Skip to main content
SpringerLink
Log in

Theoretical analysis of equivalent hydrostatic stress attenuation in surrounding rocks after excavation

  • Original Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

Energy concentration and redistribution are always accompanied by tunnel deformation and failure. This study uses a plain-strain model of circular openings under high in situ stress to derive the energy of the surrounding rocks before and after excavation based on elasticity. The study focuses on determining the areal extent of the surrounding rock significantly affected by the excavation. The relationship between dimensionless zonal radius ri/a and dimensionless stress σ0/R0 is determined based on two principles: (1) energy conservation and (2) the logarithmic relationship between consumed energy and the scale of fragmentation. The law of attenuation of stress in surrounding rock during the process of zonal fracture is theoretically explained. Preliminary values for the unknown parameters in the given formula are proposed using the data available, and the stress attenuation law corresponding to the given tunnels is presented.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

Abbreviations

σx, σy, σz :

Stress components (of surrounding rocks) in direction of x, y, and z.

τ yz :

Shear stress parallel to the yz plane.

E :

Elastic modulus.

D :

The thickness of tunnel in the axial direction.

S I,II :

The sum of surface areas in regions I and II.

σ res :

The residual stress of rock mass.

U I :

The elastic strain energy for region I.

σ r :

Radial normal stress.

τ rθ :

Tangential stress.

r :

The radius of disintegration zone.

Γ :

The surface energy density of mode I crack.

r i :

The radius corresponding to the ith, (i = 1,2…) disintegration zone.

η 2 :

The multiple of the energy in the area II relative to the initial energy in the area I after excavation.

K Ic :

The fracture toughness of the material.

\( {U}_{r_{i-1}{r}_i}^{\ast } \) :

The initial energy of block between toroidal blocks ri−1 and ri.

αi(αi > 0):

The residual stress level of surrounding rocks.

W :

The energy consumed during the formation of the non-fractured rock mass between ri−1 and ri.

τ xy :

Shear stress parallel to the xy plane.

τ xz :

Shear stress parallel to the xz plane.

ν :

Poisson’s ratio.

U I,II :

The elastic strain energy of both region I and region II.

σ 0 :

The initial in situ stress.

φ :

The elastic strain energy density.

U II :

The elastic strain energy for region II.

σ θ :

Circumferential normal stress.

a :

The tunnel radius.

s i :

The area of single ring crack.

b :

The area radius affected by the excavation.

η 1 :

The energy change of region II relative to its initial energy when the tunnel is excavated.

n i :

Physical parameter related to the thickness of the fracture zone.

R 0 :

The initial compressive strength of rock mass.

\( {U}_{r_{i-1}{r}_i}^{\ast \mathrm{res}} \) :

The residual energy of rock mass between ri−1 and ri after excavation.

V :

Volume of the non-fractured rock mass between ri−1 and ri.

d :

Scale of the non-fractured rock mass between ri−1 and ri.

“o”, “∗”:

The upper corner marks are used to distinguish the physical parameters in the surrounding rock before and after excavation.

References

Download references

Funding

The work was supported by the National Key R&D Program of China (grant number 2018YFC0604705), the National Natural Science Foundation of China (grant number 51774167), and Science and technology innovation leading talent project of Liaoning Province (grant number XLYC1802063).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Liaoning Technical University, Fuxin, 123000, China

    Yidan Sun, Yu Yang, Mengze Yang & Jinchan He

Authors
  1. Yidan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mengze Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinchan He
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Yu Yang, Yidan Sun, and Mengze Yang. The first draft of the manuscript was written by Yidan Sun and Jinchan He. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yu Yang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Responsible Editor: Zeynal Abiddin Erguler

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, Y., Yang, Y., Yang, M. et al. Theoretical analysis of equivalent hydrostatic stress attenuation in surrounding rocks after excavation. Arab J Geosci 13, 486 (2020). https://doi.org/10.1007/s12517-020-05528-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12517-020-05528-y

Keywords

Search

Navigation