i. aperThe design of vibro replacementby Heinz J Priebe, Keller Grundbau GmbH,Kaiserleistr. 44, 63067 Offenbach.

:=:,,":sl%}}iIh'- -'A}i.::~l 'il}}6!

IntroductionVibro replacement is part of the deep vibratory compactiontechniques whereby loose or soft soil is improved for buildingpurposes by means of special depth vibrators. These techniquesas well as the equipment required is comprehensively describedelsewhere'.

Contrary to vibro compaction which densifies noncohesivesoil by the aid of vibrations and improves it thereby directly,vibro replacement improves non compactible cohesive soil bythe installation of load bearing columns of well compacted,coarse grained backfill material.

The question to what extent the density of compactible soilwill be improved by vibro compaction, depends not only on theparameters of the soil being difficult to determine, but also onthe procedure adopted and the equipment provided. However,the difficulty of a reliable prognosis is balanced by the fact thatthe improvement achieved can be determined easily bysoundings.

With vibro replacement the conditions are more or lessrevers. Considerable efforts only like large-scale load tests canprove the benefit of stone columns. However, a reliable conclu-sion can be drawn about the degree of improvement whichresults from the existence of the stone columns only withoutany densification of the soil between. This is possible becausethe essential parameters attributable to the geometry of thelayout and the backfill material can be determined fairly well.In such a prognosis the properties of the soil, the equipmentand the procedure play an indirect role only and that is mainlyin the estimation of the column diameter.

Basically, the design method described was developed some20 years ago and published already'. However, in the meantimeit came to several adaptions, extensions and supplements whichjustify a new and comprehensive description of the method.Nevertheless, the derivation of the formulae is renounced withreference to literature.

It must be emphasised that the design method refers to theimproving effect of stone columns in a soil which is otherwiseunaltered in comparison to the initial state. In a first step afactor is established by which stone columns improve theperformance of the subsoil in comparison to the state withoutcolumns. According to this improvement factor thedeformation modulus of the composite system is increasedrespectively settlements are reduced. All further design stepsrefer to this basic value.

In many practical cases the reinforcing effect of stonecolumns installed by vibro replacement is superposed with thedensifying effect of vibro compaction, ie the installation ofstone columns densifies the soil between. In these cases, thedensification of the soil has to be evaluated and only then - onthe basis of soil data adapted correspondingly - the design ofvibro replacement follows.

Determination of the basic improvementfactorThe fairly complex system of vibro replacement allows a moreor less accurate evaluation only for the well defined case of anunlimited load area on an unlimited column grid. In this case aunit cell with the area A is considered consisting of a singlecolumn with the cross section Ac and the attributablesurrounding soil.

Furthermore the following idealized conditions are assumed:~The column is based on a rigid layerOThe column material is uncompressibleOThe bulk density of column and soil is neglectedHence, the column can not fail in end bearing and anysettlement of the load area results in a bulging of the columnwhich remains constant all over its length.

The improvement of a soil achieved at these conditions bythe existence of stone columns is evaluated on the assumptionthat the column material shears from the beginning whilst thesurrounding soil reacts elastically. Furthermore, the soil isassumed to be displaced already during the column installationto such an extent that its initial resistance corresponds to theliquid state: ie the coefficient of earth pressure amounts toK= 1.The result of the evaluation is expressed as basicimprovement factor n,.

Acl

li 2+f(IL ~ Ac/A)A IK~ f(IL Ac/A)

f(1L„Ac A)=I} (I 2us) 'I Ac /A)

I —I},—21} ' —21} +Ac/A

K.c = tan'(45'-9}c /2)

A poisson's ratio of lIs=1/3 which is adequate for the state offinal settlement in most cases, leads to a simple expression.

Ac [ 5 Ac/AA [4 K~ (1—Ac/A) J

GROUND ENGINEERING ~ DECEMBER ~ 1995

TOP: Figure 1.Design chartfor vibro replacement.

BOTTOM: Figure 2.Consideration of column

compressibility.

I u,qg3

The relation between theimprovement factor n0, thereciprocal area ratio A/A and the&iction angle of the backfillmaterial yc which enters thederivation, is illustrated in the wellknown diagram of Figure 1.

Consideration of the

E

column compressibilityThe compacted backfill materialof the columns is stillcompressible. Therefore, any loadcauses settlements which are not 2,0connected with bulging of thecolumns. Accordingly, in the caseof soil replacement where the arearatio amounts to A/Ac= 1, theactual improvement factor doesnot achieve an infinite value asdetermined theoretically for non 1i2

'ompressiblematerial, but itcoincides at best with the ratio ofthe constrained moduli of columnmaterial and soil. In this case for ~ I

compacted backfill material as wellas for soil, a constrained modulusis meant as found by large scaleoedometer tests. Unfortunately, inmany cases soundings are carriedout within the columns and wrong

0,0conclusions about the modulus aredrawn &om the results which are 2

sometimes only very moderate.It is relatively easy to determine

at which area ratio of column cross section and grid size(Ac/A), the basic improvement factor np corresponds to theratio of the constrained moduli of columns and soil Dc/Ds. Forexample, at ps=1/3 the lower positive result of the followingexpression (with n, = Dc/D, delivers the area ratio (Ac/A),concerned.

As an approximation, the compressibility of the columnmaterial can be considered in using a reduced improvementfactor n, which results &om the formula developed for the basicimprovement factor n, when the given reciprocal area ratioA/A is increased by an additional amount of h(A/Ac).

Ac I I/2+f(lss, Ac/A)A L K~ '(ls Ac/A)

Ac I

A A/Ac +A(A/Ac)1

A (A/Ac) = 1

In using the diagram in Figure 1, this procedure corresponds tosuch a shifting of the origin of the coordinates on the abscissawhich denotes the area ratio A/A that the improvement factor

32 n, to be drawn &om the diagram, begins with the ratio of the

6 6

Area Ratio A/Ac

6 10

pcl 10.0'

6 6 10 So 40 60 60 '~Constrained llodulus Ratio Dc/Ds

constrained moduli and not with just an infinite value. Theadditional amount on the area ratio h(A/~ depending on theratio of the constrained moduli Dc/Ds can be readily taken&om the diagram in Figure 2.

Consideration of the overburdenThe neglect of the bulk densities of columns and soil meansthat the initial pressure difference between the columns and thesoil which creates bulging, depends solely on the distribution ofthe foundation load p on columns and soil, and that it isconstant all over the column length. As a matter of fact, to theexternal loads the weights of the columns Wc and of the soilWs which possibly exceed the external loads considerably, hasto be added. Under consideration of these additional loads theinitial pressure difference decreases asymptotically and thebulging is reduced correspondingly. In other words, withincreasing overburden the columns are better supportedlaterally and, therefore, can provide more bearing capacity.Since the pressure difference is a linear parameter in thederivations of the improvement factor, the ratio of the initialpressure difference and the one depending on depth—expressed as depth factor f4 —delivers a value by which theimprovement factor n, increases to the final improvementfactor n,=Q x n, on account of the overburden pressure. Forexample, at a depth where the pressure difference amounts to50% only of the initial value, the depth factor comes to fd = 2.

GROUND ENGINEERING ~ DECEMBER ~ 1995

13

TOP: Figure 3. Determinationof the depth factor.BO'ITOM: Figure 4. Limitvalue of the depth factor.

~~ 05

e5 0,7 ~C

0,5 ~

1/3

Therefore for safety reasons, inthis diagram the lower value of thesoil ys has to be considered always.

1

ocKoc 1 Z(ts'hd)Koc Pc

0,31 5 5

Area Ratio A/Ac

0,20

0,18

0,12

8e0,08

sn',04

I ec >i 45.0',

I/4 ~ )/. Dc /Ds,butfd s 1

0,001 2 3 4 5 8

Area Ratio A/Ac

fo =1

Koc —Ws/Wc WcKoc Pc

P

Ac 1 —Ac/AA Pc/Ps

pc I/2+f(is„Ac/A)

ps K c'is ~ Ac/A)

Wc = (Yc'A4) Ws = (Ys'44)

K~ =1—sinq>c

The simplified diagram in Figure 3 considers the same bulkdensity y for columns and soil which is not on the safe side.

The depth factor fd is calculated on the assumption of alinear decrease of the pressure difference as it results from thepressure lines (pc + yc.d) K,c and (ps+ps d)(Ks=l). However,it has to be considered that with decreasing lateraldeformations the coefficient of earth pressure f'rom the columnschanges from the active value K,c to the value at rest K,c. Upto the depth where the straight line assumed for the pressuredifference meets the actual asymptotic line, the depth factor lieson the safe side. In practical cases the treatment depth is mostlyless. However, safety considerations advise not to include theadvantageous external load on the soil ps in the derivations.

Com atibili controlp ty sThe single steps of the designprocedure are not connectedmathematically and they containsimplifications andapproximations. Therefore, atmarginal cases, compatibilitycontrols have to be performedwhich guarantee that no more loadis assigned to the columns thanthey can bear at all in accordancewith their compressibility.

At increasing depths, thesupport by the soil reaches such anextent that the columns do notbulge anymore. However, eventhen the depth factor will notincrease to infinity as results fromthe assumption of a linearlydecreasing pressure difference.Therefore, the first compatibilitycontrol limits the depth factor andthereby the load assigned to thecolumns so that the settlement of

8 0 the columns resulting from theirinherent compressibility does notexceed the settlement of the

composite system. In the first place this control applies whenthe existing soil is considered pretty dense or stiff.

/sosc 1/3

D /D,f <Pc/Ps

The maximum value of the depth factor can be drawn alsofrom the diagram in Figure 4. A depth factor fd < I should notbe considered, even though it may result from the calculation.In this case the second compatibility control is imperativelyrequired which relates to the maximum value of theimprovement factor. In a certain way this control resembles thefirst one. It guarantees that the settlement of the columnsresulting from their inherent compressibility does not exceedthe settlement of the surrounding soil resulting from itscompressibility by the loads which are assigned to each. In thefirst place this second control applies when the existing soil isencountered pretty loose or soft.

n =1+—(——1)A D,A Ds

It has to be observed that the actual area ratio Ac/A has tobe appointed in the formula and not the modified value Ac/A.Because of the simple equation, an independent diagram is notrequired. 33

GROUND ENGINEERING ~ DECEMBER ~ 1995

1,0

0,8

E

5 0,8 ~ ———

I3 0,4

o.

0,2

Dasl ied Lines:m = (n ~ 1 + i le/A) / n

lido'ne::

1=(n-1)/n

pa> 1/3

(pc ~382'+

TOP: Figure 5. Proportionalload on stone columns.MIDDLE: Figure 6. Settletnentof single footings.BOTTOM: Figure 7.Settlement of strip footings.

stone columns receive anincreased portion m of the totalload m thereby which depends onthe area ratio Ac/A and theimprovement factor n.

m = (n —I+ A,/A)/n

0,01 8 8

Area Ratio A/Ac

0 10 Simplifying, the recommendeddesign procedure does notconsider the volume decrease ofthe surrounding soil caused by thebulging of the columns. Thereforeand particularly at a high arearatio, the soil receives a greaterportion of the total load thanactually calculated. In order not tooverestimate the shear resistanceof the columns when averaging onthe basis of load distribution oncolumns and soil, the proportionalload on the columns has to bereduced. The followingapproximation seems to beadequate:

00

0,8

18 g04

i1

4 8 12 18 20 24 28 32

Depth/Diameter Ratio d/D

m'= (n —I)/n

The diagram in Figure 5 shows insolid lines the proportional load ofthe columns m'nd in dashedlines the not reduced one m.

According to theproportional loads on columnsand soil, the shear resistance &omfriction of the composite systemcan be readily averaged.

8

0,8

E 0,4

0,2

0 4 8 12 18 20 24

Depth/Diameter Ratio d/D

32

C

332 '81 o

Z

tan@ = m'.tanq>, +(I—m') tan q>,

Since in most practical casespossible lines of sliding coverdMerent depths which is dif5cultto survey, it is recommended toconsider the depth factor in clear-cut cases only, ie to calculateusually with a load portion of thestone columns m,'elated to n,and not with m,'elated to theincreased factor n,=fa n,.

The cohesion of thecomposite system depends on theproportional area of the soil.

Shear values of improved groundThe shear performance of ground improved by vibroreplacement is favourable. While under shear stress rigidelements may break successively, stone columns deform untilany overload has been transferred to neighbouring columns. forexample a landslide will not occur before the bearing capacity

34 of the total group of columns installed has been activated. The

c=(i —Ac/A) cs

The installation of stone columns possibly creates damages tothe soil structure which are dificult to survey. For safetyreasons, it seems to be advisable to consider the cohesion alsoproportional to the loads, ie pretty low, although this proposalis not based on soil mechanical aspects.

GROUND ENGINEERING ~ DECEMBER ~ I 995

c'=(I-m') c,

Settlement of single and strip footingsIt is not (yet) possible to determine directly the performance ofsingle or strip footings on vibro replacement. The designensues &om the performance of an unlimited column gridbelow an unlimited load area. The total settlement s„whichresults for this case at homogeneous conditions, is readily todetermine on the basis of the forgoing description with n, as anaverage value over the depth d.

dsn=p'D

o 2

Diagrams, given in Figure 6 and Figure 7, allow toconclude &om this value the settlements of single or stripfootings on groups of columns. These diagrams —with thediameter of the stone columns D as one parameter - are basedon numerous calculations which considered load distributionon one side and a lower bearing capacity of the outer columnsof the column group below the footing on the other side.

The diagrams do not refer directly to footing extensions aswould be expected. However, there exists an indirect referencein that the grid area A required to determine the improvementfactor n, has to be derived as quotient of the footing area andthe number of columns. For example, the settlement reductionwhich a larger footing experiences normally at the same load, iscompensated widely by the lower improvement factor whichresults &om an increased area ratio as follows &om a largerfooting area on the same number of stone columns. Theapproximation given for the diagrams by this assumedcompensation seems to be acceptable for usually consideredarea ratios, ie up to some Ac/A=10.

It is clear that the diagrams are valid for homogeneousconditions only and refer to the settlement s up to a depth dwhich is the second parameter counting &om foundation level.The settlement 2((s of any layer at any depth below the footinghas to be determined as difference of the settlements up to thedepths d, and d„of the lower and upper bound of the layerconcerned with n, as an average value over its thickness hd.

hs = [(s/s„), d, -(s/s„)„d„]Do n,

Since n, increases with depth on one side due to the depthfactor, but becomes less significant with depth on the other sidedue to the load distribution of a limited footing, it is requiredeven at homogeneous conditions to subdivide greater depths.This avoids settlements being too liberally estimated.

Bearing capacity of single and stripfootingsA simple method to estimate the bearing capacity of single andstrip footings on vibro replacement exists by determining atfirst a fictitious width b of the footing, using the &iction angle (pof the improved soil below the footing and the &iction angle (psof the untreated soil on the outside, which would develop-calculated on the basis of the &iction angle (ps of the untreatedsoil only - in case of ground failure the same line of sliding

outside of the improved area as the actual footing at actualconditions. If the border line of treatment coincide with theedge of the footing - usually the case but not necessarily —thefollowing formula results:

b=b e'"n(„n„,.-/»— „,„i sin(45+ q)/2) sin(90' q),)

sin(90 —

36

Such a reduction seems to be adequate with regard to thefavourable performance of vibro replacement in seismic events.However, &om soil mechanical aspects this is not proved andhas to be verified ultimately by the increasing number ofprojects carried out worldwide.

For similar reasons as outlined at the determination of theshear values, it is recommended to use in the formula n, ratherthan n,.

A diagram for the reduction factor a is given in Figure 8.

Case study worked exampleThe design method has been used &equently in determiningthe expected behaviour of structures on treated ground.However, in most cases the application is based on parametersindirectly derived &om field tests or even just assumed. As longas the actual performance of vibro replacement excels suchforecasts, more accurate verifications are usually omitted.Some full scale field experiments about vibro replacementwhich comprise measurements beyond common practice areoutlined'. For example, enough details of a tank foundation atCanvey Island are given so that the design method can beapplied and the results verified.

The diameter of the tank concerned is 36m. it is founded ona pad of approximately i m thickness above soil reinforced by10m long stone columns in a grid with triangular spacing of1.52m and an average diameter of 0.75m measured near

0,8

a4 o,s

I 0,4

0,2 ~

01 6 s

Area Ratio A/An

practical criteria to evaluate the liquefaction potential weredeveloped rather empirically. For vibro replacement, althoughcarried out already many times against earthquake vibrations,even an empirical evaluation is difficult since - fortunately nodamage has been observed so far.

Usually, safety against liquefaction is concluded &om thecomparison of so-called cyclic stress ratios, namely the onewhich is provided by the soil on the basis of its density and theone which probably develops in a seismic event.

For a rough estimation of the efficiency of vibro replacementit is proposed to reduce the cyclic stress ratio probablydeveloped in a seismic event, in the same ratio as the load onthe soil between the columns is reduced by vibro replacement,ie to use a corresponding reduction factor a.

a= p,/p= 1/n

~l' liil~lMiiiigiil~lliiili'1~ii ~1&iii.E:8-1.0 50 pad0.0 20 top soil0.4 0.8-0.5 2 soft soll1.0 1 very soft soil1.6 1 very soft soil below

groundwater8.2 0.3-0.06 10 firm soil9.0 20 medium dense sand

1.2-0.5

At full loading of 130kN/m'ettlements were observed in therange of some 0.4m. A computation according to the designmethod (appendix) shows a final settlement of approxtmately0.38m. Taking into consideration the pockets of peat or apossible reduction of column diameter with depth, the valuewould be higher and in really good agreement.

The improvement factors n as computed on the basis offormulae, can be taken readily also &om the diagrams asfollows with reference to the first layer below the ground watertable (No5) which contributes most to the settlements:

4.53 -+ Fig. 1 o no ~ 235100 -o Fig 2 -+ A A/Ai o: 0.05 --> A/Ac = 4.58

4.58 -+ Fig. 1 -+ ni -- 2 304 58, E (7 d) = 19 1.0+ 18 0 4 + 16 0 6 + 15 0 6 + 5 6 6/2

= 61.3kN/m',130 kN/m' Fig.3 -o fo n 1.38 m n2 = fo ni = 3.17

The discrepancy to the computed value of n, = 2.94 is due tothe difference between formulae and diagram as outlined in'Consideration of the overburden'.

ConclusionsOut of the deep vibratory

+

ecI+ 38 0

compaction techniques vibroreplacement covers the widestrange with regard to theapplication in difierent soils. Whilevibro compaction is restricted tocompactible sand and gravel, theapplication of vibro replacementextends principally over the totalrange in grain size of loose soils.Even in most of the noncohesivenatural soils suitable for vibrocompaction, backfilling withcoarse grained material isrecommended to increase thecompaction efforts - and thismeans stone column installation.Pure vibro compaction hasadvanced just lately at giganticartificial deposits in different

s s 10Figure 8. Residual pressure onthe soil after vibro replacement.

surface. Including some 0.4m of top soil the treated strataconsist up to 9m depth of silty and clayey soil occasionally withpockets of peat followed by medium dense silty fine sand inwhich the columns are embedded. Referred to depths, thegiven coefficients of volume change mv and the constrainedmoduli D, (= I/mv) as used in the design computations are asfollows:

coastal regions of the world.Notwithstanding the importance of vibro replacement, the

efficiency of stone columns in soil improvement must not beoverestimated. As long as the existing soil is suitable to bedensified, this should be the preceding aim of any deepcompaction treatment including vibro replacement. However,the achievable densification depends on too many parametersto be calculable. On the contrary the improving effect of stonecolumns —possibly supplementary to an achieved densification—can be determined pretty reliably.

The application of vibro replacement which was introducedin the late 1950s, relied for a long time on the experience of thecontractors. Not until the mid-1970s were the first theoreticalapproaches submitted. In its fundamentals, the design methodoutlined originates &om this time. It has proved its reliabilitysince then. Subsequent supplements imply refinements orextensions of the application range but not a radical alterationon the fundamentals. In respect of the complexity of the matterthe design criteria have the advantage of easy use and to coverin a closed package all cases practically occurring.

Appendix A.

Vibro Replaceaent at Canvey Island, Reported 1991 by Greenwood>>~ >> ~ >*~ >>~4>>* ~ >> ~ * ~ >>>~ >>~***>~*>~ >>>~ >~ > ~>e>> ~ >~ *>>~ >>>> ~ \ ~ >

Evaluation of the soil Iaproveaent by vibro Replaceaentacc. to priebe,a.: Die Bautechnik 72, 3/1995below an Area Load on a Regular Triangular Coluan Grid

Foundation Pressure 130.00 kN/a2

Coluan DistanceKow DistanceGrid AreaLoad LevelColuan Depthconsidered Depth

1.52 ~1.32 ~2.00 82

-1.00 a10.00 820.00 8

Coluan Naterial

unit Weight 19.00 kN/a3, below 1.60 ~ Depth 12.00 kN/a3Constrained Nodulus 100.00 NN/82Friction Angle 40.0O DegreesPresa. Coefficient .22

Subsoil Strata

Keller Grundbau GabhKeieerleiarr. 44, 63067 offenbach, Tel. 069/8051210, Fax. 069/8051221prograa VIBRI, version 950904, copyright by KSLLKR Grundbau Gaba

ReferencesI Kirsch, K. 'Die Baugrundverbesserung mit Tiefenruttlern', 40 JahreSpezialtiefbau: 1953-1993,Festschrift, Werner-Veriag GmbH, Dusseldorf, 1993.2 Greenwood, DA. 'Load tests on stone columns'. ASTM Publication STP 1089,Deep Foundation Improvements: Design, Construction, and Testing, 1991.

Publications of the author to the design method:3 Abschauung des Setzungsverhaltens eines durch Stopfverdichtung verbessertenBaugrundes, Die Bautechnik 53, H.5, 1976.4 Zur Abschauung des Setzungsverhaltens eines durch Stopfverdichtungverbesserten Baugrundes, Die Bautechnik 65, H. 1, 1988.5 Abschauung des Scherwiderstandes eines durch Stopfverdichtung verbessertenBaugrundes, Die Bautechnik 55, H. 1, 1978.6 Vibro Replacement Design Criteria and Quality Control, ASTM PublicationSTP 1089, Deep Foundation Improvements: Design, Construction, and Testing,1991.7 'The prevention of liquefaction by vibro replacement'. Proc of the Int Conf onEarthquake Resistant Construction 81 Design, 1990 Balkema, Rotterdam.8 Die Bemessung von Ruttelstopfverdichtungen, Die Bautechnik 72, H.3, 1995.

1 -1.002 .003 .404 1.005 1.60e 8.2o7 9.008 10.009 20.00

.00

.75

.75

.75

.75

.60

.60

.00

.00

> ~ +**~4.534.534.534.537.087.08

>* ~ * ~ >~ >> ~ >>

50.0020.002.001.001.00

10.0020.0020.0020.00

2.005.00

50.00100.00100.0010.005.005.005.00

19.0018.0016.0015.005.007.009.009.009.00

Ground Water Table 1.60 ~Top LEOie.A

AcDCDsgaaaeayphic

Top Level of Stf'atua ConcernedColuan DiaaeterGrid Area Resp. Reference AreaCross sec'tional Are& of ColuanConetrained Nodulue of BackfillConetrained Nodulus )unit weight )Poieeon'6 Ratio ) of SoilFriction Angle )Cohesion )

No. Top L. Dia. A/AC DS DC/DS gaaaaI ~ I I ~ I INN/a21 ( ka/a3 ]

ay phi cfdeqree)(ks/a21

.33 35.00 .00

.33 25.00 5.00

.33 .00 25.00

.33 .00 20.00

.33 .00 20.00

.33 .00 30.00

.33 30.00 .00

.33 30.00 .00

.33 30.00 .00

A grid arcsb foundation widlhc cohcsiolld -inlmvcmcnt depth

dqjh ofground MuteD ~.fs—:=or

c =—'=fssashltuscong of l)gessurc

m pluporliensl load c(n stonecuhlmni

n 'ceotp area -Sagy, jassssflnslso

Wfg )tctblctktn factor sl

earthquake designumt %)eight

tl safety ~gmund SolutePoisstm's ratio

-Osf bearing elgalcuySic[ion angle

Used subscripts, dashes andapostmphes follow &om thecontext. Generally, subscriptC means column and S meanssoil. With the cxcepion of Koas coclicicnt for carlh prcssureat lest (Ka for active earthprcsstlrc) subscript 0 means a~gsslpecively~iueial

e>

I2 2.34 1.17 2.013 2 34 .09 2 31~ 2.34 .05 2.325 2.34 .05 2.326 1.'78 .52 1.727 1.78 1.17 1.65

Layer without Stone Coluana!.50 33.16 2.49 ~»*~ 1.88.57 25.41 10.84 1.16 2.68.57 25.54 8.61 1.21 2.82.57 25.54 8.61 1.27 2.94.42 19.35 17.45 1.24 2. 13.40 34.25 .00 ~ >+ ~* 1.57

Layer without Stone Columns!

.47 32.67 2.66

.63 27.73 9.34

.65 28. ~ 4 7.09

.66 28.98 6.80

.53 24.04 14.05

.36 33.90 .00

The proportional Loads on Coluana are Approxiaated to ~ 1 — I/nnod(A/AC)nl

fd

n2~1,2phil,2c1,2

Basic Iaproveaent FactorAddition to the Ares Retro (Coluan Coapreeeibility)Iaproveaent Pactor (with Coluan Compressibility)(—> Recoaaended for Failure Analyses if nl < n2)Depth Factor (overburden constraint)(>*we* —> Overridden by Control Checkinq!)Iaproveaent Factor (Add. w3th Overburden Constraint)Proportional Load on Coluana )Priction Angle of Coapound ) Attributable to nl resp. n2Cohesion of Coapound

settleaent

Depth

-1.00.00.40

1.001.608.209.00

10.00

InfiniteLoad Area

[ca].26.14

I .372.45

25.81.48.41

6.46

37.37

w/0Iapr.I ca)

.26.263.666.90

75.931.03

.656.4e

95.14

Over-burdenIkN/a21

.019.026.235.844.877.883.492.4

Soil Iaproveaent

No. no d(A/AC) nl al phil cl fd n2 a2 Phi2 c2[deqree1(kN/a2) [degree1(ka/a2)

37

GROUND ENGINEERING ~ DECEMBER ~ 1995