## 3 Friction Experiments of Granitoid Fault
### Constant-Velocity Experiment  
Constant-velocity friction experiments are fundamental for characterizing the steady-state friction strength of faults or the continental crust. These tests enable systematic observations of the shear stress-strain response, including peak strength, strain weakening, and steady sliding behavior. In recent decades, advances in experimental techniques have allowed for the simultaneous monitoring of porosity, volumetric strain, and acoustic emissions during shear. These additional datasets provide critical insights into the micromechanical processes, such as dilation, compaction, and grain-scale damage, that govern fault zone evolution during slip. Here, we mainly summarize the friction strength or coefficient changed by temperature (\(T\)), normal stress (\(\sigma_{\mathrm{n}}\)), velocity (\(V\)), and pore pressure (\(P_{\mathrm{f}}\)). Under dry conditions, granitic and quartz-feldspar materials exhibit high friction coefficients (\(\upmu\)) typically ranging from 0.6 to 0.8 across both low- and high-temperature (\(T\)) regions, consistent with [PERSON]'s law. For example, [PERSON] et al. (1986) [36] showed a high \(\upmu\), which increased slightly over a \(T\) range of \(\sim\)20-800 \({}^{\circ}\)C (normal stress ranged from 380 to 460 MPa). Also, in a study by [PERSON] [80], dry westerly granite exhibited relatively high \(\upmu\) at 300-700 \({}^{\circ}\)C (normal stress ranged from 370 to 450 MPa). [PERSON] and [PERSON] [65] conducted a shear test on dry granite rock with a bare rock surface at \(V\) = 0.01-10 \(\upmu\)m/s, further confirming high \(\upmu\). The experimental results on natural granite gouges indicate that at \(T\) = 600 \({}^{\circ}\)C and an effective normal stress (\(\sigma_{\mathrm{n}}^{\mathrm{eff}}\)) of 100 MPa, the \(\upmu\) in dry conditions remains at a value of 0.68 [9]. Compared to dry fault gouges, wet granite gouges exhibit a broader range of friction coefficients. At \(T\)s below 400 \({}^{\circ}\)C, there is no difference between dry and wet conditions; however, above 400 \({}^{\circ}\)C, the \(\upmu\) decreases significantly with increasing pore pressure (\(P_{\mathrm{f}}\)). In particular, at 600 \({}^{\circ}\)C and a low velocity (\(V\)) of <1 \(\upmu\)m/s, the \(\upmu\) values can decrease to \(\sim\)0.4 [9,37]. In addition to \(T\), \(P_{\mathrm{f}}\), and \(V\), the shear under large displacement also changed the \(\upmu\) at 600-650 \({}^{\circ}\)C. The \(\upmu\) decreases from 0.75 to 0.39 with increasing shear displacement from 4 to \(\sim\)20 mm [9,41] (Figure 3). The microstructural evidence indicates that high \(\upmu\) (>0.6) corresponds to a temperature-insensitive regime, which is dominated by frictional deformation, while low \(\upmu\) (<0.6) corresponds to a temperature-sensitive regime, which is mainly governed by frictional deformation, potentially accompanied by plastic deformation [81]. In high \(\upmu\), the deformed granite gouges shows a cataclastic frictional granular flow, and the angular grain boundaries suggest a process of grain crushing and fracturing in the slip zone. In that case, high strength is mainly determined by the actively deformed slip zones, where frictional resistance is caused by grain rotations and localized sliding along angular grains and on the fracture array. However, at lower \(\upmu\), microstructural observations reveal evidence of localized shear bands, including Riedel shear, Boundary shear, and Y-shear [82], accompanied by intergranular pressure solution and granular flow. In particular, shear localization in granular materials plays a critical role in controlling both their frictional strength and deformation characteristics. In this regime, the extremely fine-grained gauge exhibited few fracture arrays, and many nanopores were located along the grain contact surfaces, and these features are commonly observed in naturally deformed rocks from mid-crustal shear zones [83; 84; 85].