Van Eekelen Et Al 2011 BS8006 Final

8/10/2019 Van Eekelen Et Al 2011 BS8006 Final

1/15

Analysis and modication of the British Standard BS8006 for the design of piled

embankments

S.J.M. van Eekelen*, A. Bezuijen, A.F. van Tol

Deltares, Delft University of Technology, P.O. Box 177, 2600 MH Delft, The Netherlands

a r t i c l e i n f o

Article history:

Received 4 August 2010

Received in revised form

16 January 2011

Accepted 7 February 2011

Available online 5 March 2011

Keywords:

Geosynthetics

Piled embankments

British Standard BS8006

Modied British Standard BS8006

Arching effect

a b s t r a c t

The piled embankment is an increasingly popular construction method. The Dutch Design Guideline forpiled embankments (CUR 226) was published in the rst half of 2010. Several existing models have been

analysed to determine the calculation rules used in the Dutch Guideline. The British Standard BS8006

sometimes calculates tensile forces in the geosynthetic reinforcement that differ considerably from other

models. For quite thin embankments in particular, BS8006 designs a relatively strong and thus expensive

geosynthetic (basal) reinforcement in comparison with other design models. These differences are not

always fully understood, leading to uncertainty. This paper analyses BS8006 and demonstrates why it

behaves differently from other models. It also examines why this behaviour is different than would be

expected. For example, it is shown that calculations using BS8006 are based on a higher load than the

actual load.

A modication to BS8006 is proposed, which is shown to give comparable results to the German

Standard EBGEO for situations where there is no subsoil support.

The results of BS8006, Modied BS8006, and the German/Dutch guideline are compared with nite

element calculations and eld measurements. It is concluded that the results given by the Modied

BS8006 are more accurate to those using BS8006.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

The piled embankment is an increasingly popular construction

method. In the Netherlands for example, more than 20 piled

embankments have been constructed during the last 10 years.

Many more piled embankments have been reported in countries

such as Germany, England, Scandinavia, the United States, Brazil,

India, and Poland. The Dutch Design Guideline (CUR 226) was

published in therst half of 2010 (CUR 226, 2010). This Guideline

adopts major parts of the German Guideline EBGEO (2010). Several

existing models have been analysed to determine the calculation

rules used in the Dutch Guideline. The British Standard BS8006sometimes calculates tensile forces in the geosynthetic basal

reinforcement (GR) that differ considerably from other models. In

the case of quite thin embankments in particular, BS8006 designs

a relatively strong and thus expensive GR in comparison with

other design models. These differences are not always fully

understood leading to uncertainty. This paper analyses BS8006

and demonstrates why it behaves differently from other models. It

also shows why this behaviour is different than would be expec-

ted. A modication for BS8006 is proposed, referred to as the

Modied BS8006.

The tensile force in the GR must rst be calculated to design the

GR in a piled embankment. The tensile force is caused by vertical

load (trafc, soil weight) and by lateral load (active ground pressure

due to outward horizontal thrust of the embankment). This paper

only considers the tensile force calculations caused by the vertical

loads in the system.

Section 2 of this paper thoroughly analyses BS8006 for rein-

forcement in piled embankments, and identies its limitations. The

resultant proposal for the Modied BS8006 is given in Section3.The nal two sections compare the results of BS8006, the

Modied BS8006, and the German/Dutch guidelines with nite

element calculations and eld measurements.

Safety philosophy is beyond the scope of this paper, and all

safety factors in the calculation methods are therefore ignored. The

paper focuses on the tensile force calculations caused by vertical

loads in the piled embankment. Throughout the paper, pile spacing

is assumed to be identical in both directions, except in Section 3.4.

Here, equations for the Modied BS8006 are elaborated for the

situation thatsxs sy. Differences in GR stiffnessJin both directions

do not inuence the equations.* Corresponding author. Tel.:31 88 335 7287; fax:31 15 261 0821.

E-mail address: [email protected](S.J.M. van Eekelen).

Contents lists available atScienceDirect

Geotextiles and Geomembranes

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

0266-1144/$e see front matter 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.geotexmem.2011.02.001

Geotextiles and Geomembranes 29 (2011) 345e359
mailto:[email protected]://www.sciencedirect.com/science/journal/02661144http://www.elsevier.com/locate/geotexmemhttp://dx.doi.org/10.1016/j.geotexmem.2011.02.001http://dx.doi.org/10.1016/j.geotexmem.2011.02.001http://dx.doi.org/10.1016/j.geotexmem.2011.02.001http://dx.doi.org/10.1016/j.geotexmem.2011.02.001http://dx.doi.org/10.1016/j.geotexmem.2011.02.001http://dx.doi.org/10.1016/j.geotexmem.2011.02.001http://www.elsevier.com/locate/geotexmemhttp://www.sciencedirect.com/science/journal/02661144mailto:[email protected]


2/15

2. British Standard BS8006 for the design of reinforcement in

piled embankments

2.1. Introduction

British Standard BS8006 calculates the tensile force in the GR

caused by the vertical load in the following four steps:

1. The vertical load is divided into three parts

2. The load on the reinforcement is concentrated on the strips of

reinforcement between adjacent pile caps.

3. Full arching is assumed

4. The tensile force in the GR is calculated, from the vertical load

partB.

Each of these four steps will be analysed in Sections 2.2e2.5.

2.2. Step 1: dividing the vertical load into load parts

2.2.1. Load division based on the principle of arching

The load in the soil is attracted to stiff elements, in this case the

piles. This results in a tendency for the vertical load to bend off

laterally, resulting in an arch in the embankment ll. This

phenomenon is called arching.

This paper denes the division of the vertical load into parts

(due to arching) as follows (Fig.1): Load part Ais the load part that

is transferred directly to the piles. The weight of the soil wedge

below the arch is carried by both the GR and the soft subsoil. Part of

the soil wedge weight is transferred through the GR to the piles,

and is referred to as load part B. The load part that is carried by the

subsoil between the piles is referred to as C. In this paper,A,Band

Care expressed in kN/pile (per pile area, or per sx, sy, with s the

centre-to-centre distance between two piles). The next sub-section

explains howA,B and Care determined in BS8006.

List of parameters

A load part that is transferred directly to the pile (kN/

pile)

Ap area of pile cap (Ap a $ afor a square pile cap) (m2)Ar area of the reinforcement (Ar s $ s a $ a) (m2)As area that corresponds with one pile grid (As

s $ s)

(m2)

a size of pile cap, or the equivalent size in the case of

circular piles (m)

B load part that is transferred through the geosynthetic

reinforcement to the pile (kN/pile)

Bps load part that is transferred through the geosynthetic

reinforcement to the pile, assuming a plane strain

geometry (diaphragm walls instead of piles) (kN/pile)

C load part that is carried by the subsoil (kN/pile)

Cc arching coefcient adapted byJones et al. (1990)for

the piled embankment (e)

d diameter pile cap (m)

Ep pile efciencyEp 1 B C=wtot (e); in BS8006C

0, thusEp

1

B=wtot

, (kN/kN)

E Youngs modulus of soft soil (kN/m2)f maximum deection of the reinforcement in the

centre between two pile caps (m)

H height ofll above reinforcement, or height ofll

above pipe (Fig. 2) (m)

J tensile stiffness of the geosynthetic reinforcement

(kN/m)

c cohesion (kN/m2)

Kv vertical permeability (m/s)

ld length of the deformed reinforcement strip between

two adjacent pile caps (m)

p subsoil support (kN/m)

p top load on ground surface (kN/m2)

p0c vertical stress on pile cap (stress part on pile cap that istransferred directly to the pile).pc

0 A/Ap with A (kN)is the load part directly on the pile as shown in Fig. 1

andAp (m2) is the area of the pile cap; Ap a2 (kPa)

p0r average vertical stress on geosynthetic reinforcement(kPa)

p0rt average vertical stress on geosynthetic reinforcement,temporary calculation value (kPa)

q theoretical load on geosynthetic reinforcement strip

(kN/m)

s pile spacing, dened inFig. 3(m)

T tensile force generated in geosynthetic reinforcement

due to transfer of vertical load, in the GR strip in

between two pile caps, width of load strip is zero (kN)

TH horizontal component of the tensile force in the GR

strip (kN)

Trp tensile force generated in geosynthetic reinforcement

due to transfer of vertical load, in the GR strip between

two pile caps, width of load strip is equal to side of

square pile cap, a (kN/m)

TV vertical component ofT(kN)W water content (%)

WT equally distributed vertical (line) load acting on the

reinforcement strip between adjacent pile caps,

BS8006 property (kN/m)

wtot total load of trafc and soil weight in one s $ sarea,

s2(gHp) (kN/pile)X grouped variable (see equation(11)) (e)

3 strain (e)

4 angle of internal friction ()g unit weight of soil (kN/m3)

s0v average applied vertical effective stress (kPa)

Fig.1. Dividing the load into three parts: A e directly to the piles,B e via the GR to the

piles,Ce

to the soft subsoil in between the piles (C

0 in BS8006).

S.J.M. van Eekelen et al. / Geotextiles and Geomembranes 29 (2011) 345e359346


3/15

2.2.2. Determining load part A in BS8006BS8006 bases its calculation ofA on the work of Marston and

Anderson (1913),1. Marston and Anderson carried out numerous

experiments to determine the arching above a pipe in soil (Fig. 2).

The following equation was found for the load on an innitely long

pipe:

p0c;pipes0v

Cc;pipeapipeH

(1)

where p0c, pipe (kPa) e load part that is transferred to the pipedirectly;s 0v (kPa) e average vertical load directly above the pipe;Cc,pipe(e)earching coefcient. Marston and Anderson determined

the arching coefcient for several types of soft soil below and

adjacent to the pipe. For softer clay, Marston and Anderson found

a lowerCc. This means that the pipe will sink further into the softer

clay, and the pipe will attract a relatively small part of the load.

There is therefore less arching; apipe (m) diameter of the pipe; H(m)

height ofll above pipe (Fig. 2) orheight ofll above reinforcement

in a piled embankment.

Jones et al. (1990)adapted this equation for the 3-dimensional

(3D) situation of a pile by squaring the right term:

p0cs0v

Cca

H

2or p0c

Cca

H

2s0v (2)

And thus load part A is:

A

p0c

a2

Cca

H

2

a2s0v

(3)

Equation (2) has been adopted in BS8006 on page 185 (BS8006-1,

2010).Jones et al. (1990) and BS8006 also adapted how the arch-

ing coefcient Cc for the 3D geometry of a piled embankment

should be determined as follows:

End-bearing piles:

Cc 1:95Ha 0:18 (4)

Friction and other piles:

Cc 1:5 Ha 0:07 (5)

wherep0c(kPa)eload part in kPa that is transferred directly to thepile.p0c A/ApwhereA (kN) is the load part directly on the pile asshown in Fig. 1 and Ap (m

2) is the area of the pile; Ap a2; s0v(kPa)e average vertical effective stress directly above the pile cap;

Cc (e) e arching coefcient adapted byJones et al. (1990)for the

piled embankment;a (m) e size of pile cap, or the equivalent size

side in the case of circular piles; H (m) e height of ll above

reinforcement.

2.2.3. Determining load parts B and C in BS8006

Load part A has been determined in the previous sub-section.This result can be used to determine load parts B and C. BS8006

assumes that the subsoil will not support the embankment over

time. Therefore,C 0 in any design calculation with BS8006.This is a conservative (i.e. safe) assumption. Assumptions using

C> 0 can lead to unsafe situations unless it can be proven that this

case will exist in the eld. For example, a future groundwater level

decrease can result in sufcient settlement to loosen any subsoil

support, or a working platform placed on the subsoil before pile

installation may cause settlements below the mattress. In other

caseswhereit canbe proventhat minimal settlements areexpected,

calculations can reasonably include some subsoil support, as in the

German EBGEO. To validate design calculation methods with eld

tests, it is in any case necessary that calculations include subsoil

support.This is because a considerable degree of subsoil support has

been measured in the available eld studies (in the Netherlands for

example, in the N210 project (Haring et al., 2008), a rail road project

in Houten (Van Duijnen et al., 2010), and in the Kyoto Road project

(Van Eekelen et al., 2010a)). Although this support was measured

during monitoring, it may disappear in future years.

Section 2.2.2 explains howA is determined and also that BS8006

assumes C 0. This makes it possible to calculate B from thevertical equilibrium. The total load (kN/pile) on one square s $ sis:

gHps2 (6)where s is the pile spacing in m, as shown in Fig. 3.

Load partA (kN/pile) transferred directly to the piles is:

A

p0ca

2 (7)

Fig. 2. BS8006 bases its calculation of load part A on the experimental research ofMarston and Anderson (1913).

1 BS8006-1 (2010)gives the model ofHewlet and Randolph (1988) as an alter-

native. This falls beyond the scope of this paper.

S.J.M. van Eekelen et al. / Geotextiles and Geomembranes 29 (2011) 345e359 347


4/15

wherep0c is calculated from equation (2). Load part B (in kN/pile) onthe geosynthetic reinforcement is:

B p0r

s2 a2

(8)

wherep0r(kPa) e pressure on GR. p0r (B C)/(s2 a2) with B C(kN) shown in Fig. 1 and (s2 a2) (m2) is the area of the GR. InBS8006, C 0, so p0r B/Ar; B (kN/pile) e load part that is trans-ferred through the geosynthetic reinforcement to the pile.

When the subsoil support is zero, vertical equilibrium gives

Bt total load A:

p0r

s2 a2 gHps2 p0ca2 (9)

and thus,

p0rgH

p

s2

p0ca

2

s2 a2 gHpX (10)whereXis a grouped variable [e]:

X

s2 a2 p0cgHp

s2 a2 (11)

It should be noted that the equations given so far all use a fully 3-

dimensional conguration (an embankment on piles has a 3D

conguration, in contrast to an embankment on walls that has a 2D

conguration, as shown inFig. 4).

2.3. Step 2: concentration of load part B on the reinforcement strips

between the pile caps

2.3.1. Calculation of the line load WTfor a 2D conguration

BS8006 assumes that the vertical load on the GR is carried only

by the GR strips between two adjacent pile caps. These stripsare

shown shaded in Fig. 4b. It is assumed that only very limited

strain and tensile stress occur in the reinforcement between these

strips.

Jones et al. (1990) determined this line load WT for the 2D

conguration, as shown in Fig. 4a. The strip with width s is intended

to carry the entire load that rests on a square ( s a) $ s. Here, s isunity (1 m). This only becomes relevant in the 3D case. Thus Jones

et al. nd:

p0rs as WTs a / p0r WT

s or WT sp0r (12)

whereWT (kN/m) e in the 3D case (Fig. 4b): line load resting on the

reinforcement strip in between two piles. For the 2D case (Fig. 4a):

evenly distributed load acting on the reinforcement across its span

between two supporting walls per unit length of wall, with unity

widths 1 m.This is in agreement with, for example, Le Hello (2007).

Although the width of the GR strip s in the 2D case is unity

1 m, the line load is rst calculated for a strip without width.

BS8006 then reintroduces this width in the equations, see equa-

tion(23).

Combining equation (12) with the vertical equilibrium in

equation(10)gives:

WT sgHpX (13)with the grouped variable X given in equation (11). Note that

equation(13)is a mixture of the 3D-equilibrium equation(10)andthe 2D (plane strain) line load equation(12).

Equations(13) and (11) agree with equation (2) ofJones et al.

(1990). BS8006-1 (2010) adopts these equations to express the

line load in the second equation on page 186 (section 8.3.3.7.1).

This expression for the line load is for the case H 1.4(s a),which is referred to as partial arching throughout this paper.

Section 2.4 explains the concepts of partial arching and full

arching.

Fig. 4. a. The equations for the line load WTin BS8006 are determined using the 2D conguration. b. For safety reasons, BS8006 applies these equations (with the total load on the

GR) for each strip in both directions while changing the analysis to the 3D conguration.

a

a

s

s

Fig. 3. Denition ofs and a.



5/15

2.3.2. Double application of the line load WTfor a 3D conguration

Jones et al. (1990) derived the equation for the line load WTequation (13). BS8006 adopts this nearly plane strain equation.

However, BS8006 uses the recommendation of Jones et al. that this

line load shouldbe calculated both to the GR stripsperpendicular to

the load axis, and to the GR strips along the road axis, as shown in

Fig. 4b. This means that the analysis has now changed to the 3D

case by calculating the load resting on the GR twice. Jones et al.

made this choice to guarantee sufcient safety, an understandable

decision for a rst design standard in the nineties.

Fig. 4a shows the plane strain situation where the vertical

equilibrium is satised. However, BS8006 uses Fig. 4b, where the

vertical equilibrium is not satised. Equation (13) from BS8006 for

line load can be used to calculate the average load on the GR, load

partB, and the pile efciencyEp.

This paper denes load part B as the load transferred through

the GR to the piles, in kN per pile. Two GR strips lie in one s $ s

square, so thatBcan be determined using equation (13) of BS8006:

B 2WTs a 2sgHps aX (14)Note that this equation for B does not agree with (8). Vertical

equilibrium no longer exists. The average stress on the reinforce-ment resulting from the BS8006 equations is:

p0r B

s2 a2 2WTs a

2sgHps a X (15)

This gives a pile efciencyEp(kN/pile/kN/pile):

Ep 1 Bwtot

1 2sgHps aXs2gHp 1

2s as

X (16)

2.4. Step 3: assuming the existence of full arching

BS8006 assumes the existence of full arching, analogous to

McKelvey (1994)who assumes the existence of a plane of equal

settlement. The assumption is as follows: when the embankment

is sufciently high for the arch to develop fully, then the entire load

from above the arch will be transferred directly to the piles. Rein-

forcement in the bottom of the embankment will thus not feelthe

trafc load or an increasing embankment height.

BS8006 assumes that full arching occurs as soon as the height of

the embankment is greater than the arch height. The arch height is

estimated to be equal to the diagonal distance between the pile

caps, thus 1.4(s a), seeFig. 5.BS8006 assumes, with the assumption of full arching, that the

load on the GR reaches a maximum when the height of the ll is

increased. Several eld measurements are available to validate the

partial-arching situation (H< 1.4(s a)), as shown in Section6and,for example, inVan Duijnen et al. (2010) and Haring et al. (2008).

Jenck et al. (2005) compare BS8006 with 2D tests and concludesthat A is strongly overestimated when H increases beyond full

arching. In any case, insufcient data are available to satisfactorily

prove the existence of full arching for a thick embankment with

a basal GR.

The nite element calculations in Section 5 do not show the

existence of full arching. The assumption of full arching may lead to

relatively low calculated tensile forces.BS8006-1 (2010)solves this

by requiring that the GR should be designed to carry at least

a practical minimum proportion of the embankment loading

equivalent to 15% (seeBS8006-1, 2010, p. 188).

BS8006 elaborates full arching as follows: as soon as H> 1.4

(s a),the trafc load is no longer calculated to the reinforcementbut is simply set to zero (p 0) in the original partial-archingequation(13). Furthermore, the weight of the embankment above

1.4(s a) is no longer calculated for, so that H in equation (13)isreplaced by its maximum, namely 1.4(s a). In this way, theequation for the line load WTfor full arching (for H> 1.4(s a)) ofBS8006 can be found (seeBS8006-1, 2010, p. 186):

WT 1:4sgs aX (17)where Xis given in equation(11).

Equation (17) from BS8006 for the full-arching line load can be

used to derive the average load p 0ron the GR, load part B, and the

pile ef

ciencyEp. This can be used to derive the average load on theGRp0rt, for the 2D conguration given inFig. 5a and equation(12):

p0rt WT

s 1:4gs aX (18)

However, WT is calculated twice, in the same way as for partial

arching, as shown inFig. 4b. This therefore results in

p0r 2WTs a

2:8sgs as a X (19)

andB (in kN/pile) for full arching, see equation(14):

B 2WTs a 2:8sgs a2X (20)This gives a pile efciencyEp(

kN/pile/kN/pile):

Ep 1 Bwtot

1 2:8sgs a2X

s2gHp 1 2:8gs a2

sgHp X (21)

2.5. Step 4: from line load to tensile force

The equally distributed load WT on the GR strip without width is

determined in steps 2 and 3 (equations(13) and (17)). The tensile

force Tin the GR strip can be derived fromthis WT. For this purpose,

the GR strip is modelled as a tension membrane and the following

assumptions are made:

- there is no subsoil support- the line loadWTis equally distributed

- the GR strip xed at the sides of the pile caps

1.4(s-a)AA AA

C CC C C C

BBHAA AA

C CC C C C

BB BBBBBB BB

as as

Fig. 5. Left: partial arching, right: full arching.



6/15

- the tensile force is calculated at the side of the pile cap and is

therefore a maximum (not an average, as in the German

EBGEO).

The rst two assumptions result in a parabola-shaped deformed

tension membrane, as shown inAppendix 1.It is noted that several

researchers (for exampleVan Eekelen et al., 2011) found that the

greatest load is concentrated around the edges of the pile caps. This

means that the assumption of equal load distribution is closer to

reality than some other commonly used models, such as the

triangular shaped load inEBGEO (2010).

Appendix 1shows how a differential equation for the tension

membrane is derived and solved, resulting in the tensile force Tin

kN in the GR strip (the strip has a zero width):

T WTs a2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 1

63

r (22)

Dividing this by the width a of the GR strip then gives the tensile

forceTrpin the strip with width a in kN/m:

Trp

WTs a2a


63r (23)

Here, the (estimated) straineis an input parameter to calculate the

tensile force Trp. The apparent stiffness of the geosynthetic rein-

forcement can therefore be calculated as:

J Trp3

(24)

2.6. Different interpretations of BS8006 from literature

Section 2.3 showed that the BS8006 equations are based on 3D-

equilibrium equations as well as 2D equations, to concentrate the

load in line loads on the GR strips. Furthermore, the load on the GR

is calculated twice. Several authors have interpreted BS8006 in

order to compare it with other models.For example, Abusharar et al. (2009) and Le Hello (2007)

assumed that the equations were developed for a fully 2D cong-

uration. Love and Milligan (2003), Stewart and Filz (2005), and

Russell and Pierpoint (1997)on the other hand assumed that the

equations were developed for a 3D conguration. These interpre-

tations are elaborated and compared inAppendix 2.

3. Proposal for improving the BS8006

3.1. Combining a 3D conguration and 3D determination of the line

load

For quite thin embankments in particular, BS8006 designs

a relatively strong and thus expensive geosynthetic (basal) rein-forcement in comparison with other design models. These differ-

ences are not always fully understood, leading to uncertainty. The

previous section has demonstrated that one of the main reasons is

that calculations using BS8006 are based on a higher load than the

existing load.

This section proposes a modication of the British Standard

BS8006. In this Modied BS8006, the calculation for the load on the

GR is only incorporated once. Also, the line load is calculated

according to the 3D conguration given inFig. 6.

In this case, a GR strip carries half of the load on one square s $ s,

which gives:

p0r

s2 a2 2WTs a (25)

The difference between BS8006 and Modied BS8006 is the

assumed unsupported area that transfers the tensile loads onto thereinforcement strip between adjacent pile caps. BS8006 calculates

this as s(s a), see Fig. 4b. Fig. 6 calculates this ass2 a2=2 s a=2s a. The area ratio of BS8006 (Fig. 5b)/BS8006 modied (Fig. 7) is 2s=s a.

If we take as an examples 4 m anda 1 m, then the previousratio 1.6. In this example, BS8006:1995 therefore utilises a totalunsupported area 60% greater than the modied BS8006 proposal,

and thus will calculate a reinforcement tension some 60% greater

for this particular pile cap size and spacing geometry. This is the

main basis for the difference between BS8006:1995 and the

proposed BS8006 modied method.

3.2. Partial arching

Calculating vertical equilibrium for Fig. 6 gives (see equation

(10)):

p0r gHpX (26)

Fig. 6. Calculation of the load to the GR strips in modi ed BS8006.

Ary

Arx

sx

sy

a

a

x

y

Fig. 7. Pile spacing sxs

sy.



7/15

The line load WT should be calculated according to equation

(25):

WT 1

2p0rs a (27)

Combining these equations gives the basic equation for the line

loadWTfor the Modied BS8006 model:

WT 12gHps aX (28)

The average load p0r on the GR, load part B, and the pile ef-ciency Ep can be derived using this basic Modied BS8006 equation.

The followingp 0r(kN/pile) is found:

p0r 2WTs a gHpX (29)

This gives the following B (kN/pile):

B p0r*Ar 2WTs a

s2 a2

2WTs a gHp

s2 a2

X

(30)

This in turn gives a pile efciencyEp(kN/pile/kN/pile):

Ep 1 Bwtot

1 gHp

s2 a2Xs2gHp 1

s2 a2

s2 X (31)

3.3. Full arching

The assumption of full arching can be applied to the Modied

BS8006. However, it has already been argued in Section 2.4that

the assumption of full arching may lead to relatively low calcu-

lated tensile forces, which is solved in BS8006 as shown in

Section 2.4. If the Modied BS8006 applies full arching, the

tensile forces may even decrease. These equations shouldtherefore only be applied with great care. Further validation of

the full-arching theory is recommended. If full arching is

assumed in the Modied BS8006, p 0 and H 1.4(s a) areused in equation(28):

WT 0:7g

s2 a2

X (32)

The average load p0r on the GR, load part B, and the pile ef-ciency Ep can be derived using this basic Modied BS8006 equation.

The followingp 0r(kN/pile) is found:

p0r 2WTs a 1:4gs aX (33)


B p0r*Ar 2WTsa

s2 a2

2WTsa 1:4gsa

s2 a2

X

(34)This in turn gives a pile efciencyEp(kN/pile/kN/pile):

Ep 1 Bwtot

1 1:4gs a

s2 a2Xs2gHp 1

s2 a2

s2 X (35)

Table 1summarises the assumptions and starting points of Jones

equations, BS8006, and the Modied BS8006. The proposed

modication gives a fully 3D elaboration and a correct vertical

equilibrium.

3.4. Different pile spacing along and perpendicular to road axis

This section gives the equations for the Modied BS8006 if the

pile spacings along and perpendicular to the road axis are not

equal; sxs sy. The grouped variable Xin equation(11)changes in:

X

sxsy a2 p0c

gHp

sxsy a2 (36)

The GR areasArxand Ary, withsy > sx, ofFig. 7are:

Arx 12

sxsy a2

2 sxsy

Ary 12

sxsy a2sxsy

(37)

The strips in thex- andy-direction carry the loadpr0on areasArx

andAry respectively.

p0rAx WTxsx ap0rAy WTy

sy a

(38)Using equation(10)it follows:

WTxgHpXAx

sx a

WTygHpXAy

sy a

(39)

withArxand Aryand Xgiven in equations(36) and (37).

Table 1

Summary of the assumptions and starting points of Jonesequations, the original BS8006, and the modied BS8006.

Jonesa plane strain BS8006 Modied BS8006

1. Calculate load part A that passes directly to the piles (based on Marston and

Anderson, equation(2)).

Marston (equation(2)) Marston (equation(2)) Marston (equation(2))

2. Support of subsoil? No No No

3. Calculate load part Bton the reinforcement 3D equilibrium 3D equilibrium 3D equilibrium

4. Concentrate load part B on the reinforcement in between the pile caps 2D geometry 2D geometry 3D geometry

5. Double the load on the reinforcement, by applying line load to both directions

along and perpendicular to the road axis

Only 2D, thus only one

direction considered

Yes No

6. For comparison between the models: calculate back the load on the reinforcement

from the line load

2D geometry Differs per authorb 3D geometry

7. Vertical equilibrium? For partial arching Yes No Yes

8. Vertical equilibrium? For full arching No Noc No

a Jones et al. concentrated on a 2D method because thenite element studies developedfor thepaper could only modelin planestrain, i.e. 2D.Thisdoes notmean that Jones

et al. were proposing a 2D design approach, as explained in Section 2.3.2.b SeeAppendix 2, for exampleAbusharar et al. (2009)andLe Hello (2007)use a 2D geometry, whereas Love and Milligan (2003), Stewart and Filz (2005)andRussell and

Pierpoint (1997)use a 3D geometry,Chen et al. (2008) use an alternative 2D approach.c

As recognized byCorbet and Horgan (2010), in the paper in which they present the differences between BS8006:1995 and BS8006:2010.



8/15

For full arching, the height of the arch should equal the diagonal

pile spacing, giving the full-arching equation (forH>ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s2x s2yq

):

WTxgffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s2x s2yq

XAx

sx a

WTygffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s2x s2yq

XAy

sy a

(40)

4. Summary plane strain, BS8006 and Modied BS8006

Tables 2 and 3 summarise the plane strain equations, BS8006

and the Modied BS8006.

For BS8006, the vertical equilibrium is not correct. In the case of

the Modied BS8006, the vertical equilibrium is correct for partial

arching but not for full arching.

5. Comparison withnite element calculations

5.1. Geometry and properties

This section compares the results ofnite element calculations

(Plaxis) and the Modied BS8006, BS8006, and EBGEO. Moreover,

parameter variation demonstrates the inuence exerted by the

properties of thesemodels. Table 4 shows theproperties of thepiled

embankments basic geometry (also see Van Eekelen and Jansen,

2008). Comparison calculations in this paper only consider the

tensile forces due to the vertical load. Spreading forces are ignored.

For the geometry of this pile eld (s 1.75 m andd 0.5 m), thetransition between partial and full arching according to BS8006 is

whereH 1.4(s a) 1.4(1.75 0.44) 1.89 m, and the minimumembankment height according to the BS8006 isH 0.7(s a) 0.7(1.75 0.44) 0.92 m. In practice, the geometry of many piledembankments falls within the partial archingarea.

5.2. Finite element calculations

Two types of axial symmetric calculations were carried out

usingnite element analysis. The rst is a relatively simple model

(1). The second (2) is more sophisticated and was carried out to

validate the rst calculation (Van Eekelen and Jansen, 2008).

1. The soft subsoil was ignored (switched off). A one-metre-long

pile was modelled.

2. The soft subsoil was modelled using the Soft soil-creep model.

The support provided by the (drained) subsoil creeps away

below the reinforcement. In thenal situation, the subsoil is no

longer carrying any load.

In both models, the Hardening Soil model was applied to model

the granular

ll.Table 5shows the calculation parameters.

Table 2

Partial arching.

Plane strain BS8006 (Jones et al.) Modied BS8006

Total load, wtot per pile area kN/pile s2(gHp) s2(gHp) s2(gHp)

Line load on reinforcement strip, WT kN/m s(gHp)X s(gHp)X 0.5(gHp)(s a)Xa

Average pressure,p0r on geosynthetic reinforcement kPa WT

s gHpX 2WT

s a 2sgHp

s a X 2WT

s a gHpXLoad part B on geosynthetic reinforcement kN/pile (s

a)(gH

p)X 2s(s

a)(gH

p)X (s2

a2)(gH

p)X

Pile efciency, Ep 1 B/wtot kN/kN 1 s as2

X 1 2s as

X 1 s2 a2

s2 X

With:X s2 a2p0c=gHp=s2 a2.a Ifsxs sy, see equations(39) and (36).

Table 3

Full arching.

Plane strain BS8006 (Jones et al.) Modied BS8006

Total load, wtot per pile area kN/pile s2(gHp) s2(gHp) s2(gHp)

Line load on reinforcement strip, WT kN/m 1.4sg(s a)X 1.4sg(s a)X 0.7g(s2 a2)XAverage pressure,p0r on geosynthetic reinforcement kPa

WTs

1:4gs aX 2WTs a

2:8sgs as a X 1.4g(s a)X

Load part B on geosynthetic reinforcement kN/pile 1.4g(s a)2X 2.8sg(s a)2X 1.4g(s a)(s2 a2)X

Pile efciency, Ep 1 B/wtot kN/kN 1 1:4gs a2

s2gHp X 2:8gs a

2

sgHp X 1 1:4gs as2 a2

s2gHp X

Table 4

Properties of basic geometry example calculation.

Basic geometry

End-bearing or friction piles End bearing

Does the subsoil provide support? Modulus of subgrade

reaction, k

No support:

k 0 kN/m3Height embankment,H(between top pile cap and road

surface)

1.25 m

Centre-to-centre distance piles,s (along and

perpendicular to road axis)

1.75 m

Diagonal centre-to-centre distance,sdiagonal 2.47 m

(Equivalent) diameter pile caps, d 0.50 m

(Equivalent) width pile cap,a 0.44 m

Area pile caps 0.20 m2

Materialll Granular material

Materialll volume weight, g 20 kN/m3

Materialll internal friction angle, 4 37.5

Permanent weight asphalt and foundation layer 6 kPa

Trafc load,p 30 kPa

Long-term tensile stiffness geosynthetic reinforcement,

along road axis. In the BS8006 calculations, the input

strain is adapted until the calculated tensile stiffness

of the reinforcement is equal to J 1500 kN/m(calculated using equation(61)).

1500 kN/m



9/15

The geosynthetic reinforcement is modelled without interface

elements, resulting in maximal friction between granular materialand the GR.

The calculations show that models 1 and 2 give very similar

results (less than 10% difference in the total forces on the pile caps

and the tensile forces in the GR). The gures therefore only give the

results of the simple FE analysis (1).

5.3. Results of calculation comparison

Table 6 shows the calculated tensile forces for the properties

given inTable 4. The Modied BS8006 and EBGEO correlate quite

closely, agreeing more with the FE analysis than with BS8006. It is

noted that the 3D calculations of BS8006, Modied BS8006 and

EBGEO are different from the axial symmetric FE analysis. A 3D FE

analysis will calculate locally higher tensile loads than an axial

symmetric analysis. It is expected that 3D FE analysis will lead to

reinforcement loads similar to the EBGEO and modied BS8006

results.

Figs. 8e11 present several variation studies. In Figs. 8 and 11,

the geosynthetic reinforcement and the internal friction angle of

the ll are varied respectively. The geometry shown in Table 4

means that only partial arching occurs, as H 1.25


10/15

concrete pile caps (measuring 0.3 m in diameter), geogrid rein-

forcement, and 1.15 m of compacted ll (silty sand mixture).

Two geogrid layers were constructed: Fortrac 350/30e30 M

along the road axis (bottom) and Fortrac 400/30e30 M across.

Fig. 13 shows their isochrones, which can be used to determine

the time-dependent tensile stiffness J (Table 7, with a strain

of 2%).

0

150

300

450

height embankment H (m)

tensileforce(kN/m')

EBGEO

BS8006

FE analysis

Modified BS8006

1 2 3 4 5 6

Fig. 10. Tensile force with varied embankment height. Comparison of FE analysis,

EBGEO, BS8006, and modied BS8006 (the transition from full to partial arching is at

H1.4(sa)1.89 m).

0

150

300

450

1 2 3 4 5 6

height embankment H (m)

tensileforce(kN

/m')

EBGEO

BS8006

FE analysis

Modified BS8006

Fig. 11. Identical to Fig.10, butwithout fullarching. Variationin embankment height H.

Fig. 12. Layout of the Kyoto Road.

Fig. 13. Isochrones of the applied geogrids, source: Huesker Synthetic GmbH.



11/15

6.1.2. Subsoil

The local soil was excavated up to a depth of 1.15 m to remove

broken rubble. The Kyoto Road was constructed immediately

afterwards in less than four days. Therefore, the subsoil was not

able to swell before the piles and embankment were in place.

Table 8shows Youngs moduli E as determined from the drained

compression tests carried out before construction (values below

pre-consolidation stress).

From this, the modulus of subgrade reaction k can be calculated:

k E1E2E1d2 E2d1

1077*20001077*1:5 2000*1:45 477 kN=m

3

This value is probably lower than in practice, because the subsoil

did not swell fully between excavation and construction. Further-

more, the effective stress will be lower at the end of construction

than the initial stress, so the subsoil should behave more stify.

6.1.3. Properties ofll

The ll consists of a dredged silty sand containing some addi-

tives (mainly clay and cement). This ll type was used because the

re-use of waste material is environmental-friendly. Non-cohesive

granular material is normally used for embankment lls. Table 9

shows the ll properties.

6.2. Monitoring and prediction

6.2.1. Monitoring

The monitoring results are reported in Van Eekelen et al.

(2010a). Monitoring from November 2005 to May 2009 included

the total forces on top of piles eboth above the reinforcement (PSAand PNA in Fig. 12) and below the reinforcement (PNAB) e thegroundwater level, and the pore pressures below the embankment

(locations of the piezometers (ppt) inFig.12). This paper focuses on

comparing measured load distribution with predictions from

BS8006, the Modied BS8006, and EBGEO.

6.2.2. Comparison of measurements and predictionsFig.14and Table 10compare the measured and predicted values

for A, B and C. The tensile forces were not measured. The four

predictions inTable 10are:

BS8006 Modied BS8006 EBGEO without subsoil support (k 0)

EBGEO with subsoil support, with modulus of subsoil reactionk 477 andk 1000 kN/m3.

For all BS8006 calculations, the input strain has been adapted to

correspond to the tensile modulus of the geogrids J 3990 kN/mfor 1 year loaded GR (Table 7). Finally,Table 11compares the pre-

dicted tensile forces for several tensile moduli of the geogrids:

J 4375/3990/3868 kN/m (Table 7) for 1 day/1 year/10 years ofloading.

The prediction differences for short- and long-term tensile

stiffness of the geogrids are minimal due to their low creep ( Fig. 13

and Table 7). However, the long-term measurements show that

there is a constant slight increase in C, indicating that some creep

(GR deection) takes place as expected.

The differences in the predictions for different subgrade reac-

tion modules k (k 0, k 477 and k 1000 kN/m3) are consider-able. There is close agreement between the predicted and

measured B for EBGEO with k 1000 kN/m3. In this case, the k ofthe subsoil in fact seems to be higher than the determined value of

477 kN/m3. As discussed in Section6.1.2, the value ofk determined

from compression tests is probably too low. Measurements in road

N210 (Van Eekelen et al., 2010b) also tend to show that the subsoil

Table 7

Tensile stiffness of the Kyoto Road geogrid reinforcement.

Along road axis/

perpendicular to

road axis

Time

under

load

Ultimate tensile

strength, UTS

(kN/m)

Tensile stiffness

J(kN/m) (J (% of UTS/strain) UTS) (Values at 2% strain)

Along 1 day 350 (25.0/2) 350 4375Perpendicular 1 day 400 (25.0/2) 400 5000Along 1 year 350 (22.8/2) 350 3990

Perpendicular 1 year 400 (22.8/2) 400 4560Along 10 years 350 (22.1/2) 350 3868Perpendicular 10 years 400 (22.1/2) 400 4420

Table 8

Youngs moduli of subsoil.

Thickness (m) E(kN/m2)

Top layer Peat d1 1.45 m 1077Second layer Clay d2 1.50 m 2000

Table 9

Properties ofll (g unit weight, Wwater content, Kv the vertical permeability, 4

internal friction angle and c cohesion).

gwet(kN/m3)

gdry(kN/m3)

gaverage(kN/m3)

W(%) Kv(m/s)

4() c(kPa)

22.2 17.0 18.6 18.1 2.1E9 33.8 11.5

0

10

20

30

40

25-10-05

5-04

-06

14-09-06

23-02-07

4-08

-07

13-01-08

23-06-0

8

2-12

-08

13-05-0

9

loadpartC

(kN) arching

BS8006

EBGEO k=477kN/m3

measurements (total load - measured (A+B))

load on soft soil without piles

EBGEO k=1000kN/m3

0

10

20

30

40

50

25-10

-05

5-04-06

14-09

-06

23-02-07

4-08-07

13-01-0

8

23-06-0

8

2-12-0

8

13-05-0

9

loadpartB

(kN)

no arching, no soft soil supportModified BS8006

EBGEO without soft soil support (k=0)

EBGEO k =477kN/m3

measured B = (B+A)-A

EBGEO k =1000kN/m3

BS8006

0

5

10

25-10-05

5-04

-06

14-09-06

23-02-07

4-08

-07

13-01-08

23-06-08

2-12

-08

13-05-09

loadpartA(

kN

)

no arching

BS8006

EBGEO

arching

measured A

A

B

C

Fig. 14. Comparison of measured and predicted A ,B and C.



12/15

contributes more than EBGEO predicts with the k value assumed for

N210.

The determination ofB is seen as very important, as this is the

load part that directly determines the tensile force in the GR. Pre-

dictingB using the EBGEO agrees most closely with the measure-

ments.Table 11shows that for this geometry, the EBGEO without

subsoil support predicts the same tensile force as the Modied

BS8006. The tensile forces of the Modied BS8006 and EBGEO can

be identical, although B is not the same. This is because the load

distribution over the GR strip is considered differently.

Design should of course be carried out using safety margins:

subsoil support may decrease due to settlement, for example by

more than 30% due to groundwater variations (Fig. 14 and Van

Eekelen and Bezuijen, 2008).

7. Conclusions

7.1. Thin embankments

BS8006

BS8006 calculates the distributed vertical line loadWTon theGR using an equation that combines the 3D-equilibrium

equation and the 2D-calculation to concentrate the load into

a line load. BS8006 therefore incorporates both 2D and 3D.

BS8006 calculates the vertical load on the GR twice to convertto a fully 3D case. The vertical equilibrium is therefore not

correct.

Modied BS8006

Changing the BS8006 equations so that they use a 3D geometryapproach (and thus no double load calculation) resulted in the

Modied BS8006.

The Modied BS8006 approaches FE analysis-axial-symmetrymore closely than BS8006.

For thin embankments (partial arching), EBGEO and theModied BS8006 give nearly the same tensile forces, providing

that subsoil support is ignored.

Forthe geometryand properties of the Kyoto Road, EBGEO withno subsoil support and the Modied BS8006 predict the same

tensile force in the geogrids. EBGEO measurements and

predictions agree closely. If the aspect of subsoil support is

incorporated in the Modi

ed BS8006, both EBGEO and the

Modied BS8006 would give good agreement with the Kyoto

Road measurements.

It is recommended that subsoil support is incorporated in the(Modied) BS8006, at least so that the model can be validated

with eld tests where subsoil support usually occurs.

7.2. High embankments (full-arching theory)

For thick embankments (H> 1.4(s a)), BS8006 assumes thatfull arching occurs. The full-arching theory assumes that trafc

load or extra soil weight due to increased embankment height

is not carried by the reinforcement. This extra load is simply

cut off. This assumption is not conrmed by nite element

calculations. Further validation of the full-arching theory is

recommended, for example usingeld measurements on thick

embankments.

Due to the elaboration of the full-arching assumptions, anincreasing embankment height gives a dip in the predicted

tensile force in the reinforcement if a calculation using a non-

zero surcharge load is carried out.

It is recommended that the behaviour of high embankments isfurther validated before applying the Modied BS8006 for full

arching (H> 1.4(s a) or H> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2

x s2

yq

) , as the Modi

edBS8006 with full arching gives lower predicted tensile forces in

the GR than BS8006.

Elaboration of the full-arching assumption is too black-and-white to ensure a sound prediction. The transition should be

implemented more smoothly, as described byLawson (1995).

Acknowledgments

The support provided by Delft Cluster, Deltares, and CUR Bouw

& Infra is greatly appreciated. The nite element calculations were

carried out by Martin de Kant (Royal Haskoning, Netherlands) and

Piet van Duijnen (Movares, the Netherlands), both members of the

CURtask group for the design guideline for piled embankments. For

the Kyoto Road eld test, we are also grateful for the cooperationwith Van Biezen Heipalen, Kantakun, Huesker, and Delft Cluster.

Appendix 1. Elaboration of differential equation for step 4:

from line load to tensile force

The tensile force is calculated from the line load WT.

A tension membrane is considered with a tensile force T,

componentsTVand TH, and a loadq(x) in kN/m. The equilibrium of

a small particle is rst considered with a length ds(projection onx-

axis dx) given inFig.15. From the horizontal equilibrium it follows:

TH TH dTH 0 / dTH 0 (41)

From the vertical equilibrium it follows:

Table 10

Predictions of A, B, C and tensile force (kN/m) in GR, stiffness of GR is J2%, 1 year 3990 kN/m, Kyoto Road construction took place in November 2005.

BS8006 Mod. BS8006 EBGEO Kyoto Road measurements

k 0a kN/m3 k 0a kN/m3 k 0a kN/m3 k 477 kN/m3 k 1000 kN/m3 Average in 2007 Average in 2008Load part A 5.5 5.5 10.7 10.7 10.7 6.1 6.4

Load part B 48 29 24 15 9 5.8 4.2

Load part C 0 0 0 8.5 15 22.5 23.8

Tensile force,T 117 82 82 53 31

Pile efciency, Ep 0.39b 0.16 0.31 0.31 0.31 0.18 0.19a No support of subsoil.b Negative due to double calculation of load on GR.

Table 11

Predictions of tensile force (kN/m) in GR, variation of GR stiffness.

Time

under

load

J(kN/m) BS8006 Modied

BS8006

EBGEO

without

subsoil

EBGEO with

k 477 kN/m3

1 day J 4375 120 85 85 551 year J 3990 117 82 82 5310 years J 3868 116 81 81 52



13/15

TV

qdx

pdx

TV

dTV

0 / q

p

dTV

dx

(42)

As the subsoil support is ignored in BS8006:

q dTVdx

(43)

The relationship between the components THand TVof the tensile

force, dwand dx, and the angle a is:

tana TVTH

dwdx

/ TV THdw

dx (44)

This gives:

dTVdx

dTHdx

dw

dx TH

d2w

dx2 (45)

Using equation(41)and thus dTH=dx 0 it follows:

dTVdx

THd2w

dx2 (46)

Using equation(42), this gives the differential equation for rein-

forcement strips:

d2w

dx2 q

TH p

TH(47)

For BS8006, with p 0 it follows:

d2w

dx2 q

TH(48)

BS8006 assumes that q(x) is the equally distributed loadWT. Inte-

grating equation(43)gives:

TV WTx c1 (49)And integration of equation(48)gives:

THw 12WTx2 c1x c2 (50)

where c1 and c2 are integration constants. Two constraints give

expressions forc1and c2:

x 0 / w 0 / c2 0

x s a / w 0 / c1 1

2WTs a2

(51)

Thus, using equations(49) and (50):

TV WTx 12WTs a

w 12WTxs a x

TH

(52)

The extremes are:

x 0 / TV 12WTs ax s a / TV 12WTs ax 12s a / wextreme f WT

sa28TH

(53)

or, the inverse of the last equation:

TH WTs a2

8f (54)

Bouma (1989)shows the relationship between the length of the

undeformed and the deformed GR strip:

Dl 83

f2

s a or f2 3

8s aDl (55)

where F(m) e Maximal deection of the GR strip in between two

pile caps; Dl (m) e Difference of GR strip length between the

original length (s a) and the deformed length.The relationship between the (average) strain e and Dl is given

by:

Dl 3s a (56)This gives:

f s a ffiffiffiffiffi33

8r

(57)

When incorporated into equation(54)this gives:

TH WTs affiffiffiffiffiffiffiffi

243p (58)

The tensile force T in the GR strip can now be calculated:

Tx0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

T2Vx0 T2H x0q

WTs a2


63

r (59)

where Tx0 is the total tensile force (in kN) in the geosyntheticreinforcement strip with zero width. Dividing this by the width aof

the GR strip nally gives the tensile force Trp,x0 in the GR strip withwidtha, kN/m:

ds

TV+dTV

TH+dTH

Trp+dTrp

TV

TH

Trp

+d

dx

dw

x

w

w

w

q(x)

ds

TT

x

p(x)

q(x)

p(x)

f

Fig. 15. Equilibrium tension membrane.



14/15

Trp WTs a2a


63

r (60)

To summarise, this calculation is based on the following

assumptions:

- there is no subsoil support

- the line load WTis equally distributed- deformation is parabolic in shape

- the GR strip is xed at the corners of the pile caps

- the tensile force is calculated at x 0 and is thereforea maximum (and not an average, as in the German Standard

EBGEO).

In practice, equation(60)must be repeated. Here, the strain 3

has the function of an input parameter for calculating the tensile

forceTrp. This means that the apparent stiffness of the geosynthetic

reinforcement can be calculated as:

J Trp3

(61)

Appendix 2. Different interpretations of BS8006 from

literature

Introduction

Section2.3showed that the BS8006 equations are based on 3D-

equilibrium equations as well as 2D equations to concentrate the

load on the GR strips. BS8006 calculates the load on the GR twice.

Several authors have interpreted BS8006 so that it can be compared

with other models. This appendix presents their views and

compares their work.

The authors begin with the line load equations (13) and (17)and

calculate back to p0r, B or the pile efciency Ep 1 B/wtot. Theauthors usually follow either a 2D or a 3D interpretation of the 2D/

3D-BS8006.

These interpretations do not inuence the nal calculated

tensile force, as the tensile force is calculated from the line load

equations(13)or(17) and the tensile force equation (60). When

comparing BS8006 with other models, however, it is important to

realise that BS8006 is a 2De3D combination, doubling the load on

the reinforcement and assuming full arching.

Assuming a 2D conguration

For example, Le Hello (2007) assumed a 2D conguration.

Starting from equation (12) and assuming the conguration of

Fig. 4a the author nds:

p0r WTs (62)

Partial arching

For partial arching, the equation for the line load is given by

equation(13). Combining this with equation(62)gives:

p0r WT

s gHpX (63)

Continuing the assumption of a 2D conguration gives:

B s ap0r s agHpX (64)and thus a pile efciencyEp:

Ep 1 Bwtot

1 s agHpXs2gHp 1

s aXs2

(65)

Full arching

For full arching, the equation for the line load is given by


p0r WT

s 1:4gs aX (66)

Continuing the assumption of a 2D conguration gives:

B s ap0r 1:4gs a2X (67)and thus a pile efciencyEp:

Ep 1 Bwtot

1 1:4gs a2X

s2gHp (68)

Abusharar et al. (2009)also calculate the total load for deter-

mining the pile ef

ciency on the basis of 2D. This means that theyuse a total load s(gHp), thus s instead of s2. Throughout thispaper, the pile efciency is calculated using the calculated B and the

total load on one grid s $ s, thuss2(gHp).Chen et al. (2008) compared the results of 2D experiments

with e among others e BS8006. However, Yun-min did not fully

use BS8006, but instead used the original 2D equation of Marston

(equation(1)) when applying the arching coefcientsCcof BS8006

(equation(4)).

Assuming a 3D conguration

Other authors assume that BS8006 has determined its line load

(equation(12)to (11)) using the 3D conguration shown inFig. 6

(for example, seeLove and Milligan, 2003; Russell and Pierpoint,

1997; Stewart and Filz, 2005). The German Standard EBGEO

applies nearly the same conguration, except that the pile caps are

circular. The authors assume that this tensile strip carries half the

load on one square s $ s, giving:

3D : p0r

s2 a2

2WTs a / p0r 2WTs a (69)

Authors such asLove and Milligan (2003), Stewart and Filz (2005),

andRussell and Pierpoint (1997)arrive at this equation.

Partial arching

For partial arching, the equation for the line load is given by


p0r 2WTs a 2sgHp

s a X (70)


B p0r*Ar 2WTs a

s2 a2

2WTs a

2sgHps aX (71)This in turn gives a pile efciencyEp(

kN/pile/kN/pile):

Ep 1 Bwtot

1 2sgHps aXs2gHp 1

2s as

X (72)



15/15

Full arching

For full arching, the equation for the line load is given by


3D: p0r 2WTs a

2:8sgs as a X (73)

Authors such asLove and Milligan (2003), Stewart and Filz (2005),

andRussell and Pierpoint (1997)also arrived at this last equation.This gives the following B (kN/pile):

B p0r*Ar 2WTs a

s2 a2

2WTs a 2:8sgs a2X

(74)

This in turn gives a pile efciencyEp(kN/pile/kN/pile):

Ep 1 Bwtot

1 2:8sgs a2X

s2gHp 1 2:8gs a2

sgHp X (75)

Different interpretations from literature: a conclusion

Jones et al. (1990) developed the equations partly for a 3D

conguration (equilibrium), and partly for a 2D conguration (line

load determination).

Some authors assume that the equations were developed on

the basis of a fully 2D conguration. Others assume that the

equations were developed for a 3D conguration. The 2D case

results in different values forp0r,B and E, the 3D case results in thesame values forp 0r,B and Eas found in the elaboration of BS8006(Section2).

References

Abusharar, S.W., Zeng, J.J., Chen, B.G., Yin, J.H., 2009. A simplied method for

analysis of a piled embankment reinforced with geosynthetics. Geotextiles andGeomembranes 27, 39e52.Bouma, A.L., 1989. Mechanica van constructies, elasto-statica van slanke structuren,

rst ed. Delftse Uitgevers Maatschappij b.v.. 90 6562 11.British Standard, BS8006-1, 2010. Code of Practice for Strengthened/Reinforced Soils

and Other Fills, ISBN 978 0 580 53842 1.Chen, Y.M., Cao, W.P., Chen, R.P., 2008. An experimental investigation of soil arching

within basal reinforced and unreinforced piled embankments. Geotextiles andGeomembranes 26, 164e174.

Corbet, S.P., Horgan, G., 2010. Introduction to international codes for reinforced soildesign. In: Proceedings of 9ICG, Brazil, pp. 225e231.

Dutch CUR design guideline for piled embankments. CUR 226 2010, ISBN 978-90-376-0518-1.

EBGEO, 2010. Empfehlung fr den Entwurf und die Berechnung von Erdkrper mitBewehrungen als Geokunststoffen. In: Bewehrte Erdkrper auf punkt- oderlinienfrmigen Traggliedern. Deutsche Gesellschaft fr Geotechnik e.V.,(German Geotechnical Society), Ernst & Sohn, ISBN 978-3-433-02950-3(Kapitel 9).

Haring, W., Prottlich, M., Hangen, H., 2008. Reconstruction of the national road

N210 Bergambacht to Krimpen a.d. IJssel, nl: design approach, constructionexperiences and measurement results. In: Proceedings of the 4th EuropeanGeosynthetics Conference, Edinburgh, UK, paper nr. 259.

Hewlet, W.J., Randolph, M.F., Aust, M.I.E., 1988. Analysis of piled embankments.Ground Engineering, April 1988 22 (3), 12e18.

Jenck, O., Dias, D., Kastner, R., 2005. Soft ground improvement by vertical rigid pilestwo-dimensional physical modelling and comparison with current designmodels. Soils and Foundations 45 (6), 15e30.

Jones, C.J.F.P., Lawson, C.R., Ayres, D.J., 1990. Geotextile reinforced piled embank-ments. In: Den Hoedt (Ed.), Geotextiles, Geomembranes and Related Products.Balkema, Rotterdam, ISBN 90 6191 119 2, pp. 155e160.

Lawson, C.R., 1995. Basal Reinforced Embankment Practice in the United Kingdom,The Practice of Soil Reinforcing in Europe. Thomas Telford, London, pp.173e194.

Le Hello, B., 2007. Renforcement par geosynthetiques des remblais sur inclusionsrigides, etude experimentale and vraie grandeur et analyse numerique. PhDthesis, luniversite Grenoble I (in French).

Love, J., Milligan, G., March 2003. Design methods for basally reinforced pile-sup-ported embankments over soft ground. Ground Engineering, 39e43.

Marston, A., Anderson, A.O., 1913. The theory of loads on pipes in ditches and testsof cement and clay drain tile and sewer pipe. Bulletin No. 31, EngineeringExperiment Station.

McKelvey, James A, 1994. The anatomy of soil arching. Geotextiles and Geo-membranes 13, 317e329.

Russell, D., Pierpoint, N., Nov. 1997. An assessment of design methods for piledembankments. Ground Engineering, 39e44.

Stewart, M.E., Filz, G., 2005. Inuence of clay compressibility on geosyntheticloads in bridging layers for column-supported embankments. In: Proceedingsof Geo-Frontiers 2005, USA, GSP 131 Contemporary Issues in FoundationEngineering.

Van Duijnen, P.G., Van Eekelen, S.J.M., Van der Stoel, A.E.C., 2010. Monitoring ofa railwaypiledembankment.In:Proceedingsof 9ICG, Brazil,2010, pp.1461e1464.

Van Eekelen, S.J.M., Bezuijen, A., 2008. Design of piled embankments, consideringthe basic starting points of the British Standard. In: Proceedings of EuroGeo4,Number 315, September 2008, Edinburgh, UK.

Van Eekelen, S.J.M., Jansen, H., 2008. Op weg naar een Nederlandse ontwerprichtlijnvoor paalmatrassen 1, Verslag van een casestudie. GeoKunst 3 (in Dutch).

Van Eekelen, S., Bezuijen, A., Alexiew, D., 2010a. The Kyoto road, monitoring a piledembankment, comparing 3 1/2 years of measurements with design calcula-tions. In: Proceedings of 9ICG, Brazil, pp. 1941 e1944.

Van Eekelen, S., Jansen, H., Van Duijnen, P., De Kant, M., Van Dalen, J., Brugman, M.,Van der Stoel, A., Peters, M., 2010b. The Dutch design guideline for piledembankments. In: Proceedings of 9ICG, Brazil, pp. 1911e1916.

Van Eekelen, S.J.M., Lodder, H.J., Bezuijen, A., 2011. Load distribution on the geo-synthetic reinforcement within a piled embankment. In: Proceedings ofECSMGE, 2011, Greece.


Van Eekelen Et Al 2011 BS8006 Final

Documents

Transcript of Van Eekelen Et Al 2011 BS8006 Final