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GEO5

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Solution Procedure

Principle of calculation of rock slope stability for polygonal slip surface is shown in following figure.

Forces acting on multiple-block sliding surface

Suppose D1 is the vector representing the resultant of all the disturbing forces acting on block no. 1 given by:

where:

W1

-

vector due to self weight of block which is acting vertically downwards

E1

-

vector of external force due to earthquake

U1

-

force vector due to uplift water force which acts normally to the sliding surface

V1

-

vector of water force in tension cracks

If N1 denotes the unit vector for N1 and the angle of friction for plane no. 1 is ϕ1, block 1 would be an active and unstable block if the resultant falls outside the friction cone of plane no. 1 such that:

where:

R1

-

net resultant unit force of disturbing and resisting forces acting on block no. 1

N1

-

unit vector representing the upward normal of plane no. 1

ϕm1

-

mobilized angle of internal friction

For an active block, there will be a net transfer of interaction force from block 1 to the next lower block 2. The interaction force is denoted by vector I12 given by:

where:

K1

-

reaction force for block 1 which acts at an angle ϕ1 away from the normal of sliding plane 1 for the condition of equilibrium according to the Fig. 1

A similar method of analysis may be conducted for block 2 in addition to which an equal and opposite interaction force I12 has to be taken into account. The net resultant force vector R2 is given by:

where:

D2

-

resultant of all the disturbing forces acting on block no. 2

Cm2

-

vector denoting the mobilised shear force

B2

-

vector denoting the resultant of external resisting forces acting on block 1 contributed by rock bolts or sprayed concrete

I12

-

interaction force vector from block 1 to the next lower block 2

The stability analysis is hence conducted in a sequential manner for all blocks ranging from the uppermost block 1 until the lowest block n. The entire system of blocks is deemed to be stable if the resultant force of the lowest block lies within the friction cone of the sliding surface. In Figure 1, for example, where the lowest block is numbered 3, the entire system of blocks would be stable, with passive blocks supporting the active blocks of the system, provided that:

where:

R3

-

net resultant unit force of disturbing and resisting forces acting on block no. 3

N3

-

unit vector representing the upward normal of plane no. 3

ϕm3

-

mobilized angle of internal friction