🤙🏼Earthquake Engineering Unit 3 – Earthquake Ground Motion and Site Effects

Key Concepts and Terminology

• Seismic waves are elastic waves generated by an earthquake or explosion that propagate through the Earth's crust and interior
• Body waves travel through the Earth's interior and include P-waves (primary or compressional waves) and S-waves (secondary or shear waves)
  • P-waves are longitudinal waves that compress and expand the material they pass through
  • S-waves are transverse waves that cause the material to oscillate perpendicular to the direction of wave propagation
• Surface waves travel along the Earth's surface and include Rayleigh waves and Love waves
  • Rayleigh waves cause the ground to move in an elliptical motion, with both vertical and horizontal components
  • Love waves cause the ground to move side-to-side, perpendicular to the direction of wave propagation
• Seismic hazard is the probability of experiencing a certain level of ground shaking or other seismic effects at a given location within a specified time period
• Peak Ground Acceleration (PGA) is the maximum acceleration experienced by a particle on the ground during an earthquake, typically expressed as a fraction or percentage of the acceleration due to gravity (g)
• Spectral acceleration (SA) is a measure of the maximum acceleration experienced by a single-degree-of-freedom oscillator with a specific natural period and damping ratio when subjected to an earthquake ground motion
• Site effects refer to the influence of local soil and geological conditions on the amplitude, frequency content, and duration of earthquake ground motions

Seismic Wave Propagation

• Seismic waves are generated by the sudden release of energy during an earthquake, which causes the Earth's crust to vibrate and transmit energy in the form of waves
• The speed of seismic waves depends on the elastic properties and density of the material they travel through, with P-waves being faster than S-waves
• Seismic wave attenuation is the decrease in wave amplitude as the waves propagate through the Earth due to geometrical spreading, intrinsic absorption, and scattering
• Seismic wave dispersion occurs when waves of different frequencies travel at different speeds, leading to the separation of the wave packet over time
• Seismic wave reflection and refraction occur when waves encounter boundaries between materials with different elastic properties, causing the waves to change direction and partition energy
• Seismic wave interference can result in the amplification or attenuation of ground motion at specific locations due to the constructive or destructive superposition of waves
• The frequency content of seismic waves is influenced by the size and mechanism of the earthquake, as well as the properties of the medium through which the waves propagate
  • Larger earthquakes tend to generate more low-frequency content, while smaller earthquakes have more high-frequency content

Ground Motion Parameters

• Ground motion parameters are used to characterize the intensity, frequency content, and duration of earthquake ground shaking at a given location
• Peak Ground Acceleration (PGA) is the maximum acceleration experienced by a particle on the ground during an earthquake, and is an important parameter for seismic design
• Peak Ground Velocity (PGV) is the maximum velocity experienced by a particle on the ground during an earthquake, and is related to the potential for damage to structures and infrastructure
• Peak Ground Displacement (PGD) is the maximum displacement experienced by a particle on the ground during an earthquake, and is relevant for the design of long-period structures and geotechnical systems
• Spectral acceleration (SA) is a measure of the maximum acceleration experienced by a single-degree-of-freedom oscillator with a specific natural period and damping ratio when subjected to an earthquake ground motion
  • SA is often used to characterize the frequency content of ground motion and to develop design response spectra for structures
• Arias Intensity (AI) is a measure of the total energy of an earthquake ground motion, calculated by integrating the squared acceleration over the duration of the motion
• Cumulative Absolute Velocity (CAV) is another measure of the energy content of an earthquake ground motion, calculated by integrating the absolute value of the velocity over the duration of the motion
• Duration parameters, such as the significant duration (e.g., $D_{5-95}$), characterize the time over which a certain percentage of the total energy of the ground motion is accumulated

Site Classification and Soil Effects

• Site classification is the process of categorizing a location based on the properties of the near-surface soil and rock, which can significantly influence the amplitude, frequency content, and duration of earthquake ground motions
• The National Earthquake Hazards Reduction Program (NEHRP) site classification system is widely used in the United States and is based on the average shear wave velocity of the top 30 meters of soil ($V_{s30}$)
  • NEHRP site classes range from A (hard rock) to F (soils requiring site-specific evaluation)
• Soil amplification occurs when the seismic waves propagating through the soil column are amplified due to the contrast in impedance between the soil and the underlying bedrock
  • Soft soils (e.g., NEHRP site class E) tend to amplify ground motions more than stiff soils or rock
• Soil resonance can occur when the natural period of the soil column coincides with the predominant period of the earthquake ground motion, leading to significant amplification of the motion
• Soil nonlinearity can result in the reduction of soil stiffness and the increase of damping during strong ground shaking, which can limit the amount of amplification that occurs
• Liquefaction is a phenomenon in which saturated, loose granular soils lose strength and stiffness during strong ground shaking, behaving like a liquid and potentially causing significant damage to structures and infrastructure
• Landslides and other forms of ground failure can be triggered by earthquake ground shaking, particularly in areas with steep slopes or weak soil conditions
• Basin effects can cause the amplification and prolongation of ground motions in sedimentary basins due to the trapping and reverberation of seismic waves within the basin

Seismic Hazard Analysis

• Seismic hazard analysis is the process of quantifying the probability of exceeding a certain level of ground motion or other seismic effects at a given location within a specified time period
• Deterministic Seismic Hazard Analysis (DSHA) involves the estimation of ground motion parameters based on a single earthquake scenario, typically the maximum credible earthquake for a given seismic source
• Probabilistic Seismic Hazard Analysis (PSHA) accounts for the contributions of all potential earthquake sources and magnitudes, as well as their associated uncertainties, to provide a probabilistic estimate of the ground motion hazard
  • PSHA results are often expressed as hazard curves, which show the annual probability of exceedance for different levels of ground motion parameters
• Seismic source characterization involves the identification and modeling of potential earthquake sources, including faults and seismogenic zones, and the estimation of their geometry, maximum magnitude, and recurrence rates
• Ground Motion Prediction Equations (GMPEs) are empirical models used to estimate the ground motion parameters at a given site as a function of earthquake magnitude, source-to-site distance, and other relevant factors
• Logic trees are used in PSHA to capture the epistemic uncertainty in seismic source characterization and ground motion modeling by considering multiple alternative models and assigning them weights based on their relative credibility
• Deaggregation is the process of determining the relative contributions of different earthquake scenarios (magnitude-distance pairs) to the total seismic hazard at a given site and ground motion level
• Risk-targeted ground motions (e.g., $S_{a,RT}$) are seismic design parameters that correspond to a specified probability of structural collapse, taking into account the uncertainties in both the seismic hazard and the structural response

Ground Motion Prediction Equations

• Ground Motion Prediction Equations (GMPEs), also known as attenuation relationships, are empirical models used to estimate the ground motion parameters at a given site as a function of earthquake magnitude, source-to-site distance, and other relevant factors
• GMPEs are developed using regression analysis of recorded strong ground motion data from past earthquakes, considering factors such as magnitude, distance, site conditions, and tectonic setting
• The functional form of GMPEs typically includes terms for the earthquake source (e.g., magnitude), path (e.g., distance and attenuation), and site (e.g., soil conditions and basin effects)
  • Example: $\ln(Y) = a + bM + cln(R + d) + eF + fS + \epsilon$, where $Y$ is the ground motion parameter, $M$ is the magnitude, $R$ is the distance, $F$ is a fault mechanism term, $S$ is a site term, and $\epsilon$ is a random error term
• GMPEs are region-specific and are developed for different tectonic settings (e.g., active shallow crustal regions, subduction zones, and stable continental regions) to capture the unique characteristics of each region
• The selection of appropriate GMPEs for a given seismic hazard analysis is critical and should consider factors such as the tectonic setting, data availability, and the specific requirements of the project
• GMPEs are continuously updated and improved as new strong ground motion data becomes available and as our understanding of earthquake source, path, and site effects advances
• The uncertainties in GMPE predictions are typically characterized by the standard deviation of the residuals between the observed and predicted ground motions, which can be decomposed into between-event and within-event components
• Ground motion models for specific intensity measures (e.g., Arias Intensity, Cumulative Absolute Velocity) have also been developed to capture the effects of ground motion duration and energy content on structural response and damage

Site Response Analysis

• Site response analysis is the process of evaluating the influence of local soil conditions on earthquake ground motions, accounting for the propagation of seismic waves through the soil column and the potential for soil amplification, resonance, and nonlinearity
• Equivalent linear site response analysis is a simplified method that approximates the nonlinear soil behavior using strain-compatible soil properties (shear modulus and damping) derived from iterative linear analyses
  • Example: SHAKE91 is a widely used equivalent linear site response analysis software
• Nonlinear site response analysis explicitly models the nonlinear stress-strain behavior of soils using constitutive models and numerical integration techniques (e.g., finite differences or finite elements)
  • Example: DEEPSOIL is a nonlinear site response analysis software that uses a modified hyperbolic soil model and the Masing rules for unloading-reloading behavior
• The input for site response analysis includes the soil profile (layer thicknesses, densities, shear wave velocities, and nonlinear soil properties), the input bedrock motion, and the groundwater table depth
• The output of site response analysis includes the acceleration time histories, response spectra, and amplification factors at various depths within the soil profile
• One-dimensional (1D) site response analysis assumes that the soil layers are horizontally stratified and that the response is dominated by vertically propagating shear waves, while two-dimensional (2D) and three-dimensional (3D) analyses can capture more complex geometries and wave propagation effects
• The selection of input ground motions for site response analysis should consider factors such as the seismic hazard at the bedrock level, the target response spectrum, and the number and duration of motions required for a reliable analysis
• The uncertainties in site response analysis can be addressed through the use of randomized soil profiles, multiple input ground motions, and Monte Carlo simulations to quantify the variability in the predicted surface ground motions
• The results of site response analysis can be used to develop site-specific design spectra, to evaluate the potential for soil liquefaction and ground failure, and to assess the seismic performance of structures and infrastructure

Practical Applications and Case Studies

• Seismic hazard maps are developed by government agencies and research institutions to provide a spatial representation of the expected ground motion levels for different probabilities of exceedance, and are used for seismic design, risk assessment, and emergency planning
  • Example: The United States Geological Survey (USGS) National Seismic Hazard Maps display the PGA and SA values for various return periods across the country
• Seismic design codes and guidelines, such as the International Building Code (IBC) and the ASCE 7 standard, use seismic hazard information and site classification to specify the design ground motions and requirements for structures in different regions and site conditions
• Performance-based earthquake engineering (PBEE) is a framework that uses probabilistic seismic hazard analysis, site response analysis, and structural modeling to assess the seismic performance of structures and infrastructure in terms of decision variables (e.g., repair costs, downtime) that are meaningful to stakeholders
• Seismic risk assessment studies combine seismic hazard information with exposure and vulnerability data to quantify the potential losses (e.g., economic losses, casualties) from future earthquakes, and are used to inform risk reduction strategies and insurance pricing
  • Example: The Global Earthquake Model (GEM) is an international collaborative effort to develop open-source tools and datasets for seismic risk assessment worldwide
• Rapid post-earthquake damage assessment and early warning systems rely on real-time ground motion data and empirical fragility functions to estimate the extent and severity of damage in the immediate aftermath of an earthquake, enabling faster emergency response and recovery efforts
• Seismic microzonation studies provide a detailed assessment of the seismic hazard and site effects at a local scale (e.g., city or neighborhood level), considering factors such as soil conditions, topography, and basin effects, and are used for urban planning and risk mitigation
• Case studies of past earthquakes, such as the 1989 Loma Prieta earthquake in California, the 1995 Kobe earthquake in Japan, and the 2010 Haiti earthquake, provide valuable insights into the impacts of ground motion and site effects on structures and communities, and inform the development of improved seismic design and risk reduction strategies