1. PARAMETERIZED PROCESS MODELS FOR UNDERWATER MUNITIONS EXPERT SYSTEM
MR-2647
Carl T. Friedrichs
Virginia Institute of Marine Science
In-Progress Review Meeting
May 9, 2017

2. MR-2647: Parameterized Process Models for Underwater Munitions Expert System
Performer: Carl Friedrichs, VA Inst. of Marine Sci.
Technology Focus
Support of the Underwater Munitions Expert System (UnMES) for Remediation Guidance through development of observation-based parameterized models for burial, re-exposure and movement.
Research Objectives
Synthesize and parameterize effects of far-field bed processes: (1) Effects of bedforms on munitions, (2) Effects of bed fluidization.
Project Progress and Results
Progress in Year 1 (kickoff July 2016) has focused on a literature review of processes, data, and analysis approaches most relevant to parameterizing (1) burial of munitions by bedforms, and (2) burial of munitions by munitions by bed fluidization.
Technology Transition
Transfer additional parameterized models to MR-2645 “Underwater Munitions System for Remediation Guidance” (Rennie, PI), following successful precedent set by Friedrichs’s previous project MR-2224.
Burial by bedform migration
(Voropayev et al. 1999)
Burial by bed fluidization
(Catano-Lopera, Demir & Garcia 2007)

3. Social Media Content
Results of Friedrichs’s previous SERDP Munitions Response project, MR-2224 “Simple Parameterized Models for Predicting Mobility, Burial, and Re-Exposure” have been highlighted on the web:
Findings available to lay audience via SERDP & ESTCP Webinar
All of Friedrichs’s past SERDP talks (6 to date) are downloadable at his lab (Coastal Hydrodynamics and Sediment Dynamics) website:
Rennie, Brandt & Friedrichs (2017) “Initiation of motion and scour burial of objects undewater”. Ocean Engineering, Vol. 131: was highlighted on SERDP Munitions Response social media, e.g.:
on February 2, 2017
Another recent article available to highlight is Friedrichs, Rennie & Brandt & Friedrichs (2016) “Self-burial of objects on sandy beds by scour: A synthesis of observations”. In: J.M. Harris, R.J.S. Whitehouse, and S. Moxon (eds.), Scour and Erosion. CRC Press, p

4. Problem Statement
Better understand the role of independent bed movement
i.e., the “far field”
Problem being addressed: Existing data and approaches for evaluating the potential effects of far-field bed movement (e.g., bedforms and bed fluidization) on the mobility, burial and re-exposure of unexploded ordnance (UXO) and UXO-like objects have not been adequately compiled and synthesized in the past.
Limitations of previous approaches: Recent data mining (Friedrichs MR-2224) has helped constrain near-field interactions of flow with UXO (e.g., equilibrium burial by scour and initiation of UXO motion). However, relatively less literature review and synthesis has focused on interactions of far-field of flow and sediment with UXO (e.g., effects of bedforms, effects of bed fluidization).
Flow Velocity (U) in m/s
Grain Size (d) in mm
Bed regimes as a function of flow and grain size
(Modified from Stow et al. 2009)

5. Technical Objectives
1) To identify and compile existing data and analyses regarding far-field sediment effects on UXO-like objects: (1) interaction with bedforms, (2) bed fluidization.
2) To utilize these data and analyses to further develop and constrain simple, logical, parameterized relationships for these processes;
3) And to provide these improved parameterized relationships to other SERDP/ESCTP investigators for use within UnMES as well as providing them to the larger DoD, coastal engineering and scientific communities. 5

6. Technical Approach
Identify and compile existing data and analyses on interaction of UXO-like objects with bedforms and bed fluidization:
-- Internet searches (Google Scholar, Google), VIMS electronic journal and dissertation subscriptions, VIMS library, pdf reprint requests, Researchgate, interlibrary loan…
Duck, NC
Water
Burial, B
Bed
Dobject
Rapid sinking of object into fluidized sand bed in lab
(Lohse et al. 2004)
Envelope and frequency of object burial by megaripples
(Gallagher et al. 2007)

7. Technical Approach (cont.)
Further develop parameterized relationships for UXO mobility, burial and re-exposure;
Provide these improved relationships for use within UnMES as well as providing them to the larger DoD, engineering and scientific communities.
Previous SERDP projects MR-2224 (Friedrichs) and MR-2227 (Rennie) provide precedent.
Initiation of Object Motion
Equilibrium Scour Burial Depth
(Equilibrium Burial) / (Object Diameter)
(Object Diameter) / (Bed Roughness)
(Rennie, Brandt & Friedrichs 2017, Coastal Engineering)

8. Results: 1. Bedforms – Process & Importance
Bedform passing over UXO
(Voropayev et al. 1999)
Sand waves passing over UXOs
(Catano-Lopera, Demir & Garcia 2007)
Burial of object by bedform crest; additional object scour occurs in bedform trough.
Net elevation of periodically buried object is lower due to passage of bedform.

9. Results: 1. Bedforms – Bed Envelope Concept
Megaripples time-series
Duck, NC
Megaripples
Sand bar trough
(Gallagher et al. 2007)
Bed Envelope thickness = Bmax
Bmax(t) ≈ hBmax (1 – exp(-t/TBmax))
Burial, B
From mean envelope thickness
Dobject
= 20 cm
From thickness
peak frequency
As deeper troughs pass, object elevation continues to drop.
Frequency of re-exposure decreases with time.
Potential Bmax (given by bed envelope) follows exponential taper in time.
Bmax(t) ~ hBmax (1 – exp(-t/TBmax)) scales with bedform properties.

10. Results: 1. Bedforms – Bed Envelope Concept
Sand bar time-series
Duck, NC
Bed Envelope thickness = Bmax
Bmax(t) ≈ hBmax(1 – exp(-t/TBmax))
Burial, B
Dobject
= 20 cm B
Duck sand bar
(Gallagher et al. 2007)
Duck at 500 m
Bed envelopes for multiple bedform types are often superimposed.
Larger bedforms have larger envelopes that grow more slowly.
At larger time scales, larger bedforms become more important.
hBmax ~ dominant bedform height, TBmax ~ bedform cycle time.

11. Results: 1. Bedforms – Sediment, Currents, Waves
Sand
Bed regimes as a function of flow and grain size
(Modified from Stow et al. 2009)
Flow Velocity (U) in m/s
Grain Size (d) in mm
In bedform regime (Regime 2), as velocity or sand size increases, bedform height (h) and bedform length (l) increase.

12. Results: 1. Bedforms – Sediment, Currents, Waves
Sand
Bed regimes as a function of flow and grain size
(Modified from Stow et al. 2009)
Flow Velocity (U) in m/s
Shields Parameter (skin friction only) ≈
[drag by flow on sand grain] / [sand grain weight]
q = cd U2 / [(rsand/rwater-1) g dsand]
Grain Size (d) in mm
In bedform regime (Regime 2), as velocity or sand size increases, bedform height (h) and bedform length (l) increase.
Normalize velocity (U) and grain size (d) with Shields Parameter (q).
(From this point on the examples will be periodic bedforms, not bars.)

13. Results: 1. Bedforms – Sediment, Currents, Waves
Bedform regimes as a function of Wave Shields Parameter (qw) and Current Shields Parameter (qc)
(Modified from Kleinhans 2005)
Wave Shields Parameter (qw)
Current Shields Parameter (qc)
q = cd U2 / [(rsand/rwater-1) g dsand] ≈ [drag by flow] / [grain weight]
Roughly similar range of q for wave or current bedform presence.

14. Results: 1. Bedforms – Sediment, Currents, Waves
Very strong relationships of the form h = a lb.
But adding currents greatly increases maximum size of bedforms.
Wave Shields Parameter (qw)
Wave
hmax = 0.16 l0.84
h = 0.12 l0.94
Bedform height (h) in meters
Ripple height (h) in meters
h = l0.81
Current
Current Shields Parameter (qc)
(Nelson et al. 2013)
(Flemming 2000)
Bedform length (l) in meters
Ripple length (l) in meters

15. Results: 1. Bedforms – Sediment, Currents, Waves
Currents with or without waves
Waves only
(Ripple length) / (Wave orbital amplitude)
Bedform length (l) in meters
l/Ab
(Nelson et al. 2013)
Sand
Ab/d
(Wave orbital amplitude) / (Grain size)
Grain size (d) in mm
(Flemming 2000)
Bedforms appear with initial wavelengths (l) determined mainly by grain size.
With enough energy and time, dominant bedforms grow and bedforms merge.
Bedforms stop growing or decay when flow changes (e.g., new direction/decrease) or flow gets too strong (i.e., approaches plane bed/sheet flow conditions).

16. Results: 1. Bedforms – Envelope Prediction Method
Bmax(t) ≈ hBmax(1 – exp(-t/TBmax))
(Gallagher et al. 2007)
Bed Envelope thickness = Bmax
Burial, B
From mean envelope thickness
Dobject
= 20 cm
From thickness
peak frequency
Obtain information on a site’s waves, currents and grain size.
Observe or predict bedform wavelengths (l) and their variability.
Bedform heights (h) and their variability can be predicted from h = a lb.
Estimate bedform cycling times (T) from literature or bedload transport relations.
Based on estimates of h and T, Bmax envelopes can then be constructed.
The Envelope Prediction Method will be further developed in Year 2 of MR-2647.

17. Results: 2. Fluidization – Process & Importance
(Catano-Lopera, Demir & Garcia 2007)
(Traykovski, Richardson et al. 2007)
(1)
(2)
Rotary sonar shadow of mine and surrounding pit
(1) Sinking in 35 seconds of a 5 cm steel cylinder (Uwave = 88 cm/s)
(2) Sinking of a 50 cm instrumented mine in association with wash out of ripples at Martha’s Vineyard, MA (Uwave ≈ 100 cm/s)
Sheet flow and/or wash out of bedforms by intense sand transport is associated with rapid sinking of objects into sandy beds.
Sheet flow is accompanied by fluidization of the sediment transport layer of the uppermost seabed, such that its ability to support a heavy object is greatly reduced.

18. Results: 2. Fluidization – Initiation
Review previous studies that parameterized the washout of bedforms.
(Stow et al. 2009)
(Kleinhans 2005)
Flow Velocity (U) in m/s
Wave Shields Parameter (qw)
Current Shields Parameter (qc)
Grain Size (d) in mm
Effect of velocity and grain size together are normalized via Shields Parameter.
Kleinhans’s figure suggests bedform washout / sheetflow is initiated at q ≈ 0.6 .

19. Results: 2. Fluidization – Initiation
Review of previous studies that parameterized the washout of bedforms.
10.0
(cdU2)1/2/ws = 1
(Flemming 2000)
(ws = sediment
settling velocity)
(Komar & Miller 1975)
q = 1.04 d-0.4
3.0
(Nielsen 1981)
q = 1
Skin friction Shields Parameter
q = cd U2 / [(rsand/rwater-1) g d]
1.0
q/cd = 240
(Dinger & Inman 1976)
0.3
q/cd = 61 d-0.71
(Li & Amos 1999)
0.1
0.1
0.2
0.5
1.0
2.0
Sand grain size (d) in mm

20. Results: 2. Fluidization – Initiation
Review of previous studies that parameterized the washout of bedforms.
10.0
(cdU2)1/2/ws = 1
(Flemming 2000)
(ws = sediment
settling velocity)
(Komar & Miller 1975)
q = 1.04 d-0.4
3.0
(Nielsen 1981)
q = 1
(Catano-Lopera, Demir
& Garcia 2007) X
Skin friction Shields Parameter
q = cd U2 / [(rsand/rwater-1) g d]
1.0 X
q/cd = 240
(Dinger & Inman 1976)
0.3
q/cd = 61 d-0.71
(Li & Amos 1999)
0.1
0.1
0.2
0.5
1.0
2.0
Sand grain size (d) in mm
Observations and parameterizations roughly suggest qsheet flow ≈ 1 for sand d ≈ 0.15 – 0.3 mm.
(Traykovski, Richardson et al. 2007)

21. Results: 2. Depth of Burial by Fluidization
Field observations: model UXO burial by storm at Duck, NC
(Calantoni, SERDP IPR 2016)
Burial under sheet flow of up to ~ 50 cm
B/D
(Burial depth) / (Object diameter)
Lab: in loosely packed sand, settling of spheres up to depths of B/D ~ 10 is proportional to robject
(Lohse et al. 2004)
robject/rsand
(Object density) / (Sand density)
Deep burial of UXO-like objects in storms increases with object density (robject).
As object size increases (D), burial depth (B) increases proportionally.
Similar behavior is seen in lab in loosely packed and partially fluidized sand.

22. Results: 2. Depth of Burial by Fluidization
Sheet flow layer thickness under quasi-steady conditions:
(Malarkey et al. 2003)
d/d
(Layer thickness) / (Grain size)
Sand concentration (c)
Shields Parameter (q)
Steady flow solution d/d ≈ 10 q gives d ≈ O(1 cm) for sand.
This thickness on its own is far too small to fully bury UXO.
Consider pressure-gradient forces associated with time-dependence (Sleath 1999, Calantoni & Puleo 2006, Foster et al. 2006)
Combine with force balance for object settling through fluidized bed.

23. Results: 2. Depth of Burial by Fluidization
Seabed
H, L = wave height, length B
Assume heavy object sinks until Fbuoyancy = Ffriction D
(Brzinski et al. 2013, Sumer & Fredsoe 2014)
Fbuoyancy = Volobject (robj – rsed,wet) g
Ffriction ~ Net loading on interlocked sediment grains
= Areaobject a (rsand – rwater) g B [1 – f(pwave)] [1 – f(pXwave)]
Friction
coeff
Static load on interlocked grains
Vertical fluctuations in pressure
(classic liquefaction)
Horizontal gradients
in pressure
(seepage flow, piping)

24. Results: 2. Depth of Burial by Fluidization
Seabed
H, L = wave height, length B
Assume heavy object sinks until Fbuoyancy = Ffriction D
(Brzinski et al. 2013, Sumer & Fredsoe 2014)
Fbuoyancy = Volobject (robj – rsed,wet) g
Ffriction ~ Net loading on interlocked sediment grains
= Areaobject a (rsand – rwater) g B [1 – f(pwave)] [1 – f(pXwave)]
Friction
coeff
Static load on interlocked grains
Vertical fluctuations in pressure
(classic liquefaction)
Horizontal gradients
in pressure
(seepage flow, piping)
For shallow water waves over sand, fluidization burial depth:
Object density robj/rsed,wet
D (robj/rsed,wet – 1)
a [1 – 2.5 (H/L) ] [1 – f(pXwave)]
Object size D
B ≈
increases as
Friction a
Wave steepness H/L
Year 2 of MR-2647 will focus on parameterizing f(pXwave)

25. a [1 – 2.5 (H/L) ] [1 – f(pXwave)]
Transition Plan
Useful interim products:
-- Outline of envelope prediction method Bmax(t) ≈ hBmax(1 – exp(-t/TBmax))
to translate bedform properties into statistical time-dependence of future object burial.
-- Vertical force balance equation for depth of burial by fluidization gives
Transition plan for research into field use:
-- This project (MR-2647) was planned and is being executed in close collaboration with the larger SERDP project MR-2645 by Rennie & Brandt from JHU-APL entitled “Underwater Munitions Expert System for Remediation Guidance”.
-- The parameterized model relationships being developed here will be passed to Rennie for incorporation into the UnMES System which is explicitly for field use in helping guide the on site evaluation/remediation of UXO sites.
D (robj/rsed,wet – 1)
a [1 – 2.5 (H/L) ] [1 – f(pXwave)]
B ≈

26. Project Funding FY15* FY16* FY17* FY18* Total
Funds received or budgeted ($K)
$96K
$0K
% Expended
41%
N/A
Planned % Expended
Funds Remaining ($K)
$57K
*NOTE: Include a column for all fiscal years in which funds have been or are planned to be received.
NOTE: Although this project was funded with FY15 dollars, the period of performance is July 2016 to June 2018.

27. Publications
No journal publications have yet been submitted in association with MR However, two papers have recently appeared as a result of Friedrichs’s similar, previous SERDP project, MR-2224, in collaboration with MR-2227:
Friedrichs C.T., S.E. Rennie, and A. Brandt, Self-burial of objects on sandy beds by scour: A synthesis of observations. In: J.M. Harris, R.J.S. Whitehouse, and S. Moxon (eds.), Scour and Erosion. CRC Press, p
Rennie, S.E., A. Brandt, and C.T. Friedrichs, Initiation of motion and scour burial of objects underwater. Ocean Engineering, 131: