# Hybrid Machine Learning Model for Predicting Shear Strength of Rock Joints
## 1 Introduction  
A rock mass is a combination of intact rock blocks separated by rock joints [1, 2]. Generally, a rock mass consists of intact rock blocks separated by discontinuous rock joints [3, 4]. With the increase in natural resource mining engineering and underground engineering, hazards caused by joint shear slip exist widely in geotechnical engineering excavation [5, 6]. For example, Figure 1 illustrates a case of a rock slope in Jiangxi Province, China, characterized by numerous irregular rock blocks and rock joints. Shear failure of these rock joints occurs under normal boundary conditions, which poses a serious threat to pedestrians and vehicles [7, 8]. Consequently, accurate determination of the shear strength of rock joints is crucial for mitigating geological hazards and preventing engineering failures [9, 10]. Since the 1960s, the estimation of joint shear strength has remained a critical research topic in the field of civil engineering. The Mohr-Coulomb strength model, which posits that there is a linear relationship between shear strength and the normal stress acting on rock joints, has served as a foundational framework. For sawtooth joints, [PERSON] [11] established a bilinear strength model considering undulation angles. Under different shear displacement rates, [PERSON] et al. [12] modified the Patton model to obtain a shear strength model of sawtooth joints considering the shear rate. [PERSON] and [PERSON] [13] integrated the effects of friction, dilatancy, cohesion, and rock bridge strength, deriving a comprehensive shear strength model for joints containing rock bridges. Since there had been a turning point in the strength curve in the Patton model, [PERSON] [14] established a new negative exponential strength model in order to further obtain a smooth shear strength curve. [PERSON] [15] pioneered the incorporation of the joint roughness coefficient (JRC), joint wall strength, and basic friction angle into shear strength analysis. Similar to the practice in the literature [12], [PERSON] et al. [16] improved the [PERSON] shear strength model based on the direct shear test results of a series of rough joints. [PERSON] et al. [17] introduced a novel approach by distinguishing between micro-roughness and macro-undulation in joint profiles, leading to an enhanced shear strength model. Recently, the shear strength characteristics of rock joints have been explained and interpreted through the frameworks of disturbed state concept theory and renormalization group theory [18; 19; 20]. However, excessive attention to mechanical mechanisms can lead to extremely complex mechanical models, which greatly limit their applicability to practical engineering. In addition to these studies, scholars have also proposed a series of theoretical or empirical models to study the shear strength of rock joints. Classic models include the [PERSON] model [21], the [PERSON] model [22], the [PERSON] model [23], and the [PERSON] model [24]. A brief review of the existing strength models can be found in References [25; 26]. It is noteworthy that empirical regression-based strength models frequently exhibit significant deviations due to data limitations and material heterogeneity. Figure 1: A rock slope adjacent to a highway in Jiangxi Province, China (photograph by [PERSON]). The rapid advancement of computer technology has ushered civil engineering into a new era. Machine learning (ML) models have emerged as powerful tools for solving complex engineering problems without requiring explicit knowledge of the underlying physical and mathematical mechanisms [27, 28]. Extensive studies have demonstrated that ML models can not only complement but also replace certain traditional methods, offering a more efficient approach to capturing complex nonlinear relationships between input and output variables [29, 30, 31]. Under specific experimental conditions, ML models can serve as an alternative to traditional analytical models [32]. In geotechnical engineering, numerous successful applications of ML have been reported.