Updating HEC-18 Pier Scour Equations for Noncohesive Soils

Chapter 2. Data Characteristics

The development of the pier scour equation for coarse bed materials in figure 1 was based on datasets from Colorado State University (CSU), the FHWA Turner-Fairbank Highway Research Center, and the U.S. Geological Survey (USGS), which are listed as the first four datasets in table 1.⁽²⁾ These data included a range of conditions with observations of clear water and live bed scour. For the previous study, only the clear water data were used for the development of the equation in figure 1.

*Thirty-nine observations are included in both the USGS-2004 and USGS-1995 datasets.

In addition, the last dataset shown in the table (USGS-1995) will be used for the analyses in this study. Combined, these datasets provide 694 unique pier scour observations.

Selected data observations were removed from the dataset either because of incomplete data or because of inappropriate data for the study. In total, 12 observations were filtered out of the CSU laboratory dataset, and 88 observations were filtered out of the USGS-1995 dataset for the following reasons:

• USGS-1995 field data. The following changes were made:
  
  
  • Fifty-eight observations were actually 29 pairs of measured scour depths upstream and downstream of the same pier. The smaller of the two measurements was deleted (29 observations).
  • Scour depths that were minimal (measured scour depth less than 0.2 inches (5.1mm) or measured scour depths less than the reported error of field observation) were deleted (38 observations).
  • Soils that were cohesive were deleted (7 observations).
  • Observations with unusually high gradation coefficients (5 with a gradation coefficient of 12.1 and 2 with a gradation coefficient of 20.4) were deleted (7observations).
  • Soils with no gradation information were deleted (7 observations).
    
    
• CSU laboratory data. Scour depths that were minimal (measured scour depth less than 0.2 inches (5.1 mm)) were deleted (12 observations).

After filtering, 594 pier scour observations remained for further analysis. Of these, 402 were from the 3 USGS field datasets, and 192 were from the CSU and FHWA laboratory datasets.

The remaining data included a variety of pier types. Within the field data, there were 60observations with pier groups and 342 observations with single piers. The single pier types/nose types were cylindrical (8), round nose (158), sharp nose (141), square nose (27), and unknown (8). The unknown observations were treated as round nose. All of the laboratory data were for single cylindrical piers.

The data contained a broad range of grain size classes for noncohesive soils. Table 2 summarizes the grain size classification and gradation according to the system of Krumbein and Aberdeen.⁽⁹⁾ The data range from fine sand to cobble sizes based on the D₅₀. The most numerous size range represented in the data is coarse sand (215 observations).

The gradation coefficient ranges from 1.15 to 7.22. For this study, a noncohesive soil is considered uniform when the gradation coefficient is less than 1.5. With the exception of the very fine gravel, nonuniform gradations make up at least half of the observations for each soil class.

The definition of soil gradation coefficient used in this study and in HEC-18 is D₈₄/D₅₀. Another definition used is (D₈₄/D₁₆)^0.5.⁽²⁾ These two definitions are equivalent when D₈₄/D₅₀ = D₅₀/D₁₆. Landers and Mueller reported gradation coefficients for the 384 data observations included in that study.⁽⁸⁾ Each gradation coefficient was recomputed using the definition for this study and compared with the reported values. For 123 observations, the recomputed values matched the reported values. However, for 132 observations, the recomputed values exceeded the reported values, but for 129 observations, the recomputed values were less than the reported values. In all cases, the recomputed values were used for this study because they are supported by the data.

1 inch = 25.4 mm.

The distribution of the 594 bed materials by grain size classification is shown in figure 4. While the field data include observations in all 10 grain size classifications, the laboratory data from CSU and FHWA include observations in five of the classifications: medium sand, coarse sand, very coarse sand, very fine gravel, and coarse gravel. Among all grain size classes, coarse sand is the most frequently represented with more than 35 percent of the observations. The least represented is very fine gravel, with only six observations, including five from the laboratory data and one from the field.

Figure 4. Graph. Distribution of grain size classification.

The dataset includes observations of both clear water and live bed scour. If the approach velocity is greater than the critical velocity, live bed conditions exist; if not, clear water conditions govern. The critical velocity is calculated by Laursen’s critical velocity equation, as shown in figure 5.⁽¹⁾

Figure 5. Equation. Laursen’s critical velocity equation.

Where:

V_c,50 = Critical velocity based on D₅₀, ft/s (m/s).

K_u = Unit conversion constant, 11.17 for U.S. customary units (6.19 for SI units).

1 inch = 25.4 mm.