Numerical Modeling of Temperature Effect on Tensile Strength of Granitic Rock

Timo Saksala

doi:10.3390/app11104407

Abstract

The aim of this paper is to numerically predict the temperature effect on the tensile strength of granitic rock. To this end, a numerical approach based on the embedded discontinuity finite elements is developed. The underlying thermo-mechanical problem is solved with a staggered method marching explicitly in time while using extreme mass scaling, allowed by the quasi-static nature of the slow heating of a rock sample to a uniform target temperature, to increase the critical time step. Linear triangle elements are used to implement the embedded discontinuity kinematics with two intersecting cracks in a single element. It is assumed that the quartz mineral, with its strong and anomalous temperature dependence upon approaching the α-β transition at the Curie point (~573 °C), in granitic rock is the major factor resulting in thermal cracking and the consequent degradation of tensile strength. Accordingly, only the thermal expansion coefficient of quartz depends on temperature in the present approach. Moreover, numerically, the rock is taken as isotropic except for the tensile strength, which is unique for each mineral in a rock. In the numerical simulations mimicking the experimental setup on granitic numerical rock samples consisting of quartz, feldspar and biotite minerals, the sample is first heated slowly to a target temperature below the Curie point. Then, a uniaxial tension test is numerically performed on the cooled down sample. The simulations demonstrate the validity of the proposed approach as the experimental deterioration of the tensile strength of the rock is predicted with agreeable accuracy.

Highlights

Quartz-bearing rocks are susceptible to temperature effects in their material properties and, in their response under thermal loading due to the α-β transition of quartz at its Curie point (~573 ◦ C) [4]
The method includes the constitutive model for fracturing rock based on embedded discontinuity finite elements and the global solution methods to solve the thermo-mechanical equations governing the thermal cracking of rock and the uniaxial tension test
Extreme mass scaling for the mechanical problem can be used in this approach due to the quasi-static nature of the slow heating of a rock sample to a uniform temperature

Summary

Introduction

Rocks often face high temperature conditions and thermal shocks in geotechnical engineering applications, such as harvesting deep geothermal energy [1], nuclear waste disposal [2], and thermal drilling [3]. Quartz-bearing rocks are susceptible to temperature effects in their material properties and, in their response under thermal loading due to the α-β transition of quartz at its Curie point (~573 ◦ C) [4]. The temperature effects on rock mechanical properties have been extensively studied, experimentally [1,5,6,7,8,9,10,11,12,13,14] and numerically [11,12,13,14,15,16,17]

Objectives

Methods

Findings

Discussion

Conclusion