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Time-Dependent Behavior of the Tunnels in Squeezing Ground: An Experimental Study

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Abstract

The presence of squeezing ground conditions often poses significant challenges in predicting tunnel response over time and to the design of an adequate support system to stabilize the tunnel. Many analytical, empirical, observational, and numerical models have been proposed over the years for the design of tunnels in squeezing ground conditions, but they all have some limitations. The study presented in this paper focused on improving the understanding of tunnel squeezing via a unique physical model test that simulated tunnel boring machine (TBM) excavation in squeezing clay-rich rocks. The physical model included a large true-triaxial cell, a miniature TBM, a laboratory-prepared synthetic test specimen having properties similar to natural mudstone, and instrumentations to monitor deformations around the tunnel boundary during and after the excavation. Experiments were conducted at realistic in-situ stress levels to study time-dependent tunnel convergence in three-dimensions. A tunnel was excavated using the miniature TBM in a cubical rock specimen loaded in the true-triaxial cell; then the confining stress was increased in stages to values above the rock unconfined compressive strength. Strain gauges embedded in the rock specimen and a digital borehole caliper monitored tunnel wall deformations with time. The degree of tunnel squeezing was characterized using a classification system based on tunnel radial strain. A model for time-dependent tunnel longitudinal displacement profile (LDP) was proposed using measurements of the tunnel convergence at different times and different stress levels.

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References

  • Arora K, Gutierrez M, Hedayat A (2019a) Experimental setup for studying tunnels in squeezing ground conditions. In: Tunnels and underground cities. Engineering and Innovation Meet Archaeology, Architecture and Art: Naples, Italy, CRC Press, 3515–3524.

  • Arora K, Gutierrez M, Hedayat A (2019b) Miniature tunnel boring machine for simulating tunnel excavation in squeezing ground conditions. In: 4th international conference on tunnel boring machine in difficult ground: Denver, Colorado, 183–192.

  • Arora K, Gutierrez M, Hedayat A (2020a) Characterization of synthetic mudstone for physical model studies. In: 54th US rock mechanics/geomechanics symposium. American Rock Mechanics Association, Accepted.

  • Arora K, Gutierrez M, Hedayat A (2020c) New physical model to study tunnels in squeezing clay-rich rocks. Geotechnical Testing Journal, ASTM (Accpeted)

  • Arora K, Gutierrez M, Hedayat A, Xia C (2020b) Tunnels in Squeezing Clay-Rich Rocks. Underground space, Accepted

  • Aydan Ö, Akagi T, Kawamoto T (1996) The squeezing potential of rock around tunnels: theory and prediction with examples taken from Japan. Rock Mech Rock Eng 29(3):125–143

    Google Scholar 

  • Barla G (1995) Squeezing rocks in tunnels. ISRM News J 2(3):44–49

    Google Scholar 

  • Barla G (2001) Tunnelling under squeezing rock conditions. Eurosummer-school in tunnel mechanics: Innsbruck, 169–268.

  • Barla G, Debernardi D, Sterpi D (2012) Time-dependent modeling of tunnels in squeezing conditions. Int J Geomech 12(6):697–710

    Google Scholar 

  • Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech 6(4):189–236

    Google Scholar 

  • Bilgin N, Algan M (2012) The performance of a TBM in a squeezing ground at Uluabat, Turkey. Tunn Undergr Space Technol 32:58–65

    Google Scholar 

  • Bonini M, Debernardi D, Barla M, Barla G (2009) The mechanical behaviour of clay shales and implications on the design of tunnels. Rock Mech Rock Eng 42(2):361–388

    Google Scholar 

  • Cao C, Shi C, Lei M, Yang W, Liu J (2018) Squeezing failure of tunnels: a case study. Tunn Undergr Space Technol 77:188–203

    Google Scholar 

  • Carranza-Torres C, Fairhurst C (2000) Application of the convergence–confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion. Tunneling Underground Space Technol 15(2):187–213

    Google Scholar 

  • Carter BJ (1992) Size and stress gradient effects on fracture around cavities. Rock Mech Rock Eng 25(3):167–186

    Google Scholar 

  • Cristescu ND, Gioda G (1994) Visco-plastic behaviour of geomaterials. Springer, Vienna, pp 1–25

    Google Scholar 

  • Cristescu ND, Hunsche U (1998) Time effects in rock mechanics. Wiley, Chichester, pp 45–67

    Google Scholar 

  • Czurda K, Winder CG, Quigley RM (1973) Sedimentology, mineral facies, and petrofabric of the Meaford-Dundas formation (Upper Ordovician) in southern Ontario. Can J Earth Sci 10(12):1790–1804

    Google Scholar 

  • Dalgıç S (2002) Tunneling in squeezing rock, the Bolu tunnel, Anatolian Motorway. Turkey Eng Geol 67(1–2):73–96

    Google Scholar 

  • Deere DU, Peck RB, Parker HW, Monsees JE, Schmidt B (1970) Design of tunnel support systems. Highway Res Rec 339:26–33

    Google Scholar 

  • Duncan-Fama ME (1993) Numerical modelling of yield zones in weak rocks. Comprehensive Rock Eng 2:49–75

    Google Scholar 

  • Dusseault MB, Fordham CJ (1993) Time-dependent behavior of rocks. comprehensive rock engineering principles, practice and project. Rock Testing Site Characterization 3:119–149

    Google Scholar 

  • Dusseault MB, Fordham CJ (1993) Time-dependent behavior of rocks. In: Rock testing and site characterization, Pergamon, 119–149

  • Emori RI, Saito K, Sekimoto K (2008) Scale Models in Engineering (Mokei Jikken no Riron to Ohyou), (ISBN 4-7655-3252-6 C3053). Gihodo. Second print in, Tokyo, Japan

    Google Scholar 

  • Fabre G, Pellet F (2006) Creep and time-dependent damage in argillaceous rocks. Int J Rock Mech Min Sci 43(6):950–960

    Google Scholar 

  • Frash LP, Gutierrez M, Hampton J (2014) True-triaxial apparatus for simulation of hydraulically fractured multi-borehole hot dry rock reservoirs. Int J Rock Mech Min Sci 100(70):496–506

    Google Scholar 

  • Ghaboussi J, Gioda G (1977) On the time-dependent effects in advancing tunnels. Int J Numer Anal Meth Geomech 1(3):249–269

    Google Scholar 

  • Ghaboussi J, Ranken RE, Hendron Jr. AJ (1981) Time-dependent behavior of solution caverns in salt. J Geotech Geoenviron Eng ASCE 16597 Proc 107: 43–69.

  • Gioda G (1981) A finite element solution of non-linear creep problems in rocks. Int J Rock Mech Min Sci Geomech Abstracts Pergamon 18(1):35–46

    Google Scholar 

  • Gioda G (1982) On the non-linear ‘squeezing’effects around circular tunnels. Int J Numer Anal Meth Geomech 6(1):21–46

    Google Scholar 

  • Gioda G, Cividini A (1996) Numerical methods for the analysis of tunnel performance in squeezing rocks. Rock Mech Rock Eng 29(4):171–193

    Google Scholar 

  • Goel RK, Jethwa JL, Paithankar AG (1995) Tunneling through the young Himalayas—a case history of the Maneri-Uttarkashi power tunnel. Eng Geol 39(1–2):31–44

    Google Scholar 

  • Hoek E (2001) Big tunnels in bad rock. J Geotech Geoenviron Eng 127(9):726–740

    Google Scholar 

  • Hoek E, Guevara R (2009) Overcoming squeezing in the Yacambú-Quibor tunnel. Venezuela Rock Mech Rock Eng 42(2):389–418

    Google Scholar 

  • Hoek E, Marinos P (2000) Predicting tunnel squeezing problems in weak heterogeneous rock masses. Tunnels Tunnelling Int 32(11):45–51

    Google Scholar 

  • Kabwe E, Karakus M, Chanda EK (2020) Isotropic damage constitutive model for time-dependent behaviour of tunnels in squeezing ground. Comput Geotech 1(127):103738

    Google Scholar 

  • Kallhawy FH (1974) Finite element modeling criteria for underground opening in rock. Int J Rock Mech Min Sci 11:465–472

    Google Scholar 

  • Ladanyi B (1974) Use of the long-term strength concept in the determination of ground pressure on tunnel linings. In: Proceedings, 3rd congress of ISRM, National Academy of Sciences, 2: 1150–1156

  • Ladanyi B (1993) Time-dependent response of rock around tunnels. In: Analysis and design methods, Pergamon, 77–112

  • Lajtai EZ (1972) Effect of tensile stress gradient on brittle fracture initiation. Int J Rock Mech Min Sci Geomech Abstracts 9(5):569–578

    Google Scholar 

  • Lin P, Liu H, Zhou W (2015) Experimental study on failure behaviour of deep tunnels under high in-situ stresses. Tunn Undergr Space Technol 46:28–45

    Google Scholar 

  • Lo KY, Cooke BH, Dunbar DD (1987) Design of buried structures in squeezing rock in Toronto Canada. Canadian Geotech J 24(2):232–241

    Google Scholar 

  • Malan DF (2002) Simulating the time-dependent behaviour of excavations in hard rock. Rock Mech Rock Eng 35(4):225–254

    Google Scholar 

  • Manh HT, Sulem J, Subrin D, Billaux D (2015) Anisotropic time-dependent modeling of tunnel excavation in squeezing ground. Rock Mech Rock Eng 48(6):2301–2317

    Google Scholar 

  • Martin CD, Martino JB, Dzik EJ (1994) Comparison of borehole breakouts from laboratory and field tests. Rock Mech Petroleum Eng Soc Petroleum Eng. https://doi.org/10.2118/28050-MS

    Article  Google Scholar 

  • Mesri G, Febres-Cordero E, Shields D, Castro A (1981) Shear stress-strain-time behaviour of clays. Geotechnique 31(4):537–552

    Google Scholar 

  • Pan YW, Dong JJ (1991) Time-dependent tunnel convergence-II. Advance rate and tunnel-support interaction. Int J Rock Mech Min Sci 28(6):477–488

    Google Scholar 

  • Panet M (1993) Understanding deformations in tunnels. Comprehensive Rock Eng 1:663–690

    Google Scholar 

  • Panet M (1995) Calcul des Tunnels par la Me’thode de Convergence-Confinement. Presses de l’Ecole Nationale des Ponts et Chausse’es, Paris 178:11–19

    Google Scholar 

  • Pellet F, Hajdu A, Deleruyelle F, Besnus F (2005) A viscoplastic model including anisotropic damage for the time dependent behaviour of rock. Int J Numer Anal Meth Geomech 29(9):941–970

    Google Scholar 

  • Phien-wej N, Cording EJ (1991) Sheared shale response to deep TBM excavation. Eng Geol 30(3–4):371–391

    Google Scholar 

  • Phien-wej N, Thakur PK, Cording EJ (2007) Time-dependent response of tunnels considering creep effect. Int J Geomech 7(4):296–306

    Google Scholar 

  • Prassetyo SH, Gutierrez M (2018) Effect of transient coupled hydro-mechanical response on the longitudinal displacement profile of deep tunnels in saturated ground. Tunn Undergr Space Technol 75:11–20. https://doi.org/10.1016/j.tust.2018.02.003

    Article  Google Scholar 

  • Ramoni M, Anagnostou G (2006) On the feasibility of TBM drives in squeezing ground. Tunneling Underground Space Technol 21(3):262

    Google Scholar 

  • Ramoni M., Anagnostou G (2008) TBM drives in squeezing ground-Shield–Rock interaction. Building underground for the future; AFTES International Congress Monaco, Montecarlo, 163–172; Edition specifique Limonest

  • Ramoni M, Anagnostou G (2010) Thrust force requirements for TBMs in squeezing ground. Tunn Undergr Space Technol 25(4):433–455

    Google Scholar 

  • Schubert W (1996) Dealing with squeezing conditions in Alpine tunnels. Rock Mech Rock Eng 29(3):145–153

    Google Scholar 

  • Semple RM, Hendron AJ, Mesri G (1973) Effect of time-dependent properties of altered rock on tunnel support requirements. Dep of Transp, Fed Railroad Adm, Final Rep FRA-ORDD-74–30.

  • Shang Y, Xue J, Wang S, Yang Z, Yang J (2004) A case history of Tunnel Boring Machine jamming in an inter-layer shear zone at the Yellow River Diversion Project in China. Eng Geol 71(3–4):199–211

    Google Scholar 

  • Shrestha PK, Panthi KK (2015) Assessment of the effect of stress anisotropy on tunnel deformation in the Kaligandaki project in the Nepal Himalaya. Bull Eng Geol Env 74(3):815–826

    Google Scholar 

  • Singh B, Jethwa JL, Dube AK, Singh B (1992) Correlation between observed support pressure and rock mass quality. Tunn Undergr Space Technol 7(1):59–74

    Google Scholar 

  • Singh A, Kumar C, Kannan LG, Rao KS, Ayothiraman R (2018) Estimation of creep parameters of rock salt from uniaxial compression tests. Int J Rock Mech Min Sci 107:243–248

    Google Scholar 

  • Steiner W (1996) Tunnelling in squeezing rocks: case histories. Rock Mech Rock Eng 29(4):211–246

    Google Scholar 

  • Sterpi DV (2007) Ground pressure and convergence for TBM driven tunnels in visco-plastic rocks. In: Proceedings of the ECCOMAS thematic conference on computational methods in tunneling EURO: TUN, Vienna University of Technology, 1–54.

  • Sulem J (2013) Tunnel du Fréjus: Mesures géotechniques et interprétation, Manuel de Mécanique des Roches Tome IV, chap. 7, Presse des Mines

  • Sulem J, Panet M, Guenot A (1987) An analytical solution for time-dependent displacements in a circular tunnel. Int J Rock Mech Min Sci Geomech Abstracts, Pergamon 24(3):155–164

    Google Scholar 

  • Terzaghi K (1946) Rock defects and loads on tunnel supports. Rock tunneling with steel supports. In: Proctor RV, White TL (eds) Commercial shearing and stamping company. OH, Youngstown, pp 45–92

    Google Scholar 

  • Tiwari G, Pandit B, Gali ML, Babu GL (2018) Analysis of tunnel support requirements using deterministic and probabilistic approaches in average quality rock mass. Int J Geomech 18(4):1–20

    Google Scholar 

  • Tran-Manh H, Sulem J, Subrin D (2016) Progressive degradation of rock properties and time-dependent behavior of deep tunnels. Acta Geotech 11(3):693–711

    Google Scholar 

  • Vlachopoulos N, Diederichs MS (2009) Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels. Rock Mech Rock Eng 42(2):131–146

    Google Scholar 

  • Vrakas A, Dong W, Anagnostou G (2018) Elastic deformation modulus for estimating convergence when tunnelling through squeezing ground. Géotechnique 68(8):713–728

    Google Scholar 

  • Wang X, Lai J, Garnes RS, Luo Y (2019) Support system for tunnelling in squeezing ground of Qingling-Daba mountainous area: a case study from soft rock tunnels. Adv Civ Eng, 1–23.

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Acknowledegments

The authors gratefully acknowledge the financial support of the University Transportation Center for Underground Transportation Infrastructure (UTC-UTI) at the Colorado School of Mines under Grant No. 69A3551747118 from the U.S. Department of Transportation (DOT). The opinions expressed in this paper are those of the authors and not of the DOT.

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Appendices

Appendix A: Validation of the Methodology to Embed Strain Gauge

The methodology is discussed in detail by Arora et al. (2020). The strain gauge, glued on a 1 mm thick 10 × 10 × mm2 Teflon sheet, was embedded longitudinally in the cylindrical synthetic mudstone specimen, as shown in Fig. 

Fig. 14
figure 14

Validation of the embedded strain gauge technique by embedding strain gauge in cylindrical synthetic specimen and comparing the measurements with LVDT in uniaxial compression test

14. The specimen was loaded uniaxially and the strain measurement from the embedded strain gauges were compared with the average strain obtained from the linear variable differential transformer (LVDT) monitoring the axial deformation of the specimen. It can be seen from Fig. 14 that the strains from the embedded strain gauges were very close to the strains recorded by LVDT with the difference limited 15%. Hence, this technique was shown to be entirely instrumental in determining the strain inside the synthetic mudstone specimen.

Appendix B: Creep Tests and Qualitative Comparison with Model Tests

Arora (2020a) developed a synthetic mudstone for laboratory scale physical model and determined the physical, mechanical and creep properties by carrying out uniaxial compression test (UCT), triaxial tests and creep tests. The elastic properties and the Mohr–Coulomb parameters are already discussed in Table 2. Arora (2020a) also carried out unconfined compression creep tests on the cylindrical specimen of the synthetic mudstone. The tests were conducted at stress levels of 0.40σc, 0.50σc and 0.75σc as shown in Fig. 

Fig. 15
figure 15

a Creep test setup with a loaded cylindrical mudstone specimen and Sketch of the Burger’s model considering viscoelastic behavior, and Creep strain with time along with best linear fit for steady-state creep (b) 0.40σc, (c) 0.50σc, and (c) 0.75σc

15. The creep test setup used by Arora et al. (2020a) cannot be used to apply stress higher than 0.75σc.

The creep behavior of synthetic mudstone specimen is described using the Burger’s viscoelastic model as given in Fig. 15a and defined by the following equation:

$${\varepsilon }_{1}=\frac{{\sigma }_{1}}{{E}^{M}}+\frac{{\sigma }_{1}}{{\eta }^{M}}t+\frac{{\sigma }_{1}}{{E}^{K}}\left[1-exp\left(-\frac{{E}^{K}}{{\eta }^{K}}t\right)\right]$$
(8)

where EM, EK, ηM, and ηK are the Burger’s model parameter, and σ1 and ε1 are the stress and strain in the axial direction of the cylindrical specimen in the uniaxial compression creep test. Figure 15b through C shows the increase in ε1 with time for the three creep tests at stress levels of 0.40σc, 0.50σc, and 0.75σc, respectively. Burger’s model parameters obtained from the three tests and average value are provided in Table 

Table 5 Burger’s model parameters for the creep behavior of synthetic mudstone

5.

The differences and similarities between the physical model test observations and the creep test results can be summarized as follows:

  1. 1.

    In the case of creep tests, the maximum stress was 0.75σc, and hence the strains developed predominantly due to viscous and elastic behavior of the material. On the other hand, in the physical model test, the maximum stress level was 2.0σc and the strains developed due to viscous, elastic, and plastic behavior of the material.

  2. 2.

    In the physical model test, considering all lading stages and tunnel cross-sections, the tunnel strain u/R at the end of the loading stage was 1.5–2.4 times the u/R value at the beginning of the loading stage. Similarly, for the three creep tests, ε1 at the end of the test was 2.0–2.9 times that of the beginning of the test.

  3. 3.

    The trend of increase in the strain with time, for both the physical model tests and the creep tests, can be defined by the exponential functions (Eqs. (1) and (8)).

  4. 4.

    In both physical model test and creep tests, the strain value reached the steady state after a certain time (see Figs. 9 through 12 and 15).

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Arora, K., Gutierrez, M., Hedayat, A. et al. Time-Dependent Behavior of the Tunnels in Squeezing Ground: An Experimental Study. Rock Mech Rock Eng 54, 1755–1777 (2021). https://doi.org/10.1007/s00603-021-02370-w

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