Pile caps with inclined shear reinforcement and steel fibers

This experimental investigation presents results and a discussion on a series of four reinforced concrete pile caps with and without steel fibers, measuring 400 × 400 × 1000 mm3, which were tested under concentric loading. The study set the steel fiber and the inclined shear reinforcement as variables. The fiber volume fraction was 1.5%, and the concrete compressive strength was 25 MPa. The results showed a tendency to increase ductility and ultimate strength with the use of inclined shear reinforcement; the same behavior was observed with the addition of steel fibers, improving the performance of the tested pile caps. This study opens the possibility of designing slender pile caps, especially when associated with both analyzed parameters.

Foundations are among the most important structural elements used for load transfer from a building to piles or caissons. Pile caps can be classified as rigid or flexible based on criteria similar to those used for shallow foundations. Therefore, the larger and more rigid the structure is, the more complex its design becomes. According to NBR 6118 1 , rigid pile caps are not prone to diagonal tension failure; most often, failure occurs in compression struts 2 . However, some doubt remains as to whether this behavior can be modified with strut strengthening. In the literature, studies [3][4][5] have suggested limiting the height of the block as a function of the angle of inclination of the strut, ranging from 45° to 55°; this may result in an overdesign of the structure. Fighting the shear cracks through reinforcement mechanisms that can improve the performance of the blocks is an ideal way to optimize the design and safety of such structural elements. This can be achieved by using shear reinforcement and/or steel fibers to improve the mechanical properties of concrete in terms of shear, compression, and flexure; in addition, steel fiber reinforced concrete (SFRC) enhances performance in energy absorption, cracking control, and ductility 6,7 . The use of SFRC is being expanded, and its applications range from floor pavements to special structural elements or those subjected to an aggressive or corrosive environment without affecting their durability 8 .
Thus, this experimental study explores the effectiveness of inclined reinforcement and the contribution of steel fibers in improving the performance of concrete pile caps subjected to shear forces since, economically, a considerable gain in strength increase can make this approach feasible and decrease the volume of concrete in pile caps.

Calculation model
In the present study, the pile caps were designed using the strut-and-tie method (STM), which is the most widespread calculation model for the design of rigid pile caps. This design is based on the experimental works previously developed by Blévot and Frémy 4 . The model consists of designing a spatial truss inside a pile cap using tension and compression bars that are connected through nodes, as shown in Fig. 1.
The effective depth (d) of the pile cap is given by Eq. 1. To ensure adequate structural behavior of the pile cap, Blévot and Frémy 4 recommended that θ should be within a 45° ≤ θ ≤ 55° range. For the minimum spacing between the piles adopted in the work, the distance L was equal to three times the edge distance of the pile (D), according to the recommendations of Moraes 9 , (L ≥ 3⋅D).
where L is the spacing between piles; a c is the larger side of the column.
The determinations of the acting stresses near the column and the pile are calculated through Eqs. (2) and (3), respectively. The equations also define the normative verification limits for the design. www.nature.com/scientificreports/ where σ u,tc and σ u,tp represent the failure stresses of the strut in the regions of the column and the pile, respectively; A c and A p are the cross-sectional areas of the column and the pile, respectively; F d is the design load; and fc is the concrete compressive strength.
The longitudinal reinforcement area of the tie over the piles was calculated according to Eq. (4). Equation (5), proposed by Delalibera and Giongo 10 , was used to calculate the tensile force in the tie.
where A st is the total area of longitudinal steel reinforcement in the tie, R st is the tensile force on the tie, and f ys is the yield strength of the longitudinal steel reinforcement.

Experimental setup
Materials and methods. Cement, coarse aggregate, fine aggregate, and water-cement ratio (w/c) were mixed in a 1:2.90:2.10:0.55 proportion. Superplasticizer additive was used to maintain the constant workability of concrete. Table 1 lists the constituents used for the mixtures, and Table 2 lists the mechanical properties of the crimped steel fiber. Flat crimped type C fiber (Fig. 2), classified according to NBR 15530 11 , was used in this research because, according to Soroushian and Bayasi 12 and Mahakavi and Chithra 13 , hooked-end and crimped fibers are more effective at improving the performance of structural elements as a result of their additional anchoring mechanisms 14 . The concrete test specimens were molded and cured for 28 days in the laboratory with 85% relative air humidity. Table 3 presents the results of the characterization tests at 7, 14, and 28 days. There was no significant difference between the plain concrete and the concrete with fiber, so average values were adopted for both mixtures: 25.8 MPa, 1.9 MPa, and 28.4 GPa, respectively, for compressive strength (f c ), tensile strength (f ct ), and modulus of elasticity (E c ).
The steel bars used in the tests were classified according to NBR 7480 15 . Their mechanical properties were determined through axial tensile tests, following the recommendations of NBR ISO 6892-1 16 . Three samples were used in the tensile test; the test bars measured 5.0 mm, 10.0 mm and 12.5 mm in diameter and were used in the stirrups, inclined shear reinforcement and flexural reinforcement, respectively. Table 4 presents the mechanical properties of the steel used.     Instrumentation. The strains in the steels were measured using electrical resistance strain gauges (EESG, EXCEL Sensors, PA-06-125AA-120L), positioned as shown in Fig. 5. Therefore, one strain gauge was installed in the middle of the central flexural reinforcement bar, one in the inclined shear reinforcement bar, and one in the vertical stirrup at the level of the point of intersection with the inclined reinforcement (Fig. 6a), to be in the same stress line caused by the compression strut. The vertical displacements were measured using a deflectometer placed at the bottom of the pile caps at a distance of l/2 = 500 mm, as shown in Fig. 6b. Figure 7 shows the final aspect of the pile caps ready for testing.
Test setup. All pile caps were subjected to centered loading and applied on the face of the column. The test setup was composed of a hollow hydraulic jack and a hydraulic pump (Enerpac). Both the jack and the pump had a 1000 kN capacity, a digital load cell for 1000 kN, a precision of 500 N and an Amsler testing machine used as the gantry system. Figure 8 shows the test system. In all test specimens, an initial load was applied to eliminate looseness.  www.nature.com/scientificreports/ Load-displacement ratio and tenacity. This study focused only on the displacement in the center of the pile caps (l/2 = 500 mm); this way, the analyses were made based on the load-displacement (V − δ) ratio and the quantities that characterize this ratio. Although PC02 SFRC and PC04 IR had almost the same ultimate strength, Table 7 and Fig. 9 show a slight decrease in displacements with the addition of steel fiber; this effect was more pronounced with PC03 SFRC+IR , which showed lower displacements, at a 20%, and 44% reduction, respectively, compared to PC01 REF and PC04 IR . An analysis was made of tenacity (T E ), that is, the capacity of the pile caps to absorb strain energy (Table 7), based on the T E,Pilecaps /T E,REF ratio. Clearly, the fibers and the inclined reinforcement helped to improve the tenacity of the pile caps; however, the most relevant values in terms of T E were found for PC04 IR , with T E,Pilecaps / T E,REF = 3.35, where T E,Pilecaps and T E,REF were the tenacity of the pile caps with some type of additional reinforcement and the reference tenacity, respectively. In terms of displacement, the gains of the pile caps with SFRC and inclined shear reinforcement were not so substantial, mainly for PC03 SFRC+IR (with hybrid reinforcement). It is assumed that the steel fibers inhibited the action of the inclined shear reinforcement, and for this reason, the   Mobilization of the flexural reinforcement. Table 8 Table 7. Parameters defining the V − δ ratio.  Fig. 11, the results show that strain in the instrumented reinforcement of PC04 IR was higher than yield strain, with ε su, IR > ε sy = 2.42‰. However, for the pile cap with hybrid composition (fibers + inclined reinforcement), the inclined reinforcement did not have yield stress. This finding suggests that the steel fibers assumed the function of reinforcement and inhibited the strain of the inclined reinforcement. In summary, the results indicate that the use of inclined shear reinforcement together with steel fibers can lead to oversizing, i.e., the fiber restricts the action of the reinforcement and vice versa. In addition, the pile caps had similar gains in strength, ductility and tenacity, with the exception of the reference pile cap; that is, it is hardly practical and economical to use steel fibers together with inclined shear reinforcement.    (Fig. 12). The graph shows that, in general, the results had different bilinear behaviors, since one section represents the elastic phase (without the appearance of diagonal cracks), while the second section corresponds to the beginning and progress of shear cracks. Table 9 shows the coordinates that define the ultimate load (V u − ε su ) as well as the coordinate indicating the start of the second linear section (V 2L − ε 2L ). The result for strain ε su shows that yield stress occurred in the transverse reinforcement of all pile caps, ε su > ε sy = 4.63 ‰. The ε su,Pilecaps /ε su,REF ratio clearly shows that the level of strain in the stirrups of the pile caps with additional reinforcement (steel fibers and/or inclined reinforcement) is lower than the level of the reference pile cap, namely, ε su,Pilecaps /ε su,REF ∈ [0.80-0.95].

Pile cap V u (kN) δ u (mm) T E (kJ) δ u,Pilecaps /δ u,REF T E,Pilecaps /T E,REF
It can be seen that the reinforcement mechanism provided by the steel fibers and the inclined reinforcement reduces the stress in the reinforcement; therefore, for this study, the transverse reinforcement ratio or even the effective depth of the pile cap can be reduced. The analyses also show that the V 2L,Pilecaps /V 2L,REF ∈ ratio [1.00- 1.65] indicates that, at the beginning of transverse reinforcement mobilization, the stirrups of pile caps PC02 SRFC , PC03 SRFC+IR and PC04 IR underwent more stress than those of the reference pile cap. However, with increased loading, the fibers and the inclined reinforcement tend to assume the function of the main reinforcement. In  Failure of pile caps. The analysis aims to register the integrity of the pile caps after the failure of these structural elements. Figures 13 and 14 reveal the fragility of these elements and their failure mode, namely, shear by diagonal strain. P01 REF was the weakest of all, with the least pronounced diagonal crack. The pile caps  www.nature.com/scientificreports/ PC03 SFRC+IR and P04 IR demonstrated similar behavior, presenting the formation of multiple cracks. However, comparing PC03 SFRC+IR and PC02 SFRC , it can be seen that the combination of inclined reinforcement and steel fibers enhances the bearing capacity, delaying the progression of cracks and inhibiting shear efforts, with the solicitation of the fibers in tension, as the load-strain and load-displacement graphs reveal. Therefore, steel fibers and shear reinforcement improved the ductility of the pile caps.

Conclusions
The present experimental study has assessed steel fiber and inclined shear reinforcement performance in pile caps, whose variables were the use of steel fibers with and without inclined shear reinforcement. Based on the results, the following conclusions were observed: • The use of the fibers provided the same value of the bearing capacity of the pile cap with the inclined reinforcement, with a strength gain of approximately 40%, comparing PC02 SFRC and PC04 IR with PC01 REF .
• The fibers contributed to a 7% strength gain when the usage is combined with inclined shear reinforcement; comparing PC03 SFRC+IR with PC04 IR . • The analysis of the load-displacement ratio (V-δ) shows that the load-bearing capacity of the pile cap with steel fibers and inclined reinforcement (PC03 SFRC + IR ) had the best lower displacements, 20%, and 44% reduction, respectively, compared to PC01 REF and PC04 I , and exhibited greater strain capacity, with ε fu /ε f = 1.28. • Additionally, the V − δ parameters enabled the assessment of not only strength but also the influence of steel fibers and inclined shear reinforcement on the ductility and tenacity of the pile caps. These properties increased significantly in pile caps with steel fibers and/or inclined shear reinforcement, especially PC04 IR , with δ u,Pilecaps /δ u,REF = 1.20 and T E,Pilecaps /T E,REF = 3.35. • The load-strain graph (V − ε s, IR ) shows that the inclined shear reinforcement of PC03 SFRC+IR with hybrid composition (steel fibers + inclined shear reinforcement) did not carry yield stress. • The mobilization of the stirrups shows that the levels of strain in the transverse reinforcements of pile caps PC02SFRC, PC03SFRC + IR, and PC04IR were lower than that of the reference pile cap. For this reason, the additional strengthening mechanisms reduced the shear efforts. • The steel fibers restricted the strain of the inclined shear reinforcement. Therefore, it can be hypothesized that the strengthening mechanisms, under the conditions presented in this study, work satisfactorily by themselves, as the fibers tend to inhibit the action of the inclined shear reinforcement and vice versa.

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.