A bearing capacity correction forstrain-softening saturated claysby N.A. KALTEZIOTIS", B.K.MENZIES~ & A.l. TARZIt

CONVENTIONAL PREDICTIONS of bearingcapacity of strip footings on saturated claysare based on the formula

svqp = NcF +P

whereq p is the bearing capacityN, is the bearing capacity factors. is the undrained shear strengthF is the factor of safety on shear strengthp is the vertical total stress at foundation

level

The bearing capacity factor N, may beobtained from classical plasticity solutionsfor the indenting of a die in a weightlessrigid-perfectly plastic material (Calladine,1 969).

For a footing on a real soil, shear strains areinduced in the soil and vary throughout thezone of influence of the footing. For asaturated clay, the soil behaves in the shortterm like an incompressible elastic solid andthe distribution of shear strain may beobtained. Furthermore, the stress-strainbehaviour of a sensitive clay is brittle andmay be described as approximating to anelastic-plastic/strain-softening idealisation(Figs. 1 and 2).

It follows that near collapse the variation in

shear strain beneath the footing will mobiliseboth pre-peak and post-peak shear stresses.Zones at post-peak will have diminished in

shear strength and shed load to pre-peakzones. Limiting equilibrium will occur whenthe load shed by post-peak zones can onlyjust be carried by the pre-peak zones(Bishop, 1971;Menzies and Simons, 1978).A further increment in load will induceprogressive failure of the soil.

Referring to Fig. 1, it may be seen that therigid-perfectly plastic idealisation based onpeak strength will give an overestimate of thefooting collapse load. Basing the idealisationon residual strength will underestimatebearing capacity. From back-analysis of ashear failure an average mobilised rigid-perfectly plastic strength, s, may be foundglVlflg

Sp —S6 —6

Rigid- perfectlyplastic idealisations

2Sp

I0gelO

2S,

Major principal strain Et

Fig. 1. Real and idealised stress-strainrelationships for an undrained sensitivesaturated clay

rrlvielI

Ia

I0

criterion for the case of plane strain wasinvoked. Strain-softening was incorporatedutilising the above displacement controltechnique with redistribution of out-of-balance forces at the end of eachdisplacement along the strain-softeningportion of the stress-strain relationship. Thistechnique, which is described in detail byTarzi et a/ (1982), enabled the full load-displacement behaviour of the footing to beobtained in contrast to other solutions(Fraser, 1971; Hoeg et a/, 1968;Humpheson, 1976; Valliappan, 1969),which did not define completely the collapseload (Fig. 3).

Solutions were obtained for the load-dis-placement relationship for the footing (e.g.Fig. 4) ranging between the rigid-perfectlyplastic idealisations for peak and residualundrained shear strengths. As the values of Eand Sp were held constant, it may be readilyseen that the collapse load is significantlyreduced for steeper post-peak stress-strainbehaviour. Extracting the peak or collapseloads for varying strain-softening ratios andBrittleness Indices for a wide range of soils(e.g. Ladanyi, 1973; Kankare, 1969;Merrifield, 1980) gave the design chart in

Fig. 5. A correction factor may be defined as

V p= qrp/qSs

Major principal strain Q

Fig. 2. Elastic - plastic / strain — softeningidea/1'sation for an undrained sensitivesaturated clay

A finite element analysis was carried out toobtain stresses and strains in the soil fordiscrete cumulative vertical displacements ofthe footing. The movement of the footingwas thus displacement controlled andanalogous to the strain controlled triaxialcompression test. Where peak strengthshear stresses were exceeded a Tresca yield

whereqp is obtained from equation (1) andq„ is the bearing capacity obtained from the

strain-softening soil model.

Accordingly, equation (1)may be modifiedas follows:

svq,=)tpNF+ p

'The idealised soil used in the modelling possesses acombination of high compressibility and high strengthnot found in real soils. Onginally used by Hoeg ef al, thisidealised soil was also used by subsequent workersincluding the authors to enable the venous solutions to becompared.

700—Valliappan (1969) Disp(tx:ement control

—Fraser (1971)technique.

whereR, is the Residual Factor (Skempton, 1964)

for undrained shear strengthThis note presents a simple design chart

enabling the traditional bearing capacityanalysis for sensitive saturated clays to becorrected for the influence of strain-softening, The correction factor is correlatedwith Brittleness Index (Fig. 1; Bishop, 1967)

/fr = (Sp —S.)/S,

and with strain-softening ratio (Fig. 2)

SR = —

E/H'00

Q.

500L.

I (00ICl.

u. 300t

200

100

00 10

(1976)

(1968) Flexible Footing1 55m

E = 206 850 kitSuf = 120 66 kPO

= 030 7'2IIl'c.

FixedI

5020 30 /0

'Public Works Research Centre, Athens.>Gdks. Instruments Ltd., Walton-on-Thames, Surrey.tunwersity of Surrey.

Centreline displacement (mm jFig. 3, Load-settlement curves for strip load on elastic perfectly plastic soil containedin 0rigid box

30 Ground Engineering

Elastic perfectly plastic clay(Su = Su( j

7%— ~ ~ ~ ~ ~ ~

,1

400— ~

~ ~—I=I~~Curve No. SR

1 1002 403 20I 105 3396 0,

40 50

~s 2(X)CLa.

1OO

Rigid FootingE = 206,850 kFt7Sur = 120 66 kPaSur = 55'S k&v = ote

00 20 30

Centre(ine displacement (mm JFig. 4. Effect of strain softening ratio on load-settlement curve

I

10

whereq, is the bearing capacity corrected for

progressive failure in a strain-softeningsoil.

The simple model used in the analysis wasan idea(isation of true soil behaviour and wastherefore imperfect. Nevertheless the modelincorporated the crucial feature specificallyunder study of a form of soil strain-softeningand gave solutions giving modified collapseloads. For conventional bearing capacitycalculations to be retained and simplycorrected for the influence of progressivefailure in strain-softening saturated clays, thedesign chart given in Fig. 6 gives anindication of the likely magnitudes ofadjustment.

The method requires a knowledge of truefield post-peak stress-strain behaviour, to beassessed from laboratory testing (e.g.Bjerrum, 1973; Ladd et al, 1977; Poulos,1978). The factor of safety on undrainedshear strength, F, partly compensates for thedisparity between the operational strength(back-analysed from a field failure using arigid-perfectly plastic stress-strain model)and the bulk strength measured in a test on arepresentative sample. This disparity iscaused by a number of factors includingprogressive failure. To make a specificcorrection to allow for progressive failure

should enable the factor of safety to becorrespondingly reduced.

AcknowledgementThe authors gratefully acknowledge the

help of Professor N.E. Simons.

ReferencesBishop, A.W. (1976): -Progressive failure —withspecial reference to the mechanism causing it."Proc. Geotech. Conf., Oslo, 2, 142-150Bishop, A. W. (1971):"The influenceof progressivefailure on the choice of method of stabilityanalysis." Geotechnique, 21, 168-172Bjerrum, L. (1973): "Problems of soil mechanicsand construction on soft clays." Proc. Eighth Int.Conf. Soil Mech. Fdn. Engng. 3, State-of-the-artReport, Session 4. Moscow pp.109-159Calladine, CR. (1969): Engineering plasticity.Pergamon Press. London, 318ppFraser, R.A. (1971): Applications of the finiteelement method in soil mechanics. MSc Thesis,University of Manchester

Hoeg, K., Christian, J.T. & Whitman, R. Ir. (1968):"Settlement of a strip load on elasto-plastic soil."Jnl. Soil Mech. and Fdn. Engng. Div., Am. Soc. Civ.

Engrs., Vol. 94, SM2, pp.431-445Humpheson, C. (1976):Finite element analysis ofelasto-viscoplastic soils. PhD Thesis, University ofWales, Swansea

Kenkare, E. (1 969):"Geotechnical properties of theclays at the Kimola Canal area with special

1 0 —9-

0

I~~E.~9

<08I0o 06

IH

COC ~ Flexiblel,

o Rigid j V =0.a Flexible'

Rigid I~ O2

——————100———-- IO

-- 10

--: -3330

0 I I I

0 10 20 30 CO 50 60 70 80 90 100 18%

Brittleness Index

Fig. 5. Correction factor p as a function of Brittleness Index ls and strain softeningratio SR

reference to slope stability." Publ. 152, StateInstitute for Technical Research, Helsinki

Ladanyi, B. (1973): "Bearing capacity of deepfootings in sensitive clays." Proc. Eighth Int. Conf.Soil Mech. and Fdn. Engng., Moscow, Vol. 2.1,pp.159-166Ladd, C.C., Mott, R., lshihava, IC, Schlosser, F. Et

Pou/os, H.G. (1977): "Stress-deformation andstrength characteristics." Proc. Ninth int. Conf. SoilMech. Fdn. Engng. State-of-the-art Report. Tokyo.pp.421 -494Menzies, B.R. & Simons, N.E. (1978):"Stability ofembankments on soft ground." Developments in

Soil Mechanics. Applied Science Pub.: England.pp.393-435Merrifield, C.M. (1980): Factors affecting theinterpretation of the in-situ shear vane test. PhDThesis, University of Surrey, Guildford

Poulos, H.G. (1978): "Normalised deformationparameters for kaolin." Geotech. Testing Jnl. 1 (2).ASTM. 102-106Skempton, A.W. (1964): "Long-term stability ofclay slopes." Geotechnique, 14, 77-101Tanzi A.l., Kalteziotis, NA. &Menzies, B.K (1982):"Finite element analysis of strip footings on strain-softening isotropic clay." Proc. Int. Symp. on Num.Models in Geomechanics. Balkema, Rotterdam.

Valliappan, S. (1969):Discussion on "Settlementof a strip load on elasto-plastic soil". Jnl. of SoilMech. and Fdn. Engng. Div., Am. Soc. Civ. Engrs,Vol. 95, SM2, pp.676-678

Ruswroe system forsewer reliningA SEWER RELINING SYSTEM that makesuse of ferro-cement material has beenapplied to a 60m trial length of a Victorianbrick barrel sewer in Chelsea, West London.In the Ruswroe relining system, developed tomeet the problems of sewer dereliction,galvanised steel in mesh form is fixed in

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July 1984 31