How Does Fluid Inflow Geometry Control Slope
Destabilization?
I. Kock and K. Huhn
Abstract Destabilization of submarine slopes and initiation of submarine mass
wasting events depend on numerous factors e.g. transient rapid pore pressure
changes due to earthquake shaking, fast sediment accumulation, ground water
pumping or mineral dehydration to name a few. The major goal of our work is the
quantitative analysis of how local pore pressure changes affect the destabilization
of stable slope sediments. Here, we report on how the location and extent of fluid
inflow within undisturbed slope sediments affect the onset of destabilization.
We developed a 2D numerical slope model utilizing a new model approach. We
combine a granular model which simulates a sediment package with a gridded
fluid flow model. Our results indicate that the entry point of fluid flow greatly
changes the location of destabilization. Failure zones of mass movements
develop at different places, both vertically and laterally as a function of fluid
flow input. Even with a simplified model setup we were able to identify three
different destabilization scenarios.
Keywords Submarine landslide • discrete element model • fluid flow
1
Introduction
Large scale sediment mass-transport processes occur in very different geological
settings, for example passive continental margins and volcanic slopes, whereas
diffuse and smaller scale mass movements are more commonly found at accretionary
wedges (McAdoo and Watts 2004). Initiation of submarine mass wasting events
I. Kock () and K. Huhn
MARUM – Center for Marine Environmental Sciences, University of Bremen,
PO box 330 440, D-28334, Bremen, Germany
e-mail: ikock@uni-bremen.de
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
191
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I. Kock and K. Huhn
depend on numerous short and long term factors, for example oversteepening,
seismic loading and fast sediment accumulation to name a few (Sultan et al. 2004).
These factors can lead to fluid flow and transient pore pressure changes. Thus,
effective stress is reduced and instabilities on the slope can occur (Behrmann et al.
2006; Dugan and Flemmings 2000; Flemmings et al. 2008).
In-situ pore pressure measurements (Flemmings et al. 2008; Stegmann et al.
2007) confirm this theoretical model. Furthermore, many laboratory and associated
numerical studies (Biscontin et al. 2004; Sultan et al. 2004) have investigated this
effect. Large scale numerical slope models link slope failure and slide dynamics to
pore pressure changes and are able to reproduce specific slides quite well, such as
the Storrega slide (Kvalstad et al. 2005). Additionally, infinite slope stability simulations implementing pore pressure changes can be used to assess past and present
slope stability (Dugan and Flemmings 2002). However, in finite element models a
failure plane has to be predefined by incorporating a mechanically weak layer,
which limits the model interpretation significantly.
Our approach is an effort to resolve this problem. We combine two modeling
approaches: (i) a simple eulerian fluid flow model to calculate fluid pathways and
pressure distribution and (ii) a granular slope model based on the Discrete Element
Method to simulate sediment mechanical behavior and mass wasting processes.
Our goal is to analyze the onset of the slope’s destabilization in relation to fluid
flow geometry and position. In addition, we will test the potential of such models
to investigate fluid/sediment interaction on a large scale level.
2
2.1
Method and Model
Discrete Element Method
The Discrete Element Method was developed by Cundall and Strack (1978, 1979)
and has been used for the investigation of microscopic (Abe and Mair 2005; Cheng
et al. 2004; Kock and Huhn 2007a) as well as macroscopic (Campbell et al. 1995)
geologic processes. The method is based upon a granular modeling approach.
Hence, materials are built up by an assembly of spherical shaped particles. These
particles interact according to simple physical contact laws at their respective
contacts. Forces and moments between them are calculated. Resulting particle
motions are applied and their respective positions are updated which leads to a
new particle configuration where the calculation cycle begins again. For more
details see Cundall (1987, 1989), Cundall and Strack (1978, 1979, 1983) and
Cundall and Hart (1989).
We use a commercial implementation of the code, PFC2D by Itasca, Inc. (Itasca
2004). In our model the deformation at the particle scale obeys a Coulomb-like
friction law in accordance to crustal material behavior in nature. Particle fracture is
not allowed.
How Does Fluid Inflow Geometry Control Slope Destabilization?
2.2
193
Fluid Coupling
PFC2D provides a fluid coupling scheme (Itasca 2004), which solves the continuity
and Navier–Stokes equations in Eulerian Cartesian coordinates. This scheme is based
upon an approach by Tsujii et al. (1993) and has for example been successfully used
to model liquefaction of granular soils (Zeghal and El Shamy 2008). Pressure and
velocity are calculated for each grid cell. Hence, grid size has to be defined in respect
to the smallest particle diameter, because the presence of DEM particles is considered
in each cell. Thus, porosity is calculated for each cell separately.
Forces caused by fluid flow are applied to each particle, whose motions are
accordingly modified. In turn, resulting body forces from the particles’ motion
(e.g. from settling) are added to the fluid equations.
2.3
Model Setup
The model is a simplified slope with an extension of 10 km and a height of approx.
1,730 m which corresponds to a slope angle of 10° (Fig. 1, Table 1). This value
Fig. 1 Sketch of model setup. Left side: Fluid grid, particles and inflow locations. Right side:
Water column and saturated slope sediments
Table 1 Properties used in discrete
element model
Slope model
Property
Width (m)
Height (m)
Resolution
Particle radii (m)
Friction micro/macro (peak)
Particle density (kg/m3)
Fluid model
Width (m)
Height (m)
Resolution
Cell size (m)
Fluid density (kg/m3)
Fluid viscosity (Pas)
10,000
1,736
19,350 particles
25, 37.5, 50, 62.5, 75
0.5/0.34
2,500
Property
10,000
2,000
50 × 10 cells
200 × 200
1,000
1 e−3
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I. Kock and K. Huhn
represents an end member of continental slope angles (O’Grady et al. 2000).
However, the major aim of this study is to test the feasibility of this model approach.
The complete slope consists of 19,350 particles with varying radii where
3,870 particles exist for each radius (see Table 1). These particles are created
randomly in the defined slope area. Gravity is set to 9.81 m/s2 and particles are
allowed to settle after generation creating the wedge shaped geometry with a
nearly plane surface. Since all particles’ properties are identical, no stratification
exists after settling.
The properties of the particle assemblage are defined in accordance to generate
natural slope sediments (Huhn et al. 2006) by assigning microproperties for all
particles, e.g. particle friction and density (Table 1). Due to a 2D effect (Hazzard and
Mair 2003), macroscopic peak friction for the whole particle assembly is ~0.34
and thus smaller than single particle friction, but well in the range of observed friction
data for submarine landslides (Kopf et al. 2007)
The grid simulating the fluid extends over 10 km laterally and 2 km vertically to
cover the whole slope and the water column (Fig. 1). Hence, in the slope region fully
saturated sediments are simulated whereas the other part represents the pure water
column. The upper boundary is on sea level height where pressure is set to zero. Due
to gravity, pressure within the fluid increases with depth. The fluid is modeled on a
rectangular 50 × 10 grid with 200 × 200 m cell size. On average, approximately 50
particles fit into one cell. Density and viscosity of the fluid are set to 1,000 kg/m3 and
1 e−3Pas, respectively, for this first test series.
2.4
Modeling Scheme and Measurements
We conducted a suite of four numerical experiments, subsequently called E1 to E4,
where we varied only the geometry of the incoming fluid flow (Fig. 1). All other
parameters were kept constant between model runs. In addition, benchmark tests
were conducted where the effect of different initial particle packing was examined
(e.g. with model E4, see Results section).
In the initial state, fluid flow in and out of the model as well as all particle
velocities are close to zero. The left, right and lower boundaries are initially impermeable. Initial fluid velocities entering on the left boundary and right boundaries
are set to zero.
In E1, fluid flow enters from the complete left boundary, where in E2 the fluid
inflow occurs only from the bottom half of the left boundary (Fig. 2a, c). Fluid input
is set to 0–1,000 m and to 1,000–2,000 m at the lower boundary in experiments E3
and E4, respectively.
The calculation timestep throughout the simulations is governed by the DEM
and is very low (3.66 * 10−4 s). Thus, to achieve results in a reasonable amount of
computing time, fluid velocity is scaled up to 1 m/s and simulations show results
after only 1 h of inflow. However, fluid pathways and therewith location of slope
destabilization are unaffected and fluid velocities are not taken into account in our
How Does Fluid Inflow Geometry Control Slope Destabilization?
195
2000
Fluid inflow
a
Absolute
displacement
1000
0
2000
b
Relative
displacement
1000
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
2000
c
Fluid inflow
Absolute
displacement
1000
0
2000
d
Relative
displacement
1000
0
10000
0
1000
2000
0.0
3000
4000
5000
6000
0.5
normalized Displacement
7000
8000
9000
10000
1.0
Fig. 2 (a) Fluid flow and particle movement for model E1. All values normalized. Black color indicates
high displacement, white no displacement. Due to scaling, fluid flow vectors < 1*10-6 m/s are not
displayed. (b) Relative displacement for model E1. Black colors indicate high relative displacement
(shear planes) and white colors not relative displacement. (c) Fluid flow and particle movement for
model E2. Coloring same as in a). (d) Relative displacement for model E2, coloring same as in b)
interpretations. For each model run, fluid flow vectors and displacement vectors v
were normalized with:
v
− vmin
vnormalized = measured
vmax − vmin
(1)
Hence, although many parameters are recorded during simulation we concentrate
mainly on fluid flow vectors indicating fluid pathways and on particle displacement
particularly along the slope surface. Both are monitored continuously.
These data are then gridded and displayed with the software Generic Mapping
Tools (Wessel and Smith 1991). Furthermore, the gradient of displacement is computed
with GMT. Thus, relative displacement can be made visible. High relative displacement indicates shear zones and failure planes (Kock and Huhn 2007b; Morgan and
Boettcher 1999).
196
3
I. Kock and K. Huhn
Results
The fluid flow vectors in model E1 which enter from the left side are directed
towards the slope surface within the first 2,000 m (Fig. 2a). At a lateral distance
greater than 5,000 m fluid flow is extremely small compared to input (<10−6 m/s),
so that no normalized values could displayed. Particle movement is strongest at the
upper part of the slope, approximately at a distance of 1,700–2,000 m from the left
boundary. With increasing sediment depth, particle displacement decreases, most of
the movement is concentrated on the top 50–100 m. Greatest relative displacement
in terms of shear zones and shear planes mainly exist at these locations (Fig. 2b).
Some more shear planes are also found at the fluid entry and approximately at
3,000 m lateral distance on the surface of the slope.
In model E2, fluid flow vectors also are turned towards the surface after entering the
sediment (Fig. 2c). However, at the sediment/water boundary fluid vectors are almost
vertically inclined with respect to the sediment surface. Interestingly, the location
of greatest particle movement is comparable to model E1. Greatest movement
occurs between 500 and 2,000 m lateral distance on the slope surface (Fig. 2c).
In this case though, displacements reach further into the sediment and the lateral
extent is also greater (Fig. 2d). Locations of large particle movement coincide with
maximum fluid flow to a high degree. Shear planes can be observed up to 4,000 m
laterally and from top to bottom on the left boundary.
Results obtained for model E3 are very similar to model E2. Fluid vectors point
almost straight to the sediment/water boundary, and are also close to orthogonal to
the sediment surface (Fig. 3a). Thus, greatest particle movements occur between
500 to 2,000 m at the slope surface. Comparable with experiment E2, particle
movement reaches far into the sediment. Shear planes exist mainly at the top slope,
between 1,000 and 2,000 m lateral distance and reach into the sediment for ~200 m
(Fig. 3b). Furthermore, shear planes can also be found deep into the sediment at the
bottom boundary where the fluid enters the slope sediments.
Model E4 differs strongly from the previous settings. Fluid pathways at
approximately 1,500 m lateral distance point almost vertically from the bottom
boundary up to the sediment/water interface (Fig. 3c). At a greater distance of
~2,000 m, however, fluid flow vectors are directed further downslope. Consequently,
greatest particle movement occurs at two locations. The first location is comparable to the previous models is located between 1,000–2,000 m laterally on
the slope surface. The second location is situated downslope, between 3,000
and 4,000 m lateral distance on the slope surface. In between these two locations
there is considerably less sediment movement. On both locations, movement
reaches far into the sediment, in case of the second location movement increases
with increasing depth. These results are mirrored by values for relative displacement (Fig. 3d). Two foci of shear plane development exist. The first is located
upslope and close to the sediment surface whereas the second on is located downslope and well inside the slope. Additionally, shear planes also occur at the fluid
entry location, in particular at 1,500 m lateral distance. To verify these observa-
How Does Fluid Inflow Geometry Control Slope Destabilization?
197
Fig. 3 (a) Fluid flow and particle movement for model E3, coloring same as in Fig 2a). (b) Relative
displacement for model E3, coloring same as in Fig 2b). (c) Fluid flow and particle movement for
model E4. Coloring same as in (a). (d) Relative displacement for model E4, coloring same as in (b)
tions and to exclude the effect that initial particle positions govern displacement
patterns, a control run of model E4 was conducted which in essence yielded the
same results.
4
Discussion
The results presented above indicate that the position of fluid inflow affects the
location of particle movement on a sediment slope. We interpret large particle
movements as the onset of destabilization of the slope. Failure planes are indicated
by high relative movement (e.g. Fig. 3d).
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I. Kock and K. Huhn
One controlling factor leading to focused particle movement is the redirection of
fluid pathways after the fluid enters the system. The redirection of fluid flow is both
a function of inflow position and overburden pressure. Due to the high pressure
induced by the sediments upslope, fluid flow paths tend to be focused downslope.
Although fluid flow is strongest directly at the junction left boundary/slope surface
in model E1, most of the particle movement does not take place at this location, but
further down the slope. Possibly the angle between fluid vectors out of the sediment
and sediment surface plays a role, but clarification requires further experiments.
Remarkably, models E2 and E3 exhibit similar displacement patterns, although
the origin of fluid flow is conceptually very different between these cases. However,
near the sediment/water boundary fluid flow patterns are essentially the same,
both in magnitude and direction, which explains the similarities in absolute and
relative displacement.
The most interesting setting is E4, where two foci of displacement can be observed.
These foci are largely the result of two fluid flow directions which control this setting:
one vertical and one diagonal flow path. The fluid does not flow in the upslope direction,
simply because overburden pressure is lower downslope. Consequently there exists
a sharp boundary on the left side of the model where no sediment movement occurs.
Since we did not implement any fluid conduits or boundaries in terms of low or
high permeability layers, the development of distinct locations of sediment movement
in models E1 and E4 is quite unexpected. As stated above, this may be related to a
favorable combination of fluid flow magnitude and angle at the sediment surface.
This is also supported by the fact that the shear planes associated with these foci
are relative shallow, with the notable exception of the rightmost focus in model E4,
which lies deep into the sediment.
Conceptually, our models may be linked to different geological conditions. In
principle, model E1 resembles a rapid sediment accumulation model (Dugan and
Flemmings 2000), except that in our models an aquifer is not implemented. In model
E2, inflow conditions are more similar to this location, since the inflow at the bottom
left boundary could be attributed to a change in the sedimentation environment
(e.g. glacial/interglacial). On the other hand, fluid inflow from the bottom may be
linked to structural or sedimentological features further down at the basement. For
example, different fluid input locations in models E3 and E4 could be the result of
a fault ending just below the model boundary and which could serve as a conduit for
fluids. Clearly, our model setup opens the possibility for specific case studies to
investigate the above mentioned geologic settings and conditions. However, with our
current simplified model setup, we are not simulating natural environments.
Nevertheless, our results are transferable in principle to natural settings, but have to
be further extended to fully capture a specific location.
5
Conclusion
In this paper, we combined two numerical model approaches successfully to study
the onset of destabilization in relation to fluid inflow. We show that this model
approach enables us to investigate this interplay. Despite many simplifications, this
How Does Fluid Inflow Geometry Control Slope Destabilization?
199
study reveals mechanisms which are in accordance to theory and field observations.
Hence, our results indicate that sediment movement focuses in different locations
when fluid inflow location is changed (Fig. 4). We could identify three general
scenarios: (i) Fluid inflow from the upslope boundary leads to concentrated movement on the upper slope (Fig. 4a). (ii) Fluid inflow from the bottom part of this
boundary and from the bottom, but upslope side of the model leads to distributed
movement throughout the upper slope reaching deep into the sediment (Fig. 4b).
(iii) When fluid inflow is set to a region slightly further downslope two distinct foci
of displacement can be observed (Fig. 4c).
Distributed or focused sediment movement occurs both in the absence of a high
or low permeability layer which could have served as a mechanism to concentrate
fluid flow into a specific direction. Despite using a simple model, different models
may be linked to different geological processes, such as upslope rapid sediment
accumulation for model E1 and for example fluid escape conditions for model E4.
With this study we could show that our combined model approach is in principle
applicable to such a setting. Further work is in progress, especially to enhance the
model with respect to more natural conditions, such as different permeabilities
within the slope and realistic fluid flow velocities. Major goals are the investigation
of complex ocean margins settings and the detailed kinematics of mass movements
(Huhn and Kock 2008).
a
Focused sediment movement
with one focus
Fluid
inflow
Slope
Fluid
redirection
b
Distributed sediment movement
Slope
Fluid
redirection
Fluid
inflow
c
Fig. 4 Conceptual sketches.
(a) Focused sediment
movement with one focus.
(b) Distributed sediment
movement. (c) Focused
sediment movement with
multiple foci
Focused sediment movement
with multiple foci
Slope
Fluid
redirection
Fluid
inflow
200
I. Kock and K. Huhn
Acknowledgments The manuscript benefited from the helpful review of S. Abe. This work was
funded through DFG-Research Center/Excellence Cluster “The Ocean in the Earth System”.
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