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The anchor length db of rock bolts is often determined empirically by the insertion of the bond friction constant τb at the grout-rock interface. The relationship between force Fb by limit bond stress and bond length (or bond area) is their ratio. Within the same location, the anchor length can be overestimated or underestimated by usage τb = constant. In this paper, the results of load tests of passive rock bolts were analyzed across the many rocks of the Bohemian Massif using selected parameters (RQD index, GSI values, bulk density ρv, uniaxial compressive strength UCS) and their correlation. It was found that the relationship between the anchor length and the limit bound friction is non-linear and is influenced by selected parameters and the type of anchor grouting material (cement and resin). It was considered a state where τb = f (db, Fb, ρv, UCS, RQD, GSI) for 3 types of bonding (1-cement sealing, 2-cement grouting, 3-mixing of resin cartridge). The achieved and measured bond friction was verified by solving the polynomial roots using the CG (conjugate gradient) method. The accuracy of the results reached the maximum mean difference value absΔτb = 0.02 MPa and the standard deviation SD = 0.058. With this verified model, a simulation of random variables was performed by the Monte Carlo method for Fb = const. with the uniform and normal distribution with n = 1500 samples. The results were converted to diagrams represented by the mean value of the uniform distribution (best fit curves) and the normal distribution envelope curves (for 3σ).

Results and Use of Non-Linear Behavior Between Length and Bond Friction of Fully Grouted Rock Bolts in Selected Jointed Rock Masses