Research on the influence of rock micro-parameter in particle flow code (PFC) on the rock fracture morphology

Lingli Zhang; Ruirui Wang; Biao Li; Jian Hou; Nana Liu

doi:10.2478/cee-2026-0114

$Research on the influence of rock micro-parameter in particle flow code (PFC) on the rock fracture morphology Cover$

Research on the influence of rock micro-parameter in particle flow code (PFC) on the rock fracture morphology

Civil and Environmental Engineering

AHEAD OF PRINT

By: Lingli Zhang, Ruirui Wang, Biao Li, Jian Hou and Nana Liu

Open Access

|Jun 2026

Figures & Tables

Schematic diagram of the 2D linear parallel bonding model (Ni et al. 2025a, 2025b)

Table 1:

Ranges of each input micro-parameters (Ni et al. 2025a, 2025b)

Input	Symbol	Unit	Lower bounds	Upper bounds
Tensile strength	σ_mi	[MPa]	10	90
Cohesion force	c_mi	[MPa]	10	90
Radius multiplier	λ_mi	-	0.5	1
Effective modulus	$E_{p m i}^{*}$	[GPa]	10	90
Friction angle	ϕ_mi	[°]	40	60
Friction coefficient	μ_mi	-	0.1	0.9
Porosity	p_mi	-	0.1	0.15

Numerical models for data collection (Ni et al. 2025a, 2025b)

Schematic figures of different fracture morphology generated in the uniaxial compression test

Schematic figures of different fracture morphology generated in the Brazilian splitting test

Schematic figures of different fracture morphology generated in the direct shear test

The criteria areas of different fracture morphology

Table 2

Micro-parameter of the example numerical rock model

σ_mi [MPa]	c_mi [MPa]	λ_mi	$E_{p m i}^{*} [GPa]$	ϕ_mi[°]	μ_mi	p_mi
49.62	58.10	0.86	65.3	48.50	0.48	0.13

Classification of the generated fractures morphology of the example model

Table 3:

The proportion of each morphology

Uniaxial compression test			Brazilian splitting test			Direct shear test
Morphology	Number	Proportion [%]	Morphology	Number	Proportion [%]	Morphology	Number	Proportion [%]
Localized	163	10.7	Linearly penetrated	1122	74.0	Linearly penetrated	1287	84.8
Declining	914	60.3	Dumbbell	346	22.8	Large-scale	230	15.2
Large-scale	440	29.0	Large-scale	49	3.2

Fracture morphology distribution on different micro-parameters

Table 4:

Primary influencing factors on each fracture morphology

Rock test	Fracture morphology	Influencing factors
Uniaxial compression test	Localized	σ_mi, c_mi
	Declining	σ_mi, c_mi
	Large-scale	c_mi
Brazilian splitting test	Linearly	μ_mi
	Dumbbell	μ_mi
	Large-scale	σ_mi, c_mi, ϕ_mi, μ_mi, p_mi
Direct shear test	Linearly	σ_mi, c_mi
Direct shear test	Large scale	σ_mi, c_mi, $E_{p m i}^{}$ , p_mi*

Table 5:

Micro-parameters of the example numerical model

Model name	σ_mi [MPa]	c_mi [MPa]	*λ_mi*	$E_{p m i}^{*} [G P a]$	ϕ_mi [°]	μ_mi	*p_mi*
Example	82.73	88.38	0.95	16.83	50.91	0.88	0.13
The closest	82.42	73.59	0.90	30.08	46.08	0.90	0.13
The 2^nd closest	83.16	81.47	0.99	16.60	50.46	0.89	0.15
The 3^rd closest	73.12	64.72	0.94	38.77	50.39	0.72	0.13
The 4^th closest	87.64	85.28	0.85	29.84	58.44	0.81	0.12
The 5^th closest	86.95	58.35	0.95	15.28	53.51	0.67	0.14
The 6^th closest	75.01	88.69	0.81	12.68	56.02	0.80	0.11
……

Table 6:

Simulated fracture morphologies of the 5 closest models

	Uniaxial compression test	Brazilian splitting test	Direct shear test
The closest	Declining	Dumbbell	Linearly penetration
The 2^nd closest	Large-scale	Dumbbell	Linearly penetration
The 3^rd closest	Declining	Linearly penetration	Linearly penetration
The 4^th closest	Declining	Dumbbell	Linearly penetration
The 5^th closest	Declining	Dumbbell	Large-scale
The 6^th closest	Declining	Dumbbell	Linearly penetration
……
Evaluating results	Declining	Dumbbell	Linearly penetration

Simulation results of the example rock model

Table 7:

Micro-parameters of the partial of 40 randomly generated models used for verification

	σ_mi [MPa]	c_mi [MPa]	*λ_mi*	$E_{p m i}^{*} [G P a]$	ϕ_mi [°]	*μ_mi*	*p_mi*
1	72.54	79.27	0.81	34.29	57.15	0.75	0.14
2	23.17	33.43	0.93	87.36	40.08	0.29	0.12
3	27.46	82.32	0.68	39.38	53.93	0.89	0.12
4	68.40	80.92	0.81	44.96	44.54	0.19	0.12
5	13.54	10.54	0.93	12.98	41.54	0.24	0.13
6	89.82	46.19	0.56	66.44	48.51	0.31	0.10
7	51.20	39.16	0.62	73.92	49.74	0.76	0.11
8	40.58	50.71	0.73	48.10	47.27	0.56	0.14
9	17.39	31.60	0.62	27.31	50.19	0.51	0.13
10	22.46	33.27	0.63	29.81	47.42	0.34	0.15
……

Table 8:

Partial Evaluating fracture morphology of the 40 verification models

	Uniaxial compression test	Brazilian splitting test	Direct shear test
1	Declining	Dumbbell	Linearly penetrated
2	Declining	Large-scale	Linearly penetrated
3	Localized	Dumbbell	Linearly penetrated
4	Declining	Linearly penetrated	Linearly penetrated
5	Large-scale	Large-scale	Large-scale
6	Declining	Linearly penetrated	Linearly penetrated
7	Declining	Dumbbell	Linearly penetrated
8	Declining	Linearly penetrated	Linearly penetrated
9	Large-scale	Linearly penetrated	Large-scale
10	Declining	Large-scale	Large-scale

The uniaxial compression test simulation results of partial verification models

The Brazilian splitting test simulation results of partial verification models

The direct shear test simulation results of partial verification models

Frequency of the comparison results between simulated and evaluated morphology

Table 9:

Statistic results of the evaluation method applied on the 40 added simulation

	Uniaxial compression test			Brazilian splitting test			Direct shear test
	Localized	Declining	Large-scale	Linearly	Dumbbell	Large-scale	Linearly	Large-scale
Precision [%]	60.0	96.0	60.0	57.1	93.5	50.0	96.70	50.0
Recall [%]	75.0	82.8	85.7	80.0	87.9	50.0	85.30	83.3
F1-score	0.67	0.89	0.71	0.67	0.91	0.5	0.91	0.62

Table 10:

Statistic of the evaluated results by SVM and ANN

		Uniaxial compression test			Brazilian splitting test			Direct shear test
		Localized	Declining	Large-scale	Linearly	Dumbbell	Large-scale	Linearly	Large-scale
SVM	Precision [%]	100.0	83.4	57.1	50.0	90.6	50.0	94.1	67.0
	Recall [%]	50.0	89.7	57.1	40.0	87.9	100.0	94.1	66.7
	F1-score	0.67	0.86	0.57	0.44	0.89	0.67	0.94	0.67
ANN	Precision [%]	100.0	81.8	60.0	100.0	91.2	33.0	91.4	50.0
	Recall [%]	50.0	93.10	42.9	60.0	93.9	50.0	94.1	60.0
	F1-score	0.67	0.87	0.50	0.75	0.93	0.40	0.93	0.55

Table 11:

The micro-parameters of the selected samples

	σ_mi [MPa]	c_mi [MPa]	*_λ_mi*	$E_{p m i}^{*} [G P a]$	ϕ_mi [°]	*_μ_mi*	*p_mi*	Morphology
1	29.04	75.33	0.97	18.82	51.82	0.44	0.13	Declining
2	61.17	30.16	0.87	77.71	52.14	0.80	0.13	Large-scale
3	63.29	33.45	0.78	60.39	41.95	0.23	0.12	Declining
4	78.89	35.12	0.92	70.39	58.92	0.31	0.12	Declining
5	65.17	28.22	0.92	85.61	48.28	0.29	0.12	Large-scale
6	58.47	67.00	0.53	24.55	50.73	0.40	0.10	Declining
7	52.55	29.80	0.68	26.13	41.89	0.67	0.11	Large-scale
8	26.12	33.79	0.97	73.89	51.69	0.65	0.11	Declining
9	72.77	36.09	0.90	34.68	59.95	0.66	0.10	Declining
10	45.59	29.63	0.94	35.86	54.30	0.78	0.13	Large-scale

The generating and extending process of the fractures in the uniaxial compression test

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DOI: https://doi.org/10.2478/cee-2026-0114 | Journal eISSN: 2199-6512 (formerly 1336-5835) | Journal ISSN: 1336-5835

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Language: English

Submitted on: Jan 27, 2026

Accepted on: Apr 24, 2026

Published on: Jun 24, 2026

Published by: University of Žilina

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Numerical simulation,

Particle flow code,

Fractures,

Laboratory test

Related subjects:

Business and economics,

Business management,

Industries,

Environmental management

© 2026 Lingli Zhang, Ruirui Wang, Biao Li, Jian Hou, Nana Liu, published by University of Žilina
This work is licensed under the Creative Commons Attribution 4.0 License.

AHEAD OF PRINT

Research on the influence of rock micro-parameter in particle flow code (PFC) on the rock fracture morphology

Figures & Tables

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