# Random Forests and Cubist Algorithms for Predicting Shear Strengths of Rockfill Materials
## 1 Introduction  
As multiple engineering materials, rockfill materials (RFM), have been extensively employed in the construction of dams, slopes and embankments in mining and geotechnical engineering around the world [1; 2]. This material is collected either from the alluvial deposits of a river or by blasting available rock [3; 4]. The availability of information about the mechanical behavior of RFM is an important indicator in the initial stages of engineering projects, especially information concerning the shear strength of RFM, which defines the stability of a structure. Many researchers have focused on the shear behavior of rockfill in past decades. Modeling techniques [5], such as the quadratic grain size distribution technique, parallel gradation technique, replacement technique and scalping technique, are available for testing RFM. Previous experimental studies have indicated that the shear strength of materials in rockfill construction are nonlinear, and different densities induced by inhomogeneous pressure render the characterization of shear strength more complicated. The RFM can be treated as the most complex material due to the variable jointing, angularity/roundness and rock particle size distribution [6]. To understand the mechanical properties of RFM materials, [PERSON] [7] tested the shear strength of RFM by an in-situ direct shear device and measured the variation in the shear strength of rockfill along with the fill lift. [PERSON] [8] performed some experiments of large-scale shear resistance to simulate the original grain size distribution of the material and level of the expected loads. [PERSON] [1] further perfected the shear strength criteria for rockfill. However, RFM with a large particle size (maximum particle size of 1200 mm) is not conducive to testing in a laboratory [2]. Thus, [PERSON] and [PERSON] [9] proposed a strain hardening model to simulate the shear dynamic trends of rockfill. They reported that the shearing properties can be predicted with an acceptable predictive accuracy. [PERSON] et al. [10] presented a rational method based on size effects to evaluate rockfill shear strength. Strength law has been developed by [PERSON] and [PERSON] [2] to relate the shear strength parameter to some index properties of riverbed rockfill material. In addition, several other in-situ and large-scale laboratory experiments have been performed [8; 11; 12; 13; 14; 15; 16; 17]. Although these experiments seem to be trivial, they are important for future researches in certain circumstances. However, direct determination of the shear strength of RFM is considered as a costly and challenging task. Additionally, large-scale shear tests tend to be time-consuming and troublesome, and the estimation of the non-linear shear strength function is difficult without utilizing an analytical process. Therefore, several researchers have attempted to use indirect methods for assessing the mechanical properties of RFM using soft computing techniques. i.e., [PERSON] and [PERSON] [18] analyzed the security of rockfill dams based on an artificial neural network (ANN) model. [PERSON] [19] worked on the application prospect and current situation of ANNs for modeling the monotonic behaviors of multiple shapes of rockfill materials. Recently, [PERSON] [20] applied an ANN approach and obtained excellent predictions for the shear strength of the RFM. Considering that large-scale strength tests to characterize the shear strength are challenging, supervised machine learning algorithms [21; 22; 23; 24; 25; 26; 27] based on random forests [28; 29; 30; 31; 32] and Cubist [33; 34; 35; 36] development models are proposed to predict the shear strength of RFM in this paper. Compared with conventional statistical learning methods, the Cubist and random forests models are able to generate a more comprehensive predictive accuracy.