Unified analytical solution for deep circular tunnel with consideration of seepage pressure, grouting and lining

Abstract

A new unified analytical solution is presented for predicting the range of plastic zone and stress distributions around a deep circular tunnel in a homogeneous isotropic continuous medium. The rock mass, grouting zone and lining are assumed as elastic-perfectly plastic and governed by the unified strength theory (UST). This new solution has made it possible to consider the interaction between seepage pressure, lining, grouting and rock mass, and the intermediate principal stress effect together. Moreover, parametric analysis is carried out to identify the influence of the related parameters on the plastic zone radius. Under the given conditions, the results show that the plastic zone radius decreases with an increasing cohesion, internal friction angle and hydraulic conductivity of lining and unified failure criterion parameter, respectively; whereas the plastic zone radius increases with the growth of elasticity modulus of lining. Comparison of results from the new solution and the other published one shows well agreement and provides confidence in the new solution proposed.

Keywords

unified strength theory (UST) / intermediate principal stress / seepage pressure / grouting / lining / analytical solution

References

[1] MassinasS A, SakellariouM G. Closed-form solution for plastic zone formation around a circular tunnel in half-space obeying Mohr–Coulomb criterion [J]. Géotechnique, 2009, 59(8): 691-701

[2] HuL-s, WangJ-x, LuY-ru. Elastoplastic solution for deep tunnel considering influences of groundwater, grouting and lining [J]. Rock and Soil Mechanics, 2012, 33(3): 757-766

[3] LiP-f, QianF, ZhangD-li. Analytical solutions of stresses and displacements for deep circular tunnels with linings in saturated ground [J]. Journal of Zhejiang University: Science A (Applied Physics & Engineering), 2014, 15(6): 395-404

[4] SharanS K. Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(1): 78-85

[5] HuangF, ZhangD-b, SunZ-b, WuBen. Influence of pore water pressure on upper bound analysis of collapse shape for square tunnel in Hoek-Brown media [J]. Journal of Central South University of Technology, 2011, 18(2): 530-535

[6] Arranza-TorresC. Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(3): 480-481

[7] ChenR, TononF. Closed-form solutions for a circular tunnel in elastic-brittle-plastic ground with the original and generalized Hoek–Brown failure criteria [J]. Rock Mechanics and Rock Engineering, 2011, 44(2): 169-178

[8] CaiM. Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries-Insight from numerical modeling [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(5): 763-772

[9] YuM-hongUnified strength theory and its applications [M], 2004129172

[10] ZengK-h, XuJ-xiong. Unified semi-analytical solution for elastic-plastic stress of deep circular hydraulic tunnel with support yielding [J]. Journal of Central South University, 2013, 20(6): 1742-1749

[11] ZhangC-g, ZhaoJ-h, ZhangQ-h, HuX-dong. A new closed-form solution for circular openings modeled by the unified strength theory and radius-dependent Young’s modulus [J]. Computers and Geotechnics, 2012, 42: 118-128

[12] ZhangC-g, WangJ-f, ZhaoJ-hai. Unified solutions for stresses and displacements around circular tunnels using the unified strength theory [J]. Science China: Technological Sciences, 2010, 53(6): 1694-1699

[13] ZhangC-g, ZhangQ-h, ZhaoJ-h, XuF, WuC-zhou. Unified analytical solutions for a circular opening based on non-linear unified failure criterion [J]. Journal of Zhejiang University: Science A (Applied Physics & Engineering), 2010, 11(2): 71-79

[14] ZengK-h, LiJ-h, XuJ-x, YeQing. Analytical solution for stresses of deep hydraulic tunnel considering linear yielding [J]. Journal of Central South University: Science and Technology, 2012, 43(3): 1131-1137

[15] CaiM-h, CaiY-pingStructural stress calculation for hydraulic pressure tunnel [M], 2004, Beijing, China Water & Power Press: 1920

[16] LiJ-c, MaG-w, YuM-hong. Penetration analysis for geo-material based on unified strength criterion [J]. International Journal of Impact Engineering, 2008, 35(10): 1154-1163

[17] TerzaghiK. Simple tests determine hydrostatic uplift [J]. Engineering News Record., 1936, 116(25): 872-875