Optimization Effects of Load Reduction for Earth Pressure on High-Filled Cut-and-Cover Tunnels Using the Discrete Element Method

National and Provincial Joint Engineering Laboratory of Road & Bridge Disaster Prevention and Control, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu, China College of Civil Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu, China National and Provincial Joint Engineering Laboratory of Road & Bridge Disaster Prevention and Control, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu, China College of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China


Introduction
To overcome the challenges associated with mountains and less land in transportation network construction in the Loess Plateau of northwest China, a large number of high-filled cut-and-cover tunnels (HFCCTs) are applied. However, the thickness of conventional HFCCT lining structure has become a fault, and the shrinkage cracks produced by hardened concrete cause longitudinal cracking of the structure and affect its durability. Such high fill induces excessive earth pressure above the tunnel, severely affecting the safety of the HFCCT. erefore, reasonable load reduction measures should be performed to improve the safety of HFCCT. However, load reduction materials cannot achieve load reduction effects for HFCCT with ultrahigh backfills; therefore, it is necessary to increase backfill soil height and improve the bearing force capacity of HFCCT through a combination of structural cross section type optimization and laying load reduction materials. It is important to evaluate the impact of different cross section types and characteristics of load reduction materials on earth pressure distribution around HFCCT. Studies on load reduction of high backfill structures have been performed. For deeply buried culverts, Marston [1] proposed and verified the ITI unloading method, which means laying compressible flexible materials on top of the culvert to reduce earth pressure. Subsequently, they evaluated the effects of structural-soil interactions by laying flexible materials on top of the culverts. Flexible materials for load reduction include straw [2,3], sawdust [4], leaves [5], and expanded polystyrene (EPS) [6][7][8][9]. Geosynthetics have also been shown to play a certain role in load reduction on underground pipelines by Zheng et al. [10], Ahmed et al. [11], and Naggar et al. [12]. Based on the theory of culvert load reduction, Li et al. [13][14][15][16][17] performed a series of studies on load reduction in HFCCT so as to inform effective load reduction measures and evaluate various factors affecting soil arch effects of HFCCT.
In addition, the effects of cross section type of high backfill structures on earth pressure were evaluated. Various types of culverts, such as box culvert [8,[18][19][20][21][22], arch culvert [23], tubular culvert [24][25][26][27][28], and cover culvert [29] have been evaluated. For HFCCT, the influence of the slope angle [30] and vector height of arch HFCCT [31] on earth pressure has been studied. e above studies found that the cross section type of high-filled structure has a certain influence on earth pressure distribution around it.
For culverts, studies have assessed load reduction and section shapes; however, for HFCCT, studies were intensively focused on load reduction and their influence on earth pressure with different section types [31].
ere are no systematic studies on optimal coupling of load reduction in HFCCT. erefore, we considered the discreteness, inhomogeneity, and interactions of soil in the backfill soilstructure. Combined effects of optimal cross section type and load reduction material characteristics (density and laying position of EPS; width and height of concrete wedges (CW)) were studied. ree load reduction measures were compared: cross section types of HFCCT, combination of optimized cross section type with load reduction using EPS, and combination of optimized cross section type with optimized load reduction using EPS and CW. e effects of different cross section types and characteristics of load reduction materials on earth pressure distribution above HFCCT were analyzed using the PFC2D software. e optimal values for load reduction effects under the three kinds of load reduction measures were determined.

Numerical Simulations
e numerical test for load reduction in HFCCT was conducted using the commercial calculation software PFC2D (Particle Flow Code in 2D, Itasca 2016) developed by Itasca [32]. e PFC2D model consists of many disks and contact point interactions [33], which are used to calculate particle forces and displacements with two continuous cycles.

Model Establishment.
e HFCCT model was established through the similarity ratio of 1/25 according to the laboratory model test of Ma et al. [30]. Earth pressure, vertical displacement (VD), and microcontact of soil particles were evaluated by changing different influencing factors (cross section types, density and laying positions of EPS, as well as CW height and width). To assess the influence of cross section types on earth pressure around the HFCCT, we defined the concept of cross section optimization coefficient, that was, the ratio of arch height to width of HFCCT, expressed as an alphabet λ. A total of five test schemes were designed. Specific experimental schemes and model sizes are shown in Table 1 and Figure 1, respectively. e numerical model establishment processes in the working conditions shown in Table 1 were similar; therefore, the modeling process of the case C5 was given a minute description. Figure 1 shows that the ball particle was arranged to simulate the backfill soil. Two different models were selected for contact models between particles used in the PFC2D model: the linear model was used for contact between EPS particles and the linear contact bond model was selected to simulate contact characteristics for cohesive soil particles (loess). Boundary conditions (slope, HFCCT, and foundation) were simulated using wall elements. Total height of the model was 1.3 m, which included a backfill height of 1.2 m and an unfilled height of 0.1 m. e width of the foundation (D � 0.6 m), the width of HFCCT (S � 0.2 m), the slope angle (β � 70°), and the two CWs extending from the bottom of the slope to the top for the requirements were set. e backfill was layered by the IMCM method, and the thickness of each layer was 0.2 m.
To assess vertical earth pressure (VEP) above the HFCCT, lateral earth pressure (LEP) on the sides of the HFCCT, VD, porosity and coordination number of soil particles, a number of measurement circles, and displacement monitoring points were arranged in the model. e diameter of these measurement circles was 10 times the size of soil particles (6 mm), and their locations are as shown in Figure 2. Measurement circles from numbers 1 to 9 were used to measure VEP above the HFCCT, measurement circles numbered 3 to 7 were used to calculate the average VEP, while numbers 5 to 7 measurement circles were used to measure porosity and coordination number of soil particles above the HFCCT. Numbers 10 to 18 measurement circles were used to measure VD of soil particles above the HFCCT and the VEP of backfill soil between the two concrete wedges; measurement circles numbered 14 and 12 (or 14 and 16) were used to calculate relative vertical displacements (RVD) of soil particles above the HFCCT; measurement circles numbered 5, 14, and 23 to 28 were used to measure VEP at different backfill depths above HFCCT; and measurement circles numbered 19 to 22 were used to measure VEP above the CWs, while those numbered a to j (or a' to j ') were used to measure LEP on both sides of HFCCT.

Loess.
Macroscopic loess parameters were defined as described by Li et al. [34] (Table 2). e biaxial test model was established through repeated measurements and debugging.
e model size had a width of 0.5 m and a height of 1.0 m (Figure 3). Parameter calibration processes were as follows: First, the ball distribute command in PFC2D was used to balance uneven particle forces within the model. Particles reached the initial equilibrium, while the uneven force reached the set value (1E-3) in the command flow. en, particles in the model were subjected to constant pressure consolidation and axial loading by the servo control mechanism until shear failure occurred, and simulation results of loess parameters were obtained. e microscopic parameters used in the numerical model are shown in Figure 4(a). Simulation results are shown in Table 3.

Expanded Polystyrene.
Simulation of EPS was done by a disk particle element in the contact constitutive model; the distribution range of particle sizes was from 6 to 10 cm, following a standard normal curve distribution. Since earth pressure around HFCCT was far from reaching the corresponding strength of EPS when it was yielding (5%), the stress-strain curve of EPS within 5% was selected as the microscopic parameter for calibration [35]. Its microparameter calibration process was similar to that of loess. However, the difference was in selection of the contact constitutive model and compression method; that is, the      Advances in Civil Engineering linear contact model was taken as its constitutive model relation and uniaxial compression was adopted for compression. Comparison results of stress-strain curves of numerical simulation and test are shown in Figure 4(b). e stress-strain curve of the laboratory test was consistent with the stress-strain curve of numerical simulation; therefore, the calibrated EPS parameter results in Table 3 are correct.

Effects of Cross Section
Type. Taking the five cross section shapes in case C1 as research objects, the earth pressure distribution, displacement, and microscopic contact were evaluated, and cross section shapes of HFCCT were optimized. Figure 5 shows earth pressure distribution for case C1. As shown in Figure 5(a), due to differences in stiffness between HFCCT and backfill soil, analogous VEP distribution occurred on the top, and a V-shaped distribution along the central axis of HFCCT, when cross section types changed from λ � 0.4, λ � 0.7, λ � 1.0 to circle. Earth pressure concentrated on top of HFCCT decreased outwardly. at is, the more the VEP is concentrated on the HFCCT axis, the faster the decrease rate will be as the distance from the HFCCT axis increases. However, due to right-angle mutations of the rectangular cross section, the soil at the boundary of internal and external soil column subsided, and downward friction of the external soil column was transferred to the internal soil column, resulting in a greater concentration of VEP at the two sides of HFCCT and reduced VEP at the center, exhibiting an M-shaped distribution. In short, the VEP at the top of the HFCCT decreased according to λ � 1.0, circle, λ � 0.7, and λ � 0.4, and rectangle, beyond this range (the width of the HFCCT); it successively decreased in the order of λ � 0.4, λ � 0.7, circle, rectangle, and λ � 1.0. Figure 5(b) shows LEP distribution on the sides of HFCCT for case C1. e LEP can be divided into three stages along the HFCCT height: stabilization (stage 1), increase (stage 2), and decrease (stage 3). e LEP remained unchanged as the HFCCT height increased for stage 1 and gradually decreased in order of rectangular, λ � 0.4, λ � 0.7, λ � 1.0, and circle. Within the stage 2 range, LEP increased with increasing HFCCT height. In stage 3, LEP decreased with HFCCT height. e decrease in LEP was in a sequence of circle, λ � 1.0, λ � 0.7, λ � 0.4, and rectangular. e difference is that for cross section of the circle, LEP reached its maximum value at 0.8 times the height of HFCCT when cross section optimization coefficient of λ � 0.4, 0.7, 1.0, while for the rectangular cross section, LEP reached its maximum value at 0.6 times the height of HFCCT.

Earth Pressure Distribution.
Based on the above analysis of VEP and LEP, the difference in earth pressure distribution of HFCCT with different sections was not obvious. erefore, a method, equivalent load method, for determining optimal section type of HFCCT by calculating the average earth pressure was proposed. e calculated average earth pressure of HFCCT for case C1 is shown in Figure 6. e average VEP on top of HFCCT decreased first and then increased, reaching its minimum value of 17.89 kPa at λ � 1.0 and its maximum value of 20.37 kPa at the rectangular cross section. However, average LEP was inversely proportional to average VEP; the maximum value of 8.65 kPa and the minimum value of 7.26 kPa were located at λ � 1.0 for the rectangular cross section, respectively. In conclusion, the earth pressure exerted on HFCCT was the most unfavorable when the cross section was rectangular and most favorable at optimal cross section optimization coefficient of λ � 1.0. erefore, optimal cross section optimization coefficient of λ � 1.0 can be considered as the optimal cross section optimization coefficient for HFCCT without load reduction. Figure 7 shows the VD distribution of soil particles for case C1.

Variation of Displacement.
e VD of soil particles symmetrically increased with increasing distance from the HFCCT axis, presenting an inverted V-shaped distribution. As the cross section shape changed, the VD of soil particles increased with cross section optimization coefficient of λ ranging from 0.4, 0.7, to 1.0. is is because, the larger λ, the sharper the arching tendency of HFCCT, and the easier it is for soil particles to slide downward. However, the VD of soil particles was relatively small at the HFCCT axis and increased sharply at two sides of HFCCT when the cross section type was rectangular and circular. Moreover, the growth rate of VD was larger than those of the other HFCCT sections. Figure 8 shows the RVD and height of the equal settlement plane of soil particles for case C1. e RVD of soil particles was proportional to the height of equal settlement plane, which decreased first and then increased. Gradually, they both decreased as the type of cross section changed from rectangular to cross section optimization coefficient λ � 1.0; however, they gradually increased when the type changed from λ � 1.0 to circle and reached the minimum value of 0.024 mm and 0.582 m at cross section optimization coefficient of λ � 1.0, respectively. e nephograms on VD of soil particles for case C1 are shown in Figure 9. Figures 9(a)-9(d) show that the VD of soil particles on top of HFCCT was smaller than that on the sides of HFCCT. is is attributed to differences in stiffness of HFCCT and backfill soil. However, with increasing backfill height, the VD of soil particles changed slowly, while the RVD decreased gradually until there was a plane of equal settlement (see the black line in the figure). By comparing with different cross section types of HFCCT, the equal settlement plane decreased gradually as cross section type changed from rectangular to λ � 1.0 and started to increase when cross section type changed from λ � 1.0 to circle, consistent with variation results of RVD in Figure 8.
Based on the relationship of VEP, RVD, and height of equal settlement plane, in the absence of load reduction, the smaller the RVD of the external soil column and internal soil column, the lower the height of the equal settlement plane, which led to downward friction of the external soil column that was transferred to the internal soil column to be smaller, Advances in Civil Engineering making the VEP to be smaller. erefore, VEP, RVD, and height of the equal settlement plane presented the minimum value at the cross section optimization coefficient of λ � 1.0.

Variation of Microscopic Contact.
To investigate load distribution and transfer mechanism of soil particles around HFCCT for case C1, we evaluated various factors at the microscopic level, such as porosity, coordination number, and contact force chain. Figure 10 shows the relationship between porosity and coordination number for case C1. Porosity was inversely proportional to coordination number. e maximum value (0.155) of porosity and the minimum value (3.82) of coordination number simultaneously appeared when section optimization coefficient λ was 1.0. Combined with Figure 5(b), it is determined that the larger the porosity, the larger the LEP, but the smaller the coordination number of soil particles, the smaller the VEP on top of HFCCT and RVD among soil particles. Figure 11 shows the relationship between contact force chain of soil particles and cross sectional shape of HFCCT. As the cross section type of HFCCT changed from rectangular to λ � 1.0, contact force chains on top of HFCCT became sparse (see the area enclosed by the green arc in the figure); due to large impact of soil arching, it was concentrated towards the top of HFCCT (see the green arrow in the figure). However, as the cross section type of HFCCT    changed from λ � 1.0 to circular, contact force chains became denser and VEP on top of HFCCT correspondingly increased. e variation was consistent with results of earth pressure in Figure 6, indicating that cross section optimization coefficient of λ � 1.0 can be considered as the optimal cross section optimization coefficient among the HFCCT sections.

Effects of Expanded Polystyrene.
In this section, the EPS load reduction model of HFCCT was established with the same size and cross section optimization coefficient λ � 1.0 on the basis of the above HFCCT. Effects of EPS characteristics (density and laying position) on load reduction on HFCCT were analyzed. Regarding EPS characteristics, the most favorable values of thickness and width were selected [15], which were 0.15 m and 0.3 m, respectively.

Influence of Expanded Polystyrene Density.
To assess the effects of EPS density on earth pressure, the influence of density variations from 12 kg/m 3 to 30 kg/m 3 on earth pressure, VD, and microscopic contact of soil particles was determined.
(1) Earth Pressure Distribution. Figure 12 Figure 13 shows the average earth pressure of HFCCTfor case C2. e average VEP was inversely proportional to average LEP, reaching its minimum value (5.2 kPa) and maximum value (10.4 kPa) at the density of ρ � 15 kg/m 3 , respectively. erefore, 15 kg/m 3 can be regarded as the optimal density.
(2) Variation of Displacement. Figure 14 shows the VD distribution of soil particles for case C2. e VD of soil particles was distributed in a V shape. is is because EPS has a large compression deformation characteristic, which makes settlement of internal soil column to be greater than that of external soil column, resulting in negative settlement differences.
e VD of soil particles changed with EPS density, which was sequentially decreased based on EPS densities of 15 kg/m 3 , 12 kg/m 3 , 20 kg/m 3 , and 30 kg/m 3 . When the density of ρ was 15 kg/m 3 , the settlement difference and RVD between the internal and external soil column was largest while the VEP on top of HFCCT was least when the density of ρ � 15 kg/m 3 . Earth pressure distribution was most reasonable at this density.

Influence of Expanded Polystyrene Laying Position.
When the EPS laying position changed from 0 m to 0.08 m on top of HFCCT, the earth pressure, VD, and microcontact of soil particles were evaluated.
(1) Earth Pressure Distribution. e influence of different laying positions on VEP distribution is shown in Figure 15(a). e VEP on top of HFCCT was distributed in a U shape along the HFCCT central axis. As the EPS laying position increased from 0 m to 0.05 m, the VEP on top of HFCCT did not exhibit a significant change. However, as the EPS laying position was further increased (e.g., L � 0.08 m), VEP on top of HFCCT increased significantly, and the load reduction effect disappeared. Distribution of LEP with different EPS laying positions is shown in Figure 15(b). It is shown that LEP decreased with increasing EPS laying position, which occurred in a descending order: 0 m, 0.02 m, 0.05 m, and 0.08 m.
Variations in average earth pressure for case C3 are presented in Figure 16. With the increase in EPS laying position, the average VEP increased while the average LEP decreased. From the earth pressure distribution perspective, this implies that the further the EPS laying position, the greater the VEP on the top and the smaller the LEP, which means that the load on HFCCT was unfavorable.
(2) Variation of Displacement. Figure 17 shows the VD distribution of soil particles for case C3. e settlement difference in the internal soil column was greater than that of the external soil column, while the VD of soil particles decreased with increasing distance from the HFCCT axis, when the EPS laying position was within the 0.05 m range. However, as the EPS laying position increased further, the VD of soil particles gradually decreased, reaching its Advances in Civil Engineering 7 minimum value at the laying position of 0.08 m, implying that the VD of soil particles at the HFCCT axis was smaller than that on both sides of HFCCT. Moreover, EPS had no load reduction effects on earth pressure on top of HFCCT, consistent with results shown in Figure 15(a). Figure 18 shows the VD nephograms of soil particles for case C3. Due to laying of EPS, the VD of soil particles on top of HFCCT severely sunk, when compared to the VD on both sides of HFCCT. is is because of the huge deformation of EPS. Furthermore, with increasing EPS laying position, load reduction effect of EPS was away from the top of HFCCT (see the height of h in Figure 18). Figure 19 shows contact force chains of soil particles for case C3. Earth pressure distribution was significantly changed through its own compressibility, which transferred the load from the top of HFCCT to the sides of HFCCT. As a result, contact force chains were mainly distributed on side walls and foundations of HFCCT, and the distribution of contact force chains on top of HFCCT was significantly reduced due to soil arching effect formed by EPS (see the red circle in the figure). With increasing EPS laying position, contact force chain was denser and earth pressure was larger on both sides of HFCCT. However, the soil arching effect did not change (see the red circle in the figure). Moreover, the load in the area that was immediately adjacent to the top of HFCCT

Effects of Concrete Wedges.
To reduce load distribution around the HFCCT and improve load reduction efficiency, load reduction measure of the combination of optimized cross section type with load reduction using EPS and CW was evaluated. e width W � 0.3 m, density ρ � 15 kg/m 3 , laying thickness T � 0.15 m, laying position L � 0 m of EPS, and cross section optimization coefficient λ � 1.0 were selected.

Influence of Concrete Wedges Height.
To establish the effects of CW height on earth pressure, variations in earth pressure, VD, and microcontact of soil particles were analyzed as CW height changed from 0.20 m to 0.38 m.
(1) Earth Pressure Distribution. To establish the load reduction effect of CW, the column-soil stress ratio was defined as the average load ratio on top of CW to soil particles between the two CWs. Variations in the column-soil stress ratio and average VEP distribution on top of HFCCT for case C4 are shown in Figure 20. e column-soil stress ratio was inversely proportional to average VEP distribution, presenting the maximum value (11.2 kPa) and minimum value (3.25 kPa) at the CW height of H � 0.32 m.
is indicated that a large amount of earth pressure was shared with CW, which reduced the earth pressure around HFCCTat the CW height of 0.32 m.
(2) Variation of Displacement. e influence on RVD and equal settlement plane for case C4 is shown in Figure 21.
RVD was approximately the same as the height of equal settlement plane, which increased first and then decreased with increasing CW height. Both reached their maximum values, −0.155 mm and 0.885 m, respectively, at the CW height of H � 0.32 m, indicating that settlement difference between internal soil column and external soil column was obvious at the CW height of 0.32 m. Figure 22 shows VD nephograms of soil particles for case C4. Due to CW arrangement, the VD of soil particles above CW was significantly reduced (see the green area in the figure). While the VD of soil particles above HFCCT increased sharply in a certain range of CW height (see Figures 22(a)-22(b)) and then decreased with the increase of the CW height (see Figure 22(b)-22(c)), which reached the maximum value (−1.639 m) at the CW height of 0.32 m. erefore, the CW height of 0.32 m can be considered optimal.
(3) Variation of Microscopic Contact. Figure 23 shows contact force chains of soil particles for case C4. Contact force chains were mainly distributed above CW. e distribution of contact force chains on top of HFCCT was significantly reduced due to soil arching effects caused by EPS, and the scope of soil arching effect was further expanded (see the blue curve in the figure). Moreover, contact force chains on both sides of HFCCT were denser at CW height of H � 0.20 m and 0.38 m than that at CW height of H � 0.32 m, indicating that the load on both sides of HFCCT was smallest at CW height of H � 0.32 m.

Influence of Concrete Wedges Width.
Given the influence of CW width on earth pressure on HFCCT, variations in earth pressure, VD, and microcontact of soil particles were analyzed as CW width changed from 0.12 m to 0.2 m.
(1) Earth Pressure Distribution. Figure 24 shows that the column-soil stress ratio was inversely proportional to average VEP, reaching its maximum value (12.75 kPa) and minimum value (3.125 kPa), respectively, at CW width of W � 0.17 m. is indicated that CW the most earth pressure and earth pressure above HFCCT decreased the most at CW width of W � 0.17 m. erefore, earth pressure at CW width  of 0.17 m was the most reasonable, while the force around HFCCT was the most favorable.
(2) Variation of Displacement. e effect on RVD and equal settlement plane for case C5 is shown in Figure 25. RVD distribution was approximately in accordance with that of height of equal settlement plane, which increased first and then decreased with increasing CW width. Both reached the maximum values, −0.147 mm and 0.86 m, respectively, at CW width of 0.17 m.
(3) Variation of Microscopic Contact. Figure 26 shows contact force chains of soil particles for case C5. Contact force chains above CW became denser, and the trend of upper arch gradually increased above the HFCCT (see the blue curve in the figure); the load was larger as CW width increased from 0.17 m to 0.22 m (see the green arrow in the figure).

Discussion
According to simulation results of PFC2D, earth pressure distribution of HFCCT was different as load reduction measures changed. First, cross section type of the structure was optimized by changing cross section optimization coefficient to reduce earth pressure. In addition, earth pressure in HFCCT changed from inverted V-shaped distribution to      14 Advances in Civil Engineering U-shaped distribution, and earth pressure was greatly reduced by combining the optimized section type of HFCCT with EPS. Furthermore, earth pressure of HFCCT can further be reduced by combining optimized section type with EPS and CW. Under the conditions of ultrahigh backfill, the combination of optimized section type with EPS and CW can effectively reduce earth pressure and improve the safety of the structure. We evaluated the variations in earth pressure and VD of soil particles around HFCCT under three measures when backfill material around HFCCT was only loess. In the modeling process, HFCCT structure and foundation are regarded as rigid bodies. In practice, HFCCT is a three-dimensional mechanical structure, while it is only simulated as a two-dimensional structure in this paper. erefore, subsequent studies should use PFC3D simulation analyses. In addition, other influencing factors such as the height and width of EPS were not evaluated. However, we established the influence of the three measures on earth pressure distribution on HFCCT.

Conclusions
e PFC2D software was used to assess the influence of different cross section types and load reduction material characteristics on earth pressure distribution around HFCCT.
e optimal values of effects under three load reduction measures were obtained. Several conclusions can be drawn from this study: (1) Earth pressure distribution was optimized by changing the cross section optimization coefficient of HFCCT. As cross section optimization coefficient increased, average VEP, RVD, and height of equal settlement plane first decreased and then increased, while the average LEP first increased and then decreased. e turning point was the cross section optimization coefficient of 1.0. erefore, the most beneficial vault for HFCCTstructure was determined as the cross section optimization coefficient λ � 1.0 in terms of changing the cross section type.
(2) e combination of optimized section type of HFCCT with EPS load reduction significantly changed earth pressure distribution through its compressibility, which transferred the load from the top of HFCCT to the sides of HFCCT. From the perspective of changing the density and laying location of EPS, when the density of ρ was 15 kg/m 3 while the laying location of L was 0 m, the average VEP, RVD, and height of equal settlement plane was advantageous. erefore, an optimal density of 15 kg/m 3 is recommended, and EPS should be laid near the top of HFCCT during actual construction to achieve better load reduction effects.
(3) e combination of optimized section type with EPS and CW load reduction further changed earth pressure distribution, which reduced soil settlement on both sides of HFCCT and indirectly increased the settlement of internal soil column. A larger settlement difference was formed, which reduced the VEP on top of HFCCT. Moreover, the load reduction effect was different with the change in height and width of CW. When height was 0.32 m and width was 0.17 m, the average VEP, RVD, and height of equal settlement plane were favorable. us, an optimal CW height of 0.32 m and width of 0.17 m are recommended for effective load reduction.

Data Availability
e data used in this work are available from the corresponding author by request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.
Acknowledgments is study was supported by the National Natural Science Foundation of China (51668036 and 51868041) and the Basic Research Innovation Group Project of Gansu Province (21JR7RA347).