Instability of Rock Masses - Environmental Geomechanics - page 104

Unstable

Figure 4.10 . Effect of the shape of the boulder

4.5.3. Rolling with sliding

For there to actually be rolling, it is necessary for the sliding coefficient µ of the
boulder on the surface of the terrain to satisfy the condition:

mg e

⎛ ⎞

FN ≤ µ or 2 sin β + 5 cos β µ ≤ g cos β

⎜ ⎟

7 r

⎝ ⎠

If µ is given, it is necessary that (with a spherical boulder):

7µ 5 e

tg β≤− [4.32]

22 r

If this condition is not fulfilled, the boulder will slide while turning. A uniformly
accelerated motion is still obtained, but with the following characteristics:

Nmg = cos β [4.33]

F = µ g cos β [4.34]

( )

vg = sin β µβ cos t [4.35]

µ β, with the starting hypothesis of the boulder
positioned without initial velocity will depart (otherwise see section 4.5.1).

There is no movement if tg