Designing reinforced soils by columns

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1 Designing einfoed soils by olumns Mouni Bouassida, Univesity Tunis l Mana, Geotehnial ngineeing Reseah Team. National ngineeing Shool of Tunis, Tunis, Tunisia ABSTRACT The design of foundations on einfoed gound by olumns usually involves two veifiations, fist, the beaing apaity and, seond, the settlement. This ontibution details a ompehensive methodology fo detemining the optimized impoved aea atio to avoid oveestimated quantities of mateial olumns. The basis of suggested methodology onsists in estimating, fist, a minimum impovement aea atio (IAR) omplying with the allowable beaing apaity of einfoed soil; then a maximum IAR is deived fom the veifiation of allowable settlement. A tank pojet is analyzed to show up that the use of novel methodology of design, whih has been inopoated in eently developed softwae fo the design of einfoed soil by olumns, avoids an oveestimated einfoement. RÉSUMÉ Le dimensionnement d une fondation su sol enfoé pa olonnes inlut, en pemie lieu, la véifiation de la apaité potante, et, en seond lieu, la véifiation du tassement. Cette ontibution pésente une nouvelle méthode de détemination du taux d inopoation optimal pemettant d évite la su estimation de la quantité du matéiau onstitutif des olonnes. Une valeu minimale du taux d inopoation est identifiée suite à la véifiation de la apaité potante admissible; suivie de l estimation d une valeu maximale du taux d inopoation déoulant de la véifiation du tassement admissible. Un pojet de ésevoi est exposé pou monte que la mise en oeuve de la nouvelle méthodologie de dimensionnement qui a été inopoée dans le logiiel onduit à un gain su le oût du enfoement. 1 INTRODUCTION It is well known that the einfoement of weak soils by olumns aims to the inease of beaing apaity, the edution of settlement, the aeleation of onsolidation of soft soils by dained mateial olumn and the pevention of liquefation isk espeially in the ase of satuated loose sands. The ost of shemes fo einfoed soil (RS) foundation using stone olumns, ompation piles o deep mixing tehnique is essentially ontolled by the volume fation of inopoated mateial as efeed to the impovement aea atio (IAR). The Impovement Aea Ratio (IAR) is defined by the total oss setion of olumns divided by the aea of loaded foundation. Weak soils often have vey low stength and stiffness haateistis. This ategoy of soil basially inludes, high ompessible soils of undained shea stength less than 30 kpa, Young modulus lowe than 2 MPa and loose sands having a fition angle less than 30 (i.e. SPT < 10). Depending on the adopted olumna einfoed tehnique the IAR anges fom: to 0.35 fo stone olumns; the stength of olumn mateial is mainly haateized by a high fition angle (i.e. geate than 40 ) to 0.7 fo deep mixing; the stength of olumn mateial is mainly haateized by enhaned ohesion (twenty times o moe than that of initial soil) to 0.15 fo vibo ompation, with o without added mateial; the stength of olumn mateial is haateized by modeate ohesion and enhaned fition angle. The design of foundations on einfoed gound by olumns usually involves the veifiations, fist, of beaing apaity and, seond, of settlement. The design an also involve the aeleation of onsolidation when olumns behave like vetial dains and the liquefation potential in ase of loose satuated sands. The existing methods often aim to one veifiation eithe beaing apaity o settlement by adopting the unit ell model. Futhe, existing methods wee fomulated fo a unique type of olumn installation tehnique i.e. stone olumns (Piebe, 1995), (Fenh standad, 2005) o deep mixing (Boms, 2000), et. In these ontibutions the IAR was only onsideed as a given data, theefoe the optimization of quantity of olumn mateial was not disussed. Note the IAR is not taken into aount by the Fenh standad to estimate the beaing apaity of RS by the isolated olumn model. Futhe, egadless the olumn installation tehnique o the modelling of RS, none of the pevious methods of design took into aount both the beaing apaity and settlement veifiations. In ode to suggest a ompehensive design poedue, this pape pesents a novel methodology that inludes the veifiations of beaing apaity and settlement. Moe else, the suggested methodology onsides the esults of eent eseah that wee obtained in well stated famewoks. This methodology of design is detailed fo einfoed soils by end beaing and floating olumns. The onstituents of einfoed soil, i.e. the initial soil also alled weak soil and einfoing olumns ae identially modelled as a thee dimensional medium. The einfoing olumns ae loated in abitay aangement unde the

2 loaded foundation. This methodology is undetaken in thee steps to deive an optimized IAR. Theefoe, the use of goup of olumns model made it possible the use of IAR as key paamete fo the pupose of design. By pefoming the suggested methodology of design the gain in ost is shown fo a tank foundation esting on loose silt sand einfoed by end beaing stone olumns. 2 STATMNT OF TH PROBLM As fo any type of foundation the design of RS by olumns stats by the veifiation of beaing apaity whih is a neessay ondition, then it follows the veifiation of settlement that is suffiient to onlude about the stability of studied foundation. Reinfoement is done by vetial eithe end-beaing o floating olumns, of length H, installed unde loaded aea, as efeed to foundation (Fig.1). The loation of olumns of iula oss setions an be abitay and thei diamete as well (Fig. 2). Ciula olumns (Total aea A ) Figue 2. Geomety of foundation and olumns loation Seond, by the linea elastiity famewok an uppe bound of settlement is deived afte the detemination of a lowe bound of appaent modulus of RS. Then, on the basis of given allowable settlement of RS a maximum IAR is identified. Thid, an iteative alulation of settlement is aied out to find the optimized IAR. By onsequene, the oesponding design of olumna einfoed foundation annot be qualified as oveestimated. The methodology hee pesented applies fo all types of foundation (afts, footings, and embankments) shaped etangula o iula, esting on end-beaing o floating olumna soil. The pedition of beaing apaity hee pesented, in ase of puely ohesive soil einfoed by ohesive fitional olumn mateial, 3 BARING CAPACITY VRIFICATION In the famewok of limit analysis a lowe bound, Q - ult, of the ultimate load of a foundation on RS is detemined. by pefoming the stati appoah (Salençon, 1990). Fo a ohesive fitional olumn mateial the lowe bound solution of ultimate vetial stess of RS by a goup of end-beaing olumns, in funtion of the fition angle of olumns mateial (eithe < 19.5 o > 19.5 ) is given by (Bouassida et al, 1995): Figue 1. Foundation on einfoed soil by olumns The veifiation of beaing apaity is pedited by onsideing the unit weight, fition angle and ohesion of the initial soil and olumns mateial. The settlement is estimated by using the Young modulus and Poisson s atios of olumns mateial (, ) and weak soil ( s, s). Sine the einfoement aims to the inease of weak soil s stiffness then: > s. Lowe and uppe bounds of ultimate beaing apaity, obtained by limit analysis appoahes, ae onsideed to detemine the minimum IAR that haateizes the needed einfoement omplying with the allowable beaing apaity of RS. Foundation (Aea A) Q ult / A ult, s (1 ) ult, s ult, [1] Fom q (1) the pedited ultimate vetial stesses indued within olumn mateial and initial soil espetively ult, and ult,s ae expessed in tems of intenal fition angle and ohesion of olumn mateial C, and ohesion of initial soil C s. Then, the allowable vetial stess of RS, denoted all,s is intodued Conside the fato of safety against punhing of the RS, denoted F s, the allowable beaing apaity of RS is: all, s (1 ) ult, s ult, F s As fist appoximation the lowe bound estimation of the beaing apaity is assoiated to a fato of safety as: 1 < F s < 2. The allowable beaing apaity of RS, ompaed to the mean vetial stess indued by the woking load of foundation, denoted Q wok, should omply with the ondition: [2]

3 Q / A [3] wok all, s Combining qs (2) and (3) the minimum IAR, denoted min, is identified: F ( Q / A ) s atual utl, s utl, utl, s The minimum IAR identified fom q (4) oesponds to the needed quantity of olumn mateial to be inopoated in the initial soil suh that the ultimate beaing apaity ineases fom min ult, s to ult, s. Othewise, if min 0 the einfoement is unneessay sine the allowable vetial stess of uneinfoed soil omplies with the woking load exeted by the foundation. The novel methodology of design heein is extendable to the study of einfoement by floating olumns of length lowe than the statum depth H > H (Fig. 1) Bouassida et al (2009) have demonstated that lowe bounds of the ultimate beaing apaity of RS by end beaing olumns emain valid in the ase of floating olumns unde a estition on the length of olumns that usually ous in patie. Theefoe, the methodology of design heein an be also applied to pedit the minimum IAR in ase of floating olumns. 4 STTLMNT VRIFICATION In the famewok of linea elastiity the appaent Young modulus of RS by olumns, peeived as a homogenized medium, an be appoximated. In patiula, when aying out the onstution of statially allowable stess fields a lowe bound of the appaent Young modulus of RS, s [4] is detemined (Bouassida et al, 2003). Fo a igid foundation, of aea A, subjeted to the allowable woking load Q atual, and by assuming a unifom settlement of RS we have: s Q / A / H atual It is demonstated that the lowe bound of appaent Young modulus of RS is geate than the so alled homogenized Young modulus expessed by: hom = (1 ) s +. Consequently, fom Ineq (5) a moe onsevative pedition of settlement of RS denoted, is obtained: ( Q / A) H all [6] (1 ) s [5] The pedited uppe bound estimate of settlement fom q (6) is assoiated to a maximum IAR max. It is then equied that the allowable settlement of RS, as given data, should omply with as: [7] As fist veifiation of settlement we need to hek whethe the minimum IAR alulated fom q (4) omplies o not with the pesibed allowable settlement of RS. If yes, that might be the ase of impovement of vibo ompated loose sands, then the pedited minimum IAR is ageed fo the final design. min In ase minimum IAR does not omply with the allowable settlement of RS, that usually happens fo einfoed soft lays by stone olumns, then we need to inease the IAR suh that: min. The design poedue is ontinued by ombining Ineqs (5) and (6), and then one obtains: ( Q all / A)( H / s ) s max Fom Ineq (8) it is then identified a maximum IAR, denoted max, beyond whih the einfoement will be definitely oveestimated sine both pedited stess and settlement omply with allowable values. Taking aount of ineqs (4) and (8) a bounding of the IAR is obtained: min max [9] Ineqs (9) povides the tageted IAR that omplies both with allowable beaing apaity and settlement of RS. Theefoe, an optimized IAR opt [8] is detemined in funtion of the allowable settlement. In ase of floating olumns, due to linea elasti assumption that is based on the piniple of supeposition, it is postulated that the total settlement is the sum of two omponents elated espetively to the settlement of RS mass, i.e., and that of the non RS unde layes n. The settlement of RS is then estimated as detailed above fo end beaing olumns. In addition, it is neessay to veify that the total settlement tot u is allowable as well. This veifiation applies when the non einfoed unde layes belong to the ategoy of ompessible satuated lays in whih a long tem onsolidation settlement is indued. The settlement estimation of uneinfoed soil layes is pedited by the one dimensional Tezaghi s theoy of onsolidation.

4 5 ILLUSTRATIV CAS HISTORY An oil stoage tank was built at Zazis teminal on elaimed aea at Tunisian South ast Coast. The woking load of the tank is appoximated as quasi-unifom vetial stess of 120 kpa, whih exeeds the allowable beaing apaity of initial soil. Theefoe, it was aimed the inease of allowable beaing apaity at least to 120 kpa and the edution of tank s settlement to the allowable limit of 6 m whih slightly exeeds the atio 1/1,000 of diamete tank usually equied fo oil tanks pojets. Reinfoement by end-beaing stone olumns was ageed to make sue the oveall stability of tank. The einfoement was exeuted along an aveage depth of 7 m with a nominal diamete of olumns equals at 1.2 m installed in equilateal tiangula mesh. Figue 3 summaizes the geotehnial popeties of initial soil and olumn mateial. 7/54 = 0.13, then it is easonable to neglet the hoizontal omponent of displaement in the einfoed soil mass, espeially at the enteline of tank. Moeove, sine the einfoed soil aea is geate than the tank one, the assumption of zeo hoizontal displaement beomes aeptable. It has evealed min = 13 % does not omply with the allowable settlement of 6 m. Theefoe, by using Columns 1.0 it has pedited the optimal impovement aea atio opt = %. The settlement peditions ae summaized in Table 1 at the ente and the edge of tank. Table 1. Settlement peditions of Tank. Methods Settlement at Centeline (m) Reoded Bouassida et al (2003) Fenh Standad (2005) Balaam & Booke (1981) Piebe (1995) Settlement at dge (m) Figue 3. Tank on impoved soil by stone olumns 5.1 Pedition of beaing apaity By using softwae "Columns 1.0" (Bouassida & Hazza, 2011), fo the Tunisian ase histoy, it is indiated a minimum impovement aea atio min = 13 % is equied. As a matte of fat, the allowable beaing apaity of uneinfoed soil is appoximated by: 5.7 C s/3 = 47.5 kpa that is muh less than the woking load of tank of 120 kpa. Theefoe, a minimum of einfoement by stone olumns equal to 13% of tank s aea is needed to inease the allowable beaing apaity. Adding to the inease of beaing apaity it is notied that the einfoement by stone olumns has led to a signifiant edution of settlement. Fo the majoity of methods, this edution is about five times the settlement of einfoed soil. Also, the ompaison between settlement peditions fo this pojet has shown a good ageement between methods suggested by Bouassida et al (2003), Balaam & Booke (1981) and the Fenh eommendations (2005); despite the diffeene between models of einfoed soil onsideed by these methods all assuming the linea elasti behaviou fo einfoed soil onstituents of RS. In fat, the pedited settlements by these methods appea the losest to eoded data. 5.3 Adopted design The impovement aea atio equals at 35%, the total volume of added mateial is 4,908 m 3. Conside a diamete olumn equals 1.2 m, the spaing between olumns will be 1.9 m and the numbe equals 708. Meanwhile, the design by using Columns 1.0 softwae has led to = 30.64%, the spaing between olumns equals 2.06 m and the numbe of olumns 620. Theefoe, it appeas that an oveestimated design was deided fo this pojet as it an be intepeted fom Figue Pedition of settlement It is assumed that the tank aying load q= 120 kpa is unifom. Fo suh a loading, it esults, on the soil sufae, an exess of vetial stess, denoted, whih vaies with the distane fom the ente line of tank; we have ente = q, and edge = 0.48 q. The settlement of einfoed soil is pedited along a small depth H ompaed to the tank diamete: H/2R =

5 a/s 9,0 8,0 7,0 6,0 5,0 4,0 3,0 2,0 1,0 0,0 Bouassida et al (2003) Fenh standad (2005) Balaam & Booke (1981) Chow (1996) Impovement aea atio (%) Figue 4. Nomalized appaent modulus of einfoed soil vesus the impovement aea atio CONCLUSIONS A methodology has been suggested to allow a ompehensive design of foundations (afts, stip footings, et) esting on einfoed soils by olumns. This methodology suessively onsides the beaing apaity and settlement veifiations in the design poedue as egaded to pevious methods of design whih only fous on unique iteia, i.e. settlement o beaing apaity. The main advantages of the suggested methodology of design ae; its validity fo all olumns tehniques installation, abitay shaped foundations and appliability fo end-beaing and floating olumns. Fo designes, the impovement aea atio is tageted in a given ange omplying with the stability of the foundation. The study of a ase histoy has shown the effiieny of the poposed methodology in the way that an oveestimated design is avoided. In addition, fo patial pupose, the methodology was implemented in Columns 1.0 softwae whih onstitutes a viable tool fo optimized and inteative design appliable to a vaiety of geotehnial stutues. Bouassida, M., Jellali, B., Pobaha, A Limit Analysis of Rigid Foundations on Floating Columns. Intenational Jounal of Geomehanis, ASC. 9 (3) ; Boms, B.G Lime and lime/olumns. Summay and visions. Po. 4th Int. Conf. Gound Impovement Geosystems. Keynote Letue. Helsinki, Finland,June 7th-9th, Fenh Standad, Reommandations su la oneption, le alul, l exéution et le ontôle des olonnes ballastées sous bâtiments et ouvages sensibles au tassement. Revue Fançaise de Géotehnique, 111: Guetif, Z. Bouassida, M. and Debats, J.M Impoved Soft Clay Chaateistis Due to Stone Column Installation. Computes and Geotehnis. 34(2): Piebe, H The design of vibo eplaement. Gound ngineeing, De., Salençon, J An intodution to the yield design theoy and its appliations to soil mehanis. uopean J. of Meh., A. Solids, 9, (5), RFRNCS Balaam, N.P., and Booke, J.R Analysis of igid afts suppoted by ganula piles. Int. J. fo Num. and Analytial Met. in Geomeh., 5(4): Bouassida, M. and Hazza, L. Novel optimized tool of einfoed soil by olumns. Gound Impovement jounal, Aepted, Mah, Bouassida, M., de Buhan, P., and Domieux, L Beaing apaity of a foundation esting on a soil einfoed by a goup of olumns, Géotehnique, IC, 45, (1), Bouassida, M., Guetif, Z., de Buhan, P., and Domieux, L stimation pa une appohe vaiationnelle du tassement d'un sol enfoé pa olonnes. Revue Fançaise de Géotehnique, 102,