Benefit of Gathering Site-Specific Evidence In Developing Engineering Solutions to Climate Change Events
March 2016
Adeniyi Aje Ahmad Khattab
• The Context
• Case Study – Somerset 2013/14
• Typical Assessment Approach
• New Assessment Approach
• Validation of Approach
• Future Use & Benefits
• Limitations
• Questions & Answers
• Our Climate is changing with time
• Our Environment is also changing with time
• EA updates – Feb 2016
a) Increase in intensity/frequency of rainfall → increased flow rate.
Key Parameter (affecting structures along walkways)
b) Discharge Flow Rate, Q = Velocity, V x Area, A
Constant (Channel Section)
c) Climate Change → Scour in waterways around existing structures d) Factors that affect velocity and may consequently lead to scour:
• Upstream and downstream ground conditions • Laminar or turbulent flow • Discharge flow rate • Catchment run-off vs. Percolation • Channel alignment • Bed roughness • Fluid Viscosity • Obstructions • Bed slope
(Somerset) Catchment Area River Parrett
King Sedgemoor Drain
Dunball New Bridge* Dunball Old Bridge
Sluice Gate
Sluice Gate
Dunball New Bridge* Dunball Old Bridge
Open Sluice Gate
Old Abutment
Flow around Structures (Piers)
Residual Structure
Flow Direction
Displaced Rock = Hydraulic Jump
Concrete Invert Slab
Narrow Channel = Increased Velocity
Bed Conditions Slope
Approach Formulae Design Velocity
Continuity Equation for Rectangular Open Channels based on approximate channel geometry
𝑸𝑸 = 𝑽𝑽𝑽𝑽 = (𝟏𝟏.𝟎𝟎𝒏𝒏 ) × 𝑽𝑽 × (𝑹𝑹𝟐𝟐/𝟑𝟑)(𝑺𝑺𝟏𝟏/𝟐𝟐) 8.0 m/s
Critical Velocity for Live bed scour (HEC 18 – Evaluation of Scour at
Bridges) 𝑽𝑽𝒄𝒄 = (𝑲𝑲𝒖𝒖) × (𝒚𝒚𝟏𝟏/𝟔𝟔) × (𝒅𝒅) 4.6 m/s
Supercritical Flow back-analysis for rectangular channels at critical
bed velocity 𝑭𝑭𝑭𝑭 =
𝑽𝑽𝟐𝟐𝒈𝒈𝒚𝒚𝟐𝟐
> 𝟏𝟏 5.6 m/s
Single Pier Scour Hole Back- Analysis (HEC 18)
𝒚𝒚𝒔𝒔𝒚𝒚𝟏𝟏
= 𝟐𝟐.𝟎𝟎 × 𝑲𝑲𝟏𝟏 × 𝑲𝑲𝟐𝟐 × 𝑲𝑲𝟑𝟑 ×𝒂𝒂𝒚𝒚𝟏𝟏
𝟎𝟎.𝟔𝟔𝟔𝟔
× 𝑭𝑭𝑭𝑭𝟎𝟎.𝟒𝟒𝟑𝟑 10.2 m/s
a) Info Received → 1D Hydraulic Model (V=2.1m/s) → Scour Hole Depth → Upstream Flow Rate, Q≈70m3/s
b) Due Diligence/Check → Existing Formulae → Engineering Judgement
→ Observations (Site Conditions)
Tools
a) Hydraulic Model Results:
b) Further Due Diligence/Checks → New Approach Required.
Approach Estimated Design Velocity 1D Hydraulic Modelling 2.1 m/s
2D Hydraulic Modelling 3 to 4.5 m/s
Change in Bed Conditions
Angle of Current Attack
Influence of Bridge Piers
Effect of Residual Structure/ Abutment
Mismatch in results → model velocities relatively low. Effects listed above not considered.
• Diving Inspection Report
• Flood Event Videos - YouTube
• Aftermath Photos
• As-Built Drawings
• Bathymetric Surveys
• Observed Displaced Rocks (size)
a) What is actually happening? What have we observed?
b) Non-conservation of Energy
Vertical Translation Velocity Horizontal Translation Velocity
𝑣𝑣ℎ =(𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟) × 𝑔𝑔 × 𝑑𝑑𝑣𝑣
(3 × 𝐶𝐶𝐷𝐷 × 𝑑𝑑ℎ4 × 𝑑𝑑𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
+ 𝑪𝑪𝒎𝒎) × 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟
12 𝑣𝑣𝑣𝑣 =
8 × (𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟) × 𝑑𝑑𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 × 𝑔𝑔3 × 𝑪𝑪𝑳𝑳 × 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟
12
𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑤𝑤𝑖𝑖𝑤𝑤𝑖𝑖 + 𝐾𝐾𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑤𝑤𝑖𝑖𝑤𝑤𝑖𝑖 + 𝑾𝑾𝑾𝑾𝑭𝑭𝑾𝑾 𝑫𝑫𝑾𝑾𝒏𝒏𝑫𝑫 = 𝑃𝑃𝑃𝑃𝑓𝑓𝑖𝑖𝑖𝑖𝑤𝑤𝑖𝑖 + 𝐾𝐾𝑃𝑃𝑓𝑓𝑖𝑖𝑖𝑖𝑤𝑤𝑖𝑖
Scour Deposition
FD FI FB
FL
FG
(vv+vh)
• FG = Gravity (weight) Force • FL = Lift Force • FB = Buoyant Force • FD = Drag Force • FI = Inertia Force
a) Stone Ø = 0.2m b) CL = 0.25 – 0.35? c) CD = 0.47
Trends correlate with those on graph which are based on intensive experimentation
Approach Design Velocity 1D Model 2.1 m/s
2D Model 3 to 4.5 m/s
New Approach 5.4 m/s to 6.6 m/s
Velocity Forces on Submerged Rocks Design Chart
CL = 0.35
CL = 0.25
CL = 1.29
𝑣𝑣ℎ =(𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟) × 𝑔𝑔 ×
(3 × 𝐶𝐶𝐷𝐷 ×4 × + 𝐶𝐶𝑚𝑚) × 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟
12
𝑣𝑣𝑣𝑣 =8 × (𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟) × × 𝑔𝑔
3 × × 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑟𝑟
12
a) Removes the complexity of upstream effects (~7m/s) b) Based on a limited number of variables c) Uses site-specific information and engineering judgement d) Can be used in preliminary design as a simple hand calculation e) Can we use this equation to size rock (i.e. Riprap) protection?
i.e. V = known CD = known
CL = ? Displacement ≈ 0
Stone Size =