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

Review of the Analytical Calculating Methods

A stable old system is assumed in general for sizing liners as information or an accompanying effect is not yet reliable. As for the pipe-soil- system to [ATVA127b], so also must proof of stress, of deformation and of stability be provided for the pipe-in-pipe system. Non-linear FEM calculations are always to be preferred to a superimposition of analytical solvents. However, there also exist good approximations that permit a pre-sizing and qualitative checking of the FEM results for the case of failure of stability of an ideal circular liner, [Falte94a] [Glock77] [Gaube77] [ASTMF121693] [Wagne92] [Lo94] [Weith97] [Falte94b]. These empirical and analytical calculation statements also include the edge conditions of the bedded liner. Then again, they generally neglect the friction between old pipe and liner and assume a homogenous pipe walling. Entry values of the calculation formulae to [Falte94b] are always the modulus of elasticity, the wall thickness and the diameter or radius of the liner. Except for the slightly deviating Wagner equation [Wagne92], and ignoring the influence of the lateral expansion, all the statements are derived from:

and differ only in the pre-factor C and the exponent b (Table They all refer to circular profiles. FEM calculations are preferred for ovoid profiles [Mielk97].


Calculation formulae for critical buckling pressure for the even stress condition

Author Statement Coefficients Remarks
Pcrit= 2·E·(t⁄Dm)3 Free pipe
Pcrit= fs·fa·2·E·(t⁄Dm)3 fs − Empirical,
fa − Analytical
Bedded pipe with
oval deformation
Pcrit= 2.76·E·(t⁄Dm)2.2 Pipe−in−pipe
Pcrit= 2.55·E·(t⁄Dm)2.2 Pipe−in−pipe
Pcrit= 1.0·E·(t⁄Dm)2.2 Pipe−in−pipe
Pcrit= (k2−1)·2⁄3·E·(t⁄Dp)3 k2−1 − Analytical,
Dp − Analytical
Pipe−in−pipe with
ring gap
ATV−A 127
Pcrit= αD·2/3·E·(t⁄Dm)3 αD − EDP, Diagr. Bedded pipe
[Falte94a] P

Pcrit= kv·ks·1.0 ·E·(t⁄Dm)2.2

kv, ks − EDP, Diagr.
Pipe−in−pipe with
ring gap and defined
crit= K·fa·2·E·(t⁄Dm)3 fa − Analytical,
K − Empirical
Pipe−in−pipe with
oval deformation

Pcrit= C·E·(t⁄r)b
ws − Gap width
C(r⁄ws) − Empirical.
b(r⁄ws) − Empirical.
Pipe−in−pipe with
ring gap

In the equations of Lo and Zhang, Wagner and Falter, the gap width is also taken into account, whereby Lo and Zhang limit themselves to small gap widths and Wagner defines the definition region 15 S [Gaube77] [ASTMF121693] by a pre-factor.

In order to better describe the buckling behaviour of liners and also to provide long-range values of practice to the calculating equations of the critical buckling values, approx. 200 long- and short-term investigations on liners, among others, were carried out at the Louisiana Tech. University [Guice94b]. Larger ring gaps were not investigated but were limited during the insertion of the liners to a minimum.

Within the scope of the investigations, the methods available on the North American market (seven methods from five manufacturers) were tested. Individually these were the Insituform standard process, improved Insituform, NuPipe, Inline USA, Spiniello KM-liner, Paltem HL and Superliner. The liners were inserted into steel pipes (= old pipe), were approximately round and showed no visible damage or imperfections.

The sealing system used between the enveloping steel pipe and the liner is shown in (Image Measurements of various old pipe lengths have shown that with a minimum length of 1.83 m and an inside diameter of 305 mm, the buckling failure of the liner is not influenced by the clamping effect of the steel pipe. In the pipes tested, water was forced via a regulator directly between the liner and the steel pipe at a pressure of 14 bar. The system was designed for simultaneous failure of half of all the pipes under investigation.

In the short-term tests, the failure in most cases occurred 2 to 10 minutes after the start of the tests. In further tests, the buckling behaviour of a liner was also observed over a longer period and thus kept under constant pressure for this period of time.The long-term tests ended as soon as buckling failure occurred or after 10,000 hours (about 14 months). Typical buckling figures are shown in (Image and (Image Some of the liners also did not fail after 10000 hours.

Image  Layout experiment for external pressure testing of liners (Louisiana Tech University)with reference to [Guice94b] [Image: S&P GmbH]
Image  Buckling of liners during long-term experiment [Guice94b]
Image  Buckling of liners during long-term experiment (section - enlargement) [Guice94b]

The short-term investigations showed that, for small ring gap widths, the defined buckling pressures only deviated a little from those of Falter and Glock. In the long-term investigations, however, it became clear that the length of the loading must also be considered for sizing the liners when providing proof of stability, for even with lesser pressure, the buckling of the liner cannot be excluded over a longer period of operation.

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