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The primary objective of this study is to develop a parameter with a clear physical meaning to estimate the surface roughness of rock discontinuities. This parameter must be closely related to the shear strength of rock discontinuities. The first part of this study focuses on defining and computing this parameter. The estimation formula for the shear strength of a triangle within a discontinuity surface is derived based on Patton’s model. The parameter, namely, the index of roughness (

Rock masses usually contain significant discontinuities such as joints, faults, bedding planes, fractures, and other mechanical defects. The surface roughness of rock discontinuities plays an important role in the mechanical properties of rocks, including the shear strength and deformation [

Myers [_{2} to quantitatively describe the roughness of discontinuity profiles:_{2}, SF, and _{2}, Belem et al. [_{2}), and Zhang et al. [_{2} and SF, were sensitive to the sampling interval.

In conclusion, existing discontinuity roughness estimation methods can be mainly subdivided into three categories: empirical methods [_{2}, which was proposed by Myers [_{2} cannot directly reflect the influence of the basic friction angle (_{2} and the shear strength of discontinuities is not well established. As another example, Grasselli’s method can effectively estimate the 3D discontinuity roughness using the parameter

A strong connection between the roughness parameter and the shear strength of discontinuities should be established and could contribute to building a shear strength model of discontinuities. Therefore, based on the shear failure mechanism of discontinuities, a formula for the shear strength of a triangle within a discontinuity surface is derived from Patton’s model, and the roughness estimation parameter, index of roughness (

The normal stress directly affects the shear failure mechanism of discontinuities. Jaeger [

In addition, when materials fill the discontinuity gap, the shear resistance of the discontinuity can be affected by the properties of these filling materials. To simplify the discontinuities in this study, we hypothesize that the discontinuities are well-mated and that no gaps are present along them.

The teeth-discontinuity model proposed by Patton [

RTD model and its shear force analysis: (a) RTD model (modified from Patton [

Shear strength envelopes of the RTD models: (a) failure envelopes of the RTD models with different asperity angles (modified from Patton [

Discontinuities in natural rock masses are complex. For engineering purposes, additional research on the irregular-teeth-discontinuity (ITD) model, which is defined as a teeth-discontinuity model with different tooth inclinations, is very important. Figure

ITD model and its shear failure mechanism: (a) before shear failure; (b) after shear failure.

The equation

For an ITD model with a normal stress

In 3D roughness characterization, a discontinuity surface can be discretized into adjacent triangles, with each triangle orientation uniquely identified by its dip angle (_{0} is the maximum potential contact area,

Apparent dip angle

In Grasselli’s method, the potential contact triangles with equal apparent dip angle (

The data acquisition process provides a basis for estimating the roughness of discontinuities. The surface asperity features can be directly measured by several contact and noncontact tools and techniques. Contact techniques include a needle contour [

A strong connection between the roughness parameter and the shear strength of the discontinuities can contribute to establishing a shear strength model of discontinuities. Therefore, this paper proposes a new parameter,

Discontinuity model for the definition and calculation of

The parameter

The calculation procedure of

First, identify whether

After calculating the antishearing force of every potential contact triangle of

_{H} and

Additionally, the

In addition to the ten typical profiles proposed by Barton and Choubey [

Typical profiles and their models: (a) typical profiles with JRC values calculated by back analyses [

Before calculating

Linear correlation between

The corresponding shear directions of the JRC values for sixty-four profiles are known, while those for the ten typical profiles are not. Therefore, for the sixty-four profiles, the

Additionally, the influences of the sampling interval

JRC | | | |||||
---|---|---|---|---|---|---|---|

| | Average | | | Average | ||

0.4 | 0.4068 | 0.3771 | 0.3920 | 0.3195 | 0.3001 | 0.3098 | |

2.8 | 0.4611 | 0.3855 | 0.4233 | 0.4414 | 0.3468 | 0.3941 | |

5.8 | 0.5069 | 0.4406 | 0.4737 | 0.4474 | 0.3966 | 0.4220 | |

6.7 | 0.6041 | 0.6253 | 0.6147 | 0.6035 | 0.6144 | 0.6089 | |

9.5 | 0.7034 | 0.5507 | 0.6271 | 0.6641 | 0.5112 | 0.5877 | |

10.8 | 0.6364 | 0.6797 | 0.6580 | 0.6195 | 0.6497 | 0.6346 | |

12.8 | 0.8196 | 0.7106 | 0.7651 | 0.7629 | 0.6876 | 0.7253 | |

14.5 | 0.7879 | 0.8039 | 0.7959 | 0.7614 | 0.7742 | 0.7678 | |

16.7 | 1.0236 | 0.8319 | 0.9277 | 0.9640 | 0.7612 | 0.8626 | |

18.7 | 1.0718 | 1.1521 | 1.1119 | 1.0596 | 1.1075 | 1.0836 |

Jiweishan mountain is located approximately 1 km southeast of Tiekuang Township, in Wulong County, Chongqing, China (Figure ^{2}. The basic friction angle (_{c}), cohesion (

Mechanical properties of the eleven discontinuity samples.

Rock types | | _{c} (MPa) | | |
---|---|---|---|---|

Limestone | 30.5 | 90.6 | 11.2 | 44.6 |

Shale | 22.8 | 36.6 | 5.3 | 33.3 |

(a) Geographic location and (b) sampling point of the Jiweishan rockslide.

(a) Data acquisition and (b) direct shear tests for rock discontinuity specimens.

_{c} [

Results of the shear tests and roughness estimations for the eleven discontinuity specimens.

Specimens | | JRC | | |
---|---|---|---|---|

| 0.48 | 0.92 | 14.02 | 0.82 |

| 0.83 | 1.03 | 10.21 | 0.71 |

| 0.93 | 0.68 | 2.94 | 0.51 |

| 1.96 | 1.66 | 5.80 | 0.66 |

| 3.06 | 3.19 | 10.69 | 0.76 |

| 3.11 | 2.57 | 6.15 | 0.75 |

| 0.50 | 0.46 | 10.65 | 0.81 |

| 1.61 | 1.09 | 8.22 | 0.64 |

| 3.07 | 2.45 | 14.65 | 0.94 |

| 3.40 | 3.48 | 22.15 | 1.32 |

| 3.75 | 2.16 | 7.23 | 0.58 |

Modeling of discontinuity

Based on the surface data and shear test results of the eleven specimens, the estimation effects of the proposed method are analyzed as follows.

Correlation between

The results are shown in Figure

Direction (°) | |
---|---|

0 | 14.80 |

15 | 14.11 |

30 | 11.38 |

45 | 10.94 |

60 | 11.28 |

75 | 12.44 |

90 | 12.74 |

105 | 13.58 |

120 | 15.76 |

135 | 17.38 |

150 | 19.24 |

165 | 22.28 |

180 | 17.17 |

195 | 17.68 |

210 | 20.21 |

225 | 19.76 |

240 | 18.08 |

255 | 15.25 |

270 | 15.11 |

285 | 14.87 |

300 | 12.81 |

315 | 12.86 |

330 | 12.38 |

345 | 12.39 |

_{2} _{2} value of each profile model with _{2} and JRC of these profiles. The distribution of_{2} in relation to the JRC values for the seventy-four profiles is plotted in Figure _{2} and JRC is 0.803. Comparing Figures _{2} and JRC across the seventy-four profiles.

Distribution of_{2} in relation to JRC for the seventy-four profiles (

Histograms and corresponding fitting curves of

Correlation between

This study attempts to obtain a roughness parameter that is closely related to the shear strength of discontinuities. First, the shear failure mechanisms of the ITD models are analyzed based on the RTD models from Patton. Second, a formula (see (

The computational processes and estimation effects of the proposed method are presented using several applications. Specifically, the seventy-four typical profiles and the eleven discontinuities are analyzed using the proposed method. These applications show that the discontinuity roughness estimated by both 2D and 3D

Comparison analyses are performed to study the use and robustness of the proposed method. For the seventy-four profiles, the linear correlation between the _{2} and JRC. Additionally, for the eleven discontinuity specimens, the linear correlation between

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was funded by the National Key R&D Program of China (2017YFC1501305) and the Key National Natural Science Foundation of China (no. 41230637). This financial support is gratefully appreciated.

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