Evaluation of input geological parameters and tunnel strain for strain-softening rock mass based on GSI

www.nature.com/scientificreports OPEN Evaluation of input geological parameters and tunnel strain for strain‑softening rock mass based on GSI Lan Cui 1,2, Qian Sheng 1,2, Jun Zhang 3, You‑kou Dong 4* & Zhen‑shan Guo 3 The regression analysis method is being widely adopted to analyse the tunnel strain, most of which ignore the strain-softening effect of the rock mass and fail to consider the influence of support pressure, initial stress state, and rock mass strength classification in one fitting equation. This study aims to overcome these deficiencies with a regression model used to estimate the tunnel strain. A group of geological strength indexes (GSI) are configured to quantify the input strength parameters and deformation moduli for the rock mass with a quality ranging from poor to excellent. A specific semi-analytical procedure is developed to calculate the tunnel strain around a circular opening, which is validated by comparison with those using existing methods. A nonlinear regression model is then established to analyse the obtained tunnel strain, combining twelve fitting equations to relate the tunnel strain and the factors including the support pressure, GSI, initial stress state, and critical softening parameter. Particularly, three equations are for the estimation of the critical tunnel strain, critical support pressure, and tunnel strain under elastic behaviour, respectively; and the other nine equations are for the tunnel strain with different strain-softening behaviours. The relative significance between the GSI, the initial stress and the support pressure on the tunnel strain is assessed. List of symbols η Softening parameter σr , σθ Radial and tangential stresses εr(i),εθ(i) Radial and tangential strains at r = r(i) εr(i−1), εθ(i−1) Radial and tangential strains at r = r(i-1) plas plas εr ,εθ Radial and tangential plastic strains plas plas �εr(i) ,�εθ(i) Radial and tangential plastic strain increments elas,�ε elas Radial and tangential elastic strain increments �εr(i) θ(i) u(i) Radial displacement at r = r(i) p0 Initial ground stress μ Poisson’s ratio σ1, σ3 Major and minor principal stresses at failure, respectively GSI Geological Strength Index GSIp, GSIr Peak and residual values of the Geological Strength Index ψ Dilatancy angle Kψ (η) Dilatancy coefficient φ Friction angle σci Uniaxial compression strength of intact rock mb, s, a Strength parameters of the Hoek–Brown rock mass ω  mb, s and α 1 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China. 2University of Chinese Academy of Sciences, Beijing 100049, China. 3Key Laboratory of Highway Construction and Maintenance Technology in Loess Region of Ministry of Transport, Shanxi Transportation Technology Research & Development Co., Ltd., Taiyuan 030032, China. 4College of Marine Science and Technology, China University of Geosciences, Wuhan 430074, China. *email: dongyk@ cug.edu.cn Scientific Reports | (2022) 12:20575 | https://doi.org/10.1038/s41598-022-23587-x 1 Vol.:(0123456789) www.nature.com/scientificreports/ D Disturbance coefficient RMR Rock Mass Rating η* Critical value of the softening parameter σcm Strength of a rock mass σr(i),σr(i-1) Radial stresses at the inner and outer boundaries of each annulus Erp , Err Peak and residual values of the deformation modulus σr2 Radial stress at the elastic–plastic boundary The tunnel closure should be predicted appropriately as it is utilised to determine the stability of the rock mass and has been adopted in the engineering practices to guide the preliminary support design. Many analytical and numerical methods were proposed to assess the ground reaction curve with different failure criteria, flow rules, and failure behaviours of the rock mass1–6. The solutions reveal the relationship between the tunnel strain and the support pressure, which are efficacious for determining the support type with a particular geological condition. However, many solutions are often too cumbersome for practical applications due to its complicated derivation, equations, and multiple geological parameters. In this aspect, empirical methods seem to be more accessible to the engineering practisers due to their simplicity. Rock mass rating7–9, geological strength index10, and tunnelling quality index Q 11,12 are the commonly utilised systems to guide the tunnel design by adequately quantifying the strength and deformation properties of the rock mass. Based on previous case back-analysis with assumed rock mass behaviours, the empirical methods often fail to account for the input geological parameters for a specific case. Thus, the strain redistribution and support performance cannot always be well-estimated by the empirical methods. The regression analysis method has been adopted by many researchers to evaluate the tunnel strain as it takes advantage of the accuracy of the numerical tools and the convenience of the empirical schemes13–21. In the existing studies, great amount of data result was obtained using iterative procedures to analyse the large number of tunnelling cases. Multiple geological parameters for each tunnel case were simplified into a single strength parameter, and the rock mass deformation was quantified artificially as a function of the strength parameter using a nonlinear regression model. Among the studies, the functions enable to obtain the tunnel strain or the plastic zone radius for various tunnel cases with various geological scenarios. However, the limitation is obvious due to the difficulty when considering the strain of rock mass showing strain-softening behaviours, which is proved to be a common behaviour in numerous rock t ests3. Also, many studies adopted only one fitting equation in the regression model, failing to consider the support pressure, the initial stress, and the strength classification (such as RMR, GSI, and the compressive strength). As a result, the application of analysis results with one fitting equation is limited to particular initial stress or rock mass quality. In this paper, the index GSI is assigned with a group of values to represent the strength parameters and the deformation moduli for a strain-softening rock mass having various qualities. The tunnel strain around a circular opening under a hydrostatic stress state is obtained through a numerical scheme, which is validated through comparison with the previous studies. A more accurate estimation of the tunnel strain is further derived by semi-analytical procedures with different input geological parameters. Twelve fitting equations are proposed with the regression analysis method to correlate the tunnel strain with the support pressure, the GSI, the initial stress state, and the critical softening parameter; In particular, three equations are for the critical tunnel strain, the critical support pressure, and the tunnel strain in the ela (...truncated)