TAILIEUCHUNG - ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 7

Việc áp dụng áp lực không đồng đều, ngang và dọc có thể gây ra một đường hầm vòng tròn với một lớp lót linh hoạt (hoặc không có lót) để trở thành hình bầu dục. | Chapter 7 OVALIZATION OF A CIRCULAR TUNNEL The application of uneven horizontal and vertical stresses may cause a circular tunnel with a flexible lining or no lining to become oval in shape. Such uneven stresses are often found in the underground where the horizontal stresses can often be expressed as a factor multiplied by the vertical stresses see Chapter 5 . The ovalization effect due to these uneven stresses can be derived from the basic Kirsch solution 37 for a stress-free cavity with unequal stresses applied at infinity as shown by Pender 25 who deduced the incremental displacements for this case. The stresses on tunnel linings due to ovalization had already been discussed by Morgan 21 and Muir Wood 22 . The components of ovalization along the tunnel wall derived from the Kirsch solution contain a radial component ur uo cos 20 and a tangential component u0 -uo sin 20 where uo is the maximum displacement along the tunnel cavity. This boundary condition having been derived from the Kirsch solution for a stress-free cavity corresponds the case in which zero shear stresses ơrt can be expected along the tunnel periphery. This corresponds to the case in which the tunnel lining can be assumed to be frictionless. Uriel and Sagaseta 39 extended Sagaseta s original ground loss solution to include these ovalization components and obtained surface settlements which are valid for incompressible soils. Verruijt and Booker 40 extended Uriel and Sagaseta s work by using an elastic model for the underground. They obtained expressions for the displacements in the entire field for all values of Poisson s ratio and they obtained them for both the ground loss problem and for an ovalization of a tunnel. For their solution Verruijt and Booker focused on the related mode of ovalization in which zero tangential displacements are assumed along the tunnel periphery u0 0. This corresponds to the case in which the tunnel lining is rough relative to the surrounding ground and little or no

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