Cold Regions Science and Technology 76–77 (2012) 63–68

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Cold Regions Science and Technology

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Fracture of a ridged multi-year Arctic sea ice floe

J.P. Dempsey a,⁎, Y. Xie b, R.M. Adamson c, D.M. Farmer d

a Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY 13699, USAb Pacific Salmon Commission, 600-1155 Robson Street, Vancouver, BC, Canada, V6E 1B5c 108 Shadow Lake Drive, Shamong, NJ 08088, USAd Graduate School of Oceanography, University of Rhode Island, Narragansett, RI 02882, USA

⁎ Corresponding author. Tel.: +1 315 268 6517; fax:E-mail address: jdempsey@clarkson.edu (J.P. Demps

0165-232X/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.coldregions.2011.09.012

a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 May 2011Received in revised form 14 September 2011Accepted 26 September 2011

Keywords:Sea iceRidgeMulti-year floeAcousticSeismicFracture energy

As part of the 1994 Sea Ice Mechanics Initiative experimental program, fracture experiments were carried outon an 80 m diameter ridged multi-year (MY) ice floe in the Beaufort Sea. An edge cracked, quasi-circularridged floe was subjected to both cyclic and ramp loading sequences using a steel flat jack. Load, crack open-ing displacement, acoustical and seismic measurements were made during the experiments. The objectivewas to gain further insight into the fracture and constitutive properties of MY sea ice. Accurate predictionsof the strength of MY sea ice and the forces developed during interactions between MY sea ice and floatingor fixed structures are sought. Such interactions include MY ice floe collisions with offshore structures andships. The fracture resistance of MY ice is determined to be within the range 23bGcb47 J/m2 for a 80 m di-ameter ridged MY floe. This fracture energy is similar to values obtained for the fracture of FY sea ice bothin the Arctic and the Antarctic.

+1 315 268 7985.ey).

l rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Beginning in October 1991, the U.S. Office of Naval Research spon-sored a 5-year Accelerated Research Initiative on Sea Ice Mechanics(SIMI). This program supported theoretical, numerical, laboratoryand field studies to explore the mechanical behavior of sea ice at var-ious scales, ranging from 0.1 m to 100 km. As part of the March-AprilSIMI ’94 experimental program, an ice camp was setup for six weekson a drifting MY sea ice floe about 160 nautical miles north of Prud-hoe Bay, Alaska. There were many different groups at this camp at dif-ferent times. Included in these groups were John Dempsey and RobertAdamson from Clarkson University studying the constitutive andfracture behavior of sea ice, David Farmer and Yunbo Xie from the In-stitute of Ocean Sciences studying the acoustic and seismic wavesgenerated by the rafting, ridging and fracture of sea ice, while MaxCoon (Northwest Research Associates, Inc.) and Robert Pritchard (Ice-Casting, Inc.) conducted simulated ice interaction tests studying thevarious failure modes associated with the ridging process. In earlyApril 1994, Max Coon asked the Clarkson group if they could split aMY floe, and subsequently marshalled the logistical and technicalsupport of several groups. Larger flat-jacks were flown in from Dead-horse (with the assistance of L.H. Shapiro, University of Alaska-Fairbanks), and after a suitable floe was chosen by helicopter recon-naissance, many individuals were called upon to help the Clarksongroup get the test ready (M.D. Coon, D.C. Echert, G.S Knoke and R.S.

Pritchard). Test preparation took several days, April 7–9, 1994. Thetest itself was conducted on April 10, after a radial edge-crack hadbeen sawed into the chosen ridged multi-year (MY) floe, and both cy-clic and ramp loading were applied to this crack with intent to extendthe crack through the entire floe.

The floe was covered with packed uneven snow, and was frozen inplace by newly formed lead ice. The floe was cut free from this sur-rounding lead ice with chain-saws and a ditcher-saw such that thefloe would be unconstrained and free to deform. Fig. 1 shows a sche-matic of the multi-year floe. The thick central portion of the ice floewas 3 to 6 m thick and approximately 67 m in diameter, with an at-tached outer 6 to 8 m annulus of thin ice, roughly 2/3 m thick. Thepre-crack was 21 m long, however only 13.4 m of this pre-crack wascut into the thicker central portion. In the vicinity of the start of thepre-crack into thicker ice, the ice was approximately 2.5 m thick.While the first 7.6 m portion of the pre-crack was a through-the-thickness crack in the thin lead ice, the remaining 13.4 m couldbe cut to a depth of just 1.5 m, leaving a considerable uncrackedligament. Linear variable differential transformers (LVDTs) and non-contacting KAMAN gages were placed at three locations along thecrack to measure the crack opening displacements (CODs). A servo-pneumatic loading system, with closed loop control, was used toload the ice (designed by Adamson during an earlier field trip to Bar-row, Alaska between November 9–19, 1993 (Adamson et al., 1997)).The system consisted of two steel flat-jacks (0.61 m×0.91 m) whichwere inserted into the pre-crack, a high pressure nitrogen bottle,and a computer controlled servo-valve used to regulate the pressurein the flat jacks. Fig. 2 is a schematic of the pre-crack showing the

Ditch cut around MY Floe

Thin Lead IceMulti-Year Floe

Pre-cut Crack

8m13m54m

6mFJ’s

Pressure Ridge

Keel

Tent

Precutcrack

Square platetest

Chainsaw cutto free the floe

15m

Fig. 1. Schematic of multi-year floe and experimental setup.

64 J.P. Dempsey et al. / Cold Regions Science and Technology 76–77 (2012) 63–68

locations of the COD gages and the two flat-jacks. Note that the CODat Station k is given by δk, k=1,2,…,6. Both cyclic and ramp loadingsequences were applied to the ice. Ultimately the ice was loaded tofailure to split the floe. The load and COD data were recorded andviewed in real time with a triply redundant data acquisition system.Acoustic and seismic measurements of the ice cracking events duringthe cracking of the MY floe were recorded by Xie and Farmer (1994)and analyzed following the techniques developed in Farmer and Xie(1989); Xie(1991).

2. Cyclic and monotonic ramp loading

Over a time duration of approximately 40 min, six sets of cyclicloading were applied to the ice floe followed by two ramp loadings(the flat-jack pressures were corrected to account for the flat-jackloading efficiency). The first four sets of cyclic loading were haversinewaves with a frequency of 0.01 Hz and load amplitudes of 290, 610,910, and 1220 kN. Only two complete cycles of the loading at1220 kN were applied as the flat jack nearest the crack tip then failed(the flat jack located at Station 8 in Fig. 2). All loading sequences fol-lowing the failure of this flat jack used just the one flat jack. Cyclicloading at a higher frequency (0.1 Hz) was attempted but proved un-successful due to control problems. Two brief sets of cyclic loading at0.05 Hz followed with load levels of 720 and 1000 kN. After these

X

123456

78

Fig. 2. Plan view of the pre-crack cut into the multi-year floe: X1=0, X2=7.6 m,X3=11.0 m, X4=12.4 m, X5=16 m, X6=21 m, X7=11.3 m, X8=12.0 m. The crack-mouth was located at Station 1, whilst the CODs were measured at Stations 4–6 andthe centerlines of the two flat-jacks were located at Stations 7 and 8. The shaded por-tion represents the through-the-thickness crack cut into the thin lead ice. Theunshaded portion (X2bXbX6) is cut just 1.5 m deep. The flat-jack at Station 8 rupturedfirst.

sequences of cyclic loading, two monotonic loading ramps wereapplied (see Fig. 3), the first at 20 kN/s for a duration of 75 s, andthe second at 55 kN/s for a duration of approximately 33 s (cutshort because the sole remaining flat-jack blew).

Fig. 4 shows the geometry of the geo-hydrophone array system (5hydrophones and 5 geophones) deployed at the site of the MY floe.Hydrophones were deployed at 20 m depth beneath the lead icesurrounding the MY ice floe, and geophones were deployed at clearedareas on the floe surface. The maximum spacing between hydro-phones was approximately 90 m. This array constituted an over-determined system for tracking the crack positions although it turnedout that reliable correlation analyses could be obtained only throughdata recorded on the H1, H2 and H5 channels during the early stage ofthe fracturing test. This is because prior to the final fracturing, mostcracks occurred at or near the start of the uncracked ligament result-ing in higher signal-to-noise ratios on channels of the three nearesthydrophones. It was also learned that most detected cracking signalswere ms long exponentially decaying sine waves.

The root-mean-square (rms) sound level associated with crackingwas benchmarked by examining the raw acoustic signals recorded onH1. These rms values were based on statistics of the raw data slicedby a 2.5 s long window. A large amount of noise from other activitiesat the site (walking, snowmobiles) contaminated the signals, espe-cially the small cracking sounds. Nevertheless, the major cracking as-sociated with the twomonotonic ramps was very clear (see Fig. 5). Toextract cracking signals from the raw data, a digital filter was imposedto hi-pass filter the acoustic data at a cut-off frequency of 2 kHz. Thisreduced but did not eliminate the noise. A more detailed record ofrms sound level (based on windows of 185 ms long hi-pass filteredsections of data that contained cracking signals) was obtained forthese selected data sets. An immediate observation was that most ofthe cracking was loading induced, though maximum cracking activi-ties occurred prior to either peak loads or peak CODs.

To evaluate the cracking rate (number of individual cracks per sec-ond), a procedure was developed to identify individual cracks fromthe raw data. With the majority of the cracks generating ms longpulses, sudden increases of under-ice acoustic power occurred at mstime scales. Thus, an 11 ms long window was chosen to segmentthe data; the rms values of these data sets were then calculated.After many test trials, a cracking event was assumed if the rmsvalue of the data segment were greater than that of the previous seg-ment by 2.

The combined COD and acoustic recordings help elucidate thesequence of cracking events. Fig. 6 portrays the cracking trajectories,the cracking rate and the cracked distance for both the first (LHS)and second (RHS) ramps. Given that the through-the-thicknesscrack in the thin lead ice was 7.6 m long, it is clear from Fig. 6 thatafter the first ramp just the initial portion of the uncracked ligamentwas cracked (of the order of a few meters past Station 2). That is,the pre-crack was through-the-thickness for 10 m or so after thefirst ramp, having caused also a certain amount of cracking in theremaining ligament. The acoustic analyses indicated that most ofthe cracking sounds emanated from the tip of the 7.6 m through-the-thickness pre-cracked (Station 2). These sounds were generatedprimarily from the successive near-vertical fractures of the uncut lig-ament between Stations 2 and 6. Fig. 6 presents the cracking ratesversus time for the two monotonic ramps; the COD at Station 6 (δ6)versus time is also provided for comparison. The first major fracturingprocess lasted about 30 s just prior to peak load, with a total of 784individual cracks identified between 1707 s and 1797 s. Similar corre-lation analyses were carried out for a 10 s data set recorded duringthe second monotonic ramp. Xie and Farmer (1994) found that thefloe was fractured in just a few seconds, once the pre-crack becamefully through-the-thickness and started to increase in length. The in-ferred crack trajectory is shown in Fig. 6 as a function of time. The sec-ond significant fracturing process took place just 10 s prior to the

First Ramp

t [s] t [s]

P7

[MN

]

P7

[MN

]1700 1750 18000

0.5

1.0

1.5

2.0

1707

1772

Second Ramp

2320 2330 2340 2350 23600

1

22353.8

2356

.8

2357.1

Fig. 3. The two monotonic ramps applied just prior to failure of the final flat-jack.

65J.P. Dempsey et al. / Cold Regions Science and Technology 76–77 (2012) 63–68

peak load during the second ramp, with a total of 190 cracks occur-ring between 2333 s and 2363 s. During both monotonic ramps,cracking intensified as the load increased, with cracking rates reach-ing their maxima prior to the peak loads. During the second ramp,the sole remaining flat-jack located at Station 7 in Fig. 2 blew att=2356.8 s; the peak load occurred at t=2353.8 s. In the early stagesof the second ramp, it appears that two successive crack jumpsformed through-the-thickness, since the crack spontaneously closestwice. This was followed by a period of slow steady growth of thecrack. The cracking ended with a sudden increase in crack velocityapparently just as flat-jack blew, and then in less than 3 s the crackadvanced 50 m, fracturing almost the entire floe (as discoveredpost-test by Xie and Farmer (1994) via their acoustic and seismic

•

•

•

••

H1

H2

H3

H4 H5

X

Y

G1G2

G3

G4

G5

10 mscale

Atna

pre-crack

Fig. 4. Configuration of the geo-hydrophone array deployed at the MY floe. Also shownare the geometry and location of the pre-crack (reproduced from Fig. 8 in Xie andFarmer (1994)).

measurements). The cracking trajectory caused by the second rampdeviated from the direction of the pre-crack. While a spatial inhomo-geneity in tensile strength and fracture resistance is to be expected,especially with the crack aimed initially toward the ridge, a predom-inant c-axis orientation should exert a stronger influence. The factthat the pre-crack propagated the last 45 m on a straight path sup-ports the latter assertion.

After the final ramp and flat-jack failure, the Clarkson group(Dempsey and Adamson) concluded that successful splitting hadnot occurred. There were no traceable surface fractures, and thethick and uneven snow layers on the floe surface further hinderedan in situ investigation. The Clarkson Group's time at the SIMI Campwas also days over their planned exit date, and a hasty exit wasmade via Twin Otter the day after the experiment concluded. Theonly means to examine the cracking evolution further was via theacoustic and seismic measurements of Xie and Farmer (1994).

To this end, the cracking signals received by the hydrophones H1,H2 and H5 (see Fig. 4) were cross-correlated using H5 as a referencechannel. Data were hi-pass filtered (at 100 Hz) and segmented bya 90 ms window before performing correlation analyses. Peaks fromeach correlation analysis were used to estimate delays between

t [s]

rms

[cou

nts]

0 1000 20000

2000

4000

6000

First Ramp

Second Ramp

Fig. 5. Root-mean-square sound level based on the raw data recorded on the H1 chan-nel for the entire fracture experiment. The cracking associated with the two monotonicramps are clearly identified but small cracking events were masked by on-site activitiesand could not be unveiled (reproduced from Fig. 11 in Xie and Farmer (1994)), withmodifications).

First Ramp

t [s]

t [s] t [s]

t [s]

crack distance [m]

1742 1746 1750 1754 1758 17620

20

40

60

80

Second Rampcrack distance [m]

2349 2351 2353 2355 2357 23590

20

40

60

80

••••••••••••••••••

•••••••••••••••••••

First Ramp

Total=784

• cracking rateδ6 δ6

CO

D[m

m]

δ 6

CO

D[m

m]

δ 6

1700 1720 1740 1760 1780 18000

10

20

0

1

2

•

•

••••••

•••••

••••••••••••••••••

•••

••

••

•••

••

••••••

•••••

•

••••

••••••

•••••••

••

•••

•••

•

•••

•••••

Second Ramp

peakload

Total=190

• cracking rate

2330 2340 2350 23600

10

20

0

2

4

6

••

••

•• •

• ••

• •

• •

•••

••

• •

•• •

•• •• •

• •

•

•

•

••

H1

H2

H3

H4 H5

G1G2

G3

G4

G5

Atna

10 mscale

First Ramp

Cracking Trajectory

•

•

•

••

H1

H2

H3

H4 H5

G1G2

G3

G4

G5

Atna

10 mscale

Second Ramp

Cracking Trajectory

Fig. 6. Fracturing during the first (LHS) and second (RHS) monotonic ramps: acoustically inferred fracture trajectories; cracking rate (number of cracks per second) compared withthe COD at Station 6 both versus time; crack distance versus time using H1 location as reference (reproduced from Figs. 13, 14, 16 and 18 in Xie and Farmer (1994), withmodifications).

66 J.P. Dempsey et al. / Cold Regions Science and Technology 76–77 (2012) 63–68

time arrivals among the cracks detected on the three hydrophonechannels. Due to the intermittent nature of the cracking process andspatially sensitive signal strengths of cracking sounds it was neces-sary to interpolate the arrival time delays in order to obtain coherentdelay trends. Based on array geometry and floe size, an iteration rou-tine was developed to search for crack positions for any given delays.This method allowed successful inference of crack locations as a func-tion of time.

3. Fracture analysis

The six sets of cyclic loading that preceded the two monotonicramps did succeed in partially cracking the pre-existing uncracked

ligament lying between the ?7.6bXb21 m portion of the pre-crackshown in Fig. 2 as well as causing some extension of the crack tip,as indicated by the magnitude of the COD measurements at Station6. The cracking associated with the first monotonic ramp (seeFig. 3) is displayed on the left-hand side (LHS) in Fig. 6, which por-trays the cracking rate and the cracking distance versus time, respec-tively. A large number of cracks occurred, and there is no reason tobelieve that all of this sub-critical cracking all occurred in the planeof the pre-crack. Fig. 6 indicates that these cracking events did notreach Station 6. The first ramp significantly damaged the integrity ofthe uncracked ligament for approximately 10 m past Station 1, withthe partial-thickness cracks concentrated on near-vertical planesclustered in the vicinity of the plane of the uncracked ligament.

First Ramp

COD [mm]

P∗ 7

[MN

]

P∗ 7

[MN

]

0 1 2 30

1

2δ∗

4 δ∗4

δ∗6 δ∗

6

Second Ramp

COD [mm]0 2 4 6 8 10

0

1

2

Fig. 7. Load versus COD at Stations 4 and 6 during the first and second monotonic ramps. The superscript (*) denotes that the quantity was zeroed at the start of the plot.

67J.P. Dempsey et al. / Cold Regions Science and Technology 76–77 (2012) 63–68

Significant microcracking occurred ahead of, and in the vicinity of,the crack tip at Station 6, as is indicated by the LHS figure in Fig. 7,concentrated more near the top-surface of the sheet than the bot-tom-surface, since the COD at Station 4 is influenced more than thatat Station 6. The cracking rate and the cracking distance versus timeassociated with the second monotonic ramp (see Fig. 3) are displayedon the right-hand-side (RHS) in Fig. 6. There were fewer crackingevents, but in all likelihood these cracks were much more significantin areal extent of the individual cracks and in the acoustic radiation(as verified by Fig. 5). The pre-crack becomes a fully through-the-thickness crack just prior to peak load and significant, stable crackextension is occurring just before the last flat-jack at Station 7 ruptured.Fig. 7 indicates that significant crack extension occurred during theassociated unloading that occurred in the second ramp. Xie and Farmer(1994) determined that just after the flat-jack blew the crack advancedapproximately 50 m in less than 3 s.

Remember that because of a large amount of noise from other ac-tivities at the site, the cracking signals were extracted by imposing adigital filter to hi-pass filter the acoustic data at a cut-off frequencyof 2 kHz. The cracking associated with finer failure processes andvery small CODs (of the order of tens of μm) would not have beenmeasured. The actual time of extension of the major crack was infact not measured. Rather, a delayed extension was measured, associ-ated with larger CODs and the tearing of highly bridged sub-scale lig-aments. The essential hypothesis here is that the major crack wasvery nearly established by the time the flat-jack blew at the end ofthe second ramp. The work done (WD) to crack a significant portionof the floe may be idealized by the shaded area on the LHS of Fig. 8;

COD, δ∗4 [mm]

Load

,

0 2 4 6 8 100

1

2 •

•

•

a

b

c

P∗ 7

[MN

]

Fig. 8. Fracturing during the second ramp: load at Station 7 (P7) versus the COD at Station 4 (done (7900 Nm and 6300 Nm, respectively). The ?superscript (*) denotes that the quantity2356.8 s, and 2357.1 s, respectively.

if one argues that considerable work was done to establish a fully-through-thickness pre-crack (represented approximately by the ris-ing portion of P7 versus δ4 plot in Fig. 8), then a better idealizationis the shaded area on the RHS of Fig. 8. The latter shaded area is anafter-the-fact linear-elastic-fracture-mechanics (LEFM) idealization:all nonlinear behavior and sub-critical fracture processes are assumedto occur at a single mathematical point at the crack tip (there is no at-tempt to include a cohesive zone, for instance). The crack growsquasi-statically from the point at “a” (RHS of Fig. 8) and grows subjectto a constant fracture resistance to the point “b”. Too much is un-known about just exactly what happened after the final flat-jackblew, hence the shaded area on the RHS of Fig. 8 is conservative andrepresents a lower bound.

The in situ fracture energies associated with crack growth frompre-fabricated crack tips in relatively cold Arctic and Antarctic first-year (FY) sea ice has been determined to be 15 J/m2 and 13 J/m2, re-spectively (Dempsey et al., 1999, 2004), whilst the fracture energy as-sociated with stable crack growth over the distance 0bΔLb0.6 m meta rising resistance, as Gc grew from 13 J/m2 to 33 J/m2 (Wang et al.,2006). With regard to the cracked MY floe under consideration, thework-of-fracture fracture energy is given by Gc=WD/hL, in which hrepresents the thickness of the MY flow, and L the length of thenew fracture formed. No detailed thickness measurements of theMY floe were done: by looking at the sides of the floe in the waterit was determined that h=3m and h=6m represent reasonablelower and upper bounds, respectively, over the region that the newfracture formed. Assuming that a 45 m crack was formed by thework done, and taking the shaded area on the RHS of Fig. 8 as a

COD, δ∗4 [mm]

0 2 4 6 8 100

1

2 •

•

•

a

b

c

Load

,P∗ 7

[MN

]

δ4); the shaded area represents two approximations of the area equated with the workwas zeroed at the start of the plot. The points a, b and c identify the test times 2353.8 s,

68 J.P. Dempsey et al. / Cold Regions Science and Technology 76–77 (2012) 63–68

better approximation, the associated fracture energy is given by23bGcb47 J/m2.

4. Conclusions

The fracture resistance of MY ice was determined to be within therange 23bGcb47 J/m2 for a 80 m diameter ridged MY floe. This frac-ture energy is similar to values obtained for the fracture of FY seaice both in the Arctic and the Antarctic.

Acknowledgements

The research support of the U.S. National Science Foundation (ANT-0338226/JPD), the U.S. Office of Naval Research (N00014-90-J-1360/JPD, N00014-93-1-0714/JPD, and N00014-92-J-1256/DMF&YX), theCentre for Offshore Research and Engineering, the National Universityof Singapore (as a Maritime Technology Professor/JPD), the logisticalsupport of M.D. Coon and A. Heibig, and the technical support provided

by M.D. Coon, D.C. Echert, G.S Knoke, R.S. Pritchard and L.H. Shapiro aregratefully acknowledged.

References

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Dempsey, J.P., Adamson, R.M., Mulmule, S.V., 1999. Scale effects on the in-situ tensilestrength and fracture of ice. Part II: first-year sea ice at Resolute, N.W.T. Interna-tional Journal of Fracture 95, 347–366.

Dempsey, J.P., Mu, Z., Cole, D.M., 2004. In-situ fracture of first-year sea ice in McMurdoSound: Proceedings 17th IAHR Symposium on Ice, 2, pp. 299–306.

Farmer, D.M., Xie, Y., 1989. The sound generated by propagating cracks in sea ice. TheJournal of the Acoustical Society of America 85, 1489–1500.

Wang, S., Dempsey, J.P., Cole, D.M., 2006. In-situ fracture of first-year sea ice inMcMurdo Sound: Test A2-SP8: Proceedings 18th International POAC Conference2006, 3, pp. 1071–1082.

Xie, Y., 1991. An acoustical study of the properties and behaviour of sea ice. Ph.D. Thesis,The University of British Columbia:165 pp.

Xie, Y., Farmer, D.M., 1994. Acoustic and seismic perspective of ice events observed inSIMI ’94 experiment. ONR Report, December 1994. 25 pp.