30

Discussion

Soil Nailingby RJ Bridle and BIG Barr

g . g o cureithersideofa o I

o apse ta es place by fracture at the hinge,

The deformation of the nail describescribed in the Bridle paper ison y use y several workers in the field but was

acknowledged fromapubli t'6 b JThe def 'ee e ormedshapeofthenailusedembodiesa

hin Thi o d 'thth d freinforcements remov d fr

wi e eormedsha eof

I h h'ove om experiments and

ap m ro essor Jones'book onReinforcedearth

da es ve'yclearly adeformedshapeofthemd

Furthermore'

e, itis sensible tosetout tolimit the rin'earingpressure below the nail and bendin m a

o a .'

soon shows that, for rounda most inevitably be the governing c~ndit~~n

us a so esaidthataplastichin einan'

S Th"" H" "rt"

p c g sa e. e system is ve re

St t.Thi i 1''h h'

out to acture would constitute the used as reinforcementimpiest atachaincouldb

Contrasting the Jewell model and the model describeJewell model to be less prob bl Amodelimpliesaverylar e re

pro a e. part fromth e restraints, the Jewellry arge pressure below the plastic hin e. The

ea is 'ly to fail before the conditions deon i ions escribed are reached. It

side of the slip zone.es a t e nail isencasteredin in concrete like blocks either

If these blocks are moved relativel to ere a ive y to each other significant

ddi io t io 'lib ' d's

epacesoastocreatethe las'cedin the length of nail in the gap.'r tically, the moment/rotation're s ows, dia ama

'

a ions 'p orthe nail. There isanelastic section a'dsection and a strain harden' . S

bi t'd'ar ening section. Se arate "'a ionso directtensionandbendin

zeroatth poi tofm'

d'ximumending).

GROUND ENGINEERING JULY/AUGUST 1990

Reducing

T/it

f'/i

ElasticSectlan

Dynamic JumpSection

Strain HardeningSection

Figure 1:Momentlrotationr I t'i'a ions ipforuail.

The consequence is that, whatever

plastic zone'etween the blocks will be at a sigmfi gesolv d o; o gie nai and can be reso

the disturbed zone.n;a rig tanglestoit. These resolved forces support

'ng e p astic hinge is the same as Figure 5of the

Hoowever, the angular change taken u bmark dO at sio T'nsion iss owninthegapandthenailis

1 P toth o ltoth li rfItisa

a o e s 'p surface.isassumedthatthenailhasnot etfris a 'e I'ractured and is in the strain

e oads now imposed on each block are:i i i costiT. sinO = T. sing + S.c

. cosO = T;. cosy; —S;. sinj;Where g; is the angle between the reinforc

(2)

the slip surface.e rein orcement and the normal to

Supposing T; and S;are found from e uilibriq'm considerations for

maximum in the direction of slip, then the aFo h hes earsatrightan lestotg o he ail eedtobetak

d otth di tio ofth 1'e maximum stress is in the

g p. owever, thestressintheo enai inthe a . H

(T;.cos(O —(1;) + S;. sin(O —p;)). sin(O-Where A is the area of info re'rcementandy,the 'eldstr

th ltoS./A d' ban is o eexpected. Takin

1 io fo S dT.fren 'nt egapintoaccoun

;an; om both models.e fact is that thf

'conclusion drawn by Jewell and Pe

only apply if there were no rotation at thdf '

bIt can be concluded therefore that realis

'reahstic S; and T; values, the

so n 'adalongandlateraltot en'ilib'fth di t b d o

Nevertheless, consideration of the b ho e e aviour of a single nail can

DISTURBED ZONE UNDISTURBED ZONE

only be realistic if the computed distribution of the loads Tfand Si arerealistic. The main thrust of the Bridle paper was to ensurecompatibility between the deflection resulting from the forcesrequired for equilibrium of the disturbed wedge and the distribution ofthe deflections required by the kinematic model of failure.

The result of the extensive redundancy in the prediction of nailloads brings the advantage of considerable potential forredistribution. Small bearing or slight pullout failures provide releaseswhich allow load to be taken up by nails which have reserve capacity.The line of action of the natural reaction on the slip surface and that ofthe nails will adjust themselves to accommodate redistribution givingan extremely robust structure.

Finally the advantage of calculating T; and S; for a stiff nail at a steepangle is that the resistance to disequilibrium of the disturbed wedgecan be shared between friction and bearing for economy in anchoringthe nails in the undisturbed zone. To overlook this advantage wouldlead to unnecessary economic penalties.

To calibrate the design checks, stress, bearing pullout andbending, a series of large scale tests are about to be carried out atCardiff University in a three metre shear box. This series will,incidentally, give a definitive answer to the deformed shape of the nailand the validity of the approximations made to represent nailbehaviour. The results will be available shortly.

~ I

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le

Plastic hinge

Face panel

Llip surface

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o i lio li i «I ~ licll <ii«illi ii ~High stiffness earth

Low deformationSharp curvature ~ I

I~ llllllli I ~ ~ li ~ Ill i

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Higher stiffness reinforcement, lowerdeformation, slower curvature.

stiffness eorthdeform'otioncurvature

CJ ~ iiraii iwli a

'a, I ~ I.i ~

~: i,' I "II ~

Il rig,qgilffiu- - dl 'Cl ~ 11i ~ i ~ ~ I ~ ii i<,»: inri ly Pr il

o i:i CEEce ',:C;I

I C: II

" .'C I INormal S) )S, ~T

- ~TIBar fracturesat ultimate load )) 2 FRACTURE MODELS

I

Figure 2c Compared failure models.

I I -ii @I III ' 'iii

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o Iaadar Enquiry Ia 2425I 31

GROUND ENGINEERING JULY/AUGUST 1990

"Soil Nailing Design: The Role of Bending Stiffness"

by RA Jewell and MJ Pedley

32

I Authors'eply to discussion by Bridle & Barr

where lx is the distance between the points of maximum moment in

the nail. This equation uses a constant C = 6 and introduces the effectof the relative shear displacement of the nail y;. The effect of the axialforce, P, on the plastic moment capacity of the nail is introduced byBridle and Barr (1990)using the "safe" estimate suggested by Jewelland Pedley (1990)

M „=Mk I—— (c)

whereP/, = A~~istheplasticaxialcapacityofthenaiLExpressed in the general form used by the Authors, Bridle and

Barr's (1990)criterion for maximum shear force may now be written

P, 127 (I P l 6(y;ID) PPe (l ID) ( PIP I (l ID) Pk

which may be compared with the Author's equation (20), for theelastic analysis

GROUND ENGINEERING JULY/AUGUST 1990

Readers of the discussion by Bridle & Barr might conclude that theiris some fundamental disagreement concerning the action ofreinforcement in soil. However, this appears not to be the case sinceBridle &Barr (1990)have now put forward design equations verysimilar indeed to those presented by the Authors, as discussedbelow. It is hoped that these additional comments in closure will helpto clarify the position concerning the role of reinforcement bendingstiffness.

The observations made by Bridle and Barr on the deformation of areinforcing bar crossing a potential failure surface are entirelyconsistent with the loadings and model of soil-nail interactionproposed by the Authors (Figures 3and 4). Indeed, the radiographfrom a direct shear test that Bridle and Barr mention is taken directlyfrom the first named author's PhD thesis.

The rigid-plastic model in Figure 5 of the paper, which isconsidered at length in the discussion by Bridle and Barr, wasintroduced simply as a hypothetical limiting case (wherereinforcement is not loaded by the soil between the points ofmaximum moment) to establish an absolute lower limit C = 2 in therelation between the maximum shear force, P„and the maximummoment, M

P,=C ...(a)l,

The model was not considered further in the paper. Rather, theAuthors went on to determine the expected range for the constant 5)C (4, respectively from the elastic analysis proposed bySchlosser (1983), and the plastic analysis proposed by the Authors. Itis worth noting that Bridle and Barr (1990)have chosen C = 6 fortheir analysis, found from an approximate solution.

Indeed, Bridle and Barr (1990)have now presented a criterion tolimit the maximum shear'orce in the nail so as not to exceed theplastic moment capacity (taking into account the axial force carried bythe nail), exactly as described by the Authors. Their equations are foran (approximated) elastic case and may be compared with the elasticanalysis set out by the Authors. The terminology defined in the paperis used, ie. the shear force resultant S;is called P„and the axial forceresultant T; is called P.

Bridle and Barr's (1990)equation (6) describes the relation

p = 6Mmsx + 6Py; ...(b)

0.1

0.08-

i2:0.06-

00.04-

ZV)

0.02-

Case Examined:

D =25mm

E = 2i0 x i0'klvlm

K, = 50000 kNim'

0 0.2 0.4 0.6AXIAL FORCE P/Pp

0.8

Figure Dl: Comparison between theoretical limitingenvelopes ofaxial and shear force.

Pi, (l ID) Pp..(e)

Before a comparison can be made for a typical practical case, it isnecessary to calculate the shear width (l,/D). By choosing anapproximate solution, rather than solving the elastic equations as in

Schlosser (1983)and others, Bridle and Barr (1990)have arrived at anew expression for the shear width,

D= 0.30

whereas the standard elastic ——'ion is, equation (12) in the paper,

The difficulty with elastic analysis remains that there is no sensibleway to determine the constant K, for a soil, other than throughempirical charts. This is in contrast to the plastic analysis whichdepends on P 'or the soil, equation (16) in the paper.

Notwithstanding the above, the limiting envelopes can becompared for a typical steel nail of diameter 25mm and Young'smodulusE = 210 x 10 kNlm, actinginasoilwithK, = 50x10 kNIm, whichcorrespondstoasoilwithg' 38'inthe charts by Pfister et al. (1982).The limiting envelope shown in

Figure Dl is for the limiting case of insignificant shear displacementy,/D = 0. As can be seen, the new analysis by Bridle and Barr (1990)gives very similar results to the analysis described by the Authors.

This finding only adds extra support to the theoretical observationthat the magnitude of maximum shear force that can be generated in asoil nail is generally small, the conclusion that has now been confirmedby the data reported by Pedley et al (1990)in this Journal.

In their subsequent work Bridle and Barr (1990)(equation (4))have continued to use an erroneous analysis from Juran (1988),namely equation (16) in Bridle (1989).This error was pointed out bythe Authors. The purpose of the additional analysis is to determinethe relative magnitude of the maximum shear and axial forces in thenail. The suggested equation is

PP,—= 2tan20

Rupture surface

in soil

P,ee

INCORRECT EQUATION:

P,„=Psin () + P,cosoP„=Pcos() —P,sin()

Figure D2: Examinations of the equilibrium offorces actingon a soil nail atitsinteraction with the shear surface.

Co'I - ):LC:S 'L.CII.I 'L.)

I.IS:C.'.A. Q.") IJ 'l„l"-::

LJU)) "O'I'.) '.:SIgg 1;Oggsk

The authors cannot find any justification for this expression,particularly since it implies that should the shear force P,.be zero thenso must the axial force P, and vice versa.

Furthermore, the equilibrium equation from which the expressionis apparently derived is in error (equation (15) in Bridle (1989)).Theelemental section of soil nail from which the equation comes isillustrated in Figure D2. Examination of moment equilibrium aboutthe top corner of the triangular element gives Po ——P cos t), which

indicates from equation (11)in Figure D2 that the forces shown

cannot be in equilibrium unless P, = 0. In other words, if there is ashear force P, in the nail then there must be an accompanying lateral

loading on the nail which has to be considered.It would indeed be interesting to determine theoretically the

relative rate of development of the axial and shear forces in the nail

with shear deformation in the soil, such as measured in the datapresented in Figures 5 and 7 of Pedley et al (1990).But theoverwhelming conclusion which has been drawn by the Authors,supported by the data and now by the new analysis by Bridle &Barr(1990), is that the limiting maximum shear force in soil nails is sosmall, and is only mobilised at such large shear displacement, that it isbest to ignore it for design, and rely solely on the reinforcement axial

force which can be developed through the anchorage length of thenails beyond the potential rupture surface.

REFERENCESBridle, R.J. (1989).Soil nailing —analysis and design. Ground

Engineering, September, pp52-56.Bridle, R J. and Barr, B.I.G.(1990)The Analysis and Design ofSoilNails. Proceedings of the International Reinforced Sloil

Conference, Glasgow. (In press).Jewell, R.A. and Pedley, M.J. (1990).Analysis for soilreinforcement with bending stiffness. OUEL Report N'821/90,Dept. of Engineering Science, University of Oxford. (Submitted toJournal of Geotechnical Engineering, ASCE.)Juran, I., Baudrand, G. and Farrag, K. (1988)KinematicalLimitAnalysis Approach for the Design ofNailed Soil RetainingStructures. Proceedings of International Geotechnical Symposiumon Theory and Practice of Earth Reinforcement, Balkema,Rotterdam. pp301-306.Pedley, M.J.,Jewell, R.A. and Milligan, G.W.E. (1990).A LargeScale Experimental Study ofSoil-Reinforcementlnteraction.Ground Engineering, July/August 199044-50.Pfister, P., Evers, G., Guilland, M. and Davidson, R. (1982).Permanent ground anchors: Soletanche design cn teria. Report

N'D-81/150,Federal Highway Administration, Washington.Schlosser, F. (1983).Analogies et Difference dans le

Comportement et le Calcul des Ouvrages de Soutenement en TerreArmee etpar Clouage du Sol. Annales ITBTP, No 418, Sols etFondations 184, October 1983, 8-23.

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