Characterizing Earthquake Shaking:Ground Motion Parameters and the Acceleration Response SpectrumAcceleration Response Spectrum

Brady R. Cox, Ph.D., P.E.Brady R. Cox, Ph.D., P.E.The University of Arkansas

Department of Civil Engineering

Geotechnical Earthquake Engineering for Seismic Design Workshop,

Department of Civil Engineering

Port-au-Prince, Haiti, November 18-19, 2010

Good Reference for this Material

Earthquake Ground Motions

What is different about these ground motion records?Kramer (1996)

Earthquake Ground Motions are Described By:• Amplitude• Duration• Frequency Content

These Parameters are Influenced By:• Earthquake MagnitudeEarthquake Magnitude• Distance from the Site to the Fault

L l S il C diti ( k il)• Local Soil Conditions (rock versus soil)• Special effects (rupture directivity, topographic

effects, etc.)

Vibratory Motion

Kramer (1996)

Periodic Motion versus Nonperiodic Motion

Simple Harmonic MotionKramer (1996)T

A

A = amplitudeA amplitudeT = period = time to complete 1 cycle (sec) = 1/ff = frequency = cycles per second (Hz) = 1/T

Simple Harmonic Motion

A = 2f 2 Hf = 2 HzT = 1/f = 0.5 sec

A = 1f 5 Hf = 5 HzT = 1/f = 0.2 sec

Fourier Theory

Complicated motions (like earthquake ground motions) can be described

Kramer (1996)

p ( q g )as a summation of simple harmonic motions

Earthquake Amplitude Parameters

PGA

PGVPGV

PGD

Kramer (1996)Rock

Kramer (1996)Soil

Acceleration recordings from the 1989 Loma Prieta, California Earthquake; acceleration records integrated to obtain velocity and displacement

Acceleration Response SpectrumSaSa

T

Kramer (1996) PGA

Single Degree of Freedom (SDOF) oscillators(i.e. “buildings” with different heights/natural periods of vibration)

Natural Period (T) / Natural Frequency (f)T = 1/fT = 1/f

Structural Demands from Spectral AccelerationSa

Newton’s

Sa

LawF = m*aF m a

Ch (200 )

Equivalent Static Force = fso = m*Sa = W*Sa(g)

Chopra (2005)

q so (g)

Base Shear = Vbo = fso

Base Moment = fso * h

Spectral Accelerations (T = 0.5 sec)

Sa = 0 75 g S 0 60PGA PGA

Sa 0.75 g Sa = 0.60 g

T = 0.5 sec (~ 5 story building)

Input Acceleration Time Histories into SDOF oscillators (5% damping)

PGA 0 45 PGA 0 30

Rock Soil

PGA = 0.45 g PGA = 0.30 g

Kramer (1996)

Soil

Spectral Accelerations (T = 1.0 sec)

Sa = 0.30 g Sa = 0.40 g

T = 1.0 sec (~ 10 story building)

Input Acceleration Time Histories into SDOF oscillators (5% damping)

PGA 0 45 PGA 0 30

Rock Soil

PGA = 0.45 g PGA = 0.30 g

Kramer (1996)

Soil

Summary of Equivalent Static Forces

Sa = 0 75 g Sa = 0.60 gSa 0.75 gSa = 0.30 g

gSa = 0.40 g

Gilroy #1 (Rock) Gilroy #2 (Soil)~ 5 Story Building (T = 0.5 sec)Vbo = 0.75*Weight Building

~ 5 Story Building (T = 0.5 sec)Vbo = 0.60*Weight Building

~ 10 Story Building (T = 1.0 sec)V = 0 30*Weight Building

~ 10 Story Building (T = 1.0 sec)V = 0 40*Weight Building

Kramer (1996)

Vbo = 0.30 Weight Building Vbo = 0.40 Weight Building

Questions?Questions?