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Experimental and Numerical Studies on Small-Scale Direct Tension Test for Rock

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Abstract

The deformation and failure behaviors of rock play an important role in rock engineering, such as tunneling engineering, geothermal exploitation, and slope treatment; nevertheless, small-scale direct tension studies still face difficulties. To investigate the small-scale tensile properties of rock, by use of a microscope mechanical test system, we conducted systematic direct tension tests on granite, marble, and a 3D printing material, for which specifically designed dogbone specimens are used. The results show that the tensile strength is less than that obtained by the Brazilian disc test and is closer to the true value, which reflects the advantage of the small-scale direct tension test. Among all the materials, the 3D printing material exhibits low discreteness. Furthermore, the printing angle has a large effect on the tensile strength of the 3D printing material. To further investigate the failure mechanism, we reproduced the experimental results via the lattice spring model (LSM). By introducing a discontinuous surface, an adjustment coefficient, and four cohesive zone models into the LSM, the elastic modulus, tensile strength, and nonlinearity in the failure stage agreed well with the experimental result. In addition, we also conducted a cyclic direct tension test and numerical simulations. Our small-scale experimental and numerical results provide a supplement to the deep understanding of rock deformation and failure. The combination of small-scale experiments and numerical simulations strengthens the understanding of rock behavior and failure processes under tensional loading.

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Abbreviations

\(A^{D}\) :

The representative area of spring bond

\(c^{J}\) :

The cohesion of joint

D :

The diameter of the specimen

\(D_{\alpha } (u^{3D} )\) :

The damage variable of spring bond

E :

Elastic modulus

F :

Particle force

\({\mathbf{F}}_{ij}\) :

The force from particle i to particle j

\(\Delta F\) :

The difference in tension force between two images

H :

The height of the specimen

k :

Spring stiffness

\(k_{n}^{D}\) :

The normal spring stiffness

\(k_{s}^{D}\) :

The shear spring stiffness

l :

The length of spring

\(l_{AB}\) :

The distance between cross-section A and B

\(l_{i}\) :

The length of the ith spring

m :

The mass of a particle

\({\mathbf{n}}_{ij}\) :

The normal vector from particle i to particle j

P :

The force of rock failure

\(S\) :

The area of the cross-section

t :

Time

\(\Delta t\) :

Time step

\(u\) :

The deformation of spring

\(u_{dl}^{n}\) :

The dilation component of normal deformation

\(u^{*}\) :

Ultimate deformation

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

The ultimate tensile deformation

\(u_{revised}^{*}\) :

The ultimate deformation after adjustment

V :

Volume

\(V_{P}\) :

The P-wave velocity

x :

The position of a mass point

\({\mathbf{x}}^{0}\) :

The corresponding initial position

\(X_{a}\) :

Pixel a

\(X_{b}\) :

Pixel b

\(\alpha\) :

A constant in damage function

\(\beta\) :

Dimensionless parameter

\(\delta_{1}\) :

The coefficient of peak deformation

\(\delta_{2}\) :

The coefficient of post-peak turning-point deformation

\(\gamma\) :

The ratio of the strength turning point

\(\xi\) :

Adjustment coefficient

\(\sigma_{c}\) :

Uniaxial compressive strength

\(\sigma_{t}\) :

Tensile strength

\(\sigma_{t}^{J}\) :

The tensile strength of joint

\(\lambda^{4D}\) :

The 4D stiffness ratio

\(\rho\) :

Density

\(\eta\) :

The second-order polynomial equation

\(\varphi^{J}\) :

The friction angle of joint

\(\upsilon\) :

Poisson’s ratio

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Acknowledgements

This research was financially supported by the National Key R&D Program of China (Grant No. 2018YFC0406804), the National Natural Science Foundation of China (Grant No. 51979187), and the Natural Science Foundation of Tianjin, China (Grant No. 19JCZDJC39400).

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Authors and Affiliations

  1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, School of Civil Engineering, Tianjin University, Tianjin, 300354, China

    Gao-Feng Zhao, Yuliang Zhang & Senwei Hou

  2. School of Civil Engineering, Southeast University, Nanjing, 211189, Jiangsu, China

    Lei He

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  1. Gao-Feng Zhao
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Zhao, GF., Zhang, Y., Hou, S. et al. Experimental and Numerical Studies on Small-Scale Direct Tension Test for Rock. Rock Mech Rock Eng 55, 669–690 (2022). https://doi.org/10.1007/s00603-021-02683-w

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