Upper bound limit analysis of circular tunnel in cohesive-frictional soils using isogeometric analysis based on Bézier extraction

This paper focuses mainly on the stability of a square tunnel in cohesive–frictional soils subjected to surcharge loading. Large-size noncircular tunnels are quickly becoming a widespread building technology by virtue of the development of advanced tunneling machines. The stability of square tunnels in cohesive–frictional soils subjected to surcharge loading has been investigated theoretically and numerically, assuming plane strain conditions. Despite the importance of this problem, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of tunnels or openings in cohesive–frictional soils. In this study, a continuous loading is applied to the ground surface, and both smooth and rough interface conditions between the loading and soil are modelled. For a series of tunnel geometries and material properties, rigorous lower and upper bound solutions for the ultimate surcharge loading of the considered soil mass are obtained by applying recently developed numerical limit analysis techniques. The results obtained are presented in the form of dimensionless stability charts for practical convenience, with the actual surcharge loads being closely bracketed from above and below. As a handy practical means, upper bound rigid-block mechanisms for square tunnels have also been developed, and the obtained values of collapse loads were compared with the results from numerical limit analysis to verify the accuracy of both approaches. Finally, an expression that approximates the ultimate surcharge load of cohesive–frictional soils with the inclusion of shallow square tunnels has been devised for use by practicing engineers.

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Comparative study of material point method and upper bound limit analysis in slope stability analysis

Transportation Safety and Environment ◽

10.1093/tse/tdaa002 ◽

2020 ◽

Vol 2 (1) ◽

pp. 44-57

Author(s):

Lianheng Zhao ◽

Nan Qiao ◽

Zhigang Zhao ◽

Shi Zuo ◽

Xiang Wang

Keyword(s):

Stability Analysis ◽

Upper Bound ◽

Limit Analysis ◽

Slope Failure ◽

Slip Surface ◽

Material Point Method ◽

Material Point ◽

Critical Slip Surface ◽

The Stability ◽

Upper Bound Limit Analysis

Abstract The upper bound limit analysis (UBLA) is one of the key research directions in geotechnical engineering and is widely used in engineering practice. UBLA assumes that the slip surface with the minimum factor of safety (FSmin) is the critical slip surface, and then applies it to slope stability analysis. However, the hypothesis of UBLA has not been systematically verified, which may be due to the fact that the traditional numerical method is difficult to simulate the large deformation. In this study, in order to systematically verify the assumption of UBLA, material point method (MPM), which is suitable to simulate the large deformation of continuous media, is used to simulate the whole process of the slope failure, including the large-scale transportation and deposition of soil mass after slope failure. And a series of comparative studies are conducted on the stability of cohesive slopes using UBLA and MPM. The proposed study indicated that the slope angle, internal friction angle and cohesion have a remarkable effect on the slip surface of the cohesive slope. Also, for stable slopes, the calculation results of the two are relatively close. However, for unstable slopes, the slider volume determined by the UBLA is much smaller than the slider volume determined by the MPM. In other words, for unstable slopes, the critical slip surface of UBLA is very different from the slip surface when the slope failure occurs, and when the UBLA is applied to the stability analysis of unstable slope, it will lead to extremely unfavorable results.

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