## 3 Discussion  
### Effect of Elastic Modulus on Axial and Radial Pressures  
During numerical simulation, the temperature curve corresponding to varying cylinder diameters is selected and the amplitude coefficient \(k_{i}\) is adjusted so that the simulation results for radial expansive pressure are basically consistent with the test results. The preliminary simulation results suggested that the elastic modulus and Poisson's ratio of the SCA model shall be set as \(E=22.5\) GPa and \(\mu=0.3\), respectively. The time histories of radial expansive pressure obtained by tests and numerical simulations are shown in Figures 2a and 5a, respectively. It can be seen that the radial expansive pressure in cylinders with varying diameters obtained by numerical simulation has a similar trend with the test results. The expansive pressures are basically the same. The axial expansive pressure data are extracted from the modeling results and compared with the axial pressures measured during the tests, as shown in Figures 2b and 5b. When the radial expansive pressure is consistent and the same mechanical parameters are adopted, the axial pressure obtained by numerical simulation has a similar trend with the test results. However, the magnitudes are remarkably different. The axial expansive pressures for various cylinder diameters obtained by numerical simulation are significantly different from the test results. When the cylinder diameter is small (\(\phi<65\) mm), the measured axial pressure is much higher than that obtained by numerical simulation. When the cylinder diameter is greater than 65 mm, the measured axial pressure is lower than that obtained by numerical simulation. The above phenomena indicate that the linear elastic model is not good enough to describe the mechanical properties of SCA in cylinders with varying diameter and under different stress conditions. In consideration of the hydration process of SCA with constant volume in a steel cylinder, the expansion of SCA is a gradual compaction process. In this process, the elastic modulus \(E\) and the Poisson's ratio \(\mu\) may change with increasing expansive pressure. In the following numerical simulations, by adjusting the two key mechanical parameters, i.e., the elastic modulus E and Poisson's ratio \(\mu\) of SCA, the effects of the two parameters on the simulation results are investigated. By comparing the simulated axial expansive pressure curves with the test results, the mechanical parameters for numerical simulation are finally determined. First, when the radial pressure is maintained, the relationship between the elastic modulus E and the axial pressure is discussed based on the dichotomy method, as shown in Figure 6.  
It can be known from the distribution of elastic modulus that, the elastic modulus determined by the axial expansive pressures from numerical simulations and tests generally increases with increasing diameter. The amplitude is relatively large. In the model with  
Figure 5: Time histories of radial and axial expansive pressures obtained by numerical simulation: (a) radial expansive pressure, (b) axial expansive pressure. a cylinder diameter of 113 mm, the elastic modulus is close to 36 GPa. However, with further increase of cylinder diameter, the elastic modulus drops by a certain degree. This phenomenon does not conform to the general mechanical performance of an elastic body. With increasing diameter, the expansive pressure also increases and the elastic modulus is enhanced or remains unchanged under the action of expansive pressure. It can be seen from Figure 6 that: for the models with smaller cylinder diameter (\(\Phi\leq 65\) mm), the elastic modulus varies in a small range with the change of axial expansive pressure. The calculation results show that, in the models with cylinder diameter of 30 mm, 42 mm, 50 mm and 65 mm, the average elastic modulus is 2.199 GPa, 1.999 GPa, 2.11 GPa and 2.19 GPa, respectively, when the expansive pressure varies by 1.0 MPa.