ABSTRACT
This work analyzes, by using discretization with finite and infinite elements, some situation of special interest previously studied with conventional FEM models comparing them with the already achieved results. These elements, recently proposed in works concerning various field of application - wave propagation, fluid motion, stress analysis at the boundary of cavities and in proximity to loading areas, dynamical analysis of foundations and seepage problems - have shown the possibility of modeling the infinite area consistently, without the introduction of further nodal parameters. The pertinent characteristics of the FEH such as the bandwidth of the resolution system and the possibility of applying the algorithms typical of conventional fini te elements. are maintained within this scheme. Infinite elements with decay functions of reciprocal type have been used in this work using a computer program. Two practical cases were here developed: the stress-strain analysis of the Féjus motorway tunnel and the tran sient heat conduction at the contour of a haulage drive. Both these works are compared with the results of studies and researches recently carried out by Turin Polythecnic (School of Mining), on behalf of the operating companies.
INFINITE ELEMENT FEATURES
The infinite element chosen to analyze stresses and strains (1: Fréjus motorway tunnel) and the temperature field (2: at a haulage drive Campiano mine) has been constructed according to Beer and Meek scheme /5/. Two interpolation functions have been used: the first, for geometrical features of the element, which must be able to accomodate points in infinite direction of the element; the second, for the function field, constructed in order to give the decay of the analyzed phenomena, as distance from the source of perturbation increases (displacements of the tunnel wall, heat exchange by convection). The geometry of the element is described by parametric mapping of parent element /17/ and the interpolation functions, defined for every node of the infinite element, are constructed by modifying typical standard interpolation functions: the first function maps the element to the infinite (geometrical definition) and the second brings about the monotonous decay of the perturbation proportional to the distance from a point taken as the start of decay (unknown functions field). In both tested cases the start of decay coincides with the model center "cavity center") and decay function is reciprocal-type. The choice of this function must be coherent with the asymptotic behavior of the required solution. The integrals which define the element matrices are limited and can be solved by the ordinary Gauss-Le_gendre quadrature scheme. Formulas used in this work are given in de tail in /14/.
Example 1: Motorway tunnel of the Fréjus The motorway tunnel of the Fréjus, whose full-section drive (90 m2 ), was completed on April '79, links Bardonecchia (on the Italian side) to Modane (on the French side), and has a length of about 12,9OO m, and a mainly calc-schistous cover (mean thickness is some 600-700 m, with maximum values up to 17OO m). By exploration of some significant sections it has been possible to evaluate the quality of the rock mass: a fair rock according to RMR system. The supports set up immediately after the tunneling operations are: systematical bolting, safety coating with spritz-beton and, at appropriate spots, steel arches, used in very rough conditions, such as for graphite-rich schist, or highly fractured areas. The final lining followed at about 300 m from the tunnel face.