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Solutions for Displacement and Stress in Strain-Softening Surrounding Rock Incorporating the Effects of Hydraulic–Mechanical Coupling and Rockbolts Effectiveness

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Abstract

This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness. It follows the generalized Hoek–Brown failure criterion. Moreover, an improved numerical approach and stepwise procedure are proposed. This approach considers the deterioration of the strength, deformation, and dilation angle and the variation of elastic strain in the plastic region considering the effect of the hydraulic–mechanical coupling and the rockbolts effectiveness. The presented solutions were validated by FLAC results. Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming. Parametric studies are also conducted to highlight the influences of hydraulic–mechanical coupling and rockbolts effectiveness on stress and displacement. Results show that stress and displacement, incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness, are between those when hydraulic–mechanical coupling or rockbolts effectiveness is considered separately. However, this theory needs more verification from practical engineering.

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Abbreviations

k r :

Secondary permeability of the fractured rock mass (–)

k 0r :

Initial permeability of the rock mass (–)

a p :

Parameter of H–B failure criterion for peak strength (–)

a r :

Parameter of H–B failure criterion for residual strength (–)

D :

H–B constants for the rock mass (–)

e :

Elastic parts of strain (–)

E :

Young’s modulus of the rock mass (FL−2)

h :

Dilation coefficient (–)

m :

Parameter of H–B failure criterion for peak strength (–)

m r :

Parameter of H–B failure criterion for residual strength (–)

p :

Plastic parts of strain (–)

\(p_{w} = p_{w} (r,\theta )\) :

Pore pressure (F)

q :

Seepage flow rate (L)

r 0 :

Radius of the tunnel opening (L)

r :

Radial distance from the center of opening (L)

R :

Plastic radius (L)

R s :

Softening radius (L)

s :

Parameter of H–B failure criterion for peak strength (–)

s r :

Parameter of H–B failure criterion for residual strength (–)

u :

Radial displacement (L)

u R :

Radial displacement at the interface between plastic and elastic region (L)

u w :

Displacement induced by seepage force (L)

u b :

Displacement induced by boundary condition (L)

λ :

Constant of seepage force (–)

λ :

Width of the softening region (–)

γ w :

Unit weight of water (FM−1)

σ 0 :

Hydrostatic stress (FL−2)

σ c :

Uniaxial compressive strength of the rock (FL−2)

σ r :

Radial stress (FL−2)

σ θ :

Circumferential stress (FL−2)

σ 1 :

Major principal stresses (FL−2)

σ 3 :

Minor principal stresses (FL−2)

ɛ r :

Radial strain (–)

ɛ θ :

Circumferential stain (–)

ɛ 1e :

Elastic strain of the interface between plastic and elastic regions (–)

ɛ v :

Volumetric strain

η :

Constant of proportionality (coupling constant)

φ :

Dilation angle (–)

v :

Poisson’s ratio of the rock mass (–)

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Acknowledgments

This work was supported by the National Basic Research Program of China (“973” Project) (Grant No. 2013CB036004), the National Natural Science Foundation of China (Grant No. 51208523).

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, No. 22, Shaoshan South Road, Central South University Railway Campus, Changsha, 410075, Hunan Province, People’s Republic of China

    Jin-feng Zou & Zhang-qi Xia

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  1. Jin-feng Zou
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  2. Zhang-qi Xia
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Correspondence to Jin-feng Zou.

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Zou, Jf., Xia, Zq. Solutions for Displacement and Stress in Strain-Softening Surrounding Rock Incorporating the Effects of Hydraulic–Mechanical Coupling and Rockbolts Effectiveness. Geotech Geol Eng 34, 1293–1311 (2016). https://doi.org/10.1007/s10706-016-0043-5

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  • DOI: https://doi.org/10.1007/s10706-016-0043-5

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