Skip to main content
SpringerLink
Log in

A simple boundary equation technique for elastic stress analysis of underground cavities

  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Summary

A boundary integral equation approach is illustrated which does not require the solution of singular integrals in order to compute the coefficients of the final system of linear equations. This characteristic allows the carrying out of all the necessary integrations by means of numerical techniques, leading to a rather simple and compact solution algorithm. In addition the approach permits the evaluation of a measure of the error affecting the numerical solution. The stability and the accuracy of the procedure, which is based on the minimization of the difference between known boundary tractions and corresponding numerically derived stresses, are discussed with reference to some rock engineering problems and it is shown that the approach is particularly suitable for stress analyses related to underground openings. To get some insight into the overall performance of the procedure, the results obtained in the analysis of a tunneling problem of practical interest are compared with those deriving from a standard Finite Element calculation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Banerjee, P. K., Butterfield, R. (1981): Boundary Element Methods in Engineering Sciences. McGraw-Hill, London.

    Google Scholar 

  • Brady, B. H. G., Bray, J. W. 1978: The Boundary Element Method for Determining Stresses and Displacements Around Long Openings in a Triaxial Stress Field. Int. J. Rock Mechanics Min. Sci. and Geomech. Abst.15, 21–28.

    Google Scholar 

  • Brebbia, C. A. (1978): Boundary Element Method for Engineers. Pentech Press, London.

    Google Scholar 

  • Jaeger, J. C., Cook, N. G. W. (1979): Fundamentals of Rock Mechanics. Chapman and Hall, London.

    Google Scholar 

  • Ling, C. B. (1948): On the Stress in a Plate Containing Two Circular Holes. J. of Applied Physics19, 77–82.

    Google Scholar 

  • Niwa, Y., Kobayashi, S., Fukui, T. (1976): Applications of Integral Equation Method to Some Geomechanical Problems. Proc. 2nd Int. Conf. on Numerical Methods in Geomechanics, Blacksburg, Vol. 1, 120–131.

    Google Scholar 

  • Oliveira, E. R. A. (1968): Plane Stress Analysis by a General Integral Method. J. Eng. Mech. Div., ASCE94, EM1, 79–101.

    Google Scholar 

  • Poulos, H. G., Davis, E. H. (1974): Elastic Solutions for Soil and Rock Mechanics, J. Wiley and Sons, New York.

    Google Scholar 

  • Terzaghi, K., Richart, F. E. (1952): Stresses in Rock Around Cavities. Geotechnique3, 57–90.

    Google Scholar 

  • Venturini, W. S. (1983): Boundary Element Method in Geomechanics, Springer-Verlag, Berlin-Heidelberg-New York.

    Google Scholar 

  • Walker, S. (1981). Approximate Fundamental Solutions and Alternative Formulations. Proc. 3rd Int. Seminar on Boundary Element Methods, Irvine, 472–488.

Download references

Author information

Authors and Affiliations

  1. Technical University (Politecnico) of Milan, Italy

    Giancarlo Gioda

Authors
  1. Giancarlo Gioda
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gioda, G. A simple boundary equation technique for elastic stress analysis of underground cavities. Rock Mech Rock Engng 17, 147–165 (1984). https://doi.org/10.1007/BF01042547

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01042547

Keywords

Search

Navigation