Human foot encased by a boot

No.  Not really.  But not far off.

This is a sagittal section of an elephant's foot.  For those with at least a passing familiarity with human anatomy, the parallels are quite striking: tibia, heel, metatarsals, etc.  The difference is in the pad under the heel.  I found more information at the Journal of Anatomy:

The uniquely designed limbs of the African elephant, Loxodonta africana, support the weight of the largest terrestrial animal. Besides other morphological peculiarities, the feet are equipped with large subcutaneous cushions which play an important role in distributing forces during weight bearing and in storing or absorbing mechanical forces... the cushion also presumably helps to distribute the animal's weight over the entire sole... deformable foot cushions serve to absorb mechanical shock, store and return elastic strain energy, protect against local stress and keep pressures low...

In addition to the obvious mechanical functions, the cushions are important sensory structures. The high concentration of sensory receptors such as Vater–Pacinian corpuscles within the cushion and Meissner corpuscles in dermal papillae of the adjacent skin might rank an elephant's foot among the most sensitive parts of its body.

This comment sums up some of the mechanical aspects:

The heels of elephants compress as they walk along, a bit like suspension, so they can walk without their centre of mass moving up and down but maintaining it at a constant height. This means they are doing less work since they’re not having to raise and lower their mass, which because they are so large would be a huge waste of excess energy, even though it’s negligible for animals like us.

And IIRC, elephants are capable of detecting infrasound, which I presume is related to that final comment about the sensory function of the feet.

"When culling was being done in some of the parks, the elephants could clearly detect andidentify the thump-thump-thump sound of the helicopter blades from 80 to90 miles (130 to 140 kilometers) away, identify it as danger, and take off in the opposite direction." 

This is way more interesting than I initially thought.  You learn something every day.