Research on Vertical Bearing Performance of Precast Concrete Pile Reinforced with Cement-Treated Soil under Different Loading Modes

Abstract

Precast concrete pile reinforced with cement-treated soil (PCRC) is a composite pile formed by inserting a precast concrete (PC) pile into a deep cement mixing (DCM) column. It has become widely recognized and used for soft soil ground treatment. Despite its extensive application, the cooperative bearing mechanism of PCRC has not been fully investigated under diverse loading conditions. This paper presents the results of finite element analysis, comparing the bearing performances of the PCRCs under two loading forms: load applied solely to the PC pile (Form 1) and the entire cross-section (Form 2). The results reveal that the inner and outer cores of the PCRC loaded under Form 2 can synergistically work together, exhibiting a 13.2% higher ultimate bearing capacity than the PCRC with Form 1. The load sharing ratio, μ, of the inner core of the PCRC loaded under Form 2 ranges from 0.86 to 0.93, while μ of the inner core under Form 1 remains stable at approximately 0.96. Increasing the loading plate size improves the DCM column’s load sharing capacity. Furthermore, axial load tests in Form 1 underestimated the bearing capacity of PCRC to a certain extent. It is, therefore, recommended in engineering design that the top of the DCM column be positioned higher than that of the PC pile to achieve the actual force mode of Form 2.

Keywords

infrastructure geology and geoenvironmental engineering foundations of bridges and other structures piles

Precast concrete pile reinforced with cement-treated soil (PCRC) pile is a novel type of the composite pile that is constructed by inserting a precast concrete (PC) pile concentrically (known as the inner core) into a deep cement mixing (DCM) column (known as the outer core) before initial setting of cemented soil (1 –3). This composite pile design capitalizes on the high strength and large bearing capacity of precast piles, while circumventing the limitations of cemented soil’s strength (4, 5). Additionally, it helps to improve the strength of the surrounding soil, while the engineering cost of the PCRC is roughly 30% to 60% lower than that of DCM column ( 6 ). Given the minimal deformation, excellent seismic performance, and cost-effectiveness, PCRC has gained significant popularity for soft soil ground improvement in the southeastern coastal region of China and in Thailand (7 –9). As illustrated in Figure 1, PCRC can be categorized into three types: short core, equal core, and long core, based on the relationship between the lengths of inner and outer cores ( 10 ). These different types are employed in different working conditions.

In previous studies, a series of field tests, laboratory tests, and numerical analyses have been conducted to investigate the bearing mechanism of the PCRC under rigid axial and lateral loads (11 –13). Generally, the inner core of a PCRC is designed to support loads, while the outer core functions by transferring the axial force to the surrounding soil via skin friction ( 14 ), indicating that the presence of cemented soil significantly improves the bearing performance of PC piles by 30% to 50% with this double-layered load-transfer mode ( 15 ). Dong et al. ( 16 ) found by numerical analysis that the pile tip resistance was less than 7% of the load at the pile top, indicating that PCRC generally behaves as friction piles under axial loading and is susceptible to failure because of plastic deformation of the surrounding soil (17 –19). Voottipruex et al. ( 20 ) determined that the length ratio (L_pc/L_dm) has a greater impact on the vertical bearing capacity of the PCRC than the sectional area ratio (A_pc/A_dm) between these two components. Wang et al. ( 7 ) proposed a simple analytical approach for predicting the bearing capacity of the PCRC based on the shear displacement method. They found that the ultimate bearing capacity of the PCRC increases by 20% for every 100-mm increase in the diameter of the DCM column. Zhou et al. ( 11 ) observed through laboratory model tests two failure modes of PCRC, pile failure and the ratio between pile end resistance and pile top load which varied from 19.4% and 54.2%.

Given its multiple interface features, the bearing mechanism of the PCRC is more intricate than that of other types of pile that consist of a single material (21, 22), and the interface frictional behaviors between the inner and outer cores control the bearing performance of the PCRC ( 23 ). Wu et al. ( 24 ) determined that the ultimate interface friction strength can reach 0.194 times the strength of cemented soil in indoor model tests. Yu et al. ( 25 ) proposed a tri-linear interface model comprising an elastic stage, a brittle failure stage, and a shear slip stage. This model was developed based on the 3-D pile-soil interface shear tests, where the ultimate shear displacement between the concrete and cemented soil varied from 1.23 mm to 2.40 mm. Jamsawang et al. ( 26 ) revealed that the shaft friction effectively prevented the inner and outer cores from sliding through vertical pull-out tests of the PCRC. Additionally, the measured shear strength of the interface was found to be 0.4 times the compressive strength of the cemented soil. Li et al. ( 27 ) indicated that with an increase in the unconfined compressive strength of cement-soil, the mode of interface failure shifts from plastic failure to brittle failure, accompanied by a variation in the friction angle from 28° to 39°.

Previous research on in situ axial load tests for composite piles, specifically Form 1, typically applied loads directly to the inner cores (PC piles) (13, 28). However, given the collaborative load-bearing nature of the inner and outer cores in composite piles, applying loads solely to the inner cores in the current Form 1 loading configuration leads to an incomplete and inadequate representation of their load-bearing behavior. This loading method fails to accurately portray the full load-bearing characteristics of composite piles, leading to an underestimation of the contribution of the outer cores to the overall load capacity of the pile. To address this issue, it is crucial to investigate the contributions of DCM columns under external loads. Therefore, it is essential to employ a different loading method, namely Form 2, which involves applying loads simultaneously to both the inner and outer cores. This method should be used to thoroughly investigate the behavior of the PCRC under axial loads.

In this study, a comprehensive study was conducted on the working mechanisms of the PCRC through full-scale pile loading tests and numerical analysis. To achieve the research objective, taking into account the nonlinearity of the piles and the pile-soil interaction (29, 30), three-dimensional numerical (3-D) models of the single PCRC, validated against field test results, were established using the ABAQUS finite element (FE) software. Furthermore, the vertical bearing characteristics of the PCRC were studied. The research results can provide a theoretical basis for the engineering applications of this composite pile.

Site Condition and Soil Parameters

Description of the Selected Project

The geological conditions along the Jiangsu section of the Beijing–Shanghai Expressway Expansion Project in China are known for their complexity, characterized by the widespread presence of deep and thick layers of soft soils, some of which are locally over 30-m thick. It is crucial to control the post-construction settlement of the expressway. As a result, PCRC has been used to reinforce the soft soil in this area, mainly because of its remarkable bearing capacity and cost-effectiveness. In this study, four sets of single pile load tests were conducted on the PCRC. The outer core of the PCRC is formed by a DCM column with a diameter of 0.8 m. The inner core, on the other hand, consists of a precast concrete (PC) pile with a diameter of 0.4 m, a wall thickness of 95 millimeters, and a concrete grade of C50. In this project, the long-core PCRC (shown in Figure 1c) is used, where the length of the inner core is greater than that of the outer core. During the loading tests, load plates with diameters of 0.4 m and 0.8 m were selected to match the cross sections of the inner and outer cores, respectively. These two sizes of loading plates correspond to the two loading forms mentioned earlier. Detailed parameters for both are summarized in Table 1.

Table 1.

Summary of Tested Piles Configurations

Pile number	Length of inner core (m)	Length of outer core (m)	Diameter of loading plate (m)
PCRC-1	28	12	0.4
PCRC-2	28	12	0.8
PCRC-3	35	12	0.4
PCRC-4	35	12	0.8

Note: PCRC = precast concrete pile reinforced with cement-treated soil.

Materials Properties

The subsurface soil profile on site is ascertained based on the nearest closest and the results of experimental tests. The top 1.5 m is fill followed by a thin silty clay layer that extends 3.5 m. Underlying the silty clay layer is a silt layer that extends to 12 m below the ground surface. It has been observed that the modulus of compression of each layer falls below 10 MPa, indicating a pronounced tendency for soil compression within these layers. Table 2 presents a comprehensive summary of the pertinent subsurface soil parameters and profile.

Table 2.

Subsurface Soil Profile

Description	Thickness of each layer (m)	Moisture content (%)	Density (kN/m³)	Void ratio	Plasticity index	Compressibility modulus (MPa)	Cohesion (kPa)	Friction angle (°)
Fill	1.5	26.1	20.1	0.706	17.5	3.96	37.6	12.8
Silty clay	3.5	43.7	18.1	1.204	19.2	1.67	15.0	11.5
Silt	7.0	29.3	19.1	0.821	6.8	5.42	14.5	20.9
Silty clay	21	30.0	19.4	0.823	17.0	3.36	28.5	11.0

Load Form and Test Procedure

To investigate the bearing characteristics of the PCRC under various loading conditions, loading plates with diameters matching the diameters of the inner and outer cores of the piles in situ (0.4 m and 0.8 m) were employed. Figure 2 presents the schematic diagrams of the loading plate arrangement. Before loading, a layer of medium-coarse sand was placed as a thin cushion between the loading plate and the pile top to ensure a smooth contact surface, as depicted in Figure 3.

For safety considerations, the engineering piles tested in this project were subjected to non-destructive loading procedures, with the counterweight’s maximum load capacity being limited to 2,400 kN (31 –33). Based on the test results, the failure characteristics of the PCRCs were analyzed through numerical analysis. Furthermore, the inner cores of the tested piles were spliced together using several PC piles to achieve the complete designed length, which posed great difficulties for data collection on the piles’ stress. Consequently, gauges failed to be embedded in the bars during the testing process.

Axial load tests of the PCRCs were conducted in accordance with “Technical Code for Testing of Building Foundation Piles JGJ 106-2014” ( 34 ), following the Slow Load Test Method for Individual Piles.

The proposed final load is divided into 10 steps, with the first step increment being approximately 20% of the estimated final load.

After each load increment was applied, the pile top displacement was measured at intervals of 5, 15, 30, 45, and 60 min, and subsequently every 30 min.

The standard for relatively stable settlement was defined as the displacement of the pile top within each hour not exceeding 0.1 mm, and occurring twice in a row.

During unloading, the load at each level was maintained for 1 h, and the pile top settlement was measured at intervals of 5, 15, 30, and 60 min.

Load Test Results

Table 3 summarizes the results of the load tests conducted on the PCRC-1 to PCRC-4, presenting the maximum load and displacement values obtained. The applied load was restricted to the counterweight’s maximum load capacity of 2,400 kN. The maximum displacements values observed ranged from 9.40 mm to 39.22 mm. Notably, PCRC-3 may have internal defects resulting from construction practices or unfavorable geological conditions, resulting in a significant reduction in its bearing capacity relative to the other three piles. The relative displacement, defined as the ratio of displacement to the diameter of the loading plate, ranged from 1.2% to 9.8%, with the exception of PCRC-3, which had a higher relative displacement value. Importantly, all piles, except for PCRC-3, exhibited a relative displacement value of less than 4%. Additionally, the rebound rate of PCRC-1, 2, and 4 ranged from 51.0% to 82.1%, indicating that they did not reach the limit state. The load-displacement response of the pile can be characterized by three distinct regions, as observed in the current tests. Firstly, an initial linear-elastic region is identified, characterized by a steep slope, indicating a high stiffness. Subseqently, a transitional nonlinear region is observed, where the displacement increases disproportionately to the load increment. Finally, the response transitions into a final linear region, characterized by a shallow slope, indicating a decrease in stiffness. The load-displacement curves of PCRC-1 and PCRC-3 demonstrate a consistent pattern with the typical curve depicted in Figure 4. Notably, the loading stage of PCRC-2 and PCRC-4 exhibits the characteristics of the first two regions of the standard curve.

Table 3.

Summary of Full-Scale Testing Results

Pile	Maximum applied load (kN)	Maximum displacement (mm)	Relative displacement (%)	Rebound rate
PCRC-1	2,300	16.26	4.1	51.0%
PCRC-2	2400	9.40	1.2	67.4%
PCRC-3	1,560	39.22	9.8	9.5%
PCRC-4	2,400	26.83	3.4	82.1%

Note: PCRC = precast concrete pile reinforced with cement-treated soil.

Numerical Modeling

Description of Finite Element Model

FE models of the PCRCs under axial loads were developed using the ABAQUS/Standard (ABAQUS 2020) finite element–modeling program. To ensure accurate simulation, tall numerical modeling parameters were meticulously aligned with those employed during the physical pile and subsoil testing. To minimize the boundary effect, the dimensions of the soil model were set to 16 m, which is 20 times the diameter of outer cores (35, 36). Additionally, the model height was set to 40 m, and the distance between the pile tip and the bottom of the model was greater than 15 times the pile’s external diameter (29, 37, 38) (as illustrated in Figure 5).

Analysis Step and Boundary Conditions

The calculation procedure for the model is divided into two steps: initial analysis and loading analysis. During the initial analysis, the subsoils and the pile are installed, and an equilibrium state is achieved under self-weight (39, 40). Considering the uncertainty of failure load, the PCRCs are incrementally loaded based on the actual on-site loading process until the failure state is reached. For each stage, the load is increased by 300kN, starting from an initial load of 600 kN. The top surface of the model is defined as a boundary free from stress, whereas the bottom of the soil is restrained from movement in any direction, ensuring U_x = U_y = U_z = 0, with U representing translational degree of freedom (41, 42). In addition, the horizontal displacement of the adjacent sides of the soil are constrained, respectively.

Constitutive Model and Interaction

In previous works, the soft soil layers and the cemented soil were modeled using the Mohr-Coulomb (MC) model as linear elastic–perfectly plastic materials. In contrast, the concrete was modeled using a linear-elastic model (43 –45). The elastic behavior is defined by Young’s modulus, E, and Poisson’s ratio, υ, while the plastic behavior is defined by the angle of internal friction, φ, while the cohesion yield stress, c, defines material hardening. The parameters for the stratum are based on the on-site geological survey data (as shown in Table 1). Additionally, Table 4 presents the parameters for the cemented soil and concrete used for calibrating PCRC-2.

Table 4.

Material Parameters Used in Numerical Analysis

Material	E (MPa)	γ (kN/m³)	ν	c (kPa)	φ (°)
Cemented soil	120	21.0	0.3	250	27
Concrete	35,000	24.0	0.2	NA	NA

Note: NA = not available.

In this study, the pile soil and the inner–outer core interface were modeled using the tangential behavior penalty-type Coulomb’s frictional model, where relative tangential motion was restricted until the surface traction reached a critical shear stress value that was the lesser of a fraction of the interface pressure or the interface shear strength (46, 47). The friction coefficients of the pile-soil and inner-outer cores interfaces are 0.2 and 0.65, respectively. Additionally, hard contact was adopted in the normal direction to allow slippage and separation of the interface. The pile was loaded step by step according to loads for data analysis, with the loading plate activated before applying loads. The surfaces between the loading plate and the pile were bound by “tie constraint” to ensure that deformation occurred together (48 –50). To apply a distributed load to the pile, a reference point R1 was established directly above the loading plate. The surface of the loading plate and R1 were connected through “coupling constraints” to transfer the load initially to the loading plate, and then to the pile via the reference point.

Model Calibration and Verification

The finite element models are calibrated using the properties and configurations of the PCRCs, as well as soil parameters obtained from the boreholes and constitutive models. The calibration is satisfactorily achieved by comparing the tested results of PCRC-1 and PCRC-2 with the numerical results, as depicted in Figure 6. The figure demonstrates a remarkable agreement between the two curves in Figure 6a, with the curves closely overlapping during the elastic stage. As the load increases, the slope of the curve derived from the numerical analysis rises. However, this portion of the curve is positioned below the curve obtained from the tested results, albeit with a relatively small difference between them. To analyze the failure characteristics of the PCRC, the vertical load imposed on the pile was increased in the numerical analysis until the pile stopped working even after the load reached 2,400 kN.

Referring to the “Technical Code for Testing of Building Foundation Piles JGJ 106-2014” concerning the ultimate bearing capacity of an individual pile, the load value at which a displacement of 40 mm on a gradually increasing load-displacement curve is regarded as the ultimate bearing capacity. Thus, the ultimate bearing capacity of PCRC-1 and PCRC-2 are determined as 2,960 kN and 3,410 kN, respectively. This indicates a 13.2% increase in the ultimate bearing capacity of PCRC-2 compared with PCRC-1.

Results and Analysis

Axial Force Analysis

Figure 7a illustrates the behavior of the PCRC-1 under vertical load directly applied on the inner core with increasing load. The inner and outer cores collaborate to enhance the axial force exerted by the former at varying levels of loading. However, the axial force decreases gradually with depth, and the attenuation rate reduces until it stabilizes. The pile tip resistance accounts for 8% to 14.6% of the applied load, indicating the bearing characteristics of a friction pile. For the DCM column, the axial force in the pile shaft initially increases linearly with depth under loading. During the loading process, the rate of axial force growth within the 2-m to 8-m depth range of the pile body shows an initial rapid increase. Subsequently, the rate of growth becomes slower along the depth direction, eventually approaching a linear rise toward the pile tip. Given the significantly lower elastic modulus of cemented soil compared with that of concrete, the axial force in the DCM column is relatively low when a load is directly applied to the PC pile.

The PCRC-2, which has the same loading plate area as the DCM pile, demonstrates a more efficient collaboration between its inner and outer cores. A comparison between Figure 7a and Figure 8a reveals a relatively similar distribution of axial force for PC piles under the two loading modes. However, the DCM column bears an increased load in loading Form 2. Unlike the axial force development trend shown in Figure 7b, the curve in Figure 8b exhibits a larger upper and lower bottom trend. The pile top axial force reaches 380.9 kN under the ultimate load.

Skin Friction

The shaft friction resistances of this composite pile are distributed among the inner-outer core interface, the PC pile-soil and the DCM column-soil interface. Stress analysis is conducted on the micro-units of the PC pile and the DCM column, as illustrated in Figure 9.

In Figure 9

f_i and f f’_i are skin friction of the DCM column and the surrounding soil, respectively,

N_i and N_i₊₁ are the axial forces of section i and i + 1 of PC piles respectively, and

N’_i and N’_i₊₁ are the axial forces of the section i and i + 1 of the DCM column, respectively.

The force balance equations for the PC pile and the DCM column can be derived from the force balance condition of the micro-unit:

π d_{1} l_{i} f_{i} = N_{i + 1} - N_{i}

(1)

N'_{i} + π d_{2} l_{i} f'_{i} = N'_{i + 1} + π d_{1} l_{i} f_{i}

(2)

f_{i} = \frac{N_{i + 1} - N_{i}}{π d_{1} l_{i}}

(3)

f'_{i} = \frac{{N'}_{i + 1} + π d_{1} l_{i} f_{i} - {N'}_{i}}{π d_{2} l_{i}}

(4)

where

d ₁ is the outer diameter of the PC pile,

d ₂ is the outer diameter of the DCM column, and

l _i is the pile length between section i and i + 1.

Figures 10 and 11 depict the shaft friction distribution of the inner and outer cores of the PCRC-1 and PCRC-2 at varying depths. The shaft friction curves are segmented into four parts according to the soil layers. As the load increases, the value of shaft friction gradually increases. However, the growth rate of the friction resistance of each soil layer decreases as the load increases. The shaft friction of the inner and outer cores is more than twice that of the DCM column-soil, indicating that the DCM column can provide higher friction resistance for the PC pile, thereby facilitating the development of friction pile characteristics. Comparing Figure 10b and Figure 11b, it is observed that the distribution of outer core friction resistance of the PCRC remains similar under the two loading modes, suggesting that the change in loading mode has no discernible effect on the DCM column–soil interaction. However, for the composite section of the PCRC, the lateral friction of inner core of PCRC-2 exhibits a 20% increase compared with that of PCRC-1. This discrepancy is attributed to the compression of the DCM column, which enhances exertion on the inner core, resulting in an increase in its shaft friction resistance. Additionally, the shaft friction resistance of inner cores with cemented-soil reinforcement is significantly higher than that of PC piles without reinforcement.

Load Sharing Ratio of Inner and Outer Cores

The load sharing ratio, namely μ, is defined as the proportion of the load carried by the inner and outer cores of the PCRC, respectively. Figure 12 indicates that μ of the inner and outer cores of PCRC-1 remain stable at 0.96 and 0.04, respectively, as the load increases. In contrast, for PCRC-2, μ of the inner corer ranges from 0.86 to 0.93, while that of the outer core varies from 0.07 to 0.14. These results imply that when the size of the load plate matches the cross-sectional area of the DCM column, μ of the DCM column increases, resulting in a considerable enhancement in the ultimate bearing capacity of the PCRC.

Various loading conditions exert a significant influence on the stress distribution within the inner and outer cores of composite piles. Figure 13 demonstrates the variation of the stress ratio between the inner and outer cores. Concerning PCRC-1, the stress ratio between the inner and outer cores peaks given the stress concentration at the inner core top. As the applied load increases, the stress ratio exhibits a rise from 573 to 1,028 initially, followed by a sharp decrease within a depth of 2 m below the pile top within 341. With further depth, the stress ratio decreases approximately linearly, indicating the effective load transfer to the DCM column through shaft friction. With the load being applied directly to the entire PCRC-2, the inner and outer cores collaborate more effectively, resulting in a reduction in the degree of stress concentration of the pile top. The stress ratios of the inner and outer cores remain within 76.2 throughout the entire loading process.

It is worth noting that the stress ratio initially increases and then decreases as the depth varies under different load conditions. Furthermore, the location of the maximum stress value along the pile shaft shifts downwards with increasing load. Significantly, when the load reaches 3,410 kN, the entire stress ratio–depth curve shifts to the left. This shift is attributed to a substantial increase in the pile axial stress of the DCM column, from 600 kPa to 1,200 kPa, resulting in a decrease in the stress ratio of inner and outer cores as a whole. These observations indicate that the DCM column withstands a significant proportion of the load, which aligns with the trend observed in the load sharing ratio curve of the outer core of PCRC-2 depicted in Figure 12.

Suggestions for Engineering

Based on the preceding analysis, it seems that the ultimate bearing capacity of the PCRC is frequently underestimated when the design load is solely obtained from tests using Form 1 loading. This underestimation can result in unnecessary resource wastage and significant engineering expense. Consequently, several strategies to enhance piling technology and load testing methods for the PCRCs are proposed. In situations where the PCRCs have short cores and equal cores, the PC piles can be smoothly inserted into uncured cemented soil, ensuring that the DCM column head will not be lower than that of the PC pile on completion of construction. However, PC piles encounter difficulty in achieving the desired depth when dealing with stiff soil layers without cement mixing. This challenge becomes particularly pronounced in the PCRCs with long cores, where the pile tops of the inner and outer cores end up at different elevations, thereby weakening the combined force effect of the PCRCs. To optimize the design and achieve the desired force mode (Form 2), it is recommended that the top of the DCM column be higher than that of the PC pile. Moreover, it is critical to select suitable load testing methods to accurately determine the bearing capacity of the PCRC. When the PCRCs are connected to the foundation slab or beam in building foundations, or when they are part of the pile-supported embankment without pile caps, it can be challenging to transfer loads effectively to the inner and outer cores simultaneously. Consequently, loads are commonly applied directly to the PC piles using Form 1. However, in subgrade projects where pile caps are not present, embankment loads can be directly transferred to both the inner and outer cores. Adopting loading Form 2 is recommend in such cases, which involves applying the load to the entire section of the PCRC.

Conclusion

Axial load tests were conducted to investigate the bearing behaviors of the PCRCs under two different loading forms. To analyze the interaction mechanism between inner and outer cores, 3-D finite element models were established using ABAQUS software, calibrated by the test results. The main conclusions are:

(1) The combined effort of both the inner and outer cores in PCRC-2 synergistically contributes to a significant 13.2% enhancement in the ultimate bearing capacity as compared with PCRC-1.

(2) The μ for the inner core of PCRC-1 remained consistent at 0.96. In contrast, the inner core of PCRC-2 exhibited a range of values from 0.65 to 0.82, while the outer core demonstrated a range of values from 0.18 to 0.35. The increase of loading plate can improve the load sharing of the DCM column to raise the bearing power of the PCRC.

(3) For projects involving pile caps or slab, it is crucial that the DCM pile top should surpass the PC pile to avoid a lower DCM column top after pile head trimming and cap assembly. The load tests should adopt Form 1, in which the loads are directly applied to the PC piles being used. For subgrade projects without pile caps, Form 2, which involves applying the load to the entire section of the PCRC, is employed.

Footnotes

Acknowledgements

The authors would like to thank Southeast University for providing access to the software and other facilities.

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: Songyu Liu, Dingwen Zhang, Anhui Wang, Guangwei Chen; data collection: Chaozhe Zhang; analysis and interpretation of results: Anhui Wang, Chen Jiang; draft manuscript preparation: Chaozhe Zhang, Dingwen Zhang. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research work was supported by the National Natural Science Foundation of China (No. 52078129 & 42277146), Natural Science Foundation of Jiangsu Province of China (Grant No. BK20210051), and Transportation Science and Technology Project of Jiangsu Province of China. These financial supports are gratefully acknowledged.

ORCID iDs

Chaozhe Zhang

Dingwen Zhang

Data Accessibility Statement

All data generated or analyzed during this study are included within the paper.

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