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Research Collection Conference Paper Tunnel stability and deformations in water-bearing ground Author(s): Anagnostou, Georgios Publication Date: 2006 Permanent Link: https://doi.org/10.3929/ethz-a-010819313 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection . For more information please consult the Terms of use . ETH Library

Tunnel stability and deformations in water-bearing ground

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Page 1: Tunnel stability and deformations in water-bearing ground

Research Collection

Conference Paper

Tunnel stability and deformations in water-bearing ground

Author(s): Anagnostou, Georgios

Publication Date: 2006

Permanent Link: https://doi.org/10.3929/ethz-a-010819313

Rights / License: In Copyright - Non-Commercial Use Permitted

This page was generated automatically upon download from the ETH Zurich Research Collection. For moreinformation please consult the Terms of use.

ETH Library

Page 2: Tunnel stability and deformations in water-bearing ground

1 INTRODUCTION

The effects of groundwater in tunnelling are mani-fold. During tunnel excavation in a water-bearingground, seepage flow towards the opening takesplace, because the pressure at the excavationboundary is, in general, atmospheric and the tunnelacts therefore as a groundwater drain. The seepage-flow may lead to a draw-down of the water-level,to a decrease in the discharge of wells, or to con-solidation and subsidence. Besides these - in thebroader sense - environmental impacts, large waterinflows may impede excavation works or have a se-rious impact on the serviceability of the tunnelduring its operation phase.

The present paper focuses on the mechanicalaction of water: Water can affect both the stabilityand the deformations of a tunnel by reducing theeffective stress and thus resistance to shearing, bygenerating seepage forces towards the excavationboundary; and by washing out fine particles fromthe ground. Transient seepage flow in a low-permeability ground is one major cause of time-dependent effects in tunnelling. Furthermore, whentunnelling in weak ground, the seepage forces actingtowards the opening may impair its stability. Theinteractions between seepage flow and equilibrium,porewater pressure and stress field around a tunnelconstitute perhaps the most important coupledprocess in geotechnical engineering.

Figure 1. (a) Face instability; (b) Failure of an open shell; (c)Subsidence; (d) Overstressing of a grouting body in a faultzone; (e) Squeezing pressure or deformation; (f) Floor heavein swelling ground.

Keynote Lecture, Eurock 06, ISRM Symposium on Multiphysics coupling and long term behaviour in rock mechanics, Liège (Belgium), May 9 – 12, 2006

Tunnel stability and deformations in water-bearing ground

G. AnagnostouETH, Swiss Federal Institute of Technology, Zurich, Switzerland

ABSTRACT: Water can affect the stability and the deformations of a tunnel by reducing the effective stressand thus the resistance to shearing, and by generating seepage forces towards the excavation boundaries. Theseepage-flow may lead to a draw-down of the water-level and to time-dependent subsidence due to consolida-tion. Furthermore, when tunnelling in soft ground, the seepage forces acting towards the opening may impairits stability. The movement of water in a low-permeability ground is one major cause of time-dependent ef-fects in tunnelling. This paper discusses the effects of water by means of examples covering a wide range oftunnelling conditions. Emphasis is placed on practical questions of tunnel engineering, on the mechanisms gov-erning the stability and deformation of underground openings in water-bearing ground and on the significanceof poromechanical coupling.

Page 3: Tunnel stability and deformations in water-bearing ground

In the next pages the effects of water on the stabil-ity and deformations of underground openings willbe discussed by means of examples covering a widespectrum of tunnelling conditions. Rather thandelving into the details of mathematical modelling,emphasis will be placed on practical questions oftunnelling through water-bearing ground, on themechanisms governing the observed phenomena ofstability and deformation and on the significance ofporomechanical coupling. The discussion will startwith the case of shallow tunnels through weakground, and will continue with the crossing of faultzones consisting of so-called “swimming” ground,finishing with tunnelling through squeezing orswelling rock (Fig. 1). What unifies all of thesecases are the underlying mechanical principleswhich can be traced back to the fundamental worksof Terzaghi and Biot.

2 SHALLOW TUNNELS IN WEAK GROUND

2.1 Introduction

The most serious risks in tunnelling through weakground are associated with a collapse of the tunnelface. In shallow tunnels the instability may propa-gate towards the surface creating thereby a chim-ney and a crater on the ground surface (Fig. 1a).The face failure results then in excessive subsidenceand damage to overlying structures. Depending onthe construction method, i.e. on the sequence of theexcavation and temporary support works, variousother collapse mechanisms need also to be consid-ered in conventional tunnelling. For example, whentunnelling by the “top-heading and bench” method,a collapse up to the surface may occur also as aconsequence of an unsufficient bearing capacity ofthe ground beneath the footings of the temporarysupport arch (Fig. 1b). In general, the tunnel por-tion close to the heading is particularly demanding,as the application of support in this area interfereswith the excavation works. Besides the stability ofthe opening, the control of surface settlement is es-sential in urban tunneling (Fig. 1c).

The stability and deformations of tunnels in wa-ter-bearing ground depend greatly on the perme-ability of the ground. Tunnel excavation in a lowpermeability ground does not alter the water con-tent around the opening on the short-term. Instead,excess pore water pressures develop. These dissi-pate over the course of time leading thus to con-solidation and additional deformations of theground. From the standpoint of stability twostages can be distinguished: the short-term stage,corresponding to undrained shear, and the long-term stage, corresponding to drained shear. In ahigh permeability ground the water content adjusts

itself immediately to the stresses prevailing afterexcavation.

2.2 Stability

Stability issues are usually investigated by limitequilibrium analyses. As deformations are nottaken into account in such analyses, the groundmay be idealised as a plastic material obeying theMohr-Coulomb failure condition either with the ef-fective shear strength parameters (c', φ') or withthe undrained shear strength Cu. As in other prob-lems involving the unloading of the ground (i.e., areduction in the first invariant of the total stress),undrained conditions are more favourable for thestability of underground openings. For commonadvance rates (up to 20 m/d), drained conditionsare to be expected when the permeability is higherthan 10-7-10-6 m/s (Anagnostou 1995b).

When analysing the stability of the tunnel face,a simple collapse mechanism can be considered(Fig. 2a) consisting of a wedge and a prism whichextends from the tunnel crown to the surface(Davis et al. 1980, Anagnostou & Kovári 1996).With the exception of closed-shield tunnelling, thepiezometric head at the tunnel face is lower thanthat prevailing in the undisturbed ground. Conse-quently, water seeps towards the face, therebygenerating seepage forces which have a destabilisingeffect and must be taken into account in a drainedanalysis. The seepage forces are equal to the gradi-ent of the hydraulic head field. The computation ofthe seepage forces therefore calls for a three-dimensional steady-state seepage-flow analysis(Fig. 2b). Thus, a drained face stability analysisproceeds in three steps: (i) determination of thethree-dimensional hydraulic head-field by means ofa finite element computation; (ii) integration of theseepage forces acting upon the components of thespecific collapse mechanism (S, Fig. 2c); (iii) solu-tion of the limit equilibrium equations.

Fig. 2d shows the support pressure required inorder to stabilise the face as a function of thesafety factor (defined in terms of the shear strengthconstants). The upper line applies to the long-termconditions prevailing when tunneling under a con-stant water table (steady state piezometric headfield as in Fig. 2c). The face support requirementdecreases considerably if groundwater drainage iscarried-out prior to tunneling (lower line). In low-permeability ground, the face would remain stableeven without support (lowest line). The diagramshows the influence of groundwater conditions andof time on face stability.

As another example, consider a partial excava-tion with an invert closure in a distance L from theface (Fig. 3a). The overall stability of the topheading depends on the loads acting upon the tem-porary support shell and its bearing capacity, as

Page 4: Tunnel stability and deformations in water-bearing ground

well as the bearing capacity of the footings. At thelimit state, the load V from the overburden and theforces W at the shell footings can be calculated bymeans of the silo theory (Janssen, 1895) and bythe common foundation bearing capacity equations,respectively. Fig. 3b shows the safety factor of thesystem as a function of L. The diagram illustrates awell-known fact from tunneling practice: in weakground, rapid advance and closing the ring near tothe face improve stability conditions considerably.According to Fig. 3c, which shows the critical

length L as a function of the shear strength Cu, noteven short-term stability can be assured in adverseconditions and a closed support rind must be pro-vided practically immediately. Note that in therange of low strength values (Cu<150 kPa), rela-tively small variations of strength (of, e.g., ±25%),which may take place within short distances duringtunnel excavation in a heterogeneous ground, affectthe critical length L considerably from the con-structional point of view (ring closure within oneversus four diameters).

Figure 2. (a) Collapse mechanism at the tunnel face (Horn1961); (b) Numerical model for seepage flow analysis; (c)Hydraulic head field ahead of the tunnel face; (d) Results of alimit equilibrium stability analysis (geometry as in Fig. 2c)based upon the method of Anagnostou & Kovári (1996).

Figure 3. (a) Failure mechanism; (b) Safety factor as a func-tion of top heading length L; (c) Maximum length L as afunction of undrained shear strength Cu.

Page 5: Tunnel stability and deformations in water-bearing ground

1.3 Deformations

Although limit equilibrium analyses are sufficient forthe investigation of stability questions, coupledstress- and seepage-analyses provide useful insightsinto the mechanics of failure. With such analysesboth short- and long-term behaviour can be studiedconsistently, based upon the effective strength pa-rameters, i.e. without additional assumptions con-cerning the undrained strength.

Figure 4. Stability of a shallow tunnel (numerical example).(a) Crown settlement u over support pressure p at time t=0+

(undrained conditions) and t=∞ (steady state); (b) Short-term (t= 0+) plastic zone (unsupported opening); (c) Steady state(t=∞) hydraulic head field Φ , respective seepage forces f andextent of plastic zone (support = 17% of initial stress). Com-putational assumptions: Isotropic initial stress field; Elastic,perfectly-plastic material; Young’s modulus E = 50 MPa;Poisson’s number ν = 0.25, friction angle φ' = 28°, cohesionc' = 20 kPa, assoc. flow rule, γ total = 20.5 kN/m3; porosity n= 20%.

Fig. 4a shows the crown settlement u of a shallowtunnel as a function of the support resistance p(normalized by the initial stress). The condition ofconstant water content applies for the short-term de-formations, while the long-term deformations havebeen obtained by taking into account the steady statehydraulic head (Fig. 4c). In the short-term the open-ing remains stable even without support, while in thelong-term a minimum support must be provided forstability. When the support pressure approaches acritical value pcr, the ground fails up to the surface(Fig. 4c) and the settlement becomes asymptoticallyinfinite (Fig. 4a). The seepage forces reach approxi-mately 20 kN/m3 at the tunnel floor (i.e., twice thesubmerged unit weight of the ground) indicatingthereby the risk of piping in the case of an open in-vert.

Coupled analyses are indispensable for investi-gating questions of surface settlement. Fig. 5b and 5cshow the settlement troughs as well as the steadystate hydraulic head fields around a shallow tunnelfor the case of a constant or a depressed water level,respectively. In agreement with field observations(O'Reilly et al. 1991), the settlement trough deepensand widens with time while the angular distortionremains approximately constant.

3 FAULT ZONES

3.1 Introduction

Tunnel sections in soil-like materials that are subjectto high water pressures present a considerable chal-lenge to tunneling operations. In the past suchground was described as “swimming”, which aptlyemphasizes the importance of the water. The widthof such fault zones may vary from a few meters todecametres. In some cases they are accompanied lat-erally by a heavily jointed and fractured rock zone,in other cases the transition to competent rock isvery distinct. When such a zone is suddenly encoun-tered water and loose material flows into the open-ing. Often one speaks therefore of a "mud inrush",which in extreme cases can completely inundate longstretches of tunnel.

To overcome fault zones involving soil under highwater pressures the ground is drained and strength-ened ahead of the working face (Fig. 6). Experienceshow that in the case of small tunnel profiles indense ground or in ground exhibiting some cohesion,drainage alone is often sufficient to enable excava-tion.

Page 6: Tunnel stability and deformations in water-bearing ground

Figure 5. Settlement induced by tunnelling (numerical example from Anagnostou 2002): (a) Model; (b) Settlement trough andsteady state hydraulic head field for an constant water level; (c) Settlement trough and steady state hydraulic head field after draw-down of water level. Parameters: Ground: elastic, perfectly-plastic material with associated flow rule, E = 60 MPa, ν = 0.30, φ' =30°, c' = 0, porosity n=30%. Lining: d = 0.20 m, E = 20 GPa.

The ground can be strengthened and sealed eitherby grouting or by artificial freezing. Ground freez-ing however only offers a temporary solution. Indeep tunnels, in general a permanent strengtheningand sealing is required, which can only be obtainedby grouting. By injecting a fluid into the ground,which then hardens, its strength, stiffness and im-perviousness are increased. The aim is usually toobtain a cylindrical grouted body by carrying outthe grouting works in a controlled way.

1.2 Effect of seepage flow

The effect of water on the stability of groutingbodies can be explained by considering the simplecase of a circular tunnel (of radius a) in a homoge-neous and isotropic initial stress field (total stressσo, Fig. 7a). The initial water pressure at the eleva-tion of the tunnel is assumed to be uniform withthe value po. After tunnel excavation the groutedzone takes the form of a thick-walled cylinderwhose outer surface (at radius r = b) is loaded bythe surrounding untreated ground and the water.

The ground (both the grouted and the untreated)is considered to be a porous medium according tothe principle of effective stresses. Elastoplasticmaterial behaviour with Coulomb's failure criterionis assumed. Seepage effects are taken into accountbased upon Darcy's law. The permeability of thegrouted body is k, that of the untreated ground ko.The excavation boundary (r=a) represents a seep-age face, i.e. the water pressure p at that pointtakes on the atmospheric value. Under these as-sumptions the system fulfils the condition of rota-

tional symmetry, and closed-form solutions can bederived (Anagnostou & Kovári 2003).

Due to the filling of the pores, the permeabilityof the grouted zone is very low compared to thatof the untreated ground. In the borderline case of avery stiff and low-permeability grouting body, thetunnel excavation does not have any effects on thestresses and porewater pressures in the surround-ing untreated ground. The conditions at the ex-trados of the grouting cylinder are given, therefore,by the initial values of effective stress σo’ andporewater pressure po. The hydraulic head differ-ence between the untreated ground and the excava-tion boundary is dissipated entirely within thegrouting body.

Figure 6. Tunneling through a fault zone.

Page 7: Tunnel stability and deformations in water-bearing ground

Figure 7. Extent of plastic zone ρ and distribution of porewater pressure p when (a) the permeability k of the groutedzone is very low relative to the permeability ko of the un-treated ground; (b) when the grouted zone is completelydrained. Parameters: Radius a = 5 m; Radius b = 13 m; Ini-tial total stress σo = 4.2 MPa; Initial pore water pressure po

= 2 MPa; Friction angle φ’ = 30°; Uniaxial compressivestrength fc = 3 MPa. Calculation after Anagnostou & Kovári(2003).

Figure 8. Water inflow Q (normalized by the inflow Qo tak-ing place without grouting) and thickness (ρ-a) of the plasticzone (normalized by the thickness b-a of the grouting cylin-der) as a function of the permeability k of the grouted zone(normalized by the permeability ko of the untreated ground).Parameters: as in Figure 7. Calculation after Anagnostou &Kovári (2003).

The porewater pressure distribution within thegrouted body (Fig. 7a) is:

p = po

ln(r / a)ln(b / a)

(1)

The grouting cylinder is loaded by the ground pres-sure σo’ acting at r = b and by the seepage forcesassociated with the porewater pressure gradientdp/dr. Depending on the magnitude of these pa-rameters and on the strength of the grouted zone,yielding may occur. The extent of the plastic zoneis given by its radius ρ (Fig. 7a).

The effect of the seepage forces can be demon-strated best by studying the equilibrium inside theplastic zone. The equilibrium condition is

d ′ σ rdr

=′ σ t − ′ σ r

r−

dpdr

(2)

where σr’ and σt’ denote the effective radial andtangential stress, respectively. The stress fieldwithin the plastic zone fulfils, furthermore, theyield condition

′ σ t =1+ sinφ1− sinφ

′ σ r + fc (3)

where fc and φ denote the uniaxial compressivestrength and the friction angle of the grouted body,respectively. From Equations (1) to (3) we obtain:

rd ′ σ rdr

=2sinφ

1− sinφ′ σ r + fc −

po

ln(b / a) (4)

From the above we note that the effect of pore wa-ter pressure is apparently equivalent to a reductionof the uniaxial compressive strength fc by po/ln(b/a)(cf. Egger et al. 1982). In the example of Fig. 7a, theseepage forces cause an apparent strength reduc-tion from 3 to 0.9 MPa!

An extensive plastification, such as the one inFig. 7a, is in general unacceptable as it may lead toa loosening of the grouted zone and carries the riskof an uncontrollable material and water inflow (in-ner erosion). The plastification of the grouted bodycan be limited by different measures, such as ap-plying a tunnel lining of higher resistance or byproducing a grouted body of larger diameter orhigher strength. In view of the considerable effectof seepage discussed above, it is obvious that an-other very efficient measure is the systematicdrainage of the grouting body.

Note that drainage does not reduce the total loadacting upon the grouted body. Due to the seepageflow, which takes place within an extended regionsurrounding the grouted zone, the untreated groundconsolidates towards the grouted zone and the ef-fective radial stress on the external boundary of thegrouted body increases by the same amount as thatby which the water pressure decreases there. The

Page 8: Tunnel stability and deformations in water-bearing ground

effective stress at the extrados of the grouted bodybecomes equal to the total initial stress σo. Never-theless, keeping the seepage forces away from thehighly stressed grouted region leads to a considera-bly narrower plastic zone (Fig. 7b).

The technical and financial feasibility of drain-age in an actual case depends on the quantity ofwater inflows. Reduction of water inflows calls fora lower permeability grouting body and implies amore intensive stressing (Fig. 8) or, in order to limitplastification, a higher strength grouting.

4 SQUEEZING ROCK

4.1 Introduction

When driving through zones of cohesive materialsof low strength and high deformability the tunnel-ing engineer is faced with problems of a completelydifferent kind. It is almost as if the rock can bemoulded, which is why it was formerly spoken ofa "mass of dough". If suitable support measures arenot implemented, large long-term rock deforma-tions will occur, which can lead even to a completeclosure of the tunnel cross section. The rock exertsa gradually increasing pressure on the temporarylining, which can lead to its destruction. In suchcases one can speak of "genuine rock pressure” andthe ground is characterized as "squeezing". The ba-sic aspects of tunneling in zones of squeezing rockhave been presented in a concise form by Kovári(1998). Typical examples of rocks prone tosqueezing are phyllites, schists, serpentinites,claystones, certain types of Flysch and decom-posed clay and micaceous rocks.

Experience shows that high pore water pressurepromotes the development of squeezing. This isconfirmed by the observation that considerablysmaller deformations take place when the rockmass is drained in advance.

The effects of porewater pressure on the me-chanical behaviour of squeezing rock have been in-vestigated by a comprehensive laboratory testingprogram, which was carried out at ETH Zurichduring the design and exploration phase of the 57km long Gotthard highspeed railway tunnel. Heav-ily squeezing ground was expected particularly inthe so-called “northern Tavetsch massif” (TZM-N). During mountain formation this zone was sub-jected to intensive tectonic action resulting in alter-nating layers of intact and weak kakiritic gneisses,slates, and phyllites. “Kakirite” denotes an inten-sively sheared rock, which has lost a large part ofits original strength. On account of a depth of coverof 800 m, of an initial pore water pressure of 80bar and of the expected rock properties, the ap-proximately 1100 m long TZM-N was a majorchallenge to the project. The laboratory tests re-

vealed that control of porewater pressure duringtriaxial testing is indispensable. Specimen pre-saturation and maintenance of a sufficient backpressure are essential for obtaining reliable and re-producible parameters (Vogelhuber et al. 2004).Conventional triaxial tests are inadequate, as theymay lead to a serious under- or over-estimation ofthe strength parameters. Consolidated drained(CD) and consolidated undrained (CU) tests pro-vided, despite the complex structure of the kakiriticphyllite, remarkably uniform results. The distribu-tion of the strength parameters obtained by suchtests was very small in comparison with conven-tional triaxial testing data.

Squeezing normally develops slowly, althoughcases have also been known where rapid deforma-tions occur very close to the working face. The de-velopment of rock pressure or deformation maytake place over a period of days, weeks or monthsand can be traced back generally to three mecha-nisms:

(a) The three-dimensional redistribution ofstress in the region around the working face. Thismechanism cannot explain long-term rock deforma-tions, because it occurs within two or three tunneldiameters from the working face.

(b) The rheological properties of the ground. Socalled "creep" is especially evident if the rock ishighly stressed as the failure state approaches,which indicates, therefore, that it plays an impor-tant role in squeezing.

(c) The excavation of a tunnel in saturated rocktriggers a transient seepage flow process, in thecourse of which both the pore water pressures andthe effective stresses change over time. The latterleads to rock deformations. Thus we are faced herewith a coupled process of seepage flow and rockdeformation. The more impermeable the rock, theslower will process be, i.e. the more pronounced isthe time-dependency of the rock deformation orpressure.

These three mechanisms are in general superim-posed. Here attention will be paid exclusively tothe processes associated with the development anddissipation of pore water pressures. The effects ofporewater pressure will be discussed on the basisof computational results obtained with simplemodels.

A rotationally symmetric system in plane strainwill be considered (see inset in Fig. 9). At the exca-vation boundary, an atmospheric porewater pres-sure (pa = 0) and a radial stress σa corresponding tothe lining resistance apply. At the far field bound-ary, stress and porewater pressure are fixed to theirinitial values. The rock mass is modelled as a satu-rated porous medium according to the principle ofeffective stresses. Seepage flow is taken into ac-count using Darcy’s law. The mechanical behaviour

Page 9: Tunnel stability and deformations in water-bearing ground

is described by an elastic, perfectly plastic materialmodel obeying Coulomb's failure criterion.

1.2 Short- and long-term behaviour

We first consider the two limiting states of tran-sient seepage flow: the state at t = 0+ ("short-termbehaviour") and the state at t = ∞ ("long-term be-haviour"). The first is characterised by the condi-tion of a constant water content, while the secondis governed by the steady state porewater pressuredistribution. The short-term volumetric strains arezero, while the long-term deformations are associ-ated with a volume increase caused by rock dila-tancy. The short-term behaviour is therefore morefavourable than the long-term behaviour.

This can be seen clearly by comparing the re-spective ground response curves (Fig. 9), whichdescribe the interdependence of radial displacementua at the excavation boundary and lining resistanceσa.

The short-term radial displacement ua stabilisesat approximately 0.36 m even in the case of an un-supported opening (lining resistance σa = 0). Long-term, however, the tunnel would close (uppercurve).

If one assumes that about 30 - 40% of theshort-term deformation occurs before the installa-tion of the lining (ahead of the excavation or in theimmediate vicinity of the working face, cf. Panet1995) and that a temporary lining can withstand aradial displacement of 0.20 m without experiencingdamage, then it has to be dimensioned for a rockpressure of approximately 0.30 MPa (Fig. 9, PointA). Long-term however the rock pressure wouldincrease to the much higher value of 1.5 MPa(Point B).

1.3 Time-development of squeezing

To deal with the problems encountered in tunnelsections exhibiting squeezing rock conditions, basi-cally two structural concepts exist (Kovári 1998):the "resistance principle" and the "yielding princi-ple".

In the former a practically rigid lining isadopted, which is dimensioned for the expectedrock pressure. In the case of high rock pressuresthis solution is not feasible.

The yielding principle is based upon the factthat rock pressure decreases with increasing defor-mation. By applying a flexible lining, the rockpressure is reduced to a manageable value. An ade-quate overprofile and suitable structural detailing ofthe temporary lining will allow for non-damagingrock deformations, thereby maintaining the desiredclearance from the minimum line of excavation.

Interesting results concerning the efficiency ofthese two structural concepts can be obtained byinvestigating:

(a) the time-development of the rock pressureunder a fixed radial displacement ua (the "resistanceprinciple" case);

(b) the time-development of the displacement uafor a constant lining resistance σa (the “yieldingprinciple” case).

Fig. 10a shows the results of two transientanalyses carried out in respect of these two cases.The ordinates σa and ua refer to the "resistanceprinciple" (left axis) and to the "yielding principle"(right axis), respectively. For the sake of simplic-ity, it was assumed that the lining was installed af-ter the occurrence of the short-term deformations.Thus the curves have their origin at σa = 0 and ua =0, respectively.

According to Fig. 10a, the radial displacement uaof a flexible lining develops at a much slower ratethan the rock pressure σa acting upon a rigid lining.The development of rock deformations in the firstcase needs more time, because it is associated withvolumetric strains and, consequently, presupposesthe seepage of a larger quantity of water. The rockpressure σa acting upon a stiff lining (the resistanceprinciple) increases within a month to the consid-erable value of 0.5 MPa, while the correspondingdeformation of the flexible lining at 0.03 m is stillnegligible. This result is interesting from the practi-cal point of view, as it shows that with a yieldingsupport one gains time.

Figure 9. Ground response curve at t = 0+ (short-term behav-iour) and at t = ∞ (long-term behaviour). Parameters: Tunnelradius 5 m; Depth of cover 300 m; Elevation of water table250 m; Young’s modulus E = 300 MPa; Poisson’s ratio ν =0.30; Friction angle φ’ = 25°; Cohesion c’ = 50 kPa; Loos-ening factor κ = 1.2.

Page 10: Tunnel stability and deformations in water-bearing ground

Figure 10. (a) The time development of the rock pressure (re-sistance principle) and of rock deformation (yielding princi-ple) compared in the same diagram. Permeability k = 10-10

m/s, other parameters as in Fig. 9. (b) The rock pressure (re-sistance principle) and the rock deformation (yielding princi-ple) after 15 days, as a function of permeability. Other pa-rameters as in Fig. 9.

Figure 11. Shortening of the drainage path caused by perme-able interlayers.

1.4 Effect of permeability

The duration of consolidation is governed by thepermeability of the ground. Increase permeabilityby a factor of ten and the rock pressure and therock deformation will develop ten times faster. Thegreat importance of permeability soon becomesclear when one plots the rock pressure and the rockdeformation at a particular time t in the function ofpermeability (Fig. 10b).

Permeability coefficients less than 10-9 m/secare characteristic for practically impermeable rock.Since the determination of permeability in thisrange is subject to large uncertainties, reliable pre-dictions of the time development of rock pressureor deformation are extremely difficult.

Additional prediction uncertainties exist in thecase of heterogeneous rock formations. From soilmechanics it is known that the duration of consoli-dation is proportional to the square of the length ofthe drainage paths. Thin permeable layers embed-ded in a practically impermeable rock mass lead toa shortening of the drainage paths (Fig. 11) causingthus a substantial acceleration of the squeezingprocess.

For a permeability k = 10-11 to 10-9 m/s, therock pressure would increases to 0.1 - 1.2 MPawithin 15 days (Fig. 10b). For a rock pressure of0.1 MPa a light temporary lining is sufficient,while a heavy support is required in order to sus-tain a load of 1.2 MPa. The difference between thetwo cases is important from the tunneling stand-point. As a consequence of some randomly distrib-uted permeable interlayers, the tunneling engineermay experience the rock mass in one case as "com-petent", and in the other as "disturbed".

Fig. 10b shows, nevertheless, that with a flexi-ble lining the consequences of prediction uncertain-ties are alleviated. For a permeability k = 10-11 to10-9 m/s, the radial displacement ua of a flexiblelining amounts to 0 - 0.25 m. The practical conse-quences of a poor estimate of convergence aremodest compared to the consequences of a wrongestimate of the time development of rock pressureacting upon a rigid support according to the resis-tance principle (damage to the lining and the needfor re-profiling).

Page 11: Tunnel stability and deformations in water-bearing ground

5 SWELLING ROCK

5.1 Introduction

Rocks containing certain clay minerals and in somecases anhydrite swell, i.e. increase in volume whenthey come into contact with water. The swelling isdue to water adsorption by the flaky structure ofthe clay minerals (so-called osmotic swelling) and,in the case of sulphatic rocks, also due to the gyp-sification of anhydrite.

Geological formations with swelling rocks (ju-rassic claystones, tertiary marlstones or Gypsum-Keuper) are widespread in France, Switzerland andSouthern Germany.

In tunnelling, the swelling manifests itself as aheave of the tunnel floor (Fig. 12a). When theheave is constrained by an invert arch, a pressuredevelops (Fig. 12b), which may damage the lining.If the depth of cover is small, also a heave of theentire tunnel tube may occur (Fig. 12c). Swellingdevelops usually over several decades thereby seri-ously impairing the long-term serviceability andstability of underground structures (Kovári et al.1988, Amstad & Kovári 2001).

5.2 Significance of hydraulic-mechanical coupling

One interesting feature of the swelling phenomenonis that the deformations occur only in the tunnelfloor. The walls and the crown remain stable overmany years.

The first continuum-mechanical models werebased upon the hypothesis that the swelling iscaused by the stress redistribution resulting fromthe tunnel excavation. Accordingly, swelling wasconsidered as a stress-analysis problem. Since sig-nificant differences between floor and crown do notexist in respect of the geometry or the initial andboundary conditions, stress-analyses predict swel-ling not only in the tunnel floor, but also in thecrown, independently of the specific constitutivemodel. This contradicts the facts and leads to un-safe predictions concerning the resulting stresses inthe lining (overestimated axial forces, underesti-mated bending moments).

Figure 12. Phaenomena in swelling rock.

Realistic predictions of the observed deformationpattern are possible only when taking into accountthe seepage flow and the hydraulic-mechanicalcoupling (Anagnostou 1995a). In a coupled analy-sis, the displacement field depends on the porewa-ter pressures prevailing around the tunnel and, con-sequently, on the hydraulic boundary conditions.The latter are different for the tunnel crown thanthey are for the floor. In several tunnels, free watercan be observed on the floor, while the crown andwalls appear to be dry.

5.3 Sulphatic rocks

Besides clay minerals, some swelling rocks also of-ten contain anhydrite (CaSO4). In a closed system,i.e. a system without mass exchange with its sur-roundings, anhydrite dissolves in the water andgypsum begins to precipitate. Since the volume ofgypsum crystals is about 61 % bigger than that ofanhydrite, the swelling of sulphatic rocks has oftenbeen attributed to the hydration of anhydrite.

In an open system, as in situ, a great variety ofprocesses are possible. Depending on the watercirculation, and on the reaction kinetics, eitherleaching of rock or hydration may occur. In thefirst case solid matter (dissolved anhydrite) istransported away by the water. In the second casethe solid matter volume increases by about 61%.Provided that porosity remains constant, hydrationcauses a volumetric strain whose magnitude de-pends on the volume fraction of the original anhy-drite. It is also possible, however, that the forma-tion of gypsum causes a gradual stopping up of thepores, and thus a sealing of the rock. In this case, asmaller volumetric strain would occur.

So, the properties of the CaSO4 - H2O systemdo not allow for a definite statement concerning thecontribution of anhydrite to swelling. They show,nevertheless, that the seepage flow conditions mustbe decisive. This hypothesis is supported by fieldobservations: The intensity of swelling may varyconsiderably within small distances alongside atunnel even in the case of a macroscopicaly homo-geneous rock mass with constant mineralogicalcomposition. This can be explained only as a con-sequence of varying water circulation conditions.

Empirical evidence concerning the swelling ofanyhdritic rocks, actually a mechanical-hydraulic-chemical coupled process, is very limited at thepresent. The heterogeneity of sulphatic rocks (inthe specimen-scale) in combination with the ex-tremely long duration of swelling tests (severalyears even for small specimens) makes experimen-tal research very difficult. In addition, the value ofcommon laboratory tests is questionable, becausethe water circulation conditions are in general dif-ferent in situ from the ones prevailing in oedometertests.

Page 12: Tunnel stability and deformations in water-bearing ground

Field observations show that the rate of swel-ling can be reduced by applying a counterpressureon the tunnel floor. The relationship betweensteady-state heave and support pressure, which isimportant for the conceptual design of tunnels inswelling rock, is unknown.

6 CLOSING REMARKS

Water has a decisive influence on the stability andthe deformations of underground openings for awide spectrum of geotechnical conditions. Takinginto account the seepage flow by appropriate mod-elling improves our understanding of the observedphenomena and of the inherent design uncertaini-ties.

REFERENCES

Amstad, Ch. & Kovári, K. 2001. Untertagbau in quellfähi-gem Fels, Forschungsauftrag 52/94 auf Antrag desBundesamtes für Strassen (ASTRA). (in German).

Anagnostou, G. 1995a. Seepage flow around tunnels in swel-ling rock. Int. Journal Num. and Analyt. Meth. in Geo-mechanics, 19, 705-724.

Anagnostou, G. 1995b. The influence of tunnel excavationon the hydraulic head. Int. J. Num. and Analyt. Meth. inGeomechanics, 19, 725-746.

Anagnostou, G. & Kovári, K. 1996. Face Stability Condi-tions with Earth Pressure Balanced Shields. Tunnellingand Underground Space Technology, 11, No. 2, 165-173.

Anagnostou, G. 2002. Urban tunnelling in water bearingground - Common problems and soil mechanical analysismethods. 2nd Int. Conf. on Soil Structure Interaction inUrban Civil Engng., Zurich, 233-240.

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Egger, P., Ohnuki, T. & Kanoh, Y. 1982: Bau des Nakama-Tunnels. Kampf gegen Bergwasser und vulkanischesGestein. Rock Mechanics, Suppl. 12, 275-293 (in Ger-man).

Janssen, H.A., 1895. Versuche über Getreidedruck in Silozel-len. Zeitschrift des Vereins deutscher IngenieureXXXXIC(35), 1045-1049 (in German).

Kovári, K., Amstad, Ch. & Anagnostou, G. 1988. De-sign/Construction methods - Tunnelling in swellingrocks. Proc. of the 29th U.S. Symp. "Key Questions inRock Mechanics" (Eds. Cundall et al.), Minnesota, 17-32.

Kovári, K. 1998. Tunnelling in Squeezing Rock, Tunnel,Vol. 5, 12-31.

O' Reilly, M.P., Mair, R.J. & Alderman, G.H. 1991. Long-term settlements over Tunnels. an eleven-year study atGrimsby. Tunnelling'91, Inst. of Mining and Metallurgy,London, 55-64.

Panet, M. (1995), Le calcul des tunnels par la méthode con-vergence-confinement. Presses de l'école nationale desPonts et Chaussées, (in French).

Vogelhuber, M., Anagnostou, G. & Kovári, K. 2004. PoreWater Pressure and Seepage Flow Effects in SqueezingGround. Proc. X MIR Conference "Caratterizzazione de-gli ammassi rocciosi nella progettazione geotecnica",Torino.