The Layer Method is based on Simon (2000) and it is the default method (below) in USDA-ARS BSTEM Version 5.4. This method was developed specifically for bank failure applications and is derived superficially to compute failure planes through vertically heterogeneous bank sediments. The layered configuration makes it easier to formulate a stability equation for bank sediments divided into discrete horizontal layers (which is the basic configuration of BSTEM stratigraphy). The Layer Method also eliminates one cycle of iteration required in the Method of Slices which reduces runtimes in long simulations.
Force diagram for the "Layer Method" from Simon (2000).
The Layer Method solves a non-iterative equation (Equation 1, Layer Method Force Balance) for the FS that compares driving forces to resisting forces: (1) where: i = layer L = length of the failure plane S = matrix suction force U = hydrostatic uplift P = hydrostatic confining force of the water in the channel' Φ' = friction angle Φb = relationship between matrix suction and apparent cohesion'c' = effective cohesion b = angle of the failure plane
However, Equation 1 combines the driving forces in the numerator and resisting forces in the denominator, because both the numerator and denominator have negative components. Equation 2 displays the components of the Layer Method Force Balance equation, with the driving forces indicated in red and resisting forces in green. The forces in Equation 2 can be categorized into soil forces (weight of soil block, cohesion) and hydraulic forces (hydrostatic confining forces, pore water pressure). Equation 3 displays the hydraulic and soil forces of the Layer Method Force Balance equation:
