## 3 Experimental Work
### Split Hopkinson Pressure Bar Tests and Discussion  
The dynamic behavior tests for the developed ultra-high-strength concrete were carried out in a Split Hopkinson Pressure Bar (SHPB) test unit. This setup is a commonly used experimental device to determine the behavior of materials under high strain rate loadings. The SHPB test systems were first invented by [PERSON] [30] to determine the dynamical characteristics of the materials, and then improved by [PERSON] [31]. One of the detailed works on the applications of SHPB systems in concrete studies was given by [PERSON] and [PERSON] [32]. The SHPB test unit used in the present study essentially consisted of a gas tank, striker bar, incident bar, transmitter bar and an absorber system together with a section where the specimen is placed. Moreover, a pulse shaper to decrease the effects of other frequencies, a momentum trap to provide the linear transfer of the elastic wave amplitude from the striker to the incident bar, and strain gauges to measure the strain values, were used. The sample ends were lubricated with vacuum grease. A schematic illustration of the test setup is shown in Figure 5.  
A photo of a sample placed between the incident and transmitter bars is shown in Figure 6.  
The working principle of a split Hopkinson pressure bar test device is based upon the wave propagation in materials. In a split Hopkinson bar test, the impact of the striker bar on the loading block side induces a longitudinal compressive wave. After the wave arrives at the incident bar-specimen interface, a part of this wave is reflected as \(\epsilon_{\mathrm{r}}\), while the other part of the wave, denoted as \(\epsilon_{\mathrm{t}}\), continues to propagate through the specimen and into the transmitted bar. The stress wave pulses on the incident and transmitted bars are recorded by a Wheatstone bridge, formed by the strain gauges mounted on the incident and transmitted bars. In this test rig, all of the bars are made of maraging steel and have a diameter of 19 mm. The striker bar is 300 mm long while each of the incident and transmitter bars is 3340 mm long. Figure 4: Approximate length to diameter ratios of the test specimens: (**a**) L/D = 1.20; (**b**) L/D = 1.00; (**c**) L/D = 0.60. Figure 5: Schematic drawing of the Split Hopkinson Pressure Bar (SHPB) test setup. The data acquired as the time-varying voltage measurement during the experiment was evaluated to calculate the stress, the strain rate and the strain values by using Equations (1)-(3), respectively. The calculations were carried out at intervals according to the time duration observed on the time-voltage plot. An example of the time variation of the measured voltage data is given in Figure 7. It should be noted that the waves produced by the momentum trap were not considered in the calculations. \[\sigma(t) =E_{b}\frac{A_{b}}{As}\ \varepsilon_{t}(t) \tag{1}\] \[\dot{\varepsilon}(t) =\frac{-2c_{b}}{1}\varepsilon_{r}(t)\] (2) \[\varepsilon(t) =\frac{-2c_{b}}{1}\int\limits_{0}^{t}\varepsilon_{r}(\tau)d\tau \tag{3}\]  
Equations (1)-(3) are well explained in the literature regarding the Split Hopkinson Pressure Bar tests [33; 34]. In these equations, \(\varepsilon_{t}\) represents the transmitted wave, whilst \(\varepsilon_{r}\) represents the reflected wave. \(E_{b}\), \(A_{b}\) and \(c_{b}\) represent the modulus of elasticity, cross-sectional area and the elastic wave velocity, respectively. \(A_{s}\) and \(\ell\) indicate the cross-sectional area and the length of the specimen, respectively. Figure 6: The incident and transmitter bars and the specimen in the SHPB test setup. Figure 7: A sample of measured time variation of voltage during the SHPB test. The time variations of the stress and the strain for the ultra-high-strength concrete were calculated by evaluating the time-voltage data are shown in Figure 6.0 Using the data extracted from Figure 8c, the average strain rate for this test has been evaluated as 720.3 s\({}^{-1}\). The SPHB test system available does not allow much higher sample sizes.