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Predicting the performance of retaining structure under seismic loads by PLAXIS software

  • Mustafa Maadh Badr EMAIL logo und Qassun S. Mohammed Shafiqu
Veröffentlicht/Copyright: 4. April 2023
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Journal of the Mechanical Behavior of Materials
Aus der Zeitschrift Journal of the Mechanical Behavior of Materials Band 32 Heft 1

Abstract

The dynamic response of the retaining structures is a complex issue, and a major challenge in their design, especially under seismic loading conditions. So a reliable and efficient solution following a computational approach, closer to reality, is required to obtain satisfactory results. Hence, this study came to clarify the effectiveness of the PLAXIS 3D program in predicting the performance, accuracy, and reliability of retaining walls. A case study of placing compressed materials as the backfill of the retaining wall soil is analyzed in this study using PLAXIS 3D software. The results are compared with the experimental results and the results of PLAXIS 2D software. The purpose is to predict the performance of retaining walls under seismic loads. As a result, the research stated that the displacement with time was less than the results recorded depending on the program PLAXIS 2D. According to the comparison of the different analytical tools, the researchers concluded that the adoption of the PLAXIS 3D program gives results that are closer to reality, more accurate, and more reliable.

Keywords: retaining structure; seismic loading; backfill; PLAXIS 2D; PLAXIS 3D

1 Introduction

Retaining structures are walls, dams, barriers, or bins that keep Earth materials or water from advancing into an area. Building pads, highways, bridge abutments, and wharves all require retaining structures to provide stable surfaces. Retaining structures can be used to limit the volume of excavations or to make space available near a piece of land’s boundary [1,2].

The goal of the retaining structures is to securely transfer the pressure of the earth to the supporting ground. The dominating lateral earth pressure (i.e., sliding, overturning) imposed the requirements of the design. And with the nature of dynamic loading, the transmission of earth pressure securely to the supporting earth becomes considerably more difficult in the event of seismic forces [3,4].

The development of finite element analysis in two dimensions (2D) and three dimensions (3D) has substantially improved the capacity to represent complicated geotechnical issues. This research compares the results of the two- and three-dimensional models of compressed materials with the retaining wall soil backfill to estimate the performance of retaining walls under seismic stresses.

PLAXIS 3D Dynamics module can handle more advanced seismic analysis than what is available by default in PLAXIS 2D. PLAXIS 3D can accurately calculate the effects of vibrations with a dynamics analysis when the frequency of the dynamic load is higher than the natural frequency of the medium [5]. Saribas and Ok’s study is one of the studies that study the effects of using two different types of recycled aggregates with known properties as backfill materials in newly built cantilevered reinforced concrete retaining walls on the seismic performance of the walls. The study showed that partially or completely recycled aggregate can be used as a backfill in retaining walls [6]. Another study conducted by Aya and Alam mainly focuses on the position of the EPS floor foam behind the L-shaped retaining wall to control deflection under the influence of seismic forces, together with the direction of EPS Geofoam, to reduce the lateral deflection of the retaining wall L-shaped. The analysis was performed in PLAXIS 2D for both static and dynamic states [7].

2 Retaining structures and lateral earth pressure

Retaining structures’ aim is to keep the soil in place and withstand the soil’s lateral pressure on the wall. The moving soil wedge idea is the foundation of most lateral stress theories. This is predicated on the concept that, if the wall was to be abruptly removed, a soil wedge that is triangular in shape would drop down beside a rupture aircraft, and the wall would have to hold this wedge of soil [8]. In classical soil mechanics, the model of lateral pressure is part of the first organization of theories. Coulomb and Rankine devised theories for estimating passive and active lateral pressures, respectively.

Behind retaining walls, these theories yield a coefficient, which is a ratio of horizontal to vertical stress. The horizontal stress integration is used to compute lateral pressure using the ratio [5].

The well-known Mononobe–Okabe equation (M–O), is a seismic force calculation modification of the Coulomb equation. It may be used to calculate the lateral loads on a retaining structure based on ground pressure, but it ignores the inertial force that backfill exerts on the retaining structure during seismic events. One solution to this challenge is to consider both vertical and horizontal ground accelerations, with seismic coefficients for active and passive stress (K AE, and K PE) provided by the M–O equations [8].

3 Numerical model and validation

3.1 Details of the physical model

Physical model testing [9] was adopted for creating the numerical model, apparatus or Equivalent Shear Beam Container by Scotto di Santolo et al. [10], was used as a reference case model. The model wall itself was 1.15 m in depth, 4.8 m in length, 1-m in width, and it had to be built in a laminar container that is flexible. The apparatus was set up on a 3 × 3 m aluminum shaking table with a payload-carrying capacity of 3.8 tons. The frequency of the shaking can range from 1 to 100 Hz. The gadget has 21 1-D accelerometers for determining accelerations and 4 LVDTs (linear variable differential transducers) for capturing the dynamic response to see the wall bending, as well as the permanent displacement and 32 strain measurements. Figure 1 depicts the model’s size as well as the location of the experiment’s instrumentation [9,10].

Figure 1 A shaking test table’s geometry and instrumentation (dimensions in mm) [9].
Figure 1

A shaking test table’s geometry and instrumentation (dimensions in mm) [9].

The model consists of L shaped retaining structure, with a 0.6 m thick backfill lying atop a top of a 0.4 m deep soil layer. The first configuration had a 300 mm wall heel and a 50 mm toe. The wall heel was decreased by 50 mm in both Configurations 2 and 3 to make it 250 mm, and the toe was eliminated after gluing with abrasive sandpaper to increase from 23.5° to 28° frictional force of the base contact, as seen in Figure 2.

Figure 2 Various sand layers have different frequencies of shear modulus [9].
Figure 2

Various sand layers have different frequencies of shear modulus [9].

Static pull tests on the wall were used to determine the contact friction angles in situ. The foundation layer and backfill were both made of Leighton Buzzard (LB) sand (Fraction B) that had been compressed to varying levels. The experimental investigation indicated 42.5 and 33.5° as the highest friction angles of the foundation layer and backfill, based on the relative densities, Dr, of the sand produced [9].

Figure 2 depicts the total sand layers in two portions, each with a distinct frequency (f 1n ) and shear modulus (G 0). The retaining structure model was constructed using aluminum Plates made of alloy 5,083 with a thickness of 32 mm and the following properties: unit weight = 27 kN/m3, Young’s modulus E = 70 GPa, and Poisson’s ratio v = 0.3. A sinusoidal stimulation with 15 steady cycles was used to load the harmonic acceleration. A succession of increasing-amplitude sinusoidal seismic excitation amplitude was then chosen at a frequency of 7 Hz [9].

3.2 Elements

The ten-node tetrahedral elements are the primary soil elements of the 3D finite element mesh (Figure 3).

Figure 3 Soil components in three dimensions (ten-node tetrahedron) [11].
Figure 3

Soil components in three dimensions (ten-node tetrahedron) [11].

Special sorts of elements, in addition to soil elements, are utilized to model structural behavior as follows [11]:

  1. Three-node line elements are utilized for beams because They work with a soil element’s three-node edges.

  2. For plates and geogrids, six-node plate and geogrid elements are used to simulate the behavior.

  3. The behavior of the soil–structure interaction is simulated using 12-node interface components.

3.3 Soil model

In PLAXIS 3D, different soil models were employed in the investigation. Soils display non-linear behavior when under stress or pressure. In reality, the amount of stress, the stress pathway, and the strain level all influence the soil stiffness [12]. In this article, a model that has been used is Mohr–Coulomb (MC).

3.4 MC soil model

On the other hand, the MC model is a well-known and straightforward linear elastic fully plastic model that may be used to represent soil behavior. The linear elastic portion of the MC model employs Hooke’s law of isotropic elasticity. The totally plastic component is created using the MC failure criteria, which are expressed in a non-associated plasticity framework. Eq. (1) governs the MC failure criterion [12].

(1) τ = c + σ ′ tan Ø ,

where τ is the soil’s shear strength, c is its cohesion, σ′ is its effective normal stress, and φ is its friction angle.

The stress–strain plot helps to describe the linear elastic fully plastic behavior in Figure 4. The letters ε e and ε p stand for elastic and plastic strains, respectively.

Figure 4 Fundamental concept of linear elastic fully plastic behavior [12].
Figure 4

Fundamental concept of linear elastic fully plastic behavior [12].

3.5 Numerical simulations

Using PLAXIS 3D, a numerical simulation of the same size with the real shaking table model (4.8 m width and 1 m height) was created. For Configuration 3, a retaining wall with a high of 600 mm and a base-wide of 250 mm were used. The displacement histories of the wall were recorded at three nodal sites along with its height, D1, D2, and D3. The mesh utilized in this investigation is medium (Figure 5).

Figure 5 PLAXIS 3D with a finite element mesh that is employed in the numerical model for the shake table test.
Figure 5

PLAXIS 3D with a finite element mesh that is employed in the numerical model for the shake table test.

4 Analytical case study

Figure 6 shows a retaining wall model with a medium-dense backfill used as a case study model [5].

Figure 6 A retaining wall model with a medium-dense backfill.
Figure 6

A retaining wall model with a medium-dense backfill.

5 Material properties and description

The numerical study was performed for ten-node elements and plane deformation conditions. The material parameters for the sand and retaining wall have been taken similarly to those from the shake table test. When foundation, soil, and backfill materials are exposed to dynamic loads, they exhibit stress–strain behavior, which is illustrated using the MC elastoplastic model (Table 1).

Table 1

Materials characteristics that are employed in numerical simulations [9]

Material γ (KN/m3) E (KN/m2) c (KN/m2) Ø (°) v R inter
Foundation (dense sand) 16.14 53.3 × 103 1 42 0.3 0.6
Foundation (dense sand) under backfill 16.14 104 × 103 1 42 0.3 0.6
Backfill (medium-dense sand) 15.11 52 × 103 1 34 0.3 0.6

A linear-elastic material was used to simulate the retaining wall. Table 2 displays the characteristics that were used in the modeling [9].

Table 2

The retaining wall’s material qualities [9]

Parameter Symbol Value Unit
Elastic stiffness EA 2.24 × 106 (KN/m)
Flexural rigidity EI 191 (KN/m2/m)
Unit weight γ 27 (KN/m3)
Weight of wall W 0.86 (KN/m/m)
Passion ratio V 0.3 —

6 Dynamic analysis

6.1 Damping

Dynamic calculations in PLAXIS are based on the basic equation of volume change as a result of time under influence of a dynamic load. Eq. (2) is used to calculate the relative damping of mass and stiffness [12].

(2) C = α R M + β R K .

The damping matrix, stiffness matrix, and mass matrix, respectively, are C, K, and M. The Rayleigh coefficients are α and β. A link between the damping ratio and Rayleigh damping parameters may be formed given the Rayleigh damping.

(3) α R + β R ω 2 = 2 ω ξ with ω = 2 π f .

In Eq. (3), f is the frequency and ω the angular frequency (rad/s) (Hz). Eq. (2) is resolved to yield the requisite Rayleigh damping coefficients for two alternative target frequencies and related target damping ratios:

(4) α R = 2 ω 1 ω 2 ω 1 ξ 2 − ω 2 ξ 1 ω 1 2 − ω 2 2 ,

(5) β R = 2 ω 1 ξ 1 − ω 2 ξ 2 ω 1 2 − ω 2 2 .

After Rayleigh coefficients are automatically determined, the goal frequencies and damping ratios may be defined using Eqs. (4) and (5), where ξ is the desired damping of 5.0%. Explain that the first goal frequency is the natural frequency number one f 1. The second target frequency is the next odd integer bigger than the percentage f p/f 1, which is the ratio of the input motion’s predominant frequency to the soil’s natural frequency. The natural frequency of soil deposition of thickness H is related to its shape and stiffness by Eq. (6):

(6) f 1 = V s 4 H .

The shear wave of velocity in soil deposition, v s, is a function of shear stiffness modulus G. Eqs. (4)–(6) were used to compute the Raleigh damping coefficients and dynamic soil parameters, which are given in Table 3.

Table 3

Rayleigh damping coefficients of the Backfill and foundation soil [9]

Soil H (m) V s (m/s) f 1 (Hz) α β
Foundation (dense sand) 0.4 115.9 72.438 4.103 0.0001524
Foundation (dense sand) under backfill 0.4 111.6 69.750 3.997 0.0002074
Backfill (medium-dense sand) 0.6 113.8 47.416 3.832 0.0002925

6.2 Excitation

A fundamental excitation was applied to the finite element model, which represents the variable amplitude harmonic motion. The frequency of the applied harmonic input base acceleration was the agent of a medium-to-high frequency content earthquake’s usual predominant frequency. As illustrated in Figure 8, the constant frequency cyclic load was modeled using the program’s prescribed displacement feature at the base of the wall. The varied-amplitude harmonic stimulation was chosen such that the steady increase and then drop in amplitude with a set frequency resembles a real earthquake. Eq. (7) represents harmonic excitation, as seen in Figure 7 [9].

(7) α h ( t ) = α max 5 ft sin ( 2 π ft ) t ⊰ 5 f α max sin ( 2 π ft ) 5 f ⪯ t ⊰ 3 . 357 α max 5 3 . 357 + 5 f − t f sin ( 2 π ft ) 3 . 357 ⪯ t ⪯ 3 . 357 + 5 f .

The time is t, the frequency is f, and the amplitude of the acceleration is a max. The baseline model was subjected to a reference cyclic harmonic load with rising input acceleration amplitude provided at equal time intervals of 5 s at a frequency of 7 Hz, and its accelerogram was generated using Eq. (7). The numerical model employed the obtained acceleration time history as an input excitation [9].

Figure 7 Input sinusoidal motion at a frequency of 7 Hz and a 0.1 g amplitude.
Figure 7

Input sinusoidal motion at a frequency of 7 Hz and a 0.1 g amplitude.

Figure 8 The model under seismic loading in PLAXIS 3D.
Figure 8

The model under seismic loading in PLAXIS 3D.

7 Soil–structure interaction consideration

In order to represent the interaction between soil and structural units, interfaces must be identified. This is done to characterize the earth’s decreased resistance to a structured surface. Without interface components, there is no slippage or gapping, which in most cases is a non-physical assumption for the interaction between structure and soil. Strength and stiffness reductions are introduced. By using the interfaces, the parameter Rinter introduces strength and stiffness reductions. The contact strength is reduced in these studies by using a strength reduction factor of 0.60 < 1.

Interfaces are joint elements to be added to plates or geogrids to allow for proper modeling of soil–structure interaction. Interfaces may be used to simulate, for example, the thin zone of intensely shearing material at the contact between a plate and the surrounding soil. Interfaces can be created next to a plate or geogrid elements or between two soil volumes.

8 Boundary conditions

Different boundary conditions beyond the typical fixities are necessary for dynamic computations in order to depict the medium’s far-field behavior. When building a geometry model, reality is defined by an infinite domain that must be reduced to a limited domain. By absorbing the increase in stresses generated by dynamic loading and minimizing false wave reflections inside the soil body, appropriate boundary conditions can imitate far-field behavior. PLAXIS 3D comes with the option of using viscous borders by default, but there are other alternatives as well [11]. This study uses the None option for the boundaries in the y-direction, viscous in the x-direction, None in the Zmax, and viscous in Zmain.

9 Model validation

After 15 cycles of harmonic stimulation at 0.19 g accelerations at 7 Hz frequency, the maximum dynamic wall displacement as a function of time was compared between finite element analysis and shaking table testing. Figure 8 depicts an earthquake model.

Figure 9 shows a comparison between the PLAXIS 2D and PLAXIS 3D results. D1, D2, and D3 are the output points at the top, middle, and bottom of the wall, respectively. The figure demonstrates an acceptable comparison between the results from the numerical and physical models to validate the numerical model in simulating the physical model shaking table tests on retaining walls.

Figure 9 Numerical and physical model experiments under sinusoidal–harmonic stimulation (a = 0.19 g, f = 7 Hz).
Figure 9

Numerical and physical model experiments under sinusoidal–harmonic stimulation (a = 0.19 g, f = 7 Hz).

Figure 10 shows a comparison between the theoretical analytical results of the physical model (shake table testing) by different analysis tools, whether in a program PLAXIS 2D or PLAXIS 3D. D1, D2, and D3 indicate output points at the top, middle, and bottom of the wall, respectively.

Figure 10 Comparison between the PLAXIS 2D and PLAXIS 3D results for different points along the cantilever wall stem.
Figure 10

Comparison between the PLAXIS 2D and PLAXIS 3D results for different points along the cantilever wall stem.

After using the results of the analysis of the program PLAXIS 2D from the paper by Abdelkader, Sadok, and Umashankar in 2020 [9]. Figure 10 shows that the theoretical analytical results from the program PLAXIS 3D differed from the results of the program PLAXIS 2D. The displacement ratio with respect to the physical model at the top point was around 0.26%, equating to a displacement ratio with respect to the program PLAXIS 2D for the same position of 0.47%, and the displacement ratio for the PLAXIS 3D was 0.45%, as shown by extrapolation of the results for each of Figures 9 and 10. From these results, the research hypothesis is realized that the adoption of the PLAXIS 3D program gives results that are closer to reality, more accurate, and more reliable.

10 Results and discussions

  • The maximum displacement with respect to time at the top point was 0.87 mm in PLAXIS 3D, while in practice the maximum displacement was 1.03 mm per s 5.

  • The displacement ratio with respect to the physical model at the top point was approximately 0.26%, corresponding to a displacement ratio with respect to the program PLAXIS 2D for the same point of 0.47%. As for the 3D, the displacement ratio was 0.45%.

11 Conclusions

The following are the findings of the investigation:

  1. It was discovered that the theoretical analytical results of the PLAXIS 3D program are quite close to reality in terms of horizontal displacements.

  2. In PLAXIS 2D, a plane strain analysis can predict the Retaining Structure’s Performance under Seismic Loads, but the amount of the displacement must be corrected for the difference between the plane strain loading and the real axisymmetric loading. However, the difference between the plane strain loading and the true 3D loading must be taken into account when calculating the displacement.

  3. In the bottom point (D3), the theoretical and analytic consequences of a program PLAXIS 3D differed from the results of a program PLAXIS 2D. As for the middle (D2) and upper point (D1), the difference was very little.

  4. The performance of these different simulation techniques was validated and compared. The mesh pattern is very significant in PLAXIS 3D finite element studies because it allows for accurate findings without using a lot of computer memory or time. Despite the fact that the 2D as well as 3D analyses matched rather well, the 3D analysis takes significantly longer to run than the 2D analysis and creates more discretization errors due to a coarser pattern mesh.

  1. Funding information: No funding is involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors declare no conflict of interest.

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Received: 2022-04-27
Revised: 2022-08-10
Accepted: 2022-08-15
Published Online: 2023-04-04

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/jmbm-2022-0251
Schlagwörter für diesen Artikel
retaining structure; seismic loading; backfill; PLAXIS 2D; PLAXIS 3D
Creative Commons
BY 4.0

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  30. A theoretical study of mechanical source in a hygrothermoelastic medium with an overlying non-viscous fluid
  31. An atomistic study on the strain rate and temperature dependences of the plastic deformation Cu–Au core–shell nanowires: On the role of dislocations
  32. Effect of lightweight expanded clay aggregate as partial replacement of coarse aggregate on the mechanical properties of fire-exposed concrete
  33. Utilization of nanoparticles and waste materials in cement mortars
  34. Investigation of the ability of steel plate shear walls against designed cyclic loadings: Benchmarking and parametric study
  35. Effect of truck and train loading on permanent deformation and fatigue cracking behavior of asphalt concrete in flexible pavement highway and asphaltic overlayment track
  36. The impact of zirconia nanoparticles on the mechanical characteristics of 7075 aluminum alloy
  37. Investigation of the performance of integrated intelligent models to predict the roughness of Ti6Al4V end-milled surface with uncoated cutting tool
  38. Low-temperature relaxation of various samarium phosphate glasses
  39. Disposal of demolished waste as partial fine aggregate replacement in roller-compacted concrete
  40. Review Articles
  41. Assessment of eggshell-based material as a green-composite filler: Project milestones and future potential as an engineering material
  42. Effect of post-processing treatments on mechanical performance of cold spray coating – an overview
  43. Internal curing of ultra-high-performance concrete: A comprehensive overview
  44. Special Issue: Sustainability and Development in Civil Engineering - Part II
  45. Behavior of circular skirted footing on gypseous soil subjected to water infiltration
  46. Numerical analysis of slopes treated by nano-materials
  47. Soil–water characteristic curve of unsaturated collapsible soils
  48. A new sand raining technique to reconstitute large sand specimens
  49. Groundwater flow modeling and hydraulic assessment of Al-Ruhbah region, Iraq
  50. Proposing an inflatable rubber dam on the Tidal Shatt Al-Arab River, Southern Iraq
  51. Sustainable high-strength lightweight concrete with pumice stone and sugar molasses
  52. Transient response and performance of prestressed concrete deep T-beams with large web openings under impact loading
  53. Shear transfer strength estimation of concrete elements using generalized artificial neural network models
  54. Simulation and assessment of water supply network for specified districts at Najaf Governorate
  55. Comparison between cement and chemically improved sandy soil by column models using low-pressure injection laboratory setup
  56. Alteration of physicochemical properties of tap water passing through different intensities of magnetic field
  57. Numerical analysis of reinforced concrete beams subjected to impact loads
  58. The peristaltic flow for Carreau fluid through an elastic channel
  59. Efficiency of CFRP torsional strengthening technique for L-shaped spandrel reinforced concrete beams
  60. Numerical modeling of connected piled raft foundation under seismic loading in layered soils
  61. Predicting the performance of retaining structure under seismic loads by PLAXIS software
  62. Effect of surcharge load location on the behavior of cantilever retaining wall
  63. Shear strength behavior of organic soils treated with fly ash and fly ash-based geopolymer
  64. Dynamic response of a two-story steel structure subjected to earthquake excitation by using deterministic and nondeterministic approaches
  65. Nonlinear-finite-element analysis of reactive powder concrete columns subjected to eccentric compressive load
  66. An experimental study of the effect of lateral static load on cyclic response of pile group in sandy soil
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Heruntergeladen am 9.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jmbm-2022-0251/html
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