In many existing elastoplastic plane strain solutions for a circular tunnel excavated in a homogeneous, isotropic rock mass under a hydrostatic stress field, the longitudinal axial stress (or the out-of-plane stress) σ z is not correctly evaluated. The paper describes the concepts and a numerical method to calculate this stress component. The relations between rock mass dilations, tunnel displacements and in situ stress field are investigated. Mohr-Coulomb and Hoek-Brown strength criteria with proper plastic potential functions and nonassociated flow rules are used in the brittle plastic calculations. Several important conclusions are drawn from the investigations.
Pour de nombreuses solutions elasto-plastiques en deformation plane d"un tunnel circulaire excave dans masse rocheuse homogène, isotropique, sous laction d"un champ de contraintes hydrostatiques, la contrainte longitudinale axiale (ou contrainte normale au plan) σ z n"est pas evaluee correctement, Ce papierdecrit les concepts et une methode numerique pour calculer cette composante de la contrainte. Les relations entre dilations de la masse rocheuse, deplacements du tunnel et contraintes in situ sont etudiees. Les critères de rupture de Mohr-Coulomb et Hoek-Brown avec les correctes fonctions du potential plastique et des lois non associees sont utilises pour les calculations en plasticite fragile. Quelques conclusions importantes sont elaborees à la suite de cette investigation.
Innerhalb vieler bereits vorhandener Arbaiten, die sich mit elestisch-plastischen planaren Strain- Berechnungen eines Tunnels mit kreisfoemigen Querschnitt im homogenen, isotropen, im hydrostatischen Spannungsfeld befindlichen Gebirge befassen, wird die longitudinal-axiale Spannung (out-of-plane stress)σ z nicht richtig in die Berechnungen mit einbezogen. Es wird die Vorgehensweise und eine numerische Methode zur Erfassung diesser Spannungskomponente erlaeutert, wobei das Verhaeltnis der Gebirgsdehnungen, die Tunneldeformation und das in-situ Spannungsfeld beruecksichtigt werden. Die Berechnungen (sproed-plastisches Medium) basierien mit geeigneten plastischen Potentialfunktionen und unabhaengigen Fliessgesetzen. Wichtige Folgerungen lassen sich daraus ableiten.
In demonstration of the principles of underground excavation support design, and also borehole analysis in petroleum engineering, a simple axisymmetric excavation problem is often used as a basic analysis example. The problem is defined in Figure 1. Consider a circular tunnel of radius τ 0 being driven in a homogeneous, isotropic, initially elastic rock mass subjected to a hydrostatic stress field P0. The internal radial pressure pi is assumed to be the support pressure. As pi is reduced, large deviatoric stresses will arise in the rock surrounding the excavation, causing a local plastic yielding of the rock mass and a plastic zone of radius τ e will develop around the tunnel.
A large number of elastic-plastic (brittle or strain softening) closed form solutions for the problem of Figure 1 exist in the literature and were reviewed by Brown et al, (1983). In the majority of these plane strain solutions, the longitudinal axial stress (out-of-plane) σ zin the plastic zone is usually assumed to be the intermediate principal stress and is not evaluated (Wilson, 1980; Hoek and Brown, 1980; Brown et al., 1983; Detournay, 1986). In some of the solutions, the out-of- plane stress is given based on the assumptions that the axial plastic strain Є pz= 0.
