The bank failure methods employ classical, planar, analyses to compare gravitational driving forces of the soil, soil water and overburden, and frictional resisting forces (including the influences of pore water pressure) to determine the most likely failure plane through the bank and to compute whether that failure plane is stable. If the weakest failure plane is unstable, the bank fails and the sediment from the failed bank is added to the sediment transport model.
The bank stability model goes through a series of iterative computations to select potential failure planes, evaluate the factor of safety, and converge on the failure plane most likely to fail by following the steps below:
Find the critical Factor of Safety (FScr), the failure plane with the lowest Factor of Safety (FS) for nodes at several vertical locations up the bank.
Select the bounding Failure Planes (minimum and maximum angles) and compute a FS for each
Select a most probable critical failure plane (FSi ~ FScr)
Compute the FSi
Use that information to select a more likely critical failure plane (using the "bracket and Brent" optimization algorithm from Teukolsky et al., 2007) (set FSi+1 to updated estimate of FScr)
Decide when the FS is close enough to FScr to stop
If FScr is less than one, fail the bank, update the cross section, and send the bank sediments to the routing model
The failure plane selection and optimization algorithms are covered below. Since computing a FS for each failure plane (Step 3) is the physical algorithm at the core of this process, the description below starts with the basic physics and then moves to the optimization scheme. There are two basic computational approaches to computing the FS of a failure plane through the bank: