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Scientific Investigations Report 2011-5107

In cooperation with the Montana Department of Transportation

Investigation of Pier Scour in Coarse-Bed Streams in Montana, 2001 through 2007

By Stephen R. Holnbeck

Thumbnail of and link to report PDF (3.82 MB)Abstract

Determination of pier-scour potential is an important consideration in the hydraulic analysis and design of highway bridges that cross streams, rivers, and other waterways in the United States. A primary goal of ongoing research in the field of bridge scour is to improve scour-prediction equations so that pier-scour depth is neither underpredicted nor excessively overpredicted. Scour depth for piers in noncohesive, nonuniform streambeds with a mixture of sand, gravel, cobbles, and boulders (coarse-bed streams) generally is less than the scour depth in finer-grained (mostly sand) streambeds under similar hydraulic conditions. The difference in scour depth is attributed to formation of an armor layer. Pier-scour data collected by the U.S. Geological Survey were used to develop a bed-material correction factor called K4. The equation recommended by the Federal Highway Administration for computing pier scour is a version of the HEC-18 pier-scour equation that includes K4, which is referred to in this report as the HEC-18-K4Mu equation. The Montana Department of Transportation was interested in pier-scour prediction in coarse-bed streams because coarse-bed streams are common in Montana. Consequently, the U.S. Geological Survey and the Montana Department of Transportation began a cooperative study in 2001 to investigate pier scour in coarse-bed streams in Montana.

This report describes results of a study of pier scour in coarse-bed streams at 59 bridge sites during 2001–07 in the mountain and foothill regions of Montana. Drainage areas for the streams at bridge sites where measurements were collected ranged from about 3 square miles (mi2) to almost 20,000 mi2. Data collected and analyzed for this study include 103 coarse-bed pier-scour measurements. The report also describes how coarse-bed pier-scour measurements were collected, shows the extent that the coarse portion of the national pier-scour database was expanded, discusses how these new data were used to evaluate the relative accuracy of various equations for predicting scour in coarse-bed streams, and demonstrates how differences in size and gradation between surface bed material and bed material underlying the surface layer (shallow-subsurface bed material) might relate to pier scour.

Ninety-six out of 103 pier-scour measurements were made under clear-water scour conditions, when the streambed upstream from the bridge is stable and there is no substantial incoming sediment supply to the bridge opening. Of the measurements made, 50 percent had an approach velocity (Vo) that equaled or exceeded 70 percent of the critical velocity (Vc50) for incipient motion of bed material, which might indicate that scour was measured very near the threshold between clear-water and live-bed scour (Vo /Vc50 equal to 1.00) where maximum scour was shown in laboratory studies.

Pier-scour data collected for this study were compared to selected pier-scour data from the Bridge Scour Data Management System (BSDMS), a database of scour measurements made nationwide, to show the effect of bed-material size and gradation on scour depth. The relation between relative pier scour (y's /.b), or the ratio of measured pier scour (y's) to effective pier width (b), and relative velocity (Vo /Vc50) defined by an envelope curve for data collected for this study and the BSDMS data were compared to relations observed in laboratory data. The envelope curve for data used for this study displays an earlier peak, with a decrease in relative pier scour followed by an asymptotic rise. Interestingly, the first peak in the curve occurs at a lower relative velocity (Vo /Vc50 about 0.75) than the clear-water and live-bed threshold (Vo /Vc50 equal to 1.00). Also, the magnitude of this peak (maximum of 1.25) is much less than the published maximum value of 2.4 obtained from laboratory data. Furthermore, equilibrium live-bed scour is about 18 percent shallower than the maximum pier scour under clear-water conditions, a larger reduction than the 10 percent indicated in published research. Armoring associated with nonuniform coarse-bed material and unsteady-flow conditions in the field probably accounts for differences between envelope curves developed for this study and those from previous studies conducted in the laboratory using fine-grained material and steady-flow conditions.

Scour depth was computed for the measurements collected for this study using the HEC-18 equation without the K4 correction factor and five pier-scour equations that use K4 for the armoring effect of coarse bed material. The HEC-18-K4Mu equation was the best equation for predicting pier-scour depth in coarse-bed streams because the equation generally predicted pier scour in closer agreement to measured scour than the other equations used for computing pier-scour depth. Furthermore, the magnitude of the residuals of underpredicted and overpredicted scour depth was the lowest using the HEC-18-K4Mu equation.

Gradation coefficients (σg) for the surface bed-material data collected for this study ranged from 1.48 to 4.14, with a median of 2.01. For data used in this study, maximum relative pier scour was greater when σg was less than or equal to about 2.5. Pier-scour measurements collected for this study and BSDMS confirm a general lack of data for coarse-bed sites with σg greater than about 2.5.

Paired samples of surface and shallow-subsurface bed material collected for this study were analyzed and the D50 and D95 particle sizes were compared. Median D50 particle sizes for 103 surface and shallow-subsurface bed-material samples were about 49 millimeters (mm) and 32 mm, respectively, and median D95 particle sizes for 103 surface and shallow-subsurface bed material samples were 122 mm and 86 mm, respectively. The median gradation coefficients for surface and shallow-subsurface bed material associated with measurements made for this study were 2.01 and 4.14, respectively. The frequency and magnitude of the residual pier-scour depth associated with underpredicted and overpredicted scour was about the same regardless of whether surface or shallow-subsurface particle-size data were used with the HEC-18-K4Mu equation.

The combined effect that surface and shallow-subsurface bed-material characteristics might have on measured pier scour also was examined. The combined influence of relative differences in surface and shallow-subsurface bed-material size and gradation on pier scour was investigated by defining a bed-material variability index (Iv) based on ratios of particle sizes and gradation coefficients between layers for each of the 103 pier-scour measurements. Selected percentiles were determined and the relative pier scour and relative velocity for each measurement in the percentile were plotted. Envelope curves bounding the measurements in each percentile were drawn. Maximum relative pier scour associated with each envelope curve was concentrated at about the same relative velocity. Based on these curves, as differences in particle size and gradation between the surface and shallow-subsurface bed-material layers increase (higher values of Iv), pier scour decreases.

Runoff conditions during the study mostly were limited to bankfull discharge approximating the 1.5- to 2-year recurrence-interval flood, which have a 67 and 50 percent chance, respectively, of happening in any year. Lack of higher flows having greater velocity intensities may indicate that scour depths were limited by hydrologic conditions. Pier-scour depths measured in this study also may have been limited by streambed armoring and unsteady flow conditions. Conclusions presented for this study are generally limited to the range of hydraulic conditions and bed-material characteristics demonstrated in the data collected for this study and the BSDMS data.

First posted September 2, 2011

For additional information contact:
Director, USGS Montana Water Science Center
3162 Bozeman Ave.
Helena, MT 59601

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Suggested citation:

Holnbeck, S.R., 2011, Investigation of pier scour in coarse-bed streams in Montana, 2001 through 2007: U.S. Geological Survey Scientific Investigations Report 2011–5107, 67 p.




Pier Scour in Coarse-Bed Streams in Montana

Summary and Conclusions

References Cited

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