Centrifuge modelling of soil load transfer to flexible sewer liners

Aleksandar Spasojevic & Robert J. MairCambridge University, UK

John GumbelInsituform Technologies, UK

ABSTRACT: This paper presents results of a research project conceived to fill this gap in knowledge about theextent to which transferred soil and traffic loads need to be considered in the design of cured-in-place pipes orother flexible liners used for rehabilitation of gravity sewers. The Cambridge geotechnical centrifuge was used tosimulate realistic loading sequences and possible deterioration mechanisms of a sewer and its soil surround, bothbefore and after lining. The technique has for the first time enabled direct physical simulation of (a) the collapseof voids in the surrounding soil and (b) the loss in separate stages of the flexural and compressive ring stiffnessesof the host pipe as it deteriorates further. The effects of moving traffic loading have also been investigated.Test results show that in adjusting to the deterioration events the existing pipe soil-structure imposes relativelysmall, quantifiable distortions on the liner pipe. The deformation response of the liner to external loads otherthat groundwater pressure is predominantly one of bending and is governed by interactions between the liner,host pipe and the surrounding ground.

1 INTRODUCTION

The steady growth in demand for pipeline rehabilita-tion has been matched by a proliferation of trenchlesstechniques. This applies particularly in the case ofsewers, which are generally buried deeper than otherservices and for which the environmental and overallcost benefits of trenchless methods are most apparent.Despite an overall appreciation of the ‘no-dig’ phi-losophy in principle, the full potential range of useof trenchless renovation techniques remains restricteddue to a general lack of consistency in the performancecriteria and design procedures applied to the manydifferent methods and materials available. Progressin developing a more rational design approach hasbeen hampered by the lack of hard evidence, fromeither field measurements or physical experiments.This paper presents results from a research projectconceived to fill this gap in knowledge in the case ofclose-fitting polymeric liners such as ‘cured-in-placepipes’ (CIPP).

CIPP is the generic term used to describe the classof pipeline renovation techniques whereby a lining ofthermosetting resin composite is cast directly againstthe wall of a deteriorating pipe.Although there are sev-eral variations of the process, the common feature ofall of them is the use of a fabric tube impregnated withthermosetting resin. This tube is inserted by inversionor winching into the existing pipeline, inflated against

Figure 1. Schematic presentation of CIPP lining.

the pipe wall by means of fluid (water or air) pressure,and then cured in place, typically by re-circulating hotwater or steam, as shown in Figure 1. The thermalcuring process results in some shrinkage of the liner,so that a small annular gap (typically 0.1%–1.0% ofdiameter) remains between the liner and the host pipe.

Unlike previous experiments which studied theeffects of application of surface loading on buriedpipes lined with CIPP, Jones (1982), Watkins et al.(1988), Doll (2001), in this project the Cambridge Uni-versity geotechnical centrifuge was used to simulatethe effects of the gravity loading and possible deteri-oration mechanisms of a sewer and its soil surround,

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both before and after lining. In particular, the techniquehas for the first time enabled direct physical simula-tion of (a) the collapse of voids in the surrounding soil(which in the field are usually caused by soil erosioninto a leaking sewer prior to renovation), and (b) theloss in separate stages of the flexural and compressivering stiffnesses of the host pipe as it deteriorates fur-ther. The effects of moving traffic loads have also beeninvestigated.

2 PROBLEM DESCRIPTION

The effects of groundwater loading on CIPP liners havebeen well studied and the associated design problemeffectively solved. Hydrostatic pressure resistance ofthe liner was for many years estimated (e.g. ASTMF1216) by applying an empirical ‘enhancement’factor,Ke to the formula for unrestrained buckling of an elas-tic ring, Timoshenko & Gere (1961). Fully consistentnon-linear creep buckling theory which takes properaccount of the restraining effect of a rigid host pipe andassociated gap imperfections, e.g. Boot (1998), Gum-bel (2001), is however now available. The restrainedbuckling pressure, (Pe)cr , is a function of liner flex-ural modulus, E∗, and thickness-diameter ratio, t/D,but also, critically, of the size of residual annular gapbetween the liner and host pipe, φ0, as well as of oval-ity and other shape imperfections (captured by thefactor Kr).

The development of ground loads on buried pipesis a problem of some complexity. A number of broad,simplifying assumptions must be made to allow anunderstanding of the behavior. The static loading on apipe will depend on structural stiffness of the pipe,and stiffness and shear strength of the surroundingsoil, Peck (1969), Mair & Taylor (1997).

In a typical prototype situation, deterioration bylongitudinal cracking at crown, invert and springingstransforms a sound, pseudo-rigid host pipe into a kine-matical, 4-bar, mechanism. The redistribution of soil

Unrestrained pipe Rigidly encased pipe

Figure 2. The effect of constraint on the buckling pressureof CIPP liners, Gumbel (1993).

stresses which accompanies this process is very sim-ilar to the positive arching over a trap door, as shownon Figure 3.

Installation of CIPP liner and post-lining deforma-tion of the host pipe potentially changes this trend.Soil movements after the installation cause interactionbetween the host pipe and the liner.The intensity of thisinteraction depends on liner stiffness, state of deteri-oration of the host pipe, post-lining deformations andsoil density. In the worst-case scenario (collapse ofvoids in the soil), the mechanism of the load transferon the liner may lead to the negative arching, as shownon Figure 4.

The effects of the host pipe crown settlements onthe soil load transfer can be illustrated by an order-of-magnitude analysis which combines the silo effectand the deformability of the soil above the host pipe

Deformed configuration ofthe host pipe

Original configurationof the host pipe

Settlement surface

Original surface

Figure 3. Stress distribution accompanying deterioration ofthe host pipe.

Original surface

Liner

Deformed configurationof the host pipe

Gap

Collapsingvoids

Settlement surface

Figure 4. Stress distribution caused by possible deforma-tions after the installation of the liner.

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crown. This analysis shows (Spasojevic et al., 2004b)that there is approximately a linear relation between theaverage vertical stress on the host pipe/liner system,σv, and displacements of the crown of the host pipe,wHP:

where σv0/γ D represents the initial average (effective)vertical stress at depth C before deformation of thehost pipe/liner, φ is the angle of shear resistance andG and K are shear and bulk modulus of the soil, respec-tively. γ is the unit weight of soil, D diameter of thepipe, while u is horizontal displacement of the soilelements. The gradient of the linear relationship (1) isgiven by the coefficient:

The equation (1) shows that the final stress on thecrown of the pipe is roughly a linear decreasing (incase of positive arching) or increasing (in case on neg-ative arching) function of crown displacements andthat the gradient of this function depends on deforma-bility parameters and shear resistance of the soil abovethe crown of the host pipe. The last product on theright-hand side of the equation (1) shows the effect ofaverage horizontal strains, ∂u/∂x.

The effects of liner stiffness are illustrated by theanalysis of thin rings to the self-balancing interactionloading, see e.g. Calladine (1989). Using the well-known formula for the uniform compression of rings,p0 = 2Et/D(δ/D)0 and denoting amplitudes of higherbending modes by δ̄n = (δ/D)n, where n represents thenumber of lobes in the mode Spasojevic et al., (2004b)showed that the supporting vertical stress correspond-ing to any interaction loading can be presented by:

Equation (1)–(3) show that the final vertical stresson a liner, σ̄v = σv/γ D, depends on a) ring stiffness ofthe liner, Sf = E(t/R)3; b) mobilized modes of bend-ing deformation, n; c) membrane stiffness of the liner,Et/D; d) relative displacements between the soil andthe host pipe; e) mobilized shear resistance of the soil;and f ) soil deformability.

Equation (3) shows that, in general, there is no 1:1correspondence between vertical loading on the linerand its distortions, and a special procedure must beapplied to derive the specific load-distortion relation-ship from each set of test results, Spasojevic et al.(2004b).

3 DESCRIPTION OF THE PHYSICAL MODEL

The layout of the model tested on the 10 m diametergeotechnical beam centrifuge at Cambridge Universityis shown in Figure 5. Besides simulating the self-weight of soil and host pipe, the centrifuge modelalso featured small scale modeling of other processeswhich affect stresses around a deteriorating pipe,including: a) host pipe deterioration, b) CIPP lining,c) soil void formation and d) the effect of moving traf-fic surcharge. Only a brief description is given herewhile more details can be found in Gumbel et al. (2003)and Spasojevic et al. (2004a).

Host pipe deterioration was simulated by a modelwhich comprised four hinged segments, machinedfrom a piece of standard aluminium alloy tube (Dural,grade HE30-TF, ρAl = 2.8 t/m3, E = 70 GPa), Figure 6.Wall thickness of the model host pipe was t =12.7 mm,while its outer diameter (OD) was 101.6 mm; thisrepresented a massive prototype pipe with 3.0 m out-side diameter and 360 mm wall thickness. The modeldesign allowed simulation of two distinct modes ofhost pipe deterioration: 1) articulation-transformation

Figure 5. Layout of the centrifuge model.

Figure 6. Model host pipe.

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of a pseudo-rigid and sound pipe into an articulated,4-bar mechanism, and 2) circumferential shorteningof up to 2.9% of the perimeter of the host pipe.

The instrumented model CIPP liner was a standarduPVC pipe of outside diameter Dl = 75 mm and thenominal standard dimension ratio (SDR = D/t) of themodel liner 42. Young’s modulus of the pipe mate-rial was 5 GPa; the unit mass of the liner materialwas 1300 kg/m3. Normalized ring stiffness of the liner,Sf /γ D, was 0.19.

Vertical and horizontal diameter changes of theliner were measured by 0.2 mm thick leaf-springbending gauges made from heat-treated beryllium-copper (ductile alloy with relatively high yield strainεy = σy/E ≈ 1.1%). The gauges were positioned atvarious points along the inside of the model liner pipe.

Void formation and collapse in the soil backfillwere modeled using an established centrifuge tech-nique described by Mair (1979): flexible membranebladders mounted over 12.5 mm diameter mandrels,running parallel to the pipe axis either below invert oron either side of the spring lines, were inflated withwater during soil placement and gravitational accel-eration. Initial diameter 2r0 of each model void was34 mm, i.e. 2r0/D was 0.46.The pressure of fluid in themodel voids and the volume of extracted water, V ,were measured during void formation. The process isquantified by the void displacement defined as the dif-ference between the initial and current diameters of themodel void. The effects of void formation at the springline and at the invert of the host pipe were investigated.

The effects of extremely heavy traffic loading on theground surface were investigated in conjunction withother effects. They were modeled using the traffic loadsimulator illustrated in Figure 8. This relatively lightsystem (6.5 kg, 1.4% of the payload), comprising twopneumatic cylinders, was used both to track the trafficload surcharge across the model while ‘on the fly’, andto apply vertical pressure on the soil surface totaling

Host pipe

Liner

Gauges

Figure 7. Instrumentation of the model liner.

140 kPa at 30 g. The dimensions of the footings andmagnitude of pressure were designed to simulate 45units of HB2 loading in accordance with BS 5400:Part2:1978.

The soil used in all tests was Leighton Buzzardsand (grade E), a well-characterised material usedin many previous experiments at Cambridge havingD90 = 150 µm, D10 = 90 µm, coefficient of unifor-mity Cu = 1.5, minimum void ratio emin = 0.64, emaxup to 0.97, and Gs = 2.67.

The described model was subject to a total of 14centrifuge tests. The loading history in each test wasrepresented as a sequence of loading steps and dete-rioration events. Although in preliminary tests severaldifferent permutations were explored, the sequence ofsteps applied in most cases was:

G: Spinning the package up to 30 g acceleration withthe rigid cap inserted at one end of the model pipeand tapered hinge rods inserted through the conicalholes in segments of the host pipe.

A: Articulation – release of the host pipe flexural ringstiffness.

V1: First stage of void formation – controlled partialrelease of bladder fluid.

C: Circumferential shortening – release of host pipecompressive stiffness.

V2: Second stage of void formation (fluid extractionto point of soil collapse).

Additionally in several tests the model was sub-jected to several cycles of simulated traffic surcharge(T) between each of the other steps.

In this paper we refer to the results of three tests asdescribed in Table 1. More detailed presentation of theresults is given in Spasojevic et al. (2004a).

Figure 8. Model of heavy traffic loading.

Table 1. List of presented centrifuge tests.

Test Void position(s) ρd [kg/m3]/ID

H2S1 Spring line 1496/0.57H2I1 Invert 1496/0.57

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4 TEST RESULTS

Figure 9 shows plots of vertical and horizontal diam-eter changes measured during the test H2I1. Diameterchanges were fairly similar and opposite throughout –the response of the liner was apparently dominatedby the two lobe (n = 2) mode of out-of-round deflec-tion. Distortion at the end of the G phase of the testwas ∼1.3% while the V1 and V2, A and C phases ofthe test produced additional distortion of some 2.5%.Applications of model traffic loading after each majordeterioration event produced small but measurableincrement of ring distortion (∼±0.1%).

The plot on Figure 10 shows the history of verticalstress on the crown of the host pipe during test H2I1,as measured by miniature Entran (EPL) pressure sen-sors (a 1 mm thick, 5 mm diameter circular stainlesssteel sensing membrane). Despite their serious limi-tations with regard to measurement of soil pressures,

Figure 9. History of diameter changes during the test H2I1.

The effectof trafficloading

Figure 10. History of vertical stresses on the pipe crownmeasured in test H2I1.

the sensors showed fairly consistent response to thepassing of traffic loading.

Diagrams on Figure 11 show liner distortions as afunction of void displacement, with datum set at theend of the A stage of the test. The V1 stage of thetest produced less than 0.5% distortion of the linerwhile the total liner distortion produced by all post-articulation events together (V1-C-V2 with total voidformation amounting to 27% of void displacement)was ∼2%. Figure 9 again generally confirms domina-tion of low-mode, elliptical distortions in the case ofinvert void formation.

Comparison of liner distortions as a function ofvoid displacement for the lined host pipe in mediumdense sand with an invert void (as shown on Figure 9)and the corresponding results for lined host pipes inmedium dense sand but with springing voids shownon Figure 12 reveal very important aspect of the voidposition.The diameter changes presented on Figure 12show that, for a given void displacement, the liner

Figure 11. Diameter changes in terms of void displace-ments, test H2I1.

V1V2

C springing voids

springing voids

Figure 12. Diameter changes in terms of void displace-ments, tests H2I1 and H2S1.

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distortions in the case of springing voids were sig-nificantly larger than in the case of invert voids. Thedifference is particularly distinct during the first phaseof void formation (stage V1): a void displacementv/D = 0.04 produced almost 1% of elliptical distor-tion in the case with springing voids but only 0.2% inthe case with an invert void. This indicates that col-lapse of voids at the springing has a greater impact ondistortions of the liner than void collapse at the invert.

5 SUMMARY AND CONCLUSIONS

This paper has analyzed the problem of transfer ofground loading to cured-in-place pipes, CIPP. It hasbeen shown that the loading on the liner results fromthe interaction between soil, deteriorated host pipe andliner involving a) the ring and membrane stiffnesses ofthe liner, Sf and Et/D; b) activated modes of bendingdeformation, n; c) relative displacements between thesoil and the system comprising host pipe and liner;d) mobilized shear resistance of the soil; and e) soildeformability.

A non-dimensional formulation was used for designof a 1/30th scale physical model which was sub-ject to 30 g of centrifugal loading. Features of themodel included: a) a complex, two-stage deteriora-tion mechanism of the host pipe, simulating the effectsof both articulation (loss of flexural ring stiffness)and circumferential shortening (loss of compressivering stiffness); b) an instrumented close-fitting, non-bonded flexible liner; c) simulation of the formationand collapse of soil voids immediately below and oneither side of the pipe; and d) application of a moving,heavy traffic load ‘on the fly’.

Loading of the centrifuge model in a series of 14tests was designed to simulate a range of realistic‘worst-case scenarios’ for transfer of soil and trafficload to a CIPP liner. The examples of experimentalresults presented in this paper show that, under theextreme conditions applied, the response of a flexiblesewer liner to external loads other than groundwa-ter pressure is governed by interactions between theliner, host pipe and the surrounding soil. In adjustingto deterioration events and void formation, the existingpipe-soil structure imposes quantifiable out-of-rounddeflections on the liner pipe.

The insights provided by centrifuge modeling intothe conditions for transfer of ground-related strains toa close-fitting, flexible, gravity sewer liner also offerthe basis for development of an improved practicaldesign methodology for such liners.

ACKNOWLEDGEMENTS

The experimental project described has been fundedprimarily by a grant from the UK Engineering and

Physical Sciences Research Council, with additionalcontributions and guidance from Severn Trent Waterplc and Insituform Technologies Ltd.

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