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Experimental Investigation of the Peak Shear Strength Criterion Based on Three-Dimensional Surface Description

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Abstract

The three-dimensional (3D) morphology of joints is enormously important for the shear mechanical properties of rock. In this study, three-dimensional morphology scanning tests and direct shear tests are conducted to establish a new peak shear strength criterion. The test results show that (1) surface morphology and normal stress exert significant effects on peak shear strength and distribution of the damage area. (2) The damage area is located at the steepest zone facing the shear direction; as the normal stress increases, it extends from the steepest zone toward a less steep zone. Via mechanical analysis, a new formula for the apparent dip angle is developed. The influence of the apparent dip angle and the average joint height on the potential contact area is discussed, respectively. A new peak shear strength criterion, mainly applicable to specimens under compression, is established by using new roughness parameters and taking the effects of normal stress and the rock mechanical properties into account. A comparison of this newly established model with the JRC–JCS model and the Grasselli’s model shows that the new one could apparently improve the fitting effect. Compared with earlier models, the new model is simpler and more precise. All the parameters in the new model have clear physical meanings and can be directly determined from the scanned data. In addition, the indexes used in the new model are more rational.

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Abbreviations

\(\sigma_{\text{t}}\) :

Tensile strength of the intact material (MPa)

\(\sigma_{\text{c}}\) :

Uniaxial compressive strength of the intact material (MPa)

\(\varphi_{\text{b}}\) :

Basic friction angle (°)

n :

Outward normal vector of the triangle element

n 1 :

The projection vector of n

n 0 :

Outward normal vector of the shear plane

S :

The shear vector

\(\alpha\) :

The angle between n 1 and S (°)

\(\theta\) :

Dip angle of the triangle element (°)

\(\tau\) :

Shear stress applied by the testing machine (MPa)

\(\tau^{\prime}\) :

Shear stress acting on asperity (MPa)

\(\tau_{\text{p}}\) :

Peak shear strength (MPa)

\(\sigma_{\text{n}}\) :

Normal stress (MPa)

\(\sigma_{\text{j}}\) :

Normal stress acting on the joint plane (MPa)

\(\tau_{\text{j}}\) :

Shear stress along the joint plane (MPa)

A :

Total areas (mm2)

A contact :

Total areas in contact before direct shear test (mm2)

A shear :

Total areas facing the shear direction (mm2)

\(A_{{\theta^{ * } }}^{ + }\) :

Ratio between A contact and A shear

\(A_{{\theta^{ * } }}\) :

Ratio between A contact and A

\(A_{0}\) :

Ratio between A shear and A

\(\theta^{ * }\) :

Apparent dip angle (°)

\(\bar{\theta }^{ * }\) :

Characteristics angle (°)

\(\theta_{\rm max }^{ * }\) :

Maximum apparent dip angle (°)

n :

Roughness parameter characterizing the distribution of apparent dip angles over the joint surface defined by this paper

C :

Roughness parameter characterizing the distribution of apparent dip angles raised by Grasselli

h :

Average joint height (mm)

i :

Dilatancy angle (°)

i p :

Peak dilatancy angle (°)

i o :

Initial dilatancy angle (°)

\(\delta\) :

Estimation error

\(\delta_{\text{ave}}\) :

Average estimation error

\(\tau_{\text{measured}}\) :

Measured peak shear strength (MPa)

\(\tau_{\text{calculated}}\) :

Calculated peak shear strength (MPa)

JRC:

Joint roughness coefficient

JMC:

Joint matching coefficient

JCS:

Joint wall compressive strength (MPa)

\(L_{n}\) :

Real scale (mm)

\(L_{o}\) :

Standard scale (mm)

\({\text{JRC}}_{n}\) :

JRC value on real scale

\({\text{JRC}}_{o}\) :

JRC value on standard scale

\(j\) :

Number of profiles

\({\text{JRC}}_{\text{ave}}\) :

Average value of \({\text{JRC}}_{n}\)

\(\beta\) :

Angle between schistosity plane and plane normal to the joint (°)

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Acknowledgements

The authors would like to acknowledge the consistent support of the National Basic Research Program of China (973 Program) (Grant No. 2014CB046904) and the National Natural Science Foundation China (Grant No. 41130742).

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  1. The Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province, School of Civil Engineering, Wuhan University, Wuhan, 430072, Hubei, China

    Quansheng Liu, Yongchao Tian, Peiqi Ji & Hao Ma

  2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, China

    Quansheng Liu

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Liu, Q., Tian, Y., Ji, P. et al. Experimental Investigation of the Peak Shear Strength Criterion Based on Three-Dimensional Surface Description. Rock Mech Rock Eng 51, 1005–1025 (2018). https://doi.org/10.1007/s00603-017-1390-0

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