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Total scour at a ten-span river bridge: contraction, pier and abutment scour with the scour prism (HEC-18 Appendix D)

ToolBridge Scour
SourceArneson, L. A., Zevenbergen, L. W., Lagasse, P. F., and Clopper, P. E. (2012). Evaluating Scour at Bridges, 5th ed. Hydraulic Engineering Circular No. 18, FHWA-HIF-12-003, Federal Highway Administration, Washington, DC. Appendix D, Comprehensive Scour Problem (pp. D.3 to D.18); equations 6.1, 6.2, 6.4, 7.1 and 8.2.
LevelProfessional

Problem

The Ordbend Bridge over the Mainstream River is 1,200 ft long in ten equal spans on 3 ft circular columns, with spill-through abutments set back 153 ft and 431 ft from the banks. For the 120,000 ft³/s design flood a water-surface profile gives the flows, widths and depths of the main channel and the overbanks at the approach and bridge sections. Find the contraction scour in the channel and on both overbanks, the local scour at the piers and at both abutments, and the total scour across the opening.

Inputs to Enter

  • Approach main channel: depth 20.3 ft, flow 97,832 ft³/s, width 637 ft, velocity 7.57 ft/s, energy slope 0.000297; bed material D50 2.0 mm
  • Bridge main channel: flow 115,352 ft³/s, width 608 ft with five piers, depth 20.3 ft; water surface at elevation 120.0 ft
  • Left overbank under the bridge 1,694 ft³/s, 153 ft, 6.8 ft deep; right overbank 2,954 ft³/s, 431 ft, 5.8 ft deep; bank material D50 0.35 mm
  • Nine piers at stations 120 to 1,080 ft, a = 3 ft, circular, aligned with the flow; depth 23.9 ft and velocity 10.9 ft/s of the fastest stream tube at every pier; K3 = 1.1
  • Abutments, spill-through, HIRE equation: left L = 1,598 ft, 6.5 ft deep, 1.37 ft/s; right L = 2,386 ft, 4.9 ft deep, 0.90 ft/s
  • Foundation elevations 75 ft (piers) and 90 ft (abutments): illustrative, the appendix gives none
Open the Bridge Scour tool (loaded with this example)

Answers

  • Critical velocity V_c = 11.17 · 20.3^(1/6) · 0.0066^(1/3) = 3.45 ft/s (book 3.46) below the 7.57 ft/s approach velocity: live-bed scour
  • Shear velocity 0.44 ft/s, fall velocity of 2 mm sand 0.66 ft/s (Figure 6.8), ratio 0.67, so k1 = 0.64
  • Channel: y2 = 20.3 · (115,352/97,832)^(6/7) · (637/593)^0.64 = 24.47 ft, contraction scour 4.17 ft (book 24.5 ft and 4.2 ft)
  • Overbanks by the clear-water equation: y2 = 6.44 ft (left) and 4.27 ft (right), both below the existing depths: no contraction scour (book 6.4 and 4.3 ft)
  • Pier: Fr = 0.39, y_s = 2.0 · 1.0 · 1.0 · 1.1 · (23.9/3)^0.35 · 0.393^0.43 · 3 = 9.13 ft (book 3.0 a = 9.0 ft, the ratio 3.04 rounded before multiplying)
  • Abutments by HIRE: left 11.94 ft, right 8.21 ft (book 12.0 and 8.2 ft)
  • Total scour at a channel pier 4.17 + 9.13 = 13.31 ft, scour elevation 86.39 ft, the lowest across the opening

Notes

The tool's default inputs are this bridge; press Submit. The page adds what the appendix leaves to its Figure D.9: the scour elevation of every pier and abutment against a foundation elevation, the drawing of the scour prism, and HEC-23 riprap sizes. The appendix also checks a widened bridge on four-column bents at 15 degrees of skew (K2 = 1.57, 4.8 a = 14.4 ft): set a pier row to shape Group of cylinders, L = 12 ft, angle 15 and the tool gives 14.3 ft. test_bridge_scour.php (1,108 checks) reproduces every worked example of HEC-18 Chapters 6 to 8 and the HEC-23 riprap examples within the rounding of the printed intermediate values.