Optimal Skirt Spacing

Applied Ocean Research 48 (2014) 1020

Contents lists available at ScienceDirect

Applied Ocean Research

journal homepage: www.elsevier.com

Optimal skirt spacing for subsea mudmats underdegrees of freedom

X. Feng

Centre for Offsh , Craw

a r t i c l

Article history:Received 11 AReceived in reAccepted 14 Ju

Keywords:Seabed foundaBearing capacFailureNumerical moOffshore enginTorsion

mencapacl momf thee idelly thmatshe nug is pisatioratio

1. Introdu

With the exploration and exploitation of offshore oil and gasmoving into deep and ultra-deep water, skirted mudmat founda-tions have been increasingly deployed on the seabed to supportsubsea struin-line strua rectangulskirts. Peneline increaswith surfac

Capacitycient interoccur withiSo-called indations witheterogeneplug is loweat skirt-tip lmechanism

CorresponE-mail add

(X. Feng), susamark.randolph

1 Tel.: +61 82 Tel.: +61 8

respvertical load (V), moment (M) and horizontal load (H) has beeninvestigated previously by means of nite element (FE) and upperbound plasticity analysis, see e.g. Refs. [1,2,6,8,9,18]. These studiescan be applied to skirted foundations on the assumption that suf-

0141-1187/$ http://dx.doi.octures such as pipeline end terminations (PLETs) andctures. Skirted mudmat foundations typically consist ofar plate (i.e. the mat), tted with perimeter and internaltration of the skirts into stronger soil below the mud-es capacities of skirted mudmat foundations comparede foundations.

of skirted foundations can be compromised if insuf-nal skirts are provided, as soil failure mechanisms cann the soil plug under certain loading and soil conditions.ternal mechanisms are most prone to occur in foun-h low embedment ratio and soils with high strengthity. In these cases, the average strength within the soilr than the strength of soil beneath foundation level (i.e.evel), providing a path of lower resistance for the failure

within the soil plug.

ding author. Tel.: +61 8 6488 2473; fax: +61 8 6488 1044.resses: [email protected], [email protected]@uwa.edu.au (S. Gourvenec),@uwa.edu.au (M.F. Randolph).

6488 3094. 6488 3075.

cient internal skirts are provided so that the soil plug enclosed bythe perimeter skirts displaces as an intact body with the founda-tion during loading. The potential reduction in foundation capacityresulting from internal mechanisms has been demonstrated forparticular soil and loading conditions, see e.g. Refs. [3,12].

The role of internal skirts has received greater attention recentlyin response to the increased use of skirted mudmat foundations indeepwater seabeds, which typically comprise soft normally con-solidated or lightly over consolidated sediments. The high strengthgradients at shallow depth increase the tendency for internal mech-anisms between the skirts.

A simple method to determine the minimum skirt spacing forskirted foundations to resist signicant lateral loads is proposedin a marine geotechnical handbook [17] and recommends a spac-ing no greater than 1.0 d in cohesive soil (where d the skirt depthas depicted in Fig. 1). The method does not extend to generalcombined loading conditions and the recommended spacing is con-siderably closer than commonly adopted in practice. A systematicstudy of optimal skirt spacing has been proposed for skirted foun-dations under combined in-plane VMH loading, but the studywas restricted to conditions of plane strain and to only the limitsof soil strength heterogeneity [11]. Subsea mudmats are gener-ally three-dimensional in geometry and subjected to loading in sixdegrees-of-freedom (see Fig. 1), namely vertical load (V), biaxial

see front matter 2014 Elsevier Ltd. All rights reserved.rg/10.1016/j.apor.2014.07.006, S. Gourvenec1, M.F. Randolph2

ore Foundation Systems M053, University of Western Australia, 35 Stirling Highway

e i n f o

pril 2014vised form 14 July 2014ly 2014

tionsity

dellingeering

a b s t r a c t

Two- and three-dimensional nite elespacing for the maximum undrained ing (vertical, biaxial horizontal, biaxiaembedment ranging from 5% to 20% ostrength with depth. The results havspacing for mudmats subjected to fuspacing for rectangular or square mudalent foundation embedment ratio. Tunder fully three-dimensional loadingeneity index and vertical load mobilnegligible as foundation embedment

ction The/locate/apor

loading in six

ley, Perth, WA 6009, Australia

t analyses are performed to identify the optimal internal skirtity of subsea skirted mudmats. Fully three-dimensional load-ent and torsion) is considered for subsea mudmats with skirt

foundation breadth in soil with a range of linearly increasingntied the governing case for determining the optimal skirtree-dimensional loading. It is also shown that optimal skirt

can be determined in plane strain conditions using the equiv-mber of internal skirts required to ensure soil plug rigidityresented as a function of skirt embedment ratio, soil hetero-n. Results also indicate that effects of skirt roughness becomeincreases in terms of determining the optimal skirt spacing.

2014 Elsevier Ltd. All rights reserved.

onse of shallowly embedded foundations to combined

X. Feng et al. / Applied Ocean Research 48 (2014) 1020 11

y

V

HxHy

Mx

My

LRP

B

T

z

x

L

mudline

z

susum

su0d

k

1

Fig. 1. Nomenclature for foundation geometry, general loading and soil strength prole.

horizontal load (Hx, Hy), biaxial moment (My, Mx) and torsion (T),referred to here as VH2M2T loading. The generality of previ-ous ndings based on in-plane VMH loading should therefore beveried. VH2M2T load capacity of square skirted mudmats wasinvestigated for limiting cases of soil strength heterogeneity [5], butto date there has been no systematic study to dene optimal skirtspacing across a full range of foundation aspect ratios and embed-ment ratios for practical intervals of soil strength heterogeneity.

The work presented in this paper identies the optimal skirtspacing of subsea mudmats for maximum capacity (i) under fullythree-dimensional loading conditions, (ii) over the range of plangeometry from strip to square, (iii) embedment ratios from 5% to20% of the foundation breadth, (iv) and at practical intervals of soilstrength heto essentialof skirted mpresented ispacing is dfrom paralldations. Deskirt spacinembedmenmobilisatio

2. Finite el

All the carried out

2.1. Geometry and meshes

The three-dimensional nite element mesh used for the analy-sis of a typical rectangular mudmat with breadth-to-length aspectratio of B/L = 0.5 is shown in Fig. 2 (half-view). The breadth (sidelength for a square mudmat) was taken as B = 5 m for all of theanalysis, but the results are presented as normalised quantitiesso that they are independent of the selected foundation size. Themeshes extended 3B from the edges of the foundation and 3Bbeneath the foundation base (or skirt tip) level, with horizontallyconstrained nodes at the sides, and fully constrained nodes at thebase. The boundaries were shown to be sufciently remote so thatthe failure mechanism was not affected. A region of very thin ele-

was accuengttiontral dmalongiize ased

elemariauilibts arle anrainterogeneity over the full range from uniform with depthly normally consolidated. The load-carrying capacitiesudmats under fully combined loading conditions are

n the form of failure envelopes and the optimal skirtened by comparing the failure envelopes obtainedel analyses of the skirted and solid embedded foun-sign charts are proposed for determining the optimalg as a function of foundation aspect ratio, foundationt ratio, soil heterogeneity index and the vertical loadn.

ement model

nite element analyses presented from this study wereusing the commercially available software Abaqus [4].

mentsensuresoil strfoundathe cenlar muin the ment swere uhybridstress vthe eqelemenpressibfor und(a) FE mesh

Fig. 2. FE mesh for rectangular mudmats d/B = 0.1, B/L = 0.5 half mesh with planprovided at foundation level (approximately 0.3%B) torate representation of shearing, especially with highh heterogeneity. The meshes for the square mudmats maintained the same geometry and discretisation onplane (i.e. the front face in Fig. 2) as for the rectangu-ts. Fewer elements were used for square foundationstudinal direction in order to maintain a consistent ele-cross the models. Linear 8-node brick hybrid elementsfor the rectangular and square foundation models. Theent formulation uses a mixture of displacement and

bles (as opposed to solely displacement) to approximaterium equations and compatibility conditions. Hybride recommended for modelling the response of in com-d near-incompressible materials (such as is appropriateed soil conditions).

(b) Solid foundati on (c) Skirted foundation

e of symmetry through foundation centreline.

12 X. Feng et al. / Applied Ocean Research 48 (2014) 1020

LRP

exte rnal skirts

it mod

-1.5

Mo

men

t, M

y/A

Bs u

0

p

Fig. 4. Compausing explicit

A plane eral hybrid the front fawas used, aanalysis pranalyses.

The fountions with awhether a sa load referdation at mdisplacemeskirts, whethe mesh ncoupling coconstrainedthe group oThe advantthin columexplicitly (tciated withfor skirted internal ski

ateri

und wiintern al skirts

L

B

(a) Skirte d foundation

Fig. 3. Schematic of skirted foundations and implic

2

2.5 Failure envel ope

Explicit skirts

implicit skirts

2.2. M

Theuniform0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5

Horiz ontal load, Hx/Asu0

p = 0.2

p = 0.6

p = 1

p = -0.2

= -0.6

p = -4p = 4

rison of loading paths and failure envelope for a skirted foundationand implicit internal skirts: kB/sum = 100 and d/B = 0.1.

strain mesh was constructed using 4-node quadrilat-elements. The same geometry and discretisation as force of the three-dimensional mesh as shown in Fig. 2nd equivalent boundary conditions, soil conditions andocedures were modelled as in the three dimensional

dations were modelled as a solid plug or skirted founda- number, n, of internal skirts (0 n 8). The foundation,olid plug or skirted, was modelled as a rigid body withence point (LRP) dened at the centroid of the foun-udline level. In the analyses, all foundation loads andnts were applied or recovered at this point. Internalre provided, were implicitly modelled by constrainingodes at the relevant location(s) using the kinematicnstraint method, as shown schematically in Fig. 3. The

nodes were coupled to the LRP such that the motion off coupled soil nodes was limited to that of the rigid body.age of this method is that it avoids (a) the extremelyns of elements required for modelling internal skirts

0.1%B in reality), and (b) the contact iterations asso- the soilskirt interface. Therefore, the current modelsfoundations are more time-efcient and stable than ifrts are represented explicitly.

su = sum + kzk is the shheterogenewhere 0 reearly increastrength inwas consideles with inalso convenin the vicinwhere su0 =(homogene

The soil a Tresca faithe previoumodel. TheMises critesis predicts(based on pity diminishconverges fwere denesons ratio othe constantions). ThisG is the shesmall displa

The intefoundationno detachmbonded) to of a skirtedthe undersitions were For the solthe externamodelled anormal streof capacity.LRP

(b) Explicit inte rnal skirts

(c) Implicit inte rnal skirts

Kinematic coupli ng constrai nts

soil nodes

elling of internal skirts.

al properties and interface conditions

rained shear strength of the soil was modelled as eitherth depth or increasing linearly with depth according to, where sum is the shear strength at the mudline andear strength gradient with depth, z (Fig. 1). The soility is described by the dimensionless index = kB/sumpresents a uniform strength with depth and a lin-sing strength with depth with essentially zero mudlinetercept, i.e. normally consolidated. A range of 0 red to cover the whole range of linearly increasing pro-termediate values of = 2, 5, 8, 10, 20, 30 and 100. It isient to consider the local shear strength heterogeneityity of the skirt tips, which can be dened by kd = kd/su0,

sum + kd. The value of kd is constrained to lie between 0ous) and 1 (zero strength intercept at mudline).was modelled as linear elastic, perfectly plastic obeyinglure criterion to make straightforward comparison withs published data to validate the present nite element

shear strength would be adjusted appropriately if a vonrion was used. For a square foundation, Tresca analy-

3% higher vertical capacity compared with von Miseslane strain, or simple shear, strength) and the dispar-es as the foundation length increases until the solution

or plane strain conditions [10]. The elastic propertiesd by undrained Youngs modulus E = 1000su and Pois-f = 0.49 (to avoid numerical difculties associated witht-volume response of soil under truly undrained condi-

gives a relatively high rigidity index G/su of 336, wherear modulus of the soil, so that failure occurs at relativelycements to avoid problems of mesh distortion.rface between the underside of the rigid solid plug

and the subsoil was taken to be rough in shear withent between the mudmat and soil permitted (i.e. fullyrepresent the rough soilsoil interface at skirt tip level

foundation. The inside faces of the peripheral skirts andde of the foundation base plate of the skirted founda-also prescribed a fully bonded interface with the soil.id plug and skirted foundations, the contact betweenl face of the peripheral skirts and the adjacent soil wass frictionless with separation permitted under tensiless at the interface, providing a conservative prediction


(a) = 0

1.5

1.8

-1.5 -1

Mo

men

t, m

y=

My/A

Bs u

0 1.5

1.8

-1.2

s u0

B0L0, B1L1, B2L2, Solid

(c) = 3

-1.5

Mo

men

t, M

y/A

Bs u

0

2.3. Load pa

The resVH2M2TFailure enverally evaluprobe testsin Abaqus. experimentlarge sectio0

0.3

0.6

0.9

1.2

.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Horiz ontal load, Hx/As u0


-1.5

Mo

men

t, M

y/A

B(b) = 2

0

0

0.3

0.6

0.9

1.2

1.5

1.8

-1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5


B0L0, B1L1, B2L2, B3L3, Solid

(d) = 100

-1.5 -

Mo

men

t, M

y/A

Bs u

0

(e) =

0

0.3

0.6

0.9

1.2

1.5

1.8

-1.5 -1.2 -0.9 -0.6 -0.3 0 0

Mo

men

t, M

y/A

Bs u

0

Horiz ontal load, Hx

B0L

Fig. 5. Failure envelopes for mudmat foundation under in-plan

th

ponse of the mudmat foundations subjected to loading is presented in the form of failure envelopes.elopes under combined loading conditions are gen-ated through swipe tests or xed ratio displacement, implemented using the general static proceduresSideswipe tests, which have been used in previousal and numerical work, take advantage of allowingns of failure envelope to be investigated in a single

analysis, secontrolled the load paenvelope, peral VH2a proportiotion, was icomponentdetect eachfoundation0

0.3

0.6

0.9

1.2

-0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5


0.3

0.6

0.9

1.2

1.5

1.8

1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5


B0L0, B1L1,B2L2, B3L3, B4L4, Solid

.3 0.6 0.9 1.2 1.5

/Asu0

0, B1L1, B2L2, B3L3, B4L4, Solid

e VMy-Hx loading, d/B = 0.1.

e e.g. Refs. [9,16]. However, xed ratio displacementprobe tests were carried out in this study becauseth in a sideswipe test can undercut the true failurearticularly for embedded foundations [7]. For gen-M2T loading, a constant vertical load, expressed asn of the ultimate vertical capacity of a solid founda-mposed and the horizontal load, moment or torsions were applied as a series of displacement probes to

failure envelope. Failure envelopes were derived for embedment ratios d/B = 0.05, 0.1 and 0.2, for various


(a) = 0

2

2.5

-1.5 -1

Mo

men

t, M

x/A

Ls u

0 2

2.5

-1.2

s u0 B1L1, B2L2, Solid

(c) = 3

-1.5

Mo

men

t, M

x/A

Ls u

0

degrees of in planes othe ultimatwith equal tions.

3. Results

3.1. Validat

The threcomparing plasticity soon homogen0

0.5

1

1.5

.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Horiz ontal load, Hy/Asu0


(b) = 2

-1.5

Mo

men

t, M

x/A

L

2.50

0

0.5

1

1.5

2

-1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5


B0L0, B1L1, B2L2, B3L3, Solid

(d) = 10

-1.5

Mo

men

t, M

x/A

Ls u

0

(e) =

0

0.5

1

1.5

2

2.5

-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0

Mo

men

t, M

x/A

Ls u

0


B0L0, B1L1, B

Fig. 6. Failure envelopes for mudmat foundation under in-plan

shear strength heterogeneity over the range 0 ,f V/Vult = 0, 0.25, 0.5 and 0.9, where Vult is taken ase vertical bearing capacity of the solid rigid foundationembedment ratio to the corresponding skirted founda-

ion of FE model

e dimensional nite element models were validated bythe predicted vertical bearing capacity with analyticallutions for rectangular and square mudmat foundationsous soil ( = 0) as shown in Table 1. The bearing capacity

factors for sthe numeriFE results ofoundationvalues, dueresult of sm

The modconstraintsied. An eenvelope fkB/sum = 10selected loadifferent dnon-dimen0

0.5

1

1.5

-0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5


0

0.5

1

1.5

2

2.5

-1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5


B0L0, B1L1, B2L2, B3L3, B4L4, S olid

.6 0.9 1.2 1.5

2L2, B4L4, B6L6, S olid

e V-Mx-Hy loading, d/B = 0.1.

trip foundations obtained from FE analysis over-predictcal upper bound solutions [14] by approximately 2%. Thef vertical bearing capacity for the three-dimensional

geometry are bracketed by the lower and upper bound to lower overestimation of the true collapse loads, as aoothing of the Tresca yield surface in Abaqus [15].elling of the internal skirts using kinematic coupling

instead of being implemented explicitly was also ver-xample is presented in Fig. 4 showing the failureor a skirted foundation on heterogeneous soil with0 under combined HxMy loading along with severalding paths, which are the reactive forces obtained fromisplacement controlled probe tests represented by asional parameter p = ux/(By). In the analyses, the


Fig. 7. Kinematic failure mechanisms for kB/sum = 2 and d/B = 0.1; loading V/Vult = 0.5; My/BHx = 1.5.

foundation two separatimplicit aneither by ktion using cand failure skirts are evcoupling coaccuracy.

3.2. In-plan

The optijected to in

Table 1Comparison of

d/B

0.00 0.05 0.10 0.20

a FEA denotLB and UB are Fig. 8. Kinematic failure mechanisms for kB/sum = 100 and d/B = 0.1;

had one internal skirt in each direction, simulated ined models in the form of implicit and explicit skirts. Thed explicit skirts refer to skirts modelled respectivelyinematically constrained soil nodes or by discretisa-ontinuum solid elements. The identical loading pathspoints for skirted foundations with implicit and explicitident for any given value of p. Therefore, the kinematicnstraint method is effective without compromising

e VMH loading

mal internal skirt spacing for mudmat foundations sub--plane VMH loading was explored rst. Figs. 5 and 6

show the cotions, B/L = 2, 30, 100 tion and skskirts. Skirthe breadthFigs. 5 andfoundationas having envelope cimum loadleads to exincrease ofnal skirts w

vertical bearing capacity calculated by FE and plasticity analysis for uniform soil strengt

Strip B/L = 0 Rectangular B/L = 0.5

FEAa LB UB FEA LB

5.280 5.132 5.203 5.642 5.359 5.500 5.293 5.384 6.027 5.640 5.612 5.448 5.548 6.230 5.860 5.840 5.696 5.806 6.661 6.197

es results of nite element analyses from this studylower and upper bound results from Salgado et al. [14]. loading V/Vult = 0.5; My/BHx = 1.5.

mbined HM loading capacity for rectangular founda-0.5, with an embedment ratio d/B = 0.1, for kB/sum = 0,and , in a plane of V/Vult = 0.5 for a solid founda-irted foundations with different numbers of internalt conguration BnLn denotes n internal skirts along

(B) and length (L) of the foundation. As shown in 6, the innermost failure envelope corresponds to a

with peripheral skirts only, which is referred tozero internal skirts or B0L0. The outermost failureorresponds to the solid foundation dening the max--carrying capacity. The addition of internal skirtspansion of the H-M failure envelope, indicating the

load-carrying capacity. The optimal number of inter-as determined as when the failure envelope of the

h, kB/sum = 0.

Square B/L = 1.0

UB FEA LB UB

6.022 5.843 5.523 6.2216.503 6.372 5.886 6.8156.756 6.650 6.171 7.1307.116 7.136 6.590 7.524


0

0.3

0.6

0.9

1.2

1.5

0 0.3 0.6 0.9 1.2 1.5

Ho

rizo

nta

l lo

ad, H

y/A

s u0


Solid

B0L0

B1L1

Fig. 9. Failure envelopes for mudmat foundations under biaxial horizontal loading,kB/sum = 100 and d/B = 0.1.

skirted foundation coincided with that of a solid foundation orwhen the inn + 1 internations B2L2 amaximum Hlinearly inctively, for v

The failuto show theinternal skid. Figs. 7 anline cross-sfor rectanguering soil hsoil ow vesition in faithe point wcorrespondcated in theFig. 5b and

3.3. V-H2-M

Externaling in six dis thereforedeterminincase was idstudy.

The probelow for anratio d/B = 0for solid an

0

0.5

1

1.5

2

2.5

3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

Mo

men

t, M

x/A

Ls u

0

Moment, My/ABsu0

Solid

B0L0

B1L1

B2L2

B3L3

Fig. 11. Failure envelopes for mudmat foundations under biaxial moment loading,kB/sum = 100 and d/B = 0.1.

can be seenskirtntal c. 10 ing aal caadthuire

ntal a are tive mbinpplie

skirhorizs sufmob

thretionlure ele 2 l cap

t is ally reg caploading v

verincludinine crite V

g forcrease of capacity of a skirted foundation with n andl skirts was negligible. For example, the skirt congura-nd B3L3 were considered to be sufcient to mobilise thexMy load-carrying capacity for a soil strength prole

reasing with depth with kB/sum = 2 and 100, respec-ertical load mobilisation V/Vult = 0.5.re envelopes allow selection of example loading paths

transformation of soil failure mechanisms for differentrt spacings. Two such paths are shown in Fig. 5b andd 8 illustrate selected failure mechanisms at the mid-ection of the foundation for in-plane VMyHx loadinglar foundations with embedment ratio d/B = 0.1 consid-eterogeneity = kB/sum = 2 and 100. The comparison ofctors for solid and skirted foundations shows the tran-lure mechanisms with additional internal skirts, up tohere the soil plug remains intact. The load combinationsing to the failure mechanisms in Figs. 7 and 8 are indi-

failure envelopes by the constant My/BHx load path ind, respectively.

2-T loading

loads applied to subsea structures often result in load-egrees of freedom being transferred to the mudmat. It

important to identify the controlling load case(s) forg the optimal spacing of internal skirts. The critical loadentied for the range of conditions considered in this

cedure to verify the governing case is demonstrated example of a rectangular foundation with embedment.1. Fig. 9 shows the biaxial horizontal loading capacityd skirted foundations in the absence of vertical load. It

of the horizoing. FigT loadtorsionthe brethe reqhorizoanismsand acthe cocally aby theimum B1L1 ice to two orfoundathe fai

Taboptimaload. Igeneraloadinimum increasand is it is codetermthat thin-planspacin(a) Comb ined Hx-T loading

0

0.1

0.2

0.3

0.4

0.5

0 0.3 0.6 0.9 1.2 1.5

To

rsio

n, T

/AL

s

Horiz ontal load, H /As

Solid

B0L0

B1L1

0

0.1

0.2

0.3

0.4

0.5

0

To

rsio

n, T

/AL

s

Fig. 10. Failure envelopes for mudmat foundations under combined H that a single internal skirt along the breadth and lengthed foundation is required to mobilise the maximumapacity, irrespective of the direction of horizontal load-shows the failure envelopes for combined HxT and Hynd indicates that the optimal combined horizontal andpacity is also achieved with a single internal skirt along

and length of the foundation. It is to be expected thatd number of internal skirts is the same under biaxialnd torsional-horizontal loading since the failure mech-governed by soil shearing at skirt tip level and passivesoil failure against the skirts in both modes [13]. Fored HT loading, which is generated by an eccentri-d horizontal load, the additional resistance providedts can never be larger than that to mobilise the max-ontal capacity. Therefore, if the skirt conguration ofcient for maximum horizontal capacity, it must suf-ilise the maximum combined HT capacity. By contrast,e skirts are required along the breadth and length of the

to achieve optimal moment capacity, as indicated bynvelopes for biaxial moment capacity shown in Fig. 11.summarises the number of internal skirts required foracity in all planes of loading in the absence of verticalpparent that the greatest number of internal skirts isquired for mobilising maximum combined Hx(y)My(x)acity. The number of internal skirts required for max--carrying capacity has been shown to increase withertical load mobilisation for plane strain conditions [11]ed in this study, as illustrated later in Fig. 15. Therefore,ed that in-plane VMH loading is the critical case for

g optimal internal skirt spacing and it may be assertedical number of internal skirts for mudmats subjected toMH loading can be used for selection of internal skirt

mudmats under VH2M2T loading.(b) Combined Hy-T loading

0.3 0.6 0.9 1.2 1.5

Horiz ontal load, H /As

Solid

B0L0

B1L1

T loading, kB/sum = 100 and d/B = 0.1.


Table 2Optimal number of internal skirts along breadth and length of a rectangular mudmat under various loading conditions, kB/sum = 100, V/Vult = 0.

Loading condition Optimal number of internal skirts

d/B = 0.05 d/B = 0.1 d/B = 0.2

Breadth (B) Length (L) Breadth (B) Length (L) Breadth (B) Length (L)

Combined HxHy 1 1 1 1 1 1Combined MyMx 3 5 2 3 1 2Combined HxT 1 1 1 1 1 1Combined HyT 1 2 1 1 1 1Combined Hx(y)My(x) 3 6 2 3 1 2

0

0.3

0.6

0.9

1.2

1.5

1.8

-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Mo

men

t, M

/B2s u

0

B0, B1, B2, B3, B4, Solid

0

0.3

0.6

0.9

1.2

1.5

1.8

-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Mo

men

t, M

y/A

Bs u

0

B0L0, B1L1,B2L2, B3L3, B4L4, Solid

3.4. Effects number of in

The optianalysed tofailure enve(a) B/L = 0; d /B = 0.1

Horiz ontal load, H/ Bsu0

1.5

1.8 B0L0, B1L1, B2L2, B3L3, Solid

s u0(c) B/L = 0.5 ; d /L = 0.1 (d /B = 0.2)

0

0.3

0.6

0.9

1.2

-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Mo

men

t, M

x/A

Ls u

0


-1.5 -1.2

Mo

men

t, M

y(x

)/A

B

Fig. 12. Failure envelopes for different foundation shapes with equiva

of foundation shape and roughness on optimalternal skirts

mal number of internal skirts for strip foundations was investigate the effect of foundation shape. Fig. 12 showslopes for foundations with different breadth to length

aspect ratioin-plane Vthat the nuerally the sfor loadingplane paral

Fig. 13. Comparison of failure mechanisms for a rectangular and(b) B/L = 0.5; d /B = 0.1


1.5

1.8 B0L0, B1L1, B2L2, B3L3, B4L4, Solid(d) B/L = 1; d /B = 0.1

0

0.3

0.6

0.9

1.2

-0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Horiz ontal load, Hx(y)/Asu0

lent embedment ratio, kB/sum = 100.

s, B/L, but the same equivalent embedment ratio underMH loading, on soil with kB/sum = 100. It can be seenmber of internal skirts for maximum capacity was gen-ame for a given equivalent embedment ratio (i.e. d/B

in a plane parallel to the shorter side, and d/L for thelel to the longer side), irrespective of the breadth to

strip foundation, kB/sum = 100.


(a) k B/sum = 0

0

1

2

3

4

5

0 0.05 0.1 0.15 0.2

Cri

tica

l num

ber

of

inte

rnal

skir

ts

Embedment rati o, d/B

Rough skirts: 0 < v 0.25

Rough skirts: 0.25 < v 0.5

Smooth skirts: 0 < v 0.25

Smoo th skirts: 0.25 < v 0.5

(b) k B/sum =

0

1

2

3

4

5

6

7

8

9

10

0 0.05 0.1 0.15 0.2

Cri

tica

l num

ber

of

inte

rnal

skir

ts

Embedment rati o, d/B

Rough skirts: 0< v 0.25

Rough skirts: 0.25 < v 0.5

Smoo th skirts: 0 < v 0.25

Smoo th skirts: 0.25 < v 0.5

Fig. 14. Effect of roughness of internal skirts and underside of foundation baseplate on optimal number of internal skirts.

length aspect ratio. Fig. 13 demonstrates similarity of the soil failuremechanisms for a rectangular foundation and strip foundation withequivalent embedment ratio and the same number of internal skirtsunder a selected MH load path of M/BH = 1.5, for given vertical loadmobilisation, V/Vult = 0.5, reecting the observations from the fail-ure envelopes. The similarity arises as the horizontal and momentfailure mechanisms are essentially in-plane and hence independentof the length to breadth aspect ratio of the foundation. As load com-binations involve signicant vertical load mobilisation, soil failuremechanisms may extend in the out-of-plane directions for three-dimensional foundation geometry and the comparison with plane

strain conditions would become marked. Therefore, plane strainanalysis can be used to determine the optimal number of internalskirts using the relevant embedment ratio, d/B or d/L, according tothe plane of loading being considered for rectangular mudmats.

The effect of interface roughness of the internal skirts on theoptimal number of skirts for maximum capacity was explored bycomparing results for this study with results for strip foundationswith all smooth interfaces, including the skirtsoil interface andat the underside of the base plate [11]. A comparison is shown inFig. 14 and in general one additional skirt is required for foun-dations with a completely smooth foundationsoil interface to

(a) V/V

0

1

2

3

4

5

6

7

8

9

10

0

Op

tim

al n

um

ber

of

inte

rnal

skir

ts

Solid lines in order:

> 1 00

50 < 10 0

8 < 50

0 8

s/d = 5

s/d = 3 s/d = 1

) 0.25

2

3

4

5

6

7

8

9

10

0

tim

al n

um

ber

of

inte

rnal

skir

ts

Solid li nes in order:

> 1 00

20 < 10 0

10 < 20

8 < 10

0 8

s/d = 5

s/d = 3 s/d = 1

es in o

10 0 ult 0.25

0.05 0.1 0.15 0.2

Equivalent embedment ratio, d/B (d/L)

(b

0

1 Op

8

9

10

skir

ts s/d = 1 s/d = 3

Solid lin

> 1 00

20 < (c) 0.5 < V/Vult 0.9

0

1

2

3

4

5

6

7

0 0.05 0.1 0.15

Op

tim

al n

um

ber

of

inte

rnal

Equivalent embedment rati o, d/B (d/L)

s/d = 5

10 < 20

8 < 10

5 < 8

2 < 5

0 2

Fig. 15. Optimal number of internal skirts for subsea mudmat < V/Vult 0.5

0.05 0.1 0.15 0.2

Equivale nt embedment rati o, d/B (d/L)

rder: 0.2

s under VH2M2T loading.


(a) V/Vu

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

Eq

uiv

alen

t sk

irt

spac

ing r

atio

, s/

B (

s/L

) d/B (d/L) = 0.05

d/B (d/L) = 0.1

d/B (d/L) = 0.2

< V

0.8

0.9

1

0

o,

s/B

(s/

L)

d/B (d/L) = 0.05

d/B (d/L) = 0.1

0.6

eneity

mobilise threquired dufoundation becomes leratio as the

3.5. Design

Fig. 15 pnumber of equivalent fity index anratio is takethe foundatskirts acrosnumber of idation embincreasing lof internal sratios, s/d, irule of thumof internal soil heterogunconservaerogeneity unity, as repredict the

Equivales/B = 1/(n + 1tion of the lt 0.25

0.2 0.4 0.6 0.8 1

Local s oil strength heterogeneity, d = kd/su0

(b) 0.25

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Eq

uiv

alen

t sk

irt

spac

ing:r

ati

(c) 0.5 < V/Vult 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4

Eq

uiv

alen

t sk

irt

spac

ing r

atio

, s/

B (

s/L

)

Local s oil strength heterogFig. 16. Optimal skirt spacing as a function of local soil stren

e maximum available capacity. The additional skirt ise to the reduced resistance at the underside of theplate in the skirted compartment and the effect

ss pronounced with increasing foundation embedment failure mechanism is pushed towards skirt tip level.

guidance

rovides a practical guide for determining the optimalinternal skirts for subsea mudmats as a function ofoundation embedment ratio, soil strength heterogene-d vertical load mobilisation. The equivalent embedmentn as d/B for dening the number of internal skirts acrossion breadth and d/L for dening the number of internals the foundation length of a rectangular mat. The criticalnternal skirts is seen to increase with decreasing foun-edment ratio, increasing soil heterogeneity index andevel of vertical load mobilisation. The required numberkirts described by constant skirt spacing to skirt depths also shown. A value of s/d = 5, commonly taken as ab for skirt spacing, over estimates the critical number

skirts for cases of low vertical load mobilisation, loweneity index and low embedment ratio but becomestive with increasing vertical load mobilisation, soil het-index and foundation embedment ratio. An s/d ratio ofcommended by Thompson et al. [17], is shown to overrequired number of skirts for all conditions.ntly, the optimal internal skirt spacing ratio,) (or equivalent for s/L), may be plotted as a func-local soil heterogeneity index, d = kd/su0, focusing on

the local swithin the spacing vahigh as 0.5at high dembedmen

The optiwas determenvelope ofoundationwith n andthat enginegent criterion a case by

The guidered, in pastrength wseabeds. Selevel overlyIndividual cthose consi

4. Conclus

This papundrained cloading. Thcapacity hation of skirand vertica/Vult 0.5

0.2 0.4 0.6 0.8 1

Local s oil strengh t heterogeneity, d = kd/su0

d/B (d/L) = 0.2

0.8 1

, d = kd/su0

d/B (d/L) = 0.05

d/B (d/L) = 0.1

d/B (d/L) = 0.2gth heterogeneity, kd/su0.

hear strength gradient relative to the local strengthskirt compartment. Fig. 16 shows that the optimal skirtries from approximately 0.33 (though potentially as

at low vertical load) at low d down to around 0.2but with some dependence on vertical load level andt ratio.mal internal skirts spacing indicated in Figs. 15 and 16ined, as dened at the outset, as when the failure

f the skirted foundation coincided with that of a solid or when the increase in capacity of a skirted foundation

n + 1 internal skirts was negligible. It is acknowledgedering judgement may be used to determine a less strin-on, but this would be the responsibility of the designer

case basis.ance provided here is valid for the conditions consid-

rticular for soil proles with linearly increasing shearith depth, as commonly encountered in deepwaterabeds in some regions may exhibit a crust at mudlineing a deposit with linearly increasing strength prole.onsideration should be given to soil conditions outsidedered in this study.

ions

er presents results from nite element analyses of theapacity of subsea skirted mudmats under VH2M2Te optimal number of internal skirts for maximums been presented as simple to use design charts as a func-t embedment ratio, soil strength heterogeneity indexl load mobilisation. The effects of three dimensional


foundation geometry and skirt interface roughness were also quan-tied. In summary, the results have shown that:

Internal skirts of mudmat foundations can be effectively mod-elled by kinematic coupling constraint techniques.

In-plane VMH loading is the governing load combination interms of determining the required skirt spacing for skirted mud-mat foundations under general VH2M2T loading.

More internal skirts are required to mobilise maximum capac-ity of skirted mudmat foundations if the foundation undersideand internal skirtsoil interface is smooth as opposed to roughparticularly at low embedment ratios.

Plane strain analysis can be used to predict the critical numberof internal skirts along the breadth and length of a rectangularfoundation using equivalent foundation embedment ratios of d/Band d/L.

Simple to use charts can provide design guidance on the crit-ical number of skirts, or equivalent skirt spacing, for optimalfoundation capacity under VH2M2T loading as a function ofnormalised skirt embedment ratio, soil strength heterogeneityindex and level of vertical load mobilisation.

Although the primary focus of the paper has been to identifythe critical number of skirts to guarantee maximum capacity of thefoundation, results may also be implemented in simple models thatquantify the reduction in capacity for foundations containing fewerinternal skirts than critical.

Acknowledgements

This work forms part of the activities of the Centre for OffshoreFoundation Systems (COFS), currently supported as a node of theAustralian cal Science Lloyds Regprotect lifecation, pub

the research presented here derives from a collaboration betweenCOFS, Subsea 7 and BP. The authors also acknowledge the valuablecomments and suggestions from the reviewers.

References

[1] Bransby MF, Randolph MF. Combined loading of skirted foundations. Gotech-nique 1998;48(5):63755.

[2] Bransby MF, Randolph MF. The effect of embedment depth on theundrained response of skirted foundations to combined loading. Soil Found1999;39(4):1933.

[3] Bransby MF, Yun GJ. The undrained capacity of skirted strip foundations undercombined loading. Gotechnique 2009;59(2):11525.

[4] Abaqus analysis users manual. Providence, RI, USA: Simulia Corp.; 2010.[5] Feng X, Gourvenec S. Optimal shear key interval for offshore shallow founda-

tions. In: Proceeding of the 32nd international conference on ocean, offshoreand arctic engineering (OMAE 2013). 2013. p. 30817.

[6] Feng X, Randolph MF, Gourvenec S, Wallerand R. Design approach forrectangular mudmats under fully three-dimensional loading. Gotechnique2014;64(1):5163.

[7] Gourvenec S. Effect of embedment on the undrained capacity of shallow foun-dations under general loading. Gotechnique 2008;58(3):17785.

[8] Gourvenec S, Barnett S. Undrained failure envelope for skirted foundationsunder general loading. Gotechnique 2011;61(3):26370.

[9] Gourvenec S, Randolph M. Effect of strength non-homogeneity on the shapeof failure envelopes for combined loading of strip and circular foundations onclay. Gotechnique 2003;53(6):57586.

[10] Gourvenec S, Randolph M, Kingsnorth O. Undrained bearing capacity of squareand rectangular footings. Int J Geomech 2006;6(3):14757.

[11] Mana D, Gourvenec S, Martin C. Critical skirt spacing for shallow foundationsunder general loading. J Geotech Geoenviron Eng ASCE 2013;139(9):155466.

[12] Mana DSK, Gourvenec S, Randolph MF. A numerical study of the vertical bear-ing capacity of skirted foundations. In: Proceeding of the 2nd internationalsymposium on front in offshore geotechnics (ISFOG, 2010). 2010. p. 4338.

[13] Murff JD, Aubeny CP, Yang M. The effect of torsion on the sliding resistance ofrectangular foundations. In: 2nd international symposium on front in offshoregeotechnics (ISFOG, 2010). 2010. p. 43943.

[14] Salgado R, Lyamin AV, Sloan SW, Yu HS. Two- and three-dimensional bearingcapacity of foundations in clay. Gotechnique 2004;54(5):297306.

[15] Taiebat H, Carter J. Flow rule effects in the Tresca model. Comput Geotech8;35(3):5003.

FS [Psand. mpsoal eng

G, BrndraiResearch Council Centre of Excellence for Geotechni-and Engineering and as a Centre of Excellence by theister Foundation. Lloyds Register Foundation helps to

and property by supporting engineering-related edu-lic engagement and the application of research. Part of

200[16] Tan

on [17] Tho

nic[18] Yun

in uh.D. thesis] Centrifuge and theoretical modelling of conical footingsUK: University of Cambridge; 1990.n D, Rocker J, Jung B, Briaud J-L, Lin S. Handbook for marine geotech-ineering. Naval Facilities Engineering Service Centre; 2011.ansby MF. The horizontal-moment capacity of embedded foundationsned soil. Can Geotech J 2007;44(4):40924.

Optimal skirt spacing for subsea mudmats under loading in six degrees of freedom1 Introduction2 Finite element model2.1 Geometry and meshes2.2 Material properties and interface conditions2.3 Load path

3 Results3.1 Validation of FE model3.2 In-plane VMH loading3.3 V-H2-M2-T loading3.4 Effects of foundation shape and roughness on optimal number of internal skirts3.5 Design guidance

4 ConclusionsAcknowledgementsReferences

Optimal Skirt Spacing

Documents

Transcript of Optimal Skirt Spacing