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Evaluating the impact of eccentric loading on strip footing above horseshoe tunnels in rock mass using adaptive finite element limit analysis and machine learning

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Abstract

The present study investigates the ultimate bearing capacity (UBC) of a footing subjected to an eccentric load situated above an unlined horseshoe-shaped tunnel in the rock mass, following the Generalized Hoek-Brown (GHB) failure criterion. A reduction factor (Rf) is introduced to investigate the impact of the tunnel on the UBC of the footing. Rf is determined using upper and lower bound analyses with adaptive finite-element limit analysis. The study examines the influence of several independent variables, including normalized load eccentricity (e/B), normalized vertical and horizontal distances (δ/B and H/B) of the footing from the tunnel, tunnel size (W/B), and other rock mass parameters. It was found that all these parameters significantly affect the behavior of tunnel-footing interaction depending on the range of varying parameters. The findings of the study indicate that the critical depth (when Rf is nearly 1) of the tunnel decreases with increasing load eccentricity. The critical depth is found to be δ/B ≥ 2 for e/B ≤ 0.2 and δ/B ≥ 1.5 for e/B ≥ 0.3, regardless of H/B ratios. Additionally, the GHB parameters of the rock mass significantly influence the interaction between the tunnel and the footing. Moreover, this study identifies some typical potential failure modes depending on the tunnel position. The typical potential failure modes of the footing include punching failure, cylindrical shear wedge failure, and Prandtl-type failure. This study also incorporates soft computing techniques and formulates empirical equations to predict Rf using artificial neural networks (ANNs) and multiple linear regression (MLR).

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Data availability

No datasets were generated or analysed during the current study.

Abbreviations

UBC :

Ultimate bearing capacity

GHB :

Generalized Hoek-Brown

FEM :

Finite Element Method

UB :

Upper Bound

LB :

Lower Bound

DLO :

Discontinuity Layout Optimization

ANN :

Artificial Neural Network

AFELA :

Adaptive Finite Element Limit Analyis

MLR :

Multiple Linear Regression

B :

Width of strip footing (m)

H :

Horizontal distance of tunnel from central horizontal axis of footing (m)

H/B :

Normalised horizontal position of tunnel relative to the footing width

δ :

Vertical depth between the ground surface and crest of a tunnel (m)

δ/B :

Normalised vertical depth of tunnel relative to the footing width

e :

Load eccentricity (m)

e/B :

Normalised load eccentricity with the footing width

GSI :

Geological Strength index

m i :

Material constant for intact rock

D :

Disturbance factor of the rock mass

σ ci :

Unconflined compressive strength (kPa) 

R f :

Reduction factor

W :

Width of tunnel

W/B :

Height to width ratio of tunnel

q u :

Ultimate bearing capacity of strip footing resting on rock mass with underground tunnel (kPa)

\(q_u^{\prime}\) :

Ultimate bearing capacity of strip footing resting on rock mass without underground tunnel (kPa)

\(\sigma_1^{\prime}\) :

Maximum effective principal stress (kPa)

\(\sigma_3^{\prime}\) :

Minimum effective principal stress (kPa)

m b :

Material constant for rock mass strength

a, s:

GHB constants

γ :

Unit weight of rock mass (kN/m3)

Q s :

Collapse multiplier load (kPa/m)

RE :

Relative error

MSE :

Mean square error

RMSE :

Root means square error

R 2 :

Coefficient of determination

n :

Total number of samples

\(y_i^{\prime}\) :

Predicted value

y i :

Actual value or Testing data set

\(\overline{y}\) :

Mean value

\(\overline{y}_i\) :

Dependent variable

Xi1 :

Independent variable

β1 :

Slope coefficients

\(\epsilon\) :

Residual error

Nv :

Stability number

σ s :

Ultimate bearing capacity of strip footing (kPa/m)

σsci :

Stability factor

W :

Height and width of the tunnel (m)

W/B :

Normalised size of tunnel with the footing width

NNs :

Number of neurons

H n :

Hidden neurons

x :

input variables

J :

Number of input variables

N :

Number of hidden neurons

IW :

Weight matrices

K :

Output neurons

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Authors

Contributions

Aayush Kumar: Data curation, Numerical Modelling, Validation, Software, Methodology, Writing original draft, Vinay Bhushan Chauhan: Conceptualisation, Data curation, Writing - review & editing, Project administration, Supervision.

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Correspondence to Vinay Bhushan Chauhan.

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Communicated by: Hassan Babaie

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Kumar, A., Chauhan, V.B. Evaluating the impact of eccentric loading on strip footing above horseshoe tunnels in rock mass using adaptive finite element limit analysis and machine learning. Earth Sci Inform 17, 4441–4471 (2024). https://doi.org/10.1007/s12145-024-01380-w

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