Tsunami Effects on Coastal Infrastructures and How to Evaluate Them Harry Yeh Oregon State University Northwest Transportations Conference 2010 April 1, 1946 Aleutian Tsunami Nagappattinam (N10º45.785, E79º50.928) Evaluations for Tsunami Forces • June 2008: Guidelines for Design of Structures for Vertical Evacuation from Tsunamis. FEMA P646 Tsunami Inundation Map Tsunami inundation area and the maximum runup elevations are readily available from a tsunami evacuation map. Can we estimate tsunami forces from the maximum runup height found in the tsunami inundation map? Hydrodynamic and Surge Forces 1 FD = ! C D b h u 2 2 h u2 z " z% = 0.125 ! 0.235 + 0.11 $# '& g R2 R R 2 based on the elevation Impact Force FI = C M umax kˆ m m = mass of the debris k = effective stiffness umax = max. flow speed with the debris draft depth, d R = max. runup elevation. z = ground elevation d = draft depth η = d/R Example • Maximum runup height R ≈ 19.5 m • Location of a structure at z ≈ 10 m, and the column breadth 0. 76 m (30”). • ρ = 1200 kg/m3 for sediment laden sea water. • Driftwood – mass = 450 kg; effective stiffness k = 2.4 × 106 N/m; draft depth = 0.25 m hmax R z datum x l Example • Hydrodynamic and surge forces: (h u ) 2 2 " z " z% % = g R $ 0.125 ! 0.235 + 0.11$ ' ' = 124.6 m 3 sec 2 # R& & R # 2 max ( ) 1 ! Cd B h u 2 max 2 1 = 1200 kg m 3 ( 2.0 ) ( 0.76 m ) 124.6 m 3 sec 2 2 = 114 kN Fd = ( • ) ( ) Impact forces (drift wood): umax = 0.334 2 g R = 6.53m sec. Fi = Cm umax km = 2.0 ( 6.53m sec ) = 429 kN • ( 2.4 !10 6 ) N m ( 450 kg ) ζ = z/R = 0.5; η = d/R = 0.013 Design forces on a column: Fd + Fi = 114 + 429 = 543 kN (122 kips). What do we need to do to evaluate tsunami forces on bridges and other infrastructures? • The foregoing methods were developed to provide design guidelines for Tsunami Evacuation Buildings (TEB) that are usually constructed at inshore (initially dry) locations. • Coastal bridge piers are located at low elevations and initially wet; tsunamis will first propagate against the river flow prior to striking the bridge piers. • The existing methods developed for TEB can be modified for evaluation of tsunami forces on bridges, based on the existing tsunami inundation maps. Tsunami Scour Problems Bridges Kalpakkom, India, 2004 Tsunami Scour Problems Roads The 2004 Indian Ocean Tsunami: Chennai 1 Quay-wall collapse Konakano, Japan: the 1960 Chilean Tsunami. 4 2 5 3 Scour Formation Kesen-numa, Japan: the 1960 Chile Tsunami Scour hole more than 8 m deep at the entrance to the port. After Takahashi et al. (1992) Scour Formation Capsized breakwater due to foundation failure at Aonae Port, Japan Scour depth: 4 m Foundation Failure: the 1993 Okushiri Tsunami Scour Formation Runup height 4.1 m Inundation depth 0.95 m above the floor; Scour depth 1.2 m Scour span 5.0 m. Sri Lanka: photo by Patrick Lynett Scour depth ≈ 2.0 m 2004 Indian Ocean Tsunami Tsunami Scours FEMA55: Coastal Construction Manual Approach 1. Compute hypothetical but typical runup flows for idealized beach condition, viz. tsunami runup onto a plane beach with a uniform slope and uniform sediments. – Use the analytic-numeric hybrid solution given by Carrier et al. (2003) to calculate tsunami flow velocities and depths. 2. Compute the Shields parameter θ and the Rouse number Ro for this hypothetical tsunami runup. 3. Compute the analytic predictions for pore-pressureinduced scour depths (momentary-liquefaction-like scour). – Use the 1-D solution given by Tonkin et al. (2003). Model Tsunami Long-Wave Runup on a Plane Beach: Nonlinear Problem Carrier, Wu, and Yeh (2003) -- Analytic-Numeric Hybrid Approach [u' (! x' + "' )] x' + "' t ' = 0, u' t' + u' u' x' + g "' x' = 0, Nonlinear Shallow-Water-Wave Equations ⇒ 4 ! " ## $ (! "! )! = 0 Linear Cylindrical Wave Equation Initial Tsunami Form used in this Study Leading Depression N-Wave α= 1/250. Maximum positive displacement a0 = 1.4 m Breadth of approximately 60 km Resulting Flow Depth and Velocity α= 1/250. Maximum inundation distance 1160 m Maximum runup height 4.6 m Runup/drawdown process takes 16 minutes Water depth Flow velocity A very realistic runup condition of a locally generated tsunami Shields Parameter != "0 ( ) #gd s $1 = f u2 ( ) 8g d s $ 1 f = 0.01 ds = 0.35 mm s = ρs/ρ = 2.64 α = 1/250 Suspension sheet flow: θ > 2.0 Threshold of sediment motion : θc = 0.04 ~ 0.06 Rouse Number RO = ws = ws !" u* 8! # % d s %$ s " 1) g d ( 1+ 72 ! 2 3 s & " 1( (' ws = 52 mm/sec ds = 0.35 mm κ = 0.4 β = 1.0 u* = ! 0 " Possible sediment suspension: Ro < 2.5 Full sediment suspension: Ro < 1.0 • Tsunami runup is an “unsteady” flow phenomenon. – Typically tsunamis have one or a few cycles with a period in minutes or tens of minutes. – Storm waves have many cycles with a period of less than tens of seconds. – Slope instability problems associated with rapid drawdown in reservoirs and tidal inlets have a time scale of hours to days. Tsunami Tank at PWRI (NILIM) - 135 m long Cylinder embedded in gravel Scour Mechanisms • Shear stress due to water motion – Shields model • Low effective stress between sand particles Dependent on pore pressure gradient Sediment liquefies if effective stress disappears Pore pressure gradients can enhance scour due to shear stress Momentary Liquefaction Linear fit to the drawdown portion of the pressure head at the back of the cylinder 60 50 Pressure head (cm) 40 ΔT 30 20 Δp 10 0 -5 0 5 10 -10 -20 Time (s) 15 20 25 Back to Model Tsunami f = 0.01 ds = 0.35 mm s = ρs/ρ = 2.64 α = 1/250 Water-surface elevation Flow velocity Scour Enhancement Parameter Λ(0) !(0) = 2 #p . " $ b c v#T total liquefaction enhanced scour • The region where Λ > 0.5 is –300 m < x < 1200 m • At x = 450 m, the value of Λ(0) exceeds unity, i.e. total liquefaction. Spatial variation of scour depth + % d (. "p 2 s *0 . - 1 $ 4i erfc ' ! ds = # b ds -, ' 2 cv "T *0/ & ) ( ) • The maximum scour depth in the onshore area is less than 3 m. • Pore-pressure driven scour does not occur farther inland than x = –300 m. • The maximum scour depth is found to be 6.2 m deep at 450 m offshore Observed Scour Depths Scour depth 1.2 m Scour depth: 4 m Scour depth: 8 m Scour depth 2.0 m Summary for this Example α= 1/250. Maximum inundation distance: 1160 m Maximum runup height: 4.6 m Runup/drawdown process:16 minutes • This implies that offshore coastal structures (breakwaters, oil/gas berth terminals) could be vulnerable from liquefaction-induced scours. • The pore pressure effect remains important more than 1.2 km offshore from the shore. Tsunami Runup on the Tokachi River, Japan: The 2003 Tokachi-Oki Earthquake Comments We demonstrated that momentary liquefaction is important for tsunami scour during the drawdown process. It appears that when a pier is embedded in gravel, liquefaction might be suppressed. We’ve just seen the video of the tsunami runup along the river. Because of the formation of undular bore, residual liquefaction could play a role in scour during the river runup process? ? Remarks and Research Directions • Recently developed guidelines (FEMA p646) for tsunami evacuation buildings can be modified for evaluation of tsunami forces on coastal bridges and other infrastructures – prediction of the force from a given inundation map. • Likewise, tsunami induced scour and foundation failures due to momentary liquefaction can be estimated using the similar approach, i.e. based on a given inundation map. • Once estimation of tsunami effects were made, more detailed predictions for critical and vulnerable coastal infrastructures should be made with numerical simulations.
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