Risk Analysis for Hurricane-Wave Induced
Submarine Mudslides
M.C. Nodine, R.B. Gilbert, J.Y. Cheon, S.G. Wright, and E.G. Ward
Abstract Hurricane waves in the Gulf of Mexico can trigger mudslides in the
relatively weak clays in the offshore Mississippi Delta region. Mudslides can cause
extensive damage to the infrastructure that supports offshore oil and gas production,
including platforms and pipelines. This paper presents a method for assessing the
probability and risk for future mudslides in the Delta as a function of the possible
sizes of waves, bathymetry, and shear strengths of sea floor soils. The method has
been calibrated to the extent possible using historical information. The method
is transparent and can readily include either generic or site-specific information
about soil properties and wave characteristics. The method is applied regionally to
develop maps depicting the risk to locations and to pipelines. Return periods for
mudslides vary significantly across the Delta, with values less than 30 years in the
shallowest water and values greater than 1,000 years in the deepest water. Wave
period, in addition to wave height, is an important factor in mudslide vulnerability.
Mudslides are localized features, on the order of several thousand feet in lateral
extent and about 50 to 150 feet deep. The areal extent and depth of mudslides are
related to the lengths and widths of the storm waves that cause them.
Keywords Submarine landslides • mudslides • hurricanes • risk analysis
M.C. Nodine ()
GEI Consultants, Inc.,1790 38th St. #103, Boulder, CO 80302, USA
e-mail: mnodine@geiconsultants.com
R.B. Gilbert, J.Y. Cheon, and S.G. Wright
The University of Texas at Austin, Department of Civil, Architectural and Environmental
Engineering, Geotechnical Engineering Program, 1 University Station, C1792, Austin, Texas
78712-0280, USA
e-mails: bob_gilbert@mail.utexas.edu; doogiezzang@mail.utexas.edu; swright@mail.utexas.edu
E.G. Ward
Offshore Technology Research Center, Texas A&M University, 1200 Mariner Drive, College
Station, TX 77845, USA
e-mail: egward@tamu.edu
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
335
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1
M.C. Nodine et al.
Introduction
Hurricane waves in the Gulf of Mexico can trigger mudslides in the relatively weak
clays in the offshore Mississippi Delta region (Coleman et al. 1982; Hitchcock
et al. 2006). Mudslides caused extensive damage to platforms and pipelines in
Hurricanes Camille (1969), Ivan (2004) and Katrina (2005). The consequence of
this damage in Ivan and Katrina was a significant loss of capacity for offshore oil
and gas production in the Gulf of Mexico, leading to increases in the price of oil
(e.g., Thomson et al. 2005; Coyne and Dollar 2005). This paper presents a method
for assessing the probability and risk for future mudslides in the Delta as a function
of the possible sizes of waves, bathymetry, and shear strengths of sea floor soils.
The method is applied regionally to develop maps depicting the risk to lease blocks
and to pipelines. It can also be applied on a project-specific basis using site-specific
information about waves, bathymetry and soil shear strengths. The method is
described and examples are presented to demonstrate its use.
2
Mudslide Model
The conceptual framework of the risk analysis method is to characterize the hazard
caused by hurricane waves and the vulnerability caused by relatively weak soils in
the Delta, and then to compare the hazard and vulnerability to assess the potential
for mudslides. The hazard is shown schematically in Fig. 1; it is represented by
shear stresses that are applied to the soils from wave-induced bottom pressures and
from the weight of the soil when it is on a slope. These applied shear stresses can
be related to the height and length of the surface waves and the slope and unit
weight of the soil in the sea floor. Linear wave theory, with an adjustment to
Fig. 1 Schematic of wave forces imposed on the sea floor
Risk Analysis for Hurricane-Wave Induced Submarine Mudslides
337
account for the three-dimensional shape of a wave, is adopted here to characterize
the hazard (see OTRC 2008 for details).
The vulnerability is represented by the shear strength of the soil in the sea floor
acting over a potential failure surface. For the predominantly normally (and underconsolidated) marine clays that comprise the Delta sea floor, the shear strength
mobilized in wave loading is the undrained shear strength. A limit equilibrium
model, assuming a circular failure surface and constituting an extension of a model
proposed by Henkel (1970) in order to account for non-linear variations in undrained shear strength with depth below the sea floor, is adopted here to characterize
the vulnerability (see OTRC 2008 for details).
This methodology for characterizing the hazard and vulnerability has been validated by comparing predictions with observed behavior in actual hurricanes. Bea et al.
(1983) used the limit equilibrium model to analyze a mudslide that occurred in South
Pass Lease Block 70 during Hurricane Camille in 1969. The model predicted that a
mudslide would occur based on the wave hindcast and site-specific geotechnical
information. Nodine et al. (2006) used the limit equilibrium model to analyze a mudslide that occurred in Mississippi Canyon Block 20 during Hurricane Ivan in 2004.
Again, the model predicted the occurrence of the mudslide. One of the interesting
results of this analysis was the importance of the wave length on the hazard.
Increasing the wave length increases the maximum bottom pressure for the same
wave height and water depth, which may explain why Hurricane Ivan caused a comparable amount of mudslide damage to that of Hurricane Katrina despite having
smaller wave heights in the Delta (Nodine et al. 2006). A regional analysis comparing
observed to predicted mudslide activity is also presented by Nodine et al. (2006).
Predicted mudslides were found to compare well with mudslide damages reported.
Several important observations were made through applying this model of mudslides to the Delta. First, the bottom slopes in the Delta are very flat (1% to 2%)
and generally do not contribute much to potential for a mudslide. Hence, mudslides
are mainly driven by waves. Second, it takes a relatively large wave to cause a
mudslide. Nodine et al. (2007) estimated that maximum wave heights of at least 65
feet are required to cause mudslide activity. Less than 25% of all hurricanes in the
Gulf of Mexico have waves this large. Third, even if a mudslide completely remolds
the soil, the soil will not continue to move when the waves subside, and the mudslide
will not likely propagate into a large-scale regional mudflow. Therefore, the areal
extent of disturbance from a mudslide is expected to be similar in plan to the largest
ocean waves, which are sustained over several thousand feet and are hundreds to
thousands of feet across.
3
Risk Model
The risk associated with mudslides is defined as the expected damage from mudslides, which is the summation of the possible damages multiplied by their corresponding probabilities of occurrence. The primary focus in this work is to assess
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M.C. Nodine et al.
the probability of occurrence for a mudslide, both locally in terms of a specific
location or facility in the Delta and regionally in terms of the collection or system
of facilities throughout the Delta. We will also discuss briefly the factors that affect
the potential for damage from a mudslide.
3.1
Probability for Mudslide at a Particular Location
The probability that a mudslide occurs at a particular location with a given water
depth and bottom slope is assessed by dividing the problem into the hazard and the
vulnerability as follows:
P (Mudslide ) =
⎡
⎢ ∑ P Mudslide su (z ),p max ,L Hmax
all pmax ,L Hmax ⎢
⎣ all su (z)
(
∑
⎤
) P (s (z))⎥⎥⎦ P (p
u
max
,L Hmax
)
(1)
where P (Mudslide) is the probability a mudslide occurs, P(Mudslide|su (z), pmax,
LHmax) is the conditional probability that a mudslide occurs for a given profile of
undrained shear strength versus depth, su (z), together with a given combination of
maximum bottom pressure, pmax, and wave length, LHmax; P(su(z) ) is the probability
for a given profile of undrained shear strength versus depth at this location; and
P(pmax, LHmax) is the joint probability for a given combination of maximum bottom
pressure and wave length acting on the sea floor at this location.
The conditional probability of a mudslide, P(Mudslide|su(z), pmax,LHmax), is
obtained by establishing the relationship between the factor of safety against a
rotational failure in the sea floor and the maximum amplitude and wave length of
the bottom pressure acting on the sea floor. Figure 2 shows an example of this
620
600
580
Sea Floor Stable
Threshold
Wave Length of
Bottom Pressure, 560
,
LHmax (ft)
Sea Floor Not Stable
540
520
500
535
545
555
565
Amplitude of Bottom Pressure, pmax (psf)
Fig. 2 Bottom pressure wave threshold to cause a mudslide for a given profile of undrained shear
strength versus depth at a location in Delta (taken from OTRC 2008)
Risk Analysis for Hurricane-Wave Induced Submarine Mudslides
339
relationship for a particular location and a given profile of undrained shear strength
versus depth; the threshold line separates the combinations of (pmax, LHmax) that
produce a factor of safety less than one from those combinations that produce a
factor of safety greater than one. The threshold bottom pressure generally increases
as the length of the bottom pressure wave increases because the critical slip surface
is moving deeper into stronger soil. (An exception is when the soil profile includes
weaker layers at depth.) This threshold depends on the profile of undrained shear
strength versus depth as well as the bottom slope at the location of interest. The
profile of undrained shear strength with depth is extremely variable across the Delta
(Hooper 1980; Roberts et al. 1976). For the purposes of mudslide risk analysis at a
site where shear strength data are available, one shear strength profile may be
assumed to represent the site and P(su(z) ) = 1.0 for that profile, or several shear
strength profiles may be assumed to be equally probable or weighted appropriately
with different values for P(su(z) ) reflecting the available information. There may
well be uncertainty in the shear strength profile even when site-specific shear
strength data are available due to the small area sampled by a single boring relative
to the area of interest for a pipeline or a platform.
The amplitude and length of the pressure wave are related to ocean waves as
follows. The maximum pressure is approximated from the height and length of the
largest ocean wave, Hmax and LHmax, and the depth of the water, d, using linear wave
theory (Wiegel 1964) with a correction factor to account for the three-dimensional
shape of the wave, I3D (OTRC 2008):
Pmax =
⎛ 2p ⎞ ⎞
gw ⎛
d ⎟ ⎟ I3d
⎜ H max cosh ⎜
2 ⎝
⎝ LHmax ⎠ ⎠
(2)
The wave length associated with the largest wave is found by assuming that the
period for the largest wave is approximated by 90% of the peak spectral period, Tp
(the period associated with the most wave energy in a series of waves) (Haring
et al. 1976):
LHmax =
g(0.9 × Tp )2
2p
⎛ 2pd ⎞
tanh ⎜
⎟
⎜⎝ LH ⎟⎠
max
(3)
where LHmax is found implicitly, LHmax = f−1 (Tp). For a given sea state, which is
defined as an interval of time over which the mean maximum wave height, mHmax,
and peak spectral period are reasonably constant and is typically taken to be 3 h in
the Gulf of Mexico during a hurricane, the probability that the maximum wave
height exceeds a particular value during that sea state is obtained from the Forristall
probability distribution (Forristall 1978):
(
P H max > hmax m Hmax
⎡ − p ⎛⎜ 1 ⎞⎟ ⎛⎜ hmax − m ⎛⎜1+ 0.577 × 0.07
Hmax
p
⎟⎝
6 ⎜ 0.07 m H
⎝
⎢
max ⎠
= 1 − exp ⎢ −e ⎝
⎢
⎣
)
6 ⎞⎞
⎟⎟
⎠⎠
⎤
⎥
⎥
⎥
⎦
(4)
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M.C. Nodine et al.
The probability that the maximum bottom pressure exceeds a threshold for a given
sea state and three-dimensional correction factor is then obtained by combining
Eqs. 2, 3, and 4:
⎛
⎞
⎛
⎞⎞
g ⎛
2p
P ⎜ Pmax > w ⎜ hmax cosh ⎜
d ⎟ ⎟ I 3 d m Hmax , Tp , I 3 d ⎟ = P H max > hmax m Hmax
1
−
⎜⎝ LH = f Tp ⎟⎠ ⎟
2 ⎜⎝
⎜
⎟
⎠
max
⎝
⎠
(
( )
)
(5)
Therefore, Eq. 1 can be re-stated in terms of the variables defining a sea state:
P (Mudslide ) =
⎡
⎤
⎢ ∑ P Mudslide su (z ), μ Hmax ,Tp ,I 3D P (su (z ))⎥ P μ Hmax ,Tp ,I 3D
all m Hmax ,Tp ,I3D ⎢
⎥⎦
⎣ all su (z)
(
∑
)
(
)
(6)
where the threshold for pmax is established as in Fig. 5 for a given profile of undrained
shear strength versus depth and peak spectral period at a particular location (water
depth and bottom slope).
To represent the possible sea states that may occur in the future in the mudslide
prone area of the Mississippi Delta, API Bulletin 2INT-MET Interim Guidance on
Hurricane Conditions in the Gulf of Mexico (API 2007) is used. This guidance
provides a probabilistic description of possible 3-h-long sea states in terms of the
mean maximum wave height and the peak spectral period. Wave heights and peak
spectral periods are given for return periods ranging from 10 to 10,000 years. In order
to simplify the analysis, we discretized the probabilities of the mean maximum wave
heights into eight bins as shown in Fig. 3. The values of the wave heights in Fig. 3
Annual Probability of Occurrence
0.07
0.06
0.06
0.05
0.04
0.03
0.02
0.02
0.01
0.01
0.005
0.004
0.0005 0.0004 0.0001
0
(h10+h25)/2
(h50+h100)/2
(h25+h50)/2
(h200+h1000)/2 (h2000+h10000)/2
(h100+h200)/2
(h1000+h2000)/2
h10000
Mean Maximum Wave Height
Fig. 3 Probability distribution for maximum wave height at any location (taken from API 2007, where
hx is the value for mHmax with an annual probability of 1/x of being exceeded) (taken from OTRC 2009)
Risk Analysis for Hurricane-Wave Induced Submarine Mudslides
341
are dependent on the water depth, i.e. the wave height with a 10% probability of
occurrence will be larger for 500-ft-deep water than it will be for 100-ft deep water.
API (2007) provides wave heights for water depths up to about 1,000 feet, as well
as for “deep water,” in which the effect of the sea floor on the wave height is
assumed to be negligible.
The peak spectral periods of storm waves are assumed by API (2007) and in this
analysis to be independent of water depth, meaning that the periods of waves in a
given storm are directly related to the heights of the waves in deep water.
Furthermore, the peak spectral period is assumed to be related to the largest waves
in the hurricane, or the waves near the eye. To illustrate this assumption, Fig. 4 shows the
peak spectral period versus mean maximum wave height from hindcast data for
the Delta in Hurricanes Ivan and Katrina. The curve labeled “Average” represents
the average relationship between the largest mean maximum wave height and the
corresponding peak spectral period for all hurricanes in the Gulf of Mexico in
the past 60 years including Ivan and Katrina (from a proprietary database.) This
average relationship is used to relate wave height and wave period in API (2007).
The peak spectral period for the waves in the Delta in Ivan is greater than that for
the waves in Katrina and greater than the average curve (Fig. 4). The difference
between Ivan and Katrina is that the eye of Katrina passed over the Delta while that
for Ivan passed 90 miles east of the Delta. Therefore, the largest waves in Katrina
were in the Delta and the peak spectral period for these waves falls on the average
curve (Fig. 4). Conversely in Ivan, the waves in the Delta were not as high as those
near the eye, but they had a relatively large peak spectral period, approximately
equal to that near the eye (Fig. 4). Figure 4 shows why the peak spectral period is
Fig. 4 Relationship of peak spectral period with maximum wave height for Hurricanes Ivan and
Katrina in the Delta region, and the average relationship for historical hurricanes in the Gulf of
Mexico (taken from OTRC 2008)
342
M.C. Nodine et al.
such an important factor in the potential mudslides. Hurricanes Ivan and Katrina
caused similar mudslide damage in the Delta even though Ivan’s eye was well east
of the Delta and Katrina’s passed over the Delta, and even though the waves were
not as high in the Delta during Ivan as during Katrina.
In order to capture the complex relationship between peak spectral period and
mean maximum wave height (Fig. 4), the following approach is used to find the
conditional probability for a particular value of the peak spectral period, given the
mean maximum wave height. If a particular mean maximum wave height occurs in
the Delta, mHmax, delta, it means that the mean maximum wave heights in the storm are
at least as large as those in the Delta, or mHmax, anywhere ≥ mHmax, delta. In order to account
for the effects of wave height, “deep water” is used as a convenient reference point
in comparing different locations. The probability that mHmax, anywhere ≥ mHmax, delta can be
calculated from the distribution shown in Fig. 6. Likewise, the probability that the
largest mean maximum wave heights in the storm, i.e., the waves near the eye or
mHmax, eye, can be calculated as follows:
) (
P (μ
=
(
P μ Hmax,eye μ Hmax,delta = P μ Hmax,eye μ Hmax,anywhere ≥ μ Hmax,delta
H max,anywhere
> μ Hmax,delta μ Hmax,eye
(
)
) P (μ )
P μ Hmax,anywhere ≥ μ Hmax,delta
)
H max,eye
(7)
The relationship between the peak spectral period and the mean maximum wave
height near the eye (the “average” curve in Fig. 4) then provides the means to relate
the peak spectral period to the mean maximum wave height in the Delta:
(
(
P Tp = g μ Hmax,eye
)μ
H max,delta
) = P (μ
H max,eye
μ Hmax,delta
)
(8)
where Tp = g(mHmax, eye) is the “average” curve in Fig. 4. An example of the conditional probability distribution for the peak spectral period given the mean maximum wave height (in deep water) is shown in Fig. 5. Note that when there are large
waves in the Delta, it is most likely that the eye is near the Delta (the smallest
possible value for the peak spectral period in Fig. 5); however, it is also possible
that the eye was not in the Delta and the peak spectral period for the waves in the
Delta will be greater.
The correction factor in Eq. 2, I3D, accounts for the reduction in the maximum
bottom pressure due to the three-dimensional shape of the largest wave. The variability
in the pressure ratio is modeled using a simple probability distribution based on data
gathered from a selection of directional spectra from hindcasts of Hurricanes Ivan
and Katrina (OTRC 2008). The mean pressure ratio of 0.66 is assigned a probability
of 0.5, the mean plus and minus one standard deviation (0.72 and 0.60, respectively)
are each assigned probabilities of 0.25, and the probability distribution for I3D is independent of the mean maximum wave height of the peak spectral period.
The approach to establish the joint probability for the bottom pressure characteristics, P(mHmax, Tp, I3D) in Eq. 6, is depicted with the event tree shown on Fig. 6.
Risk Analysis for Hurricane-Wave Induced Submarine Mudslides
343
0.6
Given that the mean maximum wave
height is between 84 feet (h50) and 90
feet (h100) in deepwater in the Delta.
0.5
0.5
Probability
0.4
0.3
0.25
0.2
0.2
0.1
0
0
0.025
0
13.6
14.7
15.3
15.6
16.5
17.2
Peak Spectral Period (s)
0.02
0.005
17.8
18.2
Fig. 5 Conditional probability distribution for peak spectral period given that the mean maximum
wave height is between 84 and 90 feet in deep water in the Delta, or between the 50-year and
100-year return period values for any water depth in the Delta (taken from OTRC 2009)
Mean Maximum Wave
Peak Spectral Period,
Tp,for a Given μH m a x
Height, μH m a x, for a
Given Water Depth
(
p mH
max
)
(
P Tp m H
max
)
(h 10 +h 25 )/2 (.0 6)
…
13.6 s (0.0)
(h 25 +h 50 )/2 (.0 2)
…
14.7 s (0.0)
(h 50 +h 100 )/2 (.01)
…
(h 100 + h 200 )/2 (.005)
(h 200 + h 1000 )/2 (.00 4)
15.3 s (0.0)
15.6 s (0.5)
(
P I m
3D H
(h 1000 + h 2000 )/2 (.00 05) …
17.2 s (0.05)
max
)
,Tp = P (I3D
)
(
P m H max, T p , I 3D
0.72 (0 .25)
…
16.5 s (0.4)
…
Information to Establish
Magnitude and Shape
Maximum Bottom
Pressure
Bottom Pressure 3-D
Correction Factor, I3D
…
(
)
) ( )
= P(I 3D )P Tp m H max P mH max
0.66 (0 .5)
…
0.60 (0 .25)
…
= 0.25 ´ 0.5 ´ 0.005
17.8 s (0.04)
18.2 s (0.01)
(h 2000 + h 10000 )/2 (.00 04) …
h 10000 (.0 000 1)
…
Fig. 6 Event tree representing the hazard for wave-induced mudslides (taken from OTRC 2008)
Each branch in the tree represents a possible value for a parameter describing the
magnitude and shape of the wave-induced bottom pressures, and the number in
parentheses is the probability of that particular value occurring. The first set of
branches in Fig. 6 characterizes the magnitude of the sea state in terms of the mean
maximum wave height in a 3-hour period. The probabilities for these values correspond
to the probability of that mean maximum wave height occurring annually, and they
344
M.C. Nodine et al.
depend on the water depth. The next set of branches in Fig. 6 characterizes the wave
period associated with the mean maximum wave height, which depends on the wave
height at the eye of the storm and can be determined using Eq. 8. The final set of
branches characterizes the correction factor to account for the three-dimensional
shape of the maximum wave.
3.2
Consequence of a Mudslide
Assessing the risk associated with mudslides includes considering the potential
consequence or damage caused by a mudslide as well as the probability that a mudslide
will occur. The approach described above to predict the occurrence of mudslides
also provides valuable insight into the potential consequences.
The geometry of a mudslide is expected to be closely related to the geometry of
the ocean waves. The depth of disturbance is approximately 5% to 10% of the wave
length, or 50 to 100 feet below the mudline. The areal extent of disturbance from a
single wave is about the same as the length and width of the wave, or about a thousand
feet long by hundreds of feet across. The total area of disturbance may be a bit
larger due to multiple failures caused by a sustained wave passing over. Lastly, even
considering the remolded shear strength of the weak clays in the Delta, the flat sea
floor is stable without significant wave loading, meaning that the disturbed soil
does not spread beyond the area disturbed by the wave. To illustrate the expected
geometry of mudslides, waves were simulated (Zhang et al. 1999) based on the
hindcast information from Hurricane Katrina at South Pass Lease Block 70. A representative profile of undrained shear strength was used and assumed to be the same
throughout the entire block. The resulting pattern of mudslides in this simulation,
represented by the locations for which the largest bottom pressure was sufficient to
cause a factor of safety less than 1.0, is shown in Fig. 7a. The pattern of disturbance
mimics the geometry of the largest waves, and it resembles post-hurricane surveys
of actual mudslide features in the Delta (Fig. 7b). Figures 7a, b represent different
locations but the sizes and shapes of the simulated and sonar-detected disturbances
are similar. In summary, mudslides tend to be rather localized features and the total
areal extent of disturbance on the sea floor is primarily related to the length of time
over which waves large enough to cause mudslides are present.
While mudslides are localized features, they are large and deep enough to
damage pipelines and platforms if these are located within the volume of disturbance. The main concern with a pipeline is that the movement will lead to excessive
longitudinal forces (tension and/or bending) that rupture the pipeline. A mudslide
can also bury a pipeline below tens of feet of soil, making it difficult to locate and
maintain. A mudslide can even push a pipeline far enough off of its route that regulatory issues arise. With platforms, the lateral forces imposed by the rotation of
the mudslide can cause a failure of the platform legs/piles, leading to a structural
collapse. Conversely, both pipelines and platforms will not necessarily be damaged
Risk Analysis for Hurricane-Wave Induced Submarine Mudslides
345
Fig. 7 (a) Simulated pattern of mudslide during Katrina (taken from Nodine et al. 2007) and (b)
side-scan sonar images of mudslides in Delta after Ivan (adapted from Thomson et al. 2005).
by a mudslide. Pipelines in particular can span over disturbed areas and tolerate
movements without rupturing (e.g., Thomson et al. 2005). In addition, hurricanes
can damage pipelines and platforms in the Delta without mudslides occurring;
bottom currents can move pipelines large distances off alignment and waves and
winds can damage platforms.
346
4
M.C. Nodine et al.
Examples
The following examples illustrate several applications for the practical risk model
described above.
4.1
Siting a New Platform
Consider the proposed location for a new platform. The annual probability that a
mudslide will occur at a particular location in the Delta is shown in Fig. 8; the
annual probability is depicted as a return period, where the return period is equal to
inverse of the annual probability. This figure does not include site-specific geotechnical data and reflects the range of possible profiles of undrained shear strength
with depth based on a sample of borings located throughout the Delta. The differences in return period across the Delta in this regional perspective (Fig. 8) indicate
differences in water depth and bottom slope.
A location in Fig. 8 corresponds to an area affected by a single large storm wave,
on the order of several thousand feet across and taken here as 4,000 by 4,000 feet
in plan. Since a platform facility is comparable in size to the area impacted by
a single wave, the probability shown in Fig. 8 is comparable to the probability that a
mudslide will intersect the platform itself.
Fig. 8 Return periods of a mudslide occurring at a 4,000- by 4,000-ft location (taken from OTRC
2009; base map from Coleman et al. 1982)
Risk Analysis for Hurricane-Wave Induced Submarine Mudslides
347
For the specific location under consideration, the return period is 200 years (i.e.,
it is in the region with a return period between 100 and 1,000 years in Fig. 8) and
the annual probability of a mudslide is 0.005. Over the 30-year design life for this
facility, the probability of having at least one mudslide is 1 − e−30/200 = 0.14. If we
assume that the $30,000,000 facility is destroyed in a mudslide, then the expected
damage is about $4,000,000 over the lifetime of the facility.
This expected cost of a mudslide can then be compared against available options
for reducing the risk. For example, we could design the facility to be able to withstand the forces from a mudslide. If it is possible to accomplish this design for less
than $4,000,000, then it would be worthwhile to pursue. We could also abandon the
site and not build a platform. If the loss in potential revenue from not producing oil
here is less than $4,000,000, then this alternative would be worthwhile.
4.2
Value of Site-Specific Soil Boring
Let’s say it will cost $10,000,000 to strengthen the platform to withstand the forces
of a mudslide. Since the expected cost of damage over the lifetime is less
($4,000,000), it would not be worthwhile to spend that much to reduce the risk.
However, the sample of regional borings used to produce Fig. 8 includes a wide
range of profiles of undrained shear strength versus depth because the soils in the
Delta are highly variable. It may be valuable to first get site-specific geotechnical
data before deciding whether to strengthen the platform.
Each profile of undrained shear strength versus depth considered produces a
different probability that a mudslide will occur at this location over the 30-year
design life. If a site-specific boring is drilled and the calculated probability that a
mudslide will occur is greater than 1/3 (the $10,000,000 cost to strengthen the
platform divided by the $30,000,000 cost of failure), then the option of strengthening
the platform is worthwhile because it will cost less than the expected cost of damage. Based on the sample of regional borings, there is a 20% chance that a sitespecific boring will lead to strengthening the platform. In addition, we can reduce
the total expected cost (of either damage or strengthening the platform) from the
expected damage of $4,000,000 if we do not obtain a site-specific boring and
choose not to strengthen the platform to $3,000,000 if we decide whether or not to
strengthen the platform based on a site-specific boring. Therefore, the value of a
site-specific boring is $4,000,000–$3,000,000 = $1,000,000, and it would be worthwhile to obtain a site-specific boring if it will cost less than $1,000,000.
4.3
Existing Pipeline System Risk
One of the challenges associated with the distributed pipeline and platform systems
located at present in the Delta is that a single mudslide can damage the entire system.
For example, a pipeline carrying oil from production in deep water that traverses
348
M.C. Nodine et al.
the Delta can shut down a significant portion of the production from the Gulf of
Mexico if it is ruptured. In order to assess the probability of a mudslide occurring
over a larger area than the “points” considered in Fig. 8, the following assumptions
are made about how variables are related spatially:
1. The size of the storm (mean maximum wave height) and the period of the maximum
wave (relative to the wave height) are assumed to be perfectly correlated among locations with the same depth, as a storm that affects one location will similarly affect
other nearby locations and the relationship between wave height and period tends to
remain similar throughout an individual hurricane based on the hindcast data.
2. The variation in Hmax within a given sea state and the bottom-pressure correction
factor are assumed to be statistically independent between 4,000-foot by 4,000foot locations in order to realistically model the variability in maximum wave
heights and bottom pressures at nearby locations in the same storm.
3. The profile of undrained shear strength versus depth is also assumed to be statistically independent among 4,000-foot by 4,000-foot locations. This assumption
is based on the observation that soil properties vary over relatively short distances
(on the order of 1,000 feet or less) in the Delta.
With these assumptions, the variables that are statistically independent between
points in assessing the probability of a mudslide (Eq. 6) are first separated from
those that are perfectly correlated between points:
(
P Mudslide μ Hmax , Tp
⎡
) = ∑ ⎢⎣⎢ ∑( )P (Mudslide s (z), μ
i
u
all I3D
H max
all su z
⎤
, Tp , I 3D P (su (z ))⎥
⎦⎥
)
P (I 3D )
(9)
where P(Mudslide|mHmax, Tp)i is the probability of a mudslide occurring at a particular
point i with a given water depth and bottom slope. Then, the probability of at least one
occurrence of a mudslide over an area comprising n statistically independent locations:
(
)
n
(
)
P At Least One Mudslide in n points μ Hmax ,Tp = 1 - ∏ ⎡1 - P Mudslide μ Hmax ,Tp ⎤
⎣
⎦
i=1
(10)
Finally, the annual probability of at least one mudslide occurring over the total area
is obtained by summing the probabilities given a sea state over all of the possible
sea states:
P (At Least One Mudslide in n points) =
∑
all μ Hmax ,Tp
(
)(
P At Least One Mudslide in n points μ Hmax , Tp P μ Hmax , Tp
)
(11)
The map in Fig. 9 illustrates the risk of pipeline damage throughout the Mississippi
Delta region using this approach. Pipelines reported by the Minerals Management
Service as of 2006 are shown in the figure. The annual probability that a mudslide
will impact a pipeline is calculated in each of 70 sub-regions (each containing about
20 4,000-foot by 4,000-foot points). This probability is calculated by determining
Risk Analysis for Hurricane-Wave Induced Submarine Mudslides
349
Fig. 9 Return periods for mudslides impacting existing pipelines (taken from OTRC 2009; base
map from Coleman et al. 1982)
in each sub-region the number of 4,000-foot by 4,000-foot areas out of the total of
20 that contain pipelines. For example, if 50% of a sub-region is covered with
pipelines, then there are 10 of 20 possible areas where a mudslide could impact a
pipeline. Return periods of at least one mudslide impacting a pipeline in each
sub-region are represented by symbols of various sizes, with larger return periods
corresponding to larger symbols. A hollow symbol indicates that there are no pipelines
in a region, and therefore a mudslide would not cause any damage to infrastructure.
The map in Fig. 9 provides useful information for planning purposes. It shows
where the probability of a pipeline failure due to mudslides is the greatest, either
because there are a large number of pipelines or the probability of a mudslide is
high. It shows that the annual probability of mudslides impacting pipelines is high;
the return period is less than 30 years throughout much of the Delta.
5
Conclusions
A practical method is proposed for assessing the probability and risk of wave-induced
mudslides in the Mississippi Delta. The method has been calibrated to the extent possible using historical information. It is transparent and can readily include either
generic or site-specific information about soil properties and wave characteristics.
350
M.C. Nodine et al.
The following conclusions were reached in developing and applying this method:
• Return periods for mudslides vary significantly across the Delta, with values less
than 30 years in the shallowest water and values greater than 1,000 years in the
deepest water. Three major storms, Camille, Ivan, and Katrina, have caused
significant and widespread mudslide activity in the past 40 years.
• The risk for mudslide damage increases as the water depth decreases, the slope
of the bottom increases, and the amount of infrastructure in a particular area
increases.
• Wave period, in addition to wave height, is an important factor in mudslide
vulnerability. Waves in Hurricanes Ivan and Katrina had longer-than-average
periods, and Hurricane Ivan, in particular, caused significantly more mudslide
activity than other storms of its magnitude due to its very long wave periods in
the Delta.
• Mudslide vulnerability is highest in shallow water and in areas with low shear
strengths. Areas of the Delta that have these characteristics have generally experienced mudslides in large hurricanes in the past, and it is likely that these areas
will experience more mudslide activity in future storms.
• Slope angle is not a significant factor in mudslide vulnerability except in the deeper
parts of the mudslide prone area (water depths greater than about 300 feet).
• Mudslides are localized features, on the order of several thousand feet in lateral
extent and about 50 to 150 feet deep. The areal extent and depth of mudslides
are related to the lengths and widths of the storm waves that cause them.
Mudslides are not likely to lead to large-scale, regional mudflows due to the very
flat slopes in the mudslide prone area and the large amount of local variation in
soil shear strength.
Acknowledgments The Minerals Management Service provided financial support for this project
through the Offshore Technology Research Center. We also appreciate the MMS’s assistance in
providing pipeline damage information and the hurricane hindcast data used in this study. We wish
to acknowledge Prof. Jun Zhang of Texas A&M University for helping with the simulation of
wave-induced bottom pressures. We also thank representatives from BP, Shell and Exxon, J.P.
Walsh from East Carolina University and Christopher Hitchcock from William Lettis & Associates
for providing data and sharing their knowledge on the topic.
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