The Mattone Barile and Mattone Barile Grande models are based on firebrick and mortar on a 180 degree arch. We designed the arch and the entire weight of the oven to be centered evenly on the walls of the cinder block base so the added weight of an extended brick chimney CAN be held without reinforcing the slabs.
BUT - you don’t want any more than 3 layers of brick on the chimney (4 bricks per layer) unless you design a way to reinforce the chimney so the extra weight is supported by the hearth slab (cooking surface slab). You DO NOT want all that additional weight sitting on the oven’s firebrick arch as it was not designed to hold an extreme amount of weight. Adding additional rows of brick and mortar can quickly add hundreds of pounds being supported by the arch, and this can result in hairline cracking, mortar failure or oven failure (e.g. oven collapses under the additional weight. Keep in mind, each layer of brick on your chimney is about 30-35lbs of firebrick and mortar.
If you need an oven that can support the weight of a heavy chimney and/or exhaust pipe, please take a look at our Cortile Barile or Mattone Cupola ovens. They are both built with Castable Refractory and both models can support a crazy amount of additional weight.