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Soil–conduit interaction: an artificial intelligence application for reinforced concrete and corrugated steel conduits

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Abstract

Marston’s load theory is commonly used for understanding the soil–conduit interaction. However, there are no practical methods available which can estimate the Marston’s soil prism (MSP) width ratio. Moreover, the advent of soft computing methods has made many traditional approaches antiquated. The main purpose of this work is to compare and evaluate the predictive abilities of several machine learning-based models in predicting the MSP width ratio for the reinforced concrete (RC) and corrugated steel (CS) conduits. By utilizing the finite element modelling, a large-scale dataset was generated for the width of the soil prism for both types of conduit material, when buried under sandy soils of varying stiffness. After preparing the required dataset, feature validity technique based on correlation-based feature selection was employed to find the most influential parameters affecting the MSP width. Thereafter, five regression-based data driven models namely artificial neural networks (ANN), least-square support vector regression, extreme learning machine, Gaussian process regression, and multiple linear regression were developed to forecast the MSP width ratio. The results showed that the ANN outperforms the other predictive models for both the conduit types. In addition, due to the excellent overall performance of the ANN, it was translated into functional relationship for predicting the MSP width ratio for RC and CS conduits.

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Acknowledgements

This research was funded by The Higher Education Commission (HEC), Government of the Islamic Republic of Pakistan. The authors also acknowledge the assistance provided by Mrs. Saman Tariq in the extraction of images.

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Authors and Affiliations

  1. Geotechnical and Geoenvironmental Research Group, School of Engineering, Edith Cowan University, Joondalup, Perth, WA, 6027, Australia

    Muhammad Umer Arif Khan, Sanjay Kumar Shukla & Muhammad Nouman Amjad Raja

  2. Department of Civil Engineering, Mirpur University of Science and Technology, Mirpur, Azad Kashmir, Pakistan

    Muhammad Umer Arif Khan

  3. Delhi Technological University, New Delhi, Delhi, India

    Sanjay Kumar Shukla

  4. Department of Civil Engineering, School of Engineering, University of Management and Technology, Lahore, Pakistan

    Muhammad Nouman Amjad Raja

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  1. Muhammad Umer Arif Khan
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Correspondence to Muhammad Umer Arif Khan.

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Appendix: Weights and biases of the developed ANN models

Appendix: Weights and biases of the developed ANN models

1.1 RC conduit

Synaptic weights between the input and hidden layer (w1)

− 3.560

− 1.221

− 0.311

− 1.025

2.413

− 0.150

− 0.079

0.092

3.147

− 4.639

− 1.221

− 0.284

− 0.803

2.180

− 0.120

− 0.067

0.058

4.700

− 0.100

− 0.911

1.105

− 2.060

5.311

− 0.506

0.296

− 1.580

− 1.990

20.407

− 1.206

6.340

0.643

− 1.139

− 1.071

0.377

0.609

0.544

− 9.947

− 0.184

− 0.074

0.144

0.054

0.124

− 0.009

− 0.101

− 0.049

− 1.842

− 1.970

1.147

− 0.719

2.939

− 3.538

− 1.705

− 0.224

0.553

0.235

− 0.568

0.083

0.342

− 0.242

− 0.836

− 0.080

0.572

− 1.578

− 12.409

2.338

0.635

− 0.365

− 1.234

− 1.652

− 0.156

1.261

2.186

− 0.233

0.791

0.020

− 0.219

− 0.181

1.063

0.098

− 0.713

1.591

− 4.059

− 0.860

− 0.565

− 2.186

2.776

1.090

0.118

− 0.829

0.159

Synaptic weights between the hidden and output layer (w2)

− 3.394

3.108

− 0.256

− 7.023

− 7.439

0.018

2.472

0.484

2.270

0.539

Bias of hidden layer nodes (b1)

− 5.28921

− 7.15092

− 6.14941

− 0.31111

− 1.94642

− 3.0193

− 1.84741

− 10.2446

2.049577

− 4.14727

Bias of output layer node (b2)

− 0.6967.

1.2 CS conduit

Synaptic weights between the input and hidden layer (\(w_{1}\))

− 0.207

0.054

− 0.603

0.018

0.252

− 0.915

− 0.130

1.014

2.958

5.606

3.056

− 5.208

− 0.321

− 0.889

− 0.039

− 2.008

3.869

− 7.328

0.500

0.064

− 0.059

− 0.040

− 0.183

0.002

0.140

0.223

− 0.135

0.504

− 0.521

− 0.847

− 0.046

1.410

0.134

0.045

0.021

− 0.160

− 1.343

− 2.779

3.820

1.191

− 0.034

− 0.718

− 1.655

0.676

− 16.225

− 1.359

− 2.700

4.137

1.244

− 0.432

− 0.536

− 1.670

0.417

− 16.105

0.478

0.437

0.869

0.239

0.105

− 1.274

− 0.454

1.002

1.169

0.123

− 0.669

− 0.077

0.089

0.985

0.764

0.102

− 0.892

− 2.952

0.240

0.753

− 4.565

− 1.360

− 2.116

0.139

− 2.581

0.539

1.198

0.265

− 0.255

− 0.404

− 0.041

0.866

0.106

− 0.039

− 0.078

− 0.118

Synaptic weights between the hidden and output layer (w2)

− 0.990

0.639

− 0.795

1.328

4.689

− 4.602

− 0.018

− 1.113

− 0.027

− 3.244

Bias of hidden layer nodes (b1)

0.398

− 15.068

0.788

0.585

− 3.925

− 4.069

− 1.588

− 0.493

− 3.986

1.202

Bias of output layer node (b2)

2216

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Khan, M.U.A., Shukla, S.K. & Raja, M.N.A. Soil–conduit interaction: an artificial intelligence application for reinforced concrete and corrugated steel conduits. Neural Comput & Applic 33, 14861–14885 (2021). https://doi.org/10.1007/s00521-021-06125-0

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