Microcrack Growth Properties of Granite under Ultrasonic High‐Frequency Excitation

Num Anal Meth Geomechanics

2021

This paper considers numerical modeling of intensive heating induced thermo‐mechanical failure processes in granitic rock. For this end, a numerical method based on polygonal finite elements and a damage‐plasticity model is developed. A staggered scheme is employed to solve the global thermo‐mechanical problem. The rock failure is described by a Rankine‐Mohr‐Coulomb plasticity model with separate scalar damage variables for tension and compression. Consistent tangent operator is derived for this model. Special attention is given to the temperature dependence of the thermo‐mechanical material properties of heterogeneous rock. In the numerical examples, the method is first verified with an analytical solution of thermal stresses in a hollow cylinder, and then qualitatively validated with the problems of thermal cracking of concentric cylinders and uniaxial compressive test on rock under elevated temperatures. Finally, the method is applied in novel simulations inspired by the degradation of sauna stones under slow heating‐rapid cooling and the comminution by rapid heating‐cooling cycles.

α_{normalq} (θ) = 6 . 13^{- 21} θ^{6} - 1 . 38^{- 17} θ^{5} + 1 . 19^{- 14} θ^{4} - 4 . 75^{- 12} θ^{3} + 8 . 13^{- 10} θ^{2} false[1 / K false]

α_{normalf} (θ) = α_{f 0} (θ = 293 K) + K_{α_{f}}^{θ} false(θ - 293 K false) false[1 / K false], K_{α_{f}}^{θ} = \frac{α_{fmax} - α_{f 0}}{550 K}

α_{normalb} (θ) = α_{b 0} (θ = 293 K) + K_{α_{b}}^{θ} (θ - 293 K) [1 / K], K_{α_{b}}^{θ} = \frac{α_{bmax} - α_{b 0}}{550 K}

where

…”

Section: Numerical Simulationsmentioning

confidence: 66%

“…Temperature dependence of Quartz Young's modulus (A); thermal expansion coefficients for granite forming minerals (B); temperature dependence of Quartz thermal conductance (C); specific heat (D) (data after Toifl et al 7 . and Polyakova 39 )…”

Section: Numerical Simulationsmentioning

confidence: 99%

Numerical modeling of thermo‐mechanical failure processes in granitic rock with polygonal finite elements

Num Anal Meth Geomechanics

2021

“…To properly predict the failure mode in tension, the tensile strength is assumed to be heterogeneous, i.e., mineral specific. In this respect, the numerical rock consists of quartz (33%), feldspar (59%) and biotite (8%) minerals, with their respective tensile strengths [27] of 14 MPa, 11 MPa and 7 MPa. Moreover, the mode I specific fracture energies, G Ic , are [28] 40 J/m 2 for quartz and felspar, and 28 J/m 2 for biotite.…”

Section: Materials Properties and Model Parametersmentioning

confidence: 99%

Numerical Modeling of Temperature Effect on Tensile Strength of Granitic Rock

2021

Applied Sciences

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.

“…The material properties and model parameters used in the initial crack population simulations are given in Table 1. The numerical rock consists of Quartz (33%), Feldspars (59%) and Biotite (8%) minerals, and most of their properties are taken from Zhao et al [53], Mahabadi [10], and Vasquez et al [45]. The rock heterogeneity is described by random clusters of finite elements assigned with the material properties of the constituent minerals.…”

Section: Materials Properties and Model Parametersmentioning

confidence: 99%

“…Due to its importance in geology and rock engineering, the effect of microcracks on rock under various loading conditions has been widely investigated both experimentally [5,14,16,29,49,52] and numerically [5,11,13,16,18,20,22,25,26,53]. The focus in numerical modelling has been on the effect of microcracks under compression as it is the natural state of bedrock.…”

Section: Introductionmentioning

confidence: 99%

Effect of inherent microcrack populations on rock tensile fracture behaviour: numerical study based on embedded discontinuity finite elements

2021

Acta Geotech.

Inherent microcrack populations have a significant effect on the fracture behaviour of natural rocks. The present study addresses this topic in numerical simulations of uniaxial tension and three-point bending tests. For this end, a rock fracture model based on multiple intersecting embedded discontinuity finite elements is developed. The inherent (pre-existing) microcrack populations are represented by pre-embedded randomly oriented discontinuity populations. Crack shielding (through spurious locking) is prevented by allowing a new crack to be introduced, upon violation of the Rankine criterion, in an element with an initial crack unfavourably oriented to the loading direction. Rock heterogeneity is accounted for by random clusters of triangular finite elements representing different minerals of granitic numerical rock. Numerical simulations demonstrate the strength lowering effect of initial microcrack populations. This effect is substantially stronger under uniaxial tension, due to the uniform stress state, than in semicircular three-point bending having a non-uniform stress state with a clear local maximum of tensile stress.