A Model for Anisotropic Shear Strength of Rock Joints

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葛瑞伯(Gaurab Singh Thapa) 查詢紙本館藏

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論文名稱

(A Model for Anisotropic Shear Strength of Rock Joints)

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摘要(中)

本文以法向荷重為定值(CNL)的條件下，研究岩石節理異向性剪力行為。由於Barton剪力強度公式以及 Tse和Cruden的公式皆無法考慮岩石節理異向性剪力強度，因此提出新的公式解決此問題。
τ=σ_n tan⁡〖[ϕ_b+13.41*Z_2*log10⁡(JCS/σ_n ) ]+C_b* C_AR 〗
由於粗糙節理在不同方向具有異向性，因此本研究使用 Z_2(一階倒數的均方根)求粗糙節理係數 (JRC) 與最大剪力強度 (τ)，粗糙度參數包含剪力方向 (β°)，波長 (λ)，振幅 (A) 和循環數量 (N)， Z_2愈大代表粗糙度愈主導。
Z_2=√(1/2πN ∫_(x=0)^(x=2πN)▒(dy/dx)^2 )=√((A^2 sin⁡(β) (8Nπ^2 sin⁡(β)+λ sin⁡((8Nπ^2 sin⁡(β))/λ) ))/(Nλ^2 ))/2
　　本研究使用三種驗證模式對提出的模型進行適當的論證：(1)透過顆粒流軟體PFC^3D (Particle Flow Code^3D)生成不同振幅 (2mm，3mm，4mm) 與波長 (9mm，12.86mm，18mm和30mm)的正弦曲線的粗糙節理，在不同的剪力方向進行驗證； (2)用PFC^3D模擬不同傾角的三角形節理來驗證此模型； (3)使用Zhang（2019）的實驗數據對提出的模型進行了驗證。
結果顯示不同的驗證結果皆與此模型高度吻合，由於剪力方向的粗糙度發生變化，岩石節理的剪力強度 (τ) 本質上異向性的。

摘要(英)

In this study, an anisotropic shear behavior of rock joints is investigated under constant normal load condition (CNL). Barton’s shear strength formula together with Tse and Cruden’s equation cannot take into account the anisotropic shear strength of rock joints. This study proposed a new equation taking in account anisotropic shear behavior of rocks joints.
τ=σ_n tan⁡〖[ϕ_b+13.41*Z_2*log10⁡(JCS/σ_n ) ]+C_b* C_AR 〗
Because of anisotropic characteristics of joint roughness in different direction, roughness parameter Z2 (root mean square of the first derivative) is derived based on sinusoidal profile parameters and is used to find Joint roughness coefficient (JRC) and peak shear strength (τ). The parameters of roughness under consideration are shearing direction (β⁰), Wavelength (λ), Amplitude (A) and Number of cycle (N). A bigger value for this parameter (Z2) means a roughness is more dominant.
Z_2=√(1/2πN ∫_(x=0)^(x=2πN)▒(dy/dx)^2 )=√((A^2 sin⁡(β) (8Nπ^2 sin⁡(β)+λ sin⁡((8Nπ^2 sin⁡(β))/λ) ))/(Nλ^2 ))/2
Different modes of validation were used for suitable justification of the proposed models. PFC3D numerical simulation on sinusoidal profile with different amplitudes (2mm, 3mm and 4mm), wavelengths (9mm, 12.86mm, 18mm and 30mm) and normal stresses at different shearing direction (β⁰) is performed for the validation. In addition, the proposed model is validated with PFC3D numerical simulation results of triangular joints profile with different inclination angle. Furthermore, proposed model is also validated with the experimental data of Zhang, 2019. Except few combinations, good agreement is found between the results from proposed model and results from different modes of validation. It is found that shear strength of rock joint is anisotropic in nature due to roughness variation in shearing direction.

關鍵字(中)

★ 異向性剪力強度
★ 粗糙節理
★ 岩石節理
★ 裂隙
★ 直剪試驗
★ PFC

關鍵字(英)

★ Anisotropic shear strength
★ Joint roughness
★ Rock joint
★ Fracture
★ Direct shear test
★ PFC

論文目次

摘要 i
ABSTRACT ii
Acknowledgements iii
Table of Contents iv
List of Figures vi
List of Tables xi
Abbreviations and Notation xiii
CHAPTER 1 INTRODUCTION 1
1.1 Research Background 1
1.2 Research Objective 3
1.3 Research Organization 3
CHAPTER 2 LITERATURE REVIEW 5
2.1 Discontinuity 5
2.2 Anisotropy 10
2.3 Model for Shear Strength of Rock Joints 12
2.3.1 Coulomb Model 12
2.3.2 Patton’s Bilinear Criterion (1966) 13
2.3.3 Ladanyi and Archambaults Criterion (1970) 13
2.3.4 Modified Ladanyi and Archambault Criterion (Saeb, 1990) 14
2.3.5 Barton’s Shear Strength Criterion (1973) 15
2.3.6 Grasselli’s Three-dimensional Criterion (2003) 15
2.4 Relationship between JRC and Z2 16
2.5 Laboratory Study for Anisotropic Shear Behavior of Rock Joints 18
2.6 Numerical Simulation for Shear Behavior of Rock Joints 25
2.6.1 Distinct Element Method (DEM) 26
CHAPTER 3 METHODOLOGY 33
3.1 Flowchart of Research 33
3.2 Development of PFC3D Model for Rock Joints under Different Shear Direction 43
3.2.1 Generation of Planar Joint 43
3.2.2 Generation of Sinusoidal Curve Shaped Joint 44
3.2.3 Shear Directions 48
CHAPTER 4 RESULTS AND DISCUSSION 52
4.1 A New Model for Anisotropic Shear Behavior of Rock Joints 52
4.2 Contact Area Ratio (CAR) 52
4.2.1 Contact Area Ratio of Sine Profile 54
4.2.2 Contact Area Ratio of Triangular Profile 55
4.3 Z2 for Different Shear Directions 55
4.3.1 Z2 of Sine Profile 62
4.3.2 Z2 of Triangular Profile 64
4.4 Validation 73
4.4.1 Validation with Numerical Simulation on Sinusoidal Profile 74
4.4.2 Validation with Numerical Simulation on Triangular Profile 89
4.4.3 Validation with Laboratory Data- (Zhang, 2019) 92
4.5 Failure Process and Failure Mode under Different Shear Direction 98
CHAPTER 5 CONCLUSIONS 121
CHAPTER 6 RECOMMENDATIONS 123
REFERENCES 124

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指導教授

田永銘(Yong-Ming Tien)

審核日期

2020-8-19

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