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A New Elasto-Viscoplastic Damage Model Combined with the Generalized Hoek–Brown Failure Criterion for Bedded Rock Salt and its Application

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Abstract

According to the requirement of the West–East Gas Transmission Project in China, the solution-mined cavities located in the **tan bedded salt formation of Jiangsu province will be utilized for natural gas storage. This task is more challenging than conventional salt dome cavern construction and operation due to the heterogeneous bedding layers of the bedded salt formation. A three-dimensional creep damage constitutive model combined with the generalized Hoek–Brown model is exclusively formulated and validated with a series of strength and creep tests for the bedded rock salt. The viscoplastic model, which takes the coupled creep damage and the failure behavior under various stress states into account, enables both the three creep phases and the deformation induced by vicious damage and plastic flow to be calculated. A further geomechanical analysis of the rapid gas withdrawal for the thin-bedded salt cavern was performed by implementing the proposed model in the finite difference software FLAC3D. The volume convergence, the damage and failure propagation of the cavern, as well as the strain rate of the salt around the cavern, were evaluated and discussed in detail. Finally, based on the simulation study, a 7-MPa minimum internal pressure is suggested to ensure the structural stability of the **tan bedded salt cavern. The results obtained from these investigations provide the necessary input for the design and construction of the cavern project.

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Abbreviations

A 1 :

Material constant

A 2 :

Material constant

a :

Constant depending upon the rock mass’s characteristics

α:

Material constant

B :

Material constant

C 1 :

Material constant

C 2 :

Material constant

c :

Cohesion of the rock

D :

Damage factor

Δe i :

Principal strain increment (i = 1, 2, 3)

Δt :

Creep time step

e ij :

Deviatoric strain component

\( \dot{e}_{{ij}} \) :

Deviatoric portion of strain rate tensor

ε c :

Total creep strain

ε d :

Damage induced creep component

ε s :

Secondary creep component

ε t :

Transient creep component

ε vol :

Volumetric strain

\(\dot{\varepsilon }_{{ij}} \) :

Total strain rate tensor

\( \dot{\varepsilon }^{c} _{{ij}} \) :

Viscous strain rate tensor

\( \dot{\varepsilon }^{e} _{{ij}} \) :

Elastic strain rate tensor

\( \dot{\varepsilon }^{p} _{{ij}} \) :

Plastic strain rate tensor

G :

Shear modulus

I 1 :

First invariant of stress

J 2 :

Second invariant of deviatoric stress

K :

Bulk modulus

k :

Material constant

μ 0 :

Primary Poisson’s ratio

n :

Material constant

r :

Material constant

s :

Constant depending upon the rock mass’s characteristics

s ij :

Deviatoric stress component

\( \dot{s}{}_{{ij}} \) :

Deviatoric portion of stress rate tensor

σ * :

Damage equivalent stress

σ 1 :

Maximum principal stress

σ 2 :

Intermediate principal stress

σ 3 :

Minimum principal stress

σ m :

Average volumetric stress

σ n :

Effective normal stress acting on the failure plane

σ ci :

Uniaxial compression strength of the intact rock

\( \dot{\sigma }{}_{{ij}} \) :

Stress rate tensor

σ F i :

Final corrected principal stress (i = 1, 2, 3)

σ N ij :

New stress component at time step t + Δt

t :

Creep time

τ m :

Failure shear stress

φ :

Internal friction angle of the rock

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Acknowledgments

This research has been fully sponsored by the National Basic Research Program of China (973 Program, No. 2009CB724608). We would like to thank another National Basic Research Program of China (973 Program, No. 2010CB732003), whick is also supportive to our work. This support is greatly appreciated.

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Authors and Affiliations

  1. Engineering Institute of Engineering Corps, PLA University of Science and Technology, Nan**g, 210007, China

    Lin-jian Ma, **n-yu Liu, Hong-fa Xu, Hui-min **a, Er-bing Li, Shi-gang Yang & Wen-pei Li

  2. PLA University of Science and Technology, Nan**g, 210007, China

    Qin Fang

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  1. Lin-jian Ma
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Correspondence to Lin-jian Ma.

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Ma, Lj., Liu, Xy., Fang, Q. et al. A New Elasto-Viscoplastic Damage Model Combined with the Generalized Hoek–Brown Failure Criterion for Bedded Rock Salt and its Application. Rock Mech Rock Eng 46, 53–66 (2013). https://doi.org/10.1007/s00603-012-0256-8

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