Engineering Rock Mechanics

336 Design of surfuce excavations

In this diagram the force W represents the weight of the material
which overlies the foundation, and W1 and W2 represent the weight of
the two blocks 1 and 2, respectively.
Having drawn the free body dia-
gram, it is necessary to compute the re-
lations between the various virtual dis-

by accurately drawing the vectors on a
separate diagram.
One of these vectors must be given

yli

placements. This is most easily done VI

VI2

an arbitrary value in order to scale the 60"
remainder. Here, we set VI = 1.0, and t= VIH
4

sin 120 sin25

• v2 = 0.4880,

so we find VI

-- - " 3 v12 = 0.6623,

sin35 sin120

v12

u1v = u1 sin35 + vlV = 0.5736,

and

U~H = ~1 COS35 3 UIH = 0.8192.

We can now write down an expression for the external virtual work

P sin30. u.2 + Pcos30. U~V + W2 - YV - (W + Wl) e vlv = EVW

which, because U~V = 0.0, simplifies to

The internal virtual work is given by

P sin 30 1 v2 - (W + Wl) v1v = EVW.

5

sin 15

50 x 5 COS 30 * ~2 + 50 x 5 COS 30 * ~12 + - x 25 COS 20 = IVW.

For equilibrium we have EVW = IVW, and so

cos 20

sin 15

250 30 - (u2 + u12) + 125- = P sin 30. v2 - (W, + W). vIv,

from which we have

cos 20

sin 15

250.30 (~2 + ~12) + 125- + (Wi + W). viv

P=. (18.1)

sin 30 v2

We now need to compute W1 and W, the weight of block 1 and the

weight of the overburden:

x 25 = 1166.3 kN/m,

1 5

w1=- x5x -

2 tan 15

and

5

tan 15

WE- x 4 x 19 = 1418.2 kN/m.

Thus, substituting into Eq. (lS.l), we have

250 cos 30 x (0.4880 + 0.6623) + 453.8 + 2584.4 x 0.5736

sin 30 x 0.4880

P=

= 8956 kN/m.