Tools · Bridges

Scour depth

Guided step by step as per IRC 78 and the IRS Bridge Substructure and Foundation Code: silt factor, regime width, normal and maximum scour depth, maximum scour level and the foundation level that gives enough grip.

Guided · step 1 of 8

What scour is and the data needed

During a flood the river picks up bed material and the bed drops, deepest at piers, abutments and bends. Foundations must go safely below the deepest scour. Lacey’s regime theory, adopted by IRC 78 and the IRS Bridge Substructure Code, gives the scour depth from the discharge, the waterway and the bed material.

Design discharge Q = 2000 m³/s; effective linear waterway W = 150 m

Bed material: mean size dₘ = 0.323 mm

HFL = 100 m, lowest bed = 94 m; code: IRC 78

River and bridge

CodeDesign discharge Q (m³/s)From the river discharge toolIncrease for scour (%)IRC 78: 30 % up to 3000 km²Effective waterway W (m)Clear spans between abutmentsMean size dₘ (mm)Bed material (sets dₘ)Location of the foundationHFL (m)Lowest bed level (m)

Section at the pier

dₛₘ

8.97m

restricted waterway

dₘₐₓ

17.95m

below HFL

Max scour level

82.05m

Foundation level

76.07m

17.93 m below bed

Waterway against regime width

Bridge waterway W150 m

Regime width 4.8√Q244.8 m

Waterway narrower than regime: the flow is constricted and scour is worked out per metre of waterway.

Full solution, all steps at once

What scour is and the data needed
Design discharge Q = 2000 m³/s; effective linear waterway W = 150 m
Bed material: mean size dₘ = 0.323 mm
HFL = 100 m, lowest bed = 94 m; code: IRC 78
Discharge for scourQ_d = Q·(1 + increase)
Q_d = 2000 × (1 + 30100) = 2600 m³/s
Silt factorK_sf = 1.76·√d_m
K_sf = 1.76 × √0.323 = 1.76 × 0.5683 = 1
Regime width: is the waterway restricted?W_r = 4.8·√Q_d
W_r = 4.8 × √2600 = 244.75 m
W = 150 m is less than W_r: the waterway is restricted
Normal scour depth (restricted waterway)D_b = Q_dWd_sm = 1.34·(D_b²K_sf)^1/3
D_b = 2600150 = 17.333 m³/s per m
d_sm = 1.34 × (17.333²1)^1/3 = 1.34 × 6.697 = 8.974 m
(For comparison, the wide-river formula gives 6.504 m.)
Maximum scour depthd_max = k·d_sm
Right-angled bend, or at nose of piers: k = 2
d_max = 2 × 8.974 = 17.948 m below HFL
Straight reach: 1.27
Moderate bend: 1.5
Severe bend: 1.75
Right-angled bend, or at nose of piers: 2
Maximum scour levelMSL = HFL − d_max
MSL = 100 − 17.948 = 82.052 m
That is 11.948 m below the lowest bed.
Foundation level: grip below scourFoundation level ≤ MSL − d_max3
Grip = 0.333 × 17.948 = 5.983 m
Foundation level = 82.052 − 5.983 = 76.069 m (17.93 m below the bed)