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 ... shown in Figure 7. 7. From the contours in Figure 7. 7 it appears that the stresses associated with the ovalization of the tunnel are of a local nature, and it seems that mos...

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... Solution 65 7. 4 Stresses around the Tunnel 67 7. 5 Stresses on the Tunnel 68 7. 6 Displacements along the Surface 70 7. 7 Chapter Summary 72 Chapter 8. Prediction of Settlement Troughs 73 §8.1 Peck’s ... Calculation 44 §5 .7 Chapter Summary 46 Chapter 6. The Ground Loss Problem 48 §6.1 Solution of the Problem 48 §6.2 Validation of the Solution 50 ix ANALYTIC SOLUTIONS O...

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... in (3.8) and (3.9) through use of (3 .7) . We combine the series resulting from the use of (3 .7) with the analytic functions ϕ 0 (z) and ψ 0 (z) to form two new analytic functions ϕ 0 (z) and ... linearly elastic solutions for infinitely deep circular tunnels [ 37] , elasto-plastic solutions for infinitely deep circular tunnels [11, 7] , or variations of these models [45, 4]....

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... (4.20) Transformation of the Boundary Equations The boundary equation along the surface of the half-plane can be transformed to the ζ-plane by substituting (4 .7) and (4. 17) into (4.3), with the help of (4.16) and ... 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...

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... 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) , (4. 17) , (4. 27) , and ... (4. 37) that this unknown is incorporated in every coefficient of the Laurent series (4. 27) and (4.28). The value of a 0 affects the convergence of the Laurent series; in...

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... Section 5 .7 Chapter Summary 47 illustrative comparison of the solution and a Finite Element calculation shows some effect of the FEM boundary constraints along the edges of the mesh. Section ... 5 .7: The radial stresses acting on the tunnel as a function of ν. 42 Buoyancy of a Rigid Tunnel Chapter 5 an effective reduction in stiffness of the ground above the tunnel for low val...

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... 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 than a factor of 1.5 for the maximum settlement for ... intended as a validation of the solution or as a validation of the program Plaxis, but is merely an illustration of the differences that may be encountered. A linearly e...

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... 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 ... of Ground loss and Ovalization 75 latter of which is equal to the amount of ground lost around the tunnel perimeter per unit length of the tunnel in the ex...

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... 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 ... side of (C.6) by using the relation 1 + α 2 2h = α r , (C .7) Appendix C THE OVALIZATION BOUNDARY CONDITION It is the purpose of this appendix to derive the transformed Fourier...

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... 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] ... tunnel in a heavy elastic half-plane.’ International Journal for Numerical and Analytical Methods Geomechanics. In press [ 37] Timoshenko, S.P., and J.N. Goodier (1 970 ) Theor...

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