperial Valley earthquake (M5.6, D= 12 km); the 1976 Friuli earthquake (M5.9, D=18 km); and the 1983 Coalinga earthquake (M5.8, D=12 km), representing shallow crustal events recorded on soil sites were used to compute the horizontal and vertical response spectra for “soil” (Fig. 6). The V/H spectral ratio of actual recorded motions agrees reasonably well with the design recommended values from the attenuation models (Fig. 7). This V/H spectral ratio is then used to develop the vertical response spectrum from the horizontal spectral acceleration at surface as discussed below.

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Figure 6 Recorded Response Spectra from Shallow Crustal Source

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Figure 7 V/H Spectral Ratios from ground motion recordings and from design

attenuation models

5 LOCAL SITE EFFECT AND SITE RESPONSE The project site is located within a deep alluvial deposit (≈ 260 m) that mainly consists of stiff, highly plastic clay and silt. Shear wave velocities (Vs) in the upper 30 m were measured directly using the Spectral Analysis of Surface Waves (SASW) method. The Vs profiles for subsurface soils below 30 m were estimated using a site-specific empirical relationship between NSPT and Vs derived from SASW testing in the near surface materials. One-dimensional, equivalent-linear dynamic response analyses were performed to determine the amplification of the horizontal ground motion using the computer program SHAKE [8]. The computed site-specific amplification ratio was then applied to the rock acceleration response spectrum obtained from the PSHA to produce the site-specific design horizontal spectral acceleration at the ground surface.

Because of inherent uncertainty and spatial variation in shear wave velocity (Vs) across the site, a series of parametric analyses were conducted in which the shear wave velocity profile and the modulus reduction and damping curves were varied. The different Vs profiles and nonlinear property curves represented different, but plausible, characterization of the site. Knowing the limitation of equivalent linear “SHAKE” analyses, it is necessary to adjust the design response spectrum using the empirical (seismological) approaches based on actual ground motion recordings from different seismic environments.

6 DESIGN RESPONSE SPECTRUM In developing the horizontal spectral accelerations at surface, we consider the results of site response analyses (SHAKE) in conjunction with the seismological (empirical) approach. The site response analyses accurately model the actual soil layering, variations in shear wave velocity and depth to bedrock at the project site, while the empirical approach accounts for a large number of global strong motion recordings from different

seismic environments. The median amplification values from the site response analyses (SHAKE), along with the median values predicted from Atkinson and Boore [9], Choi and Steward [10], and PSHA using attenuation models for soil sites [5,9,11] are shown on Fig. 8. A similar approach was used for another project site in Jakarta as reported by Rudianto et al. [7].

The design horizontal spectrum at the surface was developed by weighting the amplification factors from different approaches (Fig. 8) and then multiplying by the design rock spectrum (horizontal) from the PSHA analyses to obtain the 500-year design horizontal response spectrum at the ground surface (Fig. 9). For T ≤ 0.5 sec., equal weighting on the SHAKE (analytical) and empirical (seismological) approaches. For T >

0.5 sec., extra weight (± 70%) is placed on the SHAKE results because it models the exact site period and soil depth, while the empirical approach involves grouping many sites with same Vs-30 m or site classes, in which the site effects get smeared between various sites with different properties (depths, Vs profiles, etc.). The design vertical response spectrum (Fig. 10) is developed by multiplying the design horizontal surface spectrum (Fig. 9) with the recommended V/H spectral ratio (Fig. 5).

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Figure 8 Design Horizontal Spectral Amplification (Surface/Rock)

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Figure 9 Design Horizontal Surface Response Spectrum for 500 years Event

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Figure 10 Design Vertical & Horizontal Surface Response Spectral (5% Damping)

7 CONCLUSIONS The vertical response spectrum was developed by: a) using the PSHA approach to determine the bedrock horizontal response spectrum and de-aggregations; b) computing the site-specific V/H spectral ratio for the dominant seismic events; c) conducting SSRA to evaluate the local site effects on the horizontal surface spectrum, and d) multiplying the V/H spectral ratio and the horizontal spectrum to obtain the surface vertical spectrum. Fig. 11 shows the site-specific vertical design spectrum, developed from Figures 5 and 9. This figure also shows for comparison the vertical spectra derived from the horizontal surface spectrum using the Newmark–Hall approach and the NRC criteria. The NRC vertical spectrum is much larger than the design vertical spectrum for all periods. The Newmark-Hall approach produces a spectrum rather similar to the design vertical spectrum. This approach is recommended if SSRA is not conducted. Based on the study results and considering the SNI standard response spectrum, for 0.2 sec. ≤ T ≤ Tc (= corner period) it is apparent that Cv = 0.5 A0 is valid for structures with some level of ductility, associated with a seismic reduction factor of R = 3.0, because the nominal vertical seismic response factor becomes Cv = 0.6 x 2.5 A0/3.0 = 0.5 A0, precisely the value as stipulated in SNI. This level of ductility is indeed the minimum that can be expected to be present in building structures. This is applicable to the new British Embassy Building with a fundamental building period of 0.712 sec. and R= 5.5. For T > Tc the SNI stipulation for Cv = 0.5 A0 becomes more conservative, because for longer natural periods, the response curve is descending, approaching the T axis asymptotically. For T < 0.2 sec. the study results indicate a higher ductility demand to the structure for reaching a value of Cv = 0.5 A0. However, structures in this period range are rare in practice.

It is concluded that the SNI stipulation Cv = 0.5 A0 is appropriate and conservative especially for high-rise building, because of the longer natural period of the structure and the higher value of the seismic reduction factor R.

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Figure 11 Comparison of Vertical Surface Spectrum

ACKNOWLEDGEMENT

The first writer expresses his sincere appreciation to Professor Paul Somerville of Macquarie University, Australia, for his advice in providing a practical approach to develop the V/H spectral acceleration ratio.

REFERENCES

1. Badan Standarisasi Nasional (2002). “Tata Cara Perencanaan Ketahanan Gempa

untuk Bangunan Gedung”, SNI 03-1726-2002 (in Indonesian).

2. Newmark,N.M. and Hall, W.J. (1982). “Earthquake Spectra and Design”, Earthquake Engineering Research Institute, pp. 103.

3. United States Nuclear Regulatory Commission (2003)

4. Abrahamson, N.A. and W.J. Silva (1997). “Empirical Response Spectral Attenuation Relations for Shallow Crystal Earthquakes”, Seismological Research Letters, Vol. 68, No. 1, pp. 94-127.

5. Campbell, K. W. (1997). “Empirical Near-Source Attenuation Relationship for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra”, Seismological Research Letters, Vol. 68, No.1, pp. 154-179.

6. Campbell, K.W. and Y, Bozorgnia (2003). “Updated Near-source Ground Motion (attenuation) Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Response Spectra”, Bulletin Seismological of America, Vol. 93, pp 314-334.

7. Rudianto, S., Rathje, E. and Soedjono, B. (2006). “Site-Specific Seismic Analyses for Deep Alluvial Jakarta Site, Indonesia“, a paper presented in the International Conference on Earthquake Engineering and Disaster Mitigation, Jakarta 12-14, May 2008.

8. Schnabel, P.B., J. Lysmer and H.B. Seed (1972). “SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites”, Report No. EERC/72-12, Earthquake Engineering Research Center, UC Berkeley, December.

9. Atkinson, Gail. M. and David M. Boore (2003). “Empirical Ground-Motion Relations Subduction-zone Earthquakes and Their Application to Cascadia and Other Regions”, Bulletin of the Seismological Vol. 93, No.4, pp. 1703-1729.

10. Choi, Y. and J.P. Stewart (2005). “Non-linear Site Amplification as Function of 30 m Shear Wave Velocity”, Earthquake Spectra, Volume 21, No.1, pp 1-30, February 2005, Earthquake Engineering Research Institute.

11. Sadigh, K., C.Y. Chang, J.A. Egan, F. Makdisi, and R.R. Youngs (1997). “Attenuation

Relationships For Shallow Crustal Earthquakes Based on California Strong Motion Data”, Seismological Research Letters, Vol. 68, No.1, pp. 180-189.

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