Geotechnical Engineering

DHARM

334 GEOTECHNICAL ENGINEERING

∴ ru = B ...(Eq. 9.28)
The pore pressure coefficient B may be determined from a triaxial test in which the
sample is subjected to increases in the principal stresses ∆σ 1 and ∆σ 3 of magnitudes expected
in the field. The resulting pore pressure is measured and B is obtained.
Once an idea of pore pressures is got, the factor of safety immediately after construction
may be obtained in the usual manner.

Effective Stress Analysis by Bishop’s Method

Bishop (1955) gave an effective stress analysis of which he took into account, at least
partially, the effect of the forces on the vertical sides of the slices in the Swedish method.

Figure 9.18 illustrates a trial failure surface and all the forces on a vertical slice which
tend to keep it in equilibrium.

Let Rn and Rn + 1 be the reactions on the vertical sides of the slice under consideration.

x

Centre of

trial circle

z

Rn+1

Rn

W

n n+1

r

S

ls

c¢l

F

P tan

F

¢f

F

P

P¢

uls

W

Trial failure surface

S (Circular arc)

P

b

a

Fig. 9.18 Bishop’s procedure for effective stress analysis of slope stability

Let the other forces on the slice be:

W : weight of slice.

P : Total normal force acting on the base of the slice.

S : Shearing resistance acting at the base of slice.

Also, let b : breadth of slice

ls : length of slice along the curved surface at the base.

z : height of the slice.

x : horizontal distance of the centre of the slice from the centre of the trial slip circle.

α : angle between P and the vertical.