Infiltration and GW Flow - Influence on Tunnel Face Stability

7/30/2019 Infiltration and GW Flow - Influence on Tunnel Face Stability

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O. Kusakabe, K. Fujita & Y. Miyazaki (eds.) Geotechnical Aspects of Underground Construction in Soft Ground, Tokyo, Japan, 2000, pp. 339-344.

Influence of Infiltration and Groundwater Flow on Tunnel Face Stability

W. BroereGeotechnical Laboratory, Delft University of Technology, The Netherlands

A.F. van TolRotterdam Public Works, The Netherlands

Geotechnical Laboratory, Delft University of Technology, The Netherlands

ABSTRACT: During the excavation of tunnels in saturated soft soils, a pressurized bentonite slurry is often usedto support the tunnel face. The slurry should form a filter cake, which is used to transfer the support pressureonto the soil. This filter cake is constantly removed by the cutter teeth of the TBM during excavation and slurrywill infiltrate into the soil while the filter cake rebuilds. This results in excess pore pressures directly in front

of the tunnel face. To quantify the influence of these excess pore pressures on the stability of the tunnel face, asimple groundwater-flow model has been incorporated in a wedge stability analysis. For a tunnel in fine sandlayers, the pore pressure distribution calculated with this model has been compared with field measurements. Itis shown that the minimal support pressure is significantly higher, compared with full-membrane calculations.

1 INTRODUCTION

During the excavation of a tunnel in soft water bearingsoils, it is often necessary to provide a temporary sup-port to prevent collapse of the working face. To estim-

ate the minimal support pressure needed a number ofmodels has been proposed over the years. Based on ob-servations made in field and laboratory tests Broms &Bennermark (1967) derived a stability ratio for purelycohesive soils. Davis et al. (1980) obtained a set ofoverburden dependant stability criteria based on thelimit analyis of a purely cohesive (Tresca) material,which corresponded well with the results of centrifugetests in clay. Using a similar approach Atkinson &Potts (1977) proposed an expression for the minimalsupport pressure in a cohesionless frictional materialand Leca & Dormieux (1990) presented a number ofupper and lower bound solutions for the more complexcase of a cohesive-frictional material. The commonfactor in all these models is that they do not incorpor-ate the effects of pore pressures or heterogeneities ofthe soil body.

In permeable soils below the water table the porepressures are often the main contribution to the forcesthat have to be supported by the shield. In order toincorporate the pore pressures in a stability analysis,Jancsecz & Steiner (1994) suggested a wedge shapedfailure mechanism loaded by a soil silo, as sketched inFigure 1. This approach is similar to the one outlinedby Horn (1961) and has parallels with the calculationmethods used for slurry filled trenches. Jancsecz &Steiner used this wedge model to calculate the minimalsupport pressures for a tunnel in a purely frictional

material and showed the effects of varying overburden.

In the model of Jancsecz & Steiner it is assumed thatthe entire support pressure is transferred onto the soilskeleton by an infinitely thin membrane at the workingface. In slurry shield tunneling bentonite, other clays

or aggregates are often added to the working chamberto provide such a filter cake. This cake should sealthe working face to prevent the slurry from infiltratingthe soil and should ensure an efficient transfer of thesupport pressure onto the soil skeleton. In fine grainedsoils a filter cake is indeed formed on top of the work-ing face and acts as an impermeable membrane.

In coarse soils however, the slurry will infiltrateinto the soil to a certain extent, see e.g. Mller--Kirchenbauer (1977), and the full-membrane assump-tion is not valid. The effectiveness of the support

decreases as the slurry penetrates the soil which un-dermines the stability of the tunnel face with increas-ing slurry penetration distance. Anagnostou & Kovri(1994) presented a wedge stability model which in-cluded this effect of slurry infiltration. They assumedthat the penetration distance of the slurry would alwaysbe greater than the cutting depth of the tunnel boringmachine (TBM) and reasoned that a constant penetra-tion distance would then establish itself during boring.They showed that in coarse soils the support pressurecalculated with a full-membrane wedge model maywell suffice during the actual excavation, but that dur-

ing stand-still the slurry penetrates into the soil andgradually undermines the stability of the tunnel face,until collapse of the face occurs.

Although the wedge stability model as presented byAnagnostou & Kovri included the influence of the

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A

B

C

D

E

F

D

C

z

x

y

Figure 1. Wedge and silo model

equilibrium pore pressures as well as the bentonitepenetration process, it does not deal with the develop-ment of excess pore pressures in front of the TBM. Ex-cess pore pressures may occur if the outflow of groundwater in the layers before the TBM is confined, for ex-ample, when tunnelingin sand lensesor layersoverlaidby impermeable clay and the filter cake at the tunnelface is somehow disturbed or too permeable.

Such a disturbance of the filter cake can be of majorimportance in fine to medium granular sands. Duringstand-still a filter cake will establish itself at the faceand the assumption that the face is sealed by an imper-meable membrane is reasonably valid. During excav-ation however, it may well occur that the cutting depthof the teeth on the cutter wheel of the TBM is so largethat the entire filter cake is removed by each passageof the cutter arms. After the filter cake is removed,the slurry will infiltrate into the soil and a new filtercake will build. During this process large amounts of

filtrate water will flow into the soil, resulting in excesspore pressures in front of the TBM.

This combination of effects adversely affects the sta-bility of the tunnel face in a number of ways. Firstlythe removal of the filter cake reduces the effectivity ofthe support pressure, as described by Anagnostou &Kovri. Unless the soil is coarse however, this is arelatively minor effect. Secondly the increase of porepressures leads to a reduction of the effective stressesand thereby a reduction of the friction capacity of thefailure wedge. And the increased pore pressures ef-fectively cancel part of the support pressure. To com-pensate for this combination of effects a higher min-imal support pressure is needed, as compared to a full-membrane model. This higher support pressure willin turn lead to an increased filtration rate and higherexcess pore pressures.

et

w

x

z

ztop

zbot

K K

Gw TT

Gs

E W

Figure 2. Definition of forces acting on the wedge and

infiltration zone (shaded area)

The Authors have incorporated a simple ground wa-ter model in a wedge stability analysis and used the

resulting model to quantify the influence of the slurryinfiltration process and excess pore pressures on thestability of the tunnel face. The results have been com-pared with field measurement obtained at the site ofthe Heinenoord tunnel in the Netherlands.

2 WEDGE STABILITY MODEL

The collapsing soil body in front of the face can beschematised as a triangular wedge loaded by a soil

silo, as sketched in Figure 1. Forces acting on thewedge are the effective weight of the wedge itself,the vertical weight of the silo, the shear forces actingalong the slanted failure plane (AEFD) as well as thetriangular side planes, the load resulting from the porewater and the support force of the slurry. For a givenvalue of the angle between the horizontal and the slipsurface, see Figure 2, the resulting equilibrium equa-tions can be solved and the required support pressure isfound iteratively by maximising the resulting supportpressure. Jancsecz & Steiner (1994) have presentedthe resulting minimal support pressures for a tunnel in

homogeneous non-cohesive soil.As the development of excess pore pressures is most

likely to occur in heterogeneous, stratified soils, wewill need to extend the basic equilibrium equations ofthe failure wedge to include soil stratification. Thiswill result in a set of equilibrium equations for eachlayer that intersects the wedge. As shown in Bro-ere (1998) it is possible to reformulate this problem interms of integrals over the entire wedge.

To this end we define w(z) the width of the wedge atdepth z and introduce the shorthand notation + and

for the goniometric relations+ = tan sin + cos (1) = tan cos sin . (2)It should be noted that the angle of internal friction

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generally depends on the depth z, i.e. (z), espe-cially when different soil layers occur within the fail-ure wedge. This also holds for the other soil proper-ties used in this Paper. However, to keep the formulaereadable this depth-dependance has not been writtenexplicitely. Of special interest is the fact that the slipangle may vary gradually or discretely within dif-ferent layers, as this allows the introduction of differ-

ent failure shapes into the stability analysis. For thenumerical examples presented in this Paper the sim-plification has been made that is constant for all z,as this significantly reduces the number of iterationsneeded to determine the minimal support pressure.

Now the vertical components of the friction forceson the slip surfaces of the wedge can be written as

K = Dztop

zbot

c

sin dz, (3)

T

= ztop

zbotc +

Ky v tan

w

dz, (4)

where K results from the friction on the slip planeAEFD and T from plane ABE. Here c denotes co-hesion, Ky is the coefficient of horizontal effectivestress and v is the vertical effective stress. The ef-fective wedge weight Gw is simply the integral of theeffective volume weight of the soil times the wedgewidth w times tunnel diameter D and the vertical loadat the top of the wedge resulting from the soil silo is

Gs=

D2 cot v

(ztop), (5)

where the effects of soil arching as well excess porepressures have to be incorporated in the calculation ofv.

For a given value of slip angle the resulting hori-zontal wedge force E can be found from

E = D Gs + Gw + K + 2Tztop

zbot

+ dz

. (6)

Now the support force S = E + W for a given angle can be calculated from the force exerted by the waterat the slip plane AEFD,

W = Dztop

zbot

p0(z) + p(w(z), z)dz. (7)

In order to calculate W the pore pressures at rest p0and the excess pore pressures p(x, z) are needed.To establish the distribution of excess pore pressurewe will take a closer look at the effects of the slurryinfiltration and groundwater flow.

2.1 Slurry Infiltration

If the slurry pressure exceeds the pore pressures in thesoil, as is needed to support the face in non-cohesive

et

pp

pfc

ps

s p0

p(w(z), z))

p(x, z)

Figure 3. Pressure drop over penetration zone and excess

pore pressure distribution

soils, the slurry will infiltrate the soil and form a fil-ter cake. The influence of this process on the stability

of vertical trenches has been studied by a.o. Mller--Kirchenbauer (1977) and Kilchert & Karstedt (1984).From their work we find that the maximal penetrationdistance emax depends primarily on the total pressuredifference over the filter cake ps , which is the dif-ference between the support pressure s and the porepressure in rest p0.

emax =ps d10

F(8)

Here d10 is the characteristic grain diameter at which10%mass passes the sieve, F the shear strength ofthe bentonite and describes the relation betweenthe grain size and the effective radius of a flow chan-nel, and normally takes values between 2 and 4, seeKrause (1984) or Kilchert & Karstedt (1984).

When during excavation the cutter teeth largely orcompletely remove the filter cake at the face, the slurrywill again start to infiltrate and a new cake will be builtover time. During this build-up process, we can nolonger assume that the support pressure is transferredonto the soil skeleton by a membrane, but seepageforces from the slurry and filtrate water will stabil-

ize the soil. Krause (1987) has shown that the time-dependant infiltration distance et can be described by

et

emax= t

a + t. (9)The timespan a is the time at which half the maximimpenetration distance is reached. This value can forexample be determined from a column infiltration test.

By linearising the dependance between the penetra-tion distance et and the pressure drop over the filtercake pf c, we can invert (8) to find the pressure dropover the partial filter cake at each moment in time as

pf c = et F

d10. (10)

In practice the infiltration distance will vary over theface with the time passed since the cutting wheel has

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Hk

p0

c

x

p(x)

Figure 4. Schematisation of semi-confined aquifer

removed the filter cake. For this model however amean pressure drop over the partial filter cake is as-sumed, which can be found by selecting a proper meaninfiltration distance et, i.e. a proper value for the time

span t since the removal of the filter cake. Field obser-vations suggest t approximately equal to half the timespan between subsequent passages of the cutter arms.We assume that the resulting pressure drop equals theseepage forces exerted by the infiltrating slurry on thesoil skeleton and the remaining excess pressure

pp = ps pf c (11)

is used to compute the hydraulic head which will beused as input for the groundwater flow model.

2.2 Groundwater Flow

Essentialy the inflow of the filtrate water into the soilis a non-stationary ground water flow problem. Usingthe filtration velocity of the slurry, which can be easilyderived from (9), the discharge of filtrate water fromthe working chamber can be estimated. Field observa-tions suggest that in situations where the build-up ofexcess pore pressures significantly influences the sta-bility of the face, the discharge of filtrate water is largeenough that an almost stationary flow will be reached

in the vicinity of the face during the excavation pro-cess. When this is the case, the ground water flow canbe approximated as a stationary flow problem, whichwill yield to a safe upper bound value for the excesspore pressures.

The basic equations of stationary flow are describedin many text books on groundwater mechanics, seee.g. Verruijt (1970). In the current application wewill schematise the soil in front of the the TBM as aone-dimensional semi-confined aquifer, see Figure4,as this is appropriate for the case history considered inthe next Section. In situations where no impermeableor semi-permeable layers are present the solution ofan unconfined radial flow might be more appropriate.

Using the hydraulic head at the far side of the par-tial filter cake pp as the necessary boundary condi-tion, the excess pore pressure distribution in the semi-

confined aquifer can be established as

p(x, z) = p(x, z) p0(z)= pp(z) exp (x/) (12)

where is the leakage factor

=

k H

c. (13)

The leakage factor can be computed from the permeab-ility k and height H of the aquifer and the hydraulicconductivity c of the overlying aquitard, see also Fig-ure 4.

2.3 Solution procedure

For a given value of the slip angle the resulting wedgeforce E can be found if the distribution of excess porepressures p(x, z) is known. This distribution in turn

depends on the excess support pressure ps , whichcan be calculated if the water force W and wedge forceE are known. In general an iterative solution proced-ure will be needed to solve this interdependance, inwhich an estimated support pressure is used as inputfor the ground water calculation and a new estimate ofthe support pressure is calculated. This process is re-peated until an equilibrium of the excess pore pressureprofile is reached.

When the support pressure for a given slip angle hasbeen found, a second iteration procedure is needed tofind the angle for which the wedge force E is max-

imal. The resulting support pressure is the requiredminimal support pressure.

3 FIELD MEASUREMENTS

The influence of excess pore pressures on the face sta-bility will be illustrated with measurements taken atthe monitoring field of the Second Heinenoord tunnel.This 8.55m diameter tunnel has been constructed un-der the River Oude Maas in the vicinity of Rotterdam

in soft Holocene and Pleistocene layers. As the build-ing site is relatively close to open sea a tidal influenceis observed in the river and a damped and retardedtidal variation is also observed in deeper sand layers.Table 1 provides an overview of the (simplified) soilstratification and parameters (Bakker, 1996). Otherparameters which have been used in the calculationsare listed in Table 2.

Using a full-membrane model to calculate the min-imal support pressure s at the tunnel axis, we find arepresentive value s = 148kPa. This is only 16kPaover the pore pressure at that depth p0

=132kPa

and compares well with findings from saturated cent-rifuge tests (Bezuijen 1997). When the influence ofexcess pore pressures is included in the calculationshowever, as outlined in this Paper, a minimal supportpressure s = 212kPa is found, approximately equal to

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Top wet(dr y ) c K0 kh c

Description [m] [kN/m3] [kPa] [] [m/s] [s]Mixture of sand and clay +2.50 17.2 (16.5) 3 27 0.58Sand, clayey 1.50 19.5 0 35 0.47Sand, clay layers 5.75 19 0 30 0.47 105Sand, clayey in places 10.0 20.5 0 36.5 0.45 1 104Sand, gravelly 17.5 20.5 0 36.5 0.50 2 104Clay, sandy in places

20.75 20 7 31 0.55

Table 1. Soil stratification and parameters for Second Heinenoord Test Field North

Tunnel axis NAP -13.2m

Water table NAP +0.0m

Bentonite shear strength F 5 PaCharacteristic grain size d10 = 4 m

Excavation speed 2 rotations/min

(5-spoke wheel)Table 2. Parameter values

the mean support pressure used. The required differ-ence between p0 and s has risen to 80kPa, a five-foldincrease compared to the fulmembrane model.

As part of a research program coordinated by theCentrum Ondergronds Bouwen (COB), a number oftest fields were set up on both sides of the river. Thelayout of the test fields has been previously describedby Leendertse et al. (1997). Of special interest are thepiezometers installed in the track of the TBM. Thesewere positioned at such a depth that they were roughly

aligned with the center of the cutter wheel and weredestroyed as the TBM passed the gauge. Up to thatpoint they provided a clear picture of the excess porepressure distribution in front of the TBM, which hasbeen plotted in Figure 5.

In Figure 5 the measured pore pressures have beenplotted against the distance to the tunnel face. In thisrepresentation the piezometric head during stand-still,approximately 120kPa, is given by the lowest pointon the downward spikes that can be observed at 1.5mintervals. A small tidal influence can be observed in

these measurements during stand-still. The remainderof the plotted line represents the excess pore pressuresmeasured. These are only measured during the actualexcavating process and immedeately afterwards. Assoon as the cutter wheel is stopped a drop in the excesspore pressures is observed and the remaining excesspore pressures dissipate.

From the support pressure s = 212kPa a mean pres-sure drop over the partial filter cake pf c = 48kPahas been calculated and the remaining excess pres-sure pp = 32kPa has been used as input for thegroundwater calculations. The resulting excess pore

pressures have also been plotted in the Figure 5. Ascan be seen prediction and measurement are in goodaccordance.

The Authors conducted a parameter study whichshowed that the calculated excess pore pressures are

highly sensitive to the leakage factor of the semi-confined aquifer. Furthermore there is a strong de-pendency on ratio of the excavation speed to the slurryinfiltration velocity, as the angular speed of the cutterwheel influences the mean infiltration distance used inthe calculations.

These observations are confirmed by measurements

taken during the construction of another tunnel in thevicinity of Rotterdam. This tunnel has been bored insomewhat coarser sands at location where no clearlydefinable impermeable overlaying strata are present.Again using the calculations outlined above, excesspore pressures up to 5kPa were expected in the vicin-ity of the tunnel face, decreasing strongly with dis-tance. This prediction corresponded very well withpore pressure measurements obtained.

4 CONCLUSIONS

When during excavation with a slurry shield the filtercake at the face is removed, the slurry will infiltrate thesoil to build a new filter cake and excess pore pressureswill develop in front of the TBM. These phenomenahave been included in a face stability model and leadto an implicite set of equations, which has been solvediteratively.

Such excess pore pressures have been shown to bea major influence on the stability of the tunnel face asthey reduce the effectiveness of the support force fromthe slurry andlowerthe effective stresses in the soil, re-ducing the friction capacity of the soil. To compensatefor these effects a higher support pressure is needed. Asignificant reduction of the face stability is most likelyto occur in heterogeneous soils and depends stronglyon the permeabilities of the different soil layers andthe mean infiltration distance of the slurry, which canbe controlled by the excavation speed of the cutting

wheel.

The minimal support pressure and excess pore pres-sures calculated withthe presented stability model cor-respond well with field measurements and experience.

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distance to gauge x in m

pore

pre

ssurep

in

kPa

35302520151050

200

190

180

170

160

150

140

130

120

110

TBMx

gauge

Figure 5. Excess pore pressure measurements taken at the Second Heinenoord Test Field North, adapted from

Bezuijen (1998), compared to calculated pore pressure distribution (dashed line)

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Infiltration and GW Flow - Influence on Tunnel Face Stability

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