1. SIMPLE PARAMETERIZED MODELS FOR PREDICTING MOBILITY, BURIAL, AND RE- EXPOSURE OF UNDERWATER MUNITIONS MR-2224 Carl T. Friedrichs Virginia Institute of Marine Science In-Progress Review Meeting May 21, 2014

2. MR-2224: Simple Parameterized Models for Predicting Mobility, Burial, and Re-Exposure of Underwater Munitions Performer: Carl Friedrichs, VA Inst. of Marine Sci. Technology Focus Development of simple, physics-based relationships for unexploded ordnance (UXO) movement, burial and re-exposure to be used by collaborators in developing an underwater munitions expert system. Research Objectives Overall: (i) Compile existing data on UXO mobility, burial & re-exposure; (ii) Further develop simple, physics-based parameterizations; (iii) Transfer results to UXO expert system (SERDP Project MR-2227). Project Progress and Results Year 2 progress focused most on (i) clearer physics-based derivation of parameters for initial motion of seabed objects and (ii) improved calibration of the formulation in close collaboration with MR-2227. Technology Transition Parameters developed in MR-2224 are now being applied as process models components within SERDP project MR-2227 “Underwater Munitions Expert System to Predict Mobility and Burial” (Rennie, PI). (Image from Rennie & Brandt, Ocean Sciences 2014)

3. Problem Statement ● Problem being addressed: Existing data on the underwater mobility, burial and re-exposure of unexploded ordnance (UXO) and UXO-like objects have not been adequately compiled and synthesized in the past. The lack of simple, robust parameterizations based on a sufficiently wide range of lab and field data limits the ability of DoD to efficiently determine the potential for underwater UXO burial and/or migration. ● Limitations of previous approaches: Some recent studies related to the mobility of underwater UXO have focused on limited parameter ranges (e.g., limited UXO sizes, limited range of bed roughness), possibly leading to incorrect conclusions when extrapolating from laboratory to field settings. 3

4. 4 Technical Objectives ● 1) To identify and compile existing quantitative data from the scientific literature and from the coastal engineering, geology and DoD communities regarding the mobility, burial and re-exposure of underwater UXO (Completed Year 1); ● 2) To utilize these data to further develop and constrain simple, logical, parameterized relationships for UXO mobility, burial and re-exposure (Focus during both Year 1 & 2); ● 3) And to provide these improved parameterized model formulations to other SERDP/ESCTP investigators for use within more sophisticated Expert Systems (Iterative focus which started toward end of Year 1) as well as providing them to the larger DoD, coastal engineering and scientific communities.

5. ● 1) Identify and compile existing quantitative data on mobility, burial and re-exposure of UXO-like objects (completed Year 1): Data for initial movement of objects larger than surrounding sediment (if any). Field measurements of natural sediment (Milhous 1973; Carling 1983; Hammond et al. 1984; Mao & Surian 2010) Lab flume containing natural sediment (Kuhnle 1993; Patel & Ranga Raju 1999; Wilcock & Kenworthy 2002 ) Lab flume with mix of glass spheres (James 1993) Lab flume with UXO-like cylinders on flat bed (Williams 2001; Davis 2007) Field measurements of UXO-like cylinders in sand under waves (Williams & Randall 2003; Wilson et al. 2008, 2009) R 2 = 0.003 Critical velocity for object motion (cm/s) Diameter of object (cm) 5 Technical Approach (#1 of 3)

6. 6 Field data: d cylinder = 50 cm, d sand = 0.13 to 0.65 mm U = 35 to 90 cm/s T = 6 to 10 sec (Bower et al. 2004, 2007; Bradley et al. 2007; Richardson & Traykovski 2002; Richardson et al. 2004; Traykovski et al. 2007; Trembanis et al., 2007; Wolfson 2005; Wolfson et al. 2007) Lab data: d cylinder = 8 to 25 cm, d sand = 0.25 mm U = 15 to 80 cm/s T = 2 to 12 sec (Catano-Lopera 2005; Catano-Lopera & Garcia, 2006; Demir & Garcia 2007) R 2 = 0.32 Wave orbital velocity (cm/s) Object scour depth (cm) Technical Approach (#1 of 3) ● 1) Identify and compile existing quantitative data on mobility, burial and re-exposure of UXO-like objects (completed Year 1):

7. 7 Technical Approach (#1 of 3) The key work on re-exposure of UXO-like objects in sand is limited largely to: -- Fahnestock & Saushild (1962) “Flume studies on the transport of pebbles and cobbles on a sand bed”. -- Articles by Voropayev et al., starting with (1999) “Dynamics of sand ripples and burial/scouring of cobbles in oscillatory flow". This limitation is being addressed by newly started or soon to start SERDP projects: -- MR-2319 Traykovski “Continuous Monitoring of Mobility, Burial and Re-Exposure of Underwater Munitions in Energetic Near-Shore Environments”. -- MR-2320 Calantoni “Long Time Series of Munitions Mobility in the Wave-Current Boundary Layer”. -- MR-2410 Garcia “Large-Scale Laboratory Experiments of Incipient Motion, Transport, and Fate of Underwater Munitions under Waves, Currents, and Combined Flows” ● 1) Identify and compile existing quantitative data on mobility, burial and re-exposure of UXO-like objects (very little data exists to constrain models):

8. 8 Velocity-based “sediment” Shields parameter  s = U w 2 /[(  sand /  water -1)gd sand ] R 2 = 0.81 Fractional scour, depth/d cylinder depth/d cylinder = 0.00608  0 + 0.145 Technical Approach (#2 of 3) ● 2) Further develop and constrain parameterized relationships for UXO burial, mobility, and re-exposure: Scour burial by waves analysis completed in Year 1 Field data: d cylinder = 50 cm, d sand = 0.13 to 0.65 mm U w = 35 to 90 cm/s T = 6 to 10 sec Lab data: d cylinder = 8 to 25 cm, d sand = 0.25 mm U w = 15 to 80 cm/s T = 2 to 12 sec

9. ● 2) Further develop and constrain parameterized relationships for UXO burial, mobility, and re-exposure: Continue from progress reached at the end of Year 1 Year 1 Approach : -- Empirically found “object” Shields parameter for initial motion of UXO- like objects to decrease with d obj /k bed (  see graph). 10 1 10 0 10 -1 10 -2 10 -3 d obj /k bed Natural sediment in streams. Natural sediment in lab flumes. Glass spheres in lab flumes. Cylinders on flat bed in flume. Field observations of cylinders in sand under waves. Velocity-based “object” Shields parameter d obj = object diameter, k bed = median bed grain size or hydraulic roughness if smooth U crit = water velocity at initial object motion,  obj /  w = object/water density, g = gravity 9 R 2 = 0.88 Technical Approach (#2 of 3)  o = (U crit ) 2 /[(  obj /  w – 1) gd obj ]

10. ● 2) Further develop and constrain parameterized relationships for UXO burial, mobility, and re-exposure: Continue from progress reached at the end of Year 1 Year 1 Approach : -- Empirically found “object” Shields parameter for initial motion of UXO- like objects to decrease with d obj /k bed (  see graph). Year 2 Approach : -- (i) Derive the physical dependence of the object Shields parameter on key object and seabed properties. -- (ii) Improve predictive skill of Shields parameter approach (reduce scatter, fill parameter space, account for waves, account for burial and scour). 10 1 10 0 10 -1 10 -2 10 -3 d obj /k bed Natural sediment in streams. Natural sediment in lab flumes. Glass spheres in lab flumes. Cylinders on flat bed in flume. Field observations of cylinders in sand under waves. d obj = object diameter, k bed = median bed grain size or hydraulic roughness if smooth U crit = water velocity at initial object motion,  obj /  w = object/water density, g = gravity 10 >1.5 orders of scatter >2 orders of scatter Empty parameter space R 2 = 0.88 Technical Approach (#2 of 3)  o = (U crit ) 2 /[(  obj /  w – 1) gd obj ] Velocity-based “object” Shields parameter

11. ● 2) Further develop and constrain parameterized relationships for UXO burial, mobility, and re-exposure: Synthesize Fahnestock & Saushild / Voropayev et al. Technical Approach (#2 of 3) 11 “Lower regime”: Exposure set by scour-burial & bedforms; cobbles don’t move downsteam. “Upper regime”: Bedforms washed out, cobbles re-exposed by scour & move downsteam.

12. ● 3) To provide improved parameterized model formulations to other SERDP/ESCTP investigators (iterative, began near end of Year 1): Advances in model parameterizations by Friedrichs MR-2224 12 Year 1 Year 2 Interaction with Rennie & Brandt MR-2227 (Figures from Brandt & Rennie, August 2013 report to SERDP) New observations by Rennie & Brandt Technical Approach (#3 of 3)

13. 13 ● 3) To provide improved parameterized model formulations to other SERDP/ESCTP investigators for use within more sophisticated Expert Systems : (Rennie & Brandt, 2014 Ocean Sciences) Technical Approach (#3 of 3) -- MR-2227 Rennie “Underwater Munitions Expert System to Predict Mobility and Burial”

14. 14 Results When does an seabed object move? Answer -- if: ( ∑ Forces) X ≥ (tan  ) ( ∑ Forces) z z U, x & F L = lift force F D = drag force F I = inertia force F W = object weight  = angle of repose  = bed slope x = downslope distance U = wave + current near top of object (Modified from Wiberg & Smith, 1987) ● 1) Derive physical dependence of Shields parameter on key object and seabed properties

15. 15 When does an seabed object move? Answer -- if: ( ∑ Forces) X ≥ (tan  ) ( ∑ Forces) z z U, x & F L = lift force F D = drag force F I = inertia force F W = object weight  = angle of repose  = bed slope x = downslope distance U = wave + current near top of object (Modified from Wiberg & Smith, 1987) F D + F I + F W sin  = (tan  ) (F W cos  – F L ) Simple to keep , but usually negligible  F D + F I + (tan  ) F L = (tan  ) F W ∑ Fluid forces = Resistance So at initial motion: Results ● 1) Derive physical dependence of Shields parameter on key object and seabed properties

16. Results (cont.) x Object moves when: F D + F I + (tan  ) F L = (tan  ) F W F D =  w ½C D A D U 2 F L =  w ½C L A L U 2 Forces d obj F W = (  obj –  w ) gV T F I =  w C I V I ∂U/∂t 16 Symbols F D,I,L,W = drag, inertia, lift force & object Weight C D,L,I = drag, lift and inertia coeffs. A D,L = object area exposed to drag, lift V T,I = object total volume and volume exposed to flow  w,obj = density of water, object d obj, e = object diameter, exposure U crit = “critical” wave + current g = gravity  = angle of repose T = sinusoidal wave period & (Modified from Kirchner et al., 1990)

17. x Object moves when: F D + F I + (tan  ) F L = (tan  ) F W F D =  w ½C D A D U 2 F L =  w ½C L A L U 2 Symbols (Modified from Kirchner et al., 1990) Forces d obj F W = (  obj –  w ) gV T F I =  w C I V I ∂U/∂t 17 = critical object Shields parameter,  o_cr (~ F D /F W ) = 1/KC, where KC = Keulegan-Carpenter # Assume (tan  ) F L /F D ≈ const., then (after algebra) at initiation of object motion (with  1,2 shape constants): U crit 2  1 (d/e) tan  (  obj /  w – 1) d obj g C D +  2 C I d obj /(UT) = F D,I,L,W = drag, inertia, lift force & object Weight C D,L,I = drag, lift and inertia coeffs. A D,L = object area exposed to drag, lift V T,I = object total volume and volume exposed to flow  w,obj = density of water, object d obj, e = object diameter, exposure U crit = “critical” wave + current g = gravity  = angle of repose T = sinusoidal wave period Results (cont.) &

18. 18 At initiation of object motion:  o = U 2 /[(  obj /  w – 1) gd] = object Shields parameter KC = UT/d obj = Keulegan-Carpenter #  1,2 = shape constants C D,I = drag and inertia coeffs.  w,obj = density of water, object d obj, e = object diameter, exposure g = gravity  = Angle of repose U = wave + current velocity T = wave period Symbols (Modified from Kirchner et al., 1990) It is easier to move an object (i.e.,  o_cr ↓ ) if objects are not “blocked” (i.e., as (d/e) ↓ or  ↓ ) and as KC = UT/d obj ↓ (i.e., as wave period T ↓ ) Results (cont.) d obj ● 1) Derive physical dependence of Shields parameter on key object and seabed properties

19. Results (cont.) kbkb kbkb kbkb d obj 19 It is easier to move an object (i.e.,  o_cr ↓ ) e e e d obj /k b  d obj /e 0.5 70 o 2.0 1.0 60 o 1.6 2.0 50 o 1.2 if objects are not “blocked” (i.e., as (d obj /e) ↓ or  ↓ ) -- As object size relative to bed roughness increases, (i.e., as d obj /k b ↑ ),  ↓ and d obj /e ↓, so  o_cr ↓. k b = bed roughness  o_cr = U crit 2 /[(  obj /  w – 1) gd] = crit. obj. Shields param. (Figures Modified from Wiberg & Smith, 1987) d obj ● 1) Derive physical dependence of Shields parameter on key object and seabed properties

20. 20 10 1 10 0 10 -1 10 -2 10 -3 Natural sediment in streams. Natural sediment in lab flumes. Glass spheres in lab flumes. Cylinders on flat bed in flume. Field observations of cylinders in sand under waves. 10 1 10 0 10 -1 10 -2 10 -3 ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour). (i) Restricted to d obj > 1 cm, improved k bed for spheres, adjusted U to expected value at z = 5 cm. d obj /k bed  o = U 2 /[(  obj /  w – 1) gd obj ] (a) After Year 1 Analysis(b) After Year 2 Analysis (i) Results (cont.)  o = U 2 /[(  obj /  w – 1) gd obj ]

21. Same as (a) plus: Smooth cylinders on varying k b. Rough cylinders on varying k b. 21 10 1 10 0 10 -1 10 -2 10 -3 Natural sediment in streams. Natural sediment in lab flumes. Glass spheres in lab flumes. Cylinders on flat bed in flume. Field observations of cylinders in sand under waves. 10 1 10 0 10 -1 10 -2 10 -3 ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour). (i) Restricted to d obj > 1 cm, improved k bed for spheres, adjusted U to expected value at z = 5 cm. (ii) Included data from Brandt & Rennie (2013) for cylinders in flume with varying d obj /k bed values. d obj /k bed  o = U 2 /[(  obj /  w – 1) gd obj ] (a) After Year 1 Analysis(b) After Year 2 Analysis (i) (ii) Results (cont.) (i)  o = U 2 /[(  obj /  w – 1) gd obj ]

22. It is easier to move an object (i.e.,  o_cr ↓ ) as KC = UT/d obj ↓ (i.e., as wave period T ↓ ) C D +  2 C I (KC) -1 KC = UT/d cylinder | F Drag + F Inertia | A D -1 ≡  w C fmax U max 2 where C fmax = C D +  2 C I (KC) -1 For an object: Evaluate denominator, “C fmax ” C fmax /C fmax0 = (KC/KC 0 ) –1.07 C fmax has been previously determined for wave forces on cylinders (Figure Modified from Sarpkaya, 1986) KC 0 ≈ 11 22 ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour). Results (cont.)

23. It is easier to move an object (i.e.,  o_cr ↓ ) as KC = UT/d obj ↓ (i.e., as wave period T ↓ ) C D +  2 C I (KC) -1 KC = UT/d cylinder | F Drag + F Inertia | A D -1 ≡  w C fmax U max 2 where C fmax = C D +  2 C I (KC) -1 For an object: Evaluate denominator, “C fmax ” C fmax /C fmax0 = (KC/KC 0 ) –1.07 C fmax has been previously determined for wave forces on cylinders (Figure Modified from Sarpkaya, 1986) KC 0 ≈ 11 23 ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour). Results (cont.) So look at  o (KC/KC 0 ) –1.07

24. Same as (a) plus: Smooth cylinders on varying k b. Rough cylinders on varying k b. Cylinders on flat bed in flume corrected for wave inertia force. 24 10 1 10 0 10 -1 10 -2 10 -3 Natural sediment in streams. Natural sediment in lab flumes. Glass spheres in lab flumes. Cylinders on flat bed in flume. Field observations of cylinders in sand under waves. 10 1 10 0 10 -1 10 -2 10 -3 ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour). (i) Restricted to d obj > 1 cm, improved k bed for spheres, adjusted U to expected value at z = 5 cm. (ii) Included data from Brandt & Rennie (2013) for cylinders in flume with varying d obj /k bed values. (iii) Accounted for effect of wave inertia force:  o_cr (KC/KC 0 ) –1.07 is tighter func. of d obj /k bed. d obj /k bed  o = U 2 /[(  obj /  w – 1) gd obj ] (a) After Year 1 Analysis(b) After Year 2 Analysis (i) (iii) (ii) Results (cont.)  o (KC/KC 0 ) –1.07 = U 2 /[(  obj /  w – 1) gd obj ] (KC/KC 0 ) 1.07

25. 25 10 1 10 0 10 -1 10 -2 10 -3 d obj /k bed -- Rennie (next!) observed several cases of  o >>  o_cr without horizontal object movement. -- Scour-induced burial changes the relevant values of tan  and (especially) e/d obj. Theoretically expect: (iv) ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour). Results (cont.)  o (KC/KC 0 ) –1.07 = U 2 /[(  obj /  w – 1) gd obj ] (KC/KC 0 ) 1.07 X X X X

26. 26 10 1 10 0 10 -1 10 -2 10 -3 d obj /k bed -- Rennie (next!) observed several cases of  o >>  o_cr without horizontal object movement. -- Scour-induced burial changes the relevant values of tan  and (especially) e/d obj. -- One way to parameterize this effect is to reduce effective d obj /k bed to account for burial. ed obj New k bed = d obj – e So new d obj /k bed = (1 – e/d obj ) –1 Then with scour-induced burial: Theoretically expect: k bed ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour). Results (cont.)  o (KC/KC 0 ) –1.07 = U 2 /[(  obj /  w – 1) gd obj ] (KC/KC 0 ) 1.07 X X X X (iv)

27. 27 Object moves approximately when: F Drag + F Inertia >  4 (tan  ) F W F D /F Dmax F I /F Imax KC = UT/d obj e/d obj 0.9 0.8 0.6 ed obj Lab experiments measuring forces on partially buried pipelines show that F Drag and F Inertia scale predictably with exposure/diameter, i.e., e/d obj. U (modified from Jacobsen et al. 1989) Results (cont.) Next suggested step: include burial conditions in force balance. ● 2) Improve predictive skill of Shields parameter approach (reduce scatter, fill in parameter space, account for waves, account for burial and scour).

28. 28 Conclusions ● Scour and motion of UXO governed by sediment and object Shields parameters, respectively Suggested focus of future work: 1)Include partial burial in force balance analysis. 2)Additional observations of movement of UXO-shaped objects in sand (especially re-exposure). 3)Effect of  object /  sand (e.g., bed fluidization) Velocity-based “object” Shields parameter

29. 29 Transition Plan ● Example interim products that are useful to the field: -- Cylindrical UXO wave scour depth in sand: depth/d cylinder ≈ C 1  s + C 2 where sediment Shields parameter  s = U w 2 /[(  sand /  w – 1)gd sand ]. -- Critical condition for initiation of UXO motion is both theoretically and empirically governed by variations in the object Shields parameter  o = U 2 /[(  obj /  w – 1)gd obj ] which scales with the diameter of the object relative to the bed roughness, d obj /k bed. ● Transition plan for research into field use. -- This project (MR-2224) was planned and executed in close collaboration with the larger SERDP project MR-2227 by Rennie & Brant from JHU-APL entitled “Underwater Munitions Expert System to Predict Mobility and Burial”. -- The parameterized model relationships developed here have been been passed to Rennie & Brant for incorporation into their Expert System which is explicitly for field use in helping guide the on site evaluation/remediation of UXO sites.