...<Xl: COVE.R f~ J Figure I. Norwegian practice regarding minimum rock cover. [redrawn after Arild Palmstrom]. ofthe1evelofsafetyfsafetyfactorlforther spec tivetunnels Itshou dbenot dthatthetwoempiri c lCUlWil u rat dnFig rl emai lmadn eba isofrafficunn sN rw y,whosecr ssctioa erm lybout50 70m2 Soic uldbeconcludedthattherl s edin mumckvsb edwh np o tp wna h smi mum Onegshouldbh ykccx a tund rdra n dcondition whichr aasu n i gd ty s pb wt11ickn s8 fko dd e si n f·3 1 D gP"P J 72 2J m n uw f wT e d b dp h i m mrockpo smflfu l For Equationds r rid c (L1 2007) whi hg vby Q 12zkL( H+h)Inl ( ) Q= a el w(m3 rockb a o n ) H=waterv ) =t icknessv n L= u neg r un elT mt d ivofEqueq lz Thf t ingt on h pck dm -gyEq 2Thjsod lh sp ks b a ampN au l I b m hodgcewh u c tab l yHowev r,ithd lrk gb ityfth unn l particularly,ng yI cy i hhip3PROPOSEDMODELSwp f neltabi ty, wopf rm ingga ckmas mo e e usv l ,wh chc tA pp x mppD (2005) w is r gof roundy zM -C lombiu g111 ckU igcf cr p gelkd o Ffim ty,nre Sy cd e dgI3(4w rB yu w ' ofck yh g d11 a dF g25 +hH leM h -C b q= 0'LA2 C h usoverL J+ P= of the level of safety (safety factor) for the respec- tive tunnels. It should be noted that the two empiri- cal curves illustrated in Figure I, are mainly made on the basis of traffic tunnels in Norway, whose cross section are normally about 50- 70m2 So it could be concluded that the curves illustrated in Figure I do not indicate any relationship between thickness of rock cover and dimension of tunnel. 2.2 Japanese minimum water inflow model The model is based on the concept that the minimum rock cover corresponds to the minimum water inflow for a subsea tunnel. For this method, Equation I is used as the criteria to predict water inflow for a tunnel (Li et al. 2007), which is given by. (I) where, Q =water inflow (m3/s); k =rock mass perme- ability around tunnel (m/s); H =water depth above tunnel (m); h =thickness of rock cover above tunnel (m); L = tunnel length (m); r = tunnel radius (m). To obtain the minimum water inflow in a tun- nel, we take the derivative of Equation I equal to zero. Then a function illustrating the relationship between rock cover, water depth and tunnel dimen- sion is given by Equation 2. r (!i+l) h=-e h 2 (2) This model has been applied to determine mini- mum rock cover in several subsea tunnels, one example is Nagashima subsea tunnel. It seems a 'reasonable' method for planning since water ingress would highly influence the cost and constructability of a sub water tunnel. However, it should be noted that the equations above do not take into account mechanical parameters of rock mass surrounding the tunnel and the stability of the tunnel, particularly, in the case that tunneling is done under high water head and rock mass has high permeability. In fact, the minimum rock cover only is only determined by water depth and tunnel dimension, without any rela- tionship with the permeability of rock mass. 3 PROPOSED MODELS From the viewpoint of tunnel stability, two models are proposed for determining optimal rock cover in subsea tunnel corresponding to cases of homo- geneous rock mass and inhomogeneous rock mass respectively, which are based on the concept that minimum rock cover is obtained when support pressure at crown reaches to the minimum. One thing should be noted that models propose here only take into account that tunnel is excavated under drained condition, which is the normal case in most of tunneling. 3.1 Homogeneous model An approximate solution for support pressure at crown is given by Dimitrios (2005), which assumes that the strength of the ground at crown is fully mobilized and complies with the Mohr-Coulomb failure criteria and is used here to deviate models on determining the minimum rock cover. Unlike undrained condition where tunnel lining could be exposed to the full hydrostatic water pres- sure, seepage force shall be taken into account in the case of drained condition. For the sake of simplicity, here we assume the distribution of water pressure above the crown is linear. So the hydraulic gradient head i and the seepage force s1 are given by. . dp H+h 1 dh h where r . =water density. (3) (4) By increasing the buoyant unit weight y of the rock mass by the seepage force ir the support pressure exerted by the ground upon the crown of a sub water tunnel, illustrated in Figure 2, can be expressed as Equation 5. r' cco.s¢ h rc 1-sm¢ H +h Pc= h sin¢ +r., h sin¢ 1+ - -- 1 'c 1 - sin¢ rc 1 - sin ¢ ater Bedrock 1\ lohr- oulomb: r.c,, qH H h (5) Figure 2. Cross section of a sub-water tunnel with homogeneous rock cover. 446 whereZ=thecurva ureradiusoftherownuniteiglltof ckma s c=cohesionockm ssfri tionanglemass T k gatp es rq=Y H=astb und·ylpad ngbedrockurfa e showsFi re3 th nEquation5nexpr dEq a on6 2 c1- in1 isth f entmechanicalperform ances Illustratedv tic lstr ym tryiABCi m den yd butedver hz Tpriman lva io k plicity, rerwoyd f ockl yersbovew h wn3 Thcn ws ss on G r yea g tun lingve - odf llldblastt sfiesIt on Ich nghao p t y,1 e thepouP S0f u 6wegq m mn sockb vwh 7 H # 1 ine+ or ,wymvEq 7 Obviou ly,itu m n s r ckm sasocd inguv AbyD i i (2005) itthaC6 p sf a hupppressur Inl vlpo 3 2 m g usI r ckvg s i there B^g df (p) dcfky (po t· u hv w h r s dZ( z2 B w( c w (pC d t bu fhev r cal d I J11R bly,pjj c p di ula b d , v dsc y Thu the j c orywi huo llu edT stapp heshpr maryP P -h atgu gJ 'loEquat3 wel ithin z ^ yf w gx n 1_e-2Kd4zlrm r(8)cif- nv 4=t n 1 Andg a o a ) 2+6 +6 7 ( =q thebound d ckff s2 b3 3 q0-1 w (lym z dm liM -C omb c 3 C fw h v ( 6 n 447 where r,: = the curvature radius of the crown; r= unit weight of rock mass; c =cohesion of rock mass; ¢ = friction angle of rock mass. Taking water pressure q = r. H = as the bound- ary load acting on the bedrock surface, shown as Figure 3, then Equation 5 can be expressed as Equation 6. h ccos¢ q -+ yfl _ rc I-sm¢ Pc - h sin¢ 1 rc 1-sin¢ (6) Generally speaking, tunneling with conven- tional method (drill and blast) satisfies the drained condition. In such case, assuming that no support is necessary, i.e. the support pressure p, $ 0, then from Equation 6 we get the required minimum thickness of bedrock above the crown h. h> y.,H - I ccos¢ y rc 1-sin¢ (7) Therefore, we can theoretically determine the minimum rock cover for a sub water tunnel from Equation 7. Obviously, it does take tunnel dimen- sion, rock mass mechanical parameters and water depth into account for determining the minimum rock cover. As mentioned...