# Deformation Behavior of Saturated Soft Clay under Cyclic Loading with Principal Stress Rotation
## 4 Test Results and Discussion  
### Pore Pressure  
Figure 5 shows the development of pore pressure with cycles \(N\) under different loading conditions. As shown in Figure 5, the pore pressure accumulates rapidly in the early stage, slowing down in the later stage and eventually stabilizing. At the same torsional cyclic stress ratio \(\eta\), the pore pressure accumulates more as the VCSR increases. At the same stress level, the increase in the degree of principal stress rotation also increased the pore pressure accumulation. In other words, the increase in both dynamic stress and the principal stress rotation can lead to an increase in the accumulated pore pressure. The development of pore pressure under cyclic loading is an important aspect of the change in the deformation strength of saturated soils. Dynamic pore pressure is also the key to analyzing the dynamic stability of soils. A correct understanding of the pore pressure development in saturated clay under cyclic loading and a suitable dynamic pore pressure model can be established to better analyze the dynamic characteristics of saturated soft clay. Based on the results of the round-trip triaxial and torsional shear tests, [PERSON] et al. (2018) found that the rate of pore pressure growth at the Nth time and the intensity of the dynamic stresses have a linear relationship in double logarithmic coordinates, and the slope of the line does not vary significantly with cycle. As a result, [PERSON] et al. (2018) proposed a dynamic pore pressure model for pore pressure growth under cyclic loading, which is given by:  
\[\Delta U_{N}=(1-U_{N-1})\overline{N}\left(\frac{\tau_{N}}{\sigma_{N-1}^{ \prime}}\right)^{\alpha} \tag{3}\]  
Figure 4: Diagram of loading waveforms. Figure 3: Method of making hollow cylindrical specimens. \[\Delta U_{N}=U_{N}-U_{N-1} \tag{4}\] \[\overline{N}=\frac{C_{1}N}{N^{C_{2}}-C_{3}} \tag{5}\]  
where \(U_{N}\) is the pore pressure after \(N\) cycles; \(U_{N-1}\) is the pore pressure after \(N-1\) cycles; \(\overline{N}\) is the cyclic effect; \(\tau_{N}\) is the shear stress after \(N\) cycles; \(\sigma^{\prime}_{N-1}\) is the effective confining pressure after \(N-1\) cycles; and \(C_{1}\), \(C_{2}\), \(C_{3}\), and \(\alpha\) are the test parameters, which depend on the soil properties and need to be determined by the tests. Figure 5: Pore pressure versus number of cycles under different cyclic loading: (**a**) \(\eta=0.00\); (**b**) \(\eta=0.25\); (**c**) \(\eta=0.50\). The soil unit under traffic loading is subjected to the continuous principal stress rotation, for which we propose a dynamic pore pressure correction model that considers the continuous principal stress rotation. Figure 6 shows the experimental relationship between the pore pressure parameter \(\frac{\Delta U_{N}}{1-U_{N-1}}\) and the effective stress ratio \(\frac{T_{N}}{\sigma_{N-1}^{2}}\), from which it can be seen that the pore pressure parameter increases with the effective stress ratio. In addition, the slope of each straight line shown in the graph is almost identical (\(\alpha=1.13\)). It is also noted in Figure 6 that the increase in pore pressure during cyclic loading is also influenced by the stress cycles. In order to evaluate the effect of stress perimeter on pore pressure, the cyclic effect is introduced, which is derived from the curve equation fitted to the experimental data shown in Figure 7. The data in Figure 7 show that the pore pressure growth decreases with the number of cycles even if the amplitude of the dynamic stress is the same. Figure 8 shows the relationship between the pore pressure model parameters \(C_{1}\), \(C_{2}\), and \(C_{3}\) and the torsional cyclic stress ratio \(\eta\). The three parameters show a good linear relationship with the torsional cyclic stress ratio \(\eta\), which can be expressed as follows:  
\[C_{1}=-2.60\eta+9.42 \tag{6}\]  
\[C_{2}=1.22 \tag{7}\]  
\[C_{3}=0.56\eta+2.16 \tag{8}\]  
Figure 4:0 Pore pressure increase with different cycles. Figure 4:1 Cycles and functions \(\overline{N}\).