FHWA Hydraulic Toolbox

Gradation Layer Calculations

Gradation layers are used in Hydraulic Toolbox as soil layers in the bridge scour and as embedment layers in other calculators. The user specifies a name, top elevation (if applicable), whether the layer is noncohesive or cohesive, and angle of repose. If the soil layer is noncohesive, the user needs to specify the gradation curve. Otherwise, the user will need to specify the critical shear strength of the soil layer.

If the soil type is noncohesive, Hydraulic Toolbox will compute the diameter for common passing percentages, uniformity coefficient, coefficient of curvature, whether the gradation is “uniformly graded,” “poorly graded,” or “well graded.” It will determine a classification according to AASHTO, UNIFIED, or USDA gradation systems, as given below. It will compute the critical shear strength and a Manning’s n value using the methods given below.

If the soil is cohesive, the user will specify the critical shear strength and the Manning’s n value will be assumed to be 0.012.

Determining the Shear Strength of Noncohesive Soil

The equation used to determine the critical shear strength of noncohesive material follows:

$\tau _{c}=ks(s-1)\ \gamma _{w}D_{50}$

Where:

τ_c = Critical shear strength, lb/ft²

ks = Shield’s number

s = Specific gravity of current layer’s soil

γ_w = Density of water, 62.4 lb/ft³ for fresh water

D₅₀ = Median diameter of soil layer, ft

The equation used to determine the shield’s number follows:

$ks={\frac {0.23}{d_{*}}}+0.054\left(1-e^{-d_{*}^{\frac {0.85}{23}}}\right)$

Where:

ks = Shield’s number

d_* = Dimensionless grain size diameter

The equation used to determine the d_* follows:

$d_{*}=\left({\frac {(s-1)g}{v^{2}}}\right)^{\frac {1}{3}}D_{50}$

Where:

d_* = Dimensionless grain size diameter

s = Specific gravity of current layer’s soil

g = Gravitational constant

v = Kinematic viscosity of water

D₅₀ = Median diameter of soil layer, ft

Determining the Manning’s N Value for a Noncohesive Soil

The equation used to determine the Manning’s n value of noncohesive material follows:

$n=(0.034\ D_{50})^{\frac {1}{6}}$

Where:

n = Manning’s n value

D₅₀ = Median diameter of soil layer, ft

Soil Gradation Classification

The classification system used by Hydraulic Toolbox is used to classify whether a material is clay, silt, sand, gravel, or riprap. It does not classify types of clays or any more in detail than the chart given below.

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Shear Decay

Shear decay is a new method to predict the amount of scour that occurs based upon the hydraulic parameters and soil profile at specific locations. The principle is that as soil is scoured away, the same flow is passing through more flow area, which results in decreased flow velocity and decreased shear. The shear is computed at increasing depth until the soil is able to resist the shear applied to the exposed surface. Maximum scour depths are also determined for specific circumstances.

The shear decay method complements traditional scour methods rather than replacing them. When shear decay is applied, first the scour is calculated as it would be without shear decay enabled.

The shear decay method is applied at a single point. It is determined for contraction scour at the thalweg of the channel, at the location of piers, and the abutments.

Shear Equation

The equation used to determine the shear follows:

$\tau =(\gamma y)^{\frac {-7}{3}}\left({\frac {nq}{k}}\right)^{2}$

Where:

τ = Shear stress at depth, lb/ft²

γ = Density of water, 62.4 lb/ft³ for fresh water

y = Depth of flow, ft

n = Manning “n” value

q = Unit discharge, ft³/s/ft

k = Constant for Manning Equation

How to Use the Shear Decay Method

The shear decay method applies to a bridge scour scenario. A bridge scour project in Hydraulic Toolbox consists of bridge geometry, soil gradation definition, and a list of scour scenarios. A scour scenario is the list of parameters that applies at a specific set of circumstances, usually referencing a recurrence interval for a given discharge that passes the bridge.

To use the shear decay method, check the box next to Compute shear decay in each scenario that you want to use the method.

Shear Decay Plots

The shear decay plots show the soil profiles with their critical shear strength at the specified location, the maximum scour depth (if applicable), and the shear applied at the specified location.

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Soil Profiles

The X axis is the shear stress, and the Y axis is the elevation. The soil profiles show the area that the soil is capable of resisting shear forces, from zero shear stress to its critical shear stress. The soil profiles are plotted according to the elevations that are specified in the Gradation section of the bridge scour project.

Shear Decay Curve

The shear decay curve is plotted from the beginning depth until the curve meets the critical shear stress or the maximum scour depth. When the curve changes from one soil layer to the next, the shear being applied may jump. The applied shear depends on the roughness of the soil layer it is applied to, so the applied shear changes when the soil type changes. At pier or abutment locations, the contraction scour shear decay curve will be given, but the curve will continue with the shear decay curve applied to the local scour conditions. This can be recognized by finding where the first curve naturally terminates at the soil’s critical shear strength or maximum scour elevation, then the curve will jump with the amplification of local scour, then continue until it meets the soil’s critical shear or the local maximum scour depth.

Thin Layers

Hydraulic Toolbox allows the user to set the minimum thickness of a layer. If the layer below the current layer is weaker than the current layer, and the layer is thinner than the specified “Minimum layer thickness”, Hydraulic Toolbox will continue the curve to the next layer.

Shear Decay Method Applied to Contraction Scour

If the governing shear method is live-bed, then the maximum scour depth will be set according to the computed maximum scour depth from the live-bed method.

Shear is then computed at an incrementally increasing scour depth until the shear no longer exceeds the critical shear strength of the current layer or the maximum scour depth is reached.

Shear Decay Method Applied to Pier Scour

The user may select whether to use the Hager equation or the CSU equation to determine the maximum scour depth.

Hager Equation

The Hager equation used to determine the maximum scour depth follows:

$y_{max}=a_{p}^{\frac {62}{100}}y^{\frac {38}{100}}\left(1.32k_{1}k_{2}\tanh \left({\frac {h^{2}}{1.97\sigma ^{\frac {3}{2}}}}\right)\right)$

Where:

y_max = Maximum scour depth, ft

a_p = Pier width, ft

y = depth of flow, ft

k1 = Correction factor for pier nose shape

k2 = Correction factor for angle of attack

h = Hager value, from next equation

σ = Sigma value from the current soil layer

The Hager value is computed using the following equation:

$h={\frac {v}{\sqrt {g(s-1)D_{50}}}}$

Where:

h = Hager value, from next equation

v = Flow velocity, ft/s

g = Gravitational constant

s = Specific gravity of current layer’s soil

D₅₀ = Median diameter of current soil layer, ft

CSU Equation

The CSU equation used to determine the maximum scour depth follows:

$y_{max}=y\left(2.0k1k2k3\left({\frac {a_{p}}{y}}\right)^{0.65}Fr^{0.43}\right)$

Where:

y_max = Maximum scour depth, ft

y = depth of flow, ft

k1 = Correction factor for pier nose shape

k2 = Correction factor for angle of attack

k3 = Correction factor for bed condition

a_p = pier width, ft

Fr = Froude number of the flow, adjusted for conditions after contraction scour

Shear is then computed at an incrementally increasing scour depth until the shear no longer exceeds the critical shear strength of the current layer or the maximum scour depth is reached.