IDENTIFICATION OF STABILITY OF CONCRETE TUNNEL LINING USING COUPLED MODELING

Transcription

1 IDENTIFICATION OF STABILITY OF CONCRETE TUNNEL LINING USING COUPLED MODELING Kaila Weiglová, Technical University in Brno, Institute of Geoechanics, Brno, Czech Republic Petr Procházka*, Czech Association of Civil Engineers, Prague, Czech Republic 33rd Conference on OUR WORLD IN CONCRETE & STRUCTURES: August 2008, Singapore Article Online Id: The online version of this article can be found at: This article is brought to you with the support of Singapore Concrete Institute All Rights reserved for CI Preier PTE LTD You are not Allowed to re distribute or re sale the article in any forat without written approval of CI Preier PTE LTD Visit Our Website for ore inforation

2 33 rd Conference on OUR WORLD IN CONCRETE & STRUCTURES: August 2008, Singapore IDENTIFICATION OF STABILITY OF CONCRETE TUNNEL LINING USING COUPLED MODELING Kaila Weiglová, Technical University in Brno, Institute of Geoechanics, Brno, Czech Republic Petr Procházka*, Czech Association of Civil Engineers, Prague, Czech Republic Abstract In the paper influence of additional structural precaution is studied for exceptional tunnel engineering in extraordinary difficult conditions. In the case considered here study on tunnel lining stiffness influence is presented in reinforceent of shallow founded tunnels being engineered in exacting conditions of clayey soils. During realization of underground structures internal forces occur, which try to change utual position of the structure and neighborhood. It is well known that the difference in behavior between structural eleents and the overall syste is deterined by coplicated questions of genesis and processes of developent in the soil or rock ass, which during its existence got past and was subdued by large extent of external and internal influences. One of the ost iportant tectonic and induced dislocations appears. Since the identification of dislocations is difficult in the research we concentrated on original physical odel prepared in stands (relatively sall basin with front glazes wall) where experients are conducted based on physically equivalent aterial being also in geoetric siilarity with the real structures. Consequently, analogy exists between original and odel structure, which enables us prediction of behavior of underground structures and their surrounding rock in these extree and extraordinary conditions. In the paper, concentration in drawn on orientation of the discontinuity surfaces with respect to the tunnel axis, which were the deterining factors influencing the structure and its neighborhood. Practical results enabled us paraetric studies in physical scale odels. Also the influence of fiber reinforced linings were one of the ost iportant arguents in the studies. Keywords: Scale odeling, fiber reinforced concrete lining, tunnels, coupled odeling, eigenparaeters, aterial identification. Introduction Based on results which had been created and easured on pilot experients on a scale : 00 in the first stage uch ore coplicated conditions were siulated on a scale : 25, where spatial probles were solved also in dependence of a variable purchase and with horizontal discontinuity surfaces.

3 Both physical scale odels (experiental) and nuerical approach confired extreely high iproveent of long-lasting stability of the underground work and settleent of the overburden. Using the coupled odeling (experiental and nuerical) enabled one to quantify the values of variables. In the paper the approach consisting in couple odeling experiental and nuerical will be described. The experients are prepared on scale odels in stands (basins with glazed front sides and the length of 2- ), where physically equivalent aterials siulate the real situation. Based on siilarity rules very good agreeent with reality is attained. In nuerical odels finite eleents are used in 3D. Using the trick described by Transforation field leads to a new nuerical procedure, which can be used in coupled odeling. A nuerical approach is proposed in such a way that internal paraeters of a atheatical physically nonlinear odel are evaluated using partial results of experiental scale odels fro equivalent aterials, which can substitute in situ easureents. Consequently, although basically strongly nonlinear probles are solved, solution of linear algebraic equations is the final step of the approach for identification of values of internal paraeters characterizing aterial properties in atheatical siulation of reality. Tunnel face stability in dependence of a length of purchase, stress changes around the tunnel, and of tunnel lining stiffness is solved in this paper using the coupled odeling. Coupled odeling (close copliance of results fro nuerical and experiental treatents with structures or structural eleents) has becoe a very powerful tool for assessent of underground and others structures in various applications and for increasing the bearing capacity of the structures and econoic optiization it plays extreely iportant role. Effective application of odern nuerical ethods to solution of exacting static and stability probles of structures is liited by reliability of basic paraeters entering into the forulation of the probles and the solution. Aside fro physically-echanical properties described in nonlinear laws being valid for particular aterials identification of internal characteristics is also necessary for attaining realistic results. Deviations fro standard behavior of rock, soil and various reinforceents of underground structures, for exaple, appear in qualification of irreversible strain field, existence of dilation, contraction, validity of principle of effective aterial properties, discrete behavior of rock and soil ass at the liit values of stresses or strains, and other factors are of great interest to engineers and researchers. Experiental echanics serves a very good tool for iproveent of such inforation, which leads us to confiration or negation of assuptions used for assessent of structures. Siilarly, easureents on site are also iportant. Both latter ethods are tieconsuing, expenses deanding ways of prediction of the behavior of structures. This disadvantage can be overcoe using feedback between atheatical (nuerical) odel and experients. This can be done in two basic anners: - Convergence analysis, coparing results fro experients and pilot nuerical analysis and successively adjusting aterial paraeters in such a way that the nuerical results are in reasonable agreeent with the experiental. - Back analysis, or coupled odeling is defined as a process, in which a qualitative and quantitative easure of agreeent with experiental results is ensured in atheatical odel and suggests approaches, by virtue of which internal paraeters of different kind are adjusted to be in copliance with experients as close as possible. In ost cases fitting of physical laws (generalized Hooke s law, creep, relaxation, aging, etc.) is sought, but soeties new geoetry arrangeent is required (this proble is not discussed in this paper). Generalized Hooke s law can be written as: σ = Dε + λ = D( ε µ ), λ = -Dµ () where σ, ε are respectively tensors of stress and strain, D is the aterial stiffness atrix, λ is the tensor of eigenstress andµ is the tensor of eigenstrain. The last equality in () arks dependency of eigenparaeters (eigenstress and eigenstrain). Note that λ can stand for prestress, relaxation stress, aging, and µ can substitute an influence of teperature, swelling, bulking, change of oisture, plastic deforations, creep, etc. In application of back analysis three ain directions are observed: Adjustent of eigenstresses, or eigenstrains, i.e. change of λ and µ in () Systeatic adjustent of aterial properties, i.e. change in D Cobination of the above entioned ite In this paper an approach leading to adjustent of eigenparaeters in back analysis is put forward. In order to siplify the explanation the proble is restricted to underground structures, for which the experiental is realized in scale odeling, which will be also briefly described. In principle, two basic procedures are described: The first is focused on atheatical and nuerical treatents

4 for coupled odeling, and the second is concerned with experients in scale odels with physically equivalent aterials and concrete treatent leading to assessent of tunnel face stability. As said before, the only proble occurs: how to assure that the experiental and nuerical results are in a good agreeent. Previously Cividini, et al., [] cae up with a successful approach leading to a coparative study of the rock and tunnel lining behavior and the reality in ters of internal paraeters (aterial properties). The paper presents a discussion on soe of the aspects of paraeter characterization probles (or back analyses) in the field of geoechanics, i.e. on the systeatic adjustent of aterial properties, i.e. change of aterial characteristics of D in (). In 992 cae up Dvorak with Transforation Field Analysis, [2], which expressed nonlinear probles in a hull of linear effects and effects of eigenparaeters, cf. (). This ethod appeared a powerful tool for solving optial prestress of a thick-walled coposite cylinder consisting of any different cylindrically orthotropic layers being loaded by unifor, axisyetric tractions and by piecewise unifor eigenstrains in the layers, [3, 4]. The first attepts have been done in [5] to involve the eigenparaeters in the coupled odeling. The starting point for this approach was elastic state and effect of eigenparaeters was expressed by cobination of products of influence atrices and eigenparaeters. The experients in scale odels are based on results issued in []. Application of siilarity in the above sense to geoechanics can be found in [7], where optiization of slopes is studied. 2. Experiental Physical scale odeling allows to study effects taking place in rock aterial in connection with construction of underground structures, for exaple to investigate echaniss of geotechnical phenoena, predicts stress changes and their deonstration during various progresses of underground construction and also during siulation of operating conditions. Basic rules of the experiental odeling and forulation of the boundary conditions for odeling coes out fro the principles of geoetrical and physical siilarity which is inferred for a consideration of diensional analysis, []. To siplify the solved proble constitutive relevant quantities v, v 2,..., v n can be selected, which posses exercise decisive influence to process taking place in the rock aterial. It can be assue that influence of the other quantities is lesser. Then physical equation involving function of relevant quantities of various diensions F( v, v 2,..., v n ) = 0, (2) describes in siplification, given by selection of these quantities, behavior of the rock aterial. In what follows the experiental odels will be described. In Fig. overall view of the stand the experients in which has been carried out is displayed. Detailed view of instruentation inside of tunnel opening with tunnel lining siulation, dilatoeters and stress gauges are seen in Fig. 2. Fig. 3 and Fig. 4 illustrate an additional loading fro above, which siulates the depth of foundation of the tunnel. The stiffness of the tunnel lining is siulated separately. Fig. 5 shows the dislocations creating a wedge typical for shallow founded tunnels. The dislocation is geoetrically transferred into nuerical odel and internal paraeters are calculated fro displaceent and stress states. 3. Nuerical odeling Nuerical odel incorporates the ideas of TFA established by Dvorak, [2]. It consists of expressing the stress σ at an arbitrary point ξ of the doain Ω describing the tunnel and its neighborhood by virtue of superposition of stress σ ext (ξ) at ξ due to external loading which is applied to purely elastic ediu, and influences of unit cohesion (shear strength) and unit internal angle of friction. Then a linear hull of, the eigenstresses λ (here substituted by cohesion and internal friction) and elastic state with no dislocation considered at points x.

5 Fig. : Overall view of the stand Fig. 2: Detailed view of the tunnel opening with dilatoeters and gauges

6 Fig. 3: The odel with additional loading fro the terrain Fig. 4: Additional loading fro above

7 Fig. 5: Dislocations created due to overburden load and weaker lining Since we assue that at each point six values of stress, and eigenstress tensors are prescribed, the relation stresses σ k at points B k, k =,...,n, and the eigenstresses and plastic stresses λ l, l =,...,n and (σ pl ) l, l =,..., n at Ω l becoes (to siplify the expressions the vector notation for stress and strain tensors is used): Without any details we can assert that siilar relations can be written for displaceents: or (u i ) k = (u ext i) k + j= (σ i ) k = (σ ext i) k + j= l = n l = (P ij ) kl (λ j ) l, i =,...,, k =,..., (3) (R ij ) kl (λ j ) l, i =,...,, k =,...,. (4) On the other hand easured stresses (σ i eas ) k, or easured displaceents (u eas i) k are available in a discrete set of points (naely the points B i ). A natural requireent is that the values of easured and coputed values be as close as possible. This leads us to the optiization of an error functional or I[(λ j ) l ]= i= I[(λ j ) l ]= i= k = k = [(σ i ) k - (σ i eas ) k ] 2 iniu, (5) [(u i ) k - (u i eas ) k ] 2 iniu () Differentiating (5) yields (A αj ) βl (λ j ) l = Y α β (7) where

8 Y α β = - i= k = (A αj ) βl = i= k = ((σ i ) k - (σ eas i) k )+ j= (R ij ) kl (R iα ) kβ, l= (R ij ) kl (λ j ) l (R iα ) kβ and siilarly for (). Fro the above forulas it follows that although nonlinear proble is solved using coupled odeling syste of linear equations is the goal of the solution. One can copare this result with Dvorak s TFA. 4. Exaple Tunnels constructed in low depths below the surface are assessed. Redistribution of the stress around the tunnel depends not only on properties of environental soils, and tunnel size and location, but also on tunnel lining stiffness. This study focuses on coupled odeling of this proble. On experiental and nuerical odels distribution of stress around horizontally located oval tunnel with diaeter about.8 in dependence on the lining stiffness was observed. The scale physical odels were constructed on a scale of : 25 in odeling stand of diensions 000 x 800 x (width x length x height) with reinforceent of its sides by steel frae (Fig. ). Tunnel of oval shape with inner horizontal diaeter 5 was odeled. The horizontal axis of the tunnel was positioned at 2.5 below the terrain, i.e. 4.2 above the botto of the stand syetrically with respect to the sidewalls of the stand. The tunnels were stiffened by an equivalent of the real lining with different strength, and prepared fro Plexiglas substituting shotcrete of various thicknesses. The purchase was uniquely considered as, which is the value corresponding to the real situation. An equivalent aterial, which has been used for the odels, has been created by copound of siliceous sand with adixture of car oil A00 (99.5 % %), balotine with adixture of car oil A00 (99 % + %), and ferrosilicon with adixture of car oil A00 (99.5 % %): volue ass ρ,447 g/c 3 strength in siple tension σ c 0,004MPa angle of internal friction φ cohesion c 0.04 MPa In Fig. geoetry of the nuerical odel is drawn. Finite eleent ethod is used for coputing elastic state and influence atrices. Finite eleents with linear distribution of displaceents are used. Since the dislocation splits the doain into two statically underdeterined parts the Uzawa algorith can generally be applied, [8], for exaple. Since we use the coupled odeling, there is no solution of contact proble necessary. Distribution of noral and shear tractions along the dislocation are observed in Figs. 7 and 8. In these both pictures thin line belongs to the largest thickness of the concrete lining (0 c in reality), the thick line to the thinnest thickness (30 c in reality). Thinner lining becoes danger for the stability of the tunnel face. Fig. : Cross-section in the iddle of the purchase - nuerical odel

9 Fig. 7: Distribution of shear tractions Fig. 8: Distribution of noral tractions 5. Conclusion If tunnels are drilled in difficult geological conditions and oreover shallow foundation of the tunnel is assued there is a necessity of accurate assessent of tunnel face stability depending on the stiffness of tunnel lining. As a tool, iproving standard assessent, it appears coupled odeling, consisting in utual influence of experiental (scale) odeling and nuerical analysis. It was proved that the dislocation being created in this case is decisive for the assessent, but on the other hand there is the sae shape of the interface between upper and lower part of the doain in the neighborhood of the purchase. Axial tractions are neglected in the analysis, although 3D proble is solved. Using siilar trick as that of Transforation field analysis, [2-5], the angle of internal friction and the cohesion (shear strength) are free, design, paraeters in the coupled odel. Fro the analysis it follows that the thickness 0 c is fully safe while 30 c becoes unsafe and even lower diension is dangerous. It is necessary to note that this coputation was carried out for the lowest foundation of the tunnel, for higher overburden the thickness of the lining has to be adequately increased. Acknowledgeent: Financial support of GACR grant nubers 03/0/24 and the second author was partly supported by CIDEAS, CTU in Prague.. References [] Cividini, A., Jurina, L., Gioda, G., 98. Soe aspects of characterization probles in geoechanice. International Journal of Rock Mechanics and Mining Science & Geoechanics Abstracts. 8,, [2] Dvorak, G.J., 992. Transforation field analysis of inelastic coposite aterials. Proc. R. Soc. London A 437, [3] Dvorak, G.J., Procházka, P., 99. Thick-walled coposite cylinders with optial fiber prestress. Coposites, Part B, 27B, [4] Dvorak, G.J., Procházka, P., Srinivas, M.V., 999. Design and fabrication of suberged cylindrical lainates-i. Int. J. Solids Structures 3, [5] Procházka, P., Trčková, J., Coupled odelling of concrete tunnel lining. In: Our World in Concrete and Structures, Singapore, [] Kožešník, J. 983., Theory of siilarity and odelling. Acadeia, Prague. [7] Koudelka, P., Procházka, P., 200. Apriori Integration Method Analysis, siilarity and optiization of slopes, Acadeia Prague. [8] Procházka, P., Sejnoha, M., 995. Developent of debond region in lag odel. Coputers and Structures 55 (2), 995,