Experimental characterisation of mechanical behaviour of concrete-like materials under multiaxial confinement and high strain rate
Introduction
Concrete-like materials, e.g., cement, concrete, mortar and geomaterials, have been widely used in civil and mining engineering projects, including hydraulic structures, underground construction and protective engineering. Those structures are frequently subjected to dynamic loadings during the service, such as earthquake, vehicle, blasting and explosion. The behaviours of concrete-like materials under dynamic loading are significantly different from those under quasi-static loading [1], [2], [3]. Cement, plain concrete and concrete are typical rate-dependent materials whose strength increases with increasing strain rate [4]. Besides, most of cement-based engineering materials exist in certain static pre-stress states such as uniaxial, biaxial and triaxial confinements. Thus, it is necessary to thoroughly investigate the dynamic properties and failure patterns of concrete-like materials under different pre-stress state [5].
Various studies have been conducted on the rate-dependence of concrete-like materials such as concrete, steel fibre reinforced concrete, high-performance concrete and mortar at strain rates from 10−5 to 103 s−1, as summarised in Table 1. The split Hopkinson pressure bar (SHPB) technique has been widely used to determine dynamic properties of concrete-like materials at high strain rate from 10 s1 to 103 s−1 [6], [7], [8], [9], [10], [11], [12], and the diameters of SHPB in Table 1 are 12.7 to 120 mm. Li et al. [13] and Wu et al. [14] conducted dynamic compression tests on reinforced concrete, and results showed that the concrete exhibited strong strain-rate dependency and dynamic strength increase near linearly with strain rate. The dynamic compressive strength of ultra-high-performance cement-based composites also increased with increasing strain rate [15], [16]. A modified SHPB with large diameter of 100 mm was applied to investigate strain rate effects, peak strain and specific energy absorption of reinforced geopolymer concrete [13]. Lv et al. [17] analysed the ‘double-peak’ phenomenon of the reflection waveform features of plain concrete based on the SHPB tests. Chen et al. [4] reported the strain rate effects on cement paste, mortar and concrete, and determined mechanical responses and failure behaviour under dynamic compressive loading conditions. Zhu et al. [18] analysed the stress distribution of concrete-like specimens during both loading and unloading processes. It is found that the stress amplitudes influence not only the stress uniformity but also the strain and average strain rate. Extensive SHPB tests have been conducted on the concrete-like materials with different cement types and specimen sizes under uniaxial dynamic loads. In terms of biaxial or triaxial simultaneous impacting, Cui et al. [19] recently developed a 3D-SHPB facility, which allows compressing the specimen synchronously in three perpendicular directions with the same amplitudes, and obtained the volumetric properties of concrete under dynamic hydrostatic pressure. However, these experiments are only subjected to dynamic loading conditions, which misses the effects of pre-confinement.
Different dynamic mechanical properties of concrete-like materials are observed under complicated stress states such as axial, biaxial and triaxial pre-stress conditions. The static strength of concrete first increases and then decreases with the increase of intermediate principal stress [30], [31], [32]. However, it is still challenging to conduct experiments by coupling the confining stress and dynamic loading. There are two approaches adopted to realise the triaxial compression in SHPB experiments. Either hydraulic triaxial cell or passive confining jacket system (e.g., shrink-fit metal sleeve or thick vessel) are used to apply radial confining pressure (σ2 = σ3) on the specimen before dynamic loading [11]. Table 2 listed typical studies on the confining effects on the dynamic properties of concrete-like materials. The pre-stress varies from 10 to 250 MPa under the active confining condition, and the maximum stress is up to 600 MPa under the passive confining system. For the active confining method, Christensen et al. [33] performed dynamic tests of nugget sandstone in 1972. Zeng et al. [34] and Yan et al. [35] investigated the dynamic compressive behaviour of concrete and plain concrete using the MTS servo-hydraulic testing system at low strain rates. Gary and Bailly [36] conducted the high strain-rate effects (uniaxial strain-rates up to 103 s−l) of concrete and proposed a mechanical model based on experimental results. Gran et al. [37] performed compression experiments of concrete using a 400 MPa dynamic triaxial loader, the axial strain rates ranged from 0.5 to 10 s−1, the confinement was up to 124 MPa, and the peak axial loads were from 103 to 393 MPa. Dynamic experiments were also conducted on rock materials at strain rates from 400 to 600 s−1 under confining pressure up to 200 MPa [38], [39]. Gabet et al. [40] and Poinard et al. [41] presented failure modes of concrete based on the triaxial and hydrostatic quasi-static tests with the confining pressure up to 650 MPa. Li et al. [42], [43] developed a modified SHPB to achieve the couple of axial static pre-stress, confining pressure and axial dynamic loading. It should be noted that the confining pressures (σ2 = σ3) considered as constant values, but it is hard to measure the changes during the impact loading simultaneously, and also has leak proneness of hydraulic fluids at high confining pressures [36], [44].
Chen and Ravichandran [45] developed a novel dynamic impact experimental apparatus which can realise the passive confinement on plain concrete specimens by using steel and aluminium jackets. The characterisation of the behaviour of plain concrete specimens under dynamic multiaxial loads was measured. Forquin [46] studied the dynamic mechanical properties of concrete under passive confining pressure up to 600 MPa. In the passive confining condition, the confining pressure depends on the gap between the specimen and sleeve, the material property and thickness of the sleeve. The gap between the specimen and sleeve is relatively difficult to precisely control, and the lateral stress is varying during dynamic loading [11]. Concrete construction is frequently subjected to various kinds of loading paths, associated with different damage modes. Deformation characteristics of concrete materials under confining stresses are substantially complex. The results are characterised by non-linearity, strain softening, intermediate principal stress effects, hydrostatic pressure effects [47], [48], [49], [50], [51]. In addition, the stiffness of confining reinforcement (elastic, elastoplastic, etc.) observably affects the behaviour of concrete, which is another important factor for concrete engineering design [52], [53]. Two factors need to be considered in both active confining and passive jacketing techniques. The first one is to precisely maintain the constant confining pressure during dynamic loading, and thus the new measurement techniques should be employed to record the real-time variation of confinement. Another factor is that the confining stresses are always in cylindrical (σ1 = σ2), rather than the true triaxial pre-stress state in the conventional SHPB tests. Cadoni and Albertini [64], [65] designed a true triaxial loading apparatus project; however, until now only uniaxial setup is presented [65]. In practical-engineering, however, most concrete structures have been already in multiaxial pre-stress states (i.e. uniaxial, biaxial and triaxial) and then subjected to dynamic loading. Therefore, it is necessary to study the characteristics of concrete-like materials under coupled multiaxial pre-stress and dynamic loadings.
This study presents detailed experiments using a recently developed triaxial Hopkinson bar (Tri-HB) system, which can investigate dynamic behaviours of geomaterials (e.g., cement, concrete and rocks) under the various pre-stress conditions including uniaxial, biaxial and triaxial compression. A series of compression experiments on cement and concrete was conducted under different pre-stress states (UC, BC and TC) and impact velocity (Vp) of 18 m/s (i.e., strain rate ranging from 80 to 180 s−1). The axial pre-stress was up to 30 MPa in uniaxial condition, and the maximum confining pre-stress was 20 MPa under the triaxial stress condition. The dynamic compressive strength, failure patterns and microscopic fractures of cement and concrete under different pre-stress conditions were analysed. In addition, the confinement effect and peak dynamic strain were also discussed in detail.
Section snippets
Specimen preparation
The cement specimens consist of water, cement (General Purpose Cement in Australian) and river sand with a ratio of 2:6:1 in weight. While for concrete specimens, the water, cement, river sand and aggregate have a ratio of 0.37:1:0.8:1.87 in weight. The specimens were firstly covered with a plastic film to prevent moisture loss in the customised cubic steel mould, and then demolded after 24 h. All specimens were conserved for 28 days in a special curing chamber at the temperature of 21 °C.
Dynamic uniaxial compression
Uniaxial compression tests were conducted at three axial pre-stress (σ1) states, including 0, 10 and 30 MPa, and the impact velocity of 18 m/s. The typical dynamic stress pulses in the bars along the X direction were recorded under different axial pre-stress status, as shown in Fig. 5. The half-sine incident pulses are proved that the shaping technique acted well during the dynamic loading. There is a peak stress platform during the incident pulse, and it means the specimen is experiencing a
Dynamic stress–strain curves
To investigate the effect of aggregates on dynamic behaviour of concrete, experiments were also conducted on concrete specimens under different pre-stress conditions. The typical dynamic stress–strain curves of concrete are shown in Fig. 15 at the impact velocity of 18 m/s under different pre-stress conditions. From Fig. 15a, we can see that the dynamic peak stress increases from 98 to 190 MPa in the σ1 axis, with the confining pressures changing from UC to TC. Besides, the peak dynamic strain
Discussion
The dynamic increase factor (DIF) is defined as the ratio of dynamic strength to static strength, and normally reported as a function of strain rate [3], [75], [76], [77]. In order to evaluate the enhancement of cement dynamic strength caused by confining stress, referred to the DIF function, the dynamic increase factor with confinement (DIFC), the ratio of the dynamic strength under confinement condition to static uniaxial compressive strength was defined aswhere
Conclusion
A series of dynamic compression experiments of cement and concrete was conducted at the impact velocity of 18 m/s (strain rate ranging from 80 to 150 s−1) under different pre-stress conditions. The experiments were carried out by using a newly developed triaxial Hopkinson bar (Tri-HB) system to achieve the dynamic responses of specimens under uniaxial, biaxial and triaxial pre-stress states. The main findings are summarised as follows.
- 1)
Under dynamic uniaxial compression, the dynamic compressive
CRediT authorship contribution statement
Pengfei Liu: Methodology, Writing - original draft. Kai Liu: Methodology. Qian-Bing Zhang: Supervision.
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
This work was supported financially by the Australian Research Council (LE150100058 and DE200101293) and the China Scholarship Council (to the first author). The specimens were scanned using the Imaging and Medical beamline (IMBL) at Australian Synchrotron (Project M13469), and special thanks to the staff members of Australian Synchrotron, Dr. Anto Maksimenko, Dr. Chris Hall, Dr. Duncan Duncan Butler and Dr. Daniel Hausermann, for their kind support.
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2022, International Journal of Mining Science and TechnologyCitation Excerpt :The formation of new cracks mainly occurred in the initial stage of stress increase, while the creeping stage mainly included the development, propagation, and penetration of microcracks, as verified by the AE characteristics in Fig. 27. Similar to those under uniaxial and conventional triaxial stress conditions, the failure characteristics of rock under true triaxial stress conditions have a significant correlation with the loading rate [113]. As observed in Fig. 28, under dynamic true triaxial stress, the main failure plane is also approximately parallel to σ2, and the damage and fragmentation degree increase with increasing loading rate but decrease as the laterally confined stress increases [92].