Tension cracks are a special case of the Method of Slices computation. Because of the vertical nature of tension cracks, they can only be computed by the Method of Slices. The USDA-ARS standalone version of BSTEM uses the Layer Method by default but switches to the Method of Slices if the tension crack parameter is defined and a tension crack is identified.
If the inter-slice normal forces are negative E less than zero the slice is in "tension". Soil generally performs very poorly under tension. Tension slices tend to be on the "upslope" portion of the failure block because there is more material "sliding away" pulling on the slice. Therefore, the code starts at the (channel side) and works inland, checking each slice interface for E less than zero.
When a slice in tension is found, the software compares the height of the slice interface to the user specified (or internally calculated) "maximum tension crack "depth". If the slice interface is greater than maximum tension crack, then no tension crack is computed at that location and the next inland interface is analyzed. Therefore the tension crack happens at the slice interface closest to the channel that fulfills the two following criteria:
- E less than 0 (i.e. the slice interface is "in tension")
- The height of the interface between the slices is less than the maximum tension crack (below)
The vertical thickness of tension cracks is soil specific and can be determined by visual field inspection of the vertical cut at the upper portion of existing bank failures. It can also be computed with the equation for the depth at which active pressure goes to zero (Equation8) (Lambe and Whitman, 1969):
|
Z_c = \frac {2c^'}{\gamma} tan \left( 45^o + \phi^' /2 \right) |
(8)
HEC-RAS currently uses this equation by default for the method of slices. The standalone version of BSTEM can override this value with a user specified maximum tension crack, but this is not available in HEC-RAS at this time.
If a tension crack is identified, the slices inland from the tension crack are excluded from the stability analysis. Because the failure plane along these inland slices is higher, the inland slices will tend to have higher suction forces and lower buoyant forces. Therefore, a tension crack that excludes these inland slices will reduce the FS and make the bank more likely to fail.
If FS is less than zero and a tension crack is computed, the failure block on the river side of the tension crack is removed from the bank and added as sediment load to the sediment model, while the inland slices remain fixed to the bank, resulting in a vertical wall.
