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Three-Dimensional Collapse Analysis for a Shallow Cavity in Layered Strata Based on Upper Bound Theorem

Hongtao Wang1,2,*, Ping Liu1,2, Lige Wang3,4,*, Chi Liu5, Xin Zhang1,2, Luyao Liu1,2

1 School of Civil Engineering, Shandong Jianzhu University, Jinan, China
2 Key Laboratory of Building Structural Retrofitting and Underground Space Engineering (Shandong Jianzhu University), Ministry of Education, Jinan, China
3 Department of Chemical and Biological Engineering, University of Sheffield, Sheffield, UK
4 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China
5 Jinan Rail Transit Group Co., Ltd., Jinan, China

* Corresponding Authors: Hongtao Wang. Email: ; Lige Wang. Email:

(This article belongs to this Special Issue: Modeling and Simulation of Fluid flows in Fractured Porous Media: Current Trends and Prospects)

Computer Modeling in Engineering & Sciences 2020, 124(1), 375-391.


Layered rock strata are observed to be common during the excavation of tunnels or cavities, and may significantly affect the deformation and failure characteristics of surrounding rock masses due to various complex forms and mechanical properties. In this paper, we propose a three-dimensional axisymmetric velocity field for roof collapse of shallow cavities in multi rock layers, by considering the influences of roof cross-section shapes, supporting pressure, ground overload, etc. The internal energy dissipation rate and work rates of external forces corresponding to the velocity field are computed by employing the Hoek-Brown strength criterion and its associated flow rule. Further, the equations of the collapse surfaces and the corresponding weight of collapsing rock masses are derived on the basis of upper bound theorem. Furthermore, we validate the proposed method by comparing the results of numerical calculations and existing research findings. The change laws of the collapse range under varying parameters are obtained for the presence of rectangular and spherical cavities. We also find that the three-dimensional mechanism is relatively safer for engineering designing actually, compared with the traditional two-dimensional mechanism. All these conclusions may provide workable guidelines for the support design of shallow cavities in layered rock strata practically.


Cite This Article

Wang, H., Liu, P., Wang, L., Liu, C., Zhang, X. et al. (2020). Three-Dimensional Collapse Analysis for a Shallow Cavity in Layered Strata Based on Upper Bound Theorem. CMES-Computer Modeling in Engineering & Sciences, 124(1), 375–391.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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