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Investigate the Mode I Fracture Characteristics of Granite After Heating/-LN2 Cooling Treatments


Thermal treatment of the warm rock mass using liquid nitrogen (LN2) is a prospective rock fracturing technology in many geo-engineering applications. This paper presents an experimental and numerical work aimed at investigating the effect of thermal treatments (i.e., heating–LN2 cooling) on fracture failure characteristics. Mode I fracture toughness as a function of thermal treatment was determined using semi-circular bending tests. The roughness of the resultant fracture surfaces was quantitatively evaluated with a 3D laser scanner and fractal theory. Experimental results show that the thermal treatment has a significant influence on the fracture toughness and roughness. The fracture toughness of the thermally treated samples shows a negative correlation with the heating temperature, except in the range of 25–200 ºC where the fracture toughness shows a slight increase. However, the fracture roughness of thermally treated samples shows an opposite trend as it gradually increases with temperature. Scanning electron microscope analysis associates these phenomena to the development of thermal microcracks. Moreover, numerical simulations using the finite-discrete element method thermo-mechanical code (FDEM-TM) were conducted to reproduce the thermo/mechanical behavior of thermally treated rock, and to help explain the influence of the thermally induced microcracks on the failure mechanisms. The thermally induced microcracks contribute to the variation of the fracture toughness and roughness according to the laboratory experiment and numerical simulation. This work provides an improved understanding of the temperature effect on rock fracture characteristics in engineering applications.


  • Fracture characteristics of the heating-cooling treated granite are investigated.

  • Fracture toughness first rises and then drops when heating temperature increases.

  • Fracture roughness shows a positive correlation with the heating temperature.

  • Numerical models reproduce the laboratory results and help to explain the failure mechanism.

  • Thermal microcracks contribute to the variation of fracture toughness and fracture roughness.

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R :

Radius of the semi-circular bend specimen

B :

Thickness of the semi-circular bend specimen

a :

Crack length in the semi-circular bend specimen

S :

Span length in the semi-circular bend specimen

K IC :

Fracture toughness

P max :

Peak load

Y I :

Dimensionless stress intensity factor


Fracture surface

D :

Fractal dimension

ε and N(ε):

Box size and the total number of the boxes

h ij :

Height of points

M :

Lumped mass matrix

C :

Damping diagonal matrix

x :

Vector of the nodal coordinates

F I, F M, F T and F C :

Vectors of internal force, mechanical force, thermal force, and contact force

σ t :

Thermal stress in element

K :

Bulk modulus

α :

Linear thermal expansion coefficient

T :


δ ij :

Kronecker’s delta


Heat capacity

ρ :

Mass density

Q s :

Source term

q :

Heat flux

k :

Thermal conductivity

J :

Temperature gradient

A, b and l :

Equivalent area, width and length of the thermal element

q + c and q c :

Heat flux across the discontinuity

k c :

Interfacial heat conductivity

T + c and T c :

Temperature at opposite discontinuity surfaces

o and s :

Opening and shear displacement

o p and s p :

Opening and sliding displacement of damage initiation

o r and s r :

Opening and sliding displacement of critical damage

d :

Dimensionless damage factor

G I and G II :

Mode I and mode II fracture energy


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This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants 341275 and National Key Research and Development Program of China 2017YFC1501300.

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Authors and Affiliations



ZS: conceptualization, methodology, and writing—original draft; LS: conceptualization, methodology, software, and writing—review and editing; KRA: writing—review and editing, and visualization; QL: supervision, writing—review and editing, and funding acquisition; GG: supervision, writing—review and editing, and funding acquisition.

Corresponding author

Correspondence to Lei Sun.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Shao, Z., Sun, L., Aboayanah, K.R. et al. Investigate the Mode I Fracture Characteristics of Granite After Heating/-LN2 Cooling Treatments. Rock Mech Rock Eng 55, 4477–4496 (2022).

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  • Thermal treatment
  • Liquid nitrogen cooling
  • Fracture roughness
  • Fracture toughness