Contribution to the numerical modelling analysis of displacements caused by tunnel construction in discontinuous rock masses: a case study of Boukhadra iron mine (Algeria)

Hamdane, Ali; Mellas, Mekki; Benghazi, Zied; Djellali, Adel

doi:10.28927/SR.2026.020325

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Case Study • Soil. Rocks 49 (3) • 2026 • https://doi.org/10.28927/SR.2026.020325 linkcopy

Contribution to the numerical modelling analysis of displacements caused by tunnel construction in discontinuous rock masses: a case study of Boukhadra iron mine (Algeria)

Authorship SCIMAGO INSTITUTIONS RANKINGS

This paper presents a comprehensive study of the stability conditions of a rock mass surrounding a tunnel, using numerical modelling analysis of displacements induced by tunnel construction. The case study focuses on the Boukhadra iron ore mine in Algeria. This research employs empirical equations from literature based on geomechanical classifications to provide the most appropriate geotechnical input data for simulation. In addition to those equations, a novel correlation equation relating the rock mass ratio (RMR) and the rock quality index (Q) was developed. This equation gives a high regression coefficient, revealing a strong correlation (R²) of 0.878. It provides a better estimation of the rock mass characteristics: Young’s moduli (E), Poisson’s ratio (ν), cohesion (c), and friction angle (φ), compared to the existing literature-based correlation equations. The estimated parameters were used to pass from a discontinuous medium to a continuous equivalent, making numerical modelling using finite element method easier. Compared with intact rock and direct equations, the numerical simulation results based on the new equation fit well with the in-situ observations, with predicted displacements remaining within the same order of magnitude as observed deformations, providing more reliable understanding of rock mass behaviour. The new equation proposed in this paper provides a substantial evaluation of the rock mass parameters required for the design process of underground structures when used within their respect acceptable ranges.

Keywords:
Tunnel stability; Rock masses; Geomechanical classifications; Failure strength; Regression analysis; Numerical modelling

	Internal friction (°)	Unite weight (kN/m³)	Cohesion (MPa)	Unconfined Compressive Strength (MPa)	Stiffness description	Young’s modulus (GPa)	Strength description	Poisson’s ratio
Limestone	37.76	26	3.65	60	extremely stiff	42	very high strength	0.22
Iron ore	49.59	27	8.56	71	very stiff	63.9	high strength	0.25
Sandstone	44.37	23	4.53	50	stiff	13.75	medium strength	0.35
Conglomerate	11.90	22	0.56	5	stiff	1.75	medium strength	0.35
Mineralised marl	29.14	24	2.19	30	moderately stiff	6.00	low strength	0.30
Multicoloured marl	8.02	19.5	0.40	5	moderately stiff	0.75	very low strength	0.38
Yellow marl	17.86	22	1.11	9	poorly stiff	1.80	very low strength	0.33

Formations	RMR		Q		RMi
Formations	Value	quality	Value	quality	Value	quality
Limestone	50	Fair	15.05	Good	1.56	high
Iron ore	70	Good	21	Good	2.34	high
Sandstone	59	Fair	19.6	Good	1.55	high
Conglomerate	19	Very Poor	3.5	Poor	0.09	low
Mineralised marl	44	Fair	14	Good	0.75	Moderate
Multicolored marl	29	Poor	9.85	Fair	0.11	Moderate
Yellow marl	39	Poor	12.95	Good	0.21	Moderate

Parameter	Estimate	Std. Error	t-value	p-value	95% CI
intercept	42.71	0.85	50.2	<0.001	41.00-44.42
ln(Q) coefficient	6.248	0.42	14.9	<0.001	5.41-7.09

Correlation	RMSE	MAE	MAPE
The new developed equation	2.43	1.80	3.50
Bieniawski (1989)	8.01	7.29	12.68
Palmström (2009)	7.64	7.27	13.62

Formations	Modelling conditions	Internal friction (°)	Unite width (kN/m³)	Cohesion (MPa)	Young’s modulus (GPa)	Poisson’s ratio
Limestone	Intact rocks	37.76	26	3.65	42.00	0.22
	Direct relations	29.40	26	0.96	10.00	0.33
	Equation 1	49.82	26	0.86	17.43	0.32
Iron ore	Intact rocks	49.59	27	8.56	63.90	0.25
	Direct relations	36.92	27	1.83	31.62	0.26
	Equation 1	50.86	27	2.03	19.64	0.32
Sandstone	Intact rocks	44.37	23	4.53	13.75	0.35
	Direct relations	31.69	23	1.16	16.79	0.30
	Equation 1	50.65	23	1.15	19.16	0.32
Mineralised marl	Intact rocks	29.14	24	2.19	6.00	0.30
	Direct relations	23.36	24	0.41	7.08	0.41
	Equation 1	49.60	24	0.34	16.98	0.32

Property of the rock mass	Empirical relation	Proposed by
Deformation modulus, E_rm (GPa)	$E_{r m} = 10^{(\frac{R M R - 10}{10})}$	Serafim & Pereira (1983)
Deformation modulus, E_rm (GPa)	$E_{r m} = 25 log Q (GPa)$	Grimstad & Barton (1993)
Friction angle, ö_m (°)	$φ_{m} = 20 σ_{c m}^{0.2}$	Aydan et al. (1993)
Friction angle, ö_m (°)	$φ_{m} = 20 + 0.5 R M R$	Aydan & Kawamoto (2001)
Cohesion, c_m (MPa)	$c_{m} = \frac{σ_{c m}}{2} \frac{1 - s i n φ_{m}}{c o s φ_{m}}$	Aydan & Kawamoto (2001)
Cohesion, c_m (MPa)	$c_{m} = (\frac{R Q D}{J_{n}} \times \frac{1}{S R F} \times \frac{σ_{c i}}{100})$	Barton (2002)
Poisson’s ratio, í_m	$ν_{m} = 0.25 (1 + e^{σ_{m} / 4})$	Aydan et al. (1993)
Poisson’s ratio, í_m	$ν_{m} = 0.5 - 0.2 \frac{R M R}{R M R + 0.2 (100 - R M R)}$	Tokashiki & Aydan (2010)

Formations	Geological Strength Index (GSI)	m_i	Disturbance factor (D)	Deformation modulus E_rm (GPa)	Unconfined Compressive Strength of the rock mass ó_rm (MPa)
Limestone	46	09	0.8	3.00	4.67
Iron ore	64	12	0.8	13.76	11.61
Sandstone	51	17	0.8	1.34	6.30
Conglomerate	14	21	0.8	0.04	0.15
Mineralised marl	38	10	0.8	0.28	1.86
Multicolored marl	21	5	0.8	0.02	0.10
Yellow marl	33	9	0.8	0.07	0.44

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[1] E_rm deformation modulus of rock mass, RMR rock mass rating, Q rock mass quality, σ_ci uniaxial compressive strength of intact rock, σ_cm uniaxial compressive strength of rock mass, RQD Rock Quality Designation, φ_m friction angle of rock mass, c_m cohesion of rock mass, ν_m Poisson's ratio of rock mass, J_n joint set rating, SRF stress reduction factor.