Effect of Grain Size on the Mechanical Behaviour of Granite Under High Temperature and Triaxial Stresses

Abstract

The optimal development of hot dry rock (HDR) geothermal is deep HDR geothermal. Because of different diagenesis environments, the mineral composition and micro-structure of deep granite are quite different than those of shallow granite. To reveal the characteristics of deep granite and guide HDR geothermal development, the difference in thermal and mechanical properties between the granite in Luya Mountain, Shanxi Province, China (coarse-grained granite) and the granite in Shandong Province, China (fine-grained granite) under high-temperature (100–400 ℃) triaxial stress was studied. The results show that the thermal expansion coefficient of the coarse-grained granite increases linearly with increasing temperature, and the thermal expansion coefficient of the coarse-grained granite is 1.52 times that of the fine-grained granite on average, and the difference reaches a maximum at 400 ℃. The elastic modulus of the coarse-grained granite increases slowly first and then decreases sharply with increasing temperature, and its threshold temperature varies with temperature at approximately 300 ℃. The elastic modulus of the fine-grained granite is 1.4–2.6 times that of the coarse-grained granite, and the difference increases with increasing temperature and confining pressure. According to the failure test under triaxial stress (confining pressure (σ_c) = 25 MPa) and at 400 ℃, for the coarse-grained granite, the peak strength, elastic modulus and its threshold temperature change with temperature are smaller, the peak strain is larger and the elasto-plastic transition occurs easier than those for the fine-grained granite. Micro-observation shows that the larger crystal particles and the extreme heterogeneity of the coarse-grained granite lead to larger thermal deformation and greater deterioration of the mechanical properties, compared with those of the fine-grained granite, further leading to higher permeability of the coarse-grained granite under high temperature and high pressure. The existence of coarse-grained granite provides a good geological foundation for high-efficiency, low-cost and large-scale construction of artificial reservoirs in the process of HDR geothermal development.

Appendix: The Derivation Process of Thermal Stress

Assuming that the axial length of a mineral crystal particle is L, the thermal expansion coefficient is α, and the temperature difference is ΔT, then the axial elongation l of the mineral crystal particle is as follows:

$$l = \alpha L\Delta T.$$

(1)

The elongation per unit length (i.e., the strain (ε)) is as follows:

$$\varepsilon = \frac{l}{L} = \alpha \Delta T.$$

(2)

If the mineral crystal particle is constrained, a compressive stress corresponding to the strain in formula (2) will be generated. Assuming that the elastic modulus of the mineral crystal particle is E, the axial stress (i.e., the thermal stress (σ)) of the mineral crystal particle is as follows (Wong et al. 1979; Wang et al. 1989):

$$\sigma = E\varepsilon = E\alpha \Delta T.$$

(3)

Then analyse the combination of different types of mineral crystal particle. Assume that E₁, α₁, E₂ and α₂ are the elastic moduli and thermal expansion coefficients of two adjacent mineral particles, respectively, the interface area is A, and that ΔT is the temperature difference. For simplicity, this paper also assumes that the mineral particles only generate stress and strain in the direction perpendicular to the interface (i.e., under one-dimensional stress state). Assuming that the stress and strain of the two mineral particles are σ₁, ε₁, σ₂ and ε₂, respectively, the relationship between stress and strain is as follows:

$$\varepsilon_{1} = \frac{{\sigma_{1} }}{{E_{1} }} + \alpha_{1} \Delta T, \varepsilon_{2} = \frac{{\sigma_{2} }}{{E_{2} }} + \alpha_{2} \Delta T.$$

(4)

Considering the axial force balance and boundary conditions, the following equations hold:

$$\sigma_{1} A + \sigma_{2} A = 0,$$

(5)

$$\varepsilon_{1} = \varepsilon_{2} .$$

(6)

According to formulas (4), (5) and (6), the thermal stresses of the two mineral crystal particles are obtained as follows:

$$\sigma_{1} = - \frac{{\left( {\alpha_{1} - \alpha_{2} } \right)E_{1} E_{2} \Delta T}}{{E_{1} + E_{2} }}, \sigma_{2} = \frac{{\left( {\alpha_{1} - \alpha_{2} } \right)E_{1} E_{2} \Delta T}}{{E_{1} + E_{2} }}.$$

(7)