Consolidation Settlements above Deep Tunnels in Fractured Crystalline Rock: Numerical Analysis of Coupled Hydromechanical Mechanisms

Consolidation Settlements above Deep Tunnels in Fractured Crystalline Rock: Numerical Analysis of Coupled Hydromechanical Mechanisms

759 CONSOLIDATION SETTLEMENTS ABOVE DEEP TUNNELS IN FRACTURED CRYSTALLINE ROCK: NUMERICAL ANALYSIS OF COUPLED HYDROMECHANICAL MECHANISMS E. Eberhardt\...

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759 CONSOLIDATION SETTLEMENTS ABOVE DEEP TUNNELS IN FRACTURED CRYSTALLINE ROCK: NUMERICAL ANALYSIS OF COUPLED HYDROMECHANICAL MECHANISMS E. Eberhardt\ K. Evans\ 0. ZangerM, S. Loew^ ^) Engineering Geology, Swiss Federal Institute of Technology (ETH Zurich), Switzerland Abstract: Recent measurements of surface displacements 800 m above the Gotthard (N2) highway tunnel in central Switzerland have shown up to 12 cm of subsidence since the tunnel was constructed. Subsidence of this magnitude in a fractured crystalline rock mass is unexpected and appears to be related to large-scale consolidation resulting from groundwater drainage and pore pressure changes around the tunnel. With the recently initiated construction of the 57 km long Gotthard Base Tunnel, which passes through similar geological conditions as the Gotthard highway tunnel and underneath several important dams (the integrity of which could bt adversely affected by differential settlements), understanding these processes and being able to predict the magnitude and extent of surface displacement becomes highly relevant. This paper focuses on the use of 2-D fmite-element models to analyse the measured subsidence magnitudes recorded over the Gotthard highway tunnel, treating the fractured rock mass as an equivalent poro-elastic medium. The provisional results reported in this paper address the hydrogeological controls and their affect on the extent of the diffusion front and the resulting shape and magnitude of the subsidence profile.

1. INTRODUCTION

Surface subsidence due to consolidation of rock in which the pore pressure has been reduced, through fluid extraction, is well known in the fields of petroleum engineering and groundwater where the problem has received wide attention. However, the phenomenon is not generally recognised as being important in fractured crystalline rock masses, even though large reductions in pore pressure can occur when driving a deep tunnel. In tunnelling, Schmidt (1989) notes that the tendency for tunnel engineers and researchers to pay little attention to consolidation settlement has often led to surprises, but that such cases have been reported in sufficient detail to identify the underlying cause. These cases almost exclusively involve tunnels excavated in soft soils. Consolidation settlement problems associated with tunnelling in fractured rock have been reported in Oslo, Norway (Karlsrud & Sander 1979), but in this case soft marine clays lying above the bedrock were still considered as being the sole consolidating material and that the fractured bedrock was reported as only providing the drainage network into the tunnel excavation. Precedence for rock mass consolidation in relation to tunnel drainage has been reported by Lombardi (1992) in relation to the driving of an investigation adit through a confined, fractured, marly-limestone aquifer near the Zeuzier dam in Switzerland. Recorded settlements at the dam site of -13 cm were measured even though the adit was

1.5 km distant. Although these settlements are small compared to those associated with some fluid extraction schemes, they can have serious consequences since only minor differential displacements are necessary to induce damage in concrete structures. In the Zeuzier case, cracks in the dam appeared which required it to be emptied and repaired over a period of several years. Zangerl (2003) describes an example of surface subsidence associated with drainage-promoted consolidation in crystalline rock. Recent highprecision levelling measurements over the Gotthard pass road in central Switzerland, have revealed up to 12 cm of subsidence over a 10 km section that passes almost a kilometre above the Gotthard highway tunnel. The levelling surveys were performed by the Swiss Federal Office of Topography prior to and after tunnel construction (i.e. 1970 and 1993/98, respectively). Earlier surveys between 1918 and 1970 showed only a steady alpine uplift rate of approximately 1 mm/year. The presence of the trough was recently confirmed by geodetic triangulation measurements supplemented with Global Positioning System data (Salvini 2002). The rock mass penetrated by the tunnel primarily consists of paragneisses and granitic gneisses (Figure 1). The majority of fractures and fracture zones are sub-vertical and strike ENEWSW. Semi-quantitative measurements of tunnel inflow during construction indicated a 3-km wide section where transient inflows were markedly

760 high, with one fracture zone producing an estimated inflow of 300 1/s. The location of this section corresponds closely to the broad trough seen in the subsidence profile, and the peak-inflow coincides with the sharp maximum displacement peak (Figure 1). This spatial correlation, and the temporal relationship between tunnel construction and settlement, points to causality between water drainage into the tunnel and surface deformation. Alternative explanations such as localized surface processes (e.g. landslides) could be excluded given the absence of local indicators and the 10 km extent over which the settlements were measured. In light of the new 57 km AlpTransit Gotthard base tunnel, which is currently under construction and whose trajectory passes close to several dams, the assessment of possible surface subsidence is of great interest. In this paper we present the results of a two-dimensional finite-element study which includes coupled fluid pressure diffusion and consolidation with the rock mass treated as an equivalent isotropic porous medium.

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I —Settlement (1970-93/98)> "5 —Alpine uplift (before tunnel o construction 1918-1970)

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Swiss coordinates, North-south axis (km)

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2. CONSOLIDATION MECHANISMS IN FRACTURED CRYSTALLINE ROCK Zangerl et al. (2003) recognised several mechanisms that might contribute to the subsidence measured over the Gotthard highway tunnel. All are triggered by reductions in pore pressure within the rock mass due to drainage into the tunnel. The mechanisms are illustrated in Figure 2 and involve: the closure of sub-horizontal joints; the deformation of sub-vertical joints and brittle fault zones through changes in the localized horizontal stress state; and the consolidation of the intact, permeable rock blocks acting as poroelastic bodies. The approach taken was to include these mechanisms in coupled hydro-mechanical numerical models and attempt to reproduce the observed subsidence. The disturbance to the model is the pore pressure depletion that reflects drainage of the rock mass at the points where major conductive fractures are intersected by the tunnel. To provide data for the modelling, a program of extensive field mapping of geological structures and laboratory tests on core samples was undertaken (Zangerl 2003). hituitively it can be expected that closure of horizontal fractures in response to reduced internal pore pressure would be the single largest contributor to subsidence. However, the major conductive structures and brittle fault zones in the Gotthard region are sub-vertical (Zangerl 2003). Numerical modelling using discontinuum techniques (i.e. distinct-element) showed that these features can contribute to subsidence in a complex manner that involve closure and shear of fractures, and vertical strains of intact block induced through a Poisson's ratio effect (Zangerl et al. 2003). The asymmetric nature of the subsidence trough and some of the local irregularity on its flanks were reproduced by these models. However, these models did not include consolidation of the intact block material and were unable to account for the observed magnitude of subsidence unless fracture compliance values were adopted which were much higher than seem reasonable. Thus, the results suggested consolidation of the intact blocks contributed significantly to the subsidence.

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Distance from tunnel north-portal (km) iPermo-carboniferous B i Granitic-gneiss and Mesozoic sediments H i Paragneiss

Figure 1. Surface settlement and measured initial water inflow rates into the Gotthard highway tunnel.

3. CONTINUUM MODELLING CONSOLIDATION SETTLEMENTS

OF

Ideally, the problem requires a fully coupled hydromechanical numerical code that incorporates flow and deformation in both the explicitly-defined

761 discrete fractures (e.g. fault zones) and the intact rock block material bounded by the fractures. Another approach that implicitly includes each of the key contributing factors outlined in Figure 2 (i.e. including matrix consolidation) and requires less expenditure of resources is to represent the discontinuities and intact blocks of the rock mass as an equivalent poro-elastic continuum. This is the approach used in producing the results reported in the remainder of the paper.

a) Model 1

-Qn ~ equals constant

Aq; = Aq,-afAp -Op changes during fracture drainage (i.e. "Poisson ratio effect)

Aperture

c) Model 3

Aq; = A(^-afAp On

On T

£

-On changes during fracture drainage (i.e. "Poisson ratio effect) -low normal and shear stiffness

intact rock^l Jiaul^ I jntact rock

d) Model 4 ult

jintac

Oij = Oij - a p 6jj -poroelastic behaviour of the intact rock mau-ix

Figure!.

Conceptual consolidation mechanisms for fractured crystalline rock masses involving: (a) horizontal joints, (b) vertical joints, (c) vertical faults, and (d) intact rock. After Zangerl (2003).

3.1 Poroelastic Formulation The pore pressure within fractures that are members of a connected network will drain when penetrated during tunnel excavation. The reduction in pore pressure will then diffuse out into the rock mass. The extent to which drainage penetrates the rock mass on the long term depends largely upon both the geometry and conductivity of the network. Generally, high conductivity and low divergence of the network, such as tends to occur in brittle fault zones, promotes deep penetration. Saturated, lowpermeability intact rock blocks that are bounded by fractures in the network are similarly obliged to adjust their internal pore pressure to maintain equilibrium at their boundaries. These pore pressure changes within the rock mass induce consolidation strains in accord with the theory of linear elasticity. Biot (1941) derived the 3-D consolidation theory, which describes the coupled hydraulic and mechanical transient response of a linear elastic, isotropic, homogeneous porous medium. One aspect of his theory is the effective stress law for elastic deformation: <

=(^u-opS,j

(1)

where a'; matrices respectively, p is the fluid pore pressure, a is Biot's coefficient, and 5ij is the Kroenecker's delta (Nur & Byerlee 1971). Biot's constant describes the fraction of pore pressure change that is felt by the solid skeleton as a deforming volumetric body force, and takes values ranging from 0 to 1. Analysis of time-dependent consolidation requires the solution of Biot's consolidation equations coupled to the equations describing flow. The transient hydro-mechanical coupling between pore pressure and volumetric strain for a linear elastic, mechanically isotropic porous medium and fully saturated with a single fluid phase (i.e. water), is given by the fluid continuity equation: de,. ^ dp k ^-y or—^ = - S ^ — + —V'p-h(2 dt dt volumetric strain

(2)

transient-flow-equation

where: Ey = volumetric strain, Q = explicit fluid source, k = permeability, \k = dynamic fluid viscosity, p = pore pressure and t = time. The

762 parameter Se refers to constrained specific storage (i.e. that which applies under zero macroscopic strain conditions: ey = 0) and is given by, S.=

y^a{\ - CCB)

(3)

KB Here Yw = specific weight of formation water, K = the drained bulk modulus, v = the drained Poisson's ratio and B is Skempton's coefficient. Simulations were performed using the commercial finite-element program VISAGE (VIPS 2003), which incorporates flow and elastic field solutions coupled through poro-elasticity. Each simulation requires as input seven independent parameters: water density, rock density, drained Young's modulus, drained Poisson's ratio, Biot's constant, Skempton's constant and the hydraulic permeability. To date, only 2-D simulations have been performed with future plans involving the analysis of 3-D models currently under development based on experiences gained through the 2-D study. The 2-D mesh was designed to allow inclusion of local topographical, geological and hydrological conditions in the study

3.2 Model Geometry and Material Properties The model geometry used in the present studies is shown in Figure 3. The profile represents an approximate North-South section taken parallel to the tunnel axis, and is thus sub-parallel to the levelling profile shown in Figure 1. The model geometry assumes a laterally extended drainage point along strike of the major permeable fault zone (i.e. out-of-plane) coinciding with the centre of the subsidence trough. This fault zone would act as a sub-vertical drain to the adjacent rock masses to the north and south. The form of the subsidence profile suggests diffusion of pore pressure drawdown both north and south from the major inflow point at the tunnel. Most certainly there is also diffusion in the EastWest direction within the conductive faults intersected by the tunnel. However, there is little data on the pattern of subsidence in these directions. Nonetheless, it seems reasonable to assume that the penetration of drainage along the major fracture zone that produced the largest inflow was extensive. In the 2-D models, it was assumed that the fracture is sufficiently conductive that is can be taken as constant potential feature at

the pressure of the tunnel. Thus, at zero time, the pressure along the set of nodes representing this fault is dropped to atmospheric. Zero displacement boundaries were applied normal to the bottom and sides of the model (shown as 'rollers' in Figure 3). Pore pressures were initialised assuming a water table coincident with the surface topography. Flow boundaries along the side were set as impermeable (i.e. no flow) and the bottom boundary was set to a constant pore pressure of 30 MPa. The surface boundary condition was set assuming a fixed pore pressure condition corresponding to recharge. Material properties were based on laboratory and field estimates whenever possible. Hydraulic conductivities were based on rock mass transmissivities derived from tunnel inflows and simple radial flow models (Luetzenkirchen 2003). The drained Young's modulus of the rock mass, Erm, was calculated using the relationship:

(4)

E^ = E

Xk„

where E is the drained Young's modulus of intact rock determined from laboratory tests as 45.5 GPa; X is the mean fracture spacing which was taken as 1 m on the basis of field mapping (Zangerl 2003); and kn is the normal stiffness of the fractures (taken as 38 MPa/mm). Material properties are given in Table 1. Where otherwise stated, these properties were assumed to be constant and isotropic.

Figure 3. 2-D model geometry and finite-element mesh used for fault zone diffusivity simulations.

763 Table 1. Model input parameters and material properties. Parameter

Value

Unit weight of rock, y 27 kN/m^ Unit weight of water, y^ 10 kN/nr' Young's modulus of rock mass, Enn 20 GPa Poisson's ratio, Vm, 0.2 Hydraulic conductivity. Km le-8 m/s Biot's coefficient, a 0.7 Skempton's coefficient, B 0.9

3.2 Model Results The material properties given in Table 1 yield a very good fit to the magnitude of subsidence (Figure 4). Parametric analysis indicates that the predicted subsidence magnitude is primarily determined by the drained bulk modulus and Biot's coefficient values, and also by the vertical extent of drainage. Indeed, the Table 1 parameter set yields a marginally better fit to the peak magnitude if the drainage along the fault zone is restricted to the lower 200 m section extending upwards from the tunnel, rather than extending to the surface. Limited vertical extent of fault zone drainage is suggested by field observations, which show that surface springs, streams and rivers were not significantly disturbed following construction of the tunnel (Zangerl 2003).

\y 165000

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—— senlement profile limitedfault drainage — fauh drained to surface 157500

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North-South Profile Distance (m)

Figure 4. Gotthard settlement profile and those modelled assuming drainage of the fault zone to surface and fault zone drainage limited to a 200 m interval above the tunnel.

Although the magnitude of the subsidence predicted in Figure 4 closely matches the observed, the form of the observed subsidence trough is broader and has detail that is not reproduced by the predicted curves. In part, the detail might reflect the contribution to the subsidence of closure on discrete fractures, as was suggested by the distinctelement modelling (Zangerl 2003). However, within the framework of the poro-elastic continuum model, two possible ways of broadening the predicted trough were examined. The first approach was to increase the horizontal diffusivity of the medium. This could be accomplished by increasing the horizontal hydraulic conductivity, Kx, or decreasing the specific storage coefficient (through decreasing a and increasing B). Increasing Kx from le-8 to 5e-8 m/s resulted in a substantial increase in the width of the subsidence trough, but also increased the magnitude. Thus, a was reduced to 0.45 to yield agreement with the observed (Figure 5). A limitation of the model is that it does not reproduce the marked asymmetry in the observed profile with respect to the northern and southern hinge points where the surface deflections begin. It also tends to under- and over-predict the subsidence along the northern and southern margins of the trough, respectively. Lastly, and perhaps most importantly, geological field observations are not consistent with higher horizontal than vertical hydraulic conductivity. Rather, the sub-vertical, ENE-WSW striking attitude of the major fault zones would suggest if anything the opposite anisotropy, leading to narrower predicted subsidence troughs. The second approach was to supplement the single drainage fracture zone at the subsidence peak with further drainage zones located 1.2 km to the north where a group of water-bearing fault zones were intersected in the tunnel (Figure 1). That these may also constitute conduits for penetrative drainage is suggested by the co-located inflection in the observed subsidence profile. The results including these extra drainage fractures are also shown in Figure 5. Parameter values were the same as those given in Table 1 except that a lower value of Biot's constant of 0.5 was used to more closely represent values derived from laboratory tests under higher hydrostatic loads (Zangerl 2003). Evidently, the inclusion of the additional drainage zones gives a marked improvement in fitting the asymmetric nature of the settlement trough. It should be noted that this study is still ongoing.

764 tunnel inflow measurements. Future modelling will also be directed towards the development of 3-D equivalent continuum models that will allow for the explicit inclusion of important geological and hydrogeological features relative to the path of the Gotthard highway tunnel axis.

REFERENCES

165000

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North-South Profile Distance (m) --— Gotthard settlement profile • • • with 2nd drainage fault

Figures.

~" single drainage fault —»*— increased horizontal ronductivir

Gotthard settlement profile and those modelled assuming additional key drainage fault structures.

4. CONCLUSIONS

The recent surface geodetic measurements above the Gotthard highway tunnel in Switzerland demonstrate that consolidation of a fractured crystalline rock mass through deep tunnel drainage can result in surface settlements of sufficient magnitude to pose a threat to the integrity of nearby large concrete structures such as arch dams. The preliminary results from this study demonstrate that fmite-element modelling based on poro-elastic formulations provides a useful means to quantitatively assess potential consolidationinduced surface settlements in fractured crystalline rock masses Results of modelling show that an equivalent rock mass deformation modulus scaled from laboratory test results, and other input parameters constrained by field observations provide a good fit to the observed maximum settlement magnitude. However, the fit to the form of the subsidence trough is not so good, particularly with regard to total width and smaller scale variations. A better fit to the width and asymmetry could be obtained by including additional tunnel drainage points in the model at the locations where significant inflows were noted during tunnel construction. Thus results emphasize the importance of geological anisotropy and asymmetry related to the location of major conductive fault zone structures intersecting the tunnel. Future modelling will concentrate on this anisotropy and asymmetry through the development of additional models incorporating more geological and material heterogeneities constrained by field data and by including tunnel flux drainage conditions based on

Biot, M.A. 1941. General theory of threedimensional consolidation. Journal of Applied Physics 12: pp. 155-164. Karlsrud, K. & Sander, L. 1979. Subsidence problem caused by rock-tunnelling in Oslo. In S.K. Saxena (ed.). Evaluation and Prediction of Subsidence. New York: American Society of Engineers, pp. 197-213. Lombardi, G. 1992. The FES rock mass model Part 2: Some examples. Dam Engineering 3(3): pp. 201-221. Luetzenkirchen, V. 2003. Structural geology and hydrogeology of brittle fault zones in the central and eastern Gotthard massif Switzerland. Department of Earth Sciences, Swiss Federal Institute of Technology (ETH Zurich), Switzerland. Nur, A. & Byerlee, J.D. 1971. An exact effective stress law for elastic deformation of rock with fluids. Journal of Geophysical Research 76(26): pp. 6414-6419. Salvini, D. 2002. Deformationsanalyse im Gotthardgebiet. Zurich: Institute of Geodesy and Photogrammetry, ETH Zurich. Schmidt, B. 1989. Consolidation settlement due to soft ground tunneling. In Proceedings of the Twelfth International Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro. Rotterdam: A.A. Balkema, pp. 797800. VIPS 2003. VISAGE - Vectorial Implementation of Structural Analysis and Geotechnical Engineering, Version 8.7. Bracknell, UK: Vector International Processing Systems Limited. Zangerl, C. 2003. Analysis of surface subsidence in crystalline rocks above the Gotthard highway tunnel, Switzerland. Department of Earth Sciences, Swiss Federal Institute of Technology (ETH Zurich), Switzeriand. Zangeri, C , Eberhardt, E. & Loew, S. 2003. Ground settlements above tunnels in fractured crystalline rock: numerical analysis of coupled hydromechanical mechanisms. Hydrogeology Journal 11(1): pp. 162-173.