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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (5) : 1066-1082     https://doi.org/10.1007/s11709-020-0651-2
TRANSDISCIPLINARY INSIGHT
A constrained neural network model for soil liquefaction assessment with global applicability
Yifan ZHANG, Rui WANG(), Jian-Min ZHANG, Jianhong ZHANG
Department of Hydraulic Engineering, State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
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Abstract

A constrained back propagation neural network (C-BPNN) model for standard penetration test based soil liquefaction assessment with global applicability is developed, incorporating existing knowledge for liquefaction triggering mechanism and empirical relationships. For its development and validation, a comprehensive liquefaction data set is compiled, covering more than 600 liquefaction sites from 36 earthquakes in 10 countries over 50 years with 13 complete information entries. The C-BPNN model design procedure for liquefaction assessment is established by considering appropriate constraints, input data selection, and computation and calibration procedures. Existing empirical relationships for overburden correction and fines content adjustment are shown to be able to improve the prediction success rate of the neural network model, and are thus adopted as constraints for the C-BPNN model. The effectiveness of the C-BPNN method is validated using the liquefaction data set and compared with that of several liquefaction assessment methods currently adopted in engineering practice. The C-BPNN liquefaction model is shown to have improved prediction accuracy and high global adaptability.

Keywords soil liquefaction assessment      case history dataset      constrained neural network model      existing knowledge     
Corresponding Author(s): Rui WANG   
Just Accepted Date: 28 June 2020   Online First Date: 14 September 2020    Issue Date: 16 November 2020
 Cite this article:   
Yifan ZHANG,Rui WANG,Jian-Min ZHANG, et al. A constrained neural network model for soil liquefaction assessment with global applicability[J]. Front. Struct. Civ. Eng., 2020, 14(5): 1066-1082.
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http://journal.hep.com.cn/fsce/EN/10.1007/s11709-020-0651-2
http://journal.hep.com.cn/fsce/EN/Y2020/V14/I5/1066
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Yifan ZHANG
Rui WANG
Jian-Min ZHANG
Jianhong ZHANG
label year country earthquake number
alla) liqb) non-liqc)
1 1962 China Heyuan ?1 0 1
2 1966 Xingtai (Mar 8) ?8 4 4
3 1966 Xingtai (Mar 22) ?7 7 0
4 1967 Hejian ?2 2 0
5 1969 Bohai ?5 5 0
6 1969 Yangjiang ?4 3 1
7 1970 Tonghai 32 17? 15?
8 1975 Haicheng 16 10? 6
9 1976 Tangshan 99 60? 39?
10 1999 Chi-Chi 82 55? 27?
11 2003 Bachu 47 21? 25?
12 1944 Japan Tohnankai ?3 3 0
13 1948 Fukui ?2 2 0
14 1964 Niigata 12 8 4
15 1968 Hososhima ?1 0 1
16 1968 Tokachi-Oki ?5 3 2
17 1978 Miyagiken-Oki (Feb 20) 14 1 13?
18 1978 Miyagiken-Oki (Jun 12) 20 14? 6
19 1980 Mid-Chiba ?2 0 2
20 1982 Urakawa-Oki ?1 0 1
21 1983 Nihonkai-Chubu 32 17? 15?
22 1984 Hososhima ?1 0 1
23 1995 Kobe 54 25? 29?
24 2011 Tohoku 55 49? 6
25 1971 USA San Fernando ?2 2 0
26 1979 Imperial Vally ?9 4 5
27 1987 Superstition Hills 12 1 11?
28 1989 Loma Prieta 25 16? 9
29 1994 Northridge ?4 3 1
30 1976 Guatemala Guatemala ?3 2 1
31 1977 Argentina Argentina ?5 3 2
32 1981 Britain West Morland ?7 3 4
33 1990 Philippines Luzon ?3 2 1
34 1999 Turkey Kocaeli 14 12? 2
35 2010 Haiti Haiti 13 11? 2
36 2010 Chile Chile 15 12? 3
total 617? 377?? 240??
Tab.1  An overview of the liquefaction data set compiled in this study
data sets Cetin 00 BI 14 Xie 84 this paper
liquefaction cases 109 135 125 377
non-liquefaction cases 88 115 76 240
data entries 9 10 9 13
critical depth (m) 1.1–20.5 1.8–14.3 0.5–18.5 0.5–23.5
effective stress (kPa) 8.1–198.7 20.3–170.9 4.3–185.5 4.0–230.4
fines content (%) 0–92 0–92 0–96
Nl (60cs) 2.2–66.1 4.6–63.7 1.4–66.0 1–69
cyclic stress ratio 0.05–0.66 0.04–0.69 0.04–0.78 0.03–0.84
magnitude 5.9–8.0 5.9–8.3 6.3–7.8 5.9–9.0
data sources
?China 9 21 174 303
?Japan 144 147 24 202
?USA 39 50 3 52
?others 5 32 0 60
Tab.2  Comparison between the data set in this study and three existing data sets
Fig.1  Data distribution of each information entry: (a) Mw; (b) amax; (c) ds; (d) dw; (e) sv; (f) sv´; (g) SPT-N; (h) FC; (i) ST; (j) CC; (k) D50; (l) ET. Note: 1) Soil types (ST) include clean sands (1-S), sands with fines (2-SF), silty sands, sand-silt mixture (3-SM), and silts and very fine sands, silty of clayey fine sands or clayey silts with slight plasticity (4-ML); 2) Earthquake type (ET) include combinations of various earthquake mechanisms (1-intraplate earthquakes, 2-interplate earthquakes and 3-subduction-zone earthquakes) and time distributions (1-isolated-shock, 2-double-shock, 3-main-shock, and 4-multi-shock). The correspondence of labels in Fig. 1(l) with earthquake mechanisms and time distributions are: 1= 1-1, 2= 1-2, 3= 1-3, 4= 1-4; 5= 2-1, 6= 2-2, 7= 2-3; 8= 2-4; 9= 3-1, 10= 3-2, 11= 3-3, 12= 3-4. 3. ‘<a’ in (e) indicates sv>300 kPa, ‘<b’ in (f) indicates sv´>200 kPa, ‘<c’ in (g) indicates SPT-N>40, ‘<d’ in (h) indicates FC>50%, and ‘<e’ in (k) indicates D50>0.55 mm.
Fig.2  Structure of the constrained BPNN (C-BPNN) model. Note: Pk is the input data, Tk is the target output, Sk and Bk are the input and output of hidden layer, Lk and Ok are the input and output of output layer, where k is the label of input sample with k = 1,2,…,m, and m is the number of input samples. wij, qj and vj, γ (i = 1,2,…,n, j = 1,2,…,p) are the connection weights and thresholds of input-hidden layer and hidden-output layer, respectively, where n is the number of input entries and p is the number of hidden neurons.
Fig.3  Illustration of the process of 5-fold cross validation.
Fig.4  The influence of momentum factor β on C-BPNN liquefaction assessment model: (a) PSR in liquefaction sites; (b) PSR in non-liquefaction sites; (c) PSR in all sites. Note: The legend shows parameters of the computation models. For simplicity, the computation model with number of hidden neurons p = 3 and learning rate α = 0.2 is abbreviated as 3-0.2 model.
Fig.5  The influence of learning rate α on C-BPNN liquefaction assessment model: (a) PSR in liquefaction sites; (b) PSR in non-liquefaction sites; (c) PSR in all sites. Note: The numbers in the legend indicate the number of hidden neurons.
Fig.6  The influence of hidden neuron number p on C-BPNN liquefaction assessment model: (a) PSR in liquefaction sites; (b) PSR in non-liquefaction sites; (c) PSR in all sites; (d) the Egeneral of C-BPNN liquefaction assessment models with different hidden neuron number p.
combinations input entry characteristics
8-entry Mw, amax, ds, dw, sv, sv´, N, FC basic information
11-entry + D50, CC, ST additional information for soil property
12-entry + ET additional information for earthquake type
Tab.3  Different combinations of input data entry
basic database year country earthquake main characteristics
1 1966 China Xingtai (Mar 8) shallow ground liquefaction with small earthquake magnitude
1966 China Xingtai (Mar 22) shallow ground liquefaction with medium magnitude
1976 China Tangshan medium ground liquefaction with large magnitude (right-beneath-city type earthquake)
1978 Japan Miyagiken-Oki (Feb 20) medium ground liquefaction with small earthquake magnitude
1978 Japan Miyagiken-Oki (Jun 12) medium ground liquefaction with medium earthquake magnitude
1989 USA Loma Prieta medium ground liquefaction with small earthquake magnitude
1994 USA Northridge deep ground liquefaction with large acceleration
1995 Japan Hyogoken-Nambu (Kobe) gravel sand liquefaction with right-beneath-city type earthquake
1999 Turkey Kocaeli high fines content
2 1968 Japan basic data set-1+Tokachi-Oki shallow ground liquefaction with large earthquake magnitude
3 2011 Japan basic data set-1+Tohoku abundant liquefaction case histories
4 1981 UK basic data set-1+West Morland high fines content with small earthquake magnitude
5 1994 USA basic data set-1-Northridge deep ground liquefaction with large acceleration
Tab.4  Basic information and main characteristics of 5 different basic data sets
Fig.7  Input data set selection for C-BPNN liquefaction assessment method: (a) PSR in liquefaction sites; (b) PSR in non-liquefaction sites; (c) PSR in all sites.
Fig.8  Constraint selection of C-BPNN liquefaction assessment method: (a) PSR in liquefaction sites; (b) PSR in non-liquefaction sites; (c) PSR in all sites. Note: BPNN on the x-coordinate refers to a model without any consideration of constraints. CN + Δ(Nl) 60 indicates the combination of constraints CN and Δ(Nl) 60.
Fig.9  Prediction of liquefaction case histories by different liquefaction assessment methods: (a) CSDB01 method; (b) CSDB10 method; (c) T-Y method; (d) JRA method; (e) NCEER method; (f) B-I14 method; (g) C-BPNN method; (h) comparison of the number of sites correctly predicted.
Fig.10  Comparison of overall PSR of different liquefaction assessment methods.
Fig.11  Liquefaction assessment for two typical boreholes in the 1999 Chi-Chi earthquake using seven different methods (data derived from Juang [43]). (a) Site 1: Boring log, SPT-N value, fines content, clay content, and prediction results at a site in Nantou (Hole No. NT-BH-3) (Liq= Liquefaction); (b) Site 2: Boring log, SPT-N value, fines content, clay content, and prediction results at a site in Wufeng (Hole No.WF-BH-8) (Non-liq= Non-liquefaction).
Fig.12  Contribution of various factors influencing liquefaction triggering. (a) 12-entry combination; (b) 8-entry combination.
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