Time‐Dependent Deformations of Excavations and Tunnels in the Greater Toronto Area
Andrew Cushing, P.Eng., M.Eng.
Associate Geotechnical and Tunnelling Engineer at Arup
Proceedings of the World Tunneling Congress, San Francisco, CA, 2016.
The shales of the Greater Toronto Area (GTA) have been known to experience time dependent deformations (TDD); those initiated by excavation‐induced stress relief which progress with time as a function of rock porewater salinity, access to freshwater (or air) of lower salinity, clay and calcite content, and the buildup of swelling pressures within the rock mass. These deformations can induce long‐term pressures on shaft walls and tunnel linings, especially if the permanent works are constructed soon after excavation, with very little time delay. This paper presents measurements of time dependent deformation of recent shaft and tunnel projects constructed in the GTA, and draws conclusions regarding the main influences on the TDD. The key input parameters for the numerical predictive model are critically assessed. Projects which are discussed include the Billy Bishop Airport Pedestrian Tunnel, Hydro One Midtown Tunnel and Hanlan Feedermain (Contract 3).
MECHANISM OF TIME DEPENDENT DEFORMATION
The Georgian Bay Shale unit consists of typically moderately weathered to fresh, grey to dark grey, fine to very fine grained fissile shale interbedded with slightly weathered to fresh grey, fine grained calcareous siltstone and limestone interbeds. There are two distinctive features of the shale in the Greater Toronto Area (GTA). One is a high horizontal stress regime, and the second is long‐term time dependent swelling behavior which develops when the following factors occur (Lo and Micic, 2010):
? Stress relief of the rock mass
? Outward salt concentration gradient from pore fluid of the rock to the ambient fluid
? Availability of fresh water
The swelling is a consequence of the reduction in confined stress in the rock which occurs upon excavation in combination with a differential gradient in salinity between the saline rock porewater and freshwater or even humid air. Osmotic and diffusive processes result in a decrease in the salinity of the rock porewater achieved by an overall increase in the water content, resulting in volumetric expansion of the shale rock over time. The development of this time dependent deformation (TDD) relative to the time 1 of installation of the permanent lining has a direct impact on the long‐term moments and forces induced on the lining. Swelling potential is defined as the average slope of the swelling strain versus the logarithm of time and is defined for a specific direction, since behavior in the vertical and horizontal directions is typically noticeably different. The swelling potential decreases as the applied pressure is increased. The pressure where swelling potential is zero and no swell occurs is called the “Critical Stress” and is defined with the result of the no‐swell test. Hawlader, Lee, and Lo (2003) studied the impact of applied load on the swelling potential of different samples. They concluded that the applied stress in one principal stress direction reduces swelling strain not only in that direction but also in the perpendicular directions. The swelling potential of shales tends to increase with decreasing calcite content, and an increasing outward salt concentration gradient from the pore fluid of the rock to the ambient fluid (Lee and Lo, 1993). Therefore, calcite content and salt concentrations (salinity) of pore water in the rock samples were also considered in the tests.
Key Rock Properties impacting Time Dependent Deformation
Swell Potential: Following the methodology developed by Lo et al. (1978), results from free swell tests, semi‐confined swell tests and no‐swell tests are used to identify the “Swelling Potential” of the rock in different directions. These tests are performed as follows:
? Free swell test: Sample is exposed to water; and vertical and horizontal deformation of sample in time is recorded.
? Semi‐confined swell test: Sample is exposed to water and a constant load is applied to the specimen. The deformation in the direction of the applied load is recorded in time.
? Nullswell test: Sample is exposed to water and variable load is applied. No deformation is allowed in the direction of the applied load. Change of load in time is recorded.
Figure 1 shows the general relationship between applied pressure and swelling potential in horizontal and vertical directions for shale samples tested for the Billy Bishop Airport Pedestrian Tunnel Project. The point of zero swelling potential (Critical stress) is also clear at the end of the lines. Similar to previous experience of other projects in the area, the free swelling potential in the vertical direction is two to three times higher than the horizontal value. A summary of swell potential data from various projects is summarized in Table 1.
In Situ Stress State (Pre‐Excavation): A summary of pre‐excavation in‐situ horizontal stress measurements taken within the shale rock of the Georgian Bay Formation within the Greater Toronto Area at depths less than 40m are summarized in Table 2. The maximum horizontal stress ranges from 2.6 to 10 MPa (with an average of approximately 5.5 MPa), while the minimum horizontal stress ranges from 2.1 to 6 MPa (with an average of approximately 3.6 MPa).
SHAFT CASE HISTORIES
Billy Bishop Airport Pedestrian Tunnel – Mainland Shaft
The mainland shaft of the Billy Bishop Airport Pedestrian Tunnel is rectangular in shape, measuring approximately 33m long, 14m wide, and 35m deep. The shaft was constructed by drilling a series of 1m diameter interlocking secant piles from the ground surface through approximately 8m thickness of saturated silty sand overburden, with the toes of the piles socketed into the underlying shale. The secant piles were supported by two levels of internal struts, as well as a rock anchor at the toe of each primary (reinforced) pile. The exposed vertical face of the sound shale below the secant pile toes did not require any additional support. Hence, the magnitude and rate of shaft sidewall TDD is a function of the degree of horizontal stress relief, which is influenced by the shaft geometry and the rate of shale excavation. The shaft was instrumented with a total of three inclinometers, two on the longer north side (0.5m and 3m from the excavation face) and one on the west side (0.5m from the face). The results showed elastic movements during each successive shaft excavation was performed, followed by very small TDD movements. It should be noted that the shaft walls were very wet, providing the ideal conditions for TDD to occur. The total (elastic + TDD) horizontal movements of the two inclinometers along the longer, northern shaft wall at El. 57.4m are provided in Figure 2 (19.3m deep relative to ground surface, or 10.6m below top of weathered rock). The final rate of TDD appears to be on the order of 4mm per log cycle of time (days).
Hanlan Feedermain Contract 3 – Shafts S5 & S7
The Hanlan Feedermain (Contract 3) has required the construction of multiple shafts, several of which have been instrumented with inclinometers. Shaft S5 (circular cross section, 13.2m diameter) was constructed almost entirely in rock, with mesh and bolt support to prevent localized block failure. Shaft S7 (trapezoidal section) was constructed through about 3m of overburden soil using shotcrete and bolts, followed by mesh and bolts within the underlying shale. The shaft support is not expected to influence the TDD in either case. Inward horizontal wall movements at Shafts S5 and S7 are reported in Figures 3 and 4 below. As the shaft excavation was complete at the end of September 2014, but earliest inclinometer readings not taken until October 8th, all the shaft movement reported is inferred to be TDD. The data shows considerable scatter since the accuracy of the instruments is close to the magnitude of the movement taking place. “Best fit” lines showing the interpreted movement have been added to the figures. Since the TDD relationship is not significantly impacted by the depth of the rock, the best fit line has been placed as an average of all movements recorded in each shaft.
TUNNEL CASE HISTORIES
Billy Bishop Airport Pedestrian Tunnel – Drift Bores & Main Tunnel
Construction of the Billy Bishop Airport Pedestrian Tunnel (BBAPT) involved the sequential drilling and mass concrete backfilling of seven 1.85m diameter drift bores within the crown of the main tunnel profile and three main tunnel excavations – center (cut 1), sidewalls (cut 2), and invert (cut 3) resulting in a final horizontal tunnel cut diameter of 10m. Initial support was light steel ribs in the drifts, no support in cut 1 and bolts and shotcrete in cut 2.
Drift Bore Convergence: Radial convergence measurements were taken over a three month period within 1.85m diameter TBM drift bore 2 (the first bore actually drilled) using a steel tape extensometer and two arrays (at Sta. 0+030 and 0+070) of four convergence studs (eye bolts) installed within the shale at the crown, invert, and sidewalls (at springline level). A total of six chords were measured at each four‐point convergence array, namely horizontal (H1), vertical (V1), and a diagonal chord in each of the quadrants (D1, D2, D3, and D4). The field convergence data for chords H1 and V1 are reported in Figure 5 in terms of the measured inward tunnel sidewall movement. The convergence of the horizontal or vertical chord length would be double these values.
Main Tunnel Convergence: The range in the inward horizontal sidewall movement (as determined by tape convergence readings) with time (days) after the central excavation (Cut 1) – with an approximate 7m wide span ‐ of the main tunnel is reported in Figure 6, with wall movements generally between 0.5mm and 0.9mm up to 56 days after excavation. Two multi‐point borehole extensometers (MPBXs) were also installed at Sta. 0+020 (two tunnel diameters from the mainland portal), one in each sidewall, in mid‐July of 2013. The MPBX data for the eastern wall has previously been reported by Hurt, et al. (2014). The total inward movements recorded by the MPBXs included two discrete elastic jumps corresponding to completion of main tunnel cuts 2 and 3 in the vicinity of Sta. 0+020. These elastic movements were removed, and the resulting trend in time‐dependent (inward) sidewall movements are superimposed on Figure 6, indicating a maximum value of 0.25mm for each sidewall after about 135 days. It is interesting to note the influence of the tunnel shape on the TDD, with the ‘square’ Cut 1, shows a higher rate of TDD than the larger excavation after Cut 2 with a more curved profile. This illustrates the importance of the shape of the excavation, which influences the extent of the area that experiences stress relief that initiates the TDD.
HydroOne Midtown Tunnel
The HydroOne Midtown Tunnel was constructed using a rock TBM in Toronto, with a cut diameter of approximately 3.3m. The tunnel was supported with ribs and boards. Convergence studs were affixed to the shale rock, and the convergence measured using a tape extensometer. However, the accuracy of the 8 measurements was less than the measurements recorded, with recorded movements over 82 days in the range of 0.2mm enlargement to 0.2mm convergence and no discernable trend.
Hanlan Feedermain Contract 3
The Hanlan Feedermain Project (Contract 3) in Mississauga, Ontario, consists of two parallel tunnels constructed in shale rock, the Hanlan Feedermain (HFM) with a 3.33m cut diameter, and the MCC Watermain with a 2.67m cut diameter. Each tunnel is excavated by a rock TBM and support consists of rock bolts and mesh in the crown. Tunnel convergence measurements were taken with a steel tape in each of the two tunnels, and the change in horizontal chord length are reported in Figure 7. The results are similar to the HydroOne Midown tunnel in that no discernable trend can be identified and it appears that the “average” result is very close to zero movement and individual results are scattered due to accuracy of the measurements.
Heart Lake Tunnel
A valuable historical reference that demonstrates damage due to TDD is reported by Lo and Yuen (1981). They provide observations ofstructural damage within the Heart Lake Storm Sewer Tunnel in Mississauga, west of Toronto. The tunnel is 1.5 km long, with a finished internal diameter of 2.7 to 3.0m and a nominal lining thickness of 300mm. The tunneled section used both TBM and drill‐and‐blast techniques. The earliest damage – longitudinal cracking at springline along the entire 183m long drill‐and‐blast section, indicative of inward tunnel sidewall movement along the springline ‐ was discovered just less than 3 years after construction of this section was completed. At this time, no damage was observed within the TBM section. Some damage was later observed within a 330m portion of the 1,050m long TBM section. Some of the longitudinal cracks opened to a width of 6mm, with differential displacement of crack faces of 4mm. Of particular interest is the correlation of the damaged zones with the in situ horizontal‐to‐vertical in situ stress ratio. In the drill‐and‐blast tunnel, this ratio ranged between 20 at the interface with the TBM section, to an ultimate high of nearly 40 (due to the lower overburden stress and high horizontal stress). For the TBM tunnel section, the in‐situ horizontal‐to‐vertical stress ratio dropped to as low as 3, as a consequence of increased overburden and lower horizontal stress. The TBM tunnel lining damage was first observed was within the zone of highest initial horizontal‐to‐vertical in situ stress ratio and progressed with time down the tunnel, but only within the length where the ratio was around in excess of 7.
Summary of Tunnel TDD
A summary of the maximum measured time‐dependent deformations along the horizontal chord of tunnels constructed in shale rock within the Greater Toronto Area are summarized in Table 4 below. The measurements are generally quite small, and it should be noted that all of the tunnels listed in Table 4 were constructed either using rock TBM, rockbreaker, or roadheader. None were constructed using drill and blast methods. It is believed that the methods of construction employed on these projects resulted in a minimum degree of damage to the surrounding rock, and that this contributes to a lesser degree of time‐dependent deformation.
ESTIMATION OF TDD
Closed‐Form Solution
There are two common design methods available to assess the impacts of TDD on the tunnel lining. Lo and Yuen (1981) developed a closed form solution method to predict the long term loads and displacement at any point in time in lining and rock. However, the closed‐form solution method does not consider the limiting effect of build‐up of time‐dependent swelling‐induced rock stress on the swelling potential of the shale rock. As a result, the closed‐form solutions for the final unlined rock swelling displacement and lining moments and forces are conservatively over‐estimated.
Numerical Solution
To obtain a more realistic estimate of the time dependent movement, a numerical model to account for swelling based on the swelling rock constitutive model in Hawlader et al. (2003; 2005) can be used, based on the Mohr‐Coulomb elastic/perfectly plastic material model. This model is based on the observations in the laboratory experiments that the swelling strains in the principal swelling directions of a Shale rock 10 specimen increase linearly with the logarithm of time, and the swelling strains are reduced in both parallel and perpendicular directions by the application of stress on the rock specimen. In this project, the model formulation was implemented for use with the two‐dimensional code FLAC in plane strain mode. Application of this approach is described in Carvalho (2015) and Hurt, et al. (2014).
Influence of Excavation Shape
The excavation shape impacts the extent of stress relief, with a circular profile generally resulting in a smaller area of rock where the stress drops to less than the critical stress than a rectangular profile. This is reflected in the Billy Bishop tunnel movements, where a higher rate of movement was encountered in the smaller rectangular tunnel compared with the larger oval tunnel, as shown in Figure 6. These two excavations have been modelled in FLAC using the swelling model, and the results correlate with the site observations, as shown in Figure 8.
Influence of ratio between in‐situ stresses
The ratio between the in‐plane stresses will also impact the area of rock where the stress drops to less than the critical stress – generally the larger the difference between the two stresses the larger the low stress area will be. Thisisillustrated in Figure 9 where two sections of the Heart Lake Tunnel with different stress rations have been modelled in FLAC. This is also a factor in why the TDD movements in tunnels (where the horizontal stress is several times the magnitude of the vertical) is typically larger than in shafts (where the horizontal stresses are often similar).
Access to Water
It is known that water is required for swelling to occur. It has been reported that humidity alone is sufficient to allow swelling (Lee and Lo, 1993). This is backed up by observations on the Billy Bishop project, where rates of swelling were observed in the shaft and the tunnel that gave similarly good agreement with the numerical models, despite very different exposure conditions to water. In the shaft, there was constant flows of water down the face of the rock wall, whereas in the tunnel the exposure to water was from humidity in the air or slow seepage through the rock mass.
SUMMARY AND CONCLUSIONS
The following conclusions can be made with regards to TDD in Georgian Bay Shale in the Toronto area.
? TDD movements are dependent on the excavation shape and the ratio between in‐situ stresses. In particular, a high horizontal stress in shallow overburden (as seen in Heart Lake tunnel) will give a high potential for swelling. Greater investment in stress measurements on projects would be useful in identifying sections with high potential for damaging TDD.
? A flexible initial support system will not impact TDD. Any rigid support system would typically see high loading unless installed well after excavation.
? Reasonable TDD predictions can be obtained using numerical solution, provided the geotechnical investigation program includes (1) free‐swell and null swell tests to define swell potential and critical stress and (2) in‐situ stress measurements. Given the potential variation of these inputs along an alignment, a parametric design approach is recommended.
? Monitoring data can provide useful verification of the design, although in smaller excavations the movements can be so small that they are less than the accuracy of the instrumentation.
REFERENCES
Carvalho, J. 2015. A Simple Numerical Approach for Modelling Time Dependent Swelling Mechanisms in Shale. Proceedings of the International Symposium on Rock Mechanics, 17p.
Hawlader, B. C., Lee, Y. N., & Lo, K. Y. 2003. Three‐dimensional Stress Effects on Time Dependent Swelling Behaviour of Shaly Rocks. Canadian Geotechnical Journal, 40 (3), 501‐511. 12
Hawlader, B. C., Lo, K. Y., & Moore, I. D. 2005. Analysis of Tunnels in Shaly Rock Considering Three‐ Dimensional Stress Effects on Swelling. Canadian Geotechnical Journal, 42 (1), 1‐12.
Hurt, J., Lee, S., Ghasemi, A., Pollak, S., and Cushing, A. 2014. Time‐dependent movements on the Billy Bishop Toronto City Airport Pedestrian Tunnel. Proceedings of the North American Tunneling Conference, Los Angeles, 908‐918.
Lee, Y. N., and Lo, K. Y. 1993. The swelling mechanism of Queenston shale. Canadian Tunnelling 1993, Tunnelling Association of Canada, 75‐97.
Lo, K. Y., and Micic, S. 2010. Evaluation of Swelling Properties of Shales for the Design of Underground Structures. ITA‐AITES 2010 World Tunnel Congress, Vancouver.
Lo, K.Y., and Morton, J.D. 1976. Tunnels in bedded rock with high horizontal stresses, Canadian Geotechnical Journal, 13 (3), 216‐230.
Lo, K. Y., and Yuen, C.M.K. 1981. Design of tunnel lining for long term time effects. Canadian Geotechnical Journal, 18 (1), 24‐39.
Lo, K.Y., Cooke, B.H., and Dunbar, D.D. 1987. Design of buried structures in squeezing rock in Toronto, Canada. Canadian Geotechnical Journal, 24 (2), 232‐241.
Lo, K.Y., Devata, M., and Yuen, C.M.K. 1979. Performance of a shallow tunnel in a shaly rock with high horizontal stresses. Proceedings of the 2nd International Symposium on Tunnelling. Institution of Mining and Metallurgy, London, UK, 1–12.
Lo, K. Y., Wai, R. S. C., Palmer, J. H. L., & Quigley, R. M. 1978. Time‐dependent deformation of shaly rock in southern Ontario, Canadian Geotechnical Journal, 15 (4), 537‐547.
Morton, J.D., Lo, K.Y., and Belshaw, D.J. 1975. Rock performance considerations for shallow tunnels in bedded shales with high lateral stresses. Proceedings, 12th Canadian Rock Mechanics Symposium, Kingston, ON, 339‐379.
Trow, W.A. and Lo, K.Y. 1989. Horizontal displacements induced by rock excavation: Scotia Plaza, Toronto, Ontario, Canadian Geotechnical Journal, 26 (1), 114‐121.
Associate Geotechnical and Tunnelling Engineer at Arup
4 年Dale Brunton
Associate Geotechnical and Tunnelling Engineer at Arup
4 年Andrew Sorrie
Civil Engineer
4 年óscar Pérez Hernández
Accurately Map Your World
4 年Very interesting read, well done.