Con

Fig. 5.6 Total stress analysis.

Taking moments about O, the centre of rotation: We = culr = cur0r = cur20 for equilibrium Restraining moment cur29

Disturbing moment We

The position of G is not needed, and it is only necessary to ascertain where the line of action of W is. This can be obtained by dividing the sector into a set of vertical slices and taking moments of area of these slices about a convenient vertical axis.

5.4.1 Effect of tension cracks

With a slip in a cohesive soil there will be a tension crack at the top of the slope (Fig. 5.7) along which no shear resistance can develop. In a purely cohesive soil the depth of the crack, hc, is given by the formula:

The effect of the tension crack is to shorten the arc AB to AB'. If the crack is to be allowed for, the angle ff must be used instead of 9 in the formula for F, and the full weight W of the sector is still used in order to compensate for any water pressures that may be exerted if the crack fills with rain water.

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