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Dynamic Model of Negative Poisson’ Ratio Bolt: Theoretical Analysis and Experimental Validation

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Abstract

The Negative Poisson's Ratio (NPR) bolt is more effective for preventing and controlling rock bursts than conventional bolts. This paper establishes a dynamic model of NPR bolts under impact forces to clarify their mechanical characteristics. The model comprises three stages: elastic deformation, structural slipping deformation, and elastic recovery. The effects of varying impact force strengths and periods on the dynamic behavior of NPR bolts were studied. The Split Hopkinson Tensile Bar (SHTB) test compared the dynamic responses of NPR and conventional bolts under different impact force wavelengths and gas pressures. The results show that during the structural slipping deformation stage, the impact force is not synchronized with the end of the structural slip deformation, with the time difference depending on the type of impact force. Even if the impact force strength is less than the constant resistance of the NPR bolt, it still transitions from elastic deformation to structural slipping deformation and back to elastic deformation with increasing impact force periods. At the same wavelength, the peak impact force of the NPR bolt is, on average, 10.6% lower than that of a conventional bolt. Due to the structural slipping deformation of the NPR bolt, its final elongation is not zero, unlike the conventional bolt, which is prone to sudden brittle fracture. The experimental data validate the accuracy and feasibility of the theoretical model in characterizing key NPR bolt characteristics, such as peak impact force and final elongation, with an absolute difference rate within 7%. A comparative field test under simulated 3-level mine earthquakes showed that NPR cable-supported roadways remained stable, while conventional ones collapsed severely. These findings provide valuable references for the anti-impact support of rock burst-prone mines.

Highlights

  • A dynamic model of NPR bolts under impact forces is established and verified, clarifying their dynamic mechanical characteristics.

  • The influence of varying impact force strengths and periods on the dynamic behavior of NPR bolts is revealed.

  • Differences in the dynamic responses of NPR and conventional bolts under varying wavelengths and gas pressures are obtained through SHTB tests.

  • A comparative study of anti-impact blasting tests (simulated grade 3 mine earthquakes) with NPR and conventional cables is conducted.

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Data Availability

All the data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

a :

Diameter of the small end of the cone (mm)

b :

Diameter of the large end of the cone (mm)

C₁, C₂, … , C₈ :

Free variables for differential equation solutions

E :

Elastic modulus of the sleeve (GPa)

f :

Static friction coefficient

f' :

Equivalent friction coefficient

f d :

Dynamic friction coefficient

F d :

Sliding friction force (kN)

h :

Length of the cone (mm)

I c :

Geometric parameter of the cone (m3)

I s :

Material parameter of the sleeve (N/m3)

k :

Stiffness of the shank rod (kN/mm)

kx :

Internal elastic force of the shank rod (kN)

m :

Mass of the shank rod and cone (kg)

M :

Mass of the face pallet and sleeve (kg)

P(t) :

Impact force as a function of time (kN)

P₀ :

Constant resistance of NPR bolt (kN)

P m :

Intensity of impact force (kN)

P max :

Maximum impact force (2Pm) (kN)

t :

Time (s)

t₁ :

End time of elastic deformation stage (s)

t₂ :

End time of structural deformation stage (s)

T :

Tension in the bolt (kN)

v :

Velocity of displacement (m/s)

v₁ :

Velocity at the end of elastic stage (m/s)

v m :

Velocity of the cone (m/s)

v m + M :

Common velocity of cone and sleeve (m/s)

v p :

P-wave velocity (m/s)

x :

Displacement of the NPR bolt (mm)

x₁ :

Maximum elastic displacement (mm)

x₂ :

Displacement at the end of structural deformation stage (mm)

x m :

Displacement of the cone during structural deformation (mm)

ẋ :

First derivative of displacement (velocity) (m/s)

ẍ :

Second derivative of displacement (acceleration) (m/s2)

α :

Inclination angle of the cone slope (°)

Δ t :

Duration of impact force (s)

Δ x :

Cyclic displacement in each stick–slip period (mm)

λ :

Duration parameter of impact force (1/ms)

μ :

Poisson's ratio of the sleeve

ω :

Natural frequency of the shank rod (rad/s)

π :

Mathematical constant pi (≈ 3.14159)

ρ :

Density (g/cm3)

φ :

Diameter symbol (e.g., φ21.7 mm) (mm)

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Funding

Funding for this work was provided by the National Natural Science Foundation of China (52,074,300), the Program of China Scholarship Council (202,206,430,024), Yueqi Young Scholars Project of China University of Mining and Technology Beijing (2602021RC84), Guizhou Province Science and Technology planning project ([2020]3007, [2020]3008).

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Authors and Affiliations

  1. State Key Laboratory for Tunnel Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

    Jiong Wang, Peng Liu, Manchao He, Lei Ma & Weili Gong

  2. School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

    Jiong Wang, Peng Liu, Manchao He, Lei Ma & Weili Gong

  3. Information Institute of the Ministry of Emergency Management of the PRC, Beijing, 100029, China

    Peng Liu

  4. College of Geosciences and Engineering, North China University of Water Resources and Electric Power, Zhengzhou, 450045, China

    Fei Zhao

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  1. Jiong Wang
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  2. Peng Liu
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  3. Manchao He
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  4. Lei Ma
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Contributions

Jiong Wang: Supervision, Project administration, Peng Liu: Data curation, Writing – original draft, Writing – review & editing, Funding acquisition, Manchao He: Validation, Lei Ma: Investigation, Fei Zhao: Methodology, Weili Gong: Resources.

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Correspondence to Peng Liu.

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Wang, J., Liu, P., He, M. et al. Dynamic Model of Negative Poisson’ Ratio Bolt: Theoretical Analysis and Experimental Validation. Rock Mech Rock Eng (2025). https://doi.org/10.1007/s00603-025-05074-7

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