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Review Articles

# Mine Impact Burial Prediction From One to Three Dimensions

[+] Author and Article Information
Peter C. Chu1

Naval Ocean Analysis and Prediction Laboratory, Naval Postgraduate School, Monterey, CA 93943pcchu@nps.edu

1

Corresponding author.

Appl. Mech. Rev 62(1), 010802 (Dec 16, 2008) (25 pages) doi:10.1115/1.3013823 History: Received January 22, 2008; Revised August 06, 2008; Published December 16, 2008

## Abstract

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.

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## Figures

Figure 1

M-coordinate with the COM as the origin of X and (im,jm) as the two axes. Here, χ is the distance between the COV (B) and Com (X), and (L,R) are the cylinder’s length and radius (after Chu (13)).

Figure 2

Mine’s COM position (x,z) and orientation ψ2 (after Chu (16))

Figure 3

Mine’s orientation is assumed constant by the one-dimensional model when it falls through a single fluid (after Chu (12))

Figure 12

The impact (resistant) force exerted on the part of the mine surface moving toward the sediment (after Chu and Fan (36))

Figure 13

Momentum and angular momentum balance for mine penetration through the water-sediment interface

Figure 14

Mine with nose, tail, and cylindrical body (after Chu and Fan (35))

Figure 15

Location of cv, cev, and cm. Here, ε is the distance between cv and cm; χ is the distance between cev and cm (after Chu and Fan (35)).

Figure 16

Mean sediment density ρs(z) and shear strength S(z) profiles in the Monterey Bay collected during the cylinder drop experiment on May 31, 2000

Figure 17

Observed (MIBEX-NPS) and predicted (IMPASCT25/28 and IMPASCT35 with Delta method) burial depths: (a) direct comparison and (b) scatter diagram. Note that the two-dimensional model (IMPACT25/28) predicts the burial depth five to ten times larger than the observed depth, and IMPACT35 with Delta method performs much better than IMPACT/28 (after Chu and Fan (36)).

Figure 18

Operational mines: (a) Manta, and (b) Rockan. Here, the Manta is an anti-invasion bottom mine, produced primarily by the Italian firm Whitehead Alenia. It is shaped as a frustum with a GRP casing, triggered either acoustically or magnetically. The Manta has a shelf life of 30years and will operate for 17months after activation. The Rockan (made in Sweden) has a gliding shape, which allows mine laying over a wide area while covering the minimal distance; its low-profile stealth shape makes it difficult to detect. Its casing is also constructed of GRP.

Figure 19

Side and top views of the model mines with different shapes for MIDEX-II experiment; (a) Manta and (b) Rockan. The construction of these model mines consisted of a three-part product process: prototype development, mold construction, and test shape casting, and finishing. This process was necessary to facilitate more efficient experimentation and to reduce the production cost of the experimental test shapes.

Figure 22

Trajectory patterns of model mines during MIDEX-II: (a) Manta and (b) Rockan mines

Figure 23

Three coordinate systems for Manta and Rockan shapes

Figure 10

Illustration of PCOV (B−), x1, and ξ− for the tail part [C(1),D(1)] for the case in Fig. 9 (after Chu and Fan (36))

Figure 11

Geometry of part D(1) (after Chu and Fan (36))

Figure 20

MIDEX-II setup: (a) MBARI test tank facility (structure above water is a movable bridge), (b) top view of the two video cameras, (c) view from underwater viewing window, and (d) calibration test cross. Here, the MBARI test tank (10×15×10m3) was filled with “standard sea water.” This water was maintained by an ozone filtration system, with no impurities that save the remnants of dye placed into the tank several weeks prior to the experiment. A sliding bridge, on which the slanted board was mounted, spanned the width of the tank (see (a)). Eight viewing windows (c) were 1.83m(6ft) below the surface of the water. The two viewing windows used were selected because of the unobstructed and near perpendicular view to the mine drop spot.

Figure 21

Examples of high-speed film frames for model mines. Here, the commercially available 3D motion analysis software, MAXTRAQ , was the primary tool utilized to perform this function.

Figure 24

Location of cv, cf, and cm. Here, χv is the distance between cv and cm; χf is the distance between cf and cm. Here, R1 and R2 are the small and large radii of the frustum.

Figure 25

Model-data comparison of Manta mines maneuvering in water column

Figure 26

Model-data comparison of Manta mines maneuvering in water column. Here, the dashed curves represent model results, and the solid curves are observations.

Figure 4

Change of mine orientation caused by momentum due to the buoyancy force (after Chu (27))

Figure 5

Effect of (a) release attitude, (b) water depth, and (c) water temperature on burial depth. Values are primarily chosen to represent all conditions under which IMPACT25 and IMPACT28 may be used (after Chu (28)).

Figure 6

Dependence of (a) burial depth (m) and (b) height protruding (m) on release altitude (m) and water depth (m). Height protruded is illustrated here to clarify the levels at which these parameters become less influential in the two-dimensional models (after Chu (28)).

Figure 7

Effect of sediment (a) density and (b) shear strength on burial depth. Density change only impacts the predicted burial depth in very soft sediments. As expected, shear strength has a dramatic impact on predicted burial depth (after Chu (31))

Figure 8

Effect of α and β on predicted burial depth (m) for different values of sedimentary density (after Chu (31))

Figure 9

Three patterns of cylinder penetration with the cross section being (a) a complete ellipse (b) cutoff ellipse with one side straight line, and (c) a cutoff ellipse with two side straight lines (after Chu and Fan (36))

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