We use numerical simulations to study the resonant interaction of relativistic electrons with rising-frequency EMIC wave packets in the H band. We find that precipitation fluxes are formed by quasi-linear interaction and several nonlinear interaction regimes having opposite effects. In particular, the influence of Lorentz force on the particle phase (force bunching) decreases precipitation for particles with low equatorial pitch angles (up to 15-25), and can even block it completely. Four other nonlinear regimes are possible: nonlinear shift of the resonance point (can cause pitch angle drift in both directions); phase bunching (slightly increases pitch angle for untrapped particles); directed scattering (strongly decreases pitch angle for untrapped particles) and particle trapping by the wave field (decreases pitch angle). Equatorial pitch angle distribution evolution during several passes of particles through the wave packet is studied. The precipitation fluxes are evaluated and compared with theoretical estimates. We show that strong diffusion limit is maintained for a certain range of energies by a wave packet with realistic amplitude and frequency drift. In this case, the quasi-linear theory strongly underestimates the precipitated flux. With increasing energy, the precipitated fluxes decrease and become close to the quasi-linear estimates.