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A Method for Calculating Passive Earth Pressure Under Finite Soil Conditions Based on Upper Bound Limit Analysis

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Abstract

The pit-in-pit phenomenon is prevalent in foundation pit engineering practice, resulting in the soil at the bottom of the foundation pit becoming limited soil. Thus, Rankine earth pressure theory based on conventional semi-infinite space is not applicable for calculating the earth pressure acting on retaining structure in case of pit-in-pit. In this paper, the calculation of passive earth pressure under finite soil condition of pit-in-pit is derived in detail based on limit analysis method. By dividing the failure modes of the pit into four cases, which are not through the inner pit, through the side wall of the inner pit, through the bottom of the inner pit and beyond the inner pit, the formulas for calculating the passive earth pressure and its ultimate slip angle are deduced, respectively, and the application of each formula is introduced in detail. Considering the pile–soil interaction force into the calculation of earth pressure, the calculation formula of earth pressure in this case is obtained. The results show that the limit slip angle is related to the internal friction angle, cohesion, calculation depth, pit size and location of the soil mass. The reasonable location of the pit can be determined by using the formula, and then, the minimum value of passive earth pressure can be determined. After considering the force between pile and soil, the passive earth pressure is obviously increased and the limit slip angle is obviously reduced compared with that without considering the force between pile and soil.

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Data Availability

Data will be made available on request.

Abbreviations

\(b_{0}\) :

A variable related to the slip angle (m)

\(B_{{\text{p}}}\) :

The width of the platform of the inner and outer pits (m)

\(G\) :

Gravity of sliding cracked soil per meter (kN/m)

\(\gamma\) :

Weight of the soil behind the wall (kN/m3)

\(H\) :

Buried depth of supporting pile (m)

\(\theta\) :

Ultimate slip angle (°)

\(K\) :

Cohesion of sliding cracked soil per meter (kN/m)

\(c\) :

Cohesion of the soil behind the wall (kN/m2)

\(W_{1}\) :

The power generated by gravity (kN/m)

\(\nu\) :

The strain rate of sliding cracked soil on the sliding surface (m/s)

\(\varphi\) :

Internal friction angle of sliding cracked soil (°)

\(W_{2}\) :

The power of earth pressure resultant force (kN/m)

\(E_{p}\) :

The reaction force of supporting structure on soil (kN/m)

\(W_{3}\) :

The internal energy dissipation rate of soil cohesion on the sliding cracked surface (kN/m)

\(h\) :

The depth of the inner pit (m)

\(b\) :

The width of the inner pit (m)

\(\tau_{1}\) :

Tangential force between piles and soil (kN/m)

\(\delta\) :

External friction Angle between piles and soil (°)

\(C_{w}\) :

Adhesion between pile and soil (kN/m2)

\(W_{4}\) :

The power of the tangential force (kN/m)

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Acknowledgements

This research work was funded by the National Natural Science Foundation of China (51409076, 51774107, 42077249, 52308344), the Natural Science Foundation of Anhui Province (2108085QD166), the Anhui Provincial Natural Science Foundation (2308085QE190), the Opening Project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (KFJJ23-05M), and the Fundamental Research Funds for the Central Universities (JZ2023HGTA0193, JZ2023HGQA0094).

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Authors and Affiliations

  1. College of Civil Engineering, Hefei University of Technology, Hefei, 230009, China

    Yalin Zhu, Qian Xu, Kun Tan, Juxiang Chen & Panpan Guo

  2. Key Laboratory of Civil Engineering Structure and Materials in Anhui Province, Hefei, 230009, China

    Yalin Zhu, Juxiang Chen & Panpan Guo

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  1. Yalin Zhu
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Correspondence to Panpan Guo.

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Zhu, Y., Xu, Q., Tan, K. et al. A Method for Calculating Passive Earth Pressure Under Finite Soil Conditions Based on Upper Bound Limit Analysis. Indian Geotech J (2024). https://doi.org/10.1007/s40098-024-00974-x

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