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The new version (incl4.6) of the Li\`ege intranuclear cascade (INC) model for the description of spallation reactions is presented in detail. Compared to the standard version (incl4.2), it incorporates several new features, the most important of which are: (i) the inclusion of cluster production through a dynamical phase space coalescence model, (ii) the Coulomb deflection for entering and outgoing charged particles, (iii) the improvement of the treatment of Pauli blocking and of soft collisions, (iv) the introduction of experimental threshold values for the emission of particles, (v) the improvement of pion dynamics, (vi) a detailed procedure for the treatment of light-cluster-induced reactions taking care of the effects of binding energy of the nucleons inside the incident cluster and of the possible fusion reaction at low energy. Performances of the new model concerning nucleon-induced reactions are illustrated by a comparison with experimental data covering total reaction cross sections, neutron, proton, pion, and composite double-differential cross-sections, neutron multiplicities, residue mass and charge distributions, and residue recoil velocity distributions. Whenever necessary, the incl4.6 model is coupled to the ABLA07 de-excitation model and the respective merits of the two models are then tentatively disentangled. Good agreement is generally obtained in the 200 MeV to 2 GeV range. Below 200 MeV and down to a few tens of MeV, the total reaction cross section is well reproduced and differential cross sections are reasonably well described. The model is also tested for light-ion induced reactions at low energy, below 100 MeV incident energy per nucleon. Beyond presenting the update of the incl4.2 model, attention has been paid to applications of the new model to three topics for which some particular aspects are discussed for the first time. The first topic is the production of clusters heavier than alpha particle. It is shown that the energy spectra of these produced clusters are consistent with coalescence. The second topic regards the longitudinal residue recoil velocity and its fluctuations. Excellent results are obtained for these quantities. It addition, it is shown that the distributions of these quantities display typical random-walk characteristics, at least for not-too-large mass losses. They are interpreted as a direct consequence of the independence of successive binary collisions occurring during the cascade process. The last topic concerns the total reaction cross section and the residue-production cross sections for low-energy incident light ions. It is shown that our new model can give a rather satisfactory account of these cross sections, offering so an alternative to fusion models and the advantage of a single model for the progressive change from fusion to pre-equilibrium mechanisms.