SIMPLE PARAMETERIZED MODELS FOR
PREDICTING MOBILITY, BURIAL, AND REEXPOSURE OF UNDERWATER MUNITIONS
MR-2224
Carl T. Friedrichs
Virginia Institute of Marine Science
In-Progress Review Meeting
May 21, 2014
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)
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
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.
4
Technical Approach (#1 of 3)
Critical velocity for object motion (cm/s)
●
1) Identify and compile existing quantitative data on mobility, burial and
re-exposure of UXO-like objects (completed Year 1):
R2 = 0.003
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)
Diameter of object (cm)
Field measurements of UXO-like cylinders
in sand under waves (Williams & Randall
2003; Wilson et al. 2008, 2009)
5
Technical Approach (#1 of 3)
Object scour depth (cm)
●
1) Identify and compile existing quantitative data on mobility, burial and
re-exposure of UXO-like objects (completed Year 1):
R2 = 0.32
Field data: dcylinder = 50 cm,
dsand = 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: dcylinder = 8 to 25 cm,
dsand = 0.25 mm
U = 15 to 80 cm/s
T = 2 to 12 sec
Wave orbital velocity (cm/s)
(Catano-Lopera 2005; Catano-Lopera &
Garcia, 2006; Demir & Garcia 2007)
6
Technical Approach (#1 of 3)
●
1) Identify and compile existing quantitative data on mobility, burial and
re-exposure of UXO-like objects (very little data exists to constrain models):
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”
7
Technical Approach (#2 of 3)
Fractional scour, depth/dcylinder
●
2) Further develop and constrain parameterized relationships for UXO burial,
mobility, and re-exposure: Scour burial by waves analysis completed in Year 1
R2
= 0.81
Field data: dcylinder = 50 cm,
dsand = 0.13 to 0.65 mm
Uw = 35 to 90 cm/s
T = 6 to 10 sec
Lab data: dcylinder = 8 to 25 cm,
dsand = 0.25 mm
Uw = 15 to 80 cm/s
T = 2 to 12 sec
depth/dcylinder = 0.00608 q0 + 0.145
Velocity-based “sediment” Shields parameter
qs = Uw2/[(rsand/rwater-1)gdsand]
8
Technical Approach (#2 of 3)
2) Further develop and constrain parameterized relationships for UXO burial,
mobility, and re-exposure: Continue from progress reached at the end of Year 1
qo = (Ucrit)2/[(robj/rw – 1) gdobj]
Velocity-based “object” Shields parameter
●
Year 1 Approach:
101
-- Empirically found “object” Shields
parameter for initial motion of UXOlike objects to decrease with dobj/kbed
( see graph).
100
10-1
10-2
10-3
R2 = 0.88
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.
dobj/kbed
dobj = object diameter, kbed = median bed grain size or hydraulic roughness if smooth
Ucrit = water velocity at initial object motion, robj/rw = object/water density, g = gravity
9
Technical Approach (#2 of 3)
2) Further develop and constrain parameterized relationships for UXO burial,
mobility, and re-exposure: Continue from progress reached at the end of Year 1
>1.5 orders of scatter
qo = (Ucrit)2/[(robj/rw – 1) gdobj]
Velocity-based “object” Shields parameter
●
101
Empty parameter
space
100
10-1
10-2
10-3
R2 = 0.88
Year 1 Approach:
-- Empirically found “object” Shields
parameter for initial motion of UXOlike objects to decrease with dobj/kbed
( see graph).
Year 2 Approach:
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.
dobj/kbed
-- (i) Derive the physical dependence
of the object Shields parameter on
key object and seabed properties.
>2 orders
of scatter
-- (ii) Improve predictive skill of
Shields parameter approach (reduce
scatter, fill parameter space, account
for waves, account for burial and
scour).
dobj = object diameter, kbed = median bed grain size or hydraulic roughness if smooth
Ucrit = water velocity at initial object motion, robj/rw = object/water density, g = gravity
10
Technical Approach (#2 of 3)
●
2) Further develop and constrain parameterized relationships for UXO burial,
mobility, and re-exposure: Synthesize Fahnestock & Saushild / Voropayev et al.
“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.
11
Technical Approach (#3 of 3)
●
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
Year 1
Year 2
Interaction with
Rennie & Brandt
MR-2227
New observations
by Rennie & Brandt
(Figures from Brandt & Rennie, August 2013 report to SERDP)
12
Technical Approach (#3 of 3)
●
3) To provide improved parameterized model formulations to other SERDP/ESCTP
investigators for use within more sophisticated Expert Systems :
-- MR-2227 Rennie “Underwater Munitions Expert System to Predict Mobility and Burial”
(Rennie & Brandt,
2014 Ocean Sciences)
13
Results
1) Derive physical dependence of Shields parameter on key object
and seabed properties
●
U, x
&
z
(Modified from
Wiberg & Smith, 1987)
FL = lift force
FD = drag force
FI = inertia force
FW = object weight
F = angle of repose
b = bed slope
x = downslope distance
U = wave + current
near top of object
When does an seabed object move?
Answer -- if:
(∑ Forces)X
≥
(tan f) (∑ Forces)z
14
Results
1) Derive physical dependence of Shields parameter on key object
and seabed properties
●
U, x
&
z
(Modified from
Wiberg & Smith, 1987)
FL = lift force
FD = drag force
FI = inertia force
FW = object weight
F = angle of repose
b = bed slope
x = downslope distance
U = wave + current
near top of object
When does an seabed object move?
(∑ Forces)X
≥
(tan f) (∑ Forces)z
FD + FI + FW sin b
=
(tan F) (FW cos b – FL)
Answer -- if:
So at initial motion:
Simple to keep b, but usually negligible 
FD + FI + (tan f) FL = (tan F) FW
∑ Fluid forces
= Resistance
15
Results (cont.)
Object moves when:
&
FD + FI + (tan F) FL = (tan F) FW
(Modified from
Kirchner et al., 1990)
x
dobj
Forces
Symbols
FD,I,L,W = drag, inertia, lift force
& object Weight
CD,L,I = drag, lift and inertia coeffs.
AD,L = object area exposed to drag, lift
VT,I = object total volume and
volume exposed to flow
rw,obj = density of water, object
dobj, e = object diameter, exposure
Ucrit = “critical” wave + current
g = gravity
F = angle of repose
T = sinusoidal wave period
FD = rw ½CDADU2
FW = (robj – rw) gVT
FL = rw ½CLALU2
FI = rw CIVI ∂U/∂t
16
Results (cont.)
Object moves when:
&
FD + FI + (tan F) FL = (tan F) FW
(Modified from
Kirchner et al., 1990)
x
dobj
Forces
Symbols
FD,I,L,W = drag, inertia, lift force
& object Weight
CD,L,I = drag, lift and inertia coeffs.
AD,L = object area exposed to drag, lift
VT,I = object total volume and
volume exposed to flow
rw,obj = density of water, object
dobj, e = object diameter, exposure
Ucrit = “critical” wave + current
g = gravity
F = angle of repose
T = sinusoidal wave period
FD = rw ½CDADU2
FW = (robj – rw) gVT
FL = rw ½CLALU2
FI = rw CIVI ∂U/∂t
Assume (tan f) FL/FD ≈ const., then (after algebra)
at initiation of object motion (with a1,2 shape constants):
Ucrit2
(robj/rw – 1) dobj g
=
= critical object Shields
parameter, qo_cr
(~ FD/FW )
a1 (d/e) tan F
CD + a2CI dobj/(UT)
= 1/KC , where
KC = Keulegan-Carpenter #
17
Results (cont.)
1) Derive physical dependence of Shields parameter on key object
and seabed properties
●
dobj
Symbols
qo = U2/[(robj/rw – 1) gd]
= object Shields parameter
KC = UT/dobj
= Keulegan-Carpenter #
a1,2 = shape constants
CD,I = drag and inertia coeffs.
rw,obj = density of water, object
dobj, e = object diameter, exposure
g = gravity
F = Angle of repose
U = wave + current velocity
T = wave period
(Modified from
Kirchner et al., 1990)
At initiation of object motion:
It is easier to move an
object (i.e., qo_cr↓)
if objects are not “blocked”
(i.e., as (d/e)↓ or F↓)
and as KC = UT/dobj ↓
(i.e., as wave period T↓)
18
Results (cont.)
1) Derive physical dependence of Shields parameter on key object
and seabed properties
dobj/kb
dobj
e
●
It is easier to move an
object (i.e., qo_cr↓)
if objects are not “blocked”
(i.e., as (dobj/e)↓ or F↓)
kb
dobj
F
dobj/e
0.5
70o
2.0
1.0
60o
1.6
2.0
50o
1.2
e
kb
dobj
kb = bed roughness
qo_cr = Ucrit2/[(robj/rw – 1) gd]
= crit. obj. Shields param.
-- As object size relative to bed roughness increases,
(i.e., as dobj/kb↑), F↓ and dobj/e ↓, so qo_cr↓ .
e
kb
(Figures Modified from
Wiberg & Smith, 1987)
19
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
(a) After Year 1 Analysis
qo =
101
100
U2/[(robj/rw – 1) gdobj]
(i)
10-3
101
qo =
(i)
U2/[(robj/rw – 1) gdobj]
100
10-1
10-2
(b) After Year 2 Analysis
10-1
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.
dobj/kbed
10-2
10-3
dobj/kbed
(i) Restricted to dobj > 1 cm, improved kbed for spheres, adjusted U to expected value at z = 5 cm.
20
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
(a) After Year 1 Analysis
qo =
101
100
U2/[(robj/rw – 1) gdobj]
(i)
(b) After Year 2 Analysis
101
qo =
(i)
U2/[(robj/rw – 1) gdobj]
100
(ii)
10-1
10-2
10-3
10-1
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.
dobj/kbed
10-2
Same as (a) plus:
Smooth cylinders on varying kb.
Rough cylinders on varying kb.
10-3
dobj/kbed
(i) Restricted to dobj > 1 cm, improved kbed for spheres, adjusted U to expected value at z = 5 cm.
(ii) Included data from Brandt & Rennie (2013) for cylinders in flume with varying dobj/kbed values.
21
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
It is easier to move an
object (i.e., qo_cr↓)
as KC = UT/dobj ↓
(i.e., as wave period T↓)
Evaluate denominator, “Cfmax”
For an object:
≡ rwCfmaxUmax2
where
Cfmax = CD + a2CI (KC)-1
Cfmax has been previously
determined for wave
forces on cylinders
CD + a2CI (KC)-1
|FDrag + FInertia| AD-1
Cfmax/Cfmax0 = (KC/KC0) –1.07
(Figure Modified from
Sarpkaya, 1986)
KC0 ≈ 11
KC = UT/dcylinder
22
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
It is easier to move an
object (i.e., qo_cr↓)
as KC = UT/dobj ↓
(i.e., as wave period T↓)
So look at qo (KC/KC0) –1.07
Evaluate denominator, “Cfmax”
For an object:
≡ rwCfmaxUmax2
where
Cfmax = CD + a2CI (KC)-1
Cfmax has been previously
determined for wave
forces on cylinders
CD + a2CI (KC)-1
|FDrag + FInertia| AD-1
Cfmax/Cfmax0 = (KC/KC0) –1.07
(Figure Modified from
Sarpkaya, 1986)
KC0 ≈ 11
KC = UT/dcylinder
23
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
(a) After Year 1 Analysis
qo =
101
100
U2/[(robj/rw – 1) gdobj]
(i)
(b) After Year 2 Analysis
qo (KC/KC0)–1.07 =
101
(i)
U2/[(robj/rw – 1) gdobj]
(KC/KC0)1.07
100
(ii)
10-1
10-2
10-3
10-1
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.
dobj/kbed
10-2
(iii)
10-3
Same as (a) plus:
Smooth cylinders on varying kb.
Rough cylinders on varying kb.
Cylinders on flat bed in flume
corrected for wave inertia force.
(iii)
dobj/kbed
(i) Restricted to dobj > 1 cm, improved kbed for spheres, adjusted U to expected value at z = 5 cm.
(ii) Included data from Brandt & Rennie (2013) for cylinders in flume with varying dobj/kbed values.
(iii) Accounted for effect of wave inertia force: qo_cr (KC/KC0)–1.07 is tighter func. of dobj/kbed .
24
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
Theoretically expect:
101
(iv)
X
X
100
X
X
10-1
10-2
qo (KC/KC0)–1.07 =
U2/[(robj/rw – 1) gdobj]
10-3
(KC/KC0)1.07
dobj/kbed
-- Rennie (next!) observed several cases of qo >> qo_cr without horizontal object movement.
-- Scour-induced burial changes the relevant values of tan F and (especially) e/dobj .
25
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
Theoretically expect:
101
(iv)
X
X
100
X
X
Then with scour-induced burial:
10-1
e
10-2
qo (KC/KC0)–1.07 =
U2/[(robj/rw – 1) gdobj]
10-3
dobj
kbed
(KC/KC0)1.07
New kbed = dobj – e
dobj/kbed
So new dobj/kbed = (1 – e/dobj)–1
-- Rennie (next!) observed several cases of qo >> qo_cr without horizontal object movement.
-- Scour-induced burial changes the relevant values of tan F and (especially) e/dobj .
-- One way to parameterize this effect is to reduce effective dobj/kbed to account for burial.
26
Results (cont.)
●
2) Improve predictive skill of Shields parameter approach (reduce scatter,
fill in parameter space, account for waves, account for burial and scour).
U
Next suggested step: include burial conditions in force balance.
Object moves approximately when: FDrag + FInertia > a4 (tan F) FW
e
dobj
e/dobj
0.9
0.8
0.6
FI/FImax
FD/FDmax
KC = UT/dobj
KC = UT/dobj
(modified from Jacobsen et al. 1989)
Lab experiments measuring forces on partially buried pipelines show that
FDrag and FInertia scale predictably with exposure/diameter, i.e., e/dobj .
27
Conclusions
Scour and motion of UXO governed by sediment and object Shields parameters, respectively
Velocity-based “object” Shields parameter
●
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 robject/rsand (e.g., bed fluidization)
28
Transition Plan
●
Example interim products that are useful to the field:
-- Cylindrical UXO wave scour depth in sand: depth/dcylinder ≈ C1 qs + C2
where sediment Shields parameter qs = Uw2/[(rsand/rw – 1)gdsand] .
-- Critical condition for initiation of UXO motion is both theoretically and empirically
governed by variations in the object Shields parameter qo = U2/[(robj/rw – 1)gdobj] which
scales with the diameter of the object relative to the bed roughness, dobj/kbed.
●
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.
29