A novel hybrid technique for lateral pressure reduction on rigid retaining walls integrating EPS cushion and lightweight foam bead backfill

1 Introduction

Retaining walls are essential geotechnical structures widely used in highway construction, urban excavation support, and hillside development to resist lateral earth pressure and maintain the stability of backfill slopes. In many practical scenarios, rigid retaining walls such as gravity walls or combined retaining structures are subjected to high lateral pressures, especially when the wall displacement is limited and the backfill soil cannot reach the active limit state (Fang and Ishibashi, 1986). These excessive lateral loads often lead to increased wall dimensions, higher material costs, and potential safety risks. Therefore, reducing lateral earth pressure acting on retaining walls has become a key concern in geotechnical engineering, particularly under limited backfill width or restricted wall movement conditions (Yang et al., 2016).

To address this challenge, various pressure-reduction techniques have been proposed and investigated. Among them, the use of compressible inclusions placed between the wall and the backfill has proven effective. Expanded polystyrene (EPS) geofoam, a lightweight and highly compressible material with stable chemical properties, has received considerable attention (Horvath, 1997). To facilitate a clear comparison of the effectiveness of these two techniques across different soil types and material parameters, the key findings from previous studies are summarized in Table 1. When installed as a cushion behind a rigid retaining wall, EPS undergoes compression upon backfilling, allowing the retained soil to mobilize its shear strength even under small wall displacements. Numerous experimental and numerical studies have demonstrated that EPS cushions can substantially reduce lateral earth pressure. Tsukamoto et al. (2002) showed through model tests that EPS blocks effectively reduce static earth pressure on rigid retaining walls. Ikizler et al. (2008) confirmed via laboratory studies that EPS geofoam works well with expansive soils. Ertugrul and Trandafir, 2011, 2013 demonstrated that EPS inclusions can significantly reduce lateral earth forces on both rigid and flexible retaining walls. Bathurst and Zarnani (2013) and Bathurst et al. (2007) further verified the effectiveness of EPS buffers under seismic conditions through shaking table tests. More recently, Zou et al. (2025) provided field evidence of EPS geofoam reducing lateral earth pressure of expansive soils, while Ni et al. (2017) investigated displacement-dependent earth pressure reduction using compressible inclusions. Numerical studies by Hatami and Witthoeft (2008) and Kim et al. (2018) also confirmed that EPS geofoam enhances the stability of retaining wall systems. Zarnani and Bathurst (2009) further supported these findings through finite element analyses.

TABLE 1. Earth pressure-reduction techniques across different soil types.

Another parallel approach to reducing lateral earth pressure is the use of lightweight backfill materials. By replacing conventional fill with low-density materials, the self-weight-induced lateral pressure can be significantly decreased. Among lightweight fill options, expanded polystyrene (EPS) beads mixed with soil or used as granular fill have shown great potential due to their ultra-low density, good workability, and ability to reduce vertical and horizontal stresses (Tsuchida et al., 2007). Tsuchida et al. (2007) investigated the mechanical properties of lightweight treated soil with EPS beads. Kazempour et al. (2021) examined the compression characteristics and lateral earth pressure coefficient of aggregate-EPS bead composites. Gao et al. (2012) explored the creep behavior of EPS composite soil, while Hou and Yang (2021) conducted model tests on lightweight soil mixed with EPS particles behind retaining walls. AbdelSalam and Azzam (2016) also investigated the reduction of lateral earth pressure using EPS geofoam. Liang et al. (2023) made preliminary attempts to investigate load-reducing effects of EPS cushion and lightweight soil, but systematic experimental quantification of their combined effect is still lacking. Kaneda et al. (2018) examined earth pressure reduction using tire-chip inclusions, while Khan and Meguid (2021) evaluated the role of geofoam properties in reducing lateral loads, further confirming the potential of compressible inclusions. Aytekin (1997) provided early numerical modeling of EPS geofoam for earth pressure reduction. It is hypothesized that by integrating both approaches—using an EPS cushion to accommodate lateral compression and EPS bead lightweight fill to reduce the driving forces—the lateral earth pressure could be reduced more effectively than by either method alone. However, most existing studies have treated EPS cushions and lightweight backfill as separate solutions, each with its own set of design parameters and effectiveness limits (Alaie and Jamshidi Chenari, 2018; Puppala, 2019; Ertugrul and Trandafir, 2011; Kim et al., 2018). To date, the interaction between the cushion and the lightweight fill, as well as their combined effect on lateral earth pressure distribution and overall load reduction performance, remains largely unexplored. Recent field studies on expansive soils and foundation treatments have highlighted the need for integrated pressure-reduction strategies.

This study aims to systematically investigate the lateral earth pressure distribution and load reduction performance of retaining walls incorporating both an EPS cushion layer and EPS bead lightweight fill. A series of laboratory model tests were conducted using a custom-built retaining wall apparatus. The test soil was taken from an actual gravity retaining wall site in Guangzhou, characterized as high-plasticity clay with high fine-particle content and low permeability. Two pressure-reduction techniques were examined: (1) placing a flexible EPS cushion of varying thickness (2–6 cm) between the wall and the backfill, and (2) mixing EPS foam beads (0.1%–0.3% by weight) into the clay to produce lightweight fill. Four levels of surcharge load were applied stepwise to simulate different service conditions. The individual and combined effects of cushion thickness and foam content on lateral earth pressure were evaluated in terms of pressure distribution, load reduction value, and load reduction rate. The results reveal the respective contributions of the cushion and the lightweight fill, their synergistic interaction, and the optimal parameter ranges for practical design.

2 Experimental materials and methods

2.1 Experimental materials

The test soil used in this study was collected from a gravity retaining wall construction site located in the Huangpu District of Guangzhou, China (Figure 1). This retaining wall was designed as part of an urban slope stabilization project, where limited backfill space and strict displacement control requirements necessitated a detailed investigation into lateral earth pressure reduction strategies. The collected clayey soil was subjected to a series of laboratory tests to determine its basic physical and mechanical properties, as summarized in Table 2. The soil has a natural density of 1.98 g/cm³, a natural water content of 20.1%, a specific gravity of 2.71, and a void ratio of 0.69. The free swelling rate is 48.3%, indicating a moderate swelling potential that should be considered in retaining wall design. The permeability coefficient is 4.55 × 10⁻⁷ cm/s, classifying the soil as having very low permeability, which implies that drainage is slow, and without appropriate drainage provisions, water pressure can build up behind the retaining wall. Atterberg limit tests gave a liquid limit of 48.5%, a plastic limit of 28.6%, and a shrinkage limit of 8.1%; the plasticity index is therefore 19.9. Using the Unified Soil Classification System (USCS), the plasticity index of 19.9 and liquid limit of 48.5% place the soil near the CL-CH boundary on the Casagrande plasticity chart (the A-line is defined as PI = 0.73 (LL − 20), giving a boundary PI of 20.8 at LL = 48.5%). The particle size distribution curve (Figure 2) shows that the soil contains 0.8% gravel (>2 mm), 28.8% sand (0.075–2 mm), 45.1% silt (0.005–0.075 mm), and 25.3% clay (≤0.005 mm). The total fine fraction (<0.075 mm) reaches 70.4%, indicating a high proportion of fine particles that tend to retain water and exhibit low shear strength under undrained conditions. The gradation is relatively well-distributed, with the curve extending smoothly from the clay to the fine sand range.

TABLE 2. Physical properties of test clay.

The combination of high fine-grained content, low permeability, and moderate swelling potential suggests that, if used as conventional backfill, this soil would generate substantial lateral earth pressure behind a rigid retaining wall, especially when the wall undergoes little to no outward movement. Therefore, this soil provides a realistic and challenging benchmark for evaluating the effectiveness of lateral pressure reduction measures. In this study, expanded polystyrene (EPS) beads, with a grain size of 1–5 mm and a bulk density of 0.032 g/cm³, were selected for testing. A specially manufactured EPS panel, featuring a sleek and even finish, was utilized as the compressible backfill cushion. This panel, which had a thickness of 20 mm and a mass per unit volume of 12 kg/m³, demonstrated an elastic modulus reaching 3 MPa during the initial, linear-elastic phase of uniaxial compression.

2.2 Test device

The experimental tests were conducted using a custom-built model box with internal dimensions of 1,000 mm in length, 600 mm in width, and 600 mm in height, as illustrated in Figure 3. The external frame of the box was welded from 30 mm square steel tubing, and the top of the box remained open. Both the side plates and the bottom plate were made of 20 mm thick ABS plastic, which were embedded and fixed within the external stainless steel frame. Ni et al. (2017) used a similar model box (2 m × 1.5 m × 1.2 m) with a rigid wall and EPS geofoam inclusion to study lateral earth pressure distribution under surcharge loading. Sealant was applied to all gaps to ensure airtightness and prevent soil leakage. The retaining wall panel was constructed from a 50 mm thick stainless steel plate. The bottom of the panel was fixed, while the top could be adjusted using rivets to change its inclination angle if required. The width of the backfill behind the retaining wall could be conveniently altered by repositioning a movable partition plate inserted into dedicated slots within the box. All EPS boards used in the tests were custom-made, with dimensions matching exactly the contact area of the retaining wall panel. To monitor the lateral earth pressure distribution, miniature earth pressure sensors were installed at five different depths along the vertical centerline of the wall panel, specifically at 100 mm, 200 mm, 300 mm, 400 mm, and 500 mm measured from the top of the backfill surface. These sensors were securely embedded to ensure full contact with the EPS cushion or backfill material. Each sensor was calibrated with the gauze wrapping in place using incremental pressure loads from 0 to 200 kPa, yielding a linear calibration curve for each sensor. For earth pressure measurement, the installation and calibration procedures follow the recommendations of Lazebnik (1998), who emphasized the importance of in-soil calibration and careful sensor placement to avoid arching-induced under-registration. The same gauze-wrapped configuration was maintained throughout both calibration and subsequent testing to ensure consistency. Repeatability tests on three sensors gave a coefficient of variation below 3%, confirming that the measurement uncertainty introduced by the gauze layer is within acceptable limits. The overall model box assembly, including the wall panel, the movable partition, and the sensor layout, is schematically shown in Figure 3.

2.3 Test methods

Given the hydrophobic nature of the expanded polystyrene (EPS) beads, special measures were taken to ensure uniform mixing with the soil during preparation of the lightweight fill. First, the EPS beads were pre-wetted by passing them through water, so that their surfaces became uniformly coated with moisture. Based on the designated mix proportions, the pre-wetted foam beads were then evenly sprinkled over the raw soil, followed by repeated and thorough mixing to achieve a homogeneous lightweight fill. The EPS foam contents (0.1%, 0.2%, and 0.3%) reported throughout this study are defined as the percentage of EPS beads by dry mass of the soil. The mixture was subsequently placed using a mass-controlled method, adopting a layered filling approach with manual compaction. All specimens, including both the lightweight fill mixtures and the untreated control soils, were prepared to a constant compaction degree of 95% relative to the maximum dry density. The untreated control soil (0% foam) achieved a dry density of 1.65 g/cm³ at this compaction degree and an optimum moisture content of 25.6%. For the lightweight fill mixtures with EPS foam contents of 0.1%, 0.2%, and 0.3% (defined as percentage by dry mass of soil), the same 95% compaction degree was maintained by applying identical compaction effort, corresponding to 1.58 g/cm³ for 0.1% foam, 1.51 g/cm³ for 0.2% foam, and 1.44 g/cm³ for 0.3% foam. This consistency allows for unambiguous evaluation of the reinforcement effects, as any observed differences in performance can be attributed solely to the presence of the binder rather than variations in initial soil conditions.

For test configurations involving an EPS flexible cushion behind the retaining wall, the cushion layer was placed along the inner face of the wall panel after the earth pressure sensors had been secured at the specified depths. The cushion was pressed tightly against the wall surface to ensure full contact. The backfill, consisting of either raw soil or the prepared lightweight fill, was then placed following the same layered compaction procedure. To prevent stress concentration on the sensors during the experiment, each sensor was wrapped with gauze before being placed into its pre-drilled cavity. This gauze layer acted as a protective barrier, avoiding direct contact between the clay backfill and the sensing surface, thereby ensuring more reliable pressure readings.

The experimental procedure began with positioning the model box and securing the retaining wall panel. The EPS board was attached to the inner surface of the wall panel using glass glue. Earth pressure sensors were then fixed onto the surface of the EPS board at five specified heights: 100, 200, 300, 400, and 500 mm from the top of the backfill. All connecting wires were carefully organized and routed out from the side edge of the wall panel to connect the sensors to a static strain acquisition system. Prior to backfilling, a simple verification test was performed by blowing air into the white ventilation tube of each sensor; a clear jump in the output value from zero, followed by a gradual return to zero after stopping, confirmed correct sensor installation. Data acquisition was then initiated with a sampling interval of 5 s.

The backfill soil was placed in six layers, each 10 cm thick, resulting in a total backfill height of 60 cm. After all layers were completed, the model was allowed to stand until the readings from the earth pressure sensors stabilized. Stepwise surcharge loading was then applied by uniformly placing weights on a wooden board to simulate a uniformly distributed load on the backfill surface, covering a width of 43 cm behind the wall. Each load increment was applied only after the measured earth pressure had stabilized. The specific load levels are listed in Table 3. Throughout both the backfilling and loading stages, the static strain acquisition system remained operational to continuously measure and record the variation of lateral earth pressure along the wall height. The surcharge loads were applied stepwise only after the measured lateral earth pressures had stabilized. Under these conditions, the tests are best interpreted as representing essentially undrained behavior of the clay matrix during the loading sequence, with any transient pore-pressure effects having largely dissipated prior to each pressure reading.

TABLE 3. Test program.

After completing the measurements for a given configuration, the surcharge load was removed, the backfill material was emptied, and the earth pressure sensors were carefully taken off. The EPS board was then replaced with a new one, and the entire procedure was repeated for the next test condition. As summarized in Table 3, a total of 14 configurations were conducted, with the cushion layer thickness varying from 0 cm to 6 cm, the foam content in the lightweight fill set to either 0% (raw soil only) or other specified values, and a stepwise vertical load ranging from 0 to 2.0, 4.0, 6.3, and finally 8.8 kPa applied to the backfill surface for each condition. It should be noted that the wall was maintained in a completely rigid state throughout the testing process, with no rotation or lateral deflection permitted. The rivet adjustment mechanism was used solely for initial positioning of the stainless steel plate prior to each test; once the desired configuration was established, the rivets were firmly secured to lock the wall in place. Under the applied load of 8.8 kPa, the structural compliance of the rigid wall system was negligible, and no measurable wall movement was detected.

3 Results and discussion

3.1 Effect of EPS cushion layer on load reduction

Figure 4 illustrates the lateral earth pressure distribution along the wall depth under different cushion thicknesses (0 cm, 2 cm, 4 cm, and 6 cm) across four consecutive load stages. It is noteworthy that in the no-cushion case, the lateral earth pressure does not increase monotonically with depth but exhibits a nonlinear distribution, first increasing and then gradually decreasing below approximately 0.3 m depth. The influence of the surcharge load applied on the backfill surface gradually diminishes with increasing depth. The development of soil arching within the backfill behind the rigid wall, arising from differential settlement and stress redistribution, can contribute to this non-monotonic pressure profile. Fan et al. (2024) found that the lateral earth pressure distribution on retaining walls with EPS inclusions under limited surcharge loading is non-linear, with the pressure changing from increasing to decreasing with depth as the surcharge load increases. Similarly, Chen et al. (2025) validated an ‘R’-shaped distribution of lateral earth pressure along the depth, attributing this pattern to soil arching effects. From the curves, a clear trend can be observed: increasing the thickness of the EPS cushion significantly reduces the lateral earth pressure acting on the retaining wall, and this effect is consistent under all four load stages. When no cushion (0 cm) is used, the lateral earth pressure increases notably with depth, reaching relatively high values at the bottom of the wall. In contrast, as the cushion thickness increases from 2 cm to 6 cm, the lateral earth pressure decreases progressively across the entire wall depth.

Under the first load stage (Figure 4A), the pressure reduction is already visible. The 2 cm cushion provides a moderate reduction, while the 4 cm and 6 cm cushions result in substantially lower pressures, especially in the lower half of the wall. This indicates that even a thin compressible layer can effectively relieve lateral stresses by allowing some lateral deformation of the backfill. As the load increases to the second and third stages (Figures 4B,C), the lateral earth pressure rises for all cushion thicknesses, but the relative reduction due to thicker cushions remains pronounced. The 6 cm cushion consistently maintains the lowest pressure profile, suggesting that a thicker EPS layer provides greater accommodation for soil movement and stress redistribution under higher surcharge loads. Under the fourth (highest) load stage (Figure 4D), the beneficial effect of thicker cushions is most evident. While the no-cushion case exhibits a steep pressure increase with depth, all cushioned cases show flatter pressure distributions, indicating a more uniform load transfer to the wall. Notably, the difference between the 4 cm and 6 cm cushions becomes smaller at higher loads, suggesting the existence of an optimal cushion thickness beyond which additional thickness yields diminishing returns in pressure reduction.

To further evaluate the pressure reduction effect of the EPS flexible cushion, lightweight fill, and their combined system on the retaining wall structure, two indices are introduced: the load reduction value △P and the load reduction rate R. These are defined in Equations 1, 2: where P ₀ represents the resultant lateral earth pressure acting on the wall when only raw soil is used as the backfill under a given surcharge load (kN/m), which is numerically equal to the area enclosed by the earth pressure distribution curve and the coordinate axis; P _n represents the resultant lateral earth pressure acting on the wall under the same surcharge load when either a cushion layer or lightweight fill (or their combination) is installed behind the wall (kN/m). To ensure the reliability and reproducibility of the experimental results, each of the 14 test configurations listed in Table 3 was independently repeated three times. For each replicate, fresh backfill material was prepared following the same mixing, compaction, and curing procedures, and new EPS cushions were used to eliminate any potential material aging or conditioning effects. The reported lateral earth pressure values at each depth, as well as the resultant lateral forces P ₀ and P _n and the derived reduction values and reduction rates, represent the arithmetic mean of the three replicate measurements.

△ P = P 0 − P n (1)

R = P 0 − P n / P 0 × 100 % (2)

As shown in Figure 5, the load-reducing value increases consistently with cushion thickness across all four loading stages. For a cushion thickness of 2 cm, the reduction in lateral earth pressure is relatively modest, ranging from approximately 0.18 kN/m under the first stage to about 0.55 kN/m under the fourth stage. When the thickness increases to 4 cm, the reduction value improves significantly, reaching approximately 0.32–0.95 kN/m. The 6 cm cushion achieves the highest reduction, with values approaching 1.24 kN/m under higher load stages. This indicates that thicker cushions provide greater accommodation for backfill deformation, thereby mobilizing more soil shear strength and transferring less load to the wall.

Figure 6 presents the corresponding load-reducing rate expressed as a percentage. The trends are consistent with those observed in Figure 5. Under the first load stage, the reduction rate for the 2 cm cushion is around 12%, while the 4 cm and 6 cm cushions achieve approximately 23% and 33%, respectively. As the vertical load increases to the fourth stage, the reduction rates for all cushion thicknesses rise noticeably. The 2 cm cushion reaches about 22%, the 4 cm cushion approaches 42%, and the 6 cm cushion attains nearly 55% reduction. This demonstrates that the efficiency of the EPS cushion improves under higher surcharge loads, likely because greater applied stress induces larger compression of the cushion, thereby enhancing its load-relief function. Another important observation is the diminishing marginal benefit of increasing cushion thickness beyond 4 cm. While the 6 cm cushion consistently outperforms the 4 cm cushion, the increment in reduction rate from 4 cm to 6 cm is smaller than that from 2 cm to 4 cm, especially under higher loads. This suggests the existence of an optimal cushion thickness-approximately 4–6 cm under the test conditions—beyond which additional thickness yields limited improvement in pressure reduction.

3.2 Effect of EPS foam on load reduction

Figure 7 presents the depth–lateral earth pressure curves (with EPS foam contents of 0%, 0.1%, 0.2% and 0.3% under four load stages). The influence of foam content on the lateral pressure distribution can be examined from a different perspective, focusing on profile shape, depth-dependent efficiency, and load-induced variations. Across all loading stages, the 0% foam (pure soil) consistently produces the highest pressures, with a distinctly concave profile that becomes steeper with depth, particularly beyond 0.4 m. The addition of only 0.1% EPS foam flattens the pressure gradient remarkably, especially in the middle and lower portions of the wall, indicating that even a tiny fraction of foam interrupts the transmission of vertical stresses into horizontal thrusts.

When the foam content is raised to 0.2% and 0.3%, the pressure curves become almost linear and shift downward as a whole. The difference between 0.2% and 0.3% is smaller than the difference between 0.1% and 0.2%, suggesting a “diminishing-return” region above 0.2% foam for this soil and compaction condition. Under the first and second load stages, the 0.3% foam curve lies only slightly below the 0.2% curve; under the third and fourth stages, the two curves almost coincide near the wall base, implying that once the foam content exceeds a threshold (around 0.2%), further increases provide marginal extra relief under heavy surcharge. A notable depth-dependent behaviour is observed: near the wall top (0–0.2 m depth), all foam contents produce similarly low pressures, because the vertical stress there is small. In contrast, at depths greater than 0.4 m, the 0% foam curve rises sharply, while all foam-amended curves remain gentle, demonstrating that foam is most efficient in reducing lateral pressure where the overburden stress is high. This explains why the load-reducing rate (not shown here) generally increases with load stage: larger vertical loads create larger overburden stresses, which are then more effectively mitigated by the lightweight foam fill.

As shown in Figure 8, the load-reducing value rises steadily with increasing foam content across all four loading stages. For 0.1% foam, the reduction value stays below 0.2 kN/m under the first stage and reaches approximately 0.35 kN/m under the fourth stage. When the foam content is raised to 0.2%, the reduction value roughly doubles, approaching 0.43 kN/m at higher loads. The 0.3% foam content produces the largest reduction, up to about 0.55 kN/m under the fourth stage. However, the increment from 0.2% to 0.3% is noticeably smaller than that from 0.1% to 0.2%, indicating diminishing marginal returns beyond 0.2% foam.

Figure 9 presents the corresponding load-reducing rate expressed as a percentage, which follows similar trends but provides clearer insight into efficiency. Under the first load stage, the reduction rate for 0.1% foam is only about 12%, while 0.2% and 0.3% foam achieve approximately 22% and 30%, respectively. As the vertical load increases to the fourth stage, the 0.1% foam reaches roughly 16%, the 0.2% foam approaches 20%, and the 0.3% foam attains nearly 25% reduction. This confirms the load-dependent sensitivity of the reduction rate. From the first to the fourth stage, the reduction rate for 0.1% foam increases by about 4 percentage points, while for 0.3% foam it decreases by approximately 5 percentage points. This suggests that higher foam content provides greater absolute reduction but degrades the load-responsive behavior, making the system less adaptable to varying surcharge conditions. Furthermore, the spacing between the curves in Figure 9 narrows from 0.1% to 0.2%–0.3%, especially under higher loads. The difference between 0.2% and 0.3% is only about 5 percentage points at the fourth stage, whereas the difference between 0.1% and 0.2% is approximately 4 percentage points. This reinforces the existence of an optimal foam content range around 0.2% in this study, beyond which additional foam yields relatively limited improvement.

3.3 Combined effect of EPS cushion and foam content on load reduction

Figure 10 illustrates the lateral earth pressure distribution along the wall depth under combined conditions of different EPS cushion thicknesses (2 cm, 4 cm, 6 cm) and EPS foam contents (0.1%, 0.2%, 0.3%) across four consecutive load stages. The interaction between the two pressure-reduction mechanisms reveals complex, load-dependent behavior that differs significantly from either technique applied independently. Under the first load stage (Figure 10a), the baseline condition (0 cm cushion +0% foam) produces the highest lateral pressures, with a pronounced increase below 0.3 m depth. Introducing either a cushion or foam alone reduces pressures, but the combined systems show distinctly different patterns. For a thin cushion (2 cm) paired with low foam content (0.1%), the pressure reduction is modest, primarily affecting the upper half of the wall. However, when the same thin cushion is combined with higher foam content (0.3%), the pressure profile flattens considerably, achieving reductions comparable to a 4 cm cushion alone. This indicates that foam content partially compensates for insufficient cushion thickness, especially under low surcharge conditions. The most pronounced enhancement appears when thicker cushions (4 cm and 6 cm) are combined with moderate to high foam contents (0.2% and 0.3%), where the integrated system achieves lower and more uniformly distributed lateral pressures than either component alone. These combinations produce pressure distributions that are not only lower in magnitude but also nearly uniform with depth, suggesting that the two mechanisms work in complementary ways. The EPS cushion primarily relieves localized stresses near the wall interface by accommodating lateral deformation, while the lightweight fill reduces the overall vertical stress transmitted through the backfill mass. Together, they create a more efficient stress redistribution system than either component alone.

Under the second and third load stages (Figures 10b,c), as surcharge loads increase, the differences between various combinations become more pronounced. The cushion-dominated combinations (thick cushion with low foam) show pressure profiles that remain concave, with higher pressures in the lower wall section. In contrast, the foam-dominated combinations (moderate cushion with high foam) produce flatter profiles, indicating that foam content plays an increasingly important role in controlling pressure buildup under higher loads. Interestingly, the combination of 4 cm cushion with 0.3% foam performs nearly as well as 6 cm cushion with 0.2% foam, demonstrating that judicious selection of both parameters can achieve target reductions without maximizing either individually.

Under the fourth (highest) load stage (Figure 10d), the combined effects reach their maximum expression. The pressure curves separate into three distinct groups. The least effective group (2 cm cushion with 0.1% foam) still shows substantial pressure buildup near the wall base. The intermediate group (2 cm/0.3% foam and 4 cm/0.1% foam) produces moderate reductions. The most effective group (4 cm/0.2% foam, 4 cm/0.3% foam, and 6 cm/0.2% foam) achieves the lowest and most uniform pressure distributions, with lateral pressures at the wall base reduced by approximately 50%–60% compared to the no-cushion, no-foam baseline.

A critical observation is that beyond certain thresholds, approximately 4 cm cushion thickness and 0.2% foam content, further increases in either parameter yield diminishing improvements when the other parameter remains low. For example, increasing foam content from 0.2% to 0.3% with a 2 cm cushion produces only marginal additional reduction, while the same foam increases with a 4 cm cushion results in noticeable improvement. This suggests a coupling effect: adequate cushion thickness is necessary to fully mobilize the benefits of higher foam content, and vice versa. The depth-dependent behavior also reveals important interactions. Near the wall top (0–0.2 m depth), all combinations produce similarly low pressures because the overburden stress is minimal. In the middle section (0.2–0.4 m depth), cushion thickness dominates the reduction effect, as lateral deformation accommodation is most relevant where intermediate stress levels exist. At greater depths (below 0.4 m), foam content becomes the dominant factor, as reducing the self-weight of the overlying soil column has the greatest impact where vertical stresses are highest. This complementary depth-dependent efficiency explains why the combined systems outperform single-parameter optimizations.

Figures 11, 12 summarises the combined effect of EPS cushion thickness (2 cm, 4 cm) and EPS foam content (0.1%, 0.2%, 0.3%) on lateral earth pressure reduction. Under the first load stage, both figures show that the reduction value and rate increase steadily with cushion thickness when foam content remains constant. However, the interaction becomes evident when comparing combinations such as 2 cm cushion with 0.3% foam versus 4 cm cushion with 0.1% foam. These two combinations yield nearly identical reduction rates (approximately 12%–14%), indicating that a deficiency in cushion thickness can be compensated by higher foam content, and vice versa. This substitutability provides design flexibility: engineers can choose between a thicker cushion or a higher foam content based on material availability and cost.

As the load progresses to the second and third stages, the interaction shifts from simple substitution to substantial enhancement. The reduction rate for 2 cm cushion with 0.2% foam increases modestly from about 10% to 14%, while 4 cm cushion with 0.2% foam jumps from approximately 18%–28%. The gap between these two combinations widens substantially, revealing that thicker cushions become more effective at mobilizing foam benefits under intermediate loads. Under the fourth (highest) load stage, the most pronounced combined effects emerge. For the 4 cm cushion, similar behavior occurs but with lower absolute values: 0.1%–0.2% gives about 10 percentage points improvement, while 0.2%–0.3% gives only about 4 percentage points. The 2 cm cushion shows the smallest improvement from foam addition, with total increase from 0.1% to 0.3% being only about 8 percentage points, indicating that very thin cushions cannot fully utilize the benefits of high foam content.

A critical interaction effect is revealed when comparing the increment due to cushion versus increment due to foam across load stages. Under low loads, foam content contributes more to reduction than cushion thickness. Under high loads, cushion thickness becomes increasingly dominant. At the fourth stage, increasing cushion from 2 cm to 4 cm with fixed 0.1% foam raises reduction rate by about 22 percentage points (from roughly 18%–40%). In contrast, increasing foam from 0.1% to 0.2% with fixed 2 cm cushion raises reduction rate by only about 10 percentage points (from 18% to 28%). This load-dependent dominance shift has important practical implications: for projects expecting high surcharge loads, prioritizing cushion thickness is more effective than maximizing foam content. The diminishing returns phenomenon is evident for both parameters but becomes more severe under higher loads. For the 4 cm cushion, the reduction rate gain from 0.1% to 0.2% foam is 17 percentage points, while from 0.2% to 0.3% is only 8 percentage points. Given the reduction efficiency is approaching the practical upper limit, and considering constructability and cost-effectiveness, the optimal design ranges are approximately 4–6 cm for cushion thickness and 0.2%–0.3% for foam content.

4 Practical implications and limitations

The test soil used in this study is a high-plasticity clay (CH) with low permeability and high fine-particle content. For granular soils, arching effects are less pronounced and stress transmission is more efficient, which may alter the performance of the EPS cushion; for expansive soils, swelling pressure may interact with the compressible inclusion in a more complex manner. Thus, while the qualitative trends and combined responses are expected to be broadly applicable, the quantitative reduction rates and optimal parameter ranges (4–6 cm cushion thickness; approximately 0.2% foam content) should be carefully adjusted when applied to other soil types. Additionally, field construction practices and long-term durability of EPS materials—including creep, aging, and degradation—may differ from laboratory conditions and warrant further investigation.

Economically, while the 4 cm cushion with 0.2% foam content proved most cost-effective for the tested clayey soil, these parameters may shift with local material costs, equipment availability, and project requirements; site-specific trials are recommended to determine optimal designs. Despite these limitations, this study clearly demonstrates the combined potential of the hybrid system and provides a systematic experimental framework adaptable to other soils and design scenarios. Future research should prioritize full-scale field validation, long-term durability assessment, and the development of numerical design tools to facilitate broader engineering adoption.

Despite these limitations, this study demonstrates the combined potential of combining EPS cushions with lightweight foam bead backfill, offering a viable and cost-effective alternative for lateral pressure reduction. For moderate surcharge conditions, a 4 cm cushion with 0.2% foam content is recommended as the near-optimal configuration, achieving 50%–60% pressure reduction under the highest load tested. Lower-demand applications may adopt a 2 cm cushion with 0.1%–0.2% foam (20%–30% reduction), whereas high-load scenarios benefit more from increasing cushion thickness (up to 6 cm) than from further raising foam content beyond 0.2%. Beyond pressure relief, the lightweight fill reduces unit weight, enhances slope stability, and is constructible with conventional equipment, offering economic advantages over traditional solutions such as wall thickening or tieback installation. Nevertheless, the quantitative findings are contingent upon the specific soil type and model scale employed. Application to granular or expansive soils, taller walls, and field conditions should be approached with caution, as arching behavior, swelling pressure, and stress-dependent EPS compressibility may alter system performance. Future research should prioritize full-scale field validation, long-term durability assessment of EPS materials, and the development of numerical design tools to facilitate broader engineering adoption.

5 Conclusion

This study systematically investigated the lateral earth pressure distribution and load reduction performance of retaining walls equipped with EPS cushion layers and EPS foam lightweight fill under varying surcharge loads. Through a series of model tests and quantitative analyses using custom-built apparatus, the individual and combined effects of cushion thickness (2–6 cm) and EPS foam content (0.1%–0.3%) on pressure reduction were evaluated across four consecutive loading stages. The main findings are summarized as follows.

• EPS cushion thickness significantly reduces lateral earth pressure. Increasing cushion thickness from 0 cm to 6 cm consistently lowered lateral pressures across all load stages. The reduction rate improved from approximately 12% for a 2 cm cushion under the first load stage to nearly 55% for a 6 cm cushion under the highest load stage. However, diminishing returns were observed beyond 4 cm, suggesting an optimal cushion thickness of approximately 4–6 cm under the tested conditions.
• EPS foam content effectively reduces lateral pressure by flattening the pressure distribution. Even a small addition of 0.1% foam notably flattened the pressure gradient, especially at greater depths. Increasing foam content to 0.2% roughly doubled the reduction value, achieving reduction rates of 22% under low loads and 20% under high loads. Further increase to 0.3% provided only marginal improvement, indicating an optimal foam content around 0.2% for this soil and compaction regime.
• The combined system of EPS cushion and foam fill exhibits strong combined effects. The most favorable combinations (e.g., 4 cm cushion with 0.2% foam) achieved lateral pressure reductions of 55%–60% at the wall base under the highest load stage, outperforming either technique applied alone. The two mechanisms work complementarily: the cushion relieves localized stresses through lateral deformation accommodation, while the foam fill reduces overall vertical stress transmission.
• Load-dependent dominance shift governs reduction efficiency. Under low surcharge loads, foam content contributed more to pressure reduction than cushion thickness. Under high loads, cushion thickness became increasingly dominant. For high-load applications, prioritizing cushion thickness (up to 4 cm) is more effective than maximizing foam content beyond 0.2%.
• Based on the quantitative thresholds identified, the optimal design ranges are: cushion thickness of 4–6 cm and EPS foam content of approximately 0.2%. Beyond these values, additional material input yields limited improvement. The observed substitutability between cushion thickness and foam content offers design flexibility, allowing engineers to balance performance, material availability, and cost.

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Footnotes

Edited by: Chaofeng Zeng, Hunan University of Science and Technology, China

Reviewed by: Kamil Bekir Afacan, Eskisehir Osmangazi Universitesi, Türkiye

N. Murali Mohan, Jawaharlal Nehru Technological University Anantapur, India