Acta Geotechnica

, Volume 12, Issue 5, pp 1089–1103 | Cite as

Failure modes and bearing capacity of strip footings on soft ground reinforced by floating stone columns

  • Haizuo Zhou
  • Yu Diao
  • Gang ZhengEmail author
  • Jie Han
  • Rui Jia
Research Paper


This study evaluates the failure modes and the bearing capacity of soft ground reinforced by a group of floating stone columns. A finite difference method was adopted to analyze the performance of reinforced ground under strip footings subjected to a vertical load. The investigation was carried out by varying the aspect ratio of the reinforced zone, the area replacement ratio, and the surface surcharge. General shear failure of the reinforced ground was investigated numerically without the surcharge. The results show the existence of an effective length of the columns for the bearing capacity factors N c and N γ. When certain surcharge was applied, the failure mode of the reinforced ground changed from the general shear failure to the block failure. The aspect ratio of the reinforced zone and the area replacement ratio also contributed to this failure mode transition. A counterintuitive trend of the bearing capacity factor N q can be justified with a shift in the critical failure mode. An upper-bound limit method based on the general shear failure mode was presented, and the results agree well with those of the previous studies of reinforced ground. Equivalent properties based on the area-weighted average of the stone columns and clay parameters were used to convert the individual column model to an equivalent area model. The numerical model produced reasonable equivalent properties. Finally, a theoretical method based on the comparison of the analytical equations for different failure modes was developed for engineering design. Good agreement was found between the theoretical and numerical results for the critical failure mode and its corresponding bearing capacity factors.


Bearing capacity Failure modes Finite difference method Limit analysis Stone columns 

List of symbols


Posison’s ratio


Area replacement ratio


Friction angle of soil


Friction angle of columns


Equivalent friction angle of reinforced zone


Equivalent friction angle of reinforced zone


Unit weight of soil


Unit weight of columns


Equivalent unit weight of reinforced zone


Bearing capacity of the footings

Nc, Nq, Nγ

Bearing capacity factors of the ground


Modulus of elasticity


Length of the columns/width of the footing


Surcharge on the ground

cu, c, cs

Cohesion of soil


Cohesion of columns


Equivalent cohesion of reinforced zone


Stress concentration ratio


Effective length of the columns


Critical surcharge


Bearing capacity at block failure


Bearing capacity factor at block failure


Base resistance of the reinforced ground


Side friction of the reinforced ground


Bearing capacity factor for clay


Undrained columns–soil adhesion


Depth factor



This research was funded by the National Natural Science Foundation of China (Grant No. 51378345). The authors appreciate the financial support.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Haizuo Zhou
    • 1
    • 2
  • Yu Diao
    • 1
    • 2
  • Gang Zheng
    • 1
    • 2
    • 3
    Email author
  • Jie Han
    • 4
  • Rui Jia
    • 1
    • 2
  1. 1.School of Civil EngineeringTianjin UniversityTianjinChina
  2. 2.Key Laboratory of Coast Civil Structure SafetyTianjin University, Ministry of EducationTianjinChina
  3. 3.State Key Laboratory of Hydraulic Engineering Simulation and SafetyTianjin UniversityTianjinChina
  4. 4.Department of Civil, Environmental, and Architectural EngineeringUniversity of KansasLawrenceUSA

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