Figuring-out which types of ground can support Bipedal Mechs of approx. the Mass of The Iron Giant

Question

(Edited:)

I've been trying to figure-out which types of ground would allow mechs that have at least roughly the same mass as that of The Iron Giant to stand, walk, and run around on without the mechs sinking into said ground, whether that be ground made of solid granite, concrete, solid steel, or even something else entirely (although I would prefer it to be a solid physical substance rather than something like, say, a forcefield).

That being said, in the story world I'm working on, I do want there to be instances of mechs walking top of regular dirt, so, once I figure-out which materials could support mechs of The Iron Giant's Mass, I'd like to see how much dirt I can put on top of those materials before the mechs start sinking into the dirt again.

Updates based on answers/comments I've received:

• What I need to do to figure this out is to find the weight of my mech over the surface of the feet in contact with the ground, and then look up what the compressive strength for different materials are; if the compressive strength can support the weight the mech puts on the ground over the surface area of the feet, then I'm good. In order to figure this out, however, I need to know what a mech the size of The Iron Giant would weigh. As for The Iron Giant himself, he would probably have to be made of some super-lightweight alien material that otherwise behaves similar to iron or steel, because he can walk around on dirt just fine. For the purposes of my research, I'm willing to start off by treating the mechs' weight as though these mechs are entirely made of real-world steel from earth, and I'd also like to assume that, unlike The Iron Giant, these mechs' upper legs are the same thickness as their lower legs and that the mechs' upper arms are the same thickness as their forearms. Given these parameters, how would I go about calculating how much these mechs would weigh? Additionally, it would be a big help if somebody knows the size of the area of the soles of The Iron Giant's feet, or, at least, could please point me in the direction of a website or app that lets me put accurate digital rulers onto digital pictures so that I can measure the objects in those pictures, to help me figure out the surface area of the feet's soles myself.

• Also, in terms of how much mechs weigh, I've been informed that Gundams seem to be in the 60-80 metric ton range, Macross mecha seem to be about 15 metric tons, and Mechwarrior mechs range from 20-100 metric tons. So now, I have a point of reference for how much a 50-foot tall mech could weigh (although I am still interested in the prospect of running the aforementioned weight calculation(s) I've listed above). (Again, if someone either knows the surface areas of the soles of those mechs' feet, or has a way to help me calculate them myself, that information would also be greatly appreciated.👍)

Other Notes:

• The Iron Giant is 50 feet tall.

Answer 1

That will depend on the exact dimensions of the mech's feet, and its total weight, but once you've decided on those, you can use the following table to determine the acceptable substrates.

Soil Bearing Capacities

Clay soil: 95 kPa

Sand or sand gravel mixture: 144 kPa

Gravel: 239 kPa

Sedimentary Rock (ex. Sandstone): 287 kPa

Crystalline Bedrock (ex. Granite): 574 kPa

Example

Assuming the mech is linearly scaled up from human by roughly a factor of 10 (for the 50' tall iron giant example), the area of the feet would be about 3.8 square meters. For a mid-range weight (70 metric tons) you would have a ground pressure of about 170kPa standing still. That is comparable to a typical automotive tire, and about 3 times the ground pressure exerted by a human, or 2 times the ground pressure exerted by a modern tank. As such a mech could stand still on a substrate as firm or firmer than gravel, or a prepared road but would sink into mud or clay. However, when walking (to say nothing of running) each foot will have to bear the weight of the mech by itself when taking a step. Ignoring the dynamic loads, the mech would exert double the ground pressure, or about 340kPa briefly during each step. Nothing short of bedrock or thick reinforced concrete could withstand this load.

However, with this baseline, you could back-calculate the size of the feet necessary to support the load. If you wanted to be able to walk on clay soil (very slowly keeping dynamic loads as low as possible) you would need to reduce the pressure by a factor of about 3.6. This would mean making the feet about 90% longer and wider than would be proportional for a human.

The thing you need to keep in mind is that when the mech walks or runs there will be dynamic loads in addition to the static loads. Each time it takes a step it needs to accelerate its mass upwards during the initial portion of the stride, then arrest its downward motion when it plants the next foot in front of the other. It's hard to find good data for this. The best I've found puts the peak vertical acceleration during each step at 1.5g for a normal human. For the mech example above (before correcting foot size), that would result in a peak ground pressure of 510kPa, just to walk around. In another study, vertical acceleration for a runner on a treadmill ranged from 2.2g at 12kph to 2.7g at 18kph. That would give you a peak pressure of 748kPa to 918kPa for an equivalent motion on the example mech. It would leave footprints in solid bedrock, assuming the legs and feet could withstand the load. To be able to run on clay soil, the feet would need to be over 3 times as long and wide as proportional human feet. Keep in mind as well, even the fastest running pace listed above wouldn't be competitive in a marathon, let alone a dead sprint. If you want your mech to actually move like a human, the feet will need to be even bigger.