Abstract
In this study, a foundation bearing capacity limit analysis upper-bound solution (FLU) was proposed under the theoretical framework of limit analysis. To be more specific, an optimized mathematical model based on a rigid block discrete system was first established, with the minimum bearing capacity as the objective function, block velocity as the main variable, and the satisfaction of velocity compatibility, associated flow rule, and functional equilibrium equations of adjacent blocks as main constraints. Then, using an optimization approach, the upper-bound value of the foundation’s bearing capacity was obtained. On this basis, the principle of establishing the value interval of the most dangerous slip depth of the two-layer clay foundation was developed by investigating the effects of varying depths on the bearing capacity of the two-layer clay foundation. Meanwhile, an approach for calculating the bearing capacity of the two-layer clay foundation was proposed to achieve the goal of reaching the foundation’s minimum bearing capacity. Furthermore, using a mathematical example, the proposed approach was proven to be rational.
Highlights
In the field of geotechnical engineering, calculating the ultimate bearing capacity of foundations has always been a great concern (Terzaghi and Peck 1967; Davis and Booker 1974; Chen 1975; Griffiths 1982; Michalowski and Lei 1996), with significant implications for underground space and engineering safety
The main reasons are as follows: 1) the number of blocks after block discretization is less than the number of finite element elements; 2) the method in this paper is based on the block interface, the limit analysis finite element is based on nodes and needs to consider the situation of overlapping nodes, and the number of block interfaces is less than the number of nodes
1) An optimized mathematical model is first established based on a rigid block discrete system with the minimum bearing capacity as the objective function, block velocity as the main variable, and the satisfaction of velocity compatibility, associated flow rule, and functional equilibrium equations of an adjacent block as main constraints in the rigid block discrete system
Summary
In the field of geotechnical engineering, calculating the ultimate bearing capacity of foundations has always been a great concern (Terzaghi and Peck 1967; Davis and Booker 1974; Chen 1975; Griffiths 1982; Michalowski and Lei 1996), with significant implications for underground space and engineering safety. Upper-bound limit analysis based on plastic mechanics is a powerful approach for calculating the ultimate bearing capacity of foundations (Lyamin and Sloan 2002; Huang and Qin 2009; Osman 2019; Shamloo and Imani 2020). An optimized mathematical model for the foundation bearing capacity was directly established in accordance with the upper-bound theorem instead of adopting the thought of introducing a significant number of assumptions in the traditional limit equilibrium approach. In this way, the foundation bearing capacity problem can be transformed into an optimization solution problem. The proposed method was proven to be rational using a mathematical example
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