Applied Ocean Research 43 (2013) 256–263

Contents lists available at ScienceDirect

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Applied Ocean Research

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p o r

uction caisson installation in sand with isotropic permeability

arying with depth

uahid Harireche

* , Moura Mehravar, Amir M. Alani epartment of Civil Engineering, Medway School of Engineering, University of Greenwich, Kent ME4 4TB, UK

r t i c l e i n f o

rticle history:

eceived 4 June 2013

eceived in revised form 21 October 2013

ccepted 22 October 2013

eywords:

aisson foundation

nstallation in sand

ormalised geometry

iping condition

ermeability varying with depth

a b s t r a c t

Suction-induced seepage is pivotal to the installation of caisson foundations in sand. Indeed, the upward

pore water flow on the inner side of the caisson wall causes a release of a fraction of soil resistance due to

the reduction of the lateral effective stress. A safe caisson installation requires a reliable prediction of soil

conditions, especially soil resistance and critical suction for piping. These soil conditions must be predicted

for the whole installation process.

In this paper, we examine the effect on such prediction of the assumed permeability profile, which is described

as a function of depth below the mudline. This study is motivated by the fact that marine sediments generally

exhibit a permeability that decreases with depth because of consolidation under gravity. Hence, the question

is whether conventional theories based on a constant permeability lead to a conservative prediction of

soil conditions or not. Our conclusion is affirmative only regarding piping condition. As for soil resistance,

a prediction based on the assumption of a constant permeability is non-conservative. This is due to an

overestimated reduction in effective stresses under suction-induced seepage. c © 2013 Elsevier Ltd. All rights reserved.

Fig. 1. Normalised geometry and finite difference mesh.

. Introduction

A suction caisson consists of a thin-walled upturned ‘bucket ’ of

ylindrical shape made from steel. This type of foundation has proven

o be efficient and versatile as a support for offshore structures and

ppears to be a very attractive option for future use in offshore wind

urbines [ 1 , 2 ].

The installation procedure starts by lowering the caisson into the

eabed where an initial penetration is achieved under caisson self-

eight. Seabed material surrounding the caisson wall above the cais-

on tip forms a natural seal which is vital to the initial installation

tage. Water trapped inside the caisson cavity is then pumped out,

hich imposes a suction that results into a pressure differential on the

aisson lid. At mudline level, inside the caisson cavity, the imposed

uction, which will be assumed uniformly distributed in this work,

nduces seepage around the caisson wall. For a caisson installation in

and, seepage causes an overall reduction in soil resistance and facil-

tates caisson penetration. It is often recognised that the downward

orce produced by suction would not overcome soil resistance for in-

tallation in sand if no soil loosening is achieved due to the induced

eepage [ 3 –8 ]. Most design procedures of caisson installation in sand

ake into account the role of porewater seepage induced by suction

* Corresponding author at: University of Greenwich at Medway, Central Avenue,

hatham Maritime, Kent ME4 4TB, UK. Tel.: + 44 01634 883787; fax: + 44 01634 883153.

E-mail addresses: ouahidharireche@msn.com , o.harireche@gre.ac.uk (O.

arireche).

141-1187/ $ - see front matter c © 2013 Elsevier Ltd. All rights reserved.

ttp://dx.doi.org/10.1016/j.apor.2013.10.008

[ 9 –12 ]. The role of suction during caisson installation in sand has also

been considered in centrifuge model testing [ 13 ] and finite element

simulations [ 14 ]. The existence of low permeability silt layers has

been considered by Tran et al. [ 15 ].

O. Harireche et al. / Applied Ocean Research 43 (2013) 256–263 257

Fig. 2. Permeability profiles: case A (constant permeability), case B ( α = 0.288) and

case C ( α = 1.204).

Nomenclature

F s frictional resisting force acting on the caisson wall

(N)

�F s change, caused by suction, in the frictional resisting

force acting on the caisson wall (N)

F t normal resisting force acting on the caisson tip (N)

�F t change, caused by suction, in the resisting force

acting on the caisson tip (N)

g , g i , g o gradient of excess porewater pressure and values at

the inner and outer sides of the caisson wall,

respectively (Pa / m)

g * normalised gradient of excess porewater pressure

(dimensionless)

h depth of caisson penetration into the seabed (m)

h * normalised penetration depth (dimensionless)

h w

water height above the mudline (m)

K lateral earth pressure coefficient (dimensionless)

k sand permeability (m

2 / Pa / s)

k ′ derivative of permeability with respect to depth

coordinate, dk / dz (m

2 / Pa / s / m)

k 0 sand permeability at the seabed surface (m

2 / Pa / s)

k ∞

sand permeability at large depth (m

2 / Pa / s)

k sand permeability, normalised with respect to the

value at the seabed surface (dimensionless)

k 1 value of normalised permeability at a given depth, z 1 (dimensionless)

L caisson height (m)

N q bearing capacity factor at the caisson tip

(dimensionless)

p 0 hydrostatic porewater pressure before caisson

installation (Pa)

p at atmospheric pressure (Pa)

p excess porewater pressure induced by suction (Pa)

p * excess porewater pressure, normalised with respect

to suction magnitude (dimensionless)

R , R i , R o caisson radius and inner and outer values,

respectively (m)

r, θ , z cylindrical coordinates (m, rad, m)

r * , z * normalised cylindrical coordinates (dimensionless)

s cr critical suction for piping (Pa)

s suction magnitude at mudline level inside the

caisson cavity (positive value) (Pa)

t wall thickness (m)

z , ζ depth below the mudline (m)

α, β constants in the expression of normalised

permeability (dimensionless)

γ w

unit weight of water (N / m

3 )

κ intrinsic permeability (m

2 )

μ dynamic viscosity of water (N-s / m

2 )

σ ′ h , σ

′ hi , σ

′ ho normal effective stress acting on the caisson

wall and values on the inner and outer sides of the

caisson wall, respectively (Pa)

σ ′ v , σ

′ vi , σ

′ vo vertical effective stress and values on the inner

and outer sides of the caisson wall, respectively (Pa)

�σ ′ h change, caused by suction, in the lateral effective

stress (Pa)

˜ σ , ̃ σi , ˜ σo vertical effective stress due to the effect of shear

resistance at the soil–caisson interface and values on

the inner and outer sides of the caisson wall,

respectively (Pa)

div ( A ) divergence of vector A

∇( A ) gradient of scalar A

During caisson installation in sand, suction must be controlled to

avoid the formation of piping channels which would prevent further

penetration and may cause the installation procedure to fail [ 16 , 17 ].

The development of design procedures with effective suction control

requires a good understanding of soil conditions and seepage around

the caisson wall. Effects of seepage on soil conditions, such as piping

and soil resistance, must be predicted for the whole installation pro-

cess to ensure that changes in suction remain within the safety limits.

Using a finite difference procedure applied to the normalised seepage

problem of caisson installation in sand, Harireche et al. [ 18 ] described

soil conditions and derived criteria for suction control during caisson

installation in sand. The numerical procedure they proposed takes

into account the actual variation in excess pressure gradient over the

installation depth.

In the present paper, the numerical procedure proposed by

Harireche et al. [ 18 ] is extended to take into account a seabed per-

meability that decreases with depth. Bryant et al. [ 19 ] reported field

data for marine sediments in the Gulf of Mexico. Their measurements

show that soil permeability generally decreases with an increasing

depth. Bennett et al. [ 20 ] have also performed in situ measurements of

porosity and permeability of selected carbonate sediments and their

reported data provide further evidence for soil permeability varying

with depth. The present study is motivated by the need to assess

whether a homogeneous seabed model is a conservative assumption

for caisson installation design.

2. Normalised seepage problem and permeability profiles

We consider a caisson of radius R , height L and we denote h the

depth of caisson penetration into the seabed. The soil consists of sand

with permeability k decreasing with the depth z below the mudline. A

problem geometry where all dimensions are normalised with respect

to the caisson radius is adopted. Fig. 1 shows a vertical section through

the meridian plane of the system caisson–soil where a cylindrical

system of coordinates r* and z* is used. The hydrostatic porewater

pressure that exists in the soil before caisson installation is denoted

p 0 and has a magnitude at depth z , p 0 = p at + γ w

h w

+ γ w

z , where

p at is the atmospheric pressure, γ w

the unit weight of water and h wthe water height above the mudline. During caisson installation the

258 O. Harireche et al. / Applied Ocean Research 43 (2013) 256–263

Fig. 3. Normalised excess porewater pressure contours for normalised penetration depths h * = 0.2, 1, 2. (a), (c), and (e): constant permeability (case A); (b), (d), and (f): permeability

with a high variability profile (case C, α = 1.204).

i

h

s

t

t

i

b

s

mposed suction induces a deviation of porewater pressure from the

ydrostatic value, which will be referred to as excess porewater pres-

ure and will be denoted as p . The suction magnitude, s imposed over

he radial distance OC

− ( Fig. 1 ) is expected to increase during installa-

ion. Indeed, as the caisson is pushed into the seabed, suction must be

ncreased to overcome the increasing soil resistance. On the mudline

oundary C

+ F outside the caisson, and on the boundaries FH and BH

ufficiently far from the zone of significant pressure disturbance, the

initial hydrostatic pressure p 0 is not affected. In order to describe the variation of permeability with depth, the

following expression is adopted ( Fig. 2 ):

k ≡ k ( z ∗)

k 0 = ( 1 − β) e −αz ∗ + β (1)

In this equation, k ≡ κ/μ, where κ is the intrinsic permeability and μ

denotes the dynamic viscosity of water.

O. Harireche et al. / Applied Ocean Research 43 (2013) 256–263 259

The coefficient k 0 denotes the permeability at the seabed surface,

z* = z / R the normalised depth and α, β are two constants such that:

α > 0; β =

k ∞

k 0 , 0 ≤ β ≤ 1 (2)

Note that for β = 1, the case of a homogeneous seabed with a con-

stant permeability k 0 is recovered. A value β = 0 corresponds to an

impervious condition at large depth, i.e., k ∞

= 0.

In order to identify the constants α and β for a given seabed profile,

k ∞

, k 0 and k 1 = k ( z ∗1 ), for a given normalised depth z ∗1 , must be speci-

fied. The coefficient β can be calculated using the second relation (2)

and α is given by:

α =

1

z ∗1 Ln

(1 − β

k 1 − β

)(3)

The porewater seepage is assumed to obey Laplace’s equation:

div ( −k∇ p ) = 0 (4)

where ∇p denotes the excess porewater pressure gradient and, div ≡(1 / r ) ∂ /∂ r + (1 / r ) ∂ /∂ θ + ∂ /∂ z .

Denoting k ′ ≡ dk / dz , Eq. (4) can be developed in axisymmetric

conditions ( ∂ /∂ θ = 0) to give:

∂ 2 p

∂ r 2 +

1

r

∂p

∂r +

∂ 2 p

∂z 2 +

k ′

k

∂p

∂z = 0 (5)

In order to draw conclusions that are not affected by the problem

dimensions, pressure is scaled by the magnitude of applied suction

and any length measure is scaled by the caisson radius [ 18 , 21 ]. Hence,

we adopt the following normalised variables:

p ∗ =

p

s , h ∗ =

h

R

, r ∗ =

r

R

( 0 ≤ r ∗ ≤ 1 on OC and 1 ≤ r ∗ < ∞ on C F ) (6)

∂ 2 p ∗

∂ r ∗2 +

1

r ∗∂p ∗

∂ r ∗+

∂ 2 p ∗

∂z ∗2 + f ∗ ( z ∗)

∂p

∂z ∗= 0 (7)

where:

f ∗ ( z ∗) ≡ −α ( 1 − β)

1 − β + βe αz ∗ (8)

As the caisson penetrates into the seabed, radial porewater flow across

the caisson wall is prevented, which is described by the boundary

condition on CD: ∂ p /∂ r = 0 and due to symmetry, this condition must

also be satisfied on the z -axis (i.e., for r = 0). As shown in Fig. 1 , the

soil domain is divided into four regions. Region ( Ω1 ) represents soil

inside the caisson, ( Ω2 ) is the region occupied by soil which passes

inside the caisson after further penetration and regions ( Ω3 ) and ( Ω4 )

are the complementary soil regions outside the caisson, surrounding

( Ω2 ) and ( Ω1 ) respectively. In addition to Eq. (7) , the normalised

excess porewater pressure p * must satisfy the boundary conditions:

p ∗ = −1 on OC

−, p ∗ = 0 on C

+ F , F H , B H and ∂p ∗

∂ r ∗= 0 on C D and O B

(9)

3. Soil resistance to caisson penetration

Water seepage caused by suction produces a hydraulic gradient

which, on both faces of the caisson wall, varies with depth. The effects

of soil deformation history that takes place during installation are

ignored in this study. Change in soil geometry around the caisson wall

is not expected to be important to the effects of a variable permeability

on soil resistance and critical suction for piping.

Fig. 3 a, c and e shows the contours of normalised excess pore pres-

sure P * for values of the normalised penetration depth h * = 0.2 (typical

of self-weight penetration), 1 and 2. These figures correspond to a ho-

mogeneous seabed with constant permeability. For comparison, Fig

3 b, d and f shows similar contours for a seabed profile that corre-

sponds to case C described in Section 2 . These figures show clearly

that the pressure distribution is affected by the permeability profile,

although this effect is not noticeable at the early stage where the

installation depth is typical of self-weight penetration ( Fig. 3 b).

Fig. 4 shows the vertical component of the normalised pressure

gradient g * ≡ ∂ p * /∂ z * on both sides of the caisson wall as a function

of normalised depth z * for the three permeability profiles (cases A, B

and C). Values of normalised penetration depth h * = 0.2, 1 and 2 have

been considered.

It can be seen that the pressure gradient on each side of the caisson

wall is higher at the early stages of the installation process. Maximum

values of the gradient occur at the caisson tip. For the homogeneous

seabed profile with constant permeability (case A), the gradient dis-

tribution over the caisson embedment tends to become uniform over

a significant depth as the installation proceeds. A gradient of higher

magnitude tends to localise around the caisson tip. For seabed pro-

files where the permeability decreases with depth (cases B and C),

such a uniformity is less pronounced, especially for the gradient on

the inner side. By comparing the normalised gradients for the three

different cases A, B and C, on both sides of the caisson wall, it can be

observed that the effect of permeability profile becomes more impor-

tant as the penetration depth increases. For the normalised gradient

on the outer side, the difference in gradient magnitude for the three

permeability profiles is not significant at shallow depths. However,

such a difference increases with depth, which is likely to affect soil re-

sistance through the increase in effective stress and this will be more

noticeable at later stages during the caisson installation process. On

the inner side of the caisson wall, the normalised gradient magnitude

is affected in a different way. Up to a normalised depth which can be

estimated to 3 / 4 of the normalised penetration depth, the normalised

gradient magnitude is lower for a higher rate of variability in the per-

meability profile. Below such depth, the opposite trend is observed.

This behaviour suggests that soil is less prone to piping for a perme-

ability that has a higher variability profile. In terms of soil resistance

to caisson penetration, it can be anticipated that a higher variability

profile is likely to correspond to less reduction in soil resistance due

to seepage. If this is the case, then we would conclude that soil resis-

tance estimations based on a constant permeability assumption are

not conservative.

These effects are now studied in more detail in order to draw final

conclusions regarding soil resistance against caisson penetration and

critical condition for piping.

3.1. Lateral frictional resistance on caisson wall

In the absence of seepage, the lateral effective pressure on the

caisson wall has the expression:

σ ′ h = K

(γ ′ z + ̃ σ

)(10)

where K is a lateral earth pressure coefficient. The vertical effective

stress near the caisson wall is enhanced by the magnitude ̃ σ due to the

effect of shear resistance that develops on the interface soil–caisson.

Under seepage conditions produced by an applied suction, the lateral

effective pressure acting on the caisson wall at depth z , inside and

outside the caisson is respectively expressed as follows:

σ ′ hi ( R, z ) = K

(γ ′ z −

∫ z

0 g i ( R, ζ ) dζ + ̃ σi ( R, z )

)(11)

σ ′ ho ( R, z ) = K

(γ ′ z −

∫ z

0 g o ( R, ζ ) dζ + ̃ σo ( R, z )

)(12)

where g i ( R , ζ ) and g o ( R , ζ ) denote the vertical component of the pres-

sure gradient on the inner and the outer sides of the caisson wall

respectively. Assuming that the enhanced effective stresses ˜ σi and ˜ σo

are not affected by seepage conditions, the change at depth z in the

260 O. Harireche et al. / Applied Ocean Research 43 (2013) 256–263

Fig. 4. Dimensionless pressure gradient as a function of normalised depth for different permeability profiles (cases A, B and C). a / h * = 0.2; b / h * = 1; c / h * = 2.

l

b

�

T

g

ateral pressure acting on the caisson wall caused by seepage is given

y:

σ ′ h ( R, z ) = K

(∫ z

0 g i ( R, ζ ) d ζ +

∫ z

0 g o ( R, ζ ) d ζ

)(13)

he pressure gradients can be expressed as follows:

o =

s g ∗o ; g i =

s g ∗i (14)

R R

where g ∗0 ≡ ∂p ∗/∂z ∗ is the normalised pressure gradient in domains

( Ω4 ), ( Ω3 ) and g ∗i ≡ ∂p ∗/∂z ∗ denotes the same quantity when evalu-

ated in domains ( Ω1 ) and ( Ω2 ). Hence, expression (13) can be rewrit-

ten under the following form:

�σ ′ h ( R, z ) = L

∗i ( z

∗) + L

∗o ( z

∗) (15)

K s

O. Harireche et al. / Applied Ocean Research 43 (2013) 256–263 261

Fig. 5. Change in the normalised lateral effective stress on caisson wall due to suction-induced seepage. a / h * = 0.2; b / h * = 1; c / h * = 2.

where, as can be seen from Fig. 4 :

L

∗i ( z

∗) ≡∫ z ∗

0 g ∗i ( 1 , ζ ∗) dζ ∗ > 0 , L

∗o ( z

∗) ≡∫ z ∗

0 g ∗o ( 1 , ζ

∗) dζ ∗ < 0 and ∣∣L

∗i ( z

∗) ∣∣ >

∣∣L

∗o ( z

∗) ∣∣ (16)

Using a numerical calculation of the integrals in (16) on the nor-

malised finite difference mesh, we obtain the normalised change of

the lateral effective stress expressed in (15) as a function of the nor-

malised depth z* , which is shown in Fig. 5 . It can be observed that

such a change increases with depth and is clearly affected by the

permeability profile. A higher rate of variability in the permeability

corresponds to a lower reduction in the lateral effective stress. Al-

though this effect is quite limited at shallow penetration depths ( Fig.

5 a), it is clearly more pronounced at larger penetration depths ( Fig.

5 b and c). This shows clearly that the assumption of a homogeneous

seabed is not in favour of a conservative estimation of soil resistance

to caisson penetration as it overestimates the effect of seepage on the

reduction of the lateral effective stress.

As a consequence, seepage causes the frictional resisting force

acting on the caisson wall to decrease by a magnitude �F s given as a

function of the normalised penetration depth h* by the expression:

�F s

2 π R

2 K s =

∫ h ∗

0 [ L

∗i ( z

∗) + L

∗o ( z

∗) ] dz ∗ (17)

3.2. Tip resistance

Seepage also causes the vertical effective stress at the caisson tip

to decrease, thereby leading to further reduction in the total resisting

force. The resisting force at the caisson tip can be expressed in the

form:

F t = 2 π R N q

∫ R e

R i

σ ′ v dr (18)

where N q is a bearing capacity factor and σ ′ v the vertical effective stress

at the caisson tip, which is assumed to vary linearly from σ ′ vi inside

the caisson (radius R i ) to σ′ vo outside (radius R o ), and these stresses

have the expressions:

σ ′ vi ( R, h ) = γ ′ h −

∫ h

0 g i ( R, ζ ) dζ + ̃ σi ( R, h ) (19)

262 O. Harireche et al. / Applied Ocean Research 43 (2013) 256–263

Fig. 6. Effect of suction-induced seepage on soil resistance at caisson tip.

σ

A

t

s

w

e

t

i

a

a

p

4

c

s

t

t

e

σ

b

w

a

m

s

a

g

s

p

a

i

Fig. 7. Critical suction for piping on the inner caisson wall. a / h * = 0.2; b / h * = 1; c / h *

= 2.

′ vo ( R, h ) = γ ′ h −

∫ h

0 g o ( R, ζ ) dζ + ̃ σo ( R, h ) (20)

ssuming that seepage does not affect the enhanced vertical stress,

he resisting force at the caisson tip decreases by the magnitude �F t uch that:

�F t

2 πRt N q s =

1

2 ( L

∗i ( h

∗) + L

∗o ( h

∗) ) (21)

here functions L

∗i ( z

∗) and L

∗o ( z

∗) are defined by expressions (16) .

Fig. 6 shows the expression ( L

∗i ( h

∗) + L

∗o ( h

∗)) as a function of pen-

tration depth ( h *) for the three permeability profiles considered in

his study. Fig. 6 and expression (21) show clearly that the reduction

n the magnitude of tip resistance is maximum when permeability is

ssumed constant (case A). Hence, constant permeability profile is not

conservative assumption when estimating tip resistance to caisson

enetration.

. Critical suction for piping condition

During caisson installation in sand, suction magnitude must be

ontrolled to avoid the formation of piping channels around the cais-

on wall, which may cause the installation procedure to fail [ 16 , 17 ].

At a generic material point of normalised coordinates r* , z* within

he soil in contact with the inner side of the caisson wall, piping

akes place when the vertical effective stress becomes zero. This is

xpressed by the equation:

′ v = γ ′ z −

∫ z

0 g i ( R, ζ ) dζ = 0 (22)

Hence, the suction magnitude that causes such condition is given

y:

s cr

γ ′ R

=

z ∗

L

∗i ( 1 , z

∗) (23)

here L

∗i (1 , z

∗) ≡ ∫ z ∗0 g

∗i (1 , ζ

∗) dζ ∗.

Note that expression (23) is similar to the one derived by Houlsby

nd Byrne [ 10 ] under the form s cr / ( γ′ R ) = h * / (1 − a ) where a is the

agnitude of the normalised pressure at the caisson tip on the inner

ide; i.e., a ≡ −p *( h *).

The present criterion extends the expression proposed by Houlsby

nd Byrne [ 10 ], taking into account the actual variation of the pressure

radient as a function of depth. At the caisson tip, it has the expres-

ion: s cr / ( γ ′ R) = h ∗/L

∗i (1 , h

∗). Note that, in addition to the variable

ressure gradient, the present criterion also takes into consideration

permeability varying with depth, which is implicitly accounted for

n the expression of L

∗i (1 , h

∗).

Fig. 7 shows the variation of the normalised magnitude of critical

suction, s cr / ( γ′ R ) as a function of depth at three different stages of

the installation process where the normalised penetration depth is

0.2, 1 and 2. The three permeability profiles have been considered at

each stage for comparison. It can be observed that the assumption of

a homogeneous soil (case A) leads to the estimation of a minimum

critical suction. Hence, as far as the condition for piping is concerned,

such an assumption is conservative. It can be observed from Fig. 7

that, while the effect of the variability with depth of permeability is

less pronounced around the caisson tip, it becomes very significant at

O. Harireche et al. / Applied Ocean Research 43 (2013) 256–263 263

shallow depth.

5. Conclusion

In this study we have considered the effect of a permeability vary-

ing with depth on the prediction of soil resistance to caisson penetra-

tion and critical suction for piping condition.

Three permeability profiles have been considered, namely: con-

stant permeability, permeability slowly varying with depth ( α =0.288), permeability with a high variability with depth ( α = 1.204).

These profiles have been motivated by the fact that marine sediments

are expected to exhibit a permeability that decreases with depth at

a rate that must also be taken into consideration as it may vary from

one type of soil to another. The effect of suction induced seepage

on soil resistance to caisson penetration has been investigated us-

ing the normalised solution of seepage around the caisson wall. It

has been observed that a constant permeability profile leads to an

under-estimation of soil resistance to caisson penetration. This high-

lights the importance of taking into account a permeability profile

with certain variability with depth for a more accurate prediction of

the required suction throughout the installation process. The investi-

gation of piping on the inner side of the caisson wall revealed that the

constant permeability assumption under-estimates the critical suc-

tion for piping. As far as the formation of piping channels is concerned,

the assumption of homogeneous seabed with constant permeability

is conservative. However, taking into account the actual variability

with depth of the permeability may lead to a more accurate estima-

tion of the critical suction with significantly less restriction on the

safe suction profile throughout the installation process.

Acknowledgement

Funding of a PhD scholarship by the University of Greenwich to

support the second author is gratefully acknowledged.

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