Research on determination of optimal distance between two unsupported tunnels when consideration to shape changes

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1 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam Reeach on detemination of optimal ditance between two unuppoted tunnel when conideation to hape change Tan Tuan Minh a *, Nguyen Duyen Phong b a Ha Noi Univeity of Mining and Geology b Mocow tate mining univeity * Coeponding autho tuanminhhumg@yahoo.com Abtact Detemination ditance between two tanpot tunnel i vey impotant poblem and ha influence on the tability calculation and tunnel deignation. Howeve, nowaday in Viet Nam thi poblem ha many diadvantage. Thi pape intoduce the tudying on detemination of optimal ditance between two tanpot tunnel when conideation to hape change bae on numeical method in Viet Nam geological condition. 1. Intoduction Vietnam i one of the mot beautiful countie located in the South Eat Aia (figue.1). In the Noth, Vietnam hae the long bodeline with China. In the Eat, Vietnam i bodeed by the Gulf of Tonkin, in the Eat and South by the South China Sea, in the South Wet by the Gulf of Thailand, and in the Wet by Cambodia and Lao. Owning to tetching the length of the Indochinee Peninula, Vietnam boat a unique hape of an elongated S and a long coatline of 3,60 km with a lot of wondeful ite. Although Vietnam lie entiely within the topic, the Vietnam climate upiingly vaie fom egion to egion with the annual aveage tempeatue fom ºC to 7ºC becaue of it topogaphy. The mountainou people of Fig.1. Location of Viet Nam Sapa in the noth might be eeking helte fom now while the uban dwelle of Ho Chi Minh City in the outh eek efuge fom mid-day heat. Although it i a mall county with the aea of 39,560km, thee ae up to 54 diffeent ethnic goup inhabiting in Vietnam, of which Kinh (Viet) people account fo nealy 86% of the whole population, and the othe ae ethnic minoity goup that epeent about 14%. To develop induty in Viet Nam in the futue we need building many hydoelectic powe plant, themal powe plant, atom powe plant and othe enegie to develop county, which can be lited a following: Hoa Binh Hydopowe plant (figue a) wa built fom 1979 to 1994 with 8 machine povide 190MW- 1/3 poductivity of Vietnam. It i not only an impotant indutial contuction but alo an attactive ighteeing fo viito. Many valuable item uch a: Ho Chi Minh tatue on Tuong hill with 18m height, the taditional aea keeping lette, memoial Vietnamee and Soviet expet acifice to built hydopowe poject. Along with the function of ocial, economic, Hoa Binh hydoelectic become an exciting detination fo viito. The Son La Hydopowe Plant (figue b) with a deigned capacity of,400 MW and ix geneato ha been completed much ealie than cheduled, binging huge economic benefit. Evey yea it will ceate a tunove of 500 million USD and ave ove five million tone of coal which will be needed to poduce an equivalent amount of electicity. Moeove, the plant will upply on aveage

2 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam 10, billion kwh/yea to the national gid, one othe hand nowaday i located in Son La povince Huoi Quang hydoelectic powe plant ha powe 50MW and built on the Nam Mu ive, which flow between Son La and Lai Chau alo i big hydoelectic powe plant in Viet Nam. a) b) Fig.. Hoa Binh and Son La hydoelectic powe plan in Viet Nam In the field of undegound contuction excavation two tunnel i tendency duing building tanpot tunnel in geneal and pecially fo vehicle tunnel. Thi wok (figue 3) will allow moe conveniently fo movement equiement than ingle tunnel, avoid taffic jam in the tunnel o ik duing ca moving in tunnel. In deignation poce and excavation tunnel the detemination appopiated ditance between two tunnel i vey impotant poblem to ecue tability fo tunnel alo degeae co ditance tunnel between them. In Viet Nam tanpot tunnel wee built a Hai Van pa tunnel poject (figue 3b). Which Contuction began in Augut 000, the poject cot ome 150 million dolla in expene and involve moe than,000 contuction woke. The tunnel egment i plit into two pat, the 4km outhen potion, contucted by Japanee contuction company Hazama, and the km nothen potion contucted by a Vietnam-South Koea joint ventue. Deo Ca tunnel (figue 3a) The poject ha a total length of 13,4km, with Ca Pa Tunnel and Co Ma Tunnel tetching 3,9km and 500m epectively. It tat fom Hoa Xuan Commune in Phu Yen Dong Hoa Ditict and end at Van Tho Commune in Khanh Hoa Van Ninh Ditict. The tunnel will be deigned in line with local expeway tandad allowing fo a deigned peed of 80km an hou. Steel and einfoced concete teel will be ued fo building the tunnel bidge, and othe tunnel poject in Viet Nam will be built in the futue. a) Deo Ca tunnel b) Hai Van tunnel Fig. 3. The ytem of two paallel tunnel in Viet Nam. The te and defomation aound ingle cicula tunnel Today poblem fo olving the te and defomation aound cicula tunnel ae accepted bae on elatic medium by many autho can be howed a following Kih, Lame [5, 6]. Howeve Tezaghi and Richat (1995) imulated poblem of haft plan in platic ock, which can be hown in figue 4.

3 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam Tezaghi and Richat (1995) howed that, component of the te and defomation at any point aound cicula tunnel with adiu a, and vetical eath peue P can be etimated by fomula a following: Fig. 4a. The concentation of the te aound cicula tunnel in ock ma 4 P a 3a 4a co (1) 4 a 3a co P 4 4 P a 3a 1 1 in 4 (3) u Pa Ed Pa Ed P 1 E a 1 1 co 4 1 v co a 1 1 co 41 v co a u1 1 v a 1 (5) d Whee - hoizontal peue atio of ock ma; E d - defomation modulu of ock ma; v - Poion atio of ock ma. It i attention that in the te fomula above, the tee don t depend on value of defomation modulu E d of ock ma. In the fact fo olving thi poblem ome extenomete had been intalled fo contol the elationhip of diplacement u 1 between the point of 1 at the poition = a and point at the poition = (figue 4). We can eceive the value of diplacement u 1 a in fomula (5). Bae on the fomula (1), () and (3) at the ditance = (4-5)a, the value of tee will be the intitute te. Aumption inne peue in tunnel i p i the olution in thi cae can be witten a following: a p i (6) a p i (7) vapi u 1 (8) E d (4) ()

4 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam The eult in thi cae how that in the fact tangential te i tenion. In pecial cae when medium i hydotatic, the olution can be hown a in figue 5. The eult how that total te of tangential and adial te will be two vetical tee at any point in ock ma, and they ae witten a following: P a a 1 p i (9) P a a 1 p i (10) P (11) vp pi a ua 1 (1) Ed The above fomula eceived fo haft plan model (longitudinal te will be zeo). The olution will be modified a litte fo haft plan medium by eplacing Poion atio in above fomula (Jaege and Cook, 1969). v v (13) 1 v Ed Ed 1 v (14) Fotunately fomula (5), (8) and (1) will be contant fo poblem in haft plan. Thee fomula can be eceived by compaion diplacement with majo tee fo haft plan poblem ( = 0) and in plan tain ( = 0 o = v( ). Recently, Caanza and Faihut (000) ecommended empiical fomula fo detemination of adial diplacement u at any ditance x in font of tunnel uface (x 0) and behind uface (x > 0) to potal of tunnel in cae cicula tunnel in hydotatic medium a following: 1.70 Fig. 4b. The ditibution of te aound cicula tunnel in hydotatic medium fo haft plan x a u e (15) u = 0.31 at x = 0 (on the tunnel uface) = 1.0 at x = = 0 at x - Radial diplacement u = u a (with p i = 0 (in fomula (1)). 3. Numeical model fo detemination optimal ditance between two tunnel Nowaday the development of compute and cience, numeical method ae moe and moe ued widely fo deignation and calculation tunnel uppot in ock engineeing alo in the field of undegound contuction. One of the mot impotant poblem in ock mechanic i mechanical alteation (changing the value of te and defomation) aound opening afte excavation [1,, 3, 4, 5]. When known thi alteation to pemit deigne effective definition of type of ock uppot and tability tunnel. To analyze and deteminate optimal ditance between two tunnel without ock uppot in thi cae we ue numeical method by Examine D bae on bounday element method [4]. Detail of paamete of ock ma fo analyi can be hown a following: unit weight of ock = 0,0 MN/m 3 ;

5 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam uniaxial compeive tength of intact ock ci = 5 MPa; defomation modulu E m = 600MPa; Poion atio of ock ma = 0,3; geological tength index GSI = ; mateial contant m i = 6; ditubance facto D = 0,3; deep tunnel located H = 5m; pan (diamete) of tunnel B (D) = 10m. By oftwae Examine D we can imulate model fo analyi and eceive the ditibution of te aound two tunnel that i hown a in figue 6. a) Cicula tunnel b) Tunnel with ac and vetical wall c) Hoe hape tunnel Figue 6. The ditibution of vetical te aound two unuppoted tunnel by Examine D One othe hand by Examine D the ditibution of total diplacement aound tunnel with othe hape can be een a in figue 7.

6 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam a) Cicula tunnel b) Tunnel with ac and vetical wall c) Hoe hape tunnel Figue 7. The ditibution of total diplacement aound tunnel by Examine D Bae on the analyi eult by Examine D and othe ditance between two tunnel above, we can eceive the value of te and diplacement in ock ma between two tunnel. By them we can etablih the elationhip te - diplacement and ditance between two tunnel, they ae een a in figue 8.

7 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam Ste 1 (MPa) Ditance two tunnel 0m Ditance two tunnel 5m Ste 1 (MPa) Ditance two tunnel 5m Ditance two tunnel 0m Ditance two tunnel 5m Total diplacement (m) Ditance two tunnel 0m Ditance two tunnel 5m a) Cicula tunnel b) Tunnel with ac and vetical wall c) Hoe hape tunnel Ste 3 (MPa) Ditance two tunnel 0m Ditance two tunnel 5m Ste 3 (MPa) Ditance two tunnel 0m Ditance two tunnel 5m Ste 3 (MPa) Ditance two tunnel 0m Ditance two tunnel 5m a) Cicula tunnel b) Tunnel with ac and vetical wall c) Hoe hape tunnel Total diplacement (m) Ditance two tunnel 0m Ditance two tunnel 5m Total diplacement (m) Ditance two tunnel 0m Ditance two tunnel 5m Total diplacement (m) Ditance 10m Ditance 15m Ditance 0m Ditance 5m Ditance 30m Ditance 35m a) Cicula tunnel b) Tunnel with ac and vetical wall c) Hoe hape tunnel (Attention: The fit point and the end point in any gaphic ae located on bounday tunnel) Figue 8. Ste and diplacement in ock ma aound two tunnel and ditance between of them

8 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam To deteminate optimal ditance between two tunnel we have to etablih the elationhip of te and diplacement of ock ma at any point fom thi tunnel to othe tunnel with othe ditance of them. When the value of te and diplacement ae equilibium to initial te, we can eceive optimal ditance between two tunnel. By Examine D we can etablih the elationhip between te and diplacement of ock ma at the middle point of ditance two tunnel a in figue 9. Vetical te 1, MPa Ditance between two tunnel, m a) Vetical te in ock ma aound two tunnel Cicula tunnel Tunnel with ac and vetical wall Hoe hape tunnel Total diplacement (m) Cicula tunnel Tunnel with ace and vetical wall Hoe hape tunnel b) Total diplacement in ock ma aound two tunnel Figue 9. The elationhip te, diplacement and ditance between two tunnel Seeing eult in figue 7 and 8 we can how that when te become initial te = H = 0,0x5 = 0,5MPa and diplacement of ock ma at the middle point two tunnel ae contant, we can eceive optimal ditance fo two tunnel. The eult in analyi alo how that in cae two tunnel ae cicula, thi ditance i ange fom 0 to 5m, hoe hape tunnel 30-35m, and two tunnel with ac and vetical wall 30-35m. 4. Concluion By above analyi we can ealize that excavation two tunnel i impotant poblem in the field of undegound contuction. The detemination ditance between two tunnel i vey difficult to olve by the cloe olution method but nowaday by numeical method bae on bounday element method (BEM) in Examine D oftwae eult can be hown the ditibution of te and diplacement of ock ma aound two tunnel. In cae of tunnel ae cicula and excavated in detail geological condition ditance between them ange fom 0-5m (4-5 time adiu of tunnel), tunnel hoe

9 Vietock015 an ISRM pecialized confeence Vietock Mach 015, Hanoi, Vietnam hape and tunnel with ac and vetical wall ditance fom thi tunnel to othe tunnel i 30-35m (5-6 time haft pan of tunnel). Commonly, damage zone aound excavated tunnel in cae of two cicula tunnel i anged fom 4-5 time adiu of tunnel. Thi eult i the ame a the eult in the cloe olution method. Howeve, in thi example becaue of changing tunnel hape tunnel with ac and vetical wall and tunnel hoe hape ae le tability moe than cicula tunnel o ditance between them ae be inceaed with ange fom 5-6 time 1/ tunnel pan. Analyi by modeling calculation will become moe quickly than othe method, when etting uppot peue inne tunnel we can etimate thi ditance fo uppoted tunnel. Refeence [1]. Nguyen Quang Phich, Rock mechanic, Ha Noi, 007. []. Nghiem Huu Hanh, Rock mechanic, Ha Noi, 004. [3]. Vo Tong Hung, Phung Manh Dac, Rock mechanic fo undegound contuction and mining, Ha Noi, 008. [4]. Nguyen Quang Phich et al, Application eeach ome numeical method fo calculation undegound contuction, B TĐ, Ha Noi, 006. [5]. B.H.G. Bady and E.T.Bown (004), Rock mechanic fo undegound mining, Dodecht. [6]. Dimitio Kolymba (005), Tunnelling and tunnel mechanic, Spinge - Velag Belin Heudelbeg Gemany. [7].