power required

It sounds as though this is not on a regular highway. Your problem is likely to be knowing the service conditions (rolling resistance). Are there any 'significant' gradients?

The hauling is to be done on asphalt road with gradients of about 15-35 degree to the horizontal

I doubt the asphalt road can take the tire (tyre?) pressures!

Call a trucking company they will help you.

500 Tonnes in one load? Gulp! And 35 degrees is one hell of an incline for a road; from my largely European experience unimagineable. If you take say a 1:5 hill (steep round here), you'd clearly need a tractive effort at the tyre contact patch of 100t. To climb that hill at 10km/h, allowing 15% for mechanical and tyre losses I calculate you'd need 3mW or 4000hp.

Gas turbine country, which is what's typically used in heavy earthmoving.

Incidentally my 'fag packet' sum has neglected the mass of the vehicle itself, as you will have noticed, and with a vehicle of this type you may be faced with losses greater than 15%. This was an initial guess.

These 360 ton mining trucks have 3200 hp. Scaling up you'd need about 4500. But perhaps you don't need to move as fast, in which case your hp could be less. Of course, there is far more to truck selection than HP. A company like Liebherr might be able to help you find the right truck.

Look for people called MEGA MOVERS they use combination methods to move things.

Yep - Mega Movers. They showed day before moving a whole house with a trailer and a Cat. dumper pulling uphill & holding from back going downhill. I bet he has seen this that is why he is mentioning. Anyway, this is not his job, he should contact the mega movers for this.