TBM tunnelling in squeezing ground represents a real challenge for all of the parties involved. It is well known from tunnelling experience that even small convergences of 100-200mm, which would not be problematic in conventional tunnelling, may lead to major problems both in the machine and in the back-up area (Ramoni and Anagnostou, 2010b).
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In the planning phase, a careful evaluation of the expected tunneling conditions is essential. For squeezing ground, the specific potential hazards that have to be evaluated include sticking of the cutter head, jamming of the shield, jamming of the back-up equipment, inadmissible convergences of the bored profile and damage to the tunnel support. In early project phases this assessment has to occur quickly and be cost-efficient. On the one hand, the general feasibility of a TBM drive in squeezing ground has to be proven. On the other hand, the tunnel sections requiring detailed investigations in later project phases have to be identified.
The authors have worked out decision aids for the planning engineer in respect of the two specific problems of jamming of the shield and damage to the tunnel support in shielded TBM tunnelling (Ramoni and Anagnostou, 2010a; Ramoni et al., 2011). These are design charts which allow for a quick and easy assessment of the thrust force required for overcoming shield skin friction (for gripper TBMs as well as for both single and double shielded TBMs) and the segmental lining loading (for both single and double shielded TBMs).
Computational model
Working out the design charts required the execution of about 20,000 calculations. Managing such a high computational effort was possible through the development of a computational method and model specifically for this purpose.
The computations have been executed applying the so called steady state method (Anagnostou, 2007; Nguyen Minh and Corbetta, 1991) – a numerical procedure implemented in the finite element code HYDMEC of the ETH Zurich which solves the advancing tunnel heading problem in just one single computational step, thus enabling major computational time saves.
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By GlobalDataThe computational model was kept deliberately simple, taking into account axial symmetry and the Mohr-Coulomb yield criterion. However, in spite of its simplicity, the computational model properly simulates all of the major system components, i.e. the shield and tunnel support with all of their main characteristics (e.g. the radial gap size between shield and ground, and the type and location of the backfilling of segmental linings), thus providing the maximum number of generally valid and valuable results with the minimum number of assumptions. For a more detailed description of the computational model, the readers are referred to Ramoni and Anagnostou (2010a, 2011b, 2011c) and Ramoni et al. (2011).
Nomograms for assessing the required thrust force
Concerning the risk of shield jamming, it is essential to have information on frictional force when designing a new TBM and when assessing the feasibility of a proposed TBM drive. Concerning the utilisation of a second-hand TBM, checks have to be made as to whether the installed thrust force is sufficiently high or whether the TBM has to be refurbished.
The thrust force Ff required for overcoming shield skin friction generally depends on all of the parameters of the problem under consideration: the material constants of the ground (Young’s modulus E, Poisson’s ratio ?, uniaxial compressive strength fc, angle of internal friction ? and dilatancy angle ?), the initial stress s0, the characteristics of the TBM (tunnel radius R, radial gap size ?R, shield length L and shield stiffness Ks), the skin friction coefficient µ and the stiffness of the lining Kl. The dimensionless nomograms are based on the numerical results of a comprehensive parametric study covering the relevant range of material constants, in situ stress and TBM characteristics. As the number of variables is still large, a trade-off has had to be made between the completeness of the parametric study and the cost of computation and data processing. For more details, as well as for a discussion of the underlying assumptions, the reader is referred to Ramoni and Anagnostou (2010a).
Each nomogram applies to a different TBM type (gripper TBM, single shielded TBM or double shielded TBM) and normalised shield length L/R as well as to a different value of the angle of internal friction ?.
Each design chart includes a band of curves (each curve corresponding to another value of the normalised uniaxial compressive strength fc/s0) showing the normalized required thrust force Ff /(µ2pRLs0) as a function of the dimensionless product of E/s0 by ?R/R. As an example, one of a total of 45 dimensionless nomograms (Ramoni and Anagnostou, 2010a), which applies for a single shielded TBM, is depicted in Figure 1.
Nomograms for assessing the segmental lining load
As regards the risk of lining overstressing, an estimation of the segmental lining load is essential to any assessment of a shielded TBM drive in squeezing ground. A realistic estimate is possible only if due account is taken of the type, location and thickness of the backfilling.
This is a challenging problem, because the thickness of the backfilling is not known a priori but depends on the intensity of the squeezing, i.e. on the deformations of the bored profile between the tunnel face and the point where the backfill is installed (see Figure 2).
Analogously to the thrust force Ff required for overcoming shield skin friction (see above), the ground pressure p acting upon the segmental lining depends on the material constants of the ground (E, ?, fc, ? and ?), on the initial stress (s0), on the characteristics of the TBM (R, ?R, L and Ks) and, additionally, on the characteristics of the backfilled segmental lining (stiffness Kl, radial gap size ?Rl and location of backfilling ?).
Figure 3 shows, by way of example, one of a total of 45 dimensionless nomograms (Ramoni et al., 2011) applying to a segmental lining that is completely backfilled with pea gravel and mortar at a distance of half a boring diameter behind the shield. Each nomogram applies to a different pair of values (?/R, KlR/E) describing the location where the backfilling occurs and the stiffness of the segmental lining, respectively. The diagrams of each figure apply to different values of the angle of internal friction ? and show the normalised ground pressure p/s0 as a function of the dimensionless parameter (E/s0)(?R/R) and of the normalised uniaxial compressive strength fc/s0. Other parameters (?, KsR/E, L/R and ?Rl./?R) have been kept constant, either because their influence on the normalised ground pressure p/s0 can be disregarded or because a conservative assumption has been made. A detailed discussion of the underlying assumptions can be found in Ramoni et al. (2011).
Application example
The suitability of the nomograms for a quick and cost-effective preliminary assessment of a TBM drive in squeezing ground will be shown by means of an application example concerning a common situation which confronts the tunnelling engineer on a regular basis in the planning phase.
The example is based on the longitudinal profile of a tunnel with a known geology (as shown schematically in the upper part of Figure 4). In this example, the tunnel has a diameter of 10m and crosses four different rock mass types (denoted by A-D) at different depths (350-550m). At issue is the identification of the critical stretches with respect to a possible jamming of the shield or to overstressing of the segmental lining under the assumption that the tunnel will be driven with a single shielded TBM.
The table in the bottom part of Figure 4 shows the preliminary assessment based upon the nomograms of Ramoni and Anagnostou (2010a) and Ramoni et al. (2011).
The hazard scenario ‘jamming of the shield’ can be assessed by comparing the required thrust force Fr with the installed thrust force Fi which is planned for the TBM. For the sake of simplicity, Figure 4 contains only the results for the operational state ‘restart after a standstill’ (the conditions during the boring process are not considered here). Please note that for this state Fr = Ff applies, i.e. the required thrust force Fr is equal to the thrust force required for overcoming shield skin friction Ff, as the boring thrust force is not taken into account when analysing this state (Ramoni and Anagnostou, 2010a).
The first step in the computation of the required thrust force Fr consists in the choice of the nomogram to be used. For example, for the tunnel section B (Figure 4) – considering the present boring diameter D of 10m (i.e. a boring radius R of 5m) and the shield length L of 10m (resulting in a ratio L/R = 2) as well as the angle of internal friction ? of 25° – the nomogram of Figure 1 applies. Taking into account the actual uniaxial compressive strength (fc = 3MPa) and the initial stress (s0 = 10MPa), the appropriate curve of Figure 1 is chosen according to the ratio fc/s0 = 0.3. In the next step, the dimensionless factor (E?R)/(s0R) = 1 is computed according to the actual values of the Young’s modulus E (1000MPa), the radial overcut of the shield ?R (50mm), the initial stress s0 (10MPa) and the boring radius R (5m). This dimensionless factor is then entered into the nomogram in order to depict the value of the normalized required thrust force for overcoming shield skin friction Ff /(µ2pRLs0), which is 0.26 in this example. Finally, a simple conversion (and bearing in mind that Fr = Ff applies in this case) allows the required thrust force to be determined. In this example Fr = 368MN, which clearly exceeds the assumed installed thrust force Fi of 150MN.
Assessment
The computational results indicate that the tunnel section B (Figure 4) is critical with respect to the risk of shield jamming. Assessing the feasibility of the TBM drive, the planning engineer should also be able to check which countermeasures would lead to a reduction of this risk. Such a preliminary assessment is possible by applying the nomograms. For example, repeating the same computation as above with ?R = 10cm (overboring) instead 50mm (normal overcut) indicates that doubling the radial gap size ?R leads to a decrease of the required thrust force Fr from 368MN to 110MN. According to this, for the example in question, the conclusion can be drawn that overboring (if it can be applied with sufficient reliability) would reduce the risk of shield jamming significantly.
The assessment of the hazard scenario ‘overstressing of the segmental lining’ can be carried out analogously by comparing the ground pressure p (load) with the bearing capacity of the lining pmax.
In this case, the appropriate nomogram is selected on the basis of the distance ? between the shieldtail and the location where the backfilling of the segmental lining is completed, the stiffness Kl of the segmental lining and the angle of internal friction ?. For example, for the tunnel section B (Figure 4) ?/R = 1, KlR/E = 1.8 (the segmental lining is assumed to be 300mm thick) and ? = 25° apply. As the nomograms of Ramoni et al. (2011) have been worked out for selected values of the ratio KlR/E (i.e. one, three and 10), the computation in this case requires a linear interpolation between different nomograms (which, for the sake of economy, is not reported here).
The output of the nomograms is the ratio between the ground pressure p acting upon the segmental lining and the initial stress s0. For the example of tunnel section B, p/s0 = 0.14 (calculated according to the main inputs fc/s0 = 0.3 and (E?R)/(s0R) = 1 as above) and therefore the result is p = 1.4, which exceeds the assumed bearing capacity of the segmental lining, which is pmax = 1.2MPa.
The computational results indicate again, in this case with respect to a possible overstressing of the segmental lining, that the tunnel section B (Figure 4) is critical and requires countermeasures such as, for example, higher quality concrete (i.e. a higher uniaxial compressive strength fc,l) for the segments in question.
In the same way, other calculations can be carried out very quickly for the other tunnel sections (A, C and D in Figure 4), thus allowing the critical tunnel sections (which are marked in red in Figure 4) to be identified rapidly.
Furthermore, a rapid sensitivity analysis could also be made in order to take due account of the fact that the intensity of squeezing may vary significantly even within a given tunnel section (for which constant material parameters may have been assumed a priori).
Closing remarks
The nomograms introduced in this paper for assessing the required thrust force show in a condensed form the statical conditions that have to be fulfilled in the design of a TBM in order to avoid jamming of the shield in squeezing ground.
When applied together with the extensive collection of TBM technical data presented in Ramoni and Anagnostou (2010a), which reviews the state of present-day TBMs, they enable quantitative statements to be made concerning the feasibility of a TBM drive as well as the effectiveness of potential design or operational measures (increase in the installed thrust force, reduction of the shield length, overboring, lubrication of the shield extrados).
The design charts for assessing the ground pressure acting upon a segmental lining enhance the set of decision aids available to the planning engineer.
Of course, the nomograms cannot eliminate the uncertainties associated with ground parameters and ground behaviour. Such uncertainties are intrinsic to every geomechanical calculation.
In the planning phase, the tunneling engineer deals with this uncertainty and utilises the computational results as a decision aid for his risk analysis. In this respect, the nomograms represent a powerful tool for decision-making in the design process.
The correctness and suitability of the methodical approaches and decision aids briefly presented in Part I and Part II of this contribution – a detailed description can be found, for example, in Ramoni and Anagnostou (2011a) – have been proven through their successful application in a series of real world projects involving TBM drives in squeezing ground. For example, during construction of the Faido Section of the Gotthard Base Tunnel in Switzerland as well as of the Uluabat and Eskisehir-Kosekoy Projects in Turkey, in the planning phase of the Lake Mead No Three Intake Tunnel in the USA and the Bosslertunnel in Germany and also in the tender design for the El Teniente New Access Tunnels in Chile.
