GeTec Ingenieurgesellschaft für Informations- und Planungstechnologie mbh. Presented by

Transcription

1 The Design of vibro replacement Dipl.-Ing. Heinz J. Priebe Presente by GeTec Ingenieurgesellschaft für Informations- un Planungstechnologie mbh Rhein-Main Office Fax Aachen Office D Aachen, Rotter Bruch 26a Fax Reprint from: GROUND ENGINEERING December 995 Technical paper GT E

2 The Design of Vibro Replacement Heinz J. Priebe Vibro Replacement is an accepte metho for subsoil improvement, at which large-size columns of coarse backfill material are installe in the soil by means of special epth vibrators. The performance of this composite system consisting of stone columns an soil, is not eterminable by simple investigation methos like sounings, an therefore, such methos are not suitable for esign purposes. However, theoretically, the efficiency of Vibro Replacement can be reliably evaluate. The metho elaborate on a theoretical basis an escribe in this contribution, is easy to survey an aaptable to ifferent conitions ue to the separate consieration of significant parameters. Practically, it comprises esign criteria for all frequently occurring applications. Introuction Vibro replacement is part of the eep vibratory compaction techniques whereby loose or soft soil is improve for builing purposes by means of special epth vibrators. These techniques as well as the equipment require is comprehensively escribe elsewhere []. ontrary to vibro compaction which ensifies noncohesive soil by the ai of vibrations an improves it thereby irectly, vibro replacement improves non compactible cohesive soil by the installation of loa bearing columns of well compacte, coarse graine backfill material. The question to what extent the ensity of compactible soil will be improve by vibro compaction, epens not only on the parameters of the soil being ifficult to etermine, but also on the proceure aopte an the equipment provie. However, the ifficulty of a reliable prognosis is balance by the fact that the improvement achieve can be etermine easily by sounings. With vibro replacement the conitions are more or less revers. onsierable efforts only like large-scale loa tests can prove the benefit of stone columns. However, a reliable conclusion can be rawn about the egree of improvement which results from the existence of the stone columns only without any ensification of the soil between. This is possible because the essential parameters attributable to the geometry of the layout an the backfill material can be etermine fairly goo. In such a prognosis the properties of the soil, the equipment an the proceure play an inirect role only an that is mainly in the estimation of the column iameter. Basically, the esign metho escribe herewith was evelope some twenty years ago an publishe alreay [3]. However, in the meantime it came to several aaptions, extensions an supplements which justify a new an comprehensive escription of the metho. Nevertheless, the erivation of the formulae is renounce with reference to literature. - -

3 Heinz J. Priebe It may be emphasize: The esign metho refers to the improving effect of stone columns in a soil which is otherwise unaltere in comparison to the initial state. In a first step a factor is establishe by which stone columns improve the performance of the subsoil in comparison to the state without columns. Accoring to this improvement factor the eformation moulus of the composite system is increase respectively settlements are reuce. All further esign steps refer to this basic value. In many practical cases the reinforcing effect of stone columns installe by vibro replacement is superpose with the ensifying effect of vibro compaction, i.e. the installation of stone columns ensifies the soil between. In this cases, first of all the ensification of the soil has to be evaluate an only then - on the basis of soil ata aapte corresponingly - the esign of vibro replacement follows. Notation A b c Gr D f K m n gri area founation with cohesion improvement epth epth of groun failure constraine moulus epth factor coefficient of earth pressure proportional loa on stone columns improvement factor p area loa resp. founation pressure s settlement W weight α reuction faktor in earthquake esign γ unit weight η safety against groun failure µ Poisson s ratio σ 0f ϕ bearing capacity friction angle Use subscripts, ashes an apostrophes follow from the context. Generally, subscript means column an means soil. With the exception of K 0 as coefficient for earth pressure at rest (K a for active earth pressure) subscript 0 means a basic respectively an initial value. 2 Determination of the Basic Improvement Factor The fairly complex system of vibro replacement allows a more or less accurate evaluation only for the well efine case of an unlimite loa area on an unlimite column gri. In this case a unit cell with the area A is consiere consisting of a single column with the cross section A an the attributable surrouning soil. Furthermore the following iealize conitions are assume: The column is base on a rigi layer The column material is uncompressible The bulk ensity of column an soil is neglecte Hence, the column can not fail in en bearing an any settlement of the loa area results in a bulging of the column which remains constant all over its length. 2

4 The Design of Vibro Replacement The improvement of a soil achieve at these conitions by the existence of stone columns is evaluate on the assumption that the column material shears from the beginning whilst the surrouning soil reacts elastically. Furthermore, the soil is assume to be isplace alreay uring the column installation to such an extent that its initial resistance correspons to the liqui state, i. e. the coefficient of earth pressure amounts to K =. The result of the evaluation is expresse as basic improvement factor n 0. n 0 A 2+ f( µ, A A) = + A K f( µ, A A) a (, = µ ) ( A A) f( µ A A) 2µ + A A K a = tan 2 ( 45 ϕ 2) A poisson s ratio of µ = which is aequate for the state of final settlement in most cases, leas to a simple expression. n 0 A 5 A A = + A 4 K ( A A) The relation between the improvement factor n 0, the reciprocal area ratio A/A an the friction angle of the backfill material ϕ which enters the erivation, is illustrate in the well known iagram of Figure. a 6 Improvement Factor n ϕ = = 45.0 ϕ = 42.5 ϕ = 40.0 ϕ = 37.5 ϕ = 35.0 µ = /3 µ B = / Area Ratio A/A Figure : Design chart for vibro replacement 3

5 Heinz J. Priebe 3 onsieration of the olumn ompressibility 2,0 Aition to the Area Ratio (A /A ),6,2 0,8 0,4 ϕ = 45.0 ϕ = 42.5 ϕ = 42.5 ϕ = 40.0 ϕ = 40.0 ϕ = 37.5 ϕ = 37.5 ϕ = 35.0 ϕ = 35.0 µ µb s = /3 0, onstraine Moulus Ratio D /D Figure 2: 2 onsieration of column compressibility The compacte backfill material of the columns is still compressible. Therefore, any loa causes settlements which are not connecte with bulging of the columns. Accoringly, in the case of soil replacement where the area ratio amounts to A/A =, the actual improvement factor oes not achieve an infinite value as etermine theoretically for non compressible material, but it coincies at best with the ratio of the constraine mouli of column material an soil. In this case for compacte backfill material as well as for soil a constraine moulus is meant as foun by large scale oeometer tests. Unfortunately, in many cases sounings are carrie out within the columns an wrong conclusions about the moulus are rawn from the results which are somtimes very moerate only. It is relatively easy to etermine at which area ratio of column cross section an gri size (A /A) the basic improvement factor n 0 correspons to the ratio of the constraine mouli of columns an soil D /D. For example, at µ = /3 the lower positive result of the following expression (with n 0 = D /D ) elivers the area ratio (A /A) concerne. A 4 Ka n = ( 2) + 5 ± A 2 ( 4 K ) a 4 Ka ( n 2) + 5 Ka n K a + 6 ( 0 ) 4 4 K a 2 4

6 The Design of Vibro Replacement As an approximation, the compressibility of the column material can be consiere in using a reuce improvement factor n which results from the formula evelope for the basic improvement factor n 0 when the given reciprocal area ratio A/A is increase by an aitional amount of (A/A ). n A 2+ f( µ, A A) = + A Ka f( µ, A A) A = A A A + ( A A ) ( AA ) = ( A A) In using the iagram in Figure this proceure correspons to such a shifting of the origin of the coorinates on the abscissa which enotes the area ratio A/A that the improvement factor n to be rawn from the iagram, begins with the ratio of the constraine mouli an not with just an infinite value. The aitional amount on the area ratio (A/A ) epening on the ratio of the constraine mouli D /D can be reaily taken from the iagram in Figure 2. 4 onsieration of the Overburen The neglect of the bulk ensities of columns an soil means that the initial pressure ifference between the columns an the soil which creates bulging, epens solely on the istribution of the founation loa p on columns an soil, an that it is constant all over the column length. As a matter of fact, to the external loas the weights of the columns W an of the soil W which possibly excee the external loas consierably, has to be ae. Uner consieration of these aitional loas the initial pressure ifference ecreases asymptotically an the bulging is reuce corresponingly. In other wors, with increasing overburen the columns are better supporte laterally an therefore, can provie more bearing capacity. ince the pressure ifference is a linear parameter in the erivations of the improvement factor, the ratio of the initial pressure ifference an the one epening on epth - expresse as epth factor f - elivers a value by which the improvement factor n increases to the final improvement factor n 2 = f n on account of the overburen pressure. For example, at a epth where the pressure ifference amounts to 50% only of the initial value, the epth factor comes to f = 2. The epth factor f is calculate on the assumption of a linear ecrease of the pressure ifference as it results from the pressure lines (p + γ ) K a an (p + γ ) (K = ). However, it has to be consiere that with ecreasing lateral eformations the coefficient of earth pressure from the columns changes from the active value K a to the value at rest K 0. Up to the epth where the straight line assume for the pressure ifference, meets the actual asymptotic line, the epth factor lies on the safe sie. In practical cases the treatment epth is mostly less. However, safety consierations avise not to inclue the avantageous external loa on the soil p in the erivations. 5

7 Heinz J. Priebe f = K0 W W + K 0 W p p = A A p A A + p p p p 2 + f( µ, A A) = K f( µ, A A) a W = Σ( γ ), W = Σ( γ ) K o = sinϕ The simplifie iagram in Figure 3 consiers the same bulk ensity γ for columns an soil which is not on the safe sie. Therefore for safety reasons, the lower value of the soil γ shoul be consiere in this iagram always. f = K0 Σ( γ ) + K p 0,3, ϕ = 45.0 f = / [ - y. Σ(γ. ) / p] f t = / [ - y. Σ (γ B t) / p] Influence Factor y 0,9 0,7 ϕ = 42.5 ϕ = 40.0 ϕ = 37.5 ϕ = 37.5 ϕ = 35.0 µ B = /3 0,5 0, Area Ratio A/A Figure 3: 3 Determination of the epth factor 6

8 The Design of Vibro Replacement 5 ompatibility ontrols The single steps of the esign proceure are not connecte mathematically an they contain simplifications an approximations. Therefore, at marginal cases compatibility controls have to be performe which guarantee that no more loa is assigne to the columns than they can bear at all in accorance with their compressibility. At increasing epths, the support by the soil reaches such an extent that the columns o not bulge anymore. However, even then the epth factor will not increase to infinity as results from the assumption of a linearly ecreasing pressure ifference. Therefore, the first compatibility control limits the epth factor an thereby the loa assigne to the columns so that the settlement of the columns resulting from their inherent compressibility oes not excee the settlement of the composite system. In the first place this control applies when the existing soil is consiere pretty ense or stiff. f D p D p 0,20 0,6 Influence Factor y 0,2 0,08 ϕ = 40.0 ϕ = 40.0 ϕ = 37.5 ϕ = 37.5 ϕ = 35.0 ϕ = 35.0 µ B s = /3 0,04 ϕ = 42.5 ϕ = 42.5 ϕ = 45.0 f t < y.. DE // DE B,, aber but ff t > 0, Area Ratio A/A Figure 4: 4 Limit value of the epth factor The maximum value of the epth factor can be rawn also from the iagram in Figure 4. By the way, a epth factor f < shoul not be consiere, even though it may result from the calculation. In this case the secon compatibility control is imperatively require which relates to the maximum value of the improvement factor. In a certain way this control resembles the first one. It guarantees that the settlement of the columns resulting from their inherent compressibility oes not excee the settlement of the surrouning soil resulting from its compressibility by the loas which are 7

9 Heinz J. Priebe assigne to each. In the first place this secon control applies when the existing soil is encountere pretty loose or soft. A D n max = + ( ) A D It has to be observe that the actual area ratio A /A has to be appointe in the formula an not the moifie value A / A. Because of the simple equation, an inepenent Diagram is not require. 6 hear Values of Improve Groun The shear performance of groun improve by vibro replacement is outmost favourable. Whilst uner shear stress rigi elements may break successively, stone columns eform until any overloa has been transferre to neighbouring columns. For example, a lanslie will not occur before the bearing capacity of the total group of columns installe has been activate. The stone columns receive an increase portion of the total loa m thereby which epens on the area ratio A /A un the improvement factor n. m = (n + A A) n implifying, the recommene esign proceure oes not consier the volume ecrease of the surrouning soil cause by the bulging of the columns. Therefore an particularly at a high area ratio, the soil receive a greater portion of the total loa than actually calculate. In orer not to overestimate the shear resistance of the columns when averaging on the basis of loa istribution on columns an soil, the proportional loa on the columns has to be reuce. The following approximation seems to be aequate: m = ( n ) n The iagram in Figure 5 shows in soli lines the proportional loa of the columns m an in ashe lines the not reuce one m. Accoring to the proportional loas on columns an soil, the shear resistance from friction of the composite system can be reaily average. tan ϕ= m tan ϕ + ( m ) tan ϕ ince in most practical cases possible lines of sliing cover ifferent epths which is ifficult to survey, it is recommene to consier the epth factor in clear-cut cases only, i. e. to calculate usually with a loa portion of the stone columns m relate to n an not with m 2 relate to the increase factor n 2 = f n. The cohesion of the composite system epens on the proportional area of the soil. c= ( A A) c 8

10 The Design of Vibro Replacement The installation of stone columns possibly creates amages to the soil structure which are ifficult to survey. For safety reasons, it seems to be avisable to consier the cohesion also proportional to the loas, i. e. pretty low, although this proposal is not base on soil mechanical aspects. c = ( m ) c,0 Proportional loa m 0,8 0,6 0,4 0,2 ϕ = 45.0 ϕ = 45.0 ϕ = 42.5 ϕ = 42.5 oli Lines: m = (n - ) / n ϕ = 40.0 ϕ = 40.0 Dashe Lines: m = (n - + A /A) / n ϕ = 37.5 ϕ = 37.5 µ s B = /3 ϕ = 35.0 ϕ = , Area Ratio A/A Figure 5: 5 Proportional loa on stone columns 7 ettlement of ingle an trip Footings It is not (yet) possible to etermine irectly the performance of single or strip footings on vibro replacement. The esign ensues from the performance of an unlimite column gri below an unlimite loa area. The total settlement s which results for this case at homogeneous conitions, is reaily to etermine on the basis of the foregoing escription with n 2 as an average value over the epth. s = p D n 2 Diagrams which are given in Figure 6 an Figure 7, allow to conclue from this value the settlements of single or strip footings on groups of columns. These iagrams - with the iameter of the stone columns D as one parameter - are base on numerous calculations which consiere loa istribution on one sie an a lower bearing capacity of the outer columns of the column group below the footing on the other sie. 9

11 Heinz J. Priebe 0,8 ettlement Ratio s/s 0,6 0,4 0, No. of tone olumns Depth/ Diameter Ratio /D Figure 6: 6 ettlement of single Footings 0,8 ettlement Ratio s/s 0,6 0,4 0, No. of tone olumn Rows Depth/ Diameter Ratio /D Figure 7: 7 ettlement of strip Footings The iagrams o not refer irectly to footing extensions as to be expecte. However, there exists an inirect reference in that the gri area A require to etermine the improvement factor n, has 0

12 The Design of Vibro Replacement to be erive as quotient of the footing area an the number of columns. For example, the settlement reuction which a larger footing experiences normally at the same loa, is compensate wiely by the lower improvement factor which results from an increase area ratio as follows from a larger footing area on the same number of stone columns. The approximation given for the iagrams by this assume compensation seems to be acceptable for usually consiere area ratios, i. e. up to some A/A = 0. Quite clear that the iagrams are vali for homogeneous conitions only an refer to the settlement s up to a epth which is the secon parameter counting from founation level. The settlement s of any layer at any epth below the footing has to be etermine as ifference of the settlements up to the epths l an u of the lower an upper boun of the layer concerne with n 2 as an average value over its thickness. p s = D n 2 [( ss ) ( ss ) ] l l u u ince n 2 increases with epth on one sie ue to the epth factor, but becomes less significant with epth on the other sie ue to the loa istribution of a limite footing, it is require even at homogeneous conitions to subivie greater epths. This avois settlements being too liberally estimate. 8 Bearing apacity of ingle an trip Footings A simple metho to estimate the bearing capacity of single an strip footings on vibro replacement exists by etermining at first a fictitious with b of the footing, using the friction angle ϕ of the improve soil below the footing an the friction angle ϕ of the untreate soil on the outsie, which woul evelop - calculate on the basis of the friction angle ϕ of the untreate soil only - in case of groun failure the same line of sliing outsie of the improve area as the actual footing at actual conitions. If the borer line of treatment coincie with the ege of the footing - being usually the case but not necessarily - the following formula results: [ ] b b e arc ( 45 ϕ 2) tan ϕ arc ( 45 ϕ 2) tan ϕ sin( 45 + ϕ 2) sin( 90 ϕ ) = sin( 90 ϕ ) sin( 45 + ϕ 2) Then, for this fictitious with the bearing capacity is etermine by using the friction angle of the untreate groun ϕ an an average cohesion accoring to the proportion of fictitious footing with an failure with outsie of the footing. In pure cohesive soil the failure with equals the footing with, thus leaing to an average cohesion of c = (c + c ) / 2. For founations on layere groun the shear values change with epth also. The etermination of the bearing capacity, e. g. accoring to the German tanar DIN 407, becomes rather complicate with the fictitious with since this with changes at each layer.

13 Heinz J. Priebe A practical approximation can be achieve as follows. At first, safeties η 0 an maximum epths of groun failure lines Gr,0 are calculate applying one after another the soil parameters of every iniviual layer, e. g. accoring to DIN 407. η = σ f p σ = ( c N ν + q N ν + γ b N ν ) b b 0 0 0f c c b b [ arc( 45 + ϕ 2) tan ϕ = b sin( 45 + ϕ 2) e ] Gr, 0 In a secon step, the final safety η an maximum epth Gr is average successively with the values of the iniviual layers as long as Gr(n-) excees u(n) being the upper boun of the layer concerne ( l(n) being the lower boun). η( n) = η0( n) + [ η( n ) η0( n) ] on ( ) Gr( n ) Gr( n ) = Gr, 0( n) + [ Gr( n ) Gr, 0( n) ] on ( ) Gr( n ) n 2 η( ) = η0( ) Gr() = When Gr,() 0 Gr n > ( ) l( n) then Gr( n ) = l( n) Though little bit uncomfortable, this proceure can still be performe manually in contrast to the iteration as outline in DIN 407. The results of both the proceures o not iffer much. 9 Liquefaction Potential of Improve Groun Vibro replacement is suitable particularly for groun improvement in seismic areas since stone columns possess a certain flexibility on one sie an prevent liquefaction on the other sie. The stabilizing effect results from the frictional resistance of the columns which carry a consierable amount of the external loa an of the weight of the soil, an their capability to reuce excess porewater pressure in the soil - at least in close vicinity - almost instantly. The steep reuction of porewater pressure towars the column is in so far important as it creates kin of a filter cake effect which maintains the lateral support require for the bearing capacity of the columns an which prevents a higher egree of soil infiltration into the columns although the column material oes not fulfill any establishe filter criteria. The complex conitions in a seismic event are investigate frequently for more or less homogeneous groun. Nevertheless, practical criteria to evaluate the liquefaction potential were evelope rather empirically. For vibro replacement although carrie out alreay many times against earthquake vibrations, even an empirical evaluation is ifficult since - fortunately - no amages have been observe so far. Usually, safety against liquefaction is conclue from the comparison of so-calle cyclic stress ratios, namely the one which is provie by the soil on the basis of its ensity an the one which probably evelops in a seismic event. 2

14 The Design of Vibro Replacement For a rough estimation of the efficiency of vibro replacement it is propose to reuce the cyclic stress ratio probably evelope in a seismic event, in the same ratio as the loa on the soil between the columns is reuce by vibro replacement, i. e. to use a corresponing reuction factor α. α= p p= n uch a reuction seems to be aequate with regar to the favourable performance of vibro replacement in seismic events. However, from soil mechanical aspects this is not prove an has to be verifie ultimately by the increasing number of projects carrie out worl-wie. For similar reasons as outline at the etermination of the shear values, it is recommene to use in the formula n rather than n 2. A iagram for the reuction factor α is given in Figure 8. 0,8 ϕ = 35.0 tress Ratio p /p 0,6 0,4 ϕ = 45.0 ϕ = 45.0 ϕ = 42.5 ϕ = 42.5 ϕ = 40.0 ϕ = 40.0 ϕ = ,2 µ Β = / Area Ratio A/A Figure 8: 8 Resiual pressure on the soil after vibro replacement 0 ase tuy Worke Example The esign metho has been use alreay frequently in etermining the expecte behaviour of structures on treate groun. However, in most cases the application is base on parameters inirectly erive from fiel tests or even just assume. As long as the actual performance of vibro replacement excels such forecasts, more accurate verifications are usually omitte. ome full scale fiel experiments about vibro replacement which comprise measurements beyon common practice are outline in [2]. For example, enough etails of a tank founation at anvey Islan are given so that the esign metho can be applie an the results verifie. 3

15 Heinz J. Priebe The iameter of the tank concerne is 36 m. It is foune on a pa of approximately m thickness above soil reinforce by 0 m long stone columns in a gri with triangular spacing of.52 m an an average iameter of 0.75 m measure near surface. Incluing some 0.4 m of top soil the treate strata consist up to 9 m epth of silty an clayey soil occasionally with pockets of peat followe by meium ense silty fine san in which the columns are embee. Referre to epths, the given coefficients of volume change m v an the constraine mouli D (= /m v ) as use in the esign computations are as follows: Depth [m] m v [m²/mn] D [MN/m²] Remarks pa top soil soft soil.0 very soft soil very soft soil below groun water firm soil meium ense san At full loaing of 30 kn/m² settlements were observe in the range of some 40 cm. A computation accoring to the esign metho (s. appenix) shows a final settlement of approximately 38 cm. Taking into consieration the pockets of peat or a possible reuction of column iameter with epth, the value woul be higher an in really goo agreement. The improvement factors n as compute on the basis of formulae, can be taken reaily also from the iagrams as follows with reference to the first layer below the groun water table which contributes most to the settlements: A/A = 4.53 Fig. n D /D = 00 Fig. 2 A/A 0.05 A/A = 4.58 A/A = 4.58 Fig. n 2.30 A/A = 4.58, Σ (γ ) = /2 = 6.3 kn/m², p = 30 kn/m² Fig. 3 f.38 n 2 = f n = 3.7 The iscrepancy to the compute value of n 2 = 2.94 is ue to the ifference between formulae an iagram as outline in paragraph 4. 4

16 The Design of Vibro Replacement onclusions Out of the eep vibratory compaction techniques vibro replacement covers the wiest range with regar to the application in ifferent soils. Whilst vibro compaction is restricte to compactible san an gravel, the application of vibro replacement extens principally over the total range in grain size of loose soils. Even in most of the noncohesive natural soils suitable for vibro compaction, backfilling with coarse graine material is recommene to increase the compaction efforts - an this means stone column installation. Pure vibro compaction has avance just lately at gigantic artificial eposits in ifferent coastal regions of the worl. Notwithstaning the importance of vibro replacement, the efficiency of stone columns in soil improvement must not be overestimate. As long as the existing soil is suitable to be ensifie, this shoul be the preceing aim of any eep compaction treatment incluing vibro replacement. However, the achievable ensification epens on too many parameters to be calculable. On the contrary the improving effect of stone columns - possibly supplementary to an achieve ensification - can be etermine pretty reliably. The application of vibro replacement which was introuce en of the fifties, relie for a long time upon the experience of the contractors. Not before the mile of the seventies first theoretical approaches were submitte. In its funamentals also the esign metho outline afore originates from this time. It has prove its reliability since then. ubsequent supplements imply refinements or extensions of the application range but not a raical alteration on the funamentals. In respect of the complexity of the matter the esign criteria have the avantage to be easy to use an to cover in a close package all cases practically occurring. References [] Kirsch, K.: Die Baugrunverbesserung mit Tiefenrüttlern, 40 Jahre pezialtiefbau: , Festschrift, Werner-Verlag GmbH, Düsselorf, 993. [2] Greenwoo, D. A.: Loa Tests on tone olumns, ATM Publication TP 089, Deep Founation Improvements: Design, onstruction, an Testing, 99. Publications of the author to the esign metho: [3] Abschätzung es etzungsverhaltens eines urch topfverichtung verbesserten Baugrunes, Die Bautechnik 53, H.5, 976. [4] Zur Abschätzung es etzungsverhaltens eines urch topfverichtung verbesserten Baugrunes, Die Bautechnik 65, H., 988. [5] Abschätzung es cherwierstanes eines urch topfverichtung verbesserten Baugrunes, Die Bautechnik 55, H., 978. [6] Vibro Replacement Design riteria an Quality ontrol, ATM Publication TP 089, Deep Founation Improvements: Design, onstruction, an Testing, 99. [7] The Prevention of Liquefaction by Vibro Replacement, Proc. of the Int. onf. on Earthquake Resistant onstruction an Design, 990 Balkema, Rotteram. [8] Die Bemessung von Rüttelstopfverichtungen, Die Bautechnik 72, H.3, 995 5

17 Heinz Appenix J. Priebe Keller Grunbau GmbH Kaiserleistr. 44, Offenbach, Tel. 069/80520, Fax. 069/80522 Program VIBRI, Version , opyright by KELLER Grunbau GmbH Vibro Replacement at anvey Islan, Reporte 99 by Greenwoo *********************************************************** Evaluation of the oil Improvement by Vibro Replacement acc. to Priebe, H.: Die Bautechnik 72, 3/995 below an Area Loa on a Regular Triangular olumn Gri Founation Pressure kn/m² olumn Distance.52 m Row Distance.32 m Gri Area 2.00 m² Loa Level -.00 m olumn Depth 0.00 m onsiere Depth m olumn Material Unit Weight 9.00 kn/m³, below.60 m Depth 2.00 kn/m³ onstraine Moulus MN/m² Friction Angle Degrees Press. oefficient.22 ubsoil trata No. TopL. Dia. A/A D D/D gamma my phi c [m] [m] [MN/m²] [kn/m³] [egree] [kn/m²] **** **** **** Groun Water Table.60 m Top L. = Top Level of tratum oncerne Dia. = olumn Diameter A = Gri Area Resp. Reference Area A = ross-sectional Area of olumn D = onstraine Moulus of Backfill D = onstraine Moulus ) gamma = Unit Weight ) my = Poisson s Ratio ) of oil phi = Friction Angle ) c = ohesion ) oil Improvement No. n0 (A/A) n m phi c f n2 m2 phi2 c2 [egree] [kn/m²] [egree] [kn/m²] Layer without tone olumns! ***** ***** Layer without tone olumns! The Proportional Loas on olumns are Approximate to m = - /n n0 = Basic Improvement Factor (A/A) = Aition to the Area Ratio (olumn ompressibility) n = Improvement Factor (with olumn ompressibility) ( > Recommene for Failure Analyses if n < n2) f = Depth Factor (Overburen onstraint) ( ***** > Overrien by ontrol hecking!) n2 = Improvement Factor (A. with Overburen onstraint) m,2 = Proportional Loa on olumns ) phi,2 = Friction Angle of ompoun ) Attributable to n resp. n2 c,2 = ohesion of ompoun ) ettlement Depth Infinite w/o Over- Loa Area Impr. buren [m] [cm] [cm] [kn/m²] Vibro Replacement by the Keller Group - the experience contractors which invente an evelope the basic features of the eep vibratory compaction methos. VIBRI - The only software for the esign of vibro replacement evelope by the author (Priebe) of the esign metho. - user frienly by graphically supporte input - easy to survey by alphanum. an graphic output For etails please contact Keller Grunbau GmbH Technical Department Kaiserleistr Offenbach/Main Tel: Fax: GERMANY 6