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Conference Paper

Tunnelling through geological fault zones

Author(s): Anagnostou, Georgios; Kovári, Kalman

Publication Date: 2005

Permanent Link: https://doi.org/10.3929/ethz-a-010819314

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TUNNELLING THROUGH GEOLOGICAL FAULT ZONES

Georg ANAGNOSTOU1 and Kalman KOVARI2

ABSTRACT

The term "fault zone" denotes a tunnel section of limited length, requiring special measures andinvolving considerable delays and high costs. Geological fault zones represent a major challengefor the design and construction of deep long tunnels. After a short overview of the problemsencountered when tunnelling in fault zones, two extreme cases of behaviour of water-bearingground and the associated construction concepts are discussed in detail. The first case concernstunnel sections in so-called “running ground”, i.e. practically cohesionless soil under high waterpressure. The second case involves tunnel sections in “squeezing ground” characterized by lowstrength cohesive material with high deformability. Running and squeezing ground define the endsof a wide spectrum of problems encountered when tunnelling in fault zones. They can beconsidered therefore as appropriate limiting cases, between which blurred transitions are possible.Both for running and squeezing ground pore water pressure and seepage flow play an importantrole. Tunnel excavation under running ground conditions is possible only after drainage andconsolidation of the ground ahead of the tunnel face. The paper discusses possible design criteriaand presents a method of dimensioning of grouting bodies. Concerning squeezing, attention is paidto the effects of pore water pressure and seepage flow on the time-dependent ground response tothe tunnelling operation.

Keywords: running ground, squeezing ground, fault zones, grouting.

INTRODUCTION

The term "fault zone" conjures up in the tunnelling engineer's mind thoughts of a tunnel section of limitedlength, requiring special measures and involving considerable delays and high costs. In contrast to the narrowgeological definition of a fault zone, the engineer's thinking is not fixed on the processes of formation, but on theinfluence of the rock's mechanical properties on driving operations. The question whether the origin is tectonic,lithologic or due to solution processes is not central in this respect. Fault zones in the geological sense are oftensuch that they do not cause any special difficulties to the tunnelling operation.

On the other hand, tunnel sections in soil subjected to water pressures present a considerable challenge to thetunnelling engineer (Fig. 1a). In the past such ground was described as “swimming”, which aptly describes theimportance of the water and the strength deficiency of the material. The width of such zones may vary from afew meters to decametres. They occur alone or as a group of fault zones with competent rock interspersedbetween them. In some cases they are accompanied laterally by a heavily jointed and fractured rock zone, inother cases the transition to competent rock is very distinct. When such a zone is suddenly encountered waterand loose material flows into the opening. Often one speaks therefore of a "mud inrush", which in extreme casescan completely inundate long stretches of tunnel. Therefore in the driving operation it is absolutely essential torecognize such zones in good time. In the exploration work the drilling device usually has to be protected againsthigh water pressures by means of a so called "preventer".

1 Professor for Underground Construction, Swiss Federal Institute of Technology, Zurich, e-mail: georg.anagnostou@igt.baug.ethz.ch2 Professor, Consulting Engineer, Zurich, Switzerland, e-mail: kalman@kovari.ch

Buried equipment due to running ground Deformations in the side drift of a Japanese tunnelin the Gran Sasso tunnel (Photo Cogefar) caused by a heavily squeezing ground

Competent rock Running ground Competent rock Squeezing ground

(a) Running ground (b) Squeezing ground

Fig. 1. Limiting cases of ground behaviour in fault zones.

When driving through zones of cohesive materials of low strength and high deformability the tunnellingengineer is faced with problems of a completely different kind (Fig. 1b). It is almost as if the rock can bemoulded, which is why formerly one spoke of a "mass of dough". If suitable preventive measures are notimplemented large long-term rock deformations occur, which can lead even to a complete closure of the tunnelcross section. The rock exerts a gradually increasing pressure on the temporary lining, which tries to resist thesedeformations, which can lead to its damage or complete destruction. In such cases one speaks of "genuine rockpressure” and the ground is characterized as "squeezing" (Kovári 1998). Experience shows that large rockdeformations and large rock pressures only occur in rocks of low strength and high deformability. Typicalexamples are phyllite, schist, serpentinite, claystone, certain types of Flysch and decomposed clay andmicaceous rocks. In fault zones portions of hard rock enclosed in "soft" rocks are often encountered. Accordingto the experience high pore water pressure favours the development of squeezing.

In the following some important aspects of tunnelling in running or squeezing ground are discussed, specialconsideration being given to the pore water pressures.

RUNNING GROUND

Measures

To overcome fault zones involving soil under water pressure the ground is drained and strengthened ahead of theworking face. In the case of small tunnel profiles in dense ground or in ground exhibiting some cohesion,drainage alone is often sufficient to enable excavation in such zones. The ground can be strengthened and sealedeither by grouting or by artificial freezing. Ground freezing however only offers a temporary solution and its

effectiveness ceases after excavation and the installation of supports. In deep tunnels, in general a permanentstrengthening and sealing is required, which can only be obtained by grouting. It creates a region of groundsurrounding the opening with improved properties. By injecting a fluid into the ground, which then hardens, itsstrength, stiffness and imperviousness are increased. The aim is usually to obtain a grouted body of cylindricalform by carrying out the grouting works in a controlled way. After excavating the solid cylinder a hollowcylinder remains, whose inner surface is supported by a temporary or a permanent lining and whose outersurface is loaded by the surrounding untreated ground. In practice grouted bodies with a diameter correspondingto two or at most three times the tunnel diameter have proved adequate. Furthermore, theoretical investigations(Kovári 1992) show that having larger grouted bodies is not justified financially because the costs increase withthe square of the increase in diameter.

The production steps for the grouted body along the tunnel axis depend primarily on the length of the fault zoneand on the tunnel diameter. In the case of short fault zones (around 20 - 40 m) one can produce the grouted bodyin a single operation working from one side from the competent rock. In the case of long fault zones the groutedbody must be produced in steps, whereby these – depending on the technical requirements – assume the form ofa truncated cone. With large excavation profiles as is the case with traffic tunnels, one divides up the groutingwork and the excavation into two parts: First, a pilot tunnel is driven under the protection of a grouted body ofsmall diameter. From it by means of radial boreholes the grouted body is increased to its final diameter. Then thepilot tunnel is widened to the final tunnel profile. The execution of systematic drainage is based on similarconsiderations. In complex geological conditions, lateral drainage galleries are constructed ahead of the groutingoperations, the execution of the work being staggered and in this way the efficiency is increased. Advancedrainage reduces the risk of uncontrollable mud inrush during the subsequent excavation stages.

Tunnelling with the aid of grouting can be extremely time-consuming and costly and therefore it should be basedon a good understanding of tunnel statics together with sound engineering judgment. In the following we treatthe problem of the required compressive strength and the required thickness of the zone to be strengthened bygrouting, i.e. we are concerned with the question of dimensioning grouted bodies.

Computational model

In Fig. 2 we consider an axisymmetric model. The fault zone is bounded by two parallel plane walls consistingof competent rock that lie normal to the axis of the tunnel. The length of the fault zone is L. The tunnel profile iscircular with a radius a, the grouted body has the form of a thick walled tube with an outer radius b, the primarystate of stress is hydrostatic amounting to σo and the lining resistance is σa. The initial water pressure in thevicinity of the tunnel is assumed to be uniform with the value po. Therefore, in the region of interest surroundingthe opening the gravitational increase of the pore water pressure with depth is neglected. More complexgeometries of the fault zone, other tunnel cross sections and non-hydrostatic primary stress states can beinvestigated numerically – albeit with considerable computational effort.

Fig. 2. Axisymmetric calculation model for the grouted body in a fault zone of length L.

The ground (both the grouted and the untreated) is considered to be a porous medium for which the principle ofeffective stresses holds. Elastic ideal-plastic material behaviour obeying Coulomb's failure criterion is assumed.Seepage effects are investigated using Darcy's law. The permeability of the grouted body is k, that of theuntreated ground ko. The excavation boundary (r=a) represents a seepage face, i.e. the water pressure pa theretakes on the atmospheric value. At a distance R from the tunnel the undisturbed groundwater pressure po acts.For deep tunnels the radius R can be assumed, for the sake of simplicity, to be equal to the height of theundisturbed water table above the tunnel (Anagnostou and Kovári 2003).

Seepage analysis

On the assumption of axial symmetry, as discussed above, the water pressure pb acting on the outer surface ofthe grouted body (r=b) may be expressed as

pb = C1 po (1)

where the coefficient C1 depends on the normalized size of the grouted body (b/a), its permeability (k/ko) andthe factor R/b (Anagnostou and Kovári 1994):

C1 = f (b/a, R/b, k/ko) = ln(b/a)

ln(b/a) + kko

ln(R/b) . (2)

The variation of water pressure within the grouted body is given by the following equation:

p(r) = pb ln(r/a)ln(b/a)

. (3)

The quantity of water inflow Q per linear meter of tunnel and per unit of time is:

Q = Qo ln(R/a)

ln(R/b) + kok

ln(b/a)

, (4)

where Qo denotes the quantity of water for the theoretical case without grouting:

Qo = 2πko po

ρw g ln(R/a) . (5)

Ground pressure acting on the grouted body

Provided that the stiffness of the grouted body is much higher than that of the untreated ground, one can showthat the following relationship between the effective radial stress σb', the primary effective stress σo' and theamount of reduction in water pressure at r=b exists (Anagnostou and Kovári 2003):

σb' = σo' + C2 (po-pb) . (6)

The coefficient C2 depends on the length L of the fault zone and on the radius R. To quantify the coefficient C2three-dimensional parametric studies using the finite element method were performed. The results can bedescribed approximately by the following relationship which is sufficiently accurate for practical purposes:

C2 = f (L/b, R/b) =

€

1

1+ 1.8 ln( R / b )− 0.7[ ] ( L / b )0.15 ln( R / b )−1.6[ ]

. (7)

For long fault zones (L>>b) C2 is equal to 1, i.e. the effective radial stress on the external boundary of thegrouted body increases by the same amount as that by which the water pressure decreases there. The total loadacting upon the grouted body, i.e. the radial stress at r=b, which is given by σb = σo' + po, remains equal to thetotal primary stress σo. Drainage reduces the total load acting upon the grouted body (C2 < 1) only in narrow

fault zones. This is due to the friction mobilised at the interface between the competent rock and the ground inthe fault zone (Anagnostou and Kovari, 2003).

Mechanical stressing of the grouted body

In the following we consider the grouted body to be an independent structural element, which is supported on itsinner surface by the lining (lining resistance σa), and is loaded on its outer surface by the water pressure pb (Eq.1) and the untreated ground (σb' according to Eq. 6). If the strength is inadequate or the loading high, the groutedbody plastifies, the strain being governed by the radius ρ (Fig. 2). An extensive plastification may lead toloosening of the grouted zone impairing thus its permeability. Limiting the plastification of the grouted bodytherefore constitutes a dimensioning criterion, whereby the amount of permissible stressing must in some casesbe chosen on the basis of safety considerations taking into account the magnitude of the ground pressure, thereliability of the drainage system etc. In the following a concise relationship is derived, which relates the radiusρ of the plastic zone with the other parameters.

To keep things simple we assume here a plane strain situation, i.e. we neglect the stabilizing effect of theneighbouring competent rock in the case of short fault zones (Kovári 1992, Kovári and Anagnostou 1996). Thestrength of the grouted body is described by Coulomb's failure criterion. The partially plastified grouted bodycan be split up into two parts, i.e. a completely plastified inner ring (range a ≤ r ≤ ρ) and a ring in the elasticstate (range ρ ≤ r≤ b). The stress analysis of the elastic outer ring is based on Hooke’s law and takesadditionally into account that the stress state at the elastic-plastic interface r=ρ fulfils the failure condition:

σt'(ρ) = 1+sinφ1-sinφ

σr'(ρ) + fc , (8)

where fc denotes the uniaxial compressive strength of the grouted body. Furthermore, the water pressure gradientis introduced into the equilibrium conditions. The analysis yields the following relationship:

€

fc =σb′ 2( b / ρ )2

( b / ρ )2 −1−σρ′

( b / ρ )2 + 1

( b / ρ )2 −1+

1+ sinφ1− sinφ

+

pb − pρ2(1−ν )

1− 2νln( b / r )

+2( b / ρ )2

( b / ρ )2 −1

(9)

where ν, pρ and σρ' denote Poisson's ratio, the water pressure at r=ρ and the effective radial stress at r=ρ,respectively. The latter is given by the stress analysis of the completely plastified inner ring (Anagnostou andKovári 1994):

€

σρ′ = ρ / a( )2 sinφ /( 1−sinφ )σa −

1− sinφ2 sinφ

fc −pb

ln( b / a )

−

1− sinφ2 sinφ

fc −pb

ln( b / a )

. (10)

By substituting the radial stress σρ' from Eq. (10) and the water pressure pρ (according to Eq. 1 with r=ρ) in Eq.

(9) one obtains, with consideration of Eq. (2) and Eq. (6), the following linear relationship between the uniaxialcompressive strength fc of the grouted body and the lining resistance σa:

fc = A - B σa , (11)with

A = f (b/a, ρ/a, φ, ν, σo', po, L/a, R/a, k/ko) = C3 σo' + [C3 C2 (1-C1 ) + C4 C1] po , (12)

B = f (b/a, ρ/a, φ) = C3 + 2 sinφ1-sinφ

, (13)

C3 = f (b/a, ρ/a, φ) =

€

2 sinφ

1− ρ / b( )2sinφ

ρ / a( )2 sinφ /( 1−sinφ )

−1+ sinφ, (14)

C4 = f (b/a, ρ/a, φ, ν) =

€

2(1−ν )+ C3 ln b / ρ( )−0.5+0.5 ρ / b( )2

2(1−ν )ln b / a( ), (15)

where C1 and C2 are given by Eq. (2) and (7), respectively. The given equations include, formally, the case of asystematic drainage of the grouted body (as limiting case for k/ko→∞).

For a particular geotechnical situation (i.e. for given values of the parameters σo', po, φ, ν, L, a, and R) and for aradius of the plastic zone ρ, selected beforehand on the basis of fundamental considerations, the coefficients Aand B only depend on the outer radius b of the grouted body and the drainage conditions (expressed by theparameter k/ko). Thus for the required uniaxial compressive strength one may write:

fc = A(b, k/ko) - B(b) σa . (16)

This equation represents the condition which the parameters chosen by the engineer have to fulfil, in order thatin a given geotechnical situation the plastification of the grouted body does not exceed the prescribed amount.Eq. (16) may be represented graphically by a family of straight lines, whereby each straight line applies for adifferent diameter of the grouted body (b) and a different drainage condition (k/ko).

Fig. 3. Interaction diagram for selected typical example.

Fig. 3 shows an example of such a diagram. The solid lines apply to grouted bodies of outer radius b = 15 m, thedashed lines for the grouted body with b = 10 m. In each case three straight lines are shown which correspond todifferent drainage conditions. In case (a) the grouted body is practically impermeable (limiting case k/ko = 0),while in case (b) it exhibits a lower permeability by a factor 10 than the untreated ground (k/ko = 0.1), and incase (c) the grouted body is systematically drained (limiting case k/ko→∞). The diagram clearly shows that theaim of limiting the stressing of the grouted body (20% plastification in this example) can be achieved byprescribing a tunnel lining of higher resistance, by producing a larger grouted body of higher strength or bysystematic drainage of the grouted body.

It may be seen that the straight line for a drained grouted body with an outer radius b = 10 m is practically thesame as that for an impermeable grouted body with b = 15 m (see points A and B). The effect of systematicdrainage therefore is statically equivalent to increasing the radius b from 10 to 15 m, which involves twice thevolume of ground to be treated by grouting. This result shows the great importance of drainage. Withoutdrainage the unreduced ground pressure (30 bar in this example) acts on the outer surface of a practicallyimpermeable grouted body. This pressure reduces to the atmospheric pressure within the grouted body; in otherwords there is a pressure gradient within the grouted body. As a result a body force, the so called seepage force,acts in the direction of the opening which is unfavourable. By means of systematic drainage however the

reduction of water pressure within an extended region in the untreated ground the seepage force in the groutedbody is eliminated. Statically this is very favourable (Fig. 3). The systematic drainage also reduces the risk ofcollapse due to inner erosion of the grouted body.

Whether drainage can be carried out in an actual case or whether it is economic, depends on the quantity ofwater inflow. Fig. 4 shows for a grouted body with b = 15 m (other data as in Fig. 3) the water inflow Q (as aratio of the water inflow Qo in the theoretical case without grouting) as a function of the permeability k of thegrouted body (as a ratio of the permeability ko of the untreated ground). With systematic drainage thepermeability k of the grouted body obviously has no influence. In this case the water inflow Q is about 40%higher than the water inflow Qo. If, e.g., one wants to reduce the water inflow to 30% of Qo, then one has toproduce a grouted body with permeability 10 times smaller than that of the untreated ground (see point A in Fig.4) and dispense with drainage. Dispensing with drainage means that the grouted body is stressed by seepageforces and therefore requires a higher strength, in the actual example twice as much (see points B and C in Fig.3).

Fig. 4. Relative quantity of flow as a function of the relative permeability.

In summarizing it may be concluded that stressing the grouted body can be limited by combinations of measures,which from the point of view of statics are equivalent. The choice of the most advantageous combination in anygiven case represents an optimization problem, because besides statics technical and economic points of viewalso have to be considered. Interaction diagrams of the type shown in Fig. 3 show in a condensed form thestatical conditions to be fulfilled in the design of the grouting measure. Thus they enable a quantitative statementto be made concerning the effectiveness of possible measures and provide a valuable contribution to decision-making in the design process.

ZONES OF SQUEEZING GROUND

Design concepts

The basic aspects of tunnelling in zones of squeezing rock have been presented in a concise form by Kovári(1998). The starting point of our discussion is the fact that rock pressure and rock deformation are closelyinterrelated. Rock pressure decreases with increasing deformation – an observation, which can also be provedbeyond question on theoretical grounds. To deal with the problems encountered in tunnel sections exhibitingsqueezing rock conditions there are basically two concepts: the "resistance principle" and the "yieldingprinciple". In the former a practically rigid lining is adopted, which is dimensioned for the expected rockpressure. In the case of high rock pressures this solution is not feasible. By contrast, in the latter, by allowingflexibility of the lining, the rock pressure is reduced to a value that is structurally manageable. An adequateoverprofile and suitable detailing of the temporary lining permit a non-damaging occurrence of rockdeformations, thereby maintaining the desired clearance from the minimum line of excavation.

Time-dependent rock behaviour

In the following we shall look more closely at various aspects of the time-dependent development of rockpressure and rock deformation. Rock deformations normally develop slowly, although cases are also known of

intense and rapid deformations occurring at the working face. The development of rock pressure or rockdeformation may take place over a period of days, weeks or months. It is encouraged by the presence ofgroundwater seepage flow or high initial pore water pressure. The gradual increase in rock deformation or rockpressure can be traced back generally to three mechanisms.

(a) The first is connected with the three-dimensional redistribution of stress in the region around the workingface. This takes place in every tunnel and is of great importance for the dimensioning of the lining (Lombardi1971). However, it cannot explain long-term rock deformations, because it occurs in proximity to the workingface within a region, whose length corresponds approximately to twice the diameter of the tunnel.

(b) The second mechanism is connected with the rheological properties of the ground. So called "creep" isespecially evident if the rock is highly stressed as the state of failure is approached, and is therefore of greatsignificance for the processes taking place under squeezing rock conditions (Fritz 1981). Creep does notnecessarily imply the presence of pore water. It is also observed in rocks with an absence of ground water flow.

(c) The excavation of a tunnel in saturated ground triggers a transient seepage flow process, in the course ofwhich both the pore water pressures and the effective stresses change with time. The latter leads to rockdeformations. Thus we are faced here with a coupled process of seepage flow and rock deformation. The moreimpermeable the rock, the slower this process takes place and the more long-term are the rock deformations – orby their prevention – is the development of rock pressures on the lining.

These three mechanisms are in general superimposed. In this contribution we are concerned exclusively with adiscussion of the processes linked to the development of pore pressures. The analysis is based on the classicalconsolidation theory of Terzaghi (1943). The ground is assumed to consist of a saturated porous medium forwhich Darcy's law holds. The deformational behaviour is described by an elastic-ideal plastic material modelobeying Coulomb's failure criterion. Special care must be taken in the experimental laboratory determination ofthe material parameters, especially the cohesion c and angle of internal friction φ. The control of pore waterpressure during triaxial testing of weak rocks prone to squeezing is indispensable. Conventional triaxial tests areinadequate in this respect, as they may lead to a serious under- or overestimation of the strength parameters.Consolidated undrained (CU) and consolidated drained (CD) tests with specimen pre-saturation and maintenanceof a sufficient back pressure are essential for obtaining reliable and reproducible parameters (Vogelhuber et al.2004).

In the following some analytical results obtained with very simple models are discussed in order to elucidate theeffect of pore water pressure in squeezing rock. The numerical calculations were performed using the finiteelement method using the computer program HYDMEC developed at the ETH (Anagnostou 1992). In thesecalculations a plane strain situation is assumed corresponding to rotational symmetry. The radial stress at theexcavation boundary corresponds to the lining resistance σa and the pore water pressure pa is atmospheric there.The far field conditions are assumed to be those given in Section 2 of the present paper (Fig. 5).

Fig. 5. Rotationally symmetric system for plane strain with boundary conditions.

The results of the analysis with a plane strain system can only be applied to the actual conditions encountered intunnelling, if seepage processes in the rock are negligible during the time of advancing the working face by alength of approximately twice the tunnel diameter (or equivalent dimension of opening). Here obviously threefactors are important: The continuity and the speed of advance, and the permeability of the rock. Further, notconsidering three-dimensional effects is only justified in cases where the ratio of the length of the disturbed zone(L) to the diameter of the tunnel (2a) is sufficiently large (Kovári 1992, Kovári and Anagnostou 1995).

Short- and long-term behaviour

We first consider the two limiting states of transient seepage flow: the state at t = 0 ("short-term behaviour") andthe state at t = ∞ ("long-term behaviour"). The first is characterised by constant water content, while for thesecond the steady state pore water pressure distribution is determinant. Whereas short-term, as a result of aconstant water content, only constant volume rock deformations occur, the long-term deformations areassociated with volumetric strains. With regard to the development of rock deformations therefore the short-termbehaviour is more favourable than the long-term behaviour.

Fig. 6. Ground response curve at t=0 (short-term behaviour) and at t=∞ (long-term behaviour).

This is seen most clearly through comparing the respective ground response curves (Fig. 6). The groundresponse curves describe the relationship between the radial displacement ua at the excavation boundary and thelining resistance σa (or, equivalently, the rock pressure). Fig. 6 presents the ground response curves of aclaystone rock mass for an assumed set of material parameters and geometrical quantities for the two limitingcases. As shown by the diagram, the short-term radial displacement ua stabilises at approximately 0.36 m even inthe case of an unsupported opening (lining resistance σa = 0). Long-term however the underground openingwould close, as shown clearly by the upper curve. If one assumes that about 30-40% of the short-termdeformation occurs before the installation of the lining (ahead of the excavation or in the immediate vicinity ofthe working face, cf. Panet 1995) and that the temporary lining can withstand a radial displacement of 0.20 mwithout experiencing damage, then it has to be dimensioned for a rock pressure of approximately 0.30 MPa (Fig.6, Point A). Long-term however the rock pressure would increase to the considerably higher value of 1.5 MPa(Point B).

These results are only of practical interest in the case of a relatively low value of permeability, since only in suchcases a pronounced short-term behaviour is possible at constant water content.

Time variation of rock pressure and rock deformation

The model studies carried-out also throw light on questions of practical interest concerning the time-development of rock pressure under conditions of full prevention of the radial displacement ua, and the time-development of displacement for a constant lining resistance σa. We explain the relationships with the aid of theparticular example previously discussed. In Fig. 7 the results are presented of the calculations based on the"resistance principle" (left) and the "yielding principle" (right). The ordinates σa and ua refer to these two designconcepts. For the sake of simplicity, for both it was assumed that the lining was installed after the occurrence ofthe short-term deformations. Thus the curves have their origin at σa = 0 and ua = 0, respectively.

From the diagram it is clear that the time development of the radial displacement ua in the case of a flexiblelining is considerably slower than that of the rock pressure σa in the case of a rigid lining. The occurrence ofrock deformations in the first case requires more time, while it accounts for the increased inflow of water. In thechosen example in Fig. 7 the rock pressure σa increases according to the resistance principle within a month tothe much higher value of 0.5 MPa, while the corresponding deformation of the flexible lining at 0.03 m is stillnegligible. Therefore, from the practical point of view this result is of interest, because it shows that with theyielding principle one gains time.

Fig. 7. The time development of the rock pressure (resistance principle) and rock deformation (yieldingprinciple) compared in the same diagram.

Fig. 8. The rock pressure (resistance principle) and the rock deformation (yielding principle) after 15 daysin function of permeability.

Influence of rock permeability

The duration of the unsteady seepage is proportional to the permeability of the rock. For permeability a factorten higher the rock pressure and the rock deformation develop ten times faster. The great importance ofpermeability soon becomes clear when one plots the rock pressure and the rock deformation at a particular time tin function of permeability (Fig. 8). One observes that permeability coefficients less than 10-9 m/sec arecharacteristic for practically impermeable rock. Since the determination of permeability in this range is oftensubject to large uncertainties, reliable predictions of the time development of rock pressure or rock deformationare extremely difficult.

Fig. 9. Shortening of the drainage path due to permeable interlayers.

In the case of inhomogeneous rock formations there are further prediction uncertainties. From consolidationtheory it is known that the duration of the period of unsteady flow is proportional to the square of the length ofthe drainage path. Thin permeable layers embedded in a practically impermeable rock mass lead to a shorteningof the drainage paths and cause therefore a substantial acceleration of the development of pressure anddeformation (Fig. 9). Also, in the neighbourhood of actual geological fault zones rock pressure phenomena dueto shortened drainage paths can be more intense, i.e. if permeable formations lie next to practically impermeablerock (Fig. 10).

Fig. 10. Shortening of the drainage path due to the vicinity of a permeable formation.

In the example of Fig. 8 the rock pressure would increase to a value between 0.1 and 1.2 MPa in 15 daysdepending on the coefficient of permeability k (between 10-11 m/sec and 10-9 m/sec). To resist a rock pressure of0.1 MPa a light temporary lining suffices. In the case of a rock pressure of 1.2 MPa however a strong liningwould be necessary. Thus the difference from the tunnelling standpoint is important. Therefore higher rockpermeability, the existence of some permeable interlayers or the vicinity of a permeable formation can mean thatthe tunnelling engineer experiences (classifies) the rock in one case as "competent", and in the other as"disturbed". Fig. 8 shows, nevertheless, that with a flexible lining the consequences of prediction uncertainties

are alleviated. For k = 10-11 to 10-9 m/sec the radial displacement ua of a flexible lining amounts to 0 - 0.25 m.The results of a poor (or wrong) estimate of convergence (in the actual example 7 - 8 m3 per tunnel metreadditional excavation and possibly more concrete for the permanent lining) are more modest than theconsequences of a wrong estimate of the time development of rock pressure according to the resistance principle(damaged lining and necessity of re-profiling).

FINAL REMARKS

Running and squeezing ground define the ends of a wide spectrum of problems encountered when tunnelling ingeological fault zones. They can be considered therefore as appropriate opposite cases, between which blurredtransitions are possible. Both for running and squeezing ground pore water pressure and seepage flow plays animportant role. The constructional measures to be taken should rely on adequate geological recognitions andbasic understanding of the mechanisms behind the phenomena observed.

REFERENCES

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Anagnostou, G., and Kovári, K. (1994), “Zur Dimensionierung von Injektionskörpern im Tunnelbau,”. In:Weiterbildungskurs "Injektionen in Boden und Fels,” Swiss Federal Institute of Technology, IGT Institute ofGeotechnical Engineering, (in German)

Anagnostou, G., and Kovári, K. (2003), The Stability of Tunnels in Grouted Fault Zones, Swiss Federal Instituteof Technology, IGT Institute of Geotechnical Engineering, Vol. 220.

Fritz, P. (1981), Numerische Erfassung rheologischer Probleme in der Felsmechanik, Mitteilung Nr. 47, Inst. fürStrassen- Eisenbahn- und Felsbau an der ETH Zürich, (in German)

Kovári, K. (1992), “Die Machbarkeit der Piora Mulde beim Gotthard-Basistunnel”, In: "Die AlpTransit-Basistunnel Gotthard und Lötschberg", SIA Dok. D085, 55-62, (in German)

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