deriving the factor of safety for a single slip circle with an arbitrarily selected radius, is included here for com-

pleteness. In order to ﬁnd the most critical condition, i.e. the minimum factor of safety, a number of slip circle calculations should be carried out using different radii. The engineer experienced in this ﬁeld is able to identify the most likely mode of failure based on a knowledge of soil parameters and boundary conditions and hence reduce the computational effort required. This iterative calculation process is time-consuming and can be more cost-effectively carried out by one of the commercial software packages for slip circle analysis that are available.

A detached house, 9 m × 9 m on plan, is to be constructed on a sloping site; a section through the proposal is as shown in

**Fig. 15.10**.

Fig. 15.10 Slip circle design example. |

Assuming an average value of cu = 50 kN/m2, consider a one metre wide strip for the case where Øu = 0, i.e. the undrained condition immediately following construction

Next set up a circular arc using compasses, to pass through the edge of the excavation for the basement of slab/footing and close to the bottom of the new embankment. Measure the radius, and compute the arc length, r = 12.5 m. The angle subtended by the arc =α= 90°. Therefore

Deduct a length (arbitrary) disturbed by excavation and subsequent ﬁlling, i.e. 19.6 − 3.6 = 16 m.

Weight of ground is F1, assuming the small area of ﬁll above the chord line equals the area omitted within the house.

Using 16 kN/m3 for existing ground and compacted ﬁll

weight, F1 = 45 × 16 = 720 kN/m

The weight of a detached house of two storeys, including external and internal load-bearing walls, when averaged per metre run, equates to 170 kN/m. Therefore

By simple geometry, the centroids of the areas are located, and scaling their lever arms

Combining these gives

2304 + 680 − 194 = 2790 kNm

Therefore

Since 3.6 is greater than 2, the factor of safety commonly adopted for slope failures involving buildings, then there is an adequate factor of safety against slip circle failure.

However, as mentioned above, other circles should be checked in order to ﬁnd the critical case.

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