Undrained stability of a trapdoor

Abstract

This paper examines the stability of a purely cohesive layer resting on a trapdoor. Although this problem has been studied for a number of years and is of considerable interest for analysing the stability of tunnels and mine workings, its exact collapse load is unknown. Rigorous bounds on the load needed to support the trapdoor against active failure are derived using two numerical techniques which employ finite elements in conjunction with the limit theorems of classical plasticity. Both of the methods assume a perfectly plastic soil model with a Tresca yield criterion and lead to large linear programming problems. The solution to the lower bound linear programming problem defines a statically admissible stress field whereas the solution to the upper bound linear programming problem defines a kinematically admissible velocity field. The upper and lower bounds derived from the numerical methods typically bracket the exact collapse load to within ten per cent over the range of trapdoor geometries considered, and are substantially tighter than existing analytical bounds. They are shown to agree well with the collapse loads that are predicted from a traditional dis-placment type of finite element analysis. L'article examine la stabilité d'une couche purement cohérente reposant sur une trappe. Bien qu'on étudie depuis quelques années ce problème de grande importance pour analyser la stabilité des travaux miniers, la charge de rupture reste encore inconnue. Des limites strictes sur le chargement nécessaire pour la rupture active au droit de la trappe contre la rupture active sont derivées à l'aide de deux techniques numériques qui emploient des éléments finis conjointement avec les théorèmes limites de la plasticité classique. Les deux méthodes admettent un modèle de sol parfaitement plastique avec un critère d'ecoulement de Tresca et conduisent à des problemes considérables en ce qui concerne la préparation de programmes linéaires. La solution du problème de la préparation des programmes linéaires à la limite inférieure définit un champ de contrainte statiquement admissible, tandis que la solution de ce problème à la limite supérieure définit un champ de vitesse cinématiquement admissible. De façon typique, les limites supérieure et inférieure dérivées à partir des méthodes numériques se situent au voisinage du chargement de rupture précis à moins de dix pour cent près pour la gamme considérée de géometries de trappe et elles sont essentiellement plus précises que les limites analytiques à present acceptées. L'article démontre qu'elles s'accordent bien avec les chargements de rupture prédits à partir d'une analyse à elements finis traditionnelle basée sur le déplacement.

Centrifuge Modeling of Granular Soil Response Over Active Circular Trapdoors

“…9(b) and straight line segments wereˆt through the data points. Both Pmin W Pi and Pult W Pi line segments showed a clear de‰ection point at about H W D＝2, which corresponded well with analytical results by Davis (1968), Gunn (1980), and Sloan et al (1990). They concluded that when H W Dº2, the trapdoor is shallow, and when H W DÀ2, the trapdoor is deep.…”

“…1g tests (Engesser, 1882;Terzaghi, 1936;McNulty, 1965;Ladanyi and Hoyaux, 1969;Evan, 1983;Tanaka and Sakai, 1993) and centrifuge tests under elevated acceleration levels (Stone and Wood, 1988;Craig, 1990;Iglesia, 1991;Abdulla and Goodings, 1994). Theoretical studies include solutions based on theory of elasticity (Finn, 1963;Chelapati, 1964), limit analysis (Davis, 1968;Gunn, 1980;Evan, 1983;Sloan et al, 1990; Singh and Basudhar, 1995; Smith, 1998), limit equilibrium (Engesser, 1882;Bierbaumer, 1913;Terzaghi, 1943;Krynine, 1945;Vardoulakis et al, 1981), andˆnite element analysis (Koutsabeloulis and Gri‹ths, 1989;Tanaka and Sakai, 1993;Nakai, et al, 1995). The focus of this paper is on physical model studies.…”

Failure Mechanisms in Pipelines Bridging a Void

“…Installations are considered to correspond to deep burial conditions when the cover depth ratio H/D exceeds approximately 2.5 (Sloan et al 1990). The electromagnetic system holding the rigid trapdoor base in place was released during centrifuge testing.…”

Geovala: um novo processo construtivo para dutos enterrados

“…Vários pesquisadores têm estudado este fenômeno (NIELSON, 1967;GETZLER et al, 1968;BURGHIGNOLI, 1981;HANDY, 1985;SLOAN et al, 1990;OKO E YAMADA, 1993;MCKELVEY III, 1994;DANCYGIER E YANKELEVSKY, 1996;SANTICHAIANANT, 2002 (BULSON, 1985). Esta altura é definida com altura de igual recalque.…”

“…Entretanto, o entendimento global do fenômeno do efeito membrana é importante para deduzir e quantificar a sua influência no processo construtivo Geovala. Vários pesquisadores têm estudado este fenômeno (NIELSON, 1967;GETZLER et al, 1968;BURGHIGNOLI, 1981;HANDY, 1985;SLOAN et al, 1990; OKO E YAMADA, 1993;MCKELVEY III, 1994; DANCYGIER E YANKELEVSKY, 1996;SANTICHAIANANT, 2002 Em que: a = raio do duto; r = raio do arco formado na região de máxima tensão cisalhante.Conhecendo-se θ pode-se calcular o valor de dp. dp R sin dr r dr rsin…”