Dynamic simulations of iceberg-seabed interactions

Cold Regions Science and Technology, 17 ( 1989 ) 137-151 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

137

D Y N A M I C S I M U L A T I O N S OF I C E B E R G - S E A B E D I N T E R A C T I O N S D.W. Bass 1 and J.H. Lever 1"2. 7Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. Johns, Nfld (Canada) 2Centre for Cold Ocean Resources Engineering, Memorial University of Newfoundland, St. Johns, Nfld (Canada)

(Received October 31, 1988; revised and accepted May 1, 1989)

ABSTRACT

A six degrees offreedom model of iceberg-seabed interaction is described. Predictions fi'om the modelling are compared to observations obtained from the DIGS series of experiments on grounding and scouring icebergs on the Labrador Shelf

INTRODUCTION

To understand better the nature and extent of iceberg-seabed interactions, a series of field observations of iceberg groundings and scourings were made during the summer of 1985 off the coast of Labrador. This program was called the Dynamics of Iceberg Grounding and Scouring ( D I G S ) experiment (Hodgson et al., in press). A number of icebergs in the DIGS study were fitted with motion sensing devices. Furthermore, the chosen icebergs were " m a p p e d " in order that their geometric characteristics could be analysed at a later date. Stereo photography and acoustic profiling were used to map their above and below water portions, respectively. Technical aspects o f the data acquisition are described elsewhere (Lever et al., 1989). The present paper describes the geometric and dynamic analysis of the icebergs, with particular reference to major dynamic events recorded by the motion sensing devices in which some form of iceberg-seabed interaction occurred. The two icebergs discussed in this paper were *Present address: U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N.H. (U.S.A.).

0165-232X/89/$03.50

chosen because of the particularly dramatic nature of the events recorded. Moreover, each demonstrates complementary aspects of the iceberg-seabed interaction process. The first of these icebergs, coded "Bertha", moved from a grounded state to free floating, periodically impacting the seabed as it moved away from the grounding site. This pitting behaviour was deduced from sidescan sonograms obtained for the seabed in the track of Bertha. The second iceberg, "Gladys", split, rolled and grounded solidly against the seabed. In this paper we describe a six degrees of freedom computer model that simulates interaction of an iceberg with the seabed. The emphasis is on the iceberg dynamics rather than on the mechanics of the soil failure process, the latter being very much more difficult to model without a greater knowledge of the seabed geology and without a better understanding of failure mechanisms within it. The computer modelling is then able to reliably simulate and predict in a qualitative manner, but it is less reliable for quantitative analysis. For example the computer model successfully predicts the motion of Bertha as it moves away from its grounded position, but is less reliable in its prediction of the depth of the pits caused in the ensuing oscillatory motion. Nevertheless, the main objective of the work was met: to simulate complex iceberg-seabed interaction behaviour of realistic iceberg geometries. In the next section we describe the geometric analysis of the icebergs. This section describes the computer model of the iceberg-seabed interaction. Results of the computer simulations are described and compared with observed motions in the section on Application.

© 1989 Elsevier Science Publishers B.V.

138

BASSAND LEVER

GEOMETRIC MODELLING

TABLE I

The geometric data obtained from the optical stereograms and acoustic profiling of the icebergs were presented in the form of horizontal cross-sections taken at various depths below and heights above the still water surface. For the geometric analysis, we processed the horizontal cross-sections to obtain vertical ones, because vertical cross-sections give a better determination of the water line intersection. From these, we derived a representation of the iceberg in terms of vertical trapezoidal prisms. The prisms could themselves be composed of a n u m b e r of smaller disconnected prisms as illustrated in Fig. 1. This pre-processing of the geometric shape data allows for efficient evaluation of geometric parameters for arbitrarily complex shapes. This is especially valuable in the time domain simulation described below where parameters such as instantaneous displacement, centre of buoyancy etc. are evaluated at each time step. The derived geometric data for Gladys and Bertha are given in Tables 1 and 2. Computer-generated three-dimensional images of Bertha and Gladys are shown in Figs. 2-5.

Geometric data for Bertha Volume above water Volume below water

= 1.98)< 105 m

Centre of gravity below water plane Draft

= 38.6 m =ll0m

= 1.16)<

3

10 6 m 3

Moments of inertia at centre of gravity (t m 2) 111 =2.7)< 109 122=2.3)< 109 133=2.9)< 109

Products of inertia at centre of gravity (t m 2 ) Ii2=4.5)< l0 s •23 = - 2 . 4 > ( 107 131-- - 4 . 9 ) < 107

where: lq =Pl I (x" x ) 6ij - xi xj) d V v

with: 60= I for i=j and t~o=0 for i¢j.

TABLE 2 Geometric data for Gladys Volume above water Volume below water

= 7.89 × 10 s m 3 = 5.64 × 106 m 3

Centre of gravity below water plane Draft

= 36.5 m = 140 m

Moments of inertia at centre of gravity (t m 2)

lit=4.1X 101° 122=4.6× 10I° 133=7.2)< 10 I° Products of inertia at centre of gravity (t m 2)

I12= 1.1)< 10I° 123=- 1.1 × 109 131 = 9 . 3 ) < 108 where: lo=pt f (x-x)c~o-xiA~/)dV u

DYNAMIC ANALYSIS

Fig. 1. Vertical cross-section showing representation of iceberg by disconnected prisms.

We conducted the dynamic analysis using a timedomain motion simulation program that calculates (at each time step) hydrostatic forces and moments, the forces and m o m e n t s associated with the

ICEBERG-SEABEDINTERACTIONS

Fig. 2. Computer generated reconstruction of Bertha showing dimensions and waterline.

Fig. 3. Computer generated reconstruction of Bertha showing dimensions and waterline.

139

140

Fig. 4. Computer generated reconstruction of Gladys showing dimensions and waterline.

Fig. 5. Computer generated reconstruction of Gladys showing dimensions and waterline.

BASSANDLEVER

ICEBERG-SEABEDINTERACTIONS

141

iceberg's penetration of the seabed and those due to currents. The simulation program tracks the position of the centre of gravity of the iceberg together with the rotation of axes fixed in the iceberg relative to axes fixed in space. More precisely, let {x,y,z} be axes fixed in space in the waterplane of the iceberg, initially above the centre of gravity, where body fixed axes {x' ,y',z' }, used to define its geometry, are located. The orientation of the body axes relative to those fixed in space is described by modified Euler angles (Blagoveshchensky, 1962 ), with a rotation ¢ (yaw) about the z-axis (in the positive sense of a right-handed system of axes), followed by a rotation ~uabout the y'-axis (pitch) and then a rotation 0 about the x'-axis (roll). The rotation matrix describing the orientation of the body axes relative to absolute axes is given by the following: C283 C 1C3~"SiS2S 3 S2 SI C2

R=

-

-

C 18283 - S I C 3 Cl C2

where St =sin 0, C, =cos 0, S2=sin ¢, C2=cos ¢, $3 = sin ~, C3 = cos ¢. The motion equations solved at each step are as follows: [M+~M]~+

[Bx]~ M g + S C F O R + CRFOR

= HSFOR-

[ I + ~ I ] t b + t o ^ [ / ] t o + [Bo~]to

modes, and where to denotes the angular velocity vector of the body fixed axes. On the right-hand side of these equations, the forces and moments HSFOR, SCFOR, CRFOR and H S M O M , SCMOM, C R M O M denote hydrostatic, scour and current drag forces and moments, respectively. All moments are relative to the centre of gravity of the body. The angular velocity vector to is related to the angular velocities of roll, pitch and yaw by the following matrix equation:

(i

C,

'(i)(1

S,G J

= to2

-S~ GC2/

o03

where: $1 = sin 0, C1 = cos 0, etc. as above. The motion equations are solved numerically using a variable order, variable time step routine of the Adams' type (predictor-corrector) (Shampine and Gordon, 1983). Estimates of the hydrodynamic coefficients in the equations of motion were based on work previously carried out by Bass and Sen ( 1986 ) using a three-dimensional linear potential model of small amplitude oscillations of large floating bodies in water of finite depth. The calculation of the forces and moments on the right-hand side of the motion equations is described below.

Hydrostatic forces and moments

= HSMOM + SCMOM + CRMOM where M is the body mass, J M is the added mass matrix for the translation modes in the x,y,z directions:

0

)

0

JM3

and [/Ix] is the matrix of damping coefficients for translation modes. I = [Io] (i,j= 1,2,3) is the symmetric inertia matrix and ~I is the added mass moment of inertia matrix:

[JIt [J/]=~

~

0

)

~I2

0

0

JI3

[BoA is the damping matrix for the rotational

The hydrostatic force acting on the iceberg (the buoyancy force) is determined by the volume of sea water displaced. The density of sea water was taken as 1.025 t m -3. The buoyancy force acts at the centre of buoyancy, which is precisely the centre of gravity of the below-water portion of the iceberg. The moment of the buoyancy force about the centre of gravity is then easily determined.

Current forces and moments The current drag term is of the form:

Fer =

1/2 p C D A N ( U - V )

IU - V l

where U is the current velocity, V = (97,~,0) is the velocity of the centre of gravity of the iceberg, Co i s the drag coefficient and AN is the orthogonally pro-

142 jected (relative to the current direction ) surface area of the iceberg. The centre of pressure for this force was taken as the centre of area of this projected surface of the iceberg, from whence the moment of the current force is calculated.

Scour forces and moments The forces and moments of soil pressure reaction to the horizontal and vertical motions o f the keel penetrating the seabed are calculated using the quasi-static modelling described in Bass and Woodworth-Lynas (1988). The most significant simplification of the soil force modelling is the decoupling of the failure modes associated with the penetration of the keel into the seabed in the horizontal and vertical directions. Thus, there is an assumed horizontal ploughing action with soil being scooped out before the forward moving face of the indenter keel, and at the same time the downward vertical motion of the keel produces failure modes typical of those associated with static vertical loadings. Doubtless there are more sophisticated models of the process, even assuming decoupling. There seems little point, however, in implementing such models when even the most rudimentary of the soil parameters are not known. The horizontal forces due to the scouring or ploughing action of the keel portion beneath the seabed are derived from the work o f C h a r i (1979). In his model the increase in depth of penetration of the iceberg keel is associated with the slope of the seabed in the linear track of the iceberg rather than the rotational and heave motions used in the model below. The direction of the horizontal reaction of the soil forces is taken to be that of the instantaneous horizontal velocity vector of the keel, characterized by the velocity of a point on the keel, assumed to be the "centre of pressure" for the soil forces. For simplicity, the indenter keel is modelled by a truncated cone of variable base radius and variable edge slope. The horizontally projected area of this cone, normal to the direction of motion is dependent only on depth of penetration and not on its direction of motion. The conical identor is an idealization of the iceberg geometry in the vicinity of the contact area with the seabed.

BASSANDLEVER Primary motivation for this model of the indenter is that it provides a simple way of modelling increase o f contact area with depth of penetration an obviously significant parameter in any soil failure mechanism. The slant edge slope a provides a single parameter to modify the rate o f increase o f contact area with depth of penetration. The motion of this idealized conical keel is characterized by the motion of a single point on the " t r u e " iceberg. The point chosen was at the deepest draft, i.e. furthest from the waterplane for the iceberg in its initial (Bertha) or final (Gladys) orientation. It is also the point chosen as centre o f pressure for the reactive soil pressures. Clearly each of these assumptions concerning the motion, shape, etc. of the keel represents a crude approximation to the " t r u e " situation. Unfortunately, " t r u e " in this case involves uncertainties in the derived data at least as significant as the approximations involved in the modelling. Because of the complicated nature o f the horizontal keel motion associated with the coupling o f the rotational and translational modes, it has been assumed that there are no " m e m o r y " effects. That is, the keel, in its time of contact with the seabed may move back into areas already cleared or partially cleared o f surficial sediment. The keel, having no memory, moves the sediment again, with similar reactive soil pressures. The point of course being that it is considered unlikely that the keel will "back out" (on a backward "swing" ) of a pit in the same direction as it moved in the first place (on a forward "swing") because of the relative phases between the various angular and linear displacements and velocities. That is not the case for the vertical motions o f Gladys where repeated entry into the iceberg formed pit is likely to occur. As is indicated below memory effects are taken into account for this motion. F H is the horizontal scour force vector in the direction of the instantaneous velocity vector Vp:

where AH= ( 2 r + s cot ot)s is the projected area o f the indenter keel of base radius r, slant edge of slope a, and depth of penetration s. The soil parameters in the formula are the submerged unit mass of the surficial sediment y, and the cohesive soil shear strength r. In the calculations, y is taken to be 1.5 t

ICEBERG-SEABED INTERACTIONS

m -3 and z as 200 kPa. The derivation of the formula of Fr~ is given in Chari (1979). In fact, his formula contains additional (second-order) terms associated with the surcharge of soil generated by the forward motion of the keel. It is derived from energy considerations by determining the work done in "scooping out" wedges of soil before the moving face of the keel. The terms in the formula for Fn represent the forces associated with "wedge weight", bottom shear and side shear of the wedge, respectively. In the derivation, the angle of soil shear resistance is assumed small and the acceleration of the soil wedge is neglected. The soil strength at the location of the events described in the simulations was not known but it is thought to be high in the general area of the field study (Hodgson et al., in press). The vertical reaction to the penetration of the keel into the seabed is determined by a simple "bearing capacity" formula Scott (1963). It is directly proportional to the vertically projected area of contact and the depth of penetration. The force is associated with the successive failure of the soil at each step and therefore is only applied as the centre of pressure, characterizing the motion of the keel, moves vertically downwards. The vertical force Fv is then given by: Fv = { [r(2~+2) +ygs]Av}k where z, y and s are as above, k is the vertical unit vector and Av is the vertically projected contact area: Av = re(r+s cot a)2 The vertical force is assumed to have memory; that is, unless there is significant horizontal motion of the keel, if the keel re-enters an already scoured pit the vertical soil pressures are taken as zero until the depth of penetration exceeds previously excavated depths.

APPLICATION It is probably worth discussing at this point, the role and implementation of computer simulations. Ideally, initial conditions, both geometric and dynamic, would be determined, model parameters theoretically or empirically derived, and the simulation undertaken. The results of that simulation

143

would then be compared with observed data, and the model rejected, modified or validated. In modelling environmental phenomena, however, it is rare that initial conditions are known to sufficient accuracy, and that model parameters can all be reliably derived theoretically or empirically. The role of the simulator is then to determine conditions and parameters as best as possible and just as importantly their likely "ranges". Results of the simulation are compared to observed data for various conditions and parameter values within likely ranges. The process of selecting the best "conditions" and parameter values is often referred to as "tuning" the model. Unfortunately, the word "tuning" carries with it connotations of chicanery. Certainly the practice is open to abuse if outlandish, unrealistic parameter values or conditions are assumed for the model. In point of fact, in a realistic but complex model, using unrealistic parameter values to improve agreement with observations frequently improves only one aspect of the agreement at the expense of another. For the simulation described below, some "tuning" was employed. It should be noted, however, that the iceberg motions are dominated by the iceberg geometry (since that determines buoyancy forces and moments). Apart from the addition of a keel to the unmapped portion of Gladys, no changes were made to the geometry. On the other hand, a significant tuning effort went into bringing about reasonable agreement between the predicted and observed pitting behaviour of Bertha (see below). For this simulation, relatively small variations in hydrodynamic coefficients and initial conditions led to significantly different pitting behaviours. This was largely due to the dominant role played by the relative phases of the roll, pitch and heave motions. These phases are considerably affected by the hydrodynamic terms in the motion equations. Some confidence could be placed on the values for the inertial hydrodynamic terms (added mass effects) and on their likely range of values. Unfortunately, rotational damping is often difficult to calculate or even estimate reliably. Despite the slow angular velocity, the Reynold's number of the flow at the extremities of the icebergs is still sufficiently high for flow separation to occur, thereby increasing the rotational damping moment (and the difficulty of making re-

144

liable estimates of it). Because of these difficulties, a simple linear damping model was assumed (i.e. a damping moment proportional to angular velocity) with "guidance" for the linear damping coefficient coming from the observed record of the decaying motions of Bertha. (For Gladys, the choice of damping coefficient was not significant since the much greater effects of soil pressures dominated the decay of its motions. ) The choice of damping coefficients was therefore guided by both the observed pitting behaviour and the observed decay of the rotational motion. There were of course other parameters and conditions subject to considerable uncertainty that were "tuned". For example the initial position of the centre of gravity of Bertha (and also, therefore, the initial penetration of the keel in the seabed) was not known since the only geometric data available for Bertha was collected sometime after it became free floating. To achieve the appropriate initial acceleration an appropriate depth of penetration had to be assumed. Other factors to be taken into account were radius of conical indenter, soil shear strength, position of centre of pressure, etc. As has already been indicated, field observations were made of two icebergs fitted with motion sensing packages. The mathematical model described above was used to simulate dramatic events that occurred to each iceberg, with the results then compared to the observations. A description of the events, simulations and comparisons for Bertha and then Gladys are given below.

Bertha At the time that the motion sensing package was deployed, Bertha was grounded. After some relatively minor calvings above and below water, the iceberg moved away from its grounding site and drifted towards the northwest, its oscillatory motions decaying rapidly. Subsequent survey work revealed the creation of a set of four pits along the direction from the initial grounding site. A plot of the potential energy or "stability" surface for Bertha is shown in Fig. 6. This was obtained using the geometric profile data acquired when the iceberg was freely floating. The stability surface shows the iceberg to be stable but with the degree of

BASS AND LEVER

stability varying considerably for different axes of rotation. In particular, the axis at approximately - 6 0 ° (i.e. 60 ° clockwise) to the x-axis is an axis of "weak stability" indicating the axis about which the iceberg was most likely to "roll". In fact, both the free roll and the "ungrounding" event, as recorded by the motion sensing devices, indicate this axis to be that about which the dominant motions occurred. Despite this qualitative confirmation of the geometric analysis of Bertha, the delay between the data acquisition and the pitting event (approximately one day, during which time several calving events took place) reduces the likelihood of good quantitative predictions. Probably one of the most significant features brought to light by the simulations was the manner in which the iceberg left the grounding site. It was apparent from the early simulations of the event that the current alone could not have accelerated the iceberg rapidly enough to account for the large initial spacings between the pits. It would seem likely that the onset of the motion was associated with a calving that caused the iceberg to push itself forward from the seabed in the direction of travel. Such an observation underscores the danger to offshore structures posed by nearby grounded icebergs. An iceberg accelerated by this mechanism could be appreciably more energetic than one accelerated by waves and currents. Initial conditions for the simulations were set so as to initiate the motion from the grounding site in this manner. Imperfect knowledge regarding the geometry of the keel, the area of the contact surface and seabed soil strength cause further doubts concerning the quantitative results from the dynamic simulation. Nevertheless, predictions from the simulations are in surprisingly good agreement with observations. Because of difficulties with the data loggers, it was not possible to obtain reliable estimates of the observed linear displacement from the measured accelerations. However, data for rotations were found to be reasonable. These rotational mode observations are compared to those obtained from the simulations in Figs. 7-9. It is apparent that there are some significant differences in the initial stages of "roll" and "pitch". These are likely associated with both the imperfect knowledge of the seabed-keel interaction parameters and its dy-

ICEBERG-SEABED INTERACTIONS

145

POTENTIAL HEIGHT

Fig. 6. Potentialor "stability" surfacefor Bertha. namic modelling and with the event initiation conditions. As the motion progresses, there is less effect of seabed penetration (see Fig. 10, showing t h e penetration of the keel in the seabed) and the amplitudes and oscillation periods show marked similarities. Some differences in amplitudes of oscillation are to be expected since the axes of rotation used in the simulation only approximately coincide with the axes for the motion sensing package. Not too much significance should be attached to the agreement between observed and predicted yaw motion, since the current speed and direction (which were not available) were chosen so as to bring about the agreement, in order that better comparisons would be made of the other two modes of rotation. The set of significant parameter values

chosen for the simulation are given in Table 3. In Fig. 10, results are shown for the motion of the indenter keel; where the height of the keel relative to the seabed is negative, a pit is formed. It is apparent that the number of pits is three or possibly four with spacing between them decreasing with distance travelled. The spacing is approximately 35, 20, 15, and 10 m. By comparison, from the sidescan sonogram, the number of pits is three with the fourth only just perceptible and the spacing 35, 25, 20, and 15 m. This again shows good agreement with the observed data. It is noted that the decreasing spacing between pits adds further evidence to the contention that the iceberg was accelerated by the energy released from a minor calving rather than by ocean current action.

146

BASS AND LEVER

g

A

OBSEI? VED. PRED.1"C TED

o

o

:j, • O0

lbo.oo

50.00

BERTHA,

1~o.oo

TIME

2bo. oo

I

2 0 0 . O0

3 0 0 . O0

I

3 5 0 . O0

400.00

(s.)

ROLL.

Fig. 7. Predicted versus observed "roll" motions of Bertha.

A

OBSERVED. PREDJ'CTED

6

I

:J .oo

5b.oo

~bo.oo

,~0.00

2~0.00

TIME (s.) BERTHA,

PITCH.

Fig. 8. Predicted versus obse~ed "pitch" motions of Be~ha.

2~0.00

3bo.oo

3~o.oo

400.00

ICEBERG-SEABED INTERACTIONS

147

OBSERVED. o

A

PREDZC

TED.

7-a o.

11M

•

O0

T

~.oo

~oo.oo

I

~5o.oo TIME

BERTHA,

T

200.00

T

~o.oo

soo.oo

3~o.oo

400.00

s~.oo

6~.oo

~.oo

88.00

(s.)

YAW.

Fig. 9. Predicted versus observed "yaw" motions of Bertha. o c;.

I,--

U

o

I0'. O0

(~.oo

2h.oo

3~.oo

4~,. oo

TRAVEL (m.) BERTHA, PITTING. Fig. 10. The motion of a "point" on the keel showing the expected "pitting" behaviour of Bertha as it moves from its grounding site.

BASSAND LEVER

148 TABLE 3 Significant simulation parameters for Bertha Current speed (m s- i ) Drag coefficient Base radius of conical indenter (m) Slant edge angle of conical indenter Keel contact point relative to C.G. (m) Added mass in heave (Mr) Added mass moment in roll and pitch (t m2) Water depth (m) Soil shear strength (kPa)

(a)

0.4 1.5 10 600 (25.1, -13.5, 78.5) 0.8 0.8• 115 200

crushed Ice zone

seabed

(b)

/

..

lo

\

?

(c)

Fig. 11. Schematic representation of the splitting, rolling and grounding of Gladys.

Gladys The event in the observed time history of Gladys to be considered was the singularly dramatic splitting of the iceberg into two pieces, with the larger of these rolling and solidly grounding. A schematic

representation o f the event is shown in Fig. 11. The shape of Gladys following this event is shown in Figs. 4 and 5. Underwater profiling of Gladys was carried out only after this event took place. For the lower segments of the keel, profile data were of particularly low quality, and an extrapolated extension o f the keel was required from 110 m depth to the seabed depth of 140 m. In fact, there were further indications that the profiling methodology was close to its limiting range of useful accuracy for this size o f iceberg (Hodgson et al., in press). Static equilibrium (in terms o f the static forces and moments of buoyancy, weight and seabed reaction) could not be attained for any reasonable position of the keel extension without assuming an ice density of 0.93 t m -3 which is obviously far too high. However it was felt that it was better to take this ice density value in the simulation runs rather than adjust the shape of the iceberg (arbitrarily) above the keel to satisfy static equilibrium requirements in the final grounded state. It should be noted that the ice density has little effect on the iceberg motions, which are predominantly determined by its geometry rather than by its mass. The potential energy plot for Gladys after it grounded (Fig. 12) illustrates the steep potential gradient along the direction followed by the iceberg during the event (approximately 10-20 ° from the x-axis). The calculated drop in potential energy for a roll of 10 ° about this axis agrees well with the calculated kinetic energy at the time of impact (Lever et al., 1989). The stability map also shows that the iceberg is stable for rotations about other axes, a fact consistent with its stable grounded condition. These consistences between the stability map and the observed behaviour of the iceberg lend some confidence to the overall shape determination. The initial configuration of the iceberg was found by rotating the measured grounded iceberg shape until orientation and above water dimensions corresponded approximately to the pre-split Gladys (as documented by surface and aerial photographs). Dynamic simulation of the motions o f Gladys immediately after the splitting are compared to the observed rotations in Figs. 13 and 14. Only the motions of roll and pitch are shown. Data for the motions of yaw and heave are of too poor quality for useful comparisons. The major error appears to be

ICEBERG-SEABEDINTERACTIONS

149 POTENTIAL HEIGHT

Approximote Axis of Roll

X

-y Fig. ! 2. Potential or "stability" surface for Gladys.

in the overprediction of the roll excursion from its initial orientation. It is likely then that the predicted pit depth (approximately 11 m) is too great and the subsequent oscillation maintains energy levels and thus roll amplitudes consistently higher than those observed. Even so the decay of the roll motion shows qualitative similarities to that observed if those portions of comparable initial amplitude are considered. Similarly for the pitch motion, amplitudes, periods of oscillation and decay behaviour show reasonable agreement, after the initial overprediction. Unfortunately due to a variety of operational problems no data could be obtained

on the pit depth or breadth etc. Significant parameters for the simulation are shown in Table 4.

CONCLUSION Despite the sometimes formidable problems of data acquisition, the DIGS experiment has shown that it is possible to obtain data of sufficient quality to test numerical modelling of the geometry and motions of icebergs. For the dynamics of the interaction of an iceberg with the seabed, only broad qualitative agreement with observations has been obtained in the modelling. It is not clear whether

150

BASS AND LEVER

g

LS

OBSEIP V E D PREDIC TED

g

g

"0 0 ~'JO

..J~. _J 0

[

:

/..

ff

g • O0

T 2 0 . O0

r 4 0 . O0

1 6 0 . O0

1" 8 0 . O0

r 1 0 0 . O0

T

1 2 0 . O0

1 1 4 0 . O0

160.00

TIME ( s . )

GL ADYS, ROLL. Fig. 13. Predicted versus observed "roll" motions for Gladys. OBSERVED PREDZCTED

g

o

~

I-

H

Q_

g

Io'. oo

ao.oo

45.00

65.00 65.00 TZME ( s . )

GLADYS, PITCH. Fig. 14. Predicted versus observed "pitch" motion for Gladys.

15o.oo

12o.oo

1~o.oo

160.00

151

ICEBERG-SEABED INTERACTIONS

TABLE 4 Significant simulation parameters for Gladys Current speed (m s-~ ) Base radius of conical indenter (m) Slant edge angle of indenter Keel contact point relative to C.G. (m) Added mass in heave (Mt) Added mass moment in roll and pitch (t m 2) Water depth (m) Soil shear strength (kPa)

0 35 90 ° ( - 0 . 7 6 , - 4 0 . 9 , - 104.1 ) 0.9 0.8• 140 200

this points to fundamental inadequacies in the interaction modelling (which by necessity is somewhat crude) or whether there were too m a n y unknown parameters (e.g. soil strength, keel shape, etc. ) for there to be any hope o f more accurate predictions. The matter may not be resolved without further careful field experiments of this type or controlled large-scale laboratory testing. Nevertheless, the relatively good qualitative performance of the model gives us some confidence that it is correctly implemented and can be applied to study realistic iceberg shapes involved in complex seabed interaction events.

ACKNOWLEDGEMENTS Major funding to perform the D I G S experiment was provided by the Canada Environmental Stud-

ies Resolving Funds, with additional support by the Canada Panel on Energy Research and Development, the Geological Survey of Canada, the Natural Sciences and Engineering Research Council of Canada, and the offshore oil and gas industry through grants to C-CORE. The authors also gratefully acknowledge the contribution to the program of the other principal investigators and numerous support personnel, and the critical role of Geonautics Ltd. coordinating the D I G S experiment.

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