Data-driven approach to solve vertical drain under time-dependent loading

doi:10.1007/s11709-021-0727-7

Front. Struct. Civ. Eng.

2021, Vol. 15

Issue (3) : 696-711 https://doi.org/10.1007/s11709-021-0727-7

RESEARCH ARTICLE

Data-driven approach to solve vertical drain under time-dependent loading

Trong NGHIA-NGUYEN^1,², Mamoru KIKUMOTO¹, Samir KHATIR³, Salisa CHAIYAPUT⁴, H. NGUYEN-XUAN⁵, Thanh CUONG-LE²(

)

¹. Department of Civil Engineering, Yokohama National University, Yokohama 240-8501, Japan
². Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City 70000, Vietnam
³. Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Faculty of Engineering and Architecture, Ghent University, Ghent 9000, Belgium
⁴. Department of Civil Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
⁵. CIRTECH Institute, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City 708300, Vietnam

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Abstract

Currently, the vertical drain consolidation problem is solved by numerous analytical solutions, such as time-dependent solutions and linear or parabolic radial drainage in the smear zone, and no artificial intelligence (AI) approach has been applied. Thus, in this study, a new hybrid model based on deep neural networks (DNNs), particle swarm optimization (PSO), and genetic algorithms (GAs) is proposed to solve this problem. The DNN can effectively simulate any sophisticated equation, and the PSO and GA can optimize the selected DNN and improve the performance of the prediction model. In the present study, analytical solutions to vertical drains in the literature are incorporated into the DNN–PSO and DNN–GA prediction models with three different radial drainage patterns in the smear zone under time-dependent loading. The verification performed with analytical solutions and measurements from three full-scale embankment tests revealed promising applications of the proposed approach.

Keywords vertical drain artificial neural network time-dependent loading deep learning network genetic algorithm particle swarm optimization

Corresponding Author(s): Thanh CUONG-LE

Online First Date: 09 June 2021 Issue Date: 14 July 2021

Cite this article:

Trong NGHIA-NGUYEN,Mamoru KIKUMOTO,Samir KHATIR, et al. Data-driven approach to solve vertical drain under time-dependent loading[J]. Front. Struct. Civ. Eng., 2021, 15(3): 696-711.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-021-0727-7
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I3/696

Fig.1 Cylinder unit cell model and lateral drainage patterns.

Fig.2 Single-ramp loading and degree of consolidation (DOC).

Fig.3 Approximate curve of DOC versus the number of divided nodes.

Fig.4 Topology of the DNN.

Tab.1 Range of data set

Tab.2 Statistical values for pattern I data set

Tab.3 Statistical values for pattern II data set

Tab.4 Statistical values for pattern III data set

Fig.5 Feature distribution in pattern I data set. (a) Distribution of value

n

;(b) distribution of value

R s

; (c) distribution of value

H

; (d) distribution of value

T h 1

Fig.6 Feature distribution in pattern II data set. (a) Distribution of value

n

;(b) distribution of value

R s

; (c) distribution of value

H

; (d) distribution of value

T h 1

Fig.7 Feature distribution in pattern III data set. (a) Distribution of value

n

;(b) distribution of value

R s

; (c) distribution of value

H

; (d) distribution of value

T h 1

Fig.8 Concept of real and image positions.

Tab.5 Training with one hidden layer network to select parameters for PSO

Fig.9 Convergence graphs of training process. (a) DNN-PSO pattern I; (b) DNN-GA pattern I; (c) DNN-PSO pattern II; (d) DNN-GA pattern II; (e) DNN-PSO pattern III; (f) DNN-GA pattern III.

Tab.6 Analysis results from pattern I data set

Tab.7 Analysis results from pattern II data set

Tab.8 Analysis results from pattern III data set

Fig.10 DOCs by the DNN–GA and by Tang and Onitsuka [24] in pattern I.

Fig.11 DOCs by the DNN–GA and by Xie et al. [26] in pattern II.

Fig.12 DOCs by the DNN–PSO and by Xie et al. [26] in pattern III.

Fig.13 Simplified loading sequences.

Tab.9 Input parameters of the DNN in pattern I

Fig.14 Comparison of the DOCs by the DNN in pattern I with field measurements.

Tab.10 Input parameters of the DNN in pattern II

Tab.11 Input parameters of the DNN in pattern III

Fig.15 Comparison of the DOCs by the DNN in pattern II with field measurements.

Fig.16 Comparison of the DOCs by the DNN in pattern III with field measurements.

c h

: coefficient of consolidation in the horizontal direction

c v

: coefficient of consolidation in the vertical direction

F c

: parameter to reflect the effect of the decay pattern

H

: soil thickness

k d

:coefficient of permeability of the drain

k h

:horizontal coefficient of permeability

k s

:horizontal coefficient of permeability of the smeared zone

k v

:vertical coefficient of permeability

m v

: coefficient of volume compressibility

q w

: discharge capacity

r d

: drain radius

r e

: equivalent radius of the influence zone

r s

: smeared zone radius

u

: excess pore water pressure

u ‾

: average excess pore water pressure

σ (t)

: the surcharge load

ε v

: vertical strain

γ w

: unit weight of water

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