The influence of distant surcharge load with a finite length on the cantilever walls

Recep Akan

doi:10.1371/journal.pone.0295442

Abstract

The behavior of a sheet pile wall constructed on saturated sand soil and exposed to a distant surcharge load with a finite length at the top of the backfill soil is examined in this study. For this aim, various internal friction angles (φ), and natural ground surface for the groundwater level are considered. Furthermore, it is considered that the sheet pile wall acts as cantilevered and supports a six-meter-high (H) excavation. The simple “45° distribution” (AP) and uniform distribution of “Beton Kalender distribution” (BK) methods are examined with Coulomb’s and Rankine’s earth pressure theories in analytical solutions, while the finite element method (FEM) is used as a numerical method. The present research has two primary goals: a) determining the best analytical approach that provides the maximum bending moment (Mmax) values that are more comparable to those of the FEM b) examining the behavior of the sheet pile wall considering several effects of load scenarios, depth (D) and section type (ST) of the wall, and the soil properties together. In this context, parametrical analyses are performed. Consequently, it is found that the distance of the surcharge load (x₁) has a pronounced effect than the intensity (q) and length (Ls) of the surcharge load on the behavior of the sheet pile, and this effect vanishes for the large values of x₁. Furthermore, Coulomb theory provides more convenient values with FEM for Mmax than those obtained from Rankine theory. The Mmax values obtained from FEM are generally less than those from BK, while they are greater than those from APC.

Citation: Akan R (2023) The influence of distant surcharge load with a finite length on the cantilever walls. PLoS ONE 18(12): e0295442. https://doi.org/10.1371/journal.pone.0295442

Editor: Shaker Qaidi, University of Duhok, IRAQ

Received: August 23, 2023; Accepted: November 22, 2023; Published: December 11, 2023

Copyright: © 2023 Recep Akan. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper.

Funding: The author(s) received no specific funding for this work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Sheet pile walls are retaining walls with the advantages of being quick to build, lightweight, resistant to driving pressure, and having a longer service life for situations above and below the water level [1].

Sheet piles can be cantilevered or anchored, depending on the height and properties of the soil, to be retained against lateral forces. Cantilever sheet pile walls are often used to build marine constructions, and they frequently encounter strip surcharge loads from vehicles or building construction behind them [2]. The surcharge load behind the walls increases the lateral pressures, maximum bending moment, and lateral deflection along the sheet pile walls. In the design of sheet pile walls, the maximum moment is one of the most important factors to be considered, especially if they built nearby constructions. Hereby, the tolerable displacement of the walls depends on the soil properties, the location, the significance and the type of nearby structures [3]. As a result, understanding how the surcharge load influences the bending moment and displacement of sheet pile walls is critical for the structural design of sheet pile walls.

The accurate computation of horizontal earth pressures is challenging in designing the sheet pile walls. Therefore, numerous studies have been presented on this subject. The most prevalent approaches for determining active earth pressure without strip load are Coulomb’s and Rankine’s earth pressure theories [2, 4–7]. Coulomb [8] initially offered a way for analytically obtaining the solution to the earth pressure issue by examining the failure wedge and applying the force equilibrium conditions. Rankine [9] proposed an alternative idea identical to Coulomb’s theory but evolved in terms of stress. Additionally, conventional design approaches are even used by Terzaghi [10], Jumikis [11], and Bowles [4], but these approaches include some drawbacks because of different assumptions and concerns [12]. Fang et al. [13] investigated the horizontal pressure caused by a strip loading on a non-yielding wall and drew some conclusions based on the experimental findings. Farzaneh et al. [14] offered a two-dimensional solution using the upper-bound theorem for the combined active earth pressure caused by soil weight and strip foundation surcharge. However, the situation in which backfill is loaded by an infinite strip surcharge load has rarely been investigated.

The elastic analysis [15–17], which mainly relies on Boussinesq’s [18] elastic theory, the simple "45° load distribution" [19], the conventional earth pressure analysis of Coulomb [8], and the approach described in Beton Kalender [20] are currently used to determine strip load-generated lateral earth pressures. These methods produce vastly diverse earth pressure distributions, which could result in either excessively conservative or unsafe solutions. Therefore, the significance of this issue and the absence of an appropriate solution have led to an increased amount of study in this field. Motta [21] developed a closed-form approach for walls with sloping fill material and variable surcharge distances. Georgiadis and Anagnostopoulos [22] performed the model experiments of sheet pile walls in the sand to explore the influence of strip loads on the behavior of walls. Ghanbari and Taheri [23] employed the horizontal slices approach and proposed a thorough formulation to estimate the effect of a line surcharge on reinforced retaining walls with frictional or cohesive-frictional backfills. Hatem et al. [24] experimented to assess the influence of surcharge intensity, sloped terrain, and relative soil density on the deflection and bending moment of sheet piles. Xiao and Xia [25] presented a variational calculus technique to compute the passive earth pressure on the rigid retaining with a distant strip surcharge on its top surface about the limit equilibrium conditions of soil mass retained by rigid retaining walls. El-Emam and Touqan [26] created a strip footing next to the non-bending basement wall, where a series of scaled-down models were used to evaluate the basement wall’s performance. Mirmoazen et al. [27] employed the lower-bound limit analysis in conjunction with the finite element discretization method and second-order cone programming to evaluate the active lateral earth pressure on geosynthetic-reinforced retaining walls subjected to overlying strip footing loadings.

Strain, deflections, stress, and bending moments are some of the factors that make geotechnical correlation solutions more complicated. Consequently, numerical modeling has become an essential solution to simplify complicated calculations and improve accuracy [4, 11–14, 28–33]. Nowadays, FEM-based computer software is frequently utilized to provide more realistic designs findings and to understand sheet pile wall behavior better. Using a variety of analytical techniques, Denver and Kellezi [34] tackled several problems and compared them with FEM applied to several typical load scenarios on free and anchored sheet piles. Using three-dimensional FE models, Zhang and Sun [35] investigated the response of piles close to surcharge loads. Rauf et al. [36] presented the deflection of the sheet pile owing to surcharge load on backfill utilizing experimental investigation and numerical analysis using FEM-based software. The stability and behavior of the rigid cantilever retaining wall that supports dry sandy soil were investigated by Al-khafaji et al. [37] regarding the location of the surcharge load using a 2D finite element model. Nandi and Choudhury [38] introduced an analytical approach for the displacement-controlled analysis of rigid embedded cantilever retaining walls with a uniform strip surcharge. Later, they compared the settlements to those obtained from the Plaxis 2D program based on FEM. Debnath and Pal [39] applied a two-dimensional nonlinear to investigate the behavior of sheet piles in sand under a uniform surcharge strip foundation load. Then, they compared the deflection and bending moments of the wall to those obtained from Plaxis 2D program based on FEM. Besides, some researchers analyzed the behavior of the sheet pile walls by using the FLAC computer program based on the finite difference method. Singh and Chatterjee [40–42] explored the role of uniform surcharge load on the soil surface at a distance away on the behavior of cantilever sheet pile walls for bending moment, lateral earth pressure, deflection, and settlement behavior. Additionally, Singh and Chatterjee [43] compared the results obtained from Coulomb’s earth pressure theory and the finite difference method to investigate the effect of distant uniform strip load.

As it is seen from the above-mentioned literature research, numerous studies have been conducted on the bending and deflection behavior of sheet pile walls adopting several methods. However, the number of studies on the influence of the location and length of a surcharge load on the sheet pile wall is still very limited. Furthermore, the combined effects of several parameters, i.e., x₁, Ls and q, φ, D, ST, and reduction coefficient of the wall-soil interface (R) on the behavior of sheet pile wall, have not been examined yet. In this research paper, an attempt is made to address this problem. Furthermore, some benchmark results for the behavior of the sheet pile walls are provided. In this context, FEM analyses are conducted to demonstrate the effects of the relevant parameters on Mmax and maximum wall deformation (Ux) of the sheet pile wall. Furthermore, four distinct analytical methods are used to solve the Mmax of the models combining Coulomb’s and Rankine’s earth pressure theories [8, 9], and AP and BK distribution approaches [19, 20] to allow one to compare the consistency of widely used analytical solutions with FEM. Consequently, the results are tabulated and illustrated, discussed in detail, and summarized.

Model

To examine the behaviors of sheet pile walls, not only 400 models are solved with analytical methods, but also 700 models are analyzed with FEM. In those models, the groundwater level is assumed to be at the natural soil surface on both sides of the wall, and the saturated unit weight of the soil γ_s = 21 kN/m³. The dilatancy angle (ψ) of the soil is assumed to be 30 degrees less than φ. Then, various analytical and numerical models are developed to examine the effects of the soil, sheet pile, and surcharge load parameters. The parameters considered in the scope of the study and a schematic representation of the relevant model are shown in Table 1 and Fig 1, respectively.

Download:

Fig 1. The geometry of the study.

https://doi.org/10.1371/journal.pone.0295442.g001

Download:

Table 1. The parameters of the study.

https://doi.org/10.1371/journal.pone.0295442.t001

Method

The analytical solutions focus on the beginning and end of the construction, while the FEM considers state changes caused by deformation in progress. Moreover, the FEM uses the matrix and determinant methods and creates approximate solutions, but analytical methods provide conclusive results. Therefore, analytical methods may provide different results from the FEM results. Since analytical methods are frequently used to solve problems when the FEM is not an option, it is helpful to understand how similar the results of analytical solutions are to the results obtained with the FEM. Hence, both analytical solutions and numerical analyses are presented in the current study, where the Matlab R2015a program is utilized to code the analytical solutions, while the Plaxis 2D V20 is used to perform the FEM analyses. It should be noted that in the analytical solutions, the earth pressure theories of Coulomb [8] and Rankine [9] are taken into account together with the load distribution methods of simple “45° distribution”(AP) [19] and uniform distribution form of "Beton Kalender distribution" (BK) [20]. In this context, four different analytical solutions are obtained, considering Coulomb’s earth pressure theory with AP and BK, and Rankine’s earth pressure theory with AP and BK, abbreviated as APC, BKC, APR and BKR, respectively.

FEM

The FEM is one of the several numerical methods that have been continuously developed and improved over the last 50 years for evaluating sheet piles [44]. Since the FEM breaks down problems into several components and generates solutions that include derivatives and integrals using matrix and determinant methods. Therefore, it is recognized as a numerical method even if it incorporates analytical approaches to studies because it reveals approximate findings [30]. The FEM-based computer software Plaxis 2D v20 which assumes a two-dimensional plane strain and axisymmetric models and lets to perform deformation, stability, and flow analysis for various geotechnical applications. Furthermore, in the related software, the finite element mesh and geometry model can be easily generated [45]. The following assumptions are considered in the numerical analyses:

The width and length of the models are considered eight times the sheet pile length behind the wall and five times the sheet pile length below the excavation level, respectively, to avoid considerable fluctuation in the findings [46].
The boundary conditions are considered to be free vertically and constrained horizontally for the vertical borders while fully fixed for the lower horizontal border.
In accordance with the open literature [28, 30, 34, 39–43, 47–56], sand is modeled in drained conditions using the Mohr-Coulomb constitutive model, while the mesh is generated in the size of “fine” using 15-noded triangular finite elements.
Elastic plate elements are used to define the sheet piles, where the interface elements are assigned on both sides of the wall to provide friction between the sheet pile wall and the soil.

Application of the interface elements allows to model the interaction of structure and soil, i.e., the structure and the soil are bound together, and relative displacement is impossible without an interface. The behavior at the interface is controlled by the R, which determines the relationship between φ and the interface’s friction angle (δ’). It is assumed to be in the range of 0.5–0.8 between wall and soil [47]. Note that R_inter represents the R in the Plaxis program, and it is assumed that R_inter = 0.67 throughout the study as it is generally considered in practice. The relationship between δ’ and φ’ is as in Eq (1).

(1)

However, it is considered as 0.33, 0.67, and 1 in the study where the impact of the interface on the behavior of the wall is investigated. The groundwater table is assumed to be located at the natural ground surface for both the front and back of the wall. Staged construction is used as the loading type, and static stress calculations for the initial conditions are made in the first step. Then, the surcharge load and sheet pile are activated in the following phases. Finally, six meters of excavation, two meters at a stage, is finished in three steps. The developed model in the Plaxis 2D v20 program and the scheme that shows the model geometry and key variables are presented in Fig 2. At the same time, the material properties of the soil and the sheet pile wall are tabulated in Table 2, where E, A, I, EA, and EI are Young’s modulus, area, moment of inertia, the axial and flexural rigidity, respectively. Note that the properties of the PZ22 and PZ40 types of sheet piles are adopted from Amer [57].

Download:

Fig 2.

a) Simulation of the model considered in Plaxis 2D v20 and of which b) the scheme.

https://doi.org/10.1371/journal.pone.0295442.g002

Download:

Table 2. The properties of soil and the sheet pile materials.

https://doi.org/10.1371/journal.pone.0295442.t002

Analytical methods

Today’s earth pressure calculations are generally based on Coulomb’s and Rankine’s theories. The primary difference between Rankine and Coulomb earth pressure theories is that Coulomb considers friction between the soil and wall [2]. Let’s consider a retaining wall with a back face inclined at β = 90° angle and a backfill made of granular soil that slopes at α = 0° angle to the horizontal to illustrate Coulomb’s active earth pressure theory. The active and passive lateral earth pressure coefficients can be calculated using Coulomb’s and Rankine’s theories as follows. (2a) (2b) (3a) (3b) where Ka and Kp are the active and passive lateral earth pressure coefficients, respectively.

In the study, AP and BK methods are considered as load distribution approaches. Cernica (1995) [19] put forth the AP method, which distributes the strip load at a 45-degree angle (Fig 3A) while the strip load spreads at an angle between φ’ and 45+φ’ in BK [20] method (Fig 3B).

Download:

Fig 3.

Approximate approaches: a) AP [19]; b) BK distribution [20, 58].

https://doi.org/10.1371/journal.pone.0295442.g003

The AP approach is frequently used in practice due to its simplicity, and the lateral force caused by the surcharge load may be derived as follows. 4 (5) (6) (7) where x₁₁, Ls₁ and Ps are the depth, length, and resultant force of the lateral pressures caused by the surcharge load, respectively.

According to Beton-Kalender [20], the lateral force caused by the surcharge load can be determined as below.

(8)

(9)

(10)

(11)

Note that it is assumed to be in Coulomb theory, while it is neglected in Rankine theory, i.e. δ’ = 0. Furthermore, the active and passive lateral earth pressures acting on the sheet pile wall are shown in Fig 4.

Download:

Fig 4. The lateral forces acting on sheet pile wall.

https://doi.org/10.1371/journal.pone.0295442.g004

Hydrostatic pressures are not included in the calculations because the water levels are the same on both sides of the wall. Effective earth pressures are considered since the soil is fully saturated. The unit weight of water is assumed to be γ_w = 9.81 kN/m³, and the effective unit weight of the soil (γ^’) is determined below.

(12)

Point A is located at a depth (Z) where the shear force is zero on the section of the sheet pile wall. Besides, Pa and Pp are the lateral resultant components of the active and passive forces until point A, respectively. Furthermore, Pa and Pp can be written as a function of Z as follows.

(13)

(14)

It should be noted that each resultant force is inclined at an angle α with the horizontal in Rankine’s theory, while they are inclined at an angle δ’ with the normal of the wall in Coulomb’s theory. Therefore, the lateral components of these forces should be considered in calculations. After, the depth of Z is derived by using the balance of the total lateral force balance that is shown below: 15

Pa, Pp, and Ps act the wall at a point that is (H+Z)/3, Z/3 and far from the base of the wall, respectively. Consequently, Mmax is determined by calculating the bending moment about the point A by the Eq (16).

16

Results and discussion

In this section, the findings of the current research are tabulated and illustrated regarding Mmax and Ux for various q, x₁, Ls, φ, D values, and STs of the sheet pile wall. It is considered that φ = 35, R = 0.67, D = 15m, q = 50kN/m and the ST is PZ40 unless otherwise stated. The analytical approaches consider Coulomb’s earth pressure theory with AP and BK and Rankine’s earth pressure theory with AP and BK, denoted by APC, BKC, APR, and BKR, respectively.

Comparison studies

Table 3 compares the Mmax values obtained from the FE, BKR, BKC, APR, and APC methods for various φ, x₁ and Ls values. The influence of φ and x₁ / H on Mmax is more pronounced in the FEM and BK methods than in the AP method and becomes more pronounced as Ls increases. Ls substantially affects Mmax more in the FEM method than in the AP and BK methods. As φ, x₁ / H, and Ls rise, the effect of the used methods on Mmax also increases. With an increase in φ and x₁ / H, the influence of Ls on Mmax reduces, but Ls does not affect Mmax for large values of x₁. Mmax values that account for Rankine earth pressures are higher than those that account for Coulomb earth pressures.

Download:

Table 3. Mmax values versus x₁ / H, φ and Ls.

https://doi.org/10.1371/journal.pone.0295442.t003

The change in Mmax values obtained from the FE, BKR, and BKC methods versus φ and x₁ is shown in Fig 5. Mmax results obtained from the BKR method are significantly higher, while Mmax results obtained from the BKC method are slightly lower than those for FEM. The difference between the results obtained by FEM and BKC methods becomes more pronounced while x₁ / H and Ls decrease.

Download:

Fig 5. The variation of Mmax values versus φ, Ls and x₁ / H.

https://doi.org/10.1371/journal.pone.0295442.g005

The change of Mmax values found using the FE, BKC, and APC methods regarding the φ and x₁ / H is shown in Fig 6. Mmax values obtained from the BKC method appear to be higher than those acquired using the APC method. The effect of the load distribution approaches on Mmax becomes more evident as the x₁ / H increase and the φ decrease. The Mmax values obtained from FEM are generally less than those from BKC, and the discrepancy gets more significant as x₁ rises. However, the results obtained using FEM are greater than those from APC. Therefore, it is more conservative to use the BK method in analytical solutions. Consequently, the evaluations show that the results of the numerical and analytical solutions are consistent. This demonstrates the worth of the FEM results. Furthermore, FEM is used for parametric study.

Download:

Fig 6. The variation of Mmax values versus φ, Ls and x₁ / H.

https://doi.org/10.1371/journal.pone.0295442.g006

Parametric studies

The effects of D, R, Ls, q, x₁, and ST on the Mmax and Ux are investigated using FEM within the parametric studies. D is anticipated to have minimal effect, whereas the others should have a significant effect.

Study 1.

Table 4 presents the variation of Mmax values versus D/H and q for different φ and Ls values where x₁ = 0. Mmax varies slightly while D/H increases, so that indicates that D/H does not influence Mmax. Additionally, Mmax increases linearly while q rises regardless of Ls and φ. Mmax reduces roughly as φ increases from 30 to 45 degrees.

Download:

Table 4. Mmax values versus φ, q, D, and Ls.

https://doi.org/10.1371/journal.pone.0295442.t004

Study 2.

Table 5 demonstrates the variation of Mmax values with respect to the R, φ, x₁ for various Ls values. Mmax increases while R decreases, and the effect of R on Mmax depends on the φ but is independent of x₁ and Ls. Note that Mmax decreases where φ = 25 and R = 0.33 as an exception. It is predicted that the system deviates from stable conditions and experiences significant movements with bearing capacity losses due to the very loose soil and insufficient interface friction.

Download:

Table 5. Mmax values versus φ, x₁ / H, and R.

https://doi.org/10.1371/journal.pone.0295442.t005

Study 3.

The variance of the Mmax values versus the ST of the sheet pile and Ls is shown in Fig 7. The Mmax values for PZ22 and PZ40 differ slightly, so the ST has a negligible impact on Mmax. The fluctuation of Mmax caused by Ls depends on x₁ / H while it is independent of the ST.

Download:

Fig 7. Mmax values versus Ls and the STs of PZ22 and PZ40.

https://doi.org/10.1371/journal.pone.0295442.g007

Study 4.

Table 6 exhibits the Ux and Mmax values depending on the distance of the endpoint of the surcharge load (x₂) for x₁ / H = 0.08 and x₁ / H = 0.5. Mmax and Ux rise with the increase in x₂ / H but once x₂ / H exceeds a certain point, the effect on Mmax and Ux disappears.

Download:

Table 6. Mmax and Ux values versus x₂ / H.

https://doi.org/10.1371/journal.pone.0295442.t006

Fig 8 shows the variation of bending moments and lateral deflections along the sheet pile wall versus the x₂ / H for x₁ = 0. The Mmax values increase nonlinearly as the x₂ / H rises but stop increasing after a certain point.

Download:

Fig 8.

The variation of a) bending moment and b) lateral deflection along the sheet pile.

https://doi.org/10.1371/journal.pone.0295442.g008

Additionally, Fig 9 depicts the change of Mmax and Ux against the x₁ where x₂ / H = 3. Mmax and Ux decrease linearly with the increase in x₁ but remain constant after x₁ reaches larger values. Therefore, the surcharge load should be considered for the safety of the wall in case the surcharge is close to the wall.

Download:

Fig 9.

The variation of a) Mmax and b) Ux versus x₁ / H.

https://doi.org/10.1371/journal.pone.0295442.g009

Study 5.

Table 7 demonstrates the fluctuation of Mmax and Ux values versus x₁ / H for Ls = 3m and Ls = 6m. Additionally, Fig 10 illustrates the variation of bending moments and lateral deflections along the sheet pile wall depending on x₁ values. As x₁ / H decreases and Ls increases, both Mmax and Ux increase. Furthermore, it can be concluded that the effect of x₁ / H on Mmax and Ux is more pronounced than that of Ls.

Download:

Fig 10.

The variation of a) bending moment and b) lateral deflection along the sheet pile.

https://doi.org/10.1371/journal.pone.0295442.g010

Download:

Table 7. The variation of Mmax and Ux versus x₁ / H.

https://doi.org/10.1371/journal.pone.0295442.t007

Conclusions

The present study examines the effect of the surcharge load with various x₁, Ls, q, φ, R, D values, and different STs on the Mmax and Ux using FEM analyses. Besides, four distinct analytical methods are used to solve the Mmax of the models combining Coulomb’s and Rankine’s earth pressure theories with AP and BK distribution approaches to allow one to compare the consistency of widely used analytical solutions with FEM. The following findings are stated briefly:

* Mmax values obtained from Rankine’s theory are higher than those for Coulomb’s theory.
* The Mmax values obtained from FEM are generally lower than those from BKC, while the results of FEM are greater than those of APC.
* The effect of the applied methods on Mmax becomes more evident for a higher distance of the surcharge load and lower internal friction angle of the soil.
* The embedment depth and section type of the sheet pile do not influence Mmax significantly.
* Mmax increases linearly while the intensity of the surcharge load rises.
* Mmax increases as internal and interface friction angle decreases, with some exceptions where the sand is very loose and the interface friction is very low.
* Mmax and Ux increase as both the surcharge load approaches the wall and the length of the surcharge load increases.
* The effect of the distance of the surcharge load is more pronounced than that of the length.

References

1. Holakoo A, Weerartne R, Kugathasan K. Sheet pile retaining walls design and construction in brown fields environment level crossing removal project 1. 8 th Aust. Small Bridg. Conf., Sydney: 2017, p. 1–29.
- View Article
- Google Scholar
2. Das BM. Principles of Foundation Engineering. Boston, MA, USA: Cengage Learning; 2014.
3. Fok P, Neo BH, Veeresh C, Wen D, Goh KH. Limiting values of retaining wall displacements and impact to the adjacent structures. Ceased 2012;5:134–9.
- View Article
- Google Scholar
4. Bowles J. Analysis Foundation And Design. 5th ed. New York, NY, USA: McGraw- Hill International Editions; 1996.
5. Wang JJ, Liu FC, Ji C Lou. Influence of drainage condition on Coulomb-type active earth pressure. Soil Mech Found Eng 2008;45:161–7.
- View Article
- Google Scholar
6. Fang Y-S, Ho Y-C, Chen T-J. Passive Earth Pressure with Critical State Concept. J Geotech Geoenvironmental Eng 2002;128:651–9. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:8(651).
- View Article
- Google Scholar
7. Wang YZ. Distribution of earth pressure on a retaining wall. Geotechnique 2000;50:83–8.
- View Article
- Google Scholar
8. Coulomb CA. Essai sur une application des regles des maximas et minmas a quelques problemes de statique relatifs a l’architecture. Mémoires l’Académie R Des Sci Present Par Divers 1776;7:343–82.
- View Article
- Google Scholar
9. Rankine WJ. II. On the stability of loose earth. Philos Trans R Soc London 1857;147:9–27.
- View Article
- Google Scholar
10. Terzaghi K. Liner-Plate Tunnels on the Chicago (Il) Subway. Trans Am Soc Civ Eng 1943;108:970–1007.
- View Article
- Google Scholar
11. Jumikis AR. Mechanics of soils. Soil Sci 1964;98.
- View Article
- Google Scholar
12. Conte E, Troncone A, Vena M. A method for the design of embedded cantilever retaining walls under static and seismic loading. Géotechnique 2017;67:1081–9.
- View Article
- Google Scholar
13. Fang YS, Tzeng SH, Chen TJ. Earth pressure on an unyielding wall due to a strip surcharge. ISOPE Int. Ocean Polar Eng. Conf., 2007, p. ISOPE-I.
- View Article
- Google Scholar
14. Farzaneh O, Askari F, Fatemi J. Active earth pressure induced by strip loads on a backfill. Int J Civ Eng 2014;12:281–91.
- View Article
- Google Scholar
15. Teng W. Foundation design. Englewood Cliffs N.J.: Prentice-Hall; 1962.
16. Jarquio R. Total lateral surcharge pressure due to strip load. J Geotech Eng Div 1981;107:1424–8.
- View Article
- Google Scholar
17. Misra B. Lateral pressures on retaining walls due to loads on surface of granular backfill. SOILS Found 1981;20:33–44.
- View Article
- Google Scholar
18. Boussinesq J. Application des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques: principalement au calcul des déformations et des pressions que 1885.
- View Article
- Google Scholar
19. Cernica JN. Geotechnical engineering: foundation design. New York, USA: John Wiley & Sons; 1995.
20. Beton-Kalender . Verlag von Wilhelm Ernst and Sohn. Munich, Germany.: 1983.
21. Motta E. Generalized Coulomb ActiveEarth Pressure for Distanced Surcharge. J Geotech Eng 1994;120:1072–9. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:6(1072)
- View Article
- Google Scholar
22. Georgiadis M, Anagnostopoulos C. Lateral Pressure on Sheet Pile Walls due to Strip Load. J Geotech Geoenvironmental Eng 1998;124:95–8.
- View Article
- Google Scholar
23. Ghanbari A, Taheri M. An analytical method for calculating active earth pressure in reinforced retaining walls subject to a line surcharge. Geotext Geomembranes 2012;34:1–10.
- View Article
- Google Scholar
24. Hatem MK, Al-Dahlaki MH, Hassan HF. Experimental investigation of model piles in sloping ground subjected to surcharge loads. Iraqi Acad Sci Journals 2017;10:158–70.
- View Article
- Google Scholar
25. Xiao S, Xia P. Variational calculus method for passive earth pressure on rigid retaining walls with strip surcharge on backfills. Appl Math Model 2020;83:526–51.
- View Article
- Google Scholar
26. El-Emam M, Touqan M. Experimental modeling of strip footing adjacent to non-yielding retaining wall. Innov Infrastruct Solut 2020;5:1–17.
- View Article
- Google Scholar
27. Mirmoazen SM, Lajevardi SH, Mirhosseini SM, Payan M, Jamshidi Chenari R. 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 2022;46:3181–92.
- View Article
- Google Scholar
28. Hashash YMA, Marulanda C, Ghaboussi J, Jung S. Novel approach to integration of numerical modeling and field observations for deep excavations. J Geotech Geoenvironmental Eng 2006;132:1019–31. https://doi.org/https://doi.org/10.1061/(ASCE)1090-0241(2006)132:8(1019).
- View Article
- Google Scholar
29. Tan Y, Paikowsky SG. Performance of Sheet Pile Wall in Peat. J Geotech Geoenvironmental Eng 2008;134:445–58. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:4(445)
- View Article
- Google Scholar
30. Chapra SC, Canale RP. Numerical methods for engineers: with programming and software applications. 3rd ed. Boston, MA, USA: WCB/McGraw-Hill; 1998.
31. Day RA, Potts DM. Modelling sheet pile retaining walls. Comput Geotech 1993;15:125–43. https://doi.org/https://doi.org/10.1016/0266-352X(93)90009-V
- View Article
- Google Scholar
32. Krabbenhoft K, Damkilde L, Krabbenhoft S. Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming. Comput Struct 2005;83:383–93. https://doi.org/https://doi.org/10.1016/j.compstruc.2004.08.016
- View Article
- Google Scholar
33. Akan R. Examination of the behavior of the single anchored sheet piles in sand utilizing analytical and numerical methods. Arab J Geosci 2021;14:1–15.
- View Article
- Google Scholar
34. Denver H, Kellezi L. Modelling of Earth Pressure from nearby Strip Footings on a Free & Anchored Sheet Pile Wall. Proc. 17th Nord. Geotech. Meet. Challenges Nord. Geotech., 2016, p. 913–21.
- View Article
- Google Scholar
35. Zhang H, Sun K. Influence of Surcharge Load on the Adjacent Pile Foundation in Coastal Floodplain. Insight ‐ Civ Eng 2020;3:17–25.
- View Article
- Google Scholar
36. Rauf I, Hrianto T, Kusnadi K. Laboratorium Experimental Of Cantilever Sheet Pile Behaviour On Soft Soil Induced By Strip Load. E3S Web Conf 2021;328:10020.
- View Article
- Google Scholar
37. Al-khafaji RS, Al-Obaydi MA, Al-Saffar QN. Effect of surcharge load location on the behavior of cantilever retaining wall. J Mech Behav Mater 2023;32.
- View Article
- Google Scholar
38. Nandi R, Choudhury D. Displacement-controlled approach for the analysis of embedded cantilever retaining walls with a distanced strip surcharge. Comput Geotech 2022;151:104970.
- View Article
- Google Scholar
39. Debnath A, Pal SK. Influence of surcharge strip loads on the behavior of cantilever sheet pile walls: A numerical study. J Eng Res 2023;11:100029.
- View Article
- Google Scholar
40. Singh AP, Chatterjee K. Influence of soil type on static response of cantilever sheet pile walls under surcharge loading: a numerical study. Arab J Geosci 2020;13:138.
- View Article
- Google Scholar
41. Singh AP, Chatterjee K. Effect of Soil–Wall Friction Angle on Behaviour of Sheet Pile Wall Under Surcharge Loading. Proc Natl Acad Sci India Sect A ‐ Phys Sci 2021;91:169–79.
- View Article
- Google Scholar
42. Singh AP, Chatterjee K. Lateral earth pressure and bending moment on sheet pile walls due to uniform surcharge. Geomech Eng 2020;23:71–83.
- View Article
- Google Scholar
43. Singh AP, Chatterjee K. The influence of strip load on the seismic design of cantilever sheet pile walls: a simplified analytical solution. Bull Earthq Eng 2022;20:5301–22.
- View Article
- Google Scholar
44. Jiang S, Du C, Sun L. Numerical analysis of sheet pile wall structure considering soil-structure interaction. Geomech Eng 2018;16:309–20. http://doi.org/10.12989/gae.2018.16.3.309" xlink:type="simple">https://doi.org/http://doi.org/10.12989/gae.2018.16.3.309
- View Article
- Google Scholar
45. Brinkgreve R, Vermeer PA. Plaxis 2D reference manual connect edition v20 2019.
- View Article
- Google Scholar
46. Singh AP, Chatterjee K. Ground Settlement and Deflection Response of Cantilever Sheet Pile Wall Subjected to Surcharge Loading. Indian Geotech J 2020;50:540–9.
- View Article
- Google Scholar
47. Tang L, Cong S, Xing W, Ling X, Geng L, Nie Z, et al. Finite element analysis of lateral earth pressure on sheet pile walls. Eng Geol 2018;244:146–58.
- View Article
- Google Scholar
48. Muni T, Devi D, Baishya S. Parametric Study of Sheet Pile Wall using ABAQUS. Civ Eng J 2021;7:71–82.
- View Article
- Google Scholar
49. Singh AP, Chatterjee K. A displacement based approach for seismic analysis and design of cantilever sheet pile walls under surcharge loading. Comput Geotech 2021;140:104481.
- View Article
- Google Scholar
50. Denver H, Kellezi L. Earth pressure from the nearby buildings on sheet pile walls. 15th Eur. Conf. Soil Mech. Geotech. Eng., IOS Press; 2011, p. 1455–60.
51. Tan Y, Lu Y. Parametric studies of DDC-induced deflections of sheet pile walls in soft soils. Comput Geotech 2009;36:902–10.
- View Article
- Google Scholar
52. Berg P V. Effect of surface loading behind earth retaining walls. Delft Geotech 1991;2:767–71.
- View Article
- Google Scholar
53. Ertugrul OL, Trandafir AC. Lateral earth pressures on flexible cantilever retaining walls with deformable geofoam inclusions. Eng Geol 2013;158:23–33.
- View Article
- Google Scholar
54. Hsiung BCB. A case study on the behaviour of a deep excavation in sand. Comput Geotech 2009;36:665–75.
- View Article
- Google Scholar
55. Bilgin Ö. Lateral Earth Pressure Coefficients for Anchored Sheet Pile Walls. Int J Geomech 2012;12:584–95.
- View Article
- Google Scholar
56. Bahrami M, Khodakarami MI, Haddad A. 3D numerical investigation of the effect of wall penetration depth on excavations behavior in sand. Comput Geotech 2018;98:82–92.
- View Article
- Google Scholar
57. Amer HAR. Effect of wall penetration depth on the behavior of sheet pile walls. University of Dayton., 2013.
58. Blum H. Beitrag zur berechnung von bohlwerken unter beruchsichtigung der wandverformung, Verlag von Wilhelm Ernst and Sohn. Munich, Germany: 1951.

[ref1] 1. Holakoo A, Weerartne R, Kugathasan K. Sheet pile retaining walls design and construction in brown fields environment level crossing removal project 1. 8 th Aust. Small Bridg. Conf., Sydney: 2017, p. 1–29.
View Article
Google Scholar

[2] View Article

[3] Google Scholar

[ref2] 2. Das BM. Principles of Foundation Engineering. Boston, MA, USA: Cengage Learning; 2014.

[ref3] 3. Fok P, Neo BH, Veeresh C, Wen D, Goh KH. Limiting values of retaining wall displacements and impact to the adjacent structures. Ceased 2012;5:134–9.
View Article
Google Scholar

[6] View Article

[7] Google Scholar

[ref4] 4. Bowles J. Analysis Foundation And Design. 5th ed. New York, NY, USA: McGraw- Hill International Editions; 1996.

[ref5] 5. Wang JJ, Liu FC, Ji C Lou. Influence of drainage condition on Coulomb-type active earth pressure. Soil Mech Found Eng 2008;45:161–7.
View Article
Google Scholar

[10] View Article

[11] Google Scholar

[ref6] 6. Fang Y-S, Ho Y-C, Chen T-J. Passive Earth Pressure with Critical State Concept. J Geotech Geoenvironmental Eng 2002;128:651–9. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:8(651).
View Article
Google Scholar

[13] View Article

[14] Google Scholar

[ref7] 7. Wang YZ. Distribution of earth pressure on a retaining wall. Geotechnique 2000;50:83–8.
View Article
Google Scholar

[16] View Article

[17] Google Scholar

[ref8] 8. Coulomb CA. Essai sur une application des regles des maximas et minmas a quelques problemes de statique relatifs a l’architecture. Mémoires l’Académie R Des Sci Present Par Divers 1776;7:343–82.
View Article
Google Scholar

[19] View Article

[20] Google Scholar

[ref9] 9. Rankine WJ. II. On the stability of loose earth. Philos Trans R Soc London 1857;147:9–27.
View Article
Google Scholar

[22] View Article

[23] Google Scholar

[ref10] 10. Terzaghi K. Liner-Plate Tunnels on the Chicago (Il) Subway. Trans Am Soc Civ Eng 1943;108:970–1007.
View Article
Google Scholar

[25] View Article

[26] Google Scholar

[ref11] 11. Jumikis AR. Mechanics of soils. Soil Sci 1964;98.
View Article
Google Scholar

[28] View Article

[29] Google Scholar

[ref12] 12. Conte E, Troncone A, Vena M. A method for the design of embedded cantilever retaining walls under static and seismic loading. Géotechnique 2017;67:1081–9.
View Article
Google Scholar

[31] View Article

[32] Google Scholar

[ref13] 13. Fang YS, Tzeng SH, Chen TJ. Earth pressure on an unyielding wall due to a strip surcharge. ISOPE Int. Ocean Polar Eng. Conf., 2007, p. ISOPE-I.
View Article
Google Scholar

[34] View Article

[35] Google Scholar

[ref14] 14. Farzaneh O, Askari F, Fatemi J. Active earth pressure induced by strip loads on a backfill. Int J Civ Eng 2014;12:281–91.
View Article
Google Scholar

[37] View Article

[38] Google Scholar

[ref15] 15. Teng W. Foundation design. Englewood Cliffs N.J.: Prentice-Hall; 1962.

[ref16] 16. Jarquio R. Total lateral surcharge pressure due to strip load. J Geotech Eng Div 1981;107:1424–8.
View Article
Google Scholar

[41] View Article

[42] Google Scholar

[ref17] 17. Misra B. Lateral pressures on retaining walls due to loads on surface of granular backfill. SOILS Found 1981;20:33–44.
View Article
Google Scholar

[44] View Article

[45] Google Scholar

[ref18] 18. Boussinesq J. Application des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques: principalement au calcul des déformations et des pressions que 1885.
View Article
Google Scholar

[47] View Article

[48] Google Scholar

[ref19] 19. Cernica JN. Geotechnical engineering: foundation design. New York, USA: John Wiley & Sons; 1995.

[ref20] 20. Beton-Kalender . Verlag von Wilhelm Ernst and Sohn. Munich, Germany.: 1983.

[ref21] 21. Motta E. Generalized Coulomb ActiveEarth Pressure for Distanced Surcharge. J Geotech Eng 1994;120:1072–9. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:6(1072)
View Article
Google Scholar

[52] View Article

[53] Google Scholar

[ref22] 22. Georgiadis M, Anagnostopoulos C. Lateral Pressure on Sheet Pile Walls due to Strip Load. J Geotech Geoenvironmental Eng 1998;124:95–8.
View Article
Google Scholar

[55] View Article

[56] Google Scholar

[ref23] 23. Ghanbari A, Taheri M. An analytical method for calculating active earth pressure in reinforced retaining walls subject to a line surcharge. Geotext Geomembranes 2012;34:1–10.
View Article
Google Scholar

[58] View Article

[59] Google Scholar

[ref24] 24. Hatem MK, Al-Dahlaki MH, Hassan HF. Experimental investigation of model piles in sloping ground subjected to surcharge loads. Iraqi Acad Sci Journals 2017;10:158–70.
View Article
Google Scholar

[61] View Article

[62] Google Scholar

[ref25] 25. Xiao S, Xia P. Variational calculus method for passive earth pressure on rigid retaining walls with strip surcharge on backfills. Appl Math Model 2020;83:526–51.
View Article
Google Scholar

[64] View Article

[65] Google Scholar

[ref26] 26. El-Emam M, Touqan M. Experimental modeling of strip footing adjacent to non-yielding retaining wall. Innov Infrastruct Solut 2020;5:1–17.
View Article
Google Scholar

[67] View Article

[68] Google Scholar

[ref27] 27. Mirmoazen SM, Lajevardi SH, Mirhosseini SM, Payan M, Jamshidi Chenari R. 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 2022;46:3181–92.
View Article
Google Scholar

[70] View Article

[71] Google Scholar

[ref28] 28. Hashash YMA, Marulanda C, Ghaboussi J, Jung S. Novel approach to integration of numerical modeling and field observations for deep excavations. J Geotech Geoenvironmental Eng 2006;132:1019–31. https://doi.org/https://doi.org/10.1061/(ASCE)1090-0241(2006)132:8(1019).
View Article
Google Scholar

[73] View Article

[74] Google Scholar

[ref29] 29. Tan Y, Paikowsky SG. Performance of Sheet Pile Wall in Peat. J Geotech Geoenvironmental Eng 2008;134:445–58. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:4(445)
View Article
Google Scholar

[76] View Article

[77] Google Scholar

[ref30] 30. Chapra SC, Canale RP. Numerical methods for engineers: with programming and software applications. 3rd ed. Boston, MA, USA: WCB/McGraw-Hill; 1998.

[ref31] 31. Day RA, Potts DM. Modelling sheet pile retaining walls. Comput Geotech 1993;15:125–43. https://doi.org/https://doi.org/10.1016/0266-352X(93)90009-V
View Article
Google Scholar

[80] View Article

[81] Google Scholar

[ref32] 32. Krabbenhoft K, Damkilde L, Krabbenhoft S. Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming. Comput Struct 2005;83:383–93. https://doi.org/https://doi.org/10.1016/j.compstruc.2004.08.016
View Article
Google Scholar

[83] View Article

[84] Google Scholar

[ref33] 33. Akan R. Examination of the behavior of the single anchored sheet piles in sand utilizing analytical and numerical methods. Arab J Geosci 2021;14:1–15.
View Article
Google Scholar

[86] View Article

[87] Google Scholar

[ref34] 34. Denver H, Kellezi L. Modelling of Earth Pressure from nearby Strip Footings on a Free & Anchored Sheet Pile Wall. Proc. 17th Nord. Geotech. Meet. Challenges Nord. Geotech., 2016, p. 913–21.
View Article
Google Scholar

[89] View Article

[90] Google Scholar

[ref35] 35. Zhang H, Sun K. Influence of Surcharge Load on the Adjacent Pile Foundation in Coastal Floodplain. Insight ‐ Civ Eng 2020;3:17–25.
View Article
Google Scholar

[92] View Article

[93] Google Scholar

[ref36] 36. Rauf I, Hrianto T, Kusnadi K. Laboratorium Experimental Of Cantilever Sheet Pile Behaviour On Soft Soil Induced By Strip Load. E3S Web Conf 2021;328:10020.
View Article
Google Scholar

[95] View Article

[96] Google Scholar

[ref37] 37. Al-khafaji RS, Al-Obaydi MA, Al-Saffar QN. Effect of surcharge load location on the behavior of cantilever retaining wall. J Mech Behav Mater 2023;32.
View Article
Google Scholar

[98] View Article

[99] Google Scholar

[ref38] 38. Nandi R, Choudhury D. Displacement-controlled approach for the analysis of embedded cantilever retaining walls with a distanced strip surcharge. Comput Geotech 2022;151:104970.
View Article
Google Scholar

[101] View Article

[102] Google Scholar

[ref39] 39. Debnath A, Pal SK. Influence of surcharge strip loads on the behavior of cantilever sheet pile walls: A numerical study. J Eng Res 2023;11:100029.
View Article
Google Scholar

[104] View Article

[105] Google Scholar

[ref40] 40. Singh AP, Chatterjee K. Influence of soil type on static response of cantilever sheet pile walls under surcharge loading: a numerical study. Arab J Geosci 2020;13:138.
View Article
Google Scholar

[107] View Article

[108] Google Scholar

[ref41] 41. Singh AP, Chatterjee K. Effect of Soil–Wall Friction Angle on Behaviour of Sheet Pile Wall Under Surcharge Loading. Proc Natl Acad Sci India Sect A ‐ Phys Sci 2021;91:169–79.
View Article
Google Scholar

[110] View Article

[111] Google Scholar

[ref42] 42. Singh AP, Chatterjee K. Lateral earth pressure and bending moment on sheet pile walls due to uniform surcharge. Geomech Eng 2020;23:71–83.
View Article
Google Scholar

[113] View Article

[114] Google Scholar

[ref43] 43. Singh AP, Chatterjee K. The influence of strip load on the seismic design of cantilever sheet pile walls: a simplified analytical solution. Bull Earthq Eng 2022;20:5301–22.
View Article
Google Scholar

[116] View Article

[117] Google Scholar

[ref44] 44. Jiang S, Du C, Sun L. Numerical analysis of sheet pile wall structure considering soil-structure interaction. Geomech Eng 2018;16:309–20. http://doi.org/10.12989/gae.2018.16.3.309" xlink:type="simple">https://doi.org/http://doi.org/10.12989/gae.2018.16.3.309
View Article
Google Scholar

[119] View Article

[120] Google Scholar

[ref45] 45. Brinkgreve R, Vermeer PA. Plaxis 2D reference manual connect edition v20 2019.
View Article
Google Scholar

[122] View Article

[123] Google Scholar

[ref46] 46. Singh AP, Chatterjee K. Ground Settlement and Deflection Response of Cantilever Sheet Pile Wall Subjected to Surcharge Loading. Indian Geotech J 2020;50:540–9.
View Article
Google Scholar

[125] View Article

[126] Google Scholar

[ref47] 47. Tang L, Cong S, Xing W, Ling X, Geng L, Nie Z, et al. Finite element analysis of lateral earth pressure on sheet pile walls. Eng Geol 2018;244:146–58.
View Article
Google Scholar

[128] View Article

[129] Google Scholar

[ref48] 48. Muni T, Devi D, Baishya S. Parametric Study of Sheet Pile Wall using ABAQUS. Civ Eng J 2021;7:71–82.
View Article
Google Scholar

[131] View Article

[132] Google Scholar

[ref49] 49. Singh AP, Chatterjee K. A displacement based approach for seismic analysis and design of cantilever sheet pile walls under surcharge loading. Comput Geotech 2021;140:104481.
View Article
Google Scholar

[134] View Article

[135] Google Scholar

[ref50] 50. Denver H, Kellezi L. Earth pressure from the nearby buildings on sheet pile walls. 15th Eur. Conf. Soil Mech. Geotech. Eng., IOS Press; 2011, p. 1455–60.

[ref51] 51. Tan Y, Lu Y. Parametric studies of DDC-induced deflections of sheet pile walls in soft soils. Comput Geotech 2009;36:902–10.
View Article
Google Scholar

[138] View Article

[139] Google Scholar

[ref52] 52. Berg P V. Effect of surface loading behind earth retaining walls. Delft Geotech 1991;2:767–71.
View Article
Google Scholar

[141] View Article

[142] Google Scholar

[ref53] 53. Ertugrul OL, Trandafir AC. Lateral earth pressures on flexible cantilever retaining walls with deformable geofoam inclusions. Eng Geol 2013;158:23–33.
View Article
Google Scholar

[144] View Article

[145] Google Scholar

[ref54] 54. Hsiung BCB. A case study on the behaviour of a deep excavation in sand. Comput Geotech 2009;36:665–75.
View Article
Google Scholar

[147] View Article

[148] Google Scholar

[ref55] 55. Bilgin Ö. Lateral Earth Pressure Coefficients for Anchored Sheet Pile Walls. Int J Geomech 2012;12:584–95.
View Article
Google Scholar

[150] View Article

[151] Google Scholar

[ref56] 56. Bahrami M, Khodakarami MI, Haddad A. 3D numerical investigation of the effect of wall penetration depth on excavations behavior in sand. Comput Geotech 2018;98:82–92.
View Article
Google Scholar

[153] View Article

[154] Google Scholar

[ref57] 57. Amer HAR. Effect of wall penetration depth on the behavior of sheet pile walls. University of Dayton., 2013.

[ref58] 58. Blum H. Beitrag zur berechnung von bohlwerken unter beruchsichtigung der wandverformung, Verlag von Wilhelm Ernst and Sohn. Munich, Germany: 1951.

Figures

Abstract

Introduction

Model

Method

FEM

Analytical methods

Results and discussion

Comparison studies

Parametric studies

Study 1.

Study 2.

Study 3.

Study 4.

Study 5.

Conclusions

References