Let G be a simple connected graph of order n ≥ 6. The third edge-connectivity of G is defined as the minimum cardinality over all the sets of edges, if any, whose deletion disconnects G and every component of the res...Let G be a simple connected graph of order n ≥ 6. The third edge-connectivity of G is defined as the minimum cardinality over all the sets of edges, if any, whose deletion disconnects G and every component of the resulting graph has at least 3 vertices. In this paper, we first characterize those graphs whose third-edge connectivity is well defined,then establish the tight upper bound for the third edge-connectivity.展开更多
Collapse shape of tunnel floor in Hoek-Brown rock media is investigated with the functional catastrophe theory. The stability of rock system in tunnel floor, which is determined by thickness, half collapse width, half...Collapse shape of tunnel floor in Hoek-Brown rock media is investigated with the functional catastrophe theory. The stability of rock system in tunnel floor, which is determined by thickness, half collapse width, half length of cave and detaching curve, has great secure and economic significance in practical engineering. To investigate the failure mechanisms and the outline of detaching block, a reliable damage model is presumed by making reference to the limit analysis theory. The analytical solutions of detaching curve, half collapse width on tunnel floor and the critical and maximum values of collapse thickness are derived based on Hoek-Brown criterion and functional catastrophe theory. The result shows that 0.5 is a most probable condition for instability, and the shape of detaching curve is a part of parabola. It is reasonable by comparing with previous theory and analogous experiments. The effects of major factors on thickness and half collapse width are further discussed. Numerical calculations and parametric analysis are carried out to illustrate the effects of different parameters on the mechanism, which is significant to the stability analysis of tunnel floor in rock media.展开更多
基金This work was supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.102055)the Natural Science Foundation of Zhejiang Normal UniversityThe second author was supported by the National Natural Science Foundation of China(Grant No.19971056).
文摘Let G be a simple connected graph of order n ≥ 6. The third edge-connectivity of G is defined as the minimum cardinality over all the sets of edges, if any, whose deletion disconnects G and every component of the resulting graph has at least 3 vertices. In this paper, we first characterize those graphs whose third-edge connectivity is well defined,then establish the tight upper bound for the third edge-connectivity.
基金Project(2013CB036004)supported by the National Basic Research Program of ChinaProject(51378510)supported by the National Natural Science Foundation of China
文摘Collapse shape of tunnel floor in Hoek-Brown rock media is investigated with the functional catastrophe theory. The stability of rock system in tunnel floor, which is determined by thickness, half collapse width, half length of cave and detaching curve, has great secure and economic significance in practical engineering. To investigate the failure mechanisms and the outline of detaching block, a reliable damage model is presumed by making reference to the limit analysis theory. The analytical solutions of detaching curve, half collapse width on tunnel floor and the critical and maximum values of collapse thickness are derived based on Hoek-Brown criterion and functional catastrophe theory. The result shows that 0.5 is a most probable condition for instability, and the shape of detaching curve is a part of parabola. It is reasonable by comparing with previous theory and analogous experiments. The effects of major factors on thickness and half collapse width are further discussed. Numerical calculations and parametric analysis are carried out to illustrate the effects of different parameters on the mechanism, which is significant to the stability analysis of tunnel floor in rock media.
