·298· 工程科学学报，第38卷，第2期 Osman A S.Stability of unlined twin tunnels in undrained clay linedtunnel at great depth.Int J Rock Mech Min Sci,2008,45 Tunnelling Underground Space Technol,2010,25(3):290 (4):486 [6]Kim S H,Burd HJ,Milligan G W E.Interaction between closely [16]Exadaktylos G,Liolios P,Stavropoulou M.A semi-nalytical e- spaced tunnels in clay /Proceedings of International Symposium lastic stress-displacement solution for notched circular openings in on Geotechnical Aspects of Underground Construction in Soft rocks.Int J Solids Struct,2003,40(5)1165 Ground.London:Balkema,1996:548 [17]Dejoie A,Mogilevskaya S G,Crouch S L.A boundary integral Wen X M.Yang J H,Zhu HH.Experimental study on reasona- method for multiple circular holes in an elastic half-plane.Eng ble distance of tunnels with small spacing.Adr Mater Res,2011, Anal Boundary Elem,2006,30(6)450 368-373:2621 [18]Chen Z Y.Analytical Method for Rock Mechanical Analysis.Bei- [8]Xu D J,Geng N G.The variation law of rock strength with in- jing:Coal Industry Press,1994 crease of intermediate principal stress.Acta Mech Solida Sin, (陈子荫.围岩力学分析中的解析方法.北京：煤炭工业出 1985,6(1):72 版社，1994) (许东俊，歌乃光.岩石强度随中间主应力的变化规律.固体 19 Deng C J,He G J,Zheng Y R.Studies on Drucker-Prager yield 力学学报，1985,6(1)：72) criterions based on M-C yield criterion and application in Shi W C,Zhu J G,Liu H L.Influence of intermediate principal geotechnical engineering.Chin J Geotech Eng,2006,28(6): stress on deformation and strength of gravel.Chin Geotech Eng, 735 2008,30(10):1449 (邓楚键，何国杰，郑颖人.基于MC准则的DP系列准则 (施维成，朱俊高，刘汉龙.中主应力对砾石料变形和强度的 在岩土工程中的应用研究.岩土工程学报，2006,28(6) 影响.岩土工程学报，2008,30(10)：1449) 735) [1]Li AZ.Zhang LQ.Mechanical Analysis of the Underground D20]Li T,Zhao G M,Meng X R,et al.Analysis on plastic zone in Tunnel Using the Function of Complex Variables.Beijing:Sci- surround rock of mime circular type gateway in non-niform stress ence Press,2007 field with centre main stress considered.Coal Eng,2014,46 (吕爱钟，张路青.地下巷道力学分析的复变函数方法，北 (3):68 京：科学出版社，2007) (李涛，赵光明，孟样瑞，等.考虑中间主应力的非均匀应力 [11]Mogilevskayasg S G,Crouch S L.A Galerkin boundary integral 场圆形巷道围岩塑性区分析.煤炭工程，2014,46(3)：68) method for multiple circular elastic inclusions with homogeneously 21] Zhao W,Cao P,Zhang G.Rock Mechanics.Central South Uni- imperfect interfaces.Int J Solids Struct,2002,39(18):4723 versity Press,2010 [12]Addenbrook T I,Potts D M.Twin tunnel interaction:surface and (赵文，曹平，章光.岩石力学.长沙：中南大学出版社， subsurface effects.Int J Geomech,2001,1 (2):249 2010) [13]Zhang LQ.Lii AZ.Study of alteration method for stress analy- 22]Zhang X B,Zhao G M,Meng X R.Elastoplastic analysis of sur- sis on surrounding rocks of two circular holes.Chin J Rock Mech rounding rock on circular road way based on Drucker-Prager Eng,1998,17(5):534 yield criterion.J China Coal Soc,2013,38(1):30 (张路青，吕爱钟.双孔圆形洞室围岩应力分析的交替法研 (张小波，赵光明，孟祥瑞.基于Drucker-Prager屈服准则的 究.岩石力学与工程学报，1998,17(5)：534) 圆形巷道围岩弹塑性分析.煤炭学报，2013,38(1)：30) [14]Su F,Chen F Q,Shi Y Z.Analytie continuation solution of deep 23]Hu J Y.Study of numerical simulation analysis of reasonable twin-unnels.Chin J Rock Mech Eng,2012,31(2)365 spacing at small-distance tunnel.Highw Tunnel,2007(4):26 (苏锋，陈福全，施有志.深埋双隧洞开挖的解析延拓法求 (胡居义.确定小净距隧道合理净距的数值模拟研究.公路 解.岩石力学与工程学报，2012,31(2)：365) 隧道，2007(4)：26) [15]Li S,Wang M.An elastic stress-isplacement solution for a工程科学学报，第 38 卷，第 2 期 ［5］ Osman A S． Stability of unlined twin tunnels in undrained clay． Tunnelling Underground Space Technol，2010，25( 3) : 290 ［6］ Kim S H，Burd H J，Milligan G W E． Interaction between closely spaced tunnels in clay / / Proceedings of International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground． London: Balkema，1996: 548 ［7］ Wen X M，Yang J H，Zhu H H． Experimental study on reasona￾ble distance of tunnels with small spacing． Adv Mater Ｒes，2011， 368 － 373: 2621 ［8］ Xu D J，Geng N G． The variation law of rock strength with in￾crease of intermediate principal stress． Acta Mech Solida Sin， 1985，6( 1) : 72 ( 许东俊，耿乃光． 岩石强度随中间主应力的变化规律． 固体 力学学报，1985，6( 1) : 72) ［9］ Shi W C，Zhu J G，Liu H L． Influence of intermediate principal stress on deformation and strength of gravel． Chin J Geotech Eng， 2008，30( 10) : 1449 ( 施维成，朱俊高，刘汉龙． 中主应力对砾石料变形和强度的 影响． 岩土工程学报，2008，30( 10) : 1449) ［10］ Lü A Z，Zhang L Q． Mechanical Analysis of the Underground Tunnel Using the Function of Complex Variables． Beijing: Sci￾ence Press，2007 ( 吕爱钟，张路青． 地下巷道力学分析的复变函数方法． 北 京: 科学出版社，2007) ［11］ Mogilevskayasg S G，Crouch S L． A Galerkin boundary integral method for multiple circular elastic inclusions with homogeneously imperfect interfaces． Int J Solids Struct，2002，39( 18) : 4723 ［12］ Addenbrook T I，Potts D M． Twin tunnel interaction: surface and subsurface effects． Int J Geomech，2001，1( 2) : 249 ［13］ Zhang L Q，Lü A Z． Study of alternation method for stress analy￾sis on surrounding rocks of two circular holes． Chin J Ｒock Mech Eng，1998，17( 5) : 534 ( 张路青，吕爱钟． 双孔圆形洞室围岩应力分析的交替法研 究． 岩石力学与工程学报，1998，17( 5) : 534) ［14］ Su F，Chen F Q，Shi Y Z． Analytic continuation solution of deep twin-tunnels． Chin J Ｒock Mech Eng，2012，31( 2) : 365 ( 苏锋，陈福全，施有志． 深埋双隧洞开挖的解析延拓法求 解． 岩石力学与工程学报，2012，31( 2) : 365) ［15］ Li S，Wang M． An elastic stress-displacement solution for a linedtunnel at great depth． Int J Ｒock Mech Min Sci，2008，45 ( 4) : 486 ［16］ Exadaktylos G，Liolios P，Stavropoulou M． A semi-analytical e￾lastic stress-displacement solution for notched circular openings in rocks． Int J Solids Struct，2003，40( 5) : 1165 ［17］ Dejoie A，Mogilevskaya S G，Crouch S L． A boundary integral method for multiple circular holes in an elastic half-plane． Eng Anal Boundary Elem，2006，30( 6) : 450 ［18］ Chen Z Y． Analytical Method for Ｒock Mechanical Analysis． Bei￾jing: Coal Industry Press，1994 ( 陈子荫． 围岩力学分析中的解析方法． 北京: 煤炭工业出 版社，1994) ［19］ Deng C J，He G J，Zheng Y Ｒ． Studies on Drucker-Prager yield criterions based on M-- C yield criterion and application in geotechnical engineering． Chin J Geotech Eng，2006，28 ( 6) : 735 ( 邓楚键，何国杰，郑颖人． 基于 M--C 准则的 D--P 系列准则 在岩土工程中的应用研究． 岩土工程学报，2006，28 ( 6) : 735) ［20］ Li T，Zhao G M，Meng X Ｒ，et al． Analysis on plastic zone in surround rock of mime circular type gateway in non-uniform stress field with centre main stress considered． Coal Eng，2014，46 ( 3) : 68 ( 李涛，赵光明，孟祥瑞，等． 考虑中间主应力的非均匀应力 场圆形巷道围岩塑性区分析． 煤炭工程，2014，46( 3) : 68) ［21］ Zhao W，Cao P，Zhang G． Ｒock Mechanics． Central South Uni￾versity Press，2010 ( 赵文，曹平，章光． 岩石力学． 长沙: 中南大学出版社， 2010) ［22］ Zhang X B，Zhao G M，Meng X Ｒ． Elastoplastic analysis of sur￾rounding rock on circular road way based on Drucker--Prager yield criterion． J China Coal Soc，2013，38( 1) : 30 ( 张小波，赵光明，孟祥瑞． 基于 Drucker--Prager 屈服准则的 圆形巷道围岩弹塑性分析． 煤炭学报，2013，38( 1) : 30) ［23］ Hu J Y． Study of numerical simulation analysis of reasonable spacing at small-distance tunnel． Highw Tunnel，2007( 4) : 26 ( 胡居义． 确定小净距隧道合理净距的数值模拟研究． 公路 隧道，2007( 4) : 26) · 892 ·