Interslice Functions
Interslice force functions used by rigorous methods.
The rigorous GLE / Morgenstern-Price method relates the interslice shear X to
the interslice normal E through an interslice function f(x):
X = lambda * f(x) * Ef(x) sets the shape of the assumed interslice-force inclination along the slip
surface; lambda (solved by GLE) sets its magnitude. The function is evaluated
at each slice interface by its relative horizontal position between the surface
entry and exit points, so the shape is correct even with non-uniform slice widths.
You select the function in the Analysis Method panel (the GLE Interslice Function control appears when GLE / Morgenstern-Price is enabled). Spencer always uses the constant function and ignores this setting.
The five functions
| Function (UI label) | Shape f(x) | Notes |
|---|---|---|
| Half Sine (Default) | sin(pi * x) | Default; peaks mid-slope, zero at the ends |
| Constant | 1 | Equivalent to Spencer |
| Clipped Sine | 0.25 + 0.75 * sin(pi * x) | A half-sine that stays positive at the ends |
| Trapezoid | ramps 0→1 over the first quarter, holds 1, ramps 1→0 over the last quarter | Flat-topped shape |
| FEA Stress | data-driven shape from the elastic stress field | Experimental (see below) |
Here x runs from 0 at the surface entry to 1 at the exit.
The FEA Stress (FEA-elastic) function
The FEA Stress function is experimental. Instead of assuming a shape, it derives one from the solved elastic stress field:
- For each internal slice interface, the kernel samples the stress tensor at seven points up the interface, integrates an approximate normal resultant from the normal stress and an approximate shear resultant from the shear stress, and forms the ratio of shear to normal resultant.
- Interfaces with a very small normal resultant are ignored, a dominant sign is chosen, the shape is smoothed and normalized to a peak magnitude of 1, and the endpoints are forced to zero.
This requires a solved elastic stress field, so selecting FEA Stress triggers the experimental FEA solve. If no valid function can be estimated, the GLE result is rejected for that surface.
Keep FEA Stress non-negative
The advanced option Keep FEA Stress GLE Interslice Function Non-Negative (default on) clips the derived shape so it cannot go negative. With it off, the derived function may take negative values where the stress field implies a reversed interslice-shear sense. See Advanced Options.
Choosing a function and checking sensitivity
- When in doubt, use the default half-sine. It is the common engineering choice and matches the half-sine function in comparable tools.
- Constant reproduces Spencer exactly and is a good cross-check.
- For most slopes the factor of safety changes only slightly across the standard
functions (half-sine, constant, clipped-sine, trapezoid); the solved
lambdachanges more. A practical check is to run two or three functions and confirm the factor of safety is stable. A large spread signals a surface whose result is sensitive to the interslice assumption and warrants closer review. - Reserve FEA Stress for exploratory comparison against a physically derived shape; it is experimental and not a primary design basis.