Bearing Capacity Design of Strength Composite Piles Considering Dominant Failure Modes and Calibrated Adjustment Coefficients

Abstract

Significant discrepancies persist between the predicted and measured bearing capacities of Strength Composite (SC) piles in engineering practice, largely due to incomplete consideration of dominant failure modes and the absence of scientifically calibrated adjustment coefficients. Existing design specifications treat side and tip resistance inconsistently and often neglect failures induced by insufficient pile material strength, which compromises accuracy and reliability. To address these limitations, this study systematically analyzed static load test data from 159 SC piles across 44 projects. Statistical evaluation revealed clear dependencies between soil type, pile–soil interface performance, and failure mechanisms, from which stratified adjustment coefficients of side resistance and the unified adjustment coefficient of tip resistance were derived. On this basis, a new calculation method for pile capacity was developed that, for the first time, explicitly integrates material strength limitations and interface failure mechanisms into design. Validation against 112 additional test piles confirmed that over 50% of predicted-to-measured ratios approximated 1.0, and 82.1% fell within ±20%. The study proposes a calculation method for SC pile bearing capacity that is broadly applicable, simple in form, and explicitly accounts for dominant failure modes, thereby providing both theoretical rigor and engineering practicality.

1. Introduction

With the rapid expansion of urban construction, excessive settlement and deformation of soft soil foundations have become a critical challenge. Ground improvement techniques such as cement-soil mixing piles and precast concrete pipe piles are widely adopted. However, each method has its own limitations: cement-soil piles are economical and easy to construct but prone to crushing due to low strength [1,2,3], whereas precast piles provide high strength and stiffness but often suffer from inefficient material utilization caused by soil failure [4,5,6]. To address these limitations, the Strength Composite (SC) pile has been developed (also known as the Stiffened Deep Cement Mixing pile in some studies). As illustrated in Figure 1, an SC pile is formed by driving a precast pile into a large-diameter cement-soil mixing pile before hardening, thereby combining the high bearing capacity of precast piles with the significant side friction of cement-soil piles [7]. As shown in Figure 2, based on the relative length of the inner and outer cores, the strength composite piles can be further classified into long-core, equal-core, and short-core types. This hybrid configuration overcomes the limitations of both pile types, offering notable technical and economic advantages. It has been increasingly used in coastal soft soil regions of China [8,9,10,11].

The SC pile, as a typical annular structure, exhibits significant advantages in mechanical behavior and bearing capacity compared to traditional pile types. Scholars worldwide have conducted extensive and in-depth research on the mechanical properties, confinement mechanisms, and design methods of annular-section concrete members. Liang et al. [12] employed numerical simulations to systematically investigate the mechanical behavior of circular double-skin concrete-filled steel tubular (DCFST) stub columns under axial compression, revealing the enhanced confinement effect provided by the outer and inner steel tubes on the core concrete. Ayough et al. [13] established the three-dimensional finite element model to analyze the influence of cross-sectional shape and confinement mechanism on the concrete strength, energy absorption capacity, and ductility of DCFST columns with a square outer tube and a circular inner tube, proposing a new design equation based on stress distribution. Teng et al. [14] demonstrated that the hybrid double-skin tubular column structural system exhibits excellent ductility and energy dissipation capacity under axial and combined bending-shear loads through experimental and numerical analyses. Zhang [15] further investigated the seismic performance of hybrid double-skin tubular columns filled with high-strength concrete under combined axial and cyclic lateral loading. Tests indicated that hybrid DSTCs possess excellent ductility and seismic resistance even when high-strength concrete with a cylinder compressive strength. These studies collectively indicate that the annular section significantly improves the strength and ductility of concrete through a multi-material synergistic confinement mechanism, resulting in mechanical properties superior to those of solid sections or single-skin tubular members [16]. The advantages of such structures in axial bearing capacity, energy dissipation, and seismic performance provide important theoretical references and practical guidance for the design of SC piles.

At present, research on SC piles by domestic and international scholars has mainly focused on their static behavior. Wang et al. [17] conducted field tests and numerical simulations to demonstrate that the unique annular-layered structure of the Stiffened Deep Cement Mixing (SDCM) pile prevents the failure of surrounding soft clay, enabling it to sustain substantial loads while ensuring the effective transfer of superstructure loads to deeper soil strata. Voottipruex et al. [18] conducted experimental studies and three-dimensional finite element analysis to demonstrate that the vertical bearing capacity of SC piles is approximately 2.2 times that of Deep Cement Mixing (DCM) piles, while the lateral bearing capacity is nearly 15 times greater. Li et al. [19] discussed the load-bearing performance of cemented soil in SDCM piles under vertical load and found that the cemented soil primarily provides lateral shaft resistance under vertical loadings through field tests and finite element simulations. Wang et al. [20] further investigated the longitudinal and lateral responses of single SC piles using theoretical and numerical methods, confirming that the surrounding cement-soil significantly reduces pile deflection and bending moments. Cao et al. [21] derived an analytical expression for the settlement of SC piles based on the Alamgir model and identified the sublayer compression modulus and pile diameter as the main influencing factors. Zhang et al. [22] proposed an analytical solution for the consolidation of composite foundations reinforced with cement-soil mixing and precast piles by employing a modified equal-strain assumption, providing theoretical guidance for settlement prediction. Wongler et al. [23] investigated that the damage mode of SDCM pile under load mainly depends on the inner-core size, area ratio of the inner-core to the DCM pile, and the strength of the DCM pile based on model experiments and numerical calculations. Yan et al. [24] integrated laboratory testing with machine learning techniques to establish a predictive model for bond–slip behavior at the core–cement-soil interface, offering a novel approach to evaluate slip-induced failure mechanisms.

Beyond static behavior, some scholars have investigated the dynamic characteristics of SC piles. Dai et al. [25] derived a three-dimensional approximate solution for the horizontal dynamic response of SC piles in fractional viscoelastic unsaturated foundations under lateral excitation at the pile tip using Timoshenko beam theory. Yan et al. [26] analyzed the influence mechanisms of physical parameters on the dynamic stiffness and damping at the pile head in a dynamic coupled system of stiffened composite piles and unsaturated soil, and concluded that appropriately increasing the pile length helps improve its seismic performance. Deng et al. [27] proposed an analytical method based on elastodynamics theory to determine the dynamic response of SC piles under vertical harmonic loading. These studies above provide the theoretical basis for analyzing the bearing mechanisms and failure modes of SC piles under dynamic loading.

Although theoretical research on SC piles has become increasingly mature, discrepancies remain between the bearing capacity values calculated using design specifications and those measured from field static load tests in engineering practice [28]. The primary reasons for these discrepancies lie in the different failure modes considered across design specifications and the lack of consensus regarding adjustment coefficients for side resistance and tip resistance. To address this issue, this study compiles and analyzes geotechnical investigation reports and static load test data from 44 engineering projects, comprising 159 test piles. The data are categorized according to soil type, pile configuration, and core inclusion ratio. By systematically comparing the Yunnan provincial specification, Jiangsu provincial specification, and the national specification, this study refines the adjustment coefficients for side and tip resistance in existing capacity formulas and proposes a more practical calculation formula to address failure modes caused by insufficient pile material strength and pile-soil interface slippage for the bearing capacity of SC piles. This calculation method better reflects practical engineering conditions and contributes to improving the theoretical framework for predicting the bearing capacity of stiffened composite piles.

2. Materials and Methods

2.1. Current Calculation Methods for Bearing Capacity of Strength Composite Piles

At present, the national specification <Technical Specification for Strength Composite Piles> (JGJ/T 327-2014) [29], the Jiangsu provincial specification <Technical Specification for Strength Composite Piles> (DGJ32/TJ 151-2013) [30], and the Yunnan provincial specification <Technical Specification for Concrete Core Mixing Piles> (YB 2007) [31] provide clear regulations on the bearing capacity of both short-core/equal-core SC piles and long-core SC Piles. The specific calculation methods are shown in

Table 1. Design methods for the bearing capacity of stiffened composite piles in the Yunnan provincial specification.

Name of the Specification	Areas of Application	Design Methods for Bearing Capacity
		Failure Modes	Short-Core/Equal-Core SC Piles	Long-Core SC Piles
<Technical Specification for Concrete Core Mixing Piles> (YB 2007)	Yunnan Province	Failure of the pile-soil interface	$\begin{array}{l}{R}_{\mathrm{a}1}=\xi u_{\mathrm{p}}{\displaystyle \sum q_{\mathrm{s}i\mathrm{a}}}{L}_i+\\ u_{\mathrm{p}}{\displaystyle \sum q_{\mathrm{s}j\mathrm{a}}}{L}_j+\alpha q_{\mathrm{pa}}{A}_{\mathrm{p}}\end{array}$	$\begin{array}{l}{R}_{\mathrm{a}1}=\xi u_{\mathrm{p}}{\displaystyle \sum q_{\mathrm{s}i\mathrm{a}}}{L}_i+\alpha q_{\mathrm{p}\alpha }{A}_{\mathrm{p}}+\\ u_{\mathrm{c}}{\displaystyle \sum q_{\mathrm{s}j\mathrm{a}}}{L}_j+q_{\mathrm{pa}}^{\mathrm{c}}{A}_{\mathrm{c}}\end{array}$
		Failure of material at the head of the pile	$R_{\mathrm{a}2}={\psi }_{\mathrm{c}}{A}_{\mathrm{c}}{f}_{\mathrm{ck}}^{\mathrm{c}}+\eta f_{\mathrm{cu}}{A}_{\mathrm{p}}$	$R_{\mathrm{a}2}={\psi }_{\mathrm{c}}{A}_{\mathrm{c}}{f}_{\mathrm{ck}}^{\mathrm{c}}+\eta f_{\mathrm{cu}}{A}_{\mathrm{p}}$
		Failure of the interface between the inner and outer pile	$R_{\mathrm{a}3}={\zeta }_{\mathrm{c}}\eta f_{\mathrm{cu}}{A}_{\mathrm{cf}}+\eta f_{\mathrm{cu}}{A}_{\mathrm{p}}$	$\begin{array}{l}{R}_{\mathrm{a}3}={\zeta }_{\mathrm{c}}\eta f_{\mathrm{cu}}{A}_{\mathrm{cf}}+\\ u_{\mathrm{c}}{\displaystyle \sum q_{\mathrm{s}i\mathrm{a}}{L}_i}+q_{\mathrm{pa}}^{\mathrm{c}}{A}_{\mathrm{c}}\end{array}$
		Failure of material below the variable cross-section	$R_{\mathrm{a}4}=\xi u_{\mathrm{p}}{\displaystyle \sum q_{\mathrm{s}i\mathrm{a}}}{L}_i+\eta f_{\mathrm{cu}}{A}_{\mathrm{p}}$	$\begin{array}{l}{R}_{\mathrm{a}4}=\xi u_{\mathfrak{p}}{\displaystyle \sum q_{\mathrm{s}i\mathfrak{a}}{L}_i}\\ +\alpha q_{\mathfrak{p}\mathfrak{a}}{A}_{\mathfrak{p}}+\psi A_{\mathrm{q}}{f}_{\mathrm{ck}}\end{array}$

Where $\xi$ is the adjustment coefficient. $q_{\mathrm{sia}}$ is the characteristic value of side resistance for layer i soil in the reinforced section of cement-soil pile. $q_{\mathrm{s}j\mathrm{a}}$ is the characteristic value of side resistance for layer i soil in the non-reinforced section of the cement-soil pile. $\alpha$ is the reduction coefficient for bearing capacity of natural foundation soil at the pile tip. $A_{\mathrm{p}}$ is the cross-sectional area of the cement-soil pile. $A_{\mathrm{c}}$ is the cross-sectional area of the inner core pile. $A_{\mathrm{cf}}$ is the cross-sectional area at the top of the inner core pile. L is the length of the pile. $f_{\mathrm{ck}}^{\mathrm{c}}$ is the axial compressive strength of concrete for the inner core pile. $f_{\mathrm{cu}}$ is the average cubic compressive strength of cement-soil test specimens under standard curing conditions at 90 days. ${\psi }_{\mathrm{c}}$ is the working condition coefficient of the inner core pile. $\eta$ is the reduction coefficient for cement-soil strength. $u_{\mathrm{p}}$ is the perimeter of the cement-soil pile. $u_{\mathrm{c}}$ is the perimeter of the inner core pile.

,

Table 2. Design methods for the bearing capacity of stiffened composite piles in the Jiangsu provincial specification.

Name of the Specification	Areas of Application	Design Methods for Bearing Capacity
		Failure Modes	Short-Core/Equal-Core SC Piles	Long-Core SC Piles
<Technical Specification for Strength Composite Piles> (DGJ32/TJ 151-2013)	Jiangsu Province	Failure of the pile-soil interface	$R_{\mathrm{a}}=U{\displaystyle \sum {\xi }_{\mathrm{s}i}{q}_{\mathrm{s}i\mathrm{a}}{l}_i}+{\xi }_{\mathrm{p}}{q}_{\mathrm{pa}1}{A}_{\mathrm{p}1}$	$\begin{array}{l}{R}_{\mathrm{a}}=U{\displaystyle \sum {\xi }_{\mathrm{s}i}{q}_{\mathrm{s}i\mathrm{a}}{l}_i}+\\ u{\displaystyle \sum q_{\mathrm{s}j\mathrm{a}}{l}_j}+q_{\mathrm{pa}2}{A}_{\mathrm{p}2}\end{array}$

Where q_sia is the characteristic value of side resistance for layer i soil in the outer core of composite section. q_sja is the characteristic value of side resistance for layer j soil in the inner core of non-composite section. q_pa1 is the characteristic value of tip resistance in the composite section. q_pa2 is the characteristic value of tip resistance in the non-composite section. l_i, l_j are the thickness of layer i soil in composite section and layer j soil in non-composite section of the SC pile. ξ_si is the adjustment coefficient for side resistance in the composite section. ξ_p is the adjustment coefficient for tip resistance in the composite section. A_p1 is the cross-sectional area of the outer core pile body in the composite section. A_p2 is the cross-sectional area of inner core pile body in non-composite section.

and

Table 3. Design methods for the bearing capacity of stiffened composite piles in the national specification.

Name of the Specification	Areas of Application	Design Methods for Bearing Capacity
		Failure Modes	Short-Core/Equal-Core SC Piles	Long-Core SC Piles
<Technical Specification for Strength Composite Piles> (JGJ/T 327-2014)	National	Failure of the interface between the inner and outer pile	$R_{\mathrm{a}}=u^{\mathrm{c}}{q}_{\mathrm{sa}}^{\mathrm{c}}{l}^{\mathrm{c}}+q_{\mathrm{pa}}^{\mathrm{c}}{A}_{\mathrm{p}}^{\mathrm{c}}$	$\begin{array}{l}{R}_{\mathrm{a}}=u^{\mathrm{c}}{q}_{\mathrm{sa}}^{\mathrm{c}}{l}^{\mathrm{c}}+\\ u^{\mathrm{c}}{\displaystyle \sum q_{\mathrm{s}j\mathrm{a}}^{\mathrm{c}}{l}_j}+q_{\mathrm{pa}}^{\mathrm{c}}{A}_{\mathrm{p}}^{\mathrm{c}}\end{array}$
		Failure of the pile-soil interface	$R_{\mathrm{a}}=u_{\mathrm{p}}{\displaystyle \sum {\xi }_{\mathrm{s}i}{q}_{\mathrm{s}i\mathrm{a}}{l}_i}+\alpha {\xi }_{\mathrm{p}}{q}_{\mathrm{pa}}{A}_{\mathrm{p}}$	$\begin{array}{l}{R}_{\mathrm{a}}=u\Sigma {\xi }_{\mathrm{s}i}{q}_{\mathrm{s}i\mathrm{a}}{l}_i+\\ u^{\mathrm{c}}{\displaystyle \sum q_{\mathrm{s}j\mathrm{a}}^{\mathrm{c}}{l}_j}+q_{\mathrm{pa}}^{\mathrm{c}}{A}_{\mathrm{p}}^{\mathrm{c}}\end{array}$

Where ξ_si is the adjustment coefficient for side resistance in the composite section. ξ_p is the adjustment coefficient for tip resistance in the composite section. $\alpha$ is the reduction coefficient for bearing capacity of the natural foundation soil. Other parameters share the same definitions as above.

.

The bearing capacity calculation methodology in the Yunnan provincial specification demonstrates the most comprehensive consideration of failure modes among regional design standards, including:

• Failure at the pile-soil interface, where the entire SC pile undergoes settlement, as shown in Figure 3a.
• Failure at the interface between the inner core pile and the outer pile, resulting in relative slippage, as shown in Figure 3b.
• Insufficient material strength at the SC pile head, leading to crushing near the pile top, as shown in Figure 3c.
• Insufficient material strength below the variable cross-section, such as crushing of the cement-soil pile at the bottom of the short-core SC piles or the section below the variable cross-section in long-core SC piles, as shown in Figure 3d.

In contrast, the bearing capacity calculation methods in the national specification and the Jiangsu specification consider relatively simpler failure modes. The national specification considers relative slippage between the inner core pile and the outer pile as well as failure at the pile-soil interface, while the Jiangsu standard only considers failure at the SC pile-soil interface. However, in practical engineering applications, failures due to insufficient material strength at the pile head account for approximately 30% of cases [6]. If this failure mode is overlooked, significant deviations can occur in the estimation of the capacity of SC piles.

Synthesizing the three specifications mentioned, it can be concluded that the bearing capacity calculation formulas involve the side resistance and tip resistance provided by the surrounding soil and the bearing capacity provided by the pile material strength. Regarding side resistance and tip resistance, three specifications provide different adjustment coefficients and reduction coefficients, along with their respective determination methods and value ranges.

The Yunnan provincial specification adopts a unified adjustment method, stipulating that the side resistance adjustment coefficient ξ ranges from 1.1 to 1.6, and the reduction coefficient α ranges from 0.4 to 0.6. In the Jiangsu provincial specification, the side resistance adjustment coefficient ξ_si is based on the core area ratio and the type of soil layers around the pile. The specific values are shown in

Table 4. Side resistance adjustment coefficient ξ_si of the composite section in the Jiangsu provincial specification.

	Name of Soil Layers	Clay	Silt	Silty Sand
Core Area Ratio
10%~20%		1.5~1.7	1.7~2.0	2.0~2.5
20%~30%		2.0~2.5	2.5~2.8	2.8~3.0
30%~40%		2.5~3.5	3.5~3.8	3.8~4.0
>40%		3.0~4.5	4.5~4.8	4.8~5.0

. The value of the adjustment coefficient ξ_p is based on the type of SC piles. The particular values are shown in

Table 5. Tip resistance adjustment coefficient ξ_p of the SC pile in the Jiangsu provincial specification.

Types of Piles	Long-Core SC Pile	Equal-Core SC Pile
MC pile	1	0.6~0.8
SMC pile	1	0.7~0.9

. In the national specification, the side resistance adjustment coefficient ξ_si and the tip resistance adjustment coefficient ξ_p adopt a layered value method based on the soil layer types. The specific values are shown in

Table 6. Side resistance adjustment coefficient ξ_si of composite section in the National specification.

Name of Soil Layers	Mud	Clay	Silt	Silty Sand	Fine Sand
Side resistance adjustment coefficient	1.30~1.60	1.50~1.80	1.50~1.90	1.70~2.10	1.80~2.30

and

Table 7. Tip resistance adjustment coefficient ξ_p of the SC pile in the National specification.

Name of Soil Layers	Mud	Clay	Silt	Silty Sand	Fine Sand
Tip resistance adjustment coefficient	—	2.00~2.20	2.00~2.40	2.30~2.70	2.50~2.90

.

In summary, although the Yunnan specification considers the most comprehensive failure modes, its approach to determining adjustment coefficients is relatively sketchy. On the other hand, the Jiangsu and national specifications, despite considering simpler failure modes, provide more precise methods for determining adjustment coefficients. As a result, the estimated bearing capacities for the same test pile often vary significantly when adopting different specifications.

To address the issues above, the following sections will employ statistical analysis based on static load test data of SC piles to revise the values of the side friction and end resistance adjustment coefficients. Moreover, a practical bearing capacity calculation formula will be proposed to better align with the actual failure modes of SC piles.

2.2. Static Load Test Data of Strength Composite Piles

To obtain valuable insights for the calculation method for bearing capacity of SC piles, we conducted static load tests on SC piles in Anhui, Jiangsu, Shandong, and Zhejiang provinces. To further expand the sample size, this study additionally collected, selected, and compiled a substantial amount of static load test data. Ultimately, the dataset encompasses tests from 44 projects, totaling 159 test piles. The specific data are presented in Table 8. The selection criteria included:

• Completeness of geotechnical and load-test records.
• Representation of major soil types.
• Variety in pile dimensions and core area ratios.
• Well-defined failure modes.

Table 8. Data of test pile projects that collected and participated.

Province	Representative Projects	Type of Piles/Number of Piles	Bearing Stratum	Remark
Anhui	A certain residential community in Fuyang	Equal-core/3	Medium sand	Participated
Beijing	A certain residential community in Tongzhou	Equal-core/3	Fine sand	Collected
Gansu	The Mingshashan Road project	Equal-core/3	Silty clay and coarse sand	Collected
Guangxi	The pile testing projects in Nanning	Equal-core/12	Silty sand and clay	Collected
Hainan	A certain residential building in Yazhou Bay	Equal-core/3	Silty clay	Collected
Henan	A commercial residential building in Zhoukou	Equal-core/3	Fine sand	Collected
Jiangsu	The Zhongtian Runyuan project in Nantong, etc.	Equal-core, short-core and long-core/60	Muddy clay, clay, silt and silty clay	Collected
	Yanglv Railway	Long-core/2	Silty clay	Participated
	Ningqi Railway	Short-core/3	Clay	Participated
Jiangxi	A certain large-scale hydrocomplex	Equal-core and Short-core/7	Rounded gravel and silty sand	Collected
Shandong	The Huaxi Yuan project in the Shandong University Town, etc.	Equal-core and Short-core/13	Silty sand, silt and clay	Collected
	Wufengshan Yangtze River Bridge	Equal-core/3	Silty sand	Participated
Shanghai	The Bailonggang Underground Wastewater Treatment Plant project, etc	Equal-core/10	Silty clay and silty fine sand	Collected
Shanxi	Hengda Jinbi Tianxia housing development, etc	Short-core/7	Silt and fine sand	Collected
Tianjin	The Phase I offshore wind power project at Tianjin Port and a project by the Tianjin Port Piling Company, etc	Equal-core, short-core and long-core/15	Silty clay and silty fine sand	Collected
Yunnan	Supporting works for the station construction of the Yuxi-Mohan Railway, etc	Equal-core, short-core and long-core/9	Clay and coarse sand	Collected
Zhejiang	A certain thermal power plant	Short-core/3	Silty sand	Participated

Table 8. Data of test pile projects that collected and participated.

Province	Representative Projects	Type of Piles/Number of Piles	Bearing Stratum	Remark
Anhui	A certain residential community in Fuyang	Equal-core/3	Medium sand	Participated
Beijing	A certain residential community in Tongzhou	Equal-core/3	Fine sand	Collected
Gansu	The Mingshashan Road project	Equal-core/3	Silty clay and coarse sand	Collected
Guangxi	The pile testing projects in Nanning	Equal-core/12	Silty sand and clay	Collected
Hainan	A certain residential building in Yazhou Bay	Equal-core/3	Silty clay	Collected
Henan	A commercial residential building in Zhoukou	Equal-core/3	Fine sand	Collected
Jiangsu	The Zhongtian Runyuan project in Nantong, etc.	Equal-core, short-core and long-core/60	Muddy clay, clay, silt and silty clay	Collected
	Yanglv Railway	Long-core/2	Silty clay	Participated
	Ningqi Railway	Short-core/3	Clay	Participated
Jiangxi	A certain large-scale hydrocomplex	Equal-core and Short-core/7	Rounded gravel and silty sand	Collected
Shandong	The Huaxi Yuan project in the Shandong University Town, etc.	Equal-core and Short-core/13	Silty sand, silt and clay	Collected
	Wufengshan Yangtze River Bridge	Equal-core/3	Silty sand	Participated
Shanghai	The Bailonggang Underground Wastewater Treatment Plant project, etc	Equal-core/10	Silty clay and silty fine sand	Collected
Shanxi	Hengda Jinbi Tianxia housing development, etc	Short-core/7	Silt and fine sand	Collected
Tianjin	The Phase I offshore wind power project at Tianjin Port and a project by the Tianjin Port Piling Company, etc	Equal-core, short-core and long-core/15	Silty clay and silty fine sand	Collected
Yunnan	Supporting works for the station construction of the Yuxi-Mohan Railway, etc	Equal-core, short-core and long-core/9	Clay and coarse sand	Collected
Zhejiang	A certain thermal power plant	Short-core/3	Silty sand	Participated

Figure 4 illustrates the regional distribution of the test piles. Among these, Jiangsu Province, characterized by extensive soft soil strata and an urgent demand for high-quality, efficient ground improvement techniques [32], has become the most prevalent region for SC pile applications, accounting for approximately 40.9% of the total cases analyzed.

Compared to conventional pile types, the design of SC piles involves more complex considerations. Various factors such as pile diameter, pile length, core area ratio, and bearing stratum of SC piles are supposed to be analyzed. Notably, the length ratio of the inner and outer piles serves as a key factor in the design process [33,34].

Based on statistical analysis of factors such as pile diameter, pile length, and core area ratio, the following conclusions can be drawn: As shown in

Table 9. Proportion of test piles with different pile diameters (inner core piles).

Diameter of Inner Core Piles/mm	200~400	400~600	600~800	>800
Proportion/%	7.4%	53.7%	28.8%	10.1%

and

Table 10. Proportion of test piles with different pile diameters (outer core piles).

Diameter of Outer Core Piles/mm	600~800	800~1000	1000~1200	>1200
Proportion/%	22.8%	43.6%	20.8%	12.8%

, it was found that the diameters of inner core piles are mainly concentrated between 400 mm and 600 mm. In comparison, the diameters of outer piles mostly exceed 800 mm. As shown in

Table 11. Proportion of SC piles with different core area ratios.

Core Area Ratios/%	0~20%	20%~40%	40%~60%	>60%
Proportion/%	13.7%	47.9%	30.8%	7.5%

, the core area ratio is predominantly distributed between 20% and 60%, with the area of the inner core pile being less than half of the outer pile area in 69% of cases. As shown in

Table 12. Proportion of inner-to-outer pile length ratios.

Types of SC Piles	Short-Core SC Piles			Equal-Core SC Piles	Long-Core SC Piles
Inner-to-outer pile length ratios	<0.5	0.5~0.7	0.7~1.0	1.0	1.0~1.5	>1.5
Number	3	14	49	76	11	6

, the test piles analyzed consist primarily of short-core piles and equal-core piles, and the length ratio of short-core piles is concentrated in the range of 0.7 to 1.0.

From the statistical analysis of the failure modes observed in test piles, it is concluded that failures occurred only at the pile-soil interface or due to failure of material in the pile head. Among these, pile head material failure accounted for 28.7%, while the remaining 71.3% of failures were attributed to pile-soil interface slippage. Figure 5 illustrates the major failure modes of test piles in practical engineering. Therefore, the practical calculation formula proposed in this research for the bearing capacity design of SC piles considers two failure modes: pile-soil interface slippage and pile head material failure.

2.3. Statistical Analysis of Bearing Capacity Adjustment Coefficients

Currently, bearing capacity calculations for SC piles in prevailing codes universally adopt adjustment coefficients for side resistance and tip resistance to modify the intact soil’s ultimate side resistance standard values and pile tip resistance standard values provided in geotechnical investigation reports.

Based on in situ measured data collected from static load tests of SC piles, this research conducted a comparative statistical analysis between measured values of side/tip resistance and standard values provided in soil investigation reports. Using different soil layer categories as classification criteria, stratified adjustment coefficients for side resistance and a unified adjustment coefficient for tip resistance were determined, respectively. The modified side resistance adjustment coefficient ξ_si and tip resistance adjustment coefficient ξ_p are calculated by the following equations:

$${\xi }_{\mathrm{s}i}={\displaystyle \frac{{q^{\prime }}_{\mathrm{s}i\mathrm{a}}}{q_{\mathrm{s}i\mathrm{a}}}},{\xi }_{\mathrm{p}}={\displaystyle \frac{{q^{\prime }}_{\mathrm{p}}}{q_{\mathrm{p}}}}$$

(1)

where $q_{sia}^{\prime }$ denotes the measured ultimate side resistance of the level i soil layer along the pile shaft (kPa). $q_{sia}$ denotes the standard ultimate side resistance of the level i soil layer along the pile shaft provided in the geotechnical investigation report (kPa). $q_p^{\prime }$ denotes the measured tip resistance (kPa). $q_p$ denotes the standard tip resistance supplied in the geotechnical investigation report (kPa).

During the data collection of the side resistance adjustment coefficient ξ_si and tip resistance adjustment coefficient ξ_p, the following principles were applied:

1.

For the side resistance adjustment coefficient (ξ_si):

Classification was based on soil layer properties. The adjustment coefficient for each soil layer was calculated as the ratio of the measured side friction resistance after pile installation to the corresponding side friction resistance provided in the pre-construction geotechnical investigation report. If the test piles lack standard values of tip resistance from the geotechnical investigation report, the recommended standard values from the <Technical Specification for Strength Composite Piles> (DGJ32/TJ 151-2013) can be adopted based on the soil layer conditions.

2.

For the end resistance adjustment coefficient (ξ_p):

The adjustment coefficient was calculated as the ratio of the measured tip resistance after pile installation to the corresponding standard bearing capacity of the pile tip soil provided in the pre-construction geotechnical investigation report. If the test piles lack standard values of end bearing capacity from the geotechnical investigation report, regional empirical values can be used instead.

Using the data collected according to the above method, the following statistical parameters were computed: mean, standard deviation, coefficient of variation, standard value, and coefficient of variation:

$$X_{\mathrm{m}}={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{X}_i}}{n}}$$

(2)

$$\sigma =\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left(X_i-X_{\mathrm{m}}\right)}^2}}{n-1}}}$$

(3)

$$\delta ={\displaystyle \frac{\sigma }{X_{\mathrm{m}}}}\times 100\%$$

(4)

$$X_{\mathrm{k}}={\gamma }_{\mathrm{s}}{X}_{\mathrm{m}}$$

(5)

$${\gamma }_{\mathrm{s}}=1\pm ({\displaystyle \frac{1.704}{\sqrt{n}}}+{\displaystyle \frac{4.678}{n^2}})\delta$$

(6)

where $X_m$ denotes the mean value of the statistical test data. $X_i$ denotes the level i statistical test data. $n$ denotes the sample size. $\sigma$ denotes the standard deviation. δ is the coefficient of variation. $X_k$ denotes the characteristic value of the statistical test data. ${\gamma }_s$ denotes the statistical correction coefficient.

Due to the influence of factors such as construction and environmental conditions, the statistical test data exhibit a certain degree of dispersion. Therefore, it is necessary to filter the data using mathematical methods during the statistical process. For example, it is required to calculate the characteristic value or mean value, inspect all sample points within the interval, and discard data with excessive deviations.

The 3-sigma criterion is a standard method for discrimination. Specifically, test data falling within the range of $X_{\mathrm{m}}-3\sigma \le X_i\le X_{\mathrm{m}}+3\sigma$ or $X_{\mathrm{k}}-3\sigma \le X_i\le X_{\mathrm{k}}+3\sigma$ can be regarded as normal values, while those outside this range are regarded as outliers and discarded. After processing, the test data should be recalculated for the mean, standard deviation, coefficient of variation, characteristic value, and statistical correction coefficient until all data fall within the specified range. Only then can further statistical analysis be conducted [35].

In data processing, the coefficient of variation δ can be used to assess the dispersion of samples and compare the variability of different test indicators. The relationship between the coefficient of variation and variability can be referenced in

Table 13. Classification of variability levels in adjustment coefficient values.

Coefficient of Variation δ	δ < 0.1	0.1 ≤ δ < 0.2	0.2 ≤ δ < 0.3	0.3 ≤ δ < 0.4	δ ≥ 0.4
Variability	Very low	Low	Medium	High	Very high

.

To obtain accurate calculation results, a confidence level of 1−α is introduced during data processing. According to the principle of standard normal distribution, the calculation result can be obtained as $X_{\mathrm{m}}\pm z_{\alpha /2}\sigma /\sqrt{n}$. Thus, the confidence interval is determined as $(X_{\mathrm{m}}-z_{\alpha /2}\sigma /\sqrt{n},X_{\mathrm{m}}+z_{\alpha /2}\sigma /\sqrt{n})$.

Figure 6 shows a schematic diagram of the confidence interval for the normal distribution. Different confidence intervals can be obtained by setting different confidence levels. Selecting different confidence levels leads to different ranges of values, and as the confidence level increases, the corresponding critical value z_α/2 also increases. Therefore, with all other factors remaining constant, a higher confidence level results in a wider confidence interval. Additionally, the size of the confidence interval is not only influenced by the confidence level but also by the sample size. When statistically determining the adjustment coefficient for composite pile bearing capacity, the principles for setting the confidence level are as follows:

1.

Meeting the required precision.

2.

Ensuring the range of values meets the required specifications.

3. Results

3.1. Range of Values and Influencing Factors for the Modified Side and Tip Resistance Adjustment Coefficients

Through statistical analysis of static load test data for SC piles, and based on the data collection methods and processing principles, the original samples of the tip resistance adjustment coefficient and the pile side resistance adjustment coefficients for different soil layers can be obtained.

The statistical summary reveals that there are 190 valid samples for the side resistance adjustment coefficient and 39 valid samples for the tip resistance coefficient. As shown in Figure 7, the pile-side soil samples primarily involve three types of soil layers: clay, silt, and sand. Among these, clay accounts for the largest number of samples, which also indicates that SC piles are suitable for soft soil layers.

For the collected original side friction adjustment coefficients and end resistance adjustment coefficients, all calculations were performed using Equation (1). Through data statistics and processing, the stratified adjustment coefficients of side resistance ξ_si in different soil layers and the unified adjustment coefficient of tip resistance ξ_p were obtained, as presented in

Table 14. Value ranges of revised layered adjustment coefficients for side resistance in different soil types and unified adjustment coefficients for tip resistance.

Coefficient Name	Adjustment Coefficients of Side Resistance ξsi			Unified Adjustment Coefficient of Tip Resistance ξp
Type of Soil Layers	Clay	Silt	Sand
Mean value	1.79	1.86	1.99	1.09
Value range	1.65–1.94	1.65–2.05	1.79–2.12	0.97–1.21
Coefficient of variation	0.20	0.22	0.31	0.33

.

As shown in Table 14, the side resistance of different soil categories has improved compared to that of undisturbed soil. Considering the construction method and process of SC piles, it can be concluded that the changes in side resistance are mainly influenced by the following factors:

1.

Relaxation effect during outer pile formation

As shown in Figure 8a, during the construction of the outer cement-soil pile, the lateral stress on the borehole wall is released, resulting in a relaxation effect that reduces soil strength and side resistance consequently. Given the large diameter of SC piles and the soft soil characteristics of the surrounding layers, this effect should not be ignored.

2.

Cement-soil diffusion effect

As shown in Figure 8b, during the construction of the outer pile of an SC pile, the binder (cement slurry or powder) penetrates the surrounding soil during grouting and mixes in situ with the foundation soil. Cement minerals such as calcium oxide and silicon dioxide react with water in the soil through hydrolysis and hydration, producing compounds like calcium hydroxide and calcium silicate hydrate. The cementation effect of these hydration products rapidly enhances the strength of the surrounding soil while ensuring that the shear strength at the pile-soil interface exceeds that of the outer soil.

3.

Compaction effect during pile installation

As shown in Figure 8c, during the driving of the pipe pile, the secondary compression on the cement-soil accelerates the drainage process in the surrounding cement-soil and adjacent soil layers. This increases the density of the surrounding soil, and the rise in effective stress further enhances side resistance.

The actual changes in side resistance indicate that the effects of cement-soil diffusion and compaction during pile installation far outweigh the relaxation effect during outer pile formation. Furthermore, based on the variation ranges of the adjustment coefficients for clay, silt, and sand, it can be observed that as soil particle size increases, the enhancement effect on side resistance becomes more pronounced. The primary reasons for this are as follows:

1.

Soil Structure and Stability

Compared to clay, sand has larger particles and a more stable structure, making it less susceptible to disturbance during drilling in the outer pile formation process. Additionally, the diffusion range of cement slurry or powder in sand is wider.

2.

Drainage Performance and Hydration Reaction

In most of the projects surveyed, wet construction methods were employed. Silt and fine sand exhibit better drainage properties, allowing excess water to drain more efficiently after ensuring sufficient moisture for the hydration reaction of cement minerals. This results in improved interfacial shear strength.

The patterns indicate that the degree of side friction enhancement is significantly correlated with soil layer properties. Based on the adjustment coefficients for side resistance of different soils and the unified adjustment coefficient for tip resistance, a new bearing capacity calculation method will be proposed next.

3.2. A Practical Calculation Method for Bearing Capacity of Strength Composite Piles

To address failure modes caused by pile-soil interface slippage or insufficient pile material strength in engineering practice, the following practical calculation method for bearing capacity is proposed, along with the formulation of the bearing capacity calculation formula:

$$R_{\mathrm{a}}=\min \{R_{\mathrm{a}1},R_{\mathrm{a}2}\}$$

(7)

where $R_{\mathrm{a}1}$ denotes the characteristic value of the vertical compressive bearing capacity of a single pile corresponding to failure due to insufficient pile material strength (kN). $R_{\mathrm{a}2}$ denotes the characteristic value of the vertical compressive bearing capacity of a single pile corresponding to failure at the pile-soil interface (kN).

When calculating the vertical compressive bearing capacity of a single pile, considering failure caused by insufficient pile material strength, this research referenced the improved calculation method for precast pile bearing capacity [36,37,38]. This method comprehensively accounts for the contributions of both the core pile concrete strength and the surrounding cement-soil pile strength to the bearing capacity:

$$R_{\mathrm{a}1}={\psi }_1(f_{\mathrm{c}}-{\psi }_{\mathrm{p}}{\sigma }_{\mathrm{ce}})A_{\mathrm{c}}+\eta f_{\mathrm{cu}}(A_{\mathrm{p}}-A_{\mathrm{c}})$$

(8)

where ${\psi }_1$ denotes the pile construction process coefficient, which can be taken as 0.85 according to the <Technical Specification for Building Pile Foundations> (JGJ94-2008) [39]. ${\psi }_{\mathrm{p}}$ denotes the residual precompression stress coefficient, which can be taken as 0.56. ${\sigma }_{\mathrm{ce}}$ denotes the effective prestress of concrete (kPa), and its value can be determined based on the type of PHC pipe pile: 4000 kPa for Type A, 6000 kPa for Type AB, 8000 kPa for Type B, and 10,000 kPa for Type C, where the classification criteria for PHC pipe piles are listed in

Table 15. Types of PHC pipe piles and classification criteria.

Type	A	AB	B	C
Reinforcement ratio/%	≥0.8	0.7~0.8	0.5~0.7	≤0.5

. $A_{\mathrm{c}}$ denotes the cross-sectional area of the inner core pile (m²). $f_{\mathrm{c}}$ denotes the design value of the axial compressive strength of concrete (kPa). $\eta$ denotes the reduction coefficient for cement-soil, with a value ranging from 0.33 to 0.4. $f_{\mathrm{cu}}$ denotes the average cubic compressive strength of cement-soil test specimens under standard curing conditions at 90 days (kPa). $A_{\mathrm{p}}$ denotes the cross-sectional area of the composite section of the pile (m²).

When calculating the vertical compressive bearing capacity of a single pile considering soil-pile interface failure, the side resistance and tip resistance are computed using the adjustment coefficients proposed in the previous section, respectively. The formula is as follows:

$$\mathrm{Short}-\mathrm{core}\mathrm{and}\mathrm{equal}-\mathrm{core}\mathrm{piles}:R_{\mathrm{a}2}=u_{\mathrm{p}}{\displaystyle \sum _{i=1}^n{\xi }_{\mathrm{s}i}}{q}_{\mathrm{s}i\mathrm{a}}{l}_i+u_{\mathrm{p}}{\displaystyle \sum _{j=1}^n{q}_{\mathrm{s}j\mathrm{a}}}{l}_j+{\xi }_{\mathrm{p}}{q}_{\mathrm{pa}}{A}_{\mathrm{p}}$$

(9)

$$\mathrm{Long}-\mathrm{core}\mathrm{piles}:R_{\mathrm{a}2}=u_{\mathrm{p}}{\displaystyle \sum _{i=1}^n{\xi }_{\mathrm{s}i}}{q}_{\mathrm{s}i\mathrm{a}}{l}_i+{\xi }_{\mathrm{p}}{q}_{\mathrm{pa}}\left(A_{\mathrm{p}}-A_{\mathrm{c}}\right)+u_{\mathrm{c}}{\displaystyle \sum _{j=1}^n{q}_{\mathrm{s}j\mathrm{a}}}{l}_j+q_{\mathrm{pa}}^{\mathrm{c}}{A}_{\mathrm{c}}$$

(10)

where $u_{\mathrm{p}}$ denotes the perimeter of the outer pile body of the SC pile (m). $u_{\mathrm{c}}$ denotes the perimeter of the inner core pile body of the SC pile (m). $l_i$ and $l_j$ denote the thicknesses of the level i soil layer in the composite section and the level j soil layer in the non-composite section of the SC pile (m). $A_{\mathrm{p}}$ denotes the cross-sectional area of the composite section of the pile (m²). $A_{\mathrm{c}}$ denotes the cross-sectional area of the inner core pile (m²). $q_{\mathrm{s}i\mathrm{a}}$ denotes the standard value of the ultimate side resistance of the level i soil layer along the pile side, as provided in the geotechnical investigation report (kPa). $q_{\mathrm{s}j\mathrm{a}}$ denotes the characteristic value of the side resistance of the level j soil layer in the non-composite section of the inner core, as provided in the geotechnical investigation report (kPa). $q_{\mathrm{pa}}^{\mathrm{c}}$ denotes the characteristic value of the tip resistance in the non-composite section (kPa), determined based on regional experience, and should adopt the tip resistance characteristic value corresponding to the respective pile type. $q_{\mathrm{pa}}$ denotes the characteristic value of the tip resistance in the composite section (kPa), determined based on regional experience, and should adopt the characteristic value of the outer tip resistance of the SC pile. ${\xi }_{\mathrm{s}i}$ denotes the adjustment coefficient for side resistance. ${\xi }_{\mathrm{p}}$ denotes the adjustment coefficient for tip resistance, with values determined according to Table 14.

4. Discussion

4.1. Validation of Formula Rationality and Applicability

To validate the rationality and applicability of the revised ultimate bearing capacity calculation formula and the bearing capacity coefficients for SC piles, an additional 112 SC piles with complete test records were selected for supplementary verification. The main failure modes observed were pile-soil interface slippage and failure due to insufficient pile head material strength. Among these, 64 piles failed due to pile-soil interface slippage, while 48 piles failed due to insufficient pile head material strength. The bearing capacities were calculated using the formulas provided in the Jiangsu provincial specification, Yunnan provincial specification, national specification, as well as the calculation method proposed in this study. These calculated values were then compared with the measured field values.

Furthermore, since the bearing capacity calculations in both the Jiangsu provincial specification and the national specification do not account for the failure mode caused by insufficient pile head material strength, only the 64 test piles that experienced pile-soil interface slippage were selected for comparative analysis.

When applying the bearing capacity calculation formula proposed by this study, we adopted the recommended values from the geotechnical investigation report. The adjustment coefficients for side resistance ${\xi }_{si}$ and tip resistance ${\xi }_p$ were assigned to the maximum values tabulated in Table 14.

As shown in Figure 9, Figure 10, Figure 11 and Figure 12, the red dush line represents the normal distribution fit applied to the data, which is used to evaluate the distribution characteristics of the ratio of calculated to measured values and its conformance to theoretical probabilistic patterns. From Figure 9 and Figure 10, it can be observed that the ratios of calculated-to-measured results obtained by adopting the bearing capacity calculation methods provided in the national specification and the Jiangsu provincial specification generally follow a normal distribution. However, the calculated values are consistently lower than the measured values, exhibiting a significant conservative bias. While the specifications ensure a safety margin in design, this approach may lead to material waste and poor economic efficiency.

Figure 11 compares the bearing capacities calculated adopting the method from the Yunnan provincial specification with the measured values. The ratios of calculated-to-measured results also approximate a normal distribution, with approximately half of the sample ratios close to 1.0, and most calculated values being lower than the measured values. However, the dispersion is considerable, with a significant number of data samples having calculated-to-measured ratios exceeding 1.2 or falling below 0.8. This indicates that the unified adjustment coefficients in the Yunnan provincial specification struggle to reliably accommodate complex and variable stratigraphic conditions, resulting in insufficient prediction accuracy and stability.

Figure 12 presents the comparison between the bearing capacities calculated adopting the method proposed in this study and the measured values. Figure 12a shows that the vast majority of data points cluster closely around the Isobar, indicating a high degree of agreement between the calculated and measured values. Furthermore, Figure 12b reveals that over 60% of the samples have a calculated-to-measured ratio close to 1.0, and an impressive 82.1% of the samples fall within the ±20% error margin. The ratio distribution exhibits a well-defined normal distribution pattern, concentrated within the 0.8–1.2 range, with very few outliers.

The case study demonstrates that the optimized bearing capacity calculation method proposed in this study is both rational and feasible. The ultimate vertical bearing capacity formula that incorporates a layered adjustment coefficient for side resistance and a unified adjustment coefficient for tip resistance delivers high accuracy and reliability. Derived from field-measured data, this new formula offers strong applicability for engineering practice and can be applied in SC pile design.

4.2. Recommendations for Adjustment Coefficients in Practical Calculation Formulas

The adjustment coefficients for side and tip resistance derived from statistical analysis are not fixed values but rather a range. Calculating the bearing capacity of SC piles solely using the minimum values may yield overly conservative results. In addition to soil layer classification, the mobilization of side friction is influenced by multiple factors. Therefore, during the preliminary design phase, adjustment coefficients for side resistance should be appropriately modified based on project characteristics and construction methods to achieve more rational and accurate predictions of single-pile bearing capacity. Combined with field test data and research from other scholars, we propose that the following two major factors be considered when selecting side friction adjustment coefficients:

1.

Construction Method

Dry and wet construction methods significantly affect side friction mobilization. Some research has experimentally demonstrated the impact of different construction methods on the shear strength of cement-soil [40,41]. The Jiangsu provincial specification specifies that the adjustment coefficient for wet construction should be 0.8 times that of dry construction. Since most static load test data collected in this research originates from wet construction, the recommended range is more suitable for wet-constructed SC piles. When calculating the bearing capacity of composite piles for dry construction, based on relevant literature [42,43,44], the adjustment coefficients of side resistance should be taken as 1.2 to 1.4 times the recommended value in Table 14.

2.

Outer Pile Material

Existing research show that higher cement content correlates positively with pile-soil interface shear strength [45,46]. In response to national “low carbon” and “green-construction initiatives”, industrial waste (e.g., silica fume, fly ash) or geopolymers have been proposed as alternatives to cement [47,48]. However, different outer pile materials exhibit distinct bonding capabilities, fluidity, and soil interactions [49]. When novel materials are employed, based on relevant literature [50,51,52], the adjustment coefficients of side resistance should be taken as 0.7 to 0.8 times the recommended value in Table 14.

4.3. Limitations and Future Works

In addition to design specifications, many scholars have investigated the bearing mechanisms of SC piles using finite element methods (FEM) and numerical simulations [36,41,49,53]. These studies provide valuable insights into stress distribution, confinement effects, and load transfer behavior, and some have examined the influence of parameters such as core ratio on ultimate bearing capacity. However, FEM-based approaches generally fail to capture the effect of pile installation processes on side resistance mobilization, and they often require extensive input data and computational resources, which limit their applicability in routine design practice.

Due to the limited statistical samples and the dispersed distribution of core ratios in this research, the test piles within the same project typically share identical structural parameters. Therefore, the statistical analysis conducted in Section 3.1 cannot provide reliable core ratio–dependent adjustment coefficients. While existing FEM studies suggest that, when the inner core pile is fixed, the bearing capacity tends to increase with the core ratio within a certain range [54,55], the detailed effect of the core ratio on side friction mobilization remains unclear. Moreover, the overly broad adjustment coefficient range specified in the Jiangsu provincial specification may compromise safety. For this reason, the core ratio is temporarily excluded from adjustment coefficient considerations in our proposed formula. Future research should incorporate more extensive datasets and experimental validation to quantify the effect of core ratio and to refine the adjustment coefficients further.

In contrast to FEM-based approaches, our proposed formula integrates dominant failure modes—pile–soil interface slippage and pile head material failure—into a simple closed-form expression calibrated against a large database of static load tests. This balance between accuracy and practicality makes it suitable for engineering design. Nevertheless, the method still relies on high-quality geotechnical investigation data, and its applicability to new pile materials and alternative construction methods requires further study. Future efforts will therefore focus on extending the formula to broader soil conditions, explicitly incorporating the influence of core ratio, and coupling with numerical simulation to enhance predictive robustness.

5. Conclusions

• Comparison of SC pile specifications between the national specification, Jiangsu provincial specification, and Yunnan provincial specification reveals significant discrepancies in the selection of adjustment coefficients for side resistance and tip resistance. Notably, certain specifications fail to consider failure modes induced by insufficient pile material strength, leading to substantial divergence in predicted bearing capacities for identical projects and compromising calculation accuracy.
• Based on static load test data from 159 test piles across 44 projects, this research employed statistical analysis methods to establish value ranges for layered side resistance and tip resistance adjustment coefficients. To enhance prediction rationality, critical influencing factors were analyzed, including construction method, core ratio, and outer pile material. Evidence-based recommendations were also provided for refining adjustment coefficients.
• Addressing the prevalent failure modes observed in engineering practice, including soil-pile interface failure and insufficient pile material strength, this study developed corresponding computational methods. By introducing proposed adjustment coefficients for side resistance and tip resistance, a comprehensive formula for calculating bearing capacity was formulated. The reliability and practical applicability of the proposed method were subsequently verified through a comparative analysis between measured and calculated values from 112 full-scale test piles.