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A Method for Selecting Optimum Microparameters’ Values in the Numerical Simulation of Rock Cutting

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Abstract

This paper deals with the numerical simulation of rock cutting laboratory tests using the discrete element method. The main objective is to provide a method for calibrating numerical DEM models of rock cutting in a systematic way so that realistic results are yielded. The numerical models are developed with the discrete element code Yade, which models rocks as a collection of bonded spheres. The models are calibrated in a four-step process based on the design of experiments method and optimization. The calibrated models are evaluated both quantitatively and qualitatively against actual laboratory cutting tests, in terms of the ratio of the simulated mean cutting force to the actual one and the cutting force time series, respectively. The fully calibrated models showed that the simulated cutting process matched qualitatively the actual cutting force recordings and underestimated the mean cutting force by approximately 3%. It is concluded that well-calibrated numerical simulations of the rock cutting process can provide not only a better understanding of the process itself but also quantitative data regarding the cutting force and energy requirements.

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Abbreviations

β i :

Coefficients (─)

γ int :

Interaction range coefficient (─)

ν :

Poisson ratio (─)

ρ :

Density (kg/m3)

σ c :

Macroscopic compressive strength (MPa)

σ c /σ t :

Macroscopic strength ratio (─)

BTS :

Brazilian tensile strength (MPa)

φ :

Internal friction angle (degrees)

a :

Distance from the design space to a star point

Actual_MCF_S{1–11} :

Actual mean cutting force cut#{1–11} (kN)

Actual_S{1–11} :

Actual cutting force curve cut#{1–11} (kN)

c :

Interparticle cohesive strength (MPa)

c/t :

Interparticle strength ratio (─)

CCC :

Central composite circumscribed

CCD :

Central composite design method

CCF :

Central composite faced

CCI :

Central composite inscribed

DE :

Discrete element

DEM :

Discrete element method

DOE :

Design of experiment

E :

Macroscopic Young’s modulus (GPa)

E eq :

Interparticle elasticity modulus (GPa)

KNKS :

Stiffness ratio (─)

MCF :

Mean cutting force (kN)

MCF PB :

Mean cutting force from the PB method (kN)

MCF CCD :

Mean cutting force from the CCD method (kN)

MCF lab :

Actual mean cutting force (kN)

MSE :

Mechanical specific energy (kJ/m3)

N :

Coordination number (─)

NIST :

National Institute of Standards and Technology

OFAT :

One-factor-at-a-time

PB :

Plackett–Burman method

phi :

Interparticle friction coefficient (degrees)

RSM :

Response surface methodology

Sim_MCF-S{1–11} :

Simulated mean cutting force Cut#{1–11} (kN)

Sim_S{1–11} :

Simulated cutting force curve Cut#{1–11} (kN)

Sim_S{1–11}_mv :

Simulated cutting force curve moving average Cut#{1–11}

SLSQP :

Sequential least square programming method (─)

t :

Interparticle tensile strength (MPa)

UCS :

Uniaxial compressive strength (MPa)

UCS/UTS :

Macroscopic strength ratio (─)

UTS :

Uniaxial tensile strength (MPa)

X1, X2 :

Main effects of the DOE

X1X2 :

Interaction

x i :

Coded microparameters

Y :

Response

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Funding

The first author was supported for this research through a Doctoral Dissertation Fellowship provided by the Research Committee of the National Technical University of Athens.

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Authors and Affiliations

  1. Laboratory of Excavation Engineering, Department of Mining Engineering, School of Mining Engineering and Metallurgy, National Technical University of Athens, Zographou Campus, 15772, Athens, Greece

    A. D. Kalogeropoulos & T. N. Michalakopoulos

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  1. A. D. Kalogeropoulos
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  2. T. N. Michalakopoulos
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Contributions

The first author conducted the research, developed the DEM simulation code, run the simulations, analyzed the results, and drafted the first version of this paper. The second author supervised the research, provided the laboratory test dataset, reviewed the analysis of results, and edited the final version of this paper. Both authors have read and agreed to the published version of the manuscript.

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Correspondence to A. D. Kalogeropoulos.

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Kalogeropoulos, A.D., Michalakopoulos, T.N. A Method for Selecting Optimum Microparameters’ Values in the Numerical Simulation of Rock Cutting. Mining, Metallurgy & Exploration 40, 211–227 (2023). https://doi.org/10.1007/s42461-022-00724-8

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