Rehabilitation and Maintenance of Drains and Sewers / Prof. Dr.-Ing. D. Stein, Dipl.-Ing. R. Stein (2004)

Glock

Glock analysed the stability program of a rigid outside-coated, linearly elastic circular ring under external water pressure with the use of geometric non-linear deformation relationships according to the energy method. Friction between pipe and outside coat, imperfections of the loading and geometry as well as non-linear material behaviour were not considered. Separation of the pipe from the coat is conditioned by the circumferential shortening resulting from the circumferential stress (EA ≠ ∞) (Image 5.3.3.7.2.3.4-1). Glock describes the deformation resulting from this with the statement:

image
Image 5.3.3.7.2.3.4-1:  The liner model according to [Glock77]

Here w1 and φ0 are free parameters that are determined according to the energy method [Glock77]. The potential energy with the buckling process of the ring is thereby dependent on three different sections or outside loads:

  • The bending moment M in the buckling region (region I) (Image 5.3.3.7.2.3.4-1) ;
  • The constant ring pressure force N acting on the whole circumference; and
  • The external pressure pcr.

The parameters w1 and φ0 can be determined from the first variation of the whole potential in general form as a function of the load so that only the critical water pressure with the dimensionless load parameter αkrit has the relationship:

On the assumption that a prevented lateral expansion exists, the equation (5-13) (Formel 5.3.2.6.1.2.3) for the full-walled pipe of wall thickness t can also be written as:

Rehabilitation and Maintenance of Drains and Sewers / Prof. Dr.-Ing. D. Stein, Dipl.-Ing. R. Stein (2004)