In short: It's the ~~cube root~~ inverse square law. The ~~damage~~ force from an explosion goes down with distance by an exponential factor (1/x^2).

So the blast force (per unit area) at 2" should be about 1/4^th the damage at 1". At 6", the force would be 1/36^th the force per unit area at 1" distance.

Think of a surface of a balloon. If the skin of the balloon (and it's thickness) represents concussive force, as the balloon gets bigger, the skin (and the force) gets smaller.

The boots work by ensuring that if you set off a mine, the mine is under one of the four prongs and away from your foot (distance = ~6") vs just under your foot (distance <1" or the thickness of your soles).

Edit: corrected damage to force. Shrapnel complicates things a bit, but in general, the further you are from the blast, the less concussive (read bone pulverizing) force you receive and the fewer and more spread out shrapnel fragments you get.

If your bones aren't pulverized and the shrapnel is less concentrated, then there's a better chance the medics can save your leg and foot.

Copying a comment on the study these boots came from:

From the study on the boots, they were way better at lowering the odds of needing an amputation after stepping on a mine than the alternatives. Even when tested against the larger mines (249g of explosive)

Check out figure 4 in the study. The competing alternatives were tested against 25g of explosive (first data point) and the measured acceleration on the test leg was 4000 -11,000 g's. The spider boots tests registered about 700 g's or less.

An alternate source to read the whole study on the spider boots:

https://www.researchgate.net/figure/Spider-Boot-tested-with-a-mechanical-surrogate-leg-at-DRDC-Suffield-Actual-and-simulated_fig3_265925569

The anti-personnel mines used in this study included the VS50 (43g RDX/TNT) and the PMA2 (100g TNT). For the Spider Boot, in all cases of detonation of the landmine under one of the pods, the limb was found to be salvageable (no amputation). In contrast, tests with conventional blast boots against the VS50 mine resulted in MTS scores requiring amputation, and contamination was observed. With the PMA2 mine (100g TNT), the foot was totally destroyed, resulting in a required amputation and severe contamination.

The boot "legs" are destroyed instead of your foot.

Here's a video about it.

https://youtu.be/g9xj5GLzT8A