The interaction behavior of the system of underground structures and rock mass depends on many factors. The most important of those are initial stress state and jointing of rock and orientation in respect to principal stresses, size and shape of the tunnel cross section. A method based on finite element techniques and factor analysis for preliminary design of non-pressurized hydraulic tunnels in jointed rock has been developed.


The shape of the cross section of a non-pressurized hydraulic tunnel is dictated by implemented tunneling technology only in the cases when shields or TBMs are used. In all other cases preliminary selection of the tunnel shape is based on recommendations of codes of practice (SNiP 1985) or rock mass classifications (Lauffer 1958, Beniawski 1973, Barton et al. 1974, Singh & Goel 1999, etc).The shortcomings of many national codes of practice, such as SNiP in Russia, include ones in which the recommendations do not take into account many significant factors influencing the working conditions of the lining of a non-pressurized tunnel. Existing rock Classifications do incorporate many factors but should be used cautiously because as a rule they are based on statistics and empirical conclusions and require repeated checks in-situ during construction.


Here we consider a method for use at the preliminary design stages based on the finite element method techniques and factor analysis applied to choosing the shape, size, and type of linings of non-pressurized tunnels. We examine the three shapes most frequently used: a square with semicircular roof (No. 1), the box shape No.2, and the circular No.3 (Fig. 1). Experiment planning theory was used to obtain factor formulas enabling one to select the best shape reliably for given conditions. The joints are reproduced in the finite-element mesh around the excavation in a region whose size corresponds to half the aperture of the tunnel b12, outside it. The rocks were simulated as a continuous homogeneous medium having an effective elastic modulus that incorporates the effects of the cracks (Figure 2). To simulate the rock blocks, we used triangular and four-node isoparametric elements, while the joints were simulated by means of special contact elements (Orekhov & Zertsalov 1999). The same contact elements were used to simulate contacts between the lining and the rock. The 2D finite element mesh contained 1344 nodes and J 746 elements, 118 of which represented the concrete lining. A linear elastic-plastic treatment for the conditions of planar strain was used (Zertsalov & Tolstikov 1988) for the above three forms of tunnel. The mesh was constructed for one form, and for the other two forms, we modified the coordinates of the mesh nodes in the region within the lining. The shapes are symmetrical, as are the loads, so we considered only half of them. The numbers of experiments and the conditions used were determined in accordance with the experiment planning matrix. It was possible to use a half-replica, i.e., to use half of the calculations denned by the planning matrix (Adler & Granovakii 1976).

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