Experimental study and analytical modeling on dynamic compressive behavior of BFRP-confined concrete under high strain rates

Abstract

The dynamic compressive behavior of FRP-confined concrete (FCC) is particularly important for its application in impact-related structures. In this paper, sperate Hopkinson pressure bar (SHPB) tests were conducted to study the dynamic compressive behavior of FCC. Experimental results show that the maximum strength and maximum axial strain of FCC are sensitive to the strain rate effect. Moreover, the axial stress–strain curves are analyzed and divided into three branches based on their trend (i.e., the initial ascending branch, the descending branch, and the second ascending branch). The strain rate histories are plotted to show that the unsynchronized change in the axial and lateral strain rate effects leads to the descending branch and the second ascending branch. The test data indicate that the dynamic confinement ratio should be larger than 0.045 to ensure sufficient confinement for the concrete. A formula is developed for the lateral and axial average strain rate relationship. Enlightened by the test results, an analytical model for dynamically loaded FCC is proposed by incorporating the concrete’s strain rate effect, the inertial confinement effect, and the FRP’s strain rate effect into a well-recognized stress–strain model of static compression.
Introduction

Applications of high-performance materials are of importance for the advancement of modern engineering structures. In recent decades, fiber-reinforced polymer (FRP) composites were widely used in practical structures owing to their high stiffness, low density and excellent corrosion resistance. It has been proven that employing FRP in building new structures and retrofitting existing structures is effective in improving structural performance[1], [2], [3], [4], [5]. One major way of using FRP composites is to employ them to confine concrete elements. Since concrete is a pressure-sensitive material[6], [7] and FRP is an ideal material for confinement, FRP-confined concrete (FCC) has improved strength and enhanced deformability than unconfined concrete[5], [8], [9].

The compressive behavior of FCC has been widely investigated in extensive studies[5], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], and most of them have focused on developing stress–strain models for FCC under static loading conditions. There are mainly two categories of FCC stress–strain models: design-oriented models and analytical models. The design model is established by directly fitting the test results and thus have simple closed form to be used directly for design applications[8], [11], [15], [16]. In contrast, analytical models are proposed by considering the concrete and FRP interaction effects and usually have a series of equations to calculate the strain curves. The analytical models need numerical iterations to obtain the FCC’s stress and strain histories and usually have higher accuracy than the designed-oriented models[10], [12], [13], [18]. Therefore, analytical models are more suitable for numerical simulations due to their better accuracy. There are extensive published studies conducted on the analytical models of FCC under static loading conditions, including the works of Teng et al.[12], Mirmiran and Shahawy[19], [20], Lim and Ozbakkaloglu[16], [18] and so on. These studies comprehensively revealed the compressive behavior of FCC and developed many models with different advantages.

Recently, the impact response of engineering structures has been the subject of numerous studies[22], [23], [24], [25], [26], [27], [28], [29] due to the increasing number of terroristic attacks and impact accidents. Therefore, the response of FCC to impact loads has drawn increasing attention from many researchers[30], [31], [32], [33], [34], [35]. As one of the important early studies, Yang et al.[34] conducted impact tests on FCC with AFRP using sperate Hopkinson pressure bar device(SHPB). The strain rate effect of FCC is studied, and empirical equations are proposed to describe the strain rate effect of the FCC’s ultimate stress. Pham and Hao[30] carried out a number of drop weight experiments on FCC columns and revealed that GFRP performs better than CFRP in increasing the impact resistance. During the tests, hoop strain histories are recorded. However, due to the uneven distribution of axial stress along the specimen, the dynamic confinement effect of FRP is not well examined in the study. Further studies have been conducted by many researchers[31], [32], [36], [37], in which SHPB tests were performed on concrete confined by AFRP, BFRP, CFRP and FFRP jackets and several strength models were proposed. Recently, the study has been extended to the investigation of the impact response of FCC with large rupture strain FRP[33] and the repeated impact response of FCC[38].

Although the impact response of FCC has been widely reported in the literature, previous papers are mostly restricted to simple analysis of the impact response and model fitting of the ultimate strength. To date, there is no study on the lateral strain history of dynamically loaded FCC. Without the lateral strain history, the FRP jackets’ contribution to the specimens’ impact response cannot be reasonably examined. Moreover, there is a notable lack of studies focusing on the analytical model of FCC under impact loadings. Therefore, experimental and analytical studies of the FCC’s dynamic behavior are still necessary.

This paper aims to explore the characteristics of dynamically loaded FCC by investigating its axial and lateral curves and to develop an analytical model. In this paper, SHPB tests with recorded lateral strain histories are conducted to investigate the behavior of dynamically compressed FCC. The lowest confinement ratio for sufficient confinement for the concrete is discussed, and an empirical formula is proposed for predicting the lateral and axial average strain rate relationship. An analytical model of the FCC is then developed by incorporating the material’s strain rate effect and FCC’s structural effect into the well-recognized Jiang and Teng model[12].
Section snippets
Materials

Self-compacting concrete (SCC) was prepared to fabricate the specimens. The binder and supplementary cementing material were ordinary Portland cement and fly ash, respectively. The fine and coarse aggregates are crushed stone and natural sand. The size ranges of the crushed stone and natural sand were 5–10 mm and 0–5 mm, respectively. The flowability of fresh SCC was increased by adding a polycarboxylate superplasticizer. The respective masses of water, cement, fly ash, crushed stone, natural
Quasistatic test

A 600 kN universal testing machine was used to perform quasistatic compressive tests on the specimens. The arrangements of the static compressive tests are presented in Fig. 2(a and b). Two 20-mm strain gauges were installed vertically on the FCC to obtain the prepeak axial strain, while displacement meters were employed to record the postpeak vertical displacement. The displacement meters have a sensitivity of 0.005 mm and a range of 25 mm. Additionally, four 10-mm strain gauges were uniformly
Quasistatic test results

Fig. 8 presents the specimens’ failure modes in the quasistatic compressive tests. The unconfined concrete failed in a typical brittle failure mode, which is characterized by inclined shear cracks. The FCC, however, exhibited FRP hoop rupture failure outside of the overlapping zone as well as concrete crushing failure, which indicated that the 85-mm-length overlapping zone was enough to avoid FRP debonding in the quasistatic tests.

The quasistatic tests showed that the strength of 3 identical
Developing an analytical model

Although several models have been developed for the impact response of FCC in existing studies[31], [32], [34], [35], there has been no analytical model in the literature. Compared with design-oriented models, analytical models have the benefits of providing a deep investigation on the response characteristics of confined concrete and have the potential to be used in concrete confined with other materials. This study proposed an analytical model for the dynamic compressive behavior of FCC using
Conclusions

The behavior of dynamically loaded FCC is studied via SHPB tests in this paper. The FCC’s axial stress–strain curves and lateral strain histories are obtained through the tests, and the response characteristics are investigated based on the test data. An analytical model is then proposed and validated using the test results. Several conclusions are made in this paper:

    1)

    The SHPB tests show that the FCC’s ultimate stress and maximum axial strain are sensitive to the strain rate, and the maximum DIF

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements

The authors are grateful for the financial support received from the National Natural Science Foundation of China (Grant No. 51978332) and the Shenzhen High-level Talents Research Start-up Project.