# A Method to Estimate Dynamic Pore Water Pressure Growth of Saturated Sand-Gravel Materials
## 3 Analysis of Dynamic Triaxial Test Results of Saturated Sand-Gravel Material  
### Dynamic Pore Water Pressure Curve  
The dynamic pore water pressure of saturated sand-gravel material increased and periodically fluctuated with periodic increases in the cyclic loading. At the initial stages of increased loading, the dynamic pore water pressure fluctuated slightly but thereafter rose steadily. With an increase in the cyclic numbers, the amplitude of the dynamic pore water pressure increased, but in general, the growth rate of the pore water pressure seemed to decrease. The dynamic pore water pressure of the saturated sand-gravel material was close to the initial effective confining pressure after reaching a certain level of loading. This level of loading was determined by the initial liquefaction of the soil, as illustrated in Figure 5. The black and red lines represent the dynamic pore water pressure of the sand-gravel material prior to and following initial liquefaction, respectively. The number of cycles required for initial liquefaction in each test (S1 to S18) and the excess pore water pressure at 5% axial strain are presented in Table 4.  
Figure 4: The stress state of the samples in dynamic triaxial tests.  
Figure 5: Pore water pressure growth curves of saturated sand-gravel. (**a**) S2 pore water pressure; (**b**) S4 pore water pressure; (**c**) S7 pore water pressure.  
[PERSON] Y et al. [28] and [PERSON] [29] explained pore water pressure growth in saturated sand. The volumetric strain of saturated sand is composed of a volumetric strain \(\varepsilon_{vc}\) due to a change in the mean effective principal stress, and a volumetric strain \(\varepsilon_{vd}\) caused by shear stress. The soil grains are broken during the shearing process so that the mean porosity decreases and the large pores disappear. This changes the soil's irreversible dilatancy component \(\varepsilon_{vd,ir}\). The slip and dislocation between the soil grains also cause a change in the soil's reversible dilatancy component \(\varepsilon_{vd,re}\). To meet the volume consistency conditions, \(\varepsilon_{vc}\) must correspondingly change, which causes the effective mean principal stress to change and cause excess pore water pressure. The monotonic increase \(\varepsilon_{vd,ir}\) causes a monotonic increase in the irreversible dynamic pore water pressure and the generation and dissipation of \(\varepsilon_{vd,re}\) causes a fluctuation in the reversible dynamic pore water pressure. The grain size distribution of the sand-gravel material is wider than sand and has larger pores between the soil grains. Slip and dislocation are, therefore, more likely to occur between the gravel and the fine sand materials, causing a monotonic increase in the pore water pressure and larger amplitudinal increases in the dynamic pore water pressure during cyclic loading of the saturated sand-gravel.  
Figure 6 shows the upper and lower envelope lines of the pore water pressure growth in the saturated sand-gravel. The sample achieves a smaller maximum pore water pressure at the same number of cycles due to the larger consolidation stress ratio before cyclic loading. This happens because the saturated sand-gravel becomes denser under the larger consolidation stress ratio, and the volume shrinkage of the soil during the shear stress is small while the volume expansion is large, which to a certain extent inhibits the accumulation of pore water pressure.