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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
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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
-
X. Feng et al. / Applied Ocean Research 48 (2014) 1020 13
(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
B0L0, B1L1, B2L2, Solid
-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
Horiz ontal load, Hx/Asu0
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
Horiz ontal load, Hx/Asu00
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
Horiz ontal load, Hx/Asu0
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
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14 X. Feng et al. / Applied Ocean Research 48 (2014) 1020
(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
B0L0, B1L1, B2L2, Solid
(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
Horiz ontal load, Hy/Asu0
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
Horiz ontal load, Hy/Asu0
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
Horiz ontal load, Hy/Asu00
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
Horiz ontal load, Hy/Asu0
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
-
X. Feng et al. / Applied Ocean Research 48 (2014) 1020 15
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
-
16 X. Feng et al. / Applied Ocean Research 48 (2014) 1020
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
Horiz ontal load, Hx/Asu0
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.
-
X. Feng et al. / Applied Ocean Research 48 (2014) 1020 17
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
Horiz ontal load, Hy/Asu0
-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
Horiz ontal load, Hx/Asu0
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.
-
18 X. Feng et al. / Applied Ocean Research 48 (2014) 1020
(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.
-
X. Feng et al. / Applied Ocean Research 48 (2014) 1020 19
(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
-
20 X. Feng et al. / Applied Ocean Research 48 (2014) 1020
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.
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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