Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion

Abstract

Based on nonlinear Mohr-Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr-Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr-Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5 to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels, appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.

Keywords

nonlinear failure criterion / twin shallow tunnels / upper bound theorem / stability number / supporting force / clear distance

References

[1] FraldiM, GuarracinoF. Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections [J]. International Journal of Solids and Structures, 2010, 47(2): 216-223

[2] ChenW FLimit analysis and soil plasticity [M], 1975, Amsterdam, Elsevier: 275-306

[3] DavisE H, GunnM J, MairR J, SeneviratneH N. The stability of shallow tunnels and underground openings in cohesive material [J]. Geotechnique, 1980, 30(4): 397-416

[4] OsmanA S, MairR J, BoltonM D. On the kinematics of 2D tunnel collapse in undrained clay [J]. Geotechnique, 2006, 56(9): 585-595

[5] KlarA, OsmanA S, BoltonM. 2D and 3D upper bound solutions for tunnel excavation using elastic flow fields [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(12): 1367-1374

[6] YangX-l, ZhangD-b, WangZ-wei. Upper bound solutions for supporting pressures of shallow tunnels with nonlinear failure criterion [J]. Journal of Central South University, 2013, 20(7): 2034-2040

[7] JiangG-liang. Limit analysis of the stability of shallow tunnels in soft ground [J]. China Civil Engineering Journal, 1998, 31(5): 65-72

[8] YangX-l, HuangFu. Slope stability analysis considering joined influences of nonlinearity and dilation [J]. Journal of Central South University of Technology, 2009, 16(2): 292-296

[9] XieJ, LiuC-g, YuH-yong. Upper bound solutions of plastic limit analysis for the stability of two parallel circular tunnels [J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(9): 1835-1841

[10] YangX L, HuangF. Three-dimensional failure mechanism of a rectangular cavity in a Hoek-Brown rock medium [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 61: 189-195

[11] ChakrabortiS, KonietzkyH, WalterK. A comparative study of different approaches for factor of safety calculations by shear strength reduction technique for non-linear Hoek-Brown failure criterion [J]. Geotechnical and Geological Engineering, 2012, 30(4): 925-934

[12] OsmanA S. Stability of unlined twin tunnels in undrained clay [J]. Tunnelling and Underground Space Technology, 2010, 25(3): 290-296

[13] YangX L, HuangF. Collapse mechanism of shallow tunnel based on nonlinear Hoek-Brown failure criterion [J]. Tunnelling and Underground Space Technology, 2011, 26(6): 686-691

[14] YangX L, WangJ M. Ground movement prediction for tunnels using simplified procedure [J]. Tunnelling and Underground Space Technology, 2011, 26(3): 462-471

[15] YangX L. Seismic passive pressures of earth structures by nonlinear optimization [J]. Archive of Applied Mechanics, 2011, 81(9): 1195-1202

[16] YangX L, ZouJ F. Cavity expansion analysis with non-linear failure criterion [J]. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 2011, 164(1): 41-49

[17] SoubraA H, DiasD, EmeriaultF, KastnerR. Three-dimensional face stability analysis of circular tunnels by a kinematical approach [J]. Geotechqiuue, 2008, 30(5): 894-901

[18] HisatakeM, OhnoS. Effects of pipe roof supports and the excavation method on the displacements above a tunnel face [J]. Tunneling and Underground Space Technology, 2008, 23(2): 120-127

[19] YangX L, YinJ H. Slope equivalent Mohr-Coulomb strength parameters for rock masses satisfying the Hoek-Brown criterion [J]. Rock Mechanics and Rock Engineering, 2010, 43(4): 505-511

[20] YangX L. Seismic bearing capacity of a strip footing on rock slopes [J]. Canadian Geotechnical Journal, 2009, 46(8): 943-954

[21] ViratjandrC, MichalowskiR L. Limit analysis of submerged slopes subjected to water drawdown [J]. Canadian Geotechnical Journal, 2006, 43(8): 802-814

[22] YangX-l, HuangFu. Stability analysis of shallow tunnels subjected to seepage with strength reduction theory [J]. Journal of Central South University of Technology, 2009, 16(6): 1001-1005

[23] SiahmansouriA, GholamnejadJ, MarjiM F. A hybridized numerical and regression method for estimating the minimum rock pillar width of twin circular tunnels [J]. Arabian Journal of Geosciences, 2014, 7(3): 1059-1066

[24] ShinH S, YounD J, ChaeS E, ShinJ H. Effective control of pore water pressures on tunnel linings using pin-hole drain method [J]. Tunneling and Underground Space Technology, 2009, 24(5): 555-561