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Simulating progressive failure in fractured saturated rock under seepage condition using a novel coupled model and the application

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Abstract

Rock mass is an inhomogeneous medium containing a large quantity of fractures and defects. The coupling interaction between seepage evolution and crack propagation is greatly significant to rock projects. In this study, a novel coupled model involving fluid pressure and mechanical damage is developed in FLAC3D. Both the pre-peak softening and post-peak mechanical degeneration of elements are considered based on their different failure types, i.e. tension failure, shear failure, and their state combinations. Investigations are carried out on the specimen with two pre-fractures and 5% defects derived from modelling cement mortar. Four test schemes of dry and saturated specimens are conducted under uniaxial and biaxial loadings. The specimens' failure process under seepage could be divided into three stages. The failure process is basically different from that under dry conditions. Both compressive and residual strengths have declined significantly, by more than 10 and 15% respectively compared with dry specimens. The volume expansion of the specimen has remarkably increased, by more than 320%. Besides, the results are well consistent with dry experiments on cement mortar, which demonstrates feasibility of the method. Finally, the proposed model is applied to explore seepage evolution, rock mass deformation and lining stability of Jiaozhou Bay subsea tunnel within excavation. A new generation method of fracture networks is developed and the simulated results match well with field monitoring data.

Article highlights

  • The novel coupled model considers both pre-peak damage and post-peak degeneration of rock.

  • Principles are based on elements' failure type, i.e. tension failure, shear failure, and their combinations.

  • Previous studies are based on elastic–plastic models, which are improved to be elastic-brittle and suit brittle rock mass better.

  • Weakened elements are developed to simulate natural defects in real rocks.

  • A new generation method of stochastic fracture networks is developed for engineering practice.

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Abbreviations

\(D\) :

Damage variable

\(\varepsilon_{t0}\) :

Threshold for damage-beginning

\(\varepsilon_{tu}\) :

Limit of tensile strain

\(E_{0}\) :

Initial elastic modulus

\(\sigma_{i}\) :

Residual strength of tension damage

\(\eta\) :

Residual strength coefficient

\(\sigma_{t}\) :

Uniaxial tensile strength

\(\overline{\varepsilon }\) :

Equivalent strain

\(\varepsilon_{c0}\) :

Strain threshold for shear damage

\(\sigma_{rc}\) :

Residual strength of shear damage

\(K^{\prime}\) :

Bulk modulus for elements after failure

\(\sigma_{t} ^{\prime}\) :

Tensile strength for elements after failure

\(G^{\prime}\) :

Shear modulus for elements after failure

\(\varphi ^{\prime}\) :

Internal friction angle for elements after failure

\(c^{\prime}\) :

Cohesion for elements after failure

\(k\) :

Permeability

\(\xi\) :

Rising rate of permeability

\(q_{i}\) :

Flow quantity

\(k_{ij}\) :

Permeability rate

\(p\) :

Seepage pressure

\(\rho_{w}\) :

Fluid density

\(g_{k}\) :

Gravity acceleration vector

\(\zeta\) :

Volume change of the fluid per unit volume in the porous solid media

\(q_{v}\) :

Intensity of source flow

\(n\) :

Porosity

\(\rho_{s}\) :

Density of solid media

\(\rho_{w}\) :

Density of fluid

\(M\) :

Biot's modulus

\(s\) :

Saturability

\(\alpha\) :

Biot’s coefficient

\(\beta\) :

Thermal expansion coefficient

\(T\) :

Temperature

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Acknowledgements

The authors express sincere appreciation to anonymous reviewers for their valuable comments on improving this study. This study is funded by National Natural Science Foundation of China (Grant No. 51608117 and 52004098), Key Specialized Research and Development Breakthrough Program in Henan province (Grant No. 192102210051).

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Authors and Affiliations

  1. School of Civil Engineering and Transportation, North China University of Water Resources and Electric Power, Zhengzhou, 450046, China

    Jinwei Fu, Huixiang Cheng & Rongbin Hou

  2. Department of Civil, Environmental, and Geo-Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Joseph F. Labuz

  3. Geotechnical & Structural Engineering Research Center, Shandong University, Jinan, 250061, China

    Weishen Zhu

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  1. Jinwei Fu
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  2. Joseph F. Labuz
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  3. Huixiang Cheng
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Contributions

JF: Theoretical derivation on the coupling model, software programming, writing-original draft, data analysis. JFL: Theoretical innovation, numerical guidance, grammar checking. HC: Simulation work of the inhomogeneous specimen and tunnel project. RH: Numerical simulation, data analysis, writing-review & editing. WZ: Field monitoring and data cooperation with Jiaozhou Bay tunnel.

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Correspondence to Jinwei Fu.

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Fu, J., Labuz, J.F., Cheng, H. et al. Simulating progressive failure in fractured saturated rock under seepage condition using a novel coupled model and the application. Geomech. Geophys. Geo-energ. Geo-resour. 8, 42 (2022). https://doi.org/10.1007/s40948-022-00354-w

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