Seismic hazard analysis is crucial for understanding earthquake risks. It involves creating hazard curves that show the likelihood of different ground motion intensities. These curves help engineers and planners make informed decisions about building design and safety measures.

Uniform hazard spectra take this analysis further by showing equal-probability ground motions across different frequencies. This tool is invaluable for seismic design, risk assessment, and infrastructure planning. It helps create safer buildings and more resilient communities in earthquake-prone areas.

Seismic Hazard Analysis

Construction of seismic hazard curves

• Probabilistic Seismic Hazard Analysis (PSHA) identifies seismic sources characterizes earthquake magnitude-recurrence relationships uses ground motion prediction equations (GMPEs)
• Annual exceedance probability calculation applies total probability theorem integrates over all possible earthquake scenarios
• Hazard curve components plot ground motion intensity measure (PGA, spectral acceleration) against annual probability of exceedance
• Curve generation process discretizes ground motion levels computes exceedance probabilities for each level
• Consideration of uncertainties accounts for aleatory variability in ground motion prediction and epistemic uncertainty in seismic source characterization

Interpretation of hazard curves

• Return period concept inverse of annual exceedance probability (Return Period = 1 / Annual Exceedance Probability)
• Reading hazard curves identifies ground motion level for a given annual probability interpolates between data points
• Common return periods in seismic design include 475 years (10% probability of exceedance in 50 years) and 2,475 years (2% probability of exceedance in 50 years)
• Conversion between probabilities and return periods uses equation $P = 1 - e^{-t/T}$ where P is probability of exceedance, t is time period of interest, T is return period

Uniform Hazard Spectra and Applications

Generation of uniform hazard spectra

• Uniform Hazard Spectrum (UHS) represents spectral accelerations with equal probability of exceedance across all periods
• UHS construction process:
  1. Generate hazard curves for multiple spectral periods
  2. Select target annual exceedance probability
  3. Extract spectral accelerations at target probability for each period
• UHS representation plots spectral period against spectral acceleration
• Comparison with deterministic spectra contrasts scenario-based vs probabilistic approach
• Limitations of UHS include conservative nature at longer return periods potential overestimation of spectral ordinates

Application in seismic design

• Seismic design applications select design ground motions determine seismic design parameters ($S_DS$, $S_D1$) implement performance-based design approaches
• Risk assessment utilization develops fragility curves estimates annual probability of structural failure conducts cost-benefit analysis for retrofit decisions
• Code-based design implementation integrates hazard information into building codes establishes site-specific hazard analysis requirements
• Infrastructure planning and resilience assesses lifeline systems risk maps regional seismic risk
• Scenario-based vs probabilistic risk assessment weighs advantages and limitations of each approach selects appropriate method based on project requirements (dam safety, nuclear power plants)