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Research on Peak Shear Strength Criterion of Rock Joints Based on the Evolution of Dilation Angle

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The surface morphology of joints directly determines the contact area and peak shear strength of rock in shearing. This research gives a detailed description of the three-dimensional roughness parameters proposed by Grasselli, and discusses the morphology characteristics of the roughness parameter C in different ranges. Quoting Xia's direct shear test data, the relationship of peak shear strength, peak shear strength/normal stress, residual strength, dilation with roughness and normal stress are studied. The deficiencies in the previous classical criteria are explained in detail. A new peak shear strength criterion is established based on the boundary conditions of the dilation angle. The nonlinear characteristic of peak shear strength is included in the peak dilation angel, so that the new criterion satisfies the Mohr–Coulomb law of nonlinear form. In the expression of the initial dilation angle, the new criterion satisfies the fact that the peak shear strength decreases after once sheared. Finally, the test data of Grasselli and Yang are used to compare the prediction accuracy of Grasselli’s criterion, Yang’s criterion, Xia’s criterion and the new criterion. In general, the new criterion has the highest degree of agreement with the test results.

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θ * :

Apparent dip angle (°)

α :

Azimuth angle (°)

θ cr * :

Threshold apparent dip angle (°)

A θ * :

Total potential contact area

C :

Roughness parameter defined by Grasselli

θ max * :

Maximum apparent dip angle (°)

A 0 :

Maximum contact area

σ n :

Normal stress (MPa)

σ c :

Uniaxial compressive strength (MPa)

σ t :

Uniaxial tensile strength (MPa)

φ b :

Basic friction angle (°)

φ r * :

Residual friction angle (°)

i p :

Peak dilation angle (°)

i 0 :

Initial dilation angle (°)

K :

Attenuation correction coefficient

β :

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

τ p :

Peak shear strength (MPa)

τ residual :

Residual strength (MPa)

τ m :

Measured peak shear strength (MPa)

τ c :

Calculated peak shear strength by the criterion (MPa)

δ avg :

Average relative error

μ :

Standard deviation of the relative error


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The authors gratefully acknowledge the financial support from National Key R&D Plan (2017YFC0404904), a research (51509163, U1765203) Grant from National Natural Science Foundation of China. And a research Grant (201501035) from Special fund project for water conservancy industry.

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Correspondence to Linnan Ding.

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Ding, L., Li, G. Research on Peak Shear Strength Criterion of Rock Joints Based on the Evolution of Dilation Angle. Geotech Geol Eng 39, 4887–4900 (2021).

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