Introduction

Tunnelling in urban areas is increasing and often requires excavation of a new tunnel to join an existing or newly constructed one. Constructing multiple tunnels, e.g. excavation of twin metro tunnels side-by-side or piggybacked, presents greater engineering challenges. As well as the geological settings along the tunnel route and stand up times, ground movements due to the excavation of an adjacent tunnel also need to be understood and the interactions between the two excavations assessed. In this paper the geological and geotechnical properties along the MTA tunnel route and the monitoring of tunnel closure are presented. The results of a finite element model (FEM) developed to investigate ground movements into the tunnel have been compared with the measured convergence values.

The location of the twin metro tunnel is illustrated in Fig. 1. Each tunnel is approximately 7 m in diameter with the distance between the centrelines being kept within 15 m. The twin tunnels were driven at shallow depth, mainly through Ankara Clay, which oedometer test results indicated to be lightly overconsolidated. Thus the Modified Cam Clay model, which was developed to represent normally or lightly overconsolidated soil behaviour, was used in the finite element (FE) analysis. The made ground over the Ankara Clay was modelled using the Drucker–Prager plasticity model in which the failure function is dependent on the intermediate principal stress. In order to achieve deformations and the 3D tunnelling effect in 2D FE analysis, the hypothetical modulus of elasticity (HME) soft lining approach was adopted.

Fig. 1
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Location of the tunnels

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Excavation of the tunnel was carried out in two stages. Firstly, the upper heading was excavated and immediately shotcreted with a 30 mm thick cover, after which steel mesh and lattice girders were emplaced and a further 170 mm of shotcrete was applied. The lower part of the tunnel was excavated and the support elements were installed in the same manner. In order to provide stability, the pull of the excavation was kept within 1–1.5 m in each advance and the lower part of the excavation followed a maximum of 6 m behind the excavation of the upper heading. Thus the support ring was closed as early as possible in order to avoid excessive displacements.

Numerical methods are widely used to analyse ground support interactions, deformations and stress re-distributions around an underground opening (Ozsan and Basarir 2003; Ozsan and Karpuz 2001; Kontogianni and Stiros 2002). Most potential hazards associated with excavations can be calculated using these methods.

The convergence of a tunnel (the amount of closure relative to the tunnel diameter) is a significant indication of the deformation. In order to maintain stability, the amount of closure should be precisely measured and the necessary support measures determined (Kovari and Amstad 1993). Short-term convergence measurements on 31-03-2003 and 10-04-2003 indicated the maximum displacement was at the crown of the right tunnel.

Geology and geotechnical properties of the construction site

The soil profile for the tunnel route consists of made ground and Ankara Clay (Fig. 2). The fill was brown in colour, and composed of uncompacted blocky gravel with rubble and sandy clay. The thickness ranged from 0.8 to 7.5 m.

Fig. 2
figure 2

Geological profiles along the MTA tunnel route

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The Ankara Clay was brown to reddish-brown in colour and composed of mainly silty, sandy clay with clayey silt. Ordemir et al. (1965) describe the Ankara Clay as fine reddish-brown clastics with a high proportion of clay while Erol (1973) found that locally there were very thin calcareous horizons, nodules and concretions at shallow depth within the clayey levels which vary in thickness. As the Ankara Clay has a low permeability, there is no clear water level. X-ray analyses show the Ankara Clay consists of the smectite group of clay minerals, illite and montmorillonite (Ordemir et al. 1977; Erguler and Ulusay 2003). According to the Unified Soil Classification System, it comprises high plasticity (CH), highly compressible inorganic silt and organic clays (MH). The fissured clay has a swelling potential due to the montmorillonite and illite contents.

The results of the Standard Penetration Tests are given in Table 1 and the results of the laboratory tests carried out on undisturbed soil samples taken from the MTA tunnel route are given in Table 2.

Table 1 Standard penetration test results for Ankara Clay
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Table 2 Soil properties of the Ankara Clay
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The stress–strain relationship was determined using the Modified Cam Clay model. The Modified Cam Clay yield function is defined in terms of the equivalent effective pressure stress (p′) and the deviator stress (q′) which are relevant to the interpretation of soil response in the conventional triaxial test (Roscoe and Burland 1968).

Parameters to locate the compression and swelling lines and specific volume at \( \ln \,{p}\ifmmode{'}\else$'$\fi = 1.0 \) in Fig. 3 have been defined in the isotropic consolidation section. The equation for the yield locus in the original Cam Clay model is given as:

$$ q = M{p}\ifmmode{'}\else$'$\fi\ln {\left( {\frac{{{p}\ifmmode{'}\else$'$\fi_{{\text{o}}} }} {{{p}\ifmmode{'}\else$'$\fi }}} \right)} $$
(1)

where \( {p}\ifmmode{'}\else$'$\fi_{{\text{o}}} \) is the isotropic pre-consolidation pressure and M is a material constant defined in terms of the angle of friction (Table 3). The shape of the yield locus is a bullet shape while the Modified Cam Clay yield locus is an elliptical shape. Then the equation becomes as follows:

$$ f = M^{2} {p}\ifmmode{'}\else$'$\fi^{2} - M^{2} {p}\ifmmode{'}\else$'$\fi_{{\text{o}}} {p}\ifmmode{'}\else$'$\fi + q^{2} = 0 $$
(2)

If the soil obeys the normality condition, i.e. the yield surfaces and plastic potential surfaces are identical, then the yield locus and plastic potential in the \( {p}\ifmmode{'}\else$'$\fi:q \) plane are given by the formula above. The recoverable strain or elastic region is assumed inside the yield locus. Beyond the ellipse—in the plastic region—irrecoverable strain occurs.

Fig. 3
figure 3

Elliptical yield locus, isotropic compression line and compression and swelling line in p′:q:e plane for the Modified Cam Clay model (after Wood 1990 )

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Table 3 Soil properties adopted in the FE analysis
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The made ground above the Ankara Clay has been modelled using the Drucker–Prager perfectly plastic model. The failure function is dependent on the value of the intermediate principal stress. Typical geotechnical materials generally include some small dependence on the intermediate principal stress. Thus, the Drucker–Prager yield model can be more accurate for soil and rock applications. The yield function is given by:

$$ f = \alpha J_{1} + {\sqrt {J_{2} } } = k $$
(3)

where α and k are the material constants that can be related to Mohr–Coulomb’s material constants c (cohesion) and φ (internal friction angle). The relationships then become:

$$ \alpha = \frac{{2\sin \,\phi }} {{{\sqrt 3 }(3 - \sin \,\phi )}} $$
(4)
$$ k = \frac{{6c\cos \,\phi }} {{{\sqrt 3 }(3 - \sin \,\phi )}}. $$
(5)

The parameter J 1 is the first invariant of the stress tensor, i.e. the sum of the principal stresses and J 2 is the second invariant of the deviatoric stress tensor given by:

$$ J_{2} = \frac{1} {6}{\left[ {{\left( {\sigma _{1} - \sigma _{2} } \right)}^{2} + {\left( {\sigma _{2} - \sigma _{3} } \right)}^{2} + {\left( {\sigma _{3} - \sigma _{1} } \right)}^{2} } \right]} $$
(6)

The yield or failure surface for Eq. 3 in principal stress space is a right-circular cone with the symmetry about the hydrostatic axis. The plastic deformation is accompanied by an increase in volume.

Finite element analysis

The Modified Cam Clay parameters adopted in the FE analysis were based on the oedometer test results, some of which are given in Fig. 4. The parameters are presented in Table 3. In order to carry out undrained analysis for the Ankara Clay the bulk modulus of water (K w), was calculated using the following expression:

$$ {K}\ifmmode{'}\else$'$\fi = \frac{{(1 + e) \times {p}\ifmmode{'}\else$'$\fi }} {\kappa } $$
(7)

where K′ is the effective bulk modulus of water, p′ is the effective mean normal stress, e is void ratio and κ is the logarithmic elastic bulk modulus. In an undrained analysis, K w is normally taken as 100×K′.

Fig. 4
figure 4

Some of the consolidation test results shown for illustrative purposes

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Finite element analysis was carried out with the 90 m×53.5 m deep mesh (Fig. 5). The detailed tunnel geometry and the structural elements are given in Fig. 6. The model was fixed in the horizontal directions on both left and right sides and the bottom part of the mesh was pinned. Non-consolidating eight-noded linear strain quadrilaterals and non-consolidating six-noded linear strain triangular elements were used for the soil medium. Shotcrete and concrete were modelled using LSQ elements.

Fig. 5
figure 5

Finite element mesh used in the analysis

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Fig. 6
figure 6

Constructed tunnel geometry (not to scale)

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As the tunnel excavation was performed in two stages in the field, the same construction method was employed in the FE analysis. Details of the excavation sequences are illustrated in Fig. 7. After achieving equilibrium at the initial stage, the upper heading of the left tunnel was excavated and solid continuum elements representing shotcrete were activated with the predetermined HME value (Karakus and Fowell 2003, 2005). This was provided to account for deformations due to volume loss, a percentage of the theoretical tunnel volume.

Fig. 7
figure 7

Construction sequences adopted in the FE analysis

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The shotcrete thickness assigned was 200 mm and the selected short-term modulus of elasticity of shotcrete was taken as 8 GPa. The concrete applied over the shotcrete was assigned a 400 mm thickness and an elasticity modulus of 20 GPa.

Each tunnel excavation and construction was carried out in five steps. Increments for each step were kept within 20 increments, which was found to be sufficient to reach equilibrium. Support elements have been introduced in a single increment. It was seen that running analyses in a small number of increments led to divergence of forces within the soil body when modelling the excavation.

Evaluation of the results

Convergence measurements were carried out after the shotcrete was applied to the tunnel periphery before the permanent 400 mm concrete wall was installed. Topographical measurement techniques were utilised to monitor the actual convergence of the tunnel. The convergence measurements points are shown in Fig. 6. It was appreciated that some measurements may be erroneous as convergence pins attached to the tunnel walls suffered some damage due to the working equipment in the tunnel. In addition, water locally trapped in the clay caused swelling which led to changes in the pin locations from time to time. Table 4 shows the observed and the calculated convergence values. The field measurements given in the table correspond to the upper and lower parts of the left tunnel excavation and the upper, left lower and the upper part of the right tunnel excavation.

Table 4 Comparison of tunnel convergence for left tunnel
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Vertical displacements corresponding to the left tunnel upper excavation, the left tunnel lower excavation and the right tunnel upper excavation are in agreement with the field observations. However, the horizontal displacements on the tunnel walls deviated from the field measurements. For the left tunnel lower excavation, however, the FEM calculations correctly predicted zero displacements; the selected shotcrete thickness being sufficient to stop excessive convergences.

Figures 8, 9, 10 and 11 shows the 10-day differential convergence observations for both left and right tunnels. No real time FEM simulation was carried out, but the displacement predictions obtained are provided in Table 4. As can be seen from Fig. 8, horizontal displacement at station L2 seem to stop around 4 mm displacement although at station L1 it continued to 7 mm and at station L3 to 9 mm displacement.

Fig. 8
figure 8

Observed horizontal displacement for the upper part of the left tunnel

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Fig. 9
figure 9

Observed vertical displacement for the upper part of the left tunnel

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Fig. 10
figure 10

Measured horizontal displacement on the upper part of the right tunnel

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Fig. 11
figure 11

Measured vertical displacement on the upper part of the right tunnel

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Compared with the horizontal displacements, the vertical displacements for the left tunnel upper excavation after 8 days were found to be much more consistent (Fig. 9). Similar observations were obtained for the right tunnel upper excavation. Differential displacement profiles for the left tunnel upper excavation are given in Figs 10 and 11. As the right tunnel was constructed after completion of the left tunnel, not only horizontal displacements but also vertical displacements were observed to be 2–3 times greater than the left tunnel observations. This indicates that the left tunnel construction increases the convergences. This could be because of the small pillar width left between the tunnels which created a larger plastic region around the left tunnel.

The vertical and horizontal displacements around the twin tunnels are given in Figs. 12 and 13. Large vertical displacements were predicted at the bottom of the tunnels (Fig. 12) which suggests that the excavation sequences adopted for tunnel construction were not appropriate. Approximately 120 mm heave at the tunnel invert was predicted. However, there are no field measurements available to verify the FEM prediction for the bottom part of the tunnels. As in many cases heave at the tunnel invert causes serious instability problems, field measurements at the bottom part of the tunnel should always be carried out to detect such movements. Horizontal displacements were also concentrated at the sidewalls and bottom part of the tunnels as shown in Fig. 13.

Fig. 12
figure 12

Vertical displacements around the twin tunnels

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Fig. 13
figure 13

Horizontal displacements around the twin tunnels

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Conclusions

The twin tunnel construction in Ankara Clay was analysed and the geotechnical parameters of the site and convergence profiles monitored during the tunnelling process are presented. The geotechnical properties of the construction site were evaluated and parameters for the Modified Cam Clay soil plasticity model were derived from oedometer test results as input data to the FEM analysis.

The results from the numerical analysis show that vertical displacements on the tunnel walls are in agreement with the observations but the horizontal displacements were found to deviate from the actual measurements. However, as the convergence measurements were carried out by topographical methods, the observed convergence could be erroneous. It is therefore considered that a more reliable technique should be used to measure convergence in soft ground.

The right tunnel was constructed after completion of the left tunnel and not only the horizontal displacements but also the vertical displacements were observed to be 2–3 times more than in the left tunnel. It is considered that the earlier left tunnel construction caused/increased in the convergence. This could be due to the small pillar width left between the tunnels which created a larger plastic region around the left tunnel.