Engineering Rock Mechanics

Foundation instability 299

Each element is

Rock slope

by discontinuities beyond its strength

Gravitational

loading

occur on both

sides

Rock foundation

I *Ed

v Blocks delineated

by discontinuities

Can occur at a

horizontal

Sliding on one

(or more)

discontinuities

Figure 17.12 Foundation instability.

(a) to postulate a geometry of discrete blocks and evaluate the associated

(b) to consider the sustainability of a postulated stress distribution

To demonstrate the fundamentals of the methods of solution, only loaded
areas are being considered, and not loads applied through structures. In
the latter case, the strength and stiffness of the structure must be taken into
account and these have a marked effect on the results.
These approaches have been used extensively in the study of plasticity.
Two fundamental theorems exist for plastic analysis, and Brown (1987),
with reference to the theory of plasticity, quotes these as:

1. Upper bound theorem. If an estimate of the plastic collapse load of a
   body is made by equating the internal rate of dissipation of energy
   to the rate at which external forces do work in any postulated
   mechanism of deformation of the body, the estimate will be either high
   or correct.

forces and instability; and

beneath the loaded region.

Load on (and applied by) superstructure

of a given magnitude & distribution

Stressing & deformation Load on foundation

of superstructure

\

Deformation of Stress in

ground surface rock mass

\I

If excessive

I

Damage to superstructure

or collapse

\/ If excessive

Failure of

rock mass

Figure 17.13 Simplified rock-structure interaction flow chart for foundation

instability (from lecture notes by S. D. Priest).