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The technology of geosynthetic mechanically stabilized earth (MSE) walls can help solve classical geotechnical earth retaining wall problems. It can also contribute to achieving the new required performance for infrastructures, such as reliance and sustainability. To further develop this technology, it is essential to analyze the history of its progress. This study summarizes the state-of-the-art research on the mechanical and soil interaction properties of geosynthetics, physical modeling and in situ measurements, analytical and numerical modeling, and reliability analyses by reviewing approximately 728 papers published in well-known international journals in this field and some notable conference paper contributions during the period of approximately 50 years from 1972 to 2023. The latest analytical methods, such as risk-based life cycle cost and CO2 emission assessments and damage/failure predictions, are introduced to evaluate the resilience and sustainability performance of geosynthetic MSE walls. Finally, the prospects of a seismic isolation technique with new types of geosynthetics and life cycle management using a long-term sensor for geosynthetic MSE walls are discussed.

Classical infrastructure design only considers basic performance aspects, such as structural safety and economic efficiency. In modern design, more advanced performance aspects, such as resilience and sustainability, are also considered (Lounis and Mcallister 2016). New infrastructure technologies related to materials, structural systems, and maintenance methods are required to satisfy these advanced performance requirements.

Geosynthetic mechanically stabilized earth (MSE) walls primarily consist of compacted backfill soils, geosynthetics, and facing materials. The performance of these structures can be controlled by varying the reinforcement conditions, such as the strength or layout conditions of the geosynthetics. Research on geosynthetic MSE walls began in the 1970s (Holtz 2017). The good performance of these wall systems has been demonstrated in both research and practice. For example, seismic damage investigations of actual structures have reported the high performance of geosynthetic MSE walls (Tatsuoka et al. 1996; White and Holtz 1997; Ling et al. 2001; Koseki 2012; Kuwano et al. 2014). Nevertheless, classical geosynthetic MSE wall technologies have considerable room for further improvement (e.g. Bathurst et al. 2005; Bathurst 2014). If a design method can be developed to reasonably determine the reinforcement conditions by considering the required performances, technology on geosynthetic MSE walls will more than ever contribute to the success of various civil engineering projects.

The keywords considered in this study are the ‘past,’ ‘present,’ and ‘future’ of research and practice regarding geosynthetic MSE walls. For the ‘past,’ research trends in geosynthetic MSE walls over the last 50 years (1972 to 2023) are reported based on a review of 728 technical papers. Changes in the number of papers, research topics, and approaches over time are visualized. For the ‘present,’ the latest analytical methods, such as risk-based life cycle costs, CO2 emission assessments, and damage/failure predictions, are presented to evaluate the performance of geosynthetic MSE walls. Finally, for the ‘future,’ the prospects for a seismic isolation technique employing new types of geosynthetics and information and communication technology (ICT)-based life cycle management with fiber optics for geosynthetics are discussed.

This manuscript was written as a journal version of the Bathurst lecture paper published in the proceedings of the 12th ICG conference held in Rome in 2023 (Miyata 2023).

Research on geosynthetic MSE walls can be divided into four categories: research on the mechanical and soil interaction properties of geosynthetics, research to clarify the mechanical behavior of geosynthetics through physical model tests and in situ measurements, research on analytical and numerical modeling to predict the mechanical behavior of geosynthetic MSE walls, and research on reliability analyses to evaluate their performance. The relationships among these four research areas are shown in Figure 1. These studies are considered to have influenced each other and advanced the technology over time.

Figure 1.

Research areas in the technology of geosynthetic MSE walls and their relationships

Figure 1.

Research areas in the technology of geosynthetic MSE walls and their relationships

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The information sources required to identify research trends in geosynthetic MSE walls include journal articles, technical reports, test standards, and design specifications. Journal articles can be obtained even if time has passed since their publication, and their contents can be easily verified. More importantly, they are peer-reviewed, and thus, their information is considered to be reliable. Therefore, this study focuses on journal articles. Nevertheless, several valuable conference papers are also cited in this review.

In many previous state-of-the-art studies on geosynthetic MSE walls, technological progress has been explained by relating important papers with significant contributions to progress in research and practice (e.g. Rowe and Ho 1993; Bathurst and Alfaro 1997; Otani et al. 1997; Rowe and Li 2003; Bathurst and Kaliakin 2005; Palmeira 2009). Giroud et al. (1993, 1994) published a two-volume book listing articles on geosynthetic engineering. This list includes information on books, journals, conference papers, theses, reports, and publications from selected authors. Many of these publications have made significant contributions not only to solving practical problems but also to setting research directions in the early stages of research on geosynthetic MSE walls. Since those publications, the accumulation of research results in this field has been remarkable. It is worth reviewing the latest status of this research field from its earliest stage to promote further research progress in the future.

The degree of technological progress is closely related to the number and content of published papers on this topic. Visualizing this information using objective indicators can facilitate our understanding of the evolution of the past and determine directions that should be taken in the future. Visualizing past achievements by analyzing published papers is a survey technique that can only be conducted after a sufficient number of articles has been accumulated. This section discusses the overall research trends in geosynthetic MSE walls and chronological changes in research topics and methods.

The technology of geosynthetic MSE walls is interdisciplinary, with relevant papers published in various fields. This study considered only journal papers published in the field of geotechnical engineering. Based on this policy, three categories of journals were examined: (1) journals covering all areas of geotechnical engineering, (2) journals specializing in geomaterials testing, and (3) journals specializing in geosynthetic engineering. Specifically, for Category 1, the following journals were reviewed: Geotechnique (Institution of Civil Engineers), the Journal of Geotechnical and Geoenvironmental Engineering (American Society of Civil Engineers), Soils and Foundations (S&F, Japanese Geotechnical Society), and the Canadian Geotechnical Journal (Canadian Geotechnical Society). These journals were first published in the 1960s and are suitable for examining long-term research trends in geosynthetics. Category 2 included the Geotechnical Testing Journal (American Society for Testing and Materials, ASTM, International). This journal publishes papers on testing and experimental methods for geosynthetics. Two journals were included in Category 3: Geotextiles and Geomembranes (G&G, Elsevier) and Geosynthetics International (GI, Institution of Civil Engineers). These are official journals of the International Geosynthetics Society (IGS), which were first published in 1983 and 1994, respectively. These journals include many studies on geosynthetic MSE walls.

The research review was conducted in the following order: article collection, content analysis, database construction, and statistical analysis. The papers were collected from the websites of each journal. Keywords were entered into the search engine of each journal website to generate a list of candidate papers. After downloading the papers, their contents were categorized, and those meeting the objectives of this review were included in the database. Table 1 presents the statistics of the collected journal papers. A total of 728 papers were collected. The largest contributor was G&G, followed by GI. The author would like to mention R.J. Bathurst's contributions in this area, as this paper summarizes the Bathurst lecture. Notably, 448 (62%) of the 728 papers collected cited papers by R.J. Bathurst.

Table 1.

Statistics of journal papers collected on the technology of geosynthetic MSE walls

Journal categoryJournal nameFirst issue yearNumber of papers
All areas of geotechnical engineeringGeotechnique 1948 26
Journal of Geotech and Geoenv Eng1956101
Soils and Foundations196056
Canadian Geotechnical Journal196334
Geomaterials testingGeotechnical Testing Journal197820
Geosynthetic engineeringGeotextiles and Geomembranes1983300
Geosynthetics International1994191

Total = 728.

The number of papers on the mechanical and soil interaction properties of geosynthetics, analytical and numerical modeling, physical modeling and in situ measurements, and reliability analyses of geosynthetic MSE walls are shown in Figures 2–5, respectively. The vertical axis represents the cumulative number of publications, and the slope of the curve represents the number of publications per year. Changes in the number of publications over time should be understood in the context of academic, practical, and social trends. Table 2 provides a chronological list of important events relevant to geosynthetic MSE walls. The curves for all four research areas can be approximated by a group of straight lines whose slopes change twice from small to large. It can be assumed that a period with a small slope represents the accumulation phase, and a period with a large slope represents the development phase. In this case, it can be understood that these phases have repeated themselves twice, and MSE wall technology is currently in the second development phase. Interestingly, the timing of the first accumulation and development phases was almost the same for the three research areas of mechanical and soil interaction properties, physical modeling and in situ measurements, and analytical and numerical modeling.

Figure 2.

Total number of papers on the mechanical and soil interaction properties of geosynthetics published in selected leading journals

Figure 2.

Total number of papers on the mechanical and soil interaction properties of geosynthetics published in selected leading journals

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Figure 3.

Total number of papers on physical modeling and in situ measurements of geosynthetic MSE walls published in selected leading journals

Figure 3.

Total number of papers on physical modeling and in situ measurements of geosynthetic MSE walls published in selected leading journals

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Figure 4.

Total number of papers on analytical and numerical modeling of geosynthetic MSE walls published in selected leading journals

Figure 4.

Total number of papers on analytical and numerical modeling of geosynthetic MSE walls published in selected leading journals

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Figure 5.

Total number of papers on reliability analyses of geosynthetic MSE walls published in selected leading journals

Figure 5.

Total number of papers on reliability analyses of geosynthetic MSE walls published in selected leading journals

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Table 2.

Events relevant to geosynthetic MSE wall technology

YearSociety and technical committee establishmentJournal launchInternational conference on geosyntheticsSymposium or workshop on soil reinforcementDesign codeMajor earthquake (Economic loss#, year; Daniell et al. 2012)
   1st (1977)   
1980     Irpinia, IT ($58.0B, 1980)
 IGS (1983) 2nd (1982)   
 ASTM/D35 (1984)GG (1984)    
 ISSMGE/TC9 (1986) 3rd (1986) ISO (1986) 2394 2nd ed. 
   IS-Kyushu (1988)   
1990  4th (1990)   
    IS-Kyushu (1992)  
  GI (1994)5th (1994) AASHTO (1994) LRFD 1st ed.Northridge, US ($79.1B, 1994)
    IS-Kyushu (1996) Kobe, JP ($187.6B, 1995)
   6th (1998) ISO (1998) 2394 3rd ed. 
2000ISO/TC221 (2000)  IS-Kyushu (2001)  
   7th (2002) CEN (2002) Eurocode Basis 
     CEN (2004¸ 2007) Eurocode 7Niigata, JP ($35.5B, 2004)
   8th (2006)IS-Kyushu (2007)  
      Sichuan, CN ($189.8B, 2008)
2010IGS/TC-R (2011) 9th (2010)   
      Tohoku, JP ($324.0B, 2011)
   10th (2014) ISO (2015) 2394 4th ed. 
       
   11th (2018)IGS WS TC-R (2018)  
2020   IGS WS TC-R (2020)AASHTO (2020) LRFD 9th ed. 
   12th (2023)   

IGS: International Geosynthetics Society, ASTM: American Society for Testing and Materials, ISSMGE: International Society for Soil Mechanics and Geotechnical Engineering, ISO: International Organization for Standardization, AASHTO: American Association of State Highway and Transportation Officials.

# 2012 HNDECI (Hybrid. Natural Disaster Economic Conversion Index); Adjusted US Dollar direct economic loss value.

As indicated in Table 2, the IGS was established during the first accumulation period, and technical committees on geosynthetics were also formed by ASTM and the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE). In addition to establishing academic societies and technical committees, an international conference on geosynthetics (ICG) and an international soil reinforcement symposium were regularly organized (Ochiai 2007). Thus, owing to the dissemination of technical information and the exchange of research ideas during the accumulation period, a development phase was achieved.

During the first development phase, several earthquakes caused significant societal losses. The high reliability of geosynthetic MSE wall technologies was demonstrated through damage investigations of these earthquakes (Tatsuoka et al. 1996; White and Holtz 1997; Koseki 2012; Kuwano et al. 2014). These studies contributed to the widespread use of MSE wall technology. Of the research topics of mechanical and soil interactions, physical modeling and in situ observations, and analytical and numerical modeling, the earliest transition from the second accumulation phase to the second development phase was achieved in research on analytical and numerical modeling. During this period, computers began to be used in all aspects of practice. This trend likely stimulated further research on analytical and numerical modeling. Research on reliability analyses began in the 2000s. The third edition of the International Organization for Standardization (ISO) 2394 on the general principles for the reliability of structures was published in 1998. It stated that the target performance of structures should be expressed in terms of probabilities. This trend is considered to have strongly influenced the research field of geosynthetic MSE walls, especially research on reliability analyses.

To identify the area with the largest number of publications in each period, – that is, the most active area of research on geosynthetic MSE walls, the ratios of the number of papers in the four areas mentioned above to the total number of papers for each year were calculated. The chronological changes were visualized, as shown in Figure 6. In the late 1970s, research on physical modeling and in situ measurements represented the largest proportion of publications. Approximately ten years later, papers on the mechanical and soil interaction properties of geosynthetics made the greatest contribution. After that, papers on mechanical modeling and interactions shifted to favor papers on analytical and numerical modeling. Currently, the proportion of papers in these three areas is approximately 30%, and the proportion of papers concerning reliability analyses is 10%, which has remained constant over the last 10 years. These changes indicate that research on geosynthetic MSE walls has progressed in the following order: understanding the macroscopic behavior of the walls, elucidation of the elemental properties, development of analysis methods, and evaluations of reliability.

Figure 6.

Changes in four research areas of geosynthetic MSE walls over time

Figure 6.

Changes in four research areas of geosynthetic MSE walls over time

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Changes have also occurred in research topics related to the mechanical and soil interaction properties of geosynthetics. This area of research can be divided into four categories: tensile behavior, creep behavior, pullout resistance, and interface shear resistance. Figure 7 depicts the temporal changes in the proportions of papers classified by the year of publication. In the early 1980s, although the total number of papers was small, most papers focused on pullout tests. In the mid-1980s, the proportion of papers on mechanical properties, such as tensile and creep behavior, increased. Subsequently, the papers on mechanical properties shifted to a greater proportion of papers on soil interactions. Presently, the ratio of papers on mechanical properties to those on soil interactions has reversed from the ratio in the mid-1980s.

Figure 7.

Changes in research topics on the mechanical and soil interactions of geosynthetics over time

Figure 7.

Changes in research topics on the mechanical and soil interactions of geosynthetics over time

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Changes in the research topics on physical modeling, in situ measurements, and analytical and numerical modeling can also be discussed. Studies in these areas can be categorized into those on static deformation properties, static stability, behavior under extreme loads such as earthquakes and rainfall, and other topics, which include case histories and environmental performance. The proportions of papers were classified by year of publication, and the changes with time are visualized in Figure 8. In the mid-1990s, the excellent seismic performance of geosynthetic MSE walls was revealed through post-disaster investigations of large earthquakes that occurred during this period. Since then, the number of studies exploring the dynamic behavior of geosynthetic MSE walls through physical modeling and numerical analyses has increased. More recently, the number of papers on hydraulic effects has increased by considering the effects of climate change. Notably, the percentage of papers on static deformation has remained almost unchanged over the past 40 years. We sometimes consider that the basic reinforcement mechanism has already been investigated. This trend indicates that such an interpretation is incorrect, and unresolved issues remain.

Figure 8.

Changes in research topics on the mechanical behavior of geosynthetic MSE walls over time

Figure 8.

Changes in research topics on the mechanical behavior of geosynthetic MSE walls over time

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The progress of geosynthetic MSE wall technology is summarized in Figure 9. The four research areas of geosynthetic walls have not been developed independently, but are interrelated. Research on the macro-behavior of geosynthetic walls has promoted research on the elemental behavior of geosynthetics. Conversely, research on elemental behavior has helped to better understand the macro-behavior of these walls. Research on macro-behavior has also contributed to the development of various modeling studies on geosynthetic walls. Conversely, the developed models were validated through research on macro-behavior. Research on models and elemental behavior involves input–output relationships. These three research areas have thus led to research on the reliability assessment of MSE structures. Such technological advances, in which disciplines influence each other, are likely to continue. One person cannot cover all these areas of research. Therefore, engineers and researchers must work together to advance the research in this area. This means it is important to have a place to exchange information and discuss various topics.

Figure 9.

Research areas in the technology of geosynthetic MSE walls and their relationships

Figure 9.

Research areas in the technology of geosynthetic MSE walls and their relationships

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In classical structural design, emphasis has traditionally been placed on indicators related to structural safety and economic efficiency. Structural safety has been evaluated based on safety factors, and economic efficiency has been evaluated based on the initial cost, – that is, the construction cost. In recent years, structural designs have required improved performance in terms of resilience and sustainability (Lounis and Mcallister 2016). Resilience refers to the ability to respond to changes. In the design of a structure, resilience is often assessed as the ability of a structure to maintain a minimum level of functionality and recover rapidly after damage from natural disasters or external events. In contrast, sustainability is more holistic and generally refers to a system or process that can continue to function without losing its environmental, social, or economic functionality. In the design of a structure, sustainability is often evaluated in terms of the degree of global environmental impact. It has been suggested that both performances must be evaluated throughout the life cycle of a structure (Bocchini et al. 2014). Damians et al. (2018) demonstrated a methodology for evaluating the sustainability of earth retaining wall structures considering the three pillars that contribute to sustainability (economics, societal/functional resilience, and environmental impact) and showed that MSE walls were more sustainable than conventional gravity and cantilever wall types performing the same function.

When evaluating the resilience and sustainability of a structure over its lifetime, it is necessary to assume potential scenarios of events that may affect the structure during its service life. Because these events include damage caused by natural disasters, the evaluation includes a high degree of uncertainty. Therefore, the assessment should be risk-based, – that is, the uncertainties in the events should be assessed probabilistically (Lounis and Mcallister 2016). As the chair of the technical committee of the IGS Japan Chapter, the author has been working on this task from its inception while advocating for the advantages of geosynthetic MSE walls in the Japanese social infrastructure development community (Miyata et al. 2010, 2013). In Sections 3.2 and 3.3, the extended analysis results of this activity are presented as an advanced analysis method in current practice.

Another important aspect when evaluating the life cycle resilience and sustainability of structures is the prediction of their damage or failure modes. The latest Japanese design standard for geostructures requires consideration of the effects of deformation, damage, and failure/beyond failure states of geostructures on adjacent roads and houses (MLIT 2015), as shown in Figure 10. Numerical analyses are expected to be employed to predict the damage or failure modes of such structures. Figure 11 shows the applicable ranges of the discrete element method (DEM) and continuum analyses using the finite element method (FEM), finite difference method (FDM), and particle method to assess the limit state of a structure. Although this classification is tentative because research on each method is ongoing to expand their application ranges, it is understood that the DEM and particle methods can be applied to reproduce structural behavior up to and after the collapse. However, these analytical methods have not been sufficiently developed for geosynthetic MSE walls. To overcome this problem, the authors’ group has been developing a particle method for geosynthetic MSE walls (Nonoyama et al. 2022). This latest analysis method is introduced in Section 3.4.

Figure 10.

Three performance levels of geosynthetic walls. (a) Deformation level, (b) Damage level, (c) Failure/beyond failure level

Figure 10.

Three performance levels of geosynthetic walls. (a) Deformation level, (b) Damage level, (c) Failure/beyond failure level

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Figure 11.

Applicability of numerical analysis to limit-state estimations of structures. (FEM = finite element method, FDM = finite difference method, DEM = discrete element method)

Figure 11.

Applicability of numerical analysis to limit-state estimations of structures. (FEM = finite element method, FDM = finite difference method, DEM = discrete element method)

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According to ISO (2015) 2394: General principles for the reliability of structures, the risk, R, is defined as follows:

1

where Pi is the probability associated with event i (probability of failure), and Ci is the magnitude of the damage if event i occurs. In this section, the discussion is limited to earthquake risks. Figure 12 shows the relationship between the performance level of the structure; the initial cost, C and the maintenance cost, M. The life cycle cost (LCC) is the sum of these three components.

2
Figure 12.

Relationship between the performance level of structures, initial cost: C, maintenance cost: M, risk: R, and life cycle cost: LCC

Figure 12.

Relationship between the performance level of structures, initial cost: C, maintenance cost: M, risk: R, and life cycle cost: LCC

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The higher the performance level of the structure, the higher the initial cost will be. In addition, the higher the performance of the structure, the lower the seismic risk will be, because the probability of failure is lower. Maintenance costs are not as strongly correlated with the performance level of the structure as are the initial costs and risks. Therefore, the total cost is represented by a downward convex curve, as shown by the top plot of the figure. A probability-based risk analysis can help to reasonably set the target performance level for a structure while considering the balance between the initial cost and risk. This section describes the risk-based life cycle cost analysis method for geostructures. The results of the analysis are shown for geosynthetic MSE walls, L-shaped retaining walls, and unreinforced embankments under simple conditions (Miyata et al. 2010). The life cycle cost concept can be applied to various risks. In this section, the evaluation method and analysis results are presented by focusing on seismic risk, which is a typical risk in geotechnical engineering.

The current Japanese design method for geosynthetic MSE walls assumes multiple failure modes, as shown in Figure 13 (PWRC 2013), and is similar to popular design specifications elsewhere in the world. Based on this, the probability of the occurrence of each failure mode Pi is calculated using the reliability analysis method. Finally, the seismic failure probability, Pf, of the geosynthetic MSE wall is calculated as follows:

3

where Π is an operator denoting the product probability. The total cost, Cf, caused by a seismic failure event can be calculated as follows:

4

where Cs is the cost of demolition and removal, Cc is the cost of reconstruction, Cj is the cost of lost time due to road damage, Cd is the cost of lost travel due to detours during reconstruction, and Cp is the cost of human losses due to damage.

LCC calculations were performed for geosynthetic MSE walls, L-shaped retaining walls, and unreinforced embankments constructed for local roads. The following conditions were assumed in the analyses: (1) Compacted backfill soil properties: unit weight: γ  = 19.0 kN/m3, cohesion: c = 0 kN/m2, angle of internal friction: ϕ  = 30°; (2) Safety factors and seismic action: required safety factor: Fs = 1.2 for permanent actions, Fs = 1.0 for seismic action; design horizontal seismic intensity kh = 0.20; (3) Service conditions: service life = 50 years, average daily traffic condition = 10 000 vehicles; (4) Collapse area: 30 m in the direction of road expansion, regardless of the seismic conditions; (5) Structural dimensions: width = 30 m, height of structures, H = 4.0, 6.0, 8.0, and 10.0 m; (6) Uncertainty of design parameters: the coefficients of variation for the compacted backfill soils, tensile strength of the geosynthetics, and seismic intensity were 10%, 5%, and 50%, respectively. Figure 14 shows the typical cross-sections that were analyzed.

Figure 13.

Failure modes considered in the current design of geosynthetic walls (PWRC 2013)

Figure 13.

Failure modes considered in the current design of geosynthetic walls (PWRC 2013)

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Figure 14.

Typical cross-sections of a geosynthetic MSE wall, L-shaped concrete wall, and unreinforced embankment. (a) Geosynthetic MSE wall, (b) L-shaped concrete wall, (c) Unreinforced embankment

Figure 14.

Typical cross-sections of a geosynthetic MSE wall, L-shaped concrete wall, and unreinforced embankment. (a) Geosynthetic MSE wall, (b) L-shaped concrete wall, (c) Unreinforced embankment

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Figure 15 shows the calculated LCC values of the soil structures. The geosynthetic MSE wall has the lowest LCC, followed by the unreinforced embankment and L-shaped retaining wall. One reason for the high LCC of the L-shaped retaining wall is that it requires more days for rehabilitation after being damaged in a disaster. The unreinforced embankment incurs the lowest initial construction costs. Compared with the risk-based LCC, the order of the embankment and geosynthetic MSE wall is reversed. This result indicates that the risk of failure should be properly considered when selecting the type of structure for road construction.

Figure 15.

Life cycle cost analysis results for a geosynthetic MSE wall, L-shaped concrete retaining wall, and unreinforced embankment. ($US = 150 Yen in 2024)

Figure 15.

Life cycle cost analysis results for a geosynthetic MSE wall, L-shaped concrete retaining wall, and unreinforced embankment. ($US = 150 Yen in 2024)

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This section briefly describes the analysis method for CO2 emissions and the advantages of using geosynthetic MSE walls with greening. Similar analyses were performed by Heerten (2012) and Damians et al. (2017). They performed rigorous environmental analyses and demonstrated the advantages of geosynthetic MSE walls. One improvement in this study is that CO2 emissions are considered in a risk-based analysis. This study presents CO2 emissions as the CO2 equivalent weight [t-CO2] based on ISO (2006) 14040 and Miyata et al. (2013). Figure 16 shows the relationship between the performance level of a structure, initial construction emissions, absorption achieved by greening of the facing, risk of disaster recovery, and total emissions. The life cycle CO2 (LCCO2) is assumed, as shown in Equation (5).

5

where Ic denotes the initial construction emissions, Sc is the absorption achieved by the greening of the facing, and Rc is the risk of disaster recovery. Rc can be evaluated by multiplying the failure probability of the structures and the CO2 emissions during disaster recovery. In this study, only the seismic risk is considered. One feature of geosynthetic MSE walls is that the facing can be selected to satisfy construction conditions. Figure 17 depicts a green geosynthetic MSE wall during construction and while in service. A CO2 emissions analysis was performed for geosynthetic MSE walls with and without greening, L-shaped retaining walls, and unreinforced embankments.

Figure 18 presents the results of the analysis. For geosynthetic MSE walls, the facing can be greened using geogrids, geotextiles, steel mesh wall materials, and greening sheets, even if the construction conditions are complex. The analysis results show that the structure with the largest LCCO2 emissions among the four cases is the L-shaped retaining wall. In contrast, the lowest LCCO2 emissions are obtained for the geosynthetic MSE wall with greening. Surprisingly, assuming a service life of 50 years, the CO2 emissions become negative. Thus, geosynthetic MSE walls can be recognized as structures contributing to carbon neutrality, – that is, sustainability.

Figure 16.

Relationship between the performance level of structures, initial construction CO2 emissions: Ic, CO2 absorption achieved by the greening of the facing: Sc, CO2 emissions risk of disaster recovery: Rc and life cycle CO2 emissions

Figure 16.

Relationship between the performance level of structures, initial construction CO2 emissions: Ic, CO2 absorption achieved by the greening of the facing: Sc, CO2 emissions risk of disaster recovery: Rc and life cycle CO2 emissions

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Figure 17.

Greening technique combining a geogrid and geotextile for a geosynthetic MSE wall (courtesy of J. Hironaka). (a) During construction, (b) Greened wall facing

Figure 17.

Greening technique combining a geogrid and geotextile for a geosynthetic MSE wall (courtesy of J. Hironaka). (a) During construction, (b) Greened wall facing

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Figure 18.

Life cycle CO2 analysis results for a geosynthetic MSE wall, L-shaped concrete retaining wall, and unreinforced embankment

Figure 18.

Life cycle CO2 analysis results for a geosynthetic MSE wall, L-shaped concrete retaining wall, and unreinforced embankment

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This section discusses a damage/failure analysis method for geosynthetic MSE walls using the particle method, and its advantages are described based on the simulation results of a full-scale loading test (Nonoyama et al. 2022). In a series of analyses, the compacted backfill soil was modeled using the non-associative Drucker–Prager elastoplastic material. Because modeling the geosynthetic material with particles would be prohibitively computationally expensive, the soil–geosynthetic–soil system was modeled as an anisotropic linear elastic material with strain-based damage criteria based on the two-mixture theory. The key points of this model are the elastic modulus and the damage criteria for the system. In this study, the average horizontal elastic modulus, Eh, of the system is evaluated using the following modified equation of the Voigt model:

6

where Es is the elastic modulus of the compacted backfill soil, Er is the elastic modulus of the geosynthetic reinforcement, α is the volume fraction of the reinforcement layers in the reinforced system, and k is an empirical parameter representing the actual complex reinforcement effects. Here, Es can be evaluated using triaxial compression tests of soil samples. Er can be evaluated using the following equation:

7

where J2%_1000h is the secant tensile stiffness of geosynthetics at 2% strain and 1000 h (Allen and Bathurst 2015; AASHTO 2020; Bathurst and Naftchali 2021), and tr is the thickness of the geosynthetics. The parameter k can be evaluated by conducting a trial analysis. The average vertical elastic modulus of the system, Ev, is assumed to be the same as Es. The damage criteria for the system are given only for the horizontal direction of the system based on the allowable limit strain, εmax, following AASHTO (2020). In this model, when the calculated horizontal strain of a reinforced soil element reaches the limit value, εmax, in one calculation step, incremental displacements are calculated in the next step by reducing the horizontal stiffness of the system to practically zero. In this analysis, εmax = 2.0%, which is recommended for rigid-facing systems (Allen et al. 2003; AASHTO 2020; Bathurst and Allen 2023). The concrete-facing panel, soil–concrete interface, and compressible bearing pads between the panels are modeled as a linear elastic material.

To validate the proposed model, a full-scale loading experiment conducted on a geosynthetic MSE wall with a height of 3.0 m by Bathurst et al. (1993) was analyzed. In this experiment, the geosynthetic MSE wall was damaged by an airbag surcharge loading on the top surface. An overview of the full-scale model is presented in Figure 19. The fill material was sandy soil with gravel with a unit volume weight γ  = 18.0 kN/m3 and a water content of w = 2%. The reinforcement material was a biaxial high-density polyethylene (HDPE) geogrid with a tensile strength Tult = 12.0 kN/m and thickness tr = 1 mm. The property values of the compacted backfill soil, soil–geosynthetic system, concrete, soil–concrete interface, and compressible bearing pads between the panels are listed in Table 3. The empirical parameter k was evaluated as k = 2.0 based on a trial analysis.

Figure 19.

Analyzed cross-section for the full-scale testing of a geosynthetic MSE wall (Bathurst et al. 1993)

Figure 19.

Analyzed cross-section for the full-scale testing of a geosynthetic MSE wall (Bathurst et al. 1993)

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Table 3.

Property values of soil, geosynthetic, and concrete materials and their interfaces

Property valuesCompacted backfill soilSoil–geosynthetic systemConcreteSoil–concrete interfaceCompressible bearing pads between panels
Elastic modulusE (kPa)38 000Equation (9)300 000169 0002
Poisson's ratioν0.30.30.20.30.33
Bulk unit weightγ (kN/m3)18.018.023.518.018.0
Cohesionc (kPa)0
Peak friction angleϕ (deg.)53
Dilation angleψ (deg.)15

Figure 20 compares the analytical and measured strain distributions along the geogrid layers at the end of construction. Good agreements are obtained for the location and magnitude of the peak strain. Figure 21 compares the measured and calculated displacements of the facing panels at surcharge loading pressures of 12, 30, 50, and 70 kPa. In both phases, the calculated values generally agree well with the measured values. Thus, the proposed particle method holds promise for deformation and damage analyses of geosynthetic MSE walls.

Figure 20.

Measured and numerical strain distributions along the geogrid reinforcement layers (Nonoyama et al. 2022). (a) Layer 1 (height = 0.25 m), (b) Layer 2 (height = 1.0 m), (c) Layer 3 (height = 1.75 m), (d) Layer 4 (height =  2.5 m)

Figure 20.

Measured and numerical strain distributions along the geogrid reinforcement layers (Nonoyama et al. 2022). (a) Layer 1 (height = 0.25 m), (b) Layer 2 (height = 1.0 m), (c) Layer 3 (height = 1.75 m), (d) Layer 4 (height =  2.5 m)

Close modal
Figure 21.

Measured and numerical horizontal panel deformations (Nonoyama et al. 2022)

Figure 21.

Measured and numerical horizontal panel deformations (Nonoyama et al. 2022)

Close modal

A scenario-based numerical analysis was used to validate the proposed method for analyzing failure/beyond failure conditions. A scenario was assumed in which the foundation directly below the geosynthetic MSE wall slides horizontally, eventually resulting in functional loss of the foundation and facing panels. This scenario was based on full-scale testing, considering foundation failures (Miyata et al. 2015). In a series of analyses, a horizontal displacement rate of 1.0 cm/s was applied to the foundation, and an initial surcharge of 60 kPa was applied to the top of the backfill. When the horizontal displacement of the foundation reached 4 cm, a group of particles representing the foundation and facing was removed from the analysis. This treatment assumed that these materials completely lost their function after the foundation slid. Figure 22 shows the displacement field of the fill material after the foundation and facing materials were removed. In previous post-disaster reports on geosynthetic MSE walls (e.g. Kuwano et al. 2014), almost no cases occurred in which the geosynthetic MSE wall completely collapsed, and many walls reached equilibrium conditions at the large-deformation stage following structural failure. The analysis results are very similar to the behavior observed in such investigations. Therefore, it can be concluded that the proposed particle method holds promise to qualitatively simulate the failure behavior of geosynthetic MSE walls.

Figure 22.

Measured and numerical horizontal panel deformations (Nonoyama et al. 2022)

Figure 22.

Measured and numerical horizontal panel deformations (Nonoyama et al. 2022)

Close modal

Geotechnical challenges are becoming increasingly complex, requiring the further development of geosynthetic MSE wall technology. One technology that requires improvement is earthquake resistance. As indicated in Table 2, severe earthquakes lead to massive economic losses and human suffering, and considerable effort is required to recover from the damage. In structural engineering, seismic isolation and dynamic load mitigation technologies have been developed to reduce seismic actions on structures and increase their resistance to earthquakes (Spencer and Nagarajaiah 2003; Ikeda et al. 2019). In geotechnical engineering, such technical developments are insufficient.

Advanced earthquake-resistance techniques have been proposed for geosynthetic MSE walls, as shown in Figure 23. Geosynthetic reinforcement integral bridges have been combined with soil improvement to improve seismic resistance (Fig. (a): Tatsuoka et al. 2009), and a vibration control system with expanded polystyrene (EPS) geofoam has been employed to attenuate dynamic loads against rigid retaining wall structures (Fig. (b): Bathurst et al. 2007; Zarnani and Bathurst 2008). Moreover, geosynthetic reinforcement combined with an EPS geofoam has also been studied (Fig. (c): Koseki 2022). However, only a few studies have investigated seismic isolation control with geosynthetics. This study considers the potential for seismic isolation using geosynthetics with three-dimensional structures that can be used as vibration-reducing materials at construction sites. In Section 4.2, primary investigation results are presented and discussed.

Figure 23.

Geosynthetic technology for the seismic resistance and vibration control of retaining walls. (a) Reinforcement with soil improvement (after Tatsuoka et al. 2009), (b) Vibration control (after Bathurst et al. 2007; Zarnani and Bathurst 2008), (c) Reinforcement with vibration control (after Koseki 2022)

Figure 23.

Geosynthetic technology for the seismic resistance and vibration control of retaining walls. (a) Reinforcement with soil improvement (after Tatsuoka et al. 2009), (b) Vibration control (after Bathurst et al. 2007; Zarnani and Bathurst 2008), (c) Reinforcement with vibration control (after Koseki 2022)

Close modal

The development of life cycle management methods is another area that requires improvement. To perform life cycle management rationally, it is necessary to periodically diagnose conditions and determine the necessity of maintenance work. The first issue in geosynthetic MSE wall life cycle management is determining which data to measure. Allen et al. (2003) showed that the reinforcement strain is an important indicator of the integrity of a geosynthetic MSE wall. They showed that the load model, which was developed using measured strain data from a large number of geosynthetic MSE walls, was useful not only for design, but also for evaluating structural integrity.

Another issue is developing methods that will allow field data to be collected rapidly, inexpensively, and securely. The authors’ research group has developed a prototype sensor system for MSE walls and has confirmed the effectiveness of ICT-based management (Miyata et al. 2012). However, issues remain regarding the provision of reinforcement strain monitoring that is applicable throughout the entire service life of a geosynthetic MSE wall. Section 4.3 discusses the applicability of ICT management and an attachment-type fiber optic sensor for geosynthetic MSE wall life cycle management. An outline of the developed sensing system is presented, and its application to real infrastructure is demonstrated.

Figure 24 shows a geosynthetic MSE wall with a seismic isolation layer. This type of structural system is expected to demonstrate high seismic performance owing to the inherent reinforcement and seismic isolation effects of the geosynthetic MSE wall. The seismic isolation layer must have frictional resistance properties to provide sufficient sliding resistance to horizontal earth pressures from the retained backfill during (operational) static loading and it must serve to reduce the shaking transmitted to the geosynthetic MSE wall during earthquakes. The author focused on applying geosynthetics, which are beginning to be used as construction vibration-reducing materials (Ogawa et al. 2022). An example geosynthetic material is shown in Figure 25. This product is made of a polyolefin elastomer and has a three-dimensional braided structure. The material and structural characteristics of the product achieve high vibration-damping properties and high friction with the soil. This product is referred to as a geopad in this paper.

Figure 24.

Concept of a geosynthetic MSE wall with a seismic isolation layer

Figure 24.

Concept of a geosynthetic MSE wall with a seismic isolation layer

Close modal
Figure 25.

Geosynthetic material with a three-dimensional structure made from polyolefin elastomer

Figure 25.

Geosynthetic material with a three-dimensional structure made from polyolefin elastomer

Close modal

Figure 26 shows a schematic of the laboratory tests conducted to investigate the seismic isolation characteristics of the product. The apparatus consisted of a vertical stress loading apparatus, a vibration machine, and a specimen mounting apparatus. In the experiment, the specimen was sandwiched between two steel plates. The active plate in the upper geopad was subjected to sinusoidal vibration, and the acceleration transmitted to the passive plate in the lower geopad was measured. The experimental results were summarized by calculating the isolation efficiency, I, from the measured acceleration on the active plate, aa(t), and on the passive plate, ap(t), where t is the time. A typical result is shown in Figure 27. From the observed aa(t) and ap(t), the acceleration root mean square (rms) values and arms values were calculated for the active and passive plates using the following equation, where T is the period:

8
Figure 26.

Laboratory model test apparatus used to investigate the isolation efficiency of geopad geosynthetic samples

Figure 26.

Laboratory model test apparatus used to investigate the isolation efficiency of geopad geosynthetic samples

Close modal
Figure 27.

Typical acceleration measurements at the upper and lower plates in the laboratory model test (Ogawa et al. 2023)

Figure 27.

Typical acceleration measurements at the upper and lower plates in the laboratory model test (Ogawa et al. 2023)

Close modal

The isolation efficiency, E, was calculated by converting the arms values using the following equation:

9

where ap_rms and aa_rms are the rms values from the measured aa(t) and ap(t), respectively. These investigations were conducted for a natural rubber sheet that is commonly used for construction vibration countermeasures, single geopad, and double geopad layers. Vibrations were applied at five frequencies ranging from 5 Hz to 80 Hz.

The experimental results are presented in Figure 28. For the natural rubber sheet, the vibration transmission is 185% at 5 Hz and 45–52% at 10–40 Hz. E exceeds 100%, indicating that the upper and lower plates reach a resonant state. The double geopad layers improve the isolation effect, transmitting only 20–30% of the vibration of the natural rubber. These experimental results demonstrate the potential of geopads to improve the seismic isolation effect of geosynthetic MSE walls. As a next step, we plan to verify the seismic isolation effect of the geopad based on shaking table experiments with geosynthetic MSE walls. Subsequently, we plan to establish a method for analyzing the seismic isolation effect and evaluating the material properties of the geopad.

Figure 28.

Relationship between the frequency of shaking and isolation efficiency (Ogawa et al. 2023)

Figure 28.

Relationship between the frequency of shaking and isolation efficiency (Ogawa et al. 2023)

Close modal

Figure 29 shows a schematic of the roles of ICT-based geosynthetic MSE wall life cycle management for the stages of ‘Design and Risk Assessment,’ ‘Construction,’ ‘Maintenance,’ and ‘Emergencies.’ The structural data is always sent to the engineering office to ensure the data can be used to make decisions for any life cycle stage of a structure. The technical reliability of geosynthetic MSE walls will be further enhanced once such a system is developed, and the corresponding management approach is put into practice. Two key issues must be addressed for the practical application of this management strategy. One concern is the need for long-term sensors to monitor the internal conditions of geosynthetic MSE walls throughout the life of the structure. Geosynthetic strain measurements can effectively assess the structural integrity of geosynthetic MSE walls (Allen et al. 2003). Therefore, corresponding long-term measurements should be developed. Hatami et al. (2009) proposed a strain-sensitive conductive geosynthetic material based on nanotechnology. Fiber optic sensing is another candidate for use in long-term measurements. Fiber optics have recently been applied to measuring civil engineering structure movements (Soga and Luo 2018). In the technical field of geosynthetic MSE walls, pioneering work has been performed by Yashima et al. (2009). The development of more advanced measurement techniques is expected.

Figure 29.

Concept of information and communication technology (ICT)-based life cycle management of geosynthetic MSE walls

Figure 29.

Concept of information and communication technology (ICT)-based life cycle management of geosynthetic MSE walls

Close modal

Remarkable progress in optical fiber sensors (OFS) has been achieved in recent years. Figure 30 presents a comparison of three types of sensors. Strain gauge measurements are limited to measurement density (number of sensors per length or area). Classical OFS measurements have limitations in terms of measurement resolution and accuracy. In the future, OFS should be developed with improved performance. The latest sensor system enables the acquisition of structural data with higher accuracy and speed. The author and research collaborators have initiated a study to confirm the applicability of the distributed fiber optic sensors examined by Kishida et al. (2022) for geosynthetic MSE walls. As a first step in the research, strain measurements were conducted at an actual infrastructure project. Figure 31 shows the site conditions. The case was a road reinforced with geosynthetics on soft ground. Soil moisture and temperature were monitored at the base and subbase. OFSs were installed on the geosynthetic material, and the geosynthetic strain was measured under actual traffic conditions. Figure 32 shows the strain distribution in the 50-m-long direction measured at 30-min intervals. The measured values vary depending on the vehicles moving on the road surface. The first stage of measurement was successful. In the next step, the measurement of reinforced soil walls is planned. In this case, the strain level is large, and the distribution is non-uniform. Further technical improvements are required to ensure success. Engineers and researchers are expected to study new long-term sensing methods for geosynthetic MSE walls.

Figure 30.

Comparison of strain gauge measurements and classical and latest optical fiber sensors (OFS)

Figure 30.

Comparison of strain gauge measurements and classical and latest optical fiber sensors (OFS)

Close modal
Figure 31.

Fiber optics applied to a field construction site with a geosynthetic reinforced soil (courtesy of H. Nagatani and J. Hironaka)

Figure 31.

Fiber optics applied to a field construction site with a geosynthetic reinforced soil (courtesy of H. Nagatani and J. Hironaka)

Close modal
Figure 32.

Field measurement results for a geosynthetic reinforced foundation with fiber optics (courtesy of H. Nagatani and J. Hironaka)

Figure 32.

Field measurement results for a geosynthetic reinforced foundation with fiber optics (courtesy of H. Nagatani and J. Hironaka)

Close modal

Another issue is the need to develop reliability analyses to utilize long-term sensor data. Using a statistical approach, Allen and Bathurst (2015) developed reinforcement tensile load prediction models for MSE walls under various operating conditions. Bathurst et al. (2019), Bathurst and Allen (2023) calibrated the load and resistance factors of geosynthetic MSE walls. Miyata et al. (2018, 2019) and Bathurst et al. (2020) demonstrated the application of this general approach to polyethylene terephthalate (PET) strap walls. Reliability analysis is a powerful tool for improving design methods using in situ data. Reliability analysis can also be used for other phases of the MSE wall life cycle. In the construction process, reliability analyses using design estimates and observed data can be used to evaluate the deviations between design assumptions and actual as-built conditions. In addition, probabilistic reliability indices can be used to consider measures, such as halting construction and changing the design, before a serious accident occurs. During the maintenance period, monitoring systems can assist in predicting the future internal conditions of a structure using reliability analysis applied to the observed data, allowing the user to consider changes to the inspection schedule and measures to be implemented. Deep learning will undoubtedly be effective for future predictions. In emergency situations where damage is caused by large actions, such as earthquakes and rainfall, data on the internal condition of the structure before and after such actions can be compared and checked for anomalies within a reliability analysis framework. Even if demolition or removal is deemed necessary, a reliability analysis using the observed data can be a useful tool for safety evaluations during planning and execution. The massive amounts of data collected by ICT management will contribute to more accurate risk estimations.

This paper discusses the ‘past,’ ‘present,’ and ‘future’ of research and practice regarding geosynthetic MSE walls. The main conclusions are summarized as follows.

To discuss the ‘past’ of geosynthetic MSE wall research and practice, research trends in geosynthetic MSE walls over the past 50 years were reported based on a review of 728 technical papers. Technological progress has reached its present state through two cycles of accumulation and development periods. The timing of these transitions was closely related to learned society proceedings, journal publications, design code development, and the occurrence of natural disasters. Research on geosynthetic MSE walls can be categorized into mechanical and soil interactions, analytical and numerical modeling, physical modeling and in situ measurements, and reliability analyses. The research topics have progressed in the following order: understanding the macroscopic behavior of the walls, elucidating their elemental properties, developing analysis methods, and evaluating reliability.

For the ‘present’ state of geosynthetic MSE walls, risk-based life cycle cost/CO2 emission assessments and a numerical simulation method were outlined as modern analysis methods developed by the author and collaborators. A life cycle assessment evaluates the LCC as the sum of the initial construction cost, maintenance cost, and seismic risk, while LCCO2 is the sum of CO2 emissions during construction and in-service combined with the seismic risk, where the risk is evaluated as a product of the seismic failure probability and recovery cost based on ISO (2015) 2394. Comparing the LCC and LCCO2 of an unreinforced embankment, L-shaped retaining wall, and geosynthetic reinforced soil wall showed that the reinforced soil wall is the most effective structural system. Further, a numerical simulation method was developed based on the particle method concept. The proposed method was demonstrated to estimate the deformation, damage, and failure of a geosynthetic MSE wall. The applicability of the proposed method for deformation and damage analysis was demonstrated by simulating a full-scale loading test conducted by Bathurst et al. (1993). The applicability of the method for failure/beyond failure analysis is demonstrated by a scenario analysis in which some important structural members lost their function.

For the ‘future,’ seismic isolation using geosynthetics and an ICT-based life cycle management method are discussed. An isolation technique concept was proposed, and simple shaking table test results were performed to validate the basic concept. The focused (geopad) product has high vibration-damping properties. The tests conducted on natural rubber sheets, single geopad, and double geopad layers demonstrated the potential for the geopad to improve the seismic isolation effect of geosynthetic MSE walls. An outline of the management technique was presented, and its application to real infrastructure was demonstrated. The developed sensing system with the latest optical fiber sensors can measure geosynthetic strain with high resolution and accuracy. Site measurements at a road reinforcement site with geosynthetics on soft ground showed the strong potential for the system to be applied to reinforced soil walls. By combining this with advanced reliability assessments, life cycle management can be performed more rationally.

The Bathurst lecture was established in recognition of the invaluable contributions of IGS Past President, R.J. Bathurst, to the technical advancement of all aspects of reinforced soil structures with geosynthetics and his overall contribution to the development of the IGS. The writer expresses sincere gratitude to the IGS council, the technical committee on soil reinforcement, and the 12th ICG organizing committee for allowing the writer to deliver this first Bathurst lecture. The writer expresses his sincere respect for R.J. Bathurst. The work described in this paper results from the collaborative effort of many talented individuals. The author would like to express his sincere gratitude to R.J. Bathurst and T.M. Allen for their guidance in research collaboration on the reliability design of MSE walls. The review work was an activity of the IGS technical committee on soil reinforcement. The writer sincerely thanks the chairperson, P. Rimoldi, and the secretary, I.P. Damians. The writer wishes to acknowledge the efforts of M. Shinoda, H. Nonoyama, and S. Miyamoto, who are members of the geotechnical research group of the National Defense Academy of Japan, and H. Nagatani and J. Hironaka who gave the author important practical information, and A. Nakagawa who jointly conducted the risk analyses in this paper. The author would also like to express his gratitude to many researchers and engineers at the PWRI, PWRC, and the IGS Japan chapter, who have allowed him to interact regularly. This work was supported by JSPS KAKENHI Grant Numbers JP 23H01507 and JP 20H02247.

Basic SI units are shown in parentheses.
aa(t)

measured acceleration on the active plate in geopad model tests (m/s2)

aa_rms

rms values from measured aa(t) (m/s2)

ap(t)

measured acceleration on the passive plate in geopad model tests (m/s2)

ap_rms

rms values from measured ap(t) (m/s2)

C

initial cost (currency)

Cc

cost of reconstruction (currency)

Cd

cost of lost travel due to detours during reconstruction (currency)

Cf

total cost (currency)

Ci

damage if event i occurs (currency)

Cj

cost of lost time due to road damage (currency)

Cp

cost of human losses due to damage (currency)

Cs

cost of demolition and removal (currency)

c

cohesion of compacted backfill soils (N/m2)

Eh

average horizontal elastic modulus of compacted backfill soils (N/m2)

Er

elastic modulus of the geosynthetics (N/m2)

Es

elastic modulus of the compacted backfill soils (N/m2)

Fs

safety factor (dimensionless)

H

height of structures (m)

I

isolation efficiency (dimensionless)

Ic

initial construction CO2 emissions (t-CO2)

J2%_1000h

secant tensile stiffness of geosynthetics at 2% strain and 1000 h (N/m)

k

an empirical parameter representing the actual complex reinforcement effects (dimensionless)

kh

design horizontal seismic intensity(dimensionless)

LCC

life cycle cost (currency)

LCCO2

life cycle CO2 emissions (t-CO2)

M

maintenance cost (currency)

Pf

probability of failure (dimensionless)

Pi

probability associated with event I (dimensionless)

R

risk (dimensionless)

Rc

CO2 emissions risk of disaster recovery (t-CO2)

Sc

CO2 absorption achieved by the greening of the facing (t-CO2)

Tult

tensile strength of geosynthetics (N/m)

t

time (s)

tr

thickness of the geosynthetics (m)

α

volume fraction of geosynthetics in the reinforced system (dimensionless)

γ

unit weight of compacted backfill soils (N/m3)

εmax

allowable limit strain for reinforced soil system (dimensionless)

ν

Poisson's ratio (dimensionless)

Π

operator denoting the product probability (dimensionless)

ϕ

internal friction angle of compacted backfill soils (°)

ψ

dilation angle of compacted backfill soils (°)

AASHTO

American Association of State Highway and Transportation Officials (USA)

ASTM

American Society for Testing and Materials (USA)

DEM

discrete element method

EPS

expanded polystyrene

FDM

finite difference method

FEM

finite element method

G&G

Geotextiles and Geomembranes

GI

Geosynthetics International

HDPE

high-density polyethylene

ICG

International Conference on Geosynthetics

ICT

information and communication technology

IGS

International Geosynthetics Society

ISO

International Organization for Standardization

ISSMGE

International Society for Soil Mechanics and Geotechnical Engineering

MSE walls

mechanically stabilized earth walls

OFS

optical fiber sensors

PET

polyethylene terephthalate

PWRC

Public Works Research Center (Japan)

rms

root mean square

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