Geotechnika - Fakulta stavební - Vysoké učení technické v Brně

76 12 th International Scientific Conference, April 20-22, 2009 Brno, Czech RepublicXah= 1 + ρ ;aXbh= 1 − ρbKnowing the average normal stress (p i ) and the radial ring deformation (u i ) then thehomogenized shear modulus (G * ) can be drawn out regarding the assumption.ua(GG*a*( G ) = 2u ( G )) + ubbGa⋅ a + G=a + bFollowing analysis step merges single homogenized rings (G i ) into one homogeneous wallsection (G *C ). The merging of rings starts off with the first two internal rings (G 1, G 2 ) making onefrom them (G *C 1). The homogenization of two adjoined rings is conditioned again with radialdisplacement on the outer ring periphery (u 0 ).*Cu0( R0, R2,G)1 =u0bi⋅ b( R , R ,G ,G )When formulae (1) for the radial displacement on the outer ring periphery (u Θ ).is implementedin condition above then the formula for (G *C ) can be extracted.1212c =R2R1;*c=R2R0;* =⎛*2 ⎞⎜c−1⎟⎛d/K ( G ,G2) d⎞⎜ 1−′0 1 2 ⎟⎝ ⎠⎝⎠d c2′′ = 2 −4μ+ 2 ; d′= 4 −4μ; d = c*2 −4μ+G c1*′d G⎛c21 21⎞⎜ − ⎟⎝ ⎠( ) ( ) 22*1Then the merging of rings advances in repetitious way joining up last homogenised one (G i *C )with the next single ring (G i+1 ) till the last sigle ring is merged and the final (G *C ) attained.ConclusionIn both approaches a true section is substituted with fictitious one. The concept of ringscooperation gives an advantage over the steel concrete design in respect with to state the truesection dimension which goes well to static analysis of tunnel lining sustaining structuredimensions. The redistribution coefficients provide for reverse estimation of stress state in the allsection materials. It facilitates to work out a time dependency of a deformation propertiesdevelopment during a shotcrete setting as a tunnel lining is built up in steps. Proposed method canbe fair enough when section materials act as elastic and there is continuous displacement onsuperficies of section parts.AcknowledgementsThis paper is part of a research program provided by Czech Grant Agency under No. GACR103/09/1438 “An investigation of the deformation and strength properties of a shotcrete shellreinforced with stiff steel truss sections“. The authors greatly appreciated this support.Literature[1] Bulytchev, N. C. Mechanika podzemnych sooruženij. Moskva : NEDRA, 1982. 270 p.