**Editor’s Note **: Jie Han, Ph.D., P.E., F.ASCE, is the third recipient of the Dr. Robert M. Koerner Award and Lecture Series. The two past recipients are George R. Koerner, Ph.D., P.E. and CQA, in 2017, and Barry Christopher, Ph.D., P.E., in 2019. The award and lecture series, given by the Geosynthetic Materials Association, is named for the late Robert M. Koerner, Ph.D., the founder and former director emeritus of the Geosynthetic Institute and the former professor emeritus in civil engineering at Drexel University.

This article summarizes the third Dr. Robert M. Koerner Lecture given by the author at the 2021 Geosynthetics Virtual Conference. This lecture series was established by the Geosynthetic Materials Association (GMA) to honor Koerner for his leadership and significant contributions to the geosynthetics industry. In the fifth edition of the classic book entitled *Designing with Geosynthetics*, Koerner (2005) stated, “The latest application area in the context of foundation and basal soil reinforcement is the use of geogrids to span deep foundations placed through compressible soils [54, 55]. The geogrids span from pile cap to pile cap, reducing localized settlement in the supported embankment system.” The two references 54 and 55 cited by Professor Koerner were published by Han and Gabr (2002) and Han and Akins (2002). The first paper was published based on a numerical study, which is theoretical, while the second paper summarized three case studies of geogrid-reinforced pile-supported embankments (now commonly referred to as geosynthetic-reinforced column-supported embankments or GRCS embankments in the U.S.), which are practical. Clearly, Koerner (2005) conveyed an important message that a successful technology involving geosynthetics not only should have solid theories but also should be practical to solve real problems. The third Dr. Robert M. Koerner Lecture entitled “Geosynthetic-reinforced column-supported embankments: Bridging theory and practice” was prepared and delivered following this philosophy. Although this article summarizes the key contents of the lecture, it emphasizes the important point: Improving practice with better theory.

**Background of technology**

Differential settlement is a common problem for civil engineering applications when superstructures or earth structures are constructed on soft soils. This problem becomes even more critical when there is a transition from soft soils to rigid supports—for example, bridge approach embankments as shown in **Figures 2a and 2b**. When the bridge abutment is supported by piles, it has minimum to nearly no settlement. However, when the approach embankment is constructed on the soft soil (**Figure 2a**), large deformation can occur, resulting in large differential settlement between the abutment and the embankment. This differential settlement at the intersection of the bridge abutment and the approach embankment is often referred to as a “bump,” a driving hazard to the public. Geosynthetic-reinforced column-supported embankments have been increasingly used to solve this bump problem because of their advantages of fast construction and effectiveness. In this technology, as shown in **Figure 2b**, columns (e.g., concrete columns, deep-mixed columns and stone columns) are used to increase bearing capacity, reduce settlement and enhance global stability. Geosynthetics (one or multiple layers) placed in the load transfer platform above the columns help transfer more vertical embankment loads to columns and carry lateral thrusts from the embankment so that lower vertical loads are applied on the soft soil and lower lateral loads are transferred to the columns. In addition, geosynthetics can reduce differential settlement between columns. This technology has also been used to solve differential settlement problems for roadway widening, retaining walls, box culverts, storage tanks, buildings and buried pipes.

The early application of this technology can be traced back to a project in 1972, in which vertical timber piles and three layers of 2.9 ounces per square yard (100 g/m^{2}) multifilament woven polyester geotextiles were used to support an approach embankment (Holtz and Massarsch 1976). Applications of this technology increased since the 1990s after the important research by Hewlett and Randolph (1988) and the publication of the design guidelines (BS8006) by the British Standards Institution (1995). One of the earliest uses of this technology in the U.S. was the construction of a storage tank on a geogrid-reinforced load transfer platform on concrete columns in Philadelphia, Pa., in 1994 (ASCE 1997).

With the increased application of this technology, GRCS embankments have become a hot research topic worldwide in the past 20 years. Many research projects and papers on this subject have been published, which have helped better understand the mechanisms involved in this system. At the same time, different theories were proposed, and different design methods were developed, which have enabled engineers to design such a system. Unfortunately, different design methods have resulted in different design requirements and performance predictions to be discussed in the following section.

**Theory** **Mechanisms**

The mechanisms for GRCS embankments depend on the location of the columns in the embankment (i.e., center or edge). This article focuses on the mechanisms associated with the columns in the center of the embankment. **Figure 3** presents the load transfer mechanisms of one unit cell from the GRCS embankment.

Since the soft soil of lower modulus deforms more than the columns of higher modulus under the embankment load, it induces shear stresses, τ_{s}, along the slip surfaces in the embankment so that the pressure applied on the geosynthetic, p_{s}, is lower than the average pressure (γH + q_{0}, γ is the unit weight of the embankment fill, H is the embankment height, and q_{0} is the surcharge) induced by the embankment fill and the surcharge. This phenomenon is referred to as soil arching by Terzaghi (1936). Soil arching ratio, defined as the pressure on the geosynthetic divided by the average pressure from the embankment load and the surcharge, is used to describe the degree of soil arching. The smaller soil arching ratio implies more soil arching. When the geosynthetic is under pressure, it deforms and develops tension, T, the vertical component of which carries the vertical load from the embankment and reduces the stress, σ_{s}, applied onto the soft soil. This mechanism is often referred to as the tensioned membrane effect. Stress reduction ratio, defined as the stress on the subsoil below the geosynthetic divided by the average pressure from the embankment load, is used to describe the benefit of combined soil arching and tensioned membrane effect. Since the soft soil (often called the subsoil) below the embankment settles more than the columns, negative skin friction (also called downdrag force), τ_{d}, develops between the columns and the soil so that the vertical stress in the subsoil decreases with depth. The reduced vertical stress in the subsoil minimizes its compression. This is the mechanism of column/subsoil interaction. The differential settlement between the columns and the subsoil depends on the relative stiffness between the columns and the subsoil, which affects the mobilization of soil arching in the embankment fill and the downdrag force in the subsoil. Rigid columns promote soil arching and downdrag force and therefore have been increasingly used in recent years. When the embankment is high enough, an equal settlement plane can develop at the critical height, H_{cr}. Van Eekelen and Han (2020) provided a list of methods to estimate this critical height, most of which yield a similar result.

In summary, the mechanisms involved in the GRCS embankment include soil arching, tensioned membrane and column/subsoil interaction. The effects of these mechanisms depend on column/subsoil relative stiffness. Many studies have shown that soil arching progressively evolves with normalized displacement, defined as the differential settlement, δ, divided by the clear spacing of the columns, s–a (s is the center-to-center spacing and a is the column diameter). Iglesia et al. (1999) proposed a ground reaction curve (GRC) to describe the evolution of the soil arching ratio with the normalized displacement. Han et al. (2017) proposed a simplified GRC using three straight lines to describe the evolution of the soil arching ratio with the normalized displacement: (1) decreasing from 1.0 (no arching) to the minimum arching ratio (i.e., the maximum arching); (2) increasing from the minimum ratio to the ultimate arching ratio (i.e., stress recovery or soil arching degradation); and (3) remaining constant at the ultimate arching ratio.

**Theoretical models**

Based on experimental and numerical studies, researchers have proposed different soil arching models (**Figure 4**) and their corresponding calculation methods for reduced stress due to soil arching. These models can be sorted into three groups in terms of their deformation patterns: (a) curved, (b) triangular and (c) vertical. However, McGuire and Filz (2008) found that these models resulted in significant differences in the calculated vertical stresses on the geosynthetic. As a result, the tensile forces in the geosynthetic calculated by these models differ by 10 times, which is not acceptable for practice. Han (2021) attributed one of the main reasons for these differences to the fact that different stages of soil arching were assumed in the development of these models. Iglesia et al. (1999) and Han et al. (2017) concluded soil arching progressively develops with the displacement from curved, triangular to vertical deformation patterns. Han (2021) found that the minimum soil arching ratio corresponds to the concentric soil arching, while the ultimate soil arching ratio corresponds to the vertical soil arching; therefore, he linked these two important states to the following two representative soil arching models to generate the simplified GRC: (1) the concentric arch model developed by van Eekelen et al. (2013) and (2) the adapted Terzaghi arch model proposed by Russell et al. (2003). Both models considered the three-dimensional effect of column patterns.

In addition to soil arching, design of GRCS embankments must determine the required maximum tension in the geosynthetic according to the tensioned membrane effect. Han and Gabr (2002) found that the maximum tension in the geosynthetic above columns occurred at the edge of columns when a single geosynthetic was used. This finding was confirmed by several later studies. Russell et al. (2003) and van Eekelen et al. (2013) both considered the net applied pressure (i.e., the difference between the pressures above and below the geosynthetic) on the geosynthetic that is eventually carried by the reinforcement strips between columns so that the higher tension in the geosynthetic is calculated using the parabolic method.

Furthermore, the column/subsoil interaction should be considered in the design. The downdrag force between columns and subsoil reduces the vertical stresses in the subsoil with depth. At a certain depth (called the neutral plane), the downdrag force becomes zero when the columns and the soil have the same deformation. The distribution of the downdrag force and the depth of the neutral plane depends on the stress on the subsoil and the properties of the columns and the subsoil, including the relative stiffness of column to subsoil. Chen et al. (2008) and Filz et al. (2019) considered the distribution of the downdrag force in the subsoil in their models.

**Unified practical solution**

To address the issue related to different soil arching models developed based on different soil arching stages, Han (2021) proposed a unified solution (**Figure 5**) by adopting the simplified GRC and the concept of the interaction diagram for soil arching, geosynthetic reinforcement and subsoil resistance proposed by Ellis and Aslam (2009). To plot all the stress values on the same figure, both the soil arching ratio and the stress reduction ratio are referred to as the normalized stress. **Figure 5** shows that the simplified GRC starts from the initial point with a normalized stress at 1.0 (i.e., no arching) corresponding to the normalized displacement equal to 0 (i.e., zero displacement). With an increase of the displacement, the normalized stress decreases to the minimum value, which can be estimated by the concentric arch model. Han et al. (2017) found that the normalized displacement corresponding to the minimum value is approximately 1.5% to 5%. After the minimum value, the normalized stress increases with the normalized displacement up to the ultimate value, which can be estimated by the adapted Terzaghi method. Han et al. (2017) also found that the ultimate value happens at the normalized displacement of approximately 10%.

According to the tensioned membrane theory, the normalized net stress carried by the geosynthetic reinforcement can be estimated based on the normalized displacement; therefore, the resistance curve for the geosynthetic can be obtained.

Considering the downdrag force distribution and the one-dimensional consolidation of the soil, the relationship between the subsoil resistance and the normalized displacement can be established.

The combined resistance from the geosynthetic reinforcement and the subsoil can be obtained by adding their resistance at the same normalized displacement. The intersection of the combined resistance curve with the GRC is the solution for the normalized displacement and the normalized stress on the geosynthetic. The location of the intersection depends on several factors including but not limited to the dimensions or properties of the embankment, the load transfer platform, the geosynthetic and the subsoil.

This unified method was verified by two field studies reported in the literature: (1) the full-scale experiment by Briançon and Simon (2012) and (2) the field project with long-term measurements by van Eekelen et al. (2020). Interestingly, the subsoil in the first study was strong and stiff so that the geosynthetic provided limited contributions. In the second study, however, the embankment lost subsoil support during its service so that the geosynthetic provided significant contributions. The verifications of the proposed solution were carried out by comparing the calculated stress on the geosynthetic, the differential settlement between columns and subsoil, and the strains in the geosynthetic with those measured. The comparisons show excellent matching between the calculations and the measurements.

**Summary**

This article provides a summary of the third Dr. Robert M. Koerner Lecture presented by the author at the 2021 Geosynthetics Virtual Conference and demonstrates the importance of bridging theory and practice for geotechnical engineering applications through GRCS embankments technology. The research conducted by many researchers in the past 20 years have helped better understand the mechanisms of the GRCS embankments including soil arching, tensioned membrane and column/subsoil interaction. The effects of these mechanisms depend on column/subsoil relative stiffness. Theoretical solutions based on these mechanisms have made it possible for engineers to design GRCS embankments. To address large discrepancies in calculated stresses and tensile forces in the geosynthetic, the author proposed a unified practical solution based on the simplified ground reaction curve and the interaction diagram to improve the accuracy of the design method.

**Acknowledgments**

I appreciate the Geosynthetic Materials Association (GMA) for selecting me for this great award and honor, and for providing the opportunity for the distinguished lecture. Professor Robert M. Koerner is one of my role models who has inspired and encouraged me to conduct research by bridging theory and practice. I am very thankful to the education, mentorship and support I received throughout my career in China, the U.S. and beyond. Credits go to all researchers and industries including my collaborators and graduate students who have helped advance this technology.

*Jie Han, Ph.D., P.E., F.ASCE, is the Glenn L. Parker Professor of Geotechnical Engineering in the Civil, Environmental, and Architectural Engineering Department at the University of Kansas in Lawrence, Kan.*

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