Influence of confining pressure-dependent Young’s modulus on the convergence of underground excavation

Abstract The actual convergence of an excavation located in fractured rock mass or the soft rock is largely different with the theoretical result in many cases. Experimental results showed that the influence of confining pressure on Young's modulus is very significant. This paper attempted to illustrate the influence of the confining pressure-dependent Young’s modulus in the ground reaction analyses of mountain tunnel. Firstly, the relationship between Young's modulus and confining pressure was described as a non-linear function according to the test results. Based on the plane strain axial symmetry assumption and the incremental theory of plasticity, equilibrium equations and compatibility equations of rock mass around a circular tunnel were deduced theoretically. Based on fourth Runge-Kutta method, a semi-analytical solution was achieved. Considering the effect of confining pressure on Young's modulus, the stress and deformation of rock mass around tunnel was calculated by both analytical and numerical methods. The influence of confining pressure-dependent Young’s modulus in surrounding rock was estimated quantitatively. Finally, Tawara saka Tunnel in Japan was taken as an example to explain the influence of confining pressure-dependent Young’s modulus. The results showed that the error with respect to the monitoring data was largely reduced with the confining pressure-dependent Young’s modulus model, which indicated the necessity of considering the non-uniform distribution of Young’s modulus.

[1]  C. Gokceoğlu,et al.  Predicting the deformation moduli of rock masses , 2003 .

[2]  Chang-Yu Ou,et al.  Evaluation of deformation parameter for deep excavation in sand through case histories , 2013 .

[3]  Giovanni Battista Barla,et al.  Impact of Advance Rate on Entrapment Risk of a Double-Shielded TBM in Squeezing Ground , 2015, Rock Mechanics and Rock Engineering.

[4]  R. Ribacchi,et al.  Practical Estimate of Deformations and Stress Relief Factors for Deep Tunnels Supported by Shotcrete , 2005 .

[5]  Xiangdong Hu,et al.  A new closed-form solution for circular openings modeled by the Unified Strength Theory and radius-dependent Young’s modulus , 2012 .

[6]  Yujing Jiang,et al.  Influence of Joint Roughness on the Shear Behaviour of Fully Encapsulated Rock Bolt , 2018, Rock Mechanics and Rock Engineering.

[7]  Murat Karakus,et al.  Predicting elastic properties of intact rocks from index tests using multiple regression modelling , 2005 .

[8]  Resat Ulusay,et al.  Deformation modulus of heavily jointed–sheared and blocky greywackes by pressuremeter tests: Numerical, experimental and empirical assessments , 2008 .

[9]  The increase in Young׳s modulus of rocks under uniaxial compression , 2014 .

[10]  Yujing Jiang,et al.  Estimating the support effect of energy-absorbing rock bolts based on the mechanical work transfer ability , 2018 .

[11]  Jun-jie Zheng,et al.  Elasto-plastic analysis of a circular opening in rock mass with confining stress-dependent strain-softening behaviour , 2015 .

[12]  M. Y. Koca,et al.  Correlation of Unconfined Compressive Strength with Young’s Modulus and Poisson’s Ratio in Gypsum from Sivas (Turkey) , 2008 .

[13]  Yujing Jiang,et al.  Ground reaction analyses in conventional tunnelling excavation , 2007 .

[14]  C. Ağan.  Determination of the deformation modulus of dispersible-intercalated-jointed cherts using the Menard pressuremeter test , 2014 .

[15]  C. Gokceoğlu,et al.  Estimating the deformation modulus of rock masses: a comparative study , 2003 .

[16]  Leandro R. Alejano,et al.  Ground reaction curves for tunnels excavated in different quality rock masses showing several types of post-failure behaviour , 2009 .

[17]  You Ming-qing.  Effect of confining pressure on the young's modulus of rock specimen and the friction in fissures , 2003 .

[18]  Xiating Feng,et al.  Deep Fracturing of the Hard Rock Surrounding a Large Underground Cavern Subjected to High Geostress: In Situ Observation and Mechanism Analysis , 2017, Rock Mechanics and Rock Engineering.

[19]  Joaquim Agostinho Barbosa Tinoco,et al.  A novel approach to predicting young’s modulus of jet grouting laboratory formulations over time using data mining techniques , 2014 .

[20]  Yujing Jiang,et al.  Theoretical estimation of loosening pressure on tunnels in soft rocks , 2001 .

[21]  Xianda Feng,et al.  Bayesian prediction of elastic modulus of intact rocks using their uniaxial compressive strength , 2014 .

[22]  Arild Palmström,et al.  The deformation modulus of rock masses — comparisons between in situ tests and indirect estimates , 2001 .

[23]  Xu-sheng Wang,et al.  Evaluation of depth-dependent porosity and bulk modulus of a shear using permeability-depth trends , 2009 .

[24]  Yingchao Wang,et al.  Elastoplastic Coupling Solution of Circular Openings in Strain-Softening Rock Mass Considering Pressure-Dependent Effect , 2018 .

[25]  A. Najibi,et al.  The effect of confining pressure on elastic wave velocities and dynamic to static Young’s modulus ratio , 2013 .

[26]  Yoshiaki Fujii,et al.  Estimation of regional stress state and Young’s modulus by back analysis of mining-induced deformation , 2013 .

[27]  T. Engelder,et al.  Pressure dependence of velocity and attenuation and its relationship to crack closure in crystalline rocks , 1996 .

[28]  H. Tian,et al.  Estimation of Elastic Moduli of Non-persistent Fractured Rock Masses , 2016, Rock Mechanics and Rock Engineering.

[29]  M. H. Leite,et al.  Determination of unconfined compressive strength and Young's modulus of porous materials by indentation tests , 2001 .

[30]  E. Hoek,et al.  Empirical estimation of rock mass modulus , 2006 .

[31]  I A Basheer,et al.  Artificial neural networks: fundamentals, computing, design, and application. , 2000, Journal of microbiological methods.

[32]  Shucai Li,et al.  Elastic analysis of stress–displacement field for a lined circular tunnel at great depth due to ground loads and internal pressure , 2008 .

[33]  F. Varas,et al.  Ground response curves for rock masses exhibiting strain‐softening behaviour , 2003 .

[34]  Yi Zhou,et al.  Bidirectional construction process mechanics for tunnels in dipping layered formation , 2013 .

[35]  Hongwei Huang,et al.  Simplified procedure for finite element analysis of the longitudinal performance of shield tunnels considering spatial soil variability in longitudinal direction , 2015 .

[36]  P. Nawrocki,et al.  Modelling of damaged zones around openings using radius-dependent Young's modulus , 1995 .

[37]  J. P. Harrison,et al.  A mechanical degradation index for rock , 2001 .

[38]  C. Fairhurst,et al.  The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion , 1999 .

[39]  Hongwei Huang,et al.  Efficient response surface method for practical geotechnical reliability analysis , 2015 .

[40]  F. J. Santarelli,et al.  Influence of stress-dependent elastic moduli on stresses and strains around axisymmetric boreholes , 1989 .