Shields Parameter Sediment Transport Calculator

Estimate whether flow can move sediment

The Shields parameter helps river engineers, geomorphologists, and restoration planners decide whether water flow is strong enough to mobilize bed material. It compares the shear stress applied by the flow to the submerged weight resisting motion for a representative grain size.

A value below the critical threshold suggests the bed is likely stable. A value above the threshold suggests grains can begin to move as bed load. The threshold is not a fixed law of nature, so this calculator uses 0.045 as a practical reference value and shows the margin above or below that value.

Formula

Bed shear stress for a wide, uniform open channel is estimated as:

τ = ρ g h S

Plain-text formulas: bedShearStress = fluidDensity * g * flowDepth * energySlope; shieldsTheta = bedShearStress / ((sedimentDensity - fluidDensity) * g * grainDiameter).

The Shields parameter is:

where ρ is fluid density, ρs is sediment density, h is flow depth, S is water-surface or energy slope, and d is median grain size converted from millimeters to meters.

The critical Shields parameter depends on particle Reynolds number, grain shape, sorting, bed structure, hydraulic conditions, and measurement uncertainty. The default value 0.045 is a screening reference, not a site-specific design threshold.

How to use the result

• θ < 0.045: sediment is probably stable for the selected conditions.
• θ near 0.045: conditions are near incipient motion; field uncertainty matters.
• θ > 0.045: bed material is likely mobile, especially if turbulence and sorting expose the grains.

The result also reports the critical bed shear stress and the approximate slope needed to reach the threshold at the depth you entered.

Field interpretation checklist

Small changes in slope, depth, or grain size can move the ratio across the threshold. Result categories use the threshold you enter: below threshold (< 90% of critical), near threshold (90% to 110% of critical), and above threshold (> 110% of critical). For design work, run a sensitivity set with low, best-estimate, and high values for depth and d50.

Worked example

For water at 1000 kg/m³, quartz sediment at 2650 kg/m³, depth of 0.8 m, slope of 0.001, and d50 of 20 mm, the bed shear stress is about 7.85 Pa and θ is about 0.024. That is below 0.045, so the selected gravel would likely remain stable in this simplified model.

Limitations

This is a screening calculation. It does not account for grain Reynolds number, hiding and exposure in mixed beds, cohesive sediment, bedforms, unsteady floods, channel curvature, vegetation, armoring, or local scour around structures. Use measured hydraulic data and a sediment transport method appropriate to your site before making design decisions.

Design use

For restoration or culvert work, pair the Shields result with site evidence. Fresh bars, exposed roots, embedded gravels, scour pools, and depositional wedges can confirm whether the modeled mobility agrees with observed behavior. If the model says stable but the channel shows recent transport, the depth, slope, grain size, or roughness assumptions may be too mild.

Report the selected critical value with the result. A threshold of 0.045 is a common screening reference, but published curves vary. Stating the threshold keeps reviews transparent and makes it easier to rerun the same site with a different incipient-motion criterion.

For monitoring, rerun the calculation after major floods or channel work using updated depth, slope, and grain-size observations. A channel that was stable before restoration can become mobile if grade control, vegetation, or bed material changes.