ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 10 pdf
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] ... D.I. (1961) ‘The elastic, heavy half-plane, weakened by holes of elliptic shape lying sufficiently close to its boundary.’ In Problems of Continuum Mechanics, Contributions...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 1 ppt
... 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 ... linearly elastic prob- lems is used to obtain several fundamental analytical solutions of tunneling problems. The method is used to derive the general mathe...
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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 ... unloaded portions of the half-plane [23, 10] . If we restrict ourselves to cases in which only a finite section of the surface of the half-plane is loaded, then the derivatives of...
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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. ... (4.4) The compactness of (4.4) is a result of the cancelation of the logarithmic terms in (3.26) along the surface, due to symmetry. Since the integration constant along one...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 4 doc
... 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 k through use of ... 4 The 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...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 5 doc
... 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 observed in the reduction of ... surface are shown in Fig- ure 5 .10 and Figure 5.11 (for the exact solution). The amount of heave appears to depend strongly on the value of Poisson’s ratio: the amount of h...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 6 potx
... from ±7 × 10 −8 for very shallow tunnels to ±8 × 10 10 for deep tunnels. These values are for ν = 0, but the maximum errors for other values of ν appear to be within an order of magnitude of the ... 0 Figure 6 .10: Surface settlements as a function of ν for r/h = 0.7. One of the more prominent features of these curves is that the settlements increase substantially (by more th...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 7 ppt
... from ±3 10 −7 for very shallow tunnels to ±5 × 10 −5 for deep tunnels. These values are for ν = 0.0. The maximum errors for other values of ν appear to be within one order of magnitude of the errors ... 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 str...
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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 ... 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...
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ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 9 pot
... 0.26 11 3.3 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 ... convergence of the tunnel. Solution r/h Num. Terms Max. Error in u/u g Max. σ surface ·h/(2µu g ) analytic 0.01 4 9.9 × 10 10 2.4 10 −15 numeric 0.01 4 1.5 10 −8 2.4 10 −15...
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