Evaluate where to lay an offshore pipeline is complex decision, D'Appolonia developed a model to assess offshore seismic slope stability. The paper presents a 1D elasto-plastic numerical model developed in OpenSees software to study the dynamic response of a submerged infinite slope in seismic conditions. Results obtained for NC soil column profile are compared with theoretical solution.

1. OFFSHORE 1D INFINITE SLOPE MODELING IN SEISMIC
CONDITIONS WITH OPENSEES
C. Piatti, L. Zuccarino & O. Zanoli
Corresponding Author Contact: claudio.piatti@dappolonia.it
The response of submerged slopes to seismic loading is often a key-element in the geohazard risk assessment for offshore projects. Seismic-induced slope failures in NC or slightly OC clays usually involve relatively large
areas but limited depths, such that the infinite slope assumption can be employed (Biscontin and Pestana, 2006). This paper describes a Finite Element numerical model which simulates the dynamic response of an
infinite submerged slope. A hypothetical uniform normally consolidated soil profile was chosen as case study. The results of transient-in-time analyses are used to develop a site specific stability plot which can be useful for
preliminary design. The outputs of the simulations are compared with pseudo-static solutions.
DYNAMIC ANALYSES
The assumed soil properties are typical of a NC medium
plasticity clay (Table 1) with a stiff to very stiff soil at
the base (Vs = 260 m/s).
The assumed shear modulus decay curve is compared
to literature curves in Figure 2. A set of seven time
historieswasselectedconsideringarangeof magnitude
between 5.0 and 7.5 and epicentral distance less than
40 km. The time histories were scaled to the stiff soil
Peak Ground Acceleration (PGA), applied at the base
of the model and propagated through the soil column.
The condition of incipient failure was assumed to
be reached when the mean permanent shear strain
exceeded 10% (established on the basis of advanced
laboratory tests results).
Strain and displacement profiles are strongly time
history dependent (Figure 3). This reflects the inherent
record to record variability in seismic response, but
also suggests that a proper selection of time histories
representative for the site is a key issue for strategic
projects.
CONCLUSION
ƒƒ The FE analysis results would correspond to apply an acceleration reduction factor β ranging from 0.10
to 0.15, i.e. significantly lower than values recommended by standard codes (e.g. Eurocode β ≥ 0.5)
ƒƒ The choice of a pseudo-static seismic coefficient without accepting some seismic displacements could
lead to a conservative slope stability assessment
ƒƒ Theeffectivenessandreliabilityof theproposedmethodologyisenhancedbyhighqualityinputgeotechnical
data and advanced laboratory test results such as bender elements, resonant column and cyclic tests
ƒƒ The methodology can be readily applied to more complex soil stratigraphy
REFERENCES
Biscontin, G. & Pestana J. M. 2006. Factors affecting seismic response of submarine slopes. Natural Hazards and Earth System Sciences 6(1): 97–107
PEER 2010. Open System for Earthquake Engineering Simulation (OpenSees) http://opensees.berkeley.edu
MODEL DESCRIPTION
The numerical model is implemented using OpenSees
(PEER,2010)softwareandconsistsof a1Dsoilcolumn
with application of suitable boundary conditions and
gravity loads to simulate an infinite slope condition
(Figure 1). The 1D model represents a 100 m high
soil column. It is constituted by 500, four nodes,
quadrilateralelementstoallowanadequatepropagation
of the desired range of frequencies. Lateral infinite
extension of the model is obtained by tied-nodes
boundary condition. The soil is represented using the
Pressure Independ Multi Yield material model. This is
a general constitutive model for cohesive soils in which
the soil strength is independent of effective stress. The
soil is modelled as a nonlinear hysteretic material with a
Von Mises multi-surface kinematic plasticity model. The
model focuses on reproduction of the soil hysteretic
elasto-plastic shear response including permanent
deformation. Plasticity is exhibited only in the deviatoric
stress-strain response. Plasticity is formulated based
on the multi-surface (nested surfaces) concept, with
an associative flow rule. The nonlinear shear stress
strain backbone curve is represented by the Kondner
hyperbolic model. Numerical damping is specified as a
combinationof stiffnessandmassproportionaldamping
matrix (Rayleigh damping). Hysteretic damping is
intrinsically developed from the nonlinear elasto-plastic
soil behavior.
Figure 2. Assumed shear stiffness degradation curve compared with
literature curves for cohesive soils.
Figure 3. Permanent shear strain and horizontal displacements at the
end of seismic motion for α = 14° and PGA= 0.3 g.
Figure 4. Stability chart: FEM results compared with pseudo-static solutions.
PSEUDO - STATIC ANALYSES
In accordance with Eurocode 8, kh
can be calculated as:
where PGA* is the peak ground acceleration on soil type A (rock), g is the acceleration of gravity, ß is an
acceleration reduction factor (0.5 for rock to 0.7 or 0.9 for soft soil depending on earthquake magnitude).
The factor of safety for a submerged slope under the assumption of infinite slope for total stress conditions
can be computed as:
where Su is the undrained shear strength, α is the slope angle, γ and γ’ are the total and submerged soil
unit weights, kh
is the horizontal seismic coefficient and z is vertical depth to the shear plane. The critical
slope angle as a function of kh
(i.e. PGA) can be obtained for the limit case of Fs =1.
RESULTS
Shear strains tend to
concentrate downslope in the
upper 5 to 10 m of the profile
(Figure 3). A stability plot
was developed to define the
boundary between stable and
unstable conditions (Figure
4). The FEM stability curve
represents the critical slope
angle as a function of PGA
values (i.e. return period).
PGA values are referred to
the acceleration applied at
the base of the model. Since
the dynamic stability analysis
is performance based, the
condition of limit stability (or
critical condition) is strictly
related to the threshold
criterion assumed (permanent
shear strain reached 10%).
The stability curve obtained
for the NC cohesive profile is
almost linear in the range of
PGAs considered.
Figure 1. Sketch of the model.
The full paper can be downloaded here