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Estimation of internal force of stabilizing piles on landslides considering nonlinear landslide thrust and soil resistance

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Abstract

A number of engineering activities are potentially threatened by adjacent slopes, and stabilizing piles as a simple and effective method can prevent and control potential landslides. However, when soil resistance conditions are not adequately considered, it can result in inconsistencies between theoretical calculations and engineering practice. Therefore, this paper established a parabolic landslide thrust and soil resistance distribution model based on the field model test and discussed their resultant force action point locations. Moreover, the calculation model and governing equation of the stabilizing pile considering nonlinear landslide thrust and soil resistance under three failure modes were established. Additionally, the general solution forms of the pile deformation and force obtained by the power series method were discussed under different soil pressure distributions. The results calculated by the method considering the nonlinear landslide thrust and soil resistance were in better agreement with the actual stress mode for single-row stabilizing piles according to the model results and two case studies. The newly proposed calculation model provides a new idea for the design and calculation of the single-row stabilizing piles on the loess slope.

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Data availability statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\(q(z)\) :

Distribution function of the landslide thrust

\(p(z)\) :

Distribution function of the soil resistance

\({p}_{\text{s}}\) :

On pile FPUL

\(z\) :

Depth of pile

\({z}_{\text{r}}\) :

Rotation depth

\(E^{\prime}\)  :

Landslide thrust value

\(E^{\prime\prime}\)  :

Soil resistance value

\(l\) :

Pile length

\({l}_{0}\) :

Pile length above the sliding surface

\({l}_{c}\) :

Pile length below the sliding surface

\({b}_{0}\) :

Calculated width of the stabilizing piles

\(b\) :

Width of the stabilizing piles with rectangular sections

\(d\) :

Diameter of stabilizing piles with circular sections

\(k\) :

Horizontal resistance factor of the foundation soil

\({k}_{\text{s}}\) :

Modulus of subgrade reaction for piles in moving soil

\({k}_{\theta }\) :

Rotational stiffness of a pile cap

\(k^{\prime}\)  :

Ratio of the resultant force action point position of landslide thrust to the \({l}_{0}\)

\(k^{\prime\prime}\)  :

Ratio of the resultant force action point position of soil resistance to the \({l}_{0}\)

\(\xi\), \(\eta\), \(\psi\) :

Coefficients of the landslide thrust distribution function

\(\xi^{\prime}\), \(\eta^{\prime}\), \(\psi ^{\prime}\) :

Coefficients of the soil resistance distribution function.

E :

Elastic modulus of the pile

I :

Sectional inertia moment of the pile

EI :

Pile bending stiffness

X :

Pile displacement in the loading section

\(\varphi\) :

Rotation angle in the loading section

M :

Bending moment in the loading section

Q :

Shear force in the loading section

X 0 :

Pile top displacement

\({\varphi }_{0}\) :

Rotation angle of the pile top

M 0 :

Bending moment of the pile top

Q 0 :

Shear force of the pile top

a i  and  a i’:

Constant coefficients

A i1 ~ G i7 (i = 1, 2, 3, 4):

Influence function values of the piles in the loaded section

A i1 ~ G i7 (i = 5, 6, 7, 8):

Influence function values of the piles in the anchoring section.

\(\beta\), \(\omega\) and \(\gamma\) :

Pile deformation coefficients.

X c :

Pile displacement in the anchoring section

\({\varphi }_{c}\) :

Rotation angle in the anchoring section

M c :

Bending moment in the anchoring section

Q c :

Shear force in the anchoring section

X B :

Pile displacement at the sliding surface

\({\varphi }_{B}\) :

Rotation angle at the sliding surface

M B :

Bending moment at the sliding surface

Q B :

Shear force at the sliding surface

\({\phi }_{1}\), \({\phi }_{2}\), \({\phi }_{3}\), and \({\phi }_{4}\) :

Effect function value of the "K" method

c :

Cohesion

\(\varphi^{\prime}\)  :

Friction angle

\({F}_{\text{s}}\) :

The design safety factor of the slope

\(\gamma^{\prime}\)  :

Unit weight of soil

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Funding

The authors are grateful for the financial and technical support provided by the National Key R&D Program of China (Grant No. 2018YFC1505302), and the National Nature Science Foundation of China (Grant No. 52278332).

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Authors and Affiliations

  1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Meng Han & Jinqing Jia

  2. School of Civil Engineering, Dalian University of Technology, Dalian, 116024, China

    Meng Han & Jinqing Jia

  3. School of Highway, Chang’an University, Xi’an, Shaanxi, 710064, China

    Zhe Li

  4. School of Resources and Civil Engineering, Northeastern University, Shenyang, Liaoning, 110819, China

    Zhenguo Zhu

  5. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 210096, China

    Lulu Liu

Authors
  1. Meng Han
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  2. Zhe Li
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  3. Jinqing Jia
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  4. Zhenguo Zhu
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  5. Lulu Liu
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Corresponding author

Correspondence to Jinqing Jia.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this.

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Han, M., Li, Z., Jia, J. et al. Estimation of internal force of stabilizing piles on landslides considering nonlinear landslide thrust and soil resistance. Bull Eng Geol Environ 82, 285 (2023). https://doi.org/10.1007/s10064-023-03292-3

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  • DOI: https://doi.org/10.1007/s10064-023-03292-3

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