Improvement of Cauchy integral method for the stresses and displacements around the deeply-buried non-circular tunnel

• Autorzy: Zhou Yulin , Lu Aizhong , Cai Hui , Ma Yaocai

Identyfikatory

DOI

10.15632/jtam-pl/145579

• Języki publikacji: EN

Abstrakty

EN

For a deeply-buried non-circular tunnel, abnormal stress and displacement arise in the region far away from the excavation boundary when the Cauchy integral method is applied. It is found that the calculation error is induced by a polynomial in the analytical function. An improved method is proposed by expanding the polynomial as a power series. The improved method is suitable for calculating the stress and displacement in the whole surrounding rock. The results obtained by the improved method are in good agreement with the numerical results of ANSYS, which proves the effectiveness of the proposed method.

Słowa kluczowe

EN

non-circular tunnel; Cauchy integral method; stress and displacement; abnormal calculations; improved method

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2022
• Tom: Vol. 60 nr 1
• Strony: 153--166
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Zhou Yulin

• North China Electric Power University, Institute of Hydroelectric and Geotechnical Engineering, Beijing, China

autor

Lu Aizhong

• North China Electric Power University, Institute of Hydroelectric and Geotechnical Engineering, Beijing, China

autor

Cai Hui

• North China Electric Power University, Institute of Hydroelectric and Geotechnical Engineering, Beijing, China

autor

Ma Yaocai

• North China Electric Power University, Institute of Hydroelectric and Geotechnical Engineering, Beijing, China

Bibliografia

• 1. Duncan J.M., Dunlop P., 1968, Slopes in stiff-fissured clays and shales, ASCE Soil Mechanics and Foundation Division Journal, 95, 467-492.
• 2. Exadaktylos G.E., Stavropoulou M.C., 2002, A closed-form elastic solution for stresses and displacements around tunnels, International Journal of Rock Mechanics and Mining Sciences, 39, 905-916.
• 3. Fakhimi A., Salehi D., Mojtabai N., 2004, Numerical back analysis for estimation of soil parameters in the Resalat Tunnel project, Tunnelling and Underground Space Technology, 19, 57-67.
• 4. Greenspan M., 1944, Effect of a small hole on the stresses in a uniformly loaded plate, Quarterly Journal of Mechanics and Applied Mathematics, 2, 60-71.
• 5. Inglis C.E., 1913, Stresses in a plate due to the presence of cracks and sharp corners, Transactions of the Royal Institution of Naval Architects, 55, 219-241.
• 6. Jiao C.M., Zhao C.F., Lou Y., Lu A.Z., Shi Z.M., 2009, Research on stochastic back analysis using of Cauchy integral method and genetic algorithm, Rock and Soil Mechanics, 30, 251-256.
• 7. Kodama J., Miyamoto T., Kawasaki S., Fujii Y., Kaneko K., Hagan P., 2013, Estimation of regional stress state and Young’s modulus by back analysis of mining-induced deformation, International Journal of Rock Mechanics and Mining Sciences, 63, 1-11.
• 8. Lei G.H., Ng C., Rigby D.B., 2001, Stress and displacement around an elastic artificial rectangular hole, Journal of Engineering Mechanics, 127, 880-890.
• 9. Lu A.Z., Zhang L.Q., 2007, Complex Variable Method for Mechanical Analysis of Underground Tunnel (in Chinese), Science Press, Beijing.
• 10. Motok M.D., 1997, Stress concentration on the contour of a plate opening of an arbitrary corner radius of curvature, Marine Structures, 10, 1-12.
• 11. Muskhelishvili N.I., 1963, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen.
• 12. Sauers T., 2012, Numerical Analysis, 2nd ed., Pearson, New York.
• 13. Sharma D.S., 2012, Stress distribution around polygonal holes, International Journal of Mechanical Sciences, 65, 115-124.
• 14. Sharma D.S., 2016, Stresses around hypotrochoidal hole in infinite isotropic plate, International Journal of Mechanical Sciences, 105, 32-40.
• 15. Shi Y.Z., Gao X.N., 2014, Complex variable function solution of stress and displacement of surrounding rock buried deep horseshoe-shaped tunnel excavation, Journal of Civil, Architectural and Environmental Engineering, 36, 101-118.
• 16. Terzaghi K., Richart F.E., 1952, Stresses in rock about cavities, Géotechnique, 3, 57-90.
• 17. Zhao G.P., Yang S.L., 2015, Analytical solutions for rock stress around square tunnels using complex variable theory, International Journal of Rock Mechanics and Mining Sciences, 80, 302-307.