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

Cross sectional values

The basis for carrying out the structural calculations are the cross sectional values of the wall structure being used. These are not only dependent on the material and the geometry but also on the loading.

The (Image 5.3.3.7.3.4-1), (Image 5.3.3.7.3.4-2) and (Image 5.3.3.7.3.4-3) show the loading ability of liners of various wall thicknesses produced according to the grouted-in-place lining process, whereby the thickness of the HD-PE hose is 2 mm in all cases and only the height of the studs , and thus the dimensions of the injection grout layer, is varied. The maximum bending moment is on the vertical axis for short-term loading (dashed line) and for the generally decisive long-term loading (solid line) that, with reference to the normal force (horizontal axis) that is at the limit of accessibility.

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Image 5.3.3.7.3.4-1:  M/N interaction for long-term loading for a 2 mm thick HD-PE hose with an injection grout thickness of 10 mm [Image: S&P GmbH]
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Image 5.3.3.7.3.4-2:  M/N interaction for long-term loading for a 2 mm thick HD-PE hose with an injection grout thickness of 13 mm [Image: S&P GmbH]
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Image 5.3.3.7.3.4-3:  M/N interaction for long-term loading for a 2 mm thick HD-PE hose with an injection grout thickness of 19 mm [Image: S&P GmbH]

The curve marked with + only limits the positive, the one with [] the negative bending moment in the condition I. Thus, there exists a wide-ranging symmetry as regards the horizontal zero line as the injection grout almost completely carries all the loads and therefore the loading capability of the cross section is almost independent of the direction of bending. The difference between the short term and long-term values is correspondingly small.

The top curve marked with o above it belongs to condition II for a positive bending moment. If, for instance, in (Image 5.3.3.7.3.4-1) one assumes a case similar to that found in practice of a relatively small normal force, one can read off a rise of the loading capability from 70 Nmm/mm to 355 Nmm/mm, that is, to more than five times as much.

In the interaction diagrams shown in (Image 5.3.3.7.3.4-1), (Image 5.3.3.7.3.4-2) and (Image 5.3.3.7.3.4-3), the required factor of safety according to ATV-M 127-2 [ATVM127-2] of 2.0 for HD-PE and 2.2 for the injection grout have already been incorporated, so that the section sizes defined under usable load can be used for sizing.

Analogous to the loading ability, the bending stiffness of the cross section at every point of the circumference is dependent on the loading and primarily on the condition (cracked or not cracked) as well as the direction of bending. Under the precondition of a small normal force, (Table 5.3.3.7.3.4-1) gives the bending stiffness for three different wall thicknesses. In this way, every cross section can be described in a form that makes a structural proof according to ATV-M 127-2 [ATVM127-2] possible.

Table 5.3.3.7.3.4-1: 

Bending stiffness in N/mm2/mm for liners produced by the anchor hose method with different nap heights (Stud sheet thickness: 2 mm) [Image: S&P GmbH]

Stud heights Condition I Condition II
Tension in stud hose
(positive moment)
Compression in stud hose
(negative moment)
[mm] Short−term Long−term Short−term Long−term Short−term Long−term
10 1,700,000 1,650,000 210,000 34,000 650 100
13 3,700,000 3,650,000 350,000 56,000 650 100
19 11,600,000 11,500,000 750,000 117,000 650 100

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