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99  b.g.s. Below ground surface [C] Damping matrix ci Viscous damping in layer i cE Viscous damping assigned to elastic half-space CSR Cyclic stress ratio (CSR = Ïco/Ïâ²v0) Dr Relative density f1 (and f2, f3, f4) Fundamental frequencies fs First mode frequency (1/Ts) fimax Maximum frequency that a layer can propagate G Secant shear modulus Gmax Maximum (i.e., low-strain) shear modulus Gmo Initial shear modulus = Gmax Gmt Shear modulus at time t Gso Initial secant modulus Gst Secant modulus at time t hi Thickness of layer I [K] Stiffness matrix k, ki element of stiffness matrix [M] Mass matrix m Element of mass matrix mi lumped mass of layer I t time OCR Over-consolidation ratio Ts First mode period (of soil deposit) Tp Predominant period (of strong-motion record) Timin Minimum period of the motion that layer i can propagate {u} Displacement vector of the single degree of freedom mass {ug} Displacement vector of the base relative to the single degree of freedom mass Vp Compression wave velocity Vs Shear wave velocity (Vs)avg Weighted-average shear wave velocity (as calculated by SHAKE) VSE Shear wave velocity of the half-space Vs30 Time-averaged shear wave velocity Vs over the upper 30 m (Vs)i Shear wave velocity of the layer i αR Rayleigh damping coefficient βR Rayleigh damping coefficient γ Shear strain γc Cyclic shear strain Abbreviations, Acronyms, Initialisms, and Symbols
100 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines γco The initial cyclic shear strain γct Cyclic shear strain at time t γtvp Volumetric threshold cyclic shear strain δ Degradation index (of soil) λ Wavelength ν Poissonâs ratio Ï Shear stress Ïco Initial cyclic shear stress Ïct Cyclic shear stress at time t Ïâ²v0 Initial vertical effective stress ξtar Target damping ratio Ï Mass density (of soil) 1D One dimensional 2D Two dimensional 3D Three dimensional BE Bender element BPT Becker penetration test CM Constitutive model CPT Cone penetration test CPTu Cone penetration test with pore water pressure measurement CyTX Cyclic triaxial (test) CyDSS Cyclic direct simple shear (test) CEUS Central and Eastern United States D Depth (below ground surface) Dw Depth of groundwater table .dll Dynamic link library DOT Department of transportation DS Dense sand EPRI Electric Power Research Institute ESA Effective-stress analysis Eq. Earthquake FDM Finite difference method FEM Finite element method FFT Fast Fourier transformation (algorithm) GLA Geo-Logic Associates, Inc. GMM Ground motion model (now used in lieu of GMPE) H Thickness of soil profile HSsmall Small strain hardening soil â total-stress constitutive model (implemented in PLAXIS) HVSR Horizontal to vertical spectral ratio LE-MC Linear-elastic MohrâCoulomb constitutive model LRFD Load and resistance factor design LS Loose sand LVDT Linear variable differential transformer M Moment magnitude (scale) MDS Medium-dense sand MKZ Matasovic-Kondner-Zelasko (constitutive model) MRD Modulus reduction and damping (curves) N/A Not applicable NEHRP National Earthquake Hazard Reduction Program NHI National Highway Institute
Abbreviations, Acronyms, Initialisms, and Symbols 101Â Â N1 SPT blow count corrected to an effective overburden stress of 1 atm (N1)60 SPT blow count corrected to 60% hammer energy ratio and an effective over burden stress of 1 atm (N1)60âCS Equivalent clean-sand corrected SPT blow count PGA Peak ground acceleration (usually reported at the ground surface) PI Plasticity index PM4SAND Pore water pressure model for sand (constitutive model) PWP Pore water pressure R Approximate site-to-source distance RC Resonant column (test) UDM User-defined model SASW Spectral analysis of surface waves sCPT Seismic cone penetration test SFSI Soil-foundation-structure interaction (the same as SSI: soil-structure interaction) SPT Standard penetration test SRA Site response analysis SSI Soil-structure interaction TI Treasure Island TSA Total stress analysis USCS Unified Soil Classification System UBCSAND University of British Columbia (constitutive model) UCSD3 University of California, San Diego (Constitutive Model No. 3) WEUS Western United States WHTL Washington Highway Test Laboratory WLA Wildlife Liquefaction Array