92 Van hung DAO．Wa r Science and Engineering。Sep．2009，Vo1．2，No．3，87-95
Plastic region radius(m) 9．5 9．O 8．5 8．0 7．5 7．0 6．5 6．0 5．5 5．0
Elastic region radius(Il1)
Fig．5 Rock stress within plastic region Fig．6 Rock stress within elastic region
Displacement“r(m)
Fig．7 Stress release coefficient of tunnel boundary Fig．8 Interactive curve between ground base and
without support along tunnel axis supporting structures for diferent initial displacements
Based on the Fenner-Pacher theory and The Vietnamese Construction Design Standard
厂Dr Underground Works(Ministry of Construction 2003)，we compared the pressure on the
supporting structures with the m aximum pressure value that the supporting structures are able
to bear(which is equal to the stress at the elasto—plastic boundary O're)to analyze the above
results．It con be concluded that：
Supporting structures installed when the initial displacement Uo：0．083 m result in the
following： There iS imm ediate consolidation after the tunnel excavation． Pressure on
supporting structures ei=6．902 M Pa> =4．019 5 MPa．W ith unfavorable operation of
supporting structures，the rock continues deforming after the support is in place．This results in
local instability．
Supporting structures installed when the initial displacement Uo：0．087 m result in the
following：Consolidation occurs at a distance of =1．O05ri= 1．708 5 m．and the stress release
coefi cient =0．481 7．Pressure on the supporting structure =3．781 8 M Pa < =
4．0 1 9 5 MPa．The rock has suficient deformation，and the tunnel is stable．
Supporting structures installed when the initial displacement Uo：0．093 m result in the
Van-hung DAO．Water Science and Engineering,Sep．2009，Vo1．2，No．3，87-95 93
一∞邕 一0= > ∞2Is 言dl乏 ； 》 h
言白 ) 2；∞∞ 口 0焉pIIo兽0u
following：Consolidation occurs at a distance of x=2．2，：=3．74 m．and the stress release
coefi cient =O．732 7．Pressure on the supporting structmcture =1．95 1 1 M Pa 《 =
4．019 5 MPa．The rock has major deformation，indicating that the tunnel can be unstable．
Supporting structures installed when the initial displacement u0=O．097 m result in the
following：Consolidation occurs at a distance of x=4 ：6．8 m，and the stress release
coefi cient =0．868．Pressure on the supporting structmcture =0．963 2 MPa 《 =
4．019 5 M Pa．Rock deformation is too great；there can be rock loosening of the tunnel roof
causing the increase of rock pressure．The tunnel is unstable． Th us，in this case，we can say that at each time，with a certain displacement u0 ranging
from 0．086 5 m to 0．09 1 9 m．we can install supporting structures that satisfy the stability and
economical requirements． 4 Conclusions
In general，the determination of initial displacement“o described in this study is more
accurate and detailed than assumptions of the initial displacement value蹦0(Vu and Do 2007)．
Values of u0 depend on the stress release effect and，when compared，provide a more
complete solution than the solution with curves that exclude the stress release effect(Hoek and
Brown 1980；Wiliams 1997)．
The survey described above has shown that the convergence—confinement method is an
efective design tool for obtaining appropriate supporting time．It
is completely different from
the traditional tunnel design method，which applies the early consolidation and quickly lining
installation rules，considers the supporting structures provisional supporting structures to bear
loads of loosened rock，and ignores the load—bearing capacity of rock masses．
However,the problem is limited to the two—dimensional elasto—plastic model，hydro—static
inital stress field and circular tunnel cross—section．Therefore．in the case of rock with a
non—hydrostatic stress field，or of non—circular tunnel cross—sections，the destructive models
such as the non．homogeneous elasto—plastic，visco—elastic，and brittle models，need to be
studied so that the convergence—confinement method can be applied more widely in tunnel design．
References
Anagnostou，G，and Kovari，K．1993．Significant parameters in elastoplastic analysis of underground openings．
JournalofGeoteehnicalEngineering，l19(3)，401-419．[doi：10．1061／(ASCE)0733—9410(1993)119：3(401)】
Brady,B．H．G，and Brown，E． 2004．Rock Mechanicsfor Underground Mining．Dordrecht：Kluwer Academic
Publishers．
Carranza Torres，C．，and Fairhurst，C．1999．The elasto—plastic response of underground excavafions in rock
masses that sarisfy the Hoek．Brown failure criterion．InternationaZ JouFnaZ ofRock Mechanics and Mining
Sciences。36(6)，777—809．
Carranza-Torres，C．，and Fairhurst，C．2000．Application of the convergence—confinement method of tunnel
design to roc k masses that sarisfy the Hoek—Brown failure criterion．Tunneling and Underground Space
Technology,15(2)，187—213．fdoi：10．1016／S0886—7798(00)00046—8】
Carranza-Torres，C．，Alonso，E．，Alejano，L．R．，Varas，F，and Fdez—Manin，G 2002．Elasto—Plastic analysis of
94 Van-hung DAO．Water Science and Engineering，Sep．2009，Vo1．2，No．3，87—95
deep tunnels in britile rock using a scaled form of the M ohr-Coulomb failure criterion．Hammah，R．，
Bawden，W ，Curran，J．，and Telesnicki，M．，eds．，Proceedings of the 5th North American Rock Mechanics
Symposium and the 17th Tunnelling Association of Canada Conference(NARMS—TAC 2002)：Mining and
Tunnelling Innovation and Opportunity，283—293．Toronto：University of Toronto．
Carranza—Torres，C．2003．Dimensionless graphical representation of the exact elasto—plastic solution of a circular
tunnel in a Mohr-Coulomb material subject to uniform far-field stressess．Rock Mechanics and Rock
Engineering，36(3)，237—253．[doi：10．1007／s00603—002—0048—7Rock]
Chern，J．C．，Shiao，E and Yu，C．W 1998．An empirical safety criterion for tunnel construction．Proceedings
ofRegional Symposium on Sedimentary Rock Engineering,222—227．Taipei，China．