## 1 Introduction  
The versatility of an earth pressure balance (EPB) shield has led it to become the most popular type of tunnel boring machine (TBM) for use in various ground conditions around the world [1, 2]. During tunnelling, an EPB shield uses the excavated soil to fill the working chamber and stabilize the tunnel face. The support pressure of the tunnel face is attained by applying pressure to the soil that fills the chamber and screw conveyor, thus preventing a sudden inflow of soil and groundwater into the machine. This distinctive tunnelling mechanism directly uses muck as a supporting material, and so the dynamic interaction between the machine and the excavated soil is more meaningful in EPB shield tunnelling than in other tunnelling methods. The mechanical relationship between the machine and surrounding soil is generally observed indirectly in real time during tunnelling via data from the TBM. These include the cutter head torque, thrust force, chamber pressure, quantity and quality of discharged muck, and abrasion of cutting tools. Analyzing these machine data is considered essential for assessing the performance of EPB shields. Collecting and interpreting machine data recorded during tunnelling is especially important to the machine operators who must carefully maintain a TBM within certain operational ranges. The appropriate operational ranges for a TBM are commonly determined by a machine superintendent and provided to the operator before each day's work. Maintaining the optimal operational conditions during tunnelling is known to enhance significantly the overall performance of a TBM [3]. Accordingly, efficient tunnelling relieson there being sufficient machine data to allow engineers and operators to analyze carefully an interaction of the machine with the soil. However, collecting enough machinery data of sufficient quality in the field for analysis is difficult, because the number of sites around the world where data can be obtained is limited and the data are generally not published. A further consideration is that the different conditions of each tunnelling site complicate the direct comparison of data. Nevertheless, many studies regarding TBM operation have been conducted using machine data accumulated from tunnelling sites, and there always has been demand for large quantities of machine data for TBM operators, engineers, and researchers [4; 5]. The limitations of collecting field data make numerical analysis a cost- and time-effective alternative for gathering and reproducing TBM tunnelling data. Many numerical approaches have been suggested to simulate tunnel construction by both conventional and machine methods. The most representative numerical methods for tunnelling simulation are finite difference methods (FDMs) and finite element methods (FEMs). The former have been used predominantly to evaluate ground displacement induced by tunnelling [6; 7; 8; 9]. A recent convergence study conducted inverse analysis of TBM parameters with an artificial neural network [10]. Tunnelling studies have also used FEMs in various ways: for example, simulation of shield tunnelling [11; 12], suggestion of critical face pressure and backfill pressure [13], dynamic load analysis on a cutterhead [14], and muck flow simulation in a EPB shield [15]. However, both FDMs and FEMs face challenges regarding the simulation of the interaction between a TBM and the soil in real time. That is, it is hard to obtain the TBM data that are significant for analysis of the dynamic interaction between machinery and the soil. To overcome the drawbacks of these methods, a discrete element method (DEM) is now widely adopted to employ the recent rapid advances in computing power in simulating tunnelling [16; 17; 18; 19]. With a number of discrete elements (e.g., particles, clumps, and blocks) whose motion follows [PERSON]'s second law and is calculated by an explicit time-stepping scheme, DEM can simulate the behavior of a granular and discrete medium like soil and rock in geotechnical engineering [20; 21].