ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 8 ppsx
ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 8 ppsx
... dimensional linearly elastic problems can be used to obtain several fundamental solutions of tunneling problems. The method was used in Chapter 3 to derive the general mathematical repre- sentation of problems ... depicted in Figure 8. 4, the magnitude of the ground loss V s in Peck’s formula has been adjusted to match the volume of the trough of the elastic solution....
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 2 ppsx
... no longer be analytic. We begin by examining the behavior of the complex potentials for large values of z. Behavior near Infinity The derivatives of ϕ(z)and ψ(z)can be continued analytically through ... functions which are analytic in R beyond the loaded portion of the surface of the half-plane, including the point at infinity [16] (these functions are also analytic in all finite...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 1 ppt
... Problem 48 §6.1 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 ... and Otto. ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, o...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 3 pot
... 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 problem is shown in Figure 4.1. ... 2. (4.30) This completes the expansion of the right-hand side of (4.21). The left-hand side can easily be expanded through substitution of (4.27) and (4. 28) in (4.21). These...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 4 doc
... expansion of the right-hand sides of both (4.21) and the modified form of (4.24) is complete. The left-hand sides of these equations can be expanded through substitution of (4.27) and (4. 28) , as ... 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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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 5 doc
... amount of heave appears to depend strongly on the value of Poisson’s ratio: the amount of heave for ν = 0 is roughly 50% more than for ν = 0.5. It would appear that this is due to 38 Buoyancy of ... 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 observ...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 6 potx
... r/h < 0.5 (6 .8) It should be emphasized that this rule of thumb is only valid for a uniform contraction of the tunnel cavity and for linearly elastic behavior. Equation (6 .8) has not been ... kN/m 2 h 16 m ν grnd 0.25 x max 80 m γ grnd 16 kN/m 3 y max 80 m E tunl 1 ×10 10 ν tunl 0.499 γ tunl 16 kN/m 3 In the table, the values of x max and y max define the range of the FEM me...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 7 ppt
... 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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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 9 pot
... 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 should be noted that part of ... ×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 th...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 10 pdf
... 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 University Press, 2002. BIBLIOGRAPHY [1] ... deforming circular tunnel in an elastic half-plane.’ International Journal for Numerical and Analytical Methods in Geomechanics 21, 77 89 [43] (19 98) ‘Deformations of an e...
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