🤙🏼Earthquake Engineering Unit 5 – Soil Dynamics and Structure Interaction

Key Concepts and Terminology

• Soil dynamics involves the study of soil behavior under dynamic loading conditions such as earthquakes, explosions, and machine vibrations
• Key soil properties influencing dynamic behavior include shear modulus, damping ratio, and Poisson's ratio
  • Shear modulus ($G$) represents the soil's resistance to shear deformation
  • Damping ratio ($\xi$) quantifies the soil's ability to dissipate energy during cyclic loading
  • Poisson's ratio ($\nu$) relates the soil's lateral and axial strains under loading
• Wave propagation in soils is characterized by body waves (P-waves and S-waves) and surface waves (Rayleigh waves and Love waves)
• Site response analysis evaluates the modification of seismic waves as they propagate through soil layers to the ground surface
• Soil-structure interaction (SSI) refers to the coupled response of soil and structure under dynamic loading, considering their mutual influence
• Dynamic soil models, such as equivalent linear and nonlinear models, are used to represent soil behavior under cyclic loading
• Analytical methods, like the substructure approach, and numerical methods, such as finite element analysis, are employed to solve SSI problems

Soil Properties and Behavior

• Soil is a complex, heterogeneous material composed of solid particles, water, and air
• The behavior of soil under dynamic loading is influenced by its composition, density, and stress history
• Strain-dependent properties, such as shear modulus and damping ratio, vary with the level of shear strain induced by dynamic loading
  • At small strains, soils exhibit linear elastic behavior with constant shear modulus and low damping
  • As strain levels increase, soils exhibit nonlinear behavior with reduced shear modulus and increased damping
• The shear wave velocity ($V_s$) is a key parameter characterizing the stiffness and dynamic response of soil
  • $V_s$ is related to the shear modulus and density of soil: $V_s = \sqrt{G/\rho}$
• Soil liquefaction is a phenomenon where saturated, loose granular soils lose strength and stiffness under cyclic loading, behaving like a liquid
• The cyclic stress ratio (CSR) and cyclic resistance ratio (CRR) are used to evaluate the liquefaction potential of soils
• The presence of groundwater and pore water pressure buildup significantly influences soil behavior under dynamic loading

Wave Propagation in Soils

• Seismic waves propagate through soil layers, undergoing refraction, reflection, and attenuation
• Body waves, including P-waves (compression waves) and S-waves (shear waves), travel through the interior of soil
  • P-waves are faster than S-waves and cause volumetric deformation
  • S-waves cause shear deformation and are more damaging to structures
• Surface waves, such as Rayleigh waves and Love waves, propagate along the ground surface
  • Rayleigh waves have both vertical and horizontal particle motion and decay exponentially with depth
  • Love waves have horizontal particle motion and are trapped in shallow soil layers
• The velocity of seismic waves in soil depends on the soil type, density, and stiffness
• Soil layering and impedance contrasts between layers can lead to wave amplification, focusing, or scattering
• Attenuation of seismic waves in soil is caused by geometric spreading, material damping, and scattering
• The predominant period of a soil deposit depends on its thickness and shear wave velocity profile

Site Response Analysis

• Site response analysis assesses the modification of seismic waves as they propagate through soil layers to the ground surface
• The objective is to determine the ground motion characteristics at the surface, considering the influence of local soil conditions
• One-dimensional (1D) site response analysis is commonly used, assuming horizontal soil layers and vertically propagating shear waves
• Equivalent linear analysis is a simplified approach that iteratively adjusts soil properties (shear modulus and damping) based on the induced strain level
• Nonlinear analysis directly models the nonlinear stress-strain behavior of soil using constitutive models (e.g., Mohr-Coulomb, Hardening Soil)
• Input motion for site response analysis is typically defined at the bedrock level, representing the seismic hazard at the site
• The output of site response analysis includes acceleration time histories, response spectra, and amplification factors at the ground surface
• Site effects, such as soil amplification and resonance, can significantly influence the characteristics of ground motion at the surface

Soil-Structure Interaction Basics

• Soil-structure interaction (SSI) refers to the coupled response of soil and structure under dynamic loading
• SSI considers the mutual influence between the soil and the structure, accounting for their stiffness, mass, and damping properties
• Inertial interaction occurs when the vibration of the structure induces dynamic forces and deformations in the surrounding soil
• Kinematic interaction results from the difference in ground motion between the free-field and the foundation level due to soil deformability and wave scattering
• Foundation type (shallow or deep) and soil conditions significantly influence the SSI effects
  • Shallow foundations (e.g., mats, spread footings) are more susceptible to rocking and sliding under dynamic loading
  • Deep foundations (e.g., piles, caissons) can provide lateral and vertical resistance, but may also be affected by kinematic interaction
• SSI can lead to changes in the natural frequencies, damping, and seismic response of the structure compared to a fixed-base assumption
• Neglecting SSI can result in an overestimation or underestimation of the structural response, depending on the relative stiffness of soil and structure

Dynamic Soil Models

• Dynamic soil models are used to represent the stress-strain behavior of soil under cyclic loading
• Equivalent linear models approximate nonlinear soil behavior using strain-dependent shear modulus and damping ratio
  • The shear modulus is reduced, and the damping ratio is increased as the strain level increases
  • Iterations are performed until the properties converge based on the induced strain level
• Nonlinear models directly capture the hysteretic stress-strain behavior of soil using constitutive relationships
  • Elastoplastic models (e.g., Mohr-Coulomb, Drucker-Prager) incorporate yield surfaces and plastic flow rules
  • Hyperbolic models (e.g., Kondner-Zelasko, Hardin-Drnevich) represent the nonlinear backbone curve and hysteretic damping
• Advanced constitutive models, such as the Hardening Soil model, consider the effects of stress history, dilatancy, and small-strain stiffness
• The selection of an appropriate soil model depends on the expected strain levels, soil type, and the desired level of accuracy and complexity
• Calibration of soil model parameters requires laboratory tests (e.g., cyclic triaxial, resonant column) or field measurements (e.g., seismic cone penetration test)

Analytical and Numerical Methods

• Analytical methods provide simplified solutions to SSI problems based on assumptions and idealized conditions
• The substructure approach decouples the SSI problem into separate analyses of the soil and the structure
  • The foundation input motion is determined by modifying the free-field motion considering kinematic interaction effects
  • The dynamic impedance functions represent the stiffness and damping of the soil-foundation system
  • The structure is analyzed using the foundation input motion and impedance functions as boundary conditions
• The direct method solves the coupled soil-structure system in a single step, considering the full interaction between soil and structure
• Numerical methods, such as the finite element method (FEM), are used to solve complex SSI problems with realistic geometry and material properties
  • FEM discretizes the soil and structure into elements connected at nodes, forming a mesh
  • The governing equations of motion are solved numerically, considering the compatibility and equilibrium conditions at the soil-structure interface
• Boundary element methods (BEM) are efficient for modeling unbounded soil domains, reducing the size of the numerical model
• Hybrid methods combine different approaches, such as FEM for the structure and BEM for the soil, to optimize computational efficiency and accuracy

Applications in Earthquake Engineering

• SSI analysis is crucial for the seismic design and assessment of structures, particularly those founded on soft soils or with massive foundations
• Nuclear power plants, high-rise buildings, and bridges are examples of structures where SSI effects can be significant
• Soil-foundation-structure interaction (SFSI) considers the combined effects of soil, foundation, and structure in a holistic manner
• Performance-based earthquake engineering (PBEE) frameworks incorporate SSI to evaluate the seismic performance of structures at different levels of ground motion intensity
• Seismic soil-pile interaction is important for the design of pile foundations in seismically active regions
  • Kinematic interaction can induce bending moments and shear forces in piles due to soil deformation
  • Inertial interaction can cause additional lateral loads on piles due to the vibration of the superstructure
• Soil-underground structure interaction is relevant for the seismic design of tunnels, pipelines, and buried structures
• SSI effects can influence the seismic response of retaining walls, quay walls, and other geotechnical structures
• Soil-foundation interaction plays a role in the seismic isolation and energy dissipation of structures using base isolation or damping devices