Anagnostou Kovari_Face Stability Conditions With Earth-pressure-balanced Shields_TUST 11 2 1996

TUNNELS AND DEEP SPACES0886--7798(96) 00017-X Face Stability Conditions with Earth-Pressure-Balanced Shields G. Anagnostou and K. Kov~ri A b s t r a c t - - E a r t h pressure balanced shields provide continuous support to the tunnel face using the freshly-excavated wet soil, which under pressure completely fills up the work chamber. EPB-shield tunnelling has been successfully applied worldwide in recent years. Under extremely unfavourable geological and hydrogeological conditions, however, face instabilities may occur. In this paper, the mechanism of face failure is analysed under drained conditions. Accordingly, a distinction is made between water-pressure and effective pressure in the chamber. The stability of the tunnel face is controlled through the combined effects of these two entities. The effective pressure can be visualized as a "grain to grain ~ contact pressure between the muck and the ground at the face. The water pressure in the chamber reduces the hydraulic head gradient in the ground and, conseqnent~Iy, the seepage forces acting in front of the face. The face is thus stabilized both by the direct support of the pressurized muck and by the redaction of the seepage forces in the ground. The greater the head-difference between ground and chamber, the higher the effective support preaaure will have to be. A high effective support pressure has, on the other hand, operational disadvantages such as excessive cutter wear, high torque etc.. It is of great practical int~,rest to investigate quantitatively the relationships between the effective support pressure required and the hydraulic head in the muck for a given geotechnical situation. In this contribution, normalized diagrams are provided which allow the assessment of tunnel face stability. R$sumd--Les boudiers ~t contrepreasion de terre fournissent un soutien continu du front du tunnel en utilisant la terre excavde qui, en pression, remplit complgtement la chambre de travail. Ces derni~res ann~es, l'excavation de tunnels en utilisant des boucliers d contrepression de terre a dtd employde avec succgspartout dane le monde. Cependant, des instabilitds de frontpeuvent avoir lieu sous des conditione gdologiques et gdotechniques trgs ddfavorables. Dana set article, le mdcanisme d'inetabilitd de front a dtd analysd pour des conditions draiwges. En conedquence, une distinction a dtd faite entre la pression d'eau et la presaion effective dane la chambre. La stabili~ du front du tunnel eat assur~e par lea effets combin~s de ces deux grandeurs. La pression effective peut gtre visualisde par une pression de contact ~grain ~ grain" entre la bouc et la terre en place au front. La pression d'eau dana la chambre rdduit le gradient hydraulique dane le terrain et, par conedquent, lea forces d'dcoulement qui agissent devant le front du tunnel. Le front eat done atabilis~ par le aoutien direct de la bone mise en pression et par la diminution des forces d'dcoulement dana le terrain. Plus la diffdrenee de pression hydraulique entre le terrain et la bone dane la chambre est grande, plus la pression effective de soutien eat dlev~e. Cependant, une preasion effective de soutien dlevde a des inconvdnients pratiques tels qu'usure des couteaux, grand moment de torsion, etc. II y a un grand intdrgt pratique d'analyser d'une fa~on quantitative lea relations entre la pression effective de aoutien requise et la pression hydraulique clans la bouc pour une situation gdotechnique donnde. Darts cet article, des abaques normalisds ontdtd donngs afin de pouvoir dvaluer rapidement lea relations entre lea diffdrents paramgtres qui ddterminent la stabilitd du front. 1. Introduction unnel construction in saturated soils is being carried out ever more t~equently using closed shields, which allow the control of surface settlement and limit the risk of tunnel face failure through the continuous support of the face during excavation. Lack of sufficient face support leads, however, to tunnel-face instability. In extreme cases, the collapse propagates up to the ground surface creating a surface depression. Seepage flow towards the face may cause inadmissible surface settlement because the piezometric head in the ground decreases and the effective stresses increase. 2hmnelling with closed shields such as compressed-air shields, slurry shields and earth pressure balanced shields (Stack 1982) has, therefore, a twofold aim: support of the excavation face and the reduction or prevention of seepage flow to the face. T Present address: Dr. G. Anagnostou and Dr. K. Kovfiri, Institut f. Geotechnik, EldgenSseische Technische Hochschule, CH-8093 Ztirich, HSnggerberg, Switzerland. Earth pressure shields (Fig. 1) provide continuous support of the tunnel face using freshly excavated soil, which under pressure completely fills up the work chamber (Fujita 1981; Nishitake 1990). The supporting pressure is achieved through control of the incoming and outgoing materials in the chamber, i.e., through regulation of the screw conveyor rotation and of the excavation advance rate. Considerable experience with earth-pressure shields has been gained in Japan, where this construction method was developed (Stack 1982). In 1980, earth-pressure shields were used for 27.8% of the total length of tunnel constructed in Japan, and by 1985 this figure had risen to 68% (Nishitake 1990). In this contribution, only the problem of face stability for machine operation in EPB mode will be analysed. Neither compressed-air application (e.g., during the execution of works in the chamber), nor deformation problems (e.g., the question of settlements caused by drainage of the ground) will be discussed. Face stability conditions in slurry-shield tunnelling have been analysed in a previous paper in this journal (Anagnostou and Kov~ri 1994b). Tunnelling and Underground Space Technology,Vol. 11, No. 2, pp. 165-173, 1996 Copyright © 1996 ElsevieT Scierce Ltd Printed in Great Britain. All rights reserved 0686-7798/96 $15.00 + 0.(30 Pergamon the mobilised shearing resistance t at each point on the slip surfaces is given by: v = c/v + o' tanC/v . Deviations from these assumptions can be considered easily in more detailed numerical analyses. The Mohr-Coulomb failure condition is assumed. in addition to sliding. Principle of the EPB shield. Leca and Panet 1988 and Leca and Dormieux 1991). As shown in Figure 2. Number 2. Face stability will be assessed by considering the limit-equilibrium of a wedge and a prismatic body. 1994). 2) may also prevail. (1980). It should be noted. therefore. as well as on the excavation advance rate. V //~///////////////" -~H i Figure 2. a simple model which idealises the three-dimensional failure mode of the tunnel face will be used. then the groundwater will seep through the tunnel face. .. F is equal to zer o. the soil is idealised as a rigid-plastic material. 2. Only the effective normal stress can be considered as an actual support pressure. the factor of safety. and the boundary tractions at the tunnel-face and at the soil surface depend on whether a drained or undrained stability analysis is carried out (Lambe and Whitmann 1979). Figure 3. Sliding mechanism (after Horn 1961). due to symmetry. This paper focuses on face stability under drained conditions. Balthaus 1988. (1) where c.e. whereby. a distinction must be drawn between the total and effective stress acting upon the face. Since a drained analysis is carried out in terms of effective stress. Figure 4 illustrates the forces acting upon the wedge at the face.1-1 m/hr or less. Furthermore.c). The question of which type of analysis is the more appropriate depends on the soil conditions.p=O ~ . which are defined by slip surfaces beginning at the face and reaching the soil surface. Because the deformation of the ground is not being taken into account. According to the results of parametric studies into the effects of the advance rate (Anagnostou 1993. and seepage forces will act towards the tunnel face (Fig. that the tensile failure mode becomes relevant only under the contradictory conditions of high cohesion and a low tensile strength (Anagnostou and Kovfiri 1994a. Consequently.* SOIL Figure 1. (iii) the resultant seepage force {F. Under drained conditions. drained conditions are to be expected when the permeability is higher than 10-Tto 10 ~ m/sec and the net excavation advance rate is 0. therefore. It has also been applied to the investigation of face stability with slurry shields (Anagnostou and Kovdri 1992. This model was first proposed by Horn (1961) and is based upon the silo theory (Janssen 1895). the ground is considered to be homogeneous and isotropic. respectively. and the effective normal stress. (ii) the vertical force V' that results from the effective normal stress %' at the wedge-prism-interface CDEF. the circular cross-section of the tunnel is approximated by a square having the same area. the body forces in the soil. drained stability conditions should be considered...1995). the piezometric head h F in the work chamber have from a stability point of view ? If it is lower than the piezometric head ho in the undisturbed state. The Computational Model The problem of face stability of tunnels has already been addressed by several other authors (see Krause 1987. The shear strength parameters. Seepage force f and effective support pressure s" 166 TUNNELLING ANDUNDERGROUNDSPACETECHNOLOGY Volume 11. i. whereas drained conditions may be more appropriate in the case of a standstill. 3). tensile stresses along ABFE (Fig. will not be considered further in this paper. What effects does the pore water pressure. F. however. W * I I L . In a predominately sandy soil. the drained angle of internal friction. In a clayey. low-permeability soil. For the case of undrained stability (Lambe and Whitmann 1979) refer to Davis et al. v and ~ denote the drained cohesion. because the work chamber is filled with excavated soil under pressure. ~ . tensile failure may occur when the ground lacks sufficient tensile strength. F]. In this study. For the sake of simplicity. and. These are: (i) the submerged weight G'. This will be termed effective support pressure and will be denoted in the following text by s'. 1996 . an additional mode of failure must be taken into consideration: Since the seepage forces are directed towards the tunnel face. ~ . L. undrained strength applies for assessing face stability during excavation. is taken to be 0. The permeability constant does not. Such a calculation yields the three-dimensional steady-state potential field. The critical inclination ~ r of the sliding surface is determined by iteratively maximizing the support force. for a given inclination w o f t h e slip surface ABFE). while the vertical load from the prism is simultaneously increased.40 for the wedge (Anagnostou and KovgLri 1994b). The frictional part of the shear strength on the vertical sliding surfaces depends essentially on the corresponding effective horizontal stresses (o '. while that in the prism above is practically vertical.e. on the effective shear strength parameters c and ¢. taking into account the seepage forces acting within the prismatic body (see Appendix). on the elevation of the water table ho. Determination of the seepage forces {Fx. Fz] calls for a numerical seepage-flow analysis. rainf~dl or an adjacent river. At the tunnel face. a no-flow boundary condition applies to the tunnel walls. a constant ratio ~ o~ horizontal to vertical stresses along the slip surfaces of the prism. 3.z) for given geometric (diameter.80 for the prism and 0. on the overburden H. by repeating steps (ii) and (iii) with different angles of inclination w. Darcy's law will be assumed for modelling seepage-flow. The face stability analysis proceeds in three steps: (i) Determination of the three-dimensional hydraulic head-field h(x. Assuming a waterproof tunnel lining. (vii) the shear forces Ton the inclined as well as on the vertical sliding surface activated by relative movement. Figure 6a represents the contour lines of the piezometric (iv) head in the vertical plane of symmetry. taking the symmetry of the system into account. Volume 11. e..g. i. the piezometric head correspondq to the water table elevation (ho). No shear force will be considered as acting on the internal slip surface DEFC. The value of~. An approximately horizontal load is exercised on the wedge.oents a seepage face.. The groundwater table is at the level of the ground surface. (vi) two horizontal normal forces resulting from the effective non~al stress acting on the vertical slip surfaces ADE and BCF of the wedge. elevation of the water table) by means of a finite element computation. the pressure is atmospheric and the piezometric head equal to the elevation at each point (h~ ~ z). This is also demonstrated when plotting the pore water pressure along the tunnel axis (Fig. the effective support pressure s" depends on the tunnel diameter D. a constant piezometric head h F < ho is prescribed. This step includes numerical integration of the seepage forces within the wedge and the prism based upon the piezometric head-field calculated in step (i) (see Appendix). In the extreme case. influence the steady state head field. Forces acting upon the wedge in front of the tunnel face. Step (i) has to be carried out only once.ld boundary condition).7" v F / Figure 4. Following Janssen's silo-theory. lake or well. there is no drawdown of the water table. This involves a continuous groundwater recharge by. as well as that of the wedge.. i. The tunnel face is under atmospheric pressure. (iii) Computation of the necessary effective face support force by applying the conditions of equilibrium and the failure criteria on the slip surfaces. in spite of drainage through the face. overburden) and boundary conditions (the piezometric head in the chamber.e. The Necessary Effective Support Pressure At limit equilibrium. At a sufficient distance from the tunnel face (the far-fi~. the pressure in the chamber is atmospheric.d i m e n s i o n a l finite e l e m e n t code H Y D M E C (Anagnostou 1991). however. As the seepage forces are oriented perpendicularly to the potential lines. Finite-element mesh for the computation of the head field. will be assumed. the resultant seepage force acting on the wedge slopes slightly downward. 1996 TUNNELLINGANDUNDERGROUNDSPACETECHNOLOGY167 . (v) the normal fi)rce N' that results from the effective normal stress on the inclined sliding surface.y. Consider a tunnel having a diameter of 10 m and an overburden of 20 m. on the piezometric head in the chamber hp. The numerical calculations were carried out by the t h r e e . the normal fi)rce S" that results from the effective support pressure s" of the muck at the tunnel face. 6b). For all of the numerical examples in this paper. The vertical force ~Wis computed by applying Janssen's silo-formulae to the prismatic body. The destabilizing effect of the seepage forces acting on the wedge is thus clearly apparent. whereas steps (ii) and (iii) are carried out simultaneously because the resultant seepage forces must be recomputed for each value of m. Figure 5 shows the central part of the finite element mesh that will be used in the numerical examples in this paper. the tunnel face repre. (ii) Computation of the forces acting upon the wedge for a specific collapse mechanism (i. on the submerged unit weight ~/(for soil Figure 5. In this example. Number 2. The increasing density of the potential lines close to the tunnel face indicates an increasing value of the seepage forces.e.. it will be assumed that. The linear approximation proposed in the German Standards ibr slurry walls (DIN 4126) will be adopted for the vertical stress distribution ~'(z) along the slip surfaces ADE and BCF of the wedge. o'). The computation is based upon the following boundary conditions. The ratio Yd /~ was taken to 1.. 1993) involves two single-lane tunnels bored by four EPB-shielded tunnel boring machines. 4. on the geometric parameters H / D and (hoD)/D. In spite of the linear relationship between s' and Ah. O. together with the diagrams in Figure 7.e.1 kN/m s. and the soil had a cohesion and a friction angle in the range 0-5 kPa and 38--42 °. cohesion c and head difference Ah=ho-h r By carrying out a dimensional analysis. the only difference being that the dry unit weight 7dis used instead of the submerged unit weight ~ . The influence of the overburden on F 1 is small. i. when the groundwater pressure is completely compensated by the fluid pressure in the chamber (see. The coefficient F I (i. h o. ~ ) ..e.i.g.e.e..F l c + F2 i A h . the shear forces depend linearly on the cohesion. the dry unit weight was equal to 16. According to the Mohr-Coulomb yield criterion. The dashed lines hold when the groundwater table is in a distance of D~2 above the tunnel crown. Result of seepage calculations in the vicinity of the tunnel face. 40°).~---_L__~ I p (kPa) 250 200 1501O0Z v Po J E O II ¢- (a) I E o "- s0 0 0 i 5 41 0 11 5 x% (b) Figure 6. 9). For these ~) reasons. Both models yield satisfactory estimates of the experimental values. it not been included in the diagram.g. Figure 7 shows that the overburden does not have any effect on the normalized support pressure F when H / D > 2 or ¢ > 25 °. Due to the high 168 TUNNELLING ANDUNDERGROUNDSPACETECHNOLOGY Volume 11. the effective support pressure depends linearly on the size of the forces acting upon the wedge.F 3 c ADh . The coefficient F 3 (the cross effect of cohesion and head difference) depends both on the overburden H / D and on the elevation of the water table (ho-D)/D. The formula (3). The upper till is a preconsolidated undisturbed soil with up to 20% clay. Number 2. (3) w h e r e F teF~ are dimensionless coefficients that depend on • q o the frictmn angle ~.60. the general linear dependency of support pressure s' on cohesion c and head difference Ah.beneath the water table)and on the dry unit weight 7d (for the soilabove the water table). Y. one obtains the following general form of the limit equilibrium condition: s'fFo i D .H. the support pressure increases linearly with the tunnel diameter. The tunnels cross glacial tills and fissured marls (Fig. The theoretical minimum face support pressure for tunnelling in dry soil is given by the following equation: s=F ydD-F1c . The diagrams havebeen computed numerically with the model described in Section 2. 1996 . The Great Belt project (Biggart et al. (2) According to the equilibrium equations. Figure 7 shows the coefficients Foto F s as functions of the friction angle ~. i. h~. gravels and glacial boulders. (4) This equation is similar to (3). Because the influence of H / D on F 3 amounts to less than 5%. the effect o~cohesion in the absence of seepage forces) does not depend on the elevation of the water table. (a) Contour-lines of piezometric head. respectively. s'=f(D. e. The coefficient F 2 expresses the effect of head difference on support pressure in a cohesionless soil. The term F ° ~D in eq. Predictions based on the model proposed in this paper are compared with the measured values from the tests.. provide a simple but powerful tool to characterize quantitatively the face stability at EPB operation in a given particular c a s e . The results discussed above concerning the effects of the overburden and of tunnel diameter are also in accordance with the experimental findings. In this case. The curves cover the relevant range of the geometric parameters H / D and (ho-D)/D.. c. respectively. and depends solely on the size of the flow domain above the crown. C a s e S t u d y . Figure 8 shows the empirically determined support pressure at collapse as a function of tunnel diameter (dashed line). The two solid lines with the black markers in Figure 8 show the support pressure according to (4) for c = 0 and c = 5 kPa. The solid lines with white markers have been obtained using the model of Leca and Dormieux (1990). The solid lines in the diagram for F o apply to cases where the water level is at the surface or above It (ho > H+D). Furthermore. a linear relationship holds between effective support pressure s'. for a given value of ~. due to the linearity of Darcy's law.T h e Storeb•lt Railway Tunnel f . to the head difference (ho--h as well. e. Passante Ferroviario Milano. the undisturbed piezometric head ho is an independent parameter because it affects the size of the flow domain. a good enough approximation for practical purposes. The other three terms express.. under a seabed or river. (b) Porewater pressure distribution along the tunnel axis. (3) is equal to the necessary support pressure in a cohesionless ground (c = O) when seepage forces do not occur (Ah = 0). In the model tests. the overburden was equal to 4D. Peron and Marcheselli 1995). the seepage forces are proportional to the head gradients and. and on the ratio of the dry to the submerged unit weight Td/~. /////////////////////////////// I I I I I I ~/////// =~- Comparison with Experimental Results Chambon and Cortd (1994) have conducted centrifugal model tests concerning face stability in dry cohesionless soils. The lines have been computed for an average friction angle of ~ = 40 °. The values of support pressure are very low due to the high friction angle of the model material (ca. on (h=D)/D or. The lower till is an extremely heterogeneous material containing irregular sand lenses.. when the water level is above the soil surface on [I/D. 5D I 0. Stack 1982).08 0. (5). as indicated by the rapid response of the piezometric heads observed after the installation of the pumps in the Moses project. Therefore. extensive drainage works have been carried out.- D-~- 1 =? 0.0 H/D= 0. Furthermore. This so-called =Moses~project reduced the seepage forces.. In order to provide a better understanding of face stability conditions. N o m o g r a m s for the d i m e n s i o n l e s s coefficients F to Fa. A(ho. 1993. i .h ~ can be obtained from eq.02 0.12 0.O. ho = h F) suffices s'=18- for face stability even when the ground shows a cohesion c as low as 10 kPa.5 ° and T' = 13 kN/ m3: 2 c + 5.->3 f i lJ ~ J J J 3 0. face stability conditions could be satisfied by maintaining a water pressure in the chamber greater than the pore water pressure in the ground.00 15 2G 25 Friction Angle 30 ¢ [°] 35 J I 0. Moreover. Darling 1993. The necessary "negative" head difference Ah can be computed from eq.O16 C (ho-h~) . the interaction between the main factors will be demonstrated by means of a parametric study concerning station 12'800 (Fig. respectively. Fujita 1981.5 I : H/D. Drained conditions are relevant because of the high l~ermeability of the till. Detailed information on the Storeb~elt project has already been given (Biggart et al. the principle of the so-called %vaterpressure-type EPB shield" is immediately obvious. In the following.10 15 20 25 Friction A n g l e 15 20 25 30 35 Friction Angle ¢ [o] 4 0. In the model.7 0. The limit equilibrium condition between effective support pressure s'. it may be seen t h a t in a cohesionless ground. the piezometric head should be maintained through the application of pressurized water in the work chamber (Abe et al. and made entry into the working chamber possible at low air pressure. For this type of machine. simplified crosspassage constructions. According to Figure 10. Whether this solution is practicable or not depends on the permeability of the ground Volume 11. ~stability calculations have been performed based on the model described above (Kov6ri and Anagnostou 1994). In other words. 9). cohesion c and head difference (ho . (5) units in [kPa] and [m] Figure 10 shows the graph of eq. In view of the great importance of the piezometric head hp in the chamber. the effects of As' = 56 kPa. if ho > H+D (ho-D)/D if ho < H+D _ _ 15 20 25 30 35 Friction Angle ¢ [o] Figure 7. the circular tunnel section (diameter 8. Both drained and undrained conditions have been studied. In the present study (and assuming a cohesionless ground). 56 kPa can be achieved either by reducing the head difference by 10 m (1 bar) or by increasing the ground cohesion by approximately 28 kPa. porewater pressures (up to 4 bar in the tills).6 (ho-hp) . the lowering of the piezometric head into the ground by pump operation represents an extremely effective measure for face stabilisation in cases with exceptionally high piezometric heads. the head in the chamber should be 3-4 m higher than the sea level in order that the effective support pressure s' is equal to zero.5 --. 1978.e.5 0.h ~ = 10 m and Ac ---28 kPa in stabilizing the tunnel face are statically equivalent. the same reduction in the required effective support pressure of approx.4 0. The depth of cover and the sea depth amount here to approximately 30 m and 10 m. (3) and the diagrams of Figure 7. 1996 TUNNELLINGANDUNDERGROUNDSPACETECHNOLOGY169 .4 30 ¢ [o] 35 O. Number 2.70 m) has been approximated by a rectangular one with a side-length of D=7 m.8 __ 0.8 [ = H/D. if ho > H+D 1 = (ho-D)/D if ho < H+D I I Hit ho 0.08 f J . with ¢= 32.04 0.1.6 z3 0. (5) by settings'=0. the required effective face support s' decreases from approximately 160 kPa to 60 kPa.2 ho 2 H+D ho= 1.6 0. Note that the compensation of the water pressure (i. Sternath 1994). when reducing the head difference by 20 m in a ground with a cohesion ofc = 30 kPa. 15 ~ I0 ~/i II y( / 0 4 I 6 I 8 I 10 I 12 I 14 Diameter D [m] . and at the exit of the screw conveyor is equal to h a. For the formation of a plug. lla). and of the muck: the more permeable the ground and the muck. 1993). Geological profile of the Storeb~elt railway tunnel (after Biggart et al. respectively. Two possible ways of reducing the seepage forces may be considered: (1) By decreasing the pore water pressure in the ground.L ~-0 (according to eqn. out of the tunnel. The piezometric head difference ho . The lower the permeability of the muck. In the extreme case. Number 2. muck properties and machinespecific details. but the excavation advance rate may then become dependent on the performance of the pump. 170 TUNNELLING ANDUNDERGROUND SPACETECHNOLOGY Volume 11. The first solution requires either the maintenance of a soil plug or the installation of a pump at the discharge port of the screw conveyor. the effective support pressure s to ensure face stability will be high. The latter method depends upon the combined effects of ground properties. a high pressure can be maintained only through a pump. If the muck is much more permeable than the undisturbed soil (k >> ko). If locally the pressure s' becomes very low. with each rotation. Apart from the injection o f pressurized water into the chamber (see end of Section 4). the hydraulic potential within the machine is equal to the head hAat the exit of the screw conveyor. shears the compacted muck in the chamber. plug formation presupposes a predominately clayey. a cave-in involving progressive instability of the face may occur. the higher the pressurized water losses towards the ground and the screw conveyor will be. 3) c=O (Leca & DotTnieux. two basic possibilities for maintaining a high water pressure in the work chamber arise from these considerations: either (1) by maintaining a high piezometric head at the exit of the screw conveyor. or (2) by decreasing the permeability of the muck. and the more water will have to be transported. the hydraulic head h F at the tunnel face corresponds to the undisturbed piezometric head h and decreases along the screw conveyor to the value h a . and let k and k denote the permeability of the ground and of the muck. 1990) Figure 8. If it is not noticed by the operator in time. and (2) by maintaining a sufficient head hv in the chamber. compressible muck. However. However. the muck becomes much more compacted. The Operational Implications of a High Effective Support Pressure s" If the difference between the water level ho and the head hFin the chamber for some reason cannot be kept low. various "water-cutoff' devices have been developed (Nishitake 1990).h A is dissipated partially within the ground and partially within the machine. thereby inhibiting the discharge (Fujita 1981). the muck in the chamber does not behave as a viscous fluid leading to a fluctuation of the distribution of the effective pressure acted on the face (Fig. 1 lc). None of these operational difficulties occurs when the muck in the chamber acts as a viscous fluid. 1996 . 3) ~ 5 kPa (Leca & Dormieux. Experimentally determined and computed support pressures as a function of tunnel diameter for dry conditions. at high effective support pressure. The third disadvantage of a high effective support pressure stems from the possible arching of the muck at the entrance to the screw conveyor (Fig. and the higher will be the piezometric head in the work chamber. but also. together with the solid matter. In a sandy or gravelly soil. 1990) ~K Measured values -- ~ 5 kPa (according to eqn. The piezometric head at a large distance from the tunnel face corresponds to the undisturbed groundwater table ho. then the head difference will be dissipated mainly within the ground ahead of the face. 12). Another implication of high effective support pressures arises from the large shear resistance of the compressed muck against the rotating cutting wheel. Consider the system represented by the machine and the surrounding ground (Fig. o o ±Om 20m 40 m 60m 80m lOOm Figure 9. The latter not only excavates the ground at the face. In the borderline case of a very low-permeability muck (k << ko). resulting in significant wear of the whole cutter head and excessive torque (Fig. the larger the portion of the head difference dissipated within the machine. 5. llb). Effective support pressure as a function of cohesion c and of hydraulic head difference (ho--h~9for a given chainage of the Storebzelt Tunnel. Consequently.250 ~ ' 200 150 . respectively). (b) Low-permeability muck Volume 11. (a) Uncontrollable support pressure distribution. Loss of head difference within the ground and along the screw conveyor: (a) High-permeability muck. the rotational speed of the screw conveyor. (b) Excessive cutter-wear and torque. where only one parameter has to be regulated (air or slurry pressure. two such parameters exist for earth pressure shields. The importance of thoroughly mixing the excavated material in the work chamber is especially great with aninhomogeneons ground (Anagnostou and K o v ~ i 1994a). both geotechnical and operational aspects will affect t-nnel face stability. However. Similar muck treatment problems may then be encountered as for slurry shields. 1996 TUNNELLINGANDUNDERGROUNDSPACETECHNOLOGY171 . the only reliable solution is the installation of a pump. Contrary to the situation with compressed air and slurry shields. and vice-versa. ?\ S. Nishitake 1990. a distinction m u s t be drawn between the effective stress s' acting on the tunnel face and the pore water pressure p in the work chamber. The larger the pore pressure p. Environmentally acceptable additives recently have been developed for use in conditioning.n n e l face is guaranteed through the joint effects of s" and p. ho Figure 12. Closing Remarks 0 0 10 20 30 40 50 Cohesion [kPa] Figure 10. 6. The stability of the t . and the excavation advance rate. the way the ground is mixed in the work chamber. when using an earth pressure shield. both the effective support pressure s' and the pore water pressurep should be controlled and adjusted according to the hydrological and soil mechanics conditions encountered. Number 2.o (b) X i ~ h (a) A (b) HIGH-PERMEABILITY SPOIL (k>> ko) LOW-PERMEABILITY SPOIL (k << ko) (c) SHIELD//" Figure 11. G ho . 100 The addition of bentonite suspensions or polymers to the excavated material (conditioning) c a n reduce both its permeability and shear strength (internal friction angle) (Babendererde 1989. (c) Arching at the entrance to the screw conveyor. the smaller the necessary effective support pressure s'. they may be difficult to control in practice. Babendererde and Babendererde 1995). (a) When using an EPB-shield. "u) Q. For high piezometric heads. Because both parameters depend on the characteristics of the excavated ground. Problems caused by a high effective support pressure s" and a high friction angle of the much. . Ein Beitrag zur Statik der Ortsbrust beim Hydroschildvortrieb. J. Baugrundtagung..: Dtisseldorfer Messegesellschaft mbH NOWEA . W. Y.) Horn. Gallerie in condizioni difficili. 1995. L. The s h e a r resistance of the m u c k also can be reduced by m a i n t a i n i n g a low effective s t r e s s s ' i n the chamber. Stability analysis for tunnelling with slurry and EPB shield. Anagnostou. Coming clean over Storebaelt. fiir Statik TU Braunschweig. Gunn. 315-320. Sugimoto. Anagnostou. 29. The Face Stability of Slurryshield-driven Tunnels. Stand der Technik und Entwicklun tendenzen beim maschinellen Tunnelvortrieb im Loekerboden. Mair. G. Handbook of Mining and Tunnelling Machinery. Leca. Zeitschrift des Vereins deutscher lngenieure ~ (35). and Kovdri.). or t h r o u g h additional m e a s u r e s (such as the i n s t a l l a t i o n of a p u m p at the exit of the screw conveyor). Bd.2. 1994. Large undersea tunnels and the progress of tunnelling technology. STUVA. ~Safety and Environmental Issues in Rock Engineering ~. Journal of Geotechnical Engineering 120(7). (in German) Lambe. 1990. 1982. Copenhagen. Application du calcul ~ la rupture la stabilit~ du front de tallle d' un tunnel. i. and P. (Ed. (M. K. Untersuchungen zur Statik des Tunnelbaus in quellf~igem Gebirge. U. etc. G.K. 1993. T. Davis. New York: John Wiley & Sons.: John Wiley & Sons. the C o n s o r t i u m for t h e Sterebeelt Crossing. Torino. A. H. Fujita. and Dormieux. the s h e a r r e s i s t a n c e of the m u c k should be k e p t as low a s possible. Kranse. Rotterdam: A. 1895. S I Version. 1981. Kov~i..12.. 10451049 (in German). Congress on Tunnelling. and Seneviratne. 1. The stability of shallow tunnels and underground openings in cohesive material. K. Babendererde. Meth. and Panet. K. and Kov~ri. April 1994. Proc. on Technology of Bored Tunnels under Deep Waterways.J. Darling. 1978. in Landeskonferenz der ungarischen Tiefbauindustrie. Use of Slurry and Earth-Pressure-Balance Shield in Japan. 1980. andCort~.-F. G.K. 1961. 130-138. Tunnels & Tunnelling 10. R. S.A.11-1. Syrup. In this case. Alagutak homlokbiztosit~s~ra hat5 vizszintes fdldnyom~svizsgfilat n~hdny eredm~nye. "Tunnelling Under Difficult Conditions ~. Rivier.. K~ln (in German). Y. and Anagnostou. G. 1993. Mitt. Int. 1992.hp = coefficient of l a t e r a l p r e s s u r e v = safety factor vertical effective stress = d r a i n e d angle of i n t e r n a l friction 03 = inclination of slip surface % = inclination of critical wedge C D 172 TUNNELLINGAND UNDERGROUNDSPACE TECHNOLOGY Volume 11. 3-10. 9553. and Analyt.. Acknowledgments The a u t h o r s wish to t h a n k MT Group. S. 487-492 (in German). In Tunnelbau-Symposium ~Probleme bei masehinellen Tunnelvortrieben ? Gerdtehersteller und Anwender berichten". Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. A. B. 1988. Friihjahrstagung der Schweiz Gesellschafl fiir Boden. M. Dissertation TU Braunschweig. Lisbon. Int. 581-606. E. G.z = Seepage forces Fo. T. Tunnelling and Underground Space Technology 9(2). 175-195. 78-84 (in German). 1987. polymers. Die Stabilit~it der Ortsbrust bei Erddruckschilden. 1986. 79-82. Chichester. 19. Proc.E U R O C K "93. 1987.und Felsmechanik 29. Versuche tiber Getreidedruck in Silozellen. and Sternath. 291-302. on Technology of Bored Tunnels Under Deep Waterways. STUVA. Sternath. 1994. Notations 63-93. R. ShallowTunnelsinCohesionless Soil: Stability of Tunnel Face. N. in Geomechanics. H. Denmark. Balthaus. 1989. der SBGF 129. 18-26.F o r operational reasons. 477-492 (in German). Anagnostou. 1994c. Peron. DIN-4126. eel. Anagnosteu. Proc. Int. Inst. 1994a.383406. E. J. In Stab ilit~itsprobleme in der Geotechnik. 5-19 (in French). Proc. Modelling seepage flow during tunnel excavation. and Babendererde. M. P. Anagnostou. P. Syrup. 1990. Balkema. K. Tunnelauskleidungen hinter grundwasserverdr~ingenden Schildvortriebmaschinen. Eisenstein. Balkema. E. K." Report prepared for the MTGroup.) m a y be n e c e s s a r y in order to reduce its friction angle. Distelmeier. Duddeck. 1. 1993. 1994. Int. 1994b. I S R M International Symposium . G. 1991. Marcheselli. Hochschule Ztirich (in German).. S. conditioning by m e a n s of lubricants (rheological foams. Copenhagen. and Whitman. "Sterebmlt Railway Tunnel . Syrup. Proc. Standsicherheit der fltissigkeitsgesttitzter Ortsbrust bei schildvorgetriebenen Tunneln. Budapest (in Hungarian). the h e a d difference b e t w e e n the c h a m b e r a n d t h e ground should be k e p t as small as possible in order to ensure face stability. 1993. Vol. 1979.. 21-24 / 06/1993. This can be achieved e i t h e r by reducing the p e r m e a b i l i t y of the m u c k w i t h i n the working c h a m b e r (with additives a n d thorough mixing). K. for t h e i r k i n d p e r m i s s i o n to reproduce r e s u l t s from the investigation into face s t a b i l i t y on the Storebeelt R a i l w a y Tunnel. H. See also "I-Iorizontaler Erddruck auf senkrechte Abschhissfliichen von Tunneln ". Leca. Anagnostou. Dtisseldorf. Chambon. In: Festschrift H. gs~ Babendererde. TU Miinchen (in German). Influence of tunnel excavation on hydraulic head. H. Development and application of environmentally acceptable new soft ground tunnellingmethod. Forschung+Praxis 3 3 . 27-34 (in German). D e p e n d i n g on the soil encountered d u r i n g tunnel excavation. References Abe. Stack.3 ~-' Coefficients in t h e d r a i n e d stability condition H = overburden h = piezometric h e a d hF = piezometric h e a d in the c h a m b e r h° = elevation of w a t e r table support pressure 8 = effective s u p p o r t p r e s s u r e ¢ = s u b m e r g e d u n i t weight ~'d = dry unit weight Ah = h o .V. Dtisseldorf). T. Schildvortriebmit fltissigkeits-underdgesttitzter Ortsbrust.Assessment of face stability. Advancedtechnologyrealizehigh-performance earth pressure balanced shield. 165-174. Kov~tri. Konstruktion und Ausfiihrung (in German). Dissertation Nr. L. AdvancedTechniques for EPB-TBM Operation. 1996 . I~zlekeddsi Dokumentttcids Vttllalat. 1995. Geotechnique 30(4). Revue Fran~aise de Gdotechnique 43. Az orsz~gos m~ly~pit6ipari konfe~encia el6adtisal. 725-746. In Franchissements souterrains pour l'Europe. Legrand. 1993. Consortium for Storebmlt Crossing. H.D. 1995. Janssen. Denmark. Int.und Grundbau e. G. Tokyo. V. Journal ofNum. J. Anagnostou.A.. Rotterdam: A. P. Tunnel 81. Techn. 94. R.y. G. Gdotechnique 40. J. 397-416. Geotechnische Sonderverfahren fiir die Vortriebe des E i s e n b a h n t u n n e l s u n t e r dem Grossen Belt. Eidg. Tunnels et Ouvrages Souterrains 128. Bauingenieur 62. N u m b e r 2. Z. Nishitake. Soil Mechanics. Biggart. Kov~Lri. La construction du tunnel ferroviaire de la liaison Passante Ferroviario a Milan.-P. 3--5 Nov. 1148-1165. d r a i n e d cohesion = d i a m e t e r of t u n n e l f~ = Seepage forces p e r unit volume F x. M.in Zusammenarbeit mit der Deutschen Gesellschaft fiir Erd. Storeb~elt RailwayTunnel--Construction. R. Ortbeton-Schlitzw~inde. and Ishihara. Tunnels et Ouvrages Souterrains 128. Budapest (German translation. 1988. The higher the frictional resistance (ktan~b). . (to) = 7~ ( .f z ' * . . the integralsymbols denote integration over the indicated surfaces ABFE. (17) v ° . the seepage-induced increase in %' is obtained by integrating the average seepage force over the height of the prism. (10) for the lower part whereby the stress a'(ho) from eq.y .. (ho _ D) /R~4. • In the general case with kl. (10) yields the following formula for the vertical effective stress sv' acting on the wedge (z=D): Gv' = RT' . The average effective vertical stress a ' at the wedgeprism-interface CDEF is computed according to silo-theory (Jarmsen 1895). c3hl-dy.tan¢ a = hoe -~*wR . In terms of effective stresses. one obtains the following equation from (14): ~. (16) This equation is more convenient than (16) for the numerical computation because it does not contain gradients of head.y. (i0) d. F. The weighting factor e -~"* ~-D~ is equal to 1 at z = D (i. ABCD. (18) ~w Ol.e. 1~'-. The stress G ' at the prism-wedge interface is obtained by solving the eqmhbrium eq.k t a n ¢ (ho .tan~p .y. in the case with a constant seepage force f. the increase in %' due to seepage is obtained by integrating a weighted seepage force over the height of the prism.y. .z): (6) The resultant seepage force {F~ F¢ F] acting on the wedge is obtained by applying Gauss's ~heorem to the body force integrals over the wedge volume: f = .yw ~}h/Dz . pD+H Yw(~ where Td denotes the dry unit weight. ~hfdx. f = .c ( 1 .e -)'tantH/s) + Xtan. the y-component of the resultant seepage force is equal to zero. 2). By means of Gauss's theorem. f = .x t a a ¢ R JD (z . 2). 1996 TUNNELLINGANDUNDERGROUNDSPACETECHNOLOGY173 .z) dy .z)dydx . (14) reveals that: • In the supposed case of a ground without internal friction (Xtan~p = 0). the seepage forces beingintroduced into the equilibrium equation. .y.. (16) is taken into account as a boundary condition: G " = (T " (h "t o-~tan~ (H + D . (9) Due to symmetry. a) Eq.tant(z-D)/Rdz . and h" is the average head over the directiony vdthin the wedge: h* = h* (x~. H.ho) /R ~.c o s t 0 fF~ JAB h* ds + JABfCD ds) . 'v -~ "°" ~ ~. Accordingly. CDEF (Fig.e-~t~*(~ *D-ho)/R . h" (7) (8) F~ (e°) = )'~ ( sm{o fASFEh*dS-fcDEFh*ds)' where eois the shear plane inclination (Fig.an~p = 0. R where R denotes the ratio of the area to the circumference of a horizontal cress-section of the prism. = JD (14) where {X = ( h o) e . Applying silotheory to the upper part yields the vertical stress acting at the level of the water table (z=ho): a~"(h o) = ~RTd-c (1.C ( l _ o_~.D ) / R d z (19) Volume 11. the case of a water level above the soil surface (ho_>H+ D) will be considered first. The Seepage Forces The seepage forces per unit volume { f j ~ f J are equal to the gradient of the numerically computed hydraulic head according to the classical silo-theory (without seepage). ' = ~ . '~ -' (13) where ** fz e-Xtant(z-D)/R d z . Water Level below Soil Surface When the water level is below the soil surface (ho< H+D). the more rapidly this factor decreases. Number 2.h** (D) + ~ ) D (D +H h **(z) e-7. the prism must be divided into two parts.APPENDIX A.y. u Water Level above Soil Surface For the sake of simplicity. For example. the increase in %' amounts to f . the vertical equilibrium equation reads as follows: dG.) = ~ 1 Da f-D~h(x. (13) gives the effective vertical stress h **(D) + ~tan¢ [ho h**(z)e . o .D ) / R _ The first term in e(l. and f ' " is the vertical seepage force averaged over the horizontal prismsection at the elevation z: (11) R = Dtano~ 2(1 + tan{o) ' ~Dtanto D/2 fz**= D2tan{o ~ o 1 f~9/2 fz(x'y'z)dydx" (12) h**(z)+~l 10D2tan{o f_D?h(x. the seepage-induced part of the effective stress ~ ' is dominated by the seepage forces in the vicinity of the tunnel crown. the second term (Tw denotes its increase due to the seepage.tan. (15) where h"(z) denotes the average hydraulic head at the horizontal prism-section at the elevation z: r Dtan o} D/2 h(x. at the wedge-prism interface CDEF) and decreases exponentially with increasing distance (z-D) from the tunnel..' Xtan. Solving eq.