Calculations of retaining wall pressures

Calculations ofretaining wall pressuresby K. COLE', BSc(Hons), MSc, FICE

RECENTLY the New Civil Engineer published (Speaker's Corner, Oct. 21, 1982, page24) an extract from a rather long and: de-tailed letter from me, drawing attention totwo serious problems which beset geo-technics practitioners in this country,namely:(i) the lack of up-to-date code guidance

on earth pressure computation andretaining wall des'ign, and

(ii) the fragmentary nature of UK codesof practice on geotechnics.

The fragmentary nature of UK codeshas two consequences, that earth-works, foundations and retaining struc-tures are treated in different mannersinstead of being part of one unifiedphilosophy, and the up-dating ofcodes out-of-step with each other ex-acerbates the problem, as at each re-vision they become more establishedin their compartmentalisation.

A further consequence of not having asingle geotechnics "core" code with aurfified philosophy applicable to all geo-technical design, is that sections badlyout-of-step (such as the now 30-years-oldCP2, Earth Retaining Structures) tend to beincorporated with revisions into othercodes as these are revised or newly writ-ten. The problem exemplified in the writingof a retaining wall design section for theCode of Practice on Falsework BS 5975:1982', is that such revisions are likely toproliferate errors and unsound designphilosophy.

I am pleased to have been invited by

vProject Director, Ove Arup a Partners

Symbols

horz

n- (o-, (rI,)

'o-„', o-„')

K, K

K,K,

pp

Meaning

densityunit weightunit weight of water (Usually taken as10 kN/m')surcharge load (uniform pressure, toinfinite distance at side of wall loaded)depthshear strength in undrained sheareffective cohesion in drained sheareffective angle of shearing resistancein drained sheartotal pressure at any point in the soilmass e.g. o-„= yh where suffix v denotesvertical pressure, and suffix h denoteshorizontal pressurewater pressure at any point (in staticconditions u = y z, where z is thedepth from the ground water surfaceimmediately above, otherwise seepagepressures must be used)effective pressure at any point in thesoil mass, where o.' o. —u

coefficients for horizonta'I active earthpressure, depending upon the values of

4', ll (wall friction) and c,„(effective

wall cohesion)coefficients for horizontal passive earthpressure, depending upon the values ofy', fi (wall friction) and c~ (effectivewall cohesion)the active pressure at any point in thesoil mass acting in a horizontal direction

the passive (resistance) pressure atany point in the soil mass acting in ahorizontal direction.

Usual units

Mg/ma

kN/ms

kN/m'N/ms

ITI

kN/ma

kN/ms

kN/ms

kN/ma

kN/ms

kN/ma

kN/ma

Symbol inBS 5975Y

pNot given

Not given

K, Kac

K,, Kac

pa

Pa

Active pressure side

Propertiesof strata

Thicknessof strata Level ground

I

c

c,

P<DFAEMNYXMZA I I

h

I—++

73 Cs ps hs u P

I—+-cs 4's hs

N.B.

(i) For static groundwater conditionsonly:—u = y z (z P h)

(ii) If groundwater is fiowing then u willnot be equal to the static ground-water pressure.

(iii) At the depths h at which pe and ppare being calculated, yh = (yt ht +y, ha + ........)

Passive resistance side

(iv) In calculating p and p use the val-ues of c'nd sf't the depth underconsideration, vis. for p use c', and'P s

ln certain circumstances c„may besubstituted for c'nd y'see text)

Ground Engineering to provide the "cor-rection note" which the New Civil Engin-eer omitted for reasons of space. In the"correction" sent to the NCE (with a copyto BSI) an attempt was made to keep tothe same symbols used in BS 5975, toavoid confusion to those wishing to amendtheir copies. The opportunity has beentaken here to use the symbols, units anddefinitions recommended by the ISSMFE',and indicate the equivalent symbols usedin BS 5975.

The following formulae apply only tolevel ground surfaces on the active andpassive sides of a retaining wa/I with ver-tical faces; any surcharge present is con-sidered as a uniformly distributed load ex-tending to infinite distances on the side ofthe wall loaded by it. These conditions areillustrated in the diagram on the left. The val-ues of K, and K„, and K„and K, shouldbe taken from the Code of Practice onEarth Retaining Structures (currently CP2:1951)', although the formulae for K, andK in Section 28.5 of BS 5975 may alsobe used as they ignore wall friction andare therefore conservative. If wall frictionis present the active and passive pres-sures do not act horizontally, see CP2 orspecialist literature such as Navfac DM74.

If the ground surfaces adjacent to t'e(concluded on page 41J

March, 1983 35

linder and the assembly returned to thescabbard whilst drilling continues to thenext test depth.

The system uses the latest wirelinetechniques with electrical cones developedboth in Holland and by Wimpey Labora-tories Ltd. The cones can be calibrated(Fig. 7) against a standard load cell, onboard, in a test frame, the cone load cellbeing set to give a resistance of 500kg/cma at a point load of 5tonnes, and thefriction sleeve to a resistance of 7.5kg/cmaat a loading of 1.125 tonnes.

During testing data are automatically re-corded graphically (Fig. 8) on a two-penchart recorder and in digital form on adata logger with a printer output, whichalso records the strain gauge excitationvoltages. Continuous records of both conetip and sleeve resistances are providedwhich enable end-bearing and skin frictionvalues to be evaluated for foundation de-sign.

A typical plot of the cone and localfriction resistances obtained during testscarried out in part of a borehole are shownin Fig. 10 whilst in Fig. 11 a condensed plotis shown for the complete borehole to-gether with the soil descriptions basedboth on a visual examjstatseal of the soilsamples taken from the borehole, and fromthe ratio (R,) of frictional resistance (f„)to cone resistance (q,) based on work byBegemann'nd Schmertmann'.

To date, plotting of the 'condensedlog'nd

calculation of the ratio (R,) has beencarried out by hand. However, in order tofacilitate rapid assessment of the CPTresults on board ship a computer-baseddata acquisition and processing system isbeing installed.

The data system includes a small digitalcomputer, disc and cassette tape datastorage, a printer and a plotter. Prior toeach test the computer's VDU shows ablank data sheet format which the soilsengineer completes by entering relevantdata of location, test number, water depthand hole depth, etc. During the test theelectrical signals from the cone and fric-tion sleeve strain gauges are recordedon both disc and tape. On completion ofthe test (or more usually after completionof the complete borehole) the plotterdraws out the cone, friction sleeve andfriction ratio values against depth to thedesired scales, As an insurance againstpossible faj'lure of the system, the straingauge signals are also fed to a two-chan-nel chart recorder for immediate plottingand all data fed into the computer for im-mediate production of a hard copy by theprinter.

A disadvantage of the earlier CPT equipment was the inability to allow testingof the soils for a few metres immediatelybelow sea bed level. This was due to theneed to obtain a certain minimum pene-tration of the drill rod into the sea bed toobtain lateral stability for the cone. Theuse of a 5000kg dead weight frame placeddirectly on the sea bed overcomes thisdisadvantage; four hydraulic rams on theframe act on the drill pipe, which passesdirectly through the frame, and providesreaction for the cone thus allowing testingfrom immediately below sea bed level.

References1. Begemann, ff. K, S. (1965): "The friction jacket

cone as an aid in determining the soil profile".Proc. 6th Int. Conf. SM at FE, Montreal

2. Sanglerar, G. (1972j. "The oenetrometer andsoil exploration". Elsevier 1972. References J. HSchmertmann's work carried out in Florida in1969, on pp. 207-211.

(i) For the general case of soils whosebehaviour may be described by an angleof shearing resistance 1k', and an effective

'ohesionc',

Active horizontal pressure at depth h

pa = [Ka (yh + q —u) —c',] + u

The term in [ ] is ignored if negativeleaving only the water pressure u.

K, and K, are obtained from CP2, orwhen tt = 0 and c = 0 may be deter-mined from the formulae

1 —sin QKa

1 + sin((r'nd Kar. = 2 +Ka

Passive horizontal pressure at depth h

p = [K (yh + q —u) + c'K„,) + u]

K„and K r are obtained from CP2, orwhen b = 0 and c„=0 may be deter-mined from the formulae

1 + sin y'

= andK„, =2 /K1-sin

y'he

above formulae are relevant also tocohesionless soils, the terms involving

c'eingomitted.

(ii) For the special case of soils exhibitinga nearly constant value of shear strength(ca) over a wide range of confining pres-sures when laboratory tested in undrainedshear, and for which the duration of activepressure and passive resistance is suffj-c'.ently short that undrained conditions inthe field may be relied upon, the followingformulae may be used:

Active horizontal pressure at depth h

p,= [(yh+ q —u) —2ca] + u

The term in [ ] is ignored if negativeleaving only the water pressure u.

Passive horizontal pressure at depth h

p„= [ (yh + q —u) + 2 ca] + u

References1. Code of Practice for Falsework, BS 5975: 1982

BSI.2. Proceedings 9th Int. Conf. SM st FE List of

Symbols, Units and Definitions recommendedby the ISSMFE Vol. 3 pp. 157-169, Tokyo 1977.

3. Code of Practice for Earth Retaining Structures,CP2 (1951) Inst Struct, Engs.

4. Navfac DM7, Naval Facilities Engineering Com-mand Publication transmittal. Design ManualSoil Mechanics, Foundations and Earth Struc-tures USA Dept. of Navy. [Note that

and some earth pressure termsxnb I errdo not include the water pressure e.g. In Figs.10.1 snd 10.2I.

Calculations ofretaining wallpressures

(continued from page 35)wall are not level, the faces of the wallin contact with the soil not vertical, or thesurcharge load not uniformly distributedto infinity on the side of the wall loaded,then recourse to specialist ljterature4 isnecessary.

~l ~ I(6~3 r~k~i L~

P~~ I~1[gIE~iPi

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La Roche model LR 925 BC combined rebarcutting and bending machine

requires a 110 volt, 50Hz single phase sup-ply of electricity.

Model LR 925 BC has a maximum capa-city of 25mm dia. mild steel or 20mm HTsteel bar size for both bending and cutting.Bending angle is adjustable between 0 and180 deg, and a 180 deg bend takes only4 secs. Cutting capacity is 30 tonnes, thecutting operation taking 3-5 sec, depend-ing on bar diameter. Bending radius for10mm dia. bars ranges between 82R and18R while for 25mm bars it is 61R to 40R.

Rapid CPTs forGlasgow UndergroundCOMPREHENSIVE site investigation at theGlasgow Underground, Broomloan Depot,Govan, has been carried out by FugroScotland Ltd. Using their independent conepenetrometer rig mounted on a flat-bed"bogie", Fugro carried out a series of 28cone penetration tests (CPTs) from therail sidings within the Underground carsheds (see Ground Engineering, May 1982,p. 29). CPTs were taken generally to 10mdepth and in certain cases to within 1mof the sides of the Underground tunnels.The soils encountered were predominantlysands with a fairly high water table.

It was necessary to carry out the in-vestigation as quickly as possible to mini-mise interference with normal depot func-tions. The CPT method of determining thein-situ density of granular soils below the

March, 1983 41