# Estimating Contact Force Chains Using Artificial Neural Network
## 1 Introduction  
It is well known that granular materials such as sand, gravel and coal exhibit a wide range of complex mechanical behaviors which are caused by the highly convoluted nature of their topological packing structure, individual grain morphology, microstructure and physical properties, as well as the contact mechanics of a large assembly of interacting grains [1; 2]. Although a significant amount of work has been dedicated to the research of granular materials over the past 50 years [3; 4; 5], there is still a lack of a holistic physical theorem that can describe the complex macro-micro mechanics of granular materials, especially down to the grain-scale behavior. Over the last two decades, X-ray microcomputed tomography (micro-CT) has been increasingly used as a powerful tool for the investigation of the grain-scale mechanical behavior of granular materials [6; 7; 8; 9; 10; 11; 12; 13; 14]. This tool makes it possible to capture and characterize the interparticle contacts of granular materials and their evolutions under the triaxial shearing condition [15; 16]. However, micro-CT has a limitation in the measurement of contact forces between interacting particles that hampers our understanding of the structure and evolution of contact force chains. Contact force chains play an important role in the mechanical properties of granular materials such as flowability, elasticity and stability. Therefore, to gain new insight into the physical processes of granular materials, it is essential to estimate the interparticle contact forces in the shearing test. Several approaches that could experimentally measure or estimate interparticle contact forces have been reported in the literature, such as the use of photo-elasticity data [17; 18], the contact force estimation of rubber balls based on micro-CT images [19] and the inverse calculation of contact forces between rubber cylinders using the granular elementmethod [20; 21]. However, all of these approaches are limited to specific types of material with simple geometries, such as 2D birefringent grains for photo-elasticity [17; 18], elastic rubber balls with an assumed contact law [19] or simple rubber cylindrical grains [20] for image-based measurement or estimation, and they thus cannot be applied to the analysis of complex granular materials such as sand. This deficiency presents a primary hurdle to achieving a holistic understanding of the mechanics of granular materials. The difficulty of directly measuring interparticle contact forces within a loaded granular material has led to the intensive use of DEM modeling by the research community as an alternative approach to obtain such information [22; 23; 24]. With full access to all the particle-scale kinetics and kinematics information, DEM has proven to be a powerful tool for investigating the micromechanics of granular materials over the past three decades [5; 25; 26; 27]. The recent incorporation of micro-CT images of sand particle morphologies into the DEM model by the authors has elevated the sophistication level of the model to a new height [27; 28]. It is anticipated that the interparticle contact forces extracted from such a one-to-one mapping model are close representations of the real contact force data of the physical sample. Machine learning (ML) is a branch of artificial intelligence that offers computers the capability to learn from existing data to solve problems that are too complex to solve with conventional programming. Among numerous ML approaches, the ANN model has been widely used [29; 30; 31] as it can adaptively estimate an accurate functional relationship between the input and output variables. The recent applications of ML to granular materials research, such as identifying structural flow defects [32], estimating fault friction from seismic signals [33], and predicting stress-strain relationship of a granular assembly based on 2D DEM datasets of biaxial testing [34] demonstrate that ML is a powerful tool for modeling the nonlinear relationships between high dimensional datasets.