Optimizing Foam Lightweight Soil Embankments: Enhancing Stability and Mitigating Settlement in Soft Soil Foundations

Abstract

Foam lightweight soil (FLS) has emerged as a promising material in geotechnical engineering due to its low density, high load-bearing capacity, and ability to incorporate industrial by-products such as fly ash. It offers significant advantages in mitigating settlement and improving stability for embankments constructed on soft soil foundations. However, the combined influence of key parameters—including layered filling thickness, bulk density, and geogrid reinforcement—on the long-term performance of FLS embankments remains insufficiently understood. This study investigates the settlement behavior and stability of FLS embankments through a combination of field experiments and finite element simulations over a 15-year period. The results indicate that layered filling thicknesses of 500–600 mm achieve the best balance between settlement control and construction feasibility. When the thickness exceeds 800 mm, not only does the uniformity deteriorate, but the settlement also increases. Experimental results showed that a medium bulk density of 6 to 8 kN/m³ is optimal as a balance between strength and settlement behavior. Furthermore, geogrid reinforcement significantly improved stability, with safety factors increasing by up to 1.87 compared to unreinforced sections. The findings provide practical guidelines for the design and construction of FLS embankments, particularly for bridge approaches and soft soil foundations. In addition to improving structural performance, the incorporation of industrial by-products highlights the potential of FLS as a sustainable and cost-effective material for future infrastructure development.

1. Introduction

Foam lightweight soil is a lightweight porous material formed by mixing and foaming cement, water, a foaming agent and the necessary admixture. The material has the advantages of low density, large compression modulus, convenient construction, and good self-compacting [1]. Han Yusheng et al. explored the reduction of load-bearing load to reduce subgrade settlement through engineering practice and numerical simulation experiments [2]. Foam lightweight soil is widely used in road reconstruction and expansion. Because of its good fluidity, light weight, and durability [3,4,5], it is often used to solve problems such as soft soil foundation treatment, embankment engineering, and differential settlement of subgrade [6,7,8,9,10]. Studies have shown that foamed lightweight soil is suitable as roadbed material [11,12,13,14]. The use of foamed lightweight soil can effectively reduce the weight of the roadbed, improve the bearing capacity, and reduce the settlement, thereby enhancing the overall stability of the road.

Zhang Delong et al. [15] explored the mechanical properties of foamed lightweight soil under different mix ratios by orthogonal test, obtained the best mix ratio of foamed lightweight soil, and predicted the compressive strength of foamed lightweight soil; Yan et al. [16] studied the strength and mechanical properties of foamed lightweight soil under different loading modes and loading boundary conditions by combining unconfined compressive strength test and triaxial shear test. Liu Chao et al. [17] analyzed the performance of foamed lightweight soil with different contents of fly ash by the laboratory test method. Han Lei et al. [18] explored the basic properties, mechanics, dynamics, and construction technology of foamed lightweight soil through laboratory tests and engineering practice. Wang [19] explored the deformation characteristics and construction technology of foamed lightweight soil subgrade under different structural forms.

While foam lightweight soil has been studied for various applications, there remains a gap in understanding the combined effect of key factors, such as layered filling thickness, bulk density, and reinforcement (e.g., geogrids), on the performance of foam lightweight soil embankments. First, most studies have focused on single parameters, such as layer thickness, bulk density, or reinforcement methods, without addressing the combined effects of these critical factors on settlement and stability [20]. Second, investigations into the long-term performance of FLS embankments remain limited, with relatively few field studies and numerical simulations extending beyond a decade. Finally, while reinforcement techniques such as geogrid inclusion have shown promise in enhancing stability, their interaction with FLS properties under complex load conditions is still not fully understood.

The present study aims to address these research gaps by systematically examining the combined influence of layered filling thickness, bulk density, and geogrid reinforcement on the settlement and stability of FLS embankments. Using both long-term field monitoring and finite element simulations (ABQUS) spanning a 15-year period, this research identifies the optimal design configurations and evaluates their performance under realistic engineering conditions. The findings are expected to provide practical recommendations for engineers in designing FLS embankments, particularly in bridge approaches and soft soil foundations, while also advancing sustainable construction practices through the utilization of industrial by-products [21].

2. Literature Review

Foam lightweight soil (FLS) has gained recognition in geotechnical engineering for its ability to mitigate settlement and enhance the stability of embankments, particularly in soft soil foundations. Despite its widespread use, there is a gap in comprehensive studies that examine the combined effects of critical parameters such as layered filling thickness, bulk density, and reinforcement techniques on the performance of FLS embankments [22].

2.1. Application in Road Embankments

Foam lightweight soil, also known as foam concrete or cellular concrete, is a material characterized by its low density and high compressive strength. The material is produced by introducing air bubbles into a cement-based slurry, resulting in a highly porous structure. The key benefits of lightweight foam soil include its low weight (often 1/4th the density of conventional soil), ease of placement, and cost-effectiveness. It is widely used in road construction, slope stabilization, and as a backfill material for embankments and bridge approaches [23].

The use of foam lightweight soil in embankment construction began in the 1980s, primarily in Japan, for road widening on slopes and soft soil stabilization [24]. Over the years, lightweight foam soil has been successfully applied to reduce the load on weak soil foundations and prevent settlement. However, challenges related to uniformity, settlement, and stability have necessitated further investigation into the optimal design of foam lightweight soil embankments [25].

2.2. Influence of Layered Filling Thickness on Settlement

The thickness of foam lightweight soil layers significantly affects the settlement behavior of embankments. In typical embankment construction, if the soil is filled in a single large layer, the pressure from the upper layers may cause over-compaction at the base, leading to uneven settlement. Several studies have shown that controlling the filling thickness in layers can help prevent this problem [26].

Zhu et al. (2016) [27] discussed the importance of layered filling in minimizing differential settlement. Their experiments indicated that lightweight foam soil layers should not exceed 500 mm to 600 mm in thickness to ensure uniform settlement and avoid excessive shrinkage. Puppala et al. (2019) [28] recommended that lightweight foam soil should be poured in layers to prevent over-compaction at the base, a phenomenon that can lead to cracking due to the rapid drying and shrinkage of the material.

In terms of the settlement analysis, the equation below can be used to estimate the settlement variation based on layered filling thickness and bulk density:

$$S={\displaystyle \frac{P.h}{E.A}}$$

(1)

where:

S = Settlement (mm)

P = Load applied (kN)

h = Layer thickness (mm)

E = Elastic modulus of foam lightweight soil (MPa)

A = Area of the base layer (m²)

This equation can help evaluate the impact of layer thickness on settlement during the filling process.

2.3. Bulk Density and Its Impact on Settlement and Stability

Bulk density is a critical parameter in the design of lightweight foam soil embankments. The density affects the material’s compressive strength, load-bearing capacity, and consolidation behavior. Studies have demonstrated a positive correlation between bulk density and the stability of foam lightweight soil embankments.

Zaolong Jiang et al. (2022) [29] observed that as the bulk density increases, the compressive strength of foam lightweight soil increases as well, leading to greater load-bearing capacity but also higher settlement values in the long run.

2.4. Reinforcement Techniques for Foam Lightweight Soil Embankments

Reinforcement, particularly the use of geogrids, has been shown to improve the stability of foam lightweight soil embankments by increasing the embankment’s load-bearing capacity and reducing plastic deformation.

Gao et al. [30] demonstrated that embedding geogrid within foam lightweight soil can significantly enhance the safety factor of the embankment. Their results showed that geogrid-reinforced foam lightweight soil embankments could withstand higher loads without significant plastic deformation.

Geosynthetics, including geogrids and geotextiles, are also commonly used in the stabilization of soft soils. Tiwari et al. [31] emphasized the use of geogrid reinforcement for improving structural integrity and long-term durability of embankments under traffic loads.

Equation for Stability of Reinforced Embankment:

The stability of a reinforced foam lightweight soil embankment can be calculated using the following equation:

$$Fs={\displaystyle \frac{L_{reinforced}}{L_{unreinforced}}}·({\displaystyle \frac{G}{S}})$$

(2)

where:

Fs = Safety factor of the embankment

L_reinforced = Length of the reinforced section (m)

L_unreinforced = Length of the unreinforced section (m)

C = Compressive strength (MPa)

S = Settlement (mm)

2.5. Gaps in Existing Research

While the literature provides valuable insights into the individual parameters affecting foam lightweight soil embankments, there is still a lack of studies that investigate the combined effect of filling thickness, bulk density, and reinforcement in ensuring optimal embankment performance. Additionally, the long-term effects of these factors on embankment stability and settlement require further exploration, particularly with the use of field tests and numerical modeling.

This research will attempt to fill these gaps by investigating the influence of these combined factors on the performance of foam lightweight soil embankments over an extended period [26].

3. Materials and Methods

The study involved both field experiments and numerical simulations using Finite Element Analysis (FEA) to simulate the behavior of foam lightweight soil embankments under various filling thicknesses and loading conditions. The objective was to analyze how different variables, such as the filling thickness and reinforcement techniques, influence the settlement and stability of the embankments over time.

3.1. Field Experiments

Field experiments were conducted on a site where foam lightweight soil was used to fill embankments of varying thicknesses. The layered filling thicknesses tested were 500 mm, 600 mm, 800 mm, and 1000 mm, with each layer applied using a controlled method to ensure uniformity and accurate measurement of settlement and stability.

Layered Filling Thicknesses: The lightweight foam soil was poured in layers to prevent over-compaction and maintain the uniformity of the embankment. The tested layer thicknesses were 500 mm, 600 mm, 800 mm, and 1000 mm.

3.2. Numerical Simulations

In addition to the field experiments, numerical simulations were conducted using finite element analysis (FEA) to predict the behavior of the foam lightweight soil embankments over time. These simulations helped in evaluating the long-term effects of different filling thicknesses, bulk densities, and reinforcement configurations. The FEA models were calibrated with experimental data to ensure the accuracy of the results [32].

3.3. Tested Parameters

Filling Thickness: The different filling thicknesses (500 mm, 600 mm, 800 mm, and 1000 mm) were tested to determine the most effective thickness for controlling settlement in foam lightweight soil embankments [33].

Bulk Density: The bulk density of foam lightweight soil was varied to analyze how changes in material density affect the settlement and stability of the embankments. Various densities were used to simulate real-world conditions and assess performance under different loading scenarios [34].

Geogrid Reinforcement: In certain cases, geogrid reinforcement was applied to the foam lightweight soil embankments to assess its effect on the stability and load-bearing capacity of the embankments. This reinforcement technique helps in improving the overall stability by reducing plastic deformation and enhancing the embankment’s resistance to external loads [35].

3.4. Selection of Layered Filling Thickness

Layered filling can effectively control and evenly distribute the settlement of each layer of light soil foam. In the case of large-volume filling, if the one-time filling is too high, the bottom soil may be over-compacted due to the greater pressure of the upper layer, resulting in uneven settlement. The reasonable thickness of layered filling is helpful to ensure the uniformity of the filling area, and at the same time, a large amount of hydration heat will be generated during the pouring process of foam lightweight soil, and layered filling can effectively reduce the shrinkage cracks caused by temperature stress during the pouring process. For foam light soil, the bubble stability has the most significant impact on the pouring thickness; the foam light soil contains a large number of bubbles, and the uniformity is not easy to control when pouring a large area [36]. The layered filling is conducive to the evaporation of water and the discharge of air, thereby accelerating the development of soil consolidation and strength. Under complex geological conditions, the layered filling can be adjusted according to the bearing capacity of the foundation at different levels so that the filling body is more suitable for the foundation conditions and the safety of the project is improved [37] and stability. Therefore, it is necessary to reasonably control the single-layer pouring thickness of foam lightweight soil.

4. Influence of Layered Placement on FLS

4.1. Determination of Layered Placement Thickness

Layered placement is an effective method to control and uniformly distribute the settlement of foamed lightweight soil during construction. In large-volume fills, excessive single-layer thickness can subject the underlying soil to significant pressure from the overlying material, potentially causing over-compaction and uneven settlement. An appropriate layered thickness helps ensure uniformity across the filled area. Furthermore, as the hydration process in foamed lightweight soil generates substantial heat, layered placement reduces the risk of shrinkage cracks caused by thermal stress. The stability of bubbles is particularly influential on the allowable placement thickness. Given the high volume of entrapped air bubbles and the challenges in maintaining uniformity over large placements [38], layered construction facilitates moisture evaporation and air escape, thereby accelerating consolidation and strength development. Under complex geological conditions, this method allows for adjustments according to the varying bearing capacities of different soil layers, enhancing the adaptability of the fill to the foundation and improving the safety and stability of the project. Therefore, it is essential to properly control the single-layer placement thickness of foamed lightweight soil [39].

1.

Vertical Stratification Ratio

Currently, there is limited quantitative research on the layered placement thickness for foamed lightweight soil. In practice, most construction projects rely heavily on empirical experience to estimate an appropriate thickness, lacking a well-defined quality control methodology. To address this gap, this study establishes a criterion for determining the optimal placement thickness, aiming to minimize initial damage caused by uneven placement. This criterion is based on the relevant code [40], which specifies that for a given strength grade, the minimum compressive strength of any individual sample should not fall below 85% of the characteristic strength—meaning the strength deviation within a group should not exceed 15%. This approach also references the engineering algorithm proposed by Zhu Junjie [27].

$${\displaystyle \frac{q_{u,\mathrm{b}}-q_{u,\mathrm{t}}}{q_{u,\mathrm{b}}}}\le \delta$$

(3)

In the equation, $q_{u,\mathrm{b}}$ and $q_{u,\mathrm{t}}$ are the compressive strengths at the bottom and top of the foamed lightweight soil within a specified depth range, respectively, in MPa; $\delta$ is the vertical stratification ratio, in percent.

The vertical stratification ratio can serve as a criterion for determining the single-layer placement thickness. When $\delta \le 15\%$ within a given depth range, the placement uniformity of the lightweight soil is considered acceptable.

2.

Vertical Stratification Test and Result Analysis

The mix proportion of foamed lightweight soil with fly ash adopted for the field construction in an actual project was selected. With a 28-day design strength of 1.0 MPa, a maximum layer thickness of 1000 mm was chosen to comprehensively evaluate the influence of layered placement thickness on embankment uniformity.

The factory-produced foamed lightweight soil was poured into prepared 1000 mm long, 100 mm diameter PVC pipes. The bottom of each pipe was sealed with disposable plastic wrap. During the pouring process, the pipes were continuously tapped with a wooden mallet to ensure compactness of the mixture. To guarantee reliability, three identical sets of specimens were prepared. After being completely filled, the pipes were sealed and cured for 28 days. Following curing, the 1000 mm long specimens were marked at 100 mm intervals and cut using a cutting machine. During cutting, surface flatness was strictly maintained; specimens exhibiting cracks or significant unevenness due to improper cutting were deemed invalid. The strength of the cut segments (numbered 1 to 10) was then measured.

Table 1. Test Results of Vertical Stratification Ratio.

Deepth/mm	Mix Proportion
	28 d Strength/MPa	δ/%
100	0.82	0
200	0.85	3.53
300	0.87	5.75
400	0.91	9.89
500	0.96	14.58
600	0.99	17.17
700	1.03	20.39
800	1.07	23.36
900	1.09	24.77
1000	1.12	26.79

presents the 28-day strength of the specimens and the vertical resolution results with depth. In the table, the 100 mm depth corresponds to the uppermost section of the 1000 mm long pipe, and this pattern continues accordingly, with the 1000 mm depth representing the bottom section.

It can be observed that the strength of the foamed lightweight soil used in the field increases with depth, accompanied by a corresponding increase in the vertical stratification ratio. This indicates that greater single-pour placement thickness leads to poorer uniformity. Furthermore, the vertical stratification ratio remains below 15% within a placement thickness of 500 mm. Therefore, based on the test results, the single-layer placement thickness of foamed lightweight soil should be controlled within 500 mm.

4.2. Settlement Analysis

To investigate the influence of layered placement thickness for foamed lightweight soil on subgrade settlement, four thicknesses—500 mm, 600 mm, 800 mm, and 1000 mm—were designed, considering the non-uniformity induced by varying thicknesses and construction practicality. A buffered step slope ratio of 1:1.5, consistent with field conditions, was adopted at the interface with the existing embankment. The embankment fill height was 12 m with a unit weight of 6 kN/m³.

1.

Final Settlement Contour

Since the final settlement contours exhibit nearly identical distribution patterns across the four working conditions, only the case with a 500 mm placement thickness is presented for illustration. Figure 1 shows the final settlement contour of the foamed lightweight soil embankment with this 500 mm layered thickness.

As can be seen from the figure, the maximum settlement after 15 years of operation occurs in the existing embankment behind the interface of the bridge approach transition zone. This indicates that the existing embankment is the most affected area during the post-construction operational phase of the bridge approach. The composite foundation of the existing embankment, improved with cement-mixing piles, shows noticeable downward penetration at the pile tips. In contrast, penetration is less apparent at the pile heads due to the presence of a gravel cushion. Furthermore, the settlement of the entire composite foundation in the bridge approach area exhibits a progressive increase along the interface.

2.

Maximum Settlement of the Bridge Approach Embankment versus Fill Height during Construction

Figure 2 illustrates the variation of the maximum settlement in the bridge approach embankment with fill height during construction. For all four layered placement thicknesses, the maximum settlement during construction increases in a convex-function pattern as the fill height increases. The settlement induced by foamed lightweight soil placement is relatively small within the initial 4 m of fill height. However, the settlement becomes more pronounced as the fill height continues to increase. Notably, the variation in layered thickness has a minimal impact on the final construction settlement of the embankment across the entire bridge approach section, with the maximum settlement values for all four thicknesses meeting the specified requirements.

The underlying mechanism for these observations is as follows. First, ignoring the subsequent consolidation settlement of the existing subgrade, the small single-layer placement thickness during construction allows for rapid surface moisture evaporation, which accelerates the hardening of the cementitious materials. Consequently, for an identical unit weight, a smaller placement thickness results in higher strength in the individual layers, enhancing their capacity to support overlying loads. This leads to reduced foundation settlement per layer. Second, after the application of the structural pavement layers and the uniformly distributed vehicle load, the load is jointly borne by the conventional fill and the foamed lightweight soil behind the abutment. This load-sharing mechanism effectively distributes the stresses caused by the weight of the structural layers and the traffic loading, thereby mitigating the overall settlement.

3.

Final Settlement of Embankment Surface

Figure 3 presents the final settlement of the embankment surface for the four layered placement thicknesses. The figure indicates that differential settlement occurred at the interface between the foamed lightweight soil embankment and the existing embankment, with a magnitude of approximately 20 mm. The underlying reason is that during post-construction operation under cyclic traffic loading, the foamed lightweight soil, due to its high strength, undergoes negligible plastic deformation. In contrast, the conventional fill is more susceptible to plastic deformation and experiences greater consolidation settlement under repeated traffic loads, leading to significant differential settlement at the interface.

4.

Post-Construction Settlement of the Bridge Approach Embankment

Table 2. Post-Construction Settlement of the Bridge Approach Embankment for the Four-Layered Placement Thicknesses.

Per-Layer Placement Thickness/mm	Construction Settlement/mm	Total Settlement at 15 Years Post-Construction/mm	Post-Construction Settlement/mm
500	−75.37	−102.26	−26.89
600	−75.53	−102.66	−27.13
800	−75.82	−102.98	−27.16
1000	−75.51	−105.51	−30

presents the post-construction settlement of the bridge approach embankment for the four layered placement thicknesses.

It can be observed that for the bridge approach embankment with the four-layered placement thicknesses, neither the construction settlement nor the total settlement at 15 years post-construction shows significant differences. However, the post-construction settlement is slightly larger for the 1000 mm placement thickness. This indicates that a greater placement thickness results in a relatively lower compactness of the foamed lightweight soil, leading to a somewhat larger settlement as the embankment undergoes gradual compaction under load.

According to specifications, the allowable post-construction settlement for bridge approaches on expressways should not exceed 100 mm. Since the backfill area behind the abutment is constructed with foamed lightweight soil, the actual post-construction settlement of the bridge approach is far less than the stipulated 100 mm. Therefore, the layered placement thickness is not a decisive factor in controlling post-construction settlement. Considering both construction convenience and post-construction settlement, a layered placement thickness of 500–600 mm is recommended for practical construction.

4.3. Stability Analysis

1.

Plastic Strain Analysis

Instability in foamed lightweight soil placement at the bridge approach primarily occurs in high-fill embankments, mainly manifesting as overall overturning of the soil mass and disturbance to the conventional fill behind the interface caused by the dynamic placement process. Given that retaining walls are constructed on both sides of the embankment during placement, and considering the high self-supporting capacity of the material, the primary concern during high-fill placement is its disturbance effect on the adjacent conventional fill. Plastic deformation develops at the base of the conventional fill, which may progress to slip failure, consequently affecting the foamed lightweight soil embankment formed behind the abutment. Figure 4 illustrates the plastic strain zones for different layered placement thicknesses of the foamed lightweight soil.

As clearly observed in Figure 4, the plastic strain zones are generally similar for placement thicknesses of 500 mm and 600 mm. These zones are primarily characterized by plastic deformation developing upward from the middle of the embankment at the interface and plastic zones progressing upward from the base of the conventional fill area. For the greater placement thicknesses of 800 mm and 1000 mm, the overall plastic strain distribution is also relatively similar. This pattern arises from deformation at the buffered step of the interface during the filling process on one hand and plastic deformation in the lower soil mass of the conventional fill area on the other.

A comparative analysis across Figure 4a–d reveals that as the layered placement thickness increases, the plastic strain zone at the interface gradually expands. Simultaneously, the plastic zone in the conventional fill area develops from the embankment base towards its lower section, showing a progressive enlargement. The underlying mechanism for this behavior is as follows. For the smaller placement thicknesses of 500 mm and 600 mm, the foamed lightweight soil, distinguished by its high strength compared to conventional fill, undergoes minimal plastic deformation itself. The smaller placement thickness also induces less additional stress on the surrounding soil, resulting in a reduced impact on the interface. Furthermore, the fill zone exhibits better overall integrity. Under this integral effect, the base of the conventional embankment primarily experiences compressive deformation. In contrast, for the larger placement thicknesses of 800 mm and 1000 mm, the increased placement thickness applies a greater instantaneous load. This generates a larger lateral force on the interface, causing it to settle with a downward and leftward shift. Consequently, a connected or continuous plastic strain zone forms throughout the right-side embankment.

2.

Safety Factor

Table 3. Safety Factor of the Embankment with Different Placement Thicknesses.

Layered Placement Thickness/mm	500	600	800	1000
Safety Factor Fs	4.1	3.8	3.2	2.9

presents the safety factors for the foamed lightweight soil embankment under different placement thicknesses.

As observed in Table 3, the safety factor of the entire bridge approach section gradually decreases with increasing layered placement thickness--a trend consistent with the development pattern of the plastic strain zones. Due to the favorable engineering properties of the foamed lightweight soil, the safety factor remains as high as 2.9 even under the most critical thickness condition. This value is considered conservative, and all cases meet the design requirements. Based on a comprehensive consideration of the development of plastic strain zones in the bridge approach and the stability safety factors, the following construction recommendation is proposed: a layered placement thickness of 500 mm or 600 mm should be adopted for the foamed lightweight soil in the bridge approach section. In addition, close attention should be paid to the stability of the buffered slope at the interface during construction to prevent potential sliding along the interface during the filling process.

5. Analysis of the Influence of Bulk Density Change of FLS

5.1. Design of Bulk Density Selection Scheme

A large number of scholars’ studies have shown that the bulk density and strength of foamed lightweight soil are important factors affecting the settlement and stability of abutment filling, and the bulk density and strength are basically positively correlated. According to the specification, the conversion is given, and the conventional relationship

Table 4. Conventional relationship table of wet bulk density grade and strength.

Wet Bulk Density Grade (kN/m3)	4	5	6	7	8	9	10
Strength CF	0.3~0.7	0.5~1.0	0.8~1.2	1.0~1.5	1.0~2.0	1.0~3.0	1.0~4.0

between wet grade and strength is given. In the process of filling the lightweight soil on the abutment back, due to the high filling height of the abutment back, according to the requirements of the design code, the strength required for the foam lightweight soil at different filling positions is different, and the strength is different. The designed lightweight soil bulk density is also different, and the detailed classification is shown in

Table 5. Wet bulk density requirements of light soil subgrade construction.

Mix Proportion Type	Embankment Part	From the Bottom of the Road Surface Distance (m)	Construction Wet Bulk Density γfw (kN/m3)
			Expressways, First-Class Highways, Urban Arterial Roads	Second-Class Highways, Urban Secondary Arterial Roads, and Other Highways
Pure cement mixture ratio	road bed	0~0.8	6 ≥ γfw ≥ 5.6	5.6 ≥ γfw ≥ 5.3
	Embankment	>0.8	5.6 ≥ γfw ≥ 5.2	5.3 ≥ γfw ≥ 5.0
Geopolymer mixture ratio	road bed	0~0.8	6 ≥ γfw ≥ 5.7	5.8 ≥ γfw ≥ 5.5
	Embankment	>0.8	5.7 ≥ γfw ≥ 5.4	5.5 ≥ γfw ≥ 5.2

. The wet bulk density design of foamed lightweight soil construction should meet the requirements of the specification. When there is no special provision, the wet bulk density of the foamed lightweight soil construction design is not less than 5.0 kN/m³, or more than 10.0 kN/m³.

In order to study the influence of bulk density of foamed lightweight soil on the settlement and stability of the bridgehead filling section, the filling height of the abutment back is set to 12 m, the slope ratio of the buffer step is set to 1:1.5, and the thickness of the layered filling is set to 500 mm. The specification clearly stipulates that the bulk density of foamed lightweight soil for construction is 5–10 kN/m³, and the design of bulk density is closely related to the mix ratio of lightweight foamed soil. Therefore, the mix ratio design corresponding to different bulk density and strength is selected for this stage of research. In order to obtain the data of bulk density, strength, and elastic modulus of foamed lightweight soil required for numerical simulation, the mix ratio obtained by laboratory test is listed in

Table 6. Foam lightweight soil bulk density mix design table.

Sample Labelling	Fly Ash /(kg/m3)	Cement /(kg/m3)	Water /(kg/m3)	Foam Volume /L/m3	Wet Bulk Density /kN/m3	Strength /MPa	Elastic Modulus /MPa
A1	0	400	220	640	9.85	1.58	455
A2	60	340	220	640	8.91	1.32	410
A3	100	300	220	640	7.84	1.24	365
A4	140	260	220	640	7.82	1.16	325
A5	180	220	220	640	6.94	1.05	275
A6	220	180	220	640	5.88	0.85	200

.

The determination of wet bulk density is carried out in accordance with the (Technical Specification for Filling Engineering of Foamed Lightweight Soil). The uniform foam lightweight soil slurry is weighed with a beaker as shown in Figure 5 and calculated according to Formula (2), and the average value of three times is taken as the wet bulk density.

$$\gamma ={\displaystyle \frac{10\left(m_1-m_0\right)}{v_0}}$$

(4)

γ—wet bulk density, kN/m³; m₁—slurry plus beaker quality g; m₀—beaker mass(g); v₀—beaker volume, cm³.

Figure 5. Wet bulk density weighing.

Figure 5. Wet bulk density weighing.

The process of preparing foamed lightweight soil is as follows: (1) Preparation of cement slurry; (2) Preparation of foam (Figure 6); (3) Mix and stir until uniform; (4) Die casting (Figure 7); (5) Maintenance (Figure 8).

The strength of foamed lightweight soil is 28 days of normal maintenance, and the data is obtained from the compression test with a universal testing machine. The elastic modulus parameters used in ABAQUS are obtained by analyzing the compressive stress-strain curve of foamed lightweight soil output by a universal testing machine.

In the current specification, it is clearly pointed out that in the filling of foamed lightweight soil subgrade on the back of the abutment, the filling of foamed lightweight soil follows the principle of high strength of the roadbed part and low strength of the part below the roadbed. The roadbed part below the pavement structure layer is subjected to the vehicle load of the pavement and the self-weight load of the pavement structure layer, so the strength design requirement of this part is greater than that of other parts. In order to study the influence of bulk density of foamed lightweight soil on the settlement of subgrade filling in the abutment back section, the scheme design is shown in

Table 7. Foam lightweight soil partition bulk density design.

Working Condition	Bulk Density of Embankment Bed (kN/m3)	The Part Above the Cushion Layer Below the Roadbed (kN/m3)
1	7	6
2	8	7
3	9	8
4	10	9

. The filling height of foam lightweight soil on the back of the abutment is 12 m. The subgrade is divided into two parts, the roadbed part (2 m below the embankment pavement structure layer) and the upper part of the cushion below the roadbed (total height 10 m), and the bulk density of each part is changed to form a new working condition.

5.2. Settlement Analysis

1.

Final settlement cloud picture

Figure 9 shows the final settlement of the embankment at the bridgehead section under four working conditions. With the increase of the bulk density of foamed lightweight soil, the overall settlement of the bridgehead section is also increasing. Among them, the settlement of working condition 4 is the largest, which is 119.25 mm, and the settlement of working condition 1 is the smallest, which is 104.09 mm, an increase of 14.56% year-on-year. Therefore, the change of bulk density has a great influence on the final settlement of the embankment, which should be paid attention to in practical engineering. It can be seen from the settlement cloud map of the subgrade that the maximum settlement of the subgrade does not appear on the surface of the subgrade filling but occurs at a certain distance from the top of the pavement. At the same time, the increase of bulk density makes the cement mixing pile of the ordinary filling embankment more obvious.

2.

The change of the maximum settlement of the embankment at the bridgehead section with the filling height during the construction period

Figure 10 shows the settlement of the 12 m filling process of foamed lightweight soil. It can be seen that with the increase of filling height, the settlement of embankment increases gradually, and the maximum settlement does not exceed 80 mm. For every 1 kN/m³ increase in bulk density, the settlement of filling increases by about 10 mm. At the same time, it can be seen from the change of embankment settlement that the settlement of foam lightweight soil as a filling material is relatively stable, and the settlement of the embankment after changing the bulk density of foam lightweight soil is also within the controllable range.

3.

Final settlement of embankment surface

Figure 11 shows the surface settlement of the embankment structure layer. It can be seen that the settlement of the top surface of the embankment in the range of 0–35 m from the abutment of the foamed lightweight soil section gradually increases, showing a linear growth, while the distance from the abutment is 35 m. There is a significant differential settlement, and the settlement is basically stable at 35–50 m from the abutment. This is because the 0–7 m from the abutment is filled with foam lightweight soil, while the foam lightweight soil itself is a light and semi-rigid material, and the buffer step is set on the connecting surface as a transition, and the settlement of this section is more uniform. 35 m away from the abutment is the division of foamed lightweight soil and the original embankment section. Due to the difference in its own bulk density, it leads to obvious differential settlement, and the greater the bulk density of foamed lightweight soil, the greater the differential settlement.

4.

Post-construction settlement

Table 8. Post-construction settlement of embankment at bridgehead section under four kinds of foam lightweight soil bulk density conditions.

Working Condition	Bulk Density of Embankment Bed (kN/m3)	The Bulk Density Above the Cushion Layer Below the Roadbed (kN/m3)	Settlement During Construction/mm	Total Settlement /mm	Post-Construction Settlement/mm
1	7	6	−78.04	−104.09	−26.05
2	8	7	−85.34	−107.16	−21.82
3	9	8	−95.36	−110.93	−15.57
4	10	9	−102.34	−119.25	−16.91

gives the post-construction settlement of the embankment at the bridgehead section under four kinds of foam lightweight soil bulk density conditions.

It can be seen that with the increase of bulk density of foamed lightweight soil, both the settlement during construction and the total settlement 15 years after construction will always increase, but it is obvious that the change of bulk density of foamed lightweight soil has a greater impact on the settlement during construction. In particular, the post-construction settlement will decrease with the bulk density of the foamed lightweight soil. This is because the increase in bulk density produces the preloading effect during the construction period. The settlement basically occurs during the construction period. The post-construction settlement is mainly caused by the compression of the foundation soil. The pre-consolidation has played an effect, and the amount of consolidation caused by the foamed lightweight soil itself is very small. Therefore, the post-construction settlement shows an opposite growth trend to the settlement during the construction period. In order to avoid the problem of abutment jumping caused by uneven settlement of the transition section between foamed lightweight soil and the original embankment, it is more appropriate to select working condition 1 or working condition 2 for the bulk density of foamed lightweight soil in view of the influence of settlement.

5.3. Stability Analysis

1.

Plastic strain analysis

The change of the bulk density of foamed lightweight soil on the stability of the whole bridge embankment is mainly manifested in two aspects: increasing the bulk density of foamed lightweight soil leads to the increase of the additional stress of the embankment, and the state of ordinary fill after the interface is affected. The strength of foamed lightweight soil increases, and the stability of the foamed lightweight soil filling area will also be affected. Figure 12 gives the plastic strain diagram of the bridge section under four working conditions.

It can be seen from Figure 12a–d that when the bulk density of foamed lightweight soil is set as working condition 1, the plastic zone of the whole embankment is mainly plastic deformation caused by the settlement of ordinary fill. If the upper load increases, there may be a risk of collapse. With the increase of bulk density to working condition 2, it can be seen that the increase of bulk density has an obvious effect on the interface, forming a plastic development zone along the interface. At the same time, the plastic strain zone at the bottom of the whole ordinary fill embankment is further increased and connected with the interface. When the bulk density is set to condition 3, the plastic strain zone of the joint surface is further expanded, while the plastic strain zone of the ordinary fill is gradually reduced. When the bulk density is set to condition 4, the plastic zone gradually develops into the bottom of the foamed lightweight soil embankment and the lowest area of the connection surface. The reason for the above phenomenon is that due to the small bulk density and low strength of the foamed lightweight soil in the initial working condition, the influence of the transition section caused by the filling is relatively small. The foamed lightweight soil is not easy to collapse due to its strong self-reliance. Therefore, there is no plastic deformation in the left filling area, and the main plastic deformation is due to the poor plasticity of the right soil itself. With the increase of bulk density, the lateral force on the right side of the soil on the interface is also greater, and the plastic zone of the interface increases. At the same time, the lateral force also makes the right ordinary fill more dense, and the plastic zone at the bottom of the right side gradually shrinks; with the increase of bulk density of foamed lightweight soil, its strength is also increasing. The strength difference of the foamed lightweight soil filling area will make the bottom of the foamed lightweight soil plastically deformed first under load, and the plastic strain zone at the bottom is also expanding with the increase of bulk density.

2.

Safety Factor

Table 9. The safety factor of bridgehead section under different bulk density conditions.

Change Bulk Density	Condition 1	Condition 2	Condition 3	Condition 4
Safety factor Fs	4.1	3.9	3.6	3.5

gives the safety factor of the foamed lightweight soil embankment under different bulk density conditions.

It can be seen from Table 9 that with the increase of bulk density, the safety factor of the whole bridgehead section gradually decreases. Combined with the development process of changing the bulk density plastic strain zone, it is found that the two indexes of bulk density and strength under the influence of bulk density still have the greatest influence on the stability, and the strength index will affect the position of the plastic zone of the bridgehead section. When the strength of foamed lightweight soil is large, its too-strong plate effect will promote its overall instability and failure rather than the shear failure caused by uneven settlement of the whole bridgehead section, resulting in local instability caused by cracks. Therefore, it is necessary to give full play to the characteristics of foam lightweight soil itself, which is lighter and has strong plate properties, and to consider the additional stress effect of the soft foundation under the soft foundation caused by the increase of bulk density and the shear stress generated on the interface. Therefore, the author believes that in the above four working conditions, working condition 1 and working condition 2 should be used as the preferred filling scheme.

6. Analysis of the Influence of Ordinary Fill Replacement Height

6.1. Replacement Height Design

The filling area of the abutment back is filled with foamed lightweight soil. The simulation results show that the settlement during the construction period and the post-construction settlement of the whole abutment section, as well as the uneven settlement, all meet the requirements. However, the cost of foamed lightweight soil is far greater than that of ordinary filling, taking into account the performance benefits and economic benefits [40,41]. Therefore, it is considered to replace the lightweight foam soil part of the abutment back with ordinary filling. In order to study the influence of foam lightweight soil replacement on the settlement and stability of the embankment at the bridgehead section, the replacement design scheme is as shown in

Table 10. Replacement design scheme.

Condition	Foam Lightweight Soil Height (m)	Replacement Fill Height (m)
1	12	0
2	9	3
3	6	6
4	3	9
5	0	12

. During the replacement process, the lightweight foam soil is always on the upper part of the replacement filling soil. The slope ratio of the abutment back connection surface is simulated by 1:1.5 in the actual working condition. The unit weight is selected from condition 1 described in 3.4.

6.2. Settlement Analysis

1.

The final settlement cloud map

Figure 13 shows the settlement cloud map of the embankment of the bridgehead transition section under different replacement heights of ordinary fill. Since the settlement cloud map without replacement has been given above, it will no longer appear here. It can be seen that with the continuous increase of the height of the replacement filling soil, the position of the maximum settlement of the whole embankment gradually moves to the left along the connection surface, and the maximum settlement is also increasing. The reason is that the replacement of the ordinary filling soil and the ordinary filling of the connection surface are gradually dense, and the adhesiveness is increased under the pressure of the dead weight load and vehicle load of the pavement structure layer. The whole is formed, so the maximum settlement is transferred to the bottom position of the connection surface.

According to the analysis of the settlement value of the cloud map, the height of the replacement fill increases from 0 m to 3 m, and the settlement increases by 5.46 mm, an increase of 5.34%. When the height of the replacement soil increases from 3 m to 6 m, the settlement increases by 37.4 mm, an increase of 34.72%. The height of the replacement filling soil increased from 6 m to 9 m, and the settlement increased by 85.05 mm, an increase of 58.61%. The height of the replacement soil increased from 9 m to 12 m, and the settlement increased by 99.51 mm, an increase of 43.23%.

2.

The maximum settlement of embankment at bridgehead section changes with filling height during construction period

Figure 14 shows the maximum settlement diagram at 12 m under different replacement heights. It can be seen that with the increase of the replacement height of ordinary fill, the maximum settlement during the filling period is also increasing. Through comparative analysis, the settlement rate caused by the filling of foam lightweight soil is much smaller than that of ordinary filling. The height of the replacement soil increases from 0 m to 3 m, and the settlement increases by 13.22 mm, an increase of 28.26%. When the height of the replacement soil increases from 3 m to 6 m, the settlement increases by 54.72 mm, an increase of 91.20%. When the height of the replacement soil increases from 6 m to 9 m, the settlement increases by 70.37 mm, an increase of 62.14%. When the height of the replacement soil increases from 9 m to 12 m, the settlement increases by 87.78 mm, an increase of 47.61%. Therefore, it can be seen that the influence of the replacement of all the common filling behind the abutment on the settlement of the embankment is obvious. In order to avoid the large settlement difference at the joint between the abutment and the abutment back embankment, it is necessary to control the replacement height of the common filling. The analysis of the line chart shows that the higher the replacement height of the ordinary fill, the greater the settlement increase, but the settlement rate does not show a consistent law. The main reason is that the entire replacement embankment is not a vertical filling but presents an ‘inverted right angle trapezoid’ replacement area. Under the same replacement height, the bottom replacement volume is small, and the additional stress applied to the bottom of the embankment is small.

3.

Final settlement of embankment surface

Figure 15 shows the settlement of embankment surface of bridge head section with five kinds of ordinary filling soil at different replacement heights. The settlement trend of the surface of the replacement embankment with the thickness of 3 m, 6 m, and 9 m is basically the same as that of the whole replacement of foamed light soil at the back of the abutment. The settlement increases linearly at 35 m from the back of the bridge, while the settlement growth rate of the whole replacement of ordinary filling soil increases first and then slows down, but the overall settlement is greater than that of the foam light soil ordinary filling mixed filling embankment. It is obvious that the total replacement of ordinary fill embankment has a large settlement difference at the top of the original joint surface at 35 m, and the difference is approximately 100 mm. It is very likely to produce uneven settlement after construction, resulting in transverse cracking of the pavement. Therefore, it is not feasible to use all replacement of ordinary fill without targeted treatment, and enough attention should be paid to the actual project. Therefore, it is necessary to lay reinforced materials at the connection between the replacement area and the existing embankment. The high toughness and tensile and shear resistance of the reinforced material itself are used to produce friction with the soil of different properties of the connection surface to play a reinforcing role so that the soil of the connection surface can form a better overall effect, and then make more reinforced soil play a network effect to resist the shear force generated by the upper load and reduce the differential settlement.

4.

Post-construction settlement

Table 11. Post-construction settlement of embankment at bridgehead section under five working conditions of common fill replacement.

Working Condition	Foam Lightweight Soil Height (m)	Replacement Fill Height (m)	Settlement During Construction /mm	Total Settlement 15 Years After Construction /mm	Post-Construction Settlement/mm
1	12	0	−75.37	−102.26	−26.89
2	9	3	−80.03	−107.72	−27.69
3	6	6	−112.57	−145.12	−32.55
4	3	9	−185.1	−230.17	−45.07
5	0	12	−279.15	−329.68	−50.53

shows the post-construction settlement of the embankment at the bridgehead section under five working conditions of ordinary fill replacement.

The results show that the post-construction settlement has been increasing with the increase of the height of ordinary filling. When all the filling is replaced with ordinary filling, the maximum post-construction settlement reaches 50.53 mm, and the maximum post-construction settlement of the bridgehead section is 100 mm, which also indirectly shows that the foundation treatment method is reasonable, and the settlement of the foundation is small in the whole process. During the post-construction operation period, the replacement embankment is subjected to vehicle load and self-weight compression and consolidation to produce settlement. When the vehicle load acts downward, the foamed lightweight soil effectively bears and transmits the load due to its good force transmission performance and high strength characteristics. In this process, the pore water of the ordinary filling under the embankment is squeezed out under the load, and the phenomenon of seepage and consolidation occurs, which is mainly reflected in the displacement of the structural particles of the subgrade filling, the reduction of the pore volume, and the compression deformation of the filling caused by the shear deformation. Over time, when the discharge of the pore water of the ordinary filling in the subgrade tends to stop, the residual stress between the filling particles is adjusted, resulting in settlement deformation. Considering the post-construction settlement of the bridgehead section and the differential settlement of the transition section, and taking into account the technical and economic indicators, the author believes that it is more reasonable to replace the ordinary fill height of 6 m.

6.3. Stability Analysis

1.

Plastic strain analysis

Figure 16 shows the plastic strain diagram of the common fill replacement heights of 3 m, 6 m, 9 m, and 12 m. The plastic strain cloud diagram of the ordinary fill replacement height of 0 m has been given in the previous section, which is not described here.

It can be seen that when the replacement height of ordinary fill is 3 m, the ordinary fill in the replacement area and the fill of the existing subgrade on the right side of the interface have a penetrating plastic strain zone. The lower part of the abutment embankment is replaced with ordinary fill, and the bulk density of the entire bridgehead embankment is increased. It can not only be seen that the additional stress applied to the soft foundation is increased. Due to the strong plasticity of the replacement soil itself, the elastic modulus of the upper foam lightweight soil is much larger than that of the replacement soil, which is similar to the semi-rigid material. After the pavement load is transferred to the lower part, the ordinary fill in the replacement area is squeezed, and the soil moves to the right side of the interface, thus forming a sliding surface connected to the right side of the ordinary fill. When the replacement height is 6 m, the plastic strain development zone only appears near the replacement height of 6 m, which has little effect on the soil on the right side of the interface. As the replacement height continues to increase, the plastic strain zone of the soil gradually develops downward. When the replacement area is all ordinary fill, a penetrating plastic strain zone appears behind the abutment, and discontinuous plastic strain appears at the bottom of the embankment on the right side of the interface. The reason for this phenomenon is that the capacity of ordinary fill is much larger than that of lightweight foam soil. When the replacement height reaches a certain level, the overall weight of the replacement area increases, and the lateral force on the right side of the interface is larger, and the compactness of the right side of the interface is better. Therefore, the plastic strain zone of the right soil is very small; the replacement of ordinary fill is too much, and the strength difference between ordinary fill and foam lightweight soil is too large. The plastic strain zone is concentrated near the interface. After all the replacement, the compactness of the soil is not enough, and there is settlement. The plastic strain zone penetrates to the bottom of the embankment and affects the ordinary fill on the right side of the interface.

2.

Safety Factor

Table 12. Safety factor of embankment at bridgehead section under five working conditions of common fill replacement.

The Common Fill Replacement Height/m	0	3	6	9	12
Safety factor Fs	4.1	3.5	3.1	2.6	1.9

gives the safety factor of the embankment at the bridgehead section under five working conditions of ordinary fill replacement.

From Table 12, it can be seen that the higher the replacement height of ordinary filling soil, the lower the safety factor of the embankment at the bridgehead section, and the faster the safety factor decays. Based on the safety factor under the condition that the abutment back is all foamed lightweight soil, the replacement height of ordinary filling soil is 3 m, the safety factor decreases by 14.6%, the replacement height is 6 m, the safety factor decreases by 24.4%, the replacement height is 9 m, the safety factor decreases by 36.6%, and for all the replacement of ordinary filling soil, the safety factor decreases by 53.7%. The safety factor is calculated by only considering the stability of the longitudinal section embankment. In the actual project, the instability problem of the cross-section slope of the high fill embankment is more prominent. Considering the economy and stability, the author thinks that it is more appropriate to replace 6 m with ordinary fill.

7. Analysis on the Influence of Slope Ratio Change of FLS and Original Embankment Connection Surface

7.1. Slope Ratio Selection

When the filling height is high, in addition to considering its own settlement, it is also necessary to pay attention to the settlement of the original embankment after the connecting surface. If the differential settlement is too large, it will also affect the stability of the roadbed [42]. Therefore, the slope ratio of the connecting surface, the step form, and the width selection are particularly important, which can effectively alleviate the differential settlement and form the settlement transition zone. The post-construction settlement of the general fill embankment and the abutment of the soft foundation section are quite different. The transition section of the foamed lightweight soil with a large longitudinal length and the reasonable connection between the foamed lightweight soil embankment and the general fill embankment are conducive to ensuring the smooth transition of the subgrade settlement.

The Technical Specification for Foamed Lightweight Soil Filling Engineering (CJJ/T177-2012) points out that the structural design should include section design and connection design. The section design should include the filling height and filling width, and the connection should include the connection form (see Figure 17) and the detailed size. The general section design size should be determined according to

Table 13. Cross-section size.

Design Content	Range	Remarks
Filling height H	0.5~15.0 m	cavity filling, except pipeline backfilling project.
Botton width BL	≥2.0 m
Bench width BT	≥0.5 m	Filling height more than 2 m Settings
Reservation width BF	0.3~0.8 m	When the filling height is more than 5 m or the back is steep slope, the setting is set.

.

Considering the construction convenience in practical engineering, the buffer slope ratio of the joint surface is selected as 1:1, 1:1.5, and 1:2 for research, and the right-angle step condition is set for comparative analysis. The modeling diagram is shown in Figure 18.

7.2. Settlement Analysis

1.

The final settlement cloud map

Figure 19 shows the embankment settlement nephograms of different slope ratios and right-angle steps of the buffer steps of the connecting surface. It can be seen that the maximum settlement position of the whole bridgehead section under different designs is at the farthest distance of the bridgehead section. For the buffer steps, the decrease of the slope ratio will cause the increase of the original embankment settlement on the right side of the slope. When the buffer step slope ratio changes from 1:1 to 1:1.5, the maximum total settlement of the original embankment after the slope increases from 9.89 cm to 10.23 cm; when the slope ratio of the buffer step changes from 1:1.5 to 1:2, the maximum total settlement of the original embankment after the slope increases from 10.23 cm to 12.90 cm, indicating that the larger the foam lightweight soil filling area behind the abutment, the greater the disturbance to the settlement of the filling soil after the slope. At the same time, the area of the filling area behind the right-angle stepped working platform is much smaller than that of the buffer step slope ratio of 1:1, and the load applied in the filling process is also smaller. However, the settlement generated when the buffer step slope ratio is 1:1 is almost the same as that of the right-angle step. Therefore, the right-angle step as a connecting surface has a non-negligible influence on the settlement after the slope.

2.

The change of the maximum settlement of the embankment at the bridgehead section with the filling height during the construction period

Figure 20 gives the maximum settlement line diagram of 12 m filling under different connection surface slope ratio designs. It can be seen that with the increase of filling height, the overall settlement of the right-angle stepped filling embankment increases linearly, while the settlement under other buffer step conditions increases with the increase of filling height. The settlement rate increases. In particular, when the slope ratio of the buffer step is designed to be 1:2, the lightweight foam soil has a large settlement at the initial stage of filling, and the settlement mainly occurs at the farthest end of the embankment of the entire bridgehead section, indicating that the initial filling under this working condition has a greater impact on the original embankment behind the slope. However, the settlement of the entire embankment is almost unchanged when the filling height is within the range of 7.5 m, that is, the filling process has little effect on the settlement of the original embankment behind the slope. Comparing and analyzing the other two working conditions, the maximum settlement of the entire embankment is a regular slow increase. During the filling process during the construction period, the decrease of the slope ratio will lead to the gentle slope of the connecting surface and the increase of the lightweight foam soil used for filling, and the settlement will inevitably increase, but the maximum settlement during the filling period of any slope ratio design is not more than 60 mm.

3.

Final settlement of embankment surface

Figure 21 shows the settlement of the embankment surface of the bridgehead section. It can be seen that whether it is a right-angle step or a buffer step, differential settlement will occur at the top of the connecting surface. For the buffer step, the smaller the slope ratio, the greater the differential settlement. The slope ratio of 1:2 has the largest differential settlement, up to 40 mm, which is more dangerous for post-construction differential settlement. Therefore, in the construction, the buffer step should be avoided as much as possible in the form of a slope ratio of 1:2.

4.

Post-construction settlement

Table 14. Post-construction settlement of embankment at bridgehead section under four types of interface forms.

Working Condition	Interface Slope Ratio	Settlement During Construction /mm	Total Settlement 15 Years After Construction /mm	Post-Construction Settlement/mm
1	1:1	−68.58	−98.93	−30.35
2	1:1.5	−75.37	−102.26	−26.89
3	1:2	−103.74	−128.98	−25.24
4	Right angle step	−12.34	−97.28	−84.94

gives the post-construction settlement of the embankment at the bridgehead section under the four types of connection surfaces.

It can be seen from the table that with the decrease of the slope ratio of the connecting surface, the post-construction settlement of the bridgehead section is also decreasing, but the overall change is not large. Therefore, the slope ratio of the connecting surface is not the main factor to control the post-construction settlement of the embankment. The bottom of the joint surface begins to design the steps from 7 m away from the abutment. Therefore, the filling amount of foamed lightweight soil during the construction period is small under the right-angle step condition, so the settlement during the construction period is small. Due to the small replacement area, after the opening of the bridge, the amount of ordinary filling in the transition section of the whole bridgehead section is relatively large. Due to the difference in the properties of the two materials, a large post-construction settlement is generated. Whether the connection surface is buffered or at a right angle, its fundamental purpose is to reduce the differential settlement between the foamed lightweight soil and the ordinary fill in the transition section of the bridgehead section rather than the overall post-construction settlement. Considering the post-construction settlement of the bridge section and the differential settlement of the transition section, as well as the convenience and economy of the construction, the author believes that it is reasonable to choose the buffer step and the slope ratio of 1:1.5.

7.3. Stability Analysis

1.

Plastic strain analysis

Figure 22 shows the change of buffer slope ratio and the change of plastic strain zone in the design of the joint surface.

It is not difficult to see from Figure 22a–c that the plastic strain zone is mainly at the bottom of the joint surface and the ordinary fill on the right side of the joint surface. The slope ratio of the joint surface decreases, and the plastic strain in the joint surface area gradually decreases. However, the plastic strain zone of the ordinary fill on the right side of the joint surface increases, and the plastic strain penetration zone after the step is more obvious. It shows that the slope ratio of the joint surface has a great influence on the filling area after the joint surface. In practical engineering, it is easy to decrease the soil strength under the action of a large vehicle load or continuous rainfall, forming slip failure. According to the plastic strain of the right-angle step in Figure 22d, it can be seen that the plastic strain of the right-angle step is large, and the connection surface is formed along the connection surface to the surface of the embankment, indicating that this treatment method is not conducive to the connection transition of the soil. It is easy to form shear failure under vehicle load, resulting in the separation of lightweight foam soil from ordinary filling and transverse cracks in the pavement structure layer.

2.

Safety Factor

Table 15. Safety factor of embankment at bridgehead section under four kinds of interface forms.

Slope Ratio of Connecting Surface	1:1	1:5	1:2	Right Angle Step
Safety factor Fs	3.7	4.1	3.6	2.4

gives the safety factor of the embankment at the bridgehead section under the four types of connection surfaces.

It can be seen from the table that in the process of decreasing the slope ratio of the connecting surface, the safety factor of the embankment at the bridgehead section increases first and then decreases. The larger the slope ratio of the buffer step is, the steeper the connecting surface will be, and then its own stability will be affected. If the slope ratio of the buffer step is too small, its stability is better, but in the filling process, more additional stress is borne by the ordinary filling on the right side of the joint surface. When the stress is too large, a large plastic strain zone will be formed, and the soil will collapse along the slip surface under ultimate load. In the actual construction, the design of the right-angle step is due to the vertical contact. Under the load, the mutual friction between the lightweight foam soil and the ordinary fill increases, and the shear stress increases. Compared with the buffer step embankment, the safety factor is reduced more. Combining the plastic strain zone and the safety factor value, the author believes that the buffer step is selected for the connecting surface, and the slope ratio is 1:1.5.

8. Conclusions

Taking the bridgehead transition section of the best soft foundation treatment method of hard shell cement mixing pile composite foundation treatment as the calculation background, 55 m on the side of the bridgehead is selected as the representative section; through the finite element ABAQUS software, the numerical model of the longitudinal section of the foam lightweight soil filling of the hard shell cement mixing pile composite foundation is established. The influence of different filling designs on the settlement and stability of the embankment at the bridgehead section is analyzed, and the best filling method of the foam lightweight soil embankment is obtained.

1.

The layered filling thickness of foamed lightweight soil has little effect on the settlement of the bridgehead section during the construction period and 15 years after construction. The post-construction settlement of the layered filling thickness of 1000 mm is slightly larger than that of the layered filling thickness of 500 mm, 600 mm, and 800 mm. In terms of stability, the safety factor of the layered filling thickness of 500 mm is the largest, and the safety factor of the layered filling thickness of 1000 mm is the smallest. According to the comprehensive settlement and stability, the optimal layered filling thickness is 500–600 mm.

2.

The bulk density of foamed lightweight soil increases, and the settlement of the embankment at the bridgehead section during the construction period and 15 years after the construction increases. At the division of foamed lightweight soil and the original embankment section, differential settlement occurs on the surface of the embankment under the structural layer, and the greater the bulk density of foamed lightweight soil, the greater the differential settlement. In terms of stability, the safety factor of condition 1 $({\gamma }_1=7 \mathrm{kN}/{\mathrm{m}}^3,{\gamma }_2=6 \mathrm{kN}/{\mathrm{m}}^3)$ is the largest, and the safety factor of condition 4 $({\gamma }_1=10 \mathrm{kN}/{\mathrm{m}}^3,{\gamma }_2=9 \mathrm{kN}/{\mathrm{m}}^3)$ is the smallest. Based on the comprehensive settlement and stability, the recommended bulk density is condition 1 and condition 2.

3.

The higher the replacement height of ordinary fill, the greater the settlement during construction and after construction, and the maximum settlement position is also changing. At the same time, the differential settlement of the embankment surface at the junction of the top of the joint surface is also greater. The differential settlement value of the working condition of all replacement ordinary fill is nearly 10 cm. In terms of stability, in the process of ordinary filling replacement, the safety factor of foam light soil in the replacement area is the largest, and the safety factor of ordinary filling in the replacement area is the smallest. Considering the settlement, stability, and economic benefits, it is more appropriate to replace the height of ordinary fill with 6 m.

4.

The change of the slope ratio of the connecting surface will not affect the maximum settlement position of the whole bridge section; the decrease of the slope ratio of the buffer step will cause the increase of the post-construction settlement of the original embankment on the right side of the slope. The right-angle step as the connecting surface has a greater impact on the post-construction settlement of the slope than the buffer step. For the buffer step, the smaller the slope ratio, the greater the differential settlement, and the design differential settlement of the slope ratio of 1:2 is the largest, up to 40 mm. In terms of stability, the safety factor of the buffer step slope ratio of 1:1.5 is the largest, the safety factor of the slope ratio of 1:2 is the smallest, and the safety factor of the right angle step is smaller than that of the buffer step. Considering the settlement and stability, the buffer step is selected as the connecting surface, and the slope ratio is designed to be 1:1.5.