SLOPE STABILITY ASSESSMENT OF THE TRÆNADJUPET SLIDE AREA
OFFSHORE THE MID-NORWEGIAN MARGIN
D. LEYNAUD and J. MIENERT
Department of Geology, University of Tromsø, N-9037 Tromsø, Norway
Abstract
Large-scale submarine slides occurred during the Holocene on the continental slope
offshore mid-Norway, north and south of the Vøring Plateau. The Trænadjupet slide
event that affected an area of 14100 km2 is located north of the Vøring Plateau. It
occurred about 4,300 years B.P., 4000 years after the giant Storegga slide that affected
an area of about 112,500 km2. A slope stability evaluation was performed in order to
explain why the sliding took place on a very gentle slope (1 degree). This was done first
with the deterministic approach using the Limit Equilibrium and the Finite Element
methods, for static, pseudo-static and dynamic cases. Then the probabilistic approach
was applied using the limit equilibrium method with the 1st and 2nd order reliability
methods (FORM and SORM) and the Monte Carlo simulation to include the parameter
uncertainties (soils parameters, seismic loading). The Finite Element modelling
indicates that the slide triggering impacted preferably the upper 40 meters of the
sediment column. The trigger could have been caused by one large earthquake of
magnitude larger than M S 5.8 (retrogressive failures) but cyclic loading due to several
earthquakes could also explain the slide, affecting the shearing resistance in the NYK
contourite drift unit (weak layer) by excess pore pressure generation.
Keywords: Submarine slide, Limit Equilibrium, Finite Element, FORM & SORM
1. Introduction
Submarine landslides are commonly observed on passive and active continental
margins, particularly on the continental slope where the steeper part of the margin
increases the effect of gravity on the downslope forces acting on a certain volume of
sediment. Among the most obvious triggers of submarine slope failures one can find
cyclic loading from earthquakes or waves, gas hydrate decomposition and excess pore
pressure, over-steepening, and undercutting of slopes.
The difficulty one faces in assessing slope stability is the fact that submarine slope
failures may occur even on very gentle slopes where the down slope forces are minor.
The failure mechanism is far from very well understood by using only geotechnical insitu measurements. As many parameters are involved in this mechanism, the
probabilistic approach is used to observe the effects of uncertainty on the likelihood of
failure. It will be used to improve our knowledge about the sediment thickness
vulnerable to failure and the failure probability during a specific time period.
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Leynaud and Mienert
2. Trænadjupet slide area: Geological and Geotechnical settings
The Trænadjupet slide field is located to the north of the Vøring Plateau (Figure 1)
while the Storegga Slide lies to the south of it. Both slides occurred during the
Holocene, the Storegga slide during a multi phase event at 8300 yrs BP (Haflidason et
al., 2001) and the Trænadjupet slide at approximately 4000yrs BP (Laberg et al. 2002)
(Figure 2). The mean continental slope angle outside the Traenadjupet slide area is
approximately 1 degree (Lindberg, 2000). The average gradient within the slide scar
area is 1.25 degrees and at the sidewall 25 degrees (Laberg et al., 2002). The slide
headwall is located at a water depth of 300 meters. The geotechnical parameters of the
last glacial interglacial sediments deposited just north and south of the Vøring Plateau
are assumed to be similar. We have used the geotechnical data from borehole 6606/3GB1 (850 m water depth) of the southern Vøring Plateau. Four soil units were defined
down to a maximum depth of 106 meters (Tables 1 and 2). The identified soil units are
described as very soft clay (unit 1), medium to stiff silty sandy clay (unit 2), stiff to very
stiff clay (unit 3) and very stiff to hard clay (unit 4).
Figure 1: Location of the trænadjupet slide offshore Norway (from Vorren et al., 1998)
and borehole 6606/3-GB1.
Figure 2: Sketch of profile along the Trænadjupet Slide (from Laberg et al., 2002).
Slope stability assessment of the Trænadjupet slide area
257
Table 1: Summary of soil conditions and the basic recommended soil parameters for borehole 6606/3-GB1
NYK slope.
Unit
1
2
3
4
Depth
(m)
Soil
descr.
0 – 1.5
1.5 - 41
41 - 81
81 - 106
Clay
Clay
Clay
Clay
γ tot
Clay
content
(%)
w
(%)
Ip
15.2 - 20.8
20.8
18.3
20.7
S DSS
u
(kPa)
1.9
1.9-1.2
1.4-1.1
1.1
2.6-6
17-140
113-213
213-276
(%)
(kN/m3 )
39
29
49
32
OCR
80-21.5
21.5
37.8
21.9
30
15.5
27.5
20
Table 2: Physical and geotechnical properties of the late weichselian glacigenic sediments and the Nyk
contourite drift sediments (from Laberg et al, 2002)
Late
Weichselian
glacigenic sed.
Nyk contourite
drift sed.
Depth
(m)
Grain size
(%C,S,S)
Water
content
(%)
Unit Weight
0-45
25,45,30
~20
45-85
50,40,10
~40
Plasticity
Sensitivity
Triaxial
compression
tests
~21
Low to
medium
~1.5
Dilatant
~18
High
>2.5
Contractant
3
(kN/m )
3. Methodology and Basic concepts
The total stress acting on sediments of a submarine slope is related to the weight of the
water (above the seafloor and in the pores space of the sediment) and the weight of the
(solids) sediment within this volume. Thus, the real stress acting on the sediment matrix
is reduced by the effect of water pressure (Terzaghi and Peck, 1967) and is called the
effective stress. The effective unit weight of the soil is then considered as the real unit
weight less the weight of water and is called the submerged unit weight of the soil. The
model used in this study defining the mechanical behaviour of the sediments to predict
the failure potential is the Mohr-Coulomb model. In this commonly used model, the
shearing resistance s per unit of area is related to the normal stress acting on the soil at a
specific depth, using an empirical equation. For the undrained case (present study), the
Mohr-Coulomb relationship becomes,
s = CU = Constant,
where s is the shear strength and Cu is the shear strenght for undrained case.
This means that in rapid, undrained loading conditions, the soil shear strength does not
depend on the applied normal stress.
4. Deterministic Slope Stability Evaluation Methods
4.1 LIMIT EQUILIBRIUM METHOD
The limit equilibrium method evaluates the forces (or stresses) resulting along an
assumed failure surface. This means that the failure occurs when the shear strength is
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Leynaud and Mienert
fully mobilized (static equilibrium). For concave failure surfaces, we have to use the
method of slices which divides the soil volume above the slip surface into vertical slices
and considers the equilibrium of each slice. The forces are estimated at the base of each
slice and are summed over the length of the failure surface to get an estimate of the
stability.
The factor of safety definition is as follow,
FOS =
resisting_forces
shear_strength
=
loading_forces shear_stress_applied
4.2 FINITE ELEMENT METHOD
The Finite Element method (FEM) is based on the concept of modelling an object with
simple blocks or small elements. Once the structure is defined with elements and nodes,
one can describe the physical behaviour of each element. Then the elements are
connected to approximate the whole soil behaviour. Also, one can estimate the strain
and stress at selected elements. Elasto-plastic analyses of geotechnical problems using
the finite element (FE) method have been widely accepted as a more accurate
procedure.
5. Description of the Probabilistic approach
While the deterministic approach uses only a constant value (mean value) for each
parameter required to describe the soil behaviour, the probabilistic approach consider
the spatial variability of these parameters and define them using a probabilistic density
function.
5.2 MONTE CARLO SIMULATION
One way to estimate the expected value and the standard deviation of the performance
function is the use of simulation methods, often referred as Monte Carlo simulation. The
performance function defines the limit state between the safe and the failure domains.
In the Monte Carlo simulation, values of the random variables are generated following
their probability distribution, and the performance function is calculated for each
generated set. This process is repeated numerous times, typically thousands, and the
expected value, standard deviation and probability distribution of the performance
function are estimated from the calculated values.
5.2 FIRST AND SECOND-ORDER RELIABILITY METHODS
The first- and second-order reliability methods (FORM and SORM respectively) are
employed to approximate the probability by linearization of the boundary of the failure
domain. The main task is to define the safety factor summing the different forces
applied on the wedges and then define a limit state function or performance
function g(X ) , such that g(X ) ≥ 0 when the slope is stable and g(X ) < 0 when the slope
Slope stability assessment of the Trænadjupet slide area
259
has failed. X represents a vector of random variables including soil properties, load
effects, geometry parameters and modelling uncertainty. The subroutines developed by
Gollwitzer et al. (1988) were used for the FORM approximation.
6. Pseudo-static and Dynamic undrained slope stability
6.1 EARTHQUAKE-INDUCED SHEAR STRESS
In 1971, Seed and Idriss proposed the following procedure for estimating the stresses
induced by earthquake. If the soil column behaves as a deformable body with a
maximum ground surface acceleration a max , the maximum shear stress on the soil
element would be,
max,def
=
⋅h
⋅ a max ⋅ rd
g
in which,
γ
is the unit weight of the soil,
h is the depth of the bottom of the soil column and rd is a stress reduction coefficient
with a value less than 1.
6.2 DYNAMIC APPROACH WITH FINITE ELEMENTS
For the Finite Element method, a representative accelerogram (acceleration vs. time) is
normalized to the Peak Ground Acceleration value expected in the area for a specific
return period (assuming a simple linear behaviour) in order to create an event providing
the expected seismic accelerations. The earthquake record used to model the seismic
loading in the study area is the Friuli Tarcento earthquake with a duration of 33.18
seconds (sampling: 0.02 sec).
6.3 SELECTION OF
a max
The Peak Ground Acceleration (PGA) represents the maximum value of the acceleration
experienced by a small particle of the soil during the earthquake motion. The horizontal
component of this parameter is used in the pseudo-static approach to have an estimate of
the acceleration-induced shear stress developed in the soil. A common way is to
consider the PGA with a probability of no exceedance during a certain period of time. In
the Eurocode-8 regulations, and for conventional buildings, a PGA value with 90%
probability of no exceedance during 50 years is required, which corresponds to a 475year return period.
The maximum PGA values considered for 475 and 10 000 year return periods for
Norway are shown in Table 3 (NORSAR, 1998):
Table 3: Peak Ground acceleration estimated for 475 and 10000 year return period.
Return period (years)
475
10000
PGA (g)
0.10 g
0.35 g
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Leynaud and Mienert
7. Softwares
7.1 SLOPE/W (Limit Equilibrium) / QUAKE/W (Finite Element)
SLOPE/W (GEO-SLOPE, 2001) is a graphical software product that uses limit
equilibrium theory to compute the factor of safety (FOS) of earth slopes. Several
methods of slices are proposed to solve the interslices force indetermination. One can
also use the stress field obtained from the Finite Element static and dynamic estimate.
Using the dynamic stress, one gets a safety factor for each time step of the seismic
acceleration time history.
QUAKE/W, a geotechnical Finite Element software for the dynamic analysis of earth
structures under earthquake loading, was used for our dynamic modelling. A linear
elastic model was considered with Young’s modulus EU defined from the following
relationship (Duncan & Buchignani, 1976),
E U = m ⋅ S DSS
with
m = 600 (empirical parameter),
U
and S DSS
is the undrained shear strength (Direct Simple Shear).
U
The Poisson’s ratio is defined from Ko values and the damping ratio fixed to 2%
according to the variation of damping ratio of fine-grained soil with cyclic shear strain
amplitude and plasticity index (Kramer, 1996). Figure 3 shows the maximum shear
strain in the soil during the seismic loading ( Maximum shear strain = 0.0046) and the
soil deformation at the end of seismic loading (Displacement magnification: 300, Time:
10 sec). One have to notice that the use of rigid boundaries in the simulation (instead of
transmitting boundaries) could exagerate the soil amplification effects.
Figure 3: Maximum shear strain (contours) and soil deformation (grid) at the end of the seismic loading
(10 sec.).
7.2 STRUREL (limit equilibrium method – two- wedge model)
The STRUREL software (Gollwitzer, 1988) allows a reliability analysis based on First(FORM) and Second-order (SORM) reliability method as well as Monte Carlo
simulation. As there is no graphic interface provided with this software, it is necessary
to define the model and thus the safety factor through a relationship involving the
different forces. A simple 2-wedge model (Figure 4, a=0.) was used to simulate a
sliding bloc (bloc 2) with a collapse mechanism (bloc 1).
Slope stability assessment of the Trænadjupet slide area
261
Figure 4. 2-wedge model used with STRUREL software (from Nadim, F., personnal communication).
8. Excess Pore Pressure generation
The earthquake-induced excess pore pressure has been estimated using the
AMPLE2000 software (Pestana & Nadim, 2000). The program simulates the 1-D site
soil response and excess pore presure under seismic loading. Different constitutive laws
defining the soil behaviour are proposed. The simple DSS (Direct Simple Shear) model
for lightly consolidated soils (Pestana & Biscontin, 2000) is used to estimate the excess
pore pressure developing with cyclic loading. As we do not have the parameters
required for the Trænadjupet area, we have used the parameters estimated for the
Helland Hansen area (southern Vøring Plateau). The earthquake record used to model
the seismic loading is the Friuli Tarcento earthquake with a duration of 33.18 seconds
(sampling: 0.02 sec). The excess pore pressure values, normalized with respect to the
vertical effective stress, are shown in Table 4.
Table 4: Excess pore pressure estimated using AMPLE_2000 for 0.10 g PGA (475 year return period) and
0.35 g PGA (10000 year return period) in % of the initial vertical effective stress.
Depth
0.10 g
(slope angle: 25 degrees)
0.35 g
(slope angle: 1 degrees)
7.5 m
1.0 %
22.5 m
0.35 %
42.5 m
0.30 %
62.5 m
0.25 %
82.5 m
0.22 %
9.2 %
5.2 %
4.2 %
3.5 %
3.2 %
The degradation of shear strength with excess pore pressure generation was estimated
using the SHANSEP relationship (Ladd and Foott, 1974).
9. Results
Backcalculation of the slide:
As the layer inclination is similar to the slope angle (1.0 degree), one cannot use the 2wedge model for this evaluation. Using SLOPE/W, the FOS is estimated to be 15.0 for
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Leynaud and Mienert
the static case and the failure is obtained (FOS < 1.0) with 0.15 g pseudo-static
acceleration. The Finite Element approach (QUAKE/W) for the dynamic loading gave a
factor of safety varying from 1.58 (assumed failure up to 30-40 meter depth) to 0.8 (1020 meter depth) as seen in Table 3. Considering the excess pore pressure generation
estimated with AMPLE_2000 (Table 2), one can calculate the degradation of strength
following the SHANSEP formula and the corresponding safety factor (Table 5).
Table 5: Factors of safety for 1 degree slope angle.
Case
Static
Pseudo-static
Dynamic
(0.35 g)
Dyn. + Excess Pore
Pressure (0.35 g)
FOS
15.0
1.0
with 0.15 g
1.58
(30-40 m depth)
1.13 (20-30m)
0.82 (10-20 m)
1.58
(30-40 m depth)
1.08 (20-30m)
0.77 (10-20 m)
In order to observe the effect of a slope angle increase (up to 3 degrees) in the area, new
slope stability assessment was performed with this new value. In this latter case, a FOS
lower than 1.0 corresponds to a failure located in the range 20-30 meter depth (Table 6).
Table 6: Factors of safety for Trænadjupet slide area with a slope angle close to 3.0 degree.
Case
FOS
Static
4.39
Pseudo-static
1.0
with 0.12 g
Dynamic
(0.35 g)
1.25 (30-40 m)
1.03(20-30 m)
Dynamic + EPP
(0.35 g)
1.20 (30-40 m depth)
0.98 (20-30 m)
Present-day slope stability:
The slope stability assessment is conducted for the South-West Sidewall where the
average slope angle is around 25 degrees (Laberg et al., 2002; Table 7). Static and
pseudo-static approaches provide similar FOS (1.72/1.85/1.74, static; 1.08/1.13 pseudostatic). The FE dynamic estimate gave a safety factor lower than 1.0 for a failure surface
up to 40 meter depth (0.1 g PGA).
Table 7: Factors of safety for present-day profile.
FOS / SLOPE/W
FOS / STRUREL
Static case
Pseudo static case (PGA=0.1 g)
1.72
1.08
1.85
1.13
FE static stress
FE dynamic stress (PGA=0.1 g)
1.74
1.33 (70 m depth)
0.98 (40 m depth)
---
---
Using the Monte Carlo simulation and FORM methods (pseudo-static case) we obtained
the following probability of failure (Table 8).
Table 8: Failure probabilities with FORM and Monte Carlo simulation methods. Present-day slope stability.
Slope stability assessment of the Trænadjupet slide area
Method
FORM
Monte Carlo
Static
Pseudo-static
6.0 E-08 %
19 %
< 1.0E-06 %
23 %
263
10. Conclusions
Backcalculation of the slide:
1.
A high FOS is found for the static case (FOS=15.0) which means that the
continental slope (1 degree slope angle) is very stable if subjected only to gravity
loading. Assuming a slope angle increase up to 3 degrees, the static FOS is reduced
to 4.39 (very stable slope).
2.
From the pseudo-static model, the pre-slide area is unstable with a 0.15 g pseudo
acceleration. Considering a similar value for the PGA and the age of the slide (4300
y. BP) on the other hand, this is in accordance with the seismic activity in the area
(0.35g PGA, 10000 year return period). The Finite Element method model a failure
in the first 20 meters depth (FOS=0.77) showing that the dynamic earthquakeinduced shear stress is enough to initiate some failures at medium depth during the
first 10 seconds. Thus, if the duration of acceleration is long enough, the modelling
shows that retrogressive failures will occur at a greater depth, depending on the new
slope angle and the decrease of acceleration with time. To confirm that, one need to
explain a complete loss of strength in the sediment (more or less liquefaction) and
this is not in agreement with the nature of this soil (not sensitive clay and no
liquefaction potential for 0.35 g); for this reason, it is necessary to get geotechnical
data in the area of the slide. So, one could not need to consider a higher slope angle
or a higher PGA seismic event to explain a failure at a greater depth though the
northernmost area of potential high ground acceleration is located on the
continental slope north of the Vøring Plateau (Dahle and Bungum, 1993). The
expected PGA is not the highest in this area (only 0.30g PGA) but the largest
historical events was located not so far from the slide (the 31.08.1819 M S 5.8
Rana earthquake and the 09.03.1866 M S 5.7 Halten Terrace earthquake)
confirming a high potential of seismic activity in terms of large events (NORSAR,
1998). From the Ambraseys’s attenuation relationship (Ambraseys, 1995), one can
expect higher PGA values in the vicinity of a magnitude M S 6.0 seismic event.
Furthermore, the Trænadjupet slide area is located exactly on the Bivrost Fracture
Zone (BFZ). From a geotechnical point of view, Laberg et al. (2002) showed that
the shearing resistance in the contourite sediments (unit 3, contractant behaviour
from triaxal compressional test) could have been reduced drastically with excess
pore pressure due to rapid deposition of overlying sediment (late Weichselian
glacigenic sediments up to 160 m thick in the slide area). With such conditions, the
triggering of the Trænadjupet slide is most likely caused by a large earthquake
associated with postglacial crustal uplift.
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Leynaud and Mienert
Present-day slope stability:
3.
Both softwares give a similar static FOS (higher than 1.0) which means that the
slope is stable (FOS=1.72, SLOPE/W; 1.85, 2-wedge model; 1.74, FE stress). The
difference between the previous values can be explained by the shape of the
assumed failure surface; circular failure with SLOPE/W and 2-wedge model with
STRUREL.
4.
For the pseudo-static model (0.1 g PGA) no failure is observed (FOS=1.08 and
FOS=1.13) with the maximum PGA value for the area (0.1 g with 10% probability
of exceedance during 50 years; 475 year return period). Using the Finite Element
method, the failure is reached with 0.1 g PGA (FOS=0.98) for the first 40 meter
depth but not for the entire slope (70 meter depth). Considering uncertainty of the
the soil parameters, the failure probability is found between 19 % and 23 %.
11. Acknowledgements
This work is a contribution to the COSTA project. We would like to thank J. Locat and
R. Urgeles for constructive reviews, N. Sultan for fruitful discussions, J. S. Laberg who
provided some figures and details on the slide area and an anonymous reviewer for
substantial improvements.
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