Lower bound limit analysis of unsupported vertical circular excavations in rocks using Hoek‐Brown failure criterion

2020 ◽  
Vol 44 (7) ◽  
pp. 1093-1106 ◽  
Author(s):  
Jyant Kumar ◽  
Obaidur Rahaman
Keyword(s):  
Lower Bound ◽  
Limit Analysis ◽  
Failure Criterion ◽  
Lower Bound Limit Analysis

Lower Bound Axisymmetric Limit Analysis Using Drucker–Prager Yield Cone and Simulation with Mohr–Coulomb Pyramid

2015 ◽  
Vol 12 (05) ◽  
pp. 1550023 ◽  
Author(s):  
Manash Chakraborty ◽  
Jyant Kumar
Keyword(s):  
Lower Bound ◽  
Nonlinear Optimization ◽  
Limit Analysis ◽  
Stability Problem ◽  
Interior Point Method ◽  
Stress Space ◽  
Logarithmic Barrier Function ◽  
Principal Stress Space ◽  
Logarithmic Barrier ◽  
Lower Bound Limit Analysis

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker–Prager (D–P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D–P yield cone with the Mohr–Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors Nc, Nq and Nγ have been computed, as a function of ϕ, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

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