Fig. 1

Apparent friction coefficient vs. slip, friction coefficients vs. viscosity, and Sommerfeld number. Experiments were performed at an acceleration of 6.5 m s⁻² and effective normal stress σ_eff up to 20 MPa, under the following environmental and hydraulic conditions: 100% water (H₂O, blue in colour dots), 60% glycerol/40% water (orange diamonds), 85% glycerol/15% water (yellow triangles), and pure glycerol (99% glycerol, purple squares). a Apparent friction coefficient vs. slip for experiment S1315 performed at σ_eff = 10 MPa in the presence of mixture 60% glycerol/40% water. μ_static, μ_peak, μ_dyn, G_c, and D_c are represented. The apparent friction coefficient is fitted following the exponential decay function proposed by Mizoguchi et al.²⁶: \(\mu = \mu _{\mathrm{dyn}} + \left( {\mu _{\mathrm{peak}} - \mu _{\mathrm{dyn}}} \right)e^{\ln \left( {0.05} \right)\,U/D_{\mathrm{c}}}\) (red line). The G_c is define as \(G_{\mathrm{c}} = \mathop {\smallint }\limits_0^{D_{\mathrm{c}}} \tau \,du\) where the weakening distance D_c is the displacement over which μ_dyn is 95% of (μ_peak − μ_dyn) (Mizoguchi et al.²⁶). b Static friction coefficient vs. viscosity η. The error bar indicate the standard deviation from the reported average values. In the semi-logarithmic diagram, the static friction coefficient slightly decreases linearly with increasing η (all values are reported in Supplementary Table 1). c Peak friction coefficients vs. Sommerfeld number