The test results have demonstrated thfollowing:

e e

a) At this site, where laboratory testresults in the weathered andpartially weathered material weri were of

ious quality and pressuremetertests in pre-formed test pocketswere unsuccessful, the RSBPprovided data. This vindicates theuse of this new instrument.

b) The new instrument is capable ofdrilling with the minimum ofdisturbance and permitsassessment of in situ total horizontalstress. To date there has been nodirect measurement of in situstresses in this material and, in thisrespect, the data are unique.

c) The improvements with this newinstrument which include a thin stiffmembranthe

rane facilitate assessment fe actual response of the rock.

0

d) The strengths measured by thepressuremeter are considerablgreater than the undrained shearstrength values from laboratorytriaxial tests. The strengthsmeasured by the RSBPare a factor ofthree lower than the HPD derivedvalues. Disturbance durinurmgpredrilling and the production of anecessarily oversized test kor HPD tests probably contribute to

produce this significant difference.

Thearid

performance of the new instrumthe results have also demonstrated

ent

that two important aspects of the 'researchneeds'utlined by Mair and Wood198 Lo

following:7) have been addressed nam I h,nameyt e

a Presessuremeters are required whichare stiff in comparison to the rockbeing tested, and which includethinner and stiffer membranes.

b) For weak rocks which degr degra euring predrilling prior to insertion

of a pressuremeter, there is a need

RSBP.to develop further the use of tho e

AchnowleftgementThe authors wish to express theirgratitude to the CEGB —for kindpermission to publish this paper and to the

forfun'cience&Engineering Research Co il

funding the development of theunc

5Q instrument.

GROUND ENGINEERING SEPTEMBER . 1989

References

3Chandler,er, RJ, Birch N and Davis, AG(1968)Enpmperties ofKeuper Marl. CIRIA. Report No. 13.10Mair, RJ and Wootsy DM (1987)Pressuremetertesting- methods and interpretation. CIRUL

13Wroth, CP (1983)British experience with the selfboring pressuremeter. Proc Symp on thePressuremeter and its marine

'applications, Institut du

o e, ratories des Ponts et Chausses, Paris.Edi'. Ilections Colloques et Seminaires

dier, RJ and Davis, AG (1973)Further work onthe engineering pmperties of Keuper Marl. CIRIA

18Windle, D and Wroth, CP (19TI).'The use of aself-boring pressuremeter to detertnine the undrainpmperties of cia '. Gys'. Ground Engineering Vol 10No. 6

e 'ed

16Al-sheikh-ali, MMH (1980).Discussion. Designparameters in geotechnical enginesengineering, Vol 4 Proc

on 'echanics and foundationengineering, Brighton, 79-81.17Chandler, RJ (1969)The effect ofweathering on theshear strength properties ofKeuper Marl.Geothchnique, 19No 3, 321-334.18Foley, GP and Davis, AG(197I)PihnMarl at Leicester. Civil en 'iner.

'engineering and public works

( )The seulement ofstructures19Davis, AG 1971founded on weathered soft rocks, with particular

per Marl Symp Interactionreference to the Keun structure and foundation. Midland

So'cs

&Foundation Eng Society, July, 1971.20 0'rien, AS and Newman, RL (1988)SelfboripressuremetertestinginLondo Cla . 'stin

'ngineeringgeology. 24 h Annn y. Field testin

'

ual Conf of theEngineering Group of the Geological SocieSunderland, September, 1989.21 Curti DC,effect on the results

'C, Ansell P 6 Leach BA (1988).'Calib'ationofpressuremeter tests in weak

useofa high ca ciErvin, MC, Burman, BCand Hughes, JMO 19es, (1980)The

capacity pressuremeter for design ofoun tions in medium strength rock. Proc Int Conf on

23 Meigh, ACstructural foundations in rock, S dne,

'g (1976)The Triassic mcks with particularreference to predicted and observed rf e ofsome major foundations. 16th Rankin

rv pe ortnanceof'

Lecture.Geottlchnique Sept 197626(3), 391-4S2.24 Maraland, A and Powell, 1e, JJM ( 988)Pressuremeter

on 's and on soft rocks; factors affecting

ogy. 24th Ann Conf of eng group of the Geol calSociety, Sunderland, September 1988.28 Leach, B Medianch, A, MecBand, JW and Sutherland, HB (1976)The ultimate hearing capacity ofbored il

euper Marl. Proc 6th Eur Conf on Soilmechani dation engineering, Vienna, 1976,mechanics and founda

'l

1.2,807-814.26JeweB, RJ and Fahey, M (1984)Measuringpmperties of rock with a high pressurepressuremeter. Proc Australia/NZ Conf onGeomechanim, Perth, 1984.27 Law, KT and Eden, WJ (1980)Effects of soildisturbance in pressuremeter tests. Prof Conf onU ting subsurface sampling of soils and rocks

28 Prevost, JH (1979)Undrained shear tests on ciaEngrs JGeotech Engng Div Jan 1979

on ys.

29 Meigh, AC and Wolski, W (1979)Desiparameters for weakor weak mcks. General report. The Eur.

Stgrt

Conf on Soil mechanics and foundation en 'erinBrightcm, 1979,Vol S, S9-79.

Soil n»»ng- analysisCLnCl CeslgIL

by R JBridle, BSc,FEng, FICE

ssm il Hi l~~~ ~ I ~cu~lsvgv il l~~ ~ I ~ i ~ I ~ si~I wow.;s mnrmm 2IIsi ~ I ~ Iso I ~II ioi I ~

~ne HI ~114 je sllwIsc u, ~ ~~ i iR1 ~ I ~ $ l ~ Lr

%lweneeore oc"~ fH i 6 '.i ~ ~ .~ w ~ I I ~ 'i I ~ I10

- el"''T

V 8Ã Il i>i fi I":i'rs is sa e iTTl "s. ~ i 'o c" ~ III

l linc 4

IntroductionSoil naQinil naQing is a direct descendant ofReinforced Earth. The Reinforced Earthmethod ofconstruction requires

e een spreadreinforcements to be laid betwand compacted layers of selectedmaterial. The technique uses the frictionbetween the selected material and the

yt eweightreinforcements, mobilised b ho e overlying material, to anchor the

e mass of soilreinforcements and reta'n thw 'c might otherwise slip away from the

In contrast, soil nailing features theinsertion of the reinforcements, known asnails, into undisturbed earth. Inconsequence, it becomes practical toinsert the nails at an angle. The angularrake considerably increases theiranchorage capacity.

The techniques may he described as'bottom up'nd'top down'ethods of

1.construction which are illustrated 'f .u1 IF.

Proposed procedureThe overall analysis of a soil nailed waQ,

herand the reinforced volume f 1eo asopemay

regarded as a wall, can he carried outin the same way as any other wall of the

ANOVEAQ FEI.OOITT

CENTAECDTATID

EFOTTDW UP

l.FFFI IE F IT

PIFCIIo AD.

I FF

TDP DOWN

ETAOE /

I"'IDI 'I

pl'OIF

I'NTEEIEEDIATEEIAEF

n/, W/

EINAC ETAGE FIFIAE ETA/EC

Flg. l.RefnforFosd earth and soil EEEEazng.

See Rrace~.

same dimensions. However, the internalstability needs tobe assessed and thefollowing procedure sets out a techniquefor doing so. The steps taken determine:(a) The position of the slip surface asrealistically as possible.(b) The out ofbalance moment required tomaintain equilibrium using characteristicmaterial strengths.(c) The direct load and shear, for the givenpattern ofnails, which each nail must carryto maintain equilibrium.(d) The distribution ofpressure along thelength of the nail in the undisturbed zone.(e) The pull out resistance (POR) underthe pressures applied to each nail.(f) The permitted bearing pressuresbelow each nail.

Once this is done the PORs at (e) arecompared with the direct loads obtainedat (c).The PORs should exceed the directloads by an appropriate material factor.

Similirly, the actual bearing pressuresobtained from the shears obtained at (c),together with the over burden pressureshould be compared with the bearingpressures obtained at (f) from theTerzaghi bearing coefficients'. Thesehearing pressures divided by anappropriate factor should not beexceeded. Appropriate factors will begiven in the forthcoming Code ofPracticeon strengthened soil structures.

(a) Detezmtuiny the slip surfaceWai-Fah-Chenz has shown that the log-spiral mechanism greatly improves thequality of the solution to the prediction of aslip surface and best matches observedresults.

The log-spiral curve is illustrated in Fig.Z.In the diagram the angle g is the anglewhich the radius makes with the horizontaland is measured positively in theanticlockwise direction. As the radiuslengthens, with depth, then a particle atthe end of the radius can move away fromthe slip plane and not into the 'at

rest'aterial.This ensures that the solution iskinematically admissible.

The equation of the log spiral is:r = ae"~ (1)a and k are constants r and g are the radiusand the angle of the radius to thehorizontal.

Now the angle between the radius and thecorresponding tangent, marked g in Fig.2, is given by:

dgae"'antP= r— =—= — ...(2)

dr kae" k

and Chen'ivesy =90 —P .(3)Where P is the angle of internal friction ofthe soil.

Murray, working at Transport &RoadResearch Laboratory, has investigated theangle Itl. This is the angle which the spiralmakes with the horizontal through the toe,as showninFlg.2. He has shown that theangle tI depends on, the slope of the facea, the angle of friction P, the slope of theground above the face, and the angle ofthe reinforcing nails. The angle of thereinforcing nails has only a minorinfluence on/ and is ignored. The generalslope ofundisturbed ground above theface is assumed, conservatively to he 15'.

These assumptions allow the use of thefollowing relationship for determining I|I.

P = (O.SP+ 0.201'+0.265a+.087) ...(4)where a and P are in radians.

Reference to Fig. 2will show:g, = 90 —y+ ~ = y + cu

g, = 180- ti—P = 90+ tt

—P ...(6)

Where co is the angle the tangent to the slipsurface makes with the vertical as itintersects withthe ground. The most likely

//IAP///~flWY//O//

~'v j0

Fig.Z. Symbols for logsyiral.

value for cu is approximately 3', which wasestablished following several trials inwhich cu was allowed to vary.

For a particular site there is a uniquecombination of H and b, see Fig.Z. sinceH ),eE. ~e, .a—= e~eEsmg2 —e~8 sjngt (>)

Slidb—= —e" Ecosg2+ e" Fcosgtaand then

(8)

b e" 'osgt —e"~'osgze" 'ings —e~e> sing

(9)

This ratio allows the points of intersectionbetween the slip surface and the ground tobe calculated.

(b) EquilibriumThe wedge is in equilibrium if the rate ofinternal energy dissipation is equal to thework done by the external forces as thewedge rotates about the centre of rotationwith an angular velocity Q. However, theangular velocity is common to bothexpressions and cancels out to leave themoment of the external forces about thecentre of rotation equal to the moment ofthe resisting forces.

The moment of the weight of the disturbedmass about the centre of rotation can befound by considering smaQ vertical slices.Drawing on the symbols and geometry setout in Fig.3.Mw ——Z;r;Ws cosg; ...(10)where Ws ——weight of slice

The additional expression for the workdone by the discrete vertical andhorizontal surcharge loads P and Ph, atxpr and ypr tsM =Z,P (racosg2+x,)+ Z,Ph,(rasing2 —yp,) ...(11)

andMT=Mw+M ...(12)GROUND ENGINEERING SEPTEMBER 19B9

53

(iiL- 9,

~nijI

I'

DIVjSjon oS

SllcZS.

$c~'-

jv sjons

aooHD.

Now the end deflection of the nail isdenoted b; andj);= Gr;d8cos(ttj+pg ...(18)

Where G = constant ofproportionalityr; = radius at 0;p; = anglebetweenthe

reinforcement and thenormal to the slip plane.

There are standard solutions for thedeflection at the end ofa pile and drawingon that works.

aS;(EI) 'k )

(18)

where EI; is the stiffness of thereinforcement at level i, k is thecoefficient of ground reaction at level iand a is a constant. Dimensional analysisshows this to be sound and so

= Grjd8cos(a+pal(El'.4(~0.6 (20)

andSj = o .G.r;d8cos(P+pgEI3

'0.6

(21)Where G is a constant ofproportionality

Hg.3.Symbols and geometry -sffoes and aalls.

0 G = OBM/Z;A;r;scos(P+pg(E@0.4(~0.6 ..(22)

The moment of resisting forces ofcohesion and friction across the slipsurface isMR

——Z; [cr;d8/costt + Wasin(0; —Itj)tan41 +P~in(8; —Itj)tang —Pjcos(19;—p)tang].r;cospwhere c = cohesion

(13)

The out ofbalance moment for all slicesOBM is thenOBM = MT —MR ...(14)This difference can be met by nails driven,fired or placed across the slip surface.

(c)Direct load and shear in the naQsHg. 4shows the shape to which the naildeforms as slip takes place. The extent towhich the nail is deformed determines theshear force and direct load supplied bythe nail.

Now p; is the angle the ith nail makes withthe normal to the slip surface. A is thecross sectional area of the nail, T; is thedirect load and S;is the shear at rightangles to the nail. So the stress in the nail in

54 the direction of the tangent is:GROUND ENGINEERING SEPTEMBER . 19B9

Juran gives the solution asT; = 2 S;tan(2.pg ...(16)

Thus when p = 8 —P —6 = 0 then T; = 0and as the nails respond to disequilibriumof the disturbed mass then(a) nails at right angles to the slip surfacewill be wholly in shear.(b) nails at a shallower angle will be intension and shear.(c)nails at a steeper angle will be incompression and shear.

And for equilibrium taking momentsabout the centre of rotation.OBM = Zj S,r; [cos(j/j+ pg

+ 2tan(2.pain(cr+ pg—sinp;.tanItj.sing + 2tan(2.pgcosp; tanPsinttj] . (I7)=Z;S;r;A;

so that the coefficient of S;r; is A;.

(Tj sin pj + Sj cos pj) cos pj (18)d

The stress is maximum when @= 0.

HenceOBM.r; cos(P+pg(El'(~Zj A, r cos(p+ pgEIJ0'4(kJa

Now it seems reasonable to replace EI;byN; where N; is the number ofbars at level iif all the nails are of identical cross section.Similarly if k .varies with depth, then Z;may be substituted for k and

OBM.r; cos(g+ p~(N~0.4(~0.6

Z; A; r,. cos(P+ pgNP4(Zg 6

T;can then be obtained from equation(16).

A computer program has been written toproduce the position of the slip surfaceand the out of balance moment. The directloads and shears necessary to maintainequilibrium are also computed for variousincrements along the slip plane and forvarious nail angles. However, theengineer must then select his own patternof nails which can then be analysed for itsacceptability.

L

SL

DELECTEO SLLAI'ESL

LLLLIIL 1.14

goAD INTENSITYA

Flg. 6shows an example which has beenanalysed for the purposes of illustration.The output is shown in 1'aMe I and isdiscussed later in this paper.

(d) Distribution ofpressure alongthe nailThe deflected shape of the nail under aload S;can be approximately representedby an exponential. Since the pressurealong the nail is proportional to thedeflection then the pressure intensity wQIfollow the same curve andp=Ae +C ...(25)

Where x = 44, see SVg.4.This permits afainily ofcurves ofvarying sharpnessdepending on m.

The extent of sharpness will depend onthe relative stiffness of nail and earth.From the assumption that the de6ectedshape is exponential, integration willdetermine shear and moment.

Ae~ AV= —+ Cx ——m m

~ (26)

C= —[m+1 —e ]m..(28)

At x = 1 the shear force will be —S/mLsince the nail length is constrained to m inequation (25).

So ——= —[[m—2]e +2+ m]mL mi ...(29)

and

p=k 6;=— S;

[ . ](e .mE+ 2(m+1) —e )m((m —2)e + 2 + m)

atx =1

(30)

M= —,+Cx' ———...(27)Ae Ax A

m m m

and since M = 0at x = 1 then

SLIEAE D.OIECE I

ISENDINC QOIIEN T

, Ae"" Cv.'x. A

Hg.4. De8ected ahape forces andmoment.that it will not pull out under the action ofT;nor will the allowable bearing pressure beexceeded as the nail bears on the eartharound it.

(e)Pullout resistanceThe pressure around the nail consists of avertical pressure of yz, together with thebearing pressure given above, and alateral pressure of ka yz (El@.5)where y isthe density, z the depth, and ka themmf6cient ofactive pressure. Hyure 8shows the symbols used and thedistribution around the bars. The pulloutresistance POR is:

Lx

l POR= 2tan41 (0 0

(p, sin8+ 2pE cos8+ p'; sin8)r d8)

+ c.2mdx....(33)

Ifthe bar is horizontal p L——,.M;

ps——k,yd and

p'; =(yd+ 1.5 ~)1.5Si

Since ~ris the mean pressurealong the bar due to S;.If the bar is at anangle to the horizontal of (8;—g3 where 0;is the angle the nail makes with the normal:othe slip surface then

p> ——yd(cos(8;+1r1$ + k sin(8;+(Ip)

pl ——k,yd

p; = (yd(cos(19;+gQ+ k, sin(19;+qg)+ 1.5~

(36)

DesignAn example of a cross section to bereinforced is given

incog.

Sand therelevant output is shown in Table l.Theprogram determines the log spiral slipsurface and prints the details necessaryfor its location. It prints out the weight ofeach vertical slice including vertical superimposed loads, there were no horizontalsuperimposed loads, and the resistingforces along the slip surface in theunreinforced state, together with thefactor of safety.

The program then assumes that thereinforcing nails are uniformly distributedalong the slip surface. S;is calculated foreach slice for three cases, 6rstly with aconstant modulus of subgrade reactionand secondly for a modulus of subgradereaction varying with depth.

Case 1 SL =OBMr/2;r,';

Case 2 S; =OBMr (2N)0 /r;r,',(~DE

The three cases for nail location are:(1)For reinforcement at a constant angleto the horizontal E, and specified by thedesigner.(2) For reinforcement at a constant angleto the normal to the slip surface, P againspecified by the designer.(3)For reinforcement normal to the slipsurface.

(37)

(38)

.--;-.,)'„.e,P.ej

derived from Terzaghi's'earing capacitycoef6cients so that

q = cN, + yz Nq+ 0.5y BNWhere q is the ultimate bearing capacity,Bis the nail diameter N the Terzaghicoef6cients.Now4.54.S;+yd$ q

Various values of m can be derived fromequations (30)and equation (19)puttinga = 2.5.For mild steel 25mm diameterbars and a k of50 000kN/m2, m is given as1.0and hence

p = —[3.5Se' 5.101] (31)

giving

p~ = —4.55~andp, = 1.55S; S;

The nail is now required to have suf6cientlength in the undisturbed sector to ensure

POR= 4rtang[yd[1+ ka]L+ 1.5

tang + 2cJrLrS;

or

..(34)

(f)BearingThe allowable bearing capacity can be

POR = 4r tang [yd(cos(8;+qg+ ka(1+ sin(e;+ ILIA))]

+ 1.5~tang+ 2cmLr . (35)S;

p1I

III

II

I/

/I

Hg.S.Pressure amund bar.GROUND ENGINEERING . SEPTEMBER 19B9

55

TaMe l.Example-Fig. 6.m=1

Slice WP1Kns101,911311,013228,0878154,17525189,0885129,8031174,9208107,892

RFI .

Kns12,25198,3310811,4242517,5223549,3164441,8693760,362344,96151

THETADegs35,1239,3643,6047,8452,0856,3160,5564,79

XSm4,594,464,203,873,382,761,991,07

YSm12,0010,619,177,696,184,653,101,55

Lim1,401,461,521,591,661,731,801,88

FOS

0.47WP=

rl r2 Thetal Theta2 SLIPm m degs degs m16,00 22,52 33,00 66,91 13,05796,892

SliceI2345678

SR.115,9105217,1633518,5275920,0039821,5997723,323925,1861727,19766

SR.297,72889105,4243113,804122,8726132,6746143,2649154,7037167,0591

SR.326,9479829,0699331,3805733,8811636,5839839,504184a,6583546,06526

TR.1-11,43179—6,848495—1,81543

3,97445410,9921119,4456730,3954744,97657

TR.2—112,8475—121,7334—131,4095—141,881-153,1993—165,428—178,6364—192,9032

5:5 And, allowing for the modulus of soil reaction varying with depth;

56

Fig. 6.Example for Table 1.

With a little calculation the reader mayshow that the output indicates that underthe calculated loads the wedge is inequilibrium in each case. In the last casethe nail will experience only shear and thedirect load is zero. In case 2 the nail mayexperience tension or compressiondepending on the angle at which the nailcrosses the slip surface. Direct loads areprinted in addition to Sand those shown asnegative are in compression. Case 3canbe used to test nails in compression wherefriction is low and nails are difficult toanchor. However, in general, small valuesof compression at small angles to thenormal are not efficient since thecompression causes an adverse momentfor which the shear component mustcompensate. This is indicated in the tablefor case 3where jttJ is —15].Furthermore,the compression in the nail lessens theresistance induced by friction on the slipplane.

The designer can now inspect the resultsand suggest a pattern of bars. The patternshould aim at two of objectives:(a) To ensure that the nails are as equallystressed as possible under full loading inthe completed structure.(h) To ensure that the nails are soarranged to ensure safety in construction.In general, construction should becarefully monitored and the movement ateach preceding line of nails should bewithin tolerance as excavation proceeds.The tolerance due to elastic lengtheningshould generally be quite small, say lessthan 0.33mm, so any significant movementmight suggest that slippage is takingplace. However the designer might havereason to account for other phenomena,for example settlement, due to increasedGROUND ENGINEERING SEPTEMBER 1989

2,3023076,74336211,6801Iz,a 783223,3704929,3730735,2968121,39959

15,7267446,0629679,78516118,0257159,6405200,6433241,1075146,1776

foundation load, as excavation increaseswhich might temporarily cause slipping.The designer should be able to makesome assessment of expected movement.This might have an effect on his choice ofdesign of, and when to place, panels. Ataround 1 in 500 safe limits for concretefacings without special precautions willbe exceeded and at 1 in 50.Safe limits forgeotextile facings will be exceeded.

Ifmovement is greater than predictedthen more nails should be inserted beforemore excavation and nailing proceeds.Uncertainty in material properties is, ofcourse, inevitable and a conservativedesign, in which appropriate soilproperties are chosen for analysis shouldhe adopted. Nevertheless, choice shouldnot be so conservative as to be inefficientand construction monitoring removes thenecessity for an over conservativeapproach by reducing the degree ofuncertainty about the completedstructure.

Construction will also requireintermediate cases at excavation stages tobe investigated.

It is evident that a trial and error process ofselection will take place in which thedesigner will, through experience, modifyhis initial choice. A further program is nowunder development to deal with particularlayouts of nails and analysis at excavationstages. The whole will be incorporated ina user-friendly package which will test

4,33652612,701522,0001432,5446944,0196355,3258466,4835440,30734

—1,65422—2,690727—1,144478

3,43291111,7850324,48942,597335,38834

—18,15966—53,1889-92,12792—136,2843—184,3369—231,6829—278,4069—168,7913

both pullout resistance and bearing foreach bar at each stage investigated.

In making his choice ofnail and to ensurethat all nails are carrying a similar load theengineer should reduce the area ofnailwhere S;is high and increase the area ofnail wherein S; is low. In addition, anglesshould be chosen to obtain the mostefficient combination of S;and T;.

ConclusionA technique has been described fordetermining the nails, their number, andarea, to restrain a mass of earth that wouldhe otherwise unstable. The requirementshave been outlined and illustrated.

A computer program as described in thispaper is available through the CardiffUniversity Industry Centre and is nowbeing extended to give comprehensiveassistance to the engineer.

Referencesl. Tersaghi, K, Theoretical soil mechanics, Wiley(1943).2.Wai-Fah-chen, Limit analysis and soil plasticity.3.Murray, R, private correspondence.4.Juran, Iet al. 'Kinematical limit analysis approach forthe design of nailed soil retaining

structures.'nternational

geotechnical symposium on theory andpractice of earth reinforcement. Fukuoka Japan. S-7Oct. 19SS.S.Matlock, H, and Reese, LC, General solutions forlaterally loaded piles.'ransactions of the AmericanSociety of Civil Engineers, Vol 127, Part 1, 1SS2.S.Bruce, DA, Soil nailing: application and practice,Part 1 Ground Engineering, Vol 19,No 2, November19SS.