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 influencing 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, USA
e-mail: aaron.bradshaw@merrimack.edu
D.R. Tappin
British Geological Survey, Nottingham, NG12 5GG, UK
e-mail: drta@bgs.ac.uk
D. Rugg
University of Texas at Austin, Austin, Texas, USA
e-mail: rugg.dennis@gmail.com
D.C. Mosher et al. (eds.), Submarine Mass Movements and Their Consequences,
Advances in Natural and Technological Hazards Research, Vol 28,
© Springer Science + Business Media B.V. 2010
117
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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 sensitivity 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 characterized 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 failure 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 landslide 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)
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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):
⎛ r
⎞ d2s ⎛ r
⎞
t ( B − Bw ) + t w Bw
T ⎛ ds ⎞
− Cd
⎜ ⎟
⎜⎝ r + Cm ⎟⎠ dt 2 = ⎜⎝ r − 1⎟⎠ g sin q −
r
A
2
Al ⎝ dt ⎠
w
w
w l
2
(1)
Where; r = bulk density of the slide block, rw = density of water, Cm = hydrodynamic 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, tw = 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, Cd = hydrodynamic 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
h
Shear Layer
α
Block
Entrained Water Layer
hw
T
B
Fig. 4 Kinematics model used in this study
Bw
θ
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:
t = ty +h
u
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:
tw = m
u
hw
(3)
Where; m = viscosity of water, hw = thickness of the entrained water layer.
Interpretation of the bathymetric and seismic data indicates that the block degenerated 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:
B = B0 − C B s
(4)
Where; B0 = initial slide length, and CB = slide length reduction coefficient. CB 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 crosssectional 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.
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A.S. Bradshaw et al.
Table 1 Summary of model parameters
Parameter
Lower
Upper
Intermediate
r (Mg/m3)
Cm
Cd
ty1 (kPa)
h1 (m)
ty2 (kPa)
h2 (m)
1.7
0.8
0.8
30
0.01
1
10
1.9
1.2
1.2
45
0.1
20
50
1.8
1.0
1.0
38
0.05
10
30
Wave tank studies by Watts (2000) indicate a slight dependence of the hydrodynamic
added mass coefficient (Cm) 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 (Cd) 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 (Sur) remains constant at large displacements 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 (ty1) 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 analysis were used, it would result in a higher estimated strength. The average Su at failure
was about 120 kPa, which corresponds to a Su / s v 0, ratio of about 0.2 where svo is the
initial effective vertical stress. Undisturbed and remolded miniature vane shear measurements taken in box core sediments at the site indicate a sensitivity (Su/Sur) 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 Sur value of 45 kPa was estimated by multiplying
the effective vertical stress by a Su / s v 0, ratio 1.5 times larger and dividing by the sensitivity of 4.
The lower bound estimate of the yield strength of the debris flow (ty2) was
obtained from remolded vane shear measurements of the box core samples. An
average Sur 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 Su within a depth of 80 m assuming a Su / s v 0, 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:
h = 0.0052t 1.12
y
(5)
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 (h1). However, interpretation 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 (h2). 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 accelerations varied from 0.35 to 0.47 m/s2.
For planar slopes, the maximum velocity occurs when the slide reaches its terminal 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 submarine 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 approximately 7 kPa to match the observed position. If hydroplaning occurs than the yield
strength must be higher (e.g., 8.5 kPa for Bw = 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, hydrodynamic drag, and basal resistance. A sensitivity analysis was performed using a range
of input parameters estimated from the literature and from measured sediment properties. 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 properties 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.
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