Authors:
Rashad Alsirawan Department of Structural Engineering and Geotechnics, Faculty of Architecture, Civil Engineering and Transport Sciences, Széchenyi István University, Győr, Hungary

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Ammar Alnmr Department of Structural Engineering and Geotechnics, Faculty of Architecture, Civil Engineering and Transport Sciences, Széchenyi István University, Győr, Hungary

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Abstract

This work aims to highlight gravity segmental retaining walls with their varied advantages. The paper investigates the dynamic behavior analysis of segmental retaining walls. The stability analysis is conducted on the basis of a pseudo-static Mononobe-Okabe theory that provides safety factors against sliding and overturning failure. The results demonstrate that the crucial safety factor of internal stability is the safety factor against overturning. Moreover, the positive wall inclination angle contributes to an improvement in the stability of the segmental retaining walls and the effect of the vertical seismic coefficient on the stability can be disregarding. Finally, a new equation is proposed for the elementary design of the segmental retaining walls.

Abstract

This work aims to highlight gravity segmental retaining walls with their varied advantages. The paper investigates the dynamic behavior analysis of segmental retaining walls. The stability analysis is conducted on the basis of a pseudo-static Mononobe-Okabe theory that provides safety factors against sliding and overturning failure. The results demonstrate that the crucial safety factor of internal stability is the safety factor against overturning. Moreover, the positive wall inclination angle contributes to an improvement in the stability of the segmental retaining walls and the effect of the vertical seismic coefficient on the stability can be disregarding. Finally, a new equation is proposed for the elementary design of the segmental retaining walls.

1 Introduction

Segmental Retaining Walls (SRWs) are gravity structures that depend on self-weight to withstand destabilizing forces caused by retained soil and surcharge loads. SRW systems are built utilizing mortarless concrete block units piled together to create a barrier, which can withstand the backfill soils as it is shown in Fig. 1. This system can be enhanced by inserting many layers of geosynthetic reinforcement into the backfill soil and between the concrete units. These types of retaining walls are characterized by their rapid and easy implementation, environmentally friendly nature, and flexible performance, a drainage face of mortarless units to decrease hydrostatic pressure, as well as the aesthetic and economic considerations and the construction of intricate architectural designs or tight curves designs or tight curves [1].

Fig. 1.
Fig. 1.

Segmental retaining wall (Source: basis on www.terraforce.com)

Citation: Pollack Periodica 18, 1; 10.1556/606.2022.00722

There are various studies on geosynthetic-reinforced segmental retaining walls in the literature. Helwany et al. [2], Koerner et al. [3] presented the results of their investigation on these retaining walls under seismic loading. The researchers investigated the behavior of these retaining walls as well as the failure mechanism since these structures are considered flexible and allow more displacement in comparison with conventional retaining walls. Over the past two decades, increasingly more numerical analysis has been used to investigate this type of SRW (Liu et al. [4], Guler et al. [5], Ren et al. [6]). For more complicated issues in geotechnical engineering, numerical analysis is deemed to be appealing [7, 8] as with terraced walls, which are considered a challenge in the design domain of the segmental retaining walls.

The literature on gravity SRWs is substantially more limited. This type of retaining wall is utilized for modest heights. The heavier masonry units can be used for larger heights or in cases where it is challenging to employ geosynthetic layers. Using geosynthetic layers necessitates a space in the behind wall for the placement of the geosynthetic layers that is roughly 70% of the wall height or more [9]. Mazni [10] performed two models of SRW in the laboratory to study the patterns of slope failures, the findings showing different failure surfaces in comparison to the Rankine theory. Latha and Manju [11] conducted numerous laboratory tests on the geocell retaining walls using the shaking table. The researchers found that the increase of the shaking table frequency increases the horizontal displacements of the retaining walls, as well as the acceleration contributing to the increase of the geocell retaining wall deformation. Toprak et al. [12] proposed utilizing gabions in retaining walls due to their high drainage efficacy. Mazni et al. [13] conducted a new model of SRW to study further the failure mechanism of this type of retaining wall.

Despite the significance of SRWs, particularly in locations where it is problematic to apply geosynthetic reinforcements, the analysis studies were quite restricted and focused on the failure mechanisms. Therefore, the main objective of this work is to revive SRWs and demonstrate their numerous features.

This paper aims to evaluate the stability of SRWs under dynamic loads (earthquakes) and highlight the characteristic of this type of retaining wall in comparison with the conventional retaining walls. Finally, an equation is proposed for the elementary design of SRWs. The internal stability of the segmental retaining walls is the only aspect of this investigation. Design Manual for Segmental Retaining Walls [1] is adopted in this study.

2 Mononobe–Okabe earth pressure theory

The pseudo-static Mononobe-Okabe (M−O) theory is employed to determine the dynamic active earth forces applied on the back surface of the SRW that is tilted towards the backfill soil at an angle ω. This is called the wall inclination angle. If this angle faces in a clockwise direction, it is regarded as positive. The backfill soil is tilted from the horizon by the angle β, which is called the backslope angle. Horizontal and vertical seismic coefficients Kh and Kv are specified as fractions of the acceleration of gravity g. For more safety in the design, the direction of the horizontal seismic force is consistent with that of failure as illustrated in Fig. 2. On the other hand, the vertical seismic force acts downward and that corresponds with the positive value of the vertical seismic coefficient. The terms Ww and W represent the weight of the retaining wall and the active soil wedge operating behind the wall, respectively.

Fig. 2.
Fig. 2.

Geometry and forces in M−O theory (Source: on the basis of [1])

Citation: Pollack Periodica 18, 1; 10.1556/606.2022.00722

The total dynamic active earth force is given as follows [1]:
PAE=0.5· 1+Kv· KAE· H2· γ,
where H(m) is the wall's height and γ(kN/m3) is the soil's unit weight, KAE is the dynamic earth pressure coefficient, calculated using the formulas below:
KAE=cos2+ωθcos(θ)·cos2(ω)·cosδω+θ1+sin+δ·sinβθcosδω+θ·cosω+β2,
where is the peak internal angle of the backfill soil; δ is the mobilized interface friction angle at the unit back, assumed to be equal to 2·/3; and θ is the seismic inertia angle is determined as follow:
θ=tan1(Kh/(1±Kv)),
where Kv is presumed to equal zero in an earthquake, since a simultaneous occurrence of the vertical and horizontal peak acceleration is unlikely. Kh is determined utilizing the specified horizontal peak ground acceleration A which is expressed as a fraction of the gravitational constant g; American Association of State Highway and Transportation Officials (AASHTO) provides the A values [14], and the permitted deflection of the SRW is d. The permitted deflection, d is the maximum lateral displacement that a retaining wall can tolerate during an earthquake. Generally, the typical value is roughly 76 mm. The horizontal seismic coefficient is calculated as follow [14]:
If d=0.0mm,  Kh=1.45A·A,
Ifd>0.0mm,  Kh=0.74·A·0.0254·A/d0.25.

Two fundamental issues should be considered in the design: θβ and kh1±kv·tanβ.

The distribution of the total seismic pressure exerted on the SRW is depicted in Fig. 3. This distribution is adopted in the internal stability analyses of this type of retaining wall.

Fig. 3.
Fig. 3.

Distribution of earth pressure as a result of soil self-weight; a) contribution of soil; b) contribution of dead load; c) dynamic increment; d) distribution of total dynamic pressure (Source: on the basis of [1])

Citation: Pollack Periodica 18, 1; 10.1556/606.2022.00722

According to the AASHTO/FHWA (Federal Highway Administration) recommendations, the total dynamic active earth force consists of the active earth pressure force PA and the increment of the dynamic earth force PDyn [1]:
PAE=PA+PDyn,
1+Kv·KAE=KA+KDyn,
where KA is the active earth pressure coefficient and KDyn is the dynamic increment active earth pressured coefficient (for more details, see [1]). According to Fig. 3, the application point of PAE varies depending on KDyn and ranges between 0.33 and 0.67 H, where H is the retaining wall height.
The internal stability at each interface between the block units is verified by calculating the Safety Factors against overturning (FSO) and sliding (FSs), according to the following formulas taking into account the distribution of earth pressure explained above. The details of these well-known formulas can be found in [1]:
FSO=Mr,iMo,iFSomin=1.1,
FSs=Ri·fPiFSsmin=1.1,
where Mr,i is the resisting moment and Mo,i is the driving moment, Ri are resisting forces and Pi are the driving forces, f is the friction coefficient.

3 Results and discussion

In this section, the internal sliding and overturning failures of the units along the wall height are investigated based on M−O theory.

A segmental retaining wall is constructed to sustain the soil behind it. The wall height, H is 7.0 m and the used unit width, b and height, h are 1.2 and 0.5 m, respectively. The unit weight of the block units γb is 22kN/m3 and the friction angle between the wall units is 40°. The surcharge load, q is 10kN/m2. The properties of the backfill soil and the foundation soil and the seismic parameters are listed in Table 1.

Table 1.

The properties of backfill and foundation soils and the seismic parameters

Backfill soil
=35°c=0(kN/m2)γ=19(kN/m3)
Foundation soil
=30°c=5(kN/m2)γ=19(kN/m3)
Seismic parameters
A=0.3d = 50 (mm)Kh=0.139
Kv=0

For the external and internal stability, the SRW software was designed in an Excel work sheet. This program is used to conduct the parametric analysis and derive an equation, which can be used in the elementary design of SRWs based on M−O theory.

Table 2 presents the summary of the parametric study in this work.

Table 2.

Parametric study program

ω (°)0, 5, 10, 15, 20
β (°)0, 5, 10, 15, 20
b/H (−)0.16, 0.18, 0.22, 0.27, 0.34, 0.48, 0.8
A (−)0, 0.05, 0.25, 0.45, 0.65, 0.85
Kv (−)(−0.66, 0, 0.66) Kh

3.1 Crucial safety factor

An extensive analysis was conducted according to Table 2 to determine the critical safety factor (safety factor against sliding or overturning) in all interfaces between the SRW units along the wall height. The results demonstrated that the safety factor against overturning is the crucial regarding the internal stability of this type of retaining wall.

Figure 4 displays the safety factors against sliding (dashed curves) and overturning (solid curves) for two scenarios, ω=0° (left) and ω=20° (right). The crucial safety factor that should be considered in the design is the safety factor against overturning in the lower interface.

Fig. 4.
Fig. 4.

Safety factors against sliding and overturning, ω=0 (left) and ω=20 (right)

Citation: Pollack Periodica 18, 1; 10.1556/606.2022.00722

3.2 Influence of angles (ω,β)

The angle ω influences positively the FSO. As ω increases, the magnitude of FSO increases, as it can be seen in Fig. 5. For the given values of ω, increasing the slope angle of the backfill soil, β reduces FSO; as the value of ω rises, so does the negative influence of β on the FSO.

Fig. 5.
Fig. 5.

Influence of ω, β on the crucial safety factors

Citation: Pollack Periodica 18, 1; 10.1556/606.2022.00722

3.3 Influence of coefficients Kh,Kv

Figure 6 depicts the common effect of KhandKv on FSO for two values of ω=0,10. The largest values of FSO obtained for Kh are less than approximately 0.2 and Kv=0.66·Kh. Nevertheless, the value of FSO computed using Kv=0.66·Kh is only 4% smaller and 4% larger than the amount obtained using Kv=0 for Kh less than 0.2, respectively. As a result, the presumption that Kv=0 is typically appropriate throughout a large range of horizontal seismic coefficient values.

Fig. 6.
Fig. 6.

Influence of Kh,Kv on the crucial safety factors for β = 0

Citation: Pollack Periodica 18, 1; 10.1556/606.2022.00722

3.4 Comparison of SRWs and conventional gravity retaining walls

As it was mentioned earlier, ω is regarded as positive if it rotates in a clockwise direction. SRWs are considered flexible as compared to the conventional gravity walls and this is one of the SRW features. In this comparison, the lateral displacement and unit weight of the conventional walls are assumed to be 15 mm and 24kN/m3, respectively. Figure 7 shows the effect of Kh and ω on FSO of the SRWs and the conventional retaining walls. The findings reveal that the positive values of ω increases FSO to values higher than those of the conventional gravity retaining walls.

Fig. 7.
Fig. 7.

Comparison of SRWs and conventional gravity retaining walls for β = 0

Citation: Pollack Periodica 18, 1; 10.1556/606.2022.00722

3.5 Equation of elementary design of SRWs

The proposed Eq. (10) is the result of an extensive parametric analysis depending on the SRW software run using an Excel work-sheet,
bH=F1·ω+F2·β2+F3·β+F4·HD1·ω+D2+H,
where F1=2.5·103·A28·103·A8·103; F2=9·103·A21·104·A+1·105; F3=1·102·A21.8·103·A+1.5·103; F4=0.4·A2+0.42·A+0.25; D1=2.5·103·A2+4.6·103·A8.1·103; D2=0.125·A2+0.405·A0.38.

The first step involves collecting 2,500 values of the dependent variable b/H for different independent variables (ω, β, H, A). The second step is choosing the ratio b/H corresponding to FSO=1.1, which represents the optimal ratio. This step is followed by statistical analysis of data based on the data structure tree concept in order to derive this equation, which can then be used in the elementary design of SRWs. Curve Expert software is employed in order determine the correlations between dependent and independent variables. The presumed independent variables are listed in Table 3.

Table 3.

Presumed values of the independent variables

ω (°)0, 5, 10, 15, 20H (m)3, 5, 7, 9
β (°)0, 5, 10, 15, 20A (−)0.1, 0.2, 0.3, 0.4

With this proposed equation, several fundamental concerns should be considered:

  • This equation is derived based on the typical properties of the backfill soil and seismic parameters in Table 1;

  • γb=22kN/m3 and q=10kN/m2;

  • The values of ω, β must be in degrees;

  • This equation can be used under static loading with A = 0.0.

Table 4 shows a comparison between the results of the proposed equation and M−O theory in term of FSO according to the following data ω = 20, β = 0.0, A = 0.3. FSs is also listed in Table 4.

Table 4.

Comparison between the results of the proposed equation and M−O theory

H (m)b (m)FSO (equ.)FSO (M−O)FSs (M−O)
20.521.101.162.12
30.711.101.152.19
40.911.101.162.25
51.111.101.172.28
61.311.101.182.31
71.521.101.192.34

4 Conclusion

In order to analyze the stability of the segmental retaining walls, a pseudo-static approach based on the Mononobe-Okabe theory was adopted in the work. Based on the outcomes of several parametric analyses presented in the paper, the following can be concluded from the segmental retaining wall analysis:

  • Between the safety factors against sliding and overturning in the internal stability, the safety factor against overturning in the lower interface of SRW units is the crucial factor. This should be considered in the design;

  • The wall inclination angle, ω contributes to improve the stability of SRWs while the backslope angle, β has a negative influence and this influence increases with higher values of ω;

  • The influence of the horizontal seismic coefficient Kh is important and contributes to a dramatic decrease in stability while the influence of the vertical seismic coefficient Kv is slight and can be negligible;

  • The positive values of ω in SRWs contributes to an improvement in stability while the influence of this parameter is negative in conventional gravity retaining walls;

  • A new equation is derived based on the M−O theory. This equation can assist engineers in the elementary design of SRWs.

References

  • [1]

    Design Manual for Segmental Retaining Walls .National Concrete Masonry Association, 3rd ed., Herndon, USA: Resimont Products, Inc., 2012.

    • Search Google Scholar
    • Export Citation
  • [2]

    M. B. Helwany, M. Budhu, and D. McCallen, “Seismic analysis of segmental retaining walls. I: Model verification,” J. Geotechnical Geoenvironmental Eng., vol. 127, no. 9, pp. 741749, 2001.

    • Search Google Scholar
    • Export Citation
  • [3]

    R. M. Koerner and T. Y. Soong, “Geosynthetic reinforced segmental retaining walls,” Geotextiles and Geomembranes, vol. 19, pp. 359386, 2001.

    • Search Google Scholar
    • Export Citation
  • [4]

    H. Liu, X. Wang, and E. Song, “Reinforcement load and deformation mode of geosynthetic-reinforced soil walls subject to seismic loading during service life,” Geotextiles and Geomembranes, vol. 29, pp. 116, 2011.

    • Search Google Scholar
    • Export Citation
  • [5]

    E. Guler, E. Cicek, M. M. Demirkan, and M. Hamderi, “Numerical analysis of reinforced soil walls with granular and cohesive backfills under cyclic loads,” Bull. Earthquake Eng., vol. 10, no. 3, pp. 793811, 2012.

    • Search Google Scholar
    • Export Citation
  • [6]

    F. Ren, F. Zheng, C. Xu, and G. Wang, “Seismic evaluation of reinforced-soil segmental retaining walls,” Geotextiles Geomembranes J., vol. 44, pp. 604614, 2016.

    • Search Google Scholar
    • Export Citation
  • [7]

    R. Alsirawan and E. Koch, “The finite element modeling of rigid inclusion-supported embankment,” Pollack Period., vol. 17, no. 2, pp. 8691, 2022.

    • Search Google Scholar
    • Export Citation
  • [8]

    J. Szép, “Modeling laterally loaded piles,” Pollack Period., vol. 8, no. 2, pp. 117129, 2013.

  • [9]

    H. Brooks and J. P. Nielsen, Basics of Retaining Wall Design, A Design Guide for Earth Retaining Structures. 10th ed., California, USA: HBA Publications, 2013.

    • Search Google Scholar
    • Export Citation
  • [10]

    D. I. Mazni, “An alternative model of retaining walls on sandy area to prevent landslides,” E3S Web of Conferences, vol. 156, 2020, Paper no. 02016.

    • Search Google Scholar
    • Export Citation
  • [11]

    G. M. Latha and G. S. Manju, “Seismic response of geocell retaining walls through shaking table tests,” Int. J. Geosynth. Ground Eng., vol. 2, no. 1, pp. 115, 2016.

    • Search Google Scholar
    • Export Citation
  • [12]

    B. Toprak, O. Sevim, and I. Kalkan, “Gabion walls and their use,” Int. J. Adv. Mech. Civil Eng., vol. 3, no. 4, pp. 23942827, 2016.

    • Search Google Scholar
    • Export Citation
  • [13]

    D. I. Mazni, A. Hakam, J. Tanjung, and F. A. Ismail, “Stability analysis of concrete block retaining wall based on a scaled laboratory,” E3S Web of Conferences, vol. 331, 2021, Paper no. 05013.

    • Search Google Scholar
    • Export Citation
  • [14]

    Standard Specifications for Highway Bridges. 17th ed., Washington, DC, USA: American Association of State Highway and Transportation Officials, 2002.

    • Search Google Scholar
    • Export Citation
  • [1]

    Design Manual for Segmental Retaining Walls .National Concrete Masonry Association, 3rd ed., Herndon, USA: Resimont Products, Inc., 2012.

    • Search Google Scholar
    • Export Citation
  • [2]

    M. B. Helwany, M. Budhu, and D. McCallen, “Seismic analysis of segmental retaining walls. I: Model verification,” J. Geotechnical Geoenvironmental Eng., vol. 127, no. 9, pp. 741749, 2001.

    • Search Google Scholar
    • Export Citation
  • [3]

    R. M. Koerner and T. Y. Soong, “Geosynthetic reinforced segmental retaining walls,” Geotextiles and Geomembranes, vol. 19, pp. 359386, 2001.

    • Search Google Scholar
    • Export Citation
  • [4]

    H. Liu, X. Wang, and E. Song, “Reinforcement load and deformation mode of geosynthetic-reinforced soil walls subject to seismic loading during service life,” Geotextiles and Geomembranes, vol. 29, pp. 116, 2011.

    • Search Google Scholar
    • Export Citation
  • [5]

    E. Guler, E. Cicek, M. M. Demirkan, and M. Hamderi, “Numerical analysis of reinforced soil walls with granular and cohesive backfills under cyclic loads,” Bull. Earthquake Eng., vol. 10, no. 3, pp. 793811, 2012.

    • Search Google Scholar
    • Export Citation
  • [6]

    F. Ren, F. Zheng, C. Xu, and G. Wang, “Seismic evaluation of reinforced-soil segmental retaining walls,” Geotextiles Geomembranes J., vol. 44, pp. 604614, 2016.

    • Search Google Scholar
    • Export Citation
  • [7]

    R. Alsirawan and E. Koch, “The finite element modeling of rigid inclusion-supported embankment,” Pollack Period., vol. 17, no. 2, pp. 8691, 2022.

    • Search Google Scholar
    • Export Citation
  • [8]

    J. Szép, “Modeling laterally loaded piles,” Pollack Period., vol. 8, no. 2, pp. 117129, 2013.

  • [9]

    H. Brooks and J. P. Nielsen, Basics of Retaining Wall Design, A Design Guide for Earth Retaining Structures. 10th ed., California, USA: HBA Publications, 2013.

    • Search Google Scholar
    • Export Citation
  • [10]

    D. I. Mazni, “An alternative model of retaining walls on sandy area to prevent landslides,” E3S Web of Conferences, vol. 156, 2020, Paper no. 02016.

    • Search Google Scholar
    • Export Citation
  • [11]

    G. M. Latha and G. S. Manju, “Seismic response of geocell retaining walls through shaking table tests,” Int. J. Geosynth. Ground Eng., vol. 2, no. 1, pp. 115, 2016.

    • Search Google Scholar
    • Export Citation
  • [12]

    B. Toprak, O. Sevim, and I. Kalkan, “Gabion walls and their use,” Int. J. Adv. Mech. Civil Eng., vol. 3, no. 4, pp. 23942827, 2016.

    • Search Google Scholar
    • Export Citation
  • [13]

    D. I. Mazni, A. Hakam, J. Tanjung, and F. A. Ismail, “Stability analysis of concrete block retaining wall based on a scaled laboratory,” E3S Web of Conferences, vol. 331, 2021, Paper no. 05013.

    • Search Google Scholar
    • Export Citation
  • [14]

    Standard Specifications for Highway Bridges. 17th ed., Washington, DC, USA: American Association of State Highway and Transportation Officials, 2002.

    • Search Google Scholar
    • Export Citation
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Editor(s)-in-Chief: Iványi, Amália

Editor(s)-in-Chief: Iványi, Péter

 

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Miklós M. Iványi

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  • Bálint Bachmann (Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Jeno Balogh (Department of Civil Engineering Technology, Metropolitan State University of Denver, Denver, Colorado, USA)
  • Radu Bancila (Department of Geotechnical Engineering and Terrestrial Communications Ways, Faculty of Civil Engineering and Architecture, “Politehnica” University Timisoara, Romania)
  • Charalambos C. Baniotopolous (Department of Civil Engineering, Chair of Sustainable Energy Systems, Director of Resilience Centre, School of Engineering, University of Birmingham, U.K.)
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  • Zoltán Siménfalvi (Institute of Energy and Chemical Machinery, Faculty of Mechanical Engineering and Informatics, University of Miskolc, Hungary)
  • Andrej Šoltész (Department of Hydrology, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Slovakia)
  • Zsolt Szabó (Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Hungary)
  • Mykola Sysyn (Chair of Planning and Design of Railway Infrastructure, Institute of Railway Systems and Public Transport, Technical University of Dresden, Germany)
  • András Timár (Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Barry H. V. Topping (Heriot-Watt University, UK, Faculty of Engineering and Information Technology, University of Pécs, Hungary)

POLLACK PERIODICA
Pollack Mihály Faculty of Engineering
Institute: University of Pécs
Address: Boszorkány utca 2. H–7624 Pécs, Hungary
Phone/Fax: (36 72) 503 650

E-mail: peter.ivanyi@mik.pte.hu 

or amalia.ivanyi@mik.pte.hu

Indexing and Abstracting Services:

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  • CABELLS Journalytics

 

2023  
Scopus  
CiteScore 1.5
CiteScore rank Q3 (Civil and Structural Engineering)
SNIP 0.849
Scimago  
SJR index 0.288
SJR Q rank Q3

Pollack Periodica
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2023  
Scopus  
CiteScore 1.5
CiteScore rank Q3 (Civil and Structural Engineering)
SNIP 0.849
Scimago  
SJR index 0.288
SJR Q rank Q3

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