Characteristic angle of shearing resistance, (j>t (deg)

Figure 9.8. Stability number required to verify limit state GEO for a finite slope with ru = 0.3 according to Eurocode 7's Design Approaches

The chart in Figure 9.8 shows the characteristic stability number Nk for different slope gradients from 1:1 to 1:4. The solid lines assume that the ratio D/H (where D is the depth to a strong layer and H is the slope height) is equal to 2. The dashed lines assume D/H = 1, i.e. the strong layer is coincident with the toe of the slope.

The charts have been derived by analysing a slope geometry for a given design angle of friction and then determining the required design value of effective cohesion c'd that gives a global factor of safety = 1.0. Due to the limited number of 9 angles used, the curves are not totally smooth.

An example illustrates how to use this chart. Imagine a 2.5m high slope which is required to stand at a gradient of 1:2. The slope comprises soil with characteristic weight density Yk = 20 kN/m3 and characteristic angle of shearing resistance 9 = 30°. From Figure 9.8, the characteristic stability number needed to verify a 1:2 slope is approximately Nk = 0.036. Hence the characteristic effective cohesion c'k that the soil must possess is: c'k = NkrkH > 0.036 x 20kN / m3 x 2.5m = 1.8kPa

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