Influence of the Internal Friction Resistance on the Vertical Compressive Bearing Capacity of Large-Diameter Steel Pipe Piles

Abstract

Current calculation methods for the vertical bearing capacity of steel pipe piles are predominantly designed for smaller diameters and do not account for the soil inside the pile. This necessitates an evaluation of their applicability to piles with diameters exceeding 2.0 m. This study aims to refine the existing formula for calculating vertical bearing capacity, as outlined in the Port Engineering Foundation Code of China, by investigating the vertical bearing capacity of large-diameter steel pipe piles through numerical simulations. By analyzing the relationship between the internal friction resistance of the soil core within the pipe and the bearing capacity for diameters ranging from 2 m to 10 m, this paper proposes a revised formula specifically tailored for steel pipe piles with diameters greater than 2 m, incorporating the effect of the soil core. The validity of the proposed formula is then confirmed through comparison with field data from four large-diameter steel pipe piles. The results demonstrate that the modified method proposed in this study performs better than the original formula when compared with the measured data.

1. Introduction

Due to China’s unique marine geological environment, large-diameter steel pipe piles are extensively used in offshore wind farms and sea-strait crossing bridge projects, becoming a primary foundation type for these applications [1,2,3]. Meanwhile, steel pile foundations have good anti-fatigue characteristics [4,5,6,7,8]. Calculating the vertical bearing capacity of steel pipe piles must consider the soil plugging effect, a critical factor [9,10]. Current methods for calculating large-diameter steel pipe piles are detailed in the “Specification for Pile Foundations of Port Engineering” [11], the “Technical Code for Building Pile Foundations” [12], the API [13], and the DNV [14] codes. These specifications define vertical bearing capacity as the sum of pile side friction resistance and end resistance but do not clarify the influence of internal friction resistance from the soil core on the ultimate vertical bearing capacity. This method is suitable for small-diameter piles but inadequate for large-diameter piles (exceeding 2 m) [15,16] where the soil core effect must be explicitly considered. The innovation of this work is to put forward an efficient method to calculate the vertical bearing capacity of steel pipe piles with diameters greater than 2 m with the consideration of inner friction resistance in the pile.

Empirical evidence suggests that for large-diameter steel pipe piles, the soil plugging effect is minimal, resulting in a nearly flat interface between the internal soil and the pile surface. Field inspection tests are limited to measuring the combined internal and external frictional resistance of the pile walls due to methodological constraints. Existing standards typically account only for external friction resistance, leaving the internal component unspecified, while base resistance is considered to act across the entire cross-section of the pile. According to API specifications, for piles without a soil plug, it is more accurate to consider only the area of the pile end ring when calculating vertical bearing capacity.

Therefore, evaluating the soil core’s effect on vertical bearing capacity across various diameters is crucial. This phenomenon has been explored by several researchers. Stefanoff [17] investigated the impact of drainage on soil plugging. He found that the pile end’s bearing capacity increased exponentially with the ratio of soil plug length to pile diameter (h/d) under drained conditions, while the soil’s internal effective stress remained relatively constant under undrained conditions. Stevens [18] examined the plugging rate’s effect on vertical bearing capacity in both cohesive and cohesionless soil conditions. Gallagher et al. [19] analyzed the vertical bearing capacity of a 0.168 m diameter steel pipe pile during penetration. They measured internal friction resistance and determined that the soil plugging effect on bearing capacity was minimal. Guo et al. [20] used the discrete element method to simulate the penetration and plugging processes of large-diameter piles. They identified pile diameter and soil plug height as critical factors influencing bearing capacity. Qin [21] and Li et al. [22,23] mentioned that soil coring inside the pipe pile also influences the lateral capacity of the piles. Li et al. [24] examined the vertical bearing capacity of pile foundations with distributed geopolymer post-grouting, demonstrating significant improvements in bearing capacity compared to traditional methods. Zhu et al. [25] explored the effect of vertical shaft resistance on the lateral behavior of large-diameter piles, highlighting the complex interactions between soil and pile under various loading conditions. However, few previous studies have focused on the effect of internal friction resistance on the vertical compressive bearing capacity of large-diameter steel pipe piles. The relevant work of other scholars over the years is shown in Table 1

Table 1. Related work of other scholars.

Main Reference	Research Object	Main Conclusion
Stefanoff (1977) [17]	Soil plug effect	Pile tip resistance increases exponentially with the ratio of soil plug length to pile diameter.
Stevens (1982) [18]	Soil plug effect	The plugging rate’s effect on vertical bearing capacity in both cohesive and cohesionless soil conditions.
Gallagher (2007) [19]	Soil plug effect	Determined that the soil plugging effect on bearing capacity was minimal.
Guo (2015) [20]	Soil plug effect	The influence of soil race in the process of large-diameter pile penetration was determined by discrete element simulation.
Qin (2022) and Li (2017), (2024) [21,22,23]	Soil plug effect	It is determined that the soil inside the pile has influence on the lateral bearing capacity of the foundation.
Li (2024) [24]	Soil plug effect	Influence of distributed grouting on bearing capacity
Zhu (2018) [25]	Size effect	Presents a numerical solution for the resisting moment that is suitable for any type of side friction model.

This paper conducts a numerical simulation of the vertical bearing capacity of large-diameter steel pipe piles. Through analyzing the relationship between internal friction resistance and the vertical capacity of pipe piles with diameters ranging from 2 to 10 m, a revised formula for calculating the vertical bearing capacity of steel pipe piles with diameters greater than 2 m is proposed. The validity of this formula is confirmed by comparing it with the measured data of four large-diameter steel pipe piles. The innovation of this work lies in putting forward an efficient method to calculate the vertical bearing capacity of steel pipe piles with diameters greater than 2 m while considering the internal friction resistance within the pile.

2. Numerical Simulation and Parameter Selection

2.1. Finite Element Model Selection

In a specific offshore wind project, large-diameter steel pipe piles were used. The steel used for the pipe piles is DH36 (a high-strength ship steel with an elastic modulus of 210 MPa and a unit weight of 78.5 kN/m³). The average pile length is 67.0 m, with a diameter of 6 m and a wall thickness varying between 5.5 cm and 7 cm along the pile length. To simplify the model, the pile parameters are summarized in Table 2. Typical soil conditions and their parameters are presented in Table 3. The soil parameters used in the study are from the CPT test in the field. In the numerical simulation, to reduce boundary effects, the soil model is defined as a cylinder with a diameter of 120 m and a height of 100 m [26,27]. The soil is characterized using the Mohr–Coulomb (M-C) model. Boundary conditions include constraints on lateral displacements in the horizontal direction and vertical displacements at the bottom surface. The contact between pile and soil is made on all sides, and the pile surface with a larger height is set as the main control surface. The tangential behavior of the contact surface is defined as a penalty function. The selection of friction coefficient is detailed in Section 2.4 below, and the normal direction of the contact surface is defined as hard contact.

Table 2. Parameters of steel pipe pile in finite element analysis.

Diameter (m)	Wall Thickness (mm)	Length of Pile (m)	Embedment Length (m)	Elastic Modulus (kPa)	Poisson’s Ratio	Constitutive Model
6	60	67	55	2.1 × 108	0.3	Ideal elastic

Table 3. Parameters of soil in Finite element analysis.

Layers No.	Soil Layer Properties	Layers Thickness (m)	Soil Density kg/m3	Compression Modulus MPa	Poisson’s Ratio	Internal Friction Angle (°)	Cohesion (kPa)
1-1	silt	2.1	1825	9.26	0.25	24	11
1-2	silty clay	5.0	1490	2.54	0.30	11.4	19
2-1	silt	4.6	1820	10.55	0.25	25	9
2-2	silty clay	2.8	1735	5.08	0.29	19.4	38.3
3-1	silt	4.6	1815	9.38	0.25	26	10
3-2	silty sand	9.1	1735	13.51	0.28	15.3	27
4-1	silty clay	13.3	1590	5.71	0.28	12.9	26.8
4-2	silty clay with sand	5.0	1785	9.61	0.23	32.5	50.0
5-1	silty clay	3.1	1715	3.44	0.28	15.9	40.5
6-1	silty sand	19.6	1810	11.16	0.23	35	8.0
7-1	silty clay	10.3	1805	8.83	0.26	18.1	65

2.2. Effects of Meshing and Interface

During the simulation, a soil model is created based on soil layer conditions. Figure 1 illustrates the foundation size and grid division results. Due to varying layer thicknesses, the mesh sizes differ. We verified that mesh size minimally affects the final result’s accuracy. Soil and pipe pile units are modeled as three-dimensional solid units (C8D8R). Assuming equal friction coefficients inside and outside the pile wall, it is expressed as tan(0.75φ) [28,29], where φ is the soil’s internal friction angle. A weighted average algorithm calculated the friction coefficient of different soil layers, resulting in an average friction coefficient μ = 0.28.

Figure 1. Model size and finite element mesh division.

2.3. Steps of Model Calculation

Figure 2 is the flow chart of the simulation calculation steps. The calculation steps of finite element analysis are divided into the ground stress balance stage, steel pipe pile installation stage, and loading stage. In it, gravity with an acceleration of 9.8 m/s² acts on all three steps:

Figure 2. Flowchart of calculation procedure.

Step1 Ground stress balance: in the first step, the whole pile foundation is invalid, and the soil mass is only once ground stress balance to approximate the actual ground stress state.

Step2 Pile foundation installation: in the second step, activate the pile foundation that was invalid in the previous step, and then invalidate the soil in the overlapping part of the pile foundation and activate the contact between the pile and the soil.

Step3 Loading stage: the last step is to apply the concentrated force load to the reference point of the pile top surface.

As can be seen from Figure 3, the vertical bearing capacity of a single pile obtained by numerical simulation is approximately 30,000 kN, whereas the vertical bearing capacity of a single pile obtained through field testing is around 32,000 kN. The main reason for this disparity is that the soil core inside the steel pipe pile is gradually compacted during the penetration process. Although a pile diameter of 2 m is considered a large-diameter pile, the penetration depth of the steel pipe pile is as deep as 55 m. Hence, the soil core inside is extremely dense and the soil plug effect is obvious, leading to a significant increase in the bearing capacity of the pile end of the soil plug. In numerical simulation, the steel pipe pile is “placed” into the soil through a one-step Model Change. As a result, any soil squeezing effect and soil plugging effect cannot be taken into account, so the simulation result will be smaller than that of the field test pile.

Figure 3. Comparison of simulation results with field tests.

2.4. Model Calculation and Loading

In offshore wind projects, the vertical load on steel pipe piles mainly comes from the piles’ own weight and the load transmitted from the superstructure. The vertical bearing capacity consists of three components: external friction resistance of the pile wall (Q_f), internal resistance (Q_i), and base resistance at the pile end (Q_b). In the numerical simulation, these components are analyzed by setting the contact relationships (friction coefficients) between the steel pipe pile and the surrounding soil. The analysis focuses on steel pipe piles with diameters of 6 m simulated under three distinct conditions:

CASE 1: This case simulates the total bearing capacity of the steel pipe pile (Q_total) with a friction coefficient of 0.28 applied to both the inner and outer surfaces.

CASE 2: Here, the friction coefficient is set at 0.28, but the internal friction coefficient is set to 0. This condition isolates the external friction force (Q_f) and the base resistance (Q_b) at the pile end.

CASE 3: In this scenario, the friction coefficient is 0.28, while the external friction coefficient is set to 0. This isolates the internal friction force (Q_i) and the base resistance (Q_b) at the pile end.

2.5. Simulation Results

In this Section, the bearing capacity of steel pipe piles was analyzed, evaluating the internal and external frictional resistances of the pile body and the base resistance under three distinct conditions (CASE 1, CASE 2 and CASE 3). Contour maps showing vertical displacement near the pile tip under ultimate load conditions are presented in Figure 4. Figure 4a shows that in CASE 2, where the internal friction coefficient is zero, the soil core settlement is nearly identical to that of the steel pipe pile. Conversely, Figure 4b shows that in CASE 3, where the external friction coefficient is zero, soil settlement occurs primarily around the pile, with significantly greater settlement beneath the pile base.

Figure 4. Contour maps of vertical displacement near pile tip: (a) settlement of soil near pile end in CASE 2 (b) settlement of soil near pile end in CASE 3.

Based on the results obtained under different conditions, Q-s curves for the steel pipe piles were derived and are shown in Figure 5. Typical bending Q-s curves were observed in CASE 1 and CASE 2, while a progressive curve was noted in CASE 3. For the progressive curve, the vertical bearing capacity reaches its ultimate stage when the settlement reaches 0.05D (where D represents the pile diameter). Therefore, in CASE 3, the pile reaches its ultimate bearing capacity when the settlement reaches 300 mm.

Figure 5. Q-s curves of steel pipe piles under different conditions.

The bearing capacities under various conditions are summarized in Table 4. During the simulation, the steel pipe pile is subjected to gravitational forces, which are not considered in the standard calculation methods specified by the criteria. Therefore, gravitational effects must be included in the results. The gravitational force on the pile is 5771 kN. Consequently, the external friction resistance of the pile wall (Q_f) is 40,918 kN, the internal friction resistance (Q_i) is 11,862 kN, and the base resistance at the pile end (Q_b) is 18,391 kN, resulting in a total bearing capacity Q_total of 71,171 kN.

Table 4. Vertical bearing capacity of steel pipe piles under different conditions.

CASE No.	Simulated Bearing Capacity (kN)	Composition of Bearing Capacity
CASE 1	71,171	Qtotal = Qf + Qi + Qb
CASE 2	59,309	Qf + Qb
CASE 3	30,253	Qi + Qb

3. Influence of Soil Coring on Large Diameter Steel Pipe Pile

3.1. Simulation Condition

To investigate the impact of soil coring on large-diameter steel pipe piles, a series of numerical simulations of their vertical bearing capacity was performed and is listed in Table 5. The study analyzed the relationships between internal friction resistance, bearing capacity, and pile diameters ranging from 2 to 10 m. Each model was simulated under the three conditions detailed in Section 2.4.

Table 5. Parameters of steel pipe piles under different diameters.

Diameter (m)	Wall Thickness (cm)	Area of Pile End (m2)	Length of Pile (m)	Embedment Depth (m)	Elastic Modulus (kPa)	Poisson’s Ratio	Constitutive Model
2	2	0.124	67	55	2.1 × 108	0.3	Ideal elastic
3	3	0.280
4	4	0.498
5	5	0.778
7	7	1.524
8	8	1.991
9	9	2.519
10	10	3.110

3.2. Result Analysis

Figure 6 illustrates the Q-s curves for piles with diameters ranging from 2 to 10 m, based on load–settlement relationships under different conditions. Table 6 presents the bearing capacities of steel pipe piles with varying diameters. The table includes external shear friction capacity, internal friction shear capacity, and bearing capacity at the pile end ring. In Figure 4, CASE 1 and CASE 2 yielded typical bending Q-s curves, while CASE 3 produced a progressive curve. For the progressive curve, the vertical bearing capacity reaches its ultimate stage when the settlement reaches 0.05D (where D is the pile diameter). Thus, in CASE 3, the pile reaches its ultimate bearing capacity when the settlement is 0.05D.

Figure 6. Q-s curves of steel pipe piles under different conditions and diameters: (a) 2 m steel pipe pile (b) 3 m steel pipe pile (c) 4 m steel pipe pile (d) 5 m steel pipe pile (e) 7 m steel pipe pile (f) 8 m steel pipe pile (g) 9 m steel pipe pile (h) 10 m steel pipe pile.

Table 6. Vertical bearing capacity of 2–10 m steel pipe pile under different conditions.

Diameter (m)	Percentage of Qfm (%)	Percentage of Qim (%)	Percentage of Qbm (%)	Weight of Piles (kN)	Bearing Capacity (kN)
					Qf	Qi	Qb	Q
2	83.59	8.72	7.69	641	16,836	1756	1549	20,141
3	75.26	13.24	11.50	1443	22,686	3991	3466	30,143
4	70.69	17.00	12.32	2565	30,513	7336	5316	43,165
5	65.25	17.56	17.19	4008	37,915	10,204	9989	58,108
6	57.49	16.67	25.84	5771	40,918	11,862	18,391	71,171
7	54.32	14.66	31.02	7855	45,767	12,352	26,137	84,256
8	48.97	13.88	37.16	10,260	47,724	13,524	36,212	97,460
9	43.59	15.03	41.38	12,985	49,160	16,952	46,674	112,786
10	39.53	18.08	42.39	16,031	52,037	23,798	55,795	131,630

Based on the results in Figure 6 and Table 6, Figure 7 illustrates the average resistances of external friction, internal friction, and pile tip stress as a function of pile diameter. Figure 7a shows that average external friction resistance decreases linearly with increasing diameter, indicating that larger pile diameters reduce support from external shear capacity. Figure 7b demonstrates that average internal friction resistance increases with diameter, suggesting that larger pile diameters enhance internal shear capacity support. Figure 7c reveals that average pile base resistance varies with diameter; it increases from 4 m to 8 m but stabilizes at 18,000 kPa for diameters exceeding 8 m.

Figure 7. The resistances of pile body and pile tip changed with diameters: the average value of (a) external friction, (b) internal friction, (c) the resistances of pile tip changed with diameters.

To further analyze the variation of friction resistance and pile tip resistance with pile diameter, we define two parameters: α, representing the sum of simulated or measured internal and external frictional resistances divided by the geotechnical recommended external resistance, and β, representing the simulated or measured bearing capacity of the pile tip divided by the geotechnical recommended bearing capacity. The dimensionless results are shown in Figure 8a,b.

Figure 8. Dimensionless parameters varied with the diameter of piles: (a) α and (b) β varied with the diameter of piles.

From Figure 8a, the relationship between α and pile diameter can be approximated by the formula α = 0.0341D + 1.0714, with a correlation coefficient of 0.86. For β, when the pile diameter ranges from 2 to 4 m, β is approximately 2.5; when the diameter exceeds 8 m, β is approximately 3.8. For diameters between 4 and 8 m, a linear interpolation is used.

4. Formula Correction

The current Chinese criteria calculate the vertical bearing capacity of large-diameter steel pipe piles by summing the lateral friction resistance and the overall end-bearing capacity. This approach is primarily designed for small-diameter piles, where the plugging effect is significant, and the internal soil within the steel pipe pile and the soil at the pile end can be considered a unified system. However, for steel pipe piles with diameters exceeding 2 m, the plugging effect is less pronounced, as shown in the force diagram in Figure 9. In such cases, treating the pile end and internal soil as a single entity is not appropriate. Instead, it is more accurate to include the internal friction force in calculating external frictional resistance. Therefore, revising the calculation formula for the bearing capacity of steel pipe piles is necessary.

Figure 9. Force diagram of steel pipe pile.

Based on the formula for calculating the vertical bearing capacity of steel pipe piles in the Port Engineering Foundation code, a revised formula for steel pipe piles with diameters greater than 2 m has been proposed:

$$Q_k=Q_s+Q_b=\alpha {\displaystyle \sum f_{si}{A}_{si}+\beta q_b}{A}_p$$

(1)

where Q_k is the standard value of the ultimate bearing capacity of single pile (kN); Q_s and Q_b are standard values of ultimate bearing capacity of pile side and pile end (kN), respectively; U is outside section of pile body(m); f_si is Standard value of ultimate lateral friction resistance of unit area (kPa), which can be valued according to specifications or local experience; As_i is the area of the pile body passing through the i layer soil (m²); q_b is the standard value of ultimate resistance per unit area (kPa), which can be valued according to specifications or local experience; A_p is the peripheral area of pile tip (m²); α is correction coefficient of the external friction, when D = 2 m, α = 1.14, D = 10 m, α = 1.41, when D = 2 m–10 m using linear difference method; β is correction coefficient of bearing capacity of pile tip, when D = 2 m–4 m, β = 2.5, when D > 8 m, β = 3.8, when D = 4 m to 8 m using linear difference method.

5. Engineering Example Verification

To validate the proposed Formula (1), two offshore wind farm projects were analyzed. These projects involved four steel pipe piles with diameters from 2 m to 2.8 m and depths over 50 m. Field test results for vertical bearing capacity, shaft capacity, and pile base capacity were compared with the revised formula, the Technical Code for Building Pile Foundations, and the Port Engineering Foundation standards.

5.1. Case Study 1

An offshore wind farm near Shanghai, featuring 38 wind turbines [30], uses steel pipe piles for its foundations. In this project, static loading tests were carried out on two piles (Figure 10). The parameters of these piles are detailed in Table 7. The primary soil layers consist of silty clay and silt, with their parameters provided in Table 8. Under a load of 50,000 kN, the pile top settlements for S1 and S2 are 46.43 mm and 40.28 mm, respectively, while the pile tip settlements are 9.25 mm and 8.28 mm, respectively. Therefore, the ultimate capacities of both S1 and S2 exceed 50,000 kN. The total bearing capacities of the piles, calculated using recommended limits for friction and end resistance, are summarized in Table 8.

Figure 10. Static loading test of piles: (a) loading equipment and (b) a structure that provides a reaction force.

Table 7. Parameters of S1 and S2 steel pipe piles.

Pile Number	Diameter (m)	Wall Thickness (mm)	Embedment Depth (m)	Pile Top Elevation (m)	Pile Tip Elevation (m)
S1	2.8	40	72.5	8.2	−85.5
S2	2.8	40	72.5	8.2	−85.5

Table 8. Parameters of soil for S1 and S2.

Pile No.	S1 and S2
Top elevation of soil layer (m)	−13.5	−27.7	−31.2	−61.5	−73.5	Total (kN)
bottom elevation of soil layer (m)	−27.7	−31.2	−61.5	−73.5	−85.5
Soil Thickness (m)	14.2	3.5	30.3	12	12
Soil layer properties	Silty clay	Silty clay	Silty sand	fine sand	fine sand
Characteristic value of bearing capacity of foundation fak (kPa)	80	110	180	230	260
Standard value of ultimate lateral resistance qsik (kPa)	15	45	60	70	80
Standard value of end face resistance qpk (kPa)	——	——	4000	5000	6000
Measured side friction (kPa)	22	56	72	101	121
Measured friction friction qsiA (kN)	2747	1723	19,181	10,656	12,766	47,073
friction resistance of each layer qsikA (kN)	1873	1385	15,984	7385	8440	35,067

The total bearing capacities of the two piles were calculated using two different codes, as summarized in Table 9. In the modified formula, α = 1.170 and β = 2.5. Table 9 shows that the bearing capacities calculated using both the Design Code for Building Foundations and the Specification for Pile Foundations of Port Engineering are lower than the measured values. However, the results from the modified formula are closer to the actual bearing capacities. This indicates that the calculation methods in the Design Code for Building Foundations and the Specification for Pile Foundations of Port Engineering are overly conservative. Therefore, the results obtained using the modified formula are more reasonable and align better with the actual bearing capacities.

Table 9. Vertical bearing capacity of S1 and S2 steel pipe piles.

Calculation Details for Compared Piles		S1	S2
Measured end resistance (kN)		2819	2823
Coefficient of soil plug effect at pile tip, λp		0.686	0.686
Standard value of ultimate end resistance (kPa)		6000	6000
Ultimate end resistance (kN)	by Standard of the design of building foundation	9047	9047
	by Specification for pile foundation of Port Engineering	3297	3297
	by modified formula	5200	5200
Total bearing capacity (kN)	by in-situ measured	49,891	49,891
	by Standard of the design of building foundation	44,114	44,114
	by Specification for pile foundation of Port Engineering	38,364	38,364
	by modified formula	46,228	46,228

5.2. Case Study 2

In this Section, vertical compressive bearing capacity tests are conducted on two steel pipe piles at a certain offshore wind farm (Figure 11), whose parameters are shown in Table 10. The main soil layers are silty clay and silt, the parameters are shown in Table 11.

Figure 11. Loading system during static loading test.

Table 10. Parameters of S3 and S4 steel pipe piles.

Pile Number	Diameter (m)	Wall Thickness (mm)	Embedment Depth (m)	Pile Top Elevation (m)	Pile Tip Elevation (m)
S3	2.0	50	71.5	−10.1	−64.0
S4	2.0	50	77.5	−10.5	−70.0

Table 11. Parameters of soil for S3 and S4.

Pile No.	Soil Thickness (m)	Soil Layer Properties	Characteristic Value of Foundation Bearing Capacity fak (kPa)	Standard Value of Side Resistance qsik (kPa)	Standard Value of End Resistance qpk (kPa)	Measured Side Resistance (kPa)	Measured Resistance of Each Layer qsiA (kN)	Calculated Resistance of Each Layer qsikA (kN)
S3	2.62	mud	40	12	——	23	378	197
	7.90	Silty clay	50	18	——	54	2679	893
	3.00	Silty sand	150	50	——	67	1262	942
	8.20	Silty sand	200	65	——	107	5510	3347
	9.80	Silty clay	70	48	——	105	6462	2954
	16.30	Silty clay	80	50	——	94	9622	5118
	1.70	Silty clay	180	65	3600	95	1014	694
	4.08	Fine sand	260	80	5600	128	3280	2050
S4	1.37	Silty sand	100	32	——	32	275	275
	7.9	Silty clay	50	16	——	40	1984	794
	3.3	Silty sand	150	50	——	63	1306	1036
	7	Silty sand	200	65	——	77	3385	2857
	10.1	Silty clay	70	48	——	80	5074	3045
	12	Silty sand	220	70	4800	103	7762	5275
	4.6	Silty clay	180	65	3600	111	3207	1878
	7.4	Silty sand	260	80	4500	135	6274	3718
	1.9	Silty clay	180	65	3600	97	1157	776
	3.93	Silt	260	70	4500	114	2814	1728

From Table 9, Table 10 and Table 11, the pile tip elevations for S3 and S4 are −63.70 m and −69.60 m, respectively, with bearing layers of fine sand and silt. The measured ultimate capacities of these piles are 32,800 kN and 34,850 kN, respectively, while the end-bearing capacities are 1724 kN and 1590 kN. The total bearing capacities of these piles, calculated using recommended limits for friction and end resistance, are summarized in Table 11. The total bearing capacities, computed using two different codes, are shown in Table 12, where α = 1.14 and β = 2.5 in the proposed formula. Table 12 shows that the calculated total bearing capacities, using both the Design Code for Building Foundations and the Specification for Pile Foundations of Port Engineering, as well as the modified formula, are lower than the measured values. However, the results from the modified formula are closer to the actual bearing capacities. This suggests that the methods prescribed by the Design Code for Building Foundations and the Specification for Pile Foundations of Port Engineering are overly conservative, and the modified formula provides a more accurate estimate of bearing capacity.

Table 12. Vertical bearing capacity of S3 and S4 steel pipe piles.

Calculation Details for Compared Piles		S3	S4
Measured end resistance (kN)		1724	1590
Coefficient of soil plug effect at pile tip, λp		0.326	0.314
Standard value of ultimate resistance (kPa)		5600	4500
ultimate end resistance (kN)	by Design code for building foundation	2306	2221
	by Specification for pile foundation of Port Engineering	1766	1766
	by modified formula	4286	3444
Total bearing capacity (kN)	by in-situ measured	31,392	34,828
	by Design code for building foundation	21,206	23,602
	by Specification for pile foundation of Port Engineering	17,962	23,147
	by modified formula	22,749	27,968

6. Conclusions

The existing calculation criterion of vertical bearing capacity of pile foundation does not consider the internal friction resistance provided by large diameter pile core. The vertical bearing capacity of large-diameter steel pipe piles is studied by the numerical simulation method. On this basis, a revised formula for calculating the vertical bearing capacity of steel pipe piles with a diameter greater than 2 m is proposed. To verify this formula, field data from two offshore wind farm projects were used to compare the field test results of vertical bearing capacity, friction resistance, and pile tip resistance with the predicted results of the revised formula, technical criteria for Building Pile Foundation, and criteria for Port Engineering Pile Foundation. The following conclusions are drawn:

• For the external friction resistance, the pile diameter has a linearly positive effect on it at 2 m < D < 10 m, while it has no influence on it when the diameter is smaller than 2 m or larger than 10 m.
• For pile tip bearing capacity, the correction coefficient β is 2.5 for diameters between 2 m and 4 m, and 3.8 for diameters over 8 m. For diameters from 4 m to 8 m, β varies linearly.
• The calculation methods in the Technical Code for Building Pile Foundations and the Specification for Pile Foundations of Port Engineering are overly conservative. The modified formula provides a more accurate estimate of bearing capacity.
• The friction resistance inside the soil core has a certain influence on the vertical bearing capacity of the steel pipe pile. Through the finite element simulation and field test results, it can be observed that the inner friction resistance of the steel pipe pile does not exceed 30% of the outer friction resistance.
• The effect of soil squeezing during pile driving and the effect of soil compaction around the pile have a great influence on the simulation results, which is also a problem to be considered in subsequent numerical simulation research.