recent advances in large diameter diaphragm wall shafts

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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.
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recent advances in large diameter diaphragm wall shafts

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