Lower Bound Solutions for Stability of Two Parallel Circular Tunnels in Cohesive Soil

Jun Xie, Xiaojun Yin

In the proceedings of: GeoRegina 2014: 67th Canadian Geotechnical Conference

Session: Transportation Geotechnics

ABSTRACT: d Solutions for Stability of Two Parallel Circular Tunnels in Cohesive Soil Jun Xie Exp Services Inc., Brampton, Ontario, Canada Xiaojun Yin University of HeLongJian Science and Technologies, Hebin, China ABSTRACT This study investigates an undrained stability of two parallel circular tunnels with same diameters in shallow soil, employing the lower bound theorem of plastic limit analysis method. The soil is assumed to be a cohesive material to obey the Trasca criterion. The collapse mechanism, with the admissible stress fields around the two tunnels, is established to estimate the lower bound of stability ratio for tunnels under the condition of plan strain. The lower bound solutions of stability ratio for two parallel circular tunnels are derived to compare with the upper bound solutions of stability ratio and the results from centrifuge testing in the laboratory. The upper and lower bounds bracket the testing results. RÉSUMÉ Cette étude examine une cohésion non drainée de deux tunnels circulaires parallèles ayant les mêmes diamètres dans des sols peu profonds, en utilisant le théorème de limite inférieur de la méthode d'analyse de limite de plasticité. Le sol est supposé être un matériau cohésif afin d'obéir au critère de Tresca. Le mécanisme d'abaissement, avec les champs de contraintes admissibles autour des deux tunnels, est établi pour estimer la limite inférieure de ratio de stabilité pour les tunnels en condition de pression du plan. Les solutions liées inférieures de ratio de stabilité pour deux tunnels parallèles circulaires sont dérivées pour comparer avec les solutions de la limite supérieure de ration de stabilité et des résultats d'essais de centrifugeuses au laboratoire. Les limites supérieures et inférieures encadrent les résultats des tests. 1 INTRODUCTION Bound theorems of plasticity theory are effective approaches to evaluate stability of tunnels in engineering practice. Usually, when it is difficult or impossible to get a true solution of stability ratio (or support force) in tunnel stability analysis, an upper bound and a lower bound can bracket the true solution and provide a good evaluation of stability ratio. In comparison with the upper bound and the lower bound, the upper bound gives a high stability ratio (a lower support force in tunnels), while the lower bound gives a lower stability ratio (a higher support force in tunnels). Due to the collapse mechanisms of the upper bound from an admissible velocity field, and the lower bound from an admissible stress field, in the view of engineering practice, the lower bound solution will lead to a safe value of the tunnel pressure, but the lower bound is more difficult to obtain than the upper bound solution. Several researchers have reported the lower bound solutions of stability ratio for tunnels. Atkinson and Potts (1977) reported the lower bound of theoretical stability results for a tunnel in cohesionless soil. Strictly, bound theorems are true only for materials whose flow rule is associated and the angle of dilation is equal to the angle of shearing resistance, but the flow rule for real soil is non-associated and the angle of shearing resistance is larger thasuggestion (1966), a lower bound solution based on the Coulomb failure criterion might still be valid even if the flow rule is non-associated. Davis et. al. (1980) gave lower and upper bounds of a single tunnel, plane strain heading and circular tunnel heading in cohesive soil. Stress characteristics fields and stress discontinuity lines were used to find lower bounds. Mulhaus (1985) used the lower bound theorem of plasticity theory to analyse tunnel stability in rock. The rock mass was idealized as an elastic perfectly plastic material. Three lower bounds for a single tunnel subjected to a uniform lining as an internal pressure, for tunnels supported by uniformly distributed forcer of anchors and the unsupported span of a tunnel near the face. Even their contributions covers lover bounds in cohesive soil, cohesiveless soil and rock mass, all of them focused on the stability problems of single tunnels. Regarding stability analysis of two parallel circular tunnels, several papers have been published in which the researchers applied numerical methods (e.g. finite element method), and laboratory model testing to investigate the stresses, displacements and stability states of two tunnels and their interactions (Addenbrooke et al.1996; Barla & Ottoviani 1974; Ghabousi & Ranken 1977; Kim et al. 1998; Wu et al. 1998; Xie et al. 2004). However, the contributions of these papers are focusing on the upper bound solutions. It is obvious that the stability ratio from upper bound theorem gives unsafe results, while the stability ratio from lower bound theorem can give a safe value of the tunnel pressure. In this paper, the lower bound solutions of two parallel circular tunnels will be derived through an approximate stress field method.

RÉSUMÉ: Bound Solutions for Stability of Two Parallel Circular Tunnels in Cohesive Soil Jun Xie Exp Services Inc., Brampton, Ontario, Canada Xiaojun Yin University of HeLongJian Science and Technologies, Hebin, China ABSTRACT This study investigates an undrained stability of two parallel circular tunnels with same diameters in shallow soil, employing the lower bound theorem of plastic limit analysis method. The soil is assumed to be a cohesive material to obey the Trasca criterion. The collapse mechanism, with the admissible stress fields around the two tunnels, is established to estimate the lower bound of stability ratio for tunnels under the condition of plan strain. The lower bound solutions of stability ratio for two parallel circular tunnels are derived to compare with the upper bound solutions of stability ratio and the results from centrifuge testing in the laboratory. The upper and lower bounds bracket the testing results. RÉSUMÉ Cette étude examine une cohésion non drainée de deux tunnels circulaires parallèles ayant les mêmes diamètres dans des sols peu profonds, en utilisant le théorème de limite inférieur de la méthode d'analyse de limite de plasticité. Le sol est supposé être un matériau cohésif afin d'obéir au critère de Tresca. Le mécanisme d'abaissement, avec les champs de contraintes admissibles autour des deux tunnels, est établi pour estimer la limite inférieure de ratio de stabilité pour les tunnels en condition de pression du plan. Les solutions liées inférieures de ratio de stabilité pour deux tunnels parallèles circulaires sont dérivées pour comparer avec les solutions de la limite supérieure de ration de stabilité et des résultats d'essais de centrifugeuses au laboratoire. Les limites supérieures et inférieures encadrent les résultats des tests. 1 INTRODUCTION Bound theorems of plasticity theory are effective approaches to evaluate stability of tunnels in engineering practice. Usually, when it is difficult or impossible to get a true solution of stability ratio (or support force) in tunnel stability analysis, an upper bound and a lower bound can bracket the true solution and provide a good evaluation of stability ratio. In comparison with the upper bound and the lower bound, the upper bound gives a high stability ratio (a lower support force in tunnels), while the lower bound gives a lower stability ratio (a higher support force in tunnels). Due to the collapse mechanisms of the upper bound from an admissible velocity field, and the lower bound from an admissible stress field, in the view of engineering practice, the lower bound solution will lead to a safe value of the tunnel pressure, but the lower bound is more difficult to obtain than the upper bound solution. Several researchers have reported the lower bound solutions of stability ratio for tunnels. Atkinson and Potts (1977) reported the lower bound of theoretical stability results for a tunnel in cohesionless soil. Strictly, bound theorems are true only for materials whose flow rule is associated and the angle of dilation is equal to the angle of shearing resistance, but the flow rule for real soil is non-associated and the angle of shearing resistance is larger tha

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Jun Xie; Xiaojun Yin (2014) Lower Bound Solutions for Stability of Two Parallel Circular Tunnels in Cohesive Soil in GEO2014. Ottawa, Ontario: Canadian Geotechnical Society.

@article{GeoRegina14Paper193,author = Jun Xie; Xiaojun Yin ,title = Lower Bound Solutions for Stability of Two Parallel Circular Tunnels in Cohesive Soil ,year = 2014}