Seismic Analysis of Concrete Dams Workshop Session 7 · Seismic Analysis of Concrete Dams Workshop Session 7 Selection of Ground Motions to Represent Seismic Hazard Moderator Robert

Seismic Analysis of Concrete Dams

Workshop

Session 7

Selection of Ground Motions to Represent Seismic Hazard

ModeratorRobert Youngs

Amec Foster Wheeler Environment & Infrastructure2017 USSD Annual Conference

April 6-7, 2017

• Starting point is seismic hazard assessment providing either a Uniform Hazard Response Spectrum (UHS) or a deterministic Maximum Credible/Considered Earthquake (MCE) spectrum

• Assume that assessment has properly accounted for seismic sources, ground motion models, and site characteristics

• Discuss issues in developing ground motion time histories to represent the specified hazard in seismic response analyses

• What should the dam response analyst be asking for from the seismic hazard analyst?

Session #7 Selection of Ground Motions to Represent Seismic Hazard

Seismic Analysis of Concrete Dams Workshop2017 USSD Annual ConferenceApril 6-7, 2017

• What spectrum should be used for selection of time histories for either deterministic MCE cases or probabilistic UHS cases

• Representation of hazard by conditional mean spectra (CMS)

• How should CMS be developed to represent hazard for important period range(s)

• Representation of variability• Development of time histories –

Scaling versus spectral matching• Representation of multiple components of motion

Topics for Discussion


• It is a statistical representation of ground motions

• Does not represent motions from an individual earthquake

• Applies to • Deterministic MCE• UHS • CMS

Seismic Hazard Spectrum


Example for Deterministic MCE –

Recording from an individual earthquake is not at the same percentile at all periods


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M 6, R 15 kmNGAW2 16th%NGAW2 MedianNGAW2 84th%Recordings

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M 7, R 35 kmNGAW2 16th%NGAW2 MedianNGAW2 84th%Recordings

Example for UHS –

Contributions from different magnitudes and distances vary with period


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2500−yr UHSRecordings, M 6, R 15 kmRecordings,M 7, R 35 km

• CMS is an approach to break the hazard into underlying scenario ground motions

• Example for UHS with target period of T0 of 1.0s

• Identify earthquake scenario having greatest contribution to 1.0 s hazard

• Spectral acceleration at T0 is some number of standard deviations above median for scenario, ε(T0)

• Correlation in ground motion amplitudes at different periods is < 1, decreasing as difference in period from T0 increases.

• CMS represents the expect value of ε(T), given ε(T0) at T0

• Expected value of ε(T) decreases as T – T0 increases

• Typically applied to UHS in probabilistic cases

• Equally valid for deterministic MCE (e.g. 84th%)

Conditional Mean Spectra (CMS)


Baker and Cornell (2006a,b), Baker and Jayaram (2008)

• CMS is a simplification of the scenario ground motions

• Provides EXPECTED spectrum for specific scenario

• Variability about expected shape for scenario

• Contributions from other scenarios

Conditional Mean Spectra


How Many CMS?

Tradeoff between more specific scenarios and number of analyses


Source: Carlton and Abrahamson (2014)

• Limited by number of analyses that can be performed and understanding of what controls response/performance of structure

• How sensitive is structural response to variability in motions

• Variability in spectral shape• Presence of ground motion pulses• Component-to-component variability

How and Where to Address Individual Earthquake Motion Variability in Evaluating Structure Response


• Design – perhaps average response is objective• Limited set of scaled records (3-5) or one or more spectrally

matched records• Performance assessment for PBEE – probability of

satisfactory performance in response to specific earthquake scenario

• Larger set of scaled records (5-7), perhaps spectrally matched• Sets for each scenario if multiple scenarios are important

• Seismic risk assessment – probabilistic assessment of performance under a range of earthquake scenarios

• Larger sets of records for multiple loading levels and scenarios

• Difficult to capture variability in structural response with a limited number of input motions

Selection of Motions Should be Based on Objective of Analyses –What Level of Variability Should Be Included?


• Scaling a set of records selected based on earthquake properties – e.g. magnitude, distance, site characteristics

• Scaling a set of records selected based on earthquake properties and record characteristics – e.g. above plus spectra shape

• Loose spectral matching – modifying a set of records to better represent statistics of target CMS (perhaps including variability)

• Tight spectral matching – producing records that closely represent target

• Component-to-component variability partially maintained by matching both components of motion

Development of Time Histories


• Depends on objective of analysis• Use of small set of scaled records implies average

response goal• Two sets of records selected by different analysts targeting

the same CMS may produce significant differences in estimated average response.

• Tight spectral matching also suggests average response is goal

• Variability in response will still occur due to variability in seed motions

• Exploring behavior of structure might argue for large set of scaled records

• Incorporation of ground motion pulse records

Which Method Should Be Used?


Spectral Matching Can Retain Phasing of Recorded Motions


As Recorded Spectrally Matched

• Most ground motion prediction equations used in hazard assessment provide the geometric mean of horizontal components of motion

• Adjustments to maximum component, fault-normal, etc., usually obtained by scaling factors based on statistical analyses – again providing a statistical estimate of component differences

• Is capturing component-to-component variability important to response?

• Can it be represented by selected time histories (e.g. two components scaled so that their geometric mean matches target spectrum

Multiple Components of Motion


• Scale both horizontal components with a common factor to match on average the target CMS

• Preserves component-to-component variability

• Should vertical be scaled using the same factor or with a different factor to match expected vertical (vertical CMS)

Example of Two Component Scaling to Geometric Mean Target Spectrum


• Separate hazard assessment using vertical GMPEs• For PSHA, the result would likely be different controlling

earthquakes for the horizontal and vertical components

• Use of vertical-to-horizontal spectral rations (V/H)• Provides vertical component for earthquake scenarios

controlling horizontal hazard• Issue of correlation of V/H ratios with horizontal motions –

residuals in V/H are negatively correlated with horizontal motion residuals

Vertical Component


1. Compute median V/H for dominant scenario at each period, use median V/Hs to scale UHS – best if vertical hazard is of primary interest

2. Compute median V/H for scenario used for horizontal CMS, use to scale horizontal CMS

3. Develop vertical CMS using scenario used for horizontal CMS, use to scale horizontal CMS – best if horizontal response of primary interest as it accounts for negative correlation between V/H and horizontal epsilons

Vertical Component Alternatives


Gülerce, Z., and Abrahamson (2011)

References


Baker, J.W., and Cornell, C.A., 2006a. Spectral shape, epsilon and record selection: Earthquake Engineering & Structural Dynamics, v. 35, no. 9. pp. 1077‐1095.Baker, J.W., and Cornell, C.A., 2006b. Correlation of response spectral values for multicomponent ground motions: Bulletin of the Seismological Society of America, v. 96, no. 1, pp. 215‐227.Baker, J., and Jayaram, N., 2008. Correlation of spectral acceleration values from NGA ground motion models: Earthquake Spectra, v. 24, pp. 299‐317.Carlton, B., and Abrahamson, N., 2014. Issues and approaches for implementing conditional mean spectra in practice: Bulletin of the Seismological Society of America, v. 104, pp. 503‐512.Gülerce, Z., and Abrahamson, N.A., 2011. Site‐specific design spectra for vertical ground motions. Earthquake Spectra, v. 27, no. 4, pp. 1023‐1047.

Bi-directional ground motions

Anil K. Chopra

USSD Workshop on Concrete DamsAnaheim, California

April 6-7, 2017

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State of practice: Tx close to Ty

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State of practice: Tx far from Ty

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CMS-UHS Composite Spectrum

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CMS-UHS Composite Spectrum

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Seismic Analysis of Concrete Dams Workshop Session 7 · Seismic Analysis of Concrete Dams Workshop Session 7 Selection of Ground Motions to Represent Seismic Hazard Moderator Robert