294 Foundation and slope instability mechanisms
this geometric check should always be performed before computing the
factor of safety.
417.4 Determine an upper bound for the collapse pressure, p, for
the foundation shown below consisting of three rock wedges formed
by the fracture sets in the rock mass.
P IAI
All angles = 60°
c'= 25 kN/m3
y = 24 kN/m3+++++++, , '>$ ,# ', , / '\
A17.4 We start by drawing free body diagrams of the blocks that
comprise the foundation. It is important to remember that the forces
drawn on a free body diagram are those required to maintain the body
in u state of equilibrium. Also, when dealing with blocks that are in
contact in the actual foundation, the forces on the common surface in
the respective free body diagrams are in equilibrium, and so must be
equal in magnitude and opposite in sense. When drawing the free body
diagrams for a multi-block system such as this, it is usually easiest
to start with the block furthest from the applied external load, as the
direction of movement - and hence the sense of the inter-block forces
- is generally evident. Using these principles, the free body diagrams
for this particular foundation are then as shown below.
block 1 block 2 block 3
D
++t titt+t
In these diagrams, each force that acts on the surface of a block is given
two subscripts in order to identify fully the two blocks it acts between,
with block 0 being the rock outside the foundation.
We assume each block to be in a state of limiting equilibrium, and that
moment equilibrium can be ignored. In order to minimise the number
of unknowns in the equilibrium equations, the solution begins with an
analysis of block 3, moves on to block 2, and finishes at block 1.