A design method forreticulated micropilestructures in slidingslopes

by R Cantoni", T Collottat, VN Ghionna f.,PC Moretti fI

i~~e tg Iugrsmuws ~ lx eelu oretc &i~ le I

sui eeeel'@su ~eeeresi ~ 0)1 BRII ler.esllzsrs 3 ee

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IntroductionThe paper deals with a design method forreticulated micropile structures adoptedto stabilise sliding slopes.

Most existing methods only enable thetotal number of micropiles to hedetermined. To overcome this limitation

the authors have set up anew methodwhich gives simple criteria for setting outthe spacing and number of rows ofmicropQes.

It is described in detail with reference tostabilising a slope along the Milan-Romemotorway, in the Apennines nearFlorence.

Descriptionofthe remedial worlasGeneral information

The sliding area was identified by meansof a ground and aerial survey together

Geometricalanti strnctt3ral characterilflcsThe chosen solution consisted (HNy l-2)of constructing four reticulated micropilestructures, directly downhill of themotorway, at a depth of Sm within thebedrock.

eecno~sRETICOLATEO~I

SOI ACTIVE ANCHORS

IIIIII ll IlailIIII IIIIII —3$0~II'l '''ll

with inclinometric instrumentation. Thearea Qanks 70m of the motorway.

Typical soil proQle is represented by twoformations: a detrital unstable upper layer13m to 16m thick made up of sandy/siltwith gravel inclusions, cobbles and rareboulders; the bedrock consists ofa Qyschformation, alternate marl and sandstone.

Average geotechnical parameters of thetwo formations are shown in TaMe I.The sliding surface, with a maximumdepth of 15m from ground level, developsalmost entirely along the interface of thesandy/silt layer and the bedrock. It isabove the maximum water table levelrecorded by piezometers installed at theslip.

According to geomorphological evidenceand stahiTity analyses, the slide may bedue to the motorway embankmentaltering the slope equilibrium and causingthe remobilization of the upper portion ofan ancient landslide.

A- Upper formationGrain size dislrihulion

Gravel: 44thSand: 20thSilt: 24thClay: 12th

Index propmtiesliquid limit: n = 39.0thPlastic limit: tP = 16.596Natural watercontent: W, = 17.190Consistencyindex :I, =0.93

Natural unit weight: y„=20kN/m Io 21kN/m

Residual angle ofshearing resistance: ps = 19'

—BedrockUnconfinedconlpfeswvestrength: q„=BMN/mz Io 10MN/mz

Rock qualitydesignation I RQI7= 6090 to 7096

Tahle IAverage yeotechnicalJsarem eterne.

The structures are stiffened by means ofreinforced concrete connecting beamsanchored to the bedrock by 90t activeanchors at 2m centres.

The micropiles were arranged accordingto an equilateral triangular array with a500mm centre to centre spacing (seeEVSy3) inclined within 4'o vertical.

Choice ofthe stabilising method

Choice of the stabilising method wasgoverned by:~ Necessity not to work along the

motorway, to avoid trafQc restrictions;~ A steep slope that did not allow access

for heavy boring machines;~ Necessity to avoid appreciable

changes in the percolating water flow;~ Necessity to avoid large diameter

borings on account of possiblepresence ofboulders in the upperformation and of the requestedembedding in the bedrock.

'aotechnical Engineer —Studio GeoteczlicoItaliano Srl- Milan

9 Geotechnical Engineer-Studio GeotecnicoItahano Srl- Milan

t. Associate Professor, Dept ofStructuralMechanics- University ofPavia

f'I Geotechnical Engineer-Societh AutostradaSpA-Rome Hfy.l. Layout of the zvrmesiiaf stroriuL

Micropiles are used to obtain soil blocksreinforced and nailed to the bedrock hymeans of steel tubes.

This can be aclueved by constructmgmicropiles at close centres in appropriatearrays, and by varying their verticalinclination.

GROUND ENGINEERING . MAY 1989

ORLLWG DRECTION

Another important design requirement isto inject the micropiles at a sufficientpressure (500kN/m'o 1000kN/m') toimprove adhesion at the interfacebetween the micropiles and the soil. Thisis due both to horizontal compactioncaused by the injection pressure and tothe injected grout.

The assumption ofmonolithic action of thedifferent structure components (steelreinforcement, grout, soil) is morerealistic for that part embedded withinfirm soil. This is due to the higher injectionpressure adopted and to the bettercharacteristics of the soil with respect tostress relaxation phenomena.

For the upper unstable layer one of therequirements (even if not sufficient) forthe formation of a monolithic structure is toavoid any plastic deformation of the soiltaking place between the micropiles. Thisis done by verifying that the resistance byarching effect between micropiles ishigher than the earth thrust caused by theunstable soil.

Proposed design method

The design criteria adopted are based onthe assumption that a totally cooperatingstructure is formed. Stability of thestructure is analysed with respect to thefollowing failure mechanisms:

a. Plastic deformation of the soQbetween adjacent micropiles

b. Sliding of the reinforced block on thefirm soil

c.Structural failure of the compositecross section of the block

IIII IIIIHg.3. Mjcnoyjfee ylan arrangement.

Condition a. determines the spacing of themicropilestransverselyto the movement;whilst conditions b. and c.establish thetotal number of micropiles and thespacing between the rows.

Evaluation of landslide thrust

The thrust of the upper sliding wedgeagainst the reticulated structure (S )hasbeen determined referring to seismicconditions as a result of a pseudostaticanalysis based on Janbu's simplifiedmethod (1973)'.A value ofS = 1850kN/mhas been obtained; this thrust has beenassumed to vary linearly with depth.

The resistance offered by the lower soilhas been evaluated following the samemethod resulting in a value S = 250kN/m;to be conservative this value has beenneglected.

Stability with respect toplastic deformation of the soilbetween adjacent micropilesStability related to plastic deformation ofsoil around the micropiles has beenverified by comparing the horizontalthrust exerted by the sliding mass of thesoil against the reticulated structure (S )

with the limit resistance developed byarching effect between two adjacentmicropiles (R,).

The evaluation ofR, has been done usingthe method proposed by Ito and Matsui(1975 1977 )

This is based on the theory ofmetalextrusion through dies and considers theequilibrium conditions of the soil archEBB'E'El{f.4) placed just behind themicr opiles.

H{f.4.Sojf ylastfc defonnatjon betweenmjcroyQee pto *Ma jsnj, l9ZS).

The soil is considered in limit conditionswith respect to failure and sliding. Themethod assumes the validity of Mohr-Coulomb's failure criterion and theexistence of a downhill resistance againstplane EE'qual to the active thrust.Furthermore the piles are consideredrigid.Equilibrium conditions of the arch

EBB'E'llow

the limit resistance R, of the frontrow of the structure to be expressed as:

R,=2 Di

)'n tP =

Kp !(kp Va tang+ Kp —I)

DiDi

D2

~ r tang tan +—Dz

e

42 H{r.2. Tpyfcaj sec{jan.

GROUND ENGINEERING MAY 1989

where, also referring to Fjg. 4:

e = Angle of shearing resistance of thesoil inside to the arch EBB'E':In thiscase s has been assumed equal to theresidual value e,

K = Passive earth pressure coefficientDi ——Centre to centre spacing between

micropilesD3 ——Net distance between adjacent

micropilesL = Thickness of the unstable layer.

The calculations give values of R,equal to 2370kN/m whichcorresponds to a partial safety factorF"~:

2370F*z= = 1.28

1850

According to De Beer and Carpentier(1977)4the method gives acceptableresults for angles of shearing resistancelower than 20 and centre to centrespacing of three to five times the diameterof the piles, which was the case of thedesigned structure.

Shding stabilityofthe reticulated structureThe analysis has been carried outcomparing the horizontal thrust (s )on thestructure with the horizontal component ofthe sliding resistance of the block (sg (seealso Lizzi, 1977 ).In such conditions the forces acting on thestructure are the following (Fig. $):

R, = Maximum earth thrust which can beresisted by the reticulated structure= Sjcosa

R( = Anchors reactionRf,a = Allowable shearing resistance of

micropile steel reinforcementsR = Soil reaction along sliding surface

R, — WORKING LOAD OF ANCHORS

R — NAXNIUM EARTH PRESSURE WHICH CAN BE RESISTEDBY THE RETICULATED STRUCTURE

RI ALLOWABLE SHEAR RESISTANCE OF MICRO. PILES

SOIL REACTION ALONG SLIDING SURFACE (REFERRED TO

THE WIDTH OF THE RETICULATED STRUCTURE)

W = WEIGHT OF RETICULATED STRUCTURE

Fig.$.$dding (sheeny) stability of thereticulated structure.

P, = Reduction factor to take into accountbending effects in the reinforcement,(Mascardi, 1979 )

4/)0 = "(/Ew)E,

E, = Young's modulus of the firm soilimproved by cement grout

E( = Threshold Young's modulusdiscriminating shearing frombending failure of the micropile. Forthe considered micropile E( can beassumed equal to 1.57x 10rkN/m2

which is close to the cement groutmodulus (Ev)

~ = allowable shear strength of thesteel reinforcement

A( = steel reinforcement section area

The calculations give the following values:/I, = 0.473r(,= 136kNR(, = 1900kN/m

Solving the polygon of forces shown in

Fig. $, the following value of R, and S,were obtained:

R, = 2250kN/mand:

S, = R, cos a = 2040kN/m

The stability of the structure with respectto sliding is therefore secured with amargin of safety F;, = 2040/1850 = 1.10.

Structural analysis of the compositecross section ofthe blockThe analysis has been carried outassuming that the reticulated structurebehaves as a monolithic body.

The structure has been assumed to act as aflexible retaining wall of flexural rigidity(E~ x J~) having:a. The upper part loaded by a given

triangular pressure distributioncorresponding to S and to the anchorsreaction R);

b. The lower part embedded in an elasticmedium having an horizontal reactionmodulus E,constant with depth. A valueof E, = 500MN/m~ has been assumed.

The bending moments and shear forcesdistribution with depth can be evaluatedusing one of the methods for elasticanalysis available in the literature.

In this case the method proposed byMatlock and Reese (1960)'as been used,obtaining the following maximum bendingmomentM = 3700 kNm/mat an approximate depth of lm below thesliding surface.

The maximum normal stresses in eachcomponent of the composite section cannow be determined using a procedure

The allowable shearing resistance of thegrout along the sliding surface has beenassumed equal to that of the soil.

The allowable shearing resistance ofmicropiles reinforcement Ria has beenevaluated by means of the followingexpression:

Rta n r(a

where:n = Number of micropiles per metrer@

——Allowable shear resistance of amicropile calculated as:ru ——)|I r

NS 1000-

00 10 12 I~

SLEXNG LASER TIECKNESS L (m)

E

l+4000-

~~1000-

O

I 0

D=200mnl0 4 =00.9mm

(14)

(4.6

R OF MICRO-PILES/ml

2 2 4 6 6 7 0 9NUMBER OF ROWS

Hp.8. Influence of the spacing of microyiles, number of rows and slidiug layerthickness on lt, and M values. 45

GROUND ENGINEERING . MAY 1989

based on the theory of the elastictransformed partially reactive sections.

For the considered case the analysis gavethe following maximum values of normalstress:—steel reinforcement: tr, = 140MN/ms—cement grout: tro = 10MN/m'

treated soil: a, = 500kN/mswhich are at the limit of the allowablevalues in spite of the close spaced patternand the large number ofmicropiles used.

ConclusionsA design method for reticulated structuresofmicropiles has been reported showingan application to a landslide problemalong the Milan-Rome motorway, in theApennines near Florence.

The method is based on the assumptionthat the structure behaves as a compositeblock. This assumption can be consideredvalid for structures built with closelyspaced micropiles having appropriate

arrays and well differentiated verticalinclinations.

The method analyses the stability of thestructure with respect to three possiblefailure mechanisms, evaluating therelevant partial safety factors which haveto be added to the main safety factorconsidered in the detentunation of thelandslide thrust.

The results obtained show that, in spite ofthe closely spaced array and the largenumber of micropiles used, the stresses inthe components of the structures are closeto the allowable values.

InQuence ofdifferent spacings ofmicropiles, numbers of rows and slidinglayer thicknesses is demonstrated inFly. (t; where R, is the limit resistanceagainst plastic deformation aroundmicropiles, M, is the allowable bendingmoment evaluated with the theory of theelastic transformed partially reactivesection.

References1.Janbu N(1973), 'Shpe stabiTity computations'.Embankment Dam Engineerin EcL Wiley aSons.3.Ito T, Matsui T (1978),'Methods to stabilise lateralforce acdng on stabiTising piles'. Soil and FoundationsVol 18No4.3.Ito T, Matsui T (1977),The effects ofpiles in a rowon the shpe stahiTity'- Proc. IXICSMFE- Tokyo.4.De Beer E, Carpentier R (1977),'scussion onmethods to estimate lateral force acdng on stabiTisingpiles.'Sail and Foundations, Vol 17No 1.8.Llsti F (1978),'ticulated root piles to correctIandsMes'SCE Convention and ExpositionChicago.8.MascatC C(1970),'Bcomportamento dei icropalisottoposti a sforso assiale, momento Setuente etaglio'. Verlag Leeman-Zurick7.Madock H, Reuse LC (1960), Oenerassed solutionsfor laterally haded piles'.Journal ofSoil Mechanicsand Foundation Division. ASCE SM8.

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47