Spencer
The Spencer method satisfying full equilibrium.
Spencer's method is a rigorous method of slices that satisfies both force and moment equilibrium. In JW Slope it is solved by the same general limit-equilibrium (GLE) kernel as Morgenstern-Price, using a constant interslice force function.
Theory summary
- Equilibrium satisfied: complete static equilibrium — both force and moment equilibrium of every slice and of the sliding mass.
- Interslice forces: the resultant interslice force on every slice interface
acts at the same constant inclination. Equivalently, the ratio of interslice
shear to interslice normal force is a single unknown that is constant along the
surface. Spencer is therefore the special case of a generalized method in which
the interslice function
f(x)is constant. - Surface type: circular or non-circular.
The single constant interslice angle is the extra unknown that lets the method
satisfy both equilibrium conditions. JW Slope solves it by the GLE procedure: for
a trial value of the interslice force scale (lambda), it advances independent
force-equilibrium and moment-equilibrium factors of safety, then searches for the
lambda at which the two agree:
FS_force(lambda) = FS_moment(lambda)That lambda, combined with the constant function, fixes the constant interslice
inclination, and the matched value is the Spencer factor of safety.
Spencer is GLE with a constant function
Internally, Spencer calls the GLE solver and forces the constant interslice
function regardless of the user-selected GLE function. Everything on the
GLE / Morgenstern-Price page about the force/moment
iteration, the lambda search, and the WASM kernel applies equally to Spencer — the
only difference is the fixed shape of f(x).
Applicability
- A robust, defensible choice for both circular and non-circular surfaces.
- Recommended where a rigorous result is required and there is no specific reason to prefer a particular interslice-function shape (in which case use GLE / Morgenstern-Price and select the function explicitly).
Notes
- Because it satisfies full equilibrium, Spencer is generally less sensitive to geometry than the simplified methods and is a good reference value.
- The method is iterative and somewhat more expensive than Bishop or Janbu, but the rigorous solve runs in the compiled WASM kernel for speed.
- Spencer and Morgenstern-Price with a constant function are theoretically equivalent and should return the same factor of safety.