In an abelian category with a Hovey triple (Q, W, R), the subclass Q_n of objects with Q-resolution dimension ≤ n itself forms a hereditary Hovey triple, yielding a model structure on Qcoh(X) with bounded Gorenstein dimensions.
Gillespie, How to construct a Hovey triple from two cotorsion pairs, Fund
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Approximations and Hovey triples by objects of finite homological dimensions: Applications to sheaves
In an abelian category with a Hovey triple (Q, W, R), the subclass Q_n of objects with Q-resolution dimension ≤ n itself forms a hereditary Hovey triple, yielding a model structure on Qcoh(X) with bounded Gorenstein dimensions.