ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 9 pot

... ×10 9 4 .9 ×10 −15 numeric 0.26 10 3.4 ×10 −8 2.2 × 10 −13 analytic 0 .9 41 1.5 × 10 −7 1.6 ×10 −13 numeric 0 .9 38 3.4 × 10 −8 1.2 ×10 −12 Section A.2 Evaluation of the Coefficients in the Potentials ... system of equations (4.38) - (4. 39) numerically and examining the behavior of p k for large values of k and different values of p 0 , as performed by Ver- ruijt [42]. It sho...

Ngày tải lên: 07/08/2014, 04:21

... terms on the left-hand side of (4.5). Section 4.1 The Complex Potentials and Geometry of the Problem 19 § 4.1 The Complex Potentials and Geometry of the Problem The problem of a buoyant tunnel with ... point on L s directly above the center of the hole. The radius of the hole is denoted by r and the depth of the center of the hole is denoted by h. The geometry of the proble...

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... 6 .9: The hoop stress around the tunnel as a function of ν. features of Figure 6 .9 is that the hoop stress is constant for ν = 0. This effect is probably related to the effect seen in the case of ... directly generate a hoop stress. In the case of a pure contraction of the tunnel boundary, the uniform contraction directly Section 6.1 Solution of the Problem 49 and ψ. The stress...

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... Solution of the Problem 48 §6.2 Validation of the Solution 50 ix ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS xii Acknowledgements ABSTRACT Analytic Solutions of Elastic Tunneling Problems The ... Program 89 §B.1 Dimensionless Complex Potentials 89 §B.2 Dimensionless Coordinates 91 §B.3 Evaluation of the Stresses and Displacements 91 §B.4 Comparison of...

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... half-plane, the problem is often solved by superimposing the reflections of solutions for an infinite plane across the boundary of the half plane. For examples of half-plane problems using the complex ... only a finite section of the surface of the half-plane is loaded, then the derivatives of the potentials (which represent the stresses in (2.4) and (2.5)) can be continued analy...

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... Summary 29 Final Form of the Transformed Solution The final form of the solution in the z-plane is given by the potentials (4.1) and (4.2). They can be expressed in terms of ζ through use of (4.7), ... of like powers of σ in the expansion of the modified form of (4.24). This results in a complicated system of equations which are simplified considerably by eliminating c k and d...

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... 0 r/h = 0.1 Figure 5 .9: The hoop stress around the tunnel as a function of ν. apparent from Figure 5 .9 that the value of Poisson’s ratio plays a much larger role in the magnitude of the hoop stress ... function of ν. 42 Buoyancy of a Rigid Tunnel Chapter 5 an effective reduction in stiffness of the ground above the tunnel for low values of Poisson’s ratio, as can also be obse...

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... for other values of ν appear to be within one order of magnitude of the errors given here. 72 Ovalization of a Circular Tunnel Chapter 7 § 7.7 Chapter Summary In this chapter an analytical solution ... ovalization of the tunnel are of a local nature, and it seems that most of the stresses have dissipated at a distance of two times the tunnel depth. For deeper tunnels the stres...

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... the Chapter 9 CONCLUSION It has been shown that the complex variable method for solving two dimensional linearly elastic problems can be used to obtain several fundamental solutions of tunneling problems. The ... negative). Larger values of ρ can be a result of grouting in very soft soils [12]. For many cases of open shield or open face tunneling, when grouting is not app...

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... deforming circular tunnel in an elastic half-plane.’ International Journal for Numerical and Analytical Methods in Geomechanics 21, 77– 89 [43] ( 199 8) ‘Deformations of an elastic half plane with a circular ... smaller zijn dan uit de theorie zou volgen. O.E. Strack, Analytic Solutions of Elastic Tunneling Problems. Ph.D. Thesis, Delft University of Technology. Delft Univ...

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