A step forward towards a comprehensive framework for assessing liquefaction land damage vulnerability: Exploration from historical data

Abstract

The unprecedented liquefaction-related land damage during earthquakes has highlighted the need to develop a model that better interprets the liquefaction land damage vulnerability (LLDV) when determining whether liquefaction is likely to cause damage at the ground’s surface. This paper presents the development of a novel comprehensive framework based on select case history records of cone penetration tests using a Bayesian belief network (BBN) methodology to assess seismic soil liquefaction and liquefaction land damage potentials in one model. The BBN-based LLDV model is developed by integrating multi-related factors of seismic soil liquefaction and its induced hazards using a machine learning (ML) algorithm-K2 and domain knowledge (DK) data fusion methodology. Compared with the C4.5 decision tree-J48 model, naive Bayesian (NB) classifier, and BBN-K2 ML prediction methods in terms of overall accuracy and the Cohen’s kappa coefficient, the proposed BBN K2 and DK model has a better performance and provides a substitutive novel LLDV framework for characterizing the vulnerability of land to liquefaction-induced damage. The proposed model not only predicts quantitatively the seismic soil liquefaction potential and its ground damage potential probability but can also identify the main reasons and fault-finding state combinations, and the results are likely to assist in decisions on seismic risk mitigation measures for sustainable development. The proposed model is simple to perform in practice and provides a step toward a more sophisticated liquefaction risk assessment modeling. This study also interprets the BBN model sensitivity analysis and most probable explanation of seismic soil liquefied sites based on an engineering point of view.

Keywords

Bayesian belief network / liquefaction-induced damage potential / cone penetration test / soil liquefaction / structural learning and domain knowledge

Introduction

Liquefaction potential and liquefaction-induced ground failures are two integral and correlated issues in the assessment of liquefaction hazard risks caused by earthquakes. The former aims to evaluate whether or not the soil liquefied after an earthquake event, while the latter not only aims to predict soil liquefaction-induced hazards occurring after soil liquefaction but also to assess the different levels of liquefaction severity. Numerous studies on seismic soil liquefaction potential and liquefaction-induced ground failures have been carried out by several researchers after the catastrophic earthquakes in Alaska and Niigata in 1964. The definition of vulnerability in this study is the degree to which the land may be damaged.

The simplified procedures (e.g., Robertson and Wride [¹]; Moss et al. [²]; Idriss and Boulanger [³]) evaluate the liquefaction potential in particular strata but do not assess the performance of the entire soil column and the consequences of liquefaction manifestations such as sand boils, lateral spreading, settlement, and ground cracks at the ground’s surface, which strongly relate to the ground damage potential and depict the entire response of the soil deposit. To evaluate the severity of liquefaction, Iwasaki et al. [⁴] recommended the liquefaction potential index (LPI), which utilizes a safety factor as an integrated effect of the likely liquefaction over the cumulative depth of the soil profile. The LPI uses the following classifications (Iwasaki et al. [⁴]): the liquefaction risk is very low if LPI= 0; low if 0<LPI≤5; high if 5<LPI≤15; and very high if LPI>15. However, the implication of the word “risk” in the cited categories was not well-defined as the index was proposed for evaluating the liquefaction severity, and other elucidations were suggested. For instance, Luna and Frost [⁵] presented the following classifications: the liquefaction severity is little to none if LPI= 0; minor if 0<LPI≤5; moderate if 5<LPI≤15; and major if LPI>15. Furthermore, certain researchers have attempted to associate the LPI, Ishihara-inspired liquefaction potential index, and liquefaction severity number (LSN) with surface manifestations (Toprak and Holzer [⁶]; Maurer et al. [⁷]; Tonkin and Taylor Ltd. [⁸]) and with ground damage potential near foundations (Hsein Juang et al. [⁹]). However, the interpretation and LPI can be utilized only if this index is appropriately adjusted with field ground damage data. The relation between LPI and ground damage vulnerability has not been evaluated systematically in one model, and it is probable that there may be a qualitative relation to certain degree.

Several researchers have applied artificial intelligence (AI) techniques in engineering, physics, and mathematical problems and have achieved comparatively satisfactory results (e.g., Hamdia et al. [¹⁰]; Anitescu et al. [¹¹]; Guo et al. [¹²]; Singh et al. [¹³]; Ghanizadeh and Rahrovan [¹⁴]). The Bayesian belief network (BBN) is considered to be an emerging modeling approach in AI research that aims to present a decision-support framework for problems involving complexity, probabilistic reasoning, and uncertainty. The BBN is used to combine experts’ knowledge and multisource information into a coherent system, particularly for complex problems in probabilistic terms such as seismic soil liquefaction and its ground damage potential. For events in which case history data are minimal and/or existing information is uncertain and indefinite, BBNs can present a suitable framework to tackle such cause-effect relations and uncertainties [¹⁵].

The twofold key contributions of this study are as follows:

1) to develop a liquefaction land damage vulnerability (LLDV) framework that integrates the multi-related factors of seismic soil liquefaction and its induced hazards into one model using a BBN approach;

2) to evaluate the performance of the proposed BBN model and compare it with that of the C4.5 decision tree (DT)-J48 model, naive Bayesian (NB) classifier, and BBN-K2 ML model.

In the following section, the construction of the BNN model is briefly described. This is followed by a case study of the development of the LLDV framework and performance evaluation indices. The results of the proposed BBN-based framework are presented in detail in the subsequent section. The final section sets out the most important conclusions and future work.

Development of a Bayesian belief network model

Bayesian belief networks (BBNs)

A BBN is a graphical model that allows a probabilistic relationship between a set of variables [¹⁶]. The BBN approach is rooted in the use of Bayes’ theorem. A BBN is a triplet (V, A, P), where

1) V is a set of variables;

2) A is a set of arcs, which together with the variables (V), comprises a directed acyclic graph G = (V, A);

3) P is the set of conditional probabilities of all the variables given with their respective parents.

Figure 1 presents a simple BBN with five variables X₁, X₂, X₃, X₄, and X₅. The network comprises the following prior and conditional probabilities: P(X₁), P(X₂|X₁), P(X₃|X₂), P(X₄|X₂), and P(X₅|X₃,X₄).

Therefore, the posterior probability in the BBN can determined by Bayesian formulas and conditional independence rules as follows:

(1)P\left(X_i|Y\right)=\frac{P\left(Y|X_i\right)\cdot P\left(X_i\right)}{P\left(Y\right)},

(2)P\left(Y|X_i\right)=\frac{P(x_1,\mathrm{...},x_n|Y)\cdot P\left(Y\right)}{P(x_1,\mathrm{...},x_n)},

(3)P(x_1,\mathrm{...},x_n)=\underset{i=1}{\overset{n}{\mathrm{\Pi }}}P\left(x_i|\pi \left(x_i\right)\right),

where x₁,…, x_n, and Y are random variables; P(X_i|Y) is the posterior probability of variable X_i given evidence Y; P(X_i) and P(Y_i) are the prior probabilities of variables X_i and Y; P(Y|X_i) is the likelihood and is proportional to the conditional probability of observing a particular event given evidence X_i; P(x₁, …, x_n) is the joint probability of variables x₁, ..., x_n; and p(x_i) is a set of values for the parents of X_i. Equation (1) corresponds to backward inferring, and Eq. (2) shows forward reasoning.

The development of a BBN primarily comprises two steps, i.e., structure learning and parameter learning.

Structure learning

Structure learning is the base of BBN modeling, and efficient structure learning is the fundamental step to develop an optimal network structure. The development of a BBN structure comprises the following three methods.

1) BBN based on experts’ knowledge referred to as domain knowledge (DK);

2) Use of machine learning (ML) algorithms to learn directly from the data;

3) Combining DK and the ML algorithm using a data fusion methodology to obtain the BBN structure.

The third method integrates the advantages of DK and ML and avoids the shortcomings of utilizing only one method to build the BBN structure, and in this paper, the third method is used to find the Bayesian network structure for the LLDV. To perform structural learning from a data set, frequently used ML algorithms such as the K2, hill-climbing and tree augmented naive (TAN) Bayes algorithms are used. In this study, the K2 algorithm [¹⁷] is applied to perform a structure learning that carries a search in accordance with the given order of nodes by means of a restricted maximum number of parent nodes. A K2 ML algorithm employs posterior probabilities as the scoring function and adds arcs to the BBN that depend on the following rules [¹⁷].

1) Calculate the Cooper-Herskovits (CH) score for according to the nodes’ order ρ.

(4)CH={\displaystyle \sum _{i=\mathrm{1}}^n{\displaystyle \sum _{j=\mathrm{1}}^{q_i}\left[\log {\displaystyle \frac{\mathrm{\Gamma }\left({\alpha }_{ij\ast }\right)}{\mathrm{\Gamma }\left({\alpha }_{ij\ast }+m_{ij\ast }\right)}}+{\displaystyle \sum _{k=\mathrm{1}}^{r_i}\log {\displaystyle \frac{\mathrm{\Gamma }\left({\alpha }_{ijk}+m_{ijk}\right)}{\mathrm{\Gamma }\left({\alpha }_{ijk}\right)}}}\right]}},

where m_{ijk} is number of samples which is subjected to X_i=k, \pi \left(X_i\right)=j, m_{ij*}={\mathrm{\sum }}_{k=1}^{r_i}{m}_{ijk},{\alpha }_{ij*}={\mathrm{\sum }}_{k=1}^{r_i}{\alpha }_{ijk}, and{\alpha }_{ijk}=P\left(X_i=k|\pi \left(X_i\right)=j\right).

2) Add an arc \left(X_i\to X_j\right)when X_i\left(i\ne j\right) makes to CH\left(X_j,{\pi }_j\cup X_i\right)the maximum. {\pi }_jrepresents the parents of X_j.

In this study, the pseudocode of the K2 algorithm [¹⁷] using the variable set X=\{X_{\mathrm{1}},X_{\mathrm{2}},X_{\mathrm{3}},\mathrm{...},X_n\}, denotes the variable nodes such as the depth of the soil deposit, groundwater table, fines content, earthquake magnitude, thickness of the soil layer, soil behavior type index, equivalent clean sand penetration resistance, liquefaction potential, liquefaction potential index, and LLDV is shown as follows.

Input: X=\{X_{\mathrm{1}},X_{\mathrm{2}},X_{\mathrm{3}},\mathrm{...},X_n\}; ρ: the order of nodes (assume it is consistent with variables’ subscripts); μ: The maximum number of parents; D: a complete dataset.

Output: Bayesian belief network structure.

Steps:

1) \xi \leftarrow acyclic graph composed by X;

2) for j=\mathrm{1}to n;

3) {\pi }_j=\phi;

4) V_{\mathrm{o}\mathrm{l}\mathrm{d}}\leftarrow CH\left(\langle X_j,{\pi }_j\rangle |D\right);

5) while (true);

6) i\leftarrowargmax \mathrm{1}\le i\le j,\hspace{0.17em}{X}_i\notin {\pi }_j CH\left(\langle X_j,{\pi }_j\cup \{X_j\}\rangle |D\right);

7) V_{\mathrm{n}\mathrm{e}\mathrm{w}}\leftarrow CH\left(\langle X_j,{\pi }_j\cup \{X_j\}\rangle |D\right);

8) if (V_{\mathrm{n}\mathrm{e}\mathrm{w}}>V_{\mathrm{o}\mathrm{l}\mathrm{d}} and ;

9) V_{\mathrm{o}\mathrm{l}\mathrm{d}}\leftarrow V_{\mathrm{n}\mathrm{e}\mathrm{w}};

10) {\pi }_j\leftarrow {\pi }_j\cup \{X_i\};

11) add an arc X_i\to X_j into \xi;

12) else;

13) break;

14) end if;

15) end while;

16) end for;

17) return ξ.

To acquire the optimal network structure, the DK is required to be included in the K2 ML algorithm. The proposed BBN structure for the LLDV assessment is developed by the K2 ML algorithm which is further fine-tuned based on the DK from respective field experts and known relationships between different input factors.

Parameter learning

Once the topological structure of the BBN is obtained, then the parameter learning can be performed. This is used to determine the conditional probability distribution of each variable node under a given BBN model. Three basic kinds of algorithms are used for acquiring a conditional probability table: the maximum likelihood estimation (MLE), gradient descent (GD), and expectation maximization (EM). The MLE is the fastest and simplest, based entirely on data and independent of prior probabilities; therefore it does not apply to models containing hidden variables, and the data set includes several missing values [¹⁸]. The EM and GD algorithms work through an iterative process, and EM is appropriate for data that contains missing values. In short, EM learning is frequently used in BNNs to perform a desired (E) step and then maximize (M) the step to find a better network [¹⁹].

Case study

Data set, predictor variable selection, and data preprocessing

The LLDV model was trained and tested with 35 select case history records derived from a cone penetration test (CPT) from the 1999 Chi-Chi (Taiwan, China), 1999 Kocaeli (Turkey), 1994 Northridge (USA), and 1989 Loma Prieta (USA) earthquakes; a summary is shown in Table 1. The case history records were chosen from the literature based on the accessibility of CPT soundings in digital format. The factors of safety (FS) against seismic soil liquefaction were calculated using the CPT-based liquefaction assessment procedure of Robertson and Wride [¹]. Previous studies [²⁰–²⁹] contributed some detailed understandings to lead the selection of variables, discretization, and classification in this study. Consequently, 11 variables were chosen from the literature as having “significant influence”, including the following: “peak ground acceleration”, “thickness of soil layer”, “soil behavior type index”, “liquefaction potential”, and “liquefaction potential index”, for a comprehensive framework of a seismic soil LLDV model. The grading standards for the seismic soil liquefaction and its induced hazard parameters are shown in Table 2. The grading standard for the LLDV is divided into five grades as per the description of ground damage status according to the domain knowledge as shown in Table 3. The statistical summary of the seismic soil liquefaction and its land damage potential is shown in Fig. 2, which indicates the following.

1) The LPI framework showed a relatively inconsistent efficacy as the observed severities of the liquefaction surface manifestation, particularly in “high” and “very high” grades, were less than the predicated values. For example (see case 28 in Table 1), the CPT sounding site Leonardini 37 (LEN-37) following the Loma Prieta earthquake on Oct 18, 1989, had no evidence of liquefaction surface manifestation, while the LPI value was 8.2, representing a “high” risk of liquefaction surface manifestation, which clearly showed disparity and inconsistency with the field data.

2) The liquefaction-induced ground failures, i.e., sand boils, ground cracks, settlement, and lateral spreading, were almost in accordance with the descriptions of ground damage potential as shown in Table 3.

Structure learning

In this research study, the K2 machine learning algorithm and DK data fusion methodology were used to find the BBN structure. Based on the K2 algorithm, structural learning was performed with MATLAB using FullBNT-1.0.7. Through the domain knowledge embedded in the K2 algorithm, the BBN structure was finally developed, as shown in Fig. 3. The network comprises 12 nodes and multiple lines. The 12 nodes relate to 12 variables, and lines connecting these nodes indicate the associations between variables. It can be seen from Fig. 3 that some soil liquefaction and its induced hazard variables demonstrated counter-intuitive results by means of the variable dependence that is entirely presented by the BBN structure. For example, “vertical effective stress” is dependent on “groundwater table depth” and “depth of soil deposit”.

Parameter learning

The BBN structure was developed in Netica software to conduct parameter learning to obtain the conditional probability distribution of the nodes. Finally, the BBN model was determined to assess the LLDV. The graphical presentation of the proposed LLDV framework after parameter learning is shown in Fig. 4.

Performance evaluation

There is no generally accepted performance index for models having multiple classes. Therefore, to evaluate the developed model, the authors compared the proposed BBN-K2 and DK model with other frequently-used predictive methods (see Table 4) in terms of overall accuracy (OA) and the Cohen’s kappa coefficient.

OA is a basic evaluation criterion designed to measure the model performance and is defined as the percentage of records correctly predicted by the model with respect to the total number of records in the classification model. OA can be calculated by:

(5)OA=\left(\frac{1}{n}\mathrm{\sum }_{i=1}^m{r}_{ii}\right)\times 100\%,

where r_ii (i= 1,2,...,m) is the cell count in the main diagonal of the confusion matrix, and n is the total number of records in the classification model.

The kappa statistic is used to compute the agreement among true and classified results [⁴¹] and is calculated as:

(6)\mathit{\kappa }=\frac{p_{\mathrm{a}}-p_{\epsilon }}{1-p_{\epsilon }},

where p_a is the proportion of observations in agreement, and p_ε is the proportion in agreement due to chance. Landis and Koch [⁴²] introduced a scale to define the degree of concordance (Table 5); the kappa ranges from “−1” (total disagreement) through “0” (random classification) to “1” (perfect agreement), as can be seen from Table 5; a value of kappa below 0.4 is an indication of poor agreement, and a value of 0.4 or above is an indication of good agreement (Landis and Koch [⁴²]; Sakiyama et al. [⁴³]).

Results and discussions

Comparative performance of multiple learners

To assess the performances of the developed BBN-K2 and DK, C4.5 (DT)-J48, NB classifier, and BBN-K2 models, the results acquired for the training and testing data sets are shown in Table 6. The developed models were trained and tested using CPT data sets of 29 and 6 case history records, respectively. The results indicated that the proposed BBN-K2 and DK model had the best performance for the training data set in terms of overall accuracy, with much higher correctly classified instances than the C4.5 (DT)-J48, NB classifier, and BBN-K2 models (from a 3% to 7% improvement over other models in the training data set). With the testing data set, the BBN-K2 and DK model showed at par overall accuracy, i.e., 83.333% performance, with the NB classifier. The same strategy was employed to analyze the results of all models (having the same training and testing data sets).

Additionally, the kappa statistics for the evaluation of the BBN-K2 and DK model for the training and testing sets were from substantial to almost perfect, while those for the C4.5 (DT)-J48 and NB techniques for the training and testing sets were substantial based on the scale of concordance introduced by Landis and Koch [⁴²]. The kappa statistics of the BBN-K2 model for the training and testing sets were moderate to substantial. Considering the comparative performance, the C4.5 DT model was found to be secondary to the proposed BBN-K2 and DK model.

The limitations of the proposed BBN-K2 and DK model need to be mentioned as well. Similar to other artificial intelligence techniques, BBNs have a limited domain of applicability and are mostly case dependent. Nevertheless, one of the most important abilities of the BBN-K2 and DK model is updating the conditional probability based on the updated data set, which will improve its predictability to enhance the previous results. Therefore, for future research, the database used in this study should be expanded to a wider range of input factors to further enhance the reliability of the model.

Probabilistic reasoning

The developed BBN model may be employed to determine the probabilistic reasoning including the calculations of posterior probability-sequential inference (from causes to results) and also causal inference-reverse inference (from results to causes).

LLDV prediction

The LLDV prediction is shown in Fig. 5 on the basis of the supposition that if the liquefaction potential is “yes” and depth to ground water table is “shallow”. In the Netica, the fixed states of “yes” and “shallow” as 100%, i.e., states of the evidence variables, are known. Subsequently, the probabilities of the BBN are updated; the changes in the probability of “liquefaction land damage vulnerability” and remaining variable nodes can be obtained. In this instance, a “very high” state probability for “liquefaction land damage vulnerability” is found to increase from 21.0% to 24.5%.

This indicates that if the liquefaction potential is “yes”, and depth to ground water table is “shallow”, then the LLDV probability of “very high” will be notably increased (see Fig. 5).

As shown in Fig. 6, in addition to the “shallow” status of groundwater table depth and “yes” status of liquefaction potential, assume that the peak ground acceleration status is “super”, and the status of “super” in “peak ground acceleration” is fixed at 100%. Thereafter, automatically updating the probabilities in the BBN, the LLDV probability of “very high” is found to further increase from 24.5% to 28.4%, which means that the LLDV probability of “very high” is higher with respect to the initial probability of 21.0%.

Furthermore, assume that the “depth of soil deposit” status is also “shallow” and is set to 100%. As depicted in Fig. 7, it can be found that the LLDV probability of “very high” further increases from 28.4% to 34.2%. This suggests that “liquefaction potential”, “groundwater table”, and “depth of soil deposit” affected the LLDV probability of “very high” to varying extents. It is noted that the change in the state of the evidence node variables affect the probability of the objective nodes, which is compatible with the engineering judgment.

Causal inference

The most significant utilization of the BBN model is to find the system fault using the diagnostic reasoning capability of the BBN model. A causal inference is conducted by selecting the evidence state “very high” in “liquefaction land damage vulnerability” as an instance. In this example, the evidence state is “very high”; therefore, the probability is 100%. As illustrated in Fig. 8, after fixing the evidence as “very high” in “liquefaction land damage vulnerability”, the probability of “yes” in “liquefaction potential” increases from 51.4% to 54.1% using the automatic updating function in Netica. Additionally, the “shallow” states of “groundwater table” and “depth of soil deposit” probability also increase from 46.9% to 49.8% and 56.3% to 58.1%, respectively. This indicates that, in the absence of other evidence, the most likely cause of the “liquefaction land damage vulnerability” increasing to a “very high” state is the “shallow” states of “groundwater table” and “depth of soil deposit”.

Most probable explanation

The most probable explanation can be found using the Netica function to determine which scenario is most likely to cause a LLDV, and the developed BBN model may be utilized to obtain the most probable explanation. For example, if the LLDV is “very high” as presented in Fig. 9, the “most probable explanation” function is used to find the set most likely to cause “liquefaction land damage vulnerability” which is [earthquake magnitude= big, peak ground acceleration= super, fines content= less, soil behavior type index= silty sand or sand with silt, equivalent clean sand penetration resistance= medium, vertical effective stress= small, groundwater table= shallow, depth of soil deposit= shallow, thickness of soil layer= thin, liquefaction potential= yes, and liquefaction potential index= very high]. This clearly indicates that the causal inference and most probable explanation set are considerably compatible when the LLDV state is “very high,” and the set is also well matched with engineering judgment.

Sensitivity analysis

There is a large and diverse literature on ​​sensitivity analyses to determine the effect of each factor on the uncertainty of the target variable. For example, Hamdia et al. [⁴⁴,⁴⁵] performed sensitivity analyses to find the key input parameters that affect the relationship between tissue structure and mechanics and the significant input parameters influencing the energy conversion factor of flexoelectric materials. Various techniques have been used in the literature to quantify the influence of uncertain input factors on uncertain model outputs, such as Vu-Bac et al. [⁴⁶], who proposed a unified framework that links different steps from generating the sample, constructing the surrogate model, and implementing the sensitivity analysis method to determine the key input parameters of an output of interest. In the Netica software, a sensitivity analysis function is utilized to find the factors that have a greater influence on the LLDV. In Netica, the target node “liquefaction land damage vulnerability” is selected for a sensitivity analysis, and the result is presented in Table 7. The information from two nodes may indicate a dependency of the nodes on one another and the closeness of their correlation [⁴⁷]. Table 7 shows that the mutual info of the “liquefaction potential index” node is the greatest, i.e., 0.00139, which indicates that it has the strongest influence on “liquefaction land damage vulnerability”, followed by “groundwater table”, “liquefaction potential”, “peak ground acceleration”, “soil behavior type index”, “liquefaction potential index”, and “depth of soil deposit”, which have mutual info equal to 0.00072, 0.00070, 0.00049, 0.00047, and 0.00028, respectively, whereas the “fines content” is the least sensitive factor with a mutual info equal to 0.00001; these results are highly compatible with the literature.

Conclusions and future work

The seismic soil liquefaction potential and its ground damage potential involves uncertainty and complexity, and this paper presented the BBN-based LLDV model that efficiently examined the complicated relationships between related factors in a semantic way. The major findings in this study are presented as follows.

1) Through comparisons with the naive Bayesian classifier, C4.5 (DT)-J48, and BBN-K2 models in terms of overall accuracy and Cohen’s kappa coefficient, it was concluded that the use of the proposed BBN-K2 and DK framework in assessing the seismic soil liquefaction potential and its ground damage potential influenced by multiple complex factors is quite promising.

2) The proposed BBN-K2 and DK model not only predicted quantitatively the seismic soil liquefaction potential and its ground damage potential probability but also identified the main reasons and fault-finding state combinations that elicit the LLDV in different states. The results prioritize the most vulnerable sites instead of identifying all sites at which the earthquake-induced liquefaction has occurred, thereby minimizing the disaster response cost. The results can support decisions on seismic risk mitigation measures for sustainable development and provide a step toward modeling liquefaction risk assessment.

3) Sensitivity analysis results concluded that the “liquefaction potential index”, “groundwater table”, “liquefaction potential”, “peak ground acceleration”, “soil behavior type index”, and “depth of the soil deposit” are the most sensitive factors in descending order in the assessment of LLDV when determining whether it is probable that seismic liquefaction will cause damage at the ground’s surface.

The general interpretation of the BBN framework corresponds well with engineering theory, which indicates the reliability of the model. However, owing to the limited available historic data of CPT soundings in digital format and certain factors that do not have a wide range in the training set, for future research, the database used in this study should be expanded to a wider range of seismic, soil, and site condition factors to enhance the reliability of model. The model can be extended to a more sophisticated model that can consider more seismic factors such as closest distance to the rupture surface in the data set and soil factors such as mean particle size. Additionally, adding nodes for the utility and decision operations in the seismic soil liquefaction and its land damage potential may eventually lead to important information for decision making in case of expected utilities of loss.

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