MR-2224 Carl T. Friedrichs Virginia Institute of Marine Science In-Progress Review Meeting

SIMPLE PARAMETERIZED MODELS FOR PREDICTING MOBILITY, BURIAL, AND RE-EXPOSURE OF UNDERWATER MUNITIONS

MR-2224Carl T. Friedrichs

Virginia Institute of Marine ScienceIn-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

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.

● 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)

R2 = 0.003

Crit

ical

vel

ocity

for

obje

ct m

otio

n (c

m/s

)

Diameter of object (cm)

5

Technical Approach (#1 of 3)

6

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

(Catano-Lopera 2005; Catano-Lopera & Garcia, 2006; Demir & Garcia 2007)

R2 = 0.32

Wave orbital velocity (cm/s)

Obj

ect s

cour

dep

th (

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


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

Velocity-based “sediment” Shields parameter qs = Uw

2/[(rsand/rwater-1)gdsand]

R2 = 0.81

Fra

ctio

nal s

cour

, dep

th/d

cylin

der

depth/dcylinder = 0.00608 q0 + 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: 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

● 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 dobj/kbed ( see graph).

101

100

10-1

10-2

10-3

dobj/kbed

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.

Vel

ocity

-bas

ed “

obje

ct”

Shi

eld

s pa

ram

eter

dobj = object diameter, kbed = median bed grain size or hydraulic roughness if smoothUcrit = water velocity at initial object motion, robj/rw = object/water density, g = gravity

9

R2 = 0.88

Technical Approach (#2 of 3)q

o =

(U

crit)

2 /[(r o

bj/r

w –

1)

gdob

j]

● 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 dobj/kbed ( 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).

101

100

10-1

10-2

10-3

dobj/kbed






dobj = object diameter, kbed = median bed grain size or hydraulic roughness if smoothUcrit = water velocity at initial object motion, robj/rw = object/water density, g = gravity

10

>1.5 orders of scatter

>2 orders of scatter

Empty parameter space

R2 = 0.88

Technical Approach (#2 of 3)q

o =

(U

crit)

2 /[(r o

bj/r

w –

1)

gdob

j]

Vel

ocity

-bas

ed “

obje

ct”

Shi

eld

s pa

ram

eter

● 2) Further develop and constrain parameterized relationships for UXO burial, mobility, and re-exposure: Synthesize Fahnestock & Saushild / Voropayev et al.


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.

● 3) To provide improved parameterized model formulations to other SERDP/ESCTP investigators (iterative, began near end of Year 1):

Advances in model parameterizations

by FriedrichsMR-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


1313

● 3) To provide improved parameterized model formulations to other SERDP/ESCTP investigators for use within more sophisticated Expert Systems :

(Rennie & Brandt, 2014 Ocean Sciences)


-- MR-2227 Rennie “Underwater Munitions Expert System to Predict Mobility and Burial”

14

Results

When does an seabed object move?

Answer -- if: (∑ Forces)X ≥ (tan f) (∑ Forces)z

z

U, x&

FL = lift force

FD = drag force

FI = inertia force

FW = object weight

F = angle of reposeb = bed slopex = downslope distanceU = wave + current near top of object

(Modified fromWiberg & Smith, 1987)

● 1) Derive physical dependence of Shields parameter on key object and seabed properties

15

When does an seabed object move?

Answer -- if: (∑ Forces)X ≥ (tan f) (∑ Forces)z

z

U, x&

FL = lift force

FD = drag force

FI = inertia force

FW = object weight

F = angle of reposeb = bed slopex = downslope distanceU = wave + current near top of object

(Modified fromWiberg & Smith, 1987)

FD + FI + FW sin b = (tan F) (FW cos b – FL)

Simple to keep b, but usually negligible FD + FI + (tan f) FL = (tan F) FW

∑ Fluid forces = Resistance

So at initial motion:

Results● 1) Derive physical dependence of Shields parameter on key object and seabed properties

Results (cont.)

x

Object moves when: FD + FI + (tan F) FL = (tan F) FW

FD = rw ½CDADU2

FL = rw ½CLALU2

Forces

dobj

FW = (robj – rw) gVT

FI = rw CIVI ∂U/∂t

16

Symbols

FD,I,L,W = drag, inertia, lift force

& object WeightCD,L,I = drag, lift and inertia coeffs.

AD,L = object area exposed to drag, lift

VT,I = object total volume and

volume exposed to flowrw,obj = density of water, object

dobj, e = object diameter, exposure

Ucrit = “critical” wave + current

g = gravityF = angle of reposeT = sinusoidal wave period

&

(Modified fromKirchner et al., 1990)

x

Object moves when: FD + FI + (tan F) FL = (tan F) FW

FD = rw ½CDADU2

FL = rw ½CLALU2

Symbols


Forces

dobj

FW = (robj – rw) gVT

FI = rw CIVI ∂U/∂t

17

= critical object Shields parameter, qo_cr

(~ FD/FW)

= 1/KC , where KC = Keulegan-Carpenter #

Assume (tan f) FL/FD ≈ const., then (after algebra)

at initiation of object motion (with a1,2 shape constants):

Ucrit2 a1 (d/e) tan F

(robj/rw – 1) dobj g CD + a2CI dobj/(UT) =

FD,I,L,W = drag, inertia, lift force

& object WeightCD,L,I = drag, lift and inertia coeffs.

AD,L = object area exposed to drag, lift

VT,I = object total volume and

volume exposed to flowrw,obj = density of water, object


Ucrit = “critical” wave + current

g = gravityF = angle of reposeT = sinusoidal wave period

Results (cont.)

&

18

At initiation of object motion:

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


g = gravity

F = Angle of repose

U = wave + current velocity

T = wave period

Symbols


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↓)

Results (cont.)

dobj


Results (cont.)

kb

kb

kb

dobj

19

It is easier to move an object (i.e., qo_cr↓)

e

e

edobj/kb F dobj/e

0.5 70o 2.0

1.0 60o 1.6

2.0 50o 1.2

if objects are not “blocked” (i.e., as (dobj/e)↓ or F↓)

-- As object size relative to bed roughness increases,

(i.e., as dobj/kb↑), F↓ and dobj/e ↓, so qo_cr↓ .

kb = bed roughness

qo_cr = Ucrit2/[(robj/rw – 1) gd]

= crit. obj. Shields param.

(Figures Modified fromWiberg & Smith, 1987)

dobj

dobj


20

101

100

10-1

10-2

10-3






101

100

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 dobj > 1 cm, improved kbed for spheres, adjusted U to expected value at z = 5 cm.

dobj/kbed dobj/kbed

qo =

U2/[(robj/rw – 1) gdobj]

(a) After Year 1 Analysis (b) After Year 2 Analysis

(i)

(i)

Results (cont.)

qo =


Same as (a) plus:

Smooth cylinders on varying kb.

Rough cylinders on varying kb.

21

101

100

10-1

10-2

10-3






101

100

10-1

10-2

10-3



(ii) Included data from Brandt & Rennie (2013) for cylinders in flume with varying dobj/kbed values.

dobj/kbed dobj/kbed

qo =



(i)

(ii)

Results (cont.)

(i) qo =


It is easier to move an

object (i.e., qo_cr↓)

as KC = UT/dobj ↓


CD +

a2C

I (K

C)-1

KC = UT/dcylinder

|FDrag + FInertia| AD-1

≡ rwCfmaxUmax2

where

Cfmax = CD + a2CI (KC)-1

For an object:

Evaluate denominator, “Cfmax”

Cfmax/Cfmax0 = (KC/KC0) –1.07

Cfmax has been previously determined for wave forces on cylinders

(Figure Modified fromSarpkaya, 1986) KC0 ≈ 11

22


Results (cont.)

It is easier to move an

object (i.e., qo_cr↓)

as KC = UT/dobj ↓


CD +

a2C

I (K

C)-1

KC = UT/dcylinder

|FDrag + FInertia| AD-1

≡ rwCfmaxUmax2

where

Cfmax = CD + a2CI (KC)-1

For an object:

Evaluate denominator, “Cfmax”

Cfmax/Cfmax0 = (KC/KC0) –1.07

Cfmax has been previously determined for wave forces on cylinders

(Figure Modified fromSarpkaya, 1986) KC0 ≈ 11

23


Results (cont.)

So look at qo (KC/KC0) –1.07

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.

24

101

100

10-1

10-2

10-3






101

100

10-1

10-2

10-3



(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 .

dobj/kbed dobj/kbed

qo =



(i) (i)

(iii)

(iii)

(ii)

Results (cont.)

qo (KC/KC0)–1.07 =


(KC/KC0)1.07

25

101

100

10-1

10-2

10-3

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 .

Theoretically expect:(iv)


Results (cont.)

qo (KC/KC0)–1.07 =


(KC/KC0)1.07

X

X

XX

26

101

100

10-1

10-2

10-3

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 .

-- One way to parameterize this effect is to reduce effective dobj/kbed to account for burial.

e dobj

New kbed = dobj – e

So new dobj/kbed = (1 – e/dobj)–1

Then with scour-induced burial:

Theoretically expect:

kbed


Results (cont.)

qo (KC/KC0)–1.07 =


(KC/KC0)1.07

X

X

XX

(iv)

27

Object moves approximately when: FDrag + FInertia > a4 (tan F) FW

FD/FDmax FI/FImax

KC = UT/dobj KC = UT/dobj

e/dobj

0.90.80.6

e dobj

Lab experiments measuring forces on partially buried pipelines show that

FDrag and FInertia scale predictably with exposure/diameter, i.e., e/dobj .

U

(modified from Jacobsen et al. 1989)

Results (cont.)

Next suggested step: include burial conditions in force balance.


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 robject/rsand (e.g., bed fluidization)

Vel

ocity

-bas

ed “

obje

ct”

Shi

elds

par

amet

er

29

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.

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MR-2224 Carl T. Friedrichs Virginia Institute of Marine Science In-Progress Review Meeting

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