What the analysis found
Thermal stress: a typical extruded lid at a constant 1,900 °F sees a maximum stress of about 10 psi from its own weight. With 1,910 °F on top and 1,900 °F underneath, the stress rises to about 1,500 psi, above the hot modulus of rupture of many refractories. Where many lids of one tunnel broke in the same campaign while the walls stood, this was the most likely cause.
Material: the hot modulus of rupture at service and upset temperatures needs a margin over the static stress, and the creep resistance should be as high as reasonably available. A lid that creeps sags in the middle and changes how it bears on the walls.
Mass: a brick tunnel with a solid lid loads the insulating firebrick below with more than 10 psi. Published ASTM data suggest that this layer deforms by a full percent within 100 hours at reformer temperatures. The furnace floor steel can deform as well. Cutting tunnel weight by 60% reduces the load on that layer by an order of magnitude, and a base component can spread it over up to five times the area.
Expansion: brick walls get fiber expansion joints every 6 to 10 ft, with mortared sections between them acting as one body. In the model, a mortared 10 ft wall section with 1,052 °C at the bottom and 1,038 °C at the top exceeded the strength of standard mortar. The same section built from separate 46 by 23 cm blocks with their own gaps stayed below about 65 psi.
The lid also grows more than the cooler base, by as much as 9.5 mm, and pushes the wall tops apart. The tunnel becomes trapezoidal and buckles more easily. When the whole tunnel grows longer than its joints allow, it snakes sideways, cracks the mortar and separates from lid and base.