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Shake Table - Seismic - Scaling

Shake Table - Seismic - Scaling

Shake Table - Seismic - Scaling

Hello Engineers

Consider a uniaxial, horizontal motion, small scale shake table used to evaluate seismic retaining wall stability (sliding and overturning); comparing resultant horiz displacements for various accelerations and durations using simplified sinusoidal input motion.

1:12 scale – similar to Chopra’s classroom shake table, using welded steel plates with a 10 inch tall plate to represent a 10 ft tall concrete wall (“inverted tee” cantilever wall).
The model backfill is compacted moist sand (wc ~ 5% to 10%, sieve #10 to #40). That is, the steel weldment is placed over a small bed of sand, then manually backfilled.

The bed dimensions: 20" wide x 20" long x 12" tall
Actuation is via a high power, high torque servo motor with control time step increments to 1/1000 second.

Here's the Question: Can you point me to references on how to scale sample recorded free field ground motion, so it is meaningful and realistic for a 1:12 scaled model for displacement and acceleration.

Sample ground motion: The 1940 El Centro max ground displacement = 8.12 inches, with max ground acceleration = 0.319g for that textbook event.

Scaled Model Peak Displacement (amplitude): Scaling down by a factor = 1 / 12 (that is, peak amplitude = 0.677 inches, normalized for sinusoidal motion),
Scaled Model Peak Acceleration: No scaling (that is, equivalent peak acceleration = 0.319g, normalized for sinusoidal motion), which means the frequency would have to increase by the root to maintain the target acceleration

Does the scaling sound right? I'm sure many universities have done this many times. Inviting comments and criticism.

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