Calculation Method for the Loose Circle of Tunnel-Surrounding Rock Considering the Strain-Softening Effect
Publication: International Journal of Geomechanics
Volume 24, Issue 10
Abstract
During tunnel excavation, stress redistribution is caused by disturbance of the surrounding rock; when the stress exceeds the strength of rock mass, the surrounding rock enters the postpeak deformation stage and then produces the strain-softening effect. This effect will lead to a decrease in rock mass strength, the expansion of the fracture zone, and a decrease in stability. To further study the influence of strain-softening effect on the loose circle of the surrounding rock, the strain-softening factor is introduced into the unified strength criterion. On this basis, the triaxial test with elastic–plastic theoretical analysis is combined, and the strain-softening model based on the unified strength criterion is proposed. Based on this strain-softening model, the stress state of the postpeak plastic zone of the surrounding rock after excavation is studied and analyzed, and the theoretical calculation formula of the loose circle radius considering the strain-softening effect is obtained. Through theoretical calculations and engineering examples, the influence of strain-softening effect and support reaction force on the radius of the surrounding rock loose circle is compared and analyzed. The results show that: (1) the strain-softening effect further deteriorates the mechanical properties of the surrounding rock in the plastic zone, the stability of the surrounding rock is reduced, and the radius of the loose circle is increased, but closer to the measured values; and (2) with the increase of supporting reaction force, the constraint ability of surrounding rock deformation increases and the radius of the loose circle gradually reduces. Therefore, by enhancing the residual strength of the surrounding rock, controlling the radius of the loose circle of the surrounding rock by improving the strength of the supporting structure, and performing primary support on time, the stability of the surrounding rock can be increased.
Practical Applications
During tunnel excavation, the process disrupts the surrounding rock, causing stress redistribution. When the local stress surpasses the strength of the rock, it results in damage, forming a loose circle and triggering strain softening. At the same time, both contribute to the expansion of the loose circle, further compromising the stability of the surrounding rock. Analyzing the distribution pattern of loose circles in the tunnel-surrounding rock considering the strain-softening effect, enhancing the residual strength of the surrounding rock, and improving the strength of the supporting structure while implementing the initial support in time can effectively control the expansion of the loose circle and improve the stability of the surrounding rock. This research provides an important theoretical basis and engineering experience for tunnel engineering to ensure construction safety and reduce construction costs.
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Data Availability Statement
Some or all data, models, or codes generated or used during the study are available from the corresponding author upon request. The data in Tables 1–3 are obtained by field measurements (original data can be provided). Tables 4 and 5 are calculated theoretically (the data model can be provided).
Acknowledgments
This research is supported by Shaanxi Province Natural Science Basic Research Program (2023-JC-YB-327) and Shaanxi Provincial Department of Education service local special project (22JC040).
Notation
The following symbols are used in this paper:
- B
- maximum tunnel excavation span;
- b
- intermediate principal stress influence coefficient;
- b
- tunnel clear width;
- C0
- integration constant;
- c(η)
- plastic zone cohesion;
- c
- cohesive force;
- cp
- initial cohesion;
- cr
- cohesion residual value;
- h
- tunnel clear height;
- i
- surrounding rock pressure increase and decrease rate;
- P0
- initial geostress;
- Pi
- support Counterforce;
- R0
- loose circle radius;
- Rp
- plastic region radius;
- r
- distance from any point around the rock to the center of the circle;
- r0
- tunnel excavation radius;
- u
- radial displacement;
- α
- tensile–compression strength ratio;
- ɛ1
- maximum principal strain;
- ɛp
- principal strain at the peak in the stress–strain curve;
- ɛr
- principal strains at residual strength in the stress–strain curve;
- η
- softening parameter;
- σ1
- maximum principal stress;
- σc
- material tensile and compressive strength limit;
- σr
- radial stress;
- σR
- radial stress at the elastoplastic interface;
- σre
- radial stress in the elastic zone;
- σrp
- radial stress in the plastic zone;
- σt
- material tensile strength limit;
- σθ
- tangential stress;
- σθe
- tangential stress in the elastic zone;
- σθp
- tangential stress in the plastic zone;
- τs
- material shear strength limit;
- φ(η)
- friction angle in the plastic zone;
- φ
- internal friction angle;
- φp
- initial internal friction angle; and
- φr
- internal friction angle residual value.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 10 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Sep 13, 2023
Accepted: Apr 12, 2024
Published online: Jul 22, 2024
Published in print: Oct 1, 2024
Discussion open until: Dec 22, 2024
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