## 1 Introduction
It can be observed that the scholarly focus primarily revolves around studying the physical and chemical mechanisms underlying the interaction between hydraulic fracturing fluid and shale, which leads to the deterioration of shale strength and subsequently increased proppant embedment. However, the impact of reservoir confining pressures on the mechanical properties of shale and their influence on proppant embedment are often disregarded in both experimental research and theoretical models. In current research, instrumented indentation testing offers an alternative and nondestructive technique for investigating the mechanical properties of monolithic and multi  
Figure 1: Schematic of proppant embedment into the fractured surfaces under in situ stresses. phase materials at various scales, providing distinct advantages over conventional uniaxial compression tests [17; 18; 19; 20; 21]. Nanoindentation, in particular, is widely employed for investigating the mechanical properties of specific phases within complex materials like shale and concrete [22; 23; 24]. Several studies have explored the mechanical responses of both individual phases and bulk rock of shale using novel nanoindentation techniques. For instance, [PERSON] et al. (2020) proposed a statistical nanoindentation method to assess the softening effects caused by water-shale interactions [25]. Similarly, [PERSON] et al. (2020) created a statistical nanoindentation technique incorporating data analytics to analyze the mechanical characteristics of shale at various length scales [26]. Their results indicate that, with adequate indentation depth, the mechanical properties derived from instrumented indentation tests can accurately reflect the overall mechanical behavior of the bulk rock. In comparison, microindentation offers advantages such as larger applied loads and indentation depths, allowing for the direct capture of the macroscopic mechanical parameters of shale. [PERSON] et al. (2021) effectively performed a sequence of microindentation experiments to assess the extent and pace of mechanical property deterioration in shale following exposure to thermo-hydro-mechanical-chemical (THMC) treatments mimicking rock-fluid interactions in deep reservoirs before and after hydraulic fracturing [27]. Additionally, [PERSON] et al. (2022) utilized microindentation tests to analyze the creep behavior of THMC-treated specimens and proposed an optimization model for proppant embedment depth and fracture conductivity based on these results [28]. Therefore, microindentation is a reliable and efficient technique used to evaluate the macroscopic mechanical behavior of shale; nevertheless, the studies mentioned above have predominantly examined shale specimens without the presence of confining pressure, leaving a notable research gap concerning the investigation of mechanical response characteristics in shale under bidirectional confining pressures. This paper presents a comprehensive study on the fundamental relationship between microindentation test results and the stress state of the Longmaxi shale. To achieve this, shale samples were subjected to bidirectional confining pressures to replicate the underground stress conditions encountered in deep reservoirs. The microindentation testing employed a spherical indenter to simulate the interaction between proppant and shale. Experimental data were collected and analyzed to investigate the effects of the confining pressure on load-displacement behavior, Young's modulus, Brinell hardness, fracture toughness, proppant embedment, and fracture conductivity. The findings from this study contribute to generating a deeper understanding of the mechanical characteristics of shale under in situ reservoir conditions and facilitate the optimization of proppant embedment and fracture conductivity calculation models for shale gas extraction.