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Front. Struct. Civ. Eng.    2021, Vol. 15 Issue (2) : 490-505    https://doi.org/10.1007/s11709-020-0669-5
RESEARCH ARTICLE
Application of machine learning algorithms for the evaluation of seismic soil liquefaction potential
Mahmood AHMAD1,2, Xiao-Wei TANG1, Jiang-Nan QIU3(), Feezan AHMAD4, Wen-Jing GU3
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. School of Economics & Management, Dalian University of Technology, Dalian 116024, China
4. Department of Civil Engineering, Abasyn University, Peshawar 25000, Pakistan
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Abstract

This study investigates the performance of four machine learning (ML) algorithms to evaluate the earthquake-induced liquefaction potential of soil based on the cone penetration test field case history records using the Bayesian belief network (BBN) learning software Netica. The BBN structures that were developed by ML algorithms-K2, hill climbing (HC), tree augmented naive (TAN) Bayes, and Tabu search were adopted to perform parameter learning in Netica, thereby fixing the BBN models. The performance measure indexes, namely, overall accuracy (OA), precision, recall, F-measure, and area under the receiver operating characteristic curve, were used to evaluate the training and testing BBN models’ performance and highlight the capability of the K2 and TAN Bayes models over the Tabu search and HC models. The sensitivity analysis results showed that the cone tip resistance and vertical effective stress are the most sensitive factors, whereas the mean grain size is the least sensitive factor in the prediction of seismic soil liquefaction potential. The results of this study can provide theoretical support for researchers in selecting appropriate ML algorithms and improving the predictive performance of seismic soil liquefaction potential models.
Keywords seismic soil liquefaction      Bayesian belief network      cone penetration test      parameter learning      structural learning     
Corresponding Author(s): Jiang-Nan QIU   
Just Accepted Date: 28 September 2020   Online First Date: 01 April 2021    Issue Date: 27 May 2021
 Cite this article:   
Mahmood AHMAD,Xiao-Wei TANG,Jiang-Nan QIU, et al. Application of machine learning algorithms for the evaluation of seismic soil liquefaction potential[J]. Front. Struct. Civ. Eng., 2021, 15(2): 490-505.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0669-5
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I2/490
machine learning algorithm description
K2 K2 [20] adds arcs with a fixed topological ordering of variables. In this method, the ordering is primarily set as a naive Bayes network where the target class variable is the first in the ordering.
HC HC [21] adds and deletes arcs with no fixed ordering of variables. This process is iterated unless the highest value of the measurement score (e.g., local Bayes) is achieved.
Tabu search Tabu search [22] is an optimal HC algorithm. This algorithm utilizes a Markov Blanket correction to the network structure after learning the network structure.
TAN Bayes In TAN Bayes [23], the tree is built by computing the maximum-weight spanning tree applying Chow and Liu’s algorithm [24].
Tab.1  Machine learning algorithms for the network structure
factor minimum maximum mean standard deviation coefficient of variation
earthquake magnitude, M 5.90 7.80 7.30 0.61 0.08
peak ground acceleration, amax (g) 0.10 0.60 0.28 0.13 0.47
cone tip resistance, qc (MPa) 0.38 26.00 6.41 5.24 0.82
mean grain size, D50 (mm) 0.016 0.48 0.17 0.10 0.61
vertical effective stress, s'v (kPa) 13.90 227.50 78.59 44.86 0.57
total vertical stress, sv (kPa) 16.70 296.30 114.43 66.25 0.58
Tab.2  Statistical aspects of the data set
factors of seismic soil liquefaction number of grade explanation range
earthquake magnitude, M 4 super
big
strong
medium		 8≤M
7≤M<8
6≤M<7
4.5≤M<6
peak ground acceleration, amax (g) 4 super
high
medium
low		 0.40≤amax
0.30≤amax<0.40
0.15≤amax<0.30
0≤amax<0.15
cone penetration resistance, qc (MPa) 4 super
big
medium
small		 10≤qc
7≤qc<10
3.5≤qc<7
0≤qc<3.5
mean grain size, D50 (mm) 4 super
big
medium
small		 2≤D50
0.425≤D50<2
0.075≤D50<0.425
0<D50<0.075
vertical effective stress, s'v (kPa) 4 super
big
medium
small		 150≤s'v
100≤s'v<150
50≤s'v<100
0≤s'v<50
total vertical stress, sv (kPa) 4 super
big
medium
small		 165≤sv
110≤sv<165
55≤sv<110
0≤sv<55
liquefaction potential 2 no
yes		 0
1
Tab.3  Grading standards for seismic soil liquefaction factors
earthquake D50 (mm) s′v (kPa) sv (kPa) amax (g) M qc (MPa) liquefaction
1964 Niigata 0.33? 35.3 52?? ?0.16 7.5 3.14 yes
0.33? 51?? 85.3 ?0.16 7.5 1.57 yes
0.33? 81.4 149.1? ?0.16 7.5 5.49 yes
0.33? 61.8 89.2 ?0.16 7.5 5.34 yes
0.33? 78.5 124.5? ?0.16 7.5 7.8? yes
0.33? 117.1? 206.9? ?0.16 7.5 9.51 yes
0.3?? 45.1 84.3 ?0.16 7.5 7.85 no
0.3?? 49?? 93.2 ?0.16 7.5 14.27? no
1971 San Fernando Valley 0.058 166.1? 167.6? 0.5 6.4 6.37 yes
0.073 182.6? 200.5? 0.5 6.4 6.86 yes
0.052 119.7? 125.7? 0.5 6.4 3.14 yes
0.045 138.9? 164??? 0.5 6.4 0.69 yes
0.16? 161.7? 209.5? 0.5 6.4 9.81 no
0.053 170.7? 227.4? 0.5 6.4 8.73 no
0.072 202.1? 290.3? 0.5 6.4 9.32 no
0.042 86.8 89.8 0.5 6.4 0.69 yes
0.095 146.7? 209.5? 0.5 6.4 10.79? no
0.069 152.7? 221.4? 0.5 6.4 13.73? no
0.082 190.2? 296.3? 0.5 6.4 6.86 no
0.072 95.8 98.8 0.5 6.4 1.96 yes
0.055 103.3? 113.7? 0.5 6.4 0.69 yes
0.067 146.7? 200.5? 0.5 6.4 0.69 no
0.13? 166.2? 239.4? 0.5 6.4 4.9? no
0.062 175.2? 257.4? 0.5 6.4 9.81 no
0.045 190.2? 287.3? 0.5 6.4 15.69? no
0.051 119.7? 122.7? 0.5 6.4 1.96 yes
0.1?? 130.2? 143.6? 0.5 6.4 1.96 yes
1975 Haicheng 0.07? 50?? 74.6 ?0.15 7.3 0.65 yes
0.08? 41.2 55.9 ?0.15 7.3 0.53 yes
0.02? 76.5 130.5? ?0.15 7.3 0.38 yes
0.016 45.6 65.2 ?0.15 7.3 1.3? yes
0.016 105.2? 191??? ?0.15 7.3 0.73 no
1976 Tangshan 0.25? 83.4 145.1? 0.4 7.8 5.59 yes
0.3?? 90.2 158.9? 0.4 7.8 7.45 yes
0.17? 16.7 16.7 0.4 7.8 1.47 yes
0.17? 20.6 24.5 0.4 7.8 0.98 yes
0.17? 24.5 33.3 0.4 7.8 4.9? yes
0.14? 33.3 37.3 0.4 7.8 2.45 yes
0.14? 42.2 55.9 0.4 7.8 2.55 yes
0.16? 51? 74.5 0.4 7.8 3.14 yes
0.16? 56.9 87.3 0.4 7.8 5.69 yes
0.16? 100???? 177.5? 0.4 7.8 8.24 yes
0.12? 34.3 50?? 0.4 7.8 4.02 yes
0.17? 26.5 28.4 0.4 7.8 5.39 yes
0.32 39.2 55.9 0.4 7.8 8.83 yes
0.48 20.6 22.6 0.4 7.8 6.86 yes
0.48 25.5 33.3 0.4 7.8 1.16 yes
0.48 32.4 47.1 0.4 7.8 4.16 yes
0.2? 108.9? 156.9? 0.4 7.8 15.46? no
0.14 73.5 97.1 0.2 7.8 17.42? no
0.17 76.5 87.3 0.2 7.8 1.62 yes
0.17 81.4 97.1 0.2 7.8 3.58 yes
0.31 36.3 53.9 0.2 7.8 4.9? yes
0.18 46.1 74.5 0.2 7.8 2.85 yes
0.18 59.8 103???? 0.2 7.8 5.94 yes
0.17 21.6 22.6 0.2 7.8 12.98? no
0.17 25.5 31.4 0.2 7.8 12.81? no
0.17 29.4 39.2 0.2 7.8 16.27? no
0.26 57.9 57.9 0.2 7.8 10.39? no
0.26 65.7 74.5 0.2 7.8 11.07? no
0.16 43.1 74.5 0.2 7.8 4.9? yes
0.14 46.1 68.6 0.2 7.8 2.2? yes
0.14 48.1 72.6 0.2 7.8 2.6? yes
0.16 34.3 52?? 0.2 7.8 4.31 yes
0.16 38.2 59.8 0.2 7.8 2.94 yes
0.08 79.4 153??? 0.2 7.8 8.83 yes
0.07 51?? 93.2 0.2 7.8 1.08 yes
0.08 103.9? 205??? 0.1 7.8 15.2?? no
0.08 107.9? 212.8? 0.1 7.8 6.37 no
0.1? 52?? 89.2 0.1 7.8 8.83 no
0.28 100??? 158.9? 0.1 7.8 18.57? no
0.16 43.1 43.1 0.2 7.8 3.45 yes
0.16 50?? 57.9 0.2 7.8 2.68 yes
0.21 51?? 59.8 0.2 7.8 4.04 yes
0.32 66.7 93.2 0.2 7.8 5.74 yes
0.13 47.1 48.1 0.2 7.8 1.84 yes
0.22 75.5 111.8? 0.2 7.8 7.85 no
?0.067 110.6? 223.6? 0.2 7.8 4.46 no
?0.067 120.4? 244.2? 0.2 7.8 5.68 no
?0.062 54.3 111.8? 0.2 7.8 2.43 yes
?0.062 55.3 118.7? 0.2 7.8 1.54 yes
?0.067 104.6? 215.7? 0.2 7.8 2.11 yes
?0.067 109.7? 225.5? 0.2 7.8 2.55 yes
?0.067 101.8? 208.9? 0.2 7.8 2.68 yes
?0.067 104.6? 214.8? 0.2 7.8 1.75 yes
?0.067 106.5? 206.9? 0.2 7.8 7.49 no
1977 Vrancea 0.2? 47.1 78.5 ?0.22 7.2 5.12 yes
0.2? 53.9 93.2 ?0.22 7.2 3.66 yes
0.2? 62.8 111.8 ?0.22 7.2 3.05 yes
0.2? 71.6 130.4 ?0.22 7.2 1.29 yes
0.2? 80.4 149.1 ?0.22 7.2 5.12 yes
1979 Imperial Valley 0.11 44.5 ?62.8 0.6 6.6 19.9?? no
0.11 44.5 ?62.8 0.6 6.6 1.8? yes
0.07 13.9 ?31.4 0.2 6.6 2?? yes
0.15 31.6 ?78.5 0.2 6.6 4.9? yes
1983 Nihonkai Cho 0.32 47.1 ?56.9 ?0.23 7.7 9.81 no
0.32 53? ?71.6 ?0.23 7.7 15.69? no
0.32 63.7 ?94.1 ?0.23 7.7 15.08? no
0.32 51? ?62.8 ?0.23 7.7 4.02 yes
0.32 65.7 ?94.1 ?0.23 7.7 7.8? yes
0.32 73.5 111.8 ?0.23 7.7 8.8? yes
1988 Sanguenay 0.1? 43.1 ?50.8 ?0.25 5.9 4.26 no
0.1? 53.1 ?70.4 ?0.25 5.9 4.91 no
0.1? 63? 90? ?0.25 5.9 2.76 yes
0.1? 72.8 109.6 ?0.25 5.9 5.71 no
0.1? 92.4 148.9 ?0.25 5.9 7.77 no
1989 Loma Prieta ?0.253 88.5 118.4 ?0.24 7.1 19??? no
?0.275 67.2 ?77.6 ?0.24 7.1 13.94? no
?0.361 78.9 100 ?0.24 7.1 18??? no
0.35 100.1? 140.9 ?0.24 7.1 13??? no
0.16 83.6 115 ?0.24 7.1 0.75 yes
0.07 66.2 108.9 ?0.16 7.1 1.9? yes
0.27 87.1 128.8 ?0.29 7.1 4.7? yes
0.26 100.6? 154.5 ?0.29 7.1 10??? yes
0.3? 82.4 111.8 ?0.29 7.1 8.7? yes
0.3? 84.6 116.5 ?0.29 7.1 6.5? yes
0.22 50.5 ?65.2 ?0.27 7.1 5.3? yes
0.22 50.5 ?65.2 0.3 7.1 6.1? yes
0.22 54.9 ?74.6 0.3 7.1 26??? no
Tab.4  Summary of training data
earthquake D50 (mm) s'v (kPa) sv (kPa) amax (g) M qc (MPa) liquefaction
1964 Niigata 0.33 56.9 ?97.1 ?0.16 7.5 ?7.06 yes
1971 San Fernando Valley 0.4? 212.5? 260.3 0.5 6.4 11.77 no
?0.068 218.5? 272.3 0.5 6.4 19.32 no
?0.044 227.5? 290.3 0.5 6.4 21.57 no
0.07 154.2? 194.5 0.5 6.4 ?1.77 no
?0.057 182.7? 251.4 0.5 6.4 ?5.39 no
0.05 131.7? 179.6 0.5 6.4 ?7.06 no
0.06 178.2? 272.3 0.5 6.4 ?8.83 no
?0.038 110.8? 128.7 0.5 6.4 ?2.94 yes
?0.059 155.7? 218.5 0.5 6.4 ?1.96 no
0.24 154.2? 191.5 0.5 6.4 20.6? no
1975 Haicheng ?0.035 80.9 139.8 ?0.15 7.3 1.2 yes
1976 Tangshan 0.06 41.2 ?55.9 0.4 7.8 ?1.67 yes
0.25 67.7 111.8 0.4 7.8 ?9.22 yes
0.16 72.6 119.6 0.4 7.8 ?3.43 yes
0.12 28.4 ?37.3 0.4 7.8 ?1.67 yes
0.12 28.4 ?39.2 0.4 7.8 ?3.43 yes
0.16 69.6 ?74.5 0.4 7.8 11.25 no
0.21 54.9 ?57.9 0.2 7.8 11.17 no
0.21 63.7 ?76.5 0.2 7.8 11.89 no
0.19 24.5 ?28.4 0.2 7.8 ?1.01 yes
0.26 59.8 ?61.8 0.2 7.8 ?8.94 no
0.16 40.2 ?68.6 0.2 7.8 1.9 yes
0.14 53.9 ?97.1 0.1 7.8 ?1.96 yes
0.1? 56.9 99? 0.1 7.8 ?2.45 no
0.1? 61.8 109.8 0.1 7.8 16.18 no
0.25 66.7 ?89.2 0.1 7.8 13.39 no
0.25 77.5 111.8 0.1 7.8 13.85 no
0.21 49? ?55.9 0.2 7.8 ?3.23 yes
0.21 55.9 ?70.6 0.2 7.8 ?2.88 yes
0.15 51? ?59.8 0.2 7.8 ?2.94 yes
0.32 77.6 103.9 0.2 7.8 ?8.83 yes
0.17 62.8 ?72.6 0.2 7.8 2.5 yes
0.17 63.7 ?74.5 0.2 7.8 ?4.41 yes
0.17 77.5 103.9 0.2 7.8 ?4.16 yes
?0.062 57.2 111.8 0.2 7.8 ?8.31 no
?0.067 101.8? 208.9 0.2 7.8 ?1.42 yes
1979 Imperial Valley 0.08 44.5 ?62.8 0.6 6.6 7? no
1983 Nihonkai Cho 0.32 45.1 53? ?0.23 7.7 ?1.76 yes
1988 Sanguenay 0.1? 82.6 129.3 ?0.25 5.9 ?6.51 no
0.1? 102.2? 168.5 ?0.25 5.9 ?7.77 no
1989 Loma Prieta ?0.303 84?? 118.4 ?0.24 7.1 16.75 no
?0.239 63?? ?69.4 ?0.24 7.1 ?9.75 no
?0.178 59.1 ?64.1 ?0.24 7.1 ?3.35 yes
?0.197 81.8 120.6? 0.24 7.1 1.2 yes
?0.244 117.1? 131.9? 0.24 7.1 5.5 no
0.1? 36.4 45.6 0.14 7.1 1.3 yes
0.1? 39.5 44.1 0.14 7.1 1.5 yes
0.12 51.8 60.4 0.14 7.1 2.5 no
0.07 66.2 108.9? 0.16 7.1 1.7 yes
0.07 66.2 108.9? 0.16 7.1 1.5 yes
Tab.5  Summary of testing data
seismic soil liquefaction factor data set minimum maximum mean standard deviation coefficient of variation
earthquake magnitude, M training 5.9 7.8 7.31 0.60 0.08
testing 5.9 7.8 7.27 0.62 0.09
peak ground acceleration, amax (g) training 0.1 0.6 0.29 0.13 0.45
testing 0.1 0.6 0.28 0.15 0.52
cone penetration resistance, qc (MPa) training 0.38 26 6.39 5.13 0.80
testing 1.01 21.57 6.46 5.54 0.86
mean grain size, D50 (mm) training 0.016 0.48 0.17 0.11 0.62
testing 0.035 0.4 0.16 0.09 0.58
vertical effective stress, s'v (kPa) training 13.9 202.1 76.40 42.25 0.55
testing 24.5 227.5 83.68 50.50 0.60
total vertical stress, sv (kPa) training 16.7 296.3 114.04 65.71 0.58
testing 28.4 290.3 115.34 68.13 0.59
Tab.6  Ranges of seismic soil liquefaction factors for training and testing data sets
Fig.1  Bayesian belief network through different machine learning algorithms. (a) K2; (b) HC; (c) TAN Bayes; (d) Tabu search.
Fig.2  BBN machine learning models after parameter learning in Netica 6.02. (a) K2; (b) HC; (c) TAN Bayes; (d) Tabu search.
item predicted class gross
yes no
actual class yes true positive (TP) false negative (FN) actual positive, AP = TP + FN
no false positive (FP) true negative (TN) actual negative, AN = FP + TN
gross predicted positive, PP = TP + FP predicted negative, PN = FN + TN TP + FN + FP + TN
Tab.7  Typical confusion matrix
Fig.3  Overall procedure flowchart for machine learning algorithms for seismic soil liquefaction potential evaluation.
model data set OA (%) AUC liquefaction non-liquefaction
precision recall F-measure precision recall F-measure
BBN-K2 training 97.4790 0.9836 0.9747 0.9872 0.9809 0.9750 0.9512 0.9630
testing 84.3137 0.8954 0.8750 0.8077 0.8400 0.8148 0.8800 0.8462
BBN-HC training 94.1176 0.9653 0.9277 0.9872 0.9565 0.9722 0.8537 0.9091
testing 78.4314 0.8538 0.7778 0.8077 0.7925 0.7917 0.7600 0.7755
BBN-TAN Bayes training 97.4790 0.9830 0.9747 0.9872 0.9809 0.9750 0.9512 0.9630
testing 84.3137 0.9054 0.8750 0.8077 0.8400 0.8148 0.8800 0.8462
BBN-Tabu search training 89.0756 0.9437 0.8916 0.9487 0.9193 0.8889 0.7805 0.8312
testing 84.3137 0.9308 0.7647 1.0000 0.8667 1.0000 0.6800 0.8095
Tab.8  Performance comparison of BBN machine learning models
node BBN-K2 BBN-HC BBN-Tabu search BBN-TAN Bayes
mutual info percent variance of beliefs mutual info percent variance of beliefs mutual info percent variance of beliefs mutual info percent variance of beliefs
liquefaction 0.99623 100.00000 0.24869 0.99430 100.00000 0.24803 0.96275 100.00000 0.23720 0.99151 100.00000 0.24706
cone tip resistance 0.00500 0.50200 0.00173 0.00947 0.95300 0.00326 0.20065 20.80000 0.06240 0.01880 1.90000 0.00645
vertical effective stress 0.00163 0.16400 0.00056 0.00244 0.24500 0.00084 0.04050 4.21000 0.01346 0.00577 0.58200 0.00198
total vertical stress 0.00140 0.14000 0.00048 0.00236 0.23700 0.00081 0.01221 1.27000 0.00408 0.00371 0.37400 0.00128
earthquake magnitude 0.00106 0.10700 0.00037 0.00008 0.00768 0.00003 0.00050 0.05210 0.00017 0.00607 0.61200 0.00208
peak ground acceleration 0.00056 0.05630 0.00019 0.00090 0.09050 0.00031 0.00222 0.23100 0.00073 0.00374 0.37700 0.00128
mean grain size 0.00055 0.05520 0.00019 0.00055 0.05570 0.00019 0.00009 0.00888 0.00003 0.00086 0.08650 0.00030
Tab.9  Sensitivity analysis result comparisons of seismic soil liquefaction
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