1. Introduction
In recent years, concrete-filled steel tubes (CFSTs) have been used in different structural applications [
1,
2]. Particularly in China, CFST solutions have been a frequent option to construct long-span arch bridges [
1,
3]. Additionally, CFST solutions are applied in high-rise buildings [
2]. In structures where a high compressive bearing capacity is needed, CFST solutions are adequate. It is well known that the transversal confinement of concrete increases the compressive strength and ductility, which effectively occurs in CFST solutions. CFSTs exhibit enhanced strength and ductility due to the combined effect of the concrete and steel tubes. The reciprocal effect between the concrete and the steel tube in CFSTs improves the mechanical properties of the structure. The concrete is confined in a steel tube, and it reinforces the steel tube due to local buckling. The strength enhancement observed in normal-strength concrete (NSC) is comparatively more significant than that observed in high- and ultrahigh-strength concrete (HSC and UHSC). The potential of CFSTs to achieve the structural requirements under high-loading conditions and the high demands of ductility has motivated and justified diverse research to understand and improve the behavior of CFSTs. The effects of different parameters, such as the concrete strength, the D/t ratio of the tubes, the slenderness, the loading application mode, and additional ways to achieve more confinement have been studied in many works [
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17]. Generally, there is consensus that the tube effect increases the concrete compressive strength and, more significantly, the ductility. The use of external reinforcement beyond the tubes also improves the behavior, especially of the ductility, a critical requirement for seismic conditions. However, according to experimental results, an increase in the confinement effect of the steel tube does not always increase the load-bearing capacity of concrete [
4,
5,
6]. This observation demonstrates an inconsistency with the conventional concept of confinement.
Much of the research on CFST solutions is based on FEM modeling. FEM modeling and analysis has provided significant contributions to the scientific development of CFSTs. However, there are some limitations and needed improvements. As an example, one could refer to [
17], a detailed Ph.D. thesis about concrete confined with external thin circular tubes. In fact, the modeling and failure theories for concrete were able to predict the loading capacity and the failure mode of the concrete inside the tube. However, the analysis was not able to predict and simulate the diagonal fracturing of the external steel tube, as clearly stated by the author. This exemplified limitation, the inconsistencies of some observed experimental results, and the expected application of complex prediction models, justify a review based on the mechanical destruction processes of concrete, as conducted in this research.
Under compressive loading, concrete suffers cracks, even inside a steel tube. Thus, an attempt to understand the mechanical behavior of the CFST solutions needs to account for the effects of cracks, which will depend on their progression, distribution, and number. From a more global perspective, brittle materials under compression loading should be considered as structural systems characterized by the presence of micro- and mini-pillars between cracks [
18]. Based on this concept, confined and unconfined concrete are different systems because the progression of cracks is different and, consequently, so too is the structural system.
Understanding the failure modes has a crucial role in determining the mechanical behavior of concrete in confined conditions such as in CFSTs. The failure modes can be related to the crack pattern of the concrete, describing indirectly what occurs inside the tube. The idea of a structural system, formed by micro-pillars between cracks, gives a mechanistic rationale to the description. Parameters such as the concrete composition, the shape and dimensions of the specimens, the stiffness of the loading system, the loading application mode, and the interaction between concrete and tubes, which affect the failure mode and load-bearing capacity of the structural systems, including CFSTs, can be accounted for in the analysis. Knowledge about the processes of cracking, the crack progression, and failures is needed. The similarities between high-strength concrete and high-strength rocks [
19,
20], as brittle materials with complex internal structure, justify the use of rock mechanics knowledge [
21,
22,
23,
24,
25,
26,
27,
28,
29,
30].
Design codes for CFSTs account for the confinement effect using different formulations [
31]. For example, Eurocode 4 [
31,
32,
33], as a reference for this work, accounts for the confinement effect when the relative slenderness ratio is lower than 0.5 and considers the eccentricity of the applied loading, which is equal to zero in uniform compression. It also considers the ratio between the tube thickness and diameter, as well as the ratio between the yield strength of steel and the compressive strength of concrete. These formulations (1)–(6) consider that the confinement decreases with a higher column slenderness and loading eccentricity, which means bending effects. Thus, to evaluate the confinement effects, compact columns are preferable.
Different researchers have conducted analyses of design code applications based on experimental results and numerical simulations [
5,
11,
12,
34]. According to [
11], Eurocode 4 provides nonconservative results with relative slenderness ratios lower than 0.4 and conservative results for relative slenderness ratios higher than 0.4. In the tests, they considered concrete compressive strengths of 56, 66, and 107 MPa. A similar trend was found in [
9].
The conclusions of [
5] show that Eurocode 4 provides good predictions for ultrahigh-strength short circular CFST columns. However, the authors of [
5] also proposed an alternative formula for ultrahigh-performance-concrete-filled steel tubes, which takes in to account the diameter-to-thickness ratio and the steel yield strength to 235 MPa ratio. Based on experimental tests with compressive-strength concrete ranging between 140 and 184 MPa, the analysis presented in [
12] shows that Eurocode 4 overestimated the confinement effect, which should be ignored.
The references above show that the different codes provide different results, concerning the underestimation or overestimation of the loading capacity. Concerning Eurocode 4, it seems relevant that an overestimation of the loading capacity appears for lower slenderness values. Taking into consideration that the slenderness implies failure modes with bending effects and even buckling, in which confinement action is not achieved, the limitations for the Eurocode 4 seem to be related to the inadequate accounting/understanding of the interaction between concrete and steel tubes.
The need for material consumption optimization with adequate behavior in extreme events, such as earthquakes, justifies the attempts to better understand how concrete and, particularly, high-strength concrete, work inside the steel tubes. The approach proposed in this work, based on the internal destruction processes of concrete, similar to other brittle materials, aims to mitigate the inconsistencies and limitations of the codes and computational analyses.
3. Interpretation of the Mechanical Behavior
3.1. Internal Destruction Processes of Brittle Materials
In the case of uniaxial compression tests of high-strength granite cylinders (height/diameter ratio h/d = 2), the measurement of strains and counting the acoustic events (indications of cracking) can enable the detection of the following limits of phases during internal destruction [
20,
21], (
Figure 12): Limit 1: the end of closing of pre-existing microcracks with favorable orientation (non-parallel to the applied loading). Limit 2: the formation of new longitudinal cracks with stable progression. Limit 3: the beginning of the unstable progression of longitudinal cracks. Limit 4 (fgk): failure due to the instability of the pillars or micro-pillars. Limits 2 and 3 can be considered as effective material properties due to their minor dependence upon external factors [
22,
23]. According to [
24], the utilization of similar measurement techniques such as the counting of acoustic events can determine a similar behavior for concrete. Limit 2 occurs at stress values in the range of 0.4–0.5 fck, and Limit 3 occurs at stress values in the range of 0.75–0.8 fck. These values are in the range of the values obtained for rocks [
20,
21,
25].
The similarities between natural rocks and concrete are advantageous because they enable the application of the concepts in field of rock mechanics for the analysis of the mechanical behavior of concrete. Several studies have been conducted on the behavior of high-strength rocks [
21,
22,
23,
24,
25,
26,
27,
28], such as granites or granodiorites.
These were considered in the present work as references to understand the destruction processes of brittle materials and, consequently, the behavior of CFST elements.
Failure in inclined planes is a relevant aspect of the behavior of compressed brittle materials. Although, failure in inclined planes is similar to that of shear failure, the process does not involve shear processes [
20]. The inclined failure planes occur due to the instability of the material as a structural system composed of micro-pillars between cracks [
30] (
Figure 13), depending upon the crack size, crack density, and loading conditions.
The effect of the steel tube on the filling concrete does not correspond to active confinement, unless some external transversal prestress is used or expansive concrete. The steel tube has a passive effect, which is generated by the internal destruction processes of the concrete corresponding to crack initiation or/and progression.
Moderate transversal confinement is effective for limiting crack progression. However, it has a limited effect on crack initiation [
22,
24,
25]. The concrete inside the steel tube, with passive confinement, corresponds to a system of cracks that can initiate but cannot have significant progression.
The mechanism of crack progression at different levels can be associated with the relative displacement of the irregular crack faces in contact [
3]. Therefore, the compressive forces exerted on the faces and the tensile forces exerted on the tips (
Figure 14) lead to crack progression [
18,
35].
The process depicted in
Figure 14 and the deformation of the mini-pillars contributes to the mobilization of the steel tube in CFST elements. This has a constraining or bracing effect, instead of an active confinement action. The effect of the steel tube is related to the crack progression because the behavior of damaged concrete is determined by the length, spacing, and distribution of the cracks. These parameters affect the slenderness, spacing, arrangement, and imperfections of micro- or mini-pillars.
According to [
24], the cracking process can lead to the confinement of the adjacent zones, where the formation or progression of new cracks is inhibited. For the cases in which the progression of cracks is significant, the resultant longer cracks have an enlarged confinement effect on the adjacent zones (
Figure 15). This contributes to a less damaged material. The failure of the resulting structural system occurs via buckling of the mini-pillars (
Figure 16 and
Figure 17) [
20]. Conversely, the limited progression of cracks implies a less enlarged confined adjacent zone (
Figure 18), which results in a higher number of distributed cracks and a severely damaged internal system. In this case, an “echelon” of cracks [
36] can be formed, with probable failure in inclined planes. Failure of unconfined high-strength brittle materials indicates the formation of long cracks, which are aligned with the applied compression forces. It leads to the separation of specimens in compact pieces [
37]. This behavior is observed in conventional short-term compression tests on specimens with dimensions h/d > 2 under monotonic loading. Conversely, the failure mode is different and occurs under loadings lower than those obtained in the conventional tests when the conditions do not permit a higher progression of cracks, such as confinement inside a steel tube.
According to [
24,
26], the application of cyclic loadings at a level that initiates cracks but does not permit their progression implies a degradation in the load-bearing capacity. Conversely, the cumulative internal damage decreases when the cyclic compression loads are sufficient to enable the progression of long cracks. The progression of a few cracks avoids the formation of adjacent cracks (
Figure 15). This indicates failure at a higher loading level because the material is internally less degraded and resists the instability of the mini-pillars.
The experimental results presented in [
25,
28] demonstrated the failure of high-strength granite samples along the inclined planes with “short axial cracks that form adjacent to the failure surface”. This type of failure is not typical in this high-strength material and is related to the test speed because the axial load was applied slowly (0.00075 MPa/s). The failure loading was lower than that obtained in conventional compression tests, in which failure does not occur with the formation of an inclined plane. When the compressive loadings are applied slowly, it inhibits the progression of cracks. The observed behavior with multiple micro-cracks corresponds to the diagram depicted in
Figure 18. It does not correspond to
Figure 16, which exhibits long cracks. The results of [
23,
26,
27,
28] demonstrated that the conditions of crack progression affect the failure modes and loading capacity. The factors that prevent crack progression but not their initiation contribute to higher internal degradation and lower loading capacity. Failure with the formation of inclined planes is related to the limited progression of cracks, corresponding to a lower loading capacity [
25]. The observations in [
25,
28] confirmed that the inclined failure plane is a result of specific loading conditions such as the loading rate, without any relation to shear processes.
3.2. Effect of Concrete Composition
The composition of concrete affects the cracking pattern of concrete under compressive loads, which affects the behavior of CFST elements. This effect is related to the differences in the behavior between confined and unconfined concrete, in particular, the level of progression and crack density, which determine the behavior of the system in terms of the failure mode and load capacity. For example, in the case of unconfined HSC, silica-fume enhances the progression of cracks, which reduces the density of cracks. The material is globally less damaged and has a high loading capacity. This behavior changes due to the presence of external elements such as steel tubes of fiber-reinforced polymers [
38], which can prevent the progression of cracks. However, these elements do not prevent crack initiation. Therefore, it is possible to explain a few of the experimental results reported in
Section 2, in which the strength index values decreased with an increase in the confinement factor. This behavior was observed when silica fume was used in the concrete composition without coarse aggregates.
The described behavior is related to the observed failure modes [
38] in which the presence of silica fume contributes to failure in the inclined planes of the confined concrete. This type of failure mode, related to the limited progression of cracks is less favorable compared with that of the failure modes observed under unconfined conditions (
Figure 16 and
Figure 17). The aggregates used in concrete composition led to favorable effects in the strength enhancement of the CFST solutions. The strength and size of the aggregates and the relative strength between the matrix and aggregates affect the cracking pattern. Consequently, this affects the slenderness, distribution, and shape of the micro-pillars (
Figure 19). The results obtained in
Section 2 (
Figure 5 and
Figure 6) demonstrated that the presence of aggregates increased the value of the strength index, even using silica fume in HSC composition. Silica fume in HSC with aggregates results in the formation of intragranular cracks, which permits longer cracks and less slender micro-pillars with related favorable effects.
The effects of steel fibers in the concrete compressive strength based on the results described in [
5] were related to the effects of the fibers in the progression of cracks. The analysis considered that the steel fibers enhanced the density of the cracks because their progression was limited (
Figure 14 and
Figure 15). A superposition of the effects of the steel fibers and the steel tube can exist in a CFST to prevent the progression of cracks and enhance the load-bearing capacity and strength index values.
3.3. Composite Effect of HSCFST Elements
The limited progression of cracks due to the steel tube effect constitutes a crucial aspect that relates the behavior of HSCFST elements to the results and analysis presented for high-strength rocks. Although these are different materials, the properties of damaged concrete as a structural system are similar to that of high-strength rocks.
Additional aspects such as shrinkage and low transversal deformability contribute to the low strength enhancement of HSCFSTs. However, these aspects do not explain the reduction in the strength index with an increase in the confinement factor.
Particularly in HSC, with a compact structure, the favorable effect of the steel tube corresponds to a bracing action on the cracked concrete. The confining action is less relevant because the steel tube is passively mobilized. The steel tube contributes to a higher density of microcracks, which promotes failure in the inclined planes and lower relative compression loadings. Therefore, increasing the confinement factor does not always increase the compressive strength of the filling concrete.
The results cited in
Section 2 were used for a comparison between the strength index values for circular and square sections. The differences were not significant. The slight differences in the strength index between the two types of sections were not in accordance with the differences based on the theoretical confinement. Circular sections should provide greater confinement than square sections. However, this was not observed for the strength index values. Therefore, it was concluded that the bracing effect of the steel tubes had a greater significance than the confinement effect.
The higher thickness of the circular tubes prevents instability in an inclined plane of the generated system of micro-pillars. Instead of one evident inclined plane, the internal destruction of concrete corresponds to the progressive crushing of micro-pillars, without a significant increase in the compression loadings but with a higher ductile behavior. A consequence of the destruction of the micro-pillars corresponds to the formation of bulges in the tube, as described in [
5] (
Figure 8).
In square sections, the transversal confinement is generated from the corners with higher effects in the central zone. The distribution of cracks is non-uniform compared with that of circular sections, which affects the mode of failure. The lower uniformity of internal damage leads to worse conditions for failure in inclined planes compared with the circular sections. Additionally, the higher flexibility of the lateral faces enables the local progression of a few cracks, which can have favorable effects.
When the concrete has a greater lateral expansive behavior and a tendency toward the formation of a dense system of micro-pillars under unconfined conditions such as in NSC or low-strength concrete (LSC), the potentially higher confinement effect of circular sections is effectively mobilized. In contrast to compact HSC, the differences between the strength enhancements of circular and square sections are in accordance with the expected confinement action of the two types of sections.
An important aspect in the interaction between concrete and a steel tube is the way that the loading is applied, simultaneously to the concrete and the steel tube or only to the concrete. Experimental studies [
39,
40] of reinforced concrete columns 2 m in length, strengthened with steel jacketing composed of channels and steel strips, show that it is possible to mobilize the external steel by loading only the concrete, with significant enhancement of the compressive strength. The measurements of the relative displacements between the steel and the concrete show higher values close to the ends and residual values in the middle of the columns. In fact, the steel mobilization occurred in the D-zone [
41], with a friction mechanism, observed as a composite action in the B-zone. According to
Figure 14, the friction benefits from the transversal pressure generated by the relative displacement of the cracks in a zone where the axial stresses and strains are not uniform.
The experimental tests in [
12] enabled evaluation of the effects of loading applied only in the concrete core and simultaneously in the concrete core and in the steel tube. Although the quantitative differences concerning the ultimate loading and compressive strength enhancement were not very significant, it was possible to identify the slip effect between the tube and the concrete in the confining stresses and in the ultimate compression loading. The friction and the effect of concrete in the external steel elements are well described in [
39,
40], according to a compression test of normal-strength-concrete square columns, strengthened with steel channels in the corners and steel strips. The relative displacement between the steel and the concrete, the tensile stresses in the steel strips, and the observed effects of the lateral pressure of the concrete on the channels, show a strong interaction between the concrete and the steel. A relevant aspect in these tests corresponds to the dimensions of the tested elements. If the ratio between the height and transversal dimension is higher, it is possible to distinguish D-zones and B-zones. According to
Figure 14, the non-uniform distribution of stresses, as expected in the ends of the tested elements [
39,
40], contributes to higher relative displacements between crack faces, with a higher lateral pressure that mobilizes the friction between steel and concrete. As demonstrated in [
39,
40], after a length of friction mobilization, the cross section works as a perfect composite. Adequate evaluation of the loading application mode should be made with specimens with higher dimensions, aiming to distinguish the D-zones and B-zones and a minimum distance for friction mobilization.
Based on
Figure 14, the parameters that determine the crack pattern, the crack length, and the roughness between their faces will influence the interaction between the concrete and the steel tube. Those parameters depend on the concrete mix, whether there is aggregate or not, the relative strength between the matrix and the aggregate, the aggregate size, the cross-section dimensions, and how the loading is applied.
The idea of the inclined failure being composed of the micro-pillars between cracks also permits a better comprehension of the interaction between the concrete and the tube, explaining, for example, the diagonal fractures in the tubes, as shown in [
5,
17]. Under compressive loading, the micro-pillars rotate, producing inclined tensile forces in the tube and the observed diagonal fracture. That lateral action creates diagonal tensile stresses in the tube, whose value will depend on the micro-pillars’ compressive strength and their length, which inherently are related to the concrete composition and strength. One contribution of this work is the conceptual model shown in
Figure 19, which can be developed in future numerical analyses of CFST solutions.
3.4. Critical Discussion
The previous subsections discussed the internal destruction processes in concrete that influence the interaction with the external tube. The rock mechanics perspective was chosen based on the similarities with concrete and on the developments in the internal destruction processes. In fact, at this stage, we can understand a conceptual model and a general approach based on the material as a structural system determined by the number, size, and distribution of cracks. This approach is applicable to different materials, including the study of the behavior of CFST elements. The proposed approach was based on an indirect understanding of the failure modes and observations in the tubes, limited by the fact that there were no direct observations in CFSTs, concerning the crack distribution and size. The experimental results were used based on an analogy between rocks and stones. However, future tests are justified to understand the crack pattern in the filling concrete, for example, using acoustic emission counting.
The proposed approach seems to also justify a numerical analysis based on the structural model for the concrete; such an analysis is not compatible with a review paper but is adequate for future work.