Geotechnical Engineering

DHARM

STABILITY OF EARTH SLOPES 341

nH b H

DH

When slip circle can pass below toe,

use full lines.

(n is indicated by dotted lines.)

H b DH

When slip circle cannot pass below toe,

use dashed lines.

Key figures

45°

30°22½°15°

1 2 3 4 5 6

b= 53° Depth factor, D N = 0.181 at D =

for all slopes

¥

0.18

0.17

0.16

0.15

0.14

0.13

0.12

0.11

0.10

0.09

0.08

0.07

0.06

0.05

Stability number

,N=c / H

gm

n=0

n=1

n=2

n=3

7½°

Fig. 9.26 Taylor’s chart for slopes with depth limitation

(After Taylor, 1948) (for β > 53°, use Fig. 9.25)

(Note: For φ = 0° and β = 90°, N = 0.26. So the maximum unsupported height of a vertical-cut in

pure clay is c/γN or 4c/γ nearly).

The use of the charts is almost self-explanatory. For example, the first chart may be

used in one of the two following ways, depending upon the nature of the problem on hand:

1. If the slope angle and mobilised friction angle are known, the stability number can be
   obtained. Knowing unit weight and vertical height of the slope, the mobilised cohesion can be
   got.
   The factor of safety may be evaluated as the ratio of the effective cohesional strength to
   the mobilised unit cohesion.


2. Knowing the height of the slope, unit weight of the earth material constituting the
   slope and the desired factor of safety, the stability number can be evaluated. The slope angle
   can be found from the chart against the permissible angle of internal friction.
   If the slope is submerged, the effective unit weight γ ′ instead of γ is to be used.
   For the case of sudden drawdown, the saturated unit weight γsat is to be used for γ; in
   addition, a reduced value of φ, φw, should be used, where:
   φw = (γ ′/γsat) × φ ...(Eq. 9.44)
   Taylor’s charts are based on the assumption of full mobilisation of friction, that is, these
   give the factor of safety with respect to cohesion.
   This is all right for a purely cohesive soil; but, in the case of a c – φ soil, where the factor
   of safety Fs with respect to shearing strength is desired, φm should be used for φ:

tan φm = tan φ/Fs ...(Eq. 9.45)
(Also φm ≈ φ/Fs)
The charts are not applicable for a purely frictional soil (c = 0). The stability then de-
pends only upon the slope angle, irrespective of the height of the slope.