Appendix 3. CALCULATING THE PRUDENT LINE
3.1. Methodology
Two separate prudent line procedures were developed based on the two dominate channel types found in El Paso County (Ayres Associates, "Prudent Line for Rural Areas, El Paso County," Draft Report, June 2000). One procedure is for channels in sandy soils and another for those incised into more erosion-resistant material. The procedure for sandy soils is a simplified approach to the procedures that have been successfully used in the Albuquerque, New Mexico area, and the erosion-resistant procedures are based on the approach used in Cottonwood Creek, Colorado.
Both procedures are simplified methodologies that should be carefully applied using reasonable engineering judgement. The procedures were developed to address channels experiencing, or potentially experiencing, erosion-related stability issues. Depositional reaches can also experience channel instability; however, the prudent-line concept may not be the best solution in these situations (Section 3.7). These methods should not be applied to channels with Q100 greater than 10,000 cfs, or to channels with unusual or unique sediment transport conditions, including alluvial fans or channels below reservoirs or detention ponds.
3.2. Prudent Line for Sandy Soils
The prudent line for sandy soils is based on a simplified sediment continuity analysis to define a potential sediment deficit. The bed material sediment transport capacity for a range of floods can be calculated based on a triangular hydrograph approximation of return period flood hydrographs (100-, 50-, 25-, 10-, 5-, and 2-year), given a sediment transport relationship in the form of Q s =aQ b. The sediment transport relationship was developed assuming sediment concentrations by weight ranging from 1,000 to 15,000 ppm.
Step 1. Calculate the sediment transport capacity for different return period events.
Apply Equation 3.1 to calculate the total bed-material sediment volume in transport (sediment transport capacity) for the 100-, 50-, 25-, 10-, 5-, and 2-year flood hydrographs:
VOL i = 6 Qp d (3.1)
Where:
VOL i = bed-material sediment volume (cf) for the i - return period flood
Qp = peak discharge (cfs) for the i - return period flood
D = hydrograph duration, (hr), as approximated by triangular hydrograph
The El Paso County Drainage Criteria Manual requires hydrology to be generated for the 100- and 5-year events. In that case, it is acceptable to plot those peak discharges on log-probability paper to estimate the intermediate return period peak flows used in Equation 3.1.
Step 2. Calculate the potential sediment deficit in any given reach of the study area.
Erosion occurs when the sediment transport capacity of any given reach exceeds the quantity of sediment supplied to that reach. In the absence of better information, assume a sediment deficit equal to 25 percent of the transport capacity is possible at any location throughout the study reach due to changes in slope, roughness, channel geometry, etc. Therefore, the potential sediment deficit for the i-return period flood in any given reach is:
Y i = 0.25 × VOL i (3.2)
This assumption is reasonable for a channel reach that is relatively similar to the next upstream reach. If significant sediment storage is occurring upstream, such as at a detention pond or constricted roadway crossing, the deficit could be substantially greater and a more complex analysis of the prudent line will be necessary.
Step 3. Calculate the average annual sediment deficit
After calculating the potential deficit for each return period event, the average annual deficit is calculated using a probability weighting approach:
Y m = 0.015Y 100 + 0.015Y 50 + 0.04Y 25 + 0.08Y 10 + 0.2Y 5 + 0.4Y 2 (3.3)
Where:
Y i represents the calculated deficit (cf) for the i - return period flood.
Step 4. Convert the calculated sediment deficit to a long-term lateral migration distance
To estimate potential long-term lateral migration, the resulting average annual deficit volume must be converted into a horizontal distance. For purposes of this analysis, it is assumed that all the sediment will be eroded from the channel bank, thus representing lateral migration. No sediment is assumed to come from the channel bed. Since the computed sediment deficit represents sediment in transport, a bulking factor must be applied to calculate the sediment volume that could be eroded from the channel boundary. Given a sand porosity of 0.4, the bulking factor would be 1.67 (i.e., 1/(1 - 0.4).
It is reasonable to assume that this long term lateral migration will occur primarily as a relatively uniform bankline retreat somewhere along the study reach. Assuming that this will occur along a 500 ft reach, the annual lateral retreat can be calculated given cross section data in the reach. This can be based on a typical cross section describing the channel and overbank geometry.
Using a 30-year period as the duration for long term erosion, the average annual migration value times 30 defines the cumulative long term erosion potential. Since the exact location of this retreat is not known, this offset should be applied to both sides of the channel along the given reach.
In summary, the calculations required in step 4 are to:
1.
Multiply the calculated average annual deficit (Equation 3.3) by 1.67 (the bulking factor).
2.
Estimate the potential lateral migration over a 500 ft reach based on a typical channel cross section (see Figure 2 for some typical examples).
3.
Multiply the calculated lateral migration by 30 and apply the computed offset to both sides of the channel, measured from the top-of-bank for the low flow channel. If a low flow channel is not apparent, measure from the location of the 10-year water surface.
Depending on reach length, channel geometry variability and changes in runoff along the reach as drainage area increases, this calculation can be based on a single reach, or multiple subreaches.
In the case of multiple reaches, the computed distance should be applied from one calculation point upstream to the next, not in the downstream direction.
Figure 2. Examples of setback calculation for long-term erosion.
Step 5. Calculate the short-term lateral migration distance
The short-term erosion potential must also be considered. This is based on the potential lateral migration during a single 100-year flood, based on the sediment deficit calculated above for the 100-year flood. However, instead of distributing this erosion in a linear fashion, as suggested for the cumulative long-term analysis, it is more reasonable to assume that such erosion in a single large event might occur as a scalloping of the bankline. Assuming a right triangle geometry with the length of one leg along the channel bankline equal to 150 ft, the length of the opposite leg (representing the scallop distance into the bankline) can be calculated given typical channel and overbank geometry. The location of this scallop is also unknown, and so the resulting offset distance should be applied to both sides of the channel along the given reach.
In summary, the calculations required in step 5 are to:
1.
Multiply the calculated 100-year flood erosion deficit by 1.67.
2.
Estimate the potential lateral migration assuming a right triangle with a 150 ft leg eroding into a bank described by the typical channel cross section (see Figure 3 for some typical examples).
3.
Apply the computed offset to both sides of the channel, measured from the top-of-bank for the low flow channel. If a low flow channel is not apparent, measure from the location of the 10-year water surface.
Depending on channel geometry variability, this calculation can also be based on a single reach, or multiple subreaches. In the case of multiple reaches, the computed distance should be applied from one calculation point upstream to the next, not in the downstream direction.
Figure 3. Example of setback calculation for short-term erosion.
Step 6. Minimum prudent line
The minimum prudent line offset recommended is 50 ft from the top-of-bank for the low flow channel. If a low flow channel is not apparent, measure from the location of the 10-year water surface.
Step 7. Tabulate and/or plot the prudent line
The prudent line for sand channels is based on an enveloping curve considering the greater of (1) the 100-year floodplain, (2) the calculated setback based long term (30 year) erosion, (3) the calculated setback based short term (100-year flood) erosion, or (4) the setback based on the low flow channel top-of-bank (or the 10-year water surface when a low flow channel is not apparent) plus 50 feet.
3.3. Prudent Line Methodology for Erosion-Resistant Material
Figure 4 presents the schematic and formula to use in defining the prudent line setback location for channels in erosion resistant material. The top of bank can be defined by reviewing topographic mapping. The bank line is represented by very closely spaced contours along the valley margins. This steep slope is different from the valley wall slope, in that the valley wall slope contours are not as closely spaced. The valley wall crest is represented by a significant change in the closeness in contour spacing.
Step 1. Calculate the maximum bank height
The bank height (BH) is defined as the height from the toe to the top of the bank as determined above. This height along with an expected maximum incision depth (ID) are added together to define the maximum bank height. The incision depth can be calculated using sediment transport procedures; however, this is a complicated analysis. Furthermore, future changes in watershed conditions complicate the prediction of long term conditions. For purposes of this methodology, the incision depth should be assumed to be 5 ft.
Step 2. Calculate the potential bank widening
The amount of bank widening is then defined by a 2H:1V bank slope given the overall bank height.
Step 3. Account for potential lateral migration
To account for future lateral migration a minimum of one valley floor width should then be added to the potential bank widening. The total setback will then be equal to 2*(BH+ID)+1VW measured from the toe of slope for each side.
Figure 4. Erosion setback definition sketch.
Step 4. Minimum setback distance
The minimum setback distance should extend out past the valley wall crest (VC) by at least 50 ft.
Step 5. Tabulate and/or plot the prudent line
The prudent line for erosion resistant materials is based on an enveloping curve considering the greater of (1) the 100-year floodplain, (2) the calculated setback based on bank slope and height considerations, or (3) the minimum allowable setback based on valley wall crest plus 50 ft.
3.4. Vertical Considerations
Even though the prudent line was developed considering primarily lateral migration, it is important to note that the prudent line also has a vertical component creating a prudent line window. Figure 5 represents a schematic of a typical stream cross section with the vertical extent of the prudent line shown. The potential lateral migration of the channel, as calculation above, defines the prudent line right-of-way. Using a minimum 2:1 sideslope and 5 ft minimum incision depth, a window of potential erosion can be defined that might occur in the channel cross section.
Infrastructure (i.e., bridges, sanitary sewers, water lines, utilities) that lie outside the window are assumed to be generally consistent with the prudent line. New infrastructure should not be proposed within this window. Existing infrastructure that lies within this window may need to be relocated or protected. Storm sewer outlets may be located within the prudent line window, but may need periodic maintenance (either lengthening or shortening pipe) as the channel migrates.
Figure 5. Schematic of typical stream cross section depicting prudent line window.
3.5. Maintenance Line
To insure long term performance of the prudent line, a maintenance line should be established inside the prudent line. The recommended maintenance line is equal to one-half the prudent line. This will provide adequate time to analyze, design and construct potential countermeasures to protect the prudent line if channel migration is greater than expected.
3.6. Sketching the Prudent Line
Given the offset distances calculated above, the prudent line can be drawn along the channel. It is important to recognize that the final location of the prudent line will require engineering judgement and a general understanding of the dynamic nature of alluvial channels. For example, channel bend geometry can change rapidly, including downstream migration of the bendway and/or a cutoff of the bend. Therefore, special consideration should be given to sketching the prudent line along reaches that are highly sinuous with sharp bends. It may be appropriate to draw the prudent line as a tangent line from the outside of one bend to the outside of the next, rather than paralleling the top of bank and forcing the prudent line to follow the bend sinuosity based on the offset distance.
If subreaches are used to define different offsets along a channel, abrupt changes from one reach to the next should be avoided. A gradual transition should always be provided, allowing the channel adequate room to adjust within the defined boundary. Areas around tributary confluences should also be carefully reviewed, to account for channel dynamics in these areas.
In contrast, if areas of competent, non-erodible material are exposed along the channel bank, it may be acceptable to reduce the size of the prudent line area. Similarly, if reaches of riprap or other bank protection exist that are in good condition, well maintained, and designed to survive a large flood, the prudent line may also be adjusted.
If legal descriptions of the prudent line are required, the final prudent line location should be defined as a series of offset tangent lines with distance and bearing descriptions.
3.7. Sediment Deposition Issues
The prudent line as outlined above is based on a channel reach that is experiencing a deficit of sediment, resulting in erosion and channel migration that could endanger adjacent property. However, a reach experiencing sediment deposition will also experience change over time resulting in unexpected channel migration, flooding and potential damage. Examples of areas where sediment deposition could be an issue include reaches upstream of a constricted road crossing, at a sudden reduction in channel slope, downstream of extensively degrading or incising reaches, or on an alluvial fan or other topographic feature that has promoted sediment deposition over time.
If sediment deposition is significant and begins to fill existing channel conveyances, it is possible that a new, radically different channel alignment may develop. The analysis of historic aerial photography may adequately define the various paths that a channel has taken over time, allowing definition of a prudent line. However, such a boundary would likely be quite large, and requires specialized knowledge to accurately define. Furthermore, based on the typically large offsets required to define a prudent line in a deposition area, the prudent line concept is typically not a cost effective or desirable approach in these basins. Maintenance activities to keep a channel defined and functional may be the preferred approach in a sediment depositional area, rather than a prudent line application.