submarine slope stability on high-latitude glaciated...

Ž .Marine Geology 162 2000 303–316www.elsevier.nlrlocatermargeo

Submarine slope stability on high-latitude glaciatedSvalbard–Barents Sea margin

Panagiotis Dimakis a,), Anders Elverhøi b,1, Kaare Høeg c,2, Anders Solheim d,3,Carl Harbitz e,4, Jan S. Laberg f, Tore O. Vorren g, Jeff Marr h

a Norwegian Water Resources and Energy Directorate, PB 5091 Majorstua, 0301 Oslo, Norwayb Institute of Geology, UniÕersity of Oslo, PB 1047, Blindern, N-0316 Oslo, Norwayc Institute of Geology, UniÕersity of Oslo, PB 1047, Blindern, N-0316 Oslo, Norway

d J.S.I. Oil and Gas Consultants AS, PB 218, 1301 SandÕika, Norwaye Norwegian Geotechnical Institute, PB 3930, UlleÕaal Hageby, N-0806, Oslo, Norway

f Institute of Geology, UniÕersity of Tromsø, N-9037, Tromsø, Norwayg Institute of Geology, UniÕersity of Tromsø, N-9037, Tromsø, Norway

h St. Anthony Falls Laboratory, UniÕersity of Minnesota, Minneapolis, MN, 55414, USA

Received 31 August 1998; accepted 10 June 1999

Abstract

Slope stability is evaluated at two locations on high latitude, deep sea fans along the Svalbard–Barents Sea margin, basedon available samples and using an ‘‘infinite slope’’ analysis. The stability evaluation uses the Mohr–Coulomb failurecriterion, and a semi-analytical approach based on Gibson’s formulation for determining the excess pore pressure build-updue to sedimentation. The main results are presented in the form of contour plots of slope safety factors in a diagram withaxes of time and thickness of deposit. The results show that during rapid sedimentation, which mostly takes place duringperiods of maximum glaciation with the ice front located along the shelf edge, slope failure will occur with a frequency

Ž .varying between 95 and 170 years. Only part of the upper sedimented layer will be mobilised 10–30 m , while theŽ .remaining thickness 40–70 m will remain at the initial sedimentation site. These results may explain why the continental

slope is characterised by relatively uniform sediment thickness from upper to lower slope. q 2000 Elsevier Science B.V. Allrights reserved.

Keywords: submarine slope stability; continental margins; glacier erosion; debris flows

) Corresponding author. Tel.: q47-22959169; fax: q47-22959216; E-mail: [email protected]

1 Tel.: q47-22856656; fax: q47-22854215; E-mail:[email protected].



4 Tel.: q47-22023000; E-mail: [email protected].

1. Introduction

Recent studies have demonstrated that the deep-sea fans of high latitude areas such as the Norwe-gian–Svalbard Sea and eastern Canadian continental

Žslope consist largely of debris flow deposits Vorren.et al., 1998 . These high-latitude fans represent ma-

jor depocenters of Late Cenozoic sediment. The Bear

0025-3227r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0025-3227 99 00076-6

( )P. Dimakis et al.rMarine Geology 162 2000 303–316304

Island Fan west of the Barents Sea contains a com-parable amount of Late Cenozoic sediment to that in

Žthe Amazon and Mississippi fans Elverhøi et al.,.1998 . Thus, formation and flow behaviour of these

debris flows represent important issues for under-standing the build-up and development of glaciatedmargins.

Here we consider the initiation of these flows byanalytical estimation of slope stability and failurecriteria of the source area sediments. The generationof these debris flows is related to relatively short

Ž .periods of maximal glaciation 3 to 5 thousand yearswhen the ice front was located at the shelf edgeŽ .Vorren et al., 1998 . During these intervals, sedi-ment was deposited at high rates on the upper conti-

Žnental slope in front of the ice margin Dowdeswelland Siegert, 1998; Dowdeswell et al., 1996, 1998;

.Vorren et al., 1998 . A hummocky surface and achaotic seismic character in the uppermost part ofthe continental slope, suggest that sediment slides

Žhave been released near the shelf break Laberg and.Vorren, 1995 . Once failure occurred, large amounts

Ž 3. Žof sediment were mobilised 10–30 km Laberg.and Vorren, 1995 . The mobilised material settled

into deposits typical of debris flows, forming lobeswith dimensions of 2–10 km wide, 10–50 m thick

Ž .and 10–200 km long Vorren et al., 1998 . While thesediment volumes of these debris flows are large, theexact source of the sediment and its failure mecha-nism are not fully understood. High resolution seis-mic data of the upper slope along the Svalbard–Barents sea margin shows very few scarps or failurescars, rather the area is characterised by sedimentlayers of fairly uniform thickness. This suggests afailure mechanism in which the sediment fails alonga single planar surface.

Various triggering mechanisms have been pro-Ž .posed for large submarine mass movements; 1

build up of excess pore pressure due to high sedi-Ž . Ž .mentation rate; 2 earthquakes; 3 oversteepening;

Ž . Ž .4 seepage of shallow methane gases; 5 erosion atthe toe of the slope. The frequent release of slides ona regional scale suggests a trigger mechanism com-

Ž .mon to these particular settings Vorren et al., 1998 .For example, on the Bear Island Fan a minimum of40 debris lobes were released during a period of

Ž .about 3000 years Laberg and Vorren, 1995 . Recentstudies indicate high rates of sediment delivery to the

margin during this period, approximately 0.5 km3

Žper year Laberg and Vorren, 1995; Dowdeswell and.Siegert, 1998 , corresponding to a sedimentation rate

of about 60 cm per year within a 5-km wide ice-Ž .proximal zone Figs. 1 and 2 .

According to present concepts, the sediment wasdelivered to the upper continental slope as deforma-

Žtion till Dowdeswell et al., 1996; Elverhøi et al.,.1997 . In other words, this sediment can be consid-

ered to have been transported out beneath the ice in a‘‘conveyor belt’’ fashion and deposited in front of

Ž . Ž .the ice margin Fig. 2 Elverhøi et al., 1997 . Thismechanism of sediment conveyance is unique in thatthe sediment is deposited without being suspended inthe water column. Thus, the properties of this sedi-ment are characteristic of what is typical for defor-mation till deposits rather than what is typicallyfound for sediment deposited sediment on a delta-feddeep-sea fan in which the sediment is suspendedbefore deposition. The transport mechanisms and therates of deposition in these high latitude systemsappear to have a significant impact on the mechani-cal properties of these tills, which in turn determinethe later stability of this sediment on the slope.Although these tills may be partly consolidated, thehigh ‘‘conveyor belt’’ rates will cause build-up ofexcess pore pressures in the underlying sedimentresulting in failures at the upper parts of the fans,despite the low slope angles observed.

High sedimentation rates clearly favour the build-up of excess pore pressures and subsequent sedimentfailure particularly in fine-grained sediment deposits.In this paper, we focus on the stability of the sedi-ment in a ‘‘hypothetical’’ ice-proximal zone offshoregrounded-ice on the shelf edge with respect to thehigh average sedimentation rates which have beenestimated for the Bear Island Fan. As examplestypical of debris flow sediments for the region, weuse the geotechnical data from two cores taken fromdebris lobes at the Bear Island Fan and the Isfjorden

Ž .Fan Fig. 1, Table 1 . The two cores consist ofŽ . Žuniform, homogeneous non-stratified diamicton ca.

.40%-2 mm, 40% silt, 20% sand and gravel .Geotechnical analysis of the samples has been car-ried out by the Norwegian Geotechnical InstituteŽ . Ž .NGI Sandbækken et al., 1986 . The Bear Islandsample was analysed according to the standard lab

Ž .procedures used by NGI Mokkelbost, 1998 , while

( )P. Dimakis et al.rMarine Geology 162 2000 303–316 305

Ž . Ž .Fig. 1. a Bathymetric map showing the Svalbard–Barents Sea margin and the location of the two cores in Table 1. b The distribution ofŽthe debris lobes as recorded by GLORIA long range side scan sonar imagery is shown at the Bear Island Fan modified from Dowdeswell et

. Žal., 1996 . The location of the core sample is also shown. BIFsBear Island Fan, BITsBear Island Trough, SFsStorfjorden Fan,.IFs Isfjorden Fan, ITs Isfjorden Trough .

the analysis of the Isfjorden sample did not followŽ .such procedures Fossen, 1996 .

Although only two samples have been analysed indetail, the composition of these two samples resem-

Fig. 2. Conceptual diagram illustrating the sediment dynamics beneath and at the front of an ice stream draining the major troughs in highlatitude areas. The deformation till under the ice stream is deposited in the ice-proximal zone in a ‘‘conveyor belt’’ fashion. The sedimentsdeposited in the ice proximal zone eventually become unstable and generate debris flows.


Table 1Core characteristics. Position, sample length, water depth, sampling device and reference

Core Number Coordinates Area Sample Water Depth Sampling Device ReferenceLatituderLongitude

X X Ž .JM96-68r1 73825 r14829 Bear Island Fan 153–183 mm 914 m Gravity corer Mokkelbost 1998X X Ž .NP90-19r1 78813.7 r8848.1 Isfjorden Fan 0.0–8.3 m 1427 m Piston corer Fossen 1996

bles other cores that have been routinely analysedŽfrom the two fans Laberg and Vorren, 1995; Ander-

.sen et al., 1996 .

2. Infinite slope stability analysis with excess porepressure

A limiting equilibrium analysis based on theMohr–Coulomb criterion is used to estimate a factorof safety against sliding under the assumption of an

Ž‘‘infinite’’ slope geometry i.e., thickness of failure.is small compared to the slope length . The parame-

ters required are the unit weight, the friction angleand cohesion intercept of the sediment, the angle ofthe submarine slope, and the pore pressure along theplane where failure is assumed to take place. Sinceno pore pressure measurements are available, the

Ž .model presented by Gibson 1958 has been em-ployed to estimate the excess pore pressure resultingfrom the consolidation of the sediment under a con-stant sedimentation rate. This approach has been

employed by many other authors to examine theeffects of sedimentation on the stability of submarine

Ž .slopes Busch and Keller, 1983; Booth et al., 1985 .Following the work of Denlinger and Iverson

Ž .1990 , we make use of their submarine infiniteslope stability equation, given as

cq g H cosuy p H yp 0 tanf� 4Ž . Ž .t c cFs 1Ž .

g H sinub c

where: Fssafety factor against slope sliding; cscohesion intercept in the Mohr-Coulomb criterion

Ž .failure law effective stresses ; usslope of sea bot-tom; fs friction angle in the Mohr–Coulomb crite-

Ž . Ž .rion effective stresses ; p h swater pressure atdepth h beneath sea floor measured normal to the

Ž .sediment surface Fig. 3 ; g s total unit weight oft

sediment; g sunit weight of water; g sg yg sw b t w

submerged unit weight of sediment; H sdistancecŽbetween failure plane and free sediment surface sea

.floor .In order to express this equation in terms of an

Žexcess pore pressure u i.e., the pore pressure ine

Fig. 3. Diagrams showing the infinite slope geometry and Gibson excess pore pressure settings.


.excess of the hydrostatic pressure we introduce theŽ .following changes Fig. 3

w x w xp H yp 0 sg Zqg H cosuqu yg Zc w w c e w

sg H cosuquw c e

where Z is the water depth and inserting this expres-Ž .sion for the pressure terms in Eq. 1 we obtain Eq.

Ž .2 giving the factor of safety in terms of the excesspore pressure.

cq g H cosuyu tanfŽ .b c eFs 2Ž .

g H sinub c

By setting Fs1, which means incipient failure, oneŽobtains an expression for the critical depth H orc

. Žcritical thickness to the theoretical failure plane Eq.Ž ..3 .

cyu tanfeH s 3Ž .c

g sinuycosu tanfŽ .b

As the excess pore pressure is a function of theŽ .thickness, Eq. 3 cannot be used in a direct manner

to obtain the critical thickness. One may thereforeuse a trial and error approach or an iterative algo-rithm to obtain the critical thickness. However, sincethe critical thickness is the thickness at which thesafety factor becomes unity, it was found easier toestimate it in the processes of estimating the safety

Ž .factor given by Eq. 2 .Ž .Gibson 1958 considers the sedimentation of a

horizontal clay layer and estimates the excess porepressure build-up and simultaneous consolidation andpore pressure dissipation for a constant sedimenta-tion rate with the assumption that the underlying

Ž .layer is impermeable Fig. 3 . The equation given for

the one-dimensional sedimentation process is as fol-lows:

x 2g b yu sg mty e 4 c te b vp c t( v

=j 2

` mj xjyj tanh cosh e dj 4Ž .4 c tH v2c 2c t0 v v

where the submerged unit weight g is defined as inbŽ .Eq. 1 , and mssedimentation rate, ts time, c sv

coefficient of consolidation, xsvertical distanceŽ .from the underlying impermeable plane Fig. 3 and

js integration variableThe integral must be evaluated numerically and

care must be taken when used in conjunction withŽ Ž . Ž ..the stability equations Eqs. 2 and 3 because x is

measured from the bottom of the layer whereas h isŽ .measured from the top of the layer Fig. 3 .

A Gauss quadrature scheme is used for the numer-ical evaluation of the integral as described by Press

Ž .et al. 1988 . The indefinite integral has been re-duced to a proper one, by setting its upper limit to2000. At first, iterative midpoint quadrature schemeswere employed using Simpson’s and Romberg’s rulesŽ .Press et al., 1988 , but convergence was slow and inmany cases failed. Several schemes involving achange of variable were also employed in order toobtain a proper integral, but these failed to improvethe performance of the iterative schemes. After ex-perimentation it was found that an upper limit of1000 was sufficient for most calculations, however,to assure that no significant errors would occur, avalue of 2000 is employed. To ensure that the nu-merical estimates are accurate, a 200 and 400 pointGauss quadrature is performed on the integral with

Ž . Ž .limits 0, 1000 and 0, 2000 , respectively. If both

Table 2Critical times obtained when failure plane is assumed to be the base of the sedimentation layer. The thickness column simply gives the

Ž .accumulated thickness of sediment at the time of failure i.e., sedimentation rate= time

Sample area Cohesion Unit weight g Coefficient of Friction Layer Critical timety3Ž . Ž .intercept c kN m consolidation c angle f thickness yearsv

2 y1Ž . Ž . Ž .kPa m yr m

Bear Island Fan 1 17.8 2.5 31 6228 10 380Isfjorden Fan 3 19.6 4 28 7830 13 050


Table 3Critical depths and times for the Bear Island and Isfjorden Fan samples. Parameter values used for each analysis

Sample area Cohesion Unit weight g Coefficient of Friction Critical Critical timety3Ž . Ž .intercept c kN m consolidation c angle f depth H yearsv

2 y1Ž . Ž . Ž .kPa m yr m

Bear Island Fan 1 17.8 2.5 31 12.8 94.6Isfjorden Fan 3 19.6 4 28 28.2 170.4

results are the same up to the 8th decimal digit, thenthe result is accepted as accurate. If they are not thesame, then the upper integral limit is raised. Theabove scheme failed only in a few extreme cases, inwhich reliable results were only obtained with a 400point Gauss quadrature and an upper limit of 10000.

3. Analysis results

The main results are divided into two categoriesbased on the assumptions made about the position of

Ž .the failure plane. With the use of Eq. 2 and estimat-ing the excess pore pressure from the Gibson equa-

Fig. 4. Safety factor contours obtained for the Bear Island Fan sample. The horizontal axis is time and the vertical axis is distance from thebase of the sediment layer. Failure occurs when the safety factor obtains a value of 1.0, whereas higher values indicate greater stability. A

Ž U .line showing the position of the top of the sediment layer has also been included. The figure also illustrates the minimum critical time t ,cŽ U . Ž .initial critical depth H , as well as the range of critical times and critical depths t and H existing within the possible failure zone.c c c


Ž Ž ..tion Eq. 4 we can analyse the stability of theslope.

3.1. Assumed failure along basal plane under sedi-ment deposit

Assume there is an impermeable basal plane onŽ .which the sediment accumulates Fig. 3 . We seek to

determine how much time it will take and how thickthe sediment layer will get before failure occursalong this basal plane.

In the case of the Bear Island Fan, having acharacteristic slope of 18, the geological data suggestan average sedimentation rate of 0.6 m yeary1. Atthis deposition rate the stability analysis of thissystem indicates that approximately 10,000 years ofsediment must accumulate before failure along thebasal plane will occur. Since the geological datasuggest an accumulation period of only 3000 to 5000years, then no failure will take place during this

period along the basal plane. It is unimaginable evento consider an ‘‘infinite’’ slope type failure with the

Ž .layer thickness proposed by these results )6 km .Since the geological evidence suggests a series ofslides in the areas of analysis, we must assume thatfailure will occur much sooner and along a failureplane other than the basal plane. A summary of theseresults as well as the similar finding determined forthe Isfjorden Fan is tabulated in Table 2.

3.2. Assumed failure inside sediment deposit

Since the position of the failure plane is unknown,one may use the following calculation scheme toestimate its location. For each year, we calculatedthe local safety factors in the sediment from thebasal plane up to the top of the sediment surface in1-m vertical increments. This approach allows us toidentify the approximate position of the failure planefor each case considered as well as the minimum

Fig. 5. Safety factor contours obtained for Isfjorden Fan sample. The horizontal axis is time and the vertical axis is distance from the base ofthe sediment layer. Failure occurs when the safety factor obtains a value of 1.0, whereas higher values indicate greater stability. A lineshowing the position of the top of the sediment layer has also been included.


time at which failure occurs. The results are sum-marised in Table 3 and shown in Figs. 4 and 5.

In all cases a slope angle of 18 and a sedimenta-tion rate of 0.6 m yeary1 was assumed. The sum-marised results can be used to determine the timeand sediment thickness at which the safety factordrops below unity. In many cases, the safety factorwas only slightly above unity for as much as adecade, before it dropped to a value of 1.

4. Discussion of results

Figs. 4 and 5 show similar patterns for the safetyŽfactor contours. The unit safety factor contour Fs

.1 is used to define the ranges of critical time andcritical depth. The minimum critical time, tU , isc

defined as the time at which we first encounter theunit safety factor contour. The critical time, t , isc

defined as any point in time greater than tU at whichc

a safety factor at or below unity exists in the sedi-Žment i.e., any time at which sediment failure could.occur . The critical depth, H , is defined as thec

depth, measured from the sediment surface, at whicha failure plane is most likely to develop. A criticaldepth is possible only after tU is exceeded. In Figs. 4c

and 5, vertical locations in the sediment are reportedin terms of the distances from the basal plane, x,where X is the location of the failure plane. Thec

total deposit thickness or sediment surface, X , istotal

the product of time, t, and sedimentation rate, m:

X s tm 5Ž .total

At times greater than the minimum critical time,X is also the sum of X and H:total

X sX qH 6Ž .total c c

Ž . Ž .By rearranging Eqs. 5 and 6 , the critical depthcan be obtained from:

H s tm yX 7Ž . Ž .c c

In Figs. 4 and 5, the critical depth can be obtaineddirectly since a line representing the sediment sur-face has been added.

The critical time and critical depth represent thetime at which failure will occur and the position ofthe failure plane according to the failure model usedherein. However, these values are valid only under

the strict assumptions of our failure model and forthe specific parameter values employed. Under morerealistic conditions, failure will occur within a rangeof safety factor values between 1.2 and 0.95. There-fore, the actual critical time and critical depth willnot, in general, coincide with the theoretical valuescalculated herein, but rather will be defined by apoint lying within the failure zone depicted in Fig. 4.

At tU , a unique initial critical depth, HU , can bec c

determined. However, at times greater than tU ac

range of critical depths, bounded by the upper andlower limits of the unit safety factor, are possible.

Ž .The upper limit Fs1, parallel to sediment surfaceattains a gradient similar to the sedimentation rateand asymptotically approaches a finite depth below

Ž .the surface of the sedimentation layer Fig. 4 . In thisway, the upper limit determines the minimum thick-ness of the failed mass. For the Bear Island Fansituation, this thickness distance seems to be ca. 8 mwhile for the Isfjorden Fan situation the thickness isca. 18 m. We therefore expect that, in general, atleast the top 10–30 m will be removed through

Žfailure processes. The lower limit of this range Fs.1, ‘‘parallel’’ to time axis slowly increases slowly

its distance from the basal plane but eventually itdecreases and reaches the basal plane at the timesgiven in Table 2. This limit defines the thickness ofthe sediment layer, X , that will remain on the slopec

after failure occurs. The lower limit is time depen-dent, but once the critical time has been exceeded,the failure should occur within a decade or two. Forthe cases studied here, the analysis suggests that atleast 40 to 70 m will remain on the slope. Thegeological implication of the existence of a lowerlimit is important, because it may explain mechanismof sediment build-up at such depocenters.

In order to apply the infinite slope criteria wemade the assumption that the depth of the failedsediment, H , was much less than the length of thec

Ž .failure, L, H rL<1 . If the application of infinitec

slope is valid for the source sediment in question,and the above values for failure thickness are reason-

Ž .able 10–30 m , then it follows that the length of thefailure is on the order of 1 to 10 km. This estimateagrees with the 5 km wide depositional zone pro-posed earlier. The regenerative process of sedimentconveyance and sheet-like failure that glacial deliv-ery and infinite slope describe, may be an explana-


tion for the uniformly thick, layered deposits ob-served in the seismic data of the source area. Fig. 6illustrates this regenerative process over one com-plete cycle. Sediment accumulates over a source

Ž .area, L, until the sediment becomes unstable FF1 .Upon failure, the sediment above the failure planemoves downslope while the sediment below the fail-ure plane remains and becomes the new surface forsediment deposition. This cycle is repeated wheneverthe sediment becomes thick enough to exceed thefailure criteria. In this way, a relatively uniform,

Ž .layered deposit is formed Fig. 6 .It is worth noting the considerable difference

between the subparallel layers of the deposits dis-cussed above and high angle deltaic formations typi-

Ž .cal of river delta outputs Hampton et al., 1996 . Inthe latter case, the build up of excess pore pressure isavoided because of high porosity and low sedimenta-tion rates of the deposit. The failure of these deposits

Fig. 6. Illustration of slope failure under the infinite slope assump-tion. For explanation refer to the text.

are controlled mainly by the mechanical propertiesŽ .friction angle of the sediment, resulting in failuresurfaces that are approximately the angle of repose

Ž .of the sediment 30–408 . In the former case, thecharacteristics of the deformation till and the buildup of pore pressure caused by rapid sedimentationresults in development of failure planes which aremore or less parallel to the basal surface of the

Ž .deposit 1–48 .

4.1. SensitiÕity analysis

A number of additional cases have been analysedin order to determine the sensitivity of the results tothe parameter values used in the analysis. The pa-rameters that directly influence the results are thesedimentation rate and coefficient of consolidation,

Ž Ž ..which are both used in the Gibson equation Eq. 4 ,and the cohesion intercept, slope angle, and frictionangle, which are used in the infinite slope equationŽ Ž ..Eq. 2 . A basic parameter in both equations is thesubmerged unit weight of the sediment layer that canbe estimated from the total unit weight of the sedi-ment.

Figs. 7 and 8 show the effects of the sedimenta-tion rate on the minimum critical time, tU , and initialc

critical thickness, HU , for the Bear Island and Isfjor-c

den fans, respectively. In both plots, HU increasesc

with decreasing sedimentation rate. The initial criti-cal thickness does not appear to be very sensitive to

Ž y1 .high sedimentation rates above 0.3 m year , butbecomes increasingly more sensitive at low rates.The minimum critical time is much more sensitive tochanges in the sedimentation rate. For high sedimen-tation rates the reduction in tU is substantial. Byc

increasing sedimentation rate from 0.3 to 0.8 myeary1 a reduction in tU from 318 years to 59 yearsc

was observed for the Bear Island Fan while for theIsfjorden Fan, the reduction was from 549 to 106years. The effect is even greater for smaller sedimen-

Ž y1 .tation rates e.g., -0.3 m year .Tables 4 and 5 show the sensitivity of results

obtained to the other parameters for the Bear Islandand Isfjorden fans, respectively. Comparisons arebased on the resulting minimum critical time, tU , thec

initial critical depth, HU , and the retention coeffi-c


Fig. 7. Sedimentation rate effects on critical time and critical thickness for the Bear Island Fan sample. As the sedimentation rate decreasesthe critical times increase dramatically, indicating that failure frequency will also decrease significantly.

cient, cU. The retention coefficient is computed as

follows:

X UcU

c s 8Ž .U UX qHŽ .c c

It represents the fraction of sediment supplied tothe source area that actually remains in the sourcearea rather than being transported downslope. Theminimum critical time and its inverse, failure fre-

Ž Ž U .y1 .quency fs t , are used interchangeably in thec

following discussion.For both the Bear Island Fan and the Isfjorden

Fan, we observe that the parameter with the smallestaffect on the results is the friction angle. Very littlechange was observed in HU , tU , or c

U with increas-c c

ing friction angle. This implies that we do not need avery precise estimate of the friction angle in order tocarry out an infinite slope analysis. All the other

Fig. 8. Sedimentation rate effects on critical time and critical thickness for the Isfjorden Fan sample. One observes the same characteristicsas those of Fig. 6 with the difference that the critical times and thicknesses are approximately twice those of the Bear Island Fan.


Table 4Sensitivity analysis obtained for the Bear Island Fan sample

Ž .Friction angle deg 29 30 31 32 33U UŽ . Ž .H m rX m 12.7r43 12.8r43.5 12.8r44 12.7r44.5 12.7r45c c

U Ž .t year 92.8 93.8 94.6 95.4 96.2cU

c 0.77 0.77 0.77 0.78 0.78

Ž .Slope angle deg 1 2 3 4U UŽ . Ž .H m rX m 12.8r44 8.0r31 6.1r24.5 5.0r20.5c c

U Ž .t year 94.6 65 51 42.5cU

c 0.77 0.79 0.80 0.80

2 y1Ž .Coefficient of consolidation m year 2 2.5 3U UŽ . Ž .H m rX m 12.1r36.5 12.8r44 13.5r51c c

U Ž .t year 81 94.6 107.5cU

c 0.75 0.77 0.79

3Ž .Submerged unit weight kNrm 7.0 7.5 8.0 8.5 9.0U UŽ . Ž .H m rX m 14.1r45 13.4r44.5 12.8r44 12.3r43.5 11.9r43c c

U Ž .t year 98.5 96.5 94.6 93 91.5cU

c 0.76 0.77 0.77 0.78 0.78

Ž .Cohesion intercept kPa 0 1 2U UŽ . Ž .H m rX m 1.2r30 12.8r44 22.4r58c c

U Ž .t year 52 94.6 134cU

c 0.96 0.77 0.72

Here HU , XU , and tU represent the initial critical depth, initial distance from basal layer to failure plane, and the minimum critical time,c c c

respectively, and are defined in the text.U Ž U U Ž U U ..c is the fraction of pre-failure sediment retained after failure c sX r X qH .c c c

Ž .The initial critical depth values are obtained by multiplying the minimum critical time with the sedimentation rate 0.6 mryear andsubtracting the XU. The minimum critical times are rounded to the nearest 0.1 years and the distances from the basal layer, XU , are roundedc c

to the nearest 0.5 m. Default parameter values used are those shown in Table 3.

parameters have had a significant effect on the anal-ysis results.

An increase in slope angle causes more frequentŽ U .slides decrease in critical time t but the slides arec

of smaller sediment thickness. For the Bear IslandŽ .case Table 4 we observe that an increase of the

slope angle from 18 to 48 will more than double theslide frequency but will reduce the amount of mo-bilised material. Increasing slide frequency has theadded affect of reducing the distance between subse-quent failure surfaces as estimated by X . We alsoc

observe that the retainment coefficient, cU , in-

creases slightly with increased slope angle. The ob-servation of larger failures on lower slopes may be

Žan explanation for why long runout distances large.sediment volumes are observed for debris flows on

Žthe Bear Island Fan slopes18, runouts100–200. Žkm and not for the Isfjordan Fan slopes48, runout

. Ž .s10–30 km Elverhøi et al., 1997 .

The coefficient of consolidation affects the fre-quency of the slides as well as the retainment coeffi-cient. In the Bear Island case an increase in thecoefficient of consolidation by 0.5 m2 yeary1 de-creases the time of failures by ca. 13 years, thusincreasing the distance between failure planes by ca.7 m. The thickness of the failures, however, isunchanged by the change in consolidation propertiesŽ .ca. 13 m . The coefficient of retainment shows anincrease with an increasing coefficient of consolida-tion suggesting that higher consolidation leads tomore trapped sediment in the source area. The Isfjor-den Fan case shows the same trends.

The sensitivity of the results to the submergedunit weight is small. By increasing this parameterover a 2 kPa range both the Bear Island and Isfjor-den fans show a slightly increase in the failurefrequency along with a slight decrease in HU. Ac

very slight increase in cU is also observed. In other


Table 5Sensitivity analysis obtained for the Isfjorden Fan sample

Ž .Friction angle deg 26 27 28 29 30U UŽ . Ž .H m rX m 28.4r72 28.3r73 28.2r74 28.5r74.5 28.4r75.5c c

U Ž .t year 167.3 168.8 170.4 171.7 173.2cU

c 0.72 0.72 0.72 0.72 0.73

Ž .Slope angle deg 1 2 3 4U UŽ . Ž .H m rX m 28.2r74 17.1r51 12.5r40 10.2r33c c

U Ž .t year 170.4 113.5 87.5 72cU

c 0.72 0.75 0.76 0.76

2 y1Ž .Coefficient of consolidation m year 3.5 4 4.5U UŽ . Ž .H m rX m 27.3r66 28.2r74 29r82.5c c

U Ž .t year 155.5 170.4 182.5cU

c 0.71 0.72 0.74

3Ž .Submerged unit weight kNrm 8.6 9.1 9.6 10.1 10.6U UŽ . Ž .H m rX m 30.9r75.5 29.1r75 28.2r74 27.4r73 26.2r72.5c c

U Ž .t year 177.3 173.6 170.4 167.3 164.5cU

c 0.71 0.72 0.72 0.73 0.73

Ž .Cohesion intercept kPa 2 3 4U UŽ . Ž .H m rX m 20.9r68.5 28.2r74 35.1r78c c

U Ž .t year 149 170.4 188.5cU

c 0.77 0.72 0.69

Here HU , XU , and tU represent the initial critical depth, initial distance from basal layer to failure plane, and the minimum critical time,c c c

respectively, and are defined in the text.U Ž U U Ž U U ..c is the fraction of pre-failure sediment retained after failure c sX r X qH .c c c

Ž .The initial critical depth values are obtained by multiplying the minimum critical time with the sedimentation rate 0.6 mry and subtractingthe XU.c

The minimum critical times are rounded to the nearest 0.1 years and the distances from the basal layer, XU , are rounded to the nearest 0.5c

m. Default parameter values used are those shown in Table 3.

words, a heavier sediment layer results in a slightlyelevated retainment of sediment, and slightly morefrequent, thinner failures.

The most influential parameter appears to be thecohesion intercept. In the case of the Bear Island FanŽ . UTable 4 we observe an increase in H of approxi-c

mately 10 m of the mobilised material per unitincrease in the cohesion intercept whereas in the case

Ž .of the Isfjorden Fan Table 5 an increase of approxi-mately 7 m is obtained. An increase in the cohesionintercept increases considerably the minimum criticaltime. For the Bear Island Fan, tU increases by aboutc

40 years per unit increase in cohesion. For theIsfjorden Fan the increase is about 20 years per unitincrease in cohesion. Finally, increasing the cohe-siveness of the sediment dramatically reduces theretainment coefficient. In summary, the more cohe-sive the sediment, the less frequently are the failures.

Failures that do occur, however, are thick, removingmuch of the source area sediments.

4.2. Limitations of analysis

There are weaknesses in our approach, one ofthem being the conditions imposed on the basal layerŽ .Fig. 3 . The basal layer cannot be entirely imperme-able, meaning that the safety factors obtained areconservative estimates, because some pore pressuredissipation will take place into the base. The ques-tion is how much this can affect the results. If theunderlying layer has a much higher degree of consol-idation than the layer on top of it, then our assump-tion of impermeability is reasonable.

In the Fig. 6, an idealised situation is depictedwhere a homogeneous distribution is assumed. Undermore realistic conditions, we expect the basal plane


to be a rough and uneven surface causing the thick-ness distribution of the pre-failed slide material tovary considerably. This variability may cause localslides to occur, but the overall effect is that thepre-failure deposit layer obtains an orientation thatroughly follows that of the deposit base.

Another weakness of our approach is related tothe constant sedimentation rate assumed. There are,very few places in the world where the geologicalrecord suggests a more-or-less steady, continuoussedimentation rate. In most cases, the rate variesconsiderably from year to year and from season toseason. Using an average sedimentation rate, as inour analysis, is a simplification that can actually leadto considerable errors in estimating safety factors.The variation of the sedimentation rate is very im-portant in terms of pore pressure and consolidation.For example, during periods of low sedimentationexcess pore pressure is allowed to dissipate andsediment consolidates resulting in failure frequenciessmaller than our results indicate. On the other hand,during periods at times of high sedimentation excesspore pressure will not be allowed to equilibrateresulting in a failure frequency larger than our resultssuggest. Even if our results are correct in the averagesense, the sedimentation rate variations may causeconsiderable uncertainties in the results obtained.However, in our particular analyses of the BearIsland and Isfjorden fans, the sedimentation condi-tions are very special. Glacier till deformation-re-lated sedimentation is more or less constant forperiods of several thousands of years and thereforewe do not expect large variations.

In the analysis, we have ignored the effects ofother influential processes. Earthquakes, wave ac-tion, erosion, and shallow gas production are someof the most important processes that can affect sub-marine slope stability and trigger submarine gravitymass flows. In the case of earthquakes, one couldemploy a simplified pseudostatic method described

Ž .by Chowdhury 1978 to estimate the effects ofearthquake shaking with the use of orthogonal accel-eration components expressed as a fraction of grav-ity.

Care must be taken when applying the specificvalues reported here to the field. The limited coredata, the complexity of the system, and the simplify-ing assumptions make it difficult for precise predic-

tions to be made. This notwithstanding, we feel thevalues reported give a good order-of-magnitude esti-mate of the thickness and frequency of the sedimentfailures which occurred in the region of the BearIsland Fan and the Isfjorden Fan during maximumglaciation.

5. Concluding remarks

The high sedimentation rates experienced overshort intervals of ca. 3000–5000 during periods ofpeak glaciations resulted in very large and frequentslope failures to occur. Despite the fact that theseslope failures along the Svalbard–Barents Sea mar-gin fans involved tens of km3 of sediments, very fewscarps have been observed. Instead, high-resolutionseismic data reveal a slope characterised by layers ofrelatively uniform thickness along the slope. Thus,the failure conditions as well as the runout mecha-nisms result in a fairly even distribution of thematerial along the ocean floor. By using the principleof infinite slope stability for a low angle slope,together with an excess pore pressure build-up due tohigh sedimentation rates, we can explain the ob-served geometry of these high latitude, deep seafans. We have a situation where sediment becomestemporarily stored at the uppermost part of the conti-nental slope. Subsequent instability causes slidingand redistribution of the sediment down the slope.Our calculations show that after 95–170 years ofhigh sedimentation rates, failures will take placewhich will remove the top 10–30 m of the depositedsediment, while 40–70 m will remain at the deposi-tion site. A sensitivity study of the model parametersindicates that good estimates of sediment propertiessuch as the cohesion intercept, submerged unit weightand coefficient of consolidation as well as sedimen-tation rate are necessary for valid results. In sum-mary, the model proposed within suggests that wenot only have build-up of sediment at the lower partsof the continental slope, but also at upper regions.Under these conditions the slope can be maintained.

Acknowledgements

This work was supported by the marine scienceand technology, ENAM II, program of EC, and the


SEABED project. Valuable comments from M.Hampton, T. Mulder and D.J.W. Piper are acknowl-edged.

Appendix A. Symbol index

F Safety factor against slope slidingc Cohesion intercept in the Mohr-Coulomb

Ž .criterion effective stressesQ Slope of sea bottomf Friction angle in the Mohr–Coulomb cri-

Ž .terion effective stressesŽ .p h Water pressure at depth h beneath sea

floor measured normal to the sedimentg Total unit weight of sedimentt

g Unit weight of waterw

g Submerged unit weight of sedimentb

u Excess pore pressure in the sedimente

Z Water depthm Sedimentation ratet Timec Coefficient of consolidationv

x Vertical distance from the underlying im-permeable plane

j Integration variabletU Minimum critical timec

t Critical timec

HU Initial critical depthc

H Critical depthc

x Distance from the basal planeX Distance from basal place to failure sur-c

faceX Total thickness of sedimentL Length of the failurec

U Retainment coefficient, fraction of pre-failure sediment retained after failure

f Failure frequency

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