ML033650191

to GEO.HBIP.02.04, Development of Response Spectra for the Hbpp Isfsi.

ML033650191
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From:	Abrahamson N, Cluff L, Mclaren M Pacific Gas & Electric Co
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HBAP C-20 Attachment 7.1 Rev. 7A Page 1 of 1 HUMBOLDT BAY POWER PLANT CALCULATION COVER SHEET File No. :

Calculation No.: GEO.HBIP.02.04 El Preliminary 0 Final Department/Group: IBPP/Geosciences Unit(s) 0 Structure, System or Component: ISFSI Geotechnical Type or Purpose of Calculation: Development of Response Spectra for the HBPP ISFSI No. of Sheets: 101 Signature Discipline/Dept Date Prepared by: By Geosciences 11/4/2002 Checked by: BY Geosciences, 11/7/2002 Approved by (Supv): if Ii0III 12/26/2002 Registered Engineer Approval: (Complete sectn A for Civil calcs. Complete A or B for others A. Insert Engineer Stamp or Seal Below B.

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RECORDS OF REVISIONS Approval Revision Prepared Checked Regis. Engr. Supvr.

Number Date Reasons for Revision By By 0 12/26/02 Initial Issue Geosci. Geosci. Geosc.i

PACIFIC GAS AND ELECTRIC COMPANY Calc Number:GEO.HBIP.02.04 GEOSCIENCES DEPARTMENT Revision: 0 CALCULATION DOCUMENT Date: 11/4/02 Calc Pages: 101 Verification Method: 3 TITLE:_Development of Response Spectra for the HBPP ISFSI PREPARED BY: g5$'- >a*.--<- DATE I// (/O -_

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Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number I of O1 Date: 11/4/02

2. PURPOSE The purpose of this calculation is to develop 84 th percentile response spectra from the maximum credible earthquake acceleration for the HBPP ISFSI incorporating the site-specific soil response that satisfy the requirements specified in the Work Plan (GEO_2002-2, rev. 0)

The resulting spectra are to be used as the basis for the development of spectrum compatible time histories (see GEO.HBPP.02.05).

3. ASSUMPTIONS 3.1 Horizontal Component Attenuation Relationships for Rock Site Conditions for Crustal Earthquakes The Abrahamson and Silva (1997), Sadigh et al. (1993), Idriss (1991; 1994; 1995), and Campbell (1997) attenuation relationships for horizontal response spectral values are assumed to be representative attenuation relations for rock sites close to large earthquakes. The basis for this assumption is that these attenuation relations represent the state-of-the practice and are widely used.

One other commonly used attenuation model is the Boore et al., 1997 model. This model is not considered applicable for this case. The Boore et al (1997) model produces very low ground motions on rock for sites close to the rupture. This is a result of the very sparse near-fault data used to derive the model and the assumption of linear site response.

Therefore, this model is not included. If this model were included, the ground motions would be lower than estimated using the other four models.

3.2 Vertical Comvonent Attenuation Relationships for Soil Site Conditions There has been very little research on non-linear vertical component site response. As an alternative to a site response study, it is assumed that the empirical attenuation relations for the vertical component can be reasonably extrapolated to very high ground motion levels. The basis for this assumption is that empirical attenuation relations (e.g.

Abrahamson and Silva, 1997) indicate that the nonlinear effects for the vertical component are much smaller than the for the horizontal component.

The Abrahamson and Silva (1997) attenuation relation for the vertical component on deep soil site conditions is assumed to be appropriate for soil sites close to large magnitude earthquakes.

The basis for this assumption is that of the four empirical attenuation relations selected for the horizontal component (assumption 3.1), only the Campbell (1997) and Abrahamson and Silva (1997) models include the models for the vertical component on deep soil sites. Since the Campbell vertical component model is based on vertical to horizontal ratios which are then scaled by the horizontal spectrum, it is sensitive to the non-linear response of the horizontal component. Therefore, this model is not considered appropriate. The only remaining model is Abrahamson and Silva (1997).

Calc Number: GEO.HBIP.02.04 Rev Number:O l Sheet Number: 2 of O1 Date: 1/4/02 3.3 Depth to Seismogenic Zone The Campbell (1997) attenuation relation uses the seismogenic distance which is defined as the closest distance between the recording site and the zone of seismogenic rupture on the fault (Campbell, 1997, page 155). Campbell (1997, page 156) states that the depth to the top of the seismogenic zone should be no less than about 2 to 4 km. For the HBPP region, the depth to the top of the seismogenic zone is assumed to be 3 km. The basis for this assumption is that it is in average of the range recommended by Campbell (1997).

3.4 Depth to Basement Rock The Campbell (1997) attenuation relationship includes a term based on the depth to basement rock. For a hard rock site, the depth to basement rock is zero. For soft-rock sites, there may be weathered rock or shallow soil over the basement rock. Campbell (1997) does not give a recommended value for the depth to basement rock for soft-rock sites. The depth to basement rock is assumed to be 1.0 km. The basis for this assumption is that the depth of the weathering or of the shallow soil is likely to be much less than 1 km. Since the Campbell (1997) model has increasing long period ground motion for increasing depth to basement rock, this assumption is conservative in terms of the resulting ground motion.

3.5 Rupture Distance The Bay Entrance Fault is the closest of the main traces of the Little Salmon fault zone to the ISFSI site. It passes under the ISFSI site at a rupture distance of 0.5 km (see Input 4.1). For computing the deterministic ground motion, the rupture distance is assumed to be zero and the seismogenic distance is assumed to be 3 km.

The basis for this assumption is that it is slightly conservative (using 0 km rather than 0.5 km results in about a 1 to 2% increase in the ground motions). This assumption avoids the uncertainty in the location of the Bay Entrance Fault impacting the ground motion calculations.

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 3 of 101 Date: 1 1/4/02 3.6 Horizontal Component Attenuation for Subduction Zone Earthquakes The Youngs et al (1997) attenuation relation is used for subduction earthquakes. The basis for this assumption is given below.

There are two types of subduction zone earthquakes: interface earthquakes and intraslab earthquakes. Although the ground motions for a given magnitude and distance can be very different for these two types of earthquakes, most ground motion attenuation studies for subduction zone earthquakes have not distinguished between these two source types.

The exceptio is Youngs et al (1997). By separating the two source types for subduction zone earthquakes, Youngs et al found a significant difference in the ground motions (ground motions from intraslab earthquakes are about 60% larger than those from interface earthquakes for the same magnitude and distance). This difference is considered to be important, so te Youngs et al (1997) attenuation relation is selected for use in this study.

3.7 Spectral Period Extrapolation to 10.0 second The four empirical attenuation relationships are defined between the period range of 0.01 seconds (i.e., PGA) and 4.0 seconds. The spectral values from these attenuation relations are extrapolated to a period of 10 seconds using linear interpolation on the log-log values (see 5.2.7).

The basis for this assumption is that it is conservative. At long periods, the spectra typically exhibit an increasing slope as a function of period in the period range of 4 to 10 seconds. Therefore, using a constant slope leads to some conservatism in the long periods range.

3.8 Extrapolation of the directivity effects to 10 seconds period The directivity effects models by Somerville et al (1997) are defined for periods up to 5 seconds. For periods between 5 and 10 seconds, the directivity scale factors are assumed to be equal to the value at T=5 seconds.

The basis for this assumption is the earthquake magnitude of interest is 7.8 which will have a rise-time on the order of 6 seconds. The directivity effects are expected to be observed at periods up to about twice the rise-time. For the fault normal/AveH ratio, Calculations GEO.DCPP.01.1 1 showed that the effect extended out periods of 10 seconds.

3.9 Spectrum for Synchronous Rupture For the case of synchronous rupture of two sources (e.g. Cascadia and Little Salmon fault zone), the response spectrum of the combined ground motion is assumed to be the square root of the sum of the squares (SRSS) of the spectra of the individual sources.

The basis for this assumption is that SRSS is the appropriate method for combining the response spectra from independent events (random vibration theory).

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 4 of 101 Date: 11/4/02 3.10 Hypocenter location for directivity The rupture is assumed to begin at the bottom of the Little Salmon fault.

The basis for this assumption is that the Little Salmon fault is modeled as a splay off of the main subduction interface. If the rupture starts on the interface at depth, the rupture would transfer to the LSF at the bottom of the fault and continue to rupture updip.

3.1 1 Hypocenter depth for the Cascadia Interface event The depth of the Cascadia Interface event is assumed to be at a depth of 20 km. The basis for this assumption is that it is the depth of the bottom of the interface. Using the Youngs et al (1997) attenuation relation, the ground motion increases as the hypocentral depth increases for the same rupture distance. Therefore, this is a conservative assumption.

3.12 V/H ratio The Vertical to horizontal ratio computed using the Abrahamson and Silva (1997) attenuation relation for M=8, Rp=7, Strike-slip, and soil site condition is assumed to be applicable to a M=8.8, Rrup=7, interface source, and soil site conditions. The basis for this assumption is given below.

The vertical / horizontal ratio is dependent on magnitude , distance, soil class, and spectral period. The Youngs et al (1997) model does not include a model for a vertical component. Therefore, a crustal model needs to be used to capture the magnitude and distance dependence of the V/H ratio. The Abrahamson and Silva (1997) model can be used with a distance of 7 km to capture the magnitude dependence of the ratio, but it is not applicable to M=8.8. The main effects of the magnitude dependence of the ratio can be captured using M=8 in the Abrahamson and Silva (1997) model. A strike-slip mechanism is selected because the spectral shape for Abrahamson and Silva (1997) is more stable for the strike-slip case than it is for the reverse case.

3.13 Interpolation of Damping Scale Factors to Other Damping Values The scale factor for 4% damping is assumed to be equal to the square root of the arithmetic value of the scale factor for 3% damping.

The basis for this assumption is that it corresponds to linear interpolation on the log of the scale factor. The log is used because the scale factors can be approximated by alog normal distribution (Abrahamson and Silva, 1996). Since the scale factor at 5% damping is unity by definition and the logarithm of 1.0 is 0, a linear interpolation of the log values is just one-half of the log value at 3% damping. One half of the log value corresponds to the square root of the arithmetic value.

3.14 Extrapolation of Damping Scale Factors to Long Periods The Abrahamson and Silva (1996) damping scale factors are given for spectral periods up to 5 seconds. The values are not given for longer spectral periods because the ground motion data beyond 5 seconds is generally not reliable (See Abrahamson and Silva, Figure 1, page 96). For long period periods, the damping scale factors are assumed to be

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 5 of 101 Date: 11/4/02 equal to the value for T=5 seconds. The basis for this assumption is that it is the simplest assumption that can be made and we have no basis for a more complex model.

3.15 Earthquake Magnitude for the Damping Scale Factors The Abrahamson and Silva (I 996) models for the damping scale factors include a dependence on the earthquake magnitude. It is assumed that a magnitude of 8.0 is appropriate for use in the damping scale factor models to estimate the scale factors for the synchronous rupture case.

The basis for this assumption is that the magnitude of the synchronous rupture, approximately 8.8 (see Input 4. 1), is outside of the range of applicability of the Abrahamson and Silva (1996) model. The largest magnitude in the data set used by Abrahamson and Silva is M=7.4 and the regression equation does not properly extrapolate for magnitudes greater than 8.5 due to the selected functional form. As a co-developer of the model, it is my judgment that it can be reasonably extrapolated up to magnitude 8.0 but it is not reliable for extrapolation of the equations to larger magnitudes. Therefore, magnitude 8.0 is used for earthquakes with magnitude greater than 8.0 3.16 Short Periods for Youngs et al (997!

The Youngs et al (1997) attenuation relation for subduction earthquakes gives equations for the peak acceleration and for a spectral period of 0.075 sec. but it does not include equations for periods less than 0.075 sec. The response spectral values for spectral periods less than or equal to 0.03 seconds are assumed to be equal to the peak acceleration.

The basis for this assumption is that the response spectra from large subduction earthquakes (e.g. 1985 Michoacan and 1985 Chile) are approximately flat (equal to the peak acceleration) for spectral periods less than 0.03 sec (see PEER strong motion data base).

Calc Number: GEO.HB[P.02.04 Rev Number:O I Sheet Number: 6 of 101 Date: 1/4/02

4. DESIGN INPUTS 4.1 Earthquake Magnitudes and Distances As described in GEO.HBPP.02.03, two seismic sources are considered in developing the deterministic ground motions: the Little Salmon Fault and the Cascadia interface. The mean magnitudes and distances for the two sources based on the Carver model are taken from GEO.HBPP.02.03 (Table 8-l). These values are listed in Tables 4-1 and 4-2.

Table 4-1. Source parameters for deterministic events for the Little Salmon Fault zone subsource Little Reference Salmon fault zone Magnitude 7.7 GEO.HBIP.02.03, Table 8-1 Rupture Distance (km) 0.0 Assumption 3-5 Seismogenic Distance (kn) 3.0 Assumption 3-3,3-5 Mechanism Reverse GEO.HBIP.02.03, Table 8-1 Table 4-2. Source parameters for deterministic events for the Cascadia Interface subsource Cascadia Reference Interface Magnitude 8.8 GEO.HBIP.02.03, Table 8-1 Rupture Distance (km) 7 GEO.HBIP.02.03, Table 8-1 Mechanism Interface GEO.HBIP.02.03, Table 8-1

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 7 of 0 1 Date: 11/4/02 4.2 Northridge High Frequency Spectral Shapes The acceleration response spectral shape (i.e., SA/PGA) from 5 strong ground motion sites on soil site conditions which recorded large horizontal PGA motions (i.e., average horizontal ground motions of 0.6 g and larger) from the Northridge earthquake was computed in GEO.HBIP.02.06 (Table 8-2). These values are listed in Table 4-3 below.

Table 4-3. Average horizontal rock spectral shape based on 12 Northridge strong motion recordings. (from GEO.HBIP.02.06 Table 8-2)

Period (sec) Average Spectral Shape (Salpga) 0.010 1.000 0.020 1.000 0.030 1.016 0.050 1.095 0.075 1.225 0.100 1.384 0.150 1.690 0.200 1.911 0.300 2.368 0.500 1.980 0.750 2.049 1.000 1.682 1.500 1.036 2.000 0.765 3.000 0.451 4.000 0.208

Calc Number: GEO.HBIP.02.04 Rev Number:O l Sheet Number: 8 of O1 Date: 1114/02 4.3 Site specific soil amplification factors As described in GEO.HBIP.02.06, the site specific soil amplification factors were developed based on three soil profiles: median, lower bound, and upper bound. For each profile three sets of time histories were used and the average amplification factors for a rock PGA value of 1.6 g are given below in Table 4-4.

Table 44. Average amplification factors for an input PGA of 1.6 g (From GEO.HBIP.02.06, Table 8-1)

Period Median Lower Upper (sec) Profile Profile Profile 0.010 0.608 0.383 0.813 0.030 0.615 0.387 0.822 0.050 0.434 0.273 0.581 0.075 0.352 0.221 0.473 0.100 0.324 0.201 0.444 0.150 0.292 0.182 0.435 0.200 0.376 0.193 0.602 0.300 0.563 0.325 0.924 0.420 0.940 0.481 1.011 0.500 0.882 0.677 0.948 0.600 0.900 0.811 1.258 0.640 0.885 0.734 1.342 0.750 1.053 0.678 1.416 0.860 1.214 0.766 1.368 1.000 1.262 0.823 1.468 1.200 1.342 1.117 1.903 1.450 1.580 1.181 2.419 1.700 1.904 1.309 2.681 2.200 2.381 1.809 2.194 2.600 2.305 2.083 1.893 3.200 1.922 2.373 1.605 3.500 1.926 2.324 1.622 4.100 1.692 2.102 1.384 4.300 1.521 1.915 1.250 5.400 1.451 1.724 1.250 6.200 1.322 1.484 1.211 7.800 1.209 1.351 1.165 10.000 1.258 1.330 1.174

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 9 of 101 Date: 1/4/02

5. METHOD AND EQUATION

SUMMARY

5.1 Methods 5.1.1 Horizontal Spectrum The method used to develop the HBPP horizontal spectra uses the following steps.

1. The 84h percentile spectrum for reference rock site conditions is computed for the Little Salmon fault zone source using the average spectrum computed from four empirical attenuation relations for crustal sources.

2. The LSF average horizontal spectrum is extrapolated to a spectral period of 10.0 seconds.

3. The LSF horizontal rock spectrum is modified to include the effects of directivity. This results in separate spectra for the fault normal and fault parallel components.

4. The 84th percentile spectrum for reference rock site conditions is computed for the Cascadia Interface source using the Youngs et al. (1997) empirical attenuation relation for subduction sources.

5. The Cascadia horizontal spectrum is extrapolated to a spectral period of 10.0 seconds.

6. The horizontal rock spectra for the LSF and Cascadia interface sources are combined to estimate the spectrum for synchronous rupture.

7. The horizontal spectrum for soil site conditions is computed by scaling the combined rock spectra by the site-specific soil amplification factors.

8. The short period part of the horizontal soil spectrum is modified to envelope the empirical spectral shape from large amplitude recordings from soil sites in the Northridge earthquake.

9. Smooth design spectra are developed for the fault normal and fault parallel components.

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 10 of 101 Date: 1/4/02 5.1.2 Vertical Spectrum The method used to develop the HBPP vertical spectrum uses the following steps.

1. The 8 4 h percentile vertical component spectrum for deep soil site conditions is computed for the Little Salmon fault zone source using the Abrahamson and Silva (1997) empirical attenuation relation.

2. The LSF vertical soil spectrum is extrapolated to a period of 10 seconds.

3. The 84th percentile horizontal spectrum for deep soil site conditions is computed for the Cascadia Interface source using the Youngs et al (1997) empirical attenuation relation for subduction sources.

4. The V/H ratio for soil sites is computed using the Abrahamson and Silva (1997) attenuation relations.

5. The Cascadia vertical soil spectrum is computed by multiplying the horizontal spectrum (step 3) by the V/ ratio (step 4).

6. The Cascadia vertical soil spectrum is extrapolated to a period of 10 seconds.

7. The vertical soil spectra for the LSF and Cascadia interface sources are combined to estimate the vertical spectrum for synchronous rupture.

5.1. 3 Spectra for Damping Values Other than 5%

1. Scale factors for scaling the 5% damped horizontal to damping values of 2%,

3%, and 7% are computed using the Abrahamson and Silva (1996) model.

2.., The horizontal scale factors at 4% damping are estimated from the scale factors for 3% damping

3. Scale factors for scaling the 5% damped vertical to damping values of 2%,

4%, and 7% are computed using the Abrahamson and Silva (1996) model.

4. The vertical scale factors at 4% damping are estimated from the scale factors for 3% damping.

5. The horizontal scale factors are applied to the 5% damped fault normal spectrum to compute the fault normal spectra at 2%, 4%, and 7% damping.

6. The horizontal scale factors are applied to the 5% damped fault parallel spectrum to compute the fault parallel spectra at 2%, 4%, and 7% damping.

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: I I of 101 Date: 1/4/02

7. The vertical scale factors are applied to the 5% damped vertical spectrum to compute tie vertical spectra at 2%, 4%, and 7% damping.

Calc Number: GEO.HBIP.02.04 Rev Number:O Sheet Number: 12 of 101 Date: I 1/4/02 5.2 Equations 5.2.1 Sadigh et al. (1993,1997) Attenuation Equation The Sadigh et al. (1997) attenuation relation for rock sites is identical to the Sadigh et al.

(1993) relation with two exceptions. First, the 1997 paper has fewer spectral periods listed. Second, there is a small change to the standard deviation model. In the 1993 model, the standard deviation becomes independent of magnitude for M>7.25. In the 1997 model, the standard deviation becomes independent of magnitude for M>7.2. This change in the standard deviation model results in a slight increase in the standard deviation for earthquakes with magnitudes greater than 7.21.

To avoid unnecessary interpolations, the 1993 relation is used for the coefficients for the median. The revised standard deviation model given in Sadigh et al (1997) is used.

The Sadigh et al (1993) median horizontal spectral acceleration attenuation relation for a strike-slip earthquake (Sass) at a rock site is given by (Sadigh et al, 1993, page 66)

In (Sass) = C + 1.1 M + C3 (8.5-M)25 + C4 n(R+exp(C 5 +C 6 M)) (5-I)

+ C 7 ln(R+2) where R is the rupture distance, and M is the magnitude. The coefficients for this model are listed in Table 5-1. Ground motions for reverse faults are computed by scaling the strike-slip values by a factor of 1.2 at all spectral periods (Sadigh et al, 1993, page 66).

For M<7.21, the standard deviation is given by the equation in the last column of Table 5-1. For M>=7.21, the standard deviation is given by using M=7.2 in the equation.

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number 13 of 1O 1 Date: 11/4102 Table 5-1. Coefficients for the Sadigh et al. (1993) attenuation relation for horizontal spectral acceleration for M > 6.5 (from Sadigh, 1993, Table 1, page 66)

Period(s) C1 C3 C4 Cs Cs C7 a (M<7.2 1) 0.00524

-12740.00 -2.00 0.-0.8451 (1997) 0.0 -1.274 0.000 -2.100 -0.48451 0.524 0.0 1.39 - 0.14M 0.05 -0.740 0.006 -2.128 -0.48451 0.524 -0.082 1.39 - 0.14M 0.07 -0.540 0.006 -2.128 -0.48451 0.524 -0.082 1.40 - 0.14M 0.09 -0.438 0.006 -2.140 -0.48451 0.524 -0.052 1.40 - 0.14M 0.10 -0.375 0.006 -2.148 -0.48451 0.524 -0.041 1.41 - 0.14M 0.15 -0.365 0.002 -2.130 -0.48451 0.524 0.0 1.42 - 0.14M 0.20 -0.497 -0.004 -2.080 -0.48451 0.524 0.0 1.43 - 0.14M 0.30 -0.707 -0.017 -2.028 -0.48451 0.524 0.0 1.45 - 0.14M 0.40 -0.948 -0.028 -1.990 -0.48451 0.524 0.0 1.48 - 0.14M 0.50 -1.238 -0.040 -1.945 -0.48451 0.524 0.0 1.50 - 0.14M 0.75 -1.858 -0.050 -1.865 -0.48451 0.524 0.0 1.52 - 0.14M 1.00 -2.355 -0.055 -1.800 -0.48451 0.524 0.0 1.53 - 0.14M 1.50 -3.057 -0.065 -1.725 -0.48451 0.524 0.0 1.53 - 0.14M 2.00 -3.595 -0.070 -1.670 -0.48451 0.524 0.0 1.53 - 0.14M 3.00 -4.350 -0.080 -1.610 -0.48451 0.524 0.0 1.53 - 0.14M 4.00 -4.880 -0.100 -1.570 -0.48451 0.524 0.0 1.53 - 0.14M 5.00 -5.364 -0.100 -1.540 -0.48451 0.524 0.0 1.53 - 0.14M 7.50 -6.180 -0.110 1-1.510 1-0.48451 0.524 0.0 1.53 -0.14M

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 14 of 101 Date: 11/4/02 5.2.2 Idriss (1991,1994.1995) Attenuation Equation The Idriss (1991) median horizontal spectral acceleration attenuation relations for rock sites use the form:

ln(Sa) = ao + exp(a I + a-,M) + (o - exp(P I + P 2M))*ln(R+20) + 0.2F (5-2a) where R is the rupture distance and F is the style-of-faulting (F=1 for reverse, F=0.5 for reverse/oblique, F=O, otherwise). driss (1991), which is summarized in the driss (1992) review paper, developed coefficients for peak acceleration and response spectral acceleration. The coefficients for this model are listed in Table 5-2.

Subsequently, the peak acceleration model was updated in driss (1995). For M>6, the updated peak acceleration is given by(Idriss, 1995, page 2114):

ln(PGA 95 )= exp(aI + a 2 M) - exp(PI1 + p2 M)*ln(R+10) + Ff (5-2b) where aI = 2.763, a 2 = -0.262, PI = 2.215, 0 2 M= -0.288, and =0.28.

The spectral shape is given by the ratio of the spectral acceleration to the peak acceleration: Sa(T)/ pga. If the spectral shape is unchanged, then at each spectral period, T,

Sa95 (T) pga 95 = Sa 9 l(T)/ pga9 l (5-3)

Therefore, Sa95 = Sag1 * (PGA9 5 / PGA9 1) (5-4)

Using eq.(5-4), the updated model for the response spectral values is computed by scaling the 1991 spectral values by the ratio of the 1995 pga to the 1991 pga.

The standard deviation for the response spectral values was updated by Idriss (1994). The equations for the updated standard deviations are given in Table 5-2. For M<7.25, the standard deviation is given by the equation in the last column of Table 5-2. For M>=7.25, the standard deviation is given by using M=7.25 in the equation.

Calc Number: GEO.HBIP.02.04 Rev Number0 I Sheet Number 15 of 101 Date: 11/4/02 Table 5-2. Coefficients for the Idriss (1991) attenuation relation for horizontal J spectral acceleration for M > 6.0 Period CO aL a2 I o p P2 a (1994) a (1994)

(s) f!r M<7.25 for M>=7.25 0.0 -0.050 3.477 -0.284 0 2.475 -0.286 1.29-0.12M 0.42 0.03 -0.050 3.477 -0.284 0 2.475 -0.286 1.29-0.12M 0.42 0.05 -0.278 3.426 -0.269 0.066 2.475 -0.286 1.29-0.12M 0.42 0.075 -0.308 3.359 -0.252 0.070 2.475 -0.286 1.29-0.12M 0.42 0.10 -0.318 3.327 -0.243 0.072 2.475 -0.286 1.32-0.12M 0.45 0.15 -0.348 3.185 -0.216 0.076 2.475 -0.286 1.35-0.12M 0.48 0.20 -0.358 3.100 -0.201 0.078 2.475 -0.286 1.37-0.12M 0.50 0.30 -0.486 2.982 -0.182 0.082 2.475 -0.286 1.39-0.12M 0.52 0.40 -0.577 2.906 -0.173 0.092 2.475 -0.286 1.41-0.12M 0.54 0.50 -0.648 2.850 -0.169 0.099 2.475 -0.286 1.42-0.12M 0.55 0.70 -0.754 2.765 -0.165 0.111 2.475 -0.286 1.44-0.12M 0.57 0.80 -0.796 2.728 -0.164 0.115 2.475 -0.286 1.45-0.12M 0.58 1.00 -0.867 2.662 -0.162 0.123 2.475 -0.286 1.47-0.12M 0.60 1.50 -0.970 2.536 -0.160 0.136 2.475 -0.286 1.47-0.12M 0.60 2.00 -1.046 2.447 -0.160 0.146 2.475 -0.286 1.47-0.12M 0.60 3.00 -1.143 2.295 -0.159 0.160 2.475 -0.286 1.47-0.12M 0.60 4.00 -1.177 2.169 -0.159 0.169 2.475 -0.286 1.47-0.12M 0.60 5.00 -1.214 2.042 -0.157 0.177 2.475 -0.286 1.47-0.12M 0.60

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 16 of 101 Date: 1114/02 5.2.3 Abrahamson and Silva (1997) Attenuation Equation The Abrahamson and Silva (1997) median spectral acceleration attenuation relation is given by (Abrahamson and Silva, 1997, eq. 3, page 105):

ln(Sa(g))=Af(M,Rrup) + Ff3 (MRrp) + HWf 4 (MRrup) + Sf 5 (PGArock) (5-5) where M is the moment magnitude, Rrup is the rupture distance, F is the style of faulting factor (F=l for reverse, F=0.5 for reverse/oblique, and F=0 otherwise), S is a site factor (S=O for rock, S=1 for soil), and HW is a hangingwall factor (HW=1 for sites on the hanging wall and HW=0 otherwise).

For M>cI the f 1(M,R) equation is given by (Abrahamson and Silva, 1997, eq. 4, page 105):

f(M,R)=a,+a 4 (M-cl)+ a 2 (8.5-M) +[a3 +aI3 (M-cI)]lnR (5-6) where c = 6.4 (Abrahamson and Silva, 1997, table 3, page 108). The distance R is given by (Abrahamson and Silva, 1997, eq. 5, page 105):

R =R2p + c42 (5-7)

For M> cl, the effect of the style-of-faulting on the spectral acceleration is given by Abrahamson and Silva, 1997, eq. 6, page 106):

f 3 (M) = a6 (5-8)

The hanging wall term, f 4(M,Rmp), is zero for Rrup < 4 km (Abrahamson and Silva, 1997, eq. 9, page 106).

The non-linear soil response (Abrahamson and Silva, 1997, eq. 10, page 106) is modeled by:

f5(PGA,,,)=alo+al ln(PGAroCk + cs) (5-9)

Substituting eq. 5-6, 5-7, and 5-8 into eq. 5-5, the median spectral acceleration for M>6,4, Rup,<4 km, on rock (S=0), is ln(Sa(g)) = a, + a 4 (M- c,)+ a.2 (8.5 - M) + [a3 + a 13 (M-c)]ln(fR2+ c2)) (5-10)

+Fa6 Substituting eq. 5-6, 5-7, 5-8 and 5-9 into eq. 5-5, the median spectral acceleration for M>6,4, Rrup< 4 km, on soil (S=1), is

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 17 of O1 Date: 1/4/02 ln(Sa(g)) =a, + a 4 (M- c,)+ a 2(8 M) + [a3 + a 3(M-c,)]In(l 2 +2))

(5-11)

+ Fa6 + 0 + a, l1n(PGA,,,k+ c)

The coefficients for eq. 5-10 and 5-11 are listed in Tables 5-3 and 5-4 for the horizontal and vertical components, respectively.

The standard deviations, for M 27.0 are given by (Abrahamson and Silva, 1997, eq. 13, page 106).

cs = b5 -2b 6 (5-12)

The coefficients for the standard deviation for the horizontal and vertical components are also listed in Tables 5-3 and 5-4.

Table 5-3. Coefficients for the Abrahamson and Silva (1997) attenuation relation for horizontal spectral acceleration (from Abrahamson and Silva, Table 3 and 4, pages 108 and 109)

Period C, a, a, a4 as as a, a, 0 all a 12 a 1,3 n cs , bo 0.0 5.60 1.640 -1.1450 .0.144 0.610 0.260 0.370 -0.417 -0.230 0.000 0.17 2 0.03 0.70 0.135 0.03 5.60 1.690 -1.1450 -0.144 0.610 0.260 0.370 -0.470 -0.230 0.014 0.17 2 0.03 0.70 0.135 0.05 5.60 1.870 -1.1450 -0.144 0.610 0.260 0.370 -0.620 -0.267 0.0280 0.17 2 0.03 0.71 0.135 0.075 5.58 2.037 -1.1450 -0.144 0.610 0.260 0.370 -0.628 -0.280 0.0300 0.17 2 0.03 0.73 0.135 0.10 5.50 2.160 -1.1450 -0.144 0.610 0.260 0.370 -0.598 -0.280 0.0280 0.17 2 0.03 0.74 0.135 0.15 5.27 2.407 -1.1450 -0.144 0.610 0.260 0.370 -0.577 -0.280 0.0050 0.17 2 0.03 0.75 0.135 0.20 5.10 2.406 -1.1150 -0.144 0.610 0.260 0.370 -0.445 -0.245 .0.0138 0.17 2 0.03 0.77 0.135 0.30 4.80 2.114 -1.0350 -0.144 0.610 0.198 0.370 -0.219 -0.195 -0.0360 0.17 2 0.03 0.78 0.135 0.40 4.52 1.860 -0.9880 -0.144 0.610 0.154 0.370 -0.065 -0.160 -0.0518 0.17 2 0.03 0.79 0.135 0.50 4.30 1.615 -0.9515 -0.144 0.581 0.119 0.370 0.085 -0.121 -0.0635 0.17 2 0.03 0.80 0.130 0.75 3.90 1.160 -0.8852 -0.144 0.528 0.057 0.331 0.320 -0.050 -0.0862 0.17 2 0.03 0.81 0.123 1.00 3.70 0.828 -0.8383 -0.144 0.490 0.013 0.281 0.423 0.000 -0.1020 0.17 2 0.03 0.83 0.118 1.50 3.55 0.260 -0.7721 -0.144 0.438 -0.049 0.210 0.600 0.040 -0.1200 0.17 2 0.03 0.84 0.110 2.00 3.50 -0.150 0.7250 -0.144 0.400 -0.094 0.160 0.610 0.040 -0.1400 0.17 2 0.03 0.85 0.105 3.00 3.50 -0.690 -0.7250 -0.144 0.400 -0.156 0.089 0.630 0.040 -0.1726 0.17 2 0.03 0.87 0.097 4.00 3.50 -1.130 -0.7250 -0.144 0.400 -0.200 0.039 0.640 0.040 -0.1956 0.17 2 0.03 0.88 0.092 5.00 3.50 -1.460 0.7250 -0.144 0.400 -. 200 0.000 0.664 0.040 -0.2150 0.171 2 0.03 0.89 0087

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 18 of 101 Date: 1/4/02 Table 5-4. Coefficients for the Abrahamson and Silva (1997) attenuation relation for vertical spectral acceleration for M > 6.4 (from Abrahamson and Silva, page 116)

Period C4 a, a3 a4 as a, a9 al0 a11 a12 a13 n CS b5 b6 (sec) I_ _ _I _

0.0 600 1.642 -1.2520 0.275 0.390 -0.050 0.630 -0.140 -0.22 0.0000 0.06 3 0.3 0.76 0.085 0.03 6.00 2.100 -1.3168 0.275 0.432 -0.050 0.630 -0.140 -0.22 0.0000 0.06 3 0.3 0.76 0.085 0.05 6.00 2.620 -1.3700 0.275 0.496 -0.050 0.630 -0.140 -0.22 -0.0002 0.06 3 0.3 0.76 0.085 0.075 6.00 2.750 -1.3700 0.275 0.545 -0.050 0.630 -0.129 -0.22 -0.0007 0.06 3 0.3 0.76 0.085 0.10 6.00 2.700 -1.3700 0.275 0.580 -0.050 0.630 -0.114 -0.22 o0.O10 0.06 3 0.3 0.76 0.085 0.12 6.00 2.480 -1.2986 0.275 0.580 -0.017 0.630 -0.104 -0.22 0.0015 0.06 3 0.3 0.74 0.075 0.15 6.00 2.170 -1.2113 0.275 0.580 0.024 0.630 4.093 0.22 -0.0022 0.06 30.3 0.72 0.063 0.17 5.72 1.960 -1.1623 0.275 0.580 0.047 0.604 -0.087 -0.220 -0.0025 0.06 3 0.3 0.70 0.056 0.20 5.35 1.648 -1.0987 0.275 0.580 0.076 0.571 -0.078 0.22 -0.00300.06 3 0.3 0.69 0.050 0.24 4.93 1.312 -1.0274 0.275 0.580 0.109 0.533 -0.069 0.22 -0.0035 0.06 3 0-3 0.69 0.050 0.30 4.42 0.878 -0.9400 0.275 0.580 0.150 0.488 -0.057 -0.22 -0.0042 0.06 3 0.3 0.69 0.050 0.40 3.77 0.478 -0.8776 0.275 0.539 0.150 0.428 -0.043 -0.22 -0.0050 0.06 3 0.3 0.69 0.050 0.50 3.26 0.145 -0.8291 0.275 0.471 0.150 0.383 -0.031 -0.22 -0.0060 06 3 0.3 0.69 0.050 0.75 2.50 -0.344 -0.7488 0.275 0.348 0.150 0.299 -0.010 -0.22 -0.0083 0.06 3 0.3 0.69 0.050 1.00 2.50 -0.602 -0.7404 0.275 0.260 0.150 0.24 0.004 -0.22 -0.0115 0.06 3 0.3 0.69 0.050 1.50 2.50 -0.966 -0.7285 0.275 0.260 0.058 0.240 0.025 -0.22 - 0 3 0.3 0.69 0.050 2.00 2.50 -1.224 -0.7200 0.275 0.260 -0.008 0.240 0.040 -0.22 -0.0240 0.06 3 0.3 0.69 0.05 3.00 2.50 -1.581 -0.7200 0.275 0.260 -0.100 0.240 0.040 -0.22 -0.0431 0.06 3 03 0.72 0.050

_ _ _ _ _ _. _ _0 3 07 . 5 4.00 2.50 -1.857 -0.7200 0.275 0.260 -0.100 0.240 0.040 -0.22 -0.0565 0.06 3 0.3 0.75 D.0 2.50 -2.053 -0.7200 0.275 0.260 -0.100 0.240 0.040 4.22 - 0.06 3 0.3 0.78 0.050

Calc Number: GEO.HBIP.02.04 Rev Number:O Sheet Number: 19 of 101 Date: 1 1/4/02 5.2.5 Campbell (1997) Attenuation Equations Campbell (1997) develops a relation for peak acceleration and a relation for spectral acceleration based on the peak acceleration. For a soft-rock site (SSR =1 and SHR =0), the mean horizontal component of peak acceleration is given by (Campbell, eq 3, page 164)

In(AH) = -3.512 + 0.904M- 1.328 InM EJS + [0.1 49exp(0.647M)] 2

+[1.125-0.1 12ln(RsEs)-0.0957M]F (5-13)

+ [0.440 - 0.171 ln(RsEIs)]

For a reverse-slip earthquake, F=1 (Campbell, 1997, page 156)

The median horizontal spectral acceleration attenuation relations for strike-slip earthquakes use the form (Campbell eq. 8, page 170):

In(Sa(g)) = n(AH) + C1 + C2 tanh[C3(M-4.7)]+(c 4 +c5M)RSEls+0.5c 6 sSR+c 6 SHR (5-14)

+ C7 tanh(cgD)(1- SHR) + fSA(D) where M is magnitude, RSEIS is the seismogenic distance, D is the depth to basement rock, SSR =1 for soft-rock and 0 otherwise, and SHR =1 for hard-rock sites and 0 otherwise. For D< 1 km, the function fsa(D) is given by fsa(D) = C6 (I-SSR)(1-D) + 0.5 C6 (I-D)SSR (5-15)

(Campbell, 1997, page 170, part of eq. 8). Note that Campbell (1997) contains an error in the equation for Fsa(D). The term (l-SSR in eq. (5-15) above is incorrectly given as (1-SHR) in Campbell (1997).

For a soft-rock site, (SSR=1, SHR=O), equation (5-14) becomes In(Sa(g)) = n(AH) + cl + c 2 tanh[c 3(M-4.7)]+(c 4 +c 5M)RsEIs+0.5c 6

+ c 7tanh(cgD) + 0.5c 6(1-D) (5-16)

The standard deviation for the horizontal component, aH, is given by (Campbell eq 10, page 171 and eq 5, page 164) 2 a, = +0.27' (5-17) where apga=0.889-0.0691 M forM<7.4 (5-18) 0.38 for M >=7.4

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 20 of 101 Date: 11/4/02 Table 5-5. Coefficients for the Campbell (1997) attenuation relation for horizontal spectral acceleration (from Campbell, page 170)

Period Ca C2 C cC Cs (sec) _ l_ _ _ _

0.05 0.05 0 0 -0.0011 0.000055 0.20 0 0 0.075 0.27 0 0 -0.0024 0.000095 0.22 0 0 0.10 0.48 0 0 -0.0024 0.000007 0.14 0 0 0.15 0.72 0 0 -0.0010 .0.00027 -0.02 0 0 0.20 0.79 0 0 0.0011 -0.00053 -0.18 0 0 0.30 0.77 0 0 0.0035 -0.00072 -0.40 0 0 0.50 -0.28 0.74 0.66 0.0068 -0.00100 -0.42 0.25 0.62 0.75 -1.08 1.23 0.66 0.0077 -0.00100 -0.44 0.37 0.62 1.0 -1.79 1.59 0.66 0.0085 -0.00100 -0.38 0.57 0.62 1.5 -2.65 1.98 0.66 0.0094 -0.00100 -0.32 0.72 0.62 2.0 -3.28 2.23 0.66 0.0100 -0.00100 -0.36 0.83 0.62 3.0 -4.07 2.39 0.66 0.0108 -0.00100 -0.22 0.86 0.62 4.0 -4.26 2.03 0.66 0.0112 -0.00100 -0.30 1.05 0.62

Calc Number: GEO.HBIP.02.04 Rev Number:O Sheet Number: 21 of 101 Date: 11/4/02 5.2.6 Computation of 8 4 th Percentile Spectral Values For a log-normal distribution, the 84'h percentile corresponds to 1.0 standard deviations above the median. The 8 4 th percentile response spectral values are given by:

Ln(Sas4 th) = In(Samed) + a (5-19) 5.2.7 Equation for log-log interpolation/extraiolation of response spectra The interpolation or extrapolation of the response spectral values is done using linear interpolation on the log spectral acceleration - log period. Given the spectral values Sal and Sa2 at periods TI and T 2 , respectively, then using linear interpolation on the log-log values, the spectral acceleration at period T is given by ln(Sa(T)) = ln(Sa(T1 )) + n(T) - n(Tl)) ln(Sa(T2 )) - n(Sa(T1 )) (5-20)

(~n(T) ln(T1 )) [ln(T 2 ) - ln(T1) 5.2.8 Somerville et al (1997) Rupture Directivity Model The Somerville et al (1997) model for rupture directivity has two effects: a scale factor for the average horizontal component and a scale factor for the fault normal (FN) and fault parallel (FP) components. The equation for the scale factor for the average horizontal component for dip-slip earthquakes is given by (Somerville et al 1997, page 210 ):

ln(Dir (Y, ,T)) = cl (T) + c 2 (T) Y cos(o) (5-21) where C (T) + C 2(T) are listed in Table 5-6, and Y and are directivity parameters defined by Somerville et al. (1997). (See Somerville et al 1997 figure 5).

The Somerville et al (1997, page 214) model for the difference between the fault normal and fault parallel components of the horizontal ground motion is given by (Somerville et al, 1997, page 214) ln(FN/AveH) = cos (20) [C 1 + C 2 ln(R+1) + C3 (M-6)] for M>6 and o<45 (5-22) ln(FN/AveH) = 0 otherwise The coefficients for this model are listed in Table 5-7. (note: Somerville et al uses the variable 4 in eq. (5-22). They state that ,=0 for dip-slip earthquakes. Only the dip-slip model is shown here.)

Caic Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 22 of 101 Date: 11/4/02 Table 5-6. Coefficients for the Somerville et al (1997) directivity model for the average horizontal component for dip-slip earthquakes (from Somerville et al 1997, Table 4 part b, page 208).

Period C, C2 (sec) 0.0 -0.60 0.000 0.000 0.75 -0.045 0.008 1.00 -0.104 0.178 1.50 -0.186 0.318 2.00 -0.245 0.418 3.00 -0.327 0.559 4.00 -0.386 0.659 5.00 -0.43 1 0.737 Table 5-7. Model Coefficients for the Somerville et al. (1997) Directivity Effects Including the dependence on the angle (from Somerville et al, 1997, Table 7, Page 209)

Period C1 C2 C3 (sec) 0.0 -.50 0.000 0.000 0.000 0.60 0.027 -0.007 0.000 0.75 0.061 -0.016 0.000 1.00 0.104 -0.026 0.000 1.50 0.164 -0.049 0.034 2.00 0.207 -0.061 0.059 3.00 0.353 -0.101 0.093 4.00 0.456 -0.128 0.118 5.00 0.450 -0.127 0.137 The average horizontal component is based on the geometric mean of the two horizontals (Abrahamson and Silva, 1997, page 105). That is AveH = FP*FN. Therefore the ratio of the FP/AveH is given by ln(FP/AveH) = - ln(FN/AveH) (5-23) where ln(FN/AveH) is given in eq. 5-22.

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 23 of 101 Date: 11/4/02 5.2.9 Combination of directivity factors The two directivity scale factors are combined to give the total effect. The scale factors for the FN and FP components are:

ScaleFN (T) = Dir(T)

• FN/AveH (T) (5-24)

ScaleFp (T) = Dir(T)

• FP/AveH (T) (5-25)

Where Dir is from eq. 5-21 and FN/AveH is from eq. 5-22, and FP/AveH is from eq. 5-23.

5.2.10 Computation of fault normal and fault parallel ground motion The directivity factors are scale factors that are used to scale ground motions from standard attenuation relations for the average horizontal component. The response spectrum for the fault normal component, including directivity effects, is computed using the following equation:

SaFN(T) = SaAveH(T)

• ScaleFN (T) (5-26)

The response spectrum for the fault parallel component, including directivity effects, is computed using the following equation:

SaFp(T) = SaAveH(T)

• ScaleFp (T) (5-27)

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 24 of 101 Date: 11/4/02 5.1.11 Youngs et al. (1997) Attenuation Relation The Youngs et al. (1997) attenuation relation for subduction zone earthquakes for rock sites is given by (Youngs et al, 1997, listed in Table 2, page 67):

ln(Sa)=0.2418+1.414M+C,+C 2 (l0-M)3 1r _n I

(3-26a)

+ C3 n(RX, + 1.7818 e0 554 ' )+ 0.00607H+ 0. 3 8 4 6 ZT where H=hypocentral depth in km and ZT is the source Type (Zr0 for interface and Z11 for intraslab).

The Youngs et al. (1997) attenuation relation for subduction zone earthquakes for soil sites is given by (Youngs et al, 1997, listed in Table 2, page 67):

In(Sa)=- 0.6687+1.438M+C,+C2 (10 - M) 3 - I

(:-/-?D)

+C3 ln(Rp +1 .097e°067AI )+0.00648H+ 0. 3 64 3 ZT The standard deviation is given by (Youngs et al, 1997, listed in Table 2, page 67):

IC.+C5 M forM<8 (5-29) 1 C4 +8C 5 forM>8 The coefficients for eq. (5-28a) and (5-28b) are given in Tables 5-8 and 5-9 for rock sites and soil sites, respectively.

Table 5-8. Coefficients for the Youngs et al (1997) attenuation relations for subduction earthquakes on rock sites (From Youngs et a. 1997, Table 2, page 67)

Period (sec) cl c2 C3 C4 C5 0.00 0 0 -2.552 1.45 -0.1 0.075 1.275 0 -2.707 1.45 -0.1 0.1 1.188 -0.0011 -2.655 1.45 -0.1 0.2 0.722 -0.0027 -2.528 1.45 -0.1 0.3 0.246 -0.0036 -2.454 1.45 -0.1 0.4 -0.115 -0.0043 -2.401 1.45 -0.1 0.5 -0.400 -0.0048 -2.360 1.45 -0.1 0.75 -1.149 -0.0057 -2.286 1.45 -0.1 1.0 -1.736 -0.0064 -2.234 1.45 -0.1 1.5 -2.634 -0.0073 -2.160 1.50 -0.1 2.0 -3.328 -0.0080 -2.107 1.55 -0.1 3.0 -4.511 -0.0089 -2.033 1.65 -0.1

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 25 of 101 Date: 1/4/02 Table 5-9. Coefficients for the Youngs et al (1997) attenuation relations for subduction earthquakes on soil sites (From Youngs et a. 1997, Table 2, page 67)

Period (sec) C1 C2 C3 C4 C5 0.00 0 0.0 -2.329 1.45 -0.1 0.075 2.400 -0.0019 -2.697 1.45 -0.1 0.1 2.516 -0.0019 -2.697 1.45 -0.1 0.2 1.549 -0.0019 -2.464 1.45 -0.1 0.3 0.793 -0.0020 -2.327 1.45 -0.1 0.4 0.144 -0.0020 -2.230 1.45 -0.1 0.5 -0.438 -0.0035 -2.140 1.45 -0.1 0.75 -1.704 -0.0048 -1.952 1.45 -0.1 1.0 -2.870 -0.0066 -1.785 1.45 -0.1 1.5 -5.101 -0.0114 -1.470 1.50 -0.1 2.0 -6.433 -0.0164 -1.290 1.55 -0.1 3.0 -6.672 -0.0221 -1.347 1.65 -0.1

Calc Number: GEO.HBIP.02.04 Rev Number:O Sheet Number: 26 of 101 Date: 1 1/4/02 5.1.12 Converting Spectral Acceleration to Psuedo-Spectral velocity response spectrum A spectral acceleration response spectrum can be converted to a psuedo-spectral velocity response spectrum based on the following equation (Hudson, 1979, page 60):

PSV(cm/s) = T*Sa(g)(980.5 cm/s) (5-30) where PSV is in units of cm/sec and Sa is'in units of g, and T is the spectral period in seconds. The inverse conversion from PSV to Sa is given by solving eq. 5-30 for Sa:

_PSV *2n( g '

Sa(g) T ( 980.5 cm/s) (5-31) 5.2.13 Equations for Scale Factors for Damping values other than 5%

The Abrahamson and Silva (1996) model for natural log of the scale factors for response spectral values at dampings other than 5% is given by I(S - C + G2 (M-6.0)+G3 (8.5 - My (5-32) where x% is the desired damping percentage (e.g. 2% or 5% or 7%). The coefficients for the horizontal component are given in Tables 5-lOa, 5-lOb, and 5-lOc. The coefficients for the vertical component are given in Tables 5-1 la, 5-1 lb, and 5-1 Ic.

The scale factor for the different damping ratio is given by Scaledamp(T,x%) = exp( n(Sax%(T)/Sa 5%(T)) ) (5-33) where ( n(Saxo/%(T)/Sa 5 o/%(T)) is given in equation (5-32). The damping scale factors are applied to the 5% damped spectrum. That is, the spectral values at x% damping are computed using the following equation:

Sax%(T) = Sa5o/%(T)

• Scaledamp(Tx%) (5-34)

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 27 of IO 1

Date: 11/4/02 Table 5-1Oa. Abrahamson and Silva (1996) coefficient Cl for damping scale factors for the horizontal component (from Abrahamson and Silva 1996, Table 44a)

Period 2% 3% 7%

(sec) damping damping dampin 0.000 0 0 0 0.020 0 0 0 0.030 0.0462 0.0273 -0.0205 0.040 0.0828 0.0490 -0.0367 0.050 0.1094 0.0648 -0.0486 0.075 0.1580 0.0936 -0.0701 0.100 0.1922 0.1138 -0.0853 0.120 0.2141 0.1268 -0.0950 0.150 0.2284 0.1353 -0.1014 0.170- 0.2379 0.1409 -0.1056 0.750 1.000 0.2365 0.1401 -0.1050 1.500 0.2309 0.1368 -0.1025 2.000 0.2239 0.1326 -0.0994 3.000 0.2095 0.1241 -0.0930 4.000 0.1957 0.1159 -0.0869 5.000 0.1830 0.1084 -0.0812 Table 5-1Ob. Abrahamson and Silva (1996) coefficient G 2 for damping scale factors for the horizontal component (from Abrahamson and Silva 1996, Table 4-5a)

Period 2% 3% 7%

(sec) damping damping damping 0.000 0 0 0 0.020 0 0 0 0.030 0 0 0 0.040 0 0 0 0.050 0 0 0 0.075 0 0 0 0.100 0 0 0 0.120 0 0 0 0.150 0 0 0 0.170- 0 0 0 0.750 1.000 0.0016 0.001 -0.0007 1.500 0.0039 0.0023 -0.0017 2.000 0.0055 0.0032 -0.0024 3.000 0.0078 0.0046 -0.0034 4.000 0.0094 0.0055 -0.0042 5.000 0.0106 0.0063 -0.0047

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 28 of 101 Date: 11/4/02 Table 5-lOc. Abrahamson and Silva (1996) coefficient G 3 for damping scale factors for the horizontal component (from Abrahamson and Silva 1996, Table 4-6a)

Period 2% 3% 7%

(sec) damping damping damping 0.000 0 0 0 0.020 0 0 0 0.030 0 0 0 0.040 0 0 0 0.050 0 0 0 0.075 0 0 0 0.100 0 0 0 0.120 0 0 0 0.150 0 0 0 0.170- 0 0 0 0.750 1.000 -0.0012 -0.0007 0.0006 1.500 -0.0030 -0.0018 0.0013 2.000 -0.0042 -0.0025 0.0019 3.000 -0.0060 -0.0036 0.0027 4.000 -0.0072 -0.0043 0.0032 5.000 -0.0082 -0.0049 0.0036

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 29 of 101 Date: 11/4/02 Table 5-11a. Abrahamson and Silva (1996) coefficient Cl for damping scale factors for the vertical component (from Abrahamson and Silva 1996, Table 4-4b)

Period 2% 3% 7%

(sec) damping damping damping 0.000 0 0 0 0.020 0 0 0 0.030 0.1232 0.0725 -0.0528 0.040 0.1844 0.1085 -0.0790 0.050 0.2072 0.1220 -0.0888 0.075 0.2488 0.1464 -0.1067 0.100 0.2818 0.1658 -0.1208 0.120 0.2890 0.1701 -0.1239 0.150 0.2932 0.1726 -0.1257 0.170 0.2910 0.1713 -0.1247 0.200 0.2839 0.1671 -0.1217 0.240 0.2776 0.1634 -0.1190 0.300- 0.2727 0.1605 -0.1169 0.750 1.000 0.2709 0.1594 -0.1161 1.500 0.2637 0.1552 -0.1131 2.000 0.2549 0.1500 -0.1093 3.000 0.2366 0.1393 -0.1014 4.000 0.2193 0.1291 -0.0940 5.000 0.2033 0.1196 -0.0871

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 30 of 101 Date: 11/4/02 Table 5-lb. Abrahamson and Silva (1996) coefficient G 2 for damping scale factors for the vertical component (from Abrahamson and Silva 1996, Table 4-5b)

Period 2% 3% 7%

(sec) damping damping dampin 0.000 0 0 0 0.020 0 0 0 0.030 0 0 0 0.040 0 0 0 0.050 0 0 0 0.075 0 0 0 0.100 0 0 0 0.120 0 0 0 0.150 0 0 0 0.170 0 0 0 0.200 0 0 0 0.240 0 0 0 0.300 - 0 0 0 0750 1.000 0.0018 0.0011 -0.0008 1.500 0.0044 0.0026 -0.0019 2.000 0.0063 0.0037 -0.0027 3.000 0.0089 0.0052 -0.0038 4.000 0.0107 0.0063 -0.0046 5.000 0.0122 0.0072 -0.0052

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 31 of 101 Date: 11/4/02 Table 5-llc. Abrahamson and Silva (1996) coefficient G 3 for damping scale factors for the vertical component (from Abrahamson and Silva 1996, Table 4-6b)

Period 2% 3% 7%

(sec) damping damping damping 0.000 0 0 0 0.020 0 0 0 0.030 0 0 0 0.040 0 0 0 0.050 0 0 0 0.075 0 0 0 0.100 0 0 0 0.120 0 0 0 0.150 0 0 0 0.170 0 0 0 0.200 0 0 0 0.240 0 0 0 0.300- 0 0 0 0.750 1.000 -0.0014 -0.0008 0.0006 1.500 -0.0034 -0.0020 0.0015 2.000 -0.0049 -0.0029 0.0021 3.000 -0.0069 -0.0040 0.0029 4.000 -0.0083 -0.0049 0.0036 5.000 -0.0094 -0.0055 0.0040

Calc Number: GEO.HBIP.02.04 Rev Number:O Sheet Number: 32 of 101 Date: 11/4/02

6. SOFTWARE No specialized computer software was used in these calculations.

Calc Number. GEO.HBIP.02.04 Rev Number:O Sheet Number: 33 of 101 Date: 11/4/02

7. BODY OF CALCULATIONS 7.1. Horizontal Spectra for Synchronous Rupture 7.1.1 SteI: 8 4 th Percentile Horizontal Spectra for the LSF Subsource The 84 percentile 5% spectral damping acceleration response spectra from the four empirical attenuation relationships are computed for a magnitude 7.7 reverse earthquake on the Little Salmon fault zone at a rupture distance of 0 km and a seismogenic distance of 3 km (input 4-1) using the Abrahamson and Silva (1997), Sadigh et al (1993), Idriss (1991,1994,1995) and Campbell (1997) attenuations relations (assumption 3.1).

The computed spectra for each relation is described below.

7.1.1.1 Abrahamson and Silva (1997)

From the inputs listed in Table 4- 1:

M =7.7 Rrup =

Mech = Reverse For a reverse mechanism, F=1. Using these inputs, the horizontal spectral acceleration based on the Abrahamson and Silva (1997) relation is given in Table 7-1. In this table, the median spectral acceleration (column #1) is computed using eq. (5-10) with coefficients from Table 5-3.

The standard deviation (column #2) is computed using eq. (5-12) with coefficients from Table 5-3.

The 84th percentile spectral acceleration (column #3) is computed using eq. (5-19) with the median spectral acceleration from column #1 and the standard deviation from column

1. 2.

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number 34 of 101 Date: 11/4/02 Table 7-1. 5% damped spectral acceleration on reference rock for the Little Salmon fault zone using the Abrahamson and Silva (1997) attenuation model.

1. 1 #2 #3 Period Median Standard 84 th (sec) Spectral Deviation Percentile Acc (Natural Spectral (g) Log Units) Acc (g) 0.000 1.129 0.43 1.735 0.020 1.129 0.43 1.735 0.030 1.197 0.43 1.841 0.050 1.446 0.44 2.245 0.075 1.716 0.46 2.718 0.100 1.965 0.47 3.144 0.150 2.579 0.48 4.168 0.200 2.754 0.5 4.541 0.300 2.281 0.51 3.799 0.500 1.554 0.54 2.667 0.750 1.074 0.564 1.887 1.000 0.803 0.594 1.455 1.500 0.472 0.62 0.877 2.000 0.316 0.64 0.599 3.000 0.169 0.676 0.333 4.000 0.103 0.696 0.206

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 35 of 101 Date: 1/4/02 7.1.1.2 Sadigh et. al. (1993.1997)

From the inputs listed in Table 4-1:

M =7.7,Rrup =0 Mech = Reverse For a reverse mechanism, F=1. Using these inputs, the horizontal spectral acceleration based on the Sadigh et al (1993) relation is given in Table 7-2. In this table, the median spectral acceleration (column #1) is computed using eq. (5-1) with coefficients from Table 5-1. The spectral accelerations in column #1 are for a strike-slip earthquake. To compute the spectral acceleration for a reverse earthquake (column #2), the values in column #1 are multiplied by 1.2.

The standard deviation (column #3) is computed using equation listed in the last column of Table 5-1 with M=7.2 (the upper limit of M for the standard deviation equations).

The 84th percentile spectral acceleration (column #4) is computed using eq. (5-19) with the median spectral acceleration for reverse faulting from column #2 and the standard deviation from column #3.

Table 7-2. 5% damped spectral acceleration on reference rock for the Little Salmon fault zone using the Sadigh et al. (1993) attenuation model.

1. 1 #2 #3 #4 Period Median Median Standard 84t (sec) Spectral Spectral Deviation Percentile Acc Acc (Natural Spectral (g) (g) Log Acc strike- Reverse Units) (g) slip 0.000 0.771 0.926 0.38 1.354 0.020 0.771 0.926 0.38 1.354 0.030 0.771 0.926 0.38 1.354 0.050 1.129 1.355 0.38 1.982 Used only to 0 . 070 interpolate 1.379 0.39 0.075 Interpolated 1.410 1.692 0.39 2.499 Used only to 0.090 interpolate 1.494 0.39 0.100 1.559 1.871 0.40 2.791 0.150 1.723 2.068 0.41 3.115 0.200 1.797 2.156 0.42 3.282 0.300 1.739 2.087 0.44 3.240 0.500 _ 1.355 1.626 0.49 2.654 0.750 0.963 1.155 0.51 1.924 1.000 0.736 0.883 0.52 1.485 1.500 0.473 0.568 0.52 0.955 2.000 0.335 0.402 0.52 0.676 3.000 0.194 0.232 0.52 0.391 4.000 0.130 0.156 0.52 0.262

Calc Number GEO.HBIP.02.04 Rev Number:0 Sheet Number. 36 of 101 Date: 11/4/02 7.1.1.3 driss(I991.19941995)

From the inputs listed in Table 4-1:

M = 7.7 Rrup =

Mech = Reverse For a reverse mechanism, F=1.

The peak acceleration is computed for the 1991 model using eq. (5-2a) with the coefficients given in Table 5-2. The PGA for the 1995 model is computed using eq. 5-2b. The resulting PGA values are:

PGA91 = 0.859 (from eq. 5-2a)

PGA 95 = 1.095 (from eq. 5-2b)

The ratio of the PGA values is PGA'5 - 1.095 = 1.275 PGA91 0.859 The horizontal spectral acceleration based on the Idriss (1991) attenuation relation is given in column #1 of Table 7-3. These values are computed using eq. (5-2a) with coefficients from Table 5-2.

The spectral acceleration, Sa95 (column #2) is computed using eq. 5-4 with the PGA ratio listed above and the Sa91 spectral acceleration listed in column #1.

The standard deviation (column #3) is computed using equation listed in the last column of Table 5-2 with M=7.25 (the upper limit of M for the standard deviation equations).

The 84kh percentile spectral acceleration (column #4) is computed using eq. (5-19) with the median spectral acceleration from column #2 and the standard deviation from column

1. 3.

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number 37 of 101 Date: 1/4/02 Table 7-3. 5% damped spectral acceleration on reference rock for the Little Salmon fault zone using the Idriss (199 1994,1995) attenuation model.

1. 1 #2 #3 #4 Period Median Median Standard 84th (sec) Spectral Spectral Deviation Percentile Acc Acc (Natural Spectral (g) (g) Log Units) Acc (g)

Sa91 Sa95 0.000 0.859 1.095 0.420 1.667 0.020 0.859 1.095 0.420 1.667 0.030 0.859 1.095 0.420 1.667 0.050 1.062 1.354 0.420 2.060 0.075 1.347 1.717 0.420 2.613 0.100 1.569 2.000 0.450 3.137 0.150 2.065 2.632 0.480 4.254 0.200 2.370 3.021 0.500 4.981 0.300 2.416 3.080 0.520 5.180 0.500 1.857 2.367 0.550 4.102 0.750 1.247 1.589 0.575 2.824 1.000 0.888 1.131 0.600 2.062 1.500 0.542 0.691 0.600 1.258 2.000 0.377 0.481 0.600 0.877 3.000 0.228 0.290 0.600 0.528 4.000 0.160 0.204 0.600 0.372

Calc Number: GEO.HBIP.02.04 Rev NumberO Sheet Number: 38 of 101 Date: 114/02 7.1.1.4 Campbell (1997)

From the inputs listed in Table 4-1 and assumption 3.4:

M =7.7 Rseis = 3 km Mech = Reverse D = 1 km (assumption 3.4)

For a reverse mechanism, F=1. Using these inputs, the peak acceleration, AH, is computed using eq. (5-13). For M=7.7, Rseis=3, and F=1, the median peak acceleration is AH = 0.874g The standard deviation of the peak acceleration is computed using eq. 5-17 and 5-18.

Using M=7.7, the standard deviation is GPGA = 0.38 natural log units.

The horizontal spectral acceleration based on the Campbell (1997) attenuation relation is given in Table 7-4. In this table, the median spectral acceleration (column #1) is computed using eq. (5-16) with coefficients from Table 5-5 with M=7.7, Rseis=O, D-1 and the PGA value of AH = 0.874g.

The standard deviation of the spectral acceleration (column #2) is computed using eq. 5-19 with aPGA = 0.38.-

The 84h percentile spectral acceleration (column #3) is computed using eq. (5-19) with the median spectral acceleration from column #1 and the standard deviation from column

1. 2.

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 39 of 101 Date: 11/4/02 Table 7-4. 5% damped spectral acceleration on reference rock for the Little Salmon fault zone using th bell 1997)attenuation model.

_______ *1 #2 #3 Period Median Standard 84 (sec) Spectral Deviation Percentile Acc (Natural Spectral (g) Log Units) Acc (g) 0.000 0.874 0.380 1.279 0.020 0.874 0.380 1.279 0.030 0.874 0.380 1.279 0.050 1.014 0.466 1.616 0.075 1.272 0.466 2.028 0.100 1.505 0.466 2.399 0.150 1.762 0.466 2.809 0.200 1.745 0.466 2.781 0.300 1.537 0.466 2.449 0.500 1.250 0.466 1.992 0.750 0.955 0.466 1.522 1.000 0.766 0.466 1.220 1.500 0.529 0.466 0.843 2.000 0.374 0.466 0.596 3.000 0.216 0.466 0.345 4.000 0.135 0.466 0.215

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 40 of 101 Date: 11/4102 7.1.1.5 Average Horizontal Spectrum The average horizontal response spectra from the Abrahamson and Silva (1997),

Campbell (1997), Idriss (991;1995) and Sadigh et al. $,1997) attenuation relationship is given the last column on the right in Table 7-5. The 84 percentile response spectra based on the four attenuation models are taken from the Tables 7-1, 7-2, 7-3, and 7-4. The spectral values for the four attenuation relations are compared in Figure 1.

Table 7-5. 84t" Percentile horizontal rock spectra for the Little Salmon fault zone subsource (M=7.7).

Period Abrahamson Campbell Idriss Sadigh et al.

(sec) & Silva (1997) (1991;1995) (1993,1997) Average (1997) 0.000 1.735 1.279 1.667 1.354 1.509 0.020 1.735 1.279 1.667 1.354 1.509 0.030 1.841 1.279 1.667 1.354 1.535 0.050 2.245 1.616 2.060 1.982 1.976 0.075 2.718 2.028 2.613 2.499 2.465 0.100 3.144 2.399 3.137 2.791 2.868 0.150 4.168 2.809 4.254 3.115 3.587 0.200 4.541 2.781 4.981 3.282 3.896 0.300 3.799 2.449 5.180 3.240 3.667 0.500 2.667 1.992 4.102 2.654 2.854 0.750 1.887 1.522 2.824 1.924 2.039 1.000 1.455 1.220 2.062 1.485 1.556 1.500 0.877 0.843 1.258 0.955 0.983 2.000 0.599 0.596 0.877 0.676 0.687 3.000 0.333 0.345 0.528 0.391 0.399 4.000 0.206 0.215 0.372 0.262 0.264

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 41 of O1 Date: 1/4/02 cm C

0 4-0 enQ Period (sec)

Figure 1. Comparison of the 8 4 th percentile horizontal spectra for the Little Salmon fault subsource for rock site based on the alternative attenuation relations,

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 42 of 101 Date: 11/4/02 7.1.2 Sten 2: Extrapolation of the LSF Subsource Spectrum from 5 seconds to 10 seconds For periods greater than 5 seconds, the average spectrum given in Table 7-5 is extrapolated using eq. (5-20) with the following values (from the last two rows of Table 7-5)

T, = 3.0 T 2 =4.0 Sal = 0.399 g Sa 2 = 0.264 g The computed spectral values at periods greater than 5 seconds are listed in Table 7-6.

These values give the average horizontal component without directivity effects. The extrapolated spectra values are also show in Figure 1.

Table 7-6. 8 4 th Percentile horizontal spectra for the Little Salmon fault zone extrapolated to 10 seconds period. (5% damping)

1. 1 #2 #3 Period (sec) Average Average SA (g) Sa (g)

(from Table 7-5) 0.000 1.509 1.509 0.020 1.509 1.509 0.030 1.535 1.535 0.050 1.976 1.976 0.075 2.465 2.465 0.100 2.868 2.868 0.150 3.587 3.587 0.200 3.896 3.896 0.300 3.667 3.667 0.500 2.854 2.854 0.750 2.039 2.039 1.000 1.556 1.556 1.500 0.983 0.983 2.000 0.687 0.687 3.000 0.399 0.399 4.000 0.264 0.264 5.000 Extrapolated 0.192 7.000 Extrapolated 0.118 10.000 Extrapolated 0.071

Caic Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 43 of 101 Date: 1 1/4/02 7.1.3 Step 3: Directivity Effects for the LSF subsource The rupture is assumed to begin at the bottom of the fault (assumption 3. 10). This corresponds to the full rupture width. Therefore the directivity parameter, Y, is 1.0 in Somerville et al (1997). For the site located at zero distance, then second directivity parameter, , is 0 degrees.

From the inputs in Table 4-2 and the hypocenter location discussed above, M=7.7 Y=1.0

=0 7.1.3.1 Directivity Effects for the Average Horizontal Component The directivity scale factor for'the average horizontal component (Table 7-6, col. #3) is computed using eq. (5-21) with coefficients from Table 5-6 and the input parameters listed above. The results are given in column #2 of Table 7-7. The scale factors at periods of 7 and 10 seconds are based on the assumption (3.8) that the factor is constant for periods > 5 seconds.

7.1.3.2 Directivity Effects for the Fault Normal Component The directivity scale factor for the FN/AveH component is computed using eq. (5-22) with the input parameters listed above and coefficients from Table 5-7. The results are given in column #3 of Table 7-7. The scale factors at periods of 7 and 10 seconds are based on the assumption (3.8) that the factor is constant for periods > 5 seconds.

The scale factor for the FN component (column #5) is computed using eq. 5-24 (column

1. 2 times column #3).

The spectral acceleration on the FN component including directivity (column #7) is computed using eq. 5-26 (column #1 time column #5). This spectrum is plotted in Figure 2.

7.1.3.3 Directivitv Effects for the Fault Parallel Component The directivity effects for the FP/AveH (column #4) is computed using eq. 5-23 with the FN/AveH value from column #3 of Table 7-7. The scale factors at periods of 7 and 10 seconds are based on the assumption (3.8) that the factor is constant for periods > 5 seconds.

The scale factor for the FP component (column #6) is computed using eq. 5-25 (column

1. 2 times column #4).

The spectral acceleration on the FN component including directivity (column #8) is computed using eq. 5-27 (column #1 time column #6). This spectrum is plotted in Figure 2.

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 44 of 101 Date: 11/4/02 Table 7-7. Horizontal Rock Spectra with directivity effects for the Little Salmon Fault event.

Ut1#2 #3 #4 #5 #6 #7 #8 AveH Directivity Scale Rock Rock Spectral Factor for Spectrum Spectrum Acc (g) The Average (g) (g)

Period (From Table Horizontal . ScaleFp FN FP (sec) 7-6) DIR FN/AveH FP/AveH ScaleFN Component Component 0.000 1.509 1 1 1.000 1.000 1.000 1.509 1.509 0.020 1.509 1 I 1.000 1.000 1.000 1.509 1.509 0.030 1.535 1 1.000 1.000 1.000 1.535 1.535 0.050 1.976 1 1 1.000 1.000 1.000 1.976 1.976 0.075 2.465 1 1 1.000 1.000 1.000 2.465 2.465 0.100 2.868 1 1 1.000 1.000 1.000 2.868 2.868 0.150 3.587 1 1 1.000 1.000 1.000 3.587 3.587 0.200 3.896 I I 1.000 1.000 1.000 3.896 3.896 0.300 3.667 I I 1.000 1.000 1.000 3.667 3.667 0.5 2.854 I _ 1.000 1.000 1.000 1.000 2.854 2.854 0.75 2.039 1.00** 1.063 0.941 1.063 0.941 2.167 1.918 1.0 1.556 1.077 1.110 0.901 1.195 0.970 1.860 1.510 1.5 0.983 1.141 1.248 0.801 1.424 0.914 1.400 0.899 2.0 0.687 1.189 1.360 0.735 1.617 0.874 1.111 0.601 3.0 0.399 1.261 1.667 0.600 2.102 0.757 0.839 0.302 4.0 0.264 1.314 1.928 0.519 2.533 0.682 0.669 0.180 5.0 0.192 1.358 1.980 0.505 2.689 0.686 0.516 0.132 7.0 0.118 1.358* 1.980* 0.505 2.689 0.686 0.317 0.081 10.0 0.071 1.358* 1.980* 0.505 2.689 0.686 0.191 0.049

• Extrapolated to long periods assuming a constant factor.

• • Value fixed to 1.0 (see text)

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 45 of 101 Date: 11/4/02 Period (sec)

Figure 2. Comparison of the fault normal and fault parallel spectra for the LSF after accounting for the effects of directivity.

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 46 of 101 Date: 11/4/02 7.1.4 Step 4: Horizontal Spectrum for Rock for the Cascadia Subsource I The parameters for the Cascadia interface subsource are given below:

M = 8.8 (Table 4-2)

Rrup = 7 km (Table 4-2)

ZT = 0 (for interface sources) (table 4-2)

H=20 km (Assumption 3-1 1)

The 84h percentile 5% spectral damping acceleration response spectra for a subduction zone earthquake is computed based on the Youngs et al. ( 997) empirical attenuation relationship (assumption 3.6). The horizontal spectral acceleration based on these input parameters is given below in Table 7-8. The median spectral acceleration values for a rock site are given in column #1 as a function of spectral period. These values were computed using equation (5-28) with the regression coefficients given in Table 5-8.

The standard deviation (column #2) is computed using equation (5-29).

The 84 'h percentile spectral acceleration (column #3) is computed using equation (5-19) with the median spectral acceleration from column #1 and the standard deviation from column #2.

Table 7-8. 5% damped spectral acceleration on reference rock for the Cascadia interface event usin Youngs et al. (1997) attenuation model.

1. 1 #2 #3 Median Standard 8 40h Percentile Spectral Deviation Spectral Period (sec) Acc (g) (LN units) Acc (g) 0.00 0.306 0.65586 0.075 0.468 0.65 0.896 0.1 0.569 0.65 1.091 0.2 0.715 0.65 1.369 0.3 0.665 0.65 1.274 0.4 0.619 0.65 1.186 0.5 0.583 0.65 1.116 0.75 0.413 0.65 0.790 1.0 0.305 0.65 0.584 1.5 0.186 0.70 0.375 2.0 0.124 0.75 0.263 3.0 0.057 0.85 0.133

Calc Number: GEO.HBIP.02.04 Rev Number:O Sheet Number: 47 of O1 Date: 11/4/02 7.1.5 Step 5: Extrapolation of Cascadia Subsource Spectrum from 3 to 10 Seconds The acceleration response spectrum for spectral periods of 0.02 and 0.03 seconds are set equal to the PGA spectral acceleration value (assumption 3.16).

The acceleration response spectra values for spectral periods of 0.05 and 0. 15 seconds were computed by interpolation using eq. 5-20.

For spectral periods greater than 3.0 seconds, the acceleration response values were computed by extrapolation using eq. 5-20 using the spectral acceleration values at T=2 and T=3 seconds.

Table 7-9. 8 4th percentile horizontal response spectrum for the Cascadia Interface event extrapolated to 10 seconds period (5% spectral damping).

1. 1 #2 #3 Extrapolated 84th Percentile 8 4 h Percentile Spectral Spectral SA (g) SA (g)

Period (sec) (From Table 7-8) 0.00 0.586 0.586 0.02 Assumption 3.16 0.586 0.03 Assumption 3.16 0.586 0.05 Interpolated 0.743 0.075 0.896 0.896 0.10 1.091 1.091 0.15 Interpolated 1.246 0.2 1.369 1.369 0.3 1.274 1.274 0.5 1.116 _ _ _ _ _ _ _ _ 1.116 0.75 o.790 0.790 1.0 0.584 0.584 1.5 0.375 _ 0.375 2.0 0.263 0.263 3.0 0.133 0.133 4.0 Extrapolated 0.082 5.0 Extrapolated 0.057 7.0 Extrapolated 0.032 10.0 Extrapolated 0.018

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number 48 of 101 Date: 1/4/02 7.1.6 Step 6: Combined Synchronous Rupture Rock Spectra The horizontal rock spectra for the Little Salmon Fault (see Table 7-7) and the Cascadia Interface event (see Table 7-9) are combined based on assumption 3.9 (i.e., SRSS).

The combined synchronous rupture rock acceleration response spectrum for the fault normal component is given in Table 7-10. The third column is the SRSS of the #1 and #2 columns. The spectra are plotted in Figure 3.

The corresponding combined synchronous rupture rock acceleration response spectrum for the fault parallel component is given in Table 7-11. The spectra are plotted in Figure 4.

Table 7-10. Combined synchronous rupture rock acceleration response spectrum for the fault normal component of motion.

1. 1 #2 #3 Little Salmon Fault Cascadia Interface Rock Rock Synchronous Fault Normal Sa(g) Rock Sa(g) (from Table 7-9) Fault Normal Period (from Table 7-7) Sa(g)

(sec) 1.509 0.586_1.619 0.000 1.509 0.586 1.619 0.020 1.509 0.586 1.619 0.030 1.535 0.586 1.643 0.050 1.976 0.743 2.111 0.075 2.465 0.896 2.623 0.100 2.868 1.091 3.069 0.150 3.587 1.246 3.797 0.200 3.896 1.369 4.130 0.300 3.6B7 1.274 3.882 0.500 2.854 1.116 3.064 0.750 2.167 0.790 2.307 1.000 1.860 0.584 1.950 1.500 1.400 0.375 1.449 2.000 1.111 0.263 1.142 3.000 0.839 0.133 0.849 4.000 0.669 0.082 0.674 5.000 0.516 0.057 0.519 7.000 0.317 0.032 0.319 10.000 0.191 0.018 0.192

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 49 of 101 Date: 11/4/02

- *;.. -- ~~~~~~~~~~~~1.......LSF FN

..... \ - - - - C sa i

- - - - -, - - - ~~Synchronous

-\ ~~~Rupture 3.

Xa 0

22.5-2- 7 1SrC4XFFU 0.5 1.5- --------....

. P 0.

0.01 0.1 1 10 Period (sec)

Figure 3. Fault normal spectra for the individual subsources and for synchronous rupture.

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 50 of lOt Date: 11/4/02 Table 7-11. Combined synchronous rupture outcropping rock acceleration response spectrum for the fault parallel component of motion. -

__ __ __ __ _ _#1 #2 #3 Little Salmon Fault Cascadia Interface Synchronous Rock Rock Rock, Fault Parallel Sa(g) Sa(g) Fault Parallel Period (from Table 7-7) (from Table 7-9) Sa(g)

(sec) 0.000 1.509 0.586 1.619 0.020 1.509 0.586 1.619 0.030 1.535 0.586 1.643 0.050 1.976 0.743 2.111 0.075 2.465 0.896 2.623 0._0 2.868 1.091 3.069 0.150 3.587 1.246 3.797 0.200 3.896 1.369 4.130 0.300 3.667 1.274 3.882 0.500 _2.854 1.116 3.064 0.750 1.918 0.790 2.074 1.000 1.510 0.584 1.819 1.500 0.899 0.375 0.974

- 2.000 0.601 0.263 0.656 3.000 0.302 0.133 0.330 4.000 0.180 0.082 0.198 5.000 0.132 0.057 0.144 7.000 0.081 0.032 0.087 10.000

_ 0.049 0.018 0.052

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 51 of 101 Date: 11/4/02 YYr-Y T i Y TTTTY! 1 11 I I I I III

.im .LSF - FP

.l.-6-4-I-4 .4.& 4 4

/ N I/

- - - - Cascadia

.3-01 4 9. 4 . I - - -- I*-l t

- - - Synchronous

//' Rupture

- i .ir - .

3- l I I -_

7_ I

__I___ _ I C

0 S..,

Eu L-a)

Z 2 ~~~___ - /.. -oi; C,

15-___

.-- X~~~SNtX 0.5- -- - -

(1.. __ W ____L-E=*1

-I0.01 .1 0.1 1 10 Period (sec)

Figure 4. Fault parallel spectra for the individual subsources and for synchronous rupture.

Calc Number GEO.HBIP.02.04 Rev Number:0 l Sheet Number. 52 of 101 Date: 11/4/02 7.1.7 Step 7: Scaling of Combined Spectra by Site Specific Soil Amplification Factors The soil spectra for the FN and FP components are computed by multiplying the horizontal rock acceleration response spectra by the soil site-specific amplification factors. The horizontal spectra (Tables 7-10 and 7-11) are first interpolated to match the spectral periods used to define the soil amplification (Table 4-4) using eq. 5-19. The interpolated values are listed in Table 7-12.

For each of the three profiles (Median, Lower Bound, and Upper Bound), the amplification factors from Table 44 are multiplied by the horizontal rock spectra given in Tables 7-12 to compute the soil ground motion for the synchronous rupture. The computed spectral acceleration values for soil are given in Tables 7-13, 7-14, and 7-15 for the median, lower bound, and upper bound profiles, respectively. In each of these three tables, the FN soil spectrum (column #4) is computed by multiplying the FN rock (column #1) by the amplification factor (column #3). Similarly, the FP soil spectrum is (column #5) is computed by multiplying the FP rock (column #2) by the amplification factor (column #3).

The FN spectra for the rock site and for each of the three soil profiles is shown in Figure

5. The FP spectra for the rock site and for each of the three soil profiles is shown in Figure 6.

Calc Number: GEO.HBIP.02.04 Rev Number Sheet Number: 53 of 101 Date: 11/4/02 Table 7-12. 5% damped spectra for the synchronous ruptu re. Interpolated to the periods rom the am litcation actors.

Period Fault Fault

__seCNormal parallel 0.00 1.619 1.619 0.02 1.619 1.619 0.03 1.643 1.643 0.05 2.111 2.111 0.075 2.623 2.623 0.1 3.069 3.069 0.15 3.797 3.797 0.2 4.130 4.130 0.3 3.882 3.882 0.42 Interpolated 3.322 3.322 0.5 3.064 3.064 0.6 Interpolated 2.697 2.571 0.64 Interpolated 2.578 2.416 0.75 2.307 2.074 0.86 Interpolated 2.130 1.843 1 1.950 1.619 1.2 Interpolated 1.706 1.288 1.A5 Interpolated 1.485 1.016 1.5 1.449 0.974 1.7 Interpolated 1.306 0.820 2 1.142 0.656 2.2 Interpolated 1.065 0.558 2.6 Interpolated 0.943 0.421 3 0.849 0.330 3.2 Interpolated 0.806 0.294 3.5 Interpolated 0.750 0.251 4 0.674 0.198 4.1 Interpolated 0.655 0.191 4.3 Interpolated 0.619 0.179 5 0.519 0.144 5.4 Interpolated OA64 0.128 6.2 Interpolated 0.380 0.104 7 0.319 0.087 7.8 Interpolated 0.273 0.074 10 0.192 0.052

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 54 of 101 Date: 1 1/4/02 Table 7-13. Soil Spectrum for synchronous rupture using the site-specific amplification factors for the median profile

1. l l #2 #3 #4 #5 Amplification Rock, Rock, Factor, Soil, Fault Normal Fault Parallel Median Profile Soil, Fault Parallel Sa(g) Sa(g) PGA=1.6 g Fault Normal Sa(g)

Period (Table 7-12) (Table 7-12) (Table 4-4) Sa (g)

(sec) 0.00 1.619 1.619 0.608 0.984 0.984 0.02 1.619 1.619 0.608' 0.984 0.984 0.03 1.643 1.643 0.615 1.010 1.010 0.05 2.111 2.111 0.434 0.916 0.916 0.075 2.623 2.623 0.352 0.923 0.923 0.1 3.069 3.069 0.324 0.994 0.994 0.15 3.797 3.797 0.292' 1.109 1.109 0.2 4.130 4.130 0.376 1.553 1.553 0.3 3.882 3.882 0.563 2.186 2.186 0.42 3.322 3.322 0.940 3.123 3.123 0.5 3.064 3.064 0.882 2.702 2.702 0.6 2.697 2.571 0.900 2.427 2.314 0.64 2.578 2.416 0.885 2.281 2.138 0.75 2.307 2.074 1.053 2.429 2.184 0.86 2.130 1.843 1.214 2.585 2.238 1 1.950 1.619 1.262 2.461 2.043 1.2 1.706 1.288 1.342 2.290 1.729 1.45 1.485 1.016 1.580 2.347 1.606 -

1.7 1.306 0.820 1.904 2.487 1.562 2.2 1.065 0.558 2.381 2.536 1.329 2.6 0.943 0.421 2.305 2.173 0.969 3.2 0.806 0.294 1.922 1.549 0.566 3.5 0.750 0.251 1.926 1.445 0.483 4.1 0.655 0.191 1.692 1.108 0.323 4.3 0.619 0.179 1.521 0.942 0.272 5.4 0.464 0.128 1.451 0.674 0.186 6.2 0.380 0.104 1.322 0.503 0.138 7.8 0.273 0.074 1.209 0.331 0.090 10 0.192 0.052 1.258 0.242 0.065

• Set to be equal to amplification at TO.OO

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 55 of 101 Date: 11/4/02 Table 7-14. Scaled combined synchronous rupture spectra for the lower bound site specific soil profile

1. 1 #2 #3 #4 #5 Amplification Factor, Soil, Rock, Rock, Lower Bound Fault Parallel Fault Normal Fault Parallel profile Sa(g)

Sa(g) Sa(g) PGA=1.6 g Soil, Period (Table 7-12) (Table 7-12) (Table 4-4) Fault Normal (sec) _________________ ______________ Sa (g) 0.00 1.619 1.619 0.383 0.620 0.620 0.02 1.619 1.619 0.383* 0.620 0.620 0.03 1.643 1.643 0.387 0.636 0.636 0.05 2.111 2.111 0.273 0.576 0.576 0.075 2.623 2.623 0.221 0.580 0.580 0.10 3.069 3.069 0.201 0.617 0.617 0.15 3.797 3.797 0.182 0.691 0.691 0.2 4.130 4.130 0.193 0.797 0.797 0.3 3.882 3.882 0.325 1.262 1.262 0.42 3.322 3.322 0.481 1.598 1.598 0.5 3.064 3.064 0.677 2.074 2.074 0.6 2.697 2.571 0.811 2.187 2.085 0.64 2.578 2.416 0.734 1.892 1.773 0.75 2.307 2.074 0.678 1.564 1.406 0.86 2.130 1.843 0.766 1.631 1.412 1.0 1.950 1.619 0.823 1.605 1.332 1.2 1.706 1.288 1.117 1.906 1.439 1 51.485 1.016 1.181 1.754 1.200 1.7 1.306 0.820 1.309 1.710 1.074 2.2 1.065 0.558 1.809 1.927 1.010 2.6 0.943 0.421 2.083 1.964 0.876 3.2 0.806 0.294 2.373 1.913 0.698 3.5 0.750 0.251 2.324 1.744 0.583 4.1 0.655 0.191 2.102 1.376 0.402 4.3 0.619 0.179 1.915 1.186 0.342 5.4 0.464 0.128 1.724 0.800 0.221 6.2 0.380 0.104 1.484 0.564 0.155 7.8 0.273 0.074 1.351 0.369 0.101 10.0 0.192 0.052 1.330 0.255 0.069

• Set to be equal to amplification at T=O.OO

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 56 of O1 Date: 1/4/02 Table 7-15. Scaled combined synchronous rupture spectra for the upper bound site specific soil profile.

1. 2 #3 #4 #5 Amplification Rock, Factor, Soil, Rock, Fault Upper Bound Fault Parallel Fault Normal Parallel Profile Sa(g)

Sa(g) Sa(g) PGA=1.6 g Soil, (Table 7-12) (Table 7-12) (Table 4-4) Fault Normal P Sa (g) 0.00 1.619 1.619 0.813 1.316 1.316 0.02 1.619 1.619 0.813 1.316 1.316 0.03 1.643 1.643 0.822 1.351 1.351 0.05 2.111 2.111 0.581 1.226 1.226 0.075 2.623 2.623 0.473 1.241 1.241 0.10 3.069 3.069 0.444 1.363 1.363 0.15 3.797 3.797 0.435 1.652 1.652 0.20 4.130 4.13 0.602 2.486 2.486 0.30 3.882 3.882 0.924 3.587 3.587 0.42 3.322 3.322 1.011 3.359 3.359 0.50 3.064 3.064 0.948 2.905 2.905 0.60 2.697 2.571 1.258 3.393 3.234 0.64 2.578 2.416 1.342 3.459 3.242 0.75 2.307 2.074 1.416 3.267 2.937 0.86 2.130 1.843 1.368 2.913 2.522 1.0 1.950 1.619 1.468 2.863 2.377 1.2 1.706 1.288 1.903 3.247 2.452 1.45 1.485 1.016 2.419 3.593 2.458 1.7 1.306 0.820 2.681 3.502 2.199 2.2 1.065 0.558 2.194 2.337 1.225 2.6 0.943 0.421 1.893 1.784 0.796 3.2 0.806 0.294 1.605 1.294 0.472 3.5 0.750 0.251 1.622 1.217 0.407 4.1 0.655 0.191 1.384 0.906 0.265 4.3 0.619 0.179 1.25 0.774 0.223 5.4 0.464 0.128 1.25 0.580 0.160 6.2 0.380 0.104 1.211 0.460 0.126 7.8 0.273 0.074 1.165 0.319 0.087 10.0 0.192 0.052 1.174 0.225 0.061

• Set to be equal to amplification at T=O.OO

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 57 of O1 Date: 11/4/02 0)

I-0' co,

%P 4) 0A uc i

Period (sec)

Figure 5. Comparison of the rock spectra and the soil spectra for the three profiles for the FN component for the synchronous rupture.

Calc Number GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 58 of 101 Date: 11/4/02 To M

0)

C 2 a) 0 cu Cu U

ca C1 1

Perod (sec)

Figure 6. Comparison of the rock spectra and the soil spectra for the three profiles for the FP component for the synchronous rupture.

J

Calc Number: GEO.HBIP.02.04 Rev Number:O l Sheet Number: 59 of O1 Date: 11/4/02 7.1.8 Step 8: Northridge High Frequency Spectrum and Corresponding Envelope Spectrum The spectral shape from the Northridge recordings is used as a constraint on the high frequency portion of the site-specific soil spectra. This spectral shape (see Table 4-3) is scaled by the largest soil PGA value from the three soil profiles (first row of Column #4 in Tables 7-13, 7-14, and 7-15). The largest PGA is 1.316g from the upper bound profile (Table 7-15). The scaled spectral shape is listed in the last column (#3) in Table 7-16.

Table 7-16. Constraint on the high frequency spectrum from the Northridge spectral shape.

__________ #1 #2 #3 High Frequency Period Spectral Largest Constraint (sec) Shape PGA (g) Sa(g) 0.000 1.000 1.316 1.316 0.020 1.000 1.316 1.316 0.030 1.016 1.316 1.337 0.050 1.095 1.316 1.441 0.075 1.225 1.316 1.612 0.100 1.384 1.316 1.821 0.150 1.690 1.316 2.224 0.200 1.911 1.316 2.515 0.300 2.368 1.316 3.116 0.500 1.980 1.316 2.606 0.750 2.049 1.316 2.696 1.000 1.682 1.316 2.214 1.500 1.036 1.316 1.363 2.000 0.765 1.316 1.007 3.000 0.451 1.316 0.594 4.000 0.208 1.316 0.274

Calc Number: GEO.HBIP.02.04 Rev Number:0 i Sheet Number: 60 of 101 Date: 11/4/02 For both the fault normal and fault parallel cases, the envelope of the following spectra was computed:

1. Soil spectrum based on the amplification factors from the median profile

2. Soil spectrum based on the amplification factors from the lower bound profile

3. Soil spectrum based on the amplification factors from the upper bound profile

4. The scaled spectral shape from Northridge.

For the fault normal case, the four spectra listed above are given in Table 7-17. The envelope of these four spectra is listed in column #5. The spectra are plotted in Figure 7.

For the fault parallel case, the four spectra listed above are given in Table 7-18. The envelope of these four spectra is listed in column #5. The spectra are plotted in Figure 8.

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 61 of 101 Date: 1/4/02 Table 7-17. Envelope acceleration response spectrum (5% spectral damping) for synchronous rupture for the fault normal component.

1. 1

______ #2 #3 #4 #5 Synchronous Soil Synchronous Soil Synchronous Soil Fault Normal Fault Normal Fault Normal (Lower Bound (Upper Bound High Period (Median profile) profile) Profile) Frequency Envelope (sec) (Table 7-13) (Table 7-14) (Table 7-15) Constraint Fault Normal 0.00 0.984 0.620 1.316 1.316 1.316 0.02 0.984 0.620 1.316 1.316 1.316 0.03 1.010 0.636 1.351 1.337 1.351 0.05 0.916 0.576 1.226 1.441 1.441 0.075 0.923 0.580 1.241 1.612 1.612 0.10 0.994 0.617 1.363 1.821 1.821 0.15 1.109 0.691 1.652 2.224 2.224 0.20 1.553 0.797 2.486 2.515 2.515 0.30 2.186 1.262 3.587 3.116 3.587 0.42 3.123 1.598 3.359 3.359 0.50 2.702 2.074 2.905 2.606 2.905 0.60 2.427 2.187 3.393 3.393 0.64 2.281 1.892 3.459 3.459 0.75 2.429 1.564 3.267 2.696 3.267 0.86 2.585 1.631 2.913 2.913 1.0 2.461 1.605 2.863 2.214 2.863 1.2 2.290 1.906 3.247 3.247 1.45 2.347 1.754 3.593 3.593 1.7 2.487 1.710 3.502 3.502 2.2 2.536 1.927 2.337 2.536 2.6 2.173 1.964 1.784 2.173 3.2 1.549 1.913 1.294 1.913 3.5 1.445 1.744 1.217 1.744 4.1 1.108 1.376 0.906 1.376 4.3 0.942 1.186 0.774 1.186 5.4 0.674 0.800 0.580 0.800 6.2 0.503 0.564 0.460 0.564 7.8 0.331 0.369 0.319 0.369 10.0 0.242 0.255 0.225 _ 0.255

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 62 of 101 Date: 11/4/02 Table 7-18. Envelope acceleration response spectrum (5% spectral damping) for synchronous rupture for the fault parallel component.

1. 1 #2 #3 #4 #5 Synchronous Synchronous Soil Soil Synchronous Fault Fault Soil Parallel Parallel Fault Parallel (Lower (Upper Average (Median Bound Bound High Envelope Period profile) profile) Profile) Frequency Fault (sec) (Table 7-13) (Table 7-14) (Table 7-15) Spectra Parallel 0.000 0.984 0.620 1.316 1.316 1.316 0.020 0.984 0.620 1.316 1.316 1.316 0.030 1.010 0.636 1.351 1.337 1.351 0.050 0.916 0.576 1.226 1.441 1.441 0.075 0.923 0.580 1.241 1.612 1.612 0.100 0.994 0.617 1.363 1.821 1.821 0.150 1.109 0.691 1.652 2.224 2.224 0.200 1.553 0.797 2.486 2.515 2.515 0.300 2.186 1.262 3.587 3.116 3.587 0.420 3.123 1.598 3.359 3.359 0.500 2.702 2.074 2.905 2.606 2.905 0.600 2.314 2.085 3.234 3.234 0.640 2.138 1.773 3.242 _ 3.242 0.750 2.184 1.406 2.937 2.696 2.937 0.860 2.238 1.412 2.522 2.522 1.000 2.043 1.332 2.377 2.214 2.377 1.200 1.729 1.439 2.452 2.452 1.450 1.606 1.200 2.458 2.458 1.700 1.562 1.074 2.199 2.199 2.200 1.329 1.010 1.225 1.329 2.600 0.969 0.876 0.796 0.969 3.200 0.566 0.698 0.472 0.698 3.500 0.483 0.583 0.407 0.583 4.100 0.323 0.402 0.265 0.402 4.300 0.272 0.342 0.223 0.342 5.400 0.186 0.221 0.160 0.221 6.200 0.138 0.155 0.126 0.155 7.800 0.090 0.101 0.087 0.101 10.000 0.065 0.069 0.061 0.069

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 63 of 101 Date: 11/4/02

---

Envelope

........ . Median Profiles 4- I--T- I I11 I 1I 1I 11

- - - Lower Bound Profile 1;1~~ Ii s1 11111 I 3.5 - - - - Upper Bound Profile

- .E- - Empirical Constraint /1V F- I I# i Ill 11I 11l

_ I _ __ I Ii_ I_

2 e.1---- ~1 - r = - - -

1._-

0) 4 11t 5- - -F - - - -;+ -M+

I- ~ - ~ ~ ~ ~ ~ ~

0.!

o- I I I I I I I _I I I fI I I I I III 0.01 0.1 i 10 Period (sec)

Figure 7. Development of the envelope for the soil spectrum for synchronous rupture for the FN component. (Table 7-17)

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 64 of 101 Date: I 1/4/02

- Envelope Median Profile 4-I I I I I I I I I

- - - - Lower Bound Profile I I I I I I I I I I I I I I 3.5 - - - - Upper Bound Profile I I

- E - Empirical Constraint V- I I l

-LI-1 1-W 2.5 ---

0 I n ==_ _7

• l rrrm__

a 2.5-co

_ __ _ -_ - i-_

0.5-

__ _ _ _ 4 _ _ X __ _ _ $;~~~~~~~~~~~~t_~

< _ _ X I

• l _ _t l , _ .

0.01 0.1 i 10 Period (sec)

Figure 8. Development of the envelope for the soil spectrum for synchronous rupture for the FP component. (Table 7-18)

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 65 of 101 Date: 1 1/4/02 7.1.9 Step 9: Horizontal Design Spectra The envelope spectra shown in Figures 7 and 8 (from Tables 7-17, 7-18) are smoothed to develop design spectra. This smoothing is to avoid peaks and troughs in the spectra. The smoothed spectra are shown in Figures 9 and 10. The values are listed in Table 7-19.

For the design spectra, the periods are selected to be commonly used periods.

Table 7-19. Smoothed design spectra (5% damping) for the horizontal components on soil.

Spectral Acc (g)

Period (sec) Fault Normal Fault Parallel 0.000 1.316 1.316 0.020 1.316 1.316 0.030 1.351 1.351 0.050 1.441 1.441 0.075 1.612 1.612 0.100 1.821 1.821 0.150 2.224 2.224 0.200 2.515 2.515 0.300 3.600 3.587 0.640 3.600 3.242 0.750 3.600 3.100 1.000 3.600 2.800 1.500 3.600 2.460 1.700 3.502 2.199 2.000 3.000 1.800 2.400 2.400 1.200 3.000 2.050 0.800 4.000 1.500 0.450 5.000 1.000 0.270 7.000 0.460 0.130 10.000 0.255 0.069

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 66 of 101 Date: 11/4/02 A

I I I I l II I I 1I. de I I IgnI11 1 I 1I I 1IIII .FN.111 1 I 111111 3.5- _FN design 4 T fI l I I tH I spectrum 3-

....... FN - Envelope -~~~~ , -_

I w j-- _

-- I. -

1L P 1~~~~~~~~~~~~~~~~~~~~~~~~~~

I II I - I I III .i

.t)2 .5- ___

C I0 1)

CL 1 b-&k-.

0. r II II I I 111I I I I _I I v~~~~ I I I I IllI I 1_ I r I I IL A

.~~~ I I 1 1 I I I I 111 11 -- I I I I 1LL I - . . . - - -

- I 0.01 0.1 i 10 Period (sec)

Figure 9. Design spectrum for synchronous rupture for the FN component. (Tables 7-17 and 7-19)

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 67 of 101 Date: 11/4/02 A

I I T I lI II FP Idesign 1111111 T14 I I 1711 1 1 I1 I1 I 110, 1r 3.5- _FPR design spectrum

.k= . . I F._ _ = _ ___

. FP - Envelope 3- . . . . . ..

I 0

C o,

.5-- -

-A -- . ..... -

i 2

V U

CU CO, 1.---- -- - - -

t i -3.

I, I= = __I I I I I I I I T IIV- --_ = -TkFI 1TH

. I I I I I I II I I 1-VI I U 12 h

. 1 1 111 1

=___ I I I 113 1 I _ _ 1_ X n

0 0.01 0.1 1 10 Period (sec)

Figure 10. Design spectrum for synchronous rupture for the FP component. (Tables 7-18 and 7-19)

Calc Number GEO.HBIP.02.04 Rev Number:O l Sheet Number 68 of O1 Date: 11/4/02 7.2 Vertical Spectra for the Synchronous Rupture 7.2.1 Step 1: 84 th Percentile Vertical Spectra for Soil Sites for the LSF Subsource The same input parameters (see Table 4-1) that were used to develop the horizontal acceleration response spectrum for the Little Salmon Fault subsource were used for the vertical component. From the inputs listed in Table 4-1:

M=7.7 Rr,,p = 0 Mech = Reverse For a reverse mechanism, F=l. The difference here is that the spectrum is computed for a soil site (S=1). Using these inputs, the vertical spectral acceleration based on the Abrahamson and Silva (1997) relation (assumption 3.2) is given in Table 7-20. In this table, the median spectral acceleration (colurn. #1) is computed using equation (5-11) with the coefficients from Table 5-4 with M=7.7, R rap =0 kn, F=1, and S=1.

Equation (5-11) has the peak acceleration on rock (PGArock) as a parameter. Using Equation (5-10), the median PGArock is computed with the coefficients from Table 5-4 with M=7.7, R rup =0 km, and F=l.

PGArock = 0.857 g The standard deviation (column #2) is computed using equation (5-12) with coefficients from Table 5-4.

The 84h percentile spectral acceleration (column #3) is computed using equation (5-19) with the median spectral acceleration from column #1 and the standard deviation from column #2.

Caic Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 69 of O1 Date: 11/4/02 Table 7-20. 5% damped vertical spectral acceleration for the Little Salmon Fault using the Abrahamson and Silva (1997) relationship for deep so site conditions.

1. 1 #2 #3 Period Median Spectral Standard Deviation 84t Percentile (sec) Acc (g) (Natural Log units) Spectral Acc (g) 0.000 0.722 0.590 1.302 0.020 0.722 0.590 1.302 0.030 1.015 0.590 1.832 0.050 1.553 0.590 2.802 0.075 1.788 0.590 3.225 0.100 1.726 0.590 3.114 0.120 1.642 0.590 2.962 0.150 1.485 0.594 2.689 0.170 1.424 0.588 2.564 0.200 1.296 0.590 2.338 0.240 1.175 0.590 2.120 0.300 1.013 0.590 1.828 0.400 0.857 0.590 1.547 0.500 0.740 0.590 1.335 0.750 0.608 0.590 1.097 1.000 0.479 0.590 0.865 1.500 0.312 0.590 0.564 2.000 0.231 0.590 0.416 3.000 0.146 0.620 0.271 4.000 0.110 0.650 0.210 5.000 0.090 0.680 0.177

Calc Number GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 70 of O1 Date: 11/4/02 7.2.2 Step 2: Extrapolation from 5.0 seconds to 10 seconds for the LSF subsource For periods greater than 5.0 seconds an extrapolation of the 84th percentile vertical acceleration response spectra was performed. The spectral velocities for the last 3 periods (3, 4, and 5 seconds) show a slight increase with period (see Figure 11 and discussion below). This trend is not expected to continue to longer periods. Therefore, spectrum was extrapolated to long periods by using a constant PSV for long periods.

The acceleration response spectrum given in Table 7-20 was converted to PSV (cm/sec) using equation (5-30). The resulting PSV values are listed in Table 7-21 (column #2).

The PSV is plotted in Figure I .This figure shows that the spectral velocity is approximately constant for periods greater than 2.0 seconds.

The geometric mean of the PSV values between the period range of 2.0 and 5.0 seconds was computed: 131.50 cm/s The vertical spectrum is set to be equal to this constant PSV value for spectral periods of 2.0 and greater. This extended vertical PSV spectrum was then converted back to spectral acceleration based on equation (5-31) and the corresponding values are listed in Table 7-22 (column #2).

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 71 of 101 Date: 11/4/02 Table 7-21. Little Salmon fault vertical spectral acceleration and psuedo-spectral velocity response spectra.

l__ _ __ #1_ _ #2 Period 84 Percentile "h 84' Percentile (sec) Spectral Acc (g) Spectral PSV (cm/s)

(From Table 7-20) 0.000 1.302 2.032 0.020 1.302 4.063 0.030 1.832 8.576 0.050 2.802 21.862 0.075 3.225 37.750 0.100 3.114 48.594 0.120 2.962 55.467 0.150 2.689 62.944 0.170 2.564 68.024 0.200 2.338 72.979 0.240 2.120 79.414 0.300 1.828 85.574 0.400 1.547 96.548 0.500 1.335 104.153 0.750 1.097 128.354 1.000 0.865 134.974 1.500 0.564 131.934 2.000 0.416 129.821 3.000 0.271 126.829 4.000 0.210 131.324 5.000 0.177 138.301

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 72 of 101 Date: 11/4/02 1000-I I I 1 I I I I I I 11 I II 1 1L

=I ~ I I -

fL0L rI IT ll r ITL II I

,_; 1W L {F

.4 An I UI U,

E T I11 .

0 I - I I I= Ll III I II 0

. 4, , . _X1 I lxr X~~~A in)

Co

/

CL V) 10- / I I

r _ _ _ . I I

____._ E I IIIIII IU I I I IIII t

- -_ PSV from Attenuation Relation

.=-_gZ _ -_ _ _ _- _ _Extrapolation I - _ _ _ 1 1 .

1 0.01 0.1 1 10 Period (sec)

Figure 11. Extrapolation of the vertical spectrum for the LSF to long spectral periods.

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 73 of O1 Date: I 1/4/02 Table 7-22. Extended vertical spectral acceleration and psuedo-spectral velocity response spectra for the Little Salmon fault.

1. 1 #2 #3 Period Extended 84th Extended 84t" (sec) Percentile Spectral Percentile Spectral PSV (crn/s) Acc (g)

(From Table 7-21) 0.000 2.032 1.302 0.020 4.063 1.302 0.030 8.576 1.832 0.050 21.862 2.802 0.075 37.750 3.225 0.100 48.594 3.114 0.120 55.467 2.962 0.150 62.944 2.689 0.170 68.024 2.564 0.200 72.979 2.338 0.240 79.414 2.120 0.300 85.574 1.828 0.400 96.548 1.547 0.500 104.153 1.335 0.750 128.354 1.097 1.000 134.974 0.865 1.500 131.934 0.564 2.000 131.50 Constant PSV 0.421 3.000 131.50 Constant PSV 0.281 4.000 131.50 Constant PSV 0.211 5.000 131.50 Constant PSV 0.169 7.000 131.50 Constant PSV 0.120 10.000 131.50 Constant PSV 0.084

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 74 of 101 Date: 1 114102 7.2.3 Step 3: Cascadia Interface Event Horizontal Soil Spectrum The same input parameters used in the development of the horizontal rock spectrum (see 7.1.4) from the Cascadia interface event were used for the soil spectrum:

M = 8.8 (Table 4-2)

R.,p =7km (Table 4-2)

ZT = 0 (for interface sources) (table 4-2)

H = 20 km (Assumption 3-11)

The horizontal soil spectral acceleration computed using the Youngs et al (1997) attenuation relation and the input parameters given above are summarized in Table 7-23.

The median spectral acceleration values ( column #1) are computed using eq. 5-28b with coefficients given in Table 5-9.

The standard deviation (column #2) is computed using equation (5-29) with coefficients given in Table 5-9.

The 84h'percentile spectral acceleration (column #3) is computed using equation (5-19) with the median spectral acceleration from column #1 and the standard deviation from column #2.

Table 7-23.5% damped horizontal spectral acceleration on soil for the Cascadia interface event usin Youngs et al. (1997) attenuation model.

1. 1 #2 #3 Median Standard 84h' Percentile Spectral Deviation Spectral Period (sec) Acc (g) (LN units) Acc (g) 0.00 0.445 0.650 0.852 0.075 0.634 0.650 1.214 0.100 0.712 0.650 1.364 0.200 0.986 0.650 1.890 0;300 0.991 0.650 1.897 0.400 0.887 0.650 1.699 0.500 0.814 0.650 1.560 0.750 0.650 0.650 1.246 1.000 0.510 0.650 0.978 1.500 0.312 0.700 0.629 2.000 0.222 0.750 0.470 3.000 0.126 0.850 0.295 4.000 0.074 0.850 0.173

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 75 of 101 Date: 11/4/02 7.2.4 Step 4: V/H Ratio for the Cascadia Interface subsource The Youngs et al (1997) attenuation relation for ground motion from subduction zone earthquakes does not include a model for the vertical component. The Abrahamson and Silva (1997) attenuation relation is used to estimate the V/H ratio that can then be applied to the horizontal spectrum for the Cascadia earthquake.

The inputs for the Cascadia event are:

M=8.8 Rrup = 7 km Source type = interface For computing the horizontal and vertical soil spectra using Abrahamson and Silva (1997), it is assumed that the following inputs will approximate the V/H ratio for the subduction events (assumption 3-12):

M=8.0 RrUP = 7 km Source type = strike-slip S = 1 (soil)

The horizontal and vertical median response spectra for soil sites are computed using (eq.

5-11) with the above inputs. First, the PGArock is computed for the horizontal component using eq. 5-10 with coefficients from Table 5-3 and for the vertical component using eq. 5-10 with coefficients from Table 5-4. He resulting PGArock values are:

horizontal PGAroCk = 0.603g vertical PGArock = 0.615g For the horizontal component, the coefficients from Table 5-3 are used with eq. 5-1 1 and with the PGArock =0.603g, M = 8.0, Rrup = 7 km, Source type = strike-slip, and S = 1.

The results are listed in column #1 of Table 7-24.

For the vertical component, the coefficients from Table 5-4 are used with eq. 5-11 and with the PGArock =0.615g, M = 8.0, Rrup = 7 km, Source type = strike-slip, and S = 1..

The results are listed in column #2 of Table 7-24.

The V/H ratio (column #3) is computed by dividing column #2 by column # 1,

Calc Number: GEO.HBIP.02.04 Rev Number:0 i Sheet Number: 76 of 1O 1 Date: 11/4/02 Table 7-24. Horizontal, vertical, and V/H ratio for a magnitude 8.0 strike-slip earthquake at a distance of 7 km from Abrahamson and Silva (1997.

1. 1 #2 #3 Period Median Horizontal Median Vertical V/H Spectral (sec) Soil Soil Ratio Spectra SA() Spectra SA (g) 0.000 0.442 0.545 1.233 0.020 0.442 0.545 1.233 0.030 0.442 0.746 1.688 0.075 0.549 1.285 2.341 0.100 0.643 1.240 1.928 0.200 1.019 0.858 0.842 0.300 1.119 0.604 0.540 0.400 1.113 0.483 0.434 0.500 1.081 0.396 0.366 0.750 0.976 0.300 0.307 1.000 0.838 0.239 0.285 1.500 0.638 0.173 0.271 2.000 0.470 0.138 0.294 3.000 0.277 0.096 0.347 4.000 0.179 0.073 0.408

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 77 of 101 Date: 11/4/02 7.2.5 Step 5: Cascadia Vertical Soil Spectrum The V/H ratio (Table 7-24, column #3) was then use to scale the previously developed 84th percentile horizontal soil acceleration response spectrum for the Cascadia interface event (Table 7-23, column #3). The V/H spectral ratio, horizontal soil spectrum, and corresponding scaled vertical soil spectrum are listed in Table 7-25 in columns #1, #2, and #3, respectively..

Table 7-25. V/H spectral ratio, horizontal, and vertical soil spectrum for the Cascadia interface event.

1. 1 #2 #3 Period V/H Spectral 84n Percentile 84 n Percentile (sec) Ratio Horizontal Spectra Vertical Spectra SA (from Table 7-24) SA (g) (g)

(from Table 7-23) 0.000 1.233 0.852 1.051 0.020 1.233 0.852 1.051 0.030 1.688 0.852 1.438 0.075 2.341 1.214 2.842 0.100 1.928 1.364 2.630 0.200 0.842 1.890 1.591 0.300 0.540 1.897 1.024 0.400 0.434 1.699 0.737 0.500 0.366 1.560 0.571 0.750 0.307 1.246 0.383 1.000 0.285 0.978 0.279 1.500 0.271 0.629 0.171 2.000 0.294 0.470 0.138 3.000 0.347 0.295 0.102 4.000 0.408 0.173 0.071

Calc Number. GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 78 of 101 Date: 11/4/02 7.2.6 Step 6: Extrapolation/Interpolation of the Cascadia Vertical Soil Spectrum The vertical soil spectrum from table 7-25 (column #3) is extrapolated to 10 seconds period using eq. 5-20 (with T 1 =3 sec and T 2 =4 sec). The extrapolated values are listed in Table 7-26 (column #2).

The vertical soil spectrum from Table 7-25 are also interpolated to the same spectral periods used for the LSF vertical soil spectrum (Table 7-22) using eq. 5-20.

Table 7-26. Vertical soil spectrum for the Cascadia interface event.

1

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ # #2 Period 84' Percentile 84' Percentile (sec) Vertical Vertical Soil Spectra Soil Spectra SA (g) SA (g)

(from Table 7-25) 0.000 1.051 1.051 0.020 1.051 1.051 0.030 1.438 1.438 0.050 Interpolated 2.102 0.075 2.842 2.842 0.100 2.630 2.630 0.120 Interpolated 2.304 0.150 Interpolated 1.960 0.170 Interpolated 1.790 0.200 1.591 1.591 0.240 Interpolated 1.305 0.300 1.024 1.024 0.400 0.737 0.737 0.500 0.571 0.571 0.750 0.383 0.383 1.000 0.279 0.279 1.500 0.17i 0.171 2.000 0.138 0.138 3.000 0.102 0.102 4.000 0.071 0.071 5.000 extrapolated 0.054 7.000 extrapolated 0.035 10.000 extrapolated 0.022

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 79 of I01 Date: 1/4/02 7.2.7 Step 7: Combined Synchronous Rupture Vertical Soil Spectra The vertical soil spectra for the Little Salmon Fault (see column #3 of Table 7-22) and the Cascadia Interface event (see Table 7-26) are combine based on assumption 3.9 (i.e.,

SRSS).

The combined synchronous rupture vertical soil acceleration response spectrum is given in Table 7-27. The third column is the SRSS of the #1 and #2 columns. These spectra are plotted in Figure 12.

Figure 13 compares the vertical and horizontal spectra for 5% damping.

Table 7-27. Combined synchronous rupture vertical soil acceleration response spectrum.

1. 1 #2 #3 Cascadia Interface Little Salmon Fault Event, Vertical Vertical Synchronous Soil SA (g) Soil SA(g) Vertical Period (from Table 7-22) (from Table 7-26) Soil SA(g)

(sec) 0.000 1.302 1.051 1.673 0.020 1.302 1.051 1.673 0.030 1.832 1.438 2.329 0.050 2.802 2.102 3.503 0.075 3.225 2.842 _4.299 0.100 3.114 2.630 4.076 0.120 2.962 2.304 3.753 0.150 2.689 1.960 3.328 0.170 2.564 1.790 3.127 0.200 2.338 1.591 2.828 0.240 2.120 1.305 2.489 0.300 1.828 1.024 2.095 0.400 1.547 0.737 1.714 0.500 1.335 0.571 1.452 0.750 1.097 0.383 1.162 1.000 0.865 0.279 0.909 1.500 0.564 0.171 0.589 2.000 0.421 0.138 0.443 3.000 0.281 0.102 0.299 4.000 0.211 0.071 0.223 5.000 0.169 0.054 0.177 7.000 0.120 0.035 0.125 10.000 0.084 0.022 0.087

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 80 of 101 Date: 11/4/02 cm a

0 2.

In co a}

0. I 0.01 0.1 I 10 Period (sec)

Figure 12. Vertical component spectra for the individual subsources and for synchronous rupture.

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: SI of O1 Date: 11/4/02 Si C

0 to 2.

a) al 0i M

cW Period (sec)

Figure 13. Comparison of the 5% damped soil spectra for the vertical, fault normal, and fault parallel components.

Calc Number: GEO.HBIP.02.04 Rev Number:O l Sheet Number: 82 of 101 Date: 1/4/02 7.3 Spectra for Damping values other than 5%.

7.3.1 Step 1: Damping Scale Factors for the Horizontal Component The natural logarithm of the scale factors for scaling the 5% damped horizontal to damping values of 2%, 3%, and 7% are computed using eq. (5-32) with coefficients from Tables 5-lOa, 5-lOb, and 5-lOc. A magnitude of 8.0 is used (assumption 3-15). The resulting values are listed in columns #1, #2, and #3 of Table 7-28.

The arithmetic values of the scale factors are computed using eq. (5-33) with the values in Table 7-28, columns # 1,#2, and #3 as the inputs. The resulting scale factors are listed in columns #1, #2, and #4 of Table 7-29.

For spectral periods of 1.7 and 2.4 seconds, the values are estimated by interpolation using eq. (5-20).

For spectral periods greater than 5.0 seconds, the damping ratio is held constant at the value for T=5 seconds (assumption 3-14).

73.2 Step 2: Damping Scale Factors for 4% damping The coefficients for the Abrahamson and Silva (1996) damping scale factors for the horizontal component (Tables 5-lOa, b, and c) are not given for 4% damping. Using assumption 3.13, the scale factor for 4% damping (Table 7-29, column #3) is computed by taking the square root of the scale factor at 3% damping (Table 7-29 column #2).

7.3.3 Step 3: Damping Scale Factors for the Vertical Component The natural logarithm of the scale factors for scaling the 5% damped horizontal to damping values of 2%, 3%, and 7% are computed using eq. (5-32) with coefficients from Tables 5-1 la, 5-1 lb, and 5-1 Ic. A magnitude of 8.0 is used (assumption 3-15). The resulting values are listed in columns #1, #2, and #3 of Table 7-30.

The arithmetic values of the scale factors are computed using eq. (5-33) with the values in Table 7-30, columns #1, #2, and #3 as the inputs. The resulting scale factors are listed in columns #1, #2, and #4 of Table 7-3 1.

For spectral periods of 1.7 and 2.4 seconds, the values are estimated by interpolation using eq. (5-20).

For spectral periods greater than 5.0 seconds, the damping ratio is held constant at the value for T=5 seconds (assumption 3-14).

7.3.4 Step 4: Damping Scale Factors for 4% damping The coefficients for the Abrahamson and Silva (1996) damping scale factors for the vertical component (Tables 5-1 la, b, and c) are not given for 4% damping. Using

Calc Number: GEO.HBIP.02.04 Rev Number:O l Sheet Number: 83 of 101 Date: 1/4/02 assumption 3.13, the scale factor for 4% damping (Table 7-3 1, column #3) is computed by taking the square root of the scale factor at 3% damping (Table 7.31 column #2).

7.3.5 Step 5: Fault Normal Spectra for 2%. 4. and 7% Damping The fault normal spectral values at 2%, 4%, and 7% damping are computed using eq. (5-

34) with the damping scale factors from Table 7-29 and the 5% damped fault normal spectrum (Table 7-19). The resulting fault normal spectral values are listed in Table 7-32.

7.3.6 Step 6: Fault Parallel Spectra for 2%, 4%. and 7% Damping The fault parallel spectral values at 2%, 4%, and 7% damping are computed using eq. (5-

34) with the damping scale factors from Table 7-29 and the 5% damped fault parallel spectrum (Table 7-19). The resulting fault normal spectral values are listed in Table 7-33.

7.3.6 Step 7: Vertical Spectra for 2%, 4%, and 7% Damping The vertical spectral values at 2%, 4%, and 7% damping are computed using eq. (5-34) with the damping scale factors from Table 7-31 and the 5% damped fault parallel spectrum (Table 7-27, column #3). The resulting fault normal spectral values are listed in Table 7-34.

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 84 of O1 Date: 114/02 Table 7-28. Natural logarithm of the damping scaling factor for the horizontal component (relative to 5% damp ing)

1. 1

___________ #2 #3 Period (sec) LN(2.0%/5%) LN(3 .0%/5%) LN(7.0%/5%)

0.000 0.0000 0.0000 0.0000 0.020 0.0000 0.0000 0.0000 0.030 0.0462 0.0273 -0.0205 0.050 0.1094 0.0648 -0.0486 0.075 0.1580 0.0936 -0.0701 0.100 0.1922 0.1138 -0.0853 0.150 0.2284 0.1353 -0.1014 0.200 0.2379 0.1409 -0.1056 0.300 0.2379 0.1409 -0.1056 0.400 0.2379 0.1409 -0.1056 0.640 0.2379 0.1409 -0.1056 0.750 0.2379 0.1409 -0.1056 1.000 0.2394 0.1419 -0.1063 1.500 0.2380 0.1410 -0.1056 2.000 0.2339 0.1384 -0.1037 3.000 0.2236 0.1324 -0.0991 4.000 0.2127 0.1258 -0.0945 5.000 0.2022 0.1198 -0.0897

. a

Calc Number: GEO.HBIP.02.04 Rev Number.0 I Sheet Number: 85 of 101 Date: 11/4/02 Table 7-29. Damping scaling factor for the horizontal component (relative to 5%

damDing)

1. 1 #2 #3 #4 Period (sec) 2.0%/5% 3.0%/5% 4%/5%* 7.0%/5%

0.000 1.000 1.000 1.000 1.000 0.020 1.000 1.000 1.000 1.000 0.030 1.047 1.028 1.014 0.980 0.050 1.116 1.067 1.033 0.953 0.075 1.171 1.098 1.048 0.932 0.100 1.212 1.121 1.059 0.918 0.150 1.257 1.145 1.070 0.904 0.200 1.269 1.151 1.073 0.900 0.300 1.269 1.151 1.073 0.900 0.400 1.269 1.151 1.073 0.900 0.640 1.269 1.151 1.073 0.900 0.750 1.269 1.151 1.073 0.900 1.000 1.271 1.153 1.074 0.899 1.500 1.269 1.152 1.073 0.900 1.700 1.267** 1.151$* 1.073** 0.900**

2.000 1.264 1.149 1.072 0.901 2.400 1.258** 1.146** 1.071** 0.903**

3.000 1.251 1.142 1.069 0.905 4.000 1.238 1.134 1.065 0.910 5.000 1.225 1.128 1.062 0.914 7.000 1.225 1.128 1.062 0.914 10.000 1.225 1.128 1.062 0.914

• The 4%/5% damping ratios are estimated as the sqrt(30/o/5%) values.

• • Interpolated using eq. 5-20

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 86 of 101 Date: 1/4/02 Table 7-30. Natural Logarithm of damping scaling factor for the vertical component (relative to 5% damping)

1. 1 #2 #3 Period (sec) LN(2.0 0/o/5%) LN(3.0 0/o/5%) LN(7.00//5%)

0.000 0.0000 0.0000 0.0000 0.020 0.0000 0.0000 0.0000 0.030 0.1232 0.0725 -0.0528 0.050 0.2072 0.1220 -0.0888 0.075 0.2488 0.1464 -0.1067 0.100 0.2818 0.1658 -0.1208 0.120 0.2890 0.1701 -0.1239 0.150 0.2932 0.1728 -0.1257 0.170 0.2910 0.1713 -0.1247 0.200 0.2839 0.1671 -0.1217 0.240 0.2776 0.1634 -0.1190 0.300 0.2727 0.1605 -0.1169 0.400 0.2727 0.1605 -0.1169 0.500 0.2727 0.1605 -0.1169 0.750 0.2727 0.1605 -0.1169 1.000 0.2742 0.1614 -0.1176 1.500 0.2717 0.1599 -0.1165 2.000 0.2663 0.1567 -0.1142 3.000 0.2527 0.1487 -0.1083 4.000 0.2386 0.1405 -0.1023 5.000 0.2254 0.1326 -0.0965

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 87 of 101 Date: 11/4/02 Table 7-31. Damping scaling factor for the vertical component (relative to 5%

damning)

______________ #1,#2 #3 #4 Period (sec) 2.00/o/5% 3.0%/5% 40 _5%* 7.00/o/5%

0.000 1.000 1.000 1.000 1.000 0.020 1.000 1.000 1.000 1.000 0.030 1.131 1.075 1.037 0.949 0.050 1.230 1.130 1.063 0.915 0.075 1.282 1.158 1.076 0.899 0.100 1.326 1.180 1.086 0.886 0.120 1.335 1.185 1.089 0.883 0.150 1.341 1.188 1.090 0.882 0.170 1.338 - 1.187 1.089 0.883 0.200 1.328 1.182 1.087 0.885 0.240 1.320 1.178 1.085 0.888 0.300 1.314 1.174 1.084 0.890 0.400 1.314 1.174 1.084 0.890 0.500 1.314 1.174 1.084 0.890 0.750 1.314 1.174 1.084 0.890 1.000 1.315 1.175 1.084 0.889 1.500 1.312 1.173 1.083 0.890 2.000 1.305 1.170 1.082 0.892 3.000 1.287 1.160 1.077 0.897 4.000 1.269 1.151 1.073 0.903 5.000 1.253 1.142 1.069 0.908 7.000 1.253 1.142 1.069 0.908 10.000 1.253 1 1.142 1.069 0.908

• The 4%/5% damping ratios are estimated as the sqrt(3%/o/5%) values.

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number 88 of 101 Date: 11/4102 The horizontal component scale factors for damping values of 2%, 4%, and 7% from Table 7-29 are listed in columns #2, #3, and #4 of Table 7-32. These values are multiplied by the fault normal spectrum at 5% damping (column #1 in Table 7-32) to computed the fault normal spectra for 2%, 4%, and 7% damping (columns #5, #6, and #7 in Table 7-32).

Table 7-32. Spectral values for the damping values of 2%, 4%, and 7% for the fault normal component.

1. 1 #2 #3 #4 #5 #6 #7 Fault Normal Fault Fault Fault 5% damp 2.00/5% 4.00/a/5% 7.00/J5% Normal Normal Normal Sa(g) scale scale scale 2% damp 4% damp 7% damp (from Table factor factor factor Sa(g) Sa(g) Sa(g) 7.19)

Period (from Table (from Table (from Table (sec) 7-29) 7-29) 7-29) 0.000 1.316 1.000 1.000 1.000 1.316 1.318 1.316 0.020 1.316 1.000 1.000 1.000 1.316 1.316 1.316 0.030 1.351 1.047 1.014 0.980 1.415 1.370 1.324 0.050 1.441 1.116 1.033 0.953 1.608 1.489 1.373 0.075 1.612 1.171 1.048 0.932 1.888 1.689 1.502 0.100 1.821 1.212 1.059 0.918 2.207 1.928 1.672 0.150 2.224 1.257 1.070 0.904 2.796 2.380 2.010 0.200 2.515 1.269 1.073 0.900 3.192 2.699 2.264 0.300 3.600 1.269 1.073 0.900 4.568 3.863 3.240 0.640 3.600 1.269 1.073 0.900 4.568 3.863 3.240 0.750 3.600 1.269 1.073 0.900 4.568 3.863 3.240 1.000 3.600 1.271 1.074 0.899 4.576 3.866 3.236 1.500 3.600 1.269 1.073 0.900 4.568 3.863 3.240 1.700 3.502 1.267 1.073 0.900 4.434 3.754 3.152 2.000 3.000 1.264 1.072 0.901 3.792 3.216 2.703 2.400 2.400 1.258 1.071 0.903 3.020 2.570 2.167 3.000 2.050 1.251 1.069 0.905 2.565 2.191 1.855 4.000 1.500 1.238 1.065 0.910 1.857 1.598 1.365 5.000 1.000 1.225 1.062 0.914 1.225 1.062 0.914 7.000 0.460 1.225 1.062 0.914 0.564 0.489 0.420 10.000 0.255 1.225 1.062 0.914 0.312 0.271 0.233

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 89 of 101 Date: 11/4/02 The horizontal component scale factors for damping values of 2%, 4%, and 7% from Table 7-29 are listed in columns #2, #3, and #4 of Table 7-33. These values are multiplied by the fault parallel spectrum at 5% damping (colunn #1 in Table 7-33) to computed the fault parallel spectra for 2%, 4%, and 7% damping (columns #5, #6, and #7 in Table 7-33).

Table 7-33. Spectral values for the damping values of 2%, 4%, and 7% for the fault parallel component.

1. 1 #2 #3 #4 #5 #6 #7 Fault Parallel Fault Fault Fault 5% damp 2.00//5% 4.0%/5% 7.00/o15% Parallel Parallel Parallel Sa(g) scale scale scale 2% damp 4% damp 7% damp (from Table factor factor factor Sa(g) Sa(g) Sa(g) 7-19)

Period (from Table (from Table (from Table (sec) 7-29) 7-29) 7-29) 0.000 1.316 1.000 1.000 1.000 1.316 1.316 1.316 0.020 1.316 1.000 1.000 1.000 1.316 1.316 1.316 0.030 1.351 1.047 1.014 0.980 1.415 1.370 1.324 0.050 1.441 1.116 1.033 0.953 1.608 1.489 1.373 0.075 1.612 1.171 1.048 0.932 1.888 1.689 1.502 0.100 1.821 1.212 1.059 0.918 2.207 1.928 1.672 0.150 2.224 1.257 1.070 0.904 2.796 2.380 2.010 0.200 2.515 1.269 1.073 0.900 3.192 2.699 2.264 0.300 3.587 1.269 1.073 0.900 4.552 3.849 3.228 0.640 3.242 1.269 1.073 0.900 4.114 3.479 2.918 0.750 3.100 1.269 1.073 0.900 3.934 3.326 2.790 1.000 2.800 1.271 1.074 0.899 3.559 3.007 2.517 1.500 2.460 1.269 1.073 0.900 3.122 2.640 2.214 1.700 2.199 1.267 1.073 0.90 2.784 2.357 1.979 2.000 1.800 1.264 1.072 0.901 2.275 1.930 1.622 2.400 1.200 1.258 1.071 0.903 1.510 1.285 1.083 3.000 0.800 1.251 1.069 0.905 1.001 0.855 0.724 4.000 0.450 1.238 1.065 0.910 0.557 0.479 0.410 5.000 0.270 1.225 1.062 0.914 0.331 0.287 0.247 7.000 0.130 1.225 1.062 0.914 0.159 0.138 0.119 10.000 0.069 1.225 1.062 0.914 0.084 0.073 0.063

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 90 of 101 Date: 11/4/02 The vertical component scale factors for damping values of 2%, 4%, and 7% from Table 7-31 are listed in columns #2, #3, and #4 of Table 7-34. These values are multiplied by the vertical spectrum at 5% damping (column #1 in Table 7-34) to computed the vertical spectra for 2%, 4%, and 7% damping (columns #5, #6, and #7 in Table 7-34).

Table 7-34. Spectral values for the damping values of 2%, 4%, and 7% for the vertical component.

1. 1 #2 #3 #4 #5 #6 #7 Vertical 5% damp Vertical Vertical Vertical Sa(g) 2.00/a/5% 4.0°/o15% 7.00/o.5% 2% damp 4% damp 7% damp (from Table scale scale scale Sa(g) Sa(g) Sa(g) 7-27) factor factor factor Period (from Table (from Table (from Table (sec) 7-31) 7-31) 7-31) 0.000 1.673 1.000 1.000 1.000 1.673 1.673 1.673 0.020 1.673 1.000 1.000 1.000 1.673 1.673 1.673 0.030 2.329 1.131 1.037 0.949 2.634 2.415 2.209 0.050 3.503 1.230 1.063 0.915 4.309 3.724 3.205 0.075 4.299 1.282 1.076 0.899 5.513 4.625 3.864 0.100 4.076 1.326 1.086 0.886 5.403 4.428 3.612 0.120 3.753 1.335 1.089 0.883 5.011 4.086 3.316 0.150 3.328 1.341 1.090 0.882 4.462 3.628 2.935 0.170 3.127 1.338 1.089 0.883 4.183 3.407 2.760 0.200 2.828 1.328 1.087 0.885 3.756 3.074 2.504 0.240 2.489 1.320 1.085 0.888 3.285 2.701 2.210 0.300 2.095 1.314 1.084 0.890 2.752 2.270 1.864 0.400 1.714 1.314 1.084 0.890 2.251 1.857 1.525 0.500 1.452 1.314 1.084 0.890 1.907 1.573 1.292 0.750 1.162 1.314 1.084 0.890 1.526 1.259 1.034 1.000 0.909 1.315 1.084 0.889 1.196 0.985 0.808 1.500 0.589 1.312 1.083 0.890 0.773 0.638 0.524 2.000 0.443 1.305 1.082 0.892 0.578 0.479 0.395 3.000 0.299 1.287 1.077 0.897 0.385 0.322 0.268 4.000 0.223 1.269 1.073 0.903 0.283 0.239 0.201 5.000 0.177 1.253 1.069 0.908 0.222 0.189 0.161 7.000 0.125 1.253 1.069 0.908 0.157 0.134 0.114 10.000 0.087 1.253 1.069 0.908 0.109 0.093 0.079

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 91 of 101 Date: 1/4/02 The response spectra at damping values of 2%, 4%, 5%, and 7% are plotted for the fault normal, fault parallel, and vertical components in Figures 14, 15, and 16, respectively.

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 92 of 101 Date: 11/4/02 LiD . . . . I .

I I i II1 2%

4.5. damping I

..... I..........

4% I~~~~~~~~~~~~I l lI 1 I I I I11 d mpn damping I I rrrr I I I T-[

4.

5% ......... .............. I *........

damping 1 z . I I F zI I - t 3.D 7%  : I 1 .7 T I IT I fI I i I il damping  ; l t . 1b-s\- \". I I I l7 I -::::JL..Z..

C 3. I . I 0 l I

l Cu O 2.5 I I I V

> 2 I4 1.5.

L I I II I II I I I 9-4-9-I I I I I I ItIf ,

I.-

%I 1- 44.9.4 *-*-9-I

'Ul I r T _ lI I = I I I 1<I I A I 1 1 T _~~ IU_ I __ LL _ A I L 0.5.

I I w i7_ _ 11 A 9--I-9 i U1

- I -

0.01 0.1 1 10 Peiod (sec)

Figure 14. Fault normal design spectrum for damping values of 2%, 4%, 5%, and 7%.

(Table 7-32)

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 93 of 101 Date: 11/4/02 I I I I 111 I LI I

_I I I 1 111II I, .

I 1 11

........ ] ..

1 1

1ZI I I

2% I I I I I I fII I I I l 1 4.5- damping Al - 7 4%

.............. I....damping...

i :N INtt I II damping I II T T I = I _

4 I 5%

damping

_ .I 3.5- 7% A I' damping

%di . . . . . ...

I ff C 3. I :a I F-0 If * , I**. A I

4I I I I 11 111 I11 I I I Ir

[

1 4'~IUI - TI. I\ I11 1 11-.

I I I Ir1- 1T I I i

rI l U .Q- I l l l l 111/ -,_rR T l I 2 i 1l X 'i\

TlmSr l l I T r r 11 A ^; Tl Ii Il i1 li11 U

l T= _ _ _ t.w

_ S

• S _

/

= _ _ = _ -1

_ 'l ,.

I r erlr a) _ § l = _ : / = = = / { r .. z r 1 § i j Tr CO, I 4 _ _ < _ ^ ,- _ _ _ l §r as 1=4 1X ^ § § r I w _ r r, , _ = = _ TFT i --;&I I I I II I

. - :5 _ . _ . Th: 7  : _ _ _ TCh17 Th: Wt I l [ @ } C r m; _-_- ___X_t t 0.5-

< l Xt l l i _.

__ = _ _ _5 S-XX l i l l ll

I T

. l I i_ R T I I

_ _ _ 18 *1 = = = rrl 1 t ¢ 11 l zL O- I J J w _ _ _ '0$ l l }[S 0.01 0.1 1 10 Period (sec)

Figure 15. Fault parallel design spectrum for damping values of 2%, 4%, 5%, and 7%.

(Table 7-33)

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 94 of 101 Date: 11/4/02 l l l I l I Il I l Il l 1 ITI! !.1 1 Iii I I1-t I I lli 2%

damping 4%

............... d mpn

.~damping 5%

- _ I . - I I_ - - - damping A

i~=

I I 7%

damping I C

0

, .U0 (a

I.-

a) 0.

CO 3-- I- - -~~~~~~~~~~A 2- _ _  ; - -~~~~~~~~~~~~~~~~~~~~~~~~~~~a

- I 0.01 0.1 1 10 Period (sec)

Figure 16. Vertical spectrum for damping values of 2%, 4%, 5%, and 7%. (Table 7-34)

Calc Number: GEO.HBIP.02.04 Rev Number:0 I Sheet Number: 95 of lO Date: 11/4/02 8 RESULTS The horizontal and vertical deterministic design response for the MCE at 2%, 4%, 5%,

and 7% damping are listed in Tables 8-1, 8-2, and 8-3 for the fault normal, fault parallel, and vertical components, respectively.

Table 8-1. 84th percentile MCE design spectra for the Fault Normal Component (from Table 7-32)

Period 2% damping 4% damping 5% damping 7% damping (sec) 0.000 1.316 1.316 1.316 1.316 0.020 1.316 1.316 1.316 1.316 0.030 1.415 1.370 1.351 1.324 0.050 1.608 1.489 1.441 1.373 0.075 1.888 1.689 1.612 1.502 0.100 2.207 1.928 1.821 1.672 0.150 2.796 2.380 2.224 2.010 0.200 3.192 2.699 2.515 2.264 0.300 4.568 3.863 3.600 3.240 0.640 4.568 3.863 3.600 3.240 0.750 4.568 3.863 3.600 3.240 1.000 4.576 3.866 3.600 3.236 1.500 4.568 3.863 3.600 3.240 1.700 4.434 3.754 3.502 3.152 2.000 3.792 3.216 3.000 2.703 2.400 3.020 2.570 2.400 2.167 3.000 2.565 2.191 2.050 1.855 4.000 1.857 1.598 1.500 1.365 5.000 1.225 1.062 1.000 0.914 7.000 0.564 0.489 0.460 0.420 10.000 0.312 0.271 0.255 0.233

Calc Number: GEO.HBIP.02.04 Rev Number:O I Sheet Number: 96 of 10 1 Date: 11/4/02 Table 8-2. 84h percentile MCE design spectra for the Fault Parallel Component (from Table 7-3 )

Period 2% damping 4% damping 5% damping 7% damping (sec) 0.000 1.316 1.316 1.316 1.316 0.020 1.316 1.316 1.316 1.316 0.030 1.415 1.370 1.351 1.324 0.050 1.608 1.489 1.441 1.373 0.075 1.888 1.689 1.612 1.502 0.100 2.207 1.928 1.821 1.672 0.150 2.796 2.380 2.224 2.010 0.200 3.192 2.699 2.515 2.264 0.300 4.552 3.849 3.587 3.228 0.640 4.114 3.479 3.242 2.918 0.750 3.934 3.326 3.100 2.790 1.000 3.559 3.007 2.800 2.517 1.500 3.122 2.640 2.460 2.214 1.700 2.784 2.357 2.199 1.979 2.000 2.275 1.930 1.800 1.622 2.400 1.510 1.285 1.200 1.083 3.000 1.001 0.855 0.800 0.724 4.000 0.557 0.479 0.450 0.410 5.000 0.331 0.287 0.270 0.247 7.000 0.159 0.138 0.130 0.119 10.000 0.085 0.073 0.069 0.063

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 97 of 101 Date: 11/4/02 Table 8-3. 84th percentile MCE design spectra for the Vertical Component (Prnm TAhIP 7AR4A Period 2% damping 4% damping 5% damping 7% damping (sec) 0.000 1.673 1.673 1.673 1.673 0.020 1.673 1.673 1.673 1.673 0.030 2.634 2.415 2.329 2.209 0.050 4.309 3.724 3.503 3.205 0.075 5.513 4.625 4.299 3.864 0.100 5.403 4.428 4.076 3.612 0.120 5.011 4.086 3.753 3.316 0.150 4.462 3.628 3.328 2.935 0.170 4.183 3.407 3.127 2.760 0.200 3.756 3.074 2.828 2.504 0.240 3.285 2.701 2.489 2.210 0.300 2.752 2.270 2.095 1.864 0.400 2.251 1.857 1.714 1.525 0.500 1.907 1.573 1.452 1.292 0.750 1.526 1.259 1.162 1.034 1.000 1.196 0.985 0.909 0.808 1.500 0.773 0.638 0.589 0.524 2.000 0.578 0.479 0.443 0.395 3.000 0.385 0.322 0.299 0.268 4.000 0.283 0.239 0.223 0.201 5.000 0.222 0.189 0.177 0.161 7.000 0.157 0.134 0.125 0.114 10.000 0.109 0.093 0.087 0.079

Calc Number: GEO.HBIP.02.04 Rev Number:0 l Sheet Number: 98 of 101 Date: 11/4/02

9. CONCLUSIONS The response spectral values given in section 8 represent the surface design response spectra for the HBIP, consistent with the specification in the Work Plan.

Limitations: Since the design spectra are based on an envelope of the response of three soil profiles and the empirical spectral shape (from Northridge), there is no single defined soil velocity model that is consistent with this spectrum. Subsequent engineering analysis should not associate a single soil profile to these design spectra. Doing so could result in unrealistic ground motion estimates at depth.

. A_/

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 99 of 101 Date: 1/4/02

10. REFERENCES Abrahamson, N. A. and W. J. Silva (1996). Empirical Ground Motion Models, Appendix A in Silva et al (1997).

Abrahamson, N. A. and W. J. Silva (1997). Empirical response spectral attenuation relations for shallow crustal earthquakes, Seism. Res. Let., vol. 68,94-127.

Boore D. M., W. Joyner, and T. Furnal (1997). Equations for estimating horizontal response spectra and peak acceleration from western North America earthquakes: a summary of recent work, Seism. Res. Let., 68, pp 12 8 - 1 5 3 .

Campbell (1997). Empirical near-source attenuation relationships for horizontal and vertical components of peak ground acceleration, peak ground velocity, and pseudo absolute accelerations response spectra, Seism. Res. Let., 68, 154-179.

Hudson, D. E. (1979) reading and interpreting strong motion accelerograms, Earthquake Engineering Research Institute, Monograph.

Idriss, I. M. (1995). An overview of earthquake ground motions pertinent to seismic zonation, Proc. Fifth International Conference on Seismic Zonation, vol. III, 2111-2126.

Idriss, I. M. (1994). Updated standard error terms, Memo to Phalkun Tan, April 17, 1994.

Idirss, I. M. (1992). Empirical procedures for estimating earthquake ground motions, Proc. SEAOC conference, October 15, 1992.

Idriss. I. M. (1991). Selection of earthquake ground motions at rock sites, report prepared for the Structures Division, Building and Fire Research Laboratory, National Institute of Standard and Technology, Department of Civil Engineering, University of California, Davis.

Sadigh K., C.Y. Chang, N. A. Abrahamson, S.. Chiou, and M. S. Power., (1993).

Specification of long period ground motions: updated attenuation relationships for rock site conditions, Proc. ATC 17-1, Volume 1, 59-70.

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, Seism. Res. Let. 568, 180-189.

Silva, W.J., N. Abrahamson, G. Toro, C. Costantino (1997). "Description and validation of the stochastic ground motion model." Draft Report to Brookhaven National Laboratory, Associated Universities, Inc. Upton, New York.

Calc Number: GEO.HBIP.02.04 Rev Number:0 Sheet Number: 100 of 101 Date: 1 1/4/02 Somerville, P. G., N. F. Smith, R. G. Graves, N. A. Abrahamson (1997). Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity, Seism. Res. Let., vol. 68, 199-222.

Youngs, R. R., S. J. Chiou, W. J. Silva, and J.R. Humphrey (1997). Strong ground motion attenuation relationships for subduction zone earthquakes, Seism. Res. Let., 68, 58-73.

Calc Number: GEO.HBIP.02.04 Rev Number:O l Sheet Number: 101 of 101 Date: 11/4/02

10. ENCLOSURES AND ATTACHMENTS : Abrahamson and Silva (1997) attenuation relations for horizontal and vertical response spectral values. : Sadigh et al. (1997) attenuation relations for the horizontal response spectral values : Sadigh et al (1993) attenuation relations for the vertical response spectral values : Idriss (1995) attenuation relation for peak acceleration : driss (1992) Attenuation relations for horizontal response spectral values. : Idriss (1994) updated standard error terms : Somerville et al (1997) Scale factors for directivity effects : Abrahamson and Silva (1996) scale factors for response spectra at various damping values