Soil　nonlinear　behavior　displays　noticeable　effects　on　the　site　seismic　response.　This　study　proposes　a　new　functional　expression　of　the　skeleton　curve　to　replace　the　hyperbolic　skeleton　curve.　By　integrating　shear　modulus　and　combining　the　dynamic　skeleton　curve　and　the　damping　degradation　coefficient,　the　constitutive　equation　of　the　logarithmic　dynamic　skeleton　can　be　obtained,　which　considers　the　damping　effect　in　a　soil　dynamics　problem.　Based　on　the　finite　difference　method　and　the　multi-transmitting　boundary　condition,　a　1D　site　seismic　response　analysis　program　called　Soilresp1D　has　been　developed　herein　and　used　to　analyze　the　time-domain　seismic　response　in　three　types　of　sites.　At　the　same　time,　this　study　also　provides　numerical　simulation　results　based　on　the　hyperbolic　constitutive　model　and　the　equivalent　linear　method.　The　results　verify　the　rationality　of　the　new　soil　dynamic　constitutive　model.　It　can　analyze　the　mucky　soil　site　nonlinear　seismic　response,　reflecting　the　deformation　characteristics　and　damping　effect　of　the　silty　soil.　The　hysteresis　loop　area　is　more　extensive,　and　the　residual　strain　is　evident.