Centrifuge models of soft-clay deposits were shaken with suites of earthquake ground motions to study site response over a wide strain range. The models were constructed in an innovative hinged-plate container to effectively reproduce one-dimensional ground-response boundary conditions. Dense sensor arrays facilitate back-calculation of modulus-reduction and damping values that show modest misfits from empirical models. Low-amplitude base motions produced nearly elastic response in which ground motions were amplified through the soil column, and the fundamental site period was approximately 1.0 s. High-intensity base motions produced shear strains higher than 10%, mobilizing shear failure in clay at stresses larger than the undrained monotonic shear strength. The authors attribute these high mobilized stresses to rate effects, which should be considered in strength-parameter selection for nonlinear analysis. This nonlinear response deamplified short-period spectral accelerations and lengthened the site period to 3.0 s. The nonlinearity in spectral amplification is parameterized in a form used for site terms in ground-motion prediction equations to provide empirical constraint unavailable from ground-motion databases. © 2013 American Society of Civil Engineers.