recent advances in large diameter diaphragm wall shafts

RECENT ADVANCES IN LARGE DIAMETER DIAPHRAGM WALL SHAFTSBenoit Virollet and Christian Gilbert, Soletanche-Bachy, Nantarre, France, andRick Deschamps, Nicholson Construction, Pittsburgh, PAOver the last 10 years the diameter of unbraced, unlined and unanchored circularshafts has grown dramatically in many parts of the world. This progress hastaken place through improvements in: construction methods; concrete rheology;and design capabilities. Excavation equipment has become more precise interms of operator control and ability to correct alignment of digging elementsleading to better alignment tolerances. Also contributing to the increases in shaftdiameters is the evolution of design models. A better understanding of soilstructure interaction is being incorporated into the analyses in terms of radial soilstresses and imposed loads on the shaft. This paper provides an overview of therecent progress made in circular shaft construction, the primary designconsiderations, and some innovative uses of efficient arc elements to developunsupported structures of other shapes. In addition, a summary of recentcircular shafts constructed worldwide is provided.IntroductionCircular diaphragm walls are constructed withthe same techniques that are used to constructplane walls. They are built in situ under a drillingfluid which stabilizes the excavation. Thesurrounding soil acts as the formwork forconstructing the concrete elements. A deeppanel trench is first excavated and stabilised bybentonite slurry. When excavated to the desireddepth, the reinforcement cage is installed andconcrete is tremie poured from the bottomdisplacing the lighter bentonite. The stability ofthe trench is ensured by both the slurry and thearching of the soil on each side of the excavatedpanel. Accordingly, the trench length is limited inorder take advantage of the arching such thatthe diaphragm wall is built through a series ofindependent panels. "Water stops" andinterlocking joints are installed between panelsto ensure the water tightness of the wall andshear transfer between panels. Excavationbegins after the panels have achieved designstrength.The tools used to excavate the panels have arectangular shape, the length of which is on theorder of three meters (Figure 1). In practice, thepanels are generally made of three "bites," twoindependent bites with a connecting smaller biteto control clamshell alignment. Therefore, thetypical panel lengths are approximately sevenmeters.The primary objective of this paper is tointroduce a cost effective construction approachfor support of excavation for circular shafts to abroader audience in the United States. Thetechniques described are used on a routinebasis and on a much greater scale in other partsof the world than are currently employed inNorth America. The technology is available interms of equipment and methods of analysis,and there are several contractors with thecapacity to competitively bid and build this work.Accordingly, it is hoped that designers willbecome familiar with the cost savings andimproved certainty of execution with thisapproach relative to alternative systems such assunken caissons. These systems are especiallyattractive solutions to the EPA mandated CSOstructures being constructed in manycommunities.Basic Mechanical Behaviour of a CircularShapeCircular walls are unique in that they cannotconverge freely when loaded externally.Consider a thin circular wall with a radius "R"that is subjected to an axisymmetrical pressure"p". The force equilibrium diagram shows that

pRR-uuN hdθdθ2N h dθ2pRdθpN hFigure 2 : Free body diagram of a circularsegment.Figure 1. Clamshell bucket.the reaction to the external pressure produces acompressive "hoop" force in the wall whichresists the tendency to converge. This isexpressed in Figure 2 where a free bodydiagram of a segment of wall is shown. Thehoop force , N h , is related to theapplied external pressure by the relationship :N h = p R (1)No extra support is required to balance theexternal forces. This is the reason why circularwalls are inherently stable provided the hoopforce does not exceed the limits of the materialproperties.A circumferential stiffness that relates theapplied pressure to the radial displacement, ∆R,can be defined as follows :P = E t ∆R / R 2 (2)"E" is Young’s modulus of ring material and t isthe wall thickness. This relationship obtained fora ring is used for the three dimensional circularwall under axisymmetrical pressure diagrams.Advantages of Circular Diaphragm WallsBased on the previous remarks, circulardiaphragm walls provide a lot of advantagescompared to plane walls. They do not needsupports such as struts or tie-back anchors.Excavation works can be achieved quicklywithout complicated construction sequence orcoordination between the excavator and anchorinstaller.Another benefit of the inherently stable circulardiaphragm walls lies in the much lessened needfor embedment to provide wall stability.Obviously other criteria for embedment must beconsidered, such as hydraulic stability (i.e.piping) and basal stability, but embedment formechanical stability of toe is unnecessary.It should also be recognized that as the hoopforce provides a stiff continuous support to thewall, the bending moment and shear force in thewall remain generally small leading to "light"reinforcement ratios.Design of Circular Diaphragm WallsWall Alignment. The design of circulardiaphragm walls can require some unusualconsiderations which leads to a need for

detailed analyses. Tied to the analysis is arigorous control of construction tolerances. Thestabilizing hoop force produces a normalcompressive stress in the structure which islimited by the strength of the concrete. Thiscompressive stress is a function not only of thehoop force but also of the thickness of the ring.As described previously, diaphragm walls areconstructed by individual panels. These panelsare excavated with a rectangular shape shovel(Figure 1) such that it isn't possible to constructa perfect ring (Figure 3). Moreover, theexcavation of the panels is done with a specifiedvertical tolerance, which makes the shape of thewall deviate further from the ideal geometry withdepth (Figure 3b). It is therefore essential to beable to control as much as possible theverticality of the excavating tool. This toleranceessentially depends on the experience of theoperator but also on the type of tool (mechanicgrab, hydraulic grab or hydrofraise), the type ofsoil (presence of boulders or not, stiffness of thesoil, etc.) and the quality control duringexcavation. This control is done through onboard instrumentation that allows for real timemeasurement of, and the ability to correct,deviation. Typical specified tolerance indeviation is in the order of 1% of the wall height,but 0.5% can be commonly achieved in practice.Regardless of the vertical tolerance achieved,the actual geometry will not be a perfect ring.The common approach used to take intoaccount the "real" geometry is to inscribe anannulus into the actual shape and calculate thewall loads neglecting the concrete outside thisannulus. This method is very conservativebecause an inscribed annulus is not anecessary condition for stability because thewall is capable of resisting bending and shearstresses. This is easily demonstrated byconsidering self stable elliptical shafts whereinan inscribed circle is not possible. An exampleis shown in Figure 4 of the Méricourt CSO shaft.Wall Shape. With elliptical shafts the externalsoil provides the required extra reaction tomaintain stability. The wall sections experiencevarying bending moments with location inaddition to the compressive stresses becausethe radial strains/displacements are no longeruniform. The stresses resulting from the actualgeometry are evaluated by modelling the wall asa horizontal beam in interaction with an elasticplastic soil on one side only. This model givesthe normal forces, N, and the bending moments,M, at each node. This model allows for theP3P2e = 0.5mL = 2.8mP4P1Φ int = 16mP5P8P6P7(a)(b)Figure 3 : Shape of a circular diaphragm wall including (la) grab geometry without deviation and(b) grab geometry and deviation.

assessment of specific concrete sections underthe varying state of stress. However, thisapproach is still conservative as it assumes thesoil pressure is constant. In reality, the soilpressure decreases with radial strain thusreducing the bending moment. Other moresophisticated methods exist such as finiteelements models, which are capable of comingcloser to the real system, but in practice aredifficult to carry out.pressure. The Hain solution takes account ofthe surrounding soil but not the threedimensional effects. The factors of safety givenby these two cases generally lead to a lowerbound of the overall factor of safety.Wall Openings. Circular walls are relatively“easy” to calculate as long as the outsideloading is symmetrical. However, theassessment of their behaviour becomes moredifficult when asymmetry occurs. For example,the case of a circular wall with an opening is athree dimensional problem. The presence ofopening affects the internal forces in the wall.Because the hoop stresses can no longer begenerated at the opening level, force equilibriumis balanced by higher stresses being generatedon both sides of the opening as shownschematically in Figure 5. This concentration incompressive stress also produces a zone ofvertical tension due to the distortional strains.Additionally, the panels adjacent to the openingtend to be "softer" producing larger bendingmoments in the ring at opening level.(3) Displacement =>Bending momentFigure 4. Elliptical unsupported CSO shaft atMéricourt, France.Wall Buckling. The high compressive hoopstresses that are generated must also beevaluated in terms of buckling. This check isdifficult to carry out as the problem is threedimensional and non-linear. Three dimensionalbecause the surrounding soil pressure varieswith depth and there is restraint from the passivesoil stress below the base and from the capbeam. It is non-linear because loads on the wallvary with strain/displacement of the wall.Fortunately, closed-form solutions weredeveloped for some simple but related casesand these allow the factor of safety againstbuckling to be estimated. Timoshenko and Gere(1961) solved the case of a cylinder fixed at itsends under a uniform pressure. Hain (1968)solved the case of a ring in interaction with anelastic soil on the exterior. The Timoshenkosolution takes into account some of the threedimensional effects but not the varying soil(1) Compression(2) TensionFigure 5. Changes in stresses aroundopenings in wall.The stress conditions can be evaluated with atwo dimensional approach. The increasedbending moment can be estimated by reducingthe hoop stiffness at the opening level. Thereduction factor is a function of the diameter of

the wall, the diameter of the opening and thecurvilinear abscissa. The tension stress and theconcentration of hoop stress is estimated with aplane plate calculationProducing Other Shaped Walls with CircularArcsAlternatives to rectangular walls can often beconstructed with circular arc segments therebyreducing or eliminating the need for anchorageor bracing. Unsupported elliptical shafts (Figure4) require relatively small a / b ratio where a andb represent the long and the short axis,respectively. Another restriction is that thesurrounding ground must be stiff. As the waterand active earth pressures are approximatelythe same around the shaft, the hoop force mustbe greater along the long side than along theshort side. In order to balance all the forces, thewall has to mobilize a strong soil reaction alongthe short side and this reaction is mobilizedthrough wall displacement. In order to maintainwall stability these induced displacements mustbe small enough so as not to generateexcessive bending moment.When the shapes of the wall componentsdeviate from continuous arcs, "flying" beams,abutment, or counterfort walls can be build tosupport the hoop forces. These combinedsystems have been successfully built in Europe,Asia and South America. The advantages of thiskind of approach include the use of thinnerwalls, lighter reinforcement, and a large openexcavation area without the need for anchorage.Conversely, construction requires goodtolerance and attention to detail. Two examplesof basins comprising circular arcs are shown inFigure 6.Example Project of Large Diameter ShaftThis example deals with a circular diaphragmwall built by Soletanche-Bachy in NorthernEurope. The internal diameter of the wall is 90m(295 ft) with a thickness of 1.20m (4 ft). Thedepth of excavation is 28m (92 ft), 24m (79 ft) ofwhich is below the ground water level. The wallis permanent and without a secondary lining.The specified maximum allowable deviation was+/-0.5% of the wall height.The primary results summarized in Figure 7show the heavily loaded wall system. Bucklingwas an important issue as the average hoopstress was equal to 10.8MPa (1565 psi). Thewall was also design to resist seismic loading,which required that the panel joints stay incompression.Seismic loads were computed with a threedimensions dynamic analysis assuming the soilremained in an elastic state and seismicincrements were superimposed to the staticcase.(a)(b)Figure 6. Multi-cell basins: (a) Hallium basin with abutment walls; (b) Lens-Levin basin with "flying"beams.

Maximum hoop force is at 23m depth and is equal to 12.5MN.Using Hain model (2D non-linear approach), buckling force is approximately equal to 95EI/R 2 =75MN.Factor of safety on buckling is larger than 6.Inscribed annulus thickness without deviation is equal to 1.158m.Maximum deviation at 23m depth = 10.5cm.Inscribed annulus thickness with +/-10.5cm deviation is equal to 0.948m.Hoop stress at 23m depth without deviations is equal to 10.8MPa.Hoop stress at 23m depth with +/-10.5cm deviations is equal to 13.2MPa.Figure 7. Example Project Information, Excavated Shaft Photo, and Idealized Cross-SectionList of example large diameter and deepshaftsA partial list of recent large diameter shaftsconstructed worldwide is summarized in Table 1.SummaryThis paper provided an overview of recentadvances in the design and construction ofcircular diaphragm wall systems. Thesesystems are especially attractive for the EPAmandated combined sewer overflow containersbecause they can be constructed to retain largefluid volumes without any internal or externalsupport. Moreover, the systems are costeffective and provide higher certainty ofexecution during construction relative tocompeting systems such as sunken caissons.Additionally, elliptical and circular arc segmentscan also be used to construct efficient systemswith different shapes. The incorporation of thearc segments allows for thinner walls, lightersteel reinforcement and minimal internal orexternal support.ReferencesHain, H. H. (1968). Zur Stabilitat ElastischGebetteter Kreisringe Und Kreiszylinderschalen,University of Hannover, Mitteilung Nr. 12.Timoshenko, S. and Gere, J. (1961) Theory ofElastic Stability, McGraw Hill, New York, 2 ndEdition.

Table 1. Recent Circular Shaft Projects Constructed Worldwide.Project’s nameDiameter(m)Depth(m)Thickness(m)Huang Pu Bridge, China 73.0 43.7 1.20Ville d’Avray Carrousel Shaft, France 7.8 63.0 1.02Viroflay Socatop Shaft, France 40.8 46.9 1.02Dubaï Palm STEP, EAU 76.2 22.0 1.00Beni Haroun STEP, Algeria 28.0 55.0 1.00HongKong Package 7 Tower, China 76.0 89.0 1.50Blackpool 2 Tanks, UK 36.0 46.044.01.001.00Ivry s/ Seine SIAAP Shaft, France 22.5 56.5 1.52Bordeaux Pkg Gds Hommes, France 57.0 24.5 0.82Colombes GCN Interceptor, France 22.5 74.4 1.50Paris Pkg Harlay, France 31.0 52.0 0.80HongKong MRTC 501 Lantau, China 50.0 70.0 1.50Sangatte Shaft, France 58.0 21.0 1.00