Gaube, starting from investigations on free pipe in the ground under external water pressure, developed a semi-empirical statement for proving the stability of embedded sewage pipes of plastics [Gaube74]. This takes into account the support effects of the soil as well as also the deformation (ovality) of the pipe attributable to the earth load.
First the buckling pressure pk0 of the free un-deformed pipe against external pressure is determined either on the basis of the trial experiments or according to equation (5-6) (Formel 126.96.36.199.1.2.1). The support effects on the pipe attributable to the surrounding soil are acquired approximately by the support factor fs with 1 s k1 of the bedded un-deformed pipe results in:
This statement is also occasionally used for supporting the sealed liner. In this case, [FI-Hoech83] recommends selecting the support factor fs = 3.
Pre-deformations are taken into account using the deformation factor fs. In order to estimate it, it is assumed that the liner is deformed elliptically with Δr ≈ Δx ≈ Δy (Image 188.8.131.52.2.3.3-1).
The semi-axes a and b of the ellipse and the larger bend radius r1 can then be determined via:
The buckling pressure of the deformed pipe is approximated in that in equation (5-5) (Formel 184.108.40.206.1.2.1) the large bend radius r1 of the elliptical equation (5-10) (Formel 220.127.116.11.1.2.2) is used for the radius r so that for the long pipe according to equation (5-5) (Formel 18.104.22.168.1.2.1) there is valid: