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Earth Pressure Calculation of High Fill Culvert Considering Inclination of Soil Column Interface

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Iranian Journal of Science and Technology, Transactions of Civil Engineering Aims and scope Submit manuscript

Abstract

In current theory of earth pressure calculations for high fill culverts, the extended modes of sliding surface and shear friction stress are always neglected, leading to great difference between theoretical calculations and field measurements. To overcome this drawback, a novel earth pressure theory for high fill culverts is developed, which takes into account extension modes of sliding surface and shear friction stress. Firstly, a finite element method (FEM) model of the high fill culvert is established by Plaxis2D. In addition, extension modes of sliding surface and directions of shear friction stress are summarized by FEM simulations. Secondly, based on the limit equilibrium theory of granular materials, theoretical equations of positive projecting (PP) and induced trench installation (ITI) culvert considering extension modes of sliding surface and shear friction stress are derived. Thirdly, the theoretical calculations are in good agreement with field measurements and numerical simulations, demonstrating the accuracy of the PP and ITI culvert theoretical equations. Finally, a parametric analysis is performed to explore how three main factors, including fill height, thickness of the expanded polystyrene (EPS) geofoam, and the ratio of the deformation modulus of fill to the EPS geofoam block, affected the earth pressure on the culvert top.

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Data availability

I, the corresponding author, confirm that all of the content, figures (drawings, charts, photographs, etc.), and tables in the submitted work are either original work created by authors listed on the manuscript or work for which permission to re-use has been obtained from the creator. The data used to support the findings of this study are available from the corresponding author upon request, and the readers can access the data supporting the conclusions of the study.

Abbreviations

B :

Culvert width (m)

B′:

Width of inner soil column (m)

L :

Culvert length (m)

H :

Distance between fill top surface and culvert top (m)

H e :

Equal settlement surface height (m)

h :

Thickness of EPS plate (m)

z :

Depth of fill (m)

S 1 :

Settlement of inner soil column (m)

S 2 :

Settlement of outer soil column (m)

ΔS :

Difference settlement between inner and outer soil column (m)

τ :

Shear friction stress (kN)

τ1, τ2 :

Shear friction stress of outer soil column (kN)

τ1 ′, τ2 ′ :

Shear friction stress of inner soil column (kN)

P :

Earth pressure (kPa)

P´:

EPS plate removes earth pressure (kPa)

P C :

Earth pressure of culvert top (kPa)

E :

Modulus of elasticity (MPa)

E S :

Modulus of elasticity of fill (MPa)

E P :

Modulus of elasticity of EPS (MPa)

c :

Cohesion (kPa)

C :

Constant (dimensionless)

σ :

Vertical stress (kPa)

σ 1, σ 2 :

Static earth pressure (kPa)

ε :

Strain (%)

γ :

Unit weight (kN/m3)

μ :

Poisson’s ratio (dimensionless)

φ :

Internal friction angle (°)

α :

Inclination angle between sliding surface and he vertical direction (°)

ρ EPS :

Density of EPS plate (kg/m3)

δ :

Vertical deformation of EPS plate (m)

K 0 :

Lateral earth pressure coefficient at-rest (dimensionless)

ω c :

Aspect ratio of rigid culvert L/B (dimensionless)

k v :

Earth pressure ratio P/γH (dimensionless)

References

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Acknowledgements

The authors are grateful for the financial support of the National Natural Science Foundation of China (No. 52078194), the National Young Top-notch Talent of "Ten Thousand Talents Program", the Science Fund for Distinguished Young Scholars of Hubei Province(2022CFA043), the Young Top-notch Talent Cultivation Program of Hubei Province, the Outstanding Young and middle-aged Science and Technology Innovation Team of colleges and universities in Hubei Province (No. T2022010), and the Innovation Demonstration Base of Ecological Environment Geotechnical and Ecological Restoration of Rivers and Lakes (No. 2020EJB004).

Author information

Authors and Affiliations

  1. School of Civil Engineering and Architecture, Hubei University of Technology, Wuhan, 430068, People’s Republic of China

    Qiang Ma, Zhuo Chen, Yiming Liu & Gaofei Zeng

  2. Key Laboratory of Intelligent Health Perception and Ecological Restoration of Rivers and Lakes, Ministry of Education, Wuhan, People’s Republic of China

    Qiang Ma, Zhuo Chen & Gaofei Zeng

  3. School of Civil Engineering, Wuhan University, Wuhan, 430072, People’s Republic of China

    Junjie Zheng

Authors
  1. Qiang Ma
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  2. Zhuo Chen
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  3. Junjie Zheng
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  4. Yiming Liu
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  5. Gaofei Zeng
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Corresponding author

Correspondence to Gaofei Zeng.

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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 paper.

Appendix

Appendix

In this paper, some of the steps for calculating the equations are omitted, mainly as follows:

Equation (1) can be derived from the following equation:

$$\begin{gathered} P\left[ {B + 2\left( {H - z} \right)\tan \alpha } \right] + \frac{1}{2}\gamma \left[ {B + 2\left( {H - z} \right)\tan \alpha + B + 2\left( {H - z} \right)\tan \alpha - 2\tan \alpha dz} \right]dz \hfill \\ = \left( {P + dp} \right)\left[ {B + 2\left( {H - z} \right)\tan \alpha - 2\tan \alpha dz} \right] - 2\tau^{\prime}\cos \alpha \hfill \\ \end{gathered}$$

Equation (3) can be derived from the following equation:

$$p\left( {B + 2H_{e} \tan \alpha } \right) + \gamma \left( {B + 2H_{e} \tan \alpha } \right)dz + \gamma \left( {B + 2H_{e} \tan \alpha } \right)K_{0} \tan fdz = \left( {p + dp} \right)\left( {B + 2H_{e} \tan \alpha } \right)$$

Equation (5) can be derived from the following equation:

$$\begin{gathered} p\left[ {B + 2\left( {H - z} \right)\tan \alpha } \right] + \frac{1}{2}\gamma \left[ {B + 2\left( {H - z} \right)\tan \alpha + B + 2\left( {H - z} \right)\tan \alpha - 2\tan \alpha dz} \right]dz \hfill \\ = \left( {p + dp} \right)\left[ {B + 2\left( {H - z} \right)\tan \alpha - 2\tan \alpha dz} \right] - 2\tau^{\prime}\cos \alpha \hfill \\ \end{gathered}$$

Equation (7) can be derived from the following equation:

$$\begin{gathered} p\left[ {B + 2\left( {H - z} \right)\tan \alpha } \right] + \frac{1}{2}\gamma \left[ {B - 2\left( {H - z} \right)\tan \alpha + B + 2\left( {H - z} \right)\tan \alpha - 2\tan \alpha dz} \right]dz \hfill \\ + 2 \times \frac{1}{2}\left[ {\gamma z + \gamma \left( {z + dz} \right)} \right]\cos^{2} \alpha dz\tan \alpha - 2\tau^{\prime}\cos \alpha = \left( {p + dp} \right)\left[ {B - 2\left( {H - z} \right)\tan \alpha + 2\tan \alpha dz} \right] \hfill \\ \end{gathered}$$

Equation (9) can be derived from the following equation:

$$p\left( {B - 2H_{e} \tan \alpha } \right) + \gamma \left( {B - 2H_{e} \tan \alpha } \right)dz + \gamma \left( {B - 2H_{e} \tan \alpha } \right)K_{0} \tan fdz = \left( {p + dp} \right)\left( {B - 2H_{e} \tan \alpha } \right)$$

Equation (11) can be derived from the following equation:

$$\begin{gathered} p\left[ {B - 2\left( {H - z} \right)\tan \alpha } \right] + \frac{1}{2}\gamma \left[ {B - 2\left( {H - z} \right)\tan \alpha + B - 2\left( {H - z} \right)\tan \alpha + 2\tan \alpha dz} \right]dz \hfill \\ + 2 \times \frac{1}{2}\left\{ {\gamma \left[ {z - \left( {H - H_{e} } \right)} \right] + \gamma \left[ {z - \left( {H - H_{e} } \right) + dz} \right]} \right\}\cos^{2} \alpha dz\tan \alpha - 2\tau^{\prime}\cos \alpha \hfill \\ = \left( {p + dp} \right)\left[ {B - 2\left( {H - z} \right)\tan \alpha + 2\tan \alpha dz} \right] \hfill \\ \end{gathered}$$

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Ma, Q., Chen, Z., Zheng, J. et al. Earth Pressure Calculation of High Fill Culvert Considering Inclination of Soil Column Interface. Iran J Sci Technol Trans Civ Eng (2024). https://doi.org/10.1007/s40996-024-01416-7

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  • DOI: https://doi.org/10.1007/s40996-024-01416-7

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