The formation of near-wavelength laser-induced periodic surface structures (LIPSS) on silicon upon irradiation with sequences of Ti:sapphire femtosecond laser pulse pairs (pulse duration 150 fs, central wavelength 800 nm) is studied theoretically. For this purpose, the nonlinear generation of conduction band electrons in silicon and their relaxation is numerically calculated using a two-temperature model approach including intrapulse changes of optical properties, transport, diffusion and recombination effects. Following the idea that surface plasmon polaritons (SPP) can be excited when the material turns from semiconducting to metallic state, the "SPP active area" is calculated as function of fluence and double-pulse delay up to several picoseconds and compared to the experimentally observed rippled surface areas. Evidence is presented that multi-photon absorption explains the large increase of the rippled area for temporally overlapping pulses. For longer double-pulse delays, relevant relaxation processes are identified. The results demonstrate that femtosecond LIPSS on silicon are caused by the excitation of SPP and can be controlled by temporal pulse shaping.