Your question was directed to internal allowances for, I assume, pigging purposes. There are other reasons to limit 'out of roundness' in a pipe.
The design allowance for 'out of round' depends on several items such as the type of lining & the type of joint.
Cement mortar lining is not as forgiving as a flexible lining. A rubber ring joint is also not as forgiving as a welded joint. The Australian Standard (buried flexible pipelines) - AS 2566, has a limitation on deflection of welded pipe (unlined or flexible lining) of 5%. A welded pipe with cement mortar lining of 3%. A steel pipe with an elastomeric joint of 2%.
Your pipe has a D/t ratio of 60 which is quite stiff for a water pipe. I recently designed a 1,400 mm (11 plate - about the same as your pipe) welded steel pipe (160 m head) with a cover of 750 mm for normal (44 tonne truck) loading. This pipe was on the limit of allowable deflection.
I then checked it out for a 250 tonne haulpak & I then required a 1 m of cement stabilised sand backfill to keep the deflection within limits. Fairly expensive method, but only for a short distance.
One way of doubling the allowable load for a limiting deflection, is to either: -
* Put temporary timber internal struts into the pipe & induce a vertical delection of the max allowable, or
* Inducing excessive compactive effort on the sides of the pipe to induce a vertical deformation.
This means that the surface load will induce a deformation from a +5% to zero, to -5%, effectively doubling the vertical allowable loading. I've never used this method & I only mention it as a theoretical concept. This concept would not apply to your pipe because of the high stiffness.
To answer your original question of a Cat D9 crossing the pipe, the bearing pressure can be quite low under a tracked machine (that is why they use tracks on machines in soft ground - because of their low soil bearing pressures). If you have any concerns of excessive surface loadings, just increase the cover a bit - remember that the surface loading is distributed two ways & dissipates quickly. I use an empirical rule of using 0.5 m of earth loading as being about the same effect as a very large truck.