🤙🏼Earthquake Engineering Unit 2 – Seismic Hazard Analysis: Probabilistic Methods

Key Concepts and Terminology

• Seismic hazard analysis assesses the probability and severity of earthquake-related hazards at a specific site or region
• Probabilistic Seismic Hazard Analysis (PSHA) is a widely used framework that incorporates uncertainties in earthquake occurrence, location, and magnitude
• Seismic source characterization identifies and models potential earthquake sources, including faults and seismic zones
• Ground motion prediction equations (GMPEs) estimate the intensity of ground shaking at a given distance from the earthquake source
  • GMPEs consider factors such as magnitude, distance, site conditions, and tectonic setting
• Aleatory variability represents the inherent randomness in earthquake processes, while epistemic uncertainty arises from incomplete knowledge and modeling limitations
• Hazard curves depict the annual probability of exceeding various levels of ground motion intensity at a specific site
• Uniform hazard spectra (UHS) provide the expected ground motion levels across a range of periods for a given probability of exceedance

Historical Context and Development

• Early seismic hazard assessment methods relied on deterministic approaches, focusing on worst-case scenarios
• Probabilistic methods emerged in the 1960s and 1970s, recognizing the inherent uncertainties in earthquake processes
• Cornell (1968) introduced the concept of PSHA, which became the foundation for modern seismic hazard analysis
• Advances in seismology, geology, and computational capabilities have refined PSHA methodologies over time
• Notable developments include the incorporation of time-dependent models, consideration of multiple seismic sources, and improved ground motion prediction equations
• Regulatory agencies and building codes have increasingly adopted PSHA for seismic design and risk assessment purposes

Probabilistic Seismic Hazard Analysis (PSHA) Framework

• PSHA aims to quantify the probability of exceeding various levels of ground motion intensity at a specific site
• The framework integrates information from seismic source characterization, ground motion prediction equations, and probability theory
• Key steps in PSHA include:
  1. Identifying and characterizing seismic sources
  2. Developing magnitude-frequency relationships for each source
  3. Selecting appropriate ground motion prediction equations
  4. Calculating the probability of exceeding ground motion levels for each source
  5. Aggregating the contributions from all sources to obtain the total hazard
• PSHA results are typically presented as hazard curves and uniform hazard spectra
• The framework allows for the explicit treatment of uncertainties and provides a consistent basis for risk-informed decision-making

Seismic Source Characterization

• Seismic source characterization involves identifying and modeling potential earthquake sources that can affect a site
• Sources can be categorized as point sources (e.g., individual faults) or area sources (e.g., seismic zones)
• Geological and seismological data are used to determine source geometry, maximum magnitude, and recurrence rates
• Fault-specific source models consider the geometry, slip rate, and rupture characteristics of individual faults
• Area source models define seismicity rates and magnitude distributions for regions with diffuse or poorly understood seismicity
• Seismic source characterization accounts for the spatial and temporal distribution of earthquakes
• Uncertainty in source parameters is incorporated through logic trees or Monte Carlo simulations

Ground Motion Prediction Equations

• Ground motion prediction equations (GMPEs) estimate the intensity of ground shaking at a given distance from the earthquake source
• GMPEs are empirically derived from strong motion data and consider factors such as magnitude, distance, site conditions, and tectonic setting
• Commonly used intensity measures include peak ground acceleration (PGA), peak ground velocity (PGV), and spectral acceleration (SA) at various periods
• GMPEs are developed for different regions and tectonic environments to capture regional variations in ground motion characteristics
• The selection of appropriate GMPEs is crucial for accurate hazard assessment and depends on the availability and applicability of regional data
• Uncertainty in GMPEs is accounted for by considering alternative models or using a logic tree approach

Uncertainty and Variability in PSHA

• PSHA explicitly addresses uncertainties in earthquake occurrence, location, magnitude, and ground motion prediction
• Aleatory variability represents the inherent randomness in earthquake processes and is typically modeled using probability distributions
  • Examples of aleatory variability include the scatter in ground motion data and the random nature of earthquake occurrence
• Epistemic uncertainty arises from incomplete knowledge and modeling limitations
  • Sources of epistemic uncertainty include seismic source characterization, choice of GMPEs, and parameter estimation
• Logic trees are commonly used to capture epistemic uncertainty by considering alternative models and parameter values
• Sensitivity analyses help identify the relative contributions of different sources of uncertainty to the overall hazard
• Proper treatment of uncertainties is essential for informed decision-making and risk assessment

Hazard Curves and Uniform Hazard Spectra

• Hazard curves represent the annual probability of exceeding various levels of ground motion intensity at a specific site
• Hazard curves are derived by integrating the contributions from all seismic sources and considering the associated uncertainties
• Uniform hazard spectra (UHS) provide the expected ground motion levels across a range of periods for a given probability of exceedance
  • UHS are constructed by interpolating hazard curves at different periods to obtain a consistent probability level
• Hazard curves and UHS are essential outputs of PSHA and serve as inputs for seismic design and risk assessment
• The shape of hazard curves and UHS can vary depending on the seismic environment, site conditions, and probability level considered
• Deaggregation of hazard curves helps identify the dominant earthquake scenarios contributing to the hazard at a specific site

Applications in Earthquake Engineering

• PSHA results are widely used in earthquake engineering for seismic design, risk assessment, and decision-making
• Building codes and design standards often specify seismic design loads based on PSHA-derived hazard levels (e.g., 2% probability of exceedance in 50 years)
• PSHA informs the development of site-specific design spectra for critical infrastructure and high-consequence facilities
• Seismic risk assessment combines PSHA results with vulnerability and exposure data to estimate potential losses and consequences
• PSHA is used in the development of seismic hazard maps, which guide land-use planning and emergency response strategies
• Insurance and reinsurance industries rely on PSHA for pricing and managing earthquake risk
• PSHA also supports the prioritization of seismic retrofitting and risk mitigation efforts

Limitations and Future Directions

• PSHA relies on assumptions and simplifications, such as the Poissonian occurrence of earthquakes and the ergodic assumption in GMPEs
• The treatment of uncertainties, particularly epistemic uncertainties, remains a challenge and requires careful consideration
• The availability and quality of seismological and geological data can limit the accuracy of PSHA in some regions
• Time-dependent models, which account for the temporal variation of earthquake occurrence rates, are an active area of research
• Incorporation of physics-based simulations and advanced ground motion models can improve the realism and accuracy of PSHA
• Integration of PSHA with other hazards (e.g., tsunamis, liquefaction) and multi-hazard risk assessment is an emerging trend
• Continued research efforts aim to refine PSHA methodologies, reduce uncertainties, and enhance the reliability of seismic hazard estimates for informed decision-making