# Study on Compaction Characteristics and Compaction Process of an Unsaturated Silt Based on PFC3D
## 2 Analysis of the Contact Effect between Particles of an Unsaturated Salt  
The PFC3D software is a particle flow analysis program developed by ITASA Consulting Group in the United States. The software is a numerical computing platform based on mesoscopic discrete element theory. It has been widely used in simulated geotechnical engineering. The advantage of this software is that it can automatically simulate the change characteristics of the soil basic properties in a stress environment. The mechanical properties of engineering an unsaturated silt soil can be well simulated by setting the mesoscopicparameters of the model through the combination of laboratory tests and simulated laboratory tests. The discrete element method allows for finite displacement of particles and a complete separation of rotating particles, and can automatically identify new contacts in the calculation process, which can make the simulation results more accurate. Therefore, this software is selected as a numerical simulation tool.  
In the PFC3D version 5.0 software, spherical particles are the main skeleton structure that constitutes the discrete element model. The mechanical properties of the materials can be expressed by the contact between the particles. Different materials give different contact characteristics. The contact model in the PFC3D discrete element simulation software cannot characterize the mechanical properties of an unsaturated silt, a soil with water between pores, well. Based on the liquid bridge structure theory, [PERSON] [16; 17] improved the linear contact model in PFC3D, and obtained the Hill contact model that can reflect the characteristics of an unsaturated soil, as shown in Figure 1.  
Compared with linear contact, Hill contact adds a suction force in the normal direction between particles to represent the water content of an unsaturated soil. The force-displacement law of the Hill contact can be expressed by Formula (1):  
\[F^{\mathrm{c}}=F^{\mathrm{s}}+F^{\mathrm{m}},M_{\mathrm{c}}=0 \tag{1}\]  
In the formula, \(F^{\mathrm{s}}\) is the surface tension and \(F^{\mathrm{m}}\) is the suction provided by the pore water.  
When there is a liquid bridge structure between the particles, there will be the suction effect of pore water. When two particles contact directly, the suction effect is the largest. With the increase in particle spacing, the suction effect attenuates exponentially, until the critical spacing is reached. The relationship between the suction effect and particle spacing can be expressed by Formula (2):  
\[F^{m}=\left(\begin{array}{c}F^{m}_{\mathrm{max}}\,g_{\mathrm{c}}<0\\ F^{m}_{\mathrm{max}}\exp\left(\frac{-g_{\mathrm{c}}}{2S_{\mathrm{cr}}}\right),0 \leq g_{\mathrm{c}}\leq 2S_{\mathrm{cr}}\\ 0,g_{\mathrm{c}}>2S_{\mathrm{cr}}\end{array}\right. \tag{2}\]  
In the formula, \(g_{\mathrm{c}}\) is the particle spacing, \(2S_{\mathrm{cr}}\) is the limit distance of the liquid bridge, \(S_{\mathrm{cr}}\) is the radius of the smallest particle in the two particles, and \(S_{\mathrm{cr}}=\min(\mathrm{R1},\,\mathrm{R2})\), \(F^{m}_{\mathrm{max}}\) is the maximum pore water pressure, which can be expressed by Formula (3).  
\[F^{m}_{\mathrm{max}}=\psi(\pi S^{2}_{\mathrm{cr}}) \tag{3}\]  
Figure 1: Hill contact diagram.  
In the formula, \(\psi\) is the matrix suction coefficient, which is related to the content of pore water between the particles.