The Kinematics of a Debris Avalanche on the Sumatra Margin

A.S. Bradshaw, D.R. Tappin, and D. Rugg

Abstract The kinematics of submarine landslides is important both for evaluating tsunami hazard potential as well as for evaluating hazards to seabed structures. This paper presents a kinematics analysis of a debris avalanche that was identified in deep water off the northwest coast of Sumatra. A numerical model is derived and used to investigate the relative influence of slide density, hydrodynamic drag, basal resistance, and hydroplaning. The model predicts a maximum slide velocity of 40–47 m/s. The slide density and shear strength of the sediments beneath the slide play a key role in the kinematics behavior.

Keywords Submarine landslide • Sumatra • debris • avalanche • kinematics • tsunami

1 Introduction

Submarine landslides have been known to generate tsunamis and have the potential for adversely affecting seabed installations. The three most important factors influ-encing gravity-driven slide motion are the mass of the slide, the hydrodynamic drag on the slide body, and the frictional resistance between the slide and the underlying sediments. Research in this area has also focused on hydroplaning, where water becomes entrained under the frontal portion of the slide body, as this seems to

A.S. Bradshaw (�)Merrimack College, North Andover, Massachusetts, MA 01845, USAe-mail: aaron.bradshaw@merrimack.edu

D.R. TappinBritish Geological Survey, Nottingham, NG12 5GG, UKe-mail: drta@bgs.ac.uk

D. RuggUniversity of Texas at Austin, Austin, Texas, USAe-mail: rugg.dennis@gmail.com

D.C. Mosher et al. (eds.), Submarine Mass Movements and Their Consequences, 117Advances in Natural and Technological Hazards Research, Vol 28,© Springer Science + Business Media B.V. 2010

118 A.S. Bradshaw et al.

explain the large run out distances observed in many submarine slides (e.g., Locat and Lee 2002; Harbitz et al. 2003; De Blasio et al. 2004a). Numerical analysis of the kinematics of documented landslide events (e.g., Locat et al. 2003; De Blasio et al. 2004b) can provide insight on the various factors involved.

This paper presents a numerical analysis of a submarine landslide event identified in deep water off the northwest coast of Sumatra. The failure was documented by a team of scientists and engineers as part of a research cruise aimed at identifying the cause of the 2004 Indian Ocean tsunami (Moran and Tappin 2006). In order to investigate the kinematics of the observed mass failure, a very simple model is derived which attempts to represent the major slide features observed in bathymetric and seismic records. A series of model runs are performed to investigate the sensi-tivity of the various factors including the slide mass, hydrodynamic drag, basal shear resistance, and hydroplaning.

2 Description of the Mass Failure

A large submarine mass failure was identified offshore off the northwest coast of Sumatra as shown in Fig. 1. Using a combination of multibeam and seismic data Tappin et al. (2007) interpreted this slide as a debris avalanche, which is character-ized by cohesive blocks that travel very rapidly a top a fine-grained sediment flow. A complete interpretation of the submarine mass failure is given in Tappin et al. (2007). However, the relevant features of the slide are described in this section to understand qualitatively the motion of the slide such that a representative kinematics model can be developed.

The mass failure, shown in the multibeam bathymetry in Fig. 2, originated from the flanks of a thrust fold in water depths of about 3,400–4,000 m. The fail-ure is characterized by a group of blocks arranged in a triangular pattern on the abyssal plane with the largest “outrunner” block forming the apex of the triangle. The landslide scarp is clearly identifiable on the upper slope of the thrust fold.

Fig. 1 Map showing the location of the land-slide site The Sumatra margin is shown by the red/dashed lines and the landslide location is indicated with a star (adapted from Tappin et al. 2007)

The Kinematics of a Debris Avalanche on the Sumatra Margin 119

The outrunner block is trapezoidal in shape with a thickness of about 80 m and a length (parallel to slope) of about 1,400 m along its base. The block is located approximately 9 km from the base of the thrust fold. The failure scarp is about 3,400 m in length and extends up from about mid-slope to the slope crest. The slope ranges from 7 degrees on the lower slope to 15 degrees on average within the scarp.

A seismic cross section taken through the blocks and lower slope (line SCS 4 in Fig. 2) indicates the presence of a blocky debris flow located between the thrust fold and the outrunner block. As shown in the cross section in Fig. 3, the bottom of the debris flow unit is horizontally planar and there is no evidence that the slide eroded the underlying sediments. The debris flow has a thickness of about 10–50 m and extends from the base of the thrust fold to beneath the outrunner block where

Fig. 2 Multibeam bathymetry looking northward showing the debris avalanche slide (Tappin et al. 2007)

Fig. 3 Seismic transect through the slide and lower slope (Tappin et al. 2007)

120 A.S. Bradshaw et al.

it pinches off in the seaward direction. This suggests that the block, or at least a significant portion of the block, traveled on top of the debris flow.

The failure scarp also runs parallel to the inclined bedding on the thrust ridge suggesting that the debris flow failed along a continuous weak sediment layer or bedding plane. The thickness of the largest outrunner block that is furthest from the base of the thrust fold is similar to the depth of the excavated failure on the thrust fold. Therefore, it is interpreted that the failed sediment formed a debris flow in the manner of Hampton (1972), disintegrating as it moved down slope and out onto the abyssal plain.

3 Kinematics Model

The purpose of the modeling was to investigate the sensitivity of the various factors influencing the kinematics behavior of the outrunner block. A simple two-dimensional kinematics model was developed as shown in the schematic in Fig. 4. The model consists of a rigid block sliding on top of a shear layer and thus is similar in concept to the model described in Imran and Parker (2001). An entrained water layer was also incorporated into the model to account for hydroplaning, which causes a reduction in the frictional resistance at the bottom of the slide. A trapezoidal block shape was assumed which resembled the shape of both the failure scarp and the outrunner block (Fig. 3). The equation of motion was derived using and approach that was consistent with Grilli and Watts (2005), Bradshaw et al. (2007), and Taylor et al. (2008):

⎛ ⎞ ⎛ ⎞ − + ⎛ ⎞+ = − − − ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠

22

2

( )1 sin

2w w w

m dw w w l l

B B Bd s T dsC g C

A A dtdt

t tr rq

r r r (1)

Where; r = bulk density of the slide block, rw = density of water, C

m = hydrody-

namic added mass coefficient, s = position of the slide block, g = acceleration due to gravity, q = slope angle, t = shear stress at the top of the shear layer, t

w = shear

stress at the top of the water layer, B = slide length, Bw = length of entrained water

layer, Al = longitudinal sectional area of slide, T = slide thickness, C

d = hydrody-

namic drag coefficient, and t = time. For a trapezoidal block, Al = TB − T2/tan a

where a = angle of the trapezoid. A Bingham model (Locat and Lee 2002) was used to model the shear behavior of the sediment in the shear layer. Assuming a linearly

Fig. 4 Kinematics model used in this study

Block

Shear Layer

BwB

h

θ

T

Entrained Water Layer α

hw

The Kinematics of a Debris Avalanche on the Sumatra Margin 121

decreasing velocity profile with depth (i.e. simple Couette flow) the shear stress at the top of the layer is given by the following equation:

= +y

u

ht t h (2)

Where; ty = plastic yield strength, h = Bingham viscosity, u = velocity of the slide

block, and h = thickness of the shear layer. Similarly, assuming a linearly velocity profile in the entrained water layer, the shear stress at the top of the layer given by the following equation:

=ww

u

ht m (3)

Where; m = viscosity of water, hw = thickness of the entrained water layer.

Interpretation of the bathymetric and seismic data indicates that the block degen-erated into a flow as it travelled down slope. Since the height of the failure scarp and the thickness of the outrunner block are consistent, it was assumed that only the slide length changed during its motion. Experiments by Watts and Grilli (2003) show that slide deformation scales with slide motion. Assuming that the rate of change of the slide length was directly proportional to velocity (i.e. no motion, no deformation) the following empirical equation was derived:

= −0 BB B C s (4)

Where; B0 = initial slide length, and C

B = slide length reduction coefficient. C

B was

iteratively adjusted during the modeling such that the final slide length was equal to that observed in the field.

4 Model Parameter Estimates

Upper and lower bound estimates were made of all model parameters based on typical values from the literature and available geotechnical data from Moran and Tappin (2006). Intermediate values of model parameters were then selected to serve as a baseline for investigating the sensitivity of each parameter individually. The parameters used in the analysis are summarized in Table 1 and the basis for their selection is discussed below.

The initial length of the slide (B0) was taken as the average length of the failure

scarp of 3,400 m. The final length was approximated to be 1,400 m based on the cross-sectional length of the outrunner block. An average angle of 10 degrees was used for the trapezoid angle (a). A slide bulk density (r) of about 1.7 Mg/m3 was measured in box core samples taken of the near surface sediments (Moran and Tappin 2006). It is anticipated that the bulk density would be higher at depth within the slide body due to overburden stress and therefore an upper bound of 1.9 Mg/m3 was assumed.

122 A.S. Bradshaw et al.

Wave tank studies by Watts (2000) indicate a slight dependence of the hydrodynamic added mass coefficient (C

m) on the ratio of water depth to slide length (D/B). At the

debris avalanche site the D/B is about one and therefore a range of 0.8 to 1.2 was assumed. The hydrodynamic drag coefficient (C

d) was also assumed to range from

0.8 to 1.2 consistent with ellipsoidal shapes (Grilli and Watts 2005).Since clay sediments are sheared undrained during slide triggering and subsequent

motion, the peak undrained strength (Su) is mobilized initially but rapidly reaches steady

state conditions after only about 2 cm of movement (Stark and Contreras 1996). The steady state strength or residual undrained strength (S

ur) remains constant at large dis-

placements and therefore can be used as an estimate of the yield strength (ty). The yield

strength of the sediments below the slide was divided into two distinct portions along its path: the strength on the failure scarp sediments (t

y1) and the strength of the debris

flow (ty2

) that was assumed to have developed down slope of the failure scarp.A static limit equilibrium slope stability analysis was used to estimate the lower

bound strength of the failure scarp sediments. If a seismic pseudo-static stability analy-sis were used, it would result in a higher estimated strength. The average S

u at failure

was about 120 kPa, which corresponds to a 0/u vS ,s ratio of about 0.2 where svo

is the initial effective vertical stress. Undisturbed and remolded miniature vane shear meas-urements taken in box core sediments at the site indicate a sensitivity (S

u/S

ur) value of

about 4. Therefore, the lower bound Sur

on the failure scarp was estimated at about 120 kPa/4 = 30 kPa. An upper bound S

ur value of 45 kPa was estimated by multiplying

the effective vertical stress by a 0/u vS ,s ratio 1.5 times larger and dividing by the sen-

sitivity of 4.The lower bound estimate of the yield strength of the debris flow (t

y2) was

obtained from remolded vane shear measurements of the box core samples. An average S

ur value of about 1 kPa was measured in the upper 15 cm of sediments

(Moran and Tappin 2006). The upper bound Sur

estimate assumes that the 80 m of sediment composing the slide mixes uniformly. Therefore, it was obtained by calculating the average S

u within a depth of 80 m assuming a

0/u vS ,s of 0.3 and dividing by a sensitivity of 4.

Studies by Locat (e.g., Locat and Lee 2002) suggest that the Bingham viscosity (h) is well correlated to the yield strength. Therefore, the following empirical correlation was used:

= 1.120.0052 yh t (5)

Parameter Lower Upper Intermediate

r (Mg/m3) 1.7 1.9 1.8C

m0.8 1.2 1.0

Cd

0.8 1.2 1.0t

y1 (kPa) 30 45 38

h1 (m) 0.01 0.1 0.05

ty2

(kPa) 1 20 10h

2 (m) 10 50 30

Table 1 Summary of model parameters

The Kinematics of a Debris Avalanche on the Sumatra Margin 123

Where; h = Bingham viscosity (in kPa), and ty = plastic yield strength (in kPa). On

the failure scarp, it is anticipated that the shear layer is thin because the failure was initiated within a continuous weak sediment layer. Therefore, a range of 1–10 cm was assumed for the shear layer thickness on the failure scarp (h

1). However, inter-

pretation of the seismic records indicates that the thickness of the debris flow ranged from 10 to 50 m and therefore this range was used for the thickness of the shear layer downslope of the failure scarp (h

2). Field observations by De Blasio

et al. (2004a) suggest the thickness of the entrained water layer (hw) is on the order

of 0.1 m which was assumed in this study.

5 Modeling Results and Discussion

The equation of motion was solved numerically using an explicit finite difference scheme. A sensitivity analysis was performed by first performing the analysis using the intermediate values of all input parameters, and then varying each parameter individually using the upper and lower bound values.

A typical time history of acceleration, velocity, position and slide length is shown in Fig. 5. The results suggest that the slide event lasted about 11 min. The maximum acceleration occurred at the start of landslide motion (Fig. 5a), which is an important aspect for tsunami generation (e.g., Watts and Grilli 2003; Grilli and Watts 2005; Harbitz et al. 2006). For block slides on planar slopes, theoretically the initial acceleration scales with slide bulk density, slope angle, basal resistance, and added mass coefficient (Watts and Grilli 2003). The modeled results are consistent

Fig. 5 Typical time histories of (a) acceleration, (b) velocity, (c) position, and (d) slide length

124 A.S. Bradshaw et al.

with the theory indicating that the initial acceleration is most influenced by the slide density, followed by the shear strength of the failure scarp sediments, followed by the added mass coefficient. Given the range of properties, the maximum accelera-tions varied from 0.35 to 0.47 m/s2.

For planar slopes, the maximum velocity occurs when the slide reaches its ter-minal velocity which scales with bulk density, slope angle, and basal resistance (Watts and Grilli 2003). However, the geometry or length of the slope may prevent a slide from reaching its theoretical terminal velocity. This was the case for this slide where maximum velocities of 40–47 m/s were reached as the slide began to move onto the abyssal plain at t ∼ 170 s (Fig. 5b). The velocity was most affected by the slide bulk density and the shear strength of the debris flow. The velocities from this study are consistent with those obtained in other numerical case studies; up to 45 m/s for the Palos Verdes debris avalanche (Locat et al. 2003) and up to 60 m/s for the Storegga slide (De Blasio et al. 2004b).

Basal resistance has a significant influence on the run out distance of a subma-rine slide (e.g., Locat et al. 2003, De Blasio et al. 2004b). Assuming that the origin is located at the middle of the failure scarp, the observed position of the outrunner block mass center is at about 13,620 m. Using the assumed range of properties, the model predicted the observed position of the outrunner block in most cases to within about 2,000 m (~15%). However, the final slide position was significantly affected by the strength properties of debris flow. When the lower bound yield strength of 1 kPa was used, the model predicted that the block would overshoot the observed position by 9,250 m (∼70%). Whereas the upper bound value predicted that the block would undershoot the observed position by 4,550 m (∼33%).

Assuming intermediate values of all parameters, additional model runs were performed to back analyze the yield strength of the debris flow required to match the observed position. The time history for this condition was shown previously in Fig. 5. If hydroplaning does not happen, the yield strength of the debris flow must be approxi-mately 7 kPa to match the observed position. If hydroplaning occurs than the yield strength must be higher (e.g., 8.5 kPa for B

w = 300 m). Both values of yield strength are

reasonable but they are higher than some of the published data for marine sediment flows, which have values typically less than about 1 kPa (Locat and Lee 2002).

6 Conclusions

This paper analyzed the kinematics of a submarine debris avalanche observed off the northwest coast of Sumatra. Based on existing bathymetric and seismic records, a kinematics model was derived which incorporates forces due to gravity, hydrody-namic drag, and basal resistance. A sensitivity analysis was performed using a range of input parameters estimated from the literature and from measured sediment prop-erties. The model predicted maximum slide accelerations ranging from 0.35 to 0.47 m/s2 and maximum velocities ranging from 40 to 47 m/s. The modeled slide position was matched to the observed position using reasonable values of input

The Kinematics of a Debris Avalanche on the Sumatra Margin 125

parameters. The parameters that had the most influence on the motion of the debris avalanche were the slide bulk density and undrained shear strength of the sediments beneath the slide block. Therefore, accurate prediction of the kinematics of future slides relies, at least in part, on accurate characterization of the bulk density and shear strength properties of the slope sediments. The prediction of the strength prop-erties of the sediments after they transition into a debris flow remains a challenge.

Acknowledgments The authors would like to thank Dr. Philip Watts and Dr. Didier Perret for their thoughtful review comments.

References

Bradshaw AS, Baxter CDP, Taylor O-DS, Grilli S (2007) Role of soil behavior on the initial kin-ematics of tsunamigenic slides. In: Lykousis V, Sakellariou D, Locat J (eds) Submarine mass movements and their consequences III: 387–394 Springer, The Netherlands.

De Blasio FV, Engvik L, Harbitz CB, Elverhøi A (2004a) Hydroplaning and submarine debris flows, J Geophys Res 109, doi:10.1029/2002JC001714.

De Blasio FV, Issler D, Elverhøi1 A, Harbitz CB, Ilstad T, Bryn P, Lien R, Løvholt F (2004b) Dynamics, velocity and run-out of the giant Storegga slide. In: Locat, J, Mienert J, Boisvert J (eds) Submarine mass movements and their consequences I: 223–230, Kluwer, The Netherlands.

Grilli ST, Watts P (2005) Tsunami generation by submarine mass failure: modeling, experimental validation, and sensitivity analyses, J Waterw P C 131(6): 283–297.

Hampton M (1972) The role of subaqueous debris flow in generating turbidity currents, J Sediment Petrol 42: 775–993.

Harbitz CB, Løvholt F, Pedersen G, Masson DG (2006) Mechanisms of tsunami generation by submarine landslides: a short review, Nor J Geol 86: 255–264.

Harbitz CB, Parker G, Elverhøi A, Marr JG, Mohrig D, Harff PA (2003) Hydroplaning of subaque-ous debris flows and glide blocks: analytical solutions and discussion, J Geophys Res 108 (B7), doi:10.1029/2001JB001454.

Imran J, Parker G (2001) A numerical model of muddy subaqueous and subaerial debris flows, J Hydrodyn Eng 127(11): 959–968.

Locat J, Lee HJ (2002) Submarine landslides: advances and challenges, Can Geotech J 39: 193–212.

Locat J, Lee HJ, Locat P, Imran J (2003) Numerical analysis of the mobility of the Palos Verdes debris avalanche, California, and its implication for the generation of tsunamis, Mar Geol 203(3–4): 269–280.

Moran K, Tappin D (2006) SEATOS 2005 Cruise Report: Sumatra Earthquake and Tsunami Off shore Survey (SEATOS). http://ocean. oce.uri.edu/seatos. Accessed 16 October 2007.

Stark TD, Contreras IA (1996) Constant volume ring shear apparatus, Geotech Test J, 19(1): 3–11.Tappin DR, McNeil LC, Henstock T, Mosher, D (2007) Mass wasting processes- offshore Sumtra.

In: Lykousis V, Sakellariou D and Locat J (eds) Submarine mass movements and their conse-quences III: 327–336, Springer, The Netherlands.

Taylor O-DS, Bradshaw AS, Baxter CDP, Grilli S (2008) The effects of basal resistance and hydro-planing on the initial kinematics of seismically induced tsunamigenic landslides. In: Reddy KR, Khire MV, Alshawabkeh AN (eds) proc GeoCongress, Am Soc Civil Eng: 522–529.

Watts P (2000) Tsunami features of solid block underwater landslides, J Waterw P C 126(3): 144–152.

Watts P, Grilli S (2003) Underwater landslide shape, motion, deformation, and tsunami generation. Proc 13th Int Offshore and Polar Eng Conf, ISOPE03 3: 364–371.