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Limit Analysis of Lateral Earth Pressure on Geosynthetic-Reinforced Retaining Structures Subjected to Strip Footing Loading Using Finite Element and Second-Order Cone Programming

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Abstract

Stability of reinforced retaining structures under a variety of surficial loadings is of particular significance in geotechnical engineering practice. In the current study, adopting the well-established lower-bound limit analysis in conjunction with the finite element discretization method and second-order cone programming, a rigorous numerical study is carried out to evaluate the active lateral earth pressure on geosynthetic-reinforced retaining walls subjected to overlying strip footing loadings. The significant influence of the length (Le) and number (n) of reinforcement layers, load intensity (q), width of strip footing (B) and its distance from the wall (a) on the lateral earth pressure is examined. It is shown that using reinforcements longer than a specific length fails to have any further significant contributions to the wall stability. With the increase in load intensity and width of the strip footing, the reinforcements are found to be further effectual in reducing the rate of increase in the value of active earth pressure coefficient. Moreover, the reinforcements are observed to be more effective in enhancing the rate of decrease in the earth pressure coefficient with the increase in the foundation-wall distance, up to a threshold value, beyond which they show the reverse influence.

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Abbreviations

\(\left[ A \right]\) :

Matrix of linear constraints

\(a\) :

The distance between the surface footing and the retaining wall

\(\left\{ b \right\}\) :

Vector of linear constraints

\(B\) :

Width of strip footing

\(H\) :

Wall height

\(I\) :

Identity matrix

\(i\) :

Number of nodes

\(K_{{\text{a}}}\) :

Active pressure coefficient

\(L_{e}\) :

Length of reinforcement layers

\(n\) :

Number of reinforcement layers

\(P_{{\text{a}}}\) :

Total active earth thrust

\(q\) :

Load intensity

\(Q_{{\text{c}}}^{3}\) :

Cone quadratic (second-order) constraint

\(x\) :

Horizontal coordinate

\(y\) :

Vertical coordinate

\(z\) :

Nodal auxiliary variable

\(\alpha\) :

Angle of each edge with the x-axis

\(\gamma\) :

Soil unit weight

\(\delta_{{{\text{sw}}}}\) :

Soil–wall interface friction angle

\(\delta_{{{\text{sr}}}}\) :

Soil–reinforcement interface friction angle

\(\eta_{{\text{a}}}\) :

Active efficiency factor

\(\xi_{i} ,\eta_{i} ,\zeta_{i}\) :

Shape function coefficients

\(\sigma\) :

Normal stress

\(\tau\) :

Shear stress

\(\varphi\) :

Internal friction angle

\(\psi\) :

Dilation angle

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Authors and Affiliations

  1. Department of Civil Engineering, Arak Branch, Islamic Azad University, Arak, Iran

    Seyed Mohamad Mirmoazen, Seyed Hamid Lajevardi & Seyed Mohammad Mirhosseini

  2. Department of Civil Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran

    Meghdad Payan & Reza Jamshidi Chenari

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  1. Seyed Mohamad Mirmoazen
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  2. Seyed Hamid Lajevardi
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  3. Seyed Mohammad Mirhosseini
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  5. Reza Jamshidi Chenari
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Correspondence to Meghdad Payan.

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Mirmoazen, S.M., Lajevardi, S.H., Mirhosseini, S.M. et al. Limit Analysis of Lateral Earth Pressure on Geosynthetic-Reinforced Retaining Structures Subjected to Strip Footing Loading Using Finite Element and Second-Order Cone Programming. Iran J Sci Technol Trans Civ Eng 46, 3181–3192 (2022). https://doi.org/10.1007/s40996-021-00793-7

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