A PARAMETER STUDY OF THE DAMAGED ROCK ZONE AROUND SHALLOW TUNNELS IN BRITTLE ROCK MASS D. SAIANG 1 and E. NORDLUND 1 1 Division of Rock Mechanics and Rock Engineering, Luleå University of Technology, Sweden. (corresponding author: david.saiang@ltu.se) As part of an ongoing study on the mechanical characteristics of the damaged rock zone (DRZ) around underground excavations and its influence on the overall performance of the excavation, a parameter study was carried out using the continuum method of numerical analysis. This assisted in identifying the sensitivity of the parameters tested, thereby laying the groundwork for further numerical investigation. The main parameters investigated include the extent of DRZ, the strength and stiffness of DRZ, and the depth of the excavation. The main quantity used to test the sensitivity of these parameters is the response of induced stresses around the excavation boundary resulting from the variation in these parameters. In the study presented in this paper, typical in-situ stress and rock mass conditions observed for shallow tunnelling projects in Sweden are used. The results clearly demonstrate the effect of DRZ on the excavation as well as the criticality of various parameter combinations. The strength of DRZ although sensitive, is the most complex to define and the tool used in this study to determine the empirical plastic strength components, namely cohesion and friction, is felt to be uncertain. Keywords: damaged rock zone, shallow tunnel, strength, stiffness, parameter study. 1. Introduction The presence of a damaged rock zone (DRZ) around a tunnel boundary can significantly influence the overall performance of the tunnel. This zone (see Figure 1), although finite in extent, is thought to be responsible for problems relating to for example; overbreak resulting in removal of additional material and uneven tunnel profile, reduced confinement due to low stiffness, reduced rock strength, increased fracture intensity leading to free inflow and outflow of water, and effects on long term stability. Any problems associated with the DRZ can create unsafe working environments and increase construction and maintenance costs. In some cases the DRZ can have a positive effect, for example in high stress environments the DRZ can protect the excavation by pushing high stresses further away from the excavation into stiffer rock, which is the basis for rock preconditioning or destressing. A synonym for DRZ is the excavation damaged/disturbed zone (EDZ). The EDZ has been widely investigated, particularly by the radioactive waste isolation agencies and reported in the for example the international EDZ workshops of 1996 (Martino and Martin, 1996), 2003 (Martino, 2003) and 2004 (Tsang et al., 2005). Some projects such as the ZEDEX in Sweden and Mine-by Experiment at URL in Canada were initiated specifically to investigate the EDZ. These studies mainly concentrated on, (i) identifying factors and mechanisms that influence the development and formation of EDZ, (ii) quantitatively measure the extent of EDZ and (iii) classifying EDZ according to its significance. In Russia the damaged rock zone around hydraulic tunnels was investigated as early as the 1960 s (Fishman and Lavrov, 1996; Mostkov, 1979). In China s massive Three Gorges Project the damage rock zone investigation is an important component of its geotechnical study program (Deng et al., 2001; Sheng et al., 2002). These studies clearly demonstrate the significance of the EDZ or the DRZ zone on the performance of an excavation, which can ultimately translate to implications on human lives and financial losses.
Numerical modelling of the DRZ can be rather difficult since much has to be known about the characteristics or condition of the rock mass within the DRZ. (Barla et al., 1999) pointed out that the success of any numerical modelling process is the level of understanding achieved in describing the rock mass conditions. The rock mass characteristic of the DRZ is complex and cannot be easily described using the existing rock mass characterisation systems, albeit they were not designed for this purpose. Other factors that complicate the process include, the confining stress conditions, anisotropic fracture patterns, presence of rock bridges, yield process of the DRZ and how to describe it, etc. With such complexities the discontinuum method of numerical modelling becomes limited since this method requires an explicit description of the rock mass. The continuum method has therefore been the alternative and had been used for EDZ investigations, see for example (Sato et al., 2000; Sheng et al., 2002). In this study, several conceptual models were developed to study the effect of the damaged rock zone on stress redistribution and ground displacements around the boundary of a shallow tunnel, with typically high horizontal stresses as experienced in the Scandinavian belt. An equivalent continuum approach of modelling is used. The results demonstrate that the DRZ does affect the induced stress and rock deformation behaviour. Undamaged rock DRZ Excavation Young's modulus (E) Deviatoric stress (σ1-σ2) Excavation DRZ Undamaged rock (a) (b) Fig. 1. (a) The damaged rock zone (DRZ) and (b) the theoretical characteristics of the rock mass around a tunnel boundary in terms of the Young s modulus (E) and deviatoric stress (σ1-σ 2). 2. Method 2.1. Model setup A single-track railway tunnel geometry shown in Figure 2(a) is used to set up the models. The geometry is typically that of a larger railway tunnel often found in Sweden (Banverket, 2002). In the actual design (Figure 2 (a)), the floor is inclined 2 o for drainage purposes, thus the wall heights differ by 0.32 m. Since symmetric models (half models) are used in this study, the tunnel height is adjusted while maintaining the overall area of the excavation, which resulted in the model crosssection shown in Figure 2 (b). In Sweden most of the railway tunnels are seated at least 10 m below the ground surface. The standard model geometry shown in Figure 3 is thus based on this rock cover depth. At shallow depths the effects due to the excavation can extend over large distances. The model size used is
thus considered sufficient based on earlier work by (Töyrä, 2004). The grid sizes are as small as 5 cm by 5 cm near the tunnel boundary in order to accurately model the DRZ. The in-situ stresses applied to the model are those given by (Stephansson, 1993) for the Fennoscandian shield, which are based on hydraulic fracturing measurements. σ V = ρgz (1) σ H = 2.8 + 0. 04z (2) σ h = 2.2 + 0. 024z (3) where σ V is the vertical stress, σh is the maximum horizontal stress, σh is the minimum horizontal stress, ρ is the rock density, g and z are gravity and depth respectively. (a) (b) Fig. 2. (a) Design geometry for a large single-track train tunnel according to Banverket (2002), (b) Model geometry with equivalent cross-sectional area. Damaged rock zone Fig. 3. A symmetric model (80 x 80 m) which represents the standard or the base case model. Stresses are initialised with stress gradients from the top to the base of the model. The left, right and base of the model are fixed with roller boundaries.
2.2. Rock mass parameters The in-situ rock mass parameters and their typical values often encountered during tunnelling projects in Sweden are shown in Table 1. The rock mass is generally considered to be of good quality. From these values the input parameter values were estimated for both the damaged and undamaged rock masses, which are shown in Table 2. These values were approximated from the Hoek-Brown failure envelope by linear regression over a range of confining stresses and subsequent projections on shear stress vs. normal stress curves. The procedure was very systematic, since the estimation of these values using Hoek-Brown failure envelope can be vulnerable due to the highly deviatoric and anisotropic stress conditions usually encountered at shallow depths. The Young s modulus (E) and compressive strength (σ cm ) for the rock mass were estimated from (Hoek et al., 2002): GSI 10 D = 40 E 1 10 (4) 2 and σ cm 2 cosφ = c 1 sinφ where D is the disturbance factor, GSI is the Geological Strength Index and c and φ are cohesion and friction angle, respectively. The empirical plastic strength parameter (c and φ) values were estimated from the shear stress vs. normal stress curve as noted earlier. For a typical drill and blast excavated tunnel the disturbance factor is assumed to be 0.75, which results in the Young s modulus of the damaged rock mass being reduced by 30%. If the simplified Hoek & Diederichs (Hoek and Diederichs, 2006) equation is used then a D value of 0.15 would give 30% reduction in the Young s modulus. The notion of disturbance factor (Hoek et al, 2002) is based on the global disturbance logic. However, in our models the disturbance is assumed to be finite and involves only the damaged rock. Table 1. Rock parameters used to derive the strength parameters for the rock mass. (5) Parameters Values Intact compressive strength (MPa) σ ci 250 Geological strength index GSI 60 Hoek-Brown rock constant mi 33 Table 2. Rock mass parameters for the base case or the standard model. Parameters Values for undamaged rock Values for the DRZ Young s modulus (GPa) 17.8 12.5 Compressive strength (MPa) 26.8 12.7 Tensile strength (MPa) 0.4 0.2 Cohesion (MPa) 2.6 1.4 Friction angle o 68 65 o
2.3. Model scenarios Six scenarios shown in Table 3 were simulated. Since it was a parameter study only one parameter was varied at a time while the others were kept constant. The Mohr-Coulomb yield model was used in simulating the scenarios. The scenario of varying the compressive strength (σ cm ) was not straightforward since σ cm is dependent on c and φ. At very low confining stress (σ 3 >1.0 MPa) the frictional effects can be considered negligible for a fractured rock with numerous rock bridges. In that case the cohesive and tensile strengths will be important. Hence, in these models the cohesion and tensile strength values were estimated from the normal stress vs. shear stress curves. This required first transforming the principal stresses into shear and normal stress components. Table 3. Model scenarios for the DRZ Scenario Model characteristics Rock cover (m) DRZ thickness (m) Rock mechanical parameters Base case 10 0.5 Base case parameters (ref. Table 2) No damage 10 0 No damage parameters Varying Young s modulus 10 0.5 17.8, 12.5 GPa, 8.9 GPa Varying compressive 10 0.5 26.8 MPa, 12.7 MPa, 8.8 MPa strength Varying DRZ thickness 10 0.2, 0.5, 0.7, 1.0 Base case parameters (ref. Table 2) Varying rock cover 2, 5, 50, 100, 200 0.5 Base case parameters (ref. Table 2) 3. Results 3.1. Varying the Young s modulus of the damaged rock (E d ) Varying the Young s modulus of the DRZ (E d ) obviously affected the magnitude and distribution of the induced differential stress around the tunnel boundary. For example, when E d was 50% of E m (i.e. the Young s modulus of the undamaged rock) the differential stress in the tunnel roof boundary was reduced by 30% (see Figure 4). This can be a notable reduction in the confining stresses when stability and strength is concerned. Also, there was a corresponding increase in induced stresses outside the damaged zone, compensating for the reduction within the DRZ as stresses were diverted to a stiffer rock mass. The observations seem to be consistent with some rule of thumb practices for boreholes and shafts where the E d at the borehole/shaft boundary is usually assumed to be about 50% of E m (Diederichs, 2005) and the induced tangential stresses varying by as much as 30%, e.g. (de la Vergne, 2003). 3.2. Varying the compressive strength of the damaged rock Varying the compressive strength of damaged rock apparently does not have any effect on the induced differential stresses at the tunnel boundary (see Figure 4). (Malmgren, 2005) also made similar observations when modelling the behaviour of EDZ around Kirunavaara underground mine drifts in Sweden. On the other hand it has been pointed out earlier in this paper that the strength parameters for the damaged rock zone are complex and could not be easily estimated
using any existing criterion. Furthermore, it has also been noted that the Mohr-Coulomb and Differential stress (MPa) 25,0 20,0 15,0 10,0 5,0 Ed =Em =17.8 GPa (no damage case) Ed =Em =11.8 GPa (base case) Ed =0.5Em =8.5 GPa (least case) Ed =Em =17.8 GPa (no damage case) Ed =Em =11.8 GPa (base case) Ed =0.5Em =8.5 GPa (least case) σd = σcm = 26.75 MPa (no damage) σd = 12.70 MPa (basecase) σd = 8.75 MPa (least case) σd = σcm = 26.75 MPa (no damage) σd = 12.70 MPa (basecase) σd = 8.75 MPa (least case) 200 m rock cover 10 m rock cover (base case) 2 m rock cover (least case) 200 m rock cover 10 m rock cover (base case) 2 m rock cover (least case) 0.2 m DRZ 0.5 m DRZ (base case) 1.0 m DRZ 0.2 m DRZ 0.5 m DRZ (base case) 1.0 m DRZ 0,0 A B A B A B A B Varying stiffness Varying strength Varying overburden Varying DRZ thickness A: Measurement from a point in the roof at the tunnel boundary. B: Measurement from a point directly above the roof at the DRZ boundary. Fig. 4. Differential stress measured from two points (A and B) in the tunnel roof for the scenarios tested. Hoek-Brown criteria may be vulnerable in accurately capturing the yield process of brittle rocks under low confining stress conditions, e.g. (Diederichs, 2003; Hajiabdolmajid et al., 2002). Therefore the results from the strength variation tests or simulations are not conclusive. 3.3. Varying overburden The least differential stress magnitude is observed when the overburden is 10 m (Figure 4). Less than 10 m it is slightly higher, which is most likely due to the highly anisotropic behaviour of the stresses at shallow depth. For overburden greater than 10 m the differential stress reaches a peak at about 200 m depth. Two additional models simulated at 500 m and 900 m overburden depth showed insignificant variation in the differential stresses from that of the 200 m depth model. The EDZ appears generally effective in pushing high tangential stresses farther into stiffer rock outside of the DRZ boundary. It does not seem to be effective at very shallow depths (<10 m). However, the kinematic behaviour may be important and needs further analyses. The effect of varying overburden demonstrates that large variation in the in-situ stresses (a scenario that is very common at shallow depths) can have a significant influence on the behaviour of the damaged rock zone. 3.4. Varying DRZ thickness The thickness of DRZ appears to have minor effect on the magnitude of the induced differential stresses at the tunnel boundary. (Malmgren, 2005) also observed minor influence in the normal force in the shotcrete lining when varying the thickness of the EDZ. The distribution of the differential stresses however was obvious, in that the peak stresses which occur at the DRZ
boundary were pushed farther into rock with decreasing magnitudes (see also for example Tang and Mitri, 2001). This characteristic is necessary for combating excessive stress accumulation near the tunnel boundary. 3.5. Ground deformation The ground deformation magnitudes and patterns were reasonably consistent with recent studies for the City-banan project (Sjöberg et al., 2006) which had similar rock mass properties and located at shallow depth. The largest deformations were inward and recorded in the tunnel walls due to high horizontal stresses. A peak deformation of 14 mm was recorded when the E m was reduced by 50% in the standard model (see Figure 5), although the 200 m model gives much higher value but may not qualify for a typical shallow depth scenario. This deformation can be considered insignificant in practical cases even though the stiffness of the damaged rock has been reduced by half. A concern though may be fallout of loose rock blocks due to low confinement. Heaving and subsidence at the ground surface are phenomena often observed in the vicinity of shallow tunnels. These phenomena were also observed in our models. However, the magnitudes of these deformations were small (>1.0 mm). Similar values were recorded by (Sjöberg et al., 2006) although their models had no damaged zone, thus indicating that the presence of the DRZ has less influence on ground surface deformation magnitudes. Wall displacement (mm) 30,0 25,0 20,0 15,0 10,0 5,0 Ed =Em =17.8 GPa (no damage case) Ed =Em =11.8 GPa (base case) Ed =0.5Em =8.5 GPa (least case) σd = σcm = 26.75 MPa (no damage) σd = 12.70 MPa (basecase) σd = 8.75 MPa (least case) 2 m rock cover (least case) 10 m rock cover (base case) 200 m rock cover 0.2 m DRZ 0.5 m DRZ (base case) 1.0 m DRZ 0,0 Varying stiffness Varying strength Varying overburden Varying DRZ thickness Fig. 5. Ground displacement at the tunnel wall for the scenarios tested. 4. Conclusions The induced boundary stresses are clearly affected by the presence of the damaged rock zone. However, the magnitudes of these stresses are largely dependent on the mechanical and physical characteristics of the damaged zone. Drastic reduction in the stiffness or the Young s modulus of the damaged rock had a notable effect on the boundary stresses and the displacement magnitudes. With large in-situ stress the effect can be amplified proportionately. Variation in the compressive strength of the damaged rock showed insignificant effect on both
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