The physics
Tilt a rough board slowly. The block slips when the pull along the board reaches friction's limit.
mg sin θ = μ mg cos θ → tan θ = μ
This angle is the angle of repose. The mass does not matter.
The floor's total push R has two parts: N and friction f. R tilts from the normal by φ, with tan φ = f / N. At the slip, tan φ = μ. This is the angle of friction.
A push inside the friction cone never moves the block, however hard. A push outside it moves the block, if it is big enough.
push α below the horizontal: F = μmg / (cos α − μ sin α)
bowl: h = R (1 − 1/√(1 + μ²)) chain: x = μL / (1 + μ)