# Non-Classical Model of Dynamic Behavior of Concrete
## 3 Comparative Analysis
### Comparisons for Dynamic Tests  
The first group of dynamic tests refers to verification of the proposed dynamic strength criterion with some experimental dynamic results available in the literature. These comparisons were performed for uniaxial compressive loading tests, biaxial compressive-compressive loading tests, and biaxial tensile-compressive loading tests. Using the dynamic strength criterion of Equation (8) for the tests of input stress rate \(\dot{\sigma}=const\), with material constants of Equation (11), enables the comparison of obtained theoretical low (C10--red line), medium (C50--green line), and high (C100--blue line) strength classes of concrete with experimental results for the uniaxial compression presented in the paper of [PERSON] and [PERSON] [48] (Figure 8). The general compatibility of the results obtained in a large range of strain rates confirms the validity of the proposed criterion for determining the dynamic strength of concrete. Figure 8: The results of the proposed dynamic strength criterion of concrete on the background of the results for the uniaxial compression presented by [PERSON] and [PERSON] [48]. Figure 7: Comparison of the proposed model with [PERSON]’s and [PERSON]’s [27] solution for biaxial compression: (a) graph of stress vs. longitudinal and lateral strains; (b) graph of stress vs. volumetric strains. Figure 9 presents the comparison of the proposed dynamic strength criterion with selected experimental results carried out by [PERSON] and [PERSON] [49] for biaxial loading tests with the type of compression-compression. The experimental results were conducted for concrete with uniaxial compressive strength \(f_{c}=9.84\)_MPa_. The experimental results presented in Figure 9 relate to the loading process with constant ratio lateral stress \(\sigma_{22}\) to axial stress \(\sigma_{11}\) of values \(\frac{\sigma_{22}}{\sigma_{11}}=\frac{0}{17},\frac{0.25}{17},\frac{0.55}{17}, \frac{0.75}{1},\frac{1}{1}\). For quasi-static strain rate \(\dot{\epsilon}=10^{-5}\)\(s^{-1}\) stresses have been obtained with values of \(\frac{\sigma_{22}/f_{c}}{\sigma_{11}/f_{c}}=\frac{0}{10},\frac{0.38}{151}, \frac{0.82}{164},\frac{125}{167},\frac{142}{142}\), while for strain rate \(\dot{\epsilon}=10^{-2}\)\(s^{-1}\), the dynamic stresses have been obtained with values of \(\frac{\sigma_{22}/f_{c}}{\sigma_{11}/f_{c}}=\frac{0}{125},\frac{0.44}{174}, \frac{0.93}{1.85},\frac{1.42}{1.90},\frac{1.83}{183}\). The static limit curve of Equation (1) was determined for the test data including \(\varphi_{cc}=1.42\) and assuming \(K=1\), \(\varphi_{t}=0.1\). In turn, the dynamic limit curve of Equation (1) was determined for the dynamic strength coefficient \(K=\psi_{d}=1.27\) calculated according to criterion of Equation (8) with material constants from Equation (11). Comparison of the results indicates a good agreement between the proposed theoretical limit curves with the experimental results, especially in relation to uniaxial and symmetrically biaxial compression. Comparison of the proposed dynamic strength criterion with selected experimental results conducted by [PERSON] and [PERSON] [50] for biaxial compressive-compressive loading tests, is presented in Figure 10. The experimental results were conducted for concrete with compressive strength \(f_{c}=20.1\)_MPa_. The experimental results presented in Figure 10 relate to the process of loading with the constant lateral confining pressure of values \(\sigma_{22}=(0\) ; \(4\) ; \(7\) ; \(10)\)_MPa_ (i.e., \(\frac{\sigma_{22}}{f_{c}}=0\) ; \(0.20\) ;\(0.35\) ; \(0.50\)). For quasi-static strain rate \(\dot{\epsilon}=10^{-5}\)\(s^{-1}\) axial stresses have been obtained with values of \(\frac{\sigma_{11}}{f_{c}}=1.00\) ; \(1.09\) ; \(1.17\) ; \(1.25\). For strain rate \(\dot{\epsilon}=10^{-2}\)\(s^{-1}\) dynamic axial stresses have been obtained with values of \(\frac{\sigma_{11}}{f_{c}}=1.36\) ; \(1.39\) ; \(1.46\) ; \(1.60\).