An Upper Bound Solution to Undrained Bearing Capacity of Rigid Strip Footings Near Slopes

  • Tingjun Chen
  • Shiguo XiaoEmail author
Research paper


The undrained ultimate bearing capacity of rigid strip footings near slopes is one of important problems in practical foundation engineering in soft clay. To solve the bearing capacity conveniently and easily, a calculation method for the undrained bearing capacity is proposed using the upper bound limit analysis. A bilateral failure mechanism is provided and involved in the analysis, and two failure modes including slope face failure and below-toe failure are pointed out considering the location relationship between the critical slip surface and the slope toe. The upper bound solution of the undrained bearing capacity based on the failure mechanism is carried specifically out via the optimization algorithm. Analysis of some typical examples shows that the results calculated by the proposed method agree well with those obtained using other analytical and numerical methods. The maximum error is about 10%. Cohesion of slope soil, slope angle, horizontal setback distance of strip footing from the slope crest, slope height, surcharge on the slope top level, and the footing depth have great influence on the undrained bearing capacity.


Undrained bearing capacity Strip footings Upper bound limit analysis Slope face failure Below-toe failure 

List of Symbols


Width of the strip footing


Cohesion of the soil, where the subscript u denotes undrained shear strength


Internal friction angle of the soil


Internal energy dissipation rate of the slope soil, where the subscript i denotes the total energy dissipation rate of admissible failure mechanism


Work rates of external forces, where the subscripts g, qu, and σ denote gravity of the slope soil, locally compressive stress on the bottom of the footing, and surcharge on the top surface of the slope, respectively


Height of the slope


Vertical depth of the intersection K between critical slip surface and slope face to the slope crest


Ratio of the distance from the footing to slope crest over the footing width


Angle between lines AC and AB in the zone ABC under the footing


Angle between lines BC and AB in the zone ABC under the footing


Dip angle of the slope face


Unit weight of the soil


Rotation angle of any point on log-spiral curves ACD or BCF from lines AC or BC


Horizontal distance from the toe of the slope P to the intersection K


Velocity of the kinematic soil body, where the subscripts D, F, x, y, C1 and C2 denote point D, point F, horizontal and vertical direction at point C, and direction perpendicular to line AC and BC at point C, respectively


Ultimate bearing capacity of the footing near the slope


Surcharge on the slope top level


Depth of the footing with respect to the top surface of the slope


Undrained bearing capacity factor



The research was supported by the National Natural Science Foundation of China (Grant Nos. 51578466 and 51278430) and the Program for New Century Excellent Talents in University (NCET-13-0976).


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Copyright information

© Iran University of Science and Technology 2019

Authors and Affiliations

  1. 1.Department of Geological EngineeringSouthwest Jiaotong UniversityChengduChina
  2. 2.Key Laboratory of High-speed Railway Engineering, Ministry of EducationSouthwest Jiaotong UniversityChengduChina

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