This example is the model for the fibration over a neighborhood of an edge point of $\Delta$ –in [7] this is called $(2,2)$ fibration. Let $B=D\times(0,1)$, where $D\subset\mathbb{C}$ is the unit disc, and let $Y=T^{2}\times B$. Define $\Sigma\subset Y$ to be the cylinder sitting above $\{0\}\times(0,1)\subset B$ defined as follows. Let $e_{1},e_{3}$ be a basis of $H_{1}(T^{2},\mathbb{Z})$. Let $S^{1}\subset T^{2}$ be a circle representing the homology class $e_{3}$. Define $\Sigma=S^{1}\times\{0\}\times(0,1)$. Now let $\pi^{\prime}:X^{\prime}\rightarrow Y^{\prime}:=Y-\Sigma$ be an $S^{1}$-bundle with Chern class $c_{1}=1$. Then $X^{\prime}$ compactifies to a manifold $X=X^{\prime}\cup\Sigma$ and there is a proper map $\pi:X\rightarrow Y$ extending $\pi^{\prime}$. We can now define $f=P\circ\pi:X\rightarrow B$ where $P:Y\rightarrow B$ is the projection. Then it is clear $f$ is a $T^{3}$ fibration with singular fibres homeomorphic to $I_{1}\times S^{1}$ lying over $\Delta:=\{0\}\times(0,1)$. If $e_{2}$ is an orbit of $\pi$, one can take $e_{1},e_{2},e_{3}$ as a basis of $H_{1}(X_{b},\mathbb{Z})$, where $X_{b}$ is a regular fibre. In this basis, $e_{2}$ and $e_{3}$ are monodromy invariant and a generator of the monodromy group of $f$ about $\Delta$ is represented in this basis by