## 1 Introduction  
The predominant soil-tool interaction of a subsoiler is the cutting of soil by horizontally moving tools (Figure 1). The soil-cutting process often involves a large draught requirement, which is the dominant limitation for determining the extent of its operation [1; 2]. To overcome the problem of tillage resistance, soil-engaging components or implements must be designed with high material strength, high structural rigidity, and high tractor power, which causes inconvenience in use and increases production and operating costs [3; 4]. For this reason, a method that can significantly reduce the tillage resistance in tillage operations, especially in subsoiling, is urgently needed. This is not only due to cost-saving considerations, but also to the electrification of agricultural machinery, automation, and the inevitable requirements of efficiency and safety [5].  
Tillage theories assume that the soil moves upwards in front of the tools along the tool surface (Figure 1b,d) [6; 7]. Therefore, existing methods to reduce draught typically focus on reducing friction and adhesion at the soil-tool interface, such as interfacial lubrication [8; 9], surfaces made of special materials [10; 11; 12], bionic non-smooth surfaces [13; 14; 15], and active or passive vibration [16; 17; 18]. However, the assumption is not always valid due to the inherent constraints of interface kinematics [19]. The actual performance of draught reduction is weakened when the surface of the tool is \"synchronized\" by boundary wedges formed by the failed soil that can barely be displaced relative to the tool [19; 20; 21; 22]. A further reduction in draught requires more radical methods. A special form of device that moves horizontally while its surface elements (or components) move upwards appears to have more potential for draught reduction. This approach has proven successful in power-driven active rotary disc tools, where draught can be reduced by over 30% compared to normal discs [4; 23; 24].  
Subsoilers are narrow tools whose working depth is much greater than their width (Figure 1f,g). To achieve the tool motion described above within the subsoiling depth, an upcutting continuous belt, as defined by [PERSON] [25] and other researchers, with a rake angle of less than 90\({}^{\circ}\) can be employed. However, the existing theories on continuous belt machines (or chain trenchers) are not applicable to such an analysis. The reason is that the corresponding kinematic and dynamic analyses do not take into account either the soil failure in front of the tool or the draught reduction performance compared to conventional subsoilers [25; 26; 27; 28]. Given the lack of relevant research, the idea of combining a subsoiler with a continuous belt motion needs to be tested.  
The discrete element method (DEM) is suitable for testing the idea because it effectively simulates the mechanical behaviors of granular materials [29; 30]. The use of DEM avoids the disadvantages of costly and time-consuming experimental methods and assumption-based analytical methods [30; 31; 32]. Its applicability and reliability have been extensively verified by simulating the soil-tool interactions of rotary tillers [33], glow discs [34], moldboard plows [35; 36; 37; 38], subsoilers [14; 18; 39; 40], and other earthmoving machines.  
The objective of this study was to investigate the ability of continuous belt motions to reduce the draught requirement of a subsoiler. An attempt was made to test the draught reduction performance of a series of narrow tools with continuous belt motions. Comparative DEM simulations between regular tools and belt tools were carried out to investigate the difference in tool force. Soil disturbance characteristics, particle velocity distribution, and deformation and soil movement patterns were analyzed to explain the difference in tool force. This study provides scientific guidance and a theoretical basis for the application of belt motions in subsoiling machinery and other earth-moving machinery.