Influence of pore water pressure on upper bound analysis of collapse shape for square tunnel in Hoek-Brown media

Abstract

To investigate the effective shape of collapsing block in square tunnel subjected to pore water pressure, the analytical solution of detaching curve was derived using upper bound theorem of limit analysis with Hoek-Brown failure criterion. The work rate of pore water pressure, which was regarded as an external rate of work, was taken into account in the framework of limit analysis. Taking advantages of variational calculation, the objective function with respect to detaching curve was optimized to obtain the effective shape of collapsing block for square tunnel. According to the numerical results, it is found that the varying pore water pressure coefficient only affects the height and width of the collapsing block, whereas the shape of collapsing block remains unchanged.

Keywords

upper bound theorem / square tunnel / pore water pressure / variational calculation / Hoek-Brown media

References

[1] MerifieldR. S., LyaminA. V., SloanS. W.. Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6): 920-937

[2] YangX.-l., YinJ.-hua.. Estimation of seismic passive earth pressures with nonlinear failure criterion [J]. Engineering Structures, 2006, 28(3): 342-348

[3] YangX.-l., ZouJ.-feng.. Stability factors for rock slopes subjected to pore water pressure based on the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(7): 1146-1152

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

[5] LecaE., DormieuxL.. Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material [J]. Geotechnique, 1990, 40(4): 581-606

[6] AssadiA., SloanS. W.. Undrained stability of shallow square tunnel [J]. Journal of Geotechnical Engineering ASCE, 1991, 117(8): 1152-1173

[7] SloanS. W., AssadiA.. Undrained stability of a square tunnel in a soil whose strength increases linearly with depth [J]. Computers and Geothehnics, 1991, 12(4): 321-346

[8] DawsonE. M., RothW. H., DrescherA.. Slope stability analysis by strength reduction [J]. Geotechnique, 1999, 49(6): 835-840

[9] MichalowskiR. L.. Slope stability analysis: A kinematical approach [J]. Geotechnique, 1995, 45(2): 283-293

[10] FraldiM., GuarracinoF.. Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(4): 665-673

[11] MerifieldR. S., LyaminA. V., SloanS. W.. Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6): 920-937

[12] Carranza-TorresC., FairhurstC.. The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(6): 777-809

[13] LiA. J., MerifieldR. S., LyaminA. V.. Stability charts for rock slopes based on the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(5): 689-700

[14] JimenezR., SerranoA., OlallaC.. Linearization of the Hoek and Brown rock failure criterion for tunnelling in elasto-plastic rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(7): 1153-1163

[15] YangX.-li.. Seismic displacement of rock slopes with nonlinear Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(6): 948-953

[16] 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

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

[18] HoekE., BrownE. T.. Practical estimate the rock mass strength [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8): 1165-1186

[19] YangX. L., YinJ. H.. Slope stability analysis with nonlinear failure criterion [J]. Journal of Engineering Mechanics, 2004, 130(3): 267-273

[20] 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

[21] YangX. L., YinJ. H.. Linear Mohr-Coulomb strength parameters from the nonlinear Hoek-Brown rock masses [J]. International Journal of Non-linear Mechanics, 2006, 41(8): 1000-1005

[22] RafaelJ., AlcibiadesS., ClaudioO.. Linearization of the Hoek and Brown rock failure criterion for tunneling in elasto-plastic rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(7): 1153-1163

[23] HoekE., BrownE. T.. Practical estimate the rock mass strength [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8): 1165-1186

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