# A Method to Estimate Dynamic Pore Water Pressure Growth of Saturated Sand-Gravel Materials
## 1 Introduction  
Soil liquefaction is a globally significant and typical seismic damage phenomenon that has become a prominent research topic in the field of soil dynamics and geotechnical earthquake engineering [1]. Sand-gravel materials are widely distributed in southwest and northwest China, which are also strong earthquake areas. Some high earth-rock dams are directly built on deep sand-gravel overburdens, and some dams are built with sand-gravel materials. The liquefaction properties of sand-gravel materials in these regions have drawn significant attention from researchers [2; 3; 4]. The study of sand liquefaction can be traced back to the 1930s, when [PERSON] [5] first proposed the concept of critical void ratio and explained the liquefaction behavior of sand at the hand of the relationship between changes in the pore water pressure and the critical void ratio during the shear deformation of saturated loose sand. [PERSON] [6] and [PERSON] et al. [7] used the saturated sand isotropic consolidation cyclic triaxial test to establish the relationship between the dynamic pore water pressure and the number of load cycles. [PERSON] et al. [8] modified [PERSON] and [PERSON]'s pore water pressure stress model by considering the influence of initial anisotropic consolidation on the dynamic pore water pressure. [PERSON] [9] also proposed an anisotropic consolidation pore water pressure calculation model that considered the effect of the initial shear stress ratio on the liquefaction of saturated sand. [PERSON] [10] defined three types of pore water pressure growth processes in saturated sand: A (the convex type), B (the concave-convex change microminiature), and C (the concave type). They also proposed corresponding calculation models for differentdynamic pore water pressure growth processes. Apart from the above stress models, the pore water pressure model also includes a strain model [11], a transient model [12], an energy model [12; 13], an endochronic theory model [14], and an effective stress path model [15]. Table 1 lists the commonly used pore water pressure growth models. Traditional research on soil dynamic liquefaction mainly focused on saturated sand and silt materials [16; 17; 18; 1; 19], and less on sand-gravel materials. It is generally believed that sand-gravel materials with coarser grain sizes are less likely to liquefy [20]. Some research [21; 22; 23; 24] has, however, shown that saturated sand-gravel materials will also liquefy under cyclic loading. In 2008, a magnitude 8.0 earthquake caused a large liquefaction area in Wenchuan, Sichuan. The gravel liquefaction area covered as much as 85% of the total liquefaction area [2; 3; 25]. After the Wenchuan earthquake, some scholars began to research the liquefaction characteristics of sand-gravel materials. [PERSON] [26] used [PERSON]'s pore water pressure model to propose a pore water pressure curve fitting model for sand-gravel materials. This model used the symmetry characteristics of the sand-gravel material relationship curve between the pore pressure ratio and the cyclic number ratio. [PERSON] [27] found that the normalized pore water pressure growth curve was close to the hyperbolic curve and proposed a hyperbolic pore water pressure growth model. In studying the dynamic pore water pressure model of sand-gravel materials, two problems must still be solved.