Bridge Scour¶
The bridge scour calculations implemented in RiverFlow2D are based on the methods developed by the U.S. Department of Transportation and described in depth in the Hydraulic Engineering Circular No. 18. RiverFlow2D includes tools to calculate pier and abutment scour using DIP.
HEC-18 Method for Pier Scour¶
The equation used to compute pier scour in this method is:
where:
\(y_s\)=Scour depth, ft or m,
\(y_1\)=Flow depth directly upstream of the pier, ft or m,
\(K_1\)=Correction factor for pier nose shape.
\(\alpha\) is the angle of attack in radians,
\(K_3\)=Correction factor for bed condition,
\(a\)=Pier width,ft or m,
\(L\) =Length of pier, ft or m,
\(Fr\)=Froude Number directly upstream of the pier \(Fr = V_1/\sqrt{g y_1}\),
\(V_1\)=Mean velocity of flow directly upstream of the pier, ft/s or m/s,
\(g\)=Acceleration of gravity, 32.2 ft/s\(^2\) in English units and 9.81 m/s\(^2\) in SI.
Pier scour in Coarse Bed material¶
The equation is only applicable to clear-water flow conditions and to coarse bed materials with \(D50 = 20\) mm and \(\sigma \ge 1.5\).
where:
\(y_s, K1, K2, a, y_1, and V_1\) are defined as beforehand:
\(FrD\)= Densimetric particle Froude Number \(= V_1 / \sqrt{g (Sg-1) D50}\),
\(Sg\) = Sediment specific gravity,
\(D50\) = Median bed material size, ft or m,
\(D84\) = D84 sediment size, ft or m,
\(\sigma\) = Sediment gradation coefficient = \(D84/D50\).
Pier scour in Cohesive Materials¶
where \(y_s, K_1, K_2, a, and V_1\) are defined before and:
\(V_c\) = Critical velocity for initiation of erosion of the material, ft/s or m/s.
Top and bottom width of pier scour holes¶
To calculate the top width of pier scour holes we use the following equation:
where:
\(W\) is the scour hole topwidth,
\(W_{bottom}\) = scour hole bottom width,
\(K\) = bottom width of the scour hole related to the depth of scour,
\(\theta\) = angle of repose of the bed material.
Abutment Scour¶
These are the equations used to calculate abutment scour.
where:
\(K_4\) = 11.17 for English units and 6.19 for SI units,
\(\gamma_w\) = 62.4 Sw for English units,
\(\gamma_w\) = 9800 Sw for SI units,
Sw is the water specific weight,
\(V = q_1/y_1\),
\(V_c\) = Critical velocity for initiation of erosion of the material, ft/s or m/s,
\(V_c = K_u y_1^{1/6} D50^{1/3}\),
Where \(K_u\) is 11.17 for English units and 6.19 for SI units,
If \(V \ge V_c\) then use live-bed conditions,
If \(V < V_c\) then use clear-water conditions.
Scour amplification factor for spill-through abutments and live-bed conditions¶
To determine the amplification factor for spill-through abutments and live-bed conditions the following regressions are used.
\(x = q2c/q_1\)
\(y = \alpha_a = Y_{max}/Yc\)
For \(x \in [1., 1.23]\)
\(y(x) = -20172x^6 + 139961x^5 - 404430 x^4 + 622994x^3 - 539598x^2 + 249172x - 47926\)
For \(x \in (1.23, 1.60]\)
\(y(x) = -1968.9x^6 + 16589x^5 - 58072x^4 + 108127x^3 - 112948x^2 + 62766x - 14497\)
For \(x \in (1.60, 3]\)
\(y(x) = 0.076x^6 - 1.136x^5+ 7.1218x^4 - 24.031x^3 + 46.166x^2 - 48.086x + 22.476\)
For \(x>3\), \(y = y(3)\). \(x < 1\) is not allowed.
Scour amplification factor for wingwall abutments and live-bed conditions¶
To determine the amplification factor for wingwall abutments and live-bed conditions the following regressions are used.
\(x = q2c/q_1\)
\(y = \alpha_a = Y_{max}/Yc\)
For \(x \in [1., 1.24]\),
\(y = 1085.1 x^5- 6379.4x^4 + 15009x^3 - 17670x^2 + 10414x - 2457.2\)
For \(x \in (1.24, 1.60]\)
\(y = -449.86x^6 + 3796.2 x^5 - 13319x^4 + 24872x^3 - 26082x^2 + 14567x - 3384.9\)
For \(x \in (1.60, 3]\)
\(y = 0.1371x^4 - 1.469x^3 + 6.0171x^2- 11.221x + 9.1721\)
For \(x>3\), \(y = y(3)\). \(x < 1\) is not allowed.
Scour amplification factor for spill-through abutments and clear-water conditions¶
To determine the amplification factor for spill-through abutments and clear-water conditions the following regressions are used.
\(x = q2c/q1\)
\(y = \alpha_b = Y_{max}/Yc\)
For \(x \in [1., 1.45]\)
\(y = 443.57x^5 - 2769.4x^4 + 6913.2x^3 - 8630.8x^2+ 5393.6x - 1349.2\)
For \(x \in (1.45, 5]\)
\(y = 0.0061x^5- 0.1193x^4 + 0.9027x^3 - 3.1887x^2 + 4.7646x - 0.2761\)
For \(x>5\), \(y = y(5)\). \(x < 1\) is not allowed.
Scour amplification factor for wingwall abutments and clear-water conditions¶
To determine the amplification factor for wingwall abutments and clear-water conditions the following regressions are used.
\(x = q2c/q1\)
\(y = \alpha_b = Y_{max}/Yc\)
For \(x \in [1., 1.18]\)
\(y = -331011x^6 + 2 10^6 x^5 - 6 10^6 x^4 + 9 10^6 x^3 - 8 10^6 x^2 + 1000000x - 632819\)
For \(x \in (1.18, 5]\)
\(y = -0.0033x^6 + 0.0639x^5 - 0.5041x^4 + 2.0151x^3 - 4.1113x^2+ 3.2197x + 2.0841\)
For \(x>5\), \(y = y(5)\). \(x < 1\) is not allowed.