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S Denton, T Christie, J Shave, A Kidd 1

PD6694-1:RECOMMENDATIONS FOR THE DESIGN OFSTRUCTURES SUBJECT TO TRAFFIC LOADING TO EN1997-1

S Denton, Parsons Brinckerhoff, Bristol, UKT Christie, Parsons Brinckerhoff, Bristol, UKJ Shave, Parsons Brinckerhoff,Bristol, UKA Kidd, Highways Agency,Bedford, UK

AbstractThis paper gives the background to the development of the provisions of PD 6694-1. It gives

guidance on the application of PD 6694-1 where it is considered that further explanation may

be helpful and identifies recommendations in PD 6694-1 which involve design principles or

procedures significantly different from those used in past practice.

The paper covers the clauses in the PD 6694-1 relating to actions, spread foundations, buried

structures and earth pressure on gravity retaining structures and bridge abutments. Traffic

surcharge and integral bridges are covered in detail in companion papers, for which references

are provided.

NotationThe same notation is used as in the Eurocodes and PD 6694-1. Other symbols are defined

within the clause in which they occur.

The Clause numbers used in the headings of this paper are the Clause numbers in PD 6694-1

to which the text refers.

IntroductionThe recommendations given in PD 6694-1 (hereafter referred to as the PD) apply to

structures that are subject to traffic surcharge and other traffic loading. The recommendationstherefore specifically relate to the rules and partial factors given for "bridges" as opposed to

"buildings" in the Eurocodes. Many of the principles described can however be applied to

earth retaining structures that are not subject to traffic loading.

BS EN 1997-1:2004 does not specifically cover aspects of design of some types of highway

and rail structures such as integral bridges and buried structures. Complementary design

recommendations and guidance is therefore included in the PD.

For highway structures, PD 6694-1 replaces BD 30/87[2](Earth Retaining Structures), BD

31/01[3]Buried Structures, BA 42/96[1]Integral Bridges and BD 74/00[5]Foundations. The

design of reinforced earth structures is neither covered in BS EN 1997-1:2004 nor in the PD.

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Basis of Design (4)

Dispersion of vertical load through fill (4.4)The justification for the 30method of dispersing vertical loads is given later in this paper in

relation to buried structure (10.2.7). The use of the 30dispersion method may however be

unsafe when the vertical pressures arising from it are favourable. For example, where sliding

resistance is dependent on the load on the base slab, it may be unsafe to assume that part of

the weight of the surcharge traffic behind the abutment is supported on the base slab because

other dispersion modes including vertical soil arching can occur which may result in the

vertical load being supported on the ground behind the base slab while the horizontal

surcharge effect is still applied to the wall.

When analysing the foundations for bearing pressure the vertical pressure on an abutment

base slab due to the traffic surcharge may be favourable or unfavourable. In some cases theadditional pressure may increase the toe pressures, but in other cases it may apply a large

enough restoring moment to reduce the toe pressure. If the effect of the vertical pressure from

traffic surcharge is favourable in respect of bearing pressure, it may be prudent to ignore it.

Model Factors on horizontal earth pressure at ULS (4.7)Following the publication of BS EN 1997-1:2004, concern was expressed that the ULS partial

factors were significantly lower than those used in pre-Eurocode standards for bridge design.

In particular it was seen that the effective ULS partial factor fL. f3specified for horizontal

earth pressure in BD 37/01[4] equalled 1.5x1.1 = 1.65 compared with a Fof 1.35 for the

critical STR/GEO limit state, Design Approach 1, Combination 1 partial factors in theEurocode (i.e.Set A1 in BS EN 1997-1:2004 and Set B in BS EN 1990:2002). This would

mean that structures designed to BS EN 1997-1:2004 could be less robust than those designed

in the past.

To address this concern, the PD states that where it is required to maintain the same levels of

safety as were applied in the past, a model factor Sd;Kmay be applied to the horizontal earth

pressure (effectively toKaorK0). The recommended value of the model factor was based on

the ratio of the pre-Eurocode factors to the STR/GEO Combination 1 factor, namely 1.65/1.35

= 1.22 (rounded down to 1.2), to give similar design values for earth pressures. Its effect was

examined for other ultimate limit states verifications.

For sliding and overturning, BD 30/87, 5.2.4.2[2]references CP 2[8]in which it says, in

relation to sliding: a factor of safety of approximately 2 should be appliedand the

angle of friction below the base is equal to the angle of friction of the soil beneath thefoundation.

On this basis, the required heel lengthBheelfor an abutment of height Z is given by:

Bheel = 2Ka;k{Z2/(2tan'

For a Eurocode design using the model factor S;dK:

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Bheel = Sd;KKa;d{Z2/(2tan'cv)}

From this is can be shown that, using the model factor and the relevant values of the partialfactors, the Eurocode value ofBheelwill not be less than the pre-Eurocode value if tancvis

not greater than about 0.9tan '. In practice tan'cvis almost invariably less than 0.9tan.

For sliding resistance of an undrained foundation CP 2[8]uses a similar method to the

Eurocode. For the CP 2[8]method with a factor of safety 2 on sliding: 2H=BcuwhereBis

the base length,Zis the height of the wall and the horizontal actionH=Ka;k Thus,

B= 2Ka;k{Z2/(2cu)}

In the Eurocode, for a retaining wall subject to permanent actions and the model factor,

GSd;kH =Bcu/Mwhere in Design Approach 1, Combination 2 G= 1 and M= 1.4.

B= 1.4 Sd;KKa;d{Z2/2cu}

From this it can be shown that based on k= 33for the backfill and the relevant values of

the partial factors, the Eurocode base length will be approximately 5% longer than the CP 2[8]

base length if the model factor is included, and approximately 13% shorter if the model factor

is not applied.

The above comparisons apply to retaining walls subject to permanent earth pressure only.

When surcharge, braking and acceleration are applied, the pre-Eurocode base lengths willtheoretically be relatively longer. In practice though, the Eurocode surcharge action is so

much larger than the pre-Eurocode surcharge action that it is unlikely that base slabs subject

to the Eurocode surcharge will be shorter than base slabs designed in the past.

Bearing resistance is frequently governed by settlement requirements at SLS for which the

ULS model factor is irrelevant. For ultimate bearing resistance it is less easy to make a direct

comparison between Eurocode and pre-Eurocode designs because of the number of different

acceptable pre-Eurocode design methods available. Specimen comparative calculations have

however shown that if the model factor is applied to the horizontal earth pressure, the

Eurocode designs for bearing resistance will usually be comparable with pre-Eurocode

designs.

In relation to overturning, CP 2[8]says "...in gravity walls the resultant thrust should not fall

outside the middle third of the base, and for other types of wall a factor of safety of at least 2

against overturning is required". Overturning is not usually an issue with conventional

gravity walls and abutments because the bearing resistance under the toe will normally

become critical before the structure overturns and the length of heel required to provided

sliding resistance is usually sufficient to give an adequate restoring moment. Overturning

could however become an issue with a mass gravity wall seated on rock or a concrete slab and

propped or keyed into the slab to prevent sliding as shown in Figure 1.

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Figure 1

For the above structure, considering overturning about A at ULS, the Eurocode effectively

requires that the maximum design overturning moment should not be greater than the

minimum design restoring moment:

Y H G;soil;supSd;kMK X V G;conc;inf

where H and V are characteristic actions and MK=Ka;d/Ka;k 1.11 at EQU and 1.25 at

STR/GEO combination 2 if ' is about 33o.

The overall factor of safety isXV/YHwhich equals (G;soil;supSd;KMK )/(G;conc;inf).

This equals (1.05 x 1.2 x 1.11/0.95) = 1.47 at EQU and (1.35 x 1.2 x 1.0/0.95) = 1.70 atSTR/GEO Combination 1.

These values reduce to 1.23 and 1.42 respectively if the model factor Sd;Kis not applied.However, it can be shown that if this structure was designed to comply with the "middle

third" rule at SLS then the factor of safety would automatically be 3.0.

From the above comparisons it can be seen that the 1.2 ULS model factor compensates for the

difference between the Eurocode and pre-Eurocode values of ULS partial factors in relation to

earth pressure, sliding resistance and ultimate bearing resistance, and it is irrelevant in regards

to settlement and overturning except in the unusual situation where a structure such as that

shown in Figure 1 is not designed to comply with the middle-third requirement at SLS.

The Eurocode surcharge loading for highway structures is substantially more onerous than the

HA and HB surcharge used in the past, and as this will result in stronger rather than weaker

structures, the 1.2 model factor is not required to be applied to the effects of traffic surcharge

loading.

The PD does not offer an opinion as to whether the pre-Eurocode standards were unduly

conservative. The option to use the model factor is for designers and clients who wish to

maintain past levels of safety in their earth retaining structures.

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Pile Foundations (6)

This clause is based on the recommendations in BD 74/00 Annex B

[5]

.

Gravity Retaining Structures and Bridge Abutments (7)

Earth pressures on retaining walls and abutments with inclined backfill (7.2.3and 7.2.4)

Active pressure on walls with long heels (

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Example 1 (Long heel)A 6m high wall with a 4m heel supports backfill inclined at 20o. Find the active characteristic

horizontal thrust applied to the structure if = 18 kN/m

3

and '= 35

o

:

When == 20o,Kafrom PD 6694-1, Table 4equals 0.30

Height of virtual face CD = 6 + 4tan20o= 7.46m

Horizontal thrust = KaCD/2 = 18x0.3x7.46/2 = 150.3kN/m width.

Figure 3. Values of

Active pressure on walls with short heels (7.2.4)When >, (that is when BC is less than ABcot as in Figure 4(c)) the critical inclined

virtual face CE is interrupted by the back face of the wall at H as shown in Figure 4(c) and the

results described in the previous paragraph will no longer apply because AH in Figure 4(c) is

a soil-to-wall surface and over that length will be wrather than '.

When = , as in Figure 4(b) on CD =. When = 90o, as in Figure 4(d), on CD equals

wbecause CD is then coincident with BA and w is applied over the full height of the wall.When lies between and 90o, the effective value of on CD therefore lies betweenand

w, and the effective value ofKaon CD (that isKa;CD) will lie betweenKa;andKa;was

described in the PD.

To determine the value ofKaon CD for an intermediate position with < < 90, the shaded

triangle AHG in Figure 4(c) was considered as a Coulomb wedge with = won AH, and

HCFG was considered as a four-sided wedge with = ' on all soil-to-soil faces. Using this

model for a number of values of it was found that although theoretically as increased from

to 90o the plot ofKa;CDfollowed a curve between Ka;andKa;w, in practice it was simpler

and marginally conservative to assume thatKa;CDincreased linearly with fromKa;to

Ka;win this range

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Figure 4(e) plots the value of the thrust on plane CA and on the whole structure as the wall

BA moves towards CD and increases from less than to 90o. The arc PQ shows the

theoretical increase in effective Ka;CD as increases from to 90

o

and the chord PQ showsthe linear variation in Ka;CDassumed in the PD.

(a) < (b) = (c) <

Linear approximation Theoretical

Horizontal

thrust on CA

as increases(a) (b) (c) (d)

on CD = w

on CD =

horiz

ontalthrust

CB

D

A

E

=

e

CB

DE

=

A

CB

DA

Hw< <

=w

=

G

F

B,C

FA,D

=

w

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recommends that when wis greater than,Kaon CD should be taken asKa;for all values of

.

Example 2 (Short heel)A 6m high wall with a 1.5m heel supports backfill inclined at 20o. Find the characteristic

active pressure applied to the structure if = 18 kN/m3and '= 35oand wis taken

conservatively as 10o:

= tan-1(6/1.5) = 76o

= from Figure 3 (above) (for= 20oand '= 35o) = 70.8o. >

When = = 20o, Ka; from PD 6694-1, Table 4 equals 0.302

When = w= 10oand= 20,Ka;w by wedge analysis or other means = 0.322

Increase inKa;CD= (Ka;w-Ka;){(-)/(90-)} = (0.322-0.302){(76-70.8)/(90-70.8)} = 0.005

Ka;CD= 0.302+0.005 = 0.307Height CD = 6 + 1.5tan20 =6.55m

Horizontal thrust = KaCD/2 = Ka6.55/2 = 18x0.307x6.55/2 = 118.5kN/m width

Walls with both and greater than 80oIt can be seen from the equation for that whenapproaches ', approaches 90o. It has

been found that in the unusual situation when both and are greater than 80o(i.e. steep

backfill with a very small heel), the value ofKa;CDstarts to increase towardsKa;when is

approximately 80o(i.e.less than ). The PD covers this situation by artificially limiting the

maximum value of to 80oin 7.2.4. This limitation only affects the heel length at which the

short heel effect becomes critical. It does not affect the valueKa;.

Compaction pressures (7.3.4)The pressure distribution shown by Clayton and Milititsky[9], Ingold[10]and others is

reproduced in Figure 5(a). In practice the position of (A) usually occurs only a short way

below the surface and it is simplest and only slightly conservative to consider the combined

active and compaction pressure having the value topgiven in the PD and being constant from

ground level to the level at which active pressure equals top as shown in Figure 5(b).

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(a) Clayton[9]& Ingold[11] (b) PD 6694-1

Figure 5. Compaction pressures

Movement Required to Generate Passive Pressure (7.5)BS EN 1997-1:2004, Annex C effectively defines the relationship between mobilised passive

pressure and wall movement by three points and one gradient (see BS EN 1997-1:2004,Annex C,Figure C.4). The three points areKoand zero movement, 0.5Kpand a movement of

v2/h andKpand a movement of v/h. By the nature of passive pressure the gradient of the

pressure/movement curve at full passive pressure is horizontal. This is illustrated in Figure 6.

In devising a formula to replicate the curve illustrated in Figure C.4in Annex C it was

considered adequate to assume that the relationship was linear betweenKo andKp/2 and the

curve betweenKp/2 andKpwas a cubic curve passing through theKp/2 andKppoints and

having a horizontal gradient atKp. The equation given in the PD achieves this. Inevitably in

some cases the gradient of the curve atKp/2 is not identical to the gradient of theKo-Kp/2 line.

The errors resulting from this are considered to be small compared to the tolerance on vp/h

and v2/hgiven in BS EN 1997-1:2004, Annex C.

Active

pressure

top

h =zKd

z

d

top

cK

h

=

toph =

Vtop 2=

A

B

0

Active

pressure

zh =zKp

h =zKa

zc

P

kh

a

c

21=

PKz ac

2

=

Phrmh

2' ==

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Buried Concrete Structures (10)This section (Clause 10) is based on BD 31/01[3]updated in line with the Eurocode

requirements.

Superimposed permanent load (10.2.2)

The model factors Sd;ecto be applied for superimposed permanent load are taken from Figure3.1 in BD 31/01[3].

Dispersal of vertical loads (10.2.7)

The dispersal of vertical loads through fill is given in the PD as 30compared to 26.6(2:1)

in BD 31/01[3]. The 30value is taken from BS EN 1991-2:2003, 4.9.1, NOTE 2.

The Boussinesq equation given in clause 3.2.1 (iii) of BD 31/01[3]has been omitted from the

PD as it underestimates the pressure when there is a rigid plane, such as the roof of a buriedstructure, located a short distance below ground level. The method in Table 2.1 of Poulos and

Davis[12]gives pressures below a point load which are marginally lower than those found

using the 30dispersion method, as can be seen from Figure 7.

Figure 7. Comparison of the 30opressures with pressures based on the Poulos &Davis[12]and Boussinesq equations for 1 m fill depth.

Longitudinal road traffic actions (10.2.8)

Traffic surcharge (10.2.8.1)The treatment of traffic surcharge for buried structures using the simplified model given in

PD 6694-1, 7.6is explained in Table 5, Note Bof the PD. Its background is given by Shave

et al[13].

Braking and acceleration (10.2.8.2)The reduction of the braking and acceleration actions with increasing depth of earth cover

given in PD 6694-1, 10.2.8.2has been retained from BD 31/01[3]in the absence of data to

justify a revaluation.

Longitudinal joints (10.5)

The 0.15Hclimitation of deflection on segmental units is taken from BD 31/01[3].

Poulos and

Davis

Boussinesq

30 degree

method

0

0.2

0.4

0.6

0.8

1

-2.5 -1.5 -0.5 0.5 1.5 2.5

Vertical

pressureperunit

load

Horizontal distance

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Soil Structure Interaction Analysis of Integral Bridges (Annex A toPD 6694-1)

See accompanying paperDenton et al[14]

.

Tables of Earth Pressures for Buried Structure (Annex B)

Maximum pressure (B.2 and tables B.1 and B.2)The values of the earth pressure coefficients given in the tables in Annex A are based on the

assumption that the maximum characteristic at rest earth pressure coefficient taking

temperature and strain ratcheting into account, is 0.6, as in BD 31/01[3]. This may be

considered as backfill with a characteristic 'of 30subject to an enhancement factor,Fenh, of

1.2 to allow for temperature, strain ratcheting and other unfavourable effects. In addition, at

ULS, the pressure coefficients are subject to the model factor Sd;K(also equal to 1.2) described

in 4.7. Using the values of Mgiven in the UK National Annex to BS EN 1997-1:2004 thevalues of the earth pressure coefficientKmaxgiven in Tables B.1 and B.2in Annex B are derived

as follows:

Characteristic EQU STR/GEO STR/GEO

Comb 1 Comb 2

d(inc M) 30o 27.7o 30o 24.8o

K0= (1-sind) 0.5 0.53 0.5 0.58

K0xFenh 0.6 0.64 0.60 0.70

Kmax=K0Fenhsdk 0.6 0.77 0.72 0.84

As traffic surcharge is not considered to be affected by temperature and strain ratcheting, and

as Sd;kis not applied to traffic surcharge (see 7.6) the design value of the at rest pressure

coefficient for traffic surcharge given in PD 6694-1, Annex B Tables B.1 and B.2 is simply

the value ofKogiven in the table above.

Minimum pressure (B.3 and Table B.3)For members which are critical with minimum horizontal earth pressure, Table B3is relevant.

The minimum characteristic earth pressure coefficient of 0.2 is as in BD 31/01[3]. This is the

characteristic value ofKafor k= 30multiplied by a reduction factor, Fred= 0.6. The values

ofKmin;dgiven in the tables are based on the equation:

Kmin;d=Fred(1-sind)/(1+sind)

where d= tan-1{(tan 30)/M*} and M* = 1/M. This gives approximately the same result as

takingFred= 1, kas 38withKa;kbased on /= 0.66 from BS EN 1997-1:2004, Figure

C.1.1and M= as before.

Figure C.1.1gives values ofKaas low as 0.13 for = 45oand = and it would therefore

be prudent to ignore active pressure altogether if it was considered that backfills with high

values of 'were relevant.

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Active pressure (B.4 and Tables B.4, B.5 and B.6)

When braking or acceleration actions are applied, active pressure based on a characteristic '

of 30is applied on the active face andKmaxis applied to the passive face as in Tables B.1andB.2, except that as the single source principle in not applied at EQU and theKmaxactions

are favourable in resisting longitudinal actions, the characteristic value of Kmax(= 0.6) is

applied at EQU in Tables B.4 andB.5.

Where it is necessary to increase the pressure on the passive face above theKmaxpressure to

resist the longitudinal traffic actions it should be noted that movements related to specific

values of K given in Table C.2of Appendix C of BS EN 1997-1:2004 are substantially

greater than those given by Hambly[10](see Table 1 above).

References

[1] BA 42/96 Amendment No. 1(2003)The design of Integral Bridges, The StationaryOffice, London

[2] BD 30/87Backfilled retaining walls and bridge abutments, The Stationary Office,

London

[3] BD 31/01The design of buried concrete box and portal frame structures, The

Stationary Office, London

[4] BD 37/01Loads for highways bridges, The Stationary Office, London

[5] BD 74/00Foundations, The Stationary Office, London

[6] BS EN 1991-2:2003 (incorporating Corrigenda December 2004 and February 2010),

Eurocode 1, Part 2, Traffic loads on bridges, BSi, London, UK

[7] BS EN 1997-1:2004(incorporating corrigendum February 2009)Eurocode 7:

Geotechnical design Part 1: General rules, BSi, London, UK[8] CP 2 (1951)Earth retaining structures, BSi, London, UK

[9] Clayton, C. R. I and Milititsky, J. (1986)Earth pressure and earth retaining structures

Surrey university Press, London

[10] Hambly, E.C. (1991)Bridge Deck behaviour, 2ndedition, London: E& FN Spon

[11] Ingold, T.S. (1979) The effects of compaction on retaining walls. Gothechnique

29(3), 265-283

[12] Poulous, H.G and Davis, E. H. (1974)Elastic solutions for soil and rock mechanics

John Wiley & Sons, Inc, London

[13] Shave, J, Christie, T. J. C, Denton, S. and Kidd, A. (2010)Development of traffic

surcharge models for highway structures, in Proceedings of Bridge Design to

EurocodesUK Implementation, Ed. by S. Denton, Nov 2010, ICE, London.

[14] Denton, S, Riches, O, Christie, T. J. C. and Kidd, A. (2010)Developments in integral

bridge design, in Proceedings of Bridge Design to EurocodesUK Implementation,

Ed. by S. Denton, Nov 2010, ICE, London.

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Appendix 1

Derivation of Earth Pressures on Walls With Long Heels andSloping Backfill

This appendix provides a derivation of the critical wedge angle , the friction angle to be

used on the vertical virtual face, and the resulting earth pressure coefficientKa, for a retaining

structure such as that illustrated in Figure A1(a) where the backfill is sloping at an angle

and the heel of the wall is long enough that >.

Figure A1(b) shows the critical wedge ECF and the forces acting on it at the boundaries,R1

andR2, and the self-weight W.

(a) (b)

Figure A1. Earth pressures with sloping backfill

Figure A2 comprises the Mohrs circle for the critical wedge ECF as it reaches a critical

state simultaneously along CE and CF (represented by points eandf). Point d represents the

stress at the vertical plane CD.

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Figure A2. Mohrs circle for the critical wedge

The angle between planes EC and ED is (90-), so this transformation of axes requires a

rotation on the Mohrs circle from point eto point dof

)90(2 =doe (A1)

Triangle geois right angled, hence'90 =goe (A2)

From (A1) and (A2),

'902)90(2'90 ==hod (A3)

The external angle of triangle gdo is therefore:

= '902jdo (A4)

By considering triangles djoand gjoand using the sine rule,

)'902sin('sin

sin)sin( == RRojdoj (A5)

Leading to:

)'902sin('sin

sin

= (A6)

Rearranging (A6) gives

=

'sin

sinsin'90

2

1 1

(A7)

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Now consider the equilibrium of the wedge component triangles EDC and CDF as shown

in Figure A3.

Figure A3. Equilibrium of wedge component triangles

The forces R1 and R2 act at the 1/3 points of CE and CF, because there is a linear stress

distribution along these lines. These points are vertically below the centroids of triangles

EDC and CDF. The forceR3 acts at the interface CD at an angle . For equilibrium the 3

forces for each triangle must intersect at a point. These intersection points must therefore be

the 1/3 points on the boundaries CE and CF, as shown in Figure A3. Using similar triangles,

the angle of the forceR3 must be identical to the slope of the backfill1, or:= (A8)

From (A7) and (A8),

=

'sin

sinsin'90

2

1 1

(A9)

By summing the angles around point O in Figure A2 to 360 degrees it can also be

demonstrated that the angle eis related to by the expression in (A10):

==

'sin

sinsin'90

2

1'90 1

e (A10)

Knowing the critical value of as given in (A9), the ratio of the horizontal to the verticalearth pressures may be determined from the Mohrs circle in Figure A2:

1

An alternative derivation of (A7) considers the triangles of forces for the component triangle EDC and the fullwedge ECF shown in Figure A3 and demonstrates that when =the horizontal thrust is equal in each case;

however the derivation is more complex and so not included here for space reasons.

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'2sin'sin1

'2sin'sin1

'2sin'sin

1

'2sin'sin

1

=

=

v

h (A11)

However, while the ratio of stresses defined in (A11) could be thought of as an earth pressure

coefficient, the values obtained from (A11) are not the same asKadefined in the conventional

way as in (A12), based on the total horizontal force Hacting on a vertical plane of height h

and assuming a vertical earth pressure of z, where is the soil density and zis the distance

below ground level.

2

21 h

HKa

= (A12)

Hmay be determined by considering the equilibrium of the wedge component triangle CDF

in Figure A3, from which:

)'tan(

1tan

2

e

= W

H (A13)

The weight W2is calculated based on the area of the triangle CDF:

)sin(

coscos

2

1 22

e

e

= hW (A14)

Combining (A8), (A12), (A13) and (A14) results in the following expression forKa:

=

)'tan(

1tan)sin(

coscos

ee

eaK (A15)

A comparison of expressions (A11) and (A15) shows that they give almost identical values up

to a slope angle of about half , but as the slope approaches the values diverge, with

(A15) giving higher values. This difference is due to the way that Ka has been defined in

(A12), which is convenient for design purposes, but this definition of Ka is not strictly the

same as the ratio of horizontal and vertical pressures when the backfill is sloping.

The values for Kapresented in Table 4 of PD6694-1 have been calculated from (A10) and

(A15) for various values ofand .

Equation (A9) may be used to check whether > . If this is not satisfied (i.e. the heel is

short) then the derivation above is not correct; the angle will lie somewhere between 0 and

, and the thrust on the wall will need to be increased as described in PD6694-1.

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