ASCE 7-10Required Procedures for Determining Site-Specific

Response Spectra

C. B. CrouseURS Corporation

November 22, 2013C.B. Crouse 2013

ASCE 7-10; Ch.21Site-Specific Ground Motion

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2008 USGS SS and SI Maps in ASCE 7-10

a

a

H1

H2

t

t

1 d.o.f.

H1

H2

Acc

.in

H2

dir e

ctio

n( g

)

Acc. in H1direction (g)

Max Sa

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Ground-Motion Prediction Equations ComputeGeometric Mean = Sa1 * Sa2

AccelerogramHorizontal Components

a

a

H1

H2

t

t

Response Spectra

H1

H2

Sa

Sa

Sa1

Sa2

Ti

Ti

T

T

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Geomean Sa vs Max Sa

1.0T (sec)

Bedrock Response Spectra

Sa

x 1.1

x 1.3

Based on:

Max Sa

Geomean Sa

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Adjustment of Site-Specific Geomean Sa for Max Direction Sa

ASCE 7-10Supplement

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Sect. 21.2.3: Site-Specific MCER

SaM(T) = min[SaProb (T), Sa

Det (T)]

Site-Specific Ground Motion ProceduresCh. 21 of ASCE 7-10: Risk-Targeted MCE (MCER)

Sect. 21.2.1: Probabilistic MCER SaProb

Sect. 21.2.2: Deterministic MCER SaDet

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ASCE 7-10: Two Methods for Probabilistic MCER

Method 2 (Exact) in Sect. 21.2.1.2

• Use “Risk Integral” Equation

• Required for foreign sites

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Probabilistic MCER

“Risk Integral”

where

• Pf = 1% probability collapse in 50 yrs

• P(a) = probability of exceeding spectral acceleration in 50 yrs

• Pf (a) = probability of collapse given spectral acceleration

Pf = P(a) dadPf (a)

da

∞∫0

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Probabilistic MCER

“Risk Integral”

“Fragility Function”(log normal distribution)

stand. dev., β = 0.6

“Hazard Curve”From PSHA

Pf = P(a) dadPf (a)

da

∞∫0

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Probabilistic MCER (Actual Calc.)

“Risk Integral” becomes:

“Fragility Function”(log normal distribution)

stand. dev., β = 0.6

“Hazard Curve” From PSHA(Annual Exceedance Freq.)

Hf = H(a) dadPf (a)

da

a2

∫a1

AnnualCollapse Freq.

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Calculation of aMCERis Iterative

• Assume aMCER= 2475-yr a

• Compute Hf

• Adjust aMCER↑ or ↓

• Repeat until Hf ≈ 0.000201

• Convert aMCERfrom geomean to max. direction

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Method 1 (Approx.) in Sect. 21.2.1.1

• Compute 2% in 50 yr Sa from PSHA

• Convert from geomean to max direction motion

• Multiply by risk coefficients, CR(T)

CRS & CR1 from USGS web site (detailed report)

ASCE 7-10: Two Methods for Probabilistic MCER

CR =aMCER

from Method 2

2475-yr a

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Deterministic MCER

1. Identify Controlling Faults

2. Postulate MMAX for each Fault

3. Use same GMPE’s & weights in PSHA

84th PercentileSa(T)

“median + 1σ”

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Example: MMAX for SAF

• MMAX = weighted average MMAX for each fault –rupture scenario

• Use USGS MMAX assigned for its Deterministic MCER

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Selection on MMAX (“Characteristic Earthquake”)San Andreas Fault

Source: Time Life Books

Highly Unlikely

M 8.5 (??)

Less Likely?

M 8 (1525?)

Likely

M 7.8 (1857)

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Uncertainty in MMAX for Given Rupture Scenario

Source: Hanks & Bakun (2008)C.B. Crouse 2013

Deterministic MCER

Use Envelop Sa

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Deterministic MCER

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Site-Specific MCER SaM

SaM = min[SaProb (T), Sa

Det (T)]

Sa = SaM ≥ 0.8 x Sa

Design Response Spectrum (Sect. 21.3)

Figure 11.4-1 (Sect. 11.4.5)

23

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Clarification

• Site-Specific Sa from Sect. 21.3 used to computeR.S. and R.H. earthquake loads

• SDS & SD1 from Sect. 21.4 are for determining Seismic Design Category, forces on non-structural components and ELF analysis.

C.B. Crouse 2013