Active and Passive Pressures for Non-Level Ground
Occasionally non-level ground surfaces and benches have to be constructed. The current version of DeepEX can handle both single angle sloped surfaces (i.e single 10degree slope angle) and complex benches with multiple points. DeepEX automatically detects which condition applies. For single angle slopes, DeepEX will determine use the theoretical Rankine, Coulomb, or Caquot-Kerisel active, or passive lateral thrust coefficients (depending on user preference).
For non level ground that does not meet the single slope criteria, DeepEX combines the solutions from a level ground with a wedge analysis approach. Pressures are generated in a two step approach: a) first, soil pressures are generated pretending that the surface is level, and then b) soil pressures are multiplied by the ratio of the total horizontal force calculated with the wedge method divided by the total horizontal force generated for a level ground solution. This is done incrementally at all nodes throughout the wall depth summing forces from the top of the wall. Wall friction is ignored in the wedge solution but pressures with wall friction according to Coulomb for level ground are prorated as discussed.
This approach does not exactly match theoretical wedge solutions. However, it is employed because it is very easy with the iterative wedge search (as shown in the figure below) to miss the most critical wedge. Thus, when lateral active or passive pressures have to be backfigured from the total lateral force change a spike in lateral pressure can easily occur (while the total force is still the same). Hence, by prorating the active-passive pressure solution a much smoother pressure envelope is generated. In most cases this soil pressure envelope is very close to the actual critical wedge solution. The wedge methods employed are illustrated in the following figures.
Surcharge loads are not considered in the wedge analyses since surcharge pressures are derived separately using well accepted linear elasticity equations.
In the 2015 version, the usIn DeepEX, user has the option of either performing a Wedge search, or performing an automatic search using the automatic failure search options. The automatic search options might produce lateral pressures that have slight abrupt changes as computed pressures are sensitive on the total computed forces. When compared to the wedge methods, the automatic search option may give slightly less conservative results when the critical failure surface is predominantly in a wedge type format. On the other hand, the automatic search option might be ideal when the general failure mass extends far beyond the typical active wedge, as is the case when clays are present when global stability is an issue.
Figure 1.a: Active force wedge search solution according to Coulomb.
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Figure 1.b: Passive force wedge search solution according to Coulomb.
Figure 2: Illustration of automatic search methods for active and passive thrusts.
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