The structural design of large non-circular GRP prefabricated linings

RERAU is divided into several programmes and the fourth programme - RERAU 4 - is devoted to prefabricated lining systems - and especially of structural GRP which is becoming more and more frequently used in France - including one-piece, multi-piece and invert only liners. For circular linings there are many available design methods – such as the SRM design approach - but calculation of non circular structural lining is far more difficult. This is why RERAU has developed:

• a simplified design formula which extends Glock’s analysis for evaluation of safety with regard to buckling
• a new design method based on finite element method analysis (F.E.M.) specially for large (man-entry), non-circular GRP linings and special non conventional loads. The design principles of this F.E.M. approach and two case studies are presented in the paper.

The first case study will present the renovation of an egg shape concrete sewer severely damaged and that was fully structurally renovated with an ovoid profile GRP full panel.
The second case study is a corrugated steel pipe arch buried in a motorway’s embankment and relined by a horseshoe GRP prefabricated lining. In this case, because of the heavy corrosion of the steel, it was considered that the host steel pipe arch would loose its hoop compressive stiffness after lining.

1. INTRODUCTION

The purpose of RERAU (Rehabilitation of Urban Network Sewers) [1] was to establish a common rational design methodology for a wide range of lining systems. The methodology is a limit state design including partial safety factor on loads and on material properties. For circular linings there are many available design methods – such as the SRM design approach (see [2]), - but structural calculation of non circular lining is far more complex. That is why RERAU has focused on non-circular lining and also because man-entry sewers are generally non-circular. The design method, based on finite element method analysis (F.E.M.), has been developed specially for large (man-entry), non-circular GRP linings and for special non conventional loads.

The lining system is designed to act as a flexible pipe with the old sewer, annulus grout (where appropriate) and soil providing the necessary support to maintain stability.

The prime design requirements on the lining are therefore (see figure 1):

• Ability to sustain the grouting pressure during installation (where appropriate).
• Ability to sustain the external head of groundwater pressure that must be considered to arise once hydraulic integrity is restored.
• And eventually ability to sustain soil loading transfer if the sewer loses its hoop compressive stiffness after lining.

2. FIRST CASE STUDY

The Water & Sewerage Department of the town of Bourg-La-Reine (France) has rehabilitated in 2004 a large sewage collector with GRP prefabricated channel linings. In total, 200m of sewer were relined using 1760 x 866 mm egg-shaped GRP lining segments.

The mechanical characteristics of the GRP channel lining was (see also figure 2):

• Height : 1761 mm
• Width : 866 mm
• Thickness : 17 mm
• Radius of the straight section : 2278 mm
• Mean Perimeter : 4430 mm
• Young modulus : 11000 MPa
• Long term modulus (wet cree value): 3700 MPa
• Bending strength : 60 MPa

2.1. The design for grouting

As a minimum requirement all lining systems should be capable of supporting the pressure of grout filling the annulus during installation. Otherwise, in some cases, excessive deformation might occur, affecting the serviceability of the lining.

The vertical height of the lining was restrained by an internal strut. Staged grouting was adopted rather than full grouting. The height of the first stage was 0.6 meter. The second stage was carried out after the grout of stage one set.

The lining deformation was verified using element analysis. The maximal deformation at the middle of the straight section was less than 9 mm (the maximal permissible deflection was 3% of the straight section = 36 mm).

2.2. The design for ground water pressure

Because lining restores hydraulic integrity and where the bond between the lining and the host cannot be relied upon in the long term, it is necessary to consider the effect of external water pressure acting directly on the lining. Where the grout is considered likely to crack due to small ground movements, groundwater may percolate through the cracks and act at the interface between the lining and the host.

The water table lies 2.3 metres above the invert.

The design pressure is equal to the pressure of the groundwater at the center of the lobe:

p_w = 10 ⋅ (2.3 - 0.7) = 16 kPa

The long-term Buckling pressure of the GRP lining was calculated with the Glock-Thepot’s analytical formula (see [3]and [4]). The parameters used are the perimeter, the radius of the straight section (where the lobe develops), the thickness and the long-term modulus:

p_cr = 0.455 ⋅ k^0.4 ⋅ E_L ⋅ [t^2.2 / (P^0.4R^1.8)]

p_cr = 0.455 ⋅ 1.32 ⋅ 3700 ⋅ [17^2.2 / (4430^0.42287^1.8)] = 35 kPa

In this case, k=2 because there are two lobes (see figure 4).

The safety factor for the stability is:

γ_F = 35/16 = 2.2 > 2

The safety factor for stability security must be greater than 2.

2.3. The design for ground and traffic loading

In most case the host structure continues to sustain the ground and traffic loading and there is normally no requirement to consider directly the transfer of any loading from the soil to the lining. But in certain circumstances significant soil loads can be transferred to the linings:

• 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.

The WRC Sewerage Rehabilitation Manual (VOL II) proposes two simplified design methods:

• The first method is for linings that form a bond to the grout, so that the renovated sewer acts as a composite section (WRc type I linings)
• The second method is for linings that form no bond with the grout (type II linings).

The first method takes into account the compressive strength of the sewer wall but no tensile strength is assumed and pin jointing (hinge) is assumed at spring level. For composite design the grout must be strong enough to transfer stress to the lining from the outer surface of the sewer.

The second method neglects the strength and the stiffness of the old sewer. It is assumed that:

• The old sewer and the grout act like the surrounding soil.
• The lining is behaving like a flexible structure in interaction with the soil.
• The effect of time is introduced by multiplying the elastic modulus by a creep factor.

The second method is recommended if we need just resistance to external water pressure. For more than 10% deflection, WRc recommends that CIPP systems should not be used as the deformations will be transferred to the liner.

WRc method is valid in most cases, for instance profiles close to egg 3:2 that are very common in Europe. But in some cases, listed by RERAU - such as special shapes, unstable soils, non conventional loads - in order to evaluate correctly the soil and traffic transfer to the lining finite element analysis is the best choice. This is why RERAU developed a new design method based on F.E.M. for non usual shapes (large channel lining for example).

A finite element analysis (see figure 5) was performed to model the transfer of the loading from the soil and the traffic loading to the lining (it was assumed that the host sewer would loose its stiffness after lining).

The long term deflection of the lining and the maximum stresses are calculated.

3. SECOND CASE STUDY : HORSESHOE GRP PREFABRICATED LINING

Here a corrugated steel pipe arch buried in a road’s embankment in France and relined in 2005 by a horseshoe GRP prefabricated lining. In this case, because of the steel corrosion, it was considered that the host steel pipe arch will loose its hoop compressive stiffness after lining.

General description of the project:

• Height of soil above the crown: 12.0 m.
• Height of the table water above the invert: 2.3 m.
• Elastic modulus of soil E_s = 10 MPa.
• Specific weight of soil γ = 20 kN/m³.
• Embedment: mixed grained soils with low fine fraction, relative compaction Dr > 95% OPN.

Mechanical characteristics of the GRP lining :

• Height: 1557 mm
• Width: 2469 mm
• Thickness: 33 mm
• Radius of the invert section: 3567 mm
• Mean Perimeter: 6500 mm
• Young modulus: 11000 MPa
• Long term modulus: 3700 MPa
• Bending strength: 60 MPa

3.1. The design for grouting

The vertical height of the lining was restrained by an internal strut. The height of the first stage was limited to 0.5 meter. Finite element analysis was used to calculate the deformation of the panel and also the hoop force in the props.

3.2. The design for ground water pressure

The design pressure is equal to the pressure of the groundwater at the invert:

p_w = 10 ⋅ (1.6 + 0.5) = 21 kPa

The Buckling pressure of the GRP lining is calculated with the Glock-Thepot’s analytical formula (see [3] and [4]). The parameters used are the perimeter, the radius of the invert section (where the lobe can develop), the thickness and the long-term modulus:

p_cr = 0.455 ⋅ k^0.4 ⋅ E_L ⋅ [t^2.2 / (P^0.4R^1.8)]

p_cr = 0.455 ⋅ 3700 ⋅ [33^2.2 / (6500^0.43567^1.8)] = 44.4 kPa

In this case, k=1 because there is only one lobe (at the invert).

The safety factor for the stability is:

γ_F = 44.4/21 = 2.1 > 2

The safety factor for stability security must be greater than 2.

3.3. The design for ground and traffic loading

A Finite element analysis was performed to model the transfer of the loading from the soil to the lining and also the traffic loading. The figure 10 shows the finite element mesh.

The vertical deflection of the lining and the maximum stresses was calculated. Two conditions must be satisfied:

• the vertical deflection must be less than 3% of the lining height;
• the maximal bending stress must be less than the bending strength divided by a safety factor of 1.5.

4. REFERENCES

[1] RERAU, 2004, Restructuration des collecteurs visitables, Lavoisier, Paris.
[2] WRc/WAA - Sewerage rehabilitation manual. UK Water Research Center / Water Authorities Association, 1994-2000.
[3] Thépot O., 2000, A new design method for non-circular sewer linings. Trenchless Technology Research, Vol. 15, No. 1, 25-41.
[4] Thépot O. 2001, Structural design of oval-shaped sewer linings, Thin-Walled Structures, Vol. 39, 499-518.
[5] Avis Technique CSTB NC Line 17/04-155 , HOBAS France. Technical specifications of GRP panels.

¹ HOBAS France, BP 216 F-95523 Cergy Pontoise, France, jeanmarie.joussin@hobas.com
² EAU DE PARIS, 21-23 rue de la Vanne, 92120 Montrouge, France, thepot@eaudeparis.fr