- freely available
Appl. Sci. 2019, 9(20), 4226; https://doi.org/10.3390/app9204226
- The BBN and C4.5 DT effective approaches are used to evaluate and compare the seismic soil liquefaction potential of the updated and relatively large cone penetration test (CPT) data set, which includes 251 case history records. In addition, the developed models are compared with the Youd et al.  and Rezania et al.  models to validate performance.
- One of the major advantages of the presented models is the consideration and addition of earthquake parameters to the dataset—the causative fault type and closest distance to rupture surface parameter.
- Data division for training and testing datasets was performed with due attention to statistical aspects, such as minimum, maximum, mean, and standard deviation of the datasets. The splitting of the datasets helped identify the predictive ability and generalization performance of the developed models, and evaluate them better.
- This study presents probabilistic reasoning, most probable explanation of seismic soil liquefied sites, and parametric sensitivity analysis of the robust model.
2. Predictive Modeling Techniques
2.1. Bayesian Belief Network (BBN)
2.2. C4.5 Decision Tree (DT) Model
3. Development of Seismic Soil Liquefaction Modeling
3.1. Dataset, Date Preprocessing, and Predictor Variables
- A training dataset is required to train the models. In this research work, the authors used 80% of the data i.e., 201 out of 251 CPT case histories are considered for the training set.
- A testing dataset is needed to predict the developed models’ performance. In this study, the remaining 20% of data i.e., 50 out of 251 CPT case histories are considered as the testing dataset.
3.2. Model Development Using BBNs
3.3. Model Development Using C4.5 Decision Tree
4. Performance Measure
- True positive (TP) and true negative (TN) indicate that the samples are predicted correctly.
- False positive (FP) represents the number of non-liquefied samples that are predicted incorrectly as positive.
- False negative (FN) denotes the number of liquefied samples that are predicted incorrectly as negative.
- Precision refers to the accuracy of the predictions for a single class (positive or negative).
- Recall measures the accuracy of predictions, considering only the predicted value.
5.1. Comparative Performance of Training and Testing Datasets
5.2. Analysis of a Robust BBN Model
5.2.1. Probabilistic Reasoning
5.2.2. Most Probable Explanation
5.2.3. Sensitivity Analysis
6. Discussion and Conclusions
- The BBN model has relatively better results, as compared to the C4.5 DT, CPT-YD, and CPT-RA models. Considering its overall predictive accuracy, MCC, precision, recall, F-measure for liquefaction and non-liquefaction instances, AUC of ROC, simplicity in practice, data-driven characteristics, and the ability to map interactions between variables, the use of the BBN model in evaluating seismic soil liquefaction by multiple complex factors is quite promising.
- The proposed robust BBN model can not only quantitatively predict seismic soil liquefaction potential probability under certain influence factors (seismic, soil, and site conditions), but also identify the main diagnostic reasons and fault-finding states’ combinations presumed to support decisions on seismic soil liquefaction mitigation measures for sustainable development.
- The sensitivity analysis results conclude that “equivalent clean sand penetration resistance”, “soil behavior type index’, “groundwater table”, “peak ground acceleration’, “vertical effective stress”, and “fines content” are the most sensitive factors in descending order in the assessment of liquefaction potential, and are well matched with the literature.
- The “most probable explanation” function is used to provide the most likely cause set of seismic soil liquefied sites, which is: earthquake magnitude = strong, peak ground acceleration = medium, closest distance to rupture surface = medium, fines content = less, soil behavior type index = silty sand or silt with sand, qc1Ncs = medium, vertical effective stress = small, total vertical stress = small, groundwater table depth = shallow, and depth of soil deposit = shallow. This is considerably compatible and well matched with engineering judgment.
- The BBN model can be used to assess vulnerability of land damage resulting from seismic soil liquefaction by adding nodes of liquefaction land damage potential.
- Additional CPT case history records should be collected and an attempt made to avoid class imbalance in the dataset (caused by updating the BBN model’s conditional probability table) and improve the performance results of prediction.
- The nodes of ‘utility’ and ‘decision operations’ should be added to seismic soil liquefaction and the BBN’s land damage potential model, which can eventually be used as important decision-making information in case of expected utility of loss.
Conflicts of Interest
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|Input : A complete dataset; . : The order of nodes (Assume it is consistent with variables’ subscripts). : The maximum number of parents. Output Bayesian belief network structure|
2: for j = 1 to n
8: if ( and )
14: end if
15: end while
16: end for
|Category||Seismic Soil Liquefaction Factors||Number of Grades||Explanation||Range|
|Seismic parameter||Earthquake magnitude, M||4||Super||8 ≤ M|
|Big||7 ≤ M < 8|
|Strong||6 ≤ M < 7|
|Medium||4.5 ≤ M < 6|
|Peak ground acceleration (PGA), amax (g)||4||Super||0.40 ≤ amax|
|High||0.30 ≤ amax < 0.40|
|Medium||0.15 ≤ amax < 0.30|
|Low||0 ≤ amax < 0.15|
|Closest distance to rupture surface, rrup (km)||4||Super||100 < rrup|
|Far||50 < rrup ≤ 100|
|Medium||10 < rrup ≤ 50|
|Near||0 < rrup ≤ 10|
|Soil parameter||Fines content, Fc (%)||3||Many||50 < Fc|
|Medium||30 < Fc ≤ 50|
|Less||0 ≤ Fc ≤ 30|
|Equivalent clean sand penetration resistance, qc1Ncs||4||Super||135 ≤ qc1Ncs|
|Big||90 ≤ qc1Ncs < 135|
|Medium||45 ≤ qc1Ncs < 90|
|Small||0 ≤ qc1Ncs < 45|
|Soil behavior type index, Ic||4||Gravelly sand to dense sand||Ic < 1.31|
|Clean sand||1.31 ≤ Ic < 1.61|
|Silty sand or sand with silt||1.61 ≤ Ic < 2.40|
|Sandy silt||2.40 ≤ Ic < 2.60|
|Site condition||Vertical effective stress, σ’v (kPa)||4||Super||150 ≤ σ’v|
|Big||100 ≤ σ’v < 150|
|Medium||50 ≤ σ’v < 100|
|Small||0 ≤ σ’v < 50|
|Total vertical stress, σv (kPa)||4||Super||165 ≤ σv|
|Big||110 ≤ σv < 165|
|Medium||55 ≤ σv < 110|
|Small||0 ≤ σv < 55|
|Groundwater table depth, Dw (m)||3||Deep||4 ≤ Dw|
|Medium||2 < Dw < 4|
|Shallow||Dw ≤ 2|
|Depth of soil deposit, Ds (m)||3||Deep||10 ≤ Ds < 20|
|Medium||5 ≤ Ds <10|
|Shallow||0 ≤ Ds <5|
|Thickness of soil layer, Ts (m)||3||Thick||10 ≤ Ts|
|Medium||5 ≤ Ts < 10|
|Thin||0 < Ts < 5|
|Seismic Soil Liquefaction Factors||Dataset||Minimum||Maximum||Mean||Standard Deviation|
|Earthquake magnitude, M||Training||5.9||9||7.01||0.55|
|Peak ground acceleration (PGA), amax (g)||Training||0.09||0.84||0.32||0.14|
|Closest distance to rupture surface, rrup (km)||Training||1||107.03||18.15||17.08|
|Fines content, Fc (%)||Training||0||85||18.65||19.92|
|Equivalent clean sand penetration resistance, qc1Ncs||Training||16.1||311.9||93.83||38.82|
|Soil behavior type index, Ic||Training||1.16||2.59||1.98||0.29|
|Vertical effective stress, σ’v (kPa)||Training||19||147||56.60||24.12|
|Total vertical stress, σv (kPa)||Training||24||210||79.90||36.48|
|Groundwater table depth, Dw (m)||Training||0.2||7.2||2.00||1.20|
|Depth of soil deposit, Ds (m)||Training||1.4||11.8||4.38||1.96|
|Thickness of soil layer, Ts (m)||Training||0.3||6.5||1.79||1.19|
|Actual Class||Yes||True Positive (TP)||False Negative (FN)|
|No||False Positive (FP)||True Negative (TN)|
|Node||Mutual Info||Percent||Variance of Beliefs|
|Equivalent clean sand penetration resistance||0.022310||2.270000||0.007442|
|Soil behavior type index||0.010800||1.100000||0.003674|
|Peak ground acceleration||0.004560||0.465000||0.001552|
|Vertical effective stress||0.003450||0.351000||0.001171|
|Total vertical stress||0.000230||0.023800||0.000079|
|Depth of soil deposit||0.000200||0.020400||0.000068|
|Closest distance to rupture surface||0.000190||0.019500||0.000065|
|Thickness of soil layer||0.000000||0.000000||0.000000|
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