Instructional Objectives

Transcription

1 GE 6477 DISCONTINUOUS ROCK 7. Shear Strength of Discontinuities Dr. Norbert H. Maerz Missouri University of Science and Technology (573) Instructional Objectives 1. Explain the differences between a simple frictional model of sliding between and the Mohr Colomb model for sliding on a discontinuity. 2. Explain the difference between peak and residual shear strength and justify the use of either model. 3. Critique the advantages and disadvantages in using triaxial vs direct shear test to establish the Mohr- Coulomb parameters. 4. Describe the shortcomings of the Mohr-Columb shear strength criterion, and how these are overcome in the Patton and Barton criteria. 5. Predict the effect of a) dilation and b) shear displacement on the fidelity of the measurements of the shear strength parameters. 1

2 Instructional Objectives 6. Justify the Patton and Barton criteria in terms of the physical representation of the roughness representations. 7. Explain what the Barton criterion has that is missing in the Patton criterion. 8. Suggest why the other shear strength models presented in this section are not widely used. 9. Predict how the scale effect would affect the behavior of rock discontinuities in shear. Image(s) from the collection of Dr. John Franklin. 2

3 Shear Strength of Joints Largely frictional property Some influence of cohesion Very sensitive to normal or confining stress Principle of peak vs. residual strength Simple Friction Model 1 R R F F' ' R ' F 3

4 Rock shear strength model Triaxial tests on discontinuities Image(s) from the collection of Dr. John Franklin. 4

5 Triaxial tests on discontinuities Traixial tests on discontinuities c 3 1 5

6 Direct shear tests Direct shear tests Image(s) from the collection of Dr. John Franklin. 6

7 Direct shear tests Review of stress- strain relationships 7

8 Direct shear test results Big direct shear tests Image(s) from the collection of Dr. John Franklin. 8

9 Mohr-Coulomb model c n c n tan M-C model vs. data 9

10 Picture(s) from Gonzales de Vallejo and Ferrer What makes a good model? 1. Accurate, faithful. 2. Simple If no one understand it, it goes nowhere. 3. Lowest possible number of parameters If there are too many it is too difficult. 4. Critical parameters are ones that are not easy to measure or estimate, and the model is especially sensitive to them. 10

11 Bilinear failure criteria What happens during shearing of rough surfaces? 1. Dilation. 2. Destruction of asperities. Bilinear failure criteria: Pattons i- angle 11

12 Bilinear failure criteria: Pattons i- angle For low normal stress p tan i n u For high normal stress p S j n tan r Picture(s) from Gonzales de Vallejo and Ferrer 12

13 Dilation Dilation 13

14 Barton s curvilinear failure criterion Empirical, curilinear three-parameter empirical shear strength model Uses Joint Roughness Coefficient, Joint (wall) Compressive Strength, and a base friction angle n tanjrc log 10 JCS n b JRC (Joint roughness coefficient). Typically estimated, or calculated from a digitized profile. Range Picture(s) from Gonzales de Vallejo and Ferrer 14

15 JCS (Joint wall Compressive Strength) from Schmidt Hardness Image(s) from the collection of Dr. John Franklin. Tilt test on core Base angle of friction tan tan b Typical guess = 30 degrees 15

16 Barton Model Barton vs Patton n tanjrc log 10 JCS b n n tan i u Equating IF THEN JCS JRC log 10 b n b u JCS JRC log 10 i n i u 16

17 Barton Model Roughness Directional. Can be thought of as a waveform. No direct relationship between roughness and shear strength. 17

18 Roughness Amplitude, wavelength, slope. Ratio of filling thickness to amplitude. Roughness to shear strength 1) Generate roughness profiles. 2) Measure some parameters on profile, such as average slope, use in Patton s model. 3) Empirical relationship to a parameter that can be used in a model, such as JRC, use in Barton s model. 18

19 Shadow Profilometry Image(s) from the collection of Dr. John Franklin. Principle of shadow profilometry 19

20 Angle of shadow profile 20

21 Shadow Profilometry Roughness Profile with Z2 (root mean square of the first derivative), i (average micro inclination angle), Rp (roughness profile index) Shadow Profilometry 21

22 Shadow profilometry Image(s) from the collection of Dr. John Franklin. Precision of shadow profilometry Greater accuracy and precision 22

23 Roughness to shear strength: Barton type curves JRC 401 R 1 p Roughness to shear strength, tilt tests on cores JRC 411 R 1 p 23

24 Shadow profilometry paper Ladanyi and Archambault model 24

25 Denby and Scoble Model B A n Reeves Model n tan t tan n t C Z 2 Uses Z 2 (root mean square of the first derivative) and empircal constants C, n to fit a power law curve. 25

26 Models superimposed Other models: Abound in literature, Suffer from obscurity. 26

27 Roughness scale effect Corrugated cardboard Rock joint surface Roughness scale effect 27

28 Shear strength scale effect Picture(s) from Gonzales de Vallejo and Ferrer Resolving shear scale effects Small portable shear machines - core sized Large lab shear machines mm on side Field shearing machines - several m on end Use small tests to get residual or ultimate or base friction. Use roughness (whichever measure) on the scale of the potential failure. Use back analysis 28

29 Time Dependent behavior of joints - rheological elements Time Dependent behavior of joints - rheological model 29