Effects of Staggered Plates on the Uplift Failure State and Bearing Capacity of NT-CEP Pile Groups

Abstract

Plate position is an important parameter of a New Type Concrete Expanded-Plate (NT-CEP) pile. In this study, two small-scale test models and two, four, six, and nine finite element models were established using a visual small-scale model of half-section piles, an undisturbed soil pull-out test, and the ANSYS finite element software R19.0. The NT-CEP pile groups were studied with the plates set at staggered positions. This study mainly analyzes the displacement contours, stress curves, and load-displacement curves under the action of vertical tension and determines the influence of staggered plate positions on the performance and bearing capacity of the NT-CEP pile group, which provides theoretical support for its application in practical engineering. The bearing plate positions affect the performance of the pile group. The stress distribution in each pile in the pile group is uneven when plate positions are staggered, and the pile with the lower plate position bears a greater force. This has a great influence on the bearing capacity of the NT-CEP pile group. If allowed, the plates can be first set at the same position. If appropriate, the plates can be set in staggered positions; however, a reasonable distance between the upper and lower plates should be considered.

1. Introduction

The variable cross-section pile is developed from the straight pile [1]. New Type Concrete Expanded-Plate (NT-CEP) piles have evolved and been optimized using various variable cross-section piles [2,3,4]. The additional bearing plate significantly improves the bearing capacity for compression, overturning, and especially uplifting [5], which makes it possible for NT-CEP piles to be utilized in large bridge projects, high-rise buildings, and other building groups with higher requirements for uplift capacity. Since the compressive resistance is usually much larger than the frictional resistance [6], the NT-CEP pile has obvious advantages in uplift bearing capacity compared with straight hole and equal cross-section pile [7]. During pile construction, pile-forming machines such as drilling, expanding, and cleaning machines are used to significantly shorten the hole-forming time, improve the hole-forming quality, and reduce mud discharge to the greatest extent possible for environmental protection. The NT-CEP pile, shown in Figure 1, is a type of variable-cross-section pile with advanced international usage in the pile foundation market. At present, a large number of theoretical and experimental studies have been carried out on the bearing capacity of single NT-CEP piles and soil failure around piles, and systematic research results have been achieved, such as the influence degree of different parameters on bearing capacity [8], the research on bearing capacity calculation formula [9], etc. However, research on NT-CEP pile groups is relatively lacking, which limits the development of NT-CEP piles [10,11]. The plate position was the main factor influencing the NT-CEP pile-bearing capacity, especially in the pile group layout. The research group previously studied the related performance of the same plate position (bearing plate in the same horizontal plane), but research on setting plates at staggered plate positions (bearing plates not in the same horizontal plane) has not yet been carried out. To expand our understanding of NT-CEP pile groups further, it is necessary to conduct in-depth research on the performance of an NT-CEP pile group when the bearing plates are set using staggered plate positions.

Compared with other software packages, ANSYS can get better simulations in static, quasi-static, and dynamic problems and linear analysis. In this study, a new type of real-time observation of the NT-CEP double pile half-section small-scale model undisturbed soil test method and an ANSYS finite element software simulation analysis method were used for comparative analysis. A single half-section NT-CEP pile model was used to reduce the actual pile body with a 1:40 ratio and convert it into a half-section form. This test method can make us observe the failure state of soil in real-time and change the status quo so that the failure process of pile foundation cannot be observed. ANSYS finite element software simulation analysis used the same real project pile size equal proportion modeling, with all parameters set with the actual project, either the same or similar, and maximized the restoration of site conditions to make the simulation results more real and effective. Models with two, four, six, and nine piles were created, including corner piles, side piles, and middle piles [12]. Five types of NT-CEP pile groups were analyzed, and the corresponding data were extracted by comparing and analyzing the test displacement images, displacement contours, stress curves, and load-displacement curves [13]. The influence of the staggered position of the bearing plate on the bearing capacity of the NT-CEP pile group and the change law of the failure state of the soil around the pile were summarized, which provided a solid theoretical basis for the subsequent research.

Due to the complexity and variability of geological conditions in practical engineering, to make the bearing plates of the NT-CEP pile group in the soil layer with better stress, it is less likely that all the bearing plates in the pile group are in the same horizontal plane. The research purposes of this paper are as follows: (1) to qualitatively analyze whether the bearing capacity of pile groups is affected by setting plates at staggered positions; (2) to indicate what are the similarities and differences of the bearing capacities of pile group foundations with different numbers of piles affected by setting plates at staggered positions; and (3) to provide a reference for further research.

2. Experimental Study on Uplift Resistance of Undisturbed Soil in Small-Scale Model of Visual Half-Section Pile

The main research topic of this study was the change in the soil failure state around NT-CEP piles. The field equal-scale test carried out in advance verified that the equal-scale reduction test corresponds well with the actual change in the soil failure state around the NT-CEP piles. Therefore, the equal-scale reduction of the specimen size has little influence on the test results, and the size effect can be ignored in this study.

2.1. Preparation of Half-Section Model Pile

A single half-section NT-CEP pile model was used to reduce the actual pile body with a 1:40 ratio and convert it into a half-section form. The main purpose of this test is to observe the change of soil failure state around piles. In pile foundation engineering, under the condition that the construction quality can be guaranteed, the pile body itself will hardly be damaged before the soil body. To ensure that the pile body will not be damaged in the test, the pile body material is aluminum alloy. Compared with other metals, the stiffness and elastic modulus of aluminum alloy are less different from those of concrete, and its price is relatively low. The detailed dimensions of the pile body are shown in Figure 2 and

Table 1. Model sizes.

Case	L1 Left Pile (mm)	L1 Right Pile (mm)	L (mm)	D (mm)	S (mm)	D (mm)	R (mm)	Slope Angle of the Plate (°)	X (mm)
A1	40	160	200	12.5	80(4R)	52.5	20	α = 36° β = 21°	37.5
A2	160	160
A3	80	120
A4	120	120

. The four cases of NT-CEP model piles manufactured for this study are shown in Figure 3.

2.2. Preparation of Undisturbed Soil Samples and Pile Soil Samples

Undisturbed silty clay was collected from the stable soil layer on the construction site in Figure 4, and its specific parameters are listed in

Table 2. Parameters.

Material	Density (t/mm3)	Elastic Modulus (MPa)	Poisson’s Ratio	Cohesion (MPa)	Friction Angle (°)	Expansion Angle (°)
Silty clay	1.488 × 10−9	25	0.35	0.04355	10.7	10.7

. After considering the boundary effect, a soil sampler made of 5 mm thick steel plate was set to 360 mm × 200 mm × 280 mm. During the test, the steel plate was replaced with tempered glass, as shown in Figure 4.

Undisturbed clay samples taken from the stabilized soil layer on the construction site were unpacked, and the double pile model was buried in the test soil samples. After the pile was buried, the pile-soil specimen was prepared, and a loading test was performed, as shown in Figure 5.

2.3. Test Equipment and Test Process

The multifunctional test bench used in this test is shown in Figure 6a. To ensure that each pile in the double pile was loaded synchronously, a synchronous loading connector designed by the research group was used. The elements of the connectors are shown in Figure 6b.

The prepared pile-soil specimens were installed on the loading table, and the loading device was installed. The specific steps were given as follows. (1) Adjusting the position of the soil sampler: we placed the soil sampler on the loading platform and handled it with care during the period. To ensure that the pull force applied to the pile top was vertical upward, it was necessary to align the model pile with the reserved loading hole of the upper beam back and forth to ensure that the force transmission tie rod was vertical. (2) Installing the soil sampler pressure plate: with the increase in load, we avoided the overall displacement between the soil sampler and model pile, which may have affected the accuracy of the test. It was necessary to fix the soil sampler on the loading platform as a whole to prevent the relative displacement between the soil sampler and the loading platform. (3) Installing vertical loading device and displacement meter: we placed the jack between the cross beam and the upper connecting plate, and the center position of the jack was aligned with the center position of the cross beam to ensure the direction of applying vertical tension. (4) Installing observation glass: we fixed the observation glass on the soil sampler with a fixing clip and stuck a layer of foam glue on the surface of the fixing clip to avoid crushing the glass. (5) Loading: after the installation of the test device, we loaded it. When loading, a special person was responsible for recording the displacement data and recording the whole loading process by video. Before 0.8 kN, 0.05 kN was used as the first-class load step, and after 0.8 kN, 0.1 kN was used as the first-class load step.

3. Analysis of Pull-Out Test Results of NT-CEP Double Piles

3.1. Analysis of Uplift Failure Process of Double Piles

Because the research group systematically studied NT-CEP double piles when setting plates at the same plate position in the early stage, the A3 case was taken as an example for analysis, and its uplift failure process is shown in Figure 7.

In the initial loading stage, the displacements at the tops of the two piles were small. When the load increased to 0.4 kN, the pile-soil separation occurred under the two pile plates, as indicated by the green arrows in Figure 7a. At the load of 0.65 kN, the soil at the ends of the two piles began to crack, as shown in Figure 7b, because the tensile stress was greater than the bond force between the particles simultaneously, and a slip zone began to appear on the plate, which is seen as a watermark in the test indicated by the red line in Figure 7b.

As the load continued to increase, the cracks at the ends of the two piles gradually expanded, and the slip area on the plate increased continuously, as shown in Figure 7c. At the same time, the relative displacement between the NT-CEP piles and the soil around the piles also increased continuously, which led to an increasingly evident separation of the piles and soil under the double piles.

When the load increased to 0.9 kN, 45° punching oblique cracks began to appear on the upper left of the two piles, as shown in Figure 7d. The pile length L1 on the right pile plate was 6R (R is the cantilever diameter of the plates) and reached a reasonable uplift position; however, punching failure still occurred. This is because the central connection between the two plates was on the 45° punching extension line of the left pile, as shown in Figure 7e. This type of punching failure of the A3′ pile was due to the punching of the A3 pile, which is called “secondary punching failure” or “integral punching failure” of two piles. The secondary punching failure has a very adverse impact on the ultimate bearing capacity of two piles, which should be avoided in practical engineering. Furthermore, the angle of two adjacent pile plates with respect to the horizontal should not be close to 45°.

3.2. Comparative Analysis of Final Failure State of Double Piles

The final failure states of the undisturbed soil pullout tests for the four cases of the half-section NT-CEP pile double pile model are shown in Figure 8.

According to our previous research results, when the load-bearing plates of two piles are set at the same position and L1 is greater than 4R, the soil between the two pile plates cracks, and the soil on the plate slips, as shown in Figure 8b,d.

When the two pile bearing plates were set at staggered positions and the angle between the connecting line of the center points of the two pile bearing plates was about 45° to the horizontal, the two piles underwent overall punching failure with a very adverse impact on the bearing capacity. The overall punching line is shown in Figure 8c. When the vertical distance between the bearing plates of the two piles was large and the left pile L1 was less than 4R, the mutual influence between the two piles was small. Punching failure occurred first, as shown by the yellow line in Figure 8a. At this point, the soil crack propagation at the end of the right pile plate was not obvious, as shown in the green circle in Figure 8a, and the bearing capacity of the pile groups could be fully exerted.

3.3. Analysis of Load-Displacement Curve of Double Piles

The load-displacement curves of the four cases of double pile tests are shown in Figure 9.

(1)

The load-displacement curves of the four cases in the initial stage of loading were essentially the same. The pile top displacement increased linearly with an increase in the load, which mainly depended on the friction between the pile and soil to bear the load.

(2)

With the increase in load, the displacement of the pile top of the A3 case was less than that of the A1 case, and the bearing capacity of the A3 case was greater than that of the A1 case because the L1 of the left pile of the A1 case was 2R, while the L1 of the left pile of the A3 case was 4R. Therefore, the bearing capacity of double piles with staggered plates depends on the single pile with the smaller L1, whereas the single pile with a larger L1 has little influence on the bearing capacity of the double piles.

(3)

The bearing capacities of cases A2 and A4 were greater than those of cases A1 and A3, indicating that the staggered position of the double piles had adverse effects on the bearing capacity.

4. Finite Element Model Construction

The basic assumptions are as follows:

(1)

This paper analyzes the failure state of soil around the NT-CEP pile group under vertical tension and the bearing capacity of the whole pile model; to make the NT-CEP pile not destroy itself under the ultimate bearing capacity, the material of the pile body is set as a linear elastic material.

(2)

The variable of the NT-CEP pile group in this paper is only the load, so the soil around the pile adopts a single soil layer. To keep consistent with the silty clay in actual engineering, the soil layer is set as a linear elastic material.

(3)

The size setting of the NT-CEP pile group model is consistent with the actual project, so the influence of size effect on the results of finite element simulation cannot be considered.

(4)

In finite element modeling, the size of the soil model (length and width) is much larger than that of the NT-CEP pile model, so the influence of boundary conditions on the analysis results cannot be considered.

(5)

In the process of finite element simulation, it is assumed that soil and pile are ideal materials with uniform material and the same property in each direction, and because the model load is continuously applied with surface load, the influence of time can be ignored.

4.1. Determination of Model Size

Referring to our previous research results [7], a reasonable pile size, pile distance, and soil range of the NT-CEP pile were determined. The pile length (L = 8000 mm), the pile diameter (D = 500 mm), the cantilever diameter (R = 800 mm), the uphill angle (α = 36°), the downhill angle (β = 21°), the plate diameter (D = 2100 mm), the pile spacing (S = 3200 mm), and the clear distance (X = 1500 mm) were held constant. The length, width, and height of the soil model were 11,000, 11,000, and 3000 mm, respectively. The models evaluated in this study are the two-, four-, six- and nine-pile cases, as presented in

Table 3. Modeling of pile case model (R = 800 mm is the cantilever diameter of plate).

	2-Pile				4-Pile		6-Pile		9-Pile
case	B1	B2	B3	B4	C1	C2	D1	D2	E1	E2
L1	2R/8R	8R/8R	4R/6R	6R/6R	5R/8R	8R/8R	5R/8R	8R/8R	5R/8R	8R/8R

.

4.2. Selection of Constitutive Relation, Element Type, Material Property and Grid Division

The elastic–plastic constitutive model was selected for the concrete constitutive model [14], the Duncan–Chang model was used for the soil model in the nonlinear elastic model [15], Solid65 [16,17] was used for the pile unit type, and Solid45 was used for the soil unit type, referring to the aforementioned small-scale test data [18]. The material properties of the soil and reinforced concrete around the piles in this study are shown in

Table 4. Setting table of pile-soil parameters.

Material	Density (t/mm3)	Elastic Modulus (MPa)	Poisson’s Ratio	Cohesion (MPa)	Friction Angle (°)	Expansion Angle (°)	Pile-Soil Friction Coefficient
Concrete	2.25 × 10−9	3.465 × 104	0.2	--	--	--	0.3
Silty clay	1.488 × 10−9	25	0.35	0.04355	10.7	10.7

, and the mapping grid division was selected for grid division [19,20].

4.3. Constraint Setting and Load Application

Constraints were imposed on the soil model to prevent the irregular displacement of the entire soil during the loading process, which affected the accuracy of the simulation results. Considering that the force of the simulation analysis is vertical tension, when constraining each surface with a hexahedral shape, the degrees of freedom of the top surface in the Y-direction are not constrained, whereas the other five surfaces are constrained. All the above parameters were invariant, and only the load value was increased for analysis. The loading of each pile was 100 kN until the curve of the finite element analysis converged.

5. ANSYS Finite Element Analysis of NT-CEP Pile Double Piles

5.1. Analysis of Y-Direction Displacement Contours of Double Piles

The corresponding Y-direction displacement contours of the B1 case with loads of 300, 600, 700, and 900 kN were selected for the loading process analysis, as shown in Figure 10.

Before the load reached 300 kN, the pile top displacement increased linearly with the load, as shown in Figure 10a. When the displacement reached 20 mm, the load was approximately 600 kN, as shown in Figure 10b. The displacement at this time was much larger than the displacement caused by the same load when the plate is set at the same plate position, which shows that the bearing capacity is greatly reduced by setting the plate at the wrong position, mainly because the pile length L1 on the left pile plate is smaller than 2R. Because the position difference between the bearing plates of the two piles was too large, there was a large vertical displacement difference, which shows a color change in the contour. With an increase in the load, the displacement difference in the Y-direction of the two piles increased continuously. As shown in Figure 10c,d, a large uneven settlement would occur in real-world applications, which should be avoided in the design phase.

5.2. Analysis of Load-Displacement Curves of Double Pile Finite Element Simulations

(1)

At the initial stage of loading, the change trends of the curves were essentially identical. At this time, the displacements of the pile tops of the four cases of model piles were small, and the displacements increased linearly with an increase in load.

(2)

By comparing curves B1 and B3 with cases B2 and B4, it was found that the bearing capacities of cases B1 and B3 were notably smaller than those of the latter, which shows that setting plates at staggered positions had a very unfavorable impact on the bearing capacity of the double piles.

(3)

The bearing capacity of the B1 case was smaller than that of the B3 case, which shows that the uplift-bearing capacity of the double piles mainly depends on the bearing plate with a smaller L1 case.

6. Comparative Analysis of Load-Displacement Curves between Pull-Out Tests of NT-CEP Double Pile Model and ANSYS Simulations

In Figure 9 and Figure 11, the curve change trend of the NT-CEP double pile was essentially the same in the initial stage of loading, and the NT-CEP double pile mainly provided the bearing capacity by measuring friction.

There are obvious inflection points in A1 and B1 at 0.6 kN and 600 kN, respectively. Combined with the experimental images and simulated contours, it can be observed that punching inclined cracks appeared in the bearing plate of the left pile. The states of the inflection points in the two figures are approximately the same, confirming the consistency between the NT-CEP double pile finite element simulation analysis and the half-section model test.

The bearing capacity sequence of the two diagrams is 2 > 4 > 3 > 1, and the general trends are similar, which shows that the test and simulation results are largely consistent, confirming each other.

7. Analysis of ANSYS Finite Element Simulation Results of Four-, Six-, and Nine-Pile Models

The above analysis proves that the basic assumptions and simulation parameters of the ANSYS finite element simulation are correct; therefore, piles four, six, and nine were primarily analyzed by finite element simulation. To avoid punching failure when L1 is less than 4R, and simultaneously avoid secondary punching failure or integral punching failure of the two piles, L1 values were selected as 5R and 8R, and the approximate modeling layouts are shown in Figure 12.

7.1. Analysis of Y-Direction Displacement Contours

By analyzing the changes in the contours in Figure 13, we can see the following.

The four-pile model displacement contour analysis indicates that in the later stage of loading, the influence range of the soil between the piles in C2 case and the soil around the two piles on the left side was larger than that of T1 case, while the influence range of the soil around the two piles on the right side was the same as that of T1 case. This is owing to the Y-direction distance between the bearing plates, and the bearing plates at the lower position will squeeze the soil between piles and thus squeeze the upper bearing plates, resulting in greater displacement of the NT-CEP piles and the soil around piles at the upper position, thus reaching the failure state first. This has a very unfavorable impact on the overall bearing capacity of NT-CEP piles.

The displacement contour of the six-pile model shows that under the limit load, owing to the Y-direction distance between the bearing plates, the displacement between the corner piles of the D2 case and the surrounding soil is larger than that of the D1 case owing to the upward squeezing of the four corner piles by the middle-side piles. This leads to the failure of the D2 and D1 cases first, thus greatly reducing the bearing capacity of the NT-CEP piles. Therefore, the construction design of the six-pile model should mainly set the plates at the same plate position.

According to the displacement contour analysis of the nine-pile model, the damage range and degree of soil around the pile in the E2 case were smaller than those in the E1 case at the later stage of loading, which was different from that of the four- and six-pile models. This is because the number of piles in the nine-pile model was excessive, and the interaction between the plates was too large. When the plates were set in staggered positions, the soil pile group effect caused by the vertical distance between plates was less than that caused by the mutual influence between the plates. Overall, the nine-pile model with a staggered plate position had a better bearing capacity than the non-staggered model. If an NT-CEP pile group with nine piles is required, a staggered plate position can be considered.

7.2. Analysis of Pile Stress Curve Results

Points on both sides of the pile bodies of cases C1 and C2 were selected for stress analysis, as shown in Figure 14. After extracting the corresponding data, the XY direction stress diagrams of the pile bodies under the limit load state were drawn, as shown in Figure 15.

Analysis of the changes in the pile stress curves in Figure 15 shows the following.

Under the action of the ultimate load, the stress of the C1 case changes greatly at three points, i.e., 12, 13, and 14, of the bearing plate position, indicating that the end bearing force provided by the bearing plate has a significant influence on the bearing performance of the uplift piles. This causes an excessive concentration of shear stress on the bearing plate and its adjacent piles, which has a stricter requirement for the strength of the bearing plate. The maximum value of the shear stress appears at position 12, that is, at the junction of the bearing plate and upper pile body. Compared with the shear stresses of positions 12 and 11, the value of the shear stress exhibits a sudden change, almost from zero to the maximum value, which is representative of the brittle failure of reinforced concrete materials.

The stress curve of the C2 case was more irregular than that of the C1 case on the same plate. Although the stress of the C2 case was still near the load-bearing plate, the stresses on the left and right sides of the C2 case were quite different, and the maximum stresses of both the left and right piles were greater than that of the C1 case. Because the position of the right pile body plate was lower when it reached the limit state, its maximum stress was greater than that of the left pile. This is due to the vertical distance between the bearing plates, which leads to an uneven distribution of the force of among the piles in the pile group. A pile with a lower bearing plate position bears more force, which should be considered in the design calculations.

7.3. Analysis of Load-Displacement Curves

Analysis of the changes in the load-displacement curves in Figure 16 shows the following.

(1)

In the four-pile models, a comparison of the curve trends of C1 (plates at the same position) and C2 (plates at staggered positions) showed that the two curves basically coincided in the middle and early stages of loading, and the Y-direction distance between bearing plates due to the staggered positioning had no significant influence on the bearing capacity. When the load reached 20 MPa, an adverse effect on the bearing capacity began to appear. The bearing capacity of the C1 case was always greater than that of the C2 case until the ultimate displacement was reached. In summary, the bearing capacity of the C1 case was more advantageous than that of the C2 case, and the overall bearing capacity of the C1 case was better for practical applications. In design and construction, after considering the geological situation and construction requirements of the site, it is more reasonable to prioritize the non-staggered plate layout for four-pile groups.

(2)

The data of D1 and D2 for six-pile models are similar to those of the four-piles in the middle and early stages of loading. However, after the load reaches 25 MPa, the influence of the Y-direction distance of the staggered plates on the bearing capacity is obviously greater than that of the four-piles groups, i.e., the slope of the D2 case curve becomes larger and faster. The pile top displacement of Case D2 occurred 100 mm earlier than that of Case D1, indicating that the overall bearing capacity of Case D2 was significantly lower than that of Case D1. In the six-pile arrangements, setting the plates at the same position remains the best choice.

(3)

In the nine-pile models, a comparison of E1 (plates at the same position) with E2 (staggered plate positions) showed that before the load reached 25 MPa, the nine-pile models performed similarly to the four- and six-pile models. However, when the load was between 25 and 62 MPa, the nine-pile model was fundamentally different from the four- and six-pile models. When the load reached 25 MPa, the influence of the Y-direction distance of the plates on the bearing capacity began to appear. Under the same load, the displacement of the E2 case was larger than that of the E1 case; however, the displacement difference between the two curves decreased continuously until the load reached 63 MPa because the soil pile group effect caused by the Y-direction distance of the load-bearing plates was almost the same as the pile group effect caused by the interaction between the plates. After reaching 62 MPa, the two curves exhibited different trends. Under the same load, the displacement of the E2 case was smaller than that of the E1 case, and failure occurred in this manner. This shows that with nine piles the bearing capacity is somewhat greater with staggered plates. Under a nine-pile arrangement, both the staggered and non-staggered plate positions were reasonable selections.

8. Conclusions

(1)

When the angle between the central point of the bearing plate of two piles and the horizontal was approximately 45°, punching failure of the two piles occurred.

(2)

The bearing capacity of double piles with staggered plates primarily depends on the single pile with a small L1.

(3)

When bearing plates of pile groups are in staggered positions, the Y-direction distance between the plates will cause oil interaction between piles to occur in the lower bearing plates. This will affect the upper bearing plates, resulting in the greater displacement of the NT-CEP piles and soil around the piles, thus reaching the failure state first.

(4)

The stress distribution in each pile in the pile group was uneven when plate positions were staggered, and the pile with the lower plate position bore a greater force.

(5)

The effect of the soil pile group caused by the Y-direction distance of the bearing force in the four- and six-pile groups was greater than that caused by the interaction of piles at the same position. Therefore, the bearing capacity of the piles at the same position was greater than that of the piles in the staggered position. The bearing capacity of the piles at the same position was greater than that at the staggered position.

(6)

Although a Y-direction distance existed between the load-bearing plates in the nine-pile group, that distance also increased. The pile group effect caused by the Y-direction distance was smaller than that caused by the mutual influence between plates with the same plate position; however, the ultimate bearing capacity was not significantly different.

Therefore, the bearing plate positions affect the performance of the pile group. If allowed, the plates can be first set at the same position. If appropriate, the plates can be set in staggered positions; however, a reasonable Y-direction distance between the upper and lower plates should be considered.

9. Outlook

In this study, the NT-CEP pile groups with staggered plates are studied by experiments and finite element analysis, which fills the blank of related research fields. However, this study only carries out qualitative analysis but does not carry out quantitative analysis. However, there are many combinations of different types of plates, and only one of them is selected in this study, which is far from enough. In the follow-up research, we should conduct qualitative and quantitative research on various types of plates, and further improve the theory of the NT-CEP pile research.