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| Citation: |
ZHOU Zhixiong, ZHOU Fengxi, LIANG Yuwang. Ultimate bearing capacity of foundations based on variational limit equilibrium method[J]. Chinese Journal of Geotechnical Engineering, 2025, 47(6): 1281-1288. DOI: 10.11779/CJGE20240146
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Based on the basic principles of the variational method and the limit equilibrium method, the ultimate bearing capacity of foundation for strip footings is analyzed. Based on the static equilibrium equation for sliding soil in the foundation, an isoperimetric model for the functional extremum of the ultimate bearing capacity of foundation is established. On this basis, the auxiliary functional under constraint conditions is constructed by introducing the Lagrange multiplier. The Euler equation is used to obtain the first-order ordinary differential equations with the potential sliding surface, normal stress on sliding surface, and Lagrange multiplier as basic unknowns, and the analysis of the ultimate bearing capacity of foundation with movable boundaries is transformed into a two-point boundary value problem under fixed boundary conditions by introducing auxiliary variables. Finally, the numerical solution of the coupled nonlinear differential equation system is carried out by using the shooting method, and the exact solution of the problem is obtained. Meanwhile, the effectiveness of the model and method is verified through numerical examples.
| [1] |
KARL T. Theoretical Soil Mechanics[M]. New York: Wiley, 1943.
|
| [2] |
MEYERHOF G G. The ultimate bearing capacity of foudations[J]. Géotechnique, 1951, 2(4): 301-332. doi: 10.1680/geot.1951.2.4.301
|
| [3] |
SAHA A, GHOSH S. Pseudo-dynamic analysis for bearing capacity of foundation resting on c-Φ soil[J]. International Journal of Geotechnical Engineering, 2015, 9(4): 379-387. doi: 10.1179/1939787914Y.0000000081
|
| [4] |
SOUBRA A H. Upper-bound solutions for bearing capacity of foundations[J]. Journal of Geotechnical and Geoenviron-mental Engineering, 1999, 125(1): 59-68. doi: 10.1061/(ASCE)1090-0241(1999)125:1(59)
|
| [5] |
WANG Y J, YIN J H, CHEN Z Y. Calculation of bearing capacity of a strip footing using an upper bound method[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25(8): 841-851. doi: 10.1002/nag.151
|
| [6] |
LI S, HUANG M S, YU J. Continuous field based upper-bound analysis for the undrained bearing capacity of strip footings resting near clay slopes with linearly increased strength[J]. Computers and Geotechnics, 2019, 105: 168-182. doi: 10.1016/j.compgeo.2018.10.002
|
| [7] |
KUMAR J. Nγ for rough strip footing using the method of characteristics[J]. Canadian Geotechnical Journal, 2003, 40(3): 669-674. doi: 10.1139/t03-009
|
| [8] |
CASCONE E, CASABLANCA O. Static and seismic bearing capacity of shallow strip footings[J]. Soil Dynamics and Earthquake Engineering, 2016, 84: 204-223. doi: 10.1016/j.soildyn.2016.02.010
|
| [9] |
李承超, 关云飞, 蔡正银, 等. 基于严格滑移线场理论临坡条形基础地基极限承载力分析[J]. 岩土工程学报, 2021, 43(8): 1408-1416. doi: 10.11779/CJGE202108005
LI Chengchao, GUAN Yunfei, CAI Zhengyin, et al. Ultimate bearing capacity of strip footings placed near slopes determined by rigorous slip line field theory[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(8): 1408-1416. (in Chinese) doi: 10.11779/CJGE202108005
|
| [10] |
MANOHARAN N, DASGUPTA S P. Bearing capacity of surface footings by finite elements[J]. Computers & Structures, 1995, 54(4): 563-586.
|
| [11] |
NGUYEN H C, VO-MINH T. The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(1): 180-196. doi: 10.1016/j.jrmge.2021.11.005
|
| [12] |
王冬勇, 陈曦, 于玉贞, 等. 基于二阶锥规划有限元增量加载法的条形浅基础极限承载力分析[J]. 岩土力学, 2019, 40(12): 4890-4896, 4924.
WANG Dongyong, CHEN Xi, YU Yuzhen, et al. Ultimate bearing capacity analysis of shallow strip footing based on second-order cone programming optimized incremental loading finite element method[J]. Rock and Soil Mechanics, 2019, 40(12): 4890-4896, 4924. (in Chinese)
|
| [13] |
KOPASCY J. Three-dimensional stress distribution and slip surfaces in earth works at rupture[C]// Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering, London, 1957.
|
| [14] |
BAKER R, SHUKHA R, OPERSTEIN V, et al. Stability charts for pseudo-static slope stability analysis[J]. Soil Dynamics and Earthquake Engineering, 2006, 26(9): 813-823. doi: 10.1016/j.soildyn.2006.01.023
|
| [15] |
周凤玺, 朱顺望, 梁玉旺, 等. 变分极限平衡法对土质边坡稳定性的精确分析[J]. 岩土工程学报, 2023, 45(7): 1341-1346. doi: 10.11779/CJGE20220360
ZHOU Fengxi, ZHU Shunwang, LIANG Yuwang, et al. Exact analysis of soil slope stability by using variational limit equilibrium method[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(7): 1341-1346. (in Chinese) doi: 10.11779/CJGE20220360
|
| [16] |
LI X G, LIU W N. Study on the action of the active earth pressure by variational limit equilibrium method[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 34(10): 991-1008.
|
| [17] |
陈建功, 胡日成, 许明. 考虑合力作用点位置的主动土压力计算[J]. 工程力学, 2016, 33(11): 132-139.
CHEN Jiangong, HU Richeng, XU Ming. Active earth pressure calculation considering force point location[J]. Engineering Mechanics, 2016, 33(11): 132-139. (in Chinese)
|
| [18] |
DIXIT R K, MANDAL J N. Bearing capacity of geosynthetic-reinforced soil using variational method[J]. Geotextiles and Geomembranes, 1993, 12(6): 543-566. doi: 10.1016/0266-1144(93)90043-N
|
| [19] |
陈榕, 栾茂田, 郝冬雪, 等. 加筋地基极限承载力的变分解法[J]. 岩土工程学报, 2010, 32(5): 774-779. https://cge.nhri.cn/article/id/13411
CHEN Rong, LUAN Maotian, HAO Dongxue, et al. The ultimate bearing capacity of reinforced foundation by variational solution[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(5): 774-779. (in Chinese) https://cge.nhri.cn/article/id/13411
|
| [20] |
ZHOU F X, MA Q. Exact solution for capillary interactions between two particles with fixed liquid volume[J]. Applied Mathematics and Mechanics, 2016, 37(12): 1597-1606. doi: 10.1007/s10483-016-2142-8
|
| [21] |
ZHOU F X, LI S R, LAI Y M. Three-dimensional analysis for transient coupled thermoelastic response of a functionally graded rectangular plate[J]. Journal of Sound and Vibration, 2011, 330(16): 3990-4001. doi: 10.1016/j.jsv.2011.03.015
|
| [22] |
宋二祥, 付浩, 李贤杰. 地基承载力机理及新计算方法[J]. 岩土工程学报, 2022, 44(1): 37-44. doi: 10.11779/CJGE202201002
SONG Erxiang, FU Hao, LI Xianjie. Mechanism and new calculation method for bearing capacity of foundations[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(1): 37-44. (in Chinese) doi: 10.11779/CJGE202201002
|
| [23] |
蒋益平, 熊巨华. 方形和圆形基础地基极限承载力分析[J]. 岩土力学, 2005, 26(12): 1991-1995.
JIANG Yiping, XIONG Juhua. Analysis of ultimate bearing capacity of square and circular foundations[J]. Rock and Soil Mechanics, 2005, 26(12): 1991-1995. (in Chinese)
|
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