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Heterogeneous Bonded Particle Modelling of Rock Fracture
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Solid Mechanics.ORCID iD: 0000-0003-1345-0740
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The dynamic fracture process of rock materials is of importance for several industries, such as the rock drilling process in geothermal and mining applications. Gaining knowledge and understanding of dynamic rock fracture through numerical simulations can enhance the rock drilling process, for example by optimising the drill bit geometry and drilling parameters. In order for a numerical simulation of rock fracture processes to be accurate, the model needs to be able to capture key aspects of rock materials. Generally, rock materials are said to be britle and heterogeneous. The heterogeneity is partly due to the varying mechanical properties of constituent minerals, and partly due to the varying sizes, shapes, and directions of these minerals. The main objective of this thesis is the development of a heterogeneous rock model to be used for dynamic drilling processes. In the first article in this thesis, a heterogeneous bonded particle model is developed. Here, the heterogeneity is introduced in two steps – a geometrical heterogeneity using statistically distributed grain shapes and sizes, and a mechanical heterogeneity by distributing bonding parameters using a Weibull distribution. The model is applied to the quasi-static Brazilian disc test and a parametric study is conducted on the heterogeneity index and intergranular cement strength. The results show that crack initiation and propagation are highly dependent on the degree of heterogeneity. In general, the model was found to replicate typical phenomena associated with britle heterogeneous materials, for example unpredictability of macroscopic strength and crack properties. In the second paper of this thesis, an extensive dynamic experimental characterization of two igneous rock materials – Kuru grey granite and Kuru black diorite – is conducted. Here, a Split-Hopkinson configuration together with high-speed photography and digital image correlation is utilized to obtain the compressive and indirect tensile behavior of the rock materials. By using a significantly high frame rate of 671,000 fps in the digital image correlation analysis, it is shown that the point in time for crack initiation in the Brazilian disc can be estimated. From this, it is shown that the main splititng crack in the Brazilian disc occurs at 70 and 77 % for the two rock materials. In the third paper of this thesis, the heterogeneous bonded particle model from the first paper is further developed and calibrated using the dynamic experimental data for Kuru black diorite from the second paper. In contrast to the first paper, where one Weibull distribution is used, three Weibull distributions are used here. The first distribution is used for assigning average bonding parameters of the grains, the second for the intragranular bonding parameters and the third for the bonding parameters of the intergranular cementing. First, a homogeneous bonded particle model, i.e., without heterogeneous grains and no statistical distribution of bonding parameters, is calibrated so that the average experimental results are replicated. Then, using this homogeneously calibrated model, the heterogeneous model is activated, and a parametric study is conducted on the heterogeneity index for the average grain properties and the intergranular cement strength. The results show that this modelling approach is able to capture key phenomena of dynamic rock fracture, such as stochastic crack initiation and propagation, as well as peak stress, overloading, strain rate and crack propagation time. In the fourth paper, the proposed heterogeneous bonded particle model from previous papers is validated using a laboratory rock drilling experiment. The rock material is dynamically characterized using the methodology from the second paper and the grain structure is obtained from a scan of the rock surface. Three of the constituent minerals are represented in the model in terms of their size, occurrence, and mechanical properties. Furthermore, the model is calibrated in both compression and tension, where both the peak stress values and fracture behavior are captured. The model is then used to simulate the laboratory rock drilling experiment, where crater depth, load and rock fragment sizes are compared with the experiments. The results show that the simulation is able to capture peak load values and the rock fragment sizes are similar to that of the experiments.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2024.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords [en]
Rock, DEM, BPM, fracture, drilling, dynamic
National Category
Other Civil Engineering
Research subject
Solid Mechanics
Identifiers
URN: urn:nbn:se:ltu:diva-104684ISBN: 978-91-8048-505-0 (print)ISBN: 978-91-8048-506-7 (electronic)OAI: oai:DiVA.org:ltu-104684DiVA, id: diva2:1845693
Public defence
2024-05-16, E632, Luleå University of Technology, Luleå, 09:00 (English)
Opponent
Supervisors
Available from: 2024-03-21 Created: 2024-03-19 Last updated: 2024-04-25Bibliographically approved
List of papers
1. A statistical DEM approach for modelling heterogeneous brittle materials
Open this publication in new window or tab >>A statistical DEM approach for modelling heterogeneous brittle materials
2022 (English)In: Computational Particle Mechanics, ISSN 2196-4378, Vol. 9, no 4, p. 615-631Article in journal (Refereed) Published
Abstract [en]

By utilizing numerical models and simulation, insights about the fracture process of brittle heterogeneous materials can be gained without the need for expensive, difficult, or even impossible, experiments. Brittle and heterogeneous materials like rocks usually exhibit a large spread of experimental data and there is a need for a stochastic model that can mimic this behaviour. In this work, a new numerical approach, based on the Bonded Discrete Element Method, for modelling of heterogeneous brittle materials is proposed and evaluated. The material properties are introduced into the model via two main inputs. Firstly, the grains are constructed as ellipsoidal subsets of spherical discrete elements. The sizes and shapes of these ellipsoidal subsets are randomized, which introduces a grain shape heterogeneity Secondly, the micromechanical parameters of the constituent particles of the grains are given by the Weibull distribution. The model was applied to the Brazilian Disc Test, where the crack initiation, propagation, coalescence and branching could be investigated for different sets of grain cement strengths and sample heterogeneities. The crack initiation and propagation was found to be highly dependent on the level of heterogeneity and cement strength. Specifically, the amount of cracks initiating from the loading contact was found to be more prevalent for cases with higher cement strength and lower heterogeneity, while a more severe zigzag shaped crack pattern was found for the cases with lower cement strength and higher heterogeneity. Generally, the proposed model was found to be able to capture typical phenomena associated with brittle heterogeneous materials, e.g. the unpredictability of the strength in tension and crack properties.

Place, publisher, year, edition, pages
Springer Nature, 2022
Keywords
Bonded DEM, Heterogeneous brittle materials, Fracture, Brazilian disc, Weibull
National Category
Other Mechanical Engineering Applied Mechanics
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:ltu:diva-83907 (URN)10.1007/s40571-021-00434-w (DOI)000692075800001 ()2-s2.0-85114114019 (Scopus ID)
Projects
GEOFIT
Funder
EU, Horizon 2020, 792210
Note

Validerad;2022;Nivå 2;2022-07-26 (hanlid)

Available from: 2021-04-23 Created: 2021-04-23 Last updated: 2024-03-19Bibliographically approved
2. Dynamic Compressive and Tensile Characterisation of Igneous Rocks Using Split-Hopkinson Pressure Bar and Digital Image Correlation
Open this publication in new window or tab >>Dynamic Compressive and Tensile Characterisation of Igneous Rocks Using Split-Hopkinson Pressure Bar and Digital Image Correlation
2022 (English)In: Materials, ISSN 1996-1944, E-ISSN 1996-1944, Vol. 15, no 22, article id 8264Article in journal (Refereed) Published
Abstract [en]

The dynamic fracture process of rock materials is of importance for several industrial applications, such as drilling for geothermal installation. Numerical simulation can aid in increasing the understanding about rock fracture; however, it requires precise knowledge about the dynamical mechanical properties alongside information about the initiation and propagation of cracks in the material. This work covers the detailed dynamic mechanical characterisation of two rock materials—Kuru grey granite and Kuru black diorite—using a Split-Hopkinson Pressure Bar complemented with high-speed imaging. The rock materials were characterised using the Brazilian disc and uniaxial compression tests. From the high-speed images, the instant of fracture initiation was estimated for both tests, and a Digital Image Correlation analysis was conducted for the Brazilian disc test. The nearly constant tensile strain in the centre was obtained by selecting a rectangular sensing region, sufficiently large to avoid complicated local strain distributions appearing between grains and at voids. With a significantly high camera frame rate of 671,000 fps, the indirect tensile strain and strain rates on the surface of the disc could be evaluated. Furthermore, the overloading effect in the Brazilian disc test is evaluated using a novel methodology consisting of high-speed images and Digital Image Correlation analysis. From this, the overloading effects were found to be 30 and 23%. The high-speed images of the compression tests indicated fracture initiation at 93 to 95% of the peak dynamic strength for granite and diorite, respectively. However, fracture initiation most likely occurred before this in a non-observed part of the sample. It is concluded that the indirect tensile strain obtained by selecting a proper size of the sensing region combined with the high temporal resolution result in a reliable estimate of crack formation and subsequent propagation.

Place, publisher, year, edition, pages
MDPI, 2022
Keywords
rock, dynamic mechanical properties, fracture, high-speed imaging, digital image correlation, Split-Hopkinson pressure bar
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:ltu:diva-94378 (URN)10.3390/ma15228264 (DOI)000887520400001 ()36431749 (PubMedID)2-s2.0-85142756512 (Scopus ID)
Funder
EU, Horizon 2020, 792210
Note

Validerad;2022;Nivå 2;2022-11-30 (joosat);

Available from: 2022-11-30 Created: 2022-11-30 Last updated: 2024-03-19Bibliographically approved
3. A statistical bonded particle model study on the effects of rock heterogeneity and cement strength on dynamic rock fracture
Open this publication in new window or tab >>A statistical bonded particle model study on the effects of rock heterogeneity and cement strength on dynamic rock fracture
2023 (English)In: Computational Particle Mechanics, ISSN 2196-4378Article in journal (Refereed) Epub ahead of print
Abstract [en]

Numerical modelling and simulation can be used to gain insight about rock excavation processes such as rock drilling. Since rock materials are heterogeneous by nature due to varying mechanical and geometrical properties of constituent minerals, laboratory observations exhibit a certain degree of unpredictability, e.g. with regard to measured strength and crack propagation. In this work, a recently published heterogeneous bonded particle model is further developed and used to investigate dynamic rock fracture in a Brazilian disc test. The rock heterogeneities are introduced in two steps—a geometrical heterogeneity due to statistically distributed grain sizes and shapes, and a mechanical heterogeneity by distributing mechanical properties using three Weibull distributions. The first distribution is used for assigning average bond properties of the grains, the second one for the intragranular bond properties and the third one for the bond properties of the intergranular cementing. The model is calibrated for Kuru black diorite using previously published experimental data from high-deformation rate tests of Brazilian discs in a split-Hopkinson pressure bar device, where high-speed imaging was used to detect initiations of cracks and their growth. A parametric study is conducted on the Weibull heterogeneity index of the average bond properties and the grain cement strength and evaluated in terms of crack initiation and propagation, indirect tensile stress, strain and strain rate. The results show that this modelling approach is able to reproduce key phenomena of the dynamic rock fracture, such as stochastic crack initiation and propagation, as well as the magnitude and variations of measured quantities. Furthermore, the cement strength is found to be a key parameter for crack propagation path and time, overloading magnitudes and indirect tensile strain rate.

Place, publisher, year, edition, pages
Springer Nature, 2023
Keywords
DEM, Heterogeneous, Rock, Split-Hopkinson pressure bar
National Category
Other Civil Engineering
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:ltu:diva-103013 (URN)10.1007/s40571-023-00688-6 (DOI)001103979400001 ()2-s2.0-85176935312 (Scopus ID)
Projects
DigiRock
Funder
Vinnova, 2021-04695
Note

Full text license: CC BY

Available from: 2023-11-27 Created: 2023-11-27 Last updated: 2024-03-19
4. A Statistical Bonded Particle Model Study on Laboratory Scale Rock Drilling
Open this publication in new window or tab >>A Statistical Bonded Particle Model Study on Laboratory Scale Rock Drilling
(English)Manuscript (preprint) (Other academic)
Keywords
BPM, DEM, Rock fracture, rock drilling, heterogeneous
National Category
Mechanical Engineering
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:ltu:diva-104683 (URN)
Projects
DigiRock
Available from: 2024-03-19 Created: 2024-03-19 Last updated: 2024-03-19

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