# The Construction of Equivalent Particle Element Models for Conditioned Sandy Pebble
## 1 Introduction  
Shield tunneling machines based on earth pressure balance (EPB) have been widely used in the construction of tunnels in urban areas. It is quite common that EPB type shield machines go through heterogeneous ground conditions, typically the sandy pebble stratum. In China, a total of 23 cities have constructed or to build metro tunnels in sandy pebble stratum, such as Chengdu, Beijing, Shenyang [1]. Japan also encountered sandy pebble in the construction of the Hiroshima Metro. Sandy pebble has attracted great interest among geotechnical researchers. Sandy pebble is a special type of geomaterial, a mixture of hard gravel and soft sand. The weakly weathered pebble grains, with high compressive strength and large grain size, are intermingled with soft and flowable sands. With pebble blocks as skeleton and weakly bonded interface, sandy pebble is a kind of loose and highly discrete noncontinuum material. Besides, it is sensitive to the external disturbance since thepoint-to-point contact between grains [2]. Obviously, sandy pebble soil cannot satisfy the requirements of EPB tunneling and it is essential to perform soil conditioning. Conditioned soil, which presents good fluidity and plasticity, can flow as well as form certain shape. So it is in a transient state between solid and fluid, and more like a solid-like material. The soil cabin system of EPB shield machine is in charge of several important tasks, such as soil excavation and tunnel face stabilization, so its performance to a large degree determines the construction efficiency and safety. However, under the complex interaction between the soil and shield machine, the soil cabin system shows both time dependency and randomness. Therefore, it is challenging to investigate the dynamic behavior of the whole system. Classical computational methods for modeling such type of systems include the discrete element method (DEM) [1; 2; 3], meshless and particle methods [4; 5; 6; 7; 8; 9], efficient remeshing techniques in the context of FEM [10; 11; 12; 13; 14], DH-PD [15; 16] and specific multiscale methods [17; 18; 19; 20]. In the DEM simulation, one of the difficult tasks is to construct the equivalent DEM model of the conditioned sandy pebble. Several types of particle are available in DEM simulation, typically single sphere, cluster of particles and bonded particles. Wherein, the single sphere is used for globular particles, while the other two for particles with irregular shape. In addition, the bonds within a cluster are impossible to break and the particles comprising the cluster remain at a fixed distance from each other, while the bonded particles are liable to separate once the suffered force exceeds its bonding strength. In reality, the grain shape of geomaterial is generally irregular. Especially for sandy pebble, which is a kind of frictional material, its friction behavior is highly sensitive to the angularity of the grains. Adopting single sphere, which is easy to roll without rolling resistance, the simulation may result in a deviation from the actuality. In contrast, the other two types can better characterize the microscopic shape of actual geomaterial. However, reconstructing the actual shape of all particles will make the complexity increase greatly; it is also impractical. [PERSON] et al. pointed out that nonspherical particles are more accurate than spherical particles. However, for nonspherical particles, when the sphericity is decreased to a certain value, the simulation results are similar. So there is no need to adopt highly precise particle shape. However, determining the parameters for discrete element model is another tricky task. Presently, there are mainly three approaches, namely analytical solution, experimental measurement and inverse analysis. Due to various simplifications of substantial material, the analytical solution proposed by [PERSON] can only provide a rough estimation and qualitative analysis [21], which remains distant for engineering application.