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EFFICIENT FINITE ELEMENT TECHNIQUES FOR LIMIT
ANALYSIS OF SUCTION CAISSONS UNDER LATERAL LOADS
By
B. Sukumaran,1 W.O. McCarron,2 P. Jeanjean,3 and H. Abouseeda4
ABSTRACT: This paper documents the use of finite element analyses techniques to
determine the capacity of suction caisson foundations founded in soft clays under
undrained conditions. The stress-strain response of the soft clay is simulated using an
elasto-plastic model. The constitutive model employed is the classical von Mises strength
criterion with linear elasticity assumed within the yield/strength surface. Both two- and
three-dimensional foundation configurations are analyzed. The three-dimensionality of
the failure surface of the actual caisson requires that computationally intensive three-
dimensional models be used. Suggestions are given on how to improve computational
efficiency by using quasi three-dimensional Fourier analyses with excellent results
instead of true three-dimensional analyses. The finite element techniques employed are
verified against available classical limit solutions. Results indicate that both hybrid and
displacement-based finite element formulations are adequate, with the restriction that
reduced-integration techniques are often required for displacement-based formulations.
1 Assistant Professor, Rowan University, 201 Mullica Hill Road, Glassboro, NJ 08028. 2 Senior Staff Engineer, Amoco Worldwide Engineering and Construction, Houston, TX 77058. 3 Engineering Specialist, Amoco Worldwide Engineering and Construction, Houston, TX 77058. 4 Project Engineer, Fugro-McClelland Marine Geosciences, Inc., Houston, TX 77274.
INTRODUCTION
As offshore exploration and development of oil fields reach water depths in the
1,000 to 3,000 m range, novel methods of anchoring production platforms become
attractive due to cost savings associated with offshore installation activities. Surface
production systems that are viable in these water depths include Tension Leg Platforms
(TLP), SPAR platforms, and laterally moored ship-shaped and semi-submersible vessels.
TLPs are floating structures anchored by vertical pretensioned tendons which exert
considerable tensile forces on the foundation. In the Gulf of Mexico, vertical design loads
for individual tendons range up to 27MN (6000 kips), resulting in foundation lateral loads
of 4MN (900 kips). Laterally moored systems, on the other hand, have the dominant load
in the horizontal direction; the horizontal load component being on the order of 9MN
(2000 kips), and the vertical component being less than half that of the horizontal
component. At this time (1998), there are five TLPs and two SPARs installed and
operating in the Gulf of Mexico. Several other TLPs and SPARs are in various stages of
design and fabrication.
For Gulf of Mexico TLPs, driven piles have been the preferred method of
anchoring tendons to the seafloor. This solution arises from a combination of
engineering, geotechnical, fabrication, installation and cost constraints. Chief among
these are the high accuracy (within 1 m) required for positioning the tendon anchoring
points, and the normally consolidated cohesive soils without appreciable strength in the
upper 20 m. These conditions combined with available offshore installation barges,
underwater hammers capable of operating in 1300 meters of water and simple fabrication
of steel pile shapes lead to the preference of driven piles. The depth of penetration of TLP
piles ranges up to 120 m.
SPARs are buoyant single-column hulls anchored by lateral moorings to
foundation elements. In water depths less than approximately 1200 m (4000 ft), TLP and
SPAR systems are competitive economically, but TLPs have a more proven construction,
technology and operating history. For greater water depths, the SPAR platform offers
some performance and economic advantages. Possible foundation systems for SPARs
include the traditional driven piles, drag anchors and suction caissons.
Suction caissons have been used in shallow waters as foundations for single point
moorings, jack-up drilling rigs, fixed platforms and as anchors for floating systems.
Initial penetration of the suction caisson into the seabed occurs due to the self weight;
subsequent penetration is by the ‘suction’ created by pumping water out from the inside
of the caisson. Suction caissons become attractive alternatives to driven piles in
deepwater because of technical challenges and costs associated with the installation
equipment. In addition, suction caissons also provide a greater resistance to lateral loads
than driven piles because of the larger diameters typically used. The terminology for this
foundation is sometimes misleading. ‘Suction’ can refer to the method of installation or a
component of foundation load resistance, or both. Figure 1 shows a schematic view of a
SPAR platform anchored by mooring to suction caissons.
The feasibility of suction caissons has been demonstrated in the North Sea
foundations for the Snorre TLP [1], Europipe 16/11-E structure [2], and with centrifuge
tests for Gulf of Mexico TLP conditions [3]. At present, the use of suction caissons are
being extended to the Gulf of Mexico. Soil conditions in the North Sea (stiff clays and
sands) have so far lead to designs with penetration to diameter ratios typically less than 2.
Because the deepwater shallow sediments in the Gulf of Mexico exhibit very low surface
shear strength, it is necessary to increase the penetration to diameter ratio of the caisson
to obtain satisfactory capacities. However, experience with the installation and behavior
of caissons with large penetration to diameter ratios (up to 10) is limited. To investigate
the installation, performance and capacity of such caissons, a series of field tests,
centrifuge tests, and numerical investigation have been commissioned by the industry.
This paper presents the findings of some numerical investigations aimed at validating
numerical procedures to calculate the lateral capacity of caissons for deepwater
foundations.
SOME BACKGROUND ON FINITE ELEMENT LIMIT ANALYSIS
Available displacement based and hybrid (combined stress and displacement
solution variables) based finite elements formulations are capable of accurately and
efficiently calculating limit loads for foundation systems. An important feature in the
successful use of displacement based finite element formulations is the use of reduced
integration techniques in many limit analysis investigations. The term ‘reduced’
integration refers to the fact that a lower level (fewer sampling points) of numerical
integration is being used than that theoretically required, to exactly integrate a
polynomial of a certain order.
Experience has indicated that the use of reduced integration techniques improves
performance under conditions of nearly incompressible (entirely deviatoric plastic
strains) response for von Mises and other pressure independent material strength models
near the limit conditions. Historical discussions on the relative merits of full and reduced
integration techniques are given by Zienkiewicz and Taylor [4] and Zienkiewicz et al.
[5]. Nagtegaal et al [6] discussed the success and failures of several fully integrated
elements with respect to their ability to accurately predict limit loads in association with
elastic-plastic material models. Sloan and Randolph [7] extended this work for plane
strain (strip) and axisymmetric (circular) footing configurations, and proposed a
triangular 15-noded element for use in axisymmetric problems. The performance of this
element was later discussed by de Borst and Vermeer [8], and Whittle and Germaine [9].
Barlow [10,11] presented mathematical arguments that reduced integration in quadratic
(8-noded) elements enhances performance and solution convergence. Griffiths [12]
presented the successful use of quadratic reduced-integration elements in plane-strain and
axisymmetric conditions. Naylor [13] discussed the elements’ performance for nearly
incompressible conditions.
Zienkiewicz and Taylor [4] demonstrate that reduced integration elements, of the
type used here, satisfy the mathematical conditions of stability and convergence required
in the ‘patch’ test. While it is beyond the intended scope of this paper to review in detail
the theoretical studies on reduced integration cited by these authors, two key findings are
summarized in the following for completeness of discussion. First, the minimum level of
numerical integration (quadrature) necessary to insure stability and convergence of
solution is that which correctly integrates the volume of the finite element. For the two-
dimensional quadratic 8-noded element used here, this implies a four-point quadrature for
reduced integration, as opposed to full quadrature which leads to a nine point
requirement. Second, reduced integration leads to a weak singularity in the single element
stiffness and fewer internal constraints on the coupling between volumetric and
deviatoric strains. This singularity does not appear in equilibrium equations when more
than one element is involved.
We therefore conclude that reduced integration techniques have a firm theoretical
basis, supporting their application. However, as with any finite element, their robustness
and accuracy in particular applications should be critically examined. Alternatives to the
use of reduced integration exist, e.g. hybrid finite elements, or very high order
displacement-based elements such as the 15-noded cubic strain triangle. Hybrid elements
are available in commercial codes, such as ABAQUS [14], and are effective in the
analysis of incompressible materials. The term hybrid stems from the use of both
displacement and stress components as solution variables. In this case, the stress
component included is the mean pressure. Detailed discussion of these elements are given
by Zienkiewicz and Taylor [4] and HKS [14]. The performance of the hybrid elements
are compared herein with results of displacement based elements.
VERIFICATION OF FINITE ELEMENT MODELING TECHNIQUES
The adequacy of the hybrid and reduced-integration elements are demonstrated in
the following by virtue of their performance in accurately calculating the limit loads for
three problems; some of which have typically proven to be problematic for a wide range
of element formulations. The analyses were performed with the program ABAQUS [14].
The first series of problems are plane strain (strip) and axisymmetric (circular) footings
on the surface of purely cohesive soil. Secondly, deeply embedded footings in cohesive
soil are considered. The final problem relates to the ultimate lateral resistance of a
circular pile cross section in a cohesive soil. The finite element analyses make use of
isotropic elasticity combined with a von Mises or Tresca type strength surface. The
implementation of the Tresca elastic-plastic constitutive model includes a non-associated
flow rule. Young’s modulus is taken as approximately one thousand times greater than
the undrained strength.
Footing analyses presented here represent rigid footings and a weightless soil. The
surface and deep footings are analyzed with smooth and perfectly rough interfaces,
respectively. The footing limit load is conventionally denoted as Pult = N⋅Su⋅A, where N is
the bearing capacity factor, Su is the undrained strength, and A is the bearing area.
Theoretical limit solutions presented here are based on the Tresca strength condition. The
Tresca and Mohr-Coulomb criteria are identical when the Mohr-Coulomb internal
friction parameter is zero, as is the case for a purely cohesive material. Finite element
strength models used here include both the von Mises and Tresca criteria. Plane strain
(strip) footings are analyzed with the von Mises condition matched to the Tresca strength
using the procedure presented by Chen [15]. For circular footings, limit loads are
presented for the Tresca criterion. Comparison of limit loads predicted by displacement
and hybrid elements for strip and circular surface footings are shown in Figure 2. The
finite element mesh is shown in Figure 2a, and the load-displacement relationship in
Figure 2b. Displacement (D) and hybrid (H) element formulations are indicated in Figure
2b, along with the order of integration, full/standard (S) and reduced (R). Thus, SD
implies a standard integration combined with a displacement formulation. A small
displacement formulation was used in the analyses to formulate the element stiffness and
equilibrium equations. Limit solutions are well defined for all conditions but the fully
integrated displacement formulation element in the circular footing case; as expected
based on previous experience. Theoretical bearing capacity factors, N for smooth and
rough circular footings are 5.69 and 6.05 [15], respectively. The theoretical bearing
capacity factor for a strip footing is 5.14. The calculated bearing capacity factors for the
strip footing range from 5.3 to 5.4. For circular footings, the calculated bearing capacity
factors range from 5.77 upwards. The RH and RD analyses with the Tresca material
model for the circular footing fall within a reasonable range of the theoretical solution.
The bearing capacity factor of 5.77 from the RH analysis is essentially the exact solution
for the smooth footing condition considered.
The finite element mesh and results of limit analysis of embedded deep strip and
circular footings are shown in Figure 3. A large displacement formulation is required for
this particular problem because of the relatively large stresses compared to the elastic
moduli. Theoretical solutions for these conditions have been given by Chen [16], using
upper-bound limit analysis, and Meyerhof [17], using limit equilibrium methods. The
ratio of the depth of embedment to footing width is 4, and the shaft of the footing is
smooth and allows no horizontal deformations. The theoretical solutions by Meyerhof
[17] result in bearing capacity factors ranging from 8.85 to 9.74 for rough strip and
circular footings, respectively. Chen [16] reported a bearing capacity factor of
approximately 9 for deep strip footings. The results for the RD analyses for strip and
circular footings indicate bearing capacity factors of 8.9 and 10.7, respectively. The RH
analyses result in bearing capacity factors of 7.7 and 9.6 for strip and circular footings,
respectively. In the present case, the fully integrated displacement elements (SD) perform
poorly and do not reach a limit (results not presented). Accurate determinations of the
bearing capacity of deep embedded footings are complicated by the fact that the
plastically deforming region is confined within an elastic region, so that the plastically
strained zone is not free to undergo the unlimited plastic deformation typically associated
with limit conditions. In the present cases, the zone of plastic behavior is contained
within about two footing diameters distance from the footing (results not shown).
The final illustrative example is that of determining the lateral resistance of a
circular pile cross section. For this analysis, a plane strain idealization and von Mises
strength criterion matched to the plane strain condition is adopted. The finite element
mesh is shown in Figure 4a. The results are shown in Figure 4b for three pile-soil
interface conditions: rough with no separation, gapping (separation allowed, no tensile
forces transmitted), and gapping with a frictional interface. The theoretical limit solutions
have been presented by Randolph and Houlsby [18]. Those authors presented lower-
bound solutions with bearing capacity factors, N of 9.14, 10.52, and 11.94 for friction
coefficients f of 0, 0.4, and 1, respectively. These correspond well with the results shown
in Figure 4b for the same conditions obtained for both reduced integration and hybrid
elements. Hamilton et al. [19] reported experimental investigations showing N values
generally between 10 to 12 for depths greater than four pile diameters. These results are
further discussed later in the paper.
Current practice in the offshore industry [20] assumes the lateral bearing capacity
factor at large depths to be N = 9. Based on the results presented here, limit solutions
[18], and experimental investigation [19], the current API practice is conservative.
LATERAL LOAD CAPACITY ANALYSES OF SUCTION CAISSONS
The ultimate holding capacity of a suction caisson anchored at a site with soil
conditions similar to that found in the Gulf of Mexico were analyzed. The soil at the site
where the suction caisson is expected to be anchored is a normally consolidated clay. The
shear strengths are assumed to be zero at the seabed and increasing linearly with depth as
given below:
SuDSS = 1.41z (kPa) (1)
where z is the depth below seabed in meters and SuDSS is the undrained static direct
simple shear strength. The submerged unit weight of the soil is 6.3 kN/m3.
The finite element analyses were conducted using ABAQUS [14]. A von Mises
shear strength idealization was used to model the clay. The von Mises model implies a
purely cohesive (pressure independent) soil strength definition. The caisson is modeled as
a weightless linear elastic material.
TWO-DIMENSIONAL LOAD CAPACITY ANALYSIS OF SUCTION CAISSONS
Two-dimensional analyses were performed to confirm the mesh and boundary
definitions selected for three-dimensional investigations are suitable for classical passive
and active pressure problems. The caisson analyzed was 6.1 m in diameter with a
penetration depth of 12.2 m below the mud line. The caisson length to diameter ratio is
L/D = 2. The caisson has a closed top during installation and operation. Initial horizontal
stresses were defined with a coefficient of lateral earth pressure Ko equal to 1. The finite
element mesh shown in Figure 5 was used for the analyses. The mesh model dimensions
of 56 m width by 36.6 m depth was intended to minimize boundary effects on response.
The mesh consists of eight-noded plane strain elements for the soil and two-noded linear
beam elements for the caisson.
The inclination of the load considered was assumed to be 28° with the horizontal,
measured counterclockwise. Several points of attachment for the mooring line were
considered to study the effect of the attachment point on the load capacity. The optimal
load attachment point is that which produces maximum capacity. Figure 6 shows a plot of
load capacity vs. point of attachment. The capacity generally increases with depth of
attachment. This is in agreement with previously published results [21,22].
Figure 7 shows the horizontal stress acting on the wall when it is constrained to
translate horizontally with no rotation occurring. Both smooth and rough soil-wall
interfaces are considered. The active and passive pressures computed at the limit
conditions display the expected linear distribution with depth, and closely match the
pressures calculated for classic active and passive pressure retaining wall response.
The effect of the load attachment point on the failure mechanism produced was
also studied. Figures 8(a), (b) and (c) shows the various failure mechanisms produced
when the load is attached above, at and below the optimum point. Figures 8(a) and (c)
show that when the load attachment point is above or below the optimal point, the caisson
rotates. The failure mechanism is more rotational than translational. The shear zone
mobilized is also less in area than if the load is attached at the optimal attachment point.
It can be seen from Figure 8(b) that when the load is attached at the optimal load
attachment point, the failure mechanism is predominately translational. From Figure 6, it
can be seen that the load capacity only decreases slightly if the attachment point is below
mid-height of the caisson.
COMPARISON OF LOAD-DEFORMATION RESPONSE OF FOURIER AND
THREE-DIMENSIONAL ANALYSES
The three-dimensional response was analyzed using both three-dimensional and
quasi three-dimensional Fourier analysis elements (CAXA) available within ABAQUS.
CAXA elements are biquadratic, Fourier quadrilateral elements. These elements were
used for the analyses of suction caissons because they allow non-linear, asymmetric
deformations and loading. Two types of CAXA elements, namely the CAXA8R2 and
CAXA8R4, were used in the analyses. These are eight-noded quadrilateral reduced
integration elements that differ in the number of Fourier modes used for interpolation.
CAXA8R2 elements use two Fourier modes for interpolation while the CAXA8R4 uses
four. The number of elements and nodes in the mesh are 180 and 3616, respectively. A
three-dimensional model having a similar mesh configuration with twenty-noded brick
elements was also developed to compare the results from a quasi three-dimensional
Fourier analysis and the actual three-dimensional response. The far boundaries of the
model are modeled as perfectly rough (no translations allowed). The modeled caisson
does not include a top plate, which results in free deformations of the top soil surface in
the caisson soil plug.
The plane of symmetry of the three-dimensional and axisymmetric models is
identical to the plane-strain model shown in Figure 5. The point of load application is at
about mid-height of the caisson (5.97 m below the mud line). The inclination of the load
was 32° with the horizontal, measured counterclockwise. The coefficient of lateral earth
pressure Ko is 0.8. The load-displacement curves for the three-dimensional model as well
as the axisymmetric analyses using two and four Fourier modes are shown in Figure 9.
The load indicated in Figure 9 represents the load vector magnitude (resultant from
horizontal and vertical components). The three-dimensional and Fourier analyses give the
same limit loads, approximately 7700 kN.
Finite element analyses with a purely horizontal applied load resulted in a limit
load of approximately 5000 kN when the load is applied at mid-height of the caisson, and
2300 kN when the load is applied at the top of the caisson. Murff and Hamilton [23]
present methods using upper-bound limit analyses, which give a capacity of 7000 kN for
the case of pile translating horizontally in a soil mass with full adhesion and suction
assumed on the back side of the pile. Those authors also compared their solutions with
experimental centrifuge tests in kaolin clay previously presented by Hamilton et al [19].
The present numerical results are compared with these limit analysis and experimental
results in the following.
Figure 10 shows the non-dimensionalized normal (radial) stresses acting on the
outside wall of the caisson from the axisymmetric-asymmetric analysis. The 0° plane is
the plane along which the load is attached. The results in Figure 10 were obtained by
dividing the soil radial stresses adjacent to the caisson by the soil strength (Eqn 1) at the
respective depth. The left side of the plot in Figure 10 represents results with an inclined
(at 32° from the horizontal) load, while the right side represents results for a purely
horizontal load. The results from the analysis with an inclined load generally show
higher non-dimensionalized pressures than that for a horizontal load. This can be
explained by the fact that the vertical load component applied on the face of the caisson
tends to reduce rotation of the caisson. The non-dimensionalized stresses generally
increase with depth when rotation of the caisson is limited, but when significant rotation
does occur, passive pressures are reduced at the leading edge of the base of the caisson.
As shown in Figure 11, the present numerical results compare reasonably with
available limit solutions and experimental results. Figure 11 includes capacities computed
from methods commonly used in the offshore industry developed by Matlock [24] for
laterally loaded piles in soft clays. Centrifuge tests performed by Hamilton et al [19,23]
resulted in a mean bearing factor of 11 over a wide range of depths. The analytical limit
solutions and experimental results in Figure 11 are for a strength profile increasing
linearly with depth at the same rate assumed for the present numerical results (Eqn 1).
Murff and Hamilton [23] attributed the scatter shown in Figure 11 at shallow depths to
‘both the low shear strength near the mud line and the inherent scatter in the soil-
resistance derivation methodology.’ The latter point refers to numerical procedures that
infer bearing pressures on model piles from measured bending strains. The present
numerically determined bearing factors are intermediate to those determined by Murff
and Hamilton [23], and Matlock [24]. Limiting bearing factors N assumed by Murff and
Hamilton, and Matlock are 12 and 9, respectively. The Matlock method results in lower
lateral bearing factors than the experimental results and other numerical and analytical
limit results shown in Figure 11.
Magnitudes of plastic strain are plotted in Figure 12 on the deformed mesh for an
inclined load analysis with Fourier elements. The zone of plastic action is contained
within a distance of three caisson diameters of the caisson axis. This is also the zone of
significant soil deformation. The mobilized soil mass is roughly conical in shape and
extends to a depth of one half diameter below the caisson base.
The authors performed limit analyses with hybrid forms of the Fourier elements
and found that these elements produced limit loads approximately 3% lower than the
displacement based formulation. It can be concluded based on these results that
CAXA8R2 or CAXA8R4 elements can be used for three-dimensional analyses of suction
caissons without loss in accuracy compared to the full three-dimensional formulations.
Further, the definition of the finite element model is much less time consuming, and limit
loads compare favorably with available experimental results.
Investigations not presented here showed that the limit loads determined from
analyses with and without the effect of soil self-weight are negligibly different. The
reason for this can be seen in the form of the failure mechanisms shown in Figure 8.
Since the passive and active wedges are the same size, the work contribution due to the
self-weights sum to zero. That is, the weight of material lifted in front of the caisson is
the same as that pulled down on the opposite side, thus resulting in no net work being
performed. Different results would be expected if separation between the caisson and soil
occurred on the active pressure side.
CONCLUSIONS
Few studies have been conducted to examine the response under loading of
suction caissons in Gulf of Mexico clays. The present analyses used linear elasticity
combined with the von Mises strength model to describe the deformation and strength
properties typical of Gulf of Mexico deepwater clays. New insights were obtained on the
extent of area in which displacements will occur due to loading of a suction caisson as
well as the magnitude of horizontal stresses that are expected to develop on the caisson
wall. The following conclusions can be drawn from the study:
• The maximum anchor capacity is obtained when the load attachment point forces the
caisson to have a translational mode of failure rather than a rotational mode of failure.
This is in agreement with earlier findings by Keaveny et al. [21], and Colliat et al.
[22] but conflicts with those of Murff and Hamilton [23] who concluded that
translational and rotational mechanisms resulted in essentially the same limit loads.
• Inclined loads applied at the face of the caisson tend to reduce caisson rotation,
resulting in greater lateral capacity.
• A pseudo three-dimensional model available in ABAQUS, utilizing the use of Fourier
interpolation to define approximate three-dimensional conditions can be used instead
of an actual three-dimensional model for analyzing the capacity of a suction caisson
with considerable computational time savings. While not pointed out elsewhere in
this paper, the authors would like to note that the use of reduced integration
procedures and the Fourier modeling technique offered large computational
efficiencies with no loss of accuracy. For the problems considered herein, using
reduced integration procedures for three-dimensional problems resulted in a 40%
reduction in solution time requirements compared to full integration procedures.
Fourier solutions required approximately 20% of the computational time of full three-
dimensional analyses.
• Limiting lateral bearing pressures on deep piles in cohesive soils are greater than
those currently used in the design of offshore piles. Other limit analysis solutions and
experimental observations support this conclusion.
• The lateral resistance of suction caissons is not affected by installation disturbance of
the soil near the caisson wall since the source of resistance is the soil in the passive
and active pressure zones.
• Accurate predictions of the capacity of suction caissons, footings and other embedded
structures can be obtained from finite element analyses. Reduced integration elements
were shown to produce well-defined limit conditions in both two- and three-
dimensional conditions. Hybrid elements generally provided lower limit loads than
displacement based formulations. The difference in caisson capacities determined by
the hybrid and displacement element formulations is relatively small.
These results have important practical implications for the estimation of the
capacity and the design of suction caissons.
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Definition of Terms
A Bearing area
B Width or diameter of footing
d Displacement
D Diameter
Suction caisson
Sea level
DSS Direct simple shear (shear strength evaluation)
f Coefficient of friction
L Length
N Bearing factor
P Load
Su Undrained shear strength of soil
z Depth
Figure 1Figure 1
61 cm
r line
4.5
5.0
5.5
6.0
6.5
7.0
-0.1
Loa
d Fa
ctor
N
SD-Misesnte
Ce Circular
Half footing
76.2 cmof 15.2 cm width
-0.05 0
Normalized Displacement (d
RD-MisesSH-MisesRH-MisesRD-TrescaRH-TrescaSD-Tresca
Figure 2b
Figure 2a
Strip
0.05 0.1
/B)
23
1.53 m25.9 m
36.6 m
27.45 m
12.2 m
5
6
7
8
9
10
11
12
-0.1 -0.05 0 0.05 0.1 0.15
Normalized Displacement (d/B)
Loa
d Fa
ctor
N
RD-MisesRH-MisesRH-TrescaRD-Tresca
Strip
Circular
Figure 3b
Figure 3a
24
0
2
4
6
8
10
12
14
0 0.01 0.02 0.03 0.04 0.05
Normalized Displacement, d/B
Rough, No Separation; SH
f=0.4, Gapping; SH
f=0.4, Gapping; RD
f=0.4, Gapping; SD
Smooth, Gapping; SHFigure 4a
3.13m diameter
14m Pile of
Figure 4b
25
27
0
3
6
9
12
15
0 40 80 120 160
Pressure (kPa)
Dep
th B
elow
Sea
bed(
m
RoughRoughSmoothSmoothClassical SmoothClassical Smooth
Active Pressure Passive Pressure
0
5
10
15
0 20 40 60 80Load Capacity (kN/m)
Horizontal Load,Rough Interface
Load Inclination =28, RoughInterfaceHorizontal Load,Friction=0.4
Figure 6
Figure 7
0
2000
4000
6000
8000
0 0.05 0.1
Normalized Displaceme
0
2
4
6
8
100
180
160
140
120
100
80
60
40
20
0.25L 0.55L
Inclined Load
u
radial
S
Figure 10
Figure 9
σ
Soil Weight Included
0.15 0.2
nt, d/D
CAXA8R2CAXA8R4C3D20R
20
40
60
80
100
120
140
160
0.75L 0.95L
Horizontal Load
31
Present Finite Element Analyses, 0° plane
Limit Analysis, Matlock method [23]
Upper bound limit analysis, Murff method [23]
Centrifuge tests [19,23]
104 6 8 2
20
16
12
8
4
Nor
mal
ized
Ulti
mat
e La
tera
l Stre
ss (P
ult/S
uD)
Depth in Pile Diameters (L/D)
Figure 11
32
Figure 1 Schematic view of a spar platform anchored to suction caissons at the seabed
Figure 2(a) Finite element mesh used in the analyses of the capacity of surface footings
Figure 2(b) Bearing capacity factor, N vs. Normalized displacement computed for surface strip and circular footings
Figure 3 Bearing capacity factor, N vs. Normalized displacement for deeply embedded circular and strip footings
Figure 4(a) Finite element mesh used for determination of lateral pile capacity
Figure 4(b) Bearing capacity factor vs. Normalized displacement for a circular pile
Figure 5 Finite element mesh used for determining the capacity of suction caissons
Figure 6 Load capacity of suction caisson (kN/m) vs. Depth to load attachment point obtained from the analyses of a plane strain
model
Figure 7 Horizontal stress acting on the wall on the active and passive side
Figure 8(a) Plot of Displacement Vectors Indicating Failure Pattern when Horizontal Load is Attached at the Top of the Caisson
Figure 8(b) Plot of Displacement Vectors Indicating Failure Pattern when Horizontal Load is Attached at the Optimal Attachment
Point
Figure 8(c) Plot of Displacement Vectors Indicating Failure Pattern when Horizontal Load is Attached Below Optimal Attachment
Point
Figure 9 Load capacity vs. Normalized displacement for the three dimensional and axisymmetric asymmetric analyses
Figure 10 Normal Stresses Acting on the Outside of the Caisson at Various Depths Below Mudline
Figure 11 Predicted versus Experimental Soil Resistance (Reproduced with permission from ASCE [Murff J.D, and Hamilton J.M., P-
Ultimate for Undrained Analysis of Laterally Loaded Piles. ASCE Journal of Geotechnical Engineering. 119 (1993) 91-107.])
Figure 12 Plastic Strains Developed in the Soil Surrounding the Caisson
34
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