A detailed description of the non-linear effects in silicon is needed when designing ring resonators in the silicon platform. The optical field propagating in the ring waveguide is strongly absorbed due to two-photon-absorption (TPA) and free-carrier-absorption (FCA), which become more prominent with increasing the input power in the ring. We present a new approach for the modelling of non-linear effects in silicon based ring resonators. We have numerically solved the non-linear problem coupling the variation of refractive index and loss due to TPA, FCA , self-heating and Shockley-Read-Hall (SRH) theory for trap-assisted recombination process. The model is validated by reproducing experimental measurements on a ring and a racetrack resonator having different Q-factors and waveguide cross-sections. As a result, we show that the SRH recombination is the origin of the dependence of free carrier lifetime on the power circulating in the ring and how this dependence is affected by the surface trap density and trap energy level. The model is then applied to the calculation of the maximum power that can incident the silicon rings designed for the Si PIC mirror of a hybrid III-V/Si widely tunable laser.