Fractional Tajimi–Kanai model for simulating earthquake ground motion

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are reached: (i) The viscoelastic behavior of the ground may be simply characterized by performing the creep (or the relaxation) test on a specimen of the ground at the given site; (ii) The number of zero crossing of the absolute acceleration at the free field that for the classical TK model is ∞ for a true white noise acceleration, remains finite for the proposed model.