Estimation of the stability of tailings dams based on genetic algorithm-supported calibration results and monitoring data

Szczepan Grosel

doi:10.2478/sgem-2026-0001

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Estimation of the stability of tailings dams based on genetic algorithm-supported calibration results and monitoring data

Studia Geotechnica et Mechanica

Volume 48 (2026): Issue 1 (March 2026)

By: Szczepan Grosel

Open Access

|Apr 2026

Figures & Tables

Solution coding into a sequence of real numbers.

Numerical model and location of nodes selected as monitoring gauges.

Unfitness and its mean (dashed) change during genetic algorithm calibration.

Match to horizontal (left) and vertical (right) displacement data of U2 gauge.

Match to piezometric data of P2 (left) and P3 (right) gauges.

Relationships between FOS and parameters or unfitness; red dot indicates true values of FOS and parameters, and R is Pearson coefficient.

Hydraulic conductivity ranges assumed to be correct identification.

FOS values for correctly identified hydraulic conductivity and angle of internal friction.

Relationship between piezometer fit (expressed as RMSE) and FOS in case 1.38.

Relationship between piezometer fit (expressed as RMSE) and FOS in case 1.48.

Relationship between piezometer fit (expressed as RMSE) and FOS in case 1.64.

FOS estimated using individuals with value above RMSE calculated on piezometers (above) or unfitness (below).

Permissible ranges of parameters being calibrated_

Material	Parameter	Min	Max
1A	E (MPa)	15.0	60.0
	ν (−)	0.20	0.40
	k _x (m/s)	1 × 10⁻¹¹	1 × 10⁻⁸
	k _y (m/s)	1 × 10⁻¹¹	1 × 10⁻⁸
	P _c0 (kPa)	300	700
	λ (−)	0.05	0.15
	R (−)	1.2	2.0
	c (kPa)	10	15
	φ (°)	15	20
	ME (−)	5	13
2B	E (MPa)	60	100
	ν (−)	0.20	0.40
	k _x (m/s)	1 × 10⁻⁹	1 × 10⁻⁶
	k _y (m/s)	1 × 10⁻⁹	1 × 10⁻⁶
	P _c0 (kPa)	300	700
	λ (−)	0.05	0.15
	R (−)	1.2	2.0
	c (kPa)	15	20
	φ (°)	20	25
3C	E (MPa)	100	200
	ν (−)	0.20	0.35
	k _x = k _y (m/s)	1 × 10⁻⁶	1 × 10⁻⁴
	c (kPa)	3	10
	φ (°)	26	36
Dykes	E (MPa)	70	120
Dykes	ν (−)	0.20	0.35
Beaches	E (MPa)	30	70
	ν (−)	0.2	0.4
	k _x (m/s)	1 × 10⁻⁷	1 × 10⁻⁵
	k _y (m/s)	1 × 10⁻⁷	1 × 10⁻⁵
Sediments	E (MPa)	10	30
	ν (−)	0.2	0.4
	k _x = k _y (m/s)	1 × 10⁻⁹	1 × 10⁻⁶

Interpretation of Pearson correlation coefficient based on [36]_

Correlation coefficient ( \| R \| \|R\| )	Strength of correlation
0.00–0.19	Very weak
0.20–0.39	Weak
0.40–0.59	Moderate
0.60–0.79	Strong
0.80–1.00	Very strong

Material parameters used to generate synthetic monitoring data_

Material	Case	E (MPa)	ν (−)	k _x (m/s)	k _y (m/s)	P _c0 (kPa)	λ (−)	R (−)	c (kPa)	φ (°)	ME (−)	γ (kN/m³)	n (−)	S _r (−)	α (1/m)	OCR (−)
1A	1.38	56.4	0.36	6.31 × 10⁻¹⁰	3.71 × 10⁻⁹	654.78	0.07	1.46	12.39	16.46	6.7	17.3	0.32	0	0.1	1.4
	1.48	55.1	0.27	1.82 × 10⁻⁹	1.44 × 10⁻⁹	476.47	0.06	1.28	11.05	17.91	11.8
	1.64	57.76	0.34	8.51 × 10⁻⁹	6.92 × 10⁻⁹	459.17	0.10	1.71	13	19.57	12
2B	1.38	72.52	0.23	1.99 × 10⁻⁸	5.37 × 10⁻⁹	640.8	0.13	1.81	15.4	20.68	—	17.7	0.33	0	0.5	1.34
	1.48	75.57	0.34	5.75 × 10⁻⁸	2.34 × 10⁻⁸	399.58	0.11	1.21	18.3	22.84
	1.64	90.39	0.27	2.69 × 10⁻⁷	1.99 × 10⁻⁹	565.64	0.09	1.23	18.45	20.47
3C	1.38	175.78	0.21	3.63 × 10⁻⁶	3.63 × 10⁻⁶	—	—	—	9.81	32.95	—	16.9	0.36	0	5	—
	1.48	109.23	0.28	2.24 × 10⁻⁶	2.24 × 10⁻⁶				6.81	35.5
	1.64	173.06	0.2	4.27 × 10⁻⁶	4.27 × 10⁻⁶				8.1	34.68
Dykes	1.38	117.8	0.23	6.61 × 10⁻⁵	2.09 × 10⁻⁴	—	—	—	20	34	—	19	0.15	0	10	—
	1.48	107.74	0.28	9.12 × 10⁻⁵	2.88 × 10⁻⁴
	1.64	114.12	0.3	2.23 × 10⁻⁵	7.08 × 10⁻⁵
Beaches	1.38	57.32	0.31	6.61 × 10⁻⁶	2.09 × 10⁻⁵	—	—	—	10	20	—	17	0.15	0	1.9	—
	1.48	41.39	0.33	9.12 × 10⁻⁶	2.88 × 10⁻⁵
	1.64	45.84	0.24	2.23 × 10⁻⁶	7.08 × 10⁻⁶
Sediments	1.38	20.86	0.32	1.44 × 10⁻⁹	1.44 × 10⁻⁹	—	—	—	10	20	—	17	0.15	0	0.75	—
	1.48	21.49	0.4	1.95 × 10⁻⁸	1.95 × 10⁻⁸
	1.64	28.62	0.28	1.35 × 10⁻⁸	1.35 × 10⁻⁸

References

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DOI: https://doi.org/10.2478/sgem-2026-0001 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365

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Language: English

Page range: 1 - 16

Submitted on: Mar 20, 2025

Accepted on: Jan 16, 2026

Published on: Apr 21, 2026

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Slope stability,

Genetic algorithms,

Monitoring data,

Numerical calculations

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2026 Szczepan Grosel, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 48 (2026): Issue 1 (March 2026)

Estimation of the stability of tailings dams based on genetic algorithm-supported calibration results and monitoring data

Figures & Tables

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Permissible ranges of parameters being calibrated_

Interpretation of Pearson correlation coefficient based on [36]_

Material parameters used to generate synthetic monitoring data_

Paradigm

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