80 research outputs found
Numerical modelling of thermal weakening of granite under dynamic loading
No full textA numerical method to predict thermal weakening of granite rock under low- and moderate rate dynamic loading conditions is developed. Thermal weakening of granite under uniform heating, leading to degradation of the material stiffness and strength, is modelled with the continuum approach, using a damage-viscoplasticity model. The viscoplastic part is based on a special power law criterion for granite under compression and the rounded tensile cut-off surface, while the damage part is equipped with separate damage variables in tension and compression. The strain rate sensitivity of rock is accounted for by viscoplasticity. The global thermo-mechanical initial/boundary value problem is solved with an explicit (in time) staggered method with mass scaling applied to increase the critical time step. Rock heterogeneity is described as random clusters of linear tetrahedral finite elements assigned with the constituent mineral, here quartz, feldspar, and biotite, material properties. The temperature dependence of the thermal and elasticity properties of the minerals is included in the model up to 850 ◦C, i.e. well beyond the α-β transition of quartz. However, as the model aims to predict the thermal weakening, the temperature dependence of the rock strength is not used as an input. In the numerical examples, low-rate uniaxial tension and compression tests are first simulated on heated and intact rock samples to demonstrate the performance of the model. Finally, crushing of heat-treated and intact granite balls by diametral dynamic compression is numerically replicated with a fair accuracy.Peer reviewe
Numerical modeling of thermo‐mechanical failure processes in granitic rock with polygonal finite elements
No full textThis paper considers numerical modeling of intensive heating induced thermo-mechanical failure processes in granitic rock. For this end, a numerical methodbased 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.Peer reviewe
Effect of Grain Level Anisotropy on Numerical Rock Fracture Behaviour under Dynamic Loading
No full textThe effect of rock crystal anisotropy is tested in numerical simulation of rock fracture at the laboratory sample level of scale. For this end, a numerical model based on the embedded discontinuity finite element method is applied here in simulations of uniaxial tension test on granitic rock. The rock material, consisting of Quartz (trigonal), Feldspar (triclinic) and Biotite (taken hexagonal here), is described as a linear elastic (up to fracture) heterogeneous and anisotropic material, which fails upon reaching the tensile strength of the individual constituent minerals. In the simulations of uniaxial tension test at two different levels of strain rate, the effect of averaged versus anisotropic elastic constants is tested. The results demonstrate that the effect of anisotropy is stronger at low strain rates (0.25 s-1 here), resulting in macrocrack planes at different locations for the isotropic and anisotropic material descriptions, while at higher rates (25 s-1 here) its notable effects disappear in the details of multiple macrocracks
Demolition of concrete by thermal shock spallation: a mesoscopic numerical study based on embedded discontinuity finite elements
No full textThis paper deals with 2D (plane strain) and axisymmetric numerical modelling of concrete fracture processes under mechanical and thermal loading. A mesoscopic modelling approach with an explicit representation of aggregates as Voronoi polygons is chosen while the concrete fracture model is based on rate-dependent embedded discontinuity finite elements with Rankine criterion indicating a new crack initiation. This choice enables the study of the effects of inherent crack populations on the response of concrete under mechanical and thermal loading. In the numerical examples, the performance of the present modelling approach is first demonstrated in the uniaxial compression and tension tests under plane strain conditions. Then, the problem of thermal spallation of concrete surface under dry conditions due to a high intensity, short duration heat flux is simulated under axisymmetric conditions. The underlying uncoupled thermo-mechanical problem is solved with an explicit time marching scheme based on the staggered approach. Different heat flux intensities and heating times as well as combined effect of surface roughness and pre-stress field are tested. The simulation results suggest that demolition of concrete structures by heat shock is a viable method.Peer reviewe
Numerical modelling of dynamic spalling test on rock with an emphasis on the influence of pre-existing cracks
No full textThis article deals with numerical modeling of rock fracture under dynamic tensileloading and the related prediction of dynamic tensile strength. A special emphasis is laid on theinfluence of pre-existing natural microcrack populations as well as structural (articial) cracks.For this end, a previously developed 3D continuum viscodamage-embedded discontinuity modelis employed in the explicit dynamic nite element simulations of the spalling test. This modelis capable of modelling the eect of natural microcracks populations always present in rocks aswell as to capture the strain rate hardening eect of quasi-brittle materials. In the numericalsimulations of spalling test on Bohus granite, it is shown that the model can predict the pull-pack velocity of the free end of the intact rock sample and the eect of structural cracks witha good accuracy. According to the simulations, the effect of microcrack populations, modeledhere as pre-embedded discontinuity populations, is weaker than the corresponding eect underquasi-static loading</jats:p
3D numerical prediction of thermal weakening effects on granite
No full textThis paper presents a numerical method to predict the temperature weakening effects on tensile and compressive strength and stiffness of granitic rock. Thermally induced cracking, leading to degradation of the material stiffness and strength, is modelled in the continuum sense by using a damage-viscoplasticity model based on the Drucker-Prager criterion with a rounded tensile cut-off surface. The governing thermo-mechanical initial/boundary value problem is solved with an explicit (in time) staggered method while using extreme mass scaling to increase the critical time step. Rock heterogeneity is described as random clusters of finite elements assigned with the constituent mineral, here Quartz, Feldspar, and Biotite, material properties further randomized by Weibull distribution. In the present approach, only Quartz thermal expansion coefficient is assumed temperature dependent due to its strong and anomalous temperature dependence upon approaching the α-β transition. In the numerical testing, the sample is first volumetrically heated to a target temperature. Then, the uniaxial tension and compression tests are performed on the cooled down numerical samples. The simulations demonstrate the validity of the proposed approach as the experimental weakening effects on the rock strength and stiffness as well as the macroscopic failure modes, both in tension and compression, are realistically predicted in a non-circular way, that is, not using the temperature dependence of any material parameter, save Quartz thermal expansion, as an input data.Peer reviewe
Numerical Modeling of Temperature Effect on Tensile Strength of Granitic Rock
No full textThe 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
Numerical modelling of rock materials with polygonal finite elements
No full textThis article presents some preliminary results on numerical modeling of rock ma-terials with polygonal finite elements. A method to describe the rock microstructure based onVoronoi diagrams, representing the rock grain texture, is sketched. In this method, the mineralsconstituting the rock are represented as Voronoi cells which themselves are polygonal finite ele-ments. A three-point bending problem under plane stress linear elasticity condition is solved inorder to compare the performance of polygonal elements to ordinary finite elements. Moreover,it is demonstrated by solving the stress state in uni-axial compression that the heterogeneitydescribed with the present method results in short-range tensile stresses which could initiatemode-I cracks.</jats:p
3D Numerical Prediction of Thermal Weakening of Granite under Tension
No full textThis paper deals with numerical prediction of temperature (weakening) effects on the tensile strength of granitic rock. A 3D numerical approach based on the embedded discontinuity finite elements is developed for this purpose. The governing thermo-mechanical initial/boundary value problem is solved with an explicit (in time) staggered method while using extreme mass scaling to increase the critical time step. Rock fracture is represented by the embedded discontinuity concept implemented here with the linear (4-node) tetrahedral elements. The rock is modelled as a linear elastic (up to fracture by the Rankine criterion) heterogeneous material consisting of Quartz, Feldspar and Biotite minerals. Due to its strong and anomalous temperature dependence upon approaching the α-β transition at the Curie point (~573 °C), only Quartz in the numerical rock depends on temperature in the present approach. In the numerical testing, the sample is first volumetrically heated to a target temperature. Then, the uniaxial tension test is performed on the cooled down sample. The simulations demonstrate the validity of the proposed approach as the experimental deterioration, by thermally induced cracking, of the rock tensile strength is predicted with a good accuracy
3D Continuum Modelling of PDC Cutting of Rock with a Simple Contact-Erosion Scheme
No full textThis paper presents a relatively simple numerical approach to predict the cutting force during PDC (polycrystalline diamond contact) cutting of rock. The rock failure model is based on a damage-viscoplasticity model, with the Drucker–Prager yield surface and the modified Rankine surface as the tensile cut-off. The damage part of the model has separate scalar damage variables for tension and compression. The PDC cutter is idealized to a rigid surface and its interaction with the rock is modelled by contact mechanics, while solving the global equations of motion explicitly in time. A damage-based erosion criterion is applied, to remove the contact nodes surrounded by heavily damaged elements. The eroded elements are left in the mesh as ghost elements that do not contribute to the load transfer but preserve the mass conservation. Numerical simulations on granite, demonstrate that the method reliably predicts the cutting force of a single PDC cutter at different cutting depths and rake angles
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