DTIC ADA551276: Mine-Impact Burial Model (IMPACT35) Verification and Improvement Using Sediment Bearing Factor Method

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34 IEEEJOURNALOFOCEANICENGINEERING,VOL.32,NO.1,JANUARY2007
Mine-Impact Burial Model (IMPACT35) Verification
and Improvement Using Sediment
Bearing Factor Method
Peter C.Chu and Chenwu Fan
Abstract—Recently, a 3-D model (IMPACT35) was developed Sea mines are big threat in naval operations. Within the
topredictafallingcylindricalmine’slocationandorientationin past 15 years three U.S. ships, the U.S.S. Samuel B. Roberts
air–water–sediment columns. The model contains the following
(FFG-58),Tripoli(LPH-10),andPrinceton(CG-59)havefallen
three components: 1) triple coordinate transform, 2) hydrody-
victim to mines. Total ship damage was $125 million while
namics of falling rigid object in a single medium (air, water, or
sediment) andin multiplemedia(air–waterand water–sediment theminescostapproximately$30000[1].Mineshaveevolved
interfaces),and3)deltamethodforsedimentresistance withthe over the years from the dumb “horned” contact mines that
transient pore pressure. Two mine-impact burial experiments damagedtheTripoliandRobertstoonesthatarerelativelyso-
were conducted to detect the mine trajectory in water column
phisticated—nonmagneticmaterials,irregularshapes,anechoic
[Carderock Division, Naval Surface Warfare Center (NSWC),
coatings, multiple sensors, and ship count routines. Despite
WestBethesda,MD,onSeptember10–14,2001],andtomeasure
themineburialvolumeinsediment(BalticSeainJune2003).The their increased sophistication, mines remain inexpensive and
existingIMPACT35predictsamine’slocationandorientationin arerelativelyeasytomanufacture,keep,andplace.
thewatercolumn,butnotinthesedimentcolumn.Sincesediment Accurate mine burial predictions are inherently difficult
resistancelargelyaffectsthemineburialdepthandorientationin
[2], because of unknown conditions in mine deployment and
sediment,anewmethod(bearingfactor)isproposedtocompute
uncertain environments such as waves, currents, and sediment
the sediment resistant force and torque. The improvement of
IMPACT35 with the bearing factor method is verified using the transports [3]. The U.S. Navy developed operational models
datacollectedfromtheBalticSeamine-impactburialexperiment. to forecast ocean environments for mine burial prediction [4],
The prediction error satisfies near-Gaussian distribution. The [5]. Recently, statistical methods such as the Monte Carlo [6]
bias of the burial volume (in percent) prediction reduces from
andtheexpertsystemmethods[3]havebeendeveloped.These
11%usingthedeltamethod(old)to0.1%usingthebearingfactor
methods have a core-physical model for falling rigid body
method (new). Correspondingly, the root-mean-square error
(rmse)reducesfrom26.8%to15.8%. through air–water–sediment columns. The U.S. Navy has a
2-D model (IMPACT28) to predict a cylinder’s trajectory and
Index Terms—Bearing factor, burial depth and orientation,
impact burial. The data collected from the mine-impact burial
dragandliftforcesandtorques,IMPACT35,mine-impactburial
prediction,sedimentresistanceforceandtorque,triplecoordinate experimentinthesurfzoneneartheNavalPostgraduateSchool,
system. Monterey, CA, shows overprediction of the burial depth (an
orderofmagnitudelarger)usingIMPACT28[7].
A 3-D model (IMPACT35) was recently developed at the
NavalPostgraduateSchooltopredictacylinder’strajectoryand
I. INTRODUCTION
impact burial [8]–[12]. The dynamical system can be simpli-
fied using the following three coordinate systems: earth-fixed
THE conclusion of the cold war culminated with the
coordinate (E-coordinate), the cylinder’s main-axis-following
UnionofSovietSocialistRepublics(U.S.S.R.)effectively
coordinate(M-coordinate),andhydrodynamicforce-following
ceasingtoexistunderinternationallawonDecember31,1991.
coordinate (F-coordinate). The origin of both M- and F-coor-
This historical event caused the U.S. military and specifically
dinates is at the cylinder’s center of mass (COM). The body
theU.S.NavyandMarineCorpTeamtoshifttacticalemphasis
forcesandtheirmomentsareeasilycalculatedusingtheE-co-
from “blue” water, deep-ocean doctrine to littoral warfare
ordinate system. The hydrodynamic forces and their moments
doctrine. This shift changed military responses dealing with a
areeasilycomputedusingtheF-coordinate.Thecylinder’smo-
widerangeofworldwideregionalcrisesrequiringforwardsea
ments of gyration are simply represented using the M-coordi-
basing,andexpeditionaryforcelandingsupport.
nate. When the mine penetrates into an interface between two
media (air–water or water–sediment), the cylinder is decom-
ManuscriptreceivedMarch28,2005;revisedMay19,2006;acceptedAu-
posedintotwopartswitheachonecontactingonemedium.The
gust8,2006.ThisworkwassupportedbytheU.S.OfficeofNavalResearch
MarineGeosciencesProgramN0001403WR20178andN0001404WR20067, body forces (such as the buoyancy force) and surface forces
bytheNavalOceanographicOffice,andbytheNavalPostgraduateSchool. (suchaspressure,hydrodynamicforce)arecomputedseparately
GuestEditor:M.D.Richardson.
forthetwoparts.Afully3-Dmodelisdevelopedforpredicting
TheauthorsarewiththeNavalOceanAnalysisandPredictionLaboratory,
DepartmentofOceanography,NavalPostgraduateSchool,Monterey,CA93943 the translation velocity and orientation of a falling cylindrical
USA(e-mail:[email protected]). mine through air, water, and sediment. The added value capa-
Colorversionsofoneormoreofthefiguresinthispaperareavailableonline
bilityofthe3-Dmodel(IMPACT35)versusthe2-Dmodel(IM-
athttp://ieeexplore.ieee.org.
DigitalObjectIdentifier10.1109/JOE.2007.890942 PACT28)isverifiedusingexperimentaldata.
0364-9059/$25.00©2007IEEE
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1. REPORT DATE 3. DATES COVERED
MAY 2006 2. REPORT TYPE 00-00-2006 to 00-00-2006
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Mine-Impact Burial Model (IMPACT35) Verification and Improvement
5b. GRANT NUMBER
Using Sediment Bearing Factor Method
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
Naval Postgraduate School,Department of REPORT NUMBER
Oceanography,Monterey,CA,93943
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)
11. SPONSOR/MONITOR’S REPORT
NUMBER(S)
12. DISTRIBUTION/AVAILABILITY STATEMENT
Approved for public release; distribution unlimited
13. SUPPLEMENTARY NOTES
14. ABSTRACT
Recently, a 3-D model (IMPACT35) was developed to predict a falling cylindrical mine?s location and
orientation in air?water?sediment columns. The model contains the following three components: 1) triple
coordinate transform, 2) hydrodynamics of falling rigid object in a single medium (air, water, or sediment)
and in multiple media (air?water and water?sediment interfaces), and 3) delta method for sediment
resistance with the transient pore pressure. Two mine-impact burial experiments were conducted to detect
the mine trajectory in water column [Carderock Division, Naval Surface Warfare Center (NSWC) West
Bethesda, MD, on September 10?14, 2001], and to measure the mine burial volume in sediment (Baltic Sea
in June 2003). The existing IMPACT35 predicts a mine?s location and orientation in the water column, but
not in the sediment column. Since sediment resistance largely affects the mine burial depth and orientation
in sediment, a new method (bearing factor) is proposed to compute the sediment resistant force and torque.
The improvement of IMPACT35 with the bearing factor method is verified using the data collected from
the Baltic Sea mine-impact burial experiment. The prediction error satisfies near-Gaussian distribution.
The bias of the burial volume (in percent) prediction reduces from 11% using the delta method (old) to
0.1% using the bearing factor method (new). Correspondingly, the root-mean-square error (rmse) reduces
from 26.8% to 15.8%.
15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF
ABSTRACT OF PAGES RESPONSIBLE PERSON
a. REPORT b. ABSTRACT c. THIS PAGE Same as 15
unclassified unclassified unclassified Report (SAR)
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CHUANDFAN:MINE-IMPACTBURIALMODEL(IMPACT35)VERIFICATIONANDIMPROVEMENT 35
Fig.1. M-coordinatewiththeCOMastheoriginXand(i ;j )asthetwo
axes.Here,(cid:31)isthedistancebetweentheCOV(B)andCOM(X);(L;R)are
thecylinder’slengthandradius[8].
Recently, two mine-impact burial experiments were con-
ducted to detect mine trajectory in the water column [Carde-
rock Division, Naval Surface Warfare Center (NSWC), West
Bethesda, MD, on September 10–14, 2001] and to measure
the mine burial in the sediment (Baltic Sea in June 2003).
The collected data are used for model verification. Section II
describes basic physics of the recently developed 3-D model
(IMPACT35).SectionIIIshowstheaddedvalueofIMPACT35
in predicting mine movement in the water column. However,
Section IV shows weakness of the existing IMPACT35 in
predictingminemovementinsediment.SectionVpresentsthe Fig. 2. Three coordinate systems. Here, (i;j;k) are the unit vectors of
E-coordinatesystem.BothM-andF-coordinatesystemssharethesameaxis,
new bearing factor method to compute the sediment resistant
i.e.,i andi arethesameunitvectors[8].
force and torque. Section VI shows the improvement of the
bearing factor method in predicting mine burial in sediment.
SectionVIIpresentstheconclusions. whichdescribestranslationofthecylinder.Thetranslationve-
locityisgivenby
II. DESCRIPTIONOFIMPACT35
(2)
The 3-D mine-impact burial prediction model (IMPACT35)
contains the following major components: 1) triple coordinate Let the orientation of the cylinder’s main axis (pointing
systems,2)momentumbalance,3)momentofmomentumbal- downward) be given by . The angle between and
ance, 4) hydrodynamics, and 5) sediment dynamics. Among is denoted by . Projection of the vector onto
them,thehydrodynamics(dragandliftforcesandtorques)have the -plane creates angle between the projection
beendescribedin[8]and[11]–[13],andwillnotbediscussed and the -axis (Fig. 2). The M-coordinate system is repre-
here. sentedby withtheorigin ,unitvectors
, and coordinates . In the plane
A. TripleCoordinateSystems consistingofvectors and (passingthroughthepoint ),
twonewunitvectors aredefinedwith perpendic-
Consider an axially symmetric cylinder with the center of
ular to the -plane, and perpendicular to in the
mass(COM) andthecenterofvolume(COV) onthemain
-plane.TheunitvectorsoftheM-coordinatesystemare
axis (Fig. 1). Let represent the cylinder’slength, ra-
givenby(Fig.2)
dius,andthedistancebetweenthetwopoints .Thepos-
itive -values refer to the nose-down case, i.e., the point (3)
is lower than the point . Three coordinate systems are used
to model the falling cylinder through the air, water, and sedi- The M-coordinate system is solely determined by the orienta-
mentphases:earth-fixedcoordinate(E-coordinate),main-axis- tionofthecylinder’smainaxis .
followingcoordinate(M-coordinate),andforce-followingcoor- The F-coordinate system is represented by
dinate(F-coordinate)systems.Allthesystemsare3-D,orthog- with the origin , unit vectors
onal,andright-handed[8]. , and coordinates . Let be the
The E-coordinate system is represented by fluid velocity. The fluid-to-cylinder velocity is represented by
with the origin , and three axes: - and -axes (horizontal) ,thatisdecomposedintotwoparts
with the unit vectors and -axis (vertical) with the unit
vector (upward positive). The position of the cylinder is (4)
representedbythepositionoftheCOM where
(1)
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36 IEEEJOURNALOFOCEANICENGINEERING,VOL.32,NO.1,JANUARY2007
TABLEI
PHYSICALPARAMETERSOFTHEMODELMINESINTHENSWC-CARDEROCKEXPERIMENT(AFTER[19])
Fig.3. Movementofmine#6(L=1.01m,(cid:26)=2:1(cid:2)10 kgm )with(cid:31)=(cid:0)0.0077mand =(cid:0)14.0 obtainedfrom(a)NSWC-Carderockexperiment,
(b)3-DIMPACT35model,and(c)2-DIMPACT28model(after[11]).
is the component paralleling to the cylinder’s main axis (i.e., [11]–[13]
along ),and
(6)
isthecomponentperpendiculartothecylinder’smainaxialdi-
rection. The unit vectors for the F-coordinate are defined by where is the gravitational acceleration, is the cylinder
(columnvectors) volume, is the rigid body density, is the cylinder
mass, isthenonhydrodynamicforcedefinedlater,and
(5) is the hydrodynamic force (i.e., surface force including drag,
lift forces). Both and are integrated for the cylinder.
The drag and lift forces are calculated using the drag and lift
The F-coordinate system is solely determined by the orienta-
laws with the given water-to-cylinder velocity . In the
tionofthecylinder’smainaxis andthewater-to-cylinder
F-coordinate, isdecomposedintoalong-cylinder and
velocity. Note that the M- and F-coordinate systems have one
across-cylinder components.Thenonhydrodynamicforce
commonunitvector (orientationofthecylinder).Useofthe
isthebuoyancyforce fortheairandwaterphases
F-coordinate system simplifies the calculations forthe lift and
dragforcesandtorquesactingonthecylinder.
(7)
B. MomentumBalance
where are the air and water densities and is the
The3-Dtranslationvelocityofthecylinder isgoverned resultantofbuoyancyforce ,andshearingresistanceforce
by the momentum equation in the E-coordinate system [8], forthesedimentphase.
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CHUANDFAN:MINE-IMPACTBURIALMODEL(IMPACT35)VERIFICATIONANDIMPROVEMENT 37
Fig.4. Movementofmine#5(L=1.01m,(cid:26) =2:1(cid:2)10 kgm )with(cid:31) =0.0045mand =42:2 obtainedfrom(a)NSWC-Carderockexperiment,
(b)3-DIMPACT35model,and(c)2-DIMPACT28model.
Fig.5. Movementofmine#2(L=0.505m,(cid:26)=2:1(cid:2)10 kgm )with(cid:31)=0and =87:0 obtainedfrom(a)NSWC-Carderockexperiment,(b)3-D
IMPACT35model,and(c)2-DIMPACT28model(after[11]).
C. MomentofMomentumEquation neglected.Thus,wehave
ThemomentofmomentumequationiswrittenintheM-co-
ordinatesystem,whichrotateswiththeangularvelocityof
(8) Thisleadstozerocentripetaland“Coriolis”terms
Usually, the angular velocity around the mine’s main axis
(i.e., self-spinning velocity) is very small and (9)
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38 IEEEJOURNALOFOCEANICENGINEERING,VOL.32,NO.1,JANUARY2007
Fig.6. ModelverificationfrompredictionoftheCOMpositionxusingtheNSWC-Carderockexperimentdataatseveraltimeinstances:0.32,0.64,0.96,and
1.28s.Here,thefirstcolumnisthedata-IMPACT28comparison,thesecondcolumnisthedata-IMPACT35comparison,thethirdcolumnshowsthehistograms
ofthemodelerror((cid:14)x)forIMPACT28,andthefourthcolumnshowsthehistogramsofthemodelerror((cid:14)x)forIMPACT35.
Theinertialterm locityissmall.ThemomentofmomentumequationintheM-co-
ordinatesystemcanbesimplifiedby
(10) (11)
onlyhasthecomponentalongthedirectionof (mine’smain where and are the nonhydrodynamic and hydrody-
axis). This term may be neglected when the self-spinning ve- namic force torques. In the M-coordinate system, the moment
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CHUANDFAN:MINE-IMPACTBURIALMODEL(IMPACT35)VERIFICATIONANDIMPROVEMENT 39
Fig.7. ModelverificationfrompredictionoftheCOMpositionzusingtheNSWC-Carderockexperimentdataatseveraltimeinstances:0.32,0.64,0.96,and
1.28s.Here,thefirstcolumnisthedata-IMPACT28comparison,thesecondcolumnisthedata-IMPACT35comparison,thethirdcolumnshowsthehistograms
ofthemodelerror((cid:14)x)forIMPACT28,andthefourthcolumnshowsthehistogramsofthemodelerror((cid:14)x)forIMPACT35.
ofgyrationtensorfortheaxiallysymmetriccylinderisadiag- The gravity force, passing the COM, does not induce the mo-
onalmatrix ment.Thebuoyancyforceinducesthemomentinthe direc-
tioniftheCOMdoesnotcoincidewiththeCOV(i.e., )
(13)
(12)
D. SedimentDynamics
where , ,and arethemomentsofinertia.Thenonhydro- IntheexistingIMPACT35model,thesedimentresistanceis
dynamicforceusuallycontainsthegravityandbuoyancyforces. calculatedusingthedeltamethod.Thismethodisbasedonthe
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40 IEEEJOURNALOFOCEANICENGINEERING,VOL.32,NO.1,JANUARY2007
Fig.8. Modelverificationfrompredictionoftheorientation usingtheNSWC-Carderockexperimentdataatseveraltimeinstances:0.32,0.64,0.96,and1.28
s.Here,thefirstcolumnisthedata-IMPACT28comparison,thesecondcolumnisthedata-IMPACT35comparison,thethirdcolumnshowsthehistogramsofthe
modelerror((cid:14) )forIMPACT28,andthefourthcolumnshowsthehistogramsofthemodelerror((cid:14) )forIMPACT35.
assumption that the cylinder pushes the sediment and leaves namic forces (per unit area) at the point over the cylinder’s
space in the wake as it impacts and penetrates into the sedi- surface, is the area of the cylinder’s surface below the
ment.Thisspaceisrefilledbywaterandthewatercavityispro- water–sedimentinterface, istheporewaterpressureforce
duced.Attheinstantofpenetration,thetotalresistantforceon onthewholecylinder,and -functionisdefinedby
thecylinderisrepresentedby[16]–[18]
(14) (15)
where and are the sediment buoyancy and which shows that the sediment buoyancy and shear resistance
shear resistance forces and water buoyancy and hydrody- forces act when the cylinder moves towards them. Here, is
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CHUANDFAN:MINE-IMPACTBURIALMODEL(IMPACT35)VERIFICATIONANDIMPROVEMENT 41
Fig.9. TemporalevolutionofmodelperformanceevaluatedusingtheNSWC-Carderockdata:(a)observationaldatanumber,(b)rmseofx,(c)rmseofz,(d)rmse
of ,(e)STDof(cid:14)x,(f)STDof(cid:14)z,and(g)STDof(cid:14) withthesolidcurvesforIMPACT28anddashedcurvesforIMPACT35from(b)to(g).
thevelocityatpoint (representedintheM-coordinate)onthe the only explosive-related test pond in the United States with
cylindersurface thecapabilityofprovidinghigh-speedunderwaterphotography
given its exceptional water clarity. In addition, the facility’s
(16)
concretefloorthicknessandreinforcementissufficienttoallow
impact of 45-kg cylinders without additional floor protection.
III. VERIFICATIONOFIMPACT35INTHEWATERCOLUMN Thepondinplanviewis aregularpentagonwitheachsideof
The NSWC–Carderock experiment was conducted on 41 m. During the experiment, six model mines (Table I) with
September 10-14, 2001 in the Explosion Test Pond, which is massvaryingfrom16.96to45.85kgwerereleasedtothepond
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