Slope Stability Assessment of the Helland Hansen Area Offshore

Marine Geology 213 (2004) 457 480 www.elsevier.com/locate/margeo

Slope stability assessment of the Helland Hansen area offshore the mid-Norwegian marginD. Leynauda,*, J. Mienerta, F. Nadimbb a Department of Geology, University of Troms, NO-9037 Troms, Norway International Centre for Geohazards/Norwegian Geotechnical Institute, NO-0806, Oslo, Norway

Accepted 30 September 2004

Abstract Numerous large-scale submarine slides affected the continental slope offshore mid-Norway during the Holocene. One of them, the Storegga slide, is located south of the Vbring Plateau, stretching from the North Sea Fan to the Helland Hansen arch. With a volume of 3200 km3 and an influenced area of 95,000 km2, the Storegga slide, which occurred about 8250 years before present (BP), represents one of the largest submarine slides worldwide. The slope stability assessment concentrates on the northern sidewall (Helland Hansen area) where gas hydrates are suspected from the presence of a bottom-simulating reflector (BSR) on reflection seismic data and where few slope stability investigations have been performed compared to the Ormen Lange area. The limit equilibrium and finite element methods (FEM) were used for the evaluation of static and dynamic (seismic) stabilities of the dipping seabed. To account for the uncertainties in the soil parameters, a probabilistic approach was applied by coupling the limit equilibrium model with the first- and second-order reliability methods (FORM and SORM) and the Monte Carlo simulation. The finite element simulation for the seismic loading indicates that a strong earthquake (N6.5 Ms) could be a potential trigger for slope failure but only down to 30 m subsurface. Obviously, one needs a significant pore pressure build-up and loosening of the sediments to explain the slide on such gentle slopes. More critical preconditions to failure in the deeper sediments should exist to explain the thickness of the sliding slab, knowing that the northern sidewall is approximately 150 m high. Cyclic loading due to a series of earthquakes could explain the slide, affecting the shearing resistance in a marine clay unit (weak layer) by excess pore pressure generation (drained conditions). The degradation of undrained shear strength with cyclic loading plays a major role in the instability process. D 2004 Elsevier B.V. All rights reserved.Keywords: Storegga slide; risk assessment; slope failure; limit equilibrium; finite element; first- and second-order reliability methods

1. Introduction* Corresponding author. Tel.: +33 298 22 42 57; fax: +33 298 22 45 70. E-mail addresses: [email protected], [email protected] (D. Leynaud). 0025-3227/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.margeo.2004.10.019

Submarine landslides are frequent both on passive and active continental margins, especially on the continental slope (e.g., Mienert et al., 2002). This is

458 D. Leynaud et al. / Marine Geology 213 (2004) 457480 Fig. 1. (a) Location of the Storegga slide offshore Norway (Stor). Tr&nadjupet and Bjbrnbyrenna slides areas are shown (grey areas). (b) Location of boreholes 6405/2, 6404/5, long sample MD99-2288, and seismic line NH9651-202 on the enlargement.

D. Leynaud et al. / Marine Geology 213 (2004) 457480

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the steeper part of the margin, where the effects of gravity on the downslope sediments are increased. Rapid deposition of sediment can often play a destabilizing role in this area. Cyclic loading from earthquakes or waves, gas hydrate dissociation, and excess pore pressure generation are among the most obvious triggers of submarine failures. Inasmuch as many parameters are involved in causing seabed instability, not all failure mechanisms are fully understood. The probabilistic approach is thus applied to observe the effect of uncertainty of each parameter on the likelihood of failure and the failure probability during a specific time period. As the modelling uses some simplifications, the aim is also to verify the quality of the results (safety factor and failure probability) to ensure the reliability of the different approaches and the similarity of the final estimates.

2. Storegga slide area: geological and geotechnical settings The Storegga slide complex is located to the south of the Vbring Plateau (Fig. 1). The slide occurred during a multiphase event approximately 8250 years ago (Haflidason et al., 2001). The headwall is 290 km long and is located at a water depth of 200300 m (Haflidason et al., 2003). The calculated slope angle inside the failed area, southwest of the working area, is between 1.178 and 1.328 (0.558 to 1.148 eastward) (Haflidason et al., 2003). The location of the two major Holocene slides (Storegga and Tr&nadjupet slides) on the mid-Norwegian margin suggests a relation with the deeper structures and processes on

the margin (Berndt et al., 2001). Topographic difference defining the Vbring high (inferred to play a stabilizing role on the margin) have been increased by differential subsidence and uplift of the margin (Bryn et al., 2002). The slides are defined as translational from the slip planes and the thickness of removed sediment (compared to the lateral extension). The slip planes (corresponding to the seismic horizons TNS, TNR, and INO3) correspond to marine clay units (Bryn et al., 2002). Excess pore pressure within the marine clays due to rapid loading of glacial deposits is considered as one of the main destabilization factors, reducing the effective strength of the sediments (Bryn et al., 2003). The geotechnical parameters come from borehole 6404/5-GB1 (966 m water depth), 6405/ 2 (532 m water depth), and long piston corer sample MD99-2288 southwest of Helland Hansen (NGI, 1998 and 2000) (Fig. 1). Six soil units (from very soft to very hard clays) were defined from borehole 6404/5 down to a maximum depth of 309 m (Table 1).

3. Methodology 3.1. Basic concepts 3.1.1. Soil shear strength A soil element below the seafloor is subjected to a total stress that depends on the weight of the water above the element, the weight of the solid (sediment) particles up to the seafloor, and possible existing excess pore pressure. The effective stress affecting the sediment matrix corresponds to the total stress minus

Table 1 Summary of soil conditions and the basic recommended soil parameters for borehole 6404/5-GB1/1A. EOB is 309 m below seabed Unit 1 2 3 4 5 6 Depth (m) 030 3065 65123 123152 152270 270EOB Clay Very soft to soft Medium to stiff Very stiff Very stiff to hard Hard becoming very hard Hard Clay content (%) 42 43 41 35 43 34 c tot (kN/m3) 16.0 17.8 18.3 17.4 18.9 17.6 w (%) 71.0 43.4 38.5 47.2 33.3 43.0 St 3.9 2.4 3.3 3.1 4.6 4.6 Ip (%) 35.7 27.4 26.4 29.0 28.3 32.0 OCR 1.71.2 1.2 1.2 1.2 1.2 1.2 s DSS u (kPa) 380 80130 130260 260325 325580 580700

c tot, g, total unit weight; w, water content; S t , sensitivity; Ip, plasticity index; OCR, over consolidation ratio; s DSS, undrained shear strength u (direct simple shear).

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the effect of water pressure (Terzaghi and Peck, 1967). In absence of excess pore pressure, one can use the effective (submerged) unit weight of the soil (total unit weight minus the unit weight of water) to evaluate effective stresses. The shear strength of the sediments typically follows the MohrCoulomb model where the shearing resistance s per unit of area is related to the effective normal stress acting on the soil at a specific depth as in the following equation: s cV rn uV Vtan 1Fig. 2. Infinite slope analysis (adapted from Nash, 1987).

where cV is the cohesion of the soil, rV is the effective n normal stress, and uV is the internal friction angle. For the undrained case (present study, uV=0 ), the equation becomes s su constant 2

Inasmuch as the slope is considered infinite, interslice forces are parallel to the slope and cancel each other out ( Q L=Q R) so one gets: P W cosb rl so W r cos2 b r vertical stress b T W sinb sl so W s sinbcosb s mobilized shear stress b

where s u is the undrained shear strength. Undrained loading conditions mean that the loading process is (relatively) rapid enough so that excess pore pressure does not have time to dissipate through the porous medium. 3.1.2. Slope stability evaluation by limit equilibrium method In the limit equilibrium method, one analyses the forces (or stresses) acting on an assumed failure surface (plane, circular, concave, log-spiral, etc. . .). Failure occurs when the mobilized shear strength required for equilibrium exceeds the maximum shear strength available. The factor of safety (FOS) is defined as P P resisting forces resisting moments F P % P loading forces loading moments available shear strength 3 mobilized shear strength The simplest case occurs when a slab of soil is assumed to slide on a plane parallel to the ground surface (Fig. 2; infinite slope analysis). This approach is appropriate to model the Storegga slide using a back-analysis (translational slide from the observed slip planes).

4

5

where W is the slice weight (W=czb), c is the total unit weight of the soil, and cV is the effective unit weight of the soil. As the undrained case is considered (u=0), the failure criterion becomes s=s u. As mentioned earlier, the factor of safety F is defined as the shear strength divided by the mobilized shear stress, i.e., (Nash, 1987) s su 6 F s cVzsinbcosb By including a uniform horizontal seismic acceleration one gets su F 7 cVzsinbcosb KX czcos2 b where K X is the maximum horizontal component of seismic acceleration in g (0.1 means 10% of g). For concave failure surfaces, the soil volume above the assumed slip surface is divided into vertical slices. Consequently, one considers the equilibrium of forces


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applied to each slice to estimate the stability along the failure surface (method of slices) (Nash, 1987). 3.1.3. Finite element method (FEM) The concept of the FEM is to model an object with simple blocks or small elements. The physical behaviour is modelled for the elements defining the structure, and the connection between the elements approximates the behaviour of the soil continuum. Hence, strains and stresses can thus be estimated at any location. This procedure has been widely used for modelling strongly nonlinear geotechnical problems by using the elasto-plastic analyses (Griffiths and Lane, 1999). 3.2. Pseudostatic and dynamic undrained slope stability 3.2.1. Pseudostatic approach The evaluation of slope stability under earthquake loading is commonly based on pseudostatic analyses. In the latter, the inertial force caused by ground acceleration is applied as an effective static load equal to the mass of soil times the peak or the effective acceleration. The pseudostatic analyses provide the factor of safety against slope instability as a function of the peak earthquake acceleration. The ground acceleration giving a FOS of unity in the pseudostatic analysis is called the cut-off acceleration. It is not physically possible to transmit accelerations higher than the cut off value to the soil mass because the shear strength is fully mobilized along a slip surface. If the slope is subjected to an earthquake with peak acceleration higher than the cut-off value, permanent deformations along the slip surface will take place. Newmark (1965) pointed out that a pseudostatic FOS having less than unity during the maximum-earthquake-induced load does not necessarily indicate a slope failure with large movement of soil masses. The maximum earthquake loads only last a fraction of a second, and, as long as the soil does not completely lose its shear strength, the consequence of full mobilization of soil shear strength along a slip surface is a limited permanent deformation. Newmark (1965) presented the sliding block model for computing the seismically induced permanent displacements in dams, embankments, and slopes. For these geotechnical structures, the earthquake-induced sliding

occurs only in one direction, and the permanent displacements accumulate during an earthquake in a stepwise fashion. The seismic performance of the geotechnical structure under consideration is deemed acceptable if the earthquake-induced permanent deformation is less than the cut-off value to the soil mass. For a clay-rich submarine slope, the pseudostatic FOS is believed not to be a good measure of the seismic performance of the slope during an earthquake event. However, some key questions regarding the stability of a clayey slope under a strong earthquake are the following: ! Will the soil mass experience essentially elastic deformations during the earthquake, or will nonreversible plastic deformations occur? If plastic deformations do occur, how large will be the permanent displacements? Will the earthquake loading trigger creep of the slope sediments, leading to large shear displacements after the earthquake? Will the soil keep its shear strength after being exposed to the high cyclic shear stresses induced by the earthquake, or will it completely loose its strength and develop into a slide? The latter situation would be the case if, for example, liquefaction takes place.

!

!

3.2.2. Earthquake-induced shear stress A simplified procedure for estimating the earthquake-induced stresses has been proposed by Seed and Idriss (1971). The maximum shear stress on a soil element (deformable body behaviour) subjected to a ground surface acceleration a max is, smax;def ch amax rd g 8

in which c is the unit weight of the soil, h is the depth of the base of the soil column, and r d is a stress reduction coefficient with a value less than 1 (Fig. 3). 3.2.3. Dynamic approach with finite elements In the dynamic approach, the seismic-accelerationinduced shear stress (total stress approach) is modelled through the FEM using a representative accelerogram (horizontal acceleration vs. time) normalized

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Fig. 3. Determination of maximum shear stress (from Seed and Idriss, 1971).

to the peak ground acceleration (PGA) value expected in the area for a specific return period (475- or 10,000year return period in our case; ENV, 1998-1-1) to get an event providing the expected seismic accelerations (PGA). The earthquake records used to model the seismic loading in the study area is the Friuli Tarcento earthquake (Ms=6.2, PGA=0.08 g) with a duration of 10 s (sampling=0.02 s) and the El Centro earthquake (Ms=7.2, PGA=0.35 g) with a duration of 10 s (sampling=0.02 s). 3.2.4. Selection of a max The peak ground acceleration (PGA) represents the maximum acceleration experienced by a small particle of the soil during the course of the earthquake motion. A common way is to consider a pseudostatic acceleration related to the PGA. As seen previously, the use of PGA (lasting a fraction of second) overestimates the lower average effective acceleration acting on the soil during a longer period and leads to conservative results. Hynes-Griffin et al. (1984) stated that using a seismic coefficient equal to one-half the PGA, deformations would be acceptably small for a FOS greater than 1.0 (for dams). So, one will use onehalf of PGA to represent the pseudostatic seismic acceleration. In the absence of a seismic event record (related to large-magnitude seismic events) providing PGA for each seismic area, PGA is commonly defined 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. This corresponds to a 475-year return period. For back-calculation, a 10,000-year return period was used. 3.3. Sediment-loosening potential To initiate the slide on a very gentle slope (18 slope angle for the Storegga slide case study), one has to consider a more or less complete loss of strength in the soil to move the soil mass. The failure (FOS lower than 1.0) is not sufficient to explain the slide on such regional scale and slope angle (gravity forces insignificant on 18 slope angle) if permanent deformation is not large enough. Different soil conditions could explain such liquefaction, providing a much easier way to remove the soil mass in the upper tens of meters of the sub-seabed. 3.3.1. Liquefaction of sand Liquefaction occurs in sand when the vertical effective stress is cancelled by the pore pressure in excess. In this case, the sediment has no internal shear strength, resulting in a liquid behaviour. Depending on clay content and liquid limit (Andrews and Martin, 2000), a high excess pore pressure (95%) could be expected in case a strong earthquake occurs. Subsequently, this could trigger some liquefaction. The


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FOS against liquefaction can then be estimated from the cyclic stress approach developed by Seed and Idriss (1971):FSL cyclic shear stress required to cause liquefaction equivalent cyclic shear stress induced by earthquake scyc;L CRRL scyc CSR

9

CRR and CSR are related to a representative number of cycles corresponding to the seismic event considered. 3.3.2. Extra sensitive clay Sensitivity is defined as the ratio of the peak shear strength to the residual strength of a material. In some circumstances, when the sensitivity of the clay is very high (sensitivity higher than 30), one can observe another type of liquefaction which corresponds to the complete destruction of the delicate particles packing.

3.3.3. Melting of gas hydrates The presence of gas-hydrate-bearing sediments in the study area is inferred from the observation of a well-defined bottom-simulating reflection (BSR) on seismic profiles (Stoll and Bryan, 1979) from the NE flank of the slide scar (Bugge, 1983; Mienert et al., 1998; Bunz and Mienert, 2004; Fig. 4). Dissociation of gas hydrates can increase the excess pore pressure of the gas phase up to a critical value (percent of vertical effective stress) and thus may trigger an isotropic loss of strength in the soil.

4. Description of the probabilistic approach Contrary to the deterministic approach which uses one single constant value (mean value in general) for each parameter describing the soil behaviour, the probabilistic approach considers their variability and define them using a mean and a standard deviation value.

Fig. 4. Seismic profile NH9651-202 with borehole 6404/5-GB1/1A and sidewall locations.

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4.1. Monte Carlo simulation The expected mean value and standard deviation of the performance function is estimated using a simulation method, often referred to as Monte Carlo or Stochastic simulation, the performance function defining the boundary between safe and unsafe (failure) domains. Random variable values are generated according to their probability distribution, and the performance function is calculated for each set generated. Considering numerous trials, typically several thousands, the expected mean value, standard deviation, and probability distribution of the performance function is derived from the calculated values (Fig. 5). 4.2. First- and second-order reliability methods The basic concepts of first- and second-order reliability methods (FORM and SORM, respectively) are transformation of arbitrary random uncertainty vectors into independent, standard normal vectors and approximation of the failure boundary in a certain point of this area. Let X represents a vector of random variables (such as soil properties, load effects, geometry parameters, and modelling uncertainty). A limit state function g(x) or performance function is defined such that g(X)z0 when the domain is stable and g(X)b0 when the domain has failed. This limit state function can be represented by a function defining the FOS less unity. The subroutines devel-

oped by Gollwitzer (1999) were used for the FORM and SORM approximation. The FORM approximation (Fig. 6) is done in two steps: (1) The vector of basic random variables X=(X 1,X 2) is transformed into a vector U=(U 1,U 2) of independent Gaussian variables with zero mean and unit standard deviation using Rosenblatts (1952) transformation. The (transformed) limit state function is linearised at the point of maximum probability density. This is the most likely bfailureQ point and is referred to as the bdesign point.Q The design point is found by optimisation techniques.

(2)

In the transformed space, the probability of failure P f is: ! n X Pf % P gU b0 P ai U i bb0 U bi1

10 where P(. . .) reads bthe probability that,Q ai is the direction cosine of random variable Ui (transform of X i), b is the distance between the origin, and the hyperplane g(U)=0, n is the number of basic random variables X, and U is the standard normal distribution function. The vector of the direction cosines of the random variables (ai) is called the vector of sensitivity factors, and the distance b is called the reliability index.

Fig. 5. Example of Monte Carlo simulation outputs.


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Fig. 6. Basic principles for FORM method for two random variables.

The square of the direction cosines or sensitivity factors (a2), which sum is equal to unity, quantifies in i a relative manner the contribution of the uncertainty in each random variable X i to the total uncertainty. The performance function for the slope stability was defined as: g eF Facceptable 11

where F is the computed safety factor, F acceptable is the acceptable minimum safety factor. Typically, for conventional static loading, F acceptable is unity. The random variable e is introduced to account for the modelling uncertainty. The expected value of e is 1.0 for an unbiased analysis method.

to the user to solve the interslice force indetermination. The general limit equilibrium method (Fredlund and Krahn, 1977) was used in our evaluation. Once the geometry is defined, one applies for each layer an average effective unit weight and undrained shear strength representative of the soil profile (static). As the earthquake acceleration affects the total soil mass (including water), one corrects the pseudostatic acceleration value to get a similar earthquake-induced effect according to the following relationship: corrected PSA average total unit weight PSA average effective unit weight 12

5. Softwares 5.1. Slope/W (limit equilibrium)

where PSA is the pseudostatic seismic acceleration. This is done to avoid computation problems related to the water mass. 5.2. Quake/W (Geo-slope, 2001)

Slope/W (Geo-slope, 2001) uses the limit equilibrium theory to compute the FOS of earth slopes. A large and complete set of methods of slices is available

This product is a geotechnical finite element software for the dynamic analysis of earth structures

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Table 2 Elastic (linear) parameters used for the dynamic approach (Quake/W) Depth (m) 020 2030 3040 4070 7090 90110 110140 140360 E modulus (kPa) 9000 15,000 33,000 56,000 91,000 126,000 165,000 290,000 Poissons ratio (v) 0.5

5.4. STRUREL (limit equilibrium methodtwo-wedge model) Reliability analyses were performed using the STRUREL software (Gollwitzer, 1999). This analysis is based on first- and second-order reliability methods (FORM and SORM). No graphic interface is provided, and thus one has to consider a specific model to define the FOS. A two-wedge slope stability model was developed to simulate a sliding block (wedge 2) with a collapsing mechanism (wedge 1) (Fig. 7). A closed-form solution for FOS can be obtained by considering the equilibrium of the two wedges and assuming the same safety factor F on all slip planes:Fmax max max S1 cosb a S2 sinb a S3 Pcosa W1 sinbcosb a W2 sina X1 cosbcosb a X2 Pcosa

Poissons ratio corresponding to constant volume (undrained conditions).

under earthquake loading and was used for our dynamic modelling. Total stresses computed with finite elements (static and dynamic) can be used in Slope/W to get a more accurate evaluation. Two-dimensional elements with a quadrangular mesh were used (4040 and 2060 m or more depending on the model. The deformation analysis of the soil subjected to earthquake shaking uses a Newmark-type procedure (Newmark, 1965). This implies that permanent movement of the sliding mass occurs during specific time period when the FOS falls below 1.0 (when the average acceleration becomes larger than the yield acceleration). We considered a linear elastic model (Table 2) with a Youngs modulus E U estimated from the following relationship (Duncan and Buchignani, 1976): EU am sDSS u 13

14max max max where S 1 , S 2 , and S 3 and are the maximum shear resistance along the sliding planes shown on Fig. 1, W 1 and W 2 are the submerged weights of wedge 1 and wedge 2, and P is the passive lateral resistance at the toe of the slope. X 1 and X 2 correspond to the forces (respectively on wedges 1 and 2) due to the seismic acceleration. The angles a and b are defined on Fig. 7. Recently, this model has been improved (Nadim et al., 2003). The first improvement concerns the geometry of the two-wedge model. In this new model, one considers the possibility to have one failure coming out within the slope (this corresponding to a negative a parameter, Fig. 7). The second one is

where a m=600 (NGI, 1998) (empirical parameter), and DSS s u is the undrained shear strength in direct simple shear. The Poissons ratio m is constant (m=0.5) considering undrained conditions (no volume change during loading). According to the variation of damping ratio of fine-grained soil with cyclic shear strain amplitude and plasticity index (Kramer, 1995), damping ratio has been fixed to 2%. 5.3. Sigma/W (Geo-slope, 2001) The Sigma/W software for finite element stress and deformation analysis was used to estimate the FOS using the shear strength reduction technique (Matsui and San, 1992).

Fig. 7. Modified two-wedge model used with STRUREL software (Nadim et al., 2003). L1, L2, Li, Ln: sediment layers with different mechanical properties.


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related to the undrained shear strength values, which are corrected for overconsolidation ratio (OCR) and effective vertical stress according to the Stress History and Normalized Soil Engineering Properties (SHANSEP) relationship. The latest improvement concerns the strength anisotropy which is taken into account C DSS through a global anisotropy factor j=S u /S u (defined for the entire soil profile). Thus, the following correction is applied to the s u values for computing the shear resistance: sub sDSS 1 j 1sin2b u 15

soil in the vicinity of the sidewall (Fig. 8 and Table 3). The northern sidewall slope angle is found to be around 58 from both the seismic profile and the highresolution bathymetric map (Fig. 9). The average preslide slope angle (for the back-analysis) was considered to be 18. 6.2. Undrained shear strengthSHANSEP model The Stress History and Normalized Soil Engineering Properties (SHANSEP) model, which includes the effects of overconsolidation and vertical effective stress, has been used in this work (Ladd and Foott, 1974). This approach allows defining more realistic s u values from overconsolidation ratio (OCR) and effective stress conditions. One can also estimate the s u reduction related to excess pore pressure generation. This model has been used with the limit equilibrium method (twowedge and circular failure models). The s u values have been reestimated near the sidewall, according to the SHANSEP approach. One define the undrained shear strength in each layer by the following SHANSEP-type equation: su ap0 DuOCRm V p0 Dp Du m V ap0 Du V p0 Du V

where b is the angle of the failure plane with the horizon. The program works in two steps. First, it looks for the critical geometry (criticals length a and angle b providing the lowest safety factor), and then (second step) it calculates the probability of failure around these values (with reliability index).

6. Input parameters for modelling 6.1. Soil geometry Using the NH9651_202 seismic profile (Figs. 1 and 4), several horizons have been defined to fit the layers reported in the borehole 6404-5/GB1. The geotechnical report (NGI, 1997) provides the main horizon locations in term of depth (m) and two-way time (ms). Assuming a laterally constant P wave velocity distribution in each layer, one can estimate the horizon location along the seismic line. Thus, one obtains a geometrical model for the

16

where s u is the reference undrained shear strength, pV 0 is the vertical effective stress assuming hydrostatic s conditions, a rVu NC = ratio of undrained shear ac strength to vertical effective stress for normally consolidated clay; OCR is the overconsolidation

Fig. 8. Interpreted horizons from seismic line NH9651-202.

468 Table 3 Summary of depths for seismic units Unit Depth (m) 015 1530 3048 4865 65123 123152 152170 170207 207234 234270 Period


Horizons

TWT (ms) 13111330 13301350 13501372 13721395 13951468 14681506 15061528 15281575 15751606 16061651

Estimated Vp (m/s) 1579 1500 1636 1478 1589 1526 1636 1574 1742 1600

Estimated depth at the sidewall (m) 0? ?16 1626 2633 3361 6177 7785 8593 ... ?134

Estimated s DSS u at the sidewall (kPa) 2.1? ?29 2946 4658 58122 122153 153171 171189 ... . . . 285

HH0 HH1 HH2 HH3 HH4 HH5 HH6 HH7 HH8 HH9

Holocene Middle Weichselian M.W. M.W. Eemian/E. Weichselian Late Saalian Saalian Saalian Saalian Saalian

SeabedBNA0 BNA0BNA1 BNA1BNA2 BNA2BNA3 BNA3BNA4 BNA4BNA5 BNA5BNA6 BNA6TNC1 TNC1TNC TNCBSR

Model estimated at the sidewall.

ratio=PV/( pV Du), pV is the maximum past consolc 0 c idation stress=pV +DpDu, Dp is the removed over0 burden stress=pVpV +Du, m is a dimensionless c 0 exponent (typically between 0.65 and 0.90), and Du is the excess pore pressure (assumed to be due to incomplete consolidation). The long sediment core MD99-2288 (NGI, 2000) located near the sidewall provides some undrained DSS shear strength in the direct simple shear mode (s u ) values ranging from 35 to 37 kPa at 1819 m depth (s u estimated around 3133 kPa from SHANSEP relationship using a=0.25; Table 3). This confirms a good

estimate for the undrained shear strength profile at the sidewall location concerning the first 20 m depth. DSS A comparison of SHANSEP modelling, s u C (direct simple shear) and s u (CAUC triaxal test) profiles is shown on Fig. 10. 6.3. Peak ground acceleration (PGA) in the Helland Hansen area PGA values considered for 475- and 10,000-year return periods in the Helland Hansen area are shown in Table 4. These correspond to the maximum value

Fig. 9. Slope angle around the seismic line area. SURFER software and high-resolution bathymetric data (200200 m; Norsk Hydro).


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Fig. 10. SHANSEP modelling compared to s DSS and s C values. u u

offshore Norway, with 90% probability of no exceedance (NORSAR, 1998). Fig. 11 shows the historical seismic activity on the Norwegian continental margin. Using the seismic activity parameters from NORSAR (1998) and a public software (SEISRISKIII, Bender and Perkins, 1987), we made a simplified seismic hazard map for the area in the vicinity of the Storegga slide area (Fig. 12) to get an outline of the PGA potential spatial distribution in this area. It follows that the maximum PGA value offshore Norway occurs in the vicinity of the Storegga slide headwall. 6.4. Earthquake records It is well known that the same value of peak ground acceleration (PGA) can be due to different combinations of magnitude and distance. In spite of the same PGA, the frequency content of the ground motion can be quite different because highmagnitude events contain more energy in low frequencies and have longer duration. Therefore,Table 4 Maximum peak ground acceleration with 90% probability of no exceedance for 475- and 10,000-year return period offshore Norway (NORSAR, 1998) 90% probability of no exceedance during (years) 50 1000 Return period (years) 475 (present-day) 10,000 (backcalculation) PGA ( g) 0.10 0.35 Pseudostatic acceleration ( g) 0.05 0.175

it is relevant to consider accelerograms corresponding to large- as well as medium-magnitude events in our study. 6.4.1. Friuli earthquake; May 6, 1976; Ms=6.5 The Friuli seismic event contains mainly high frequencies (periods lower than 0.5 second). The peak

Fig. 11. Historical seismic activity (for magnitudes above 4.4) on the Norwegian continental margin (from NORSAR, 1998) with outlines of the major slides. Largest seismic events in the vicinity of the Storegga slide: 1866, Ms=5.7 (Lat/Lon: 65.2/6.0); 1895, Ms=5.3 (65.0/6.0); 1913, Ms=5.0 (64.3/6.3); 1958, Ms=5.0 (65.2/6.5); 1969, Ms=5.0 (65.1/6.5); 1988, Ms=5.3 (63.68/2.44).

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Fig. 12. Simplified seismic hazard map in the vicinity of the Storegga slide area for a 10,000-year return period (PGA value with 90% probability of no exceedance during 1000 years). Ambraseys attenuation relationship (1995; 50th percentile curve). Seismic zonation from NORSAR. GMT software (Wessel and Smith, 1988). Grid smoothed using a Gauss filter/200 km.

ground acceleration (PGA) is 0.082 g, and a maximum spectral acceleration of 0.30 g is reached for 0.25 s (Fig. 13). 6.4.2. El Centro (Imperial Valley) earthquake; May 18, 1940; Ms=7.2 The El Centro seismic event contains low and high frequencies (periods between 0.25 and 1.0 s). The PGA is equal to 0.35 g, and a maximum spectral

acceleration of 0.80 g is reached for 0.25- and 0.6-s periods (Fig. 14). 6.4.3. Site effect (Friuli earthquake) Using AMPLE2000 software (Pestana and Nadim, 2000), one have estimated the 1-D seismic response of the site assuming a Friuli-type earthquake normalized to 0.1 g on the bedrock (Fig. 15). The isotropic linear elastic model has been used with the initial shear

Fig. 13. Acceleration time history (A) and spectral acceleration for the Ms 6.5 Friuli earthquake (damping=5%).


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Fig. 14. Acceleration time history (A) and spectral acceleration for the Ms 7.2 El Centro earthquake (damping=5%).

stiffness at small strains G max defined as follows (NGI, 1998): Gmax z 50 1620*z with Gmax shear force=unit area kPa and angular deformation z depthmeter 17

The dynamic approach has been performed using these seismic events to observe the effects of the magnitude (frequency content and spectral accelerations) on the shear stress and excess pore pressure generation.

7. Excess pore pressure generation The earthquake-induced excess pore pressure can play a major role in the decrease of shearing resistance and thus in the sliding mechanism. AMPLE2000 software (Pestana and Nadim, 2000) has been used to simulate the 1-D site soil response and excess pore pressure generation under seismic loading. The simple direct simple shear (DSS) model for lightly consolidated soils (Pestana and Biscontin, 2000) is considered to estimate the amount of excess pore pressure developing with cyclic loading. The simple DSS model parameters for the Helland Hansen area were provided within AMPLE2000 software package (failure ratio, b=0.35; slenderness parameter, m=0.5; large

Once the site effect of the submarine soil (accelerogram on soft soil equivalent seafloor) has been estimated (elastic behaviour), we use it as input seismic event in the finite element software (Quake/ W) to model a more realistic dynamic approach with an accelerogram which models the seismic response of the soft soil. It should be noted that soil response effects will filter out the high frequencies and reduce the seabed accelerations significantly with respect to the bedrock accelerations given in Table 4. Earlier site response studies performed for the Helland Hansen area indicate that this reduction could be a factor of two or more (NGI, 1997).

Fig. 15. Accelerogram and Spectral acceleration estimated at the seafloor level (red line) using an elastic model (AMPLE2000 software) compared to the accelerogram recorded on the bedrock (black line). Friuli earthquake, 1.5% damping.

472


Table 5 Earthquake-induced excess pore pressure ratio estimated using AMPLE2000 for 0.10 g PGA (475-year return period) and 0.35 g PGA (10,000-year return period) in percent of the initial vertical effective stress Depth PGA=0.10 g (slope angle: 58) PGA=0.35 g (slope angle: 18) 7.5 m 1.0% 9.2% 22.5 m 0.35% 5.2% 42.5 m 0.30% 4.2% 62.5 m 0.25% 3.5% 82.5 m 0.22% 3.2%

8. Slope stability assessment of the Helland Hansen area 8.1. Back-calculation of the slide 8.1.1. Infinite slope analysis The infinite slope analysis, with the layer thicknesses and the undrained shear strength profile estimated at the headwall, provides an FOS around 14.0 for the static case (Table 8), suggesting a very stable situation. Considering a 0.175-g pseudostatic seismic acceleration (half of the PGA value) and the nonlinear shear mass participation factor (Mwz6.8, 0.23bamax) from Seed et al. (2001), one gets a FOS related to the depth (Fig. 16). The FOS is above unity using the mean value of rd but remains lower than unity down to approximately 50 m depth, considering rd mean plus one standard deviation. It was used considering the uncertainty of the pseudostatic approach (using the half of the PGA). Furthermore, Makdisi and Seed (1978) proposed some displacements computed by Newmarks method as a function of the acceleration ratio ((k)/(a max)) (k, seismic coefficient reducing the safety factor to unity; a max, expected peak acceleration). For an acceleration ratio around 0.5 (k=0.175; PGA=0.35 g) and for a 7.5magnitude seismic event, the curves show that displacements are still acceptably small. One have to notice that these curves correspond to embankments with a height ranging from 15 to 75 m. Considering that the equivalent depth to bedrock is much higher in the

Ms 6.5 Friuli Tarcento earthquake (1.5% damping).

strain obliquity angle, W=28; backbone curve parameter, G p=10; h=25; k=30). Two earthquake records have been used to model the seismic loading: the Ms 6.5 Friuli earthquake (high-frequency content) and the Ms 7.1 El Centro earthquake (low frequency content). Excess pore pressure values, normalized with respect to the vertical effective stress, are shown in Tables 5 and 6. One observes a large difference for the excess pore pressure generation (Tables 5 and 6), depending on the frequency content of the seismic acceleration. It is noticed that the excess pore pressure generation is higher with a 0.1 g PGA low-frequency seismic event (Table 6) than with a 0.35 g PGA high-frequency event (Table 5). As the undrained shear strength remains constant with excess pore pressure generation (after complete consolidation), one has to consider the drained case to find out whether or not this latter is more critical than the former one (whether drained shear strength is lower than undrained shear strength). The excess pore pressure generation estimated with the El Centro earthquake (low frequencies) will be used in the present-day slope stability assessment to consider a low-frequency generation.

Table 6 Earthquake-induced excess pore pressure ratio estimated using AMPLE2000 for 0.10 g PGA (475-year return period) and 0.35 g PGA (10,000-year return period) in percent of the initial vertical effective stress Depth PGA=0.10 g (slope angle: 58) PGA=0.35 g (slope angle: 18) 7.5 m 12% 40% 22.5 m 8% 20% 42.5 m 5% 15% 62.5 m 3% 12% 82.5 m 3% 12% Fig. 16. Safety factor (infinite slope analysis) with 0.175-g pseudostatic acceleration depending on depth and shear stress reduction factor curves.

Ms 7.2 El Centro earthquake (5% damping).


473

Helland Hansen area, this approach underestimates displacements and thus overestimates the stability in our area (FOS). With the present values, the Makdisi and Seeds approach does not consider any large displacement in the shallow part of the seafloor. 8.1.2. Slope/WQuake/W softwares The finite element approach (Quake/W) for the dynamic loading provides a stress state in the soil with a 0.35 g PGA seismic acceleration generated by an ElCentro-type earthquake. Using a computed timevarying shear stress, Slope/W returns a critical dynamic FOS around 0.9 (down to 2030 m depth) (Table 8). However, permanent displacements calculated on the failure surface when the critical acceleration is reached (FOS lower than 1.0) remain small between 20 and 30 m depth. 8.1.3. Drained conditions As the earthquake-induced excess pore pressure generation affects drained shear strength, one needs to check the stability using the drained conditions to test the more critical case which could lead to failure. To do that, we use the following relationship: s c V rV tanuV n 18Fig. 17. Shear strength profiles vs. depth for drained (0%, 25%, and 50% excess pore pressure) and undrained conditions.

at 80% excess pore pressure). Thus, it is not possible to evaluate the safety factor against liquefaction (corresponding to 95% excess pore pressure) but only a safety factor against 80% excess pore pressure generation or failure. CSR 0:65 amax rvo rd g rV vo

where c is the cohesion of the soil (7 to 10 kPa; borehole 6405/2), r n is the effective normal stress, V and u is the internal friction angle (28 to 29.5 kPa, borehole 6405/2). Using c and / parameters (NGI, 2000), we find that the drained shear strength is still less critical than the undrained one (Fig. 17). It is estimated that an excess pore pressure generation exceeding 50% of the vertical effective stress is necessary to reach more critical conditions in the area compared to undrained case. Previous results show that excess pore pressure generation modelling remains below 50% even with the more critical seismic event considered (Tables 5 and 6). 8.1.4. Cyclic stress approach Using the cyclic DSS test performed on the borehole 6405/2-GB1 (Unit 2, 10.5 m depth), one gets a cyclic shear stress value for the failure; considering 10 cycles for the maximum seismic event (Ms=7.0), one observe that failure occurs for s cyc/ DSS s u =0.995 (failure occurring before any liquefaction

CSR=0.47 with a max=0.35 g at 10.5 m depth, 10 cycles, decrease to CSR=0.13 with a max=0.1 g, same depth and cycles number) at 10.5 m depth: s u=18 kPa, r vo =57 kPa V scyc CRRfield V 0:9CRRSS rvo CRRSS 0:31 so CRRfield 0:28 FS80% EPP FScyclic failure 0:6DSS Assuming the same cyclic ratio [(s cyc/s u )=0.995; 10.5 m depth] at a greater depth (similar clay content down to 270 m depth: 3443%), one shows that 80% excess pore pressure can be reached down to 30 m depth with a 0.35 g PGA acceleration and a 10-cycle seismic event (Ms 7.0 earthquake) (Fig. 18). The

CRRfield 0:28 0:47 CSR

474


Fig. 18. Safety factor against 80% excess pore pressure (and failure) vs. depth for different peak ground seismic accelerations (a max), assuming a constant cyclic behaviour of the soil for the first 100 m depth.

reduction factor proposed by Seed et al. (2001) has been used for this estimate, taking into account the magnitude, horizontal PGA, and shear wave velocity (mean value). Using a reduction factor corresponding to the mean value plus one standard deviation (M wz6.8, 0.23ba max) (Seed et al., 2001), the factor of safety against 80% excess pore pressure (or failure) remains below unity down to 80 m depth. In addition, a high sand content has been found at 20 m depth (borehole MD99-2288) with plasticity index Ip=20 and liquid limit WL=35, suggesting that the liquefaction potential could be much higher at this location and depth (Sultan et al., 2004a). 8.1.5. Sensitive clay No high sensitive clay has been observed in the boreholes 6404/5-GB1/1A [sensitivity=4.6 or lower; end of Boring (EOB) is 309 m below seabed] or 6405/ 2-GB1 (sensitivity=4.0 or lower; EOB is 124 m depth below seabed). However, here, an uncertainty in the spatial variability of the sensitivity has to be considered. 8.1.6. Gas hydrate dissociation Sultan et al. (2004b) proposed a model to explain some retrogressive failures from gas hydrates dissociation at the top of the gas hydrate stability zone

(GHSZ) related to the postglacial temperature, pressure, and gas solubility changes, with approximately a 30-kPa excess pore pressure generation (4% of the vertical effective stress) at 100 m depth below seafloor. Assuming that gas hydrates dissociation results in a reduction of the undrained shear strength corresponding to the drop from the peak to the residual strength values, the FOS could be obviously drastically reduced. Considering that the main hydrates dissociation took place between 80 and 120 m depth below seafloor (Fig. 19) and the sensitivity at this depth (sensitivity=4.6, borehole 6404/5; Tables 1 and 3), the shear strength should drop to a residual value which is around 44 kPa. The FOS is then estimated using the infinite slope analysis (Table 7), including the shear stress reduction factor with depth. As the uncertainty concerning the stress reduction factor is very large at such depth (100 m depth), one cannot efficiently propose any FOS with a high accuracy, although failure is very unlikely to occur. The limit equilibrium method (Slope/W) combined to the finite element stress model (using Quake/W software) computes only small permanent displace-

Fig. 19. Excess pore pressure generation estimated from gas hydrates dissociation. 10,000 years BP (from Sultan et al., 2004b).

D. Leynaud et al. / Marine Geology 213 (2004) 457480 Table 7 Factor of safety estimated using the infinite slope analysis (pseudostatic approach, 0.175 g) and the residual shear strength at 100 m depth (44 kPa) corresponding to gas hydrate dissociation for different values of the shear strength reduction factor with depth (100 m) Shear strength reduction factor (r d; 100 m depth) Factor of safety (pseudostatic acc=0.175 g slope angle: 18) 0 0.05 0.1

475

The two-wedge model (new geometry+OCR correction+strength anisotropy) gives a lower FOS (3.9) (Table 9); this corresponds to a more realistic modelling, particularly for the shear strength distribution in the soil around the sidewall (s u deduced from OCR distribution). 8.2.2. Pseudostatic and dynamic cases Using a 0.11-g corrected pseudostatic seismic acceleration (Eq. (12); PSA=0.05 g), the soil geometry (thicknesses), and the s u profile estimated at the sidewall, the limit equilibrium (Slope/W) provides a critical pseudostatic FOS around 1.9 (circular failure). The modified two-wedge model gives a lower FOS in the range 1.631.67 (a SHANSEP=0.25) and 1.371.4 (a SHANSEP=0.21) (Table 9). The FE dynamic modelling using Quake/W software (stress distribution with time) and different accelerograms (0.1 g PGA) combined to the limit equilibrium method (Slope/W software) gives some FOS ranging from 4.1 (Friuli-type earthquake) to 3.0 (El-Centro-type earthquake) (Table 10). The El-Centro-type seismic event remains the most critical one regarding the dynamic FOS. One have to notice that the critical failure surface does not correspond to the time of the PGA (2.1 s for the El Centro accelerogram) but later on (after 5.0 s for both cases). Figs. 21 and 22 show the most critical failure surfaces (with critical FOS) depending on the length of the failure surface (ElCentro-type earthquake, a SHANSEP=0.25). The twowedge model allows us to get a pseudostatic approach, including the reduction factor accounting for the shear stress reduction with depth, and gives a FOS around 2.26 (a SHANSEP=0.21) similar to the dynamic one (FOS=2.3, a SHANSEP=0.21) (Table 11). A summary of present-day FOS is shown on Fig. 23.

3.1

1.45

0.95

r d=0.05 means that equivalent acceleration for estimating induced shear stress at 100 m depth is 0.175 g 0.05=0.0875 g.

ments (1.0 E03 m) on a failure plane at 100 m depth with a 0.35 g PGA seismic acceleration (El-Centrotype earthquake) considering residual shear strength at 100 m depth from gas hydrate dissociation (s u reduced to 44 kPa). The previous modelling results are summarized in Table 8, and a sketch shows the results in Fig. 20. 8.2. Present-day slope stability The slope stability assessment is conducted for the north sidewall where the steepest slope observed on the seismic line NH9651-202 is around 58. The slope angle in the vicinity of the seismic profile has been checked on using a high-resolution bathymetric map (200200 m, Norsk Hydro; Fig. 9). The highest slope angle (around 58) observed for the sidewall (Fig. 9) confirms the value obtained from the seismic line (Fig. 4). 8.2.1. Static case The Geoslope products provide similar FOS: 4.7 using the limit equilibrium method (Slope/W) and 4.9 for the shear strength reduction method (Sigma/W).

Table 8 Factors of safety for 18 slope angle (horizontal component for earthquake loading) Case Static Pseudostatic (0.175 g PGA) Dynamic approach (0.35 g PGA) Cyclic stress approach (0.35 g PGA) Seed and Idriss (1971) Failure (FSb1.0) down to 30 m depth Gas hydrate dissociation (s u=44 kPa at 100 m depth) +0.175 g PGA Method/ software Factor of safety Infinite slope Higher than 10 Infinite slope Failure (FSb1.0) down to 50 m depth Slope/W+Quake/W Failure (FSb1.0) down to 30 m depth Infinite slope Failure very unlikely at 100 m depth +0.35 g PGA Slope/W+Quake/W No failure (FOSN1.0) at 100 m depth

476


Fig. 20. Maximum failure depth modelling for different approaches (failure but no large permanent deformation expected from finite element approach).

Using the Monte Carlo simulation (using Slope/W software) and FORM/SORM methods (STRUREL; two-wedge model) for the pseudostatic case, one gets some probability of failure for the present-day sidewall (Table 12). Table 13 shows failure probabilities (FORM/SORM with two-wedge model) using the most critical undrained shear strength profile (a SHANSEP=0.21).

9. Discussion For the back-analysis and considering the low slope angle, the sliding depends on the permanent deformation occurring on a failure surface. If the average acceleration is larger than the yield acceleration (leading to a FOS below 1.0) during few time steps, the cumulative permanent displacement would be insufficient to move the soil mass on the sliding

Table 9 Factors of safety for present-day profile Software Slope/W STRUREL Sigma/w (SSRM) 4.7 STRUREL (new geometry) 3.9 1.63

plane. This would be much easier with the present-day profile which exhibits a larger slope angle and consequently an increased downslope gravity component, resulting in a situation much more prone to sliding after the failure occurs. For both cases, the effect of strength degradation with cyclic loading (Cascone et al., 1998) was not considered. The degradation index which represents the ratio of the undrained shear strength after cyclic loading to the initial one prior to cyclic loading depends not only on the number of cycles but also the cyclic stress ratio, the type of soil (plasticity index Ip), and the overconsolidation ratio. The input acceleration below the critical one can trigger permanent deformation after few cycles because of the significant reduction in undrained shear strength. This illustrates that strength degradation, as expected, will affect the development of slope displacement. Zhou and Gong (2001) propose a model for strain degradation of saturated clay under cyclic loading with parameters such as OCR, cyclic stress ratio, and cycles frequency. They show that

Table 10 Factors of safety for present-day profile (dynamic approach) Earthquake type Dynamic FOS (Slope/W+ QUAKE/W) a SHANSEP=0.25. Friuli (0.1 g) 4.1 Friuli+Site Effect (0.2 g) 3.4 (6.8 s) El Centro (0.1 g) 3.0 (5.6 s)

Static FOS Pseudostatic (acc=0.05 a S=0.25) Pseudostatic (acc=0.05 a S=0.21)

FOS g FOS g

4.9 1.9

4.2 1.67

1.40

1.37


477

Fig. 21. Present-day slope stability assessment. Critical failure surface obtained with the dynamic approach (El Centro earthquake; 0.1 g PGA). FS=3.0 at 5.6 s. Vertical exageration=2:1.

low frequencies have a higher effect on degradation. Additionally, Vucetic and Dobry (1988) show that low plasticity clays are more prone to a higher degradation for a given cyclic strain. Kramer (1995) notes that cyclic strength of a cohesive soil element depends on the combination of average shear stress and cyclic shear stress, showing that monotonic strength at the end of an earthquake shaking is related to cyclic strain amplitudes. For more accurate slope stability evaluations in this area, investigations should focus on degradation of marine sediment with cyclic loading. Finally, using one cyclic DSS test, one could also explain a failure down to 30 m depth which is far from the 110 m height of the sidewall. Obviously, one needs to assume a failure process along with liquefaction (complete loss of strength in the sediment) to explain the mass movement on a gentle slope (18 slope angle). This is not in agreement with the nature of the soil (no extrasensitive clay and no liquefaction potential from cyclic DSS test for 0.35 g PGA), but a spatial variability has to be taken into account on a such slide scale. However, one needs some other factors to increase the thickness of the sliding sediments

(Hydrates, higher PGA, etc. . .). The site effect (time history acceleration on the seafloor or soft soil) could be high enough to initiate some failures at a greater depth. The highest expected PGA offshore the midNorwegian margin is in the vicinity of the Storegga slide area (0.35 g PGA) with one of the largest historical events (the 09.03.1866 Ms 5.7 Halten Terrace earthquake). This confirms a high potential of seismic activity in terms of large events (NORSAR, 1998). From the Ambraseys attenuation relationship (Ambraseys, 1995), one can expect higher PGA values in the vicinity of a magnitude Ms 7.0 seismic event (0.43 g PGA for a 10-km depth event).

10. Conclusions Back-calculation of the slide: (1) A high FOS (FOSN10.0; static case) shows that the continental slope (18 slope angle) is very stable if subjected only to gravity loading. The pseudostatic approach (0.175 g) using the infinite slope analysis explains a failure down to

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Fig. 22. Present-day slope stability assessment. Longest critical failure surface (fully specified) obtained with the dynamic approach (El Centro earthquake; 0.1 g PGA). FS=3.9 at 5.3 s. Vertical exaggeration=2:1.

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D. Leynaud et al. / Marine Geology 213 (2004) 457480 Table 12 Failure probabilities with FORM and SORM and Monte Carlo simulation methods Method FORM (SHANSEP) 418/a=0 1.2 E15 0.4% FORM/SORM (SHANSEP+ new geometry) b=188/a=337 m 3.2 E16 0.75% 1.4 E09% (FORM) 1.1 E09% (SORM) Monte Carlo

Table 11 Factors of safety for present-day profile (dynamic approach) Approach Softwares FOS a SHANSEP=0.21 a SHANSEP=0.21. Dynamic+El Centro (0.1 g PGA) Quake/W+Slope/W 2.30 (6.0 s) Pseudostatic (0.05 g)+(r d ) Two-wedge model (modified) 2.26

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50 m depth (FOSb1.0 between 0 and 50 m depth). The finite element stress distribution model a critical state at 30 m depth (failure) with a 0.35 g PGA seismic event, but with only small displacements (decimeter scale). The earthquake-induced shear stress could initiate some failures with large displacements (meter) in the first 20 m depth during the first 10 s of an ElCentro-type earthquake. Furthermore, the Storegga slide area is located exactly on the Eastern Jan Mayen Fractured Zone (EJMFZ). Including the effect of gas hydrate dissociation (Sultan et al., 2004b), a 30-kPa excess pore

Static Pseudostatic (0.05 g) Pseudostatic (0.05 g)+r d

0.23%

Present-day slope stability. a SHANSEP=0.25.

pressure generation (4% of the vertical effective stress) is not sufficient to destabilize the slope. One has to consider the residual shear strength value (assuming remoulding of sediment) to reduce drastically the initial static safety factor (static FOS=3.10 with ((s u)/(sensitivity)) at 100 m depth) and reach a critical FOS (FOS below 1.0) with 0.175 g pseudostatic acceleration (r d=0.1 to 100 m depth, infinite slope analysis). However, the uncertainty related to the shear

Fig. 23. Summary of safety factors vs. methods for present-day evaluation.

D. Leynaud et al. / Marine Geology 213 (2004) 457480 Table 13 Failure probabilities with FORM and SORM methods Method FORM/SORM (SHANSEP+new geometry) b=188/a=337 m 2.3 E07% (FORM) 1.8 E07% (SORM)

479

Pseudostatic (0.05 g)+r d

Present-day slope stability. a SHANSEP=0.21.

stress reduction factor value at 100 m depth is very high and does not allow one to draw any conclusion. The finite element approach (shear stress distribution with time) does not model any critical state (failure) at 100 m depth with a similar configuration. Although the triggering of the Storegga slide is most likely caused by a large earthquake (postglacial crustal uplift), one needs deeper and more critical preconditions to failure to fully explain the slide (100 m high sidewall). One candidate is associated with gas hydrate melting, but the effect of excess pore pressure in the marine clays due to the rapid loading by the overlying glacigenic sediments has to be considered as well, and could explain weak layers development in deeper sediments. Present-day slope stability: (1) Both softwares provide a similar static FOS which means that the slope is stable (FOS above 3.9). The pseudostatic approach (0.05 g pseudostatic acceleration) models no failure (FOS above 1.0) even with the critical SHANSEP modelling (a S=0.21). No failure is expected from the finite element modelling with 0.1 g PGA (FOS=3.0, El-Centro-type earthquake). The Friuli Tarcento earthquake (high-frequency content) has less effect on the shear stress (FOS=4.1). This confirms that the PGA parameter is not sufficient to perform a realistic pseudostatic or dynamic slope stability assessment and that one needs to consider the frequency content of the seismic acceleration. One can state that the slope is stable even with a 0.1-g PGA seismic event occurring in this area, but the site effect (soil response to seismic loading) could be much more critical than the expected one. The

dynamic FOS drops to 2.3, with the critical SHANSEP shear strength profile estimated using a S=0.21 to fit the s u DSS profile. The pseudostatic approach combined to the shear stress reduction factor (modified two-wedge model) gives a FOS similar to the dynamic one (FOS=2.26), confirming that the present-day slope is stable in this area. The corresponding failure probability (SORM method) is around 1.8 E07%. This last parameter is mainly relevant to define the critical slope stability area at a local or regional scale, considering parameter uncertainties.

Acknowledgements This work is a contribution to the COSTA project. We would like to thank Norsk Hydro for providing a complete set of data in the Storegga slide area, N. Sultan for fruitful discussions and data concerning gas hydrates dissociation modelling, Dr. C. Lindholm and Dr. H. Bungum for information regarding the fine seismic zonation for Norway. An insightful review of Drs. N. Sultan and R. Popescu significantly improved the manuscript. ReferencesAndrews, D.C.A., Martin, G.R., 2000. Criteria for liquefaction of silty soils. Proceedings 12th World Conference on Earthquake Engineering, Auckland, New Zealand, Paper vol. 0312. Ambraseys, N.N., 1995. The prediction of earthquake peak ground acceleration in Europe. Earthq. Eng. Struct. Dynam. 24, 467 490. Bender, B., Perkins, D.M., 1987. SEISRISK III: a computer program for seismic hazard estimation. U.S. Geol. Surv. Bull., 1772. Berndt, C., Planke, S., Tsikalas, F., Rasmussen, T., 2001. Seismic volcanostratigraphy of the Norwegian margin: constraints on tectono-magmatic breakup processes. J. Geol. Soc. 158, 413 426. Bryn, P., Berg, K., Lien, R., Solheim, A., Ottesen, D., Rise, L., 2002. The Storegga geomodel and its use in slide risk evaluation: geological and geotechnical site investigation in the Storegga slide area. Offshore Site Investigation and Geotechnics, pp. 219 232. Bryn, P., Solheim, A., Berg, K., Lien, R., Forsberg, C.F., Haflidason, H., Ottesen, D., Rise, L., 2003. The Storegga slide complex: repeated large scale sliding in response to climatic cyclicity. In: Locat, J., Mienert, J. (Eds.), Submarine Mass Movements and their Consequences. Kluwer Academic Publishers, pp. 215 222.

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Slope Stability Assessment of the Helland Hansen Area Offshore

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