state of the art in deep mixing technology. part iv:design considerations
TRANSCRIPT
State of the art in deep mixing technology. Part IV:design considerationsA. PORBAHAOf®ce of Infrastructure Research, Department of Transportation, State of California, 5900Folsom Blvd., Sacramento, CA, 95819, USA (formerly Technical Research Institute, TOACorporation, Yokahama, Japan)
This paper examines various issues related to analysis anddesign of deep mixing (DM) technology. The signi®canceof site characterization in cost-effective design is high-lighted, along with major design considerations, designprinciples based on the allowable-stress or limit stateapproach, and methods to analyse composite ground. Inaddition, a comprehensive design methodology is out-lined, incorporating various modes of external and internalfailure and an optimization scheme. Empirical equationsand coef®cients are provided to be used in the analysis ofcomposite ground. Guidelines and design examples areprovided for special applications of DM to support opencuts, to maintain embankment stability, to prevent baseheave during excavation and for seepage control for damsand levees using DM cut-off walls. Further discussions arepresented of deformation characteristics on the basis ofcentrifuge and ®eld tests, settlement analysis and ®nite-element analysis, coupled with an outline of researchneeds in terms of the analytical aspects of DM.
Keywords: bearing capacity; deep soil mixing; de-sign methods & aids; embankments; slope stability
Cet expose s'inteÂresse aux diffeÂrents aspects lieÂs auxanalyses et aux calculs en technologie de mixage profond(DM). Nous soulignons l'importance de la caracteÂrisationdu site pour la rentabilite de la conception ; noussoulignons aussi d'autres facteurs importants dans lecalcul, entre autres les principles de conception baseÂs surla meÂthode de contrainte admissible ou d'eÂtat limite, et lesmeÂthodes pour analyser un sol composite. De plus, nouspreÂsentons une meÂthodologie de conception compleÁte,incorporant divers modes de ruptures externes et interneset un plan d'optimisation. Nous donnons des eÂquations etcoef®cients empiriques aÁ utiliser dans l'analyse du solcomposite. Nous proposons des linges directrices et desexemples de calcul pour des applications DM speÂciales,pour soutenir les entailles aÁ ciel ouvert, maintenir lastabilite des talus, empeÃcher un boursou¯ement de la basependant l'excavation et controÃler les suintements pour lesbarrages et les digues au moyen de murs eÂcrans DM. NouspreÂsentons d'autres discussions sur les caracteÂristiques dedeÂformation en nous basant sur des essais centrifuges etdes essais sur le terrain, des analyses de tassement, desanalyses d'eÂleÂments ®nis, tout en deÂcrivant les besoins dela recherche au regard des aspects analytiques de DM.
Ground Improvement (2000) 3, 111±125 111
1365-781X # 2000 Thomas Telford Ltd
Introduction
To achieve the full bene®t of ground improvement usingdeep mixing (DM) technology, it is necessary for the designengineer to know the merits and the limitations of thetechnology and to have a clear understanding of theprinciples, estimating procedures and methodology requiredfor analysis and design. A comprehensive site characteriza-tion is indispensable, which should be planned with theunderstanding that reliable estimation of ground propertiesis an integral part of the design solution (see next section)which signi®cantly affects the project cost.
In a broad perspective, the design of DM is composed ofgeomaterial design and geometrical design. Part III in thisseries of papers (Porbaha, 2000) focused on geomaterialdesign, whereas this paper presents issues related to geome-trical design of DM.
The analysis and design process of DM is composed ofseveral steps to evaluate the external stability of the treated
ground under various potential modes of failure, and also toexamine the internal stability, ensuring that the stressesinduced inside the treated ground remain within ranges thatdo not exceed the material capacity. The ®nal design isbased on optimization of the cross-section to include thelong-term serviceability of the treated ground and incorpora-tion of a factor of safety for different modes of failure basedon regional codes of practice.
The engineers involved in design and construction ofDM should be aware that (a) the design process isempirical and based on a trial and error approach, and(b) the design and construction of DM are closelyinterrelated, taking into consideration the availability ofthe construction machinery in the regionÐsince the costof mobilization and demobilization may be quite substan-tial. The past experience or current expertise of thecontractor(s) with the particular type of project (i.e. anoffshore, nearshore or land-based project) is also animportant consideration.
The objective of this paper is to examine several issuesassociated with the analysis and design of deep mixing. Adesign process is outlined, incorporating various modes of
(GI 062) Paper received 28 September 1998; accepted 15 December1999.
external and internal failure along with an optimizationscheme. In addition, guidelines and design examples areprovided to support open cuts, maintain embankmentstability, prevent base heave during excavation, and controlseepage for dams and levees using DM cut-off walls.
Signi®cance of site characterization
Site investigation and reliable estimation of the groundproperties play signi®cant roles in cost-effective design ofDM, and thereby in the total construction cost of a project.For instance, Fig. 1 (Tsuchida and Tanaka, 1995) shows thedesigned cross-sections of a revetment founded on a founda-tion improved by deep cement mixing using two types ofshear strength pro®le. According to the Technical StandardManual for Port and Harbour Facilities in Japan (OverseasCoastal Development Institute of Japan, 1991), the shearstrength of a clay deposit is half of the mean uncon®nedcompressive strength qu. Obtained from site investigationand laboratory tests, pro®les A and B in Fig. 1 representdifferent estimations of the soil strength pro®les at theproject site. The width of the DM improved ground, asshown in the lower part of Fig. 1, is 95 m for the designbased on the shear strength represented by pro®le A, and59 m for the design based on pro®le B. The large differencein volume of the improvement is caused predominantly bythe difference in the estimations of the shear strength pro®leof the ground. The estimated construction cost, which was33 million yen per metre using pro®le A, was reduced to 22million yen owing to enhancement of the characterization ofthe ground pro®le.
Design considerations
The purpose of geometrical design is to determine thepattern, dimensions, improvement area ratio and con®gura-tion of DM on the basis of the following considerations:
· choice of the analytical framework (i.e. allowable-stressdesign or limit state design approaches, effective/total-stress analysis, drained/undrained conditions and 2D/3Danalysis), access to tools for numerical simulation anddesign optimization, and margin of safety (i.e. load factorsand partial or global factors of safety)
· consideration of various loading conditions during thelifetime of the project (i.e. inertia due to earthquakes inseismically prone areas, cyclic load due to machineryvibration, traf®c load, etc.) and load transfer mechanisms(i.e. ¯oating versus bearing)
· consideration of the relative stiffness of the treated soiland the surrounding soil with respect to the function ofthe improvement and the loading condition
· incorporating various modes of failure (i.e. sliding, over-turning, bearing failure, rotational sliding and extrusion)for the designated pattern of DM
· consideration of soil±structure interaction· consideration of displacement (vertical and lateral) and
rotation of the stabilized ground.
Design basis
The traditional design of foundations is based on theallowable-stress design (ASD) basis, which is determinedfrom the ultimate load capacity. However, the limit statedesign (LSD) basis is the current practice in some ®elds,such as structural design. In LSD partial factors are appliedto various elements of the design according to the reliabilitywith which the parameters are known or can be calculated.However, the application of the limit state design philoso-phy to geotechnical design is currently under extensivedebate among the scholars and practitioners (Manfred, 1997;European Foundations, 1997; Driscoll, 1997; EFFC's technicalworking group, 1997). Whereas allowable-stress concepts,such as `allowable strength', are widely accepted and under-stood by geotechnical engineers, the LSD approach is beingprogressively adopted by the new Eurocode (EuropeanCommittee for Standardization, 1993; Gulvanessian andHolicky, 1996). Accordingly, the adoption of a designprinciple is essential for all geotechnical designs, includingdesign of DM.
Methods of analysis
Analyses are carried out in the following frameworks toevaluate the stability and long-term serviceability of im-proved ground.
(a) Analysis of a rigid body: the improved ground isregarded as a rigid structure, and its stability isevaluated under various modes of failure using theconcepts of classical solid mechanics.
(b) Analysis of composite ground: the improved groundand the surrounding soil are regarded as a compositecontinuum. The representative mean shear strengthsare used to examine the stability of the compositesystem.
(c) Analysis of soil±structure interaction: the de¯ectionsand stresses of the improved ground at various loadingstages are examined by analysing the soil±structureinteraction using a numerical technique, such as the®nite-element or the ®nite difference method.
Figure 2 illustrates schematically the DM improvementfor the foundation of an embankment.
Fig. 1. Design for a revetment based on different undrained strengthpro®les
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Porbaha
General design procedure
Design process
The ¯ow chart shown in Fig. 3 outlines the generalmethodology for the analysis and design of DM. Some ofthese steps may be simpli®ed for certain projects. Forinstance, if the structure is not in an earthquake-prone area,then obviously the seismic response analysis is not required.
The ground improved by DM has a large shear strengthand modulus of deformation and a relatively small strain atfailure, compared with the soft unimproved soil. Hence, thestabilized body, regarded as a rigid structure, is analysed byexamining (a) different modes of failure (external stability)and (b) the stresses induced inside the body (internalstability) to ensure that the stresses are within the allowableranges. Accordingly, the most cost-effective cross section ofthe DM is designed on the basis of the data obtained fromthe project site, with consideration of long-term stability andserviceability, in a trial and error process. The regionalstandard codes of practice should be consulted to establishthe safety margins and performance criteria.
External stability
The analysis of the external stability of the improvedground is aimed at examining different modes of failure ofthe DM, including sliding, overturning and bearing-capacityfailure. In addition, the global stability of the system shouldbe examined for a potential rotational sliding failure (or slipalong a plane of weakness) using conventional analyticaltechniques. In this case the slip surface, containing the entirestructure, is passed underneath the treated body. Figure 4illustrates different potential modes of failure of DM for acase of a retaining structure.
As an example, the free-body diagram of the externalloads acting on ground improved by DM for a caisson-typesea wall is shown in Fig. 5. The loads include gravity forces,active and passive earth and water pressures, groundreaction, surcharge loads, the inertia exerted by an earth-quake, and the adhesion representing interaction of the softsoil with the boundaries of the DM.
In the analysis the adhesion between treated and un-treated soil is sometimes disregarded, mainly owing to lackof understanding of the soil±structure interaction. However,several studies have addressed the signi®cance of incorpor-ating adhesion in the analysis of DM (e.g. Tanaka, 1993).
Internal stability
Any safe design requires that the stresses induced insidethe body of a structure due to the external loads do notexceed the capacity of the material. Therefore, it is necessaryto establish allowable stresses for the internal-stability analy-sis. The empirical relationships presented here correlate theallowable strengths (compressive, tensile and shear) with themean uncon®ned compressive strength of a DM obtainedfrom the ®eld, quf. The limitations of the uncon®ned com-pression test for representing the actual ®eld conditionswere discussed in Part III (Porbaha, 2000). The allowablestrengths are given by
óca � á
Fsquf (1a)
á � á1á2á3 (1b)
ôa � 0:50óca (2)
and
ó ta � 0:15óca (3)
where óca is the allowable compressive strength, ôa is theallowable shear strength, ó ta is the allowable tensilestrength and Fs is the factor of safety. á denotes theuncertainties (either systematic or due to data scatter)associated with the con®guration of the DM machine,construction technique, soil variability and so on. á1 is thecorrection factor for the effective width of the treatedcolumn, as shown in Fig. 6 (Japanese Geotechnical Society,1988); á2 represents the reliability of the overlapping(usually less than 1´0); and á3 is a measure of the scatteredstrength. Table 1 summarizes these empirical coef®cients onthe basis of the current practice in Japan (Cement DeepMixing Association of Japan, 1994). Evidently, furtherrecords of case histories will provide better estimates ofthese uncertainties, incorporating regional soil variabilityand construction practice.
If the mean uncon®ned compressive strength of the speci-mens prepared in the laboratory, ql, is used in Equation 1a,then the following relation is applicable:
quf � ëql (4a)
ë � ë1ë2ë3 (4b)
where ë is the overall correction factor representing the
Embankment
Activezone
Passivezone
Improved zone Improved zone
R
r
τfill
τsoil
τc
Potential slipsurface
Fig. 2. Conceptual design approaches
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Deep mixing technology. Part IV
discrepancy of the ®eld and laboratory test results. ë1 is thecorrection factor for variations in geomaterial manufacturingin the ®eld; ë2 is the time-dependent coef®cient correlatingthe geomaterial strength at time t with the long-termstrength; and ë3 is the coef®cient of durability due toenvironmental effects. The coef®cients in Equation 4b are yetto be established through further research and ®eld obser-vations.
Although the uncon®ned compression test is consideredhere, some attempts to use the triaxial test were reported byHashimoto et al. (1994).
The internal stress distribution may be evaluated using anumerical technique, such as the ®nite-element method,under various loading conditions during and after construc-tion.
Fig. 3. Design process for DM
Translational sliding Overturning
Bearing failure Rotational sliding
Potentialslipsurface
Fig. 4. Idealized potential modes of failure of DM
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Porbaha
Extrusion failure
In the case of wall-type DM there is a possibility that theuntreated soft soil in between the long walls may besqueezed out owing to the unbalanced forces caused byactive and passive earth pressures acting on the DM. Thisphenomenon is referred to as extrusion failure (Terashi et al.,1983), breakthrough or tunnel action.
Several methods are available for the analysis of extrusionfailure on the basis of the assumed failure patterns. Onemethod is to assume that the soft soil in between the longwalls moves as a rigid prism with an oval section directedalong a tunnel. The oval is bounded by the space between
the long walls with a length equal to the width of theimproved ground, as shown in Fig. 7. The height of the ovalis estimated from balance of the forces acting, while the topportion of the oval is ®xed to the bottom of the short wall.The extruding force acts at one end of the prism (the ®llingside), directed towards the sea. On the basis of thissimpli®ed model, the safety factor for extrusion failure isde®ned as the ratio of resistance force to extruding force,and is calculated as (Honjo, 1981)
Fs � Pr=Pe (5a)
Pr Bs(ða� 2ma)[C0 � C1(Ds � 2(m� 1)=2)] (5b)
and
Pe � ÄP(ða2=4� ma2) (5c)
where Pr is the resistance force, Pe is the extruding ordriving force, ÄP is the lateral force increment on theback®ll side, Bs and Ds are the width and length of the shortwall, respectively, a is the thickness of the unimproved partand m is the shape factor, which is de®ned as
m � 0:25ð[1� 8(C0=aC1 � Ds=aÿ 0:25ð� 0:50)]0:5 ÿ 1 (5d)
where C0 and C1 are the intercept and rate of increase ofcohesion with depth, respectively.
Pw1
Pc1
Pc2
Pa
W1
W2
Hk1
Hk2
Pw2Pp
Surcharge
Fig. 5. Schematic diagram of external forces acting on DM-improved ground
Dx
D y
l x
l y
ax = l x/Dxay = l y/Dy
Fig. 6. Illustration of effective width of DM
Table 1. Empirical reduction coef®cients
Coef®cient Current range of practice
á1 0´7±0´9
á2 0´8±0´9
á3 0´50±0´66
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Deep mixing technology. Part IV
Design optimization
In the design procedure discussed earlier, the differentmodes of failure are examined independently. Evidently, itis unlikely that all of these failures will occur simulta-neously. In many situations, depending on the type ofstructure, loading and site conditions, the potential for oneor more failure mechanism(s) may be predominant. Accord-ingly, optimization of the geometrical design of DM iscarried out on the basis of trial and error to obtain the mostreliable and cost-effective cross-section.
As an example, the revetment shown in Fig. 8 (Terashi etal., 1983) is a concrete caisson retaining structure to beconstructed on a soft clay layer underlain by a bearingstratum of dense sand. In this hypothetical case the ®rstestimate of the DM width is shown by the dotted linesenclosing the base of the caisson and the sand mound. Thewidth of the foundation (B) is calculated by extending theimproved ground beyond the caisson, as de®ned by a and/or b, so as to satisfy the designated factor of safety. The threelines (I, II and III) plotted in the ®gure suggest the minimumwidth of the DM satisfying the requirements of sliding (lineI), induced shear stress at the toe (line II) and the shearstress in the vertical plane in front of the superstructure (lineIII). The arrows on the lines show the direction towards ahigher factor of safety. The hatched zone satis®es therequirements of stability, and point A, representing theminimum width of the DM, is considered to be the optimumdesign. According to Terashi et al. (1983), for this exampleoverturning, bearing capacity and extrusion were not gov-erning modes of failure.
Recent advances in reliability theory and its application in
civil engineering (e.g. Ditlevsen, 1981; Dai and Wang, 1992;Low and Tang, 1997) prompt the need for developing areliability-based methodology for the design of DM-im-proved ground. In addition, numerical simulations arepowerful tools for stress analysis and optimization of thedesigned section (as will be discussed later on), incorporat-ing long-term serviceability.
Design of column-type DM
Group column DM has been applied in a variety ofground improvement projects (Porbaha et al., 1998). For thedesign of column-type DM, stability analysis is usuallycarried out with the assumption that the composite ground(i.e. the DM and the surrounding soil) has a mean weightedshear strength, denoted as ôc and expressed as (Fig. 9)
ôc � acôcol � (1ÿ ac)ôsoil (6)
where ôcol is the mean shear strength of the DM columns,ôsoil is the mean shear strength of the soft ground and ac isthe replacement area ratio, de®ned as the area of thecolumns to the total area of the improved ground.
On the basis of ®eld observations, as shown in Fig. 10(Amano et al., 1986; Hayashi, 1990), DM columns subjectedto embankment loading have exhibited deformation patternsconsistent with bending failure.
The ultimate shear strength ôf of a lime/cement columnunder an embankment loading, considering bending failure,as shown in Fig. 11 (Kivelo, 1997), is as follows:
ôf � 24
ð
�����������������������������������Mucu2
D3(1� Cu2=Cu1)
s(7a)
Mu,max � 1
12óucc D3 (7b)
where Mu is the moment capacity of a column section, óucc
is the compressive strength of the column, Cu1 and Cu2 arethe undrained cohesion of the soil inside and below theassumed failure surface respectively, and D is the diameterof the column.
This mode of failure is not currently incorporated into thedesign procedure, mainly owing to lack of understanding ofthis phenomenon. Consequently, further research is neededto shed light on the potential bending failure of DM.
Seabed
Short wallShort wall
Long wall Long wall
Caisson
Tunnel action
Improved zone
D
B
Fig. 7. Examination of extrusion failure of wall-type DM
Fig. 8. Example of design optimization
Column
Soil
Strain
She
ar s
tren
gth
Composite ground
Column
Slip surface
Soil
τc
τs
τsτc
τcompositeτcτs
Fig. 9. Stress±strain diagram of composite ground
116
Porbaha
Design guidelines for specialapplications
Guidelines and design examples are presented here formaintaining stability of open cuts and embankments on softground, for protecting the bottom of an excavation fromheave action and for cut-off walls for seepage control.
Design of DM for stability of open cuts
GeneralThe purpose of DM for open cuts is to act as a permanent
support system maintaining stability of the excavated areaagainst the lateral soil pressure, while controlling deforma-tion and settlement of the adjacent structures.
Design exampleA cross-section of the DM designed for a permanent open
cut at Tokyo international airport is shown in Fig. 12 (Shiomiet al., 1996). The stability against sliding was analysed byexamining the balance of horizontal forces acting on theDM. The safety factor against sliding is then expressed as
(Fs)sliding � (Pp � S)=Pa (8)
where Pp and Pa are the total passive and active earthpressures, respectively, acting on the rigid body and S is the
total shearing resistance mobilized along the bottom of theDM.
The stability against overturning was analysed by examin-ing the moment of the external forces acting at the toe of therigid block on the excavated side. The factor of safety foroverturning is then calculated as
(Fs)Ov � (Pp lp �Wlw)=(Pa la) (9)
where W is the weight of the treated soil mass, lw is themoment arm of W from the excavated side, and lp and la
are the moment arms of Pp and Pa from the bottom of theDM. The simpli®ed design for this project was not sorigorous as to consider deformation of the supportingground, and thus the centre of rotation was unlikely to be atthe toe.
The distribution of contact pressures along the bottom ofthe DM was estimated from the equilibrium of Pa, Pp, Wand S. The contact pressure at the corner of the excavatedside (t1) is much larger than that at the back (t2) owing tothe large tilting moment induced by the active side (Pa la). Ifthe maximum contact pressure t1 is larger than the bearingcapacity of the native ground below the treated soil, then thesafety factor against bearing capacity failure becomes lessthan one, which may lead to failure.
To take full advantage of the shearing resistance of thebearing stratum and to avoid problems associated with a¯oating-type DM, a decision was made to rest the bottom ofthe DM on a bearing layer at a depth of 20 m below theground surface. Hence, the remaining part of the design wasto calculate the width of the improved ground. The resultsof the stability analysis are presented in Table 2, where thesafety factors against sliding and overturning for all cases
Fig. 10. Lateral displacement of DM columns
Soil 1
Soil 2
Passivezone
Shear Bending
Assumed slip surface
Fig. 11. DM subject to embankment loading
Contact pressure
Pp
Pa
lp
lw
t1t2
la
w
S
w = 10 kPa
Fig. 12. Free-body diagram of DM at Tokyo international airport
Table 2. Summary of calculated safety factors�
Case
Width of
DM: (m)
Safetyfactor
(sliding)
Safetyfactor
(overturning)
Bearing capacity(qa and t1):
kPa
I 16´5 1´67 3´10 429 , 455
II 13´2 1´59 2´36 506 . 446III 10´0 1´51 1´77 659 . 436
� qa � allowable bearing capacity.t1 � maximum contact pressure.
Shear strength of ground (kPa): 35 � 2´1z (where z is the depth).
117
Deep mixing technology. Part IV
are more than the minimum value of 1´2 adopted. On theother hand, if the width is less than 16´5 m, the contactpressure t1 is greater than the allowable bearing capacity(qa) of the original ground. Therefore, the width wascalculated on the basis of the maximum contact pressure t1
with the aim of making this less than the allowable bearingcapacity. The internal stability was examined by ®nite-element analysis, assuming that the treated soil was a linearelastic material. The ®nal design cross-section of the DM-improved ground is shown in Fig. 13 (Shiomi et al., 1996).
Design of DM for embankment support
GeneralThe construction of an embankment on soft ground
requires improvement at the shoulder or at the toe, or fullimprovement of the base, to maintain stability and to controlsettlement (Amano et al., 1986; Evstatiev et al., 1995; Xu,1996).
Design exampleFor the construction of an embankment on deep soft
ground with an undrained shear strength of 20 kPa, calcula-tions showed that the factor of safety for the embankmentwithout improvement was 1´13, and that slip surfaces with afactor of safety less than 1´5 extended to a depth of about10 m below the ground level (Carlsten, 1995). The completedroad embankment represented a load of 67 kPa. Thediameter of and spacing between the columns were obtainedby performing a stability analysis, as summarized in Table 3.
The calculations show that in terms of stability, fewercolumns are required if lime±cement columns are installedinstead of lime columns. For lime columns 500 mm indiameter, 16 columns are needed over the width of thereinforced area, which is equivalent to 13´3 columns permetre of road for a column spacing of 1´2 m. For lime±
cement columns 600 mm in diameter, 14 columns areneeded, which is equivalent to 11 columns per metre run at1´4 m spacing.
Design for excavation support
GeneralSeveral projects reported the use of soil±cement for
excavation control in soft ground (Mihashi et al., 1987;Furuya et al., 1988, Ou et al., 1996). In the case of deepexcavation of soft ground, stability against heave action is amajor problem during construction. The conventional meth-od to examine the stability against base failure is the slipcircle method. The dimensionless stability charts based onthe Janbu method (1954) are available (O'Rourke andO'Donnell, 1997) to evaluate the deep rotational slip of tieback excavation in clay (Figure 14). A typical design chartfor the case of è � 10 (where è is the inclination of the tieback to the horizontal) is shown in Figure 15.
To increase the bending resistance of a soil±cement wall
16·5
1·0 1·01·58·0 5·0
20·5
14·0
4·0
2·5
Improved zone
Bs
Ac1
Ac1
Ac2
As1
+2·5
–4·0
–7·0
–16·0
–18·0
0
Fig. 13. Final design section of DM for open cut (dimensions in metres)
Critical centre
Anchor bond zone
Firm base
3 m
B X
YH
D
W
θ
X = x0HY = y0H
Fig. 14. Tie-back anchored wall
6·5
6·0
5·5
1·6
1·4
1·2
1·0
0·6
0·4
0·2
0
Sta
bilit
y nu
mbe
r N
sU
nit c
entr
e or
dina
te y
0U
nit c
entr
e ab
scis
sa x
0
0 0·5 1·0 2·01·5 2·5Width/height of excavation B/H
W/H1·50
1·50
1·25
1·25
1·00
1·00
1·50
1·25
1·00
Fig. 15. Dimensionless stability charts for evaluating deep rotational slip fortie-back excavation in clay
Table 3. Maximum column spacing (centre to centre) for safety factor >1.5�
Type of column d � 500 mm d � 600 mm
Lime columns: (m) 1´1 1´3Lime±cement columns: (m) 1´2 1´4
� d � diameter of the column.Width of improvement � 20 m.
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Porbaha
for excavation, a core steel reinforcement (such as wide-¯ange H-beam or sheet piles) is sometimes used to counter-act lateral earth pressure. The structural design of the H-beam is similar to the design of a ¯exible wall, and thespacing between the vertical beams is estimated on the basisan internal-stress analysis of the soil±cement (using anumerical technique, such as ®nite-element analysis), andmaintaining the stresses within the allowable limits. Figure16 (Pearlman and Himick, 1993) shows a cross-section of acore-reinforced soil mix wall for an excavation. Two modelsfor bending and shear were applied to design the spacingbetween the steel soldier piles.
Design exampleDM was applied to increase the passive resistance and
thus to maintain the base stability of an excavation site atTokyo international airport in Japan, as schematically shownin Figs 17 and 18 (Tanaka, 1994). Stability analysis wasconducted using the slip circle method, with the centre ofthe circle assuming to act at the lowest strut. Following therecommendations of Janbu (1954) and Peck (1969), thestability factor Nt for rotational sliding was de®ned as
Nt � ãH=Su (10)
where ã is the unit weight of the untreated soil, H is theexcavated depth and Su is the undrained shear strength of
the untreated soil at the bottom of the excavation. It wasfound that a stability factor of 4±5 was required to maintainstability against base heave.
The excavation of Boston blue marine clay for the BostonCentral Artery/Tunnel project presented many challengesfor the design engineers (Lambrechts and Roy, 1997).O'Rourke and O'Donnell (1997) reported a tie-back excava-tion for this project. A combination of a soil mix wall and jetgrouting was used to reinforce the excavated base againstdeep rotational failure.
Other projects that have used soil±cement for excavationare the Cypress freeway project in Oakland, California, andexcavation of a bay mud for a box sewer in San Francisco(Schaefer, 1997).
Design for seepage control
GeneralThe prime issue in the design of DM as a cut-off wall for
seepage control is the coef®cient of permeability, which isin¯uenced by many factors, including the soil type, cementcontent, water±cement ratio, bentonite content, grout injec-tion rate, time (or age) and curing environment. Therefore,
Lateral pressure
Lateral pressure
C L C L C L
C L C L
Soldier pile
Soldier pile Soldier pile
Soldier pileSpan
SMW
SMW
v v
Model for checking shear
Model of soil–cement arch
Fig. 16. A core-reinforced soil±cement wall for an excavation (SMW = SoilMixed Wall)
3·4
3·1
3·1
3·1
2·9
3·4
9·5
29·0
Cla
y 1
San
dC
lay
2
Ground level
Deepsoilmixing
Jetgrouting
1·0
5·25 5·256·65 6·6
30·5
6·65
1·0
Fig. 17. Design of DM for base heave (dimensions in metres)
Deepsoilmixing
Lowest strut
H
q
x ′
α
Su
dθ
W
Fig. 18. Design method for base stability
119
Deep mixing technology. Part IV
the design of DM for cut-off wall is mainly associated withgeomaterial design (Porbaha 2000). A cut-off wall in deepalluvium under a high earth/rock®ll dam should resist ahigh con®ning pressure. Thus, the stresses and deformationsof a deep cut-off wall should also be examined so that theydo not exceed the allowable limits.
Some test results from laboratory samples for a pilotstudy are shown in Fig. 19 (Taki and Yang, 1991). Thepermeability test results range from 10ÿ5 to 10ÿ8 cm=s andare based on laboratory testing of ®eld-wet samples obtainedduring trial construction. A coef®cient of permeability of1 3 10ÿ6 cm=s or less is usually required for permanentseepage control.
Further studies on permeability were reported by Mori etal. (1990) and Kurita et al. (1990). Suttoh et al. (1983) reportedbasic studies of a soil±cement mixture for a cut-off wall.
Design examplesFor the Lockington Dam project in Ohio, USA, Walker
(1994) reported twelve soil±cement±bentonite mix designsfor cut-off wall construction. The permeability of the mix-ture, measured on the basis of ASTM D-5084 (AmericanSociety for Testing and Materials 1997), was speci®ed as1 3 10ÿ6 cm=s, and the minimum cement content was 6% byweight of the mixture. The cement/water ratios by weightranged from 14 to 33%. Using an auger ¯ight 0´9 m indiameter, a total of 6200 m2 of wall was installed down to amaximum depth of 6´5 m.
For the spillway of Lake Cushman in Washington, a soil±cement core wall 61 cm thick was installed to a maximumdepth of 43 m to reach the bedrock (Cotton and Butler, 1990;Sehgal et al., 1992). The core material had an averagecompressive strength of 2´254 MPa and a permeability of1 3 106 cm=s. The cement content used for this project wasquite high, ranging from 350 to 550 kg per cubic metre of insitu soil.
Nishikiguri et al. (1988) and Matsumura et al. (1989)reported a cut-off wall for the Tadami Dam project in Japan.
Deformation characteristics
Centrifuge tests
The deformation characteristics of ground improved by agroup of cement-treated columns subject to embankmentloading, obtained using a geotechnical centrifuge, are shownin Fig. 20 (Miyake et al., 1991). A model ground with areplacement area ratio of 50% (cases 1 and 2) and 23% to38% (case 3) in three different con®gurations was subjectedto embankment loading. Figure 21 (Miyake et al., 1991)illustrates how the reinforcement con®guration affects thedeformation pattern of the ground improved by the DM.
The deformation characteristics of ground improved bywall-type DM, obtained using a geotechnical centrifuge, areshown in Fig. 22 (Kitazume and Terashi, 1991) for threecases with different improvement area ratios. Large displa-cements and a large-diameter slip circle were observed forcase 1, without any reinforcement. In the second case, with asmall improved area (40 mm wide), large displacement tookplace in the upper half of the ground and an almost linearfailure surface was observed in the passive side of thetreated soil, rather than a curvilinear slip surface. In case 3,where the width of the improved area was doubled, thedisplacement remained small and there was a tendency forrotational sliding.
The limitations of model tests for the quanti®cation ofdeformation require one to be cautious when the results areextrapolated to a real-world case, mainly owing to theproblems associated with scaling and boundary effects.These effects have been addressed in a number of investiga-tions (e.g. Foray et al., 1998; Sartoris et al., 1998).
Field test
The behaviour of column and wall-type DM was studiedin a ®eld test of a 5 m high embankment on soft Bangkokclay. A plan and cross-section of the test embankment areshown in Figs 23 and 24 (Honjo et al., 1991). The foundationof the embankment was improved by a wall-type pattern inone side and a column-type pattern in the other side. Anamount of 100 kg of Portland cement was used for one cubicmetre of treated soil. The laboratory uncon®ned compressivestrength of the stabilized mass, cured for 28 days, was up to20 times that of the native soil. As shown in Fig. 25 (Honjoet al., 1991), the settlements and lateral movements of thewall-type improved ground were less than that of thecolumn-type improved ground when subjected to the sameloading conditions. Furthermore, the deformation pattern ofthe column type was tilting, i.e. simple shear deformation,while the deformation pattern of the wall type was sliding.Unsurprisingly, the wall-type DM was found to be moreeffective in reducing the lateral and vertical deformations.
Example of a project
Soil mix walls with anchored tie-backs were applied forthe support of an excavation 13´9±19´4 m deep and 59±87 mwide in Boston clay. The patterns of the maximum horizon-tal movements were found to have a close correlation withthe thickness of the stabilized ground. Figure 26 (O'Rourkeet al., 1998) shows the lateral displacements at two inclin-ometers, where dH and Hc are the maximum differentialmovement from the bottom of the marine clay and thethickness of the lower-strength clay, respectively. The meanstrength of the soil±cement obtained from uncon®ned com-pression tests was 3´83 MN=m2, with an standard deviation
Fig. 19. Variation of coef®cient of permeability with cement content forthree projects
120
Porbaha
Embankment Embankment Embankment
1·50 1·50 1·500·75
1·50
1·25
Improved zone Improved zone Improved zone(50%) (50%) (23%and 38%)
Fig. 20. Deformation characteristics of DM columns (dimensions in metres)
10 mm
10 m
m
10 mm
10 m
m
10 mm
10 m
m
Embankment
Embankment
Embankment
Improved zone
Improved zone
Improved zone
Fig. 21. Displacement vectors of improved ground
Caisson
Caisson
Caisson
Sand mound
Sand mound
Sand mound
Case 1
Case 2
Case 3
Improved zone
Improved zone
Displacement: mm0–1 1–2 2–3 3–4 4–6 6–8 8–
Fig. 22. Deformation characteristics of DM walls
121
Deep mixing technology. Part IV
of 1´87 MN=m2 for 37 specimens 37 mm in diameter. Themaximum horizontal movement occurred at approximatelyelevation 20�5, where stiff overconsolidated clay (upper clay)grades into lower-strength marine clay at depth.
Settlement analysis
The consolidation settlement of improved ground withcolumn reinforcement is estimated from the followingrelationships (Fig. 27):
S � âS0 (11a)
â � óc
ó� 1
(nÿ 1)ap � 1(11b)
S0 � mvo Hc Äp (11c)
where óc is the stress applied to untreated soil, ó is thestress increment, ap is the replacement area ratio, mvo is thecoef®cient of volume compressibility of the untreated soil(óp=óc � mvo=mvp, in which mvp is the coef®cient of volumecompressibility of the treated soil), n is the stress concentra-tion ratio, Hc is the thickness of the improved zone and Äp
is the load increment (Cement Deep Mixing Association ofJapan, 1994).
Yoshikuni and Nakanoda (1974, 1975) proposed theconcept of consolidation potential, in which the treated ground
GL 05·0
8·0 1·
0
6·5
2·8
7·0 5·0
55
77
152·0
6·515
Toeexcavation
Toeexcavation
Embankment
GL
0
GL
+ 5
·0
Excavation depth: 2 mExcavation slope: 1:1
Fig. 23. Plan and cross-section of test embankment improved by DM(dimensions in metres)
GL –20
GL –10
GL +50
5 5 5 7 93 1 3 3 31 1 1Movement: cmMovement: cm Ground level
IWTF
IWUF
IWTB
IWUB
IPTB
IPUB
IPTF
IPUF
3
5
7
9
11
Dep
th: m
Wall-type DM Column-type DM
Fig. 24. Lateral movement of wall- and column-type DM after 71 days
Embankment
Improved
Unimproved
0
–5
–20
–10
–15
–25
–30
–35
–40
Set
tlem
ent:
m
0 2 4 6 8 10 12 14Horizontal distance: m
Fig. 25. Settlement of embankment at a depth of 1 m after 71 days
122
Porbaha
is assumed to be an elastic material without radial ¯ow,owing to low permeability. When the applied load isconstant with time, the rate of consolidation of the compo-site ground is expressed as
@U=@ t � Cvu @2u=@z2 � îduav=dt (12)
where Cvu is the coef®cient of consolidation of the untreatedsoil, uav is the average pore water pressure and î is aconstant denoting the stress concentration, which is a func-tion of the improvement area ratio (ap) and coef®cient ofvolume compressibility (mv). When the ground is unim-proved (î � 0) there is no lateral deformation of treated soil,and thereby the equation is equivalent to Terzaghi's con-solidation equation. A three-dimensional analysis of consoli-dation settlement was applied to ground stabilized usinglime/cement columns, as reported by Baker (1999).
Finite-element analysis
The ®nite-element method (FEM) is a powerful numericaltechnique that is widely applied for solution of variousengineering problems. A great deal of literature about theprinciples of the FEM modelling technique is available (e.g.Britto and Gunn, 1987; Zienkiewicz and Taylor, 1990). Anumber of issues arise when this technique is used for theanalysis of practical problems (Woods and Clayton, 1993),which can be divided into the following categories:
· geometric modelling and discretization: issues related tomesh size, boundaries, element size, interface elements,etc.
· constitutive modelling and parameter selection: issuesrelevant to non-homogeneity, anisotropy, small-strain be-haviour, linearity, yielding and normality
· simulating the construction process and modelling theinstallation, and pore pressure equalization
· problems related to computational dif®culties relevant todisparate stiffnesses the incremental solution scheme,drained/undrained conditions, etc.
Despite these dif®culties the FEM has been applied for anumber of cases (e.g. Okabayashi and Kawamura, 1991;Babasaki et al., 1992; Lambrechts and Roy, 1997; Nicholsonet al., 1998). Fukutake and Ohtsuki (1995) reported a three-dimensional effective-stress analysis for liquefaction preven-tion of ground improved by the deep mixing method.
The behaviour of excavations using the column type ofDM can theoretically be evaluated by simulating the actualdistribution of the soil columns and the excavation sequenceusing a 3D ®nite-element method (Ou et al., 1996). However,this generally requires a large amount of computer storageand computation time because a ®ne ®nite-element mesh isrequired. For this reason, a method for evaluating the overallmaterial properties of the treated soil mass was proposed by
35
30
25
20
15
10
5
–5
0
Ele
vatio
n: m
35
30
25
20
15
10
5
–5
0E
leva
tion:
m
0 20 40 60 80Lateral displacement: mm
0 20 40 60 80Lateral displacement: mm
Fill
Organic silt
Marine clay
Fill
Organic silt
Marine clay
Upper GM
Lower GM
Lower GM
Glacial tillGlacial till
Glaciofluvial
Deepsoil
mixing
Deepsoil
mixing
Tie-backs Tie-backs
Hc
dH
Fig. 26. Horizontal displacement of a DM-improved excavation in Boston clay
Hc
S
σ = ∆P
σp
σc
Soil
Column
Fig. 27. Settlement analysis of DM-improved ground
123
Deep mixing technology. Part IV
Ou et al. (1996), in which the treated soil area was replacedby a single material during analysis. By this means, the 3Danalysis was then performed with less computer storage andcomputation.
Summary and research needs
This paper has presented various issues related to theanalysis and design of DM, covering design considerations;design principles; methods of analysis, coupled with a ¯owchart for comprehensive design; and empirical relations andcoef®cients. In addition, guidelines have been provided forspecial applications of DM, the deformation characteristicsof column-type and wall-type DM, settlement analysis, andnumerical analysis using the ®nite-element method.
Despite the large number of DM projects applied forvarious purposes around the world, the design of DM is stillhighly empirical. Some of the research needs in terms ofanalysis and design of DM can be outlined as follows:
· understanding the soil±structure interaction· investigating the effect of relative stiffness (treated and
untreated) on the behaviour of the improved ground· investigating the ¯exural rigidity of column-type DM
subject to the bending failure mechanism· reports of case histories with the aim of improvement of
the empirical coef®cients currently being used in theanalysis
· developing a reliability-based design methodology· elaboration on the analysis of DM based on the limit state
design (LSD) principle.
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Discussion contributions on this paper should reach thesecretary by 25 October 2000
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