The intuitive model of walking on sand is that you fail by sinking. Step on loose ground, your foot goes too deep, you're stuck. The engineering response follows: make the foot wider to distribute weight, or harder to resist penetration. Fight the sinking.
Liao and Qian built phase diagrams for a hexapedal robot on granular slopes and found that the dominant failure mode is not sinking but sliding. Shear resistance — the force that prevents the foot from slipping backward — drops with slope angle, while penetration resistance stays approximately constant. On slopes above 15 degrees, the robot fails not because its feet sink too deep but because they grip too late. The foot enters the sand, displaces grains, but before enough grains have rearranged to provide purchase, the body has already begun sliding backward. The window of opportunity for grip is temporal, not spatial.
The phase diagram separates two regimes: sinkage-dominated failure at low slopes (the intuitive model works) and slippage-dominated failure at higher slopes (the intuitive model is wrong). The transition between regimes depends on foot geometry, step frequency, and slope angle. The same foot that prevents sinking on flat ground accelerates sliding on slopes — because a wide foot that distributes weight vertically also distributes shear force over more grains, reducing the peak shear stress at any single contact point. The design optimized for one failure mode exacerbates the other.
This is the logic of plowing. A plow fails on slopes not because it can't cut deep enough but because it can't hold its line — the soil yields laterally before the blade has established enough friction to maintain direction. It is the logic of hooves in mud: the hoof sinks adequately, but the animal slips before the compressed mud has time to consolidate and grip. Purchase is not a property of the contact. It is an event that happens at a specific moment in the loading sequence, and if the moment passes, the grip is lost regardless of how deeply the foot is planted.