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Front. Struct. Civ. Eng.    2021, Vol. 15 Issue (1) : 80-98    https://doi.org/10.1007/s11709-021-0682-3
TRANSDISCIPLINARY INSIGHT
Evaluation of liquefaction-induced lateral displacement using Bayesian belief networks
Mahmood AHMAD1,2, Xiao-Wei TANG1, Jiang-Nan QIU3(), Feezan AHMAD4
1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
2. Department of Civil Engineering, University of Engineering and Technology Peshawar (Bannu Campus), Bannu 28100, Pakistan
3. Faculty of Management and Economics, Dalian University of Technology, Dalian 116024, China
4. Department of Civil Engineering, Abasyn University, Peshawar 25000, Pakistan
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Abstract

Liquefaction-induced lateral displacement is responsible for considerable damage to engineered structures during major earthquakes. Therefore, an accurate estimation of lateral displacement in liquefaction-prone regions is an essential task for geotechnical experts for sustainable development. This paper presents a novel probabilistic framework for evaluating liquefaction-induced lateral displacement using the Bayesian belief network (BBN) approach based on an interpretive structural modeling technique. The BBN models are trained and tested using a wide-range case-history records database. The two BBN models are proposed to predict lateral displacements for free-face and sloping ground conditions. The predictive performance results of the proposed BBN models are compared with those of frequently used multiple linear regression and genetic programming models. The results reveal that the BBN models are able to learn complex relationships between lateral displacement and its influencing factors as cause–effect relationships, with reasonable precision. This study also presents a sensitivity analysis to evaluate the impacts of input factors on the lateral displacement.
Keywords Bayesian belief network      seismically induced soil liquefaction      interpretive structural modeling      lateral displacement     
Corresponding Author(s): Jiang-Nan QIU   
Just Accepted Date: 07 February 2021   Online First Date: 24 March 2021    Issue Date: 12 April 2021
 Cite this article:   
Mahmood AHMAD,Xiao-Wei TANG,Jiang-Nan QIU, et al. Evaluation of liquefaction-induced lateral displacement using Bayesian belief networks[J]. Front. Struct. Civ. Eng., 2021, 15(1): 80-98.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-021-0682-3
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I1/80
method technique reference
simplified analytical methods sliding block model Newmark [3], Olson and Johnson [4], Yegian et al. [5], Baziar [6],
minimum potential energy model Towhata et al. [7]
shear strength loss and strain re-hardening model Byrne [8]
viscous model Hamada et al. [9]
numerical
methods		 finite element method and finite difference techniques Soroush and Koohi [10], Finn et al. [11]
soft computing methods neural networks Baziar and Ghorbani [12], Wang and Rahman [13]
genetic programming (GP) Javadi et al. [14]
adaptive neuro-fuzzy inference system Javdanian [15]
empirical methods regression analysis Jafarian and Nasri [16], Youd et al. [17], Youd and Perkins [18], Raunch [19], Bardet et al. [20], Hamada et al. [21]
Tab.1  Methods for lateral displacement evaluation
Fig.1  Working procedure for BBN-based liquefaction-induced lateral displacement evaluation.
Fig.2  Topography-related descriptive variables.
earthquake year no. of records no. of free face records no. of ground slope records fault type input and output parameters
W (%) S (%) R (km) PGA (g) M D5015 (mm) T15 (m) F15 (%) DH (m)
San Francisco, California, United States 1906 ??2 ??2 ??0 SS 17.76–22.02 NA 24–27 0.24–0.26 7.9 0.16–0.25 1.50–7.20 23–30 0.92–1.84
Anchorage, Alaska, United States 1964 ??7 ??4 ??3 R 7.03–48.98 0.05–0.10 35–100 0.20–0.24 9.2 0.07–1.47 3.10–19.70 12.0–66.0 0.31–2.45
Niigata, Japan 1964 299 139 160 R 1.64–55.68 0.11–1.09 21 0.32 7.5 0.10–0.59 0.50–16.70 2.0–32.0 0.42–10.16
San Fernando, California, United States 1971 ?23 ?18 ??5 RO 4.70–20.47 1.23 0.2–0.5 0.68–0.70 6.4 0.06–0.08 1.00–6.50 47–59 0.47–3.26
Imperial Valley, California, United States 1979 ?31 ?29 ??2 SS 3.08–10.66 0.56 2.0–6.0 0.36–0.49 6.5–6.6 0.04–0.12 0.20–4.00 15–70 0.01–4.25
Nihonkai-Chubu, Japan 1983 ?72 ?0 ?72 R NA 0.20–5.90 27 0.29 7.7 0.35 1.00–3.70 0–4 0.38–3.11
Borah Peak, Idaho, United States 1983 ??4 ?0 ??4 N NA 11 2 0.51 6.9 2.30–12.00 0.01–3.00 16–29 0.01–1.01
Superstition Hills, California United States 1987 ??6 ?6 ??0 SS 7.50–41.38 NA 23 0.15 6.6 0.07–0.09 1.70–3.60 22–44 0.01–0.24
Loma Prieta, California, United States 1989 ??2 ?2 ??0 RO 29.73–33.54 NA 27.2 0.2 7 0.60–0.80 2.70–3.40 1.0–2.0 0.26–0.29
Hyogo-Ken Nanbu (Kobe), Japan 1995 ?19 ?19 ??0 SS 5.16–56.80 NA 5.5–8.0 0.34–0.39 6.8 0.47–1.98 12.50–16.0 10–14.60 0.34–2.83
Chi-Chi, Taiwan China 1999 ?26 ?26 ??0 R 5.70–57.70 NA 5.00 0.67 7.6 0.10–0.18 0.45–1.80 13.00–48.50 0–2.96
Koacaeli, Turkey 1999 ??2 ??2 ??0 SS 6–8 NA 0.50 0.57 7.4 0.55–7.70 1.20–1.70 11.00–31.00 0.10–0.90
Tab.2  Summary of case studies in database and their respective parameter statistics
category factor (FRi) factors of liquefaction-induced lateral displacement number of grade explanation range
seismic parameter FR1 earthquake magnitude, M 4 super
big
strong
medium		 8≤M
7≤M<8
6≤M<7
4.5≤M<6
FR2 closest horizontal distance to seismic energy source, R (km) 4 super
far
medium
near		 100<R
50<R≤100
10<R≤50
0<R≤10
FR3 peak ground acceleration (PGA), amax (g) 4 super
high
medium
low		 0.40≤amax
0.30≤amax<0.40
0.15≤amax<0.30
0≤amax<0.15
geotechnical parameter FR4 average fines content (particles<0.075 mm) in T15, F15 (%) 3 many
medium
less		 50<F15
30<F15≤50
0≤F15≤30
FR5 average mean grain size in T15, D5015 (mm) 4 super
big
medium
small		 2≤D5015
0.425≤D5015<2
0.075≤D5015<0.425
0<D5015<0.075
FR6 cumulative thickness of saturated layers with corrected SPT number (N1)60<15, T15 (m) 3 thick
medium
thin		 10≤T15
5≤T15<10
0<T15<5
topographic parameters FR7 free-face ratio, W (%) 3 high
medium
low		 20<W
10≤W≤20
1<W<10
slope of surface topography, S (%) 2 steep
gentle		 6<S
S≤6
output FR8 lateral displacement (LD), DH (m) 4 none
small
medium
large		 0
0<DH≤0.1
0.1<DH≤0.3
0.3<DH
Tab.3  Grading standards for liquefaction-induced lateral displacement factors
category factors of liquefaction-induced lateral displacement data set minimum maximum mean standard deviation
seismic parameter earthquake magnitude, M T 6.4 9.2 7.26 0.51
T* 6.4 9.2 7.3 0.49
closest horizontal distance to seismic energy source, R (km) T 0.5 100 15.1 11.61
T* 0.5 60 16.1 10.61
peak ground acceleration (PGA), amax (g) T 0.15 0.68 0.4 0.15
T* 0.15 0.68 0.38 0.13
geotechnical parameter average fines content (particles<0.075 mm) in T15, F15 (%) T 1 70 18.83 13.71
T* 2 66 13.96 12.14
average mean grain size in T15, D5015 (mm) T 0.04 7.7 0.36 0.65
T* 0.07 1.98 0.39 0.42
cumulative thickness of saturated layers with corrected SPT number (N1)60<15, T15 (m) T 0.2 16.7 7.8 5.16
T* 0.5 16 7.98 5.2
topographic parameters free-face ratio, W (%) T 1.64 57.7 11.69 9.96
T* 2.11 48.98 10.08 9.77
output lateral displacement (LD), DH (m) T 0 10.16 2.45 2.26
T* 0 8.39 2.17 2.21
Tab.4  Parameter statistics used in development of free-face model
category factors of liquefaction-induced lateral displacement data set minimum maximum mean standard deviation
seismic parameter earthquake magnitude, M T 6.4 9.2 7.53 0.29
T* 6.6 9.2 7.59 0.29
closest horizontal distance to seismic energy source, R (km) T 0.2 100 22.16 7.82
T* 6 100 24.39 11.65
peak ground acceleration (PGA), amax (g) T 0.2 0.7 0.32 0.07
T* 0.2 0.36 0.3 0.02
geotechnical parameter average fines content (particles<0.075 mm) in T15, F15 (%) T 0 59 9.03 10.62
T* 0 68 7.69 10.33
average mean grain size in T15, D5015 (mm) T 0.06 12 0.46 1.11
T* 0.07 0.65 0.34 0.08
cumulative thickness of saturated layers with corrected SPT number (N1)60<15, T15 (m) T 0.01 19.7 6.69 3.8
T* 0.07 13.1 6.35 3.75
topographic parameters slope of surface topography, S (%) T 0.1 11 0.96 1.61
T* 0.05 5.9 0.99 1.27
output lateral displacement (LD), DH (m) T 0.01 5.36 1.91 0.95
T* 0.01 3.5 1.87 0.89
Tab.5  Parameter statistics used in development of sloping ground model
FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 factor (FRi)
O V O O O O V FR1
V O O O O V FR2
O O O O V FR3
V O O V FR4
O O V FR5
O V FR6
V FR7
FR8
Tab.6  SSIM for liquefaction-induced lateral displacement factors
FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 factor (FRi)
1 0 1 0 0 0 0 1 FR1
0 1 1 0 0 0 0 1 FR2
0 0 1 0 0 0 0 1 FR3
0 0 0 1 1 0 0 1 FR4
0 0 0 0 1 0 0 1 FR5
0 0 0 0 0 1 0 1 FR6
0 0 0 0 0 0 1 1 FR7
0 0 0 0 0 0 0 1 FR8
Tab.7  IRM for liquefaction-induced lateral displacement factors
FRi FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 driving power
FR1 1 0 1 0 0 0 0 1 3
FR2 0 1 1 0 0 0 0 1 3
FR3 0 0 1 0 0 0 0 1 2
FR4 0 0 0 1 1 0 0 1 3
FR5 0 0 0 0 1 0 0 1 2
FR6 0 0 0 0 0 1 0 1 2
FR7 0 0 0 0 0 0 1 1 2
FR8 0 0 0 0 0 0 0 1 1
dependence power 1 1 3 1 2 1 1 8 18/18
Tab.8  FRM for liquefaction-induced lateral displacement factors
iteration factor (FRi) reachability set R(FRi) antecedent set A(FRi) intersection set R(FRi) ∩ A(FRi) level (Li)
1 1 1,3,8 1 1 –
2 2,3,8 2 2 –
3 3,8 1,2,3 3 –
4 4,5,8 4 4 –
5 5,8 4,5 5 –
6 6,8 6 6 –
7 7,8 7 7 –
8 8 1,2,3,4,5,6,7,8 8 L1
2 1 1,3 1 1 –
2 2,3 2 2 –
3 3 1,2,3 3 L2
4 4,5 4 4 –
5 5 4,5 5 L2
6 6 6 6 L2
7 7 7 7 L2
3 1 1 1 1 L3
2 2 2 2 L3
4 4 4 4 L3
Tab.9  Level partitions by iteration
Fig.3  Interpretive structural modeling of LD for (a) free-face and (b) sloping ground conditions.
Fig.4  Graphical result presentation of BBN-based LD models for (a) free-face and (b) sloping ground conditions.
predicted actual total UA (%)
1 2 … m
1 r11 r21 … r1m r1+ (r11/r1+ ) × 100%
2 r21 r22 … r2m r2+ (r22/r2+ ) × 100%
… … … … … … …
m rm1 rm2 … rmm rm+ (rmm/rm + ) × 100%
total r+1 r+1 … r+m
PA (%) (r11/r+1) × 100% (r22/r+2) × 100% … (rmm/r+m) × 100%
Tab.10  Confusion matrix
kappa statistic interpretation
0.81–1.00 almost perfect
0.61–0.80 substantial
0.41–0.60 moderate
0.21–0.40 fair
0.00–0.20 slight
- 1.00–0.00 poor
Tab.11  Strength agreement measure related to kappa statistic
predicted observed total UA (%)
none small medium large
none 0 0 0 0 0 –
small 0 3 0 0 3 100
medium 0 0 4 1 5 80
large 3 0 0 187 190 98.421
total 3 3 4 188 198
PA (%) 0 100 100 99.5 OA= 97.98% kappa= 0.771
Tab.12  Confusion matrix and performance measures of BBN–W model based on training data set of lateral displacement for free-face condition
predicted observed total UA (%)
none small medium large
none 0 0 0 0 0 –
small 0 1 0 0 1 100
medium 0 0 0 0 0 –
large 0 1 0 195 196 99.49
total 0 2 0 195 197
PA (%) – 50 – 100 OA= 99.492% kappa= 0.664
Tab.13  Confusion matrix and performance measures of BBN–S model based on training data set of lateral displacement for sloping ground condition
predicted observed total UA (%)
none small medium large
BBN–W model
none 0 1 0 1 2 0
small 0 0 0 0 0 -
medium 0 0 3 0 3 100
large 1 1 3 39 44 88.636
total 1 2 6 40 49
PA (%) 0 0 50 97.5 OA= 85.714% kappa= 0.448
Javadi et al. [14]–GP model
none 0 0 0 0 0 -
small 0 0 0 0 0 -
medium 0 0 1 0 1 100
large 1 2 5 40 48 83.33
total 1 2 6 40 49
PA (%) 0 0 16.67 100 OA= 83.673% kappa= 0.175
Bardet et al. [20]–MLR model
none 0 0 0 0 0 -
small 0 0 1 2 3 0
medium 0 0 0 2 2 0
large 1 2 5 36 44 81.8181
total 1 2 6 40 49
PA (%) 0 0 0 90 OA= 73.469% kappa= - 0.022
Jafarian and Nasri [16]–MLR model
none 0 0 0 0 0 -
small 0 0 1 0 1 0
medium 0 0 1 0 1 100
large 1 2 4 40 47 85.106
total 1 2 6 40 49
PA (%) 0 0 16.67 100 OA= 83.673% kappa= 0.236
Tab.14  Confusion matrices and performance measures based on testing data set of lateral displacement for free-face condition
predicted observed total UA (%)
none small medium large
BBN–S model
none 0 0 0 0 0 -
small 0 1 0 0 1 100
medium 0 0 0 0 0 -
large 0 0 0 48 48 100
total 0 1 0 48 49
PA (%) - 100 - 100 OA= 100% kappa= 1.0
Javadi et al. [14]–GP model
none 0 1 0 0 1 0
small 0 0 0 0 0 -
medium 0 0 0 1 1 0
large 0 0 0 47 47 100
total 0 1 0 48 49
PA (%) - 0 - 97.92 OA= 95.918% kappa= 0.324
Bardet et al. [20]–MLR model
none 0 1 0 0 1 0
small 0 0 0 0 0 -
medium 0 0 0 1 1 0
large 0 0 0 47 47 100
total 0 1 0 48 49
PA (%) - 0 - 97.92 OA= 95.918% kappa= 0.324
Jafarian and Nasri [16]–MLR model
none 0 0 0 0 0 -
small 0 1 0 0 1 100
medium 0 0 0 0 0 -
large 0 0 0 48 48 100
total 0 1 0 48 49
PA (%) - 100 - 100 OA= 100% kappa= 1.0
Tab.15  Confusion matrices and performance measures based on testing data set of lateral displacement for sloping ground condition
node BBN–W BBN–S
mutual variance of mutual variance of
info beliefs info beliefs
lateral displacement 1.74898 0.4540909 1.42415 0.3294491
peak ground acceleration 0.07718 0.0129344 0.12110 0.0209899
D5015 0.02282 0.0032952 0.05334 0.0070218
earthquake magnitude, M 0.01737 0.0031323 0.01358 0.0023004
free-face ratio, W 0.01363 0.0025745 - -
R 0.00494 0.0009073 0.01185 0.0020273
F15 0.00103 0.0001581 0.01884 0.0024999
T15 0.00097 0.0001781 0.00557 0.0012092
slope of surface topography, S - - 0.01413 0.0015986
Tab.16  Sensitivity analysis of “lateral displacement” using proposed BBN models
  Fig. A-1 Graphical result of lateral displacement prediction of single sample when evidence states are known in proposed BBN models for (a) free-face and (b) sloping ground conditions.
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