Inter-slice shear force in cohesive slope stability 4

[A Smith]

In the Morgenstern-Price method the ratio between the inter-slice (vertical) shear force and the inter-slice normal (horizontal) force is often defined by a half-sine function. So the ratio would be zero at both ends of a slip surface. Yet the normal force near the top of the slip surface approaches zero as tension cracks form. So the cohesive shear force divided by the normal force tends towards infinity rather than zero.

Shear isn’t as directly related to horizontal forces as the ratio suggests. Shear may be negligible beneath a gentle slope whatever the horizontal forces (it would be ignored beneath a non-sloping surface) and could much larger in parts of non-circular slips than in circular ones. We all know about tan phi as a ratio between the total shear and normal forces, but we don’t think it’s a good idea when cohesion is involved. Beyond Bishop, why doesn’t there seem to be a more rational method of slices based on finite element analyses?

 

[geotechguy1]

The example Krahn quotes is specifically for a slip surface exiting at the toe (where there would be a shear stress concentration), which is a case where there is a bigger difference (and the LE model was conservative in that case anyway).

>Suppose it was possible to construct a slope using separate blocks of soil of different heights. These would be allowed to settle and bulge, then their sides would be trimmed so they could all be fitted together and fused to form a single soil mass. It would then be valid to ignore the previous ground settlements, so any of the “general” methods would be sensible ways to analyse this slope. But of course this isn’t the way slopes are formed either naturally or artificially, so it’s no wonder that the “general” methods can give consistent yet misleading results. These methods are solving a different problem.

Back to the supercomputer DEM model to run a simulation of a few million years of geological history based on your preferred geological story, then?

You should chat with an engineering geologist or geomorphologist sometime - they'll tell you that all of this slope stability modeling civil engineers turned geotech engineers do is a load of total rubbish anyway (at least for natural slopes); perhaps the point about using bishops method / and or slope stability charts isn't so bad.

 

[A Smith]

There is nothing unusual about slip circles exiting at the toe, and it’s important to know how different assumptions can affect the resulting FoS.

I thought we’d agreed that mathematical sophistication is often unnecessary along with the need for a supercomputer.

Nor do I have a preferred geological history going back millions of years. When an embankment is constructed, the higher part settles more and this induces vertical shear stresses. Such stresses also occur when overburden is removed to form a cutting. It seems obvious these stresses should be taken into account when engineers use a method of slices requiring vertical shear stresses to be estimated.

Artificial slopes are the province of the engineer and natural slopes are more the province of geologists. Where a watercourse has made a cutting through alluvium this seems akin to an artificial cutting, but where the soil on a slope has weathered in-situ from rock I think your reference to engineering geologists is instructive. The weathering process probably destroys earlier shear stresses and a FE analysis that treated the soil as alluvium or artificial fill would probably be invalid. So I agree that Bishop or any other time-honoured approach wouldn’t be at all bad in these circumstances.

A rational method of slices would therefore need to distinguish between different types of soil origin. But FE or other software that’s even more sophisticated should also take account of geological considerations and hence be acceptable to geologists. Why doesn’t this seem to be the case?