Compressive Strength of Concrete-Filled Steel Pipe Pile Head with Inner Ribs

Abstract

Pile foundation failures during earthquakes can cause severe structural damage, emphasizing the importance of accurate strength evaluation. This study focuses on concrete-filled steel pipe pile heads with inner ribs, which play a crucial role in resisting compressive loads. Compression tests were conducted on specimens simulating pile heads to investigate stress transfer between the steel pipe and infill concrete. A numerical analysis model was developed using ABAQUS 6.14 and validated against experimental results, successfully reproducing load-deformation relationships and stress transfer mechanisms. Simulations extended the study by analyzing the bearing strength of the infill concrete under rib-induced pressure, with varying diameter-to-thickness ratios D/t. The results show that the compressive strength is primarily governed by the combined effects of steel pipe buckling resistance and concrete bearing resistance of a single layer of inner ribs. The proposed evaluation formula provides a lower-bound estimate of compressive strength and effectively captures key parameters influencing performance.

1. Introduction

1.1. Research Backgound

In recent major earthquakes in Japan, such as the Tohoku Region Pacific Ocean Earthquake (the Great East Japan Earthquake) in 2011 and the Kumamoto Earthquake in 2016, a considerable number of buildings were demolished due to global inclination caused by pile foundation damage, even though the superstructure sustained only minor damage [1,2]. In the Noto Peninsula earthquake that occurred at the beginning of 2024, many buildings suffered foundation damage, leading to tilting, with some even collapsing [3]. The seven-story reinforced concrete building supported by prestressed concrete (PC) piles that collapsed had a slenderness ratio of approximately 2. It is estimated that significant compressive forces acted on the piles during the earthquake. As a result, the piles on the compressive side failed, causing the building to topple as it sank into the weak ground, unable to support its weight. Additionally, the large P-Delta moment caused the pile head connections to pull apart, completely losing their resistance to collapse [4,5]. The seismic damage to pile foundations has brought to light the insufficient examination of the failure mechanisms of pile foundations. In response to these seismic events, the Architectural Institute of Japan is in the process of introducing a plastic design method for pile foundations. This approach aims to establish a performance-based design method that can predict the collapse mechanisms of entire buildings, including their pile foundations, under major seismic events [4,5].

Among various pile foundation types, steel pipe piles demonstrate high ductility during earthquakes when properly designed. Their failure mechanisms under seismic forces can be classified into two main types: overall flexural buckling and local buckling at the pile head. The former assumes pile foundations constructed on ultra-soft ground in coastal areas and has been extensively studied [6,7,8,9,10,11,12,13]. These findings are included in the Recommendations for Design of Building Foundation by the Architectural Institute of Japan [5] and the Eurocode [14]. In contrast, the latter assumes more typical ground conditions with horizontal subgrade reaction and remains less understood, particularly in terms of stress distribution, the stress–deformation relationship of the pile, and the prediction of failure mechanisms.

Figure 1 illustrates the typical configuration of a steel pipe pile head connected to a reinforced concrete pile cap, which is commonly used in Japan [5,15]. In this configuration, concrete is filled at the pile head to connect it to the reinforced concrete pile cap, and two layers of inner ribs are welded inside the pile head to resist rotational movement of the steel pipe relative to the infill concrete. As a result, the steel pipe pile foundation consists of a lower hollow steel pipe section and an upper concrete-filled steel pipe section. The compressive and bending strengths of the pile head are expected to increase due to the presence of inner ribs and infill concrete, as indicated by the red dashed line in Figure 1. In general cases, the pile head typically behaves as a fixed support [16,17], resulting in a bending moment distribution that peaks at the pile head. Therefore, evaluating the compressive and bending strengths of each cross-section is essential for predicting the ultimate mechanism of steel pipe pile foundations. Previous studies [16,17,18,19,20] propose the moment–curvature relationship of hollow steel pipe piles considering local buckling. However, the stress transfer mechanism and strength evaluation of steel pipe pile heads under seismic conditions, where inner ribs are provided inside the steel pipe and concrete is filled, remain insufficiently established.

1.2. Related Previous Research and Issues for Consideration

To propose a method for evaluating the ultimate strength of the concrete-filled steel pipe pile head section (the cross-section enclosed by the red dashed line in Figure 1), it is necessary to clarify the following three points:

• The stress transfer mechanism via inner ribs transferring forces from the steel pipe to the filled concrete and the load-bearing mechanism of the steel pipe pile head section when the local buckling of the steel pipe and the damage to the infill concrete progress simultaneously.
• The evaluation of the local buckling strength of the steel pipe and whether the filled concrete provides a restraining effect against buckling progression.
• The evaluation of the bearing strength of the infill concrete under pressure from the inner ribs.

A typical example of a member with concrete filled into a steel tube is the CFT (Concrete-Filled Steel Tube) [21,22]. In reference [23], centrifugal loading tests were conducted using a scaled model that assumes a concrete-filled steel tube (CFT) pile with concrete filled along the entire length of the pile. The plane section assumption was applied to propose yield and ultimate bending strengths. However, as shown in Figure 1, it is difficult to consider that the plane section assumption holds in concrete-filled steel pipe pile heads where only the pile head is filled with concrete, and stress transfer is achieved via inner ribs.

For steel pipes partially filled with concrete, references [24,25,26] numerically simulated the hysteretic behavior and failure modes under cyclic horizontal loading with a constant compressive force, considering steel pipes with inner ribs at a 1D pitch. Although this study provides highly useful information for constructing numerical analysis models of the heads of concrete-filled steel tube piles, it does not evaluate the strength of the members or clarify the contribution of inner ribs to the member strength. Reference [27] conducted horizontal load tests under constant axial force on specimens modeling the concrete-filled steel pipe pile head, as shown in Figure 1. The experiment shows that, within a low axial force ratio range (≤0.3), the bending strength of the CFT [25] aligns well with the predictions. However, when the axial force ratio increases to as high as 0.6, the bending strength of the CFT becomes an unsafe-side evaluation. This is considered to be because the CFT bending strength formula overestimates the contribution of the compressive force borne by the infill concrete. Therefore, reference [27] proposes the cumulative ultimate bearing strength of the steel pipe and the bearing strength of the infill concrete at the inner ribs as a bending strength evaluation formula. As a bearing strength of infill concrete, the formula proposed in references [28,29] was adopted, which was developed from push-out tests on concrete-filled steel pipes with inner ribs. This approach has already been adopted in the Recommendations for Design of Building Foundation by the Architectural Institute of Japan [4,5]. In the recommendations, the shear connector strength is calculated by considering the number of inner ribs based on references [28,29]. For the steel pipe, the compressive strength is calculated using the yield strength of the steel material.

From the above, the following considerations appear to be lacking for fully developing a method to evaluate the ultimate strength of the concrete-filled steel pipe pile head.

• In related references, the stress transfer mechanism from the steel pipe to the filled concrete via inner ribs has remained unclear.
• In the presence of concrete on the side surface of the thin-plate steel element, it has been noted in reference [30] that the progression of local buckling is restrained, leading to an increase in the strength of the steel pipe. However, in references [24,25,26,27], the local buckling restraint effect of the filled concrete has not been clearly identified, nor has it been explicitly addressed.
• Under the current guidelines, the bearing capacity of filled concrete for shear connectors adopts the bearing capacity formula based on the results of concrete push-out tests from references [28], and the bearing capacity is considered for the number of inner ribs. However, in the concrete-filled steel pipe pile head shown in Figure 1, the stress in the steel pipe is not entirely transferred to the infill concrete, as in push-out tests. Instead, the steel pipe and the infill concrete act as parallel springs. Therefore, it remains unclear whether the bearing stress carried by the inner ribs at the ultimate state of the concrete-filled steel pipe pile head reaches the concrete bearing strength specified in reference [28].

1.3. Research Purpose

To construct an interaction curve for the bending and compressive strengths of the concrete-filled steel pipe pile head section in accordance with the Japanese specifications shown in Figure 1, it is essential to establish the ultimate mechanism and strength evaluation formula for the pile head under compressive forces. This paper evaluates the compressive strength of concrete-filled steel pipe pile heads and clarifies the contribution of infill concrete. Section 2 describes compression tests on specimens simulating concrete-filled steel pipe pile heads, based on reference [27], to investigate stress transfer behavior from the steel pipe to the infill concrete up to the ultimate state. Section 3 develops an analytical model to reproduce these experimental results, while Section 4 applies a similar model to replicate push-out test results from reference [28]. This analysis confirms the bearing strength of the inner ribs for various diameter-to-thickness ratios D/t of the steel pipe and concrete strengths. Finally, Section 5 calculates the compressive strength of concrete-filled steel pipe pile heads for different parameters and proposes a compressive strength evaluation formula.

2. Compression Loading Tests on the Concrete-Filled Steel Pipe Pile Head

2.1. Test Setup and Test Parameters

Figure 2 illustrates the specimen of the concrete-filled steel pipe pile head along with the details of the welded sections. The specimen is a half-scale model of a full-size steel pipe pile. The shape of the test specimen was primarily based on the specimens used in the biaxial loading tests of concrete-filled steel pipe pile heads [27]. As shown in Figure 2a and Figure 3, the specimen is positioned upside down under the Amsler testing machine; in this orientation, the bottom end of the specimen represents the pile head. To ensure that the failure mechanism forms in the concrete-filled steel pipe pile head (enclosed by the red dashed lines in Figure 1), the specimen is divided into two main parts: the TEST Section and the LOADING Section. The TEST Section represents the head part of a concrete-filled steel pipe pile with two layers of inner ribs. Since the inner ribs are arranged at a pitch of 1/4D, the Test Section length is 1/2 D. This part is designed to examine the compressive buckling strength of the steel pipe and the concrete’s bearing capacity under pressure from the inner ribs during the experiments. The influence of steel pipe length on the local buckling resistance of cold-formed steel pipes is analytically examined in Section 5.2, confirming that the effect is minimal within the range of diameter-to-thickness ratio D/t typically used in steel pipe piles. The loading section has a steel pipe with doubled thickness, ensuring it does not yield until the TEST Section exhibits local buckling and strength deterioration under compressive force. The test pipe has dimensions of D = 488 mm with t = 9 and is fabricated by bending a steel plate (SS400, JIS G 3101 [31]) into a circular shape, followed by welding along the seam. The diameter-to-thickness ratio is D/t = 54. The loading pipe measures ϕ508 × t19 and is made of general structural carbon steel (STK490, JIS G 3444 [32]). The length of the test steel pipe l is equal to the height of the second rib, which is half the diameter of the steel pipe D (see Figure 1 and Figure 2). The diameter-to-thickness ratio of the test section, D/t = 54, was chosen as a relatively large value within the range of D/t = 30–60 typically employed for steel pipe piles in actual buildings. This selection was made because the objective of this study is to elucidate the contribution of the filled concrete to the compressive strength of the concrete-filled steel pipe pile head. It is anticipated that with a relatively large D/t ratio, the proportion of compressive strength borne by the filled concrete will be comparatively higher.

The inner ribs inside the test pipe have a thickness of s = 6 mm and a width of w = 25 mm, fabricated from rolled steel plates (SS400). The size of the inner ribs was determined following the Japanese design specifications for steel pipe piles [33]. Hereafter, the lower inner rib will be referred to as “inner rib 1”, and the upper inner rib will be referred to as “inner rib 2”, as defined in Figure 2a.

Figure 2c provides a detailed view of the welding joints: between the test pipe and the loading pipe, and between the steel pipe and the inner ribs. Inner ribs 1 and 2 were attached to the test pipe using fillet welding on the bottom sides of the inner ribs, following the specifications [33]. For inner rib 2, the rib was pre-welded to the test pipe 10 mm below the welding surface between the test pipe and the loading pipe, which also served as a backing ring for the butt joint between the test pipe and the loading pipe during the V-groove fillet welding process. The inner ribs have a gap width x of 35 mm (2% of the circumference) to ensure proper fitting to the circumference of the test pipe. The fillet weld strength at each stop was designed to exceed twice the maximum bearing reaction force from the concrete filling, as determined from the experimental results in Section 2.2. Normal concrete with a maximum aggregate size of 20 mm was used and filled to a height of 1.0D from the bottom of the TEST Section (Figure 2). The concrete was poured from the top of the loading section, which was the same casting direction used in reference [27].

Table 1. List of specimens for compression test.

Specimen	TEST Section				LODATING Section			Inner Rib		Concrete
	D	t	D/t	l	D’	t’	l’	s	w
A-E	488	9	54	244	508	19	294	6	25	NAN
A-N								NAN		1.0D
A								6	25	1.0D
B				488			50	6	25	1.0D

presents the experimental variables and dimensions of each part used in the compression loading test. The test specimens are categorized into four types:

• Specimen A-E, a hollow steel pipe with two inner ribs and a TEST Section length of l = 0.5D, which corresponds to Specimen A without infill concrete.
• Specimen A-N, a hollow steel pipe without inner ribs but filled with concrete, corresponding to Specimen A without inner ribs.
• Specimen A, a hollow steel pipe with inner ribs and filled with concrete, regarded as the standard specimen, as shown in Figure 2a and Figure 3.
• Specimen B, a variation of Specimen A where the length of the TEST Section is increased to l = 1.0D.

The symbols used in Table 1 are defined in Figure 2.

Figure 3 illustrates the locations where the displacement transducers were installed and the positions where the strain gauges were attached. Displacement was measured at four circumferential points around the steel pipe, capturing both the displacement of the TEST Section δ_t and the overall displacement δ. From this point onward, δ_t and δ will be calculated as the average of the measured values at these four points. As shown in Figure 3 (right), vertical strains were measured at the heights of sections (i) and (ii) at eight circumferential locations, while for sections (iii) to (v), they were measured at four circumferential locations per surface.

Figure 4 provides an overview of the compression loading test conducted on the head part of a concrete-filled steel pipe pile. The loading is monotonic compressive loading, with a loading rate of 4–5 kN/s. The test was performed using a 10,000 kN Amsler testing machine. The compressive load was applied until the specimen lost its compressive strength, which was defined as 80% of the maximum strength, as a result of the progression of local buckling in a steel pipe. Prior to the main loading test, a preliminary load of 100 kN was applied. The strain distribution around the circumference of the steel pipe, as measured by strain gauges (Figure 3), was adjusted to achieve uniformity using thin stainless steel plates placed between the top of the steel pipe and the Amsler head.

Table 2. Material properties.

Steel Pile (TEST Section)
Young’s Modulus Es (×103 N/mm2)	yield Strength σsy (N/mm2)	Ultimate Strength σsu (N/mm2)
200	298	431
Concrete
	Compressive Strength σcc (N/mm2)	Slitting Tensile Strength σcs (N/mm2)
	28.8	3.7

presents the material properties of the test steel pipe (t = 9.0, SS400) and the infill concrete. The Young’s modulus E_s, yield and ultimate stresses of the test steel pipe σ_sy, σ_su were determined through tensile tests on coupons cut from the rolled steel pipe (ϕ488 × t9, SS400), avoiding the seam. The properties of the concrete were obtained from compression and splitting tests conducted on test specimens. In Figure 5, the stress–strain relationship obtained from the tensile test of the test steel pipe is presented. The shape of the tensile test specimens cut from the steel pipe followed the No. 12 specimen specified in [34], and the gripping sections were flattened before conducting the test. The tensile test was conducted in accordance with [34]. The tensile stress σ is calculated by dividing the applied tensile force N by the initial cross-sectional area of the test specimen A₀. The strain ε_gage is taken as the average of the strain values measured using gauges attached to both the front and back of the test specimen. From Figure 5, it is noted that the stress–strain relationships for the steel pipe used in the TEST Section exhibit a distinct yield point and a yield plateau, unlike those of the actual steel pipe, as discussed in Section 3.2.

2.2. Maximum Strength and Failure Mode

Figure 6 illustrates the relationship between the compressive load N applied to the specimens of the concrete-filled steel pipe pile head and the normalized deformation ratio μ of the TEST Section. The normalized deformation ratio μ is defined as the average strain of the test steel pipe ε_t (= δ_t /l) divided by the yield strain ε_sy (= σ_sy/E_s). In the figure, the maximum strength ratios η_m, defined as the maximum load N_max divided by the yielding axial strength of the steel pipe _sN_y (= σ_sy A_s), are also shown. A solid black line in Figure 6 (left) represents the elastic stiffness of the test steel pipe (E_s A_s), while a horizontal dashed line in Figure 6 (right) indicates the yielding axial strength _sN_y of the steel pipe. Here, E_s and σ_sy are defined in Table 2, and A_s is the cross-sectional area of the steel pipe. From the left-side figure of Figure 6, no significant differences in elastic stiffness were observed under low loads where μ ≤ 0.2. Beyond μ = 0.2, the stiffness of specimens A-E, A-N, and B remained similar, while only Specimen A exhibited an approximate 15% increase in stiffness. From Figure 6 (left), the compressive loads of specimens A-E, A-N, and B were nearly equal to the yielding axial strength _sN_y of the steel pipe, and no increase in stress capacity was observed after the yielding of the steel pipe until the strength began to deteriorate. In other words, in this test specimen, the improvement in compressive strength due to the local buckling restraint effect provided by the concrete filling was not observed. On the other hand, Specimen A showed an increase in compressive load N of approximately 1000 kN compared with the other specimens. This increase is attributed to the transfer of compressive force from the steel pipe to the infill concrete via the inner ribs. The stress transfer mechanism between the steel pipe and the infill concrete is described in detail in Section 2.3.

Figure 7 shows the specimens after the loading test. For the concrete-filled specimens A-N, A, and B, the condition of the infill concrete, photographed after removing the steel pipe, is also presented. From Figure 7a,b, specimens A-E and A-N exhibited local buckling at the lower half of the TEST Section. The lower end of the steel pipe in the TEST Section, placed flat on the loading plate, has a smaller out-of-plane rotational restraint compared with the upper end, which is fixed with butt welding to the thicker steel pipe of the loading section (with twice the plate thickness). The buckling location shifted upward in Specimen A-N compared with that of Specimen A-E. This may be because the infill concrete restrains the rotation of the steel pipe, resulting in more moderate strength degradation compared with Specimen A-E. From Figure 7b, the infill concrete remained intact in Specimen A-N. From Figure 7c, Specimen A exhibited local buckling of the steel pipe at the upper part of the TEST Section (between the inner ribs). Observing the infill concrete, it was confirmed that the surface of the concrete directly below inner rib 2 was significantly spalled while almost no damage was observed below inner rib 1. This indicates that the buckling deformation concentrated between two inner ribs; inner rib 2 moved downward, spalling infill concrete, while inner rib 1 stayed the same height. Observing the infill concrete, it was confirmed that the surface of the concrete directly below inner rib 2 was significantly spalled, whereas almost no damage was observed below inner rib 1. This indicates that the buckling deformation was concentrated between the two inner ribs: inner rib 2 moved downward, causing the spalling of the infill concrete, while inner rib 1 remained almost at the same height. Therefore, it can be inferred that the bearing pressure transferring the compressive force from the steel pile to the infill concrete was greater for inner rib 2 than for inner rib 1. In Specimen A, no cracks were observed in the fillet welds of the inner ribs in this specimen, nor was any noticeable residual deformation of the inner ribs detected. From Figure 7d, for Specimen B with a length of l = 1.0D, local buckling occurred above inner rib 2. At this time, no significant damage was observed in the infill concrete near the inner ribs. This is likely because the maximum load carried by the gross cross-section at the height of inner rib 2 was limited by the buckling strength of the steel pipe, as shown in Figure 6. Further details are discussed in Figure 9.

2.3. Stress Transfer Mechanism Between Steel Pipe and Infill Concrete

The strains measured on the inner and outer surfaces of the steel pipe at sections (i)–(iii) shown in Figure 2 are presented in Figure 8. The inner strain represents the average values of measurements taken from the strain gauges attached to the inner surface of the steel pipe, while the outer strain represents the average values of measurements taken from the strain gauges attached to the outer surface of the steel pipe, as also shown in Figure 4. The average strain ε_s,avg was calculated as the axial strain obtained by averaging the inner and outer strain values. The yield strain ε_sy =1490 μ is indicated with a horizontal black line in the figure.

Based on Figure 8a, for Specimen A-E, the strain values on the inner and outer surfaces of the steel pipe begin to diverge around μ = 0.5. This indicates that local buckling deformation of the steel pipe began to progress at this point. From Figure 8b, for Specimen A-N, which does not have inner ribs, the divergence of inner and outer strain values starts earlier, around μ = 0.2. The results for specimens A-E and A-N suggest that the inner ribs restrained the local buckling deformation of the steel pipe in its initial stages, which, however, did not increase yielding force, as shown in Figure 6. From Figure 8c, in Specimen A, a difference in the average strains ε_s,avg at sections (i) and (ii) appears immediately after loading begins. The strain at section (i) consistently remains smaller than that at section (ii). This suggests that part of the compressive force in the steel pipe was transferred to the infill concrete between sections (ii) and (i). In specimens A-E, A-N, and A, the average strain ε_s,avg at section (iii), where the steel pipe thickness is twice that of sections (i) and (ii), was approximately half of the strain at sections (i) and (ii). Based on Figure 8d, for Specimen B, in which the TEST Section length was doubled, the strain at section (iii), where buckling had progressed, exhibited the most significant increase. In contrast, there was no notable difference in the average strains ε_s,avg between sections (i) and (ii), compared with Specimen A.

In Figure 9, the relationship between the applied load N and the normalized deformation ratio μ of the steel pipe in specimens A-N, A, and B, which are filled with concrete, is shown by black lines. Additionally, the sectional force of the steel pipe _sN_i at section (ii), located between the inner ribs, is shown in red. The difference between the applied load N and _sN_ii, represented as N − _sN_ii, is shown in blue, while the difference between _sN_ii and the sectional force _sN_i at section (i), represented as _sN_ii − _sN_i, is shown in green. The difference N − _sN_ii represents the transfer force from the steel pipe to the infill concrete above section (ii), while _sN_ii − _sN_i represents the transfer force between sections (i) and (ii). Figure 10 provides supplementary explanations for Figure 9. The sectional forces _sN_i and _sN_ii of the steel pipe were simply calculated by multiplying the stress, derived from the axial strain ε_s,avg shown in Figure 8, by the cross-sectional area A_s and Young’s modulus E_s of the test steel pipe. For this calculation, the stress–strain relationship of the steel pipe is assumed to follow a perfectly elastic-plastic model based on Figure 5. In Figure 9, solid lines represent the range where the axial strain ε_s,avg at sections (i) or (ii) shown in Figure 8 does not exceed the yield strain ε_sy, while dashed lines indicate the range where the strain exceeds ε_sy. The initial stiffness of the sectional force _sN_ii (red line) is indicated by a black dashed line, and the theoretical stiffness calculated from the Young’s modulus E_s and cross-sectional area A_s of the steel pipe shown in Table 2, it is additionally illustrated in orange.

Figure 10 illustrates the force transfer mechanism from the steel pile to the infill concrete, which occurs through the bond force between the steel pile and the infill concrete, as well as through the bearing force exerted by the inner ribs on the infill concrete. In the figure, _cN₁ and _cN₂ represent the bearing force exerted by the inner ribs 1 and 2 on the infill concrete, respectively.

In Specimen A-E, shown in Figure 9a, which is a hollow steel pipe with inner ribs, the initial stiffness of the compressive force _sN_ii at section (ii) corresponds well to the theoretical stiffness calculated by multiplying the Young’s modulus E_s of the steel material and the cross-sectional area A_s obtained from material testing.

In Specimen A-N, shown in Figure 9b, which is a steel pipe filled with concrete but without inner ribs, an increase in the initial stiffness of the compressive load N (represented by the black line in the figure) was observed compared with the hollow steel pipe Specimen A-E (Figure 9a). However, this increase was marginal. In Specimen A-N, the blue line (N − _sN_ii) and the green line (_sN_ii − _sN_i) can be interpreted as the bond force between the steel pipe and the infill concrete, as illustrated in Figure 10b. From Figure 9b, it is evident that the bond force is significantly smaller than the steel pipe sectional force _sN_ii. Additionally, the concrete bond force has negligible influence when the slope of _sN_ii begins to decrease from its initial gradient. The maximum bond force is estimated to be approximately 250 kN. Assuming that the bond force is uniformly distributed and reaches the concrete bond strength over the height of the infill concrete, this corresponds to a bond stress of 0.35 N/mm². As a reference, the bond strength between circular steel pipes and concrete suggested in the Structural Design Guidelines and Commentary for Steel Reinforced Concrete Structures [35] is 0.34 N/mm², which is close to the value obtained for this specimen.

In Specimen A of Figure 9c, the initial stiffness of the compressive load N (black line in the figure) increased more significantly than Specimen A-N and the hollow steel pipe (Specimen A-E in Figure 9a). N − _sN_ii (blue line) and _sN_ii − _sN_i (green line) include not only the bonding force but also the bearing force (_cN₁ and _cN₂ in Figure 10) transmitted to the infill concrete through the inner ribs. From Figure 9c, the total of N − _sN_ii (blue line) and _sN_ii − _sN_i (green line) was 3.3 times that of Specimen A-N (Figure 9b) at μ = 0.5, which transmits compressive force to the infill concrete solely through concrete bonding force. Until the steel pipe sectional force _sN_ii reached the yield axial force _sN_y, N − _sN_ii (blue line) and _sN_ii − _sN_i (green line) were approximately equal. This indicates that, during the elastic phase of the steel pipe, the compressive force borne by the steel pipe section of the TEST Section between inner ribs 1 and 2 exceeded that between the pile head and inner rib 1. As a result, local buckling progressed between inner ribs 1 and 2, as shown in Figure 7c. After reaching μ = 1.0, _sN_ii − _sN_i decreased and bore almost no compressive force. In contrast, N − _sN_ii began to increase, reaching 950 kN. It is considered that, while the stiffness of the steel pipe decreased due to the initiation of local buckling and yielding between two inner ribs, the bearing stiffness of the infill concrete compressed at the inner ribs relatively increased. This caused more compressive force to be transmitted to the infill concrete in the region above section (ii). In Specimen A-N of Figure 9b, bonding force nearly disappeared at μ = 1.0. Therefore, in Specimen A, N − _sN_ii and _sN_ii − _sN_i after μ = 1.0 are considered to be almost equivalent to _cN₂ and _cN₁ defined in Figure 10, respectively. Since it has been confirmed that the concrete directly below inner rib 2 of Specimen A spalled off, it suggests that N − _sN_ii = _cN₂ = 950 kN represents the concrete’s bearing capacity at the inner rib in this test specimen.

In Specimen B, where local buckling occurred further above inner rib 2 as shown in Figure 9d, the steel pipe sectional force _sN_ii at section (ii) below inner rib 2 did not reach the yield axial force _sN_y. Additionally, the compressive force borne by the infill concrete remained smaller compared with that of Specimen A.

Based on the above, it can be concluded that the effect of the infill concrete can be fully expected when the ultimate failure occurs at the concrete-filled steel pipe pile head with inner ribs.

3. Analytical Model to Simulate Compressive Behavior of the Concrete-Filled Steel Pipe Pile Head

3.1. Configuration of Analytical Model

The numerical analysis was conducted using the finite element program ABAQUS 6.14 [36]. ABAQUS has been shown in the references [24,25,26,37,38], for example, to reasonably reproduce experimental results of concrete-filled steel tubes (CFTs). The reference [37] also demonstrates in detail that it can effectively replicate both the confinement effects of the infill concrete by the outer steel pipe.

The numerical analysis model shown in Figure 11 simulates the specimen of the concrete-filled steel pipe pile head discussed in Figure 2. The steel pipe was modeled using shell elements S4R, while the infill concrete and inner ribs were modeled using three-dimensional solid elements C3D8R available in the ABAQUS library. In the study [39], which analytically evaluated the ultimate bending strength of steel pipes with local buckling, it was shown that using 40 or more elements per 1D in the longitudinal direction, related to the local buckling waveform, ensures convergence of the analysis results. Additionally, while the details of the steel pipe pile head examined in this paper differ, the study [24,25,26], which analytically evaluated the ultimate bending strength of concrete-filled steel tubes with inner ribs, adopted 30 elements per 1D. In this analysis, for the TEST Section where local buckling occurs, 30 elements were used for every 0.5D of length, providing a sufficiently dense mesh. The nodes of the shell elements representing the steel pipe were positioned along the coordinates of the pipe’s inner diameter (Figure 11, center right). The inner ribs and the steel pipe were integrated using tie constraints [36], which restricted the relative displacements and rotational displacements between the paired coordinates on the contact surfaces (Figure 11, center right). Additionally, inner rib 2 was restrained to the loading steel pipe using tie constraints [36]. The boundary conditions were set as fully fixed at both the bottom end of the steel pipe and the bottom end of the concrete. The loading was applied by incrementally increasing the vertical displacement, with the condition that the vertical displacements of the node group at the top end of the steel pipe remained equal at all times.

3.2. Interface Modeling Between Steel and Infill Concrete

When concrete is filled inside a steel pipe, the expansion caused by concrete damage is restrained by the steel pipe, resulting in an increase in the compressive strength of the concrete. This confinement effect is sometimes incorporated directly into the concrete constitutive law, as in reference [40]. However, in this study, the confinement effect is reproduced by separately defining the concrete damage model in Section 3.3 and specifying the contact interaction between the concrete and the steel pipe.

The pressure generated between the steel pipe and the filled concrete, as well as between the inner ribs and the filled concrete, is accounted for using the contact model implemented in ABAQUS [36]. This is based on references [24,25,26], where the hysteretic behavior and failure modes of concrete-filled steel pipes with inner ribs were examined through ABAQUS simulations. The respective surfaces are defined as contact pairs. Therefore, it was determined that defining contact as surface-to-surface interaction using ABAQUS’s contact pair model better represents the actual behavior compared with modeling interaction as node-to-node interactions. This is because, in the target analysis, the steel pipe moves downward against the filled concrete while undergoing local buckling. The surface of the filled concrete was defined as the slave surface, and a hard contact [36] was applied to ensure that the concrete surface does not penetrate the steel pipe or the inner rib surfaces, which were defined as the master surfaces during contact.

The friction and bonding forces between the two elements during contact were not considered because N − _sN_ii and _sN_ii − _sN_i (blue and green lines in Figure 9, respectively) became nearly zero after the yielding of the steel pipe for Specimen A-N (Figure 9b).

3.3. Constitutive Models for Infill Concrete and Steel Pipe

Among the Concrete Damage Plasticity models for the constitutive law of infill concrete, such as the one described in reference [41], the Drucker–Prager hyperbolic function [42], available in the ABAQUS material library [36], was employed. The Drucker–Prager-based damage-plasticity model is noted for its numerical stability and has been adopted in numerical analyses considering the interaction between steel and concrete, such as in CFT columns [24,25,26] and composite beams [43,44]. References [24,25,26] and [44] indicate that while reproducing degradation behavior remains challenging, the model effectively replicates the hysteretic behavior of steel–concrete composite structures up to their ultimate strength. The plastic potential function, yield function, and coefficients in the damage-plasticity model are fundamentally the same as those used in references [24,25,26,42,43,44]. The material dilation angle ψ, which represents the volumetric change in concrete under shear deformation, was set to 30°, based on reference [45], which conducted simulation analyses in ABAQUS to simulate the results of compression tests on concrete-filled steel pipe columns.

Figure 12 illustrates the schematic stress–strain relationship, and

Table 3. Constitutive law for concrete material.

	Tension			Compression
ascending region	Linear with stiffness of Ec			Euro Code [49]
				${\sigma }_c=\left\{{\displaystyle \frac{kX-X^2}{1+\left(k-2\right)X}}\right\}{\sigma }_{cc}$	(3)
				$X={\displaystyle \frac{{\epsilon }_c}{{\epsilon }_{cc}}}$
				${\epsilon }_{cc}=0.0022$
				$k=1.05E_c{\displaystyle \frac{{\epsilon }_c}{{\sigma }_{cc}}}$
descending region	Uchida, et al. [46]			Modified Popovics [50]
	${\sigma }_c={\left\{1+0.5{\displaystyle \frac{{\sigma }_{ct}}{G_F}}w\right\}}^{-3}{\sigma }_{ct}$	(1)		${\sigma }_c=\left\{{\displaystyle \frac{1}{n}}+{\displaystyle \frac{\left(n-1\right){\left({\epsilon }_c/{\epsilon }_{cc}\right)}^m}{n-1+{\left({\epsilon }_c/{\epsilon }_{cc}\right)}^{nm}}}\right\}{\sigma }_{cc}$		(4)
	$G_F=10{d_{\max }}^{1/3}{{\sigma }_{cc}}^{1/3}$	(2)	[47]	m = 0.5: normal concrete
	$d_{\max }=20$			n = 6.5: W/C = 65%
	$w=\epsilon l_{el}$			$k=1.05E_c{\displaystyle \frac{{\epsilon }_c}{{\sigma }_{cc}}}$
	lel: representative element length
	${\sigma }_{ct}=0.291{{\sigma }_{cc}}^{0.637}$	(5)	[51]

describes the material constitutive law for infill concrete. For the tensile side of the stress–strain relationship, the response is elastic up to the tensile strength, and the post-peak stress decline adopts a tensile softening curve (an inverse cubic equation) considering the fracture energy G_F of concrete (Equation (1) in the table of Figure 12) based on reference [46]. The fracture energy G_F is calculated using Equation (2) in the table of Figure 12, which uses the maximum coarse aggregate size and compressive strength as parameters [47]. The Young’s modulus E_c of concrete is determined according to reference [48], and the Poisson’s ratio is set to 1/6. For the compressive side of the stress–strain relationship, the ascending region adopts the formula from Eurocode 2 [49], and the descending region uses the empirical equation proposed by Tanigawa et al. [50] (Equations (3) and (4) in the table of Figure 12). In the numerical analyses simulating the experimental results of Section 2 presented in Section 3.2, the compressive strength σ_cc and tensile strength σ_ct of concrete correspond to the compressive strength σ_cc shown in Table 2. In the numerical analyses in Section 4 and Section 5, where the steel pipe diameter, concrete strength, and inner rib thickness are varied as parameters, the tensile strength is calculated using Equation (5) in the table of Figure 12, which is derived from the specified concrete compressive strength σ_cc [51].

Figure 13 illustrates the material constitutive law for steel pipes used in the numerical analysis. The vertical and horizontal axes represent the true stress σ′ and true strain ε′, respectively. The black solid line in Figure 13 represents the constitutive law with a distinct yield point and yield plateau, determined based on Figure 5 and Table 2, for reproducing the experiments in Section 2. The material constitutive law, particularly for the post-yielding behavior, was established through a trial-and-error process to replicate the test results of Specimen B. Specifically, it reproduces the relationship between axial force and axial deformation of the TEST Section shown in Figure 6, as well as the sectional force _sN_ii at section (ii) of the test steel pipe shown in Figure 9. The true stress–true strain relationship used in the numerical analysis was calculated using Equation (6) in Figure 13.

$${{\epsilon }_s}^{\prime }=\ln \left(1+{\epsilon }_s\right),{{\sigma }_s}^{\prime }={\sigma }_s\left(1+{\epsilon }_s\right)$$

(6)

3.4. Initial Imperfection

The initial imperfection applied to the steel pipe was based on the first-mode shape obtained from an eigenvalue analysis of the steel pipe, with an identical amplitude along the same height. The magnitude of the initial imperfection was set to 4%, as it best reproduced the compressive load degradation slope of Specimen B, where local buckling of the steel pipe occurred above the inner ribs. The material constitutive law for the inner ribs was assumed to follow the material properties of the steel pipe (Table 2, Figure 13). Figure 14 illustrates the first-mode shape ϕ used as the initial imperfection applied to the steel pipe for specimens A and B. The horizontal axis of the first-mode shape ϕ is normalized by its maximum value ϕ_max.

3.5. Reproduction Analysis Results and Stress Transmission from Steel Pipe to Infill Concrete

Figure 15 illustrates the horizontal displacement distribution u_s of the test steel pipe at μ = 1 and 5. As shown in Figure 14, the first mode of Specimen A does not necessarily form a convex wave shape between the upper and lower inner ribs. However, at μ = 5, local buckling progressed between the upper and lower inner ribs, which closely resembles the experimental results shown in Figure 7. The analysis also successfully simulated buckling deformation of Specimen B.

Figure 16 compares the experimental results of specimens A and B shown in Figure 9 with the numerical analysis results. The lower part of Figure 16 provides an enlarged view of the bearing forces _cN₁ and _cN₂ at inner ribs 1 and 2. The experimental results are represented by plotted points, while the analysis results are shown with solid lines. Here, the steel pipe sectional force _sN represents the sectional force between the inner ribs 1 and 2. For Specimen A, plots of estimated forces based on strain gage data are shown up to the point when any of the gauges at section (ii) became unreadable. From Figure 16b, it can be confirmed that the analytical model described in Section 3.1 and Section 3.2 sufficiently captures the experimental results for the compressive load N and the steel pipe sectional force _sN in Specimen B, even in the load reduction region.

From the lower parts of Figure 16a,b, it can be observed that the analysis results for the concrete bearing forces _cN₁ and _cN₂ capture the experimental trends well up to μ = 0.5. for beyond μ = 0.5, the discrepancy between the experimental results and the analysis increases. As a result, the compressive load N acting on the system is approximately 5% smaller than the experimental results. This indicates that the analysis cannot reproduce the rapid increase in the load carried by the inner ribs observed in the experiment, which occurs as the steel pipe yields and local buckling progresses, leading to a reduction in the axial stiffness of the steel pipe. However, the maximum value of _cN₂ experimentally estimated corresponded well with the analytical results. Therefore, it is considered that the ultimate strength of concrete-filled steel pipe pile heads, in cases where local buckling occurs in the steel pipe at the pile head, can be sufficiently reproduced using this analytical model.

For Specimen B shown in the lower part of Figure 16b, the analysis reproduces the experimental trend observed after μ = 0.5, where _cN₂ remains relatively constant while _cN₁ decreases. Similarly, for Specimen A, shown in Figure 16a, the analysis also reflects the experimental trend observed after μ = 0.6, where the bearing force _cN₁ at inner rib 1 begins to decrease. Furthermore, after μ = 1.0, the majority of the compressive force transferred to the infill concrete is supported by the bearing force _cN₂, a trend also observed in the experimental results.

Figure 17 shows the equivalent plastic strain (PEEQ [36]) of the infill concrete between the shear connectors at μ = 5.0. From Figure 17, it can be observed that in the numerical analysis, as in the experimental results (Figure 7c,d), Figure 7a Specimen B exhibited almost no damage progression, while Figure 7b Specimen A showed the progression of plastic strain along the tip of inner rib 2.

From the above, it was confirmed that using the numerical analysis model shown in Figure 11 and Figure 12 and Table 3 allows for reproducing the effect of inner ribs on the compressive strength of the concrete-filled steel pipe pile head, including the yielding and local buckling of the steel pipe. Furthermore, it was also analytically demonstrated that the compressive strength of the concrete-filled steel pipe pile head can be approximately determined as the sum of the axial yield strength of the steel pipe and the concrete bearing strength exerted by a single layer of inner ribs.

4. Simulation Analysis of Concrete Bearing Strength Under Inner Rib-Induced Pressure Based on Previous Push-out Test

Reference [28] reports that the push-out strength of infill concrete in steel pipes with inner ribs increases as the diameter-to-thickness ratio D/t decreases. In Section 3, the analysis successfully reproduced the experimental results for concrete-filled steel pipe pile heads described in Section 2, but the examination was limited to a single diameter-to-thickness ratio of D/t = 54. Therefore, in this section, it is verified whether the push-out test results for concrete presented in reference [28] can also be simulated under basically the same analytical conditions as those in Section 3.

4.1. Configuration of Analytical Model

Figure 18 illustrates the analytical model used to simulate the push-out test specimen described in reference [28]. The test specimens consist of steel pipes with a single row of inner ribs, filled with concrete.

Table 4. List of parameters for push-out test [28].

Diameter-Thickness Ratio D/t	Compressive Strength σcc (N/mm2)
15, 25, 35, 55, 95	25, 39, 44

summarizes the experimental parameters of the push-out tests reported in reference [28]. In both the test specimens and the analytical model, the inner diameter of the steel pipe remains consistent across all diameter-to-thickness ratios D/t. The inner diameter is 191.1 mm, and the thickness of the inner ribs is s = 6 mm.

The analytical element models for each component, the method of attaching the inner ribs to the steel pipe, the definition of contact elements, and the supporting and loading conditions are identical to those shown in Figure 11 and Figure 12 and detailed in Table 3. The analysis is conducted using the same variables listed in Table 4. The yield strength of the steel pipe was set to 408 N/mm² in accordance with reference [28], while the Young’s modulus, which was not specified, was assumed to be 205,000 N/mm². The material constitutive law for the steel pipe was defined as perfectly elastic-plastic, and the second gradient of the stress–strain relationship was set to 1/1000 of the elastic stiffness.

4.2. Simulation Analysis Results of Push-out Test

Figure 19 shows the correlation between the analysis results simulating the push-out test and the experimental results. The analysis results successfully capture the experimental trend that the concrete bearing capacity generally increases as the steel pipe diameter-to-thickness ratio D/t decreases, with an error of approximately 20%.

5. Evaluation of Compressive Strength for the Concrete-Filled Steel Pipe Pile Head

Section 3 confirmed through analysis that the local buckling behavior of the steel pipe and the transfer of compressive stress to the infill concrete via inner ribs could be reproduced until the concrete-filled steel pipe pile head reached its ultimate state. Furthermore, in Section 4, push-out analysis of infill concrete in steel pipes equipped with shear connectors, with the diameter-to-thickness ratio D/t as a variable, demonstrated that the variations in concrete bearing capacity due to changes in the D/t ratio could also be reproduced through analysis.

Building on these findings, this section conducts a parametric study using the previously validated analytical model and proposes a method for evaluating the compressive strength of the concrete-filled steel pipe pile head.

5.1. Simulation Parameters

Parametric analyses are conducted using the analytical model following the configuration in Figure 11 and Figure 12 and Table 3. Similarly to the test specimens discussed in Section 2 and Section 3, the analytical models were also based on a 1/2-scale model. Element and mesh pattern follow the test part of Figure 10. The analysis parameters are shown in

Table 5. Simulation list of parametric study on concrete-filled steel pipe pile head.

Model	Test Part			Inner Rib		Concrete
	L	D	D/t	s	w	σcc
Specimen model	0.5D	400	40, 54, 70, 120	6	25	20, 30, 40
		488		6, 8	25
		600		6	32

. The diameter of steel pipe piles used to support buildings in Japan typically ranges from D = 500 mm to 1200 mm. Therefore, in the analysis, the test specimen diameter of D = 488 mm from Section 2 was used as a reference, and diameters of D = 400 mm and D = 600 mm were also examined. The diameter-to-thickness ratio D/t was set to D/t = 40, 70, and 120, in addition to the test specimen with D/t = 54 from Section 2. Diameter-to-thickness ratios less than D/t = 40 exhibited a tendency for solution divergence, particularly after the initiation of yielding in the steel pipe during analysis. Therefore, these cases were excluded from the scope of this study. The diameter-to-thickness ratio D/t = 120 exceeds the width-to-thickness ratio limit of 100 for circular steel pipe columns and is not typically used for steel pipe piles due to transportation and construction constraints [4,15]. However, this parameter was included to examine the trends in compressive axial resistance and bearing resistance provided by inner ribs in concrete-filled steel pipe pile heads with high diameter-to-thickness ratios D/t. Concrete compressive strength parameters σ_cc was set to 20, 30, and 40 N/mm², which are commonly used for foundations. For the inner rib thickness, the value s = 6 mm, as employed in the test specimens in Section 2, was used as the standard.

The local buckling behavior of steel pipes is generally verified using test specimens with a standard member length of L =3.0D. Based on the experimental results, evaluation formulas for the local buckling strength of steel pipes _sN_u in relation to the diameter-to-thickness ratio D/t have been proposed [52,53]. To evaluate the stress increase ratio η_m of the steel pipe section in cases where failure is governed within the pile head region (within 0.5D from the pile head) with infill concrete and inner ribs, additional numerical analyses were conducted. These analyses examined the effects of member length (L = 3.0D and 0.5D) and the presence of inner ribs at the middle height on the stress increase ratio η_m of the steel pipe.

Table 6. Standard simulation model for steel pipe.

Model	Test Part			Inner Rib		Concrete
	L	D	D/t	s	w	σcc
L3.0-rNAN	3.0D	500	30, 40, 45, 54, 70, 90, 120	NAN		NAN
L0.5-rNAN	0.5D			NAN
L0.5-r6 1	0.5D			6	25

¹ Model L0.5-r6 has a single inner rib at the middle height of the pile.

presents the additional simulation parameters used to investigate the effect.

Figure 20 illustrates the material constitutive law of the steel pipe used in the numerical analysis. The vertical and horizontal axes represent the true stress σ′ and true strain ε′, respectively. As shown in Figure 5 and Figure 6, the steel pipe used in the specimens of Section 2 exhibited a stress–strain relationship with a relatively clear yield point and yield plateau. In contrast, cold-formed steel pipes typically exhibit a Round House-type (RH-type) constitutive law without a distinct yield plateau. According to references [52,53], the post-yield stress increase rate of cold-formed steel pipes (STK materials) varies significantly between specimens, even for those with the same diameter-to-thickness ratio D/t. In some cases, the stress increase rate η_m reached as high as 1.5. Based on these findings, two types of material constitutive laws with different stress increase rates (depicted as red and blue solid lines in Figure 17) are considered. The Round House-type constitutive law is modeled using the Ramberg–Osgood empirical formula (Equation (7) in Figure 17) from reference [53]. In Equation (7), the yield stress σ_sy is defined as the stress that induces a residual strain of 0.2%. The red solid line in Figure 17 represents the case where m = 10.5 (RH-1), which reasonably simulates the experimental results of one of the specimens from reference [52] (D/t = 52.6, yield strength σ_sy = 319 N/mm², stress increase rate η = 1.22). The blue solid line represents the case where m =17.5 (RH-2), which refers to the values approximated by Equation (7) in reference [53] for the stress–strain relationship of cold-formed steel pipes. For RH-2, the yield strength σ_sy is also set at 319 N/mm², consistent with RH-2. Regarding the variability in the stress increase ratio η_m of cold-formed steel pipes (STK material) summarized in previous studies [53], RH-1 represents an average value, while RH-2 provides approximately the lower bound. Details are explained in Section 5.2.

$${\epsilon }_s={\displaystyle \frac{{\sigma }_s}{E_s}}+0.002{\left({\displaystyle \frac{{\sigma }_s}{{\sigma }_{sy}}}\right)}^m$$

(7)

Figure 21 shows (a) the first mode shape used as initial imperfections applied to the steel pipe with diameter-to-thickness ratios D/t of 40, 54, 70, and 120, and (b) the out-of-plane displacement distribution u_s of the TEST Section steel pipe at a plasticity ratio μ = 20. Regardless of the initial imperfection applied based on the first mode shape, the steel pipe with D/t = 54, 70, and 120 exhibited local buckling progression between the upper and lower displacement restraints. On the other hand, for D/t = 40, local buckling progressed in both the region between the upper and lower inner ribs and the region between the pile head and the inner rib 1. Additionally, a bulging deformation occurred at inner rib 1.

5.2. Stress Increase Ratio of Steel Pipes for Concrete-Infill Steel Pipe Pile Head

Figure 22 illustrates the stress increase ratio η_s,max of steel pipes with respect to the normalized diameter-to-thickness ratio 1/β, where 1/β = σ_sy/E_s (D/t). The stress increase ratio η_s,max in the test specimen model was calculated as the ratio of the maximum sectional stress of the steel pipe, measured between inner ribs 1 and 2, to its yield stress. For reference, diameter-to-thickness ratios D/t of the steel pipe are also shown at the bottom of the figure. These D/t correspond to the material properties for RH-1 and RH-2, as defined in Figure 17, with E_s = 205,000 N/mm² and σ_sy = 319 N/mm². The small gray hollow circles in the figure represent previous experimental results of cold-formed steel pipes summarized in reference [53], with the regression line shown in black (Equation (13)). These gray circles also include data reported in reference [53], which was used to establish the constitutive model RH-1 (Figure 17). The numerical analysis results for the reference series L3.0-rNAN, L0.5-rNAN, and L0.5-r6 are plotted in black and gray for the material constitutive models RH-1 and RH-2, respectively.

Focusing first on the reference series L3.0-rNAN, indicated by the black and gray ● symbols in Figure 22, the stress increase ratio η_s,max for the L3.0-rNAN series with the RH-1 constitutive model (black ●) closely aligns with the regression line of the previous experimental data (Equation (8)). In contrast, the RH-2 constitutive model (gray ●), which exhibits a lower increase in stress after yielding (Figure 20), falls below Equation (8) and approaches the lower limit of the experimental data set. Additionally, the stress increase ratio η_s,max of the steel pile of Specimen A from Section 2, represented by the yellow markers in Figure 22, exhibits a stress increase ratio η_s,max at the lower bound of the experimental data for cold-formed steel pipes. This is attributed to the steel pipe used in Specimen A, which has a constitutive model characterized by a distinct yield point and yield plateau.

From Figure 22, no notable difference in the stress increase ratio η_s,max attributable to the length of steel pipes and the addition of inner ribs can be observed when comparing the L3.0-rNAN series with the L0.5-rNAN series and L0.5-r6 series. To examine the effect of infill concrete on the stress increase ratio η_s,max of the steel pipe, η_s,max for the specimen models is presented in Figure 22. The material constitutive model RH-1 was selected as a representative constitutive model for cold-formed steel piles. In the specimen models, η_s,max increased by up to approximately 10% in the range of small diameter-to-thickness ratios D/t, and no reduction in the axial strength of the steel pipe due to concrete filling was observed across all the parameters examined in this study. This indicates that, in the case of the concrete-filled steel pipe pile head, the counteracting effect of confining the infill concrete, as exerted by inner ribs, on the compressive strength of steel pipes is negligible.

Equation (9), represented by the red line in Figure 20, indicates the short-term allowable stress of steel pipes as specified in the Recommendations for Structural Design of Building Foundations by the Architectural Institute of Japan [4] for the axial strength of steel pipe piles at the damage limit state. It is notable that Figure 22 shows Equation (9) evaluates the compressive strength of the steel pipe too conservatively. If the converged value of the stress increase ratio η_s,m in Equation (9) is adjusted from 0.8 to 0.9, the lower bounds of both the experimental data (gray ○) and the numerical analysis results for RH-2 are better evaluated (Equation (10)).

$${\eta }_{s,m}=0.792{\beta }^{0.137}$$

(8)

$${\eta }_{s,m}=0.8+{\displaystyle \frac{5}{D/t}}$$

(9)

$${\eta }_{s,m}=0.9+{\displaystyle \frac{5}{D/t}}$$

(10)

5.3. Adjustment Factor for Bearing Strength of Infill Concrete Under Rib-Induced Pressure

In the Japanese design standards for prestressed concrete structures [54] and the ACI code [55], the bearing strength of concrete σ_cb is determined by multiplying the concrete strength by the square root of the ratio between the bearing area A_c and the loaded area A_s, as expressed in Equation (11). In addition, the recent version of Japanese design standards considers that the bearing strength of concrete does not increase linearly as the compressive strength of concrete σ_cc becomes higher [55]. Therefore, Equation (12) is used to define the compressive strength of concrete σ_cc’ related to the bearing strength.

$${\sigma }_{cb}=\sqrt{{\displaystyle \frac{A_c}{A_s}}}{{\sigma }_{cc}}^{\prime }$$

(11)

A_c: cross-sectional bearing area of concrete

A_s: loaded area subjected to bearing pressure

$${{\sigma }_{cc}}^{\prime }=1.8{\sigma }_{cc}^{(0.8-{\sigma }_{cc}/2000)}$$

(12)

σ_cc: compressive strength of concrete (N/mm²)

Reference [28] introduces the bearing strength factor α to adjust the concrete bearing strength σ_cb to the maximum load N_max obtained from the push-out test results of infill concrete in steel pipes with inner ribs. Figure 23 illustrates the relation between the bearing strength factor α and the diameter-to-thickness ratio D/t in the grey plots for the maximum load N_max from the push-out test results [28]. The gray dashed line represents the related approximation lines. Since α tends to decrease as the diameter-to-thickness ratio D/t of the steel pipe increases, it is considered to reflect the confining effect of the steel pipe on the infill concrete. The current Japanese design recommendations for foundations [4] adopt Equation (14), represented by the black line in the figure, as the lower limit of the maximum load N_max from the push-out test results [28], to determine the concrete bearing strength of the inner ribs in concrete-filled steel pipe pile heads. In reference [4], the sectional area of infill concrete is adopted as the bearing area A_c, while the cross-sectional area of inner ribs considering two layers is adopted as the loaded area A_s in Equation (11).

$${\sigma }_{cir}=\alpha {\sigma }_{cb}$$

(13)

$$\alpha =5.05-0.053D/t (\alpha \ge 1.0)$$

(14)

Based on the analysis results simulating the head of a concrete-filled steel pipe pile, the bearing strength coefficient α is modified. Here, the concrete bearing area of a single layer of the inner rib A_ir is adopted as the loaded area A_s in Equation (11), referencing the findings from Section 2 and Section 3. Figure 23 shows the adjustment factor α for the shear resistance bearing strength. The numerical analysis results are presented for the material constitutive model RH-1 (m = 10.5) used in the test specimen series. The numerical analysis results for the adjustment factor α, associated with the concrete bearing strength of the concrete-filled steel pipe pile head, were generally lower than those corresponding to the maximum load N_max observed in the push-out tests [28]. In the push-out tests, the compressive force acting on the concrete was completely transferred to the steel pipe through the inner ribs. In contrast, at the concrete-filled steel pipe pile head, the compressive force from the steel pipe is borne in parallel by both the steel pipe and the infill concrete. In the latter case, the progression of damage in the infill concrete due to the bearing pressure of the inner ribs, along with the yielding and local buckling of the steel pipe, occurs within the same cross-section. Therefore, it is considered that the confining effect provided by the steel pipe did not enhance the bearing strength to the extent given by Equation (14). Based on the above considerations, the red dashed line in Figure 23, given by Equation (15), is proposed to represent the lower bound of the adjustment factor α for the shear resistance bearing strength of the infill concrete in the concrete-filled steel pipe pile head. For D/t < 50, considering the increase in α at D/t = 40, the gradient of α with respect to D/t was determined with reference to the gradient in Equation (12). For D/t < 40, further investigation is required in the future.

$$\alpha =3-0.05D/t (\alpha \ge 0.5)$$

(15)

5.4. Ultimate Compressive Strength of the Concrete-Filled Steel Pipe Pile Heads

The maximum compressive force obtained from the numerical analysis presented in the former sections is evaluated by the combined strength of the local buckling resistance of the steel pipe and the bearing resistance of a single layer of inner ribs (Equations (16)–(18)). The ultimate axial strength of the steel pipe section _sN_u considers the post-yield stress increase and local buckling. Here, for the stress increase ratio η_s,m, derived from the regression line of previous compression test results on cold-formed steel pipes (Equation (8)), is adopted. The maximum bearing capacity _cN of the infill concrete section is evaluated using Equations (12), (13), and (15).

$$N_u={}_{s}N_u+{}_{c}N$$

(16)

$${}_{s}N_u=A_s{\sigma }_{sc}$$

(17)

$${}_{c}N=A_{ir}{\sigma }_{cir}$$

(18)

$${\sigma }_{sc}={\eta }_{s,m}{\sigma }_{sy}$$

σ_sc: compressive stress of steel pipes considering post-yield stress increase and local buckling.

Figure 24 illustrates the correlation between the evaluation values calculated using the proposed formula for the compressive strength of the concrete-filled steel pipe pile head and the numerical analysis results. In the figure, the hollow plots represent the compressive strength of the steel pipe alone, while the solid plots indicate the compressive strength of the concrete-filled steel pipe pile head as evaluated by Equation (15). The figure also includes data for Specimen A from Section 2. From Figure 24, it can be observed that within the range examined in this study, the modified evaluation formula provides an accurate assessment of the compressive strength of the concrete-filled steel pipe pile head.

6. Conclusions

In this study, a compressive strength evaluation formula for the concrete-filled steel pipe pile head, in accordance with the Japanese specifications shown in Figure 1, was proposed. To achieve this, Section 2 presented compression tests on specimens simulating the pile head, and Section 3 conducted reproduction analyses of the compression test results from Section 2. Section 4 examined whether the bearing resistance of concrete provided by the inner ribs, which is critical for evaluating the compressive strength of the concrete-filled steel pipe pile head, could be analytically reproduced based on previous push-out test results, and Section 5 proposed a method for evaluating the compressive strength of the concrete-filled steel pipe pile head.

The main findings are summarized as follows:

(1)

The compression experiments (Section 2) and numerical simulations (Section 3) conducted on the concrete-filled steel pipe pile head (D/t = 54) with two inner ribs arranged in accordance with Japanese specifications [33] demonstrated the compressive strength of the pile head significantly increases when inner ribs are installed inside the steel pipe. It was observed that the local buckling of the steel pipe occurred between the two ribs, and the infill concrete beneath inner rib 2, located farther from the pile head, experienced bearing failure due to the bearing pressure transmitted from the inner rib. The experiments and simulations revealed that under conditions where yielding and local buckling of the steel pipe progressed, inner rib 2 primarily transmitted stress to the filled concrete, while inner rib 1 contributed minimally to compressive force transmission.

(2)

Based on the compression experiments in Section 2 and the numerical simulations in Section 5, within the scope of this study, no significant effect was observed on the local buckling strength of the steel pipe due to the presence of filled concrete or the welding of inner ribs to the inner surface of the steel tube. The steel tube section at the concrete-filled steel pipe pile head with inner ribs was found to fully demonstrate the ultimate compressive strength equivalent to that of the steel pipe alone.

(3)

It was demonstrated that the bearing resistance of the concrete, provided by the inner ribs, at the ultimate state of the concrete-filled steel pipe pile head under compressive force does not reach the push-out resistance obtained from push-out tests on concrete-filled steel pipes with inner ribs (Equation (14) [28]). This is because, in the concrete-filled steel pipe pile head, the steel pipe and the infill concrete share the compressive force in a parallel spring mechanism. Equation (15) was proposed as the evaluation formula for the bearing resistance of concrete provided by the inner ribs in the compressive strength of the concrete-filled steel pipe pile head.

(4)

The compressive strength of the concrete-filled steel pipe pile head can be evaluated as the sum of the steel pipe’s compressive strength and the bearing resistance provided by a single layer of inner ribs (Equations (16)–(18)). In Section 5, the average stress increase ratio η_s,m derived from previous experimental results (Equation (8) [53]) was adopted to evaluate the compressive strength of the steel pipe alone. However, for design purposes, it is recommended to use a formula that, in some cases, provides a lower bound.

As a result, the bearing strength formula of the filled concrete due to inner ribs in the ultimate flexural strength equations of references [4,27] was revised, and the necessary insights were obtained for establishing the M–N curve at the ultimate state of the concrete-filled steel pipe pile head under seismic forces.

In this study, a compressive strength evaluation formula for the concrete-filled steel pipe pile head was proposed under the condition that the pile head is fully fixed. However, in practical situations, the steel pipe pile head is supported by concrete members, which reduces the axial resistance stiffness of the steel pipe in the parallel resistance mechanism involving the steel pipe and the bearing resistance of the infill concrete provided by the inner ribs. Consequently, the bearing failure mechanism of the infill concrete due to the inner ribs is expected to approach the conditions of the push-out tests more closely. From Figure 23, since Equation (15) provides the lower bound of the bearing resistance of the inner ribs, the compressive strength evaluation formula proposed in this study can be considered to give the lower bound of the compressive strength of the concrete-filled steel pipe pile head.

This study evaluated the compressive strength of the concrete-filled steel pipe pile with inner ribs, assuming specifications for steel pipe piles used in Japanese buildings [33]. The use of inner rib shapes and arrangements outside the current specifications remains a subject for future research, aimed at improving the existing standards.