SUBSIDENCE OVERHARDR ROCK TUNNELS
Prof Erik Eberhardt, University of British Columbia, Dr Christian Zangerl, of alps GmbH, Centre for Natual Hazard Management, and Prof Simon Low, Swiss Federal Institute of Technology, discuss asymmetrical subsidence associated with deep hard rock tunnels
A prime concern in any shallow tunnelling project is the impact that the excavation process may have on the surface environment. In most cases, the immediate concern involves differential settlements caused by ground /volume loss leading to damage to sensitive surface structured. In water-bearing ground, tunnel drainage may also lead to differential displacements due to time-dependent consolidation and subsidence. Reported cases almost exclusively involve shallow tunnels excavated in soft, unconsolidated soils.
. Above: Fig1-(a) Typical surface subsidence profile based on an inverted Guassian normal distribution curve; (b) Meadured ling-term subsidence profile above a tunnel in soft soils
Consequently, the analytical and numerical procedures available to predict the extent of surface subsidence are largely based on continuum mechanics where the subsidence profile calculated is symmetric about the vertical tunnel axial plane. In many cases, the profile is approximated by an inverted Gaussian normal distribution curve (figure 1a). this assumption is generally valid for soft ground conditions where the presence of geological heterogeneity is restricted to horizontal layering(e.g.[,figure 1b )
In contrast, consolidation subsidence related to hard rock tunneling is rarely considered, although some precedence does exist. Karlsrud & Sander report cases in Oslo, Norway where tunnels driven in fractured bedrock at depths of 20m-40m drained the overlying sediments resulting in up to 35cm of subsidence. In these cases, the soft marine clays above the bedrock were considered as being the sole consolidating material, with the fractured rock mass below only serving as a conduit for drainage during excavation. Lombardi reported the case of the Zeuzier double arch dam in western Switzerland, where 13cm of vertical settlement was measured at the dam in relation to the driving of an investigation adit 1.5km away. These displacements resulted in the cracking of the dam. Initially, no clear explanation could be provided as to the source of the settlements and the reservoir was ordered drained. After investigating and discounting a number of alternative causes, suspicion fell on water inflows into the adit, which was driven through a confined, fractured, marly-limestone aquifer. The adit excavation works were then ordered stopped and the cracks in the dam body repaired.
Above: Fig2-(a)Levelling profile along the Gotthard pass road showing measured surface subsidence relative to earlier measured periods of alpine uplift;(b)Measured initial inflow rates into the Gotthard safety tunnel/100minterval during excavation
In 1998, the Swiss Federal Office of Topography completed a routine high-precision leveling survey over the Gotthard pass road in central Switzerland. Comparison of results with those from a survey over the same route in 1970 revealed that up to 12cm of downward displacement had occurred over a 10km section (figure 2a) . This sharply conflicted with earlier surveys made between 1918 and 1970, which showed upward displacements of 1mm/yuar in agreement with measured alpine uplift rates for the region. The presence of the subsidence trough was late confirmed by geodetic trough was later confirmed by geodetic triangulation measurements supplemented with GPS date . Field investigations performed to determine the origin of the subsidence quickly ruled out localized surface phenomena (e.g. a deep-seated landslide)given the absence of local indicators and the 10km extent over which the settlements weer measured. Instead, spatial and temporal relationships between the measured settlements and the nearby Gotthard highway tunnel pointed to causality between tunnel drainage and surface deformation (figure 2b).
The Gotthard highway tunnel
The 19.6km long Gotthard highway tunnel was constructed between 1970 and 1977. The geology encountered consists primarily of paragneisses and granitic gneisses of the central Gotthard massif. These rock bodies were overprinted by alpine metamorphism, mostly in greenschist facies.
Construction of the highway tunnel included that of a smaller safety tunnel, which was excavated several hundred meters ahead of the main tunnel with a 12-18 month lag time. This allowed the safety tunnel to serve both as an investigation and drainage adit for the main tunnel. Water inflows into the safety tunnel were measured periodically, for which a 3km zone was encountered in the Gamsboden granitic gneiss that produced especially high inflows (figure 2b). Steeply inclined brittle fault zones acted as the primary drainage conduits into the tunnel, two of which, situated 23m apart, produced initial inflows of 300 l/s. The location of this interval and that of the 3km zone closely corresponds to the centre of the broad subsidence trough seen in the settlement profile, with the point of peak water inflow coinciding with that of maximum subsidence(figure 2)
Based on this correlation, a working hypothesis was developed that pointed to tunnel-induced surface subsidence associated with deep drainage and consolidation of the fractured crystalline rock mass . An extensive field, laboratory and numerical modeling campaign was then undertaken to explore and explain the processes and mechanisms responsible for the measured subsidence . Most of the focus was placed on the major fault zones and meso-scale fractures mapped the region and understanding the phenomenon of fracture consolidation and that of low-porosity intact rock (<1% intact matrix porosity).
Treatments of consolidation subsidence
Analytical solutions for consolidation settlement are primarily based on Terzagh’s one-dimensional consolidation theory, where the vertical strain is calculated for a given change in pore presser acting across a compressible stratum. The key assumption here is that the zone of influence around the tunnel can be delineated and that the change in pore pressure is uniform across it. This neglects the influence of any geological heterogeneity and/or permeability anisotropy between the free drainage boundary condition represented by the tunnel opening and the far field boundary conditions. Such factors would significantly influence the distribution and evolution of pore pressures during tunnel drainage and groundwater drawdown.
Empirical databases compiled for subsidence prediction almost exclusively focus on shallow urban tunnels in granular and cohesive soils. From these, design charts are developed that depict trends for maximum subsidence and shape of the subsidence profile based on that of the symmetrical inverted normal distribution curve (e.g. figure 1a). In one such study, Rankin found that the overall trough width of detectable surface settlements can be estimated as three times the tunnel depth. However, it should be noted that the case histories used in Rankin’s assessment are heavily weighted towards the influence of ground loss during excavation.
This points to a general deficiency of empirical databases in that they are ‘holistic’ and disregard details of the underlying mechanisms. In Rankin’s empirical study[, the influence of both ground loss and long-term consolidation are combined together in the observations used to form his empirical relationships. Thus, if ground loss is not an issue, as is the case for the Gotthard highway tunnel, then such empirical relationships are likely not applicable. As an aside, the width of the measured subsidence trough over the Gotthard highway tunnel is more than ten times its depth. Care must be taken that the case histories on which empirical relationships are based are applicable to the case in question.
More recently, the advance of numerical methods has led to the finite-element method (FEM) becoming the standardized tool by which to solve consolidation settlement problems. Again, treatment has generally focused on granular and cohesive soils that can be treated as a uniform geological continuum (e.g.). For fractured rock, the rock mass must be equated to that of an equivalent continuum, where fractures are treated implicitly. Solutions often invoke Biot’s 3-D consolidation theory, which describes the transient coupled hydro-mechanical response of a linear elastic, isotropic, homogeneous porous medium.
Figure 3 shows the results of a finite element analysis carried out for the Gotthard highway tunnel problem, where the flow and elastic field solutions are coupled through a poroelastic formulation. Several independent input parameters are required including drained Young’s modulus and Poisson’s ratio, Biot’s and Skempton’s coefficients, and the permeability tensor. These were established through laboratory tests and field-based estimates scaled to field values through mapping and rock mass characterization The 2-D mesh was designed to replicate local topographical, geological and hydrological conditions in the study area (figure 3a-b). Of key importance was the representation of the fracture drainage network intersecting the tunnel. This consisted of a primary sub-vertical drainage conduit (figure 3a), representing the steeply inclined brittle fault zone that produced the peak tunnel inflows (figure 3b ), fed by a less permeable equivalent-continuum domain representing the smaller-scale fracture permeability network.
Above: Fig3-(a)Schematic model geometry and boundary condition for contimuum-based Gotthard highway tunnel consolidation subsidence analysis;(b)Associated finite-element results and measured Gotthard subsidence profile
Results from the continuum analysis (figure 3c) showed that a good fit could be achieved with the observed maximum settlement magnitude when constrained by field observations. However, the fit to the shape of the subsidence trough was poor, and for the most part, the magnitudes of vertical displacement were under predicted.
Discontinuum analysis
In reality, the nature of the rock mass tunneled through in the Gotthard example is much more heterogeneous than that afforded by an equivalent continuum treatment. The presence of jointing and faulting would result in a deformation mechanism that is largely discontinuous. Zangerl et al developed several deformation models to explain consolidation subsidence in fractured crystalline rock. These included the closure of sub-vertical joints and brittle fault zones through changes in effective normal stress and the poroelastic consolidation of the intact rock matrix(figure 4)
Intuitively, the frequency and normal stiffness of sub-horizontal fractures would have the most impact on surface subsidence as closure of these fractures (figure4a) would directly contribute to vertical displacements. However mapping of the major conductive structures in the Gotthard highway tunnel region(i.e. brittle faults, figure5a)showed that the majority of these structures were steeply inclined (figure 5b), forming a fan-like structure along the tunnel alignment (figure 5c)
In the case of vertical faults, both the total and effective stresses acting normal to the fracture plane are assumed to change during drainage, but the vertical stress remains constant (figure 4b-c).The resulting drop in the effective normal stress would enable vertical slip to occur along the fracture. In addition, decreases to the constant vertical stress would generate strains within the intact rock blocks, resulting in a “Poisson’s ratio” effect where the intact rock would experience expansion in the horizontal and shortening in the vertical direction.
Based on these fracture deformation models Zangerl , performed a series of numerical simulations using the distinct-element code UDEC . The distinct-element method treats the problem domain as an assemblage of impermeable, deformable blocks for which the dynamic equations of equilibrium are solved until the boundary conditions and laws of contact and motion are satisfied. The method accounts for complex non-linear interaction between blocks (i.e. slip and/or opening/closing along discontinuities ),and through the effective stress law and an aperture-flow coupling relationship, is capable of modeling the hydro-mechanical response of a fracture network to tunnel drainage.
For the Gotthard analysis, discrete fractures were added to the model (figure 6a) based primarily on the steeply inclined brittle fault zones mapped on surface and from within the safety tunnel that runs parallel to the highway tunnel (figure5). Thus, the fracture spacing and geometry for there faults were a direct (i.e. explicit) representation of those mapped in situ. Normal and shear stiffness values for the faults were assumed to be constant and equal to 0.5 and 0.1MPa/mm, respectively. The transition from elastic shear displacement along the faults to plastic ship was dictated using a Coulomb-slip low where cohesion was set to zero and the joint friction angle to 30°.Next horizontal joints were added to the model to provide connectivity for fluid flow. The normal set spacing for these joints were based on mapping data, with spacing values decreasing with depth. Normal stiffness values for the horizontal joints were based on a semi-logarithmic closure law, where values were varied with depth (i.e. as a function of increasing normal stress)
Integration of the conceptual hydrogeological model into UDEC was achieved by calibrating the sub-vertical hydraulic conductivities of the representative fault zones based on their transmissivities. Hydraulic boundary conditions along the side boundaries were set as impermeable (i.e. no flow boundaries). A mean water-table was set 500m above the tunnel elevation, with surface recharge being accounted for through a constant pore pressure condition applied to the upper boundary (figure 6b).
Above: Fig-(a) Distinct-element model with explicit re3presentation of brittle fault zones maped within Gotthard highway safety tunnel;(b)Model boundary conditions;（c）Discontimuum results showing shear displacements along discontimuities;(d)Comparison of distinct-element results and measured Gotthard subsidence profile
Results from the discontinuum models showed that vertical displacements are generated through shear deformation and slip along the steeply inclined faults upon tunnel drainage (figure 6c).Furthermore, the models also confirmed the presence of the Poisson ratio effect as previously described. Of key importance though, was that the distinct-element models were able to reproduce most of the asymmetry and small-scale inflections with respect to the shape of the subsidence profile (figure 6d). It should be notes though, that these models could only reproduce 75% of the total surface settlement magnitudes (assuming low normal stiffness values), as limitations in the UDEC formulation, where the blocks are treated as being impermeable, do not enable the contributing poroelastec effects to the intact rock matrix to be considered. Laboratory tests by Zangerl suggest that
ACKNOWLEDGMENTS
The authors would like to thank the maintenance team of the gotthard highway tunnel for their kind support of this work and the AlpTransit Gotthard AG for the permission to publish the settlement data. These are sizeable and should not be discounted.
Discussion and conclusions
Conventional methods used to calculate tunnel-induced consolidation subsidence are largely based on continuum mechanics the consequence of which is a pofile. In hard rock tunneling, the heterogeneous and discontinuous nature of the ground mass where fractures (joints, faults, etc.) open, slip and shear when the effective stress conditions change, mean that any tunnel-induced surface displacement will largely be asymmetrical.
This was the case for the subsidence trough that developed, completely unforeseen, over the Gotthard highway tunnel, a tunnel excavated at several hundred meters depth through fractured crystalline rock. The implications are thus significant for the 57km long Gotthard Base Tunnel currently under construction, as its trajectory passes through similar rock mass conditions and close to several important concerte dams. Already, small vertical settlements as well as horizontal strains have been recorded close to the Nalps dam in relation to the Gotthard Base Tunnel excavations near Sedrun.
Comparison of numerical results based on continuum and discontinuum techniques demonstrated that finite-element (i.e. continuum) models were able to reproduce the maximum settlement magnitude measured when constrained by field observations, but could not reproduce the asymmetric shape of the subsidence profile. This resulted in the under-prediction of vertical displacements away from the centre of the width and asymmetry to the subsidence profile was instead achieved by distinct-element (i.e. discontinuum) models where mapped geological structures intersecting the tunnel could be explicitly included.
Through Zangler’s study , it has been established that detrimental consolidation settlements in relation to a deep hard rock tunnel project are possible by means of fracture drainage and consolidation. Results further demonstrate the importance of detailed field investigation, monitoring and selection of the correct analysis method for the given ground conditions encountered. One of the major limitations to the present case study, was that pore pressure drawdown due to tunnel drainage could not be well constrained; prior to construction, the prospect of generating surface displacements several hundred meters above the tunnel was not considered and therefore data relating to pore pressure evolution was not recorded. In future, continuous spatial and temporal deformation and pore pressure measurements may be necessary in cases where a deep hard rock tunnel excavation will pass under strain sensitive surface structures.
