The limit equilibrium method’s analysis index cannot be measured by on‐site monitoring equipment and cannot be used for monitoring and early warning of rock instability. The existing rock stability evaluation methods based on vibration information cannot evaluate the stability of rocks quantitatively. In this paper, the slope’s constraints on the rock were simplified to springs and a three‐dimensional analysis model of rock vibration was established. The equation for calculating the natural frequency of rock that includes the spring stiffness as an indicator was derived. The rock stability calculation function containing the index of natural frequency was brought into the traditional rock stability coefficient calculation equation, and a new rock stability analysis method based on natural frequency was established. The experiment proved the measurability of the index of the natural frequency of rock and the method’s effectiveness for the stability analysis of the rock based on natural frequency.

In this study, through an analysis of vibration response characteristics of joint surface stiffness on dangerous rock mass, the relationship formula between amplitude ratio of the dangerous rock mass to the bedrock and the length of the bonding section of the joint surface is determined. The stability of the rock mass can be evaluated by combining the formula with the existing rock-mass limit equilibrium theory. This study proposes the existence of a resonance bonding length for the dangerous rock mass. When the length of the bonding section reaches the resonance bonding length, the dangerous rock mass has the largest response to the bedrock vibration. The study found that when the length of the bonding section of the dangerous rock mass is longer than the resonance bonding length, the amplitude ratio increases with the decrease of the bonding section and increases with the increase of the vibration frequency of the bedrock. When the length of the bonding section of the dangerous rock body is shorter than the resonance bonding length, the amplitude ratio decreases with the decrease of the bonding section and decreases with the increase of the vibration frequency of the bedrock. Indoor experiments were conducted by collecting the vibration time-history curves of rock blocks and stone piers and performing analysis and calculation, which proved the accuracy of the analytical results. Through the amplitude ratio of the dangerous rock mass and the bedrock, the bonding length can be calculated. This method can improve the calculation accuracy of the stability coefficient K of the dangerous rock mass.

The accurate judgment of topographic bias tunnels is directly related to reasonable tunnel design and construction safety. In this study, numerical simulations were carried out to determine the unsymmetrical coefficient of topographic unsymmetrical-loaded tunnels, according to the critical thickness of the cover layer of the topographic bias tunnel proposed in the Chinese Code. The unsymmetrical coefficient was analyzed via control variable method and orthogonal test method. The results showed that it is appropriate to take 1.2 as the criterion for all types of topographic unsymmetrical-loaded tunnel in practical application. The influence of different topographic factors, mechanical properties of the surrounding rock, rock quality, construction methods and tunnel spans on the unsymmetrical coefficient were summarized by the control variable method. The results of multifactor analysis under an orthogonal design revealed that the influence of Uc is in the following order: slope angle, overburden thickness, construction method, surrounding rock quality, and height-to-span ratio. Article Highlights The Chinese code for topographic unsymmetrical-loaded tunnels presents a the determination of the corrected unsymmetry coefficient. Single-factor analysis determines the change pattern of the corrected unsymmetry coefficient under the influencing factors. Polar analysis based on orthogonal tests determines the strength of the factors influencing the corrected unsymmetry coefficient.