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A statistical DEM approach for modelling heterogeneous brittle materials
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Solid Mechanics.ORCID iD: 0000-0003-1345-0740
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Solid Mechanics.ORCID iD: 0000-0001-5206-6894
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Solid Mechanics.ORCID iD: 0000-0003-0910-7990
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Solid Mechanics.ORCID iD: 0000-0001-5218-396x
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. Vol. 9, no 4, p. 615-631
Keywords [en]
Bonded DEM, Heterogeneous brittle materials, Fracture, Brazilian disc, Weibull
National Category
Other Mechanical Engineering Applied Mechanics
Research subject
Solid Mechanics
Identifiers
URN: urn:nbn:se:ltu:diva-83907DOI: 10.1007/s40571-021-00434-wISI: 000692075800001Scopus ID: 2-s2.0-85114114019OAI: oai:DiVA.org:ltu-83907DiVA, id: diva2:1546986
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
In thesis
1. Towards Discrete Element Modelling of Rock Drilling
Open this publication in new window or tab >>Towards Discrete Element Modelling of Rock Drilling
2021 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The method of percussive rotary drilling is recognized as the most efficient method for hard rock drilling. Despite the clear advantages over conventional rotary meth-ods, there are still uncertainties associated with percussive rotary drilling. For geothermal applications, it is estimated that 50 % of the total cost per installed megawatt of energy is associated with drilling and well construction, with drill bit wear being a predominant cost factor. Numerical modelling and simulation of rock drilling, calibrated and validated towards rigorous experiments, can give insight into the rock drilling process. This thesis is focused on the prerequisites of numer-ical simulations of rock drilling, i.e. the development of a numerical model and experimental characterization of rock materials. A new approach for modelling brittle heterogeneous materials was developed in this work. The model is based on the Bonded Particle Method (BPM) for the Discrete Element Method (DEM), where heterogeneity is introduced in two ways. Firstly, the material grains are rep-resented by random, irregular ellipsoids that are distributed throughout the body. Secondly, these grains are constructed using the BPM-DEM approach with mi-cromechanical parameters governed by the Weibull distribution. The model was applied to the Brazilian Disc Test (BDT), where crack initiation, propagation, coalescence and branching could be investigated for different levels of heterogene-ity and intergranular cement strengths. The initiation and propagation of the cracks were found to be highly dependent on the level of heterogeneity and cement strengths. In the experimental study, the static and dynamic properties of two rock materials - Kuru grey granite and Kuru black diorite - were obtained from uniaxial compression and indirect tension tests. A Split-Hopkinson Pressure Bar was used to obtain the dynamic properties. Using high-speed photography with frame rate 663,000 fps, the crack initiation and propagation could be studied in de-tail, and the full-field exterior deformation fields of the samples were evaluated by using digital image correlation. From the high-speed images, the onset of unstable crack growth was detected. The crack-damage stresses, associated with unstable crack growth, was approx. 90 % of the peak strength in the dynamic compression tests, whereas the tensile crack-damage stress was approx 70 % of the tensile peak strength.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2021
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
Keywords
DEM Rock Dynamic Drilling
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:ltu:diva-83911 (URN)978-91-7790-836-4 (ISBN)978-91-7790-837-1 (ISBN)
Presentation
2021-06-18, E632, 09:00 (English)
Opponent
Supervisors
Available from: 2021-04-23 Created: 2021-04-23 Last updated: 2023-09-05Bibliographically approved
2. Heterogeneous Bonded Particle Modelling of Rock Fracture
Open this publication in new window or tab >>Heterogeneous Bonded Particle Modelling of Rock Fracture
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
Rock, DEM, BPM, fracture, drilling, dynamic
National Category
Other Civil Engineering
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:ltu:diva-104684 (URN)978-91-8048-505-0 (ISBN)978-91-8048-506-7 (ISBN)
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

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Wessling, AlbinLarsson, SimonJonsén, PärKajberg, Jörgen

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