from the simulation of a NATM tunnel using finite element method in three ... finite element model was based on the construction of Fort Canning Tunnel, ...
Volume 5, Number 1, March 2009, pp.33-38
[INVITED PAPER]
Three dimensional numerical modelling of a NATM tunnel Chong Hun YEO*, Fook Hou LEE*, See Chee TAN**, Osamu HASEGAWA***, Hitoshi SUZUKI*** & Masato SHINJI**** * Dept. of Civil Engineering, National University of Singapore ** CPG Corporation Pte Ltd *** Sato Kogyo (S) Pte Ltd ****Dept. of Civil and Environmental Engineering, Yamaguchi University Received 06 10 2008; accepted 22 12 2008
ABSTRACT The design of NATM tunnels are often done in two dimensions, even though there are limitations. This paper uses the results from the simulation of a NATM tunnel using finite element method in three dimensions to illustrate a few observations that may aid in practical designs. These observations are three dimensional effects, which will not be apparent in two dimensional analyses. The finite element model was based on the construction of Fort Canning Tunnel, Singapore, which is an approximately 15m wide vehicular tunnel that has been constructed using NATM with applications of steel pipe umbrella method. Keywords: Tunnel, NATM, Finite element method, Field observations, Steel pipe umbrella method
1. INTRODUCTION In tunnelling, the importance of ensuring stability during tunnel driving and limiting deformations on adjacent structures is well recognized (e.g. Peck 1969). Ground movement is not readily evaluated using conventional methods of analyses such as closed form solutions, limit equilibrium, stress fields and plastic analyses, owing to the complexities in geometry, construction sequence, soil stratification and soil behaviour, which are often encountered in the field. In such instances, numerical analysis such as finite element and finite difference is often employed. In spite of the widespread use of numerical analysis, most of the analyses used to-date are mainly two-dimensional (2D) analyses. However, 2D analysis may not satisfactorily account for many of the events which occur around the heading. For instance, the primary lining is usually installed after some degree of inward ground de-formation at the heading. In 2D analyses, this event must be modelled by means of artificially specifying a percentage unloading (e.g. Panet and Guenot, 1982; Allouani et al., 1994), tunnel volume loss (e.g. Stallebrass et al., 1994), an artificial gap between tunnel wall and lining (e.g. Rowe and Lee, 1992) or some hypothetically soft lining to allow some amount of tunnel convergence (e.g. Powell et al., 1997; Karakus and Fowell, 2003; Karakus and Fowell, 2005). In addition, very often, one of the main objectives of such analyses is to evaluate the lining stresses. While 2D analysis may appear satisfactory for secondary linings, they may be unrealistic for primary linings because of three-dimensional changes in principle stress © JCRM All rights reserved.
directions around the tunnel heading. Another issue is that concerning the modelling of the pipe arch. Steel pipe umbrella arches are often used to bridge the unsupported gap as the tunnel face advances. Its action is longitudinal and therefore cannot be captured by a 2D analysis modelling just the tunnel section. On the other hand, it has been widely recognised that the situation at the tunnel heading is highly three-dimensional. Three-dimensional (3D) analyses are much less widely used in practice although they have been studied quite substantially in research in recent years. For example, Dasari et. al. (1996) studied the differences between 2D and 3D approaches with the consideration of non-linear soil behaviour and time-dependant lining Young’s modulus and showed the significance of early gains in shotcrete stiffness to control deformation. Ng et. al. (2004) modelled twin NATM tunnels in 3D with coupled analyses to investigate the effects of lagging distance between the two tunnels’ progress on ground deformation and lining loads. Yazdchi et. al. (2006) modelled NATM tunnel in 3D with non-linear soil behaviour, anisotropic shear moduli and time dependant gain in lining strength and studied the interactions between advance rate and ground deformation. Using a well-instrumented NATM tunnel as a case study, the paper hopes to illustrate how very detailed and high-resolution 3D numerical analysis can be applied to realistic problems. Furthermore, comparison with field data shows how, by so doing, realistic results and useful insight into the behaviour of pipe arch supported, shotcrete lined sequential tunnels can be obtained.
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2. FORT CANNING TUNNEL
2.1 Background and Site Conditions The Fort Canning Tunnel is a three-lane road tunnel which lies beneath the North Eastern edge of Fort Canning Park and aligns along the back of the National Museum of Singapore in an approximately southeast-northwest direction. It connects the Stamford-Road-Armenian-Street junction with Penang Road. The tunnel length, width and height are approximately 350 m, 15 m and 11 m, respectively. The soil cover above the tunnel varies from 3 m to 9 m. The central segment of 180m which passes beneath Canning Rise, was constructed according to the principles of NATM, with sequential tunnelling and a two-pass lining process. The remaining entrance and exit segments were constructed by cut-and-cover method. The Tunnel was driven through residual soils of the Fort Canning Boulder Bed (FCBB) and Jurong Formation. The FCBB consist of boulders in hard sandy silt or sandy silty clay matrix, the colour of the matrix can be deep red, or red and white or mottled red, yellow and white, which is commonly found in downtown area of Singapore (Shirlaw et. al. 2003). The boulders show varying degrees of weathering. The Jurong Formation, which consists of sedimentary rocks of various types, such as sandstones, mudstone, shale, phyllite, limestone, slate and conglomerate (Zhao et al., 1999), lies far beneath the tunnel soffit.
tunnel. The steel pipes, with perforations along the entire length, were injected with chemical grout after insertion into the ground. The AGF was installed from within the tunnel and consisted of a single row of steel pipes drilled at 400 mm spacing in the crown of the tunnel top heading. Each steel pipe has a length of 12.5 m, an outer diameter of the 114 mm, and a wall thickness of 6 mm. The steel pipes were installed at a 7-degree outwards angle. The lap length between successive pipe arches was 3.5 m. After excavating a 9m long tunnel section the next grouted steel pipe arch in sequence was installed. Upon completion of the initial shotcrete lining and the waterproofing system, the secondary lining, 300 mm thickness of cast in-situ concrete, was installed to complete the tunnel structure. 3. FINITE ELEMENT MODEL The software used in this analysis was the commercial software ABAQUS v6.4. The modelled domain was 120 m in length, 50 m in width and 29 m in depth, as Figure 2 shows. The soil domain consisted of 38064 linear brick elements with pore pressure degrees of freedom, hybrid formulation and reduced integration. By taking advantage of symmetry, only half the tunnel was modelled. The coarse elements at both ends of the model served to isolate the central finer mesh from the boundary effects. Results from the central fine mesh, a length of 40 m, will be used to compare against the field measurements. Results from the coarse elements were disregarded.
2.2 Construction and excavation sequence As shown in Figure 1, the Fort Canning Tunnel was constructed following a top heading and bench excavation sequence. Tunnel construction progressed from the South Portal towards the North Portal. The top heading has a temporary invert which was subsequently removed during the bench excavation. A 300 mm thick reinforced shotcrete primary lining was installed after each round of excavation.
Figure 2. Mesh used in 3D analyses.
Figure 1. Cross-sectional profile of Fort Canning Tunnel, NATM. A steel pipe umbrella arch known as ―All Ground Fastened‖ (AGF), was installed over the entire length of the
The duration of excavation, duration for placement of shotcrete and the hardening rate of shotcrete will influence the volume loss to some degree. These were standardised for every excavation cycle. In the actual construction cycle, each excavation length in the top heading is 1 m, thus elements within the central fine mesh is meshed in 1 m length to closely model the construction sequence. The plasticity model chosen was the Mohr-Coulomb plasticity model with non-associated flow rule. The Young’s modulus and strength was prescribed to increase with depth. The lateral earth pressure coefficient at rest is assumed to be 0.8. As shown in Figure 2, the pore water pressure profile at the vertical faces A and B was kept unchanged throughout the analyses, so that these faces acted as the recharge boundary. Various phreatic levels were studied. In cases where the phreatic level lies below the ground level, a suction zone was prescribed above. This is not unreasonable given that the soil is a silty clay, which can hold a small amount of negative
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pore pressure. The shotcrete lining was modelled as elastic shells with, a thickness of 300 mm and Poisson’s ratio of 0.3. The hardening of the shotcrete was modelled by increasing its Young’s modulus with age, i.e. elapsed time after placement, in the shotcrete. The time-dependant Young’s modulus was calculated from compressive strength based on the following empirical relation by Mindess & Young (1981),
E(GPa)= 4.73 f c (MPa)
(1)
The development of strength of the shotcrete follows that shown in Table 1. As data pertaining to the strength development of shotcrete in the field is scarce, references were made according to values obtained from field site trials. Table 1. Shotcrete properties with age.
Figure 3. Beam elements for modeling steel pipe umbrella arch. The construction sequence is shown in Table 2, this was prescribed to follow the actual construction sequence as far as possible. The durations are according to construction plan 4. RESULTS
Time (days)
Strength (MPa)
Young’s modulus (GPa)
0
0
0
4.1 Calculated surface settlement
0.5
6
12
1
12
16
3
30.7
26
7
37.7
29
28
40
30
As mentioned earlier, the analyses described herein were conducted prior to construction and therefore represented a real predictive exercise, or a type A prediction (Lambe 1973). As field data became available during construction, they allowed the validity of the analyses to be assessed. The surface settlement contour of a typical 3D finite element analysis prediction is as shown in Figure 4a, in which a bench length of 20 m was modelled. It shows that the maximum settlement does not occur around the face or the unsupported gap, it occurs well back from the tunnel face. The surface settlement contour of field measurements during construction is as shown in Figure 4b, where the bench length was also 20 m, and Figure 4c, where the top heading and bench end has passed beyond chainage 360 m. In the field observations, the maximum settlement occurred far behind the face as predicted. The predicted maximum settlement for the segment with 9 m overburden, between chainage 300 m and 340 m, varies from 0.14 m to 0.20 m. The predictions fairly capture the field measurements of maximum settlement at the end of construction along this segment, which varies from 0.11 m to 0.15 m.
The steel pipes were modelled as beam elements tied to nodes in the finite element mesh as shown in Figure 3. To simplify mesh generation, the beams were aligned horizontally. Various researchers had modelled the umbrella arch in FEM as discreet beams (Nishimaki et. al. 1995, Eclaircy-Caudon et. al. 2006) or smeared elastic shell elements (Golser & Schubert 2003, Kotake et. al. 1994, Ohtsu et. al. 1995). Eclaircy-Caudon et. al. (2006) modelled the tilt in the forepoling and noted that this resulted only in slight differences in the settlement. A lap length of 3.5 m was prescribed between succeeding segments during construction and this was also replicated in the model. The beam elements were fully tied to the solid elements, so any sliding between beam and solid elements was not modelled.
Table 2. Simulation sequence in Fort Canning Tunnel model. Location and activity
Modelling activity
Duration in hours
top heading excavation
remove solid elements
10.5
Top heading lining construction
add shell elements
1.5
Bench excavation
remove solid elements
10.5
bench invert lining construction
add shell elements
1.5
top heading AGF installation
add beam elements
60
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360
top heading position
Chainage: m
335 bench end position
310
285
260 -25
0
25
-25
0
25
-25
0
25
Offset from tunnel centre-line: m (a)
(b)
(c)
Figure 4. Surface settlement contours, mm: (a) prediction from 3D finite element analysis; (b) field measurements during construction; (c) field measurements at the end of construction.
settlement monitoring marker position surface
0.00
X2
-0.04
0.00
top heading position
X1
bench position
-0.04 vertical displacement, m
vertical displacement, m
+ve
-0.08
-0.12 prediction field observation -0.16
-0.08
-0.12 prediction field observation -0.16
-0.20 -80
-60
-40
-20
0
20
40
60
80
X1
top heading position, m
(a)
-0.20 -80
-60
-40
-20
0
20
40
60
80
X2
bench position, m
(b)
Figure 5. Vertical displacements at a monitoring point against progresses in: (a) top heading; (b) bench.
Figure 5a & 5b show the computed and measured settlement of a point on the ground surface with horizontal distance from the top heading and bench, as defined in the inset. A greater proportion of settlement occurred after the top heading has passed, as Figure 5a show. The settlement only
ceases when invert closure was completed, so that the final steady state settlement occurred at some point after the bench, as Figure 5b shows. Thus expedient invert closure will help to reduce settlement.
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4.2 Effects of lining permeability Effects of lining permeability on the surface settlement profile were investigated by considering two extreme cases, one with permeable linings and one with impermeable lining. Permeable linings were modelled by setting the pore pressure on the exposed wall of the tunnel and shotcrete to atmospheric. As Figure 6 shows, impermeable lining leads to smaller settlement except for the zone within one tunnel diameter of the tunnel centreline, thereby giving a narrower settlement trough.
(kPa)
(b) Figure 7. Pore pressure contours of model: (a) with permeable linings; (b) without permeable linings.
Vertical displacement, m
0.0
4.3 Differences in Phreatic Level Figure 8 shows the settlement trough arising from the ground water table at ground surface and 5m below ground surface. The difference in settlement can be explained by considering the effect of ground water table regime on the undrained strength distribution in the soil. With a higher groundwater table, the pore pressure is also higher and effective stress level at corresponding depths is corresponding lower. Since the strength of the soil depends upon the effective stress, having a higher groundwater table means having a weaker soil, in general.
-0.1
-0.2
-50
field measurements permeable lining impermeable lining
0
50 0.0
Figure 6. Transverse settlement profiles. This can be explained by looking into the resulting ground water regimes, as shown in Figure 7a and 7b. With permeable linings modelled, the tunnel was acting like a buried drain that drew down the ground water table. Thus the permeable lining allows water to drain out of the soil and into the tunnel, thereby generating a consolidation basin which is relatively large in lateral extent. At the same time, the permeable boundary also facilitates swelling of the soil underlying the tunnel which reduces the overall settlement of the ground directly overlying the tunnel.
Vertical displacement, m
Distance from tunnel centreline, m
-0.1
field measurements GWT at 5m below GWT at surface
-50
0
50
Distance from tunnel centreline, m
(a)
(kPa)
(a)
Normalised vertical displacement
0
field measurements GWT at 5m below GWT at surface
-1
-8
-4
0
4
8
normalised distance from tunnel centreline, x/i
(b)
Figure 8. Transverse settlement profiles: (a) predicted and field measurements; (b) normalised.
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4.4 Effects of steel pipe umbrellas on settlement response Figure 9 illustrates the effect of the steel pipe arch on ground settlement. As expected, without the steel pipe arch, the settlement is manifestly larger. This difference is particularly striking given that the length of the unsupported gap is only 1m. This is due to the fact that the hardening of the shotcrete is replicated in the model. The shotcrete only gains substantial stiffness after about 3 days, which is when the top heading has progress a further 6 m. Thus, the length of tunnel which needed support is much more than just the 1m-length of unlined gap; the segment with the newly placed, hardening shotcrete also requires support.
0.00
Vertical displacement, m
-0.02
-0.04
-0.06 beam elements enabled beam elements disabled
-0.08
-0.10 -40
-20
0
20
Top heading position, m
Figure 9. Vertical displacements at a monitoring point against progresses in top heading.
CONCLUSIONS Modern finite element software enables very detailed and high-resolution 3D analysis to be conducted for realistic scenarios. With such tools, one no longer needs to make relatively arbitrary assumptions relating to tunnel convergence or stress relief. In addition, the results of 3D analyses, properly conducted, shows a richness and realism which cannot be matched by those of 2D analyses. REFERENCES Allouani, M., Bahar, R., Cambou, B., & Rezgui, B., 1994. Evaluation of displacements during tunnelling in soft soil, Proceedings of the Eighth International Conference on Computer Methods and Advances in Geomechanics, Morgantown, West Virginia, USA, Siriwardane and Zaman (ed), pp. 2353-2540. Dasari, G., R., Rawlings, C., G., and Bolton, M., D., 1996. Numerical modelling of a NATM tunnel construction in London clay, Proceedings of International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, City University, Balkema, pp. 491-49. Eclaircy-Caudron, S., Disa, D., Kastner, R., & Chantron, L., 2006. Numerical modelling of a reinforcement process by umbrella arch, Proceedings of the International Conference on Numerical Modelling of Construction Processes in Geotechnical
Engineering for Urban Environment, Bochum, Germany, March 2006. Golser, H., & Schubert, W., 2003. Application of numerical simulation at the tunnel site, Numerical Simulation in Tunnelling, Gernot Beer (ed.), chapter 15. Karakus, M., & Fowell R., J., 2003. Effects of different tunnel face advance excavation on the settlement by FEM, Tunnelling and Underground Space Technology, 18, pp. 513–523. Karakus, M., & Fowell, R., J., 2005. Back analysis for tunnelling induced ground movements and stress redistribution, Tunnelling and Underground Space Technology, 20, pp. 514–524. Kotake, N., Yamamoto, Y. & Oka, K., 1994. Design for umbrella method based on numerical analyses and field measurements, Tunnelling and ground conditions, pp. 501-508. Lambe, T., W., 1973. Predictions in soil engineering. Géotechnique 23, no. 2, pp. 149-202. Mindess, S., & Young, J., F., 1981. Concrete, Englewood Cliffs, N.J., Prentice Hall. Ng, C., W., W., Lee, K., M., & Tang, D., K., W., 2004. Three-dimensional numerical investigations of new Austrian tunnelling method (NATM) twin tunnel interactions, Canadian Geotechnical Journal, v.41, pp. 523-539. Nishimaki, A., Mitarashi, Y., & Uematsu, S., 1995. Study on the effects of the AGF method (Proposal of a simplified AGF design technique), South East Asian Symposium on Tunnelling and Underground Space Development, Japan Tunnelling Association, Bangkok, pp. 125-132. Ohtsu, H., Hakoishi, Y., Nago, M., & Taki, H., 1995. A prediction of ground behaviour due to tunnel excavation under shallow overburden with long length forepilings, South East Asian Symposium on Tunnelling and Underground Space Development, Japan Tunnelling Association, Bangkok, pp. 157-164. Panet, M., & Guenot, A., 1982. Analysis of convergence behind the face of a tunnel, Tunnelling '82, Papers Presented at the 3rd International Symposium, Brighton, England, pp. 197-204. Peck, R., B., 1969. Deep excavations and tunnelling in soft ground, in State Of-The-Art Report of 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico, 1969. Powell, D., B., Sigl, O., & Beveridge, J., P., 1997. Heathrow-Express—design and performance of platform tunnels at Terminal 4. Tunnelling’ 97. IMM, London, pp. 565–593. Rowe, R., K., & Lee, K., M., 1992. An evaluation of simplified techniques for estimating 3-dimensional undrained ground movements due to tunnelling in soft soils, Canadian Geotechnical Journal, Vol. 29, No. 1, pp. 39-52. Shirlaw, J., N,., Broome, P., B., Chandrasegaran, S., Daley, J., Orihara K., Raju G., V., R., Tang, S., K., Wong, I., H., Wong, K., S., & Yu, K., 2003. The Fort Canning Boulder Bed. Proceedings of Underground Singapore 2003, Engineering Geology Workshop. Stallebrass, S., E., Jovicic, V., & Taylor, R., N., 1994. The influence of recent stress history on ground movements around tunnels, in Pre-Failure Deformation of Geomaterials (eds Shibuya, S., Mitachi, T. and Miura, S.), vol. 1, pp. 615–620. Balkema. Yazdchi, M., Macklin, S., R., & Yeow, H., C., 2006. 3D modelling of sprayed-concrete-lined tunnels in clay, Geotechnical Engineering, v.159, pp. 243-250. Zhao, J., Liu, Q., Lee, K., W., Choa, V., & The, C., I., 1999. Underground cavern development in the Jurong sedimentary rock formation, Tunnelling and Underground Space Technology, Volume 14, Issue 4, pp. 449-459.
