This paper focuses on the analytical derivation and the numerical simulation analyses to predict the interaction influences between a landslide and a new tunnel in mountain areas. Based on the slip-line theory, the di...This paper focuses on the analytical derivation and the numerical simulation analyses to predict the interaction influences between a landslide and a new tunnel in mountain areas. Based on the slip-line theory, the disturbance range induced by tunneling and the minimum safe distance between the tunnel vault and the sliding belt are obtained in consideration of the mechanical analyses of relaxed rocks over the tunnel opening. The influence factors for the minimum safe crossing distance are conducted,including the tunnel radius, the friction angle of surrounding rocks, the inclination angle of sliding belt,and the friction coefficient of surrounding rocks. Secondly, taking account of the compressive zone and relaxed rocks caused by tunneling, the Sarma method is employed to calculate the safety factor of landslide. Finally, the analytical solutions for interaction between the tunnel and the landslide are compared with a series of numerical simulations, considering the cases for different perpendicular distances between the tunnel vault and the sliding belt. Resultsshow that the distance between the tunnel vault and the slip zone has significant influence on the rock stress and strain. For the case of the minimum crossing distance, a plastic zone in the landslide traversed by tunneling would be formed with rather large range, which seriously threatens the stability of landslide. This work demonstrates that the minimum safe crossing distance obtained from numerical simulation is in a good agreement with that calculated by the proposed analytical solutions.展开更多
A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once.It is known that the list edge chromatic numberχ′l(G)of any outer-1-planar g...A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once.It is known that the list edge chromatic numberχ′l(G)of any outer-1-planar graph G with maximum degreeΔ(G)≥5 is exactly its maximum degree.In this paper,we proveχ′l(G)=Δ(G)for outer-1-planar graphs G withΔ(G)=4 and with the crossing distance being at least 3.展开更多
基金financial support provided by Natural Science Foundation of China (Grant No. 51008188)by Shanghai Natural Science Foundation (Grant No. 15ZR1429400)+2 种基金by Open Project Program of State Key Laboratory Breeding Base of Mountain Bridge and Tunnel Engineering (Grant No. CQSLBF-Y15-1)by Open Project Program of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Grant No. SKLGP2015K015)by the Open Project Program of Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Land and Resources (Grant No. 2015k005)
文摘This paper focuses on the analytical derivation and the numerical simulation analyses to predict the interaction influences between a landslide and a new tunnel in mountain areas. Based on the slip-line theory, the disturbance range induced by tunneling and the minimum safe distance between the tunnel vault and the sliding belt are obtained in consideration of the mechanical analyses of relaxed rocks over the tunnel opening. The influence factors for the minimum safe crossing distance are conducted,including the tunnel radius, the friction angle of surrounding rocks, the inclination angle of sliding belt,and the friction coefficient of surrounding rocks. Secondly, taking account of the compressive zone and relaxed rocks caused by tunneling, the Sarma method is employed to calculate the safety factor of landslide. Finally, the analytical solutions for interaction between the tunnel and the landslide are compared with a series of numerical simulations, considering the cases for different perpendicular distances between the tunnel vault and the sliding belt. Resultsshow that the distance between the tunnel vault and the slip zone has significant influence on the rock stress and strain. For the case of the minimum crossing distance, a plastic zone in the landslide traversed by tunneling would be formed with rather large range, which seriously threatens the stability of landslide. This work demonstrates that the minimum safe crossing distance obtained from numerical simulation is in a good agreement with that calculated by the proposed analytical solutions.
基金supported by the National Natural Science Foundation of China (Nos. 11871055,11301410)the Youth Talent Support Plan of Xi’an Association for Science and Technology,China (2018-6)
文摘A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once.It is known that the list edge chromatic numberχ′l(G)of any outer-1-planar graph G with maximum degreeΔ(G)≥5 is exactly its maximum degree.In this paper,we proveχ′l(G)=Δ(G)for outer-1-planar graphs G withΔ(G)=4 and with the crossing distance being at least 3.
