1 50 10 1 5 10 50 90 99 Fracture stress σ [MPa] Cumulative fracture probability Fi [%] Static bending σb Static splitting σts Static compression σc Impact tension σit Impact splitting σits Impact compression σic Figure 3: Cumulative fracture probability of concrete strengths. TABLE 3 EXPERIMENTAL RESULTS OF STATISTICAL ANALYSIS BY WEIBULL PLOTS Test σb σts σc σit σits σic Number of samples n 13 23 15 14 15 14 Shape parameter m 10.66.3 9.8 5.2 6.5 14.6 Scale parameter [MPa] ξ 5.7 3.1 29.3 6.8 5.2 36.9 Mean [MPa] µ 5.4 2.9 27.8 6.2 4.9 33.7 Standard deviation [MPa] s.d. 0.5 0.6 3.4 0.9 0.9 2.8 Strain Rate Sensitivity of Concrete In this measuring method the tensile stress region developed in the axial direction of a specimen bar varies with time. Therefore it is necessary to find the beginning time when a specimen bar is broken after starting of tensile stress waves superposition, in other words, the gage length that the tensile stress waves have reached until the initiation of tensile break. The broken time of a specimen was measured using crack gages pasted on it, while the starting time of superposition of tensile stress waves was done by strain gages. A typical example of response signals measured by the strain and crack gages is presented in Figure 4. The solid blue line denotes the stress response at the broken position of a specimen bar, estimated from the stress response of the strain gage 2, while the red line denotes the response from crack gages. It can be found that the beginning time of tensile stress generation and tensile break is 431 µsec and 548 µsec, respectively, after an incident compressive stress is transmitted into the specimen bar. Then the gage length of tensile stress region is calculated as l = 2c0 ∆t = 0.85 m, considering that the tensile stress region is initiated at the center of a specimen bar and progresses on both sides. Subsequently the strain rate can be found as, ε& = v/l = 1.35 sec-1 by making use of the relation between impact stress σ and particle velocity v, v = σ / ρ c0. The corresponding impact tensile strength is about 9.2 MPa. Repeating the same procedure to each measuring result shown in Figure 3 and a series of experimental results on higher impact tensile stresses applied to concrete specimens, the relation of the impact tensile stress and the strain rate of the concrete used for the present test was obtained in Figure 5. The impact splitting tensile (Brazilian) results are also depicted in addition. The impact tensile strength of concrete at the strain rate of about 100 sec-1 may be found to be approximately twice of the static tensile strength, and it is remarkably
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