Propagation of high amplitude acoustic pulses is studied in a 1D waveguide, connected to a lattice of Helmholtz resonators. An homogenized model has been proposed by Sugimoto (J. Fluid. Mech., 244 (1992)), taking into account both the nonlinear wave propagation and various mechanisms of dissipation. This model is extended to take into account two important features: resonators of different strengths and back-scattering effects. The new model is derived and is proved to satisfy an energy balance principle. A numerical method is developed and a better agreement between numerical and experimental results is obtained.