Experimental study on shear behavior of prestressed reactive powder concrete I-girders

Abstract

As a new generation of concrete, RPC(Reactive Powder Concrete) has attracted great research attention for its ultra-high strength and high durability. In the present paper, experimental results from tests on eight prestressed RPC I-section girders failing in shear are reported herein. The beams with RPC of 120 MPa in compression were designed to assess the ability to carry shear stress in thin webbed prestressed beams with stirrups. The test variables were the level of prestressing, shear span-depth ratio (a/d) and stirrup ratio. Shear deformation, shear capacity and crack pattern were experimentally investigated in detail. With regard to the shear resistance of the test beams, the predictions from three standards (AFGC, JSCE and SIA) on the design of UHPC structures were compared with the experimental result suggesting that the experimental strength is almost always higher than predicted. RPC, as a new concrete, was different from normal concrete and fiber reinforced concrete. Further study should be needed to develop an analytical method and computation model for shear strength of RPC beams.

Keywords

prestressed concrete / RPC(Reactive Powder Concrete) / concrete beams / shear strength, experimental study

Introduction

As a new generation of concrete, RPC (Reactive Powder concrete) has attracted great research attention for its ultra-high strength and high durability. RPC, one type of UHPC(Ultra-High Performance Concrete), is a better alternative to High Performance Concrete and has the potential to structurally compete with steel. RPC, which was developed in the mid-1990s by Bouygues’ laboratory in France, is a special type of ultra-high strength cementitious composite reinforced with short fibres [¹,²].

UHPC has been used worldwide for a number of structural applications including the first prestressed RPC Pedestrian Bridge with single span of 60 meters and crossing the river of Magog in Sherbrook in Canada [³]; the Seonyugyo in South Korea with a single arch spanning 120 meters and supporting a 30 mm thick RPC deck [⁴]; the first RPC highway traffic bridge constructed by VSL at Shepherd’s Gully Creek in NSW, Australia [⁵]; a kind of high-durability panel entirely made of RPC was used for railway bridge walkways in Qinghai-Tibet railway in China [⁶,⁷]; Wapello County Mars Hill Bridge, the first highway bridge (in North America) built with Ductal was successfully completed and opened to the public in 2006 [⁸], this bridge is a significant step toward “The Bridge of the Future”.

Experimental studies on shear performance of prestressed RPC were very limited. Voo YL and Foster SJ et al. [⁹,¹⁰]. tested ten Prestressed RPC beams without stirrups with the variables of the quantity and types of fibres. Voo YL et al. [¹¹]. tested another eight prestressed RPC beams without stirrups with the variables of the a/d , quantity and types of steel fibres. Those tests showed that the quantity and types of fibres in the concrete mix did not significantly affect the initial shear cracking load but increased the failure load of the beams with the volume of fibres grew. Moreover, as prestressing added, their ultimate shear strength and the stiffness of the beams also increased.

So far, there has been lack of research on prestressed RPC with shear reinforcement. As a consequence, the purpose of this preliminary study is to conduct shear tests on prestressed RPC beams with shear reinforcement and investigate the understanding of the failure modes and strength behaviour in shear. In this research, shear deformation, shear capacity, crack pattern and stirrup strain were experimentally investigated in detail. All of this information can be used for more advanced shear analysis of prestressed RPC beams.

Experimental investigation

Design of the test beams

The details of those tested pre-tensioned prestressed RPC beams are shown in Fig. 1 and Table 1. The beams were 2,400 mm long, with a simply-supported span of 2,100 mm and a total depth of 300 mm. The webs of the beams were 50 mm wide. The top flanges were 300 mm wide and contained four rolled plain bars in diameter of 8 mm. The bottom flanges were 100 mm wide and contained three deformed bars and three 15.2 mm diameter strands, as shown in Fig. 1. In the beams containing stirrups, deformed bars in diameter of 6 mm were used for vertical stirrups. The primary test variables of 8 specimens as shown in Table 1 were focused on the shear-span ratio a/d (1.1, 2 and 3, repectively); the prestressing level {{\displaystyle \sigma }}_{\mathrm{c}\mathrm{o}\mathrm{n}}/{{\displaystyle f}}_{\mathrm{p}\mathrm{t}\mathrm{k}} (0, 30, 60 in percentage, respectively) and the stirrup ratio (0.63 and 1.26 in percentage, respectively). In the test specimen designations, the character “B” referred to Beam, the first series number (1, 2 and 3) after B indicated the ratio of shear-span to depth (a/d), the second series number (0, 30 and 60) represented the prestressing level, and the last (90, 180) indicated the spacing of stirrups. More details of the beams were explained in Table 1.

Material properties

The constituents of RPC whose mix proportions listed in Table 2 were as follows: cement with fines of 3400 cm²/g (42.5 Portland cement made in China ); quartz sand with grain size from 0.23 mm to 0.45 mm; high-quality silica fume with a specific surface exceeding 200,000 cm²/g and average grain size of 0.1 µm; superplasticizer with water reduction ratio above 25%; and straight steel fibers with 12±1 mm long by 0.16±0.005 mm diameter with tensile strength above 2000 MPa volume fraction was 1.6%. The aspect ratio of the fibers was 75. All of the tests contained 1.6% by volume of straight steel fiber.

The cubic and prismatic compressive strength f_cu and f_c of the RPC used were determined form the cubes of 100 mm×100 mm×100 mm and prisms of 100 mm×100 mm×400 mm under load control at rate of 20 MPa per minute, respectively; The split tensile strength f_t^s of the material was obtained by cubes of 100 mm×100 mm×100 mm loaded at 1.0 MPa per minute. The axial tensile strength f_t of the RPC was calculated by f_t =0.75 f_t^s [¹²]. The compressive elastic modulus E₀ of the RPC was obtained from the stress-strain curves of 100 mm×100 mm×400 mm prisms in compression under strain control at rate between 25\mathrm{\mu }\mathrm{\epsilon }and 150\mathrm{\mu }\mathrm{\epsilon }per minute over a period of approximately 2 hours. The properties of RPC tested were summarized in Table 1.

The mechanical properties of reinforcing bar and tendons were summarized in Table 3. The stirrups had yield strength of about 586 MPa and a Young’s modulus of 190 GPa. The tendon had yield strength of about 1420 MPa (taken as the 0.2% proof stress) and Young’s modulus of 195 GPa.

Construction of the test beams

A reinforced concrete open box structure as shown in Fig. 2 was first built to form a stretching bed for tendon’s pre-tension and a pool for RPC beam’s heat curing at the same time, a pair of beams could be prefabricated in the concrete box. The prestressing strands were pre-tensioned the day prior to RPC casting of the beams. The tension force, stress and elongation in the strands were measured by load cell at the stretch end of the strands, strain gauges attached on the strands and LVDTs beside the hydraulic jacks separately as shown in Fig. 2.

After 24 hours, the beams were demoulded. Afterwards, they were cured for 48 h in 80±2 °C hot water and gradually cooled for another 48 h in water in the concrete box. Those cubes and prisms for determining the properties of RPC were cured at the same manner as the test specimens. Eight days after casting, the prestress was transferred to the RPC beams by cutting the wires outside of the beams. Immediate prestress losses in tendons and effective pre-compression stress at the bottom of the beam due to tendon release were measured by the strain gauge readings on the strands and bottom surface. At last, the beams were stored in the laboratory until the day of test.

Test setup and procedure

The test setup consisted of a simply supported beam under two-point load with a steel distribution beam, as shown in Fig. 3. At the supports, load was transferred to the beam using a 51 mm diameter roller and 100 mm×150 mm×25 mm steel plates. At the point load, a 50mm diameter roller was sandwiched between 100 mm×150 mm ×25 mm steel bearing plates.

The applied load was measured by a load cell while deflections were measured by linear variable differential transformers (LVDTs) at mid-span, load points and the supports. In addition, strain gauges were attached to both the prestressing strands and reinforcing bars. Strain gauges were attached to stirrups to measure the contribute of stirrups. Rectangular rosette was located in the web regions of the specimens to measure concrete principal strains and the angle of inclination of diagonal compressive stress. The crack width was measured by using a microscope with precision 0.02 mm. Load was applied in 10 kN increment up to the cracking load, then, 20 kN increment was used. After the beam entered into the remarkable nonlinear range, the loading was controlled using the deflection increment of 3~5 mm at mid span until final failure of the beam.

Experimental results

The experimental results of the shear tests were summarized in Table 4, in which V_{\mathrm{c}\mathrm{r},\mathrm{i}}was the flexural cracking load, V_{\mathrm{c}\mathrm{r},\mathrm{w}} was the initial web-shear cracking load, and V_uwas the maximum load recorded during the experiments.

Load-deflection behaviour

Load-versus-displacement plots at the mid-span in Fig.4 were used to evaluate the overall response of the beams. To evaluate the effect of a/d on shear behaviour, Specimen B-1-60-90, B-2-60-90 and B-3-60-90 were compared synthetically (Fig.4 (a)). The only difference between these three specimens was the a/d. As exhibited in this plot, the ultimate shear capacity of beams decreased as the a/d increased. In very short beams (B-1-60-90), inclined cracks occur along the line between load and reaction. Thus, most of the shear force is transferred by arch action.

To estimate the effect of stirrup ratio on shear behaviour, Specimen B-2-60-90 was compared with Specimen B-2-60-180 (Fig. 4(b)). The only difference between these two specimens was the stirrup ratio. As exhibited in this plot, the load-deflection relationship before the failure of B-2-60-180 was barely influenced by the stirrup ratio, whereas the growth in stirrup ratio increased the ultimate shear capacity of concrete beams. This phenomenon was also observed in the test results of the specimens B-2-0-90 and B-2-0-180 (Fig.4(c)), and the specimens B-2-30-90 and B-2-30-180 (Fig. 4(d)). As shown in Fig. 4(e) and (f), the ultimate shear capacity of the RPC beams increased when prestressing forces added. Based on a comparison of the applied loads when the slope of the load-deflection curve flattened out, it was obvious that the prestressing force delayed the occurrence of cracks.

Crack pattern

All specimens failed in shear. Figure 5 shows typical shear failure patterns observed in some of the specimens. For Specimens B-1-60-90 (the a/d is only 1.1), inclined cracks occurred along the line between load and reaction support. Thus, most of the shear force was transferred by arch action, compression strut failure by crushing the web along the line of the crack. In short beam (B-2-60-90 with a/d=2.0), a diagonal crack propagated along the tension steel causing splitting between the concrete and the longitudinal bars (Fig. 5 (b)). This is called a shear-tension failure. The diagonal cracks propagated toward the top of the beam resulting in crushing of the compression zone. This is called as shear-compression failure. In slender beams (B-3-60-90 with a/d=3.0), the diagonal cracks continue to propagated towards the top and bottom of the beam and cause yield of the tension steel. The beam called as diagonal tension failure may split into two pieces at failure, as shown in Fig. 5(c).

Figure 6 illustrates crack patterns observed at the maximum load for all the tested beams. Thick black line in Fig.6 represents the principal damage cracks. Flexural cracks appeared first in the maximum moment region. As the load increased, some of these cracks were gradually inclined toward the loading point. Most of the beams which failed after one or two significant diagonal cracks had developed. The location of the significant diagonal crack was between the loading and supporting points. Similar crack patterns were observed in those specimens with the same a/d.

For calculating the contribution of shear reinforcement to capacity, the most important angle of web-shear cracking is that of the dominant crack. Figure 6 described the Shear failure cracks after attainment of ultimate load for prestressed RPC beams, Table 5 presented the dominant and range web-shear crack angle.

These comparisons of the angles of cracking in the web-shear region are useful for assessing the appropriateness and conservation of approaches taken in codes of practice for calculating the contribution of shear reinforcement. The results of this testing program are summarized in Table 5. For the slender beam (B-3-60-90 with a/d=3.0), it is highly conservative to calculate the contribution of the shear reinforcement using the number of stirrups that are calculated to cross a 45 degree crack, which is quoted in ACI 318-11.

Effects of experimental parameters

The primary objective of the test was to evaluate the influences of the a/d, the stirrup ratio, and the prestressing forces on the response of the beams, which were cast using reactive powder concrete(RPC). The influences of three parameters were investigated by considering the normalized shear stress at failure load. The normalized shear stress was defined as {{\displaystyle v}}_n=v/\sqrt{{{\displaystyle f}}_c^{\text{'}}}={{\displaystyle v}}_u/\left({{\displaystyle b}}_w\cdot d\cdot \sqrt{{{\displaystyle f}}_c^{\text{'}}}\right), as shown in Table 4.

Beams with different a/d

Load-deflection curves were compared in Fig. 4(a) for the specimens with different shear span to depth ratios (a/d). The normalized shear stress obtained from tests of the same stirrups ratio and prestressing forces having various a/d were shown in Fig. 7. As could be seen from the Fig. 8, the normalized shear stress at failure was affected by the a/d. For the beams had stirrups ratio 1.26%, the normalized shear stress of B-1-60-90 (a/d=1.1) was 2.71, while that of B-2-60-90 (a/d=2) and B-3-60-90 (a/d=3) were 2.32、2.06, respectively. The normalized shear stress of B-3-60-90 (a/d=3) was 76% of that of B-1-60-90.

Beams with different stirrup ratio

Load-deflection curves were compared in Fig. 4(b), (c) and (d) for the specimens with different shear stirrup ratios. The normalized shear stress versus stirrup ratio were shown in Fig. 8. As stirrup ratio increased, their shear strength and deflection at maximum load increased accordingly. The contribution of stirrups was investigated by the shear strength at failure load subtracted the Diagonal cracking load V_{\mathrm{c}\mathrm{r},\mathrm{w}}. By increasing stirrup ratio by 2 times from 0.62% for the spacing of stirrups equal to 90mm to 1.26% for the spacing equal to 180 mm, the contribution of stirrups increased by 16%, 26% and 55% for {{\displaystyle \sigma }}_{\mathrm{c}\mathrm{o}\mathrm{n}}/{{\displaystyle f}}_{\mathrm{p}\mathrm{t}\mathrm{k}}equal to 0, 0.3 and 0.6, respectively. The contribution of the stirrups increased is inversely proportional to the spacing of the stirrups. The best reason why the increment less than 100% was that most stirrups (stirrup ratio equal to 1.26%) did not yield.

Beams with different prestressing stress

Load-deflection curves were compared in Fig. 4(e) and (f) for the specimens with different prestressing stress. The figure shows that at different levels of prestressing, as prestressing stress increased, their ultimate shear strength and the stiffness of the beams increased, but deflection at maximum load decreased.

To examine the influence of prestressing stress on web-cracking and failure load, the normalized shear stress of web-cracking and failure of the beams with a/d equal to 2.0 shown in Fig. 9. Comparison of the Normalized shear stress showed that the prestressing level had a more significant influence on the shear cracking load than on the failure load. Setting the beam without prestressing stress as the basis reference, the beams that the stirrups ratio equal to 1.26%, shear cracking load increased by 80.0%, 192.5%, failure load increased by only 14.7%, 17.9% for {{\displaystyle \sigma }}_{\mathrm{c}\mathrm{o}\mathrm{n}}/{{\displaystyle f}}_{\mathrm{p}\mathrm{t}\mathrm{k}} equal to 0.3 and 0.6, respectively.

Analytical models to predict shear resistance

Currently,three design codes are available for UHPFRC and the corresponding structures design: Japanese Recommendations JSCE-2006 [¹³], French standard NF P18-710-2016 [¹⁴], Swiss Standard SIA-2016 [¹⁵]. The formulas in these three standards are used for predicting the ultimate shear resistance of the tested beams.

The experimental strength is almost always higher than predicted.The shear resistance predicted by the four standards are summarized and compared with the test result in Table 6. For the test beams, the average V_{\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}/V_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{u}} for JSCE-2006 is 1.44 with a coefficient of variation of 0.15. The corresponding results were 1.86 and 0.24 for the NFP18-710-2016, and 1.47 and 0.20 for SIA-2016.

Conclusion

Eight Prestressed RPC I-beams were tested to study the shear behaviour. The test variables were shear-span to depth ratio (a/d), stirrup ratio and the level of prestressing. From the experimental study, the following conclusions were drawn:

(1) As stirrup ratio increased, their shear strength and deflection at maximum load increased accordingly. By increasing stirrup ratio by 2 times from 0.62% for the spacing of stirrups equal to 90 mm to 1.26% for the spacing equal to 180 mm, the contribution of stirrups increased by 16%, 26% and 55% for {{\displaystyle \sigma }}_{\mathrm{c}\mathrm{o}\mathrm{n}}/{{\displaystyle f}}_{\mathrm{p}\mathrm{t}\mathrm{k}} equal to 0, 0.3 and 0.6, respectively.

(2) Comparison of the normalized shear stress showed that the prestressing level had a more significant influence on the initial shear cracking load than the failure load. In addition, not only did the ultimate shear strength of the specimens increase with increasing prestress but the prestress also influenced the stiffness of the beams.

(3) With regard to the shear resistance of the test beams, the predictions from three standards (AFGC, JSCE and SIA) on the design of UHPC structures were compared with the experimental result suggesting that the experimental strength is almost always higher than predicted.

(4) RPC, as a new Concrete, was different from normal concrete and fiber reinforced concrete. Further study should be needed to develop an analytical method and computation model for shear strength of RPC beams.

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