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 February 12, 2013

2. Problem Statement ● Problem being addressed: Existing data on mobility, burial and re- exposure of underwater 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, lack of surrounding sand), possibly leading to incorrect conclusions when extrapolating from laboratory to field settings. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 2

3. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 3 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; ● 2) To utilize these data to further develop and constrain simple, logical, parameterized relationships for UXO mobility, burial and re- exposure; ● 3) And to provide these improved parameterized model formulations to other SERDP/ESCTP investigators for use within more sophisticated Expert Modeling Systems as well as providing them to the larger DoD, coastal engineering and scientific communities.

4. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 4 Technical Approach ● 1) Identify and compile existing quantitative data on mobility, burial and re-exposure of underwater UXO and UXO-like objects: -- Internet searches (Google Scholar, Google), VIMS journal subscription, VIMS electronic Dissertation subscription, VIMS library, pdf reprint requests, interlibrary loan… -- Results from lab experiments… Catano-Lopera et al. (2007) Buffington et al. (1992)

5. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 5 Technical Approach (cont.) ● 1) Identify and compile existing quantitative data on mobility, burial and re-exposure of underwater UXO and UXO-like objects (cont.): -- Results from field measurements… Williams & Randall (2003) Carling (1983)

6. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 6 Technical Approach (cont.) ● 1) Identify and compile existing quantitative data on mobility, burial and re-exposure of underwater UXO and UXO-like objects (cont.): -- Lots of digitization and data retrieval… Kuhnle (1993) Catano (2005)

7. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 7 Technical Approach (cont.) ● 2) Further develop and constrain simple, rational, parameterized relationships for UXO mobility, burial and re-exposure: -- Leading candidates: Keulegan-Carpenter #, Shields Parameter Origin of Keulegan-Carpenter #, KC = UT/d KC scales the length of the wave’s orbital motion (~ UT) relative to the length of the object (d). Origin of Shields Parameter,  =  /[  (S-1)gd]  scales the force of flow on an object or sediment clast (~  d 2 ) relative to the submerged weight of the object or clast (~  (S-1)gd 3 ).

8. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 8 Technical Approach (cont.) ● 2) Further develop and constrain simple, rational, parameterized relationships for UXO mobility, burial and re-exposure: -- Kuelegan-Carpenter Number (e.g, Used for scour burial of cylinders in sand in wave tank.) Keulegan-Carpenter #, KC = UT/d 1 10 100 Percent Scour Burial of cylinder 100 10 1 U = max wave orbital velocity T = wave period d = diameter of cylinder Catano-Lopera & Garcia (2006)

9. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 9 Technical Approach (cont.) ● 2) Further develop and constrain simple, rational, parameterized models for UXO mobility, burial and re-exposure (cont.): -- Shields Parameter (Used for initial motion of cylinders on a flat laboratory flume bed under waves.) Non-dimensionalized cylinder diameter,  p = Peak wave- induced bed stress (away from cylinder) s =  cylinder /  water  =  water g = accel. of gravity d = diameter of cylinder = kinematic viscosity of water Shields Parameter  = Williams & Randall (2003)

10. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 10 Technical Approach (cont.) ● 2) Further develop and constrain simple, rational, parameterized relationships for UXO mobility, burial and re-exposure (cont.): -- Modified Shields Parameter  /  in   U 2 (Used for rolling of cylinders along flat laboratory flume bed under steady current.) Modified Shields Parameter,  0 = U 2 /[(S-1)gd] Velocity of rolling cylinder Water velocity U = Water velocity S =  cylinder /  water g = acceleration of gravity d = diameter of cylinder Davis et al. (2007)

11. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 11 Technical Approach (cont.) ● 3) To provide these improved parameterized model formulations to other SERDP/ESCTP investigators for use within more sophisticated Expert Modeling Systems : Mann et al. (2006) Example Mine Burial Expert System

12. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 12 Results ● 1) Improved parameterized model relation for predicting final object burial depth after scour (as in figure (f) below). ● 2) Improved parameterized model relation for predicting whether object will roll away before being buried (i.e., “critical transport condition” for object). Demir & Garcia (2007) Options: Keulegan-Carpenter #, KC = UT/d Modified Shields Parameter,  0 = U 2 /[(S-1)gd] Classic Shields Parameter,  =  /[  (S-1)gd] Others? (e.g., d object /d sand,  object /  sand, object shape)

13. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 13 Results (cont.) ● 1) Parameterized model relation for predicting object scour depth. (i) Dimensional data: Scour depth vs. wave orbital velocity. 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)

14. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 14 Results (cont.) ● 1) Parameterized model relation for predicting object scour depth. (ii) Non-dimensionalized data: Fractional scour depth vs. Kuelegan-Carpenter #. Kuelegan-Carpenter #, KC = UT/d cylinder (c.f. Catano-Lopera & Garcia, 2006) R 2 = 0.061 Fractional scour, depth/d cylinder 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)

15. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 15 Results (cont.) ● 1) Parameterized model relation for predicting object burial depth. (iii) Non-dimensionalized data: Percent burial vs. Shields Parameter. Sediment Shields Parameter  =  /[  (S sand -1)gd sand ] = 0.5 f w U 2 /[(S sand -1)gd sand ] 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 Lab data: d cylinder = 8 to 25 cm, d sand = 0.25 mm U = 15 to 80 cm/s T = 2 to 12 sec (c.f. Friedrichs, 2007) R 2 = 0.79 S sand =  sand /  water  =  water g = accel. of gravity f w = wave friction factor = func.(U,T, d sand ) (Swart, 1974) Fractional scour, depth/d cylinder depth/d cylinder = 2.09 

16. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 16 Results (cont.) ● 1) Parameterized model relation for predicting object burial depth. (iv) Non-dimensionalized data: Percent burial vs. modified Shields Parameter. Modified Sediment Shields Parameter  0 = U 2 /[(S sand -1)gd sand ] 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 Lab data: d cylinder = 8 to 25 cm, d sand = 0.25 mm U = 15 to 80 cm/s T = 2 to 12 sec R 2 = 0.81 S sand =  sand /  water  =  water g = accel. of gravity f w = wave friction factor = func.(U,T, d sand ) (Swart, 1974) Fractional scour, depth/d cylinder depth/d cylinder = 0.00608  0 + 0.145

17. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 17 Results (cont.) ● 2) Parameterized model relation for predicting whether object will move. (i) Dimensional data: Critical fluid velocity for movement vs. object diameter. 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)

18. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 18 Results (cont.) ● 2) Parameterized model relation for predicting whether object will move. (ii) Partially non-dimensionalized data: Critical Shields Parameter vs. object diameter. R 2 = 0.14  crit = 0.05 for homogenous (i.e., single size) natural sediment Diameter of object, d object (cm) 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)  crit for object motion =  crit /[  (S object -1)gd object ] -- Isolated objects more more easily than homogenous objects.

19. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 19 Results (cont.) ● 2) Parameterized model relation for predicting whether object will move. (iii) Non-dimensionalized data:  crit vs. object diameter divided by bottom roughness. R 2 = 0.90 Bottom physical roughness, k bed, for natural sediment beds is defined here as the median sediment grain diameter for that bed. Bottom physical roughness, k bed, for flat-bottom lab flume experiments is defined here as 30 z 0, where z 0 is the hydraulic roughness for a smooth turbulent boundary layer. d object /k bed  crit = 0.05 for homogenous (i.e., single size) natural sediment Field measurements of natural sediment. Lab flume containing natural sediment. Lab flume with mix of glass spheres. Lab flume with UXO-like cylinders on flat bed. Field measurements of UXO-like cylinders in sand under waves.  crit for object motion =  crit /[  (S object -1)gd object ] -- The larger exposed objects are relative to their surroundings, the more more easily they move.

20. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 20 Results (cont.) ● 2) Parameterized model relation for predicting whether object will move. (iv) Non-dimensionalized data:  0crit vs. object diameter divided by bottom roughness. R 2 = 0.88 Bottom physical roughness, k bed, for natural sediment beds is defined here as the median sediment grain diameter for that bed. Bottom physical roughness, k bed, for flat-bottom lab flume experiments is defined here as 30 z 0, where z 0 is the hydraulic roughness for a smooth turbulent boundary layer. Field measurements of natural sediment. Lab flume containing natural sediment. Lab flume with mix of glass spheres. Lab flume with UXO-like cylinders on flat bed. Field measurements of UXO-like cylinders in sand under waves. 10 1 10 0 10 -1 10 -2 10 -3  0crit for object motion = (U crit ) 2 /[(S object -1)gd object ] d object /k bed

21. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 21 Results (cont.) ● Why is object diameter relative to bottom roughness (d object /k bed ) so important to the initial movement condition for objects (  crit )? Ans: large d/k results in object exposure to flow, small d/k shelters object from flow. ● This means UXO in sand may be easier to move than a jumbled pile of UXO. d/k > 1 d/k < 1 large d/k small d/k (Kerchner et al., 1990)

22. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 22 Conclusions ● Scour and motion of UXO governed by Sediment and Object Shields Parameters, respectively What’s still missing? 1)Sufficient observations of movement of UXO-shaped objects in sand 2)Better understanding of shape effects 3)Effect of  object /  sand (e.g., bed fluidization)

23. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 23 Future Work ● When do UXO-like objects “sink” into sand and when do they “float” on sand? ● Also, still need to parameterize sand moving over stationary objects (i.e., sand bedform migration, sandy beach profile evolution) Metal cylinder in sand in lab wave flumeCobbles on beach in northern California Catano-Lopera et al. (2007)Photo by Friedrichs (2012)

24. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 24 Action Items ● No SERDP Technical Committee/Program Office action items listed in SEMS for this project to date.

25. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 25 Transition Plan ● Interim products that are useful to the field: --UXO scour depth in sand: depth/d cylinder = 2.09  where Sediment Shields Parameter  =  /[(  sand -  water )gd sand ]. --Clear demonstration that large underwater objects, such as UXO, may be much easier to move when in sand than would be the case for a homogenous collection of UXO-sized objects. (More lab and field data is needed.) ● Transition plan for research into field use. --This project was proposed in close collaboration with a partner SERDP project by Rennie & Brant from JHU-APL entitled “Underwater Munitions Expert System to Predict Mobility and Burial” which has also been funded. --The parameterized model relationships developed here are being 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.

26. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 26 Issues ● No unanticipated or unresolved issues for this project to date.

27. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 27 BACKUP MATERIAL These charts are required, but will only be briefed if questions arise.

28. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 28 Project Funding FY10*FY11*FY12*FY13*Total Funds received or budgeted ($K) $0K$43K$42K$0K$85K % Expended N/A84% Planned % Expended N/A100% Funds Remaining ($K) N/A$7K NOTE: If substantial funds remain from FY10 (or previous years), please contact your Program Manager in advance of the IPR. *NOTE: Include a column for all fiscal years in which funds have been or are planned to be received.

29. Carl Friedrichs -- Parameterized Models for Mobility/Burial of Underwater Munitions 29 Publications ● No publications, patents, awards, etc., resulting from this project to date.