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**Ground Motions Geotechnical Earthquake Engineering: Steve Kramer**

Department of Civil and Environmental Engineering University of Washington Seattle, WA

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**All are becoming more common**

Ground Motions PSHA (or DSHA) provides uniform hazard spectrum Codes generally produce design spectrum For linear structural analysis, response spectrum is all you need – no need for individual ground motions For nonlinear analyses time histories are required Nonlinear structural analyses Nonlinear geotechnical analyses Nonlinear SSI analyses All are becoming more common Goal is to identify / create one or more motions that have amplitudes, frequency contents, and durations that are consistent with the ground shaking hazard at the site of interest.

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**Ground Motions Sources:**

PEER NGA Database (http://peer.berkeley.edu/nga/)

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**Ground Motions Sources:**

PEER NGA Database (http://peer.berkeley.edu/nga/search.html) Can search for records with characteristics similar to those controlling hazard at site of interest

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**Ground Motions http://db.cosmos-eq.org/scripts/search.plx Sources:**

COSMOS Database Can search for records with characteristics similar to those controlling hazard at site of interest

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Ground Motions Problem: Find ground motion(s) that “match” target spectrum Two common approaches: Simulation – single spectrum-compatible ground motion Scaling – suite of motions with matching ensemble average Required information: Target spectrum Uniform hazard spectrum (UHS) Code spectrum Fundamental period of structure Intent of analyses for which motions are to be used Mean or median response Mean / median and indication of variability of response Sa T To

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**Ground Motion Scaling Simulation**

Alter characteristics of motion to “match” target spectrum Two common approaches: Time domain – wavelets (actually, time and frequency domains) Example: RSPMATCH (Norm Abrahamson) Frequency domain – Fourier analysis Example: RASCAL (Walt Silva) Both approaches start with some initial ground motion Important that initial motion has “correct” duration Spectrum-compatible motions are useful for determining the mean or median response of a system. They do not provide direct insight into the variability of that response.

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**Ground Motion Scaling Simulation Example: Spectrum after matching**

Initial motion too strong Initial motion too weak After Norm Abrahamson COSMOS workshop presentation

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**Ground Motion Scaling Original Modified Simulation Example:**

After Norm Abrahamson COSMOS workshop presentation

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**Ground Motion Scaling Original Modified Simulation Example:**

After Norm Abrahamson COSMOS workshop presentation

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**Ground Motion Scaling Original Modified Simulation Example:**

After Norm Abrahamson COSMOS workshop presentation

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**Ground Motion Scaling Simulation Example:**

After Norm Abrahamson COSMOS workshop presentation

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Ground Motion Scaling Simulation Example: Note: In areas where seismic hazards come from multiple sources, different parts of UHS may be controlled by different sources – single motion producing entire UHS may not be physically possible. In that case, use of spectrum-compatible motion may be quite conservative. After Norm Abrahamson COSMOS workshop presentation

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**Ground Motion Scaling Scaling**

Alternatively, we can identify and scale actual recorded motions for (ensemble average) consistency with a target spectrum Use deaggregation to find representative (mean / modal) values of: Magnitude Distance Style of faulting Select consistent motions from database (e.g. PEER NGA database) based on seismological properties Similar magnitude (within +/- 0.5 provides reasonable duration) Similar distance range Similar spectral shape (or epsilon) Same style of faulting Candidate motions should be consistent with these characteristics

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**Ground Motion Scaling Scaling**

Scale motions by constant factor to “match” target spectrum What constitutes a match? Match is in average sense – average of suite of motions May be defined in terms of SRSS spectra (multi-directional components) Usually need to exceed target over significant period range For structures, typically 0.2To – 1.5To Lower periods (higher frequencies) covers higher mode response Higher periods (lower frequencies) covers damage-induced softening

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**Significant period range**

Ground Motion Scaling Scaling Select large suite of ground motions (50 – 100 or so) Use deaggregation to find representative (mean / modal) values of: Magnitude Distance Style of faulting Select consistent motions from database (e.g. PEER NGA database) based on seismological properties Similar magnitude (within +/- 0.5 provides reasonable duration) Similar distance range Similar spectral shape (or epsilon) Same style of faulting Significant period range

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**Ground Motion Scaling Epsilon Scaled negative e motion is too strong**

Be careful – look for local peaks and valleys in candidate motions prior to scaling Scaled positive e motion is too weak

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**Ground Motion Scaling Epsilon**

Baker (2007) took 382 representative ground motions Computed e values for each, chose 20 highest and 20 lowest Computed spectra after scaling to same Sa(T=0.8)

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**Hazard Analysis and Ground Motions**

Summary Design levels of ground motion determined by seismic hazard analysis DSHA – deterministic PSHA – probabilistic Attenuation behavior is critical Prediction of response spectrum may be sufficient Ground motions may be required Synthetic motions – describe mean/median level of shaking Scaled motions Reflect actual earthquake characteristics Suite of motion required – can account for record-to-record variability Results of site response analyses will be sensitive to ground motion inputs – need to pay careful attention to this issue

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1J. Baker Jack Baker Civil & Environmental Engineering Stanford University Ground motions for the PEER Transportation Systems Research Program.

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