The F\'elix--Tanr\'e rational model for the polyhedral product of a fibre inclusion is considered. In particular, we investigate a tractable rational model for the polyhedral product of a pair of Lie groups corresponding to arbitrary simplicial complex and the rational homotopy group of the polyhedral product.  Furthermore, it is proved that for a partial quotient $N$ associated with a toric manifold $M$,the following conditions are equivalent: (i) $N=M$. (ii) The odd-degree rational cohomology of $N$ is trivial.(iii) The torus bundle map from $N$ to the Davis--Januszkiewicz space is formalizable.This work is based on the paper On F\'elix and Tanr\'e rational models for polyhedral products, Fundam. Math. 267 (2024), 243--265.