Spatial Analysis of Shallow Slope Instability
Incorporating an Engineering Geological
Ground Model
B. Mackenzie, J. Hooper, and D. Rushton
Abstract Within a GIS (geographical information system), spatial analysis techniques
can be used to apply deterministic methods for identifying and mapping areas
susceptible to shallow submarine mass movements. This paper describes such a
method which allows spatially widespread, rapid, repeatable and cost-effective
evaluation of shallow submarine slope risk. A deterministic approach has the
advantage of providing a quantitative output; useful in subsequent project risk
assessment. The use of GIS in this way is well established. Many of the method
limitations described in the literature can now be overcome. This paper describes
some advances through which these limitations are being addressed, and the compromises that still need to be made. The paper places emphasis on GIS modeling
of the full three-dimensional variation of geotechnical input parameters. This
approach allows the type of sophisticated ground model now becoming available
from regional engineering geological and geohazard studies to be harnessed and
exploited. The approach described in the paper has been applied on deepwater oil
and gas projects having development areas of over 1,000 km2.
Keywords Submarine landslide • geographical information system • GIS •
shallow slope stability • soil model • ground model • geotechnical spatial
variability • risk assessment
1
Introduction
Submarine slope instability is a risk to many offshore oil and gas developments,
particularly in deepwater areas. Authors have described risks and associated
mitigating measures in various deepwater regions (Jeanjean et al. 2005;
B. Mackenzie (), J. Hooper, and D. Rushton
Fugro GeoConsulting Limited, Fugro House, Hithercroft Road, Wallingford, Oxfordshire,
OX10 9RB, UK
e-mail: b.mackenzie@fugro.co.uk
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
365
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B. Mackenzie et al.
Hooper and Prior 1989 (Gulf of Mexico); Kvalstad et al. 2002 (Norwegian Sea);
Evans et al. 2007 (West Nile Delta); Orren and Hamilton 1998 (Caspian Sea) ).
In order to design, install and successfully bring onstream an oil and gas development
in an area of potential submarine slide activity, the slide instability risks must not
only be understood, but must be quantified. This is the only way that the project can
relate and balance the risks, and mitigating effort, to the overall project value.
The overall quantified slope instability risk is an aggregate of component probabilities and consequences, including: (i) the probability of slide occurrence, (ii) the
probability of the slide then spatially impacting development infrastructure, and (iii)
the probability that this impact will cause damage having a cost. This paper focuses
on the first stage of this quantitative risk assessment process – the prediction of slide
occurrence. However, it will be seen that, if a predictive method can also output key
physical slide attributes such as spatial extent and thickness, then the method also
helps quantify the damage consequence, another step in the risk assessment process.
2
Landslide Prediction Methods and GIS Applicability
Different techniques exist to predict slide occurrence. Some authors (Soeters and
Van Westen 1996; Van Westen et al. 1997; Dai and Lee 2001) have placed these
techniques into four categories: inventory, heuristic, statistical and deterministic.
Each method has its relative merits and limitations, as summarized in Table 1.
All the techniques originate from methods first developed for slope stability
assessment in onshore environments. However, they are also generally applicable in
the submarine environment, for instance by using high resolution seabed bathymetry
data in place of aerial imagery to perform submarine slide inventory mapping.
Table 1 can be viewed as showing a progression, from top to bottom, from qualitative to quantitative stability risk assessment. All of the methods also lend themselves to GIS implementation. In the simplest case, a GIS represents an ideal tool
to compile, manage and present a landslide inventory, with the added advantage
that that the accompanying slide parameters can be included in a GIS attribute
table. Hitchcock et al. (2006) describe the implementation of a heuristic approach
using GIS technology to map mudflow susceptibility in the Gulf of Mexico. Here,
the relative contributions of geology, slope, and bathymetric drivers were ranked
and captured in an expert-assigned scoring system. These scores were then aggregated and assigned a mudflow susceptibility class (low, moderate, high, very high)
which was then mapped over the study area.
Authors have previously described the use of GIS to apply deterministic slope
stability methods (Graham 1984; Wu and Sidle 1995; Dai and Lee 2001). Jeanjean
et al. (2005) describe the application of a deterministic method to identify areas
having a low safety factor against shallow slope failure, over an entire field of interest. The input soil strength varied over the field, but was a constant value with
depth at any given location. In the case of the deterministic method, GIS spatial
analysis techniques can be used directly to realize the method’s key advantage - the
calculation of factors of safety (FOS) against slide failure. Via probabilistic methods
Spatial Analysis of Shallow Slope Instability
367
Table 1 Summary of predictive methods for landslide occurrence
Technique
Description
Advantage(s)
Limitation(s)
Inventory
Shows location of existing Straight-forward;
Basic; time-consuming;
landslides on a map,
yields good insight
does not directly identify
accompanied by key
into whole slope
areas susceptible to new
characterization
instability record
landslides
parameters: e.g. type,
of an area
subtype, size, activity
Heuristic
Use algorithms to
Incorporates expert
Poor reproducibility of
estimate landslide
opinion
results due to high
potential based on
reliance on expert expeterrain input variables
rience; high subjectivity
in weightings and
ratings assigned
Statistical
Statistical determination
Mathematically
Complexity of analysis,
of combinations of
incorporates
especially with large
variables that have
existing knowledge
numbers of causative
led to past failures.
into predictive
terrain parameters
Statistical methods
tool; data-driven;
include multi-variate or
objective
Bayesian approaches
Deterministic Use slope stability
Yields quantitative
Landslide mechanisms
analysis and limit
results; repeatable
need to be assumed
equilibrium methods
and simplified, e.g.
to calculate factor
one-dimensional infinite
of safety
slope theory; requires
detailed input data and
good knowledge of
ground conditions
(e.g., Nadim et al. 2003), the FOS can be developed into a probability of failure
thus enabling fully quantified risk assessment. Building on the assertion that a
quantified risk assessment is ultimately required for an offshore oil and gas development to achieve sanction, it follows that a deterministic approach should be
applied at some stage. This paper focuses on the implementation, using GIS, of the
deterministic method to obtain FOS against shallow slide failure. It is nevertheless
important to emphasize that a deterministic approach should still be preceded and
substantiated by other methods, and that no one method should be applied alone in
achieving an overall understanding of the slope instability risk to a project.
3
3.1
Deterministic Slope Stability Analysis
Limitations and Advances
The limitations of the deterministic method include its reliance on detailed input
data and a good knowledge of the seabed conditions. However, advances in deepwater bathymetric and geotechnical data acquisition, twinned with advances in
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B. Mackenzie et al.
engineering geology and geohazard assessment (e.g., Thomas et al. 2009) are
reducing the uncertainties inherent with these limitations. These advances are
leading to the availability of sophisticated and spatially resolute terrain and soil models
for many of the world’s slide-prone deepwater development areas. The amount of
information available would form an overwhelming dataset for interpretation in
anything other than a GIS-based terrain analysis.
Another previously noted limitation of GIS implementation of deterministic
models is the inability to model the influence of neighboring pixels (neighborhood operations), and the inability to model the third dimension (depth). This
need no longer be a limitation, as will be described, with an emphasis on modeling
depth variability.
Table 1 also notes that landslide mechanisms need to be simplified for implementation in a numerical-based GIS mapping algorithm. This might be true for a
solution performed completely within GIS. However, parallel advances using
hybrid solutions are reducing the reliance on simplified models. Xie at al. (2003)
describe a method enabling full 3D analysis through a combination of GIS spatial
analysis and an external column-based 3D slope stability model.
Overall, GIS implementation of a deterministic slope analysis remains a technical
compromise, but one in which not all of the current limitations need apply. In the
analysis described herein, the modeled landslide is maintained at a relatively simple
level (one-dimensional infinite slope), but incorporates a complex, spatially resolute and depth-dependent ground model. The use of numerical-based mapping
methods in GIS enables this analysis to be performed rapidly over wide areas.
Furthermore, despite the complexity of the ground model, it remains a model and
is consequently subject to uncertainty. However, the use of GIS also allows the
rapid design and execution of sensitivity studies in which the ground model can be
parametrically varied.
3.2
Infinite Slope Theory Formulation
The basic formula giving FOS against shallow mass movement is as follows,
where shear resistance and shear load are calculated over the same hypothesized
failure surface:
FOS
available shear resistance
applied shear load
=
(1)
For an infinite slope under static submerged conditions, and where mass movement
results simply from an imbalance between downslope gravity load and soil undrained shear strength, Eq. 1 can be expressed:
FOS
=
su
g ' z sin b cos b
(2)
Spatial Analysis of Shallow Slope Instability
369
where: su = soil undrained shear strength (kPa) at depth z
z = depth of failure plane below, and parallel to, seabed (m)
g ' = soil submerged unit weight, average to depth z (kN/m3)
b = seabed slope (°)
Equation 2 can be further modified to model drained soil response, and also to
incorporate non-static loading such as the effect of a downslope seismic acceleration, as follows:
FOS =
(su / z ) + (g ' cos2 b − g kseis cos b sin b )tan f'
g ' cos b sin b + g kseis cos2 b
(3)
where: g = soil total unit weight (kN/m3)
f' = soil effective friction angle (°)
kseis = seismic acceleration coefficient (-)
The product of the seismic acceleration coefficient, kseis, and the acceleration due
to gravity gives the seismic acceleration. The use of the seismic acceleration
coefficient in this way represents a recognized simplification where the additional
downslope load is applied as a quasi-static load equal to the product of the soil mass
and its resolved downslope acceleration.
Further adaptations can be made to Eq. 3 to incorporate the effects of excess
pore-water pressure in the soil, and also the influence of external loads, such as
might be imposed by seabed structures or pipelines on the seabed. Equation 3, and
variants, allowing for external structure loading and excess pore-water pressure,
have been used by the author in region-wide GIS assessments of seabed susceptibility
to shallow mass movements. These assessments have used, as their input, GIS
ground models derived from regional engineering geological studies. A description
of the type of ground model typically now available is given below, followed by a
description of its actual implementation in a GIS slope stability assessment.
4
4.1
GIS Ground Model Availability – State of the Art
Ground Model Components
The term ground model, in this context, encompasses the data required to characterize
seabed topography and the geotechnical and geological conditioning factors,
including the temporal element. Combined, these govern the occurrence, size and
extent of shallow slide events. A typical process for the development of the ground
model is described by Thomas et al. (2009). Seabed topography is now typically
available to the slope stability engineer as a digital three-dimensional surface
derived from ultra-ultra high resolution autonomous underwater vehicle (AUV)
survey data. AUV bathymetry data typically exist at a resolution of 2.5 m, or finer,
for today’s deepwater development projects.
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B. Mackenzie et al.
The geotechnical and geological conditioning factors are those parameters
required to compute soil shear resistance and loading, the balance between
which governs stability. With reference to Eqs. 2 and 3, these include undrained
shear strength (su), total and submerged unit weight (g, g '), and effective friction
angle (f').
4.2
Representation of Full Spatial Variability
In reality the above parameters vary spatially as a function of depth as well as location. The seabed model sourced by the GIS stability analysis should ideally reflect
this. A convenient means of defining the geotechnical variability across a site is to
use terrain systems or soil provinces (Campbell 1984). A soil province is defined
as an area within which soil conditions share a similar stratigraphic sequence; usually
the soils within a given soil province have shared a similar geological and geomorphological history. There is often a visible correlation between soil province
mapping and bathymetry, since the seabed bathymetry can reveal much about the
process by which the soil has arrived at its present state.
Figure 1a shows a portion of seabed terrain, and highlights four individual
locations which have each been subject to different geological or geomorphological
processes. The simple block model in Fig. 1b depicts these processes schematically.
Consequently, each location has a different shear strength profile (Fig. 2), a key
parameter in assessing shallow slide potential.
Fig. 1 (a) Three-dimensional seabed rendering (×2.5 vertical exaggeration) of shallow slope
instabil-ity study area, showing locations affected by different geological or geomorphological
processes. Marked areas: (1) normally consolidated deposit, (2) underconsolidated debris flow
deposit, (3) pull-apart window, exposing overconsolidated deposit, and (4) block slide on failure
plane having residual strength. (b) Simple block model idealizing typical locations of the four
different processes marked in Fig. 1a
Spatial Analysis of Shallow Slope Instability
a
Undrained Shear Strength, Su (kPa)
10
20
30
b
40
0
0
4
4
8
8
Depth (m)
Depth (m)
0
371
12
16
20
20
0
Undrained Shear Strength, Su (kPa)
10
20
30
4
h
Undrained Shear Strength, Su (kPa)
10
20
30
40
h
8
Depth (m)
Depth (m)
0
0
8
12
40
d
40
0
4
Undrained Shear Strength, Su (kPa)
10
20
30
12
16
c
0
12
16
16
20
20
Fig. 2 Characteristic design undrained shear strength profiles for each location highlighted in
Fig. 1. (a) Location 1 (normally consolidated); (b) Location 2 (underconsolidated); (c) Location
3 (overconsolidated); and (d) Location 4 (residual/previous slide). Each location’s profile (bold
line) is superimposed on a composite of the other profiles (faint lines). The dashed profiles represent the strength profiles derived directly from cone penetration test data. ‘h’ denotes the elevation
to a strength profile discontinuity
On Fig. 1a, Location 1 sits in a normally consolidated depositional environment,
for which one would expect a low shear strength at the immediate seabed, below
which the strength would increase linearly with depth (constant shear strength
gradient). Location 2 represents an underconsolidated deposit. Here, owing to recent
higher deposition rates, or in this case loading from an earlier mass movement
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event, the soil contains excess pore-water pressure and hence exhibits a lower
strength than if normally consolidated. At Location 3 the soils are slightly overconsolidated; here surface soil has been removed by previous slide activity and the
underlying unloaded soil is slowly weakening, just like an excavation on land – but
remains stronger than a normally consolidated seabed soil. Location 4 has been
subject to previous slide movement, and comprises a layer of disturbed, weaker
mass flow deposit separated from the underlying soil by a shear plane.
Examination of the seabed and sub-seabed in this way, especially if assisted by
shallow geophysical and geotechnical site investigation data, allows delineation
into soil provinces. These provinces lend themselves to GIS mapping and subsequent spatial analysis of the seabed and sub-seabed extremely well. An important
point to note is that, within any soil province, the layer change elevations (denoted
at depth ‘h’ in Fig. 2c, d) need not be a fixed GIS attribute for that soil province.
Rather, and better still, these elevations are themselves defined in a GIS isopach
layer resulting from a geophysical interpretation. In other words, although the soil
layering follows a set sequence within a soil province, the layer thicknesses and
hence the soil parameters are fully spatially variable. The cross-referencing of
stratigraphic elevations from isopach maps allows for computational efficiency, as
opposed to storing depth-variable data on a per-location basis.
5
5.1
GIS Implementation and Results
Implementation
The required numeric seabed model parameters are captured in a suite of GIS raster
surfaces. A raster surface is a grid of pixels, or raster cells, where each cell has a
value assigned based on the soil province in which the cell lies (or based on an
isopach layer in the case of continuously mapped stratigraphic elevation).
For the depth-variable parameters such as undrained shear strength (su), raster
surfaces defining su at the top of each stratigraphic layer, and defining the gradient
of su within each layer, are produced. These are readily generated from a GIS soil
province map, likely to have initially been created as a vector map with lines or
polygons delineating the soil provinces. A GIS soil province vector map is a
convenient and effective data management tool, since all key parameters can be
captured as data attributes.
Figure 3 reproduces the GIS attribute table for the study area introduced earlier
in Fig. 1. The soil province map, and its underlying attribute table, is then used to
spawn individual parameter surfaces on a stratigraphic layer-by-layer basis. At the
same time, these individual parameter surfaces are converted into raster format.
Through the resulting suite of raster surfaces, the GIS then has the full ‘picture’ of
the spatial variability of the key parameters over the study area, including buried
strength discontinuities on previous slide planes.
Spatial Analysis of Shallow Slope Instability
373
Fig. 3 Example attribute table for a soil province polygon map. Each data row corresponds to a
mapped soil province. A suite of raster surfaces is produced using this attribute table, with raster
call values corresponding to each attribute field. The stratigraphic boundary depths, such as captured in the data field ‘L1_z_base’ above, can alternatively be sourced from an isopach map to
give a truly continuous variation over the study area
GIS spatial analysis is used to perform raster-based algebraic operations using
the seabed model. The slope stability equation is evaluated in a raster algebra
expression which yields an output raster surface of FOS. This is calculated on a
cell-by-cell basis, using the appropriate strength, density, slope, and other geological
controls, and triggering factors captured in the suite of input raster maps. In the case
of an included seismic load, the seismic acceleration coefficient, kseis, is also
required in the raster algebra expression. This can be programmed as a region-wide
constant, or alternatively taken from GIS map layer, where a seismic ground
response analysis has been performed and peak ground acceleration mapped as a
variable with soil province or proximity to source.
5.2
Results
The spatial analysis is repeated on a soil layer-by-layer basis. This is not a computationally intensive task, although geoprocessing techniques can further increase
efficiency. The analysis outputs a suite of predicted FOS surfaces, each showing the
spatial variation of predicted safety factor appropriate for each layer top or base.
These can be analyzed in further raster algebra operations to seek and map, for
example, the minimum safety factor in each raster cell (Fig. 4a, b), and the depth
at which the minimum safety factor is predicted to occur (Fig. 4c). Figure 4c is
essentially a color scale map of critical shear depth, which could alternatively be
output as a contour map. This critical shear depth map enlightens us in two ways:
firstly, by examination, it reveals the existence and size of potentially spatially
extensive failure planes. Secondly, it indicates the probable thickness of a potential
slide block, a key physical attribute used when assessing the damage level caused
by a slide on a seabed structure.
Superposition of a slope aspect map (Fig. 4d) helps indicate slide direction,
and where unstable zones might move in unison, diverge, or collide. From the
results mapping, simple risk metrics can also be generated, such as percentage of
overall study area predicted to be at risk, for differing assumed input conditions.
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B. Mackenzie et al.
a
b
Minimum FOS
<VALUE>
1.0 - 1.1
1.1 - 1.25
1.25 - 1.5
1.5 - 2.0
2.0 - 2.5
c
d
Critical Shear Depth (m)
<VALUE>
1.5 - 3.0
3.0 - 4.5
4.5 - 6.0
6.0 - 7.5
7.5 - 9.0
9.0 - 10.5
Slope Aspect
<VALUE>
N - NE
NE - E
E - SE
SE - S
S - SW
SW - W
W - NW
NW - N
Fig. 4 (a) (top left): Seabed terrain image – selected portion of study area, focusing on topographical
high and associated scarp. (b) (top right): GIS spatial analysis results for selected area showing
color-shaded factor of safety against shallow slope failure. (c) (bottom left): Results showing predicted
slide thickness. (d) (bottom right): Results showing slope aspect of slide-susceptible zones
Of more importance to the facilities engineer is the identification of at-risk zones
which are coincident with, or close to, planned seabed infrastructure. The ability to do
this in a GIS requires a simple overlay operation with the proposed infrastructure map
6
Conclusions
The paper has described a method allowing a spatially resolute and fully variable
soil model to be incorporated in a deterministic analysis of seabed slide instability
within a GIS. The use of a deterministic analysis needs to be accompanied by other
expert-applied assessments; however, a deterministic approach is ultimately
required to deliver the numerical information required to perform a quantified
project risk assessment.
Spatial Analysis of Shallow Slope Instability
375
The ability to capture the full depth variability in the ground model, including
strength profile discontinuities, represents a key advance. This approach allows the
analysis to estimate the likelihood of slide re-activation as well as new movements.
It also allows estimation of slide thickness. Slide thickness is a key parameter used
in the soil-structure interaction analysis to assess the damage consequence for seabed structures.
Simplifications regarding slide mechanics still currently need to be made in
order to implement a deterministic slide analysis in a GIS. However, this compromise is balanced by the ability of the method to analyze rapidly such large extents
of seabed, while using a more representative ground model. This makes it a costeffective option for performing parametric sensitivity studies, arguably not possible
by any other means.
Acknowledgements The authors acknowledge the valuable opportunities and input given by
individuals from external organizations over the years, and the assistance and discussion provided
by colleagues in the Fugro Group, together which have enabled the production of this
manuscript.
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