Ultimate bearing capacity of strip footings placed near slopes determined by rigorous slip line field theory

LI Cheng-chao; GUAN Yun-fei; CAI Zheng-yin; JIANG Peng-ming; HAN Xun

doi:10.11779/CJGE202108005

Volume 43 Issue 8

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Geotechnical Engineering > 2021 > 43(8): 1408-1416. > DOI: 10.11779/CJGE202108005

LI Cheng-chao, GUAN Yun-fei, CAI Zheng-yin, JIANG Peng-ming, HAN Xun. 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. DOI: 10.11779/CJGE202108005

Citation:

PDF (1720 KB)

Ultimate bearing capacity of strip footings placed near slopes determined by rigorous slip line field theory

1.
Department of Geotechnical Engineering, Nanjing Hydraulic Research Institute, Nanjing 210024, China
2.
Department of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, China

More Information

Received Date: August 08, 2020
Available Online: December 02, 2022

Graphical Abstract

Abstract

Abstract

Calculating the ultimate bearing capacity of strip footings placed near slopes has long been a critical component in geotechnical design. In order to obtain the accurate solution of this issue, the statically and kinematically admissible conditions should be satisfied beforehand. Based on the rigorous slip line field theory, the equations for characteristic line and the three kinds of basic boundary value problems are solved together to establish the slip line field of the footing-on-slope system that satisfies the stress and velocity boundaries simultaneously. Then, five types of unilateral failure modes are proposed to determine the corresponding ultimate bearing capacity. The effects of soil shear strength, slope geometry and setback distance from footing edge to slope on the ultimate bearing capacity and the failure mechanism are evaluated in this study. The results indicate that the proposed solutions show good agreement with the experimental results found in the literature. The parametric analysis presents that the ultimate bearing capacity increases with the shear strength, and decreases with an increase in the slope height and the slope angle. When the slope height reaches the critical value, the ultimate bearing capacity is no longer affected by the slope height. Meanwhile, the ultimate bearing capacity increases with the relative distance from footing edge to slope shoulder, and it finally remains unchanged. When the placement position of the footing reaches the critical value, the ultimate bearing capacity is no longer affected by the slope stability. At this point, the failure mechanism obeys the Prandtl’s bearing capacity failure. The failure mechanism gradually transits from the face bearing capacity failure to the face sliding failure or the deep sliding failure and finally follows the Prandtl’s bearing capacity failure with an increase in the relative distance. In this process, the critical sliding range gradually increases until the footing-on-slope system obeys the Prandtl’s failure mode, which results in the corresponding variation in the ultimate bearing capacity.
- strip footing near slope,
- ultimate bearing capacity,
- slip line field theory,
- boundary value problem

FullText(HTML)

References (22)

References

[1]	尉学勇, 王晓谋, 怀超. 斜坡地基极限承载力上限解计算与分析[J]. 岩土工程学报, 2010, 32(3): 381-387. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201003014.htm YU Xue-yong, WANG Xiao-mou, HUAI Chao. Calculation and analysis of upper limit solution of ultimate bearing capacity of sloping ground[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(3): 381-387. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201003014.htm
[2]	尹鑫, 周海祚, 郑刚. 地震作用下临近边坡的条形基础极限承载力研究[J]. 岩土工程学报, 2017, 39(增刊2): 95-98. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2017S2025.htm YIN Xin, ZHOU Hai-zuo, ZHENG Gang. Seismic bearing capacity of strip footings adjacent to slopes[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(S2): 95-98. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2017S2025.htm
[3]	TERZAGHI K. Theoretical Soil Mechanics[M]. New York: Wiley, 1943.
[4]	MEYERHOF G G. Some recent research on the bearing capacity of foundations[J]. Canadian Geotechnical Journal, 1963, 1(1): 16-26. doi: 10.1139/t63-003
[5]	马庆宏, 朱大勇, 雷先顺, 等. 无黏性土斜坡地基承载力模型试验研究[J]. 岩土工程学报, 2014, 36(7): 1271-1280. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201407013.htm MA Qin-hong, ZHU Da-yong, LEI Xian-shun, et al. Model tests on bearing capacity of footing on sand slopes[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(7): 1271-1280. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201407013.htm
[6]	TURKER E, SADOGLU E, CURE E, et al. Bearing capacity of eccentrically loaded strip footings close to geotextile-reinforced sand slope[J]. Canadian Geotechnical Journal, 2014, 51(8): 884-895. doi: 10.1139/cgj-2014-0055
[7]	HUANG C C. Effects of restraining conditions on the bearing capacity of footings near slopes[J]. Soils and Foundations, 2019, 59(1): 1-12. doi: 10.1016/j.sandf.2018.08.016
[8]	胡卫东, 曹文贵. 基于双侧非对称破坏模式的临坡地基承载力极限平衡分析方法[J]. 土木工程学报, 2015, 48(1): 120-128. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201501015.htm HU Wei-dong, CAO Wen-gui. The limit equilibrium method for ultimate bearing capacity of ground foundation adjacent to slopes based on bilateral asymmetry failure mode[J]. China Civil Engineering Journal, 2015, 48(1): 120-128. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201501015.htm
[9]	胡卫东, 曹文贵. 基于滑移线场理论的临坡地基承载力简化分析方法[J]. 湖南大学学报(自然科学版), 2017, 44(7): 162-169. doi: 10.16339/j.cnki.hdxbzkb.2017.07.021 HU Wei-dong, CAO Wen-gui. Simplified analysis method of ultimate bearing capacity for footings near slope based on slip line theory[J]. Journal of Hunan University (Natural Sciences), 2017, 44(7): 162-169. (in Chinese) doi: 10.16339/j.cnki.hdxbzkb.2017.07.021
[10]	胡卫东, 曹文贵, 袁青松. 基于非对称双侧破坏模式的临坡地基承载力上限分析[J]. 岩土力学, 2016, 37(10): 2787-2794. doi: 10.16285/j.rsm.2016.10.007 HU Wei-dong, CAO Wen-gui, YUAN Qing-song. An upper-bound limit analysis of ultimate bearing capacity of ground foundation adjacent to slope based on asymmetric and bilateral failure mode[J]. Rock and Soil Mechanics, 2016, 37(10): 2787-2794. (in Chinese) doi: 10.16285/j.rsm.2016.10.007
[11]	蒋洋, 王晓谋, 郭建坤, 等. 基于滑移线场理论斜坡条基极限承载力解析解[J]. 地下空间与工程学报, 2018, 14(1): 92-100. https://www.cnki.com.cn/Article/CJFDTOTAL-BASE201801014.htm JIANG Yang, WANG Xiao-mou, GUO Jian-kun, et al. Analytical solutions of ultimate bearing capacity for strip foundations on slopes based on slip line theories[J]. Chinese Journal of Underground Space and Engineering, 2018, 14(1): 92-100. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BASE201801014.htm
[12]	YANG S C, LESHCHINSKY B, CUI K, et al. Influence of failure mechanism on seismic bearing capacity factors for shallow foundations near slopes[J]. Géotechnique, 2021, 71(7): 594-607.
[13]	LESHCHINSKY B. Bearing capacity of footings placed adjacent to c'-φ' slopes[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 141(6): 04015022.
[14]	郑刚, 于晓旋, 杜娟, 等. 临近边坡的条形基础地基极限承载力数值分析[J]. 岩土力学, 2018, 39(10): 3812-3820, 3829. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201810039.htm ZHENG Gang, YU Xiao-xuan, DU Juan, et al. Numerical analysis of ultimate bearing capacity of strip footings near slopes[J]. Rock and Soil Mechanics, 2018, 39(10): 3812-3820, 3829. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201810039.htm
[15]	赵明华, 胡啸, 张锐. 临坡地基承载力极限分析上限有限元数值模拟[J]. 岩土力学, 2016, 37(4): 1137-1143, 1152. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201604029.htm ZHAO Ming-hua, HU Xiao, ZHANG Rui. Numerical simulation of the bearing capacity of a foundation near slope using the upper bound finite element method[J]. Rock and Soil Mechanics, 2016, 37(4): 1137-1143, 1152. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201604029.htm
[16]	LI C C, ZHOU A Z, JIANG P M. Eccentric bearing capacity of embedded strip footings placed on slopes[J]. Computers and Geotechnics, 2020, 119: 103352.
[17]	ZHANG R, XIAO Y, ZHAO M H, et al. Seismic bearing capacity of strip footings placed near c-φ soil slopes[J]. Soil Dynamics and Earthquake Engineering, 2020, 136: 106221.
[18]	沈珠江. 不连续解在极限土压力计算中的应用[M]//沈珠江土力学论文集. 北京: 清华大学出版社, 2005. SHEN Zhu-jiang. Discontinuous solution in limit earth pressure computation application[M]//Selected Works on Soil Mechanics of Shen Zhujiang. Beijing: Tsinghua University Press, 2005. (in Chinese)
[19]	LI C C, JIANG P M, ZHOU A Z. Rigorous solution of slope stability under seismic action[J]. Computers and Geotechnics, 2019, 109: 99-107.
[20]	KUMAR J, KOUZER K M. Effect of Footing Roughness on Bearing Capacity Factor N_γ[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133(5): 502-511.
[21]	VESIC A S. Analysis of ultimate loads of shallow foundations[J]. Journal of the Soil Mechanics and Foundation Division, 1973, 99(1): 45-73.
[22]	HANSEN J B. A Revised and Extended Formula for Bearing Capacity[M]. Copenhagen: Danish Geotechnical Institute, 1970.