Abstract
The semispatial static allowable stress field was constructed by three‐dimensional stress columns, and the analytical lower‐bound solution of bearing capacity of Mohr–Coulomb foundation beneath circular uniformly distributed load was put forward for the first time. The influence of the amount of stress columns and soil shear strength parameters on the lower‐bound solution of the foundation‐bearing capacity is analyzed. The research showed that (1) when the number of stress columns is more than 9 (n > 4) and the friction angle is less than 30°, the relative error between the lower‐bound solution of the bearing capacity and exact solution is less than 6.6%, (2) the suggested analytical solution is applicable for common clayey materials; thus, the application scope of the analytical lower‐bound solution is further expanded, and (3) the influence of cohesion on bearing capacity is linear. However, with the increase of the friction angle, the bearing capacity increases faster and faster under all cohesion levels. The correctness and effectiveness of the proposed method were verified by literature comparison.
Highlights
In the 1950s, Drucker and Prager combined the static field with the kinematical field and put forward the limit analysis method for geotechnical problems, which provided a new tool for solving the limit load of foundations. e limit analysis method includes upper-bound and lower-bound theorems
Singh and Basudhar [4] dealt with the prediction of lower-bound-bearing capacity of smooth and rough strip footings based on finite elements and nonlinear programming
Huang [5] derived the lower-limit solution of the ultimate bearing capacity of a rigid strip footing based on finite element by using second-order cone programming
Summary
In the 1950s, Drucker and Prager combined the static field with the kinematical field and put forward the limit analysis method for geotechnical problems, which provided a new tool for solving the limit load of foundations. e limit analysis method includes upper-bound and lower-bound theorems. Huang [5] derived the lower-limit solution of the ultimate bearing capacity of a rigid strip footing based on finite element by using second-order cone programming. In order to determine the ultimate bearing capacity (Pc) of the foundation as an elastoplastic material, two methods are usually adopted: one is to investigate the whole evolution process of the foundation, from the elastic deformation state to the plastic limit state, which is based on the theory of plastoelasticity mechanics (Figure 1(b)). E second is to ignore the process of elastic deformation, regard the material as a rigid-plastic body, and focus on the behavior of the structure in the plastic limit state, namely, the limit analysis method (Figure 1(c)) It can effectively simplify the analysis process and reflect the most essential content in the plastic deformation, so it is widely used in the engineering field. If the upper limit is equivalent to the lower limit, the ultimate load is a complete solution
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