Time-dependent longitudinal responses of a shield tunnel induced by surcharge load: Theoretical prediction and analysis

Abstract

The surcharge load at the ground surface inevitably breaks the original equilibrium state between the underneath tunnel and the surrounding soil, which will impact the service performance of a subway tunnel. This paper presents a novel semi-analytical approach for assessing the time-dependent, longitudinal responses of a subway tunnel in soft soil strata induced by the surcharge load. The solution is developed based on the framework of the classical ‘‘two-stage method” but innovatively incorporates the effects of ground stratification, the consolidation process, and the longitudinal stiffness reduction of the lining. Biot’s poroelastic theory in conjunction with the Laplace- Fourier transform technique is selected to model the deformation of the stratified ground, while the Timoshenko beam on a Pasternak foundation is employed to model the mechanical responses of the tunnel. The proposed semi-analytical solution is validated not only by comparison with benchmark solutions and a finite element model, but also by predicting a well-documented field measurement. Parametric analyses are conducted to investigate the effects of the elastic modulus and the permeability coefficient of the stratified ground on the longitudinal responses of the tunnel. It is expected that the proposed solution can serve as a useful tool for evaluating the effects of the surcharge load on the longitudinal responses of a subway tunnel.

Keywords

Time-dependent / Longitudinal responses / Stratified ground / Subway tunnels / Ground surface surcharge / Consolidation

References

[1] Ai Z. Y., Cheng Y. C., & Zeng W. Z. (2011). Analytical layer-element solution to axisymmetric consolidation of multilayered soils. Comput- ers and Geotechnics, 38(2), 227-232.

[2] Biot M. A. (1941). General theory of three-dimensional consolidation. I. Journal of Applied Physics, 12(2), 155-164.

[3] Booker J. R., & Small J. C. (1982). Finite layer analysis of consolidation. I. International Journal for Numerical and Analytical Methods in Geomechanics, 6(2), 151-171.

[4] Chang C. T., Sun C. W., Duann S. W., & Hwang R. N. (2001). Response of a taipei rapid transit system (TRTS) tunnel to adjacent excavation. Tunnelling and Underground Space Technology, 16(3), 151-158.

[5] Cue´llar P., Mira P., Pastor M., Merodo J. A. F., Baeßler M., & Ru¨ cker W. (2014). A numerical model for the transient analysis of offshore foundations under cyclic loading. Computers and Geotechnics, 59, 75-86.

[6] Cui G., Cui J., Fang Y., Chen Z., & Wang H. (2020). Scaled model tests on segmental linings of shield tunnels under earth and water pressures. International Journal of Physical Modelling in Geotechnics, 20(6), 338-354.

[7] Fan Y., Guo X. H., Deng Z. J., & Xu Y. Z. (2014). Deformation analysis of shield tunnel with loading and unloading above. Construction Technology, 43, 107-109 (in Chinese).

[8] Franza A., & Viggiani G. M. B. (2021). Role of shear deformability on the response of tunnels and pipelines to single and twin tunneling. Journal of Geotechnical and Geoenvironmental Engineering, 147(12), 04021145.

[9] Han J. Y., Zhao W., Jia P. J., Guan Y. P., Chen Y., & Jiang B. F. (2018). Risk analysis of the opening of shield-tunnel circumferential joints induced by adjacent deep excavation. Journal of Performance of Constructed Facilities, 32(1), 04017123.

[10] Hu, Z. F., Yue, Z. Q., Zhou, J., & Tham, L. G. (2003). Design and construction of a deep excavation in soft soils adjacent to the Shanghai Metro tunnels. Canadian Geotechnical Journal, 40(5), 933-948.

[11] Huang H. W., & Zhang D. M. (2016). Resilience analysis of shield tunnel lining under extreme surcharge: Characterization and field application. Tunnelling and Underground Space Technology, 51, 301-312.

[12] Huang Z., Zhang H., Fu H., Ma S., & Liu Y. (2020). Deformation response induced by surcharge loading above shallow shield tunnels in soft soil. KSCE Journal of Civil Engineering, 24(8), 2533-2545.

[13] Koizumi J., Murakami H., & Saino K. (1988). Modelling of longitudinal structure of shield tunnel. Journal of Japan Society of Civil Engineers, 394, 79-88, in Japanese.

[14] Liang F. Y., Fang Y. Q., Yuan Q., & Li J. P. (2021a). Experimental study of the influence of surface surcharge on tunnel lateral deforma- tion in soft and hard soil. Journal of Tongji University (Natural Science), 49(3), 322-331, in Chinese.

[15] Liang F. Y., Yuan Q., Li J. P., & Zhang S. X. (2020). Influences of soil characteristics on longitudinal deformation of shield tunnels induced by surface surcharge. Chinese Journal of Geotechnical Engineering, 42 (1), 63-71, in Chinese.

[16] Liang F. Y., Yuan Q., Song Z., Li J. P. & Zhang S. X. (2021b). Longitudinal responses of shield tunnel subjected to surcharge considering the dislocation. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 174(4), 342-354.

[17] Liang R. Z., Wu W. B., Yu F., Jiang G. S., & Liu J. W. (2018). Simplified method for evaluating shield tunnel deformation due to adjacent excavation. Tunnelling and Underground Space Technology, 71, 94-105.

[18] Liang R. Z., Xia T. D., Huang M. S., & Lin C. G. (2017). Simplified analytical method for evaluating the effects of adjacent excavation on shield tunnel considering the shearing effect. Computers and Geotechnics, 81, 167-187.

[19] Liu X., Fang Q., & Zhang D. L. (2018). Mechanical responses of existing tunnel due to new tunnelling below without clearance. Tunnelling and Underground Space Technology, 80, 44-52.

[20] Liu X., Fang Q., Zhang D. L., & Wang Z. J. (2019). Behaviour of existing tunnel due to new tunnel construction below. Computers and Geotechnics, 110, 71-81.

[21] Pasternak P. L. (1954). On a new method of analysis of an elastic foundation by means of two foundation constants. Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, 1, 1-56, in Russian.

[22] Prassetyo S. H., & Gutierrez M. (2016). Effect of surface loading on the hydro-mechanical response of a tunnel in saturated ground. Under- ground Space, 1(1), 1-19.

[23] Puswewala U. G. A., & Rajapakse R. K. N. D. (1988). Axisymmetric fundamental solutions for a completely saturated porous elastic solid. International journal of engineering science, 26(5), 419-436.

[24] Rajapakse R. K. N. D., & Senjuntichai T. (1993). Fundamental solutions for a poroelastic half-space with compressible constituents. ASME. Journal of Applied Mechanics, 60( 4), 847-856.

[25] Schapery R.A. (1962). Approximation methods of transform inversion for viscoelastic stress analysis. In: Proceedings of the Fourth U.S. National Congress of Applied Mechanics, 1075-1085.

[26] Shen S. L., Wu H. N., Cui Y. J., & Yin Z. Y. (2014). Long-term settlement behaviour of metro tunnels in the soft deposits of Shanghai. Tunnelling and Underground Space Technology, 40, 309-323.

[27] Shiba Y., Kawashima K., Obinata N., & Kano T. (1988). An evaluation method of longitudinal stiffness of shield tunnel linings for application to seismic response analyses. Doboku Gakkai Ronbunshu, 319-327, in Japanese.

[28] Shiba Y., Kawashima K., Obinata N., & Kano T. (1989). Calculation method on sectional forces of longitudinal structure of shield tunnel under earthquake force based on response deformation method. Journal of Japan Society of Civil Engineers, 385-394, in Japanese.

[29] Talbot A. (1979). The accurate numerical inversion of Laplace trans- forms. IMA Journal of Applied Mathematics, 23(1), 97-120.

[30] Tanahashi H. (2004). Formulas for an infinitely long Bernoulli- Euler beam on the Pasternak model. Soils and foundations, 44(5), 109-118.

[31] Wei Z., & Jiang Y. (2021). A simplified analysis method for the deformation response of an existing tunnel to ground surcharge based on the Pasternak model. Applied Sciences, 11(7), 3255.

[32] Winkler E. (1867). Die Lehre von der Elastizita¨ t und Festigkeit. Prag, H. Dominicus. (in Germany).

[33] Wu H. N., Huang R. Q., Sun W. J., Shen S. L., Xu Y. S., Liu Y. B., & Du S. J. (2014). Leaking behavior of shield tunnels under the Huangpu River of Shanghai with induced hazards. Natural Hazards, 70(2), 1115-1132.

[34] Wu H. N., Shen S. L., Liao S. M., & Yin Z. Y. (2015). Longitudinal structural modelling of shield tunnels considering shearing dislocation between segmental rings. Tunnelling and Underground Space Technology, 50, 317-323.

[35] Wu H. N., Shen S. L., Yang J., & Zhou A. N. (2018). Soil-tunnel interaction modelling for shield tunnels considering shearing disloca- tion in longitudinal joints. Tunnelling and Underground Space Technology, 78, 168-177.

[36] Xu L. (2005). Study on longitudinal settlement of shield tunnel in soft soil. Shanghai : Tongji University, Doctoral dissertation. (in Chinese)

[37] Yamamoto K., Lyamin A. V., Wilson D. W., Sloan S. W., & Abbo A. J. (2014). Stability of dual square tunnels in cohesive-frictional soil subjected to surcharge loading. Canadian Geotechnical Journal, 51(8), 829-843.

[38] Yu J., Li H., Huang M., Li Y., Tan J. Q. W., & Guo Y. (2022). Timoshenko-beam-based response of existing tunnel to single tunnel ing underneath and numerical verification of opening and dislocation. Computers and Geotechnics, 147, 104757.

[39] Zhang C. R., Zhu J. R., Huang M. S., & Yu J. (2019b). Winkler load- transfer analysis for pipelines subjected to surface load. Computers and Geotechnics, 111, 147-156.

[40] Zhang D. M., Huang Z. K., Li Z. L., Zong X., & Zhang D. M. (2019a). Analytical solution for the response of an existing tunnel to a new tunnel excavation underneath. Computers and Geotechnics, 108, 197-211.

[41] Zhang J. Z., Huang H. W., Zhang D. M., Zhou M. L., Tang C., & Liu D. J. (2021). Effect of ground surface surcharge on deformational performance of tunnel in spatially variable soil. Computers and Geotechnics, 136, 104229.

[42] Zhang Z. G., Huang M. S., & Wang W. D. (2013). Evaluation of deformation response for adjacent tunnels due to soil unloading in excavation engineering. Tunnelling and Underground Space Technology, 38, 244-253.