Cnoidal wave theory is appropriate to periodic wave progressing in water whose depth is less than 1/10 wavelength. However, the cnoidal wave theory has not been widely applied in practical engineering because the formula for wave profile involves Jacobian elliptic function. In this paper, a cnoidal wave-seabed system is modeled and discussed in detail. The seabed is treated as porous medium and characterized by Biot's partly dymic equations (u-p model). A simple and useful calculating technique for Jacobian elliptic function is presented. Upon specification of water depth, wave height and wave period, Taylor's expression and precise integration method are used to estimate Jacobian elliptic function and cnoidal wave pressure. Based on the numerical results, the effects of cnoidal wave and seabed characteristics, such as water depth, wave height, wave period, permeability, elastic modulus, and degree of saturation, on the cnoidal wave-induced excess pore pressure and liquefaction phenomenon are studied.
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