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Proceedings of OMAE’0424

th International Conference on Offshore Mechanics and Arctic Engineering

June 20-25, 2004, Vancouver, Canada

OMAE2004-51564

EFFECT OF SKIRT-TIP GEOMETRY ON SET-UP OUTSIDE SUCTION ANCHORS IN

SOFT CLAY

Knut H. AndersenNorwegian Geotechnical InstituteP.O. Box 3930 Ullevaal Stadion

N-0588 Oslo, NorwayEmail: [email protected]

Lars AndresenNorwegian Geotechnical InstituteP.O. Box 3930 Ullevaal Stadion


Hans Petter JostadNorwegian Geotechnical InstituteP.O. Box 3930 Ullevaal Stadion


Edward C. ClukeyBP America Production Company501 WestLake Park Blvd.

Houston, Texas 77079, USAEmail: [email protected]

Keywords: Suction Anchor, Soft Clay, Set-up, Finite Element

Analyses, Tapered Skirt Tip

ABSTRACTAn important part of suction anchor design is the

determination of the shear strength along the outside skirt wall.

Previous work has suggested that when a suction anchor in clayis installed by applying underpressure inside the anchor, the

external skin friction may be reduced compared to the skin

friction expected for driven piles. The primary reason for this

reduction is that the movement of soil at and beneath the

caisson tip during installation will be influenced by whether the

anchor is penetrated by weight or by underpressure. To further

investigate the impact of installation by underpressure,

additional finite element analyses have been performed where

the skirt installation process has been better followed than in

the previous analyses. The movement of soil around the caisson

wall was studied for both a flat caisson tip and a tip with a

tapered edge of 45º towards the outside of the anchor. The

tapering was made to see if it would cause more of the

displaced soil to move outside the anchor and thereby increase

the mean total stresses and the shear strength along the outside

anchor wall. The analyses were made with two separate wall

roughness factors for a typical anchor in soft clay.

INTRODUCTIONSuction anchors are cylindrical steel units closed at the top

and open at the bottom. They are installed by penetrating the

cylinder wall, also called “skirt”, into the seabed. The first part

of the penetration is achieved by the self-weight of the anchor

Further penetration requires application of an underpressure

below the top lid inside the anchor to generate an additiona

driving force (e.g. Andersen and Jostad, 1999). Suction anchors

have been widely used to anchor various types of floaters

world wide during the last decade.

During self-weight penetration, a significant part of thesoil displaced by the skirt wall will move outside the skirt wall

as for driven piles. When underpressure is applied, however

most of the clay displaced by the skirt is expected to move into

the anchor. In addition, the underpressure may cause shear

strains in the soil beneath and outside the anchor that will also

lead to soil movements into the anchor. The outward soi

movement during weight penetration will cause a significant

increase in the mean total stresses in the soil outside the skirt

wall, whereas the movement of soil into the anchor during

penetration by underpressure is likely to give significantly

smaller mean total stress increases, or even stress reduction

outside the skirt wall.

During penetration, a thin zone of clay along the skirt wall

will be remolded, and the shear strength in the clay along the

skirt wall will be equal to the remolded shear strength. This

zone of remolded clay will have a high excess pore pressure in

soft normally consolidated clay. With time, the excess pore

pressure in the remolded zone will dissipate, and the effective

stresses and the shear strength will increase. There will also be

a shear strength increase due to thixotropy. The effect of

penetration on the mean total stresses outside the skirt wal

gives the potential for higher effective stresses and shear

1 Copyright © 2004 by ASME

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FINITE ELEMENT MODELstrength along the outside skirt wall for anchors penetrated byweight than for anchors penetrated by underpressure.

Geometry and finite element meshAndersen and Jostad (2002) proposed a method to

calculate the shear strength along the outside skirt wall (i.e. the

“set-up”) with time. They assumed that all the displaced soil

moves inside the caisson when it is penetrated by

underpressure, thus giving no mean total stress change outsidethe caisson immediately after installation. This assumption was

based on prototype and model test experience and some small

strain, small displacement finite element analyses for caissons

with a flat skirt tip. Consolidation analyses showed that even

with no change in mean total stress, the difference in

compressibility of the remolded zone and the intact soil gave

reduced effective stresses in the remolded zone along the

outside of the anchor wall as the excess pore pressure due to

total stress changes, remolding and shear strains dissipated.

Andersen and Jostad (2002) suggested from their analyses that

for typical anchors in normally consolidated plastic clay, the

strength along the outside of the skirt wall after full set-up

would be in the order of the initial shear strength in the case ofself-weight penetration and about 65% of the initial strength

when underpressure was applied. The factor will depend on

plasticity, sensitivity, overconsolidation ratio, anchor geometry

and wall thickness.

The finite element analyses were performed with an

axisymmetric model with an inside anchor diameter of D = 3.8

m, a skirt wall thickness of t = 0.033 m (~1.25''), an outer mesh

radius of 3.5 D and a mesh height of 5 D, as shown in Figure

1a. The analyses were for practical reasons started from a penetration depth of 3 D (11.4m) and continued to a

penetration depth of 4.2 D (16m). Two different skirt tip

geometries were used, one with a flat tip and one with a tapered

tip (Figure 1b).

The finite element analyses were made with the program

PLAXIS v. 8.1 (PLAXIS, 2003). The finite element mesh is

shown in Figure 2. The model was discretized using 3367 15-

noded axisymmetric elements with a refined mesh at and below

the skirt tip. Interface elements were used to model the

disturbed zone of clay between the intact clay and the inside

and outside skirt walls, and the interface between the clay and

the skirt tip. Interface elements were also used in the clay

around the skirt tip, as shown in Figure 1 marked as dottedlines with + and - signs, in order to model the failure

mechanism around the skirt tip more accurately.

Modelling of skirt penetrationThe reduced strength after full set-up along the outsideskirt wall of anchors penetrated by underpressure may in some

cases have an important effect on the holding capacity of a

suction anchor, and it is therefore of interest to check the

assumption that all the displaced soil moves into the caisson

when it is penetrated by underpressure and to investigate means

of increasing the set-up. One way to increase the set-up may be

to taper the skirt tip in an attempt to force some of the displaced

soil to move outside the anchor also when the anchor is

penetrated by underpressure. This effect from the taper

increases the mean total stresses outside the anchor as during

self-weight penetration. The soil heave inside the anchor will

also be reduced if more displaced soil moves outside the

anchor, reducing the extra skirt length to accommodate soil

heave.

The finite element model was designed to analyze the

process of penetrating the skirt tip 4.6 m from the skirt tip at a

depth of 3·D (11.4 m) to the skirt tip at depth of 4.2·D (16 m).

The 4.6 m penetration of the skirt was modeled by changing the

geometry configuration of the FE-model in a series of 28

penetration steps. In each step the penetration length of the

skirt was increased by switching material from clay to steel and

reducing the shear strength in the interface elements along the

skirt according to the roughness factor αwall. For each step, afterthe switching of material, the loading of the anchor was

increased until the penetration resistance (steady-state plastic

failure condition) for the new penetration depth was achieved.

When the final depth of 16 m was reached, the load on the

anchor was removed (unloaded) such that all external loads

were zero. This was done both for the weight and the

underpressure cases. The situation before unloading is more

representative for the weight case, since the self-weight wil

remain after penetration. The situation for the underpressure

case will in a prototype situation be between the end of loading

and the unloading cases, as the underpressure will be removed

but the anchor weight will remain.

To further investigate the impact of penetration by

underpressure on the displacement pattern and the stress

changes outside the skirt wall, additional finite element

analyses were performed. The numerical scheme used in these

analyses followed the skirt installation process better than the

previous analyses. This methodology was used to assess

movement of soil around the caisson wall for both a flat skirt

tip and a tip with a tapered edge of 45º towards the outside of

the caisson. The analyses were performed both for penetration

by weight and for penetration by underpressure, and for

roughness factors of 0.5 and 0.25 at the interface between the

skirt wall and the clay.

LoadingPenetration of the anchor by weight or underpressure is

modeled by applying tractions on top of the axisymmetric

model (Figure 3). For weight loading only, the traction p acting

on the annulus with area Atip is activated. For loading by

underpressure both this traction p and a traction p⋅Atip/A baseacting on the base area A base in the opposite direction, are


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a)

1/2D 3D

t = 0.033 m

~ 1.25 ''

t = 0.033 m

~ 1.25 ''

Start penetration

depth 3D= 11.4 m

End penetration

depth 4.2D= 16 m

D=3.8 m

3 D

2 D

p

p*Atip/Abase

Abase = 11.34 m2

Atip = 0.397 m2

Figure 3. Load system

activated. The anchor is brought to penetration failure by

increasing the traction p for each penetration depth using the

automatic incremental-iterative solving procedure in PLAXIS

The penetration resistance can then be calculated as p ⋅Atip both

for weight and underpressure loading.

Material properties

b)

2.7cm

0 . 6 c m

45o

The undrained shear strength of the clay is modeled as

being isotropic and increasing linearly with depth from the

seabed according to:

su = 1.25⋅z (kPa) for self-weight penetration

su = 1.0+1.25⋅z (kPa) for penetration by underpressure

The shear strength for the underpressure penetration

analyses has a small intercept at the surface in order to avoid

numerical problems when loading a boundary (surface of the

soil plug) with zero shear strength.

The clay is modeled as being elastic-perfectly plastic using

the PLAXIS Mohr-Coulomb material model with a normalized

shear modulus G/su= 100. The stress-strain relationship for theclay is illustrated in Figure 4.Figure 1. Finite element model. a) Overall geometry b)

Detail of flat and tapered skirt tips The skirt is modeled as steel by an elastic material model

with the Young's modulus E = 2.1⋅108 kPa.

The shear strength along the interface between the intact

clay and the skirt wall is set equal to the clay shear strength

times a roughness factor αwall.

The clay material is modeled as being weightless meaning

that the calculated stresses are stress changes from the initial

stresses before anchor installation.

γ

τ

G

1%

unload/

reload

Figure 2. FE-mesh and zoomed in detail around skirt tipFigure 4. Shear stress – shear strain relationship


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Table 1. Identification of cases analyzed

a)

11.4

11.9

12.4

12.9

13.4

13.9

14.4

14.9

15.4

15.9

0 500 1000 1500 2000 2500

Total penetration force [kN]

P e n e t r a t i o n d e p t h [ m ]

case 1-flat,r=0.5,selfweight

case 2-flat,r=0.5,suction

case 3-flat,r=0.25,selfweight

case 4-flat,r=0.25,suction

case 5-tapered,r=0.5,selfweight

case 6-tapered,r=0.5,suction

case 7-tapered,r=0.25,selfweight

case 8-tapered,r=0.25,suction

No αwall Penetration

Type

Tip

Geom

1 0.5 Weight Flat

2 0.5 Underpr Flat

3 0.25 Weight Flat

4 0.25 Underpr Flat

5 0.5 Weight Tapered

6 0.5 Underpr Tapered

7 0.25 Weight Tapered

8 0.25 Underpr Tapered

CASES ANALYZEDThe 8 cases summarized in Table 1 were analyzed. They

cover flat and tapered skirt tips of skirts with roughness factorsof αwall = 0.5 and 0.25 penetrated by weight and underpressure.

The tapering was 450 towards the outside of the caisson from a

6mm flat portion of the 33mm thick skirt (Figure 1b). The

roughness factors correspond to soil sensitivity values of

St=1/αwall = 2 and 4, assuming that the skirt wall is rough

enough for the failure along the skirt wall to occur in the

remolded clay. This is believed to be the case unless the skirt

wall is painted or prepared in other ways, has variation in

thickness, or the anchor has stiffeners.

b)

11.4

11.9

12.4

12.9

13.4

13.9

14.4

14.9

15.4

15.9

0 50 100 150 200

Tip penetration force [kN]


RESULTS

Penetration resistance

The total penetration resistance Ftot at a given penetrationdepth is calculated by multiplying the penetration failure stress,

pfail, obtained from the load-displacement curve for each of the

28 penetration steps by the tip area Atip. The results are given in

Figure 5a, which shows that the penetration resistance is

roughly proportional to the roughness factor, αwall. The

penetration resistance is consistently higher for penetration by

underpressure than for penetration by weight. The reason for

this is the difference in the shear strength profile with a 1kPa

intercept at the clay surface in the case with penetration by

underpressure. The effect of skirt tip tapering is negligible

compared to the total penetration resistance.

The effect of skirt tip tapering is studied more closely by

isolating the skirt tip resistance. The skirt tip resistance iscalculated by subtracting the resistance caused by the shear

strength along the inside and outside skirt wall from the total

penetration resistance, i.e. Ftip= Ftot - Ffrict. The portion of the

penetration resistance that is caused by the shear strength along

the inside and outside skirt wall is calculated by:

Figure 5. a) Total penetration resistance and b) skirt tip

resistance versus penetration depth.

sutip : undrained shear strength at skirt tip depth

susurface : undrained shear strength at the clay surface

αwall : skirt wall roughness factor

Askirt : area of penetrated skirt wall (inside and

outside)Ffrict = 1/2⋅(su

tip+ susurface) αwall⋅Askirt

where


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The calculated skirt tip resistance is presented in Figure 5b.

The result shows that there is an effect of roughness factor, but

as expected the effect is much less than proportional to the

roughness factor, since the failure will occur through the clay.

There is also a difference between resistances from penetration

by weight and by undrepressure. This difference is attributed to

the difference in shear strength profile, as discussed above forthe total resistance. Tapering has only small or no effect on the

tip resistance. For cases with penetration by weight the effect of

tapering is 10% or less, and there is essentially no effect for

cases with penetration by underpressure.

Displacement pattern around skirt tipThe calculated displacement pattern around the skirt tip is

shown in Figure 6a and b, for roughness factors of αwall = 0.5

and 0.25, respectively. The displacements in Figure 6 are the

incremental displacement vectors at failure when the skirt tip is

at depth 13.7 m, the midpoint between start and end of

penetration.

The incremental displacements at failure show that- about half the displaced soil moves outside the anchor

when it has a flat skirt tip and is penetrated by weight

- essentially all the displaced soil moves inside the anchorwhen it has a flat skirt tip and is penetrated by

underpressure

- tapering of the skirt tip causes more clay to move outsidethe anchor than for a flat tip, both for penetration by weight

and by underpressure

- the displacement pattern is not significantly influenced bythe roughness factor, but there is a tendency for more soil to

move inside the anchor for the lower roughness factor

The displacements shown in Figure 6 are due to (1) penetration

of the skirt tip into the soil and (2) displacements of the soil plug due to the shear stresses along the skirt wall and the

underpressure applied at the top of the clay plug inside the

anchor, if the anchor is penetrated by underpressure. For an

anchor penetrated by underpressure, the relative magnitude of

these displacement components depends on how close the

underpressure is to causing an inverse bearing capacity failure

of the soil plug at skirt tip level. It is therefore expected that

more soil will move into the anchor as the depth to diameter

ratio increases. The cases analyzed here are not close to inverse

bearing capacity failure.

Development of mean total stress at depth of 13.7m

Examples of the change in the mean total stress, ∆σmean=1/3 (∆σ1 + ∆σ2 + ∆σ3), in two monitoring points at 0.33 m and

0.56 m outside the skirt wall at depth 13.7 m are shown for two

cases in Figure 7 (σ1, σ2 and σ3 are the principal total stresses).

The two cases are Case 4 (anchor with flat tip and roughness

factor of 0.25 penetrated by underpressure) and Case 5 (anchor

with tapered tip and roughness factor of 0.5 penetrated by

weight). The change in mean stress is plotted against the

penetration depth for 8 selected penetration depths starting

when the tip passes 13.7 m depth and ending at the final

penetration depth of 16 m.

The plots in Figure 7 show that the mean stress at 13.7m

depth decreases with penetration depth after the tip passes

13.7m. A near "steady-state" situation representative for an

infinitely long anchor is approached at a penetration depth of

about 16m. However, the plot shows that some additionareduction of the mean total stress can be expected for further

penetration (i.e. deeper than 16m). The trend of stress reduction

with depth shown for Cases 4 and 5 in Figure 7 is believed to

be representative also for the other cases.

Mean total stress distribution with depthFigures 8 and 9 show the contour shadings of changes in

mean total stress at the final penetration depth after unloading

the penetration force. The stress concentrations outside the skir

wall above 13.7m are caused by the analyses starting with the

“wished-in-place” condition at 11.4m depth. The effect of this

artificial starting point is reflected down to a penetration depth

of less than 13.7m for anchors penetrated by underpressure. Foranchors penetrated by weight, the stresses at 13.7m may have

some minor influence from the starting conditions at 11.4m.

There is also some stress concentrations around the skirt

tip, indicating that the stresses will not be fully uniform along

the whole skirt wall after penetration. The stress concentrations

around the skirt tip do not extend very far up along the skirt

wall when the anchor is penetrated by underpressure, and

normalized stresses at 13.7m will be reasonably representative

for the whole skirt length.

The stress concentrations extend further up along the wall

for anchors penetrated by weight, and the stresses at 13.7m will

tend to underestimate the stresses along the lower part of the

skirt for anchors penetrated by weight. This stress

concentration influences the stresses almost one anchor radius

above the skirt tip for anchors with flat skirt tip and roughness

factor of 0.5. The influence decreases with decreasing

roughness factor and is reduced by tapering.

The contours show some local stress variations along the

skirt wall between the zone influenced by the starting

conditions and the zone influenced by the concentrations

around the skirt tip. These variations are due to the finite size of

the penetration steps. Smaller steps would have evened out

these variations.

Mean total stress at depth 13.7m as function of radius

The change in mean total stress,∆σ

mean, outside the skirtwall along a horizontal section at depth 13.7 m after the skirt

has been penetrated to 16 m is plotted in Figures 10 and 11

before and after the penetration force is unloaded, respectively

The stresses in the zone close to the skirt wall are average

stresses over a large enough depth interval to even out the

stress concentrations along the skirt wall.

The stress change at the skirt wall at 13.7m depth is

summarized in Table 2. The stress change is normalized to the

initial in situ effective mean stress of σ’mean, initial= 62kPa, based


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Case1

Flat tip, r = 0.5,

Selfweight

Case5

Tapered tip, r = 0.5,

Selfweight

Case2

Flat tip, r = 0.5,

Suction

Case6


Suction

Case3

Flat tip, r = 0.25,Selfweight

Case7

Tapered tip, r = 0.25,Selfweight

Case4Flat tip, r = 0.25,

Suction

Case8


Suction

Figure 6a. Incremental displacements at failure when skirt

tip is at 13.7m. Roughness factor wall=0.5. Black arrows

give displacement direction where vectors may be unclear.

Figure 6b. Incremental displacements at failure when skirt

tip is at 13.7m. Roughness factor wall=0.25. Black arrowsgive displacement direction where vectors may be unclear.

on a submerged unit weight of γ ’= 6.5kN/m3 and a coefficient

of earth pressure at rest of K 0 = 0.55. These normalized stressesare representative for the conditions along the part of the wall

away from the zone influenced by the local variations around

the skirt tip.

highest for the high roughness factor.

- penetration by weight gives a significant increase in the

mean total stress at the anchor wall for all cases (32-46%

before unloading the penetration force). The stress increases

to a radius of more than 1.75-2.25 times the anchor radius

(1.4-2.4m from the wall).The data in Figures 10 and 11 and in Table 2 show that

- penetration by weight gives significantly higher mean totalstress increase than penetration by underpressure. The

difference depends strongly on the roughness factor, and is

- penetration by underpressure gives only a modest increasein the mean total stress outside a distance of about 1.25

times the anchor radius (0.5m from the wall). At the wall,


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the mean total stress after unloading decreases by 26-32%

of the initial mean effective stress for a roughness factor of

0.5 and increases by 2-16% for a roughness factor of 0.25.

It is assumed that the penetration force is unloaded in this

case.

The largest stress reduction for the highest roughness

factor for an anchor penetrated by underpressure can beexplained by the penetration resistance increasing with

increasing roughness factor. A higher penetration resistance

will require a higher underpressure at the top of the clay

plug inside the caisson, and this unloading causes a higher

reduction in the horizontal total stresses in the clay outside

the anchor at and below the anchor tip depth. As the skirt

penetrates into and through this zone, the reduced

horizontal total stresses will be “locked in” and give a

permanent reduction in the horizontal total stress along the

skirt at this depth.

- tapering gives somewhat higher mean total stress increasethan flat tips, but the effect is relatively modest, with

tapering giving 2-6% increase for a roughness factor of 0.5and 12-14% increase for a roughness factor of 0.25. These

ranges assume that the penetration force is not unloaded

when the anchor is penetrated by weight, and that it is

unloaded when the anchor is penetrated by underpressure.

Effect of mean total stress change on shear strengthalong outside skirt wall

The effect that the mean total stress change will have on

the shear strength along the outside skirt wall requires a finite

element consolidation analysis with modeling of the total stress

variation with radius (both in the remolded clay along the wall

and in the intact clay outside the remolded zone), the excess

pore pressure in the remolded zone, the shear induced pore

pressure in the intact clay, and the compressibility and

consolidation characteristics of the remolded and intact zones

(Andersen and Jostad, 2002). The shear strength change will

therefore not be proportional to the total stress change.

Generally, however, the stress changes calculated by the

new finite element analyses seem to support the

recommendations by Andersen and Jostad (2002). For anchors

penetrated by weight, they assumed that the mean total stress

changes outside the anchor would be large enough to restore

the initial shear strength with time as the excess pore pressure

dissipates, and that there would be no total stress change

outside an anchor penetrated by underpressure. Even if definite

conclusions can not be drawn without consolidation analyses,

the high calculated total stress change outside anchors

penetrated by weight is in line with their assumption.

For anchors penetrated by underpressure, Andersen and

Jostad (2002) assumed that no mean total stress change would

occur outside the anchor. The new calculations give a total

stress increase of 2-16% for a roughness factor of 0.25 and a

reduction of 32-26% for a roughness factor of 0.5. The first

numbers in the ranges are for flat skirt tips and the second

numbers are for tapered skirt tips. For a roughness factor of

0.25, the set-up factor will thus be very close to the set-up

factor from Andersen and Jostad (2002) for a flat tip, whereas

tapering may give potential for some small increase in the set-

up factor. For a roughness factor of 0.5, the set-up factor

related to effective stresses is likely to become smaller than

calculated by Andersen and Jostad (2002), for both flat and

tapered skirt tips. However, as shown by Andersen and Jostad(2002), thixotropy is likely to govern the shear strength if the

roughness factor is already 0.5 (sensitivity of 2), and a

thixotropy factor of only 1.3 is needed to reach a set-up facto

of 0.65.

Table 2. Mean total normal stress change at outside skirt

wall at 13.7m depth when the skirt is penetrated to 16m.

No αwall Penetr. Tip∆σmean/σ’mean,initia

l

Effect of

Tapering

Type Geom. No

Unl’d

After

Unl’d

No

Unl’d

After

Unl’d

1 0.5 Weight Flat 44% 33%

5 0.5 Weight Tapered 46% 35% 2% 2%2 0.5 Underpr Flat -31% -32%

6 0.5 Underpr Tapered -21% -26% 10% 6%

3 0.25 Weight Flat 32% 24%

7 0.25 Weight Tapered 44% 32% 12% 8%

4 0.25 Underpr Flat 6% 2%

8 0.25 Underpr Tapered 21% 16% 15% 14%

13.66

14.16

14.66

15.16

15.66

0 10 20 30 40 50 60 7

Sig_mean [kPa]


0

Case 5 r= 2.26 m

Case 5 r=2.5 m

Case 4 r= 2.26 m

Case 4 r=2.5 m

Figure 7. Changes of mean total stress, σmean,

during penetration for Cases 4 and 5 in two points(Depth 13.7m and radius 2.26m and 2.5m)


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Case 1

Flat tip, r = 0.5,

Self weight

< -50 kPa

Case 1

Flat tip, r = 0.5,

Self weight

< -50 kPa

Case 5


Self weight

< -50 kPa

Case 5


Self weight

< -50 kPa

Case 2

Flat tip, r = 0.5,

Suction

> 5 0 k P a

Case 2

Flat tip, r = 0.5,

Suction

> 5 0 k P a

Case 6


Suction

> 5 0

k P a

Case 6


Suction

> 5 0

k P a

Case 3

Flat tip, r = 0.25,

Self weight

< -50 kPa

Case 3

Flat tip, r = 0.25,

Self weight

< -50 kPa

Case 7


Self weight

Case 7


Self weight

Case 4

Flat tip, r = 0.25,

Suction

> 5 0 k P

a

Case 4

Flat tip, r = 0.25,

Suction

> 5 0 k P

a

Case 8


Suction

> 50 kPa

Case 8


Suction

> 50 kPa

Figure 8. Distribution of change in mean total stress,

σmean, for skirt penetrated to 16 m and thenunloaded. Roughness factor wall=0.5. Note that

compression is negative in these plots.

Figure 9. Distribution of change in mean total stress,

σmean, for skirt penetrated to 16 m and thenunloaded. Roughness factor wall=0.25.Note that

compression is negative in these plots.


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SUMMARY AND CONCLUSIONSTapering the skirt tip is thus giving potential for somesmall increase in the set-up factor for a roughness factor of

0.25, but tapering is not likely to have an effect for a roughness

factor of 0.5, since the set-up is then governed by thixotropy.

Stronger tapering of the skirt tip with a higher angle from the

horizontal is likely to give more effect than the 450 tapering

analyzed here, but one then needs to consider that a highertapering angle may weaken the skirt at the tip.

The installation of suction anchors has been simulated by

finite element analyses in order to study the impact of

installation by underpressure on the displacement pattern

beneath the anchor and the stress changes outside the anchor

wall. Both flat and tapered skirt tips were analyzed to assess the

potential benefit that a tapered skirt tip may have. The analyseswere made both for weight penetration and for penetration by

underpressure, and for roughness factors at the interface

between skirt wall and clay of 0.5 and 0.25.

The results of the analyses show that the displacemen

pattern of the soil depends strongly on whether the anchor is

penetrated by weight or by underpressure. Roughly half the soi

displaced by the anchor wall moves into the anchor when the

anchor is penetrated by weight, whereas essentially all the

displaced soil moves into the anchor when it is penetrated by

underpressure. Tapering causes more clay to move outside the

anchor than a flat tip in all cases, i.e. both for penetration by

weight and by underpressure and for roughness factors of 0.5

and 0.25.

-30

-20

-10

0

10

20

30

40

1.932 2.932 3.932 4.932 5.932 6.932 7.932 8.932 9.932

Radius [m]

S i g_

m e a n [ k P a ]

flat,r=0.5,selfweight


flat,r=0.5,suction

flat,r=0.25,suction

tapered,r=0.5,selfweight

tapered,r=0.5,suction



Penetration by weight gives significantly higher mean tota

stresses than penetration by underpressure, both at the outside

skirt wall and away from the wall. The difference is highest for

the highest roughness factor because more underpressure is

needed to penetrate the anchor. Tapering gives higher tota

stresses, but the effect is relatively modest, with a stress

increase of 2-6% for a roughness factor of 0.5 and 12-14% for

a roughness factor of 0.25.Figure 10. Distribution of mean total stress change, σmean,outside the skirt wall along horizontal section at depth

13.7m for skirt penetrated to 16m. Before unloading.Penetration by weight gives an increase in the mean tota

stress in all cases. The increase at the skirt wall is about 32-

46%, and the increase is highest for the highest roughness

factor and for tapered skirt tips.

-30

-20

-10

0

10

20

30

1.932 2.932 3.932 4.932 5.932 6.932 7.932 8.932 9.932

Radius [m]

S i g_

m e a n [ k P a ]



flat,r=0.5,suction

flat,r=0.25,suction





Penetration by underpressure gives only a modest increase

in the mean total stress outside a distance of about 0.5 m from

the wall. At the wall, the stress decreases by ~26-32 % of the

initial mean effective stress for a roughness factor of 0.5, but

increases by ~2-16% for a roughness factor of 0.25. Tapering

gives the highest stresses. Higher tapered angles may further

increase the mean total stress and ultimately the shear strength

along the outside anchor wall.

The calculated total stress changes for anchors penetrated

by underpressure agree reasonably well for a roughness factor

of 0.25 with the assumption of no total stress change outside

the anchor wall made by Andersen and Jostad (2002). The

calculated stress changes for roughness factor of 0.5, however

gives lower stresses than assumed by Andersen and Jostad

(2002). Considering both stress changes and thixotropy

however, the resulting set-up factor is likely to be very close to

the set-up factor recommended by Andersen and Jostad (2002).Figure 11. Distribution of mean total stress change, σmean,outside the skirt wall along horizontal section at depth

13.7m for skirt penetrated to 16m. After unloading.Tapering the skirt tip by 450 gives potential for some smal

increase in the set-up factor for a roughness factor of 0.25, but

tapering is not likely to have an effect for a roughness factor of

0.5, since the set-up is then governed by thixotropy.

The shear strength along the skirt wall will not be

proportional to the total stress, and additional consolidation


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analyses are needed to fully assess the detailed impact of

tapering and stress changes on the shear strength along the skirt

wall with time.

The analyses involve some simplifications, like small

strain and small displacement finite element formulations,

isotropic initial stresses and shear strength, and an elastic-

perfectly plastic soil model with a constant normalized shearmodulus. It is believed that the analyses still give reasonable

results, especially with respect to the relative effect of tapering

the skirt tips.

REFERENCES(1) Andersen, K. H. and Jostad, H. P. (1999). Foundation

design of skirted foundations and anchors in clay. Offshore

Technology Conference, Houston, Proc., Paper 10824.

(2) Andersen, K. H. and Jostad, H. P. (2002). Shear strengthalong outside wall of suction anchors in clay after

installation. Proc., XII ISOPE Conference, Kyushu, Japan,

26 – 31 May 2002

(3) PLAXIS, (2003) www.plaxis.nl

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