Numerical Modeling of Temperature Effect on Tensile Strength of Granitic Rock

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.

3D numerical prediction of thermal weakening effects on granite

“…As to the temperature dependence of rock forming minerals, the previous study by Saksala 22 is followed here in that only the thermal expansion coefficient of Quartz depends explicitly on temperature. This is in contrast to all, save Saksala, 20,22 of the previous mentioned above studies, which feed the temperature dependence of rock strength and stiffness into the constitutive description and then “predict” that same data. In addition, oftentimes the laboratory level data is, confusingly, predicted only at the material point level using a single element mesh, while the correspondence between macro‐ and mesolevel fails upon macroscopic failure of the sample.…”

“…Quartz bearing rocks, such as granite and gneiss, are particularly prone to temperature weakening due to its α‐β transition at about 573°C 4 . An extensive body of both experimental 1,5–16 and numerical 11–14,16–22 studies naturally exist on the temperature effects in various rocks.…”

“…[1][2][3] As high temperature has a detrimental effect on rock strength, especially in case of Quartz bearing rocks, good understanding of the weakening effects and their prediction by numerical or analytical methods is an asset of substantial importance in rock engineering. Quartz bearing rocks, such as granite and gneiss, are particularly prone to temperature weakening due to its α-β transition at about 573 • C. 4 An extensive body of both experimental 1,[5][6][7][8][9][10][11][12][13][14][15][16] and numerical [11][12][13][14][16][17][18][19][20][21][22] studies naturally exist on the temperature effects in various rocks.…”

“…Saksala 20,22 used the embedded discontinuity FEM to successfully predict thermal weakening effect under uniaxial tension. Nevertheless, rock materials are mostly under compression in engineering applications.…”

Comparative Numerical Study on the Weakening Effects of Microwave Irradiation and Surface Flux Heating Pretreatments in Comminution of Granite

“…The specimens were heated at 5 °C/min up to target temperatures and then the temperature was kept constant for 4 h. The reduction in the uniaxial compressive strength of the coarse-grained granite specimens was reported to be lower than that for the fine-grained granite specimens. Saksala [19] predicted the temperature effect on the tensile strength of granitic rock. Rock samples were heated uniformly up to target temperatures of 300 °C and 500 °C.…”