Numerical Analysis of Pile-Supported Reinforced Embankments in Deep Soft Soil Regions Based on Soft Soil Creep Parameter Optimization

Abstract

When analyzing the engineering characteristics of pile-supported embankments in deep soft soil regions, the creep behavior of soft soils cannot be overlooked. In previous numerical analyses, empirical formulas were often used to determine related parameters, which limited the accuracy of the calculations. This study validated the reliability of the soft soil creep (SSC) model using measurement data and proposed an optimized process for SSC parameter selection, aiming to improve both accuracy and practical applicability. A numerical model was established based on actual engineering to study the effects of different pile lengths and spacing on settlement, soil arching, and reinforcement material stress. Key findings include as follows: (1) The SSC model outperforms the Mohr–Coulomb and soft soil models in predicting settlement and stress concentrations. (2) An optimized SSC parameter selection process is proposed, providing reference values for typical soft soils in Zhejiang, China. (3) Settlement increases significantly when pile spacing exceeds 2.8 m in this project, suggesting the existence of a threshold effect of pile spacing on settlement. (4) Increasing pile length reduces differential settlement and the tensile force on reinforcement material, with differential settlement decreasing from 0.268 to 0.114 mm and tensile force dropping from 106 to 89 kN/m as pile length increases from 24 to 30 m. This finding shows the importance of balancing pile length and reinforcement material strength, which can reduce project costs while ensuring the stability and quality of the embankment. This study provides a theoretical basis for the design of pile-supported reinforced embankments in soft soil regions.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

In recent years, with the rapid advancement of highway construction in China, many highways inevitably pass through coastal soft soil areas. The characteristics of soft soil, such as high water content, low shear strength, and high compressibility, pose severe challenges to highway construction quality. Resulting issues, such as the difficulty of controlling postconstruction settlement and road surface damage caused by uneven settlement [1], have significantly impacted road safety [2]. As an effective engineering solution, pile-supported reinforced embankments provide a feasible method for addressing these challenges [3, 4].

Numerous researchers have conducted extensive studies on this topic. Zhang and Lin [5] employed laboratory model tests and finite element method (FEM) modellings and analyzed the soil-arching geometry and embankment deformation in pile-supported reinforced embankments. The study revealed that filling cohesion significantly impacts embankment load distribution, with the pile–soil stress ratio decreasing as filling cohesion increases. Lang et al. [6] applied the finite-element method to investigate the dynamic behavior of piled embankments under train loading. The study considered various factors such as train speed, track irregularity, and embankment structure parameters. Meena et al. [7] employed a two-dimensional finite element simulation, demonstrating that pile shaft modulus, embankment modulus, and friction angle notably influence the soil-arching mechanism. Pham and Dias [8] examined the effects of traffic load cycles, vehicle speed, and embankment height on soil arching and cumulative settlements using Abaqus. They also showed that the hypoplastic model better represents soil-arching reduction and cumulative settlement under cyclic loading than the linear elastic–perfectly plastic model. Ding et al. [9] used ABAQUS to build a 3D model of geosynthetic-reinforced embankment without drainage consolidation. They simulated traffic loads via a Fortran subroutine, modeled materials, and used infinite elements to reduce boundary effects and studied the impacts of reinforcement type, overload, and load velocity on the embankment. Zhang et al. [10] introduced a novel 2D–3D conversion method for calculating maximum strain in geosynthetic reinforcement within pile-supported embankments, significantly reducing the computational complexity. Samira et al. [11] employed a linear elastic model to simulate the foundation soil and piles, analyzing how foundation soil stiffness affects load transfer and noting that foundation stiffness has minimal effect on soil arch height.

In summary, while numerical simulation studies on pile-supported reinforced embankments have made substantial progress, there remains a lack of research focused on coastal areas with deep soft soils. Zhang et al. [12] proposed a multi-effect coupling model for the piled embankment in the coastal expressway. The model took into account the coupling effects of the soil arching effect, the membrane-pulling effect, and the pile–soil interaction, and studied key factors such as the pile spacing and the tensile stiffness of the reinforcement material. Gu et al. [13] took the embankment on the soft soil subgrade of the southern extension line of the Xintai Expressway in Guangdong as a case study and investigated problems such as sliding and cracking of the embankment formed by the reinforcement of soft soil foundations with rigid piles in the deep soft soil area. Previous studies indicate that the creep deformation of soft soil under self-weight stress is a primary cause of settlement in such coastal areas [14, 15]. Therefore, creep compression in deep soft soil layers must be considered when analyzing the settlement of pile-supported reinforced embankments. However, in numerical calculations, the creep parameters of soft soil are often based on empirical formulas, which limits the accuracy of the calculation results.

To address the limitations of existing research, this study first verifies the reliability of the soft soil creep (SSC) model using measured data. Second, to improve both the accuracy and practical applicability of SSC parameter selection, an optimized process for SSC parameter determination is proposed. Finally, based on this optimized process, a numerical model of a pile-supported reinforced embankment in deep soft soil regions was established to analyze the impacts of varying pile lengths and spacings on settlement, soil-arching effects, and the stress in reinforcement material, providing a theoretical basis for the design of pile-supported reinforced embankments in deep soft soil areas.

2. SSSC Model Verification

To verify the reliability of the SSC model in simulating the consolidation and settlement of soft soil, as well as the accuracy of calculating the stress in reinforcement material, Zhang’s laboratory test on a pile-supported reinforced embankment [16] was used as a benchmark. A schematic diagram of the model test is shown in Figure 1, while the SSC-based numerical model is presented in Figure 2.

[figure(s) omitted; refer to PDF]

Zhang [16] and Zhao [17] used the Mohr–Coulomb and soft soil (SS) models, respectively, to simulate this test. The total foundation settlement results under different models are shown in Figure 3. The Mohr–Coulomb model underestimates settlement compared to the measured values, and the soft soil model’s error grows progressively with increasing load. In contrast, the SSC model’s predictions are slightly higher than the measured values but with minimal error, favoring safety. Figure 4 shows the distribution of tensile forces in geogrid under different models (In this test, the reinforcement material is geogrid). The soft soil model cannot predict peak tensile forces at the pile edge. In contrast, the Mohr–Coulomb and SSC models reflect the observed stress concentration of the geogrid at the pile edge, with the SSC model achieving lower error. These results demonstrate that the SSC model can effectively predict settlement and internal stress characteristics in pile-supported reinforced embankments.

[figure(s) omitted; refer to PDF]

The same conclusion has also been verified in Yue and Liu’s research [18]. It was pointed out that, compared with the results of traditional constitutive models, the SSC model could better reflect the creep characteristics of soft clay. Compared with the Mohr–Coulomb model, the SSC model was more suitable for calculating the settlement of buildings founded on soft clay foundations, and its calculation results were more consistent with the actual situation.

3. Optimization Process for Selecting SSC Parameter Values

In the SSC model, creep parameters can be accurately obtained through one-dimensional consolidation tests. However, in practical engineering, geotechnical investigation reports typically do not include this test. Since there is a certain correlation between creep parameters and compression modulus $E_{s1-2}$, empirical formulas are often used to estimate these values in numerical simulations [19–21].

Nevertheless, Li et al.’s [22] study on SSC model parameter sensitivity indicates that the modified compression index ${\lambda }^{\ast }$determines the deformation in the initial development stage of foundation settlement, while the modified creep index ${\mu }^{\ast }$ primarily affects long-term settlement. Niu et al. [23] investigated the influence laws of the modified compression index ${\lambda }^{\ast }$ and the modified rebound index ${\kappa }^{\ast }$ on embankment settlement and lateral displacement. When the value of ${\lambda }^{\ast }$ varies within the range of −20% to 20%, the absolute value of the settlement change rate reaches 15%. As its value increases, both the lateral displacement and the surface settlement at the same location increase, and its impact on settlement is much greater than that on lateral displacement. When ${\kappa }^{\ast }$ decreases by 20%, the settlement decreases by 2.04% and the lateral displacement decreases by 13.05%; when it increases by 20%, the settlement increases by 2.38% and the lateral displacement increases by 13.05%. Therefore, the impact of ${\kappa }^{\ast }$ on lateral displacement is greater than that on settlement.

Therefore, the above-mentioned research on the sensitivity analysis of modified compression index ${\lambda }^{\ast }$, modified rebound index ${\kappa }^{\ast }$, and modified creep index ${\mu }^{\ast }$ that the impacts of these parameters on the deformation of soft soil foundations are significant and complex. In practical engineering modeling, the values of these parameters must be determined with caution. Otherwise, it will greatly affect the accuracy of settlement predictions.

Although parameters derived from one-dimensional consolidation tests are precise, such tests require undisturbed soil samples and sufficient time and resources, making them challenging to conduct in projects with tight construction schedules, limited personnel, or budget constraints.

To enhance both the accuracy and practical applicability of SSC parameter selection, an optimized process is proposed as follows: (1) Based on the compression modulus $E_{s1-2}$ from the geological survey report, estimated values for modified compression index ${\lambda }^{\ast }$, modified rebound index ${\kappa }^{\ast }$ and modified creep index ${\mu }^{\ast }$ are obtained; (2) Compare the estimated value with the test value of typical local soft soil. If the estimated value is within the range of the test value, use the estimated value. If the estimated value exceeds the testing range, the average of the test values of local soft soil is adopted; (3) When testing conditions permit, undisturbed soil samples are taken directly from the project site to conduct relevant tests and calculate precise ${\lambda }^{\ast }$, ${\kappa }^{\ast }$, and ${\mu }^{\ast }$ values, as shown in Figure 5.

[figure(s) omitted; refer to PDF]

To verify the feasibility of this method, a series of laboratory tests were conducted on typical soft soils in the Zhejiang region, as shown in Figure 6. The relationship between test values of the modified compression index ${\lambda }^{\ast }$, modified rebound index ${\kappa }^{\ast }$, and modified creep index ${\mu }^{\ast }$ with the compression modulus $E_{s1-2}$ for soils from Taizhou, Ningbo, and Wenzhou were examined. The discrepancies between test values and estimated values were analyzed. The test results are shown in Figure 7. Overall, the smaller the $E_{s1-2}$ value, the greater the deviation in each parameter. The compression modulus $E_{s1-2}$ for Taizhou soft soils ranges from 1.89 to 6.68 MPa, for Ningbo from 1.41 to 2.55 MPa, and for Wenzhou from 1.44 to 4.99 MPa. The ${\lambda }^{\ast }$, ${\kappa }^{\ast }$, and ${\mu }^{\ast }$ values for Taizhou soils are generally lower than the estimated values, those for Ningbo are mostly within the estimated range, and those for Wenzhou are predominantly above the estimated range. Therefore, using estimated values to calculate settlement for soft soil embankments would overestimate settlement in Taizhou and underestimate it in Wenzhou. The range of ${\lambda }^{\ast }$, ${\kappa }^{\ast }$, and ${\mu }^{\ast }$ test values for typical soft soils in Zhejiang is summarized in Table 1, providing reference data for future SSC parameter selection research.

[figure(s) omitted; refer to PDF]

Table 1

The range of soft soil creep parameters for typical soft soils in Zhejiang.

Area	${\lambda }^{\ast }$	${\kappa }^{\ast }$	${\mu }^{\ast }$
Taizhou	0.011–0.042	0.0013–0.0053	0.00045–0.00173
Ningbo	0.036–0.096	0.0045–0.0131	0.00151–0.00483
Wenzhou	0.027–0.105	0.0034–0.0199	0.00174–0.00654

4. Performance Evaluation of Pile-Supported Reinforced Embankments Based on the SSC Model

4.1. Project Overview

In practical engineering, only by using reasonable SSC parameters, the numerical model can accurately simulate the responses of embankment settlement, soil arching effect, and stress in the reinforcement material when the pile spacing and pile length change. This not only helps to deeply understand the interaction mechanism among various factors but also provides a powerful basis for the design optimization of the embankment. Therefore, in this study, a numerical model was established based on the optimized SSC parameters to evaluate the engineering characteristics of pile-supported reinforced embankments.

The pile-supported reinforced embankment project is located on an expressway in Wenzhou, Zhejiang Province. The design section is located on the main road section behind the toll station of the expressway, as shown in Figure 8. The preliminary design is as follows: the embankment is 32 m wide and 4.5 m high and has a slope of 1 : 1.5. The pipe piles have a diameter of 0.4 m, a wall thickness of 0.06 m, and a length of 26 m, with a spacing of 2.8 m. The piles are made of C60 concrete. The pile cap measures 1.2 × 1.2 × 0.3 m, made of C30 concrete. The effects of changes in pile length and spacing on embankment settlement, pile–soil stress ratio, and reinforcement material stress will be analyzed through numerical simulation to guide subsequent design optimization.

[figure(s) omitted; refer to PDF]

4.2. Establishment of the Numerical Model

The numerical model of pile-supported reinforced embankment in this project is shown in Figure 9. A semi-symmetric model was adopted, with model boundaries x_min = 0 m, x_max = 50 m, y_min = 0 m, y_max = 10 m, z_min = −40 m, and z_max = 5 m. A borehole was created at the origin, and the thickness parameters and physical parameters of silty clay, silt, and clay were set. Using the optimized SSC model parameters mentioned earlier, suitable parameters for this project were determined, as shown in Tables 2 and 3. According to the geological survey report, the depth of groundwater is set to −2.82 m. Considering the extremely poor permeability of the clay at the bottom, the seepage boundary conditions are x_max = open, x_min = closed, y_max = closed, y_min = closed, z_min = closed, and z_max = open. This model allows for the evaluation of the impacts of different design schemes on settlement, pile–soil stress ratios.

[figure(s) omitted; refer to PDF]

Table 2

The parameter of soft soil creep model for soft soil.

Soil type	Thickness (m)	$\gamma$ (kN/m3)	$e$	${\lambda }^{\ast }$	${\kappa }^{\ast }$	${\mu }^{\ast }$	$c\prime$ (kPa)	$\phi \prime$ (°)	$k$ (m/day)
Silty clay	2.2	17.9	1.161	0.0264	0.0121	6.71E−4	6	26	3.45E−3
Silt	21.2	15.8	1.884	0.0578	0.0184	1.02E−3	2	22	8.64E−5
Clay1	1.0	17.4	1.302	0.0279	0.0127	7.11E−4	6	26	4.32E−4
Clay2	11.2	18.7	0.949	0.0177	0.0068	6.25E−4	7	25	4.32E−4

Table 3

The material parameters of the pile-supported embankment.

Material Type	$\gamma$ (kN/m3)	$E$ (kPa)	ν	$c\prime$ (kPa)	$\phi \prime$ (°)	$k$ (m/day)	$F_{\text{max\hspace{0.17em}}}$ (kN)	$EA$ (kN/m)	$N_{\text{max\hspace{0.17em}}}$ (kN/m)
Pile cap	25	30E6	0.2	—	—	—	—	—	—
Pile	19	60E6	0.2	—	—	—	340	—	—
Cushion	22	15E3	0.2	1	33	1E−2	—	—	—
Roadbed	20	15E3	0.2	1	35	1E−2	—	—	—
Pavement	25	20E6	02	—	—	—	—	—	—
Reinforcement material	—	—	—	—	—	—	—	47.76E3	400

The modeling is consistent with the construction process, which is generally divided into the construction period and the postconstruction operation period. The construction period lasts for 12 months, and the postconstruction operation period is 15 years. The construction process is divided into two stages: 6 months of surcharge preloading and 6 months of embankment filling. The load of surcharge preloading is equivalent to the height of 4.5 m of fill (i.e., equal-load preloading). During the operation period, the traffic load is simplified, and an upper load of 10.5 kPa is adopted.

5. Results and Discussion

5.1. Pile Spacing Effects

5.1.1. Influence of Pile Spacing on Settlement

The relationship between time and settlement under different pile spacings is shown in Figure 10, where the settlement observation point is the intersection point between the centerline of the embankment and the ground. Under different pile spacings, the rate of settlement growth during the operation period is less than that during the construction period. However, the rate of settlement increase in the operation period increases as pile spacing increases. When the pile spacing exceeds 2.8 m, the settlement curve continues to have a steep slope, indicating that the embankment is still experiencing significant settlement, and the settlement does not converge after 15 years of operation. At this point, further increasing the pile spacing will significantly reduce the safety of the embankment project.

[figure(s) omitted; refer to PDF]

To further analyze settlement changes during and after construction, the settlement values during construction, postconstruction settlement, and total settlement are plotted in the same figure, as shown in Figure 11. During the construction period, settlement gradually increases from 4.1 to 5.8 cm as pile spacing increases, while postconstruction settlement increases from 7.4 to 21.2 cm. As pile spacing increases, both construction-period and postconstruction settlement increase, but the increase in postconstruction settlement is more significant than that during construction. Therefore, controlling total settlement primarily depends on controlling postconstruction settlement. The total settlement increases with increasing pile spacing, with a notable threshold for the growth rate. In this project, when the pile spacing is 2.4, 2.6, and 2.8 m respectively, the slopes of the curves are −0.053, −0.115, and −0.170 respectively. That is, when the pile spacing exceeds 2.8 m, the growth rate of the total settlement increases significantly. Considering the characteristic that the settlement is difficult to converge when the pile spacing exceeds 2.8 m, the critical value of the pile spacing in this project can be determined as 2.8 m.

[figure(s) omitted; refer to PDF]

From a mechanical mechanism perspective, as pile spacing increases, soil particle interactions change significantly. In granular mechanics, soil comprises numerous particles. With a small pile spacing, particles are compact, and stable force chains transfer load to piles and underlying soil. When the spacing widens, the soil between piles has more room to deform, breaking some force chains connected to piles. The redistributed load increases stress on these soil particles. Given their limited bearing capacity, the soil between piles compresses and deforms more, leading to settlement growth. Also, a larger pile spacing reduces the proportion of load transferred to the pile tops. Instead, the load becomes more concentrated on the soil between piles, worsening its settlement. This cumulative effect causes postconstruction and total settlement to increase notably when the pile spacing exceeds a certain value.

5.1.2. Influence of Pile Spacing on Soil Arch Height

Figure 12 shows the vector diagram of the major principal stress in the embankment filling unit. A clear stress concentration occurs at the top of the pile cap, with the major principal stress in the soil units near the pile cap deflecting toward it. This creates an arch structure, where the stress direction above the arch is vertical, but within the arch, it deflects towards the pile cap. As a result, the earth pressure between the piles decreases, while the pressure at the top of the pile cap increases rapidly. This deflection leads to stress redistribution, which is the essence of the soil arching effect.

[figure(s) omitted; refer to PDF]

Figure 13 illustrates the relationship between soil arch height and pile spacing. Both the height and span of the soil arch increase with pile spacing, with the height between four piles being significantly greater than between two piles. This is consistent with the concentric circular arch model [24].

[figure(s) omitted; refer to PDF]

To study the pile–soil stress states, the pile at the central axis and the surrounding soil are analyzed. The stress at the pile top is taken from the central pile cap, and the soil stress between piles is averaged. The pile top load is calculated by multiplying the stress by the pile cap area, while the soil load is calculated by multiplying the soil stress by the area between piles, as shown in Figure 14. By comparing the numerical calculation results with the Chinese code (DB33/T 904-2021) [25] and the British code (BS 8006) [26], it can be seen that the variation trend of the numerical simulation results is similar to that of the Chinese code. When the pile spacing exceeds 2.8 m, the pile–soil load ratio decreases more rapidly. However, the numerical simulation results are larger than those of the Chinese code. Although the variation of the British code generally shows a linear decrease, the values are closer to the numerical simulation results, with a maximum error of no more than 10%.

[figure(s) omitted; refer to PDF]

This is because the British code calculates the pile–soil load ratio based on the hemispherical shell theory of Hewlett and Randolph. Its theoretical system is relatively complete, and the mechanical analysis of the pile–soil interaction is relatively in-depth, considering a variety of complex mechanical mechanisms, which makes the calculation results closer to the numerical simulation results in value. In contrast, the Chinese code (DB33/T 904-2021) is based on Chen Yunmin’s spatial soil arch limit analysis method and determines the pile–soil load ratio by looking up tables. Although this method simplifies the design process to a certain extent, due to its large safety margin, the calculated pile–soil load ratio is often smaller than the actual numerical simulation results.

Therefore, in practical engineering design, numerical simulation and codes can be combined and flexibly applied according to specific geological conditions to provide a more scientific and reasonable basis for pile foundation design.

Although increasing pile spacing can reduce project costs, it also increases the load on the soil between the piles. Therefore, selecting an optimal pile spacing requires balancing cost, settlement control, and pile–soil load distribution to ensure long-term project stability.

5.2. Pile Length Effects

5.2.1. Influence of Pile Length on Settlement

The pile spacing is set at 3.0 m, and the pile lengths are adjusted to 22, 24, 26, 28, and 30 m, ensuring that the position of the central pile remains unchanged. The pile groups are symmetrically distributed according to the corresponding spacing with no piles placed outside the embankment. The pile lengths are summarized in Table 4. When the pile length is 22 m, the bearing stratum at the bottom of the pile is silt and the calculation results do not converge, indicating that the pile foundation fails to meet the bearing capacity requirements.

Table 4

Different pile length settings.

Pile length (m)	22	24	26	28	30
Pile bottom bearing stratum	Silt (computational nonconvergence)	Clay1	Clay1	Clay2	Clay2

In the context of pile–soil interaction, when the pile length increases, the side friction resistance and end resistance change in distinct ways. The side friction resistance, which is the frictional force between the pile side and the surrounding soil, increases as the pile length grows. This is because the contact area between the pile and the soil along the pile side expands. For instance, in a homogeneous soil profile, a longer pile will have more surface area in contact with the soil, thereby generating greater side friction.

The end resistance, determined by the bearing capacity of the soil at the pile tip, also changes with pile length. If the pile penetrates deeper into a stronger soil layer as the length increases, the end resistance will increase. These alterations in side friction and end resistance jointly influence the pile–soil load ratio. As the pile length increases, the enhanced side friction and end resistance allow the pile to bear a larger proportion of the load, thus reducing the load borne by the soil.

This change in the pile–soil load ratio has a direct impact on the settlement. As shown in Figure 15, which depicts the relationship between time and settlement under different pile lengths, as the pile length increases, the total settlement decreases. For pile lengths of 24, 26, 28, and 30 m, the total settlement is 32.7, 20.0, 15.4, and 11.8 cm, respectively. When the pile–soil load ratio shifts in favor of the pile bearing more load, the overall settlement of the embankment system is reduced because the pile is more effective in transferring the load to deeper and more stable soil layers.

[figure(s) omitted; refer to PDF]

For pile lengths between 26 and 30 m, the postconstruction settlement gradually converges because the bearing stratum is clay. However, for a pile length of 24 m, the postconstruction settlement rate increases significantly and the settlement continues to increase with time. This can be attributed to the relatively poor load-bearing capacity of the soil at this pile length, which results in an unfavorable pile–soil load ratio, causing more load to be borne by the soil and leading to larger settlement.

To further analyze the changes in construction and postconstruction settlement, the relationship between pile length, construction settlement, postconstruction settlement, and total settlement is shown in Figure 16. During construction, settlement gradually decreases from 9.1 to 3.9 cm as the pile length increases, while postconstruction settlement decreases from 23.6 to 11.8 cm. The change in the pile-soil load ratio due to the increase in pile length affects both the construction period settlement and the postconstruction settlement. When the pile length is 24 m, settlement during and after construction increases sharply, as the bearing stratum is a poorer clay layer. This indicates that the soil properties of the bearing layer at the bottom of the pile play a crucial role in determining the settlement, and they also interact with the pile–soil load ratio to influence the overall settlement behavior.

[figure(s) omitted; refer to PDF]

Therefore, pile length has a significant impact on postconstruction settlement and total settlement. Specifically, the soil properties of the bearing layer at the bottom of the pile are a key influencing factor for settlement during construction, and they are closely related to the pile-soil load ratio which in turn affects the settlement characteristics.

5.2.2. Influence of Pile Length on Stress of Reinforcement Material

Figure 17 illustrates the relationship between reinforcement tensile force and pile length. For pile lengths of 24, 26, 28, and 30 m, the reinforcement tensile forces are 106, 94.5, 91.8, and 89 kN/m, respectively. As the pile length increases, the tensile force in the reinforcement decreases.

[figure(s) omitted; refer to PDF]

When using the Chinese code (DB33/T 904-2021) [25] or the British code (BS 8006) [26], the tensile force in the reinforcement remains constant, regardless of pile length—149.4 and 117 kN/m, respectively. This is because both codes do not account for the effect of pile length on reinforcement stress.

Figure 18 shows the differential settlement at various stages of construction. For pile lengths of 24, 26, 28, and 30 m, the total differential settlement is 0.268, 0.173, 0.137, and 0.114 mm, respectively. As the pile length increases, the differential settlement decreases significantly, particularly after construction. An increase in pile length enhances side friction and, with stronger soil layers, increases end resistance, thus improving overall bearing capacity and stability. More surrounding soil contributes to load-sharing, which reduces differential settlement.

[figure(s) omitted; refer to PDF]

Figure 19 shows the displacement and tensile force distribution of reinforcement material in the pile-supported embankment (Pile length = 28 m). Due to the significantly lower modulus of the soil between the piles compared to the piles, the settlement of the reinforcement material above the soil between the piles is much greater than that above the pile cap. This differential settlement leads to relative sliding between the pile top and the soil between the piles, causing tensile deformation in the reinforcement. Stress concentration at the edges of the pile cap causes a sharp increase in the tensile force in the reinforcement at this location.

[figure(s) omitted; refer to PDF]

In conclusion, in deep soft soils, pile length significantly affects differential settlement at each construction stage, which in turn impacts reinforcement stress. Therefore, considering longer piles to reduce differential settlement can enhance project quality and reduce costs.

6. Conclusions

In summary, this study confirmed the reliability of the SSC model using measured data, providing a foundation for accurate analysis. Additionally, an optimized SSC parameter selection process was proposed to enhance both the precision and practical accessibility of parameter determination. Using these refined parameters, a numerical model of a pile-supported reinforced embankment in deep soft soil regions was established, enabling analysis of the effects of varying pile lengths and spacings on settlement, soil arching behavior, and reinforcement material stresses. The following main conclusions can be drawn:

1. The SSC model has good predictive performance for the settlement and stress characteristics of pile-supported reinforced embankments. Compared with the Mohr–Coulomb model and the Soft Soil model, the SSC model has the least error in predicting settlement and leans towards safety and can accurately reflect the stress concentration phenomenon of the reinforcement material at the pile edges.

2. An optimized process for SSC parameter selection was proposed, summarizing the range of test values for the modified compression index, modified rebound index, and modified creep index for typical soft soils in Zhejiang. This provides a reference for future studies related to SSC parameter selection.

3. The total settlement increases with increasing pile spacing, with a notable threshold for the growth rate. In this project, when pile spacing exceeds 2.8 m, the growth rate of total settlement increases significantly. It is not recommended to exceed this threshold for pile spacing in this project.

4. For deep soft soil areas, increasing pile length can significantly reduce differential settlement, thereby reducing the tensile force of reinforcement material. When the pile length increased from 24 to 30 m in this project, the differential settlement decreased from 0.268 to 0.114 mm and the tensile force of reinforcement material decreased from 106 to 89 kN/m. Therefore, a balance between pile length and reinforcement material strength can be achieved to reduce project costs.

5. However, this study also has several limitations. First, the soil properties and engineering conditions in other regions may vary significantly, which may limit the universality of the SSC model and the optimized parameter selection process. Second, the influence of some complex factors, such as the long-term environmental effects (e.g., temperature variations, groundwater level fluctuations) and the interaction between the embankment and superstructure, were not fully considered in the model. Future research could focus on expanding the scope of research areas, collecting more field data, and further improving the model to account for these complex factors to enhance the accuracy and applicability of the research results.

Author Contributions

The authors confirm contribution to the paper as follows: Bin Mao, Wei-Kang Lin: study conception and design; Bing Duan, Xiao-Wu Tang: data collection; Xiao-Dong Pan and Hao-Chen Xue: analysis and interpretation of results; Hong-Yue Sun and Xiao-Dong -Pan: draft manuscript preparation. All authors reviewed the results and approved the final version of the manuscript.

Acknowledgments

This research was funded by Key R & D Project of Zhejiang Communication (No. ZJXL-JTT-202201A); National Natural Science Foundation of China (52378377); Natural Science Foundation of Zhejiang Province (LTZ21E080001); Key Laboratory of Geotechnical and Under-ground Engineering of Ministry of Education, Tongji University (KLE-TJGE-B2202); Zhejiang Province Public Welfare Technology Application Research Project (LGG22E080002); Key Water Science and Technology Project of Zhejiang Province (RB2027); and Cultural Heritage Bureau of Zhejiang Province (2023006).

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