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Analytical Model for Prediction of Tunnel Deformations in Soft Rocks Considering the Softening and Expansion Effects

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Abstract

Accurate prediction of surrounding rock deformation can effectively prevent tunnel failure. To accurately predict the displacement of soft rock, an optimized prediction model is proposed, which simultaneously considered the phased release of geostress and the characteristics of soft rock. The existing stress release formula is modified based on the stress release law of three steps excavation. Considering the softening effect of soft rock, the softening factor is established and introduced into the Mohr-Columb strength criterion. At the same time, the influence of the expansion effect and rheological effect is considered in the derivation. Analytical model is used to verify actual soft rock tunnel engineering. The results show that the model can accurately predict the displacement. Combined with the actual engineering parameters, the calculated final displacement is 810.39 mm, which is less different from the actual monitoring vault displacements of 779.70 mm, 778.72 mm and 780.74 mm. The error of the final displacement is 3.787%, 3.907% and 3.658%, and the average error is 3.784%. Therefore, the analytical model has good applicability for similar soft rock tunnels, which can accurately calculate the displacement. The analytical model can be used to analyse the stability of soft rock tunnels.

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Abbreviations

λ(x) :

The stress release coefficient

α :

The initial stress release parameter

R L :

The influence radius of the face

x :

The distance between the section and the tunnel face.

R 0 :

The influence radius of the upper step

R 1 :

The influence radius of the middle step

R 2 :

The influence radius of the lower step

X 1 :

The distance between the middle step face and the tunnel face

X 2 :

The distance between the lower step face and the tunnel face

p(t) :

The release of geostress

p 0 :

The initial geostress

\(\sigma_{r}\) :

The radial pressure of the tunnel

\(\sigma_{\theta }\) :

The r tangential pressure of the tunnel

r :

The distance to the centre of the tunnel

u :

The radial displacement of the surrounding rock

\(\varphi\) :

The internal friction angle

c :

The cohesive force

\(\phi\) :

The softening coefficient

\(\Delta c\) :

The variation in cohesive force

\(\Delta \varepsilon_{r}^{p}\) :

The variation in radial plastic strain

\(\varepsilon_{r}^{e}\) :

The radial strain in the elastic zone

\(\varepsilon_{\theta }^{e}\) :

The tangential strain in the elastic zone

\(\varepsilon_{r}^{p}\) :

The radial strain in the plastic zone

\(\varepsilon_{\theta }^{p}\) :

The tangential strain in the plastic zone

h :

The expansion coefficient of the plastic zone

\(\varepsilon_{r}^{b}\) :

The radial strain in the broken zone

\(\varepsilon_{\theta }^{b}\) :

The tangential strain in the broken zone

h 1 :

The expansion coefficient of the broken zone

\(\varepsilon^{c}\) :

Creep strain

\(g(\sigma )\) :

A function of equivalent stress

\(f(t)\) :

A function of the time effect

G c :

The creep modulus

\(\eta\) :

The viscosity coefficient

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Acknowledgements

This research was financially supported by the National Natural Science Foundation of China (Grant Nos. 51408054 sponsored), the Natural Science Foundation (2017JM5136) by the Science and Technology Department of Shaanxi Province.

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Authors and Affiliations

  1. School of Civil and Architecture Engineering, Xi’an Technological University, Xi’an, 710021, China

    Xiang-hui Deng, Yun-cai Wang, Rui Wang & Wei-ping Cao

  2. Xi’an Key Laboratory of Civil Engineering Testing and Destruction Analysis On Military-Civil Dual Use Technology, Xi’an, 710021, China

    Xiang-hui Deng & Rui Wang

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  1. Xiang-hui Deng
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  2. Yun-cai Wang
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  3. Rui Wang
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Correspondence to Yun-cai Wang or Rui Wang.

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Deng, Xh., Wang, Yc., Wang, R. et al. Analytical Model for Prediction of Tunnel Deformations in Soft Rocks Considering the Softening and Expansion Effects. Int J Civ Eng 21, 101–117 (2023). https://doi.org/10.1007/s40999-022-00760-x

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