Geotechnical Engineering

DHARM

340 GEOTECHNICAL ENGINEERING

The line of action of U will pass through the centre of the circle.

The resultant of W and U is the actuating force B.

The triangle of forces will consist of the forces B, Cm and R.

9.3.4 Taylor’s Method
For slopes made from two different soils the ratio cm/γH has been shown to be the same for
each slope provided that the two soils have the same angle of friction. This ratio is known as
the ‘stability number’ and is designated by the symbol, N.

∴ N = cm/γH ...(Eq. 9.43)

where N = stability number (same as Sn of Eq. 9.15)

cm = Unit cohesion mobilised (with respect to total stress)

γ = Unit weight of soil

and H = Vertical height of the slope (Similar to z of Eq. 9.15).

Taylor (1948) prepared two charts relating the stability number to the angle of slope,

based on the friction circle method and an analytical approach. The first is for the general case

of a c – φ soil with the angle of slope less than 53°, as shown in Fig. 9.25. The second is for a soil

with φ = 0 and a layer of rock or stiff material at a depth DH below the top of the embankment,

as shown in Fig. 9.26. Here, D is known as the depth factor; depending upon its value, the slip

circle will pass through the toe or will emerge at a distance nH in front of the toe (the value of

n may be obtained from the curves). Theoretically, the critical arc in such cases extends to an

infinite depth (slope angle being less than 53°), however, it is limited to the hard stratum. For

φ = 0 and a slope angle greater than 53°, the first chart is to be used.

5°10°

f=0°

15°

20° 25°

0.24

0.20

0.16

0. 12

0.08

0.04

0 1020304050 60708090

Slope angle, °b

Stability number

,N=c / H

m

g

Fig. 9.25 Taylor’s charts for slope stability (After Taylor, 1948)

(for φ = 0° and β < 53°, use Fig. 9.26)