The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

1.
Arnone
,
R. A.
, and
Bowen
,
L. E.
, 1980, “
Prediction Model of the Time History Penetration of a Cylinder Through the Air-Water-Sediment Phases
,” Naval Coastal Systems Center, NCSC Technical Note 734-36.
2.
Satkowiak
,
L. J.
, 1987, “
Modifications to the NCSC Impact Burial Prediction Model
,”
Naval Coastal Systems Center
, NCSC Technical Note 883-87.
3.
Satkowiak
,
L. J.
, 1987, “
User’s Guide for the Modified Impact Burial Prediction Model
,” Naval Coastal Systems Center, NCSC TN 884-87.
4.
Hurst
,
R. B.
, 1992, “
Mine Impact Burial Prediction Model-Technical Description of Recent Changes and Developments (U)
,” (Restricted), Defense Scientific Establishment, DSE Report 149.
5.
Mulhearn
,
P. J.
, 1992, “
Experiments on Mine Burial on Impact-Sydney Harbour
,”
U.S. Navy Journal of Underwater Acoustics
,
43
, pp.
1271
1281
.
6.
Chu
,
P. C.
,
Gilles
,
A. F.
,
Fan
,
C. W.
, and
Fleischer
,
P.
, 2000, “
Hydrodynamics of Falling Mine in Water Column
,”
Proceedings of the Fourth International Symposium on Technology and the Mine Problem
,
Naval Postgraduate School
,
Monterey, CA
, p.
10
.
7.
Chu
,
P. C.
,
Taber
,
V. L.
, and
Haeger
,
S. D.
, 2000, “
Environmental Sensitivity Studies on Mine Impact Burial Prediction Model (Two-Dimensional)
,”
Proceedings of the Fourth International Symposium on Technology and the Mine Problem
, p.
10
.
8.
Taber
,
V. L.
, 1999, “
Environmental Sensitivity Studies on Mine Impact Burial Prediction Model
,” Master thesis, Naval Postgraduate School, Monterey.
9.
Smith
,
T. B.
, 2000, “
Validation of the Mine Impact Burial Model Using Experimental Data
,” Master thesis, Naval Postgraduate School, Monterey.
10.
Chu
,
P. C.
,
Evans
,
A. D.
,
Gilles
,
A. F.
,
Smith
,
T.
, and
Taber
,
V.
, 2004, “
Development of Navy’s 3D Mine Impact Burial Prediction Model (IMPACT35)
,”
Proceedings of the Sixth International Symposium on Technology and the Mine Problem
,
Naval Postgraduate School
,
Monterey, CA
, p.
10
.
11.
Chu
,
P. C.
, and
Fan
,
C. W.
, 2007, “
Mine Impact Burial Model (IMPACT35) Verification and Improvement Using Sediment Bearing Factor Method
,”
IEEE J. Ocean. Eng.
0364-9059,
32
(
1
), pp.
34
48
.
12.
Chu
,
P. C.
, 2002, “
Hydrodynamics of Mine Impact Burial
,”
ONR Impact Burial Annual Workshop
,
La Jolla
,
CA
, Jan. 15–17.
13.
Chu
,
P. C.
,
Fan
,
C. W.
,
Evans
,
A. D.
,
Gilles
,
A. F.
, and
Fleischer
,
P.
, 2003, “
Three-Dimensional Hydrodynamic Model for Prediction of Falling Cylinder Through Water Column
,”
The OCEANS 2003 MTS/IEEE Conference Proceedings
,
San Diego
,
CA
, p.
10
.
14.
Chu
,
P. C.
,
Fan
,
C. W.
, and
Evans
,
A. D.
, 2004, “
Three-Dimensional Rigid Body Impact Burial Model (IMPACT35)
,”
Advances in Fluid Mechanics
,
5
, pp.
43
52
.
15.
Evans
,
A. D.
, 2002, “
Hydrodynamics of Mine Impact Burial
,” Master thesis, Naval Postgraduate School, Monterey.
16.
Chu
,
P. C.
,
Fan
,
C. W.
,
Evans
,
A. D.
, and
Gilles
,
A. F.
, 2004, “
Triple Coordinate Transforms for Prediction of Falling Cylinder Through the Water Column
,”
ASME J. Appl. Mech.
0021-8936,
71
, pp.
292
298
.
17.
Lamb
,
H.
, 1932,
Hydrodynamics
,
Cambridge University Press
,
ASME, Cambridge
.
18.
Milne-Thomson
,
L. M.
, 1968,
Theoretical Hydrodynamics
,
Macmillan
,
New York
.
19.
Aref
,
H.
, and
Jones
,
S. W.
, 1993, “
Chaotic Motion of a Solid Through Ideal Fluid
,”
Phys. Fluids A
0899-8213,
5
(
12
), pp.
3026
3028
.
20.
Aref
,
H.
, and
Jones
,
S. W.
, 1994, “
Motion of a Solid Body Through an Ideal Fluid
,”
College of Engineering, University of Illinois at Urbana-Champaign
, Report No. 772.
21.
Holmes
,
P.
,
Jenkins
,
J.
, and
Leonard
,
N. E.
, 1998, “
Dynamics of the Kirchhoff Equations I: Coincident Centers of Gravity and Buoyancy
,”
Physica D
0167-2789,
118
(
3–4
), pp.
311
342
.
22.
Field
,
S. B.
,
Klaus
,
M.
,
Moore
,
M. G.
, and
Nori
,
F.
, 1997, “
Chaotic Dynamics of Falling Disks
,”
Nature (London)
0028-0836,
388
(
6639
), pp.
252
254
.
23.
Mahadevan
,
L.
,
Ryu
,
W. S.
, and
Aravinthan
,
D. T. S.
, 1999, “
Tumbling Cards
,”
Phys. Fluids
1070-6631,
11
(
1
),
1
3
.
24.
Kochin
,
N. E.
,
Kibel
,
I. A.
,
Roze
,
N. V.
, 1964,
Theoretical Hydromechanics
,
Intersciences
,
New York
.
25.
Kozlov
,
V. V.
, 1989, “
Heavy Rigid Body Falling in an Ideal Fluid
,”
Izv AN SSSR, Mekhanika Tverdogo Tela
,
24
(
5
), pp.
10
17
.
26.
Satkowiak
,
L. J.
, 1988, “
Modified NCSC Impact Burial Prediction Model with Comparisons to Mine Drop Tests
,” Naval Coastal Systems Center, NCSC TN 486-88.
27.
Chu
,
P. C.
, 2002, “
Ensemble Mine Impact Burial Prediction
,”
ONR Impact Burial Modeling Workshop
, Phoenix, AZ, March 5–7.
28.
Chu
,
P. C.
,
Taber
,
V. L.
, and
Haeger
,
S. D.
, 2000, “
A Mine Impact Burial Model Sensitivity Study
,” Naval Postgraduate School, NPS-IJWA-00-003.
29.
Stanley
,
E. M.
, 1969, “
Viscosity of Sea Water at Moderate Temperatures and Pressures
,”
J. Geophys. Res.
0148-0227,
74
,
3415
3420
.
30.
Krone
,
R. B.
, “
A Study of Rheological Properties of Estuarine Sediments
,” Technical Bulletin No. 7.
31.
Chu
,
P. C.
,
Smith
,
T. B.
, and
Haeger
,
S. D.
, 2001, “
Mine Impact Burial Prediction Experiment
,” Naval Postgraduate School, NPS-IJWA-01-007.
32.
Chu
,
P. C.
,
Smith
,
T. B.
, and
Haeger
,
S. D.
, 2002, “
Mine Impact Burial Prediction
,”
Proceedings of the Fourth International Symposium on Technology and the Mine Problem
,
Naval Postgraduate School
, Monterey, CA, p.
10
.
33.
Crowe
,
C. T.
,
Roberson
,
J. A.
, and
Elger
,
D. F.
, 2001, “
Engineering Fluid Mechanics
,”
7th ed.
,
Wiley
,
New York
, pp.
1
714
.
34.
Chu
,
P. C.
,
Gilles
,
A. F.
,
Fan
,
C. W.
,
Lan
,
J.
, and
Fleischer
,
P.
, 2002, “
Hydrodynamics of Falling Cylinder in Water Column
,”
Advances in Fluid Mechanics
,
4
, pp.
163
181
.
35.
Chu
,
P. C.
, and
Fan
,
C. W.
, 2005, “
Pseudo-Cylinder Parameterization for Mine Impact Burial Prediction
,”
ASME J. Fluids Eng.
0098-2202,
127
, pp.
1515
1520
.
36.
Chu
,
P. C.
, and
Fan
,
C. W.
, 2006, “
Prediction of Falling Cylinder Through Air-Water-Sediment Columns
,”
ASME J. Appl. Mech.
0021-8936,
73
, pp.
300
314
.
37.
Chu
,
P. C.
, and
Ray
,
G.
, 2006, “
Prediction of High Speed Rigid Body Maneuvering in Air-Water-Sediment Column
,”
Advances in Fluid Mechanics
,
6
, pp.
123
132
.
38.
Chu
,
P. C.
,
Ray
,
G.
,
Fleischer
,
P.
, and
Gefken
,
P.
, 2006, “
Development of Three Dimensional Bomb Maneuvering Model
,”
Proceedings of the Seventh Monterey International Symposium on Technology and Mine Problems
,
Naval Postgraduate School
,
Monterey, CA
, p.
10
.
39.
Rouse
,
H.
, 2006,
Fluid Mechanics for Hydraulic Engineers
,
1st ed.
,
McGraw-Hill Book
,
New York
, p.
422
.
40.
Von Mises
,
R.
, 1959,
Theory of Flight
,
Dover
,
New York
, pp.
564
585
.
41.
Sumer
,
B. M.
, and
Fredsøe
,
J.
, 1997,
Hydrodynamics Around Cylindrical Structures
,
World Scientific
,
Singapore
, p.
530
.
42.
White
,
F. M.
, 1974,
Viscous Fluid Flow
,
McGraw-Hill Inc.
,
New York
, p.
712
.
43.
Hansen
,
N. E. O.
,
Simonsen
,
B. C.
, and
Sterndoff
,
M. J.
, 1994, “
Soil Mechanics of Ship Beaching
,”
Proceedings of 24th International Conference on Coastal Engineering
,
Kobe, Japan
, p.
3030
3044
.
44.
Aubeny
,
C. P.
, and
Shi
,
H.
, 2007, “
Effect of Rate-Dependent Soil Strength on Cylinders Penetrating Into Soft Clay
,”
IEEE J. Ocean. Eng.
0364-9059,
32
(
1
), pp.
49
56
.
45.
Gilles
,
A. F.
, 2001, “
Mine Drop Experiment
,” Master thesis, Naval Postgraduate School, Monterey.
46.
Chu
,
P. C.
,
Gilles
,
A. F.
, and
Fan
,
C. W.
, 2005, “
Experiment of Falling Cylinder Through the Water Column
,”
Exp. Therm. Fluid Sci.
0894-1777,
29
, pp.
555
568
.
47.
Abelev
,
A. V.
,
Valent
,
P. J.
, and
Holland
,
K. T.
, 2007, “
Behavior of a Large Cylinder in Free Fall Through Water
,”
IEEE J. Ocean. Eng.
0364-9059,
32
(
1
), pp.
10
20
.
48.
Holland
,
K. T.
,
Green
,
A. W.
,
Abelev
,
A.
, and
Valent
,
P. J.
, 2004, “
Parameterization of the In-Water Motions of Falling Cylinders Using High-Speed Video
,”
Exp. Therm. Fluid Sci.
0894-1777,
37
, pp.
690
770
.
49.
Elmore
,
P. A.
,
Wilkens
,
R.
,
Weaver
,
T.
, and
Richardson
,
M. D.
, 2005, “
IMPACT 28 and 35 Simulations of 2003 Baltic Sea Cruise: Model Results and Comparison with Data
,”
Fifth Annual ONR Workshop on Mine Burial Prediction
,
Kona
,
HI
, Jan. 31–Feb. 2.
50.
Elmore
,
P. A.
,
Richardson
,
M. D.
, and
Wilkens
,
R. H.
, 2007, “
Exercising a Deterministic Mine Burial Prediction System for Impact and Scour Burial for Operational Navy Use
,”
IEEE J. Ocean. Eng.
0364-9059,
32
(
1
), pp.
273
283
.
51.
Chu
,
P. C.
,
Allen
,
C. R.
, and
Fleischer
,
P.
, 2006, “
Non-Cylindrical Mine Impact Experiment
,”
Proceedings of the Seventh Monterey International Symposium on Technology and Mine Problems
,
Naval Postgraduate School
,
Monterey, CA
, p.
10
.
52.
Allen
,
C. R.
, 2006, “
Mine Drop Experiment II with Operational Mine Shapes (MIDEX-II)
,” Master thesis, Naval Postgraduate School, Monterey.
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