recent advances in large diameter diaphragm wall shafts

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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.
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Page 7: Table 1. Recent Circular Shaft Proj

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