The French recommendations for the structural design of large sewer linings
Mar 04, 2008
The French National project of research and experimentation named RERAU (Rehabilitation of Urban Network Sewers) has published in 2004 its recommendations for the structural design of large sewer linings after a five years period of preparation and discussion. The design method works for circular or non circular linings and takes into account the exact geometry of the lining (curve radius and imperfections) and the interaction with the existing host. The concept based on an approximate analytical solution, supports simple formula and diagram usage for stress, deformation and stability analyses. The method gives formulas for the buckling pressure of non circular linings (egg-shaped linings). Geometrical imperfections (ovality, gap, local intrusion, flat spot) are treated individually using reduction factors for the buckling pressure and amplification factors for the stresses (bending moment and axial force) and the deflection.
- Improve the quality of structure diagnoses;
- Define the field and the conditions of use of renovation techniques;
- Establish a rational design methodology for sewer rehabilitations.
The first operation concerns the diagnosis and the testing of man entry sewers. The second operation is devoted to the sprayed concrete (with or without reinforcement); a rehabilitation technique used in large man entry sewers.
- Ability to sustain the grouting pressure during installation (when appropriate).
- Ability to sustain the external head of groundwater pressure that must be considered to rise, once hydraulic integrity is restored.
- And eventually ability to sustain soil loading transfer, if the sewer loses its hoop compressive stiffness after lining.
The buckling pressure of the one lobe mode is lower than the buckling pressure of the two lobes. So the designer shows generally the one lobe mode.
On one hand, if the curvature and the extension angle of the arc where the lobe develops are sufficient, the deflection at the center of the lobe increases but the lobe angle remains constant or decreases, the lobe does not extends. There is a limit pressure where the lobe buckles, see Figure 6(a).
On the other hand, for instance in the case of an oval shape or an egg shape with straight sides, the lobe may extend continuously over the entire lining and there is no buckling pressure. The first behavior is named “ critical ” and the second “ sub-critical ”.
Pcr = 2.02 ⋅ K0.4 ⋅ [(EI0.6EA0.4) / (p0.4R1.8)]
Note that the formula calls into play both the flexural stiffness (at power 0.6) and the compressive stiffness (at power 0.4), whereas Timoshenko’s formula uses only the flexural stiffness. This is because the lining must shorten in order to separate from the host, which calls its compressive stiffness into play. In the case of a plain wall and homogeneous material of t, the formula can be simplified as follow:
pcr = 0.455 ⋅ k0.4 ⋅ EL ⋅ [(t2.2) / (P0.4R1.8)]
Pcr = 0.308 ⋅ EL ⋅ [t / H]2.2
Pcr = 1.0 ⋅ EL ⋅ [t / D]2.2
M(pW) = [0.5 ⋅ (pW/pcr) Mcr] / [1 - 0.5 ⋅ (pW/pcr)2]
N(pW) = (pW/pcr) Ncr
d(pW) = dcr [1 - [1 - (pW/pcr)]0.5]
Ncr = 1.26pcrR
Mcr = 1.2 (EI / R)
r1: The radius of the crown
r2: The radius of the invert
L: The length of the straight section
P: The perimeter of lining
EA: The compressive stiffness of the lining
EI: The Flexural stiffness
λ: The relative deflection of the straight section (3%)
θ1 = [r1 / L]
θ2 = [r2 / L]
λ = [dL / L]
β = [EId / EAd] ˙ [P / L3]
m = [EId / L3]
g12 = 1 + √(r1/r2)
120β + 9λ2 + g12θ2(120β + 18λ2)α2 + (12λθ2 + 9λ2g212θ22)α22 - 12λg212θ32α42 - 16g12θ23α25 = 0
Then two quantities are defined:
η = 1 + α2θ2g12 and γ = g12θ22α23
Expression of the pressure:
pλ = [(4π4m) / η4) ⋅ λ [(1+ (γ2 / 9βη)) - (γ / 4β)γ + (η / 8β)λ2]
The gap angle α1 must be lower than half the arc angle of the invert.
For man entry linings, staged or partial grouting are generally adopted rather than full grouting. The first stage involves grouting the annulus up to a third or a quarter of the vertical height, and this is followed by a second stage, carried out after the grout of stage one as set; finally a third possible stage supplements the filling of annular space.
- The degree of restraint provided during grouting. Hardwood wedges are normally used as packing. Restrains of the vertical height of the lining by an internal strut may be very important.
- The height of grouting at the first stage.
- The shape of the lining and particularly the curvature of the straight section.
- The bending stiffness of the lining material (not the hoop stiffness).
- The unit weight of the grout.
- If the host sewer loses its hoop compressive stiffness after lining.
- If a subsequent excavation near the renovated pipe is undertaken.
- If the host sewer is obviously in an unstable ground, where the source of instability is not eliminated by lining.
- Firstly initial stresses are generated in the soil by specifying the head of soil, the specific weight of soil and the coefficient of earth pressure at rest.
- Secondly the equilibrium forces are calculated at the interface between the soil and the lining. These equilibrium force are actually sustained by the host structure.
- And thirdly the reversed forces, are applied to the lining.
 Thépot O., 2000, A new design method for non-circular sewer linings. Trenchless Technology Research, Vol. 15, No. 1, 25-41.
 Glock D., 1977, Behavior of liners for rigid pipeline under external water pressure and thermal expansion, Der Stahlbau, Vol. 46, No. 7, 212-217.
 Falter B.,1996, Structural analysis of sewer linings, Trenchless Technology Research, Vol. 11, No. 2, 27-41.
 Falter B., 2001, Structural design of linings, Proceedings of the International Conference on Underground Infrastructure Research, Kitchener, Ontario, Balkema publishers, 49-58.
 Hall D.E., Zhu M., 2001, Creep induced contact and stress evolution in thin-walled pipe liners, Thin-Walled Structures, Vol. 39, 939-959.
 Moore ID., 1998, Tests for pipe liner stability: what we can and cannot leran, Proceedings of North American No-Dig 98, NASTT, Albuquerque, 443-457.
 Thépot O. 2001, Structural design of oval-shaped sewer linings, Thin-Walled Structures, Vol. 39, 499-518.
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Dr O. Thépot (Eau de Paris)
+33 (0) 1 40 92 24 93
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