TY - JOUR
AU - Jalal,, Mostafa
AB - Abstract In this paper, an approach for soil liquefaction evaluation using probabilistic method based on the world-wide SPT databases has been presented. In this respect, the parameters’ uncertainties for liquefaction probability have been taken into account. A calibrated mapping function is developed using Bayes’ theorem in order to capture the failure probabilities in the absence of the knowledge of parameter uncertainty. The probability models provide a simple, but also efficient decision-making tool in engineering design to quantitatively assess the liquefaction triggering thresholds. Within an extended framework of the first-order reliability method considering uncertainties, the reliability indices are determined through a well-performed meta-heuristic optimization algorithm called hybrid particle swarm optimization and genetic algorithm to find the most accurate liquefaction probabilities. Finally, the effects of the level of parameter uncertainty on liquefaction probability, as well as the quantification of the limit state model uncertainty in order to incorporate the correct model uncertainty, are investigated in the context of probabilistic reliability analysis. The results gained from the presented probabilistic model and the available models in the literature show the fact that the developed approach can be a robust tool for engineering design and analysis of liquefaction as a natural disaster. Graphical Abstract Open in new tabDownload slide Graphical Abstract Open in new tabDownload slide liquefaction hazard, probabilistic approach, reliability analysis, optimization algorithm, hybrid PSO-GA Highlights New computer-aided approach for liquefaction as a natural disaster. Standard penetration test-based reliability model with parameter uncertainty. Application of hybrid genetic algorithm and particle swarm optimization. Bayes’ theorem to capture the failure probability. 1. Introduction Several methods for evaluating the liquefaction potential of sandy soils have been suggested, in which the deterministic analysis has been widely used among the geotechnical experts due to its simplicity. Although the factor of safety of soils can be determined utilizing deterministic methods by applying the certain and non-dispersion parameters, some facts such as anisotropy and non-uniformity of the soils, uncertainties in the seismic parameters, mismatch between the employed assumptions in modelling, and the actual in-situ conditions, as well as human and instrumental errors, cause unreliable results for these methods. Thus, in order to overcome these difficulties, probabilistic evaluation of liquefaction in which the degree of conservatism can be quantified in terms of PL can be a good option. Hence, geotechnical engineers can interpret the probability of liquefaction occurrence (PL) simplicity in terms of lacking knowledge of the associated uncertainties by calibrating the safety factor (Fs) with the liquefaction field manifestation and by developing the mapping function on the basis of the Bayes’ theorem of conditional probability for preliminary calculations of the liquefaction probability (Goharzay, Noorzad, Mahboubi Ardakani, & Jalal, 2017). However, using reliability assessment methods by considering both of the parameter and model uncertainties and utilizing the probability distribution curves of the parameters instead of only a certain amount for each one, we can provide the soil liquefaction probability curve. Desired constitutive modelling of liquefiable soil is very difficult, even with considerable laboratory testing. Hence, cyclic stress-based simplified methods based on in-situ tests such as standard penetration test (SPT), cone penetration test (CPT), and Shear wave velocity (Vs) measurements along with the post-liquefaction case histories-calibrated empirical relationships have been used widely by the geotechnical engineers to evaluate the liquefaction potential of soils throughout most part of world (Youd et al., 2001, Cetin et al., 2004; Idriss & Boulanger, 2004; Idriss & Boulanger, 2008). SPT-based method is the most widely used method among the available in-situ test methods for the evaluation of resistance of soil against the occurrence of liquefaction. Nowadays, CPT is becoming more acceptable as it is consistent, repeatable, and able to identify a continuous soil profile. Thus, CPT is being used as a valuable tool for assessing various soil properties, including liquefaction potential of soil. The main advantages of the CPT are that it provides a continuous record of penetration resistance and is less vulnerable to operator error than the SPT. The main disadvantages of the CPT are the difficulty in penetrating layers that have gravels or very high penetration resistance and need to perform companion borings or soundings to obtain actual soil samples. The use of Vs as an in-situ test index of liquefaction resistance of soil is very well accepted because both Vs and cyclic resistance ratio (CRR) are similar, but not proportional, and influenced by void ratio, effective confining stresses, stress history, and geologic age. The main advantages of using Vs for the evaluation of liquefaction potential are as follows: Vs measurements are possible in soils that are difficult to penetrate with SPT and CPT or difficult to extract undisturbed samples; (ii) Vs is a basic mechanical property of soil materials, directly related to small-strain shear modulus; and (iii) the small-strain shear modulus is a parameter required in analytical procedures for estimating dynamic soil response and soil-structure interaction analyses. However, the following are the disadvantages of utilizing Vs for liquefaction resistance evaluations: (i) seismic wave velocity measurements are made at small strains, whereas pore-water pressure build-up and the liquefaction triggering are medium- to high-strain phenomena; (ii) seismic testing does not provide samples for the classification of soils and the identification of non-liquefiable soft clay-rich soils; and (iii) thin, low Vs strata may not be detected if the measurement interval is too large. Therefore, it is preferred to drill sufficient boreholes and conduct in-situ tests (SPT or CPT) to detect thin liquefiable strata, non-liquefiable clay-rich soils, and silty soils above the ground water table. Whitman (1971) first proposed to use liquefaction case histories to characterize liquefaction resistance in terms of measured in-situ test parameters. Seed and Idriss (1971) did a pioneer work in developing a simplified empirical model, using laboratory tests and post-liquefaction field observations in earthquakes for evaluating liquefaction susceptibility of soils. Based on this procedure, liquefaction charts have been developed that correlate soil resistance to earthquake-induced stresses. Early efforts to develop such charts involved using laboratory tests to evaluate stresses needed for soil liquefaction (Seed & Lee, 1966; Seed & Peacock, 1970). Such studies typically quantified soil resistance in terms of relative density. However, it was soon realized that grain disturbance during sample extraction from the field significantly altered soil resistance, necessitating considerable judgement to estimate in-situ properties from test results (Seed & Idriss, 1982). Iwasaki (1978) proposed the liquefaction potential index (LPI) to assess the damage potential of liquefaction. Iwasaki et al. (1982) calibrated the values of LPI with the severity of liquefaction-induced damage using data mostly for sandy soils, as provided by 87 SPT borings in liquefied and non-liquefied sites in Japan that severe liquefaction should be expected if LPI > 15 but not if LPI < 5. This criterion for liquefaction manifestations is referred to as the Iwasaki criterion. The LPI value is inversely proportional to the FS and the depth of the saturated layers; the higher the index, the greater the potential for liquefaction. Damage to infrastructure is more likely to result from moderate or severe liquefaction; the probability of damaging liquefaction at LPI = 5 ranges from 0.05 to 0.17. Thus, the Iwasaki criterion is more applicable for assessing the damage potential, rather than the occurrence of liquefaction. Zhou (1980) first published liquefaction correlation directly based on case history CPT database of the 1978 Tangshan earthquake. He presented the critical value of cone penetration resistance separating liquefiable from non-liquefiable conditions to a depth of 15m. Seed and Idriss (1981) as well as Douglas, Olsen, and Martin (1981) proposed the use of correlations between the SPT and CPT to convert the available SPT-based charts for use with the CPT data. Seed, Idriss, and Arango (1983) extended their previous work in developing a modified model in which they used CSR (τav/σ′v) instead of peak ground acceleration (amax) as a measure of seismic action and overburden pressure-corrected SPT value (N1) instead of relative density (Dr) as the site parameter representing its resistance to liquefaction. Robertson and Campanella (1985) developed a CPT-based method for the evaluation of liquefaction potential, which is a conversion from SPT-based method using empirical correlation of SPT–CPT data and follows the same stress-based approach of Seed and Idriss (1971). This method has been revised and updated by some researchers (Suzuki, Tokimatsu, Taya, & Kubota 1995; Olsen, 1997; Robertson & Wride, 1998). Robertson and Wride (1998) developed an integrated procedure to evaluate the liquefaction resistance of sandy soils based solely on CPT data. Comparison of Robertson and Wride’s CPT-based method with SPT-based methods and other CPT-based methods has demonstrated that Robertson and Wride’s method is reliable and convenient (Gilstrap, 1998; Juang, Rosowsky, & Tang, 1999). In addition, Juang et al. (1999) found that the degree of conservatism in the Robertson and Wride method is comparable to that in the Seed and Idriss (1971, 1982) SPT-based method that has been widely used in geotechnical practice around the world for more than 20 years. Youd et al. (2001) published a summary paper of 1996 and 1998 NCEER workshop in which the updates and augmentations to the original ‘simplified procedure’ of Seed and Idriss (1971), Seed et al. (1983), and Seed, Tokimatsu, Harder, and Chung (1985) for the evaluation of liquefaction potential are recommended using SPT-based methods and are still followed as the current state of the art on the subject of liquefaction potential evaluation. Cetin et al. (2004) proposed new correlations for the assessment of liquefaction triggering in soil. Although the above SPT-based method remains an important tool for evaluating liquefaction resistance, it has some drawbacks, primarily due to the variable nature of the SPT (Robertson & Campanella, 1985; Skempton, 1986). Moss (2003) and Moss, Seed, Kayen, Stewart, and Tokimatsu (2005) presented a CPT-based probabilistic model for the evaluation of liquefaction potential using reliability approach and a Bayesian updating technique. Juang, Yuan, Lee, and Lin (2003) investigated the uncertainties of the Robertson and Wride model (Robertson & Wride, 1998) in order to assess the liquefaction potential based on the CPT through the reliability analysis. Hwang, Yang, and Juang (2004) proposed a new practical approach for reliability evaluation of soil liquefaction potential. They calculated the earthquake-induced cyclic shear stress probability density function utilizing the acceleration attenuation relationships related to Taiwan area (Chi Chi earthquake data in 1999) and applied first-order second moment method for the combination of cyclic shear stress probability density function and cyclic shear strength of soil and developed probability models in order to determine the reliability index (β) and the related liquefaction probability (PL) using factor of safety (Fs). Juang, Jiang, and Andrus (2005) studied the uncertainties of the Andrus and Stoke model (Andrus & Stokoe, 2000) to assess the soil liquefaction based on the shear wave velocity by means of the first-order reliability method (FORM). They obtained a probability model to estimate the liquefaction occurrence. Hanna, Ural, and Saygili (2007) based on Turkey and Taiwan earthquake databases in 1999, taking into account 12 dynamic and soil parameters, established a neural network model for liquefaction potential in sandy soil deposits. Their proposed general regression neural network model (GRNN) propounded a complex relationship between soil and dynamic parameters. The accuracy of the prediction model was verified by comparing of GRNN model results against the results of the simplified methods. Jha and Suzuki (2009) analysed soil liquefaction potential using analytical approximation methods and Monte Carlo simulation approach based on SPT databases. For this purpose, they presented a comparative study of the reliability approaches in order to obtain the liquefaction probability related to each factor of safety. Lee, Chi, Juang, and Lee (2010) presented a reliability model to evaluate the liquefaction potential of the Yuanlin city of Taiwan by considering the uncertainties in seismic forces and soil strength parameters through the FORM method. Das and Muduli (2013) used Chi-Chi earthquake data in order to investigate the soil liquefaction potential based on genetic programming (GP). Gene expression programing (GEP) was also recently used in earlier study of the authors to develop deterministic model for liquefaction (Goharzay et al., 2017). In recent years, artificial intelligence and optimization techniques have been successfully applied in various applications in civil and mechanical engineering such as civil engineering materials (Ashrafi, Jalal, & Garmsiri, 2010; Jalal & Ramezanianpour, 2012; Jalal, Ramezanianpour, Pouladkhan, & Tedro, 2013; Fathi, Jalal, & Rostami, 2015; Jalal, 2015), composites (Jodaei, Jalal, & Yas, 2012,2013; Jalal, Moradi-Dastjerdi, & Bidram, 2019), product manufacturing (Garmsiri & Jalal, 2014; Jalal, Mukhopadhyay, & Goharzay, 2018; Jalal & Goharzay, 2019; Jalal, Mukhopadhyay, & Grasley, 2019), etc. Though GEP modelling and optimization algorithms have been implemented to solve some complex geotechnical problems, their use in liquefaction potential evaluation is very limited. In recent years, a lot of work has been done to assess the liquefaction potential in terms of the probability of liquefaction. A precise estimation of the probability of liquefaction requires information of both parameter and model uncertainties. In this research, the issue of the uncertainties has been addressed through rigorous meta-heuristic optimization algorithm-based reliability analysis, which is considered to be significant. In the present study, an approach for soil liquefaction evaluation using probabilistic methods based on the world-wide SPT databases as presented in Appendix 1 (Cetin, 2000) has been employed in order to analyse the effects of parameter and model uncertainty in liquefaction probability on the basis of the obtained GEP models (Goharzay et al., 2017) for liquefaction resistance and potential evaluation. In this respect, the parameters’ and model uncertainties for liquefaction probability have been taken into account within an extended framework of the FORM. The reliability indexes (β) are determined through a well-performed meta-heuristic optimization algorithm called hybrid particle swarm optimization (PSO) and genetic algorithm (GA) in order to find the most accurate liquefaction probabilities (PL) through the notional failure concept. In addition, the empirically calibrated mapping functions with the liquefaction field manifestation are developed utilizing Bayes’ theorem in order to infer the relationship between the obtained reliability index (β) and the related probability of liquefaction (PL). Finally, the effect of the level of parameter uncertainty on liquefaction probability (PL), as well as the quantification of the limit state model uncertainty in order to incorporate the correct model uncertainty, is investigated by comparing the Bayesian mapping functions (β–PL curves) obtained for each uncertainty level in the context of probabilistic reliability analysis. 2. Methodology and Analysis 2.1. Reliability analysis Generally, there are several uncertainties in geotechnical engineering, especially in liquefaction analysis (e.g. errors associated with the dispersion of the measured data, systematic errors, human errors, etc.). Referring to the inability of the deterministic methods to take into account the geotechnical uncertainties, They are not applicable to be used in the analysis of the soil liquefaction potential. Figure 1 represents the probability density functions of a specified safety factor. The failure probabilities (PL) are shown by the dark areas, which are defined as the zones of the probability density functions with Fs < 1. According to the figure, as a curve with a higher mean value has more uncertainties than the one with lower mean value, the former curve has a greater failure probability than the latter. Therefore, it can be seen that the greater Fs does not necessarily mean a less chance of failure mode. So, the reliability analysis is required in order to consider both model and parameter uncertainties. The first step of a reliability analysis is to define a performance function. In the liquefaction potential evaluation, CSR and CRR are represented in the form of the random variables Q and R, respectively. In this study, each variable is assumed to follow a lognormal distribution, which has been shown to provide a good fit to the measured geotechnical parameters (Jefferies & Wright, 1988). The safety margin (Z) is defined as the difference between ‘resistance’ and ‘loading’, which also has a lognormal distribution. The performance function of the liquefaction potential assessment is presented as (Baecher & Christian, 2003) $$\begin{eqnarray} Z = R - Q. \end{eqnarray}$$(1) In terms of Z < 0, the liquefaction is more likely to occur and the failure mode is expected. When Z = 0, the performance function is on the limit state boundary, which discriminates between the liquefaction and non-liquefaction cases. If Z > 0, no liquefaction is predicted. The reliability index (β) is defined as the inverse of the covariance coefficient, as (Baecher & Christian, 2003) $$\begin{eqnarray} \beta = \frac{{{\mu _z}}}{{{\sigma _z}}} = \frac{{{\mu _R} - {\mu _Q}}}{{\sqrt {\sigma _R^2 + \sigma _Q^2 - 2{\rho _{RQ}}{\sigma _R}{\sigma _Q}} }},\ \end{eqnarray}$$(2) where μR and μQ are the mean values of R and Q, respectively; σR and σQ are the standard deviations of R and Q, respectively; σ2R and σ2Q are the variances of R and Q, respectively, and ρRQ is the correlation coefficient between R and Q. The probability of liquefaction (PL) can be calculated through the notional failure concept, presented as $$\begin{eqnarray} {p_f} = {P_L} = P \left[ {Z \le 0} \right] = \ = \ \Phi \ \left( { - \frac{{{\mu _z}}}{{{\sigma _z}}}} \right) = \Phi \ \left( { - \beta } \right) = \ 1 - \Phi \left( \beta \right), \end{eqnarray}$$(3) where Φ is the cumulative distribution function for a standard normal variable. Figure 1: Open in new tabDownload slide Comparison of the failure probabilities corresponding to the two different probability density functions of the factor of safety. Figure 1: Open in new tabDownload slide Comparison of the failure probabilities corresponding to the two different probability density functions of the factor of safety. Despite the method’s simplicity, it has some significant drawbacks. For example, when the failure function is linearized around the average values of the random variables, different reliability indices can be obtained by choosing different functions for the same problem. The above problem is solved by Hasofer and Lind (1974), since they proposed a geometric interpretation of the reliability index, which is defined as the shortest distance between the failure surface and the origin of the standard normal coordinate system. They suggested to use a linear approximation of the failure surface at the design point. Based on the Hasofer–Lind approach, all the normal random variables are transformed to their reduced form in standard normal space with zero mean and unit standard deviation. Thus, R′ and Q′as the standard normal variables and d as the distance of the limit state line from origin can be expressed as equations (4–6), respectively. $$\begin{eqnarray} R^{\prime} = \frac{{R - {\mu _R}}}{{{\sigma _R}}}\ \end{eqnarray}$$(4) $$\begin{eqnarray} Q^{\prime} = \frac{{Q - {\mu _Q}}}{{{\sigma _Q}}}\ \end{eqnarray}$$(5) $$\begin{eqnarray} d = \frac{{{\mu _R} - {\mu _Q}}}{{\sigma _R^2 + \sigma _Q^2}}\\ \nonumber \end{eqnarray}$$(6) As the liquefaction performance function (equation 1) depends on multiple variables, it can be represented as Z = R – Q = g(z), in which z is a vector of uncorrelated random variables, z = {(N1)60, FC, σv, |$\sigma^\prime_v$|amax, Mw}. Equation (6) can be extended to six random variables, which are first converted to standard normal variables (zi′), as follows: $$\begin{eqnarray} d = \sqrt {z_1^{{{\prime 2}}} + z_2^{{{\prime 2}}} + \ldots + z_6^{{{\prime 2}}}} \ = \sqrt {{z^{{{\prime T}}}}z^{\prime}}. \ \end{eqnarray}$$(7) Thus, the Hasofer–Lind reliability index is stated as (Der Kiureghian, Lin, & Hwang, 1987) $$\begin{eqnarray} \beta = \min {\left( {{z^{{{\prime T}}}}{\rho ^{ - 1}}{z^{\prime}}} \right)^{0.5}}\ \mathrm{ in}\ \mathrm{ terms}\ \mathrm{ of}\ g\left( z \right) = 0,\ \end{eqnarray}$$(8) where ρ is the correlation matrix of the variables and g(z) = 0 is the constraint function in the optimization problem. In order to determine the characteristics of the lognormal distribution, the mean and standard deviation of equivalent normal variables are calculated as equations (9) and (10), respectively. $$\begin{eqnarray} {\xi _i} = \sqrt {ln\left( {1 + \delta _{zi}^2} \right)} \ \end{eqnarray}$$(9) $$\begin{eqnarray} {\lambda _i} = \ ln{\mu _{zi}} - 0.5\xi _i^2\\ \nonumber \end{eqnarray}$$(10) in which ξi is the standard deviation of the equivalent normal variable, λi is the mean of the equivalent normal variable, μzi is the mean of the random variable zi, and δzi is the coefficient of variation (COV) of zi. The various numerical methods can be utilized in order to find out the minimum value of the reliability index (β). A new hybrid evolutionary algorithm combining the PSO algorithm and the GA referred to as HPSO-GA is presented in order to exploit the advantages and reduce the weaknesses of these two algorithms for solving optimization problems. As these modern meta-heuristic optimization algorithms do not deal with the problem details, they depend only on the quality of the response variables. On the Contrary most traditional gradient-based non-linear search and optimization methods (e.g. gradient, conjugate directions, quasi-Newton, and Newton) require knowledge of derivatives of the objective functions, which may not be easy to obtain those of the different cost functions for the sophisticated problems, such as for reliability analysis. The benefits of utilizing these approaches provide a fast and easy search mechanism of the solution space in order to find the optimal values of the objective functions for the constrained or unconstrained optimization problems by using the computers. In the current study, the simulations are performed by developing the hybrid optimization algorithm code in the MATLAB2013a software. 2.1.1. Optimization algorithm GAs, first introduced by Holland (1975), were implemented on the basis of the principles of natural selection as a class of evolutionary algorithms (EAs). In the GA, a set of chromosomes, which are in fact a set of possible answers to the optimization problem, is considered as the initial population. After generating the initial candidate solutions in the form of strings, the new chromosomes known as offspring (child chromosomes) must be created using the genetic operations (e.g. crossover and mutation). After the creation of children population, by evaluating each of the candidate solutions through the selection process, which is based on the fitness value for each individual in the population, the best chromosomes as the feasible and good quality solutions can be selected. Therefore, after several generations, the population will converge towards the optimal solutions to the optimization problem. PSO algorithm is a population-based stochastic optimization technique developed by Eberhart and Kennedy (1995), originated from the flocking-behaviour simulation of the birds. In the PSO, each particle represents a possible solution and has an associated fitness value based on the relevant objective function. Each particle alone has a personal velocity (vi) and position (xi), which can be updated by taking into account the influence of both personal best experience (p best) and the successful experiences of neighbouring particles or the global best experiences (g best) attained by the whole swarm population. So, each particle is pulled towards the best position it has personally found in the search space so far, as well as the best position that any particle has ever found within the entire swarm. The particles adjust their own positions and velocities according to the previous best solutions as defined in the following relations: $$\begin{eqnarray} {v^i}\! \left[ {t + 1} \right] = w{v^i}\! \left[ t \right] + {c_1}{r_1}\! \left( {{x^{i,best}}\left[ t \right] - {x^i}\left[ t \right]} \right) + {c_2}{r_2}\!\left( {{x^{g,best}}\left[ t \right] - {x^i}\left[ t \right]} \right) \end{eqnarray}$$(11) $$\begin{eqnarray} {x^i}\! \left[ {t + 1} \right] = {x^i}\! \left[ t \right] + {v^i}\! \left[ {t + 1} \right], \end{eqnarray}$$(12) where i and t are the numbers of particle and iteration, respectively, xi and vi are the position and velocity of the particle, respectively, xi,best and xg,best are the optimal position of the particle and of the whole particles, respectively, and ω is an inertia weight, which controls the momentum of the particle and provides a balance between exploration and exploitation within the search algorithm. The parameters r1 and r2 are two random values uniformly distributed between 0 and 1, which are used in order to maintain an appropriate diversity among the feasible solutions represented by the particles, and in this way a rapid and comprehensive search is performed over the whole search space. The parameters c1 and c2 are the personal and global learning coefficients, respectively, which quantify the contributions of personal and social experiences. Both GA and PSO algorithms begin with an initial random population and the evolutionary progression will follow by assessing the fitness of each component, the information sharing among the particles and generating a new population until reaching a stopping criterion. However, the information flow mechanisms in these two algorithms are different. In the GA, all chromosomes share information with each other. Thus, the whole population as a group moves towards the optimal region, whereas in the PSO algorithm only the personal best (p best) and global best (g best) give out information to the other particles. In the course of evolution, the particles’ movement is affected by the best solutions; therefore, the PSO algorithm has a higher convergence rate than the GA. Generally, the random search algorithms have two fundamental objections concerning their performance. First, these algorithms are likely to be stuck into the local optima and in this way, the premature convergence can happen. On the other hand, although PSO is able to find good solutions much faster than many other evolutionary algorithms, the quality improvement of the PSO solutions cannot be seen noticeably during the search process, due to the large-scale information flow, which leads to the emergence of similar birds (reducing the variety of answers), as well as focusing of all the birds at one point known as the global best, which is between the personal and social optimal positions. Second, these heuristic optimization algorithms have an affiliate performance to the problems. This dependence is often the result of the way of selecting the algorithm parameters, which are chosen individually for each problem. Therefore, selecting different values for them can lead to great changes in the algorithm performance. These difficulties can be managed by blending the PSO algorithm with the other intelligent optimization algorithms such as the GA. The combination of these two algorithms was first proposed by Angeline (1998), which revealed that the performance and efficiency of the PSO can be significantly improved by adding a selection process similar to that which occurs in the evolutionary algorithms. Angeline empirically demonstrated that the selection-based PSO algorithm can enhance the local search ability of this algorithm. Thus, a combination of the PSO algorithm with the concepts of selection, crossover, and mutation from the GA seems to be a logical approach and can provide the better results. Figure 2 illustrates the flowchart of the proposed HPSO-GA algorithm. Figure 2: Open in new tabDownload slide Flowchart of the hybrid of particle swarm optimization and genetic algorithm. Figure 2: Open in new tabDownload slide Flowchart of the hybrid of particle swarm optimization and genetic algorithm. 3. Development of SPT-based Reliability Models The liquefaction probability (PL) can be determined for a given reliability index (β) through a calibration with field manifestations of case history databases on the basis of the Bayesian theory as follows (Juang et al., 1999): $$\begin{eqnarray} P\left( {{^{L}\! /\! _{\beta }}} \right)\ = \frac{{{f_\mathrm{ L}}\left( \beta \right)P\left( L \right)}}{{{f_\mathrm{ L}}\left( \beta \right)P\left( L \right) + {f_{\mathrm{ NL}}}\left( \beta \right)P\left( {NL} \right)}}\ \end{eqnarray}$$(13) in which P(L/β) is the liquefaction probability for a given β, fL(β) and fNL(β) are the probability density functions of β for the liquefied cases and non-liquefied cases of the database, respectively, and P(L) and P(NL) are the prior probabilities of liquefaction and non-liquefaction, respectively. In the absence of the prior information, P(L) can be considered equal to P(NL). Thus, equation (13) can be summarized as $$\begin{eqnarray} {P_\mathrm{ L}} = \frac{{{f_\mathrm{ L}}\left( \beta \right)}}{{{f_\mathrm{ L}}\left( \beta \right) + {f_{\mathrm{ NL}}}\left( \beta \right)}}.\ \end{eqnarray}$$(14) The classification of liquefaction likelihood is specified in Table 1. Figure 4: Open in new tabDownload slide Flowchart of the reliability analysis using HPSO-GA as an optimization tool. Figure 4: Open in new tabDownload slide Flowchart of the reliability analysis using HPSO-GA as an optimization tool. Table 1: Liquefaction likelihood classification (Das & Muduli, 2013). Class . Liquefaction probability (PL) . Description of likelihood . 1 PL< 0.15 Almost certain that it will not liquefy 2 0.15 ≤ PL < 0.35 Unlikely to liquefy 3 0.35 ≤ PL < 0.65 Liquefaction and no liquefaction are equally likely 4 0.65 ≤ PL < 0.85 Very likely to liquefy 5 PL ≥ 85 Almost certain that it will liquefy Class . Liquefaction probability (PL) . Description of likelihood . 1 PL< 0.15 Almost certain that it will not liquefy 2 0.15 ≤ PL < 0.35 Unlikely to liquefy 3 0.35 ≤ PL < 0.65 Liquefaction and no liquefaction are equally likely 4 0.65 ≤ PL < 0.85 Very likely to liquefy 5 PL ≥ 85 Almost certain that it will liquefy Open in new tab Table 1: Liquefaction likelihood classification (Das & Muduli, 2013). Class . Liquefaction probability (PL) . Description of likelihood . 1 PL< 0.15 Almost certain that it will not liquefy 2 0.15 ≤ PL < 0.35 Unlikely to liquefy 3 0.35 ≤ PL < 0.65 Liquefaction and no liquefaction are equally likely 4 0.65 ≤ PL < 0.85 Very likely to liquefy 5 PL ≥ 85 Almost certain that it will liquefy Class . Liquefaction probability (PL) . Description of likelihood . 1 PL< 0.15 Almost certain that it will not liquefy 2 0.15 ≤ PL < 0.35 Unlikely to liquefy 3 0.35 ≤ PL < 0.65 Liquefaction and no liquefaction are equally likely 4 0.65 ≤ PL < 0.85 Very likely to liquefy 5 PL ≥ 85 Almost certain that it will liquefy Open in new tab The assessment of the reliability index (β) associated with solving the constrained minimization problem, is performed by applying the proposed optimization algorithm (HPSO-GA) in order to determine the optimal reliability index (β) for each case history considered in the present study through the FORM in the case of the lack of knowledge of the model uncertainty. The specifications of the hybrid optimization algorithm are given as MaxIt: 500, MaxSubItPSO: 3, MaxSubItGA: 1, nPop: 50, Pcrossover = 0.7, Pmutation = 0.2, and ωinertia weight damping ratio = 0.8. The parameters c1 and c2 are calculated based on the following equations (Clerc & Kennedy, 2002): $$\begin{eqnarray} \chi \ = \frac{2}{{\emptyset - 2 + \sqrt {{\emptyset ^2} - 4\emptyset } }}\ \end{eqnarray}$$(15) $$\begin{eqnarray} {\emptyset _1},\ {\emptyset _2} > 0{\rm{\ }}\quad\emptyset \buildrel \Delta \over = {\emptyset _1} + {\emptyset _2} > 4 \end{eqnarray}$$ $$\begin{eqnarray} \omega \ = \ \chi ,\ \ \ {c_1} = \ \chi .{\emptyset _1},\ \ {c_2} = \ \chi .{\emptyset _2}.\\[-6pt] \nonumber \end{eqnarray}$$ In optimal conditions, $$\begin{eqnarray} \ {\emptyset _1} = \ {\emptyset _2} = \ 2.05,\quad\ \omega \ = \ 0.7298,\quad\ {c_1}, \ {c_2} = \ 1.4962, \end{eqnarray}$$ where |$\ \omega $| is an inertia weight, |${\emptyset _1}$| and |${\emptyset _2}$| are the random positive numbers, and |$\chi $| is a constriction coefficient. The penalty function method is a common approach in order to transform a constrained optimization problem into an unconstrained one by adding (or multiplying) a certain value to the original objective functions based on the total amount of constraint violation errors to form the adjunct function. Hence, the corresponding objective function can be defined as follows (Yeniay, 2005): $$\begin{eqnarray} \hat{z} = \ z.\left( {1 + \alpha v} \right) \end{eqnarray}$$(16) $$\begin{eqnarray} v\ = \ {\rm{max}}\left( {\frac{{\mathrm{ CRR}}}{{\mathrm{ CS}{\mathrm{ R}_{7.5}}}} - 1, 0} \right),\\ \nonumber \end{eqnarray}$$(17) where |$\hat{z}$|⁠, |$\ {z_.}$|⁠, α, and v are the adjunct function, the original objective function (e.g. reliability index), the coefficient of penalty function, and the amount of violation, respectively. Cyclic stress ratio (CSR7.5) is denoted as (Seed & Idriss, 1971) $$\begin{eqnarray} CS{R_{7.5}} = \ 0.65\left( {\frac{{{a_{\mathrm{ max}}}}}{g}} \right)\left( {\frac{{{\sigma _v}}}{{\sigma _v^\prime }}} \right)\left( {{r_\mathrm{ d}}} \right)/\mathrm{ MSF}.{K_\sigma }.{K_\alpha }, \end{eqnarray}$$(18) where CSR7.5 is the cyclic stress ratio adjusted to a benchmark earthquake of moment magnitude of 7.5 and σvc′ = 101 kPa; amax is the peak horizontal ground surface acceleration; g is the ground acceleration; |$\sigma^\prime_v$| and σv are the effective and total vertical stresses at the depth study, respectively, rd is the depth-dependent shear stress reduction coefficient, MSF is the magnitude scaling factor, Kσ is the overburden correction factor for CSR, and Kα is the static shear stress correction factor. The values of Kσ for all of effective pressures less than 3 atm (1 atm = 101 kPa) are obtained according to Fig. 3, where the soil is divided into three areas based on Dr and (N1)60 of soil. In Fig. 3, (N1)60 is the corrected SPT blow count, and Dr is the relative density. In this plot, the value of α is equal to the static active shear stress applied to horizontal plane, which corresponds to the vertical effective stress in that plane. Figure 3: Open in new tabDownload slide Suggested Kα for effective pressures less than 3 atm (1 tsf = 96 kPa). Figure 3: Open in new tabDownload slide Suggested Kα for effective pressures less than 3 atm (1 tsf = 96 kPa). Several amendments for rd have been proposed by various researchers. In this study, rd is calculated based on the relationship presented by Idriss and Boulanger (2010) as follows (Idriss & Boulanger, 2010): $$\begin{eqnarray} {r_\mathrm{ d}} = \ \mathrm{ exp}\left[ {\alpha \left( z \right) + \beta \left( z \right).{M_w}} \right] \end{eqnarray}$$(19) $$\begin{eqnarray} \alpha \left( z \right)\ = \ - 1.012 - 1.126sin\left[ {5.133 + \left( {\frac{z}{{11.73}}} \right)} \right] \end{eqnarray}$$(20) $$\begin{eqnarray} \beta \left( z \right)\ = \ 0.106 + 0.118sin\left[ {5.142 + \left( {\frac{z}{{11.28}}} \right)} \right],\\ \nonumber \end{eqnarray}$$(21) where Mw is the moment magnitude and z is the depth in metres. MSF can be defined as $$\begin{eqnarray} \mathrm{ MSF}\ = \ - 0.058 + 6.9{\rm{exp}}\left( {\frac{{ - {M_w}}}{4}} \right) \le 1.8. \end{eqnarray}$$(22) The cyclic loading laboratory test results demonstrate that the soil susceptibility to the cyclic liquefaction will rise up by increasing the overburden effective stress. In order to consider a non-linear relationship between CSR and |$\sigma^\prime_v$|, the adjustment factor Kσ is calculated as (Seed, 1983) $$\begin{eqnarray} {K_\sigma } = \ 1 - {C_\sigma }{\rm{ln}}\left( {\frac{{\sigma _v^{\prime}}}{{{P_a}}}} \right) \le 1.1 \end{eqnarray}$$(23) $$\begin{eqnarray} {C_\sigma } = \frac{1}{{18.9 - 2.55\sqrt {{{\left( {{N_1}} \right)}_{60,cs}}} }}\ \le 0.3,\\ \nonumber \end{eqnarray}$$(24) where Pa is the atmosphere pressure (101 kPa). CRR is considered as the upper limit of CSR that a soil can resist before liquefying (Juang et al., 2000); in the search algorithm N1,60, FC and |$\sigma^\prime_v$| values are kept constant and by changing CSR7.5 (increase/decrease depends on the location of the data points), the hypothetical data points on the limit state curve can be found out. These data points are applied to estimate the limit state function in the form of CRR = f(N1,60, FC, |$\sigma^\prime_v$|) by the GEP software (Goharzay et al., 2017). A brief summary of the databases (Cetin, 2000) used for model development is presented in Table 2. The information includes the maximum and minimum values of the mean and the COV of the different variables considered as inputs and output of the GEP. Table 2: Summary of the databases utilized for the development of the models in this research. Model variables . Max. mean value . Min. mean value . Max. COV value . Min. COV value . d (m) 20.400 1.100 Nm 37.000 1.500 0.815 0.007 FC (%) 92.000 1 2.000 0.037 |$\sigma_{v}$|(kPa) 383.930 15.470 0.280 0.031 |$\sigma^{^\prime}_{v}$|(kPa) 198.660 8.140 0.378 0.044 amax(g) 0.693 0.090 0.300 0.011 Mw 8.000 5.900 0.025 0 Model variables . Max. mean value . Min. mean value . Max. COV value . Min. COV value . d (m) 20.400 1.100 Nm 37.000 1.500 0.815 0.007 FC (%) 92.000 1 2.000 0.037 |$\sigma_{v}$|(kPa) 383.930 15.470 0.280 0.031 |$\sigma^{^\prime}_{v}$|(kPa) 198.660 8.140 0.378 0.044 amax(g) 0.693 0.090 0.300 0.011 Mw 8.000 5.900 0.025 0 Open in new tab Table 2: Summary of the databases utilized for the development of the models in this research. Model variables . Max. mean value . Min. mean value . Max. COV value . Min. COV value . d (m) 20.400 1.100 Nm 37.000 1.500 0.815 0.007 FC (%) 92.000 1 2.000 0.037 |$\sigma_{v}$|(kPa) 383.930 15.470 0.280 0.031 |$\sigma^{^\prime}_{v}$|(kPa) 198.660 8.140 0.378 0.044 amax(g) 0.693 0.090 0.300 0.011 Mw 8.000 5.900 0.025 0 Model variables . Max. mean value . Min. mean value . Max. COV value . Min. COV value . d (m) 20.400 1.100 Nm 37.000 1.500 0.815 0.007 FC (%) 92.000 1 2.000 0.037 |$\sigma_{v}$|(kPa) 383.930 15.470 0.280 0.031 |$\sigma^{^\prime}_{v}$|(kPa) 198.660 8.140 0.378 0.044 amax(g) 0.693 0.090 0.300 0.011 Mw 8.000 5.900 0.025 0 Open in new tab For the development of the proposed CRR models, approximately 70% of the databases are randomly selected as training and the rest of them as testing data. Among numerous GEP-based CRR models, the best model is chosen on the basis of the statistical performance [e.g. coefficient of determination (R2) and MSE]. The proposed GEP-based CRR model outputs have a good conformity with the results obtained based on the Idriss and Boulanger equations (Idriss & Boulanger, 2010), which demonstrates the competency of the GEP in estimating the comprehensive predictive models. Equation (25) is found to be the most appropriate prediction model of CRR through the GEP (Goharzay et al., 2017). $$\begin{eqnarray} CRR &=& \frac{{{{({N_1})}_{60}}^{54}}}{{\sigma _v^\prime - FC}} + \sin \Big\{ {\sqrt[4]{{\sin \left( {\sigma _v^\prime } \right)}} \times \sigma _v^\prime \times {{({N_1})}_{60}}^2}\nonumber\\[10pt] && {\times \left[ {{{({N_1})}_{60}} - FC} \right]} \Big\} + \sqrt[4]{{FC}} \times {\left( {{N_1}} \right)_{60}}^3 \times \left[ {{{({N_1})}_{60}} - \sigma _v^\prime } \right]\nonumber\\[10pt] && \times\, 1.190887 + \frac{{\sqrt[4]{{{{\left[ {{{\left( {{N_1}} \right)}_{60}} + 0.37854} \right]}^3}}}}}{{{{\left( {{N_1}} \right)}_{60}}^2 + FC + 4.669555}}, \end{eqnarray}$$(25) where (N1)60 is the corrected SPT blow count and FC is the fine content percentage. The correlation coefficients among six input variables are given in Table 3 (Juang, Fang, & Li 2008). The reliability indices (β) for the total 94 cases (59 liquefied and 35 non-liquefied cases) of the databases, for which the statistical specifications are available, can be determined utilizing the HPSO-GA. The flowchart of solving optimal reliability index (β) by the proposed optimization algorithm is shown in Fig. 4. Table 3: Correlation coefficients among the input variables (Lee et al., 2010). . Input parameters . Input parameters . (N1)60 . FC . |$\sigma^\prime_{v}$| . σv . amax . Mw . (N1)60 1 0 0.3 0.3 0 0 FC 0 1 0 0 0 0 |$\sigma^\prime_{v}$| 0.3 0 1 0.9 0 0 σv 0.3 0 0.9 1 0 0 amax 0 0 0 0 1 0.9 Mw 0 0 0 0 0.9 1 . Input parameters . Input parameters . (N1)60 . FC . |$\sigma^\prime_{v}$| . σv . amax . Mw . (N1)60 1 0 0.3 0.3 0 0 FC 0 1 0 0 0 0 |$\sigma^\prime_{v}$| 0.3 0 1 0.9 0 0 σv 0.3 0 0.9 1 0 0 amax 0 0 0 0 1 0.9 Mw 0 0 0 0 0.9 1 Open in new tab Table 3: Correlation coefficients among the input variables (Lee et al., 2010). . Input parameters . Input parameters . (N1)60 . FC . |$\sigma^\prime_{v}$| . σv . amax . Mw . (N1)60 1 0 0.3 0.3 0 0 FC 0 1 0 0 0 0 |$\sigma^\prime_{v}$| 0.3 0 1 0.9 0 0 σv 0.3 0 0.9 1 0 0 amax 0 0 0 0 1 0.9 Mw 0 0 0 0 0.9 1 . Input parameters . Input parameters . (N1)60 . FC . |$\sigma^\prime_{v}$| . σv . amax . Mw . (N1)60 1 0 0.3 0.3 0 0 FC 0 1 0 0 0 0 |$\sigma^\prime_{v}$| 0.3 0 1 0.9 0 0 σv 0.3 0 0.9 1 0 0 amax 0 0 0 0 1 0.9 Mw 0 0 0 0 0.9 1 Open in new tab 4. Results and Discussion 4.1. Parameter uncertainty impact on liquefaction probability without consideration of the model uncertainty In the following, corresponding probabilities (PL) are derived from the notional probability concept (equation 3) and the Bayesian mapping function (equation 14) without taking into account the model uncertainty. A difference is observed between the two probability curves depicted in Fig. 5. As the accuracy of the calculated notional probability depends on the accuracy of the reliability index (β), due to the lack of consideration of uncertainty associated with the model in the reliability analysis, the calculated β in this case (β in terms of lacking knowledge of model uncertainty is called β1) and the corresponding notional probability may be either underestimated or overestimated and cannot be expected to give the reliable results. While, as the Bayesian probability curve is calibrated empirically with the field observations of the databases, the effect of the uncertainty related to the limit state model is inherent in the probability calculations, it is supposed to provide a good approximation of the true probability of liquefaction. Figure 5: Open in new tabDownload slide Comparison of the Bayesian probability with the notional probability obtained from the FORM analysis without considering the model uncertainty. Figure 5: Open in new tabDownload slide Comparison of the Bayesian probability with the notional probability obtained from the FORM analysis without considering the model uncertainty. The investigation of the effect of the level of parameter uncertainty on the liquefaction probability can be performed by comparing the Bayesian mapping functions derived for each uncertainty level. Figure 6 shows the effect of five levels of the uncertainty (COVs = 0.10, 0.25, 0.40, 0.55, and 0.70) of the parameter N1,60 alone on the β1–PL curves (Bayesian mapping function). The results show that within the cases between COV = 0.1 and 0.25 the level of N1,60 uncertainty has little effect on the probability curves and the effect of the uncertainty becomes significant at the greater COV values. In a similar vein, the effect of the uncertainty of the FC parameter for four different COV values (COVs = 0.10, 0.75, 1.25, and 2.00) is investigated. As expected, the FC does not have a remarkable effect on the Bayesian probability curve (Fig. 7). In order to study the effect of the levels of uncertainty of the parameter |$\sigma^\prime_v$|⁠, four different scenarios of COVs (0.05, 0.15, 0.25, and 0.35) are performed. Figure 8 shows that within some ranges of COVs (COV = 0.05–0.15 and COV = 0.25–0.35) the level of σv´ uncertainty has a noticeable effect on the β1–PL relationship, but no significant difference is observed within the COV (0.15–0.25). In a similar manner, six different scenarios are studied (COV amax = 0.1 and COV Mw = 0.01, COV amax = 0.1 and COV Mw = 0.02, COV amax = 0.2 and COV Mw = 0.01, COV amax = 0.2 and COV Mw = 0.02, COV amax = 0.3 and COV Mw = 0.01, and COV amax = 0.3 and COV Mw = 0.02) for assessing the effect of the levels of uncertainty of the parameters amax and Mw. As indicated in Fig. 9, in spite of the little influence of the Mw uncertainty, the COV of amax has a significant impact on the probability curves. According to the results obtained through the reliability analysis, it can be concluded that each developed Bayesian probability function is efficient for the relevant parameter uncertainty level and the suggested Bayesian mapping functions may not be applicable if the uncertainty levels of a future case study differ remarkably from those of the previous analysis. As it is not reasonable to develop Bayesian probability functions for each level of the parameter uncertainty, a rigorous reliability analysis, which considers both of the associated uncertainties (parameter and the limit state model uncertainties), is highly recommended. Figure 6: Open in new tabDownload slide Investigation of the effect of COV of parameter (N1)60 on the Bayesian mapping function. Figure 6: Open in new tabDownload slide Investigation of the effect of COV of parameter (N1)60 on the Bayesian mapping function. Figure 7: Open in new tabDownload slide Investigation of the effect of COV of parameter FC on the Bayesian mapping function. Figure 7: Open in new tabDownload slide Investigation of the effect of COV of parameter FC on the Bayesian mapping function. Figure 8: Open in new tabDownload slide Investigation of the effect of COV of parameter |$\sigma^\prime_v$| on the Bayesian mapping function. Figure 8: Open in new tabDownload slide Investigation of the effect of COV of parameter |$\sigma^\prime_v$| on the Bayesian mapping function. Figure 9: Open in new tabDownload slide Investigation of the effect of COV of parameters amax and Mw on the Bayesian mapping function. Figure 9: Open in new tabDownload slide Investigation of the effect of COV of parameters amax and Mw on the Bayesian mapping function. 4.2. Estimation of the model uncertainty The accurate determination of the probabilities is not possible unless the effect of model uncertainty is incorporated within the reliability analysis. In order to evaluate the liquefaction probability of soils, a random variable referred to as model factor (cmf) is considered to quantify the uncertainties related to the limit state model in the FORM analysis. Since the CRR model is obtained on the basis of the CSR model, the uncertainty in the CRR model shall be considered alone, which is also recommended as the appropriate limit state model by Juang et al. (2005) as follows: $$\begin{eqnarray} g \left( z \right) = {c_{\mathrm{ mf}}} R - Q\ = \ {c_{\mathrm{ mf}}}\mathrm{ CRR }- \mathrm{ CSR} \end{eqnarray}$$(26) in which g(z) is the limit state function in terms of considering model uncertainty and z is a vector of random variables, z = {cmf, (N1)60, FC, σv, |$\sigma^\prime_v$|, amax, Mw}. Similar to other variables, the model factor is assumed to follow a lognormal distribution. The estimation of model uncertainty includes finding out two statistical characteristics of the model factor, namely the mean (μcmf) and the COV. As the model factor has a weak dependence on the other input variables (Phoon & Kulhawy, 2005), in the present study no correlation is considered between cmf and other six input parameters. The model uncertainty is correctly estimated if the reliability indices (β in terms of considering the model uncertainty is called β2) and the related notional probabilities are most compatible with those based on the Bayes’ theorem, as well as by plotting the β2 values against the calibrated probabilities, PL found to be 0.5 in the case of β2 = 0, in which the most unbiased evaluation of liquefaction potential of soils can be rest assured. In the current study, a simple trial-and-error approach is implemented in order to estimate the model uncertainty within the efficient reliability analysis based on a Bayesian framework. Figure 10 shows the four scenarios of model uncertainty with μcmf = 1, in terms of COVs (0.0, 0.1, 0.2, and 0.3). For each scenario, the reliability indices and the corresponding probabilities are calculated taking into account the effect of model uncertainty for 94 cases of the databases through the FORM analysis and Bayesian technique. According to Fig. 10, at μcmf = 1 and COV = 0.2, PL = 0.519 at β2 = 0. Thus, the COV component of model uncertainty is considered constant at 0.2 for subsequent reliability analyses. Afterwards, the five scenarios of model uncertainty in terms of COV = 0.2 and μcmf = (0.90, 0.95, 1.00, 1.05, and 1.10) are investigated (Fig. 11). It has been observed that the mapping function is transmitted from left to right, and the corresponding probabilities increase as the μcmf value increases. In the third scenario (μcmf = 1 and COV = 0.2), β2 and the corresponding PL are 0 and 0.5186, respectively, whereas in the second scenario (μcmf = 0.95 and COV = 0.2), the PL value is equal to 0.4857 in terms of β2 = 0. Finally, the μcmf value is estimated as 0.97 by using a conjectural interpolation. Similar to the first mode, four scenarios of model uncertainty with μcmf = 0.97 and COVs = 0–0.3 are implemented through the series of reliability analyses. According to Fig. 12, the statistical characteristics of model factor are chosen as μcmf = 0.97 and COV = 0.2, which presents PL = 0.5 at β2 = 0. Figure 10: Open in new tabDownload slide Investigation of the effect of COV of the model factor on the liquefaction probability. Figure 10: Open in new tabDownload slide Investigation of the effect of COV of the model factor on the liquefaction probability. Figure 11: Open in new tabDownload slide Investigation of the effect of μcmf on the liquefaction probability. Figure 11: Open in new tabDownload slide Investigation of the effect of μcmf on the liquefaction probability. Figure 12: Open in new tabDownload slide Investigation of the effect of COV of model factor on the liquefaction probability in order to find the most unbiased model. Figure 12: Open in new tabDownload slide Investigation of the effect of COV of model factor on the liquefaction probability in order to find the most unbiased model. The effect of the COV component of model uncertainty on the reliability indices is investigated by plotting the β1 values (β without considering model uncertainty) against the β2 values (β considering model uncertainty) in Fig. 13, which indicate that the slope of the line passing through the points decreases as the COV of the model factor increases. Figure 14 shows the effect of the μcmf component of model uncertainty on the reliability indices in five scenarios, which illustrate that the intercept of the linear trend line increases by increasing the μcmf value. Figure 15 demonstrates a comparison between the liquefaction probabilities obtained from the Bayesian theory in terms of lacking knowledge of the model uncertainty (PL1, μcmf = 1, COV = 0), and the probabilities considering the true model uncertainty (PL2, μcmf = 0.97, COV = 0.2). The very good agreement (R2 = 0.98839) between both the cases indicates the robustness of the Bayesian mapping approach in estimating the liquefaction probabilities (PL) in terms of unknown model uncertainty specifications. A comparison between the calibrated liquefaction probabilities calculated using the Bayesian mapping function without considering the model uncertainty (PL1, μcmf = 1, COV = 0), and the notional probabilities considering the true model uncertainty (PL2, μcmf = 0.97, COV = 0.2) is presented in Fig. 16, which indicates the strong agreement (R2 = 0.97164) between the two liquefaction probability sets. It can be concluded that the estimated notional probabilities are accurate if the true model factor characteristics are incorporated within the reliability analysis. Figure 13: Open in new tabDownload slide Investigation of the effect of COV of model factor on the reliability index (β2). Figure 13: Open in new tabDownload slide Investigation of the effect of COV of model factor on the reliability index (β2). Figure 14: Open in new tabDownload slide Investigation of the effect of μcmf on the reliability index (β2). Figure 14: Open in new tabDownload slide Investigation of the effect of μcmf on the reliability index (β2). Figure 15: Open in new tabDownload slide Comparison of the liquefaction probabilities obtained from the Bayesian mapping function in two different conditions (with/without consideration of model uncertainty). Figure 15: Open in new tabDownload slide Comparison of the liquefaction probabilities obtained from the Bayesian mapping function in two different conditions (with/without consideration of model uncertainty). Figure 16: Open in new tabDownload slide Comparison of the liquefaction probabilities obtained from the Bayesian mapping function without considering the model uncertainty with the notional probabilities in terms of considering the true model uncertainty. Figure 16: Open in new tabDownload slide Comparison of the liquefaction probabilities obtained from the Bayesian mapping function without considering the model uncertainty with the notional probabilities in terms of considering the true model uncertainty. 5. Two Examples In the following, two cases of the databases are investigated to verify the accuracy of the above study. The first example is the Miyagi-ken-oki earthquake that occurred in Japan on 12 June 1978. As a liquefied case, the seismic and soil parameters at the critical depth (z = 3.7 m) are given below: $$\begin{eqnarray} {N_m} = 3.7,{C_B} = 1,{C_S} = 1,{C_R} = 0.77,{C_E} = 1.09,FC = 10\% , \\ {\sigma _v} = 58.83{\rm{\, kPa}},\sigma^\prime_v = 36.28\,{\rm{kPa}},{a_{\mathrm{ max}}} = 0.2{\rm{\,g}},{M_w} = 7.4. \end{eqnarray}$$ The COVs of the parameters Nm, FC, |${\sigma _v}, \sigma^\prime_v$|⁠, amax, and Mw are 0.189, 0.2, 0.217, 0.164, 0.2, and 0.1, respectively. By implementing the meta-heuristic optimization algorithm (HPSO-GA) and considering the estimated true model uncertainty (μcmf = 0.97, COV = 0.2) within the FORM analysis, the reliability index (β2) and the corresponding notional liquefaction probability (PL) using equation (3) are found out to be −1.41 and 0.921, respectively, and Juang et al. (2008) reported the corresponding notional probability for this case as 0.91. The liquefaction probability can also be obtained from the Bayesian mapping function (Fs–PL) proposed by Goharzay et al. (2017) by considering only the mean values of the input variables. The calculated safety factor and the corresponding Bayesian PL are predicted as 0.573 and 0.943, respectively. These two analyses yield consistent results, which confirm the field observation of liquefaction and support the accuracy of different estimation approaches used to predict the liquefaction probabilities. The second example is the San Juan earthquake that occurred in Argentina on 23 November 1977. As a non-liquefied case, the seismic and soil parameters at the critical depth (z = 2.9 m) are as follows: $$\begin{eqnarray} {N_m} = 15.2,{C_B} = 1,{C_S} = 1,{C_R} = 0.72,{C_E} = 0.75,FC = 3\% , \\ {\sigma _v} = 45.61{\rm{ }}\,kPa,\sigma^\prime_v = 38.14{\rm{\, kPa}},{a_{\mathrm{ max}}} = 0.2{\rm{g}},{M_w} = 7.4. \end{eqnarray}$$ The COVs of the parameters Nm, FC, σv, |$\sigma^\prime_v$|, amax, and Mw are 0.026, 0.333, 0.107, 0.085, 0.075, and 0.1, respectively. In the similar way, β2 and the corresponding notional probability (PL) in terms of considering the true model uncertainty are calculated as 0.468 and 0.32, respectively. Juang et al. (2008) also investigated this case and obtained β2 and the notional PL as 0.533 and 0.297, respectively. The liquefaction probability can also be obtained from the Bayesian mapping function (Fs–PL) proposed by Goharzay et al. (2017) by considering only the mean values of the input variables. The calculated safety factor and the corresponding Bayesian PL are predicted as 1.241 and 0.247, respectively. The results prove the case to be non-liquefied, which indicates the robustness of the methodology used in this study. 6. Conclusions The following concluding remarks can be obtained from this study: Easy implementation, fast computing, and the low memory requirements of the PSO algorithm, making it superior to the other algorithms. Therefore, HPSO-GA by combining the strengths of PSO and GA, as an appropriate optimization tool for solving complex problems (e.g. reliability analysis), speeds up the convergence rate besides providing the accurate solutions. The development of the mapping function for each level of parameter uncertainty to interpret the probability of liquefaction occurrence is not practical. Hence, the reliability analysis, which does not depend only on the mean values of input parameters and takes into account effects of both uncertainties associated with the input parameters and the limit state model, is suggested in order to achieve more accurate estimation of the right liquefaction probability. If the uncertainties related to the limit state model have a significant impact on the probability assessment, by disregarding them during the analysis, the reliability indices (β1) and thus, the corresponding notional probabilities (PL) will include some errors. Nevertheless, the Bayesian mapping function, which is calibrated empirically with the field observations of the case history databases, covers the effect of the associated uncertainties of the databases implicitly and consequently, provides more accurate predictions in terms of lacking knowledge of model uncertainty. Due to obtaining compatible results from the Bayesian mapping function with and without considering the model uncertainty, it can be concluded that the calibrated Bayesian functions can produce excellent predictions of the liquefaction probability in terms of lacking knowledge of the limit state model uncertainties. The comparison of the Bayesian probabilities with those based on the notional concept in terms of not considering the model uncertainty effect and considering the true model factor characteristics (μcmf = 0.97, COV = 0.2), respectively, implies the good consistency of the results derived from both methods, which demonstrates that the model uncertainty is well incorporated in the reliability analysis. Conflict of interest statement Declarations of interest: none. References Andrus R. D. , Stokoe K. H. II ( 2000 ). Liquefaction resistance of soils from shear-wave velocity . Journal of Geotechnical and Geoenvironmental Engineering , 126 ( 11 ), 1015 – 1025 . 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Post-liquefaction SPT-based Data (Cetin, 2000) Used for Reliability Analysis Mean depth (m) . Mean σv (kPa) . COV σv . Mean |$\sigma^\prime_v$|(kPa) . COV |$\sigma^\prime_v$| . Mean amax (g) . COV . Mean Nm . COV Nm . Mean Mw . COV Mw . Mean FC (%) . COV FC . CR . CS . CB . CE . Liquefied? . 4.2 69.61 0.149 51.85 0.107 0.24 0.2 6 0.333 7.4 10 0.2 0.8 1 1 1.09 Yes 5.2 89.15 0.085 57.29 0.084 0.4 0.1 11.7 0.248 8 2 0.5 0.85 1 1 1.22 Yes 3 49.07 0.118 22.22 0.139 0.24 0.2 7 0.229 7.4 12 0.167 0.73 1 1 1 Yes 4.5 73.26 0.078 46.37 0.08 0.2 0.075 6 0.017 7.4 50 0.1 0.82 1 1 0.75 Yes 3.7 58.83 0.217 36.28 0.164 0.2 0.2 3.7 0.189 7.4 10 0.2 0.77 1 1 1.09 Yes 4.7 72.78 0.157 35.43 0.189 0.17 0.265 7.8 0.449 6.5 0.02 40 0.075 0.83 1 1 1.05 No 6 102.7 0.123 67.73 0.103 0.24 0.2 9.9 0.424 7.4 10 0.2 0.88 1 1 1.09 No 9.9 184.6 0.179 135.57 0.126 0.4 0.1 17.5 0.154 6.9 0.016 20 0.25 1 1 1 1.22 No 3.5 53.89 0.057 44.04 0.073 0.26 0.096 13 0.238 7 0.017 3 0.333 0.76 1 1 1 Yes 8.5 137.8 0.105 69.39 0.109 0.1 0.2 9.5 0.158 7.3 0.015 5 0.4 0.95 1 1 1 Yes 5.5 90 0.095 45.05 0.109 0.095 0.011 4.6 0.087 6.1 13 0.077 0.86 1 1 1.09 No 11.4 211 0.054 116.24 0.068 0.18 0.15 24.7 0.121 7.5 0.015 8 0.25 1 1 1 1.21 No 6.2 112.6 0.04 93.48 0.044 0.54 0.074 10.3 0.155 6.7 0.019 38 0.605 0.89 1 1 1.13 Yes 3.2 52.82 0.133 30.77 0.137 0.09 0.2 2.7 0.556 7.5 0.015 5 0.4 0.74 1 1 1.22 Yes 10.7 200.1 0.106 110.44 0.106 0.4 0.1 26 0.096 8 0 0 1 1 1 1.22 No 2.4 38.18 0.093 27.02 0.113 0.24 0.2 11.5 0.191 7.4 7 0.143 0.68 1 1 1.12 Yes 6.5 117.4 0.036 83.12 0.053 0.22 0.045 13 0.315 7 0.017 5 0.2 0.9 1.1 1 0.92 Yes 6 82.08 0.066 57.57 0.072 0.165 0.079 4 0.35 7 0.017 25 0.2 0.88 1.1 1 0.92 Yes 8.9 159.8 0.043 142.12 0.049 0.693 0.087 20 0.22 6.7 0.019 43 0.302 0.97 1 1 1.13 Yes 7.9 129.6 0.194 66.05 0.169 0.13 0.2 8.4 0.19 7.3 0.015 67 0.104 0.94 1 1 0.83 Yes 7.9 143.2 0.137 88.63 0.121 0.24 0.2 19.3 0.13 7.4 5 0.2 0.94 1 1 1.21 No 2.7 44.57 0.28 22.52 0.257 0.12 0.2 4.6 0.348 6.7 5 0.2 0.71 1 1 1 Yes 5 84.97 0.206 44.91 0.185 0.1 0.2 8.8 0.318 6.7 0 0 0.84 1 1 1.09 No 3.7 60.52 0.162 32.09 0.156 0.24 0.2 8.8 0.42 7.4 0 0 0.77 1 1 1 Yes 3.7 58.83 0.217 36.28 0.164 0.12 0.2 3.7 0.189 6.7 10 0.2 0.77 1 1 1.09 No 5.5 97.24 0.069 52.15 0.089 0.35 0.2 18.1 0.088 8 0.011 20 0.15 0.86 1 1 1 Yes 2.5 35.74 0.089 30.84 0.113 0.18 0.111 10.9 0.202 6.7 0.019 30 0.167 0.69 1 1 1.05 No 5.7 94.84 0.108 38.48 0.153 0.116 0.155 8.9 0.079 7.7 0.013 3 0.333 0.87 1 1 1.22 Yes 2.9 45.74 0.238 25.71 0.207 0.2 0.2 5.6 0.143 7.9 20 0.15 0.72 1 1 1.17 Yes 8.5 155.1 0.15 120.82 0.102 0.4 0.1 19.7 0.142 6.9 0.016 20 0.25 0.95 1 1 1.22 No 7.7 146.5 0.24 94.08 0.192 0.34 0.029 5.7 0.246 6.9 0.016 20 0.25 0.93 1 1 1.22 Yes 4.7 84.15 0.096 40.83 0.196 0.19 0.105 21 0.024 6.7 0.019 18 0.167 0.83 1 1 1.05 No 3.5 61.66 0.206 38.13 0.171 0.22 0.2 19.7 0.157 8 0.011 5 0.6 0.76 1 1 1 No 4.5 72.31 0.118 40.16 0.118 0.13 0.2 9.5 0.263 8 0.011 12 0.25 0.81 1 1 1 Yes 4.5 65.59 0.117 41.08 0.102 0.09 0.278 4.5 0.778 6.2 0.023 75 0.133 0.81 1 1 1.05 No 7.2 127.4 0.156 78.84 0.126 0.25 0.1 20 0.205 7.6 19 0.105 0.92 1 1 0.65 Yes 3.5 53.41 0.065 48.51 0.053 0.28 0.2 11 0.245 7.4 5 0.4 0.76 1 1 1 Yes 2 30.93 0.257 16.28 0.256 0.2 0.3 1.8 0.333 8 27 0.111 0.64 1 1 1.17 Yes 3 49.72 0.12 29.14 0.126 0.32 0.2 15.5 0.31 7.4 4 0.25 0.73 1 1 1.12 No 4.6 68.04 0.099 57.01 0.1 0.14 0.093 4.6 0.717 7 0.017 30 0.233 0.82 1.1 1 0.92 No 2.4 41.9 0.223 26.96 0.188 0.225 0.111 14.4 0.153 7.9 5 0.4 0.68 1 1 1.21 No 2.6 41.67 0.181 28.44 0.144 0.32 0.2 5.2 0.385 7.4 4 0.25 0.7 1 1 1 Yes 5.7 94.84 0.108 38.48 0.153 0.213 0.141 8.9 0.079 7.8 3 0.333 0.87 1 1 1.22 Yes 6 87.58 0.066 63.07 0.067 0.13 0.1 4 0.35 7 0.017 25 0.12 0.88 1.1 1 0.92 Yes 4.5 75.4 0.089 60.7 0.069 0.5 0.2 29.4 0.139 8 0.011 10 0.2 0.81 1 1 1 No 4.2 66.67 0.115 54.66 0.142 0.28 0.2 13.2 0.424 7.4 0 0 0.8 1 1 1.21 No 3.6 57.38 0.18 39.24 0.13 0.12 0.2 2 0.4 6.7 60 0.083 0.77 1 1 1 No 5.3 81.54 0.073 70.93 0.086 0.45 0.1 3.4 0.265 6.6 55 0.091 0.85 1 1 1.13 Yes 6.6 96.57 0.071 87.5 0.085 0.46 0.109 10.2 0.363 7 0.017 27 0.185 0.9 1 1 1.13 Yes 6 101.6 0.093 63.9 0.084 0.24 0.2 21 0.09 7.4 0 0.88 1 1 1.12 No 3.3 51.47 0.188 33.55 0.142 0.09 0.256 5.9 0.288 5.9 0.025 31 0.097 0.75 1 1 1.05 No 4.5 65.59 0.117 41.08 0.102 0.17 0.118 4.5 0.778 5.9 0.025 75 0.133 0.81 1 1 1.05 Yes 7.5 123.1 0.226 53.4 0.23 0.227 0.154 7.6 0.224 7.7 0.013 1 1 0.93 1 1 1.22 Yes 4.2 66.08 0.131 51.14 0.091 0.13 0.077 6.4 0.516 6.5 0.02 92 0.109 0.8 1 1 1.05 No 4.7 72.78 0.147 35.43 0.148 0.1 0.05 7.8 0.449 6.2 0.023 40 0.075 0.83 1 1 1.05 No 3.6 57.38 0.18 39.24 0.13 0.24 0.2 2 0.4 7.4 60 0.083 0.77 1 1 1 Yes 9.2 158.3 0.056 77.4 0.085 0.15 0.2 13.1 0.229 7.1 0 0 0.97 1 1 1.22 No 9.5 174.8 0.17 130.65 0.119 0.4 0.1 30.2 0.235 6.9 0.016 20 0.25 0.98 1 1 1.22 No 3 49.07 0.118 22.22 0.139 0.12 0.2 7 0.229 6.7 12 0.167 0.73 1 1 1 No 4.5 76.85 0.124 55.93 0.097 0.24 0.2 11.9 0.227 7.4 26 0.192 0.82 1 1 1.09 No 2.5 39.27 0.092 34.37 0.078 0.24 0.104 17.9 0.173 7 0.017 1 2 0.69 1 1 1 No 3.4 54.08 0.172 37.9 0.225 0.47 0.106 10.6 0.302 6.5 0.02 37 0.135 0.76 1 1 1.13 No 4.1 68.41 0.205 45.87 0.15 0.27 0.093 15 0.22 7 0.017 1 2 0.79 1 1 1 No 3.5 53.57 0.169 36.9 0.125 0.29 0.086 6.1 0.557 7 0.017 2 1 0.76 1 1 1 Yes 5.2 85.16 0.123 42.66 0.146 0.16 0.15 7.9 0.177 7.5 0.015 8 0.25 0.85 1 1 1.09 Yes 6 82.08 0.119 57.57 0.084 0.15 0.087 3.9 0.487 7 0.017 50 0.1 0.88 1.1 1 0.92 Yes 5.5 104.4 0.155 71.52 0.122 0.225 0.111 25.5 0.067 7.9 5 0.4 0.86 1 1 1.21 No 3.5 54.98 0.153 37.83 0.118 0.25 0.22 9.7 0.227 7.7 0.013 1 1 0.76 1 1 1.22 Yes 4.5 73.01 0.15 53.9 0.103 0.24 0.104 15.7 0.204 7 0.017 1 2 0.82 1 1 1 Yes 3.7 60.52 0.162 32.09 0.156 0.12 0.2 8.8 0.42 6.7 0 0 0.77 1 1 1 No 6.5 123.3 0.051 113.51 0.087 0.24 0.1 37 0.038 7 0.017 7 0.286 0.9 1.2 1 0.92 No 7.5 122.3 0.124 57.72 0.152 0.16 0.15 9.4 0.16 7.5 0.015 8 0.25 0.93 1 1 1.09 Yes 11.4 210.5 0.225 136.98 0.171 0.34 0.118 11.6 0.31 6.9 0.016 20 0.25 1 1 1 1.22 Yes 5.2 88.44 0.119 71.78 0.081 0.4 0.125 20.7 0.454 6.9 0.016 18 0.222 0.85 1 1 1.22 No 7 117.4 0.108 63.66 0.119 0.2 0.2 12.4 0.056 7.3 0.015 48 0.104 0.91 1 1 1 Yes 4.2 66.08 0.142 51.14 0.179 0.19 0.132 6.4 0.516 5.9 0.025 92 0.109 0.8 1 1 1.05 Yes 3.5 56 0.199 32.48 0.166 0.22 0.2 5.9 0.136 8 0.011 3 0.667 0.76 1 1 1 Yes 4.7 82.08 0.128 35.52 0.165 0.25 0.16 8.5 0.247 6.9 0.016 20 0.35 0.83 1 1 1.22 Yes 2.7 44.57 0.28 22.52 0.257 0.32 0.2 4.1 0.39 7.4 5 0.2 0.71 1 1 1 Yes 8.2 131.4 0.031 95.58 0.046 0.2 0.075 9 0.233 7.4 20 0.15 0.95 1 1 0.75 Yes 7.9 130.5 0.137 61.06 0.161 0.16 0.15 8.8 0.25 7.5 0.015 8 0.25 0.94 1 1 1.09 Yes 4.2 66.08 0.131 51.14 0.091 0.174 0.115 6.4 0.516 6.7 0.019 92 0.109 0.8 1 1 1.05 No 4.2 69.32 0.26 37.46 0.215 0.2 0.2 4.8 0.583 7.7 0.013 15 0.267 0.8 1 1 1.22 Yes 7.5 131.4 0.082 70.63 0.106 0.24 0.2 20.5 0.215 7.4 17 0.176 0.93 1 1 1.12 No 9.9 183.8 0.139 115.18 0.115 0.34 0.118 9.5 0.137 6.9 0.016 20 0.25 1 1 1 1.22 Yes 1.1 15.47 0.243 8.14 0.378 0.16 0.281 5.8 0.241 6.5 0.02 80 0.125 0.5 1 1 1.05 Yes 3.3 51.47 0.188 33.55 0.142 0.51 0.098 5.9 0.288 6.5 0.02 31 0.097 0.75 1 1 1.05 Yes 6 108.3 0.066 61.46 0.077 0.18 0.15 30 0.097 7.5 0.015 0 0 0.88 1 1 1.21 No 4.9 85.81 0.181 59.83 0.13 0.25 0.1 34.2 0.216 7.6 19 0.105 0.84 1 1 0.65 No 4.2 69.61 0.149 51.85 0.107 0.14 0.171 6 0.483 6.7 10 0.2 0.8 1 1 1.09 No 2.9 49.88 0.163 39.1 0.169 0.156 0.128 26.4 0.394 6.7 0.019 25 0.16 0.72 1 1 1.13 No 4.2 71.87 0.067 40.01 0.095 0.2 0.2 10.4 0.538 8 0.011 5 0.6 0.8 1 1 1 Yes 1.1 15.47 0.243 8.14 0.378 0.19 0.105 5.8 0.241 6.7 0.019 80 0.125 0.5 1 1 1.05 No 6.2 117.8 0.048 85.96 0.057 0.25 0.04 6 0.65 7 0.017 8 0.375 0.89 1.1 1 0.92 Yes 3.7 61.59 0.214 24.99 0.231 0.16 0.15 3.9 0.179 7.5 0.015 10 0.3 0.77 1 1 1.09 Yes 7.9 141.6 0.053 98 0.054 0.4 0.125 25.9 0.193 6.9 0.016 2 0.5 0.94 1 1 1.22 No 4.7 72.78 0.148 35.43 0.249 0.23 0.087 7.8 0.449 5.9 0.025 40 0.075 0.83 1 1 1.05 Yes 5.9 91.33 0.119 74.9 0.114 0.14 0.171 9 0.2 6.7 5 0.6 0.88 1 1 1 No 12.1 165.6 0.187 78.98 0.155 0.135 0.111 13 0.269 7.5 3 0.333 1 1 1 0.75 No 4.5 73.95 0.153 33.27 0.176 0.12 0.183 7.7 0.091 7.1 0 0 0.81 1 1 1.22 Yes 7 115.4 0.084 92.84 0.062 0.41 0.122 20 0.165 7 0.017 13 0.154 0.91 1 1 1.13 Yes 9.1 129 0.238 54.35 0.213 0.135 0.111 4.3 0.302 7.5 3 0.333 0.97 1 1 0.75 Yes 6.5 98.26 0.086 82.58 0.063 0.46 0.109 9 0.1 7 0.017 15 0.133 0.9 1 1 1.13 Yes 4.5 65.59 0.117 41.08 0.102 0.2 0.2 4.5 0.778 6.6 0.02 75 0.133 0.81 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.14 0.2 9 0.233 6.7 20 0.15 0.74 1 1 1.09 No 7.5 135.6 0.119 80.04 0.108 0.18 0.15 17.5 0.063 7.5 0.015 8 0.25 0.93 1 1 1.21 No 4.7 80.68 0.066 37.36 0.105 0.17 0.118 21 0.024 5.9 0.025 18 0.167 0.83 1 1 1.05 No 9.2 172.4 0.045 120 0.048 0.51 0.118 24.4 0.123 6.7 0.019 25 0.2 0.97 1 1 1.13 Yes 4.2 133.4 0.122 105.94 0.072 0.2 0.2 23.3 0.094 7.4 10 0.2 0.8 1 1 1.21 No 4.2 69.32 0.26 37.46 0.215 0.15 0.2 4.8 0.583 7.1 15 0.267 0.8 1 1 1.22 No 4 65.91 0.183 32.15 0.211 0.225 0.111 4.5 0.156 7.9 5 0.4 0.79 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.24 0.2 4.3 0.581 7.4 10 0.2 0.73 1 1 1 Yes 4.5 65.59 0.118 41.08 0.104 0.18 0.106 4.5 0.778 6.5 0.02 75 0.133 0.81 1 1 1.05 Yes 3.3 53.17 0.224 32.21 0.175 0.4 0.3 3.6 0.278 7.3 0 0 0.75 1 1 1.17 Yes 4.7 72.78 0.147 35.43 0.148 0.18 0.028 7.8 0.449 6.6 0.02 40 0.075 0.83 1 1 1.05 Yes 3.5 53.06 0.157 38.2 0.123 0.2 0.3 6 0.333 8 13 0.077 0.76 1 1 1.17 Yes 1.7 26.7 0.15 19.35 0.166 0.25 0.1 6.5 0.062 7 0.017 35 0.143 0.61 1 1 1 Yes 6 86.4 0.12 66.79 0.078 0.42 0.119 8 0.45 7 0.017 22 0.136 0.88 1 1 1.13 Yes 4.2 65.12 0.154 47.19 0.114 0.2 0.3 1.5 0.4 8 25 0.12 0.8 1 1 1.17 Yes 3.9 61.38 0.144 46.19 0.183 0.24 0.104 10.2 0.039 7 0.017 3 0.333 0.79 1 1 1 Yes 6 86.01 0.091 71.3 0.145 0.37 0.135 9 0.244 7 0.017 8 0.25 0.88 1 1 1.13 Yes 5 81.53 0.076 38.4 0.114 0.16 0.15 4.4 0.364 7.5 0.015 0 0 0.84 1 1 1.09 Yes 20.4 383.9 0.04 198.66 0.065 0.4 0.1 8.5 0.259 8 − 10 0.3 1 1 1 1.22 Yes 7.5 140 0.071 95.86 0.068 0.25 0.04 12 0.425 7 0.017 10 0.1 0.93 1.1 1 0.92 Yes 7.5 137.9 0.168 103.54 0.117 0.4 0.125 14.5 0.407 6.9 0.016 25 0.2 0.93 1 1 1.22 Yes 3.4 54.08 0.179 37.9 0.235 0.13 0.154 10.6 0.302 6.7 0.019 37 0.135 0.76 1 1 1.13 No 14.4 238.5 0.044 105.28 0.074 0.095 0.011 3.6 0.167 6.1 27 0.037 1 1 1 1.09 No 4.5 73.95 0.153 33.27 0.176 0.278 0.144 7.7 0.091 7.7 0.013 0 0 0.81 1 1 1.22 Yes 8.7 152.6 0.056 101.11 0.058 0.4 0.125 11 0.236 6.9 0.016 2 0.5 0.96 1 1 1.22 Yes 2.5 35.74 0.075 30.84 0.099 0.16 0.125 10.9 0.183 5.9 0.025 30 0.167 0.69 1 1 1.05 No 6.5 106.4 0.142 67.22 0.119 0.18 0.15 12 0.25 7.5 0.015 0 0 0.9 1 1 1.09 No 4.2 71.34 0.158 53.42 0.112 0.24 0.2 9.6 0.448 7.4 3 0.333 0.8 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.12 0.2 4.3 0.581 6.7 10 0.2 0.73 1 1 1 No 2.5 35.74 0.079 30.84 0.102 0.16 0.119 10.9 0.202 6.5 0.02 30 0.167 0.69 1 1 1.05 No 2.4 39.26 0.182 27.31 0.144 0.2 0.075 13.9 0.007 7.4 4 0.375 0.68 1 1 0.75 No 3.2 47.09 0.157 32.88 0.266 0.47 0.106 2.7 0.815 6.5 0.02 29 0.155 0.74 1 1 1.13 Yes 4.2 71.34 0.158 53.42 0.112 0.14 0.2 9.6 0.448 6.7 3 0.333 0.8 1 1 1.09 No 6.2 94.92 0.072 84.47 0.077 0.45 0.1 7.2 0.333 6.6 50 0.1 0.89 1 1 1.13 Yes 5 84.97 0.206 44.91 0.185 0.2 0.2 8.8 0.318 7.4 0 0 0.84 1 1 1.09 Yes 3.2 47.09 0.166 32.88 0.276 0.15 0.133 2.7 0.815 6.7 0.019 29 0.155 0.74 1 1 1.13 No 11.6 181.8 0.052 133.22 0.05 0.2 0.075 11.4 0.14 7.4 20 0.15 1 1 1 0.75 Yes 7.9 132.2 0.197 90.83 0.143 0.35 0.3 16.1 0.155 7.3 4 0.25 0.94 1 1 1.3 Yes 8.5 124.5 0.068 70.58 0.077 0.41 0.122 18.5 0.151 7 0.017 20 0.15 0.95 1 1 1.13 Yes 8.3 104.3 0.186 63.97 0.121 0.135 0.111 14.9 0.154 7.5 3 0.333 0.95 1 1 0.75 No 4.7 83.3 0.095 47.19 0.101 0.2 0.2 9.8 0.204 8 0.011 12 0.25 0.83 1 1 1 Yes 3.5 53.41 0.065 48.51 0.053 0.14 0.2 11 0.209 6.7 5 0.4 0.76 1 1 1 No 2.9 45.61 0.107 38.14 0.085 0.2 0.075 15.2 0.026 7.4 3 0.333 0.72 1 1 0.75 No 4.2 68.93 0.221 41.97 0.202 0.18 0.056 6 0.55 7 0.017 20 0.2 0.8 1.1 1 1.13 Yes 5.9 91.33 0.119 74.9 0.114 0.24 0.2 9 0.444 7.4 5 0.6 0.88 1 1 1 Yes 2.4 38.18 0.093 27.02 0.113 0.12 0.2 11.5 0.191 6.7 7 0.143 0.68 1 1 1.12 No 1.1 15.47 0.243 8.14 0.378 0.17 0.118 5.8 0.241 5.9 0.025 80 0.125 0.5 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.24 0.2 9 0.256 7.4 20 0.15 0.74 1 1 1.09 Yes 13.5 240.2 0.045 141.19 0.058 0.4 0.125 5.8 0.483 6.9 0.016 18 0.222 1 1 1 1.22 Yes 6.5 119.9 0.037 88.49 0.045 0.4 0.1 9.5 0.074 6.7 0.019 37 0.135 0.9 1 1 1.13 Yes 6.1 111.1 0.043 80.23 0.085 0.22 0.045 12.6 0.246 7 0.017 3 0.333 0.88 1.1 1 0.92 Yes 7.5 121.3 0.14 62.7 0.13 0.2 0.2 10.3 0.32 7.3 0.015 5 0.4 0.93 1 1 1 Yes 3.4 54.08 0.17 37.9 0.124 0.26 0.096 10.5 0.067 7 0.017 2 1 0.76 1 1 1 Yes 2.9 49.88 0.163 39.1 0.169 0.47 0.106 26.4 0.394 6.5 0.02 25 0.16 0.72 1 1 1.13 No 2.6 41.67 0.181 28.44 0.144 0.12 0.2 5.2 0.385 6.7 4 0.25 0.7 1 1 1 No 3.3 51.47 0.188 33.55 0.142 0.16 0.125 5.9 0.288 6.7 0.019 31 0.097 0.75 1 1 1.05 No Mean depth (m) . Mean σv (kPa) . COV σv . Mean |$\sigma^\prime_v$|(kPa) . COV |$\sigma^\prime_v$| . Mean amax (g) . COV . Mean Nm . COV Nm . Mean Mw . COV Mw . Mean FC (%) . COV FC . CR . CS . CB . CE . Liquefied? . 4.2 69.61 0.149 51.85 0.107 0.24 0.2 6 0.333 7.4 10 0.2 0.8 1 1 1.09 Yes 5.2 89.15 0.085 57.29 0.084 0.4 0.1 11.7 0.248 8 2 0.5 0.85 1 1 1.22 Yes 3 49.07 0.118 22.22 0.139 0.24 0.2 7 0.229 7.4 12 0.167 0.73 1 1 1 Yes 4.5 73.26 0.078 46.37 0.08 0.2 0.075 6 0.017 7.4 50 0.1 0.82 1 1 0.75 Yes 3.7 58.83 0.217 36.28 0.164 0.2 0.2 3.7 0.189 7.4 10 0.2 0.77 1 1 1.09 Yes 4.7 72.78 0.157 35.43 0.189 0.17 0.265 7.8 0.449 6.5 0.02 40 0.075 0.83 1 1 1.05 No 6 102.7 0.123 67.73 0.103 0.24 0.2 9.9 0.424 7.4 10 0.2 0.88 1 1 1.09 No 9.9 184.6 0.179 135.57 0.126 0.4 0.1 17.5 0.154 6.9 0.016 20 0.25 1 1 1 1.22 No 3.5 53.89 0.057 44.04 0.073 0.26 0.096 13 0.238 7 0.017 3 0.333 0.76 1 1 1 Yes 8.5 137.8 0.105 69.39 0.109 0.1 0.2 9.5 0.158 7.3 0.015 5 0.4 0.95 1 1 1 Yes 5.5 90 0.095 45.05 0.109 0.095 0.011 4.6 0.087 6.1 13 0.077 0.86 1 1 1.09 No 11.4 211 0.054 116.24 0.068 0.18 0.15 24.7 0.121 7.5 0.015 8 0.25 1 1 1 1.21 No 6.2 112.6 0.04 93.48 0.044 0.54 0.074 10.3 0.155 6.7 0.019 38 0.605 0.89 1 1 1.13 Yes 3.2 52.82 0.133 30.77 0.137 0.09 0.2 2.7 0.556 7.5 0.015 5 0.4 0.74 1 1 1.22 Yes 10.7 200.1 0.106 110.44 0.106 0.4 0.1 26 0.096 8 0 0 1 1 1 1.22 No 2.4 38.18 0.093 27.02 0.113 0.24 0.2 11.5 0.191 7.4 7 0.143 0.68 1 1 1.12 Yes 6.5 117.4 0.036 83.12 0.053 0.22 0.045 13 0.315 7 0.017 5 0.2 0.9 1.1 1 0.92 Yes 6 82.08 0.066 57.57 0.072 0.165 0.079 4 0.35 7 0.017 25 0.2 0.88 1.1 1 0.92 Yes 8.9 159.8 0.043 142.12 0.049 0.693 0.087 20 0.22 6.7 0.019 43 0.302 0.97 1 1 1.13 Yes 7.9 129.6 0.194 66.05 0.169 0.13 0.2 8.4 0.19 7.3 0.015 67 0.104 0.94 1 1 0.83 Yes 7.9 143.2 0.137 88.63 0.121 0.24 0.2 19.3 0.13 7.4 5 0.2 0.94 1 1 1.21 No 2.7 44.57 0.28 22.52 0.257 0.12 0.2 4.6 0.348 6.7 5 0.2 0.71 1 1 1 Yes 5 84.97 0.206 44.91 0.185 0.1 0.2 8.8 0.318 6.7 0 0 0.84 1 1 1.09 No 3.7 60.52 0.162 32.09 0.156 0.24 0.2 8.8 0.42 7.4 0 0 0.77 1 1 1 Yes 3.7 58.83 0.217 36.28 0.164 0.12 0.2 3.7 0.189 6.7 10 0.2 0.77 1 1 1.09 No 5.5 97.24 0.069 52.15 0.089 0.35 0.2 18.1 0.088 8 0.011 20 0.15 0.86 1 1 1 Yes 2.5 35.74 0.089 30.84 0.113 0.18 0.111 10.9 0.202 6.7 0.019 30 0.167 0.69 1 1 1.05 No 5.7 94.84 0.108 38.48 0.153 0.116 0.155 8.9 0.079 7.7 0.013 3 0.333 0.87 1 1 1.22 Yes 2.9 45.74 0.238 25.71 0.207 0.2 0.2 5.6 0.143 7.9 20 0.15 0.72 1 1 1.17 Yes 8.5 155.1 0.15 120.82 0.102 0.4 0.1 19.7 0.142 6.9 0.016 20 0.25 0.95 1 1 1.22 No 7.7 146.5 0.24 94.08 0.192 0.34 0.029 5.7 0.246 6.9 0.016 20 0.25 0.93 1 1 1.22 Yes 4.7 84.15 0.096 40.83 0.196 0.19 0.105 21 0.024 6.7 0.019 18 0.167 0.83 1 1 1.05 No 3.5 61.66 0.206 38.13 0.171 0.22 0.2 19.7 0.157 8 0.011 5 0.6 0.76 1 1 1 No 4.5 72.31 0.118 40.16 0.118 0.13 0.2 9.5 0.263 8 0.011 12 0.25 0.81 1 1 1 Yes 4.5 65.59 0.117 41.08 0.102 0.09 0.278 4.5 0.778 6.2 0.023 75 0.133 0.81 1 1 1.05 No 7.2 127.4 0.156 78.84 0.126 0.25 0.1 20 0.205 7.6 19 0.105 0.92 1 1 0.65 Yes 3.5 53.41 0.065 48.51 0.053 0.28 0.2 11 0.245 7.4 5 0.4 0.76 1 1 1 Yes 2 30.93 0.257 16.28 0.256 0.2 0.3 1.8 0.333 8 27 0.111 0.64 1 1 1.17 Yes 3 49.72 0.12 29.14 0.126 0.32 0.2 15.5 0.31 7.4 4 0.25 0.73 1 1 1.12 No 4.6 68.04 0.099 57.01 0.1 0.14 0.093 4.6 0.717 7 0.017 30 0.233 0.82 1.1 1 0.92 No 2.4 41.9 0.223 26.96 0.188 0.225 0.111 14.4 0.153 7.9 5 0.4 0.68 1 1 1.21 No 2.6 41.67 0.181 28.44 0.144 0.32 0.2 5.2 0.385 7.4 4 0.25 0.7 1 1 1 Yes 5.7 94.84 0.108 38.48 0.153 0.213 0.141 8.9 0.079 7.8 3 0.333 0.87 1 1 1.22 Yes 6 87.58 0.066 63.07 0.067 0.13 0.1 4 0.35 7 0.017 25 0.12 0.88 1.1 1 0.92 Yes 4.5 75.4 0.089 60.7 0.069 0.5 0.2 29.4 0.139 8 0.011 10 0.2 0.81 1 1 1 No 4.2 66.67 0.115 54.66 0.142 0.28 0.2 13.2 0.424 7.4 0 0 0.8 1 1 1.21 No 3.6 57.38 0.18 39.24 0.13 0.12 0.2 2 0.4 6.7 60 0.083 0.77 1 1 1 No 5.3 81.54 0.073 70.93 0.086 0.45 0.1 3.4 0.265 6.6 55 0.091 0.85 1 1 1.13 Yes 6.6 96.57 0.071 87.5 0.085 0.46 0.109 10.2 0.363 7 0.017 27 0.185 0.9 1 1 1.13 Yes 6 101.6 0.093 63.9 0.084 0.24 0.2 21 0.09 7.4 0 0.88 1 1 1.12 No 3.3 51.47 0.188 33.55 0.142 0.09 0.256 5.9 0.288 5.9 0.025 31 0.097 0.75 1 1 1.05 No 4.5 65.59 0.117 41.08 0.102 0.17 0.118 4.5 0.778 5.9 0.025 75 0.133 0.81 1 1 1.05 Yes 7.5 123.1 0.226 53.4 0.23 0.227 0.154 7.6 0.224 7.7 0.013 1 1 0.93 1 1 1.22 Yes 4.2 66.08 0.131 51.14 0.091 0.13 0.077 6.4 0.516 6.5 0.02 92 0.109 0.8 1 1 1.05 No 4.7 72.78 0.147 35.43 0.148 0.1 0.05 7.8 0.449 6.2 0.023 40 0.075 0.83 1 1 1.05 No 3.6 57.38 0.18 39.24 0.13 0.24 0.2 2 0.4 7.4 60 0.083 0.77 1 1 1 Yes 9.2 158.3 0.056 77.4 0.085 0.15 0.2 13.1 0.229 7.1 0 0 0.97 1 1 1.22 No 9.5 174.8 0.17 130.65 0.119 0.4 0.1 30.2 0.235 6.9 0.016 20 0.25 0.98 1 1 1.22 No 3 49.07 0.118 22.22 0.139 0.12 0.2 7 0.229 6.7 12 0.167 0.73 1 1 1 No 4.5 76.85 0.124 55.93 0.097 0.24 0.2 11.9 0.227 7.4 26 0.192 0.82 1 1 1.09 No 2.5 39.27 0.092 34.37 0.078 0.24 0.104 17.9 0.173 7 0.017 1 2 0.69 1 1 1 No 3.4 54.08 0.172 37.9 0.225 0.47 0.106 10.6 0.302 6.5 0.02 37 0.135 0.76 1 1 1.13 No 4.1 68.41 0.205 45.87 0.15 0.27 0.093 15 0.22 7 0.017 1 2 0.79 1 1 1 No 3.5 53.57 0.169 36.9 0.125 0.29 0.086 6.1 0.557 7 0.017 2 1 0.76 1 1 1 Yes 5.2 85.16 0.123 42.66 0.146 0.16 0.15 7.9 0.177 7.5 0.015 8 0.25 0.85 1 1 1.09 Yes 6 82.08 0.119 57.57 0.084 0.15 0.087 3.9 0.487 7 0.017 50 0.1 0.88 1.1 1 0.92 Yes 5.5 104.4 0.155 71.52 0.122 0.225 0.111 25.5 0.067 7.9 5 0.4 0.86 1 1 1.21 No 3.5 54.98 0.153 37.83 0.118 0.25 0.22 9.7 0.227 7.7 0.013 1 1 0.76 1 1 1.22 Yes 4.5 73.01 0.15 53.9 0.103 0.24 0.104 15.7 0.204 7 0.017 1 2 0.82 1 1 1 Yes 3.7 60.52 0.162 32.09 0.156 0.12 0.2 8.8 0.42 6.7 0 0 0.77 1 1 1 No 6.5 123.3 0.051 113.51 0.087 0.24 0.1 37 0.038 7 0.017 7 0.286 0.9 1.2 1 0.92 No 7.5 122.3 0.124 57.72 0.152 0.16 0.15 9.4 0.16 7.5 0.015 8 0.25 0.93 1 1 1.09 Yes 11.4 210.5 0.225 136.98 0.171 0.34 0.118 11.6 0.31 6.9 0.016 20 0.25 1 1 1 1.22 Yes 5.2 88.44 0.119 71.78 0.081 0.4 0.125 20.7 0.454 6.9 0.016 18 0.222 0.85 1 1 1.22 No 7 117.4 0.108 63.66 0.119 0.2 0.2 12.4 0.056 7.3 0.015 48 0.104 0.91 1 1 1 Yes 4.2 66.08 0.142 51.14 0.179 0.19 0.132 6.4 0.516 5.9 0.025 92 0.109 0.8 1 1 1.05 Yes 3.5 56 0.199 32.48 0.166 0.22 0.2 5.9 0.136 8 0.011 3 0.667 0.76 1 1 1 Yes 4.7 82.08 0.128 35.52 0.165 0.25 0.16 8.5 0.247 6.9 0.016 20 0.35 0.83 1 1 1.22 Yes 2.7 44.57 0.28 22.52 0.257 0.32 0.2 4.1 0.39 7.4 5 0.2 0.71 1 1 1 Yes 8.2 131.4 0.031 95.58 0.046 0.2 0.075 9 0.233 7.4 20 0.15 0.95 1 1 0.75 Yes 7.9 130.5 0.137 61.06 0.161 0.16 0.15 8.8 0.25 7.5 0.015 8 0.25 0.94 1 1 1.09 Yes 4.2 66.08 0.131 51.14 0.091 0.174 0.115 6.4 0.516 6.7 0.019 92 0.109 0.8 1 1 1.05 No 4.2 69.32 0.26 37.46 0.215 0.2 0.2 4.8 0.583 7.7 0.013 15 0.267 0.8 1 1 1.22 Yes 7.5 131.4 0.082 70.63 0.106 0.24 0.2 20.5 0.215 7.4 17 0.176 0.93 1 1 1.12 No 9.9 183.8 0.139 115.18 0.115 0.34 0.118 9.5 0.137 6.9 0.016 20 0.25 1 1 1 1.22 Yes 1.1 15.47 0.243 8.14 0.378 0.16 0.281 5.8 0.241 6.5 0.02 80 0.125 0.5 1 1 1.05 Yes 3.3 51.47 0.188 33.55 0.142 0.51 0.098 5.9 0.288 6.5 0.02 31 0.097 0.75 1 1 1.05 Yes 6 108.3 0.066 61.46 0.077 0.18 0.15 30 0.097 7.5 0.015 0 0 0.88 1 1 1.21 No 4.9 85.81 0.181 59.83 0.13 0.25 0.1 34.2 0.216 7.6 19 0.105 0.84 1 1 0.65 No 4.2 69.61 0.149 51.85 0.107 0.14 0.171 6 0.483 6.7 10 0.2 0.8 1 1 1.09 No 2.9 49.88 0.163 39.1 0.169 0.156 0.128 26.4 0.394 6.7 0.019 25 0.16 0.72 1 1 1.13 No 4.2 71.87 0.067 40.01 0.095 0.2 0.2 10.4 0.538 8 0.011 5 0.6 0.8 1 1 1 Yes 1.1 15.47 0.243 8.14 0.378 0.19 0.105 5.8 0.241 6.7 0.019 80 0.125 0.5 1 1 1.05 No 6.2 117.8 0.048 85.96 0.057 0.25 0.04 6 0.65 7 0.017 8 0.375 0.89 1.1 1 0.92 Yes 3.7 61.59 0.214 24.99 0.231 0.16 0.15 3.9 0.179 7.5 0.015 10 0.3 0.77 1 1 1.09 Yes 7.9 141.6 0.053 98 0.054 0.4 0.125 25.9 0.193 6.9 0.016 2 0.5 0.94 1 1 1.22 No 4.7 72.78 0.148 35.43 0.249 0.23 0.087 7.8 0.449 5.9 0.025 40 0.075 0.83 1 1 1.05 Yes 5.9 91.33 0.119 74.9 0.114 0.14 0.171 9 0.2 6.7 5 0.6 0.88 1 1 1 No 12.1 165.6 0.187 78.98 0.155 0.135 0.111 13 0.269 7.5 3 0.333 1 1 1 0.75 No 4.5 73.95 0.153 33.27 0.176 0.12 0.183 7.7 0.091 7.1 0 0 0.81 1 1 1.22 Yes 7 115.4 0.084 92.84 0.062 0.41 0.122 20 0.165 7 0.017 13 0.154 0.91 1 1 1.13 Yes 9.1 129 0.238 54.35 0.213 0.135 0.111 4.3 0.302 7.5 3 0.333 0.97 1 1 0.75 Yes 6.5 98.26 0.086 82.58 0.063 0.46 0.109 9 0.1 7 0.017 15 0.133 0.9 1 1 1.13 Yes 4.5 65.59 0.117 41.08 0.102 0.2 0.2 4.5 0.778 6.6 0.02 75 0.133 0.81 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.14 0.2 9 0.233 6.7 20 0.15 0.74 1 1 1.09 No 7.5 135.6 0.119 80.04 0.108 0.18 0.15 17.5 0.063 7.5 0.015 8 0.25 0.93 1 1 1.21 No 4.7 80.68 0.066 37.36 0.105 0.17 0.118 21 0.024 5.9 0.025 18 0.167 0.83 1 1 1.05 No 9.2 172.4 0.045 120 0.048 0.51 0.118 24.4 0.123 6.7 0.019 25 0.2 0.97 1 1 1.13 Yes 4.2 133.4 0.122 105.94 0.072 0.2 0.2 23.3 0.094 7.4 10 0.2 0.8 1 1 1.21 No 4.2 69.32 0.26 37.46 0.215 0.15 0.2 4.8 0.583 7.1 15 0.267 0.8 1 1 1.22 No 4 65.91 0.183 32.15 0.211 0.225 0.111 4.5 0.156 7.9 5 0.4 0.79 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.24 0.2 4.3 0.581 7.4 10 0.2 0.73 1 1 1 Yes 4.5 65.59 0.118 41.08 0.104 0.18 0.106 4.5 0.778 6.5 0.02 75 0.133 0.81 1 1 1.05 Yes 3.3 53.17 0.224 32.21 0.175 0.4 0.3 3.6 0.278 7.3 0 0 0.75 1 1 1.17 Yes 4.7 72.78 0.147 35.43 0.148 0.18 0.028 7.8 0.449 6.6 0.02 40 0.075 0.83 1 1 1.05 Yes 3.5 53.06 0.157 38.2 0.123 0.2 0.3 6 0.333 8 13 0.077 0.76 1 1 1.17 Yes 1.7 26.7 0.15 19.35 0.166 0.25 0.1 6.5 0.062 7 0.017 35 0.143 0.61 1 1 1 Yes 6 86.4 0.12 66.79 0.078 0.42 0.119 8 0.45 7 0.017 22 0.136 0.88 1 1 1.13 Yes 4.2 65.12 0.154 47.19 0.114 0.2 0.3 1.5 0.4 8 25 0.12 0.8 1 1 1.17 Yes 3.9 61.38 0.144 46.19 0.183 0.24 0.104 10.2 0.039 7 0.017 3 0.333 0.79 1 1 1 Yes 6 86.01 0.091 71.3 0.145 0.37 0.135 9 0.244 7 0.017 8 0.25 0.88 1 1 1.13 Yes 5 81.53 0.076 38.4 0.114 0.16 0.15 4.4 0.364 7.5 0.015 0 0 0.84 1 1 1.09 Yes 20.4 383.9 0.04 198.66 0.065 0.4 0.1 8.5 0.259 8 − 10 0.3 1 1 1 1.22 Yes 7.5 140 0.071 95.86 0.068 0.25 0.04 12 0.425 7 0.017 10 0.1 0.93 1.1 1 0.92 Yes 7.5 137.9 0.168 103.54 0.117 0.4 0.125 14.5 0.407 6.9 0.016 25 0.2 0.93 1 1 1.22 Yes 3.4 54.08 0.179 37.9 0.235 0.13 0.154 10.6 0.302 6.7 0.019 37 0.135 0.76 1 1 1.13 No 14.4 238.5 0.044 105.28 0.074 0.095 0.011 3.6 0.167 6.1 27 0.037 1 1 1 1.09 No 4.5 73.95 0.153 33.27 0.176 0.278 0.144 7.7 0.091 7.7 0.013 0 0 0.81 1 1 1.22 Yes 8.7 152.6 0.056 101.11 0.058 0.4 0.125 11 0.236 6.9 0.016 2 0.5 0.96 1 1 1.22 Yes 2.5 35.74 0.075 30.84 0.099 0.16 0.125 10.9 0.183 5.9 0.025 30 0.167 0.69 1 1 1.05 No 6.5 106.4 0.142 67.22 0.119 0.18 0.15 12 0.25 7.5 0.015 0 0 0.9 1 1 1.09 No 4.2 71.34 0.158 53.42 0.112 0.24 0.2 9.6 0.448 7.4 3 0.333 0.8 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.12 0.2 4.3 0.581 6.7 10 0.2 0.73 1 1 1 No 2.5 35.74 0.079 30.84 0.102 0.16 0.119 10.9 0.202 6.5 0.02 30 0.167 0.69 1 1 1.05 No 2.4 39.26 0.182 27.31 0.144 0.2 0.075 13.9 0.007 7.4 4 0.375 0.68 1 1 0.75 No 3.2 47.09 0.157 32.88 0.266 0.47 0.106 2.7 0.815 6.5 0.02 29 0.155 0.74 1 1 1.13 Yes 4.2 71.34 0.158 53.42 0.112 0.14 0.2 9.6 0.448 6.7 3 0.333 0.8 1 1 1.09 No 6.2 94.92 0.072 84.47 0.077 0.45 0.1 7.2 0.333 6.6 50 0.1 0.89 1 1 1.13 Yes 5 84.97 0.206 44.91 0.185 0.2 0.2 8.8 0.318 7.4 0 0 0.84 1 1 1.09 Yes 3.2 47.09 0.166 32.88 0.276 0.15 0.133 2.7 0.815 6.7 0.019 29 0.155 0.74 1 1 1.13 No 11.6 181.8 0.052 133.22 0.05 0.2 0.075 11.4 0.14 7.4 20 0.15 1 1 1 0.75 Yes 7.9 132.2 0.197 90.83 0.143 0.35 0.3 16.1 0.155 7.3 4 0.25 0.94 1 1 1.3 Yes 8.5 124.5 0.068 70.58 0.077 0.41 0.122 18.5 0.151 7 0.017 20 0.15 0.95 1 1 1.13 Yes 8.3 104.3 0.186 63.97 0.121 0.135 0.111 14.9 0.154 7.5 3 0.333 0.95 1 1 0.75 No 4.7 83.3 0.095 47.19 0.101 0.2 0.2 9.8 0.204 8 0.011 12 0.25 0.83 1 1 1 Yes 3.5 53.41 0.065 48.51 0.053 0.14 0.2 11 0.209 6.7 5 0.4 0.76 1 1 1 No 2.9 45.61 0.107 38.14 0.085 0.2 0.075 15.2 0.026 7.4 3 0.333 0.72 1 1 0.75 No 4.2 68.93 0.221 41.97 0.202 0.18 0.056 6 0.55 7 0.017 20 0.2 0.8 1.1 1 1.13 Yes 5.9 91.33 0.119 74.9 0.114 0.24 0.2 9 0.444 7.4 5 0.6 0.88 1 1 1 Yes 2.4 38.18 0.093 27.02 0.113 0.12 0.2 11.5 0.191 6.7 7 0.143 0.68 1 1 1.12 No 1.1 15.47 0.243 8.14 0.378 0.17 0.118 5.8 0.241 5.9 0.025 80 0.125 0.5 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.24 0.2 9 0.256 7.4 20 0.15 0.74 1 1 1.09 Yes 13.5 240.2 0.045 141.19 0.058 0.4 0.125 5.8 0.483 6.9 0.016 18 0.222 1 1 1 1.22 Yes 6.5 119.9 0.037 88.49 0.045 0.4 0.1 9.5 0.074 6.7 0.019 37 0.135 0.9 1 1 1.13 Yes 6.1 111.1 0.043 80.23 0.085 0.22 0.045 12.6 0.246 7 0.017 3 0.333 0.88 1.1 1 0.92 Yes 7.5 121.3 0.14 62.7 0.13 0.2 0.2 10.3 0.32 7.3 0.015 5 0.4 0.93 1 1 1 Yes 3.4 54.08 0.17 37.9 0.124 0.26 0.096 10.5 0.067 7 0.017 2 1 0.76 1 1 1 Yes 2.9 49.88 0.163 39.1 0.169 0.47 0.106 26.4 0.394 6.5 0.02 25 0.16 0.72 1 1 1.13 No 2.6 41.67 0.181 28.44 0.144 0.12 0.2 5.2 0.385 6.7 4 0.25 0.7 1 1 1 No 3.3 51.47 0.188 33.55 0.142 0.16 0.125 5.9 0.288 6.7 0.019 31 0.097 0.75 1 1 1.05 No Open in new tab Mean depth (m) . Mean σv (kPa) . COV σv . Mean |$\sigma^\prime_v$|(kPa) . COV |$\sigma^\prime_v$| . Mean amax (g) . COV . Mean Nm . COV Nm . Mean Mw . COV Mw . Mean FC (%) . COV FC . CR . CS . CB . CE . Liquefied? . 4.2 69.61 0.149 51.85 0.107 0.24 0.2 6 0.333 7.4 10 0.2 0.8 1 1 1.09 Yes 5.2 89.15 0.085 57.29 0.084 0.4 0.1 11.7 0.248 8 2 0.5 0.85 1 1 1.22 Yes 3 49.07 0.118 22.22 0.139 0.24 0.2 7 0.229 7.4 12 0.167 0.73 1 1 1 Yes 4.5 73.26 0.078 46.37 0.08 0.2 0.075 6 0.017 7.4 50 0.1 0.82 1 1 0.75 Yes 3.7 58.83 0.217 36.28 0.164 0.2 0.2 3.7 0.189 7.4 10 0.2 0.77 1 1 1.09 Yes 4.7 72.78 0.157 35.43 0.189 0.17 0.265 7.8 0.449 6.5 0.02 40 0.075 0.83 1 1 1.05 No 6 102.7 0.123 67.73 0.103 0.24 0.2 9.9 0.424 7.4 10 0.2 0.88 1 1 1.09 No 9.9 184.6 0.179 135.57 0.126 0.4 0.1 17.5 0.154 6.9 0.016 20 0.25 1 1 1 1.22 No 3.5 53.89 0.057 44.04 0.073 0.26 0.096 13 0.238 7 0.017 3 0.333 0.76 1 1 1 Yes 8.5 137.8 0.105 69.39 0.109 0.1 0.2 9.5 0.158 7.3 0.015 5 0.4 0.95 1 1 1 Yes 5.5 90 0.095 45.05 0.109 0.095 0.011 4.6 0.087 6.1 13 0.077 0.86 1 1 1.09 No 11.4 211 0.054 116.24 0.068 0.18 0.15 24.7 0.121 7.5 0.015 8 0.25 1 1 1 1.21 No 6.2 112.6 0.04 93.48 0.044 0.54 0.074 10.3 0.155 6.7 0.019 38 0.605 0.89 1 1 1.13 Yes 3.2 52.82 0.133 30.77 0.137 0.09 0.2 2.7 0.556 7.5 0.015 5 0.4 0.74 1 1 1.22 Yes 10.7 200.1 0.106 110.44 0.106 0.4 0.1 26 0.096 8 0 0 1 1 1 1.22 No 2.4 38.18 0.093 27.02 0.113 0.24 0.2 11.5 0.191 7.4 7 0.143 0.68 1 1 1.12 Yes 6.5 117.4 0.036 83.12 0.053 0.22 0.045 13 0.315 7 0.017 5 0.2 0.9 1.1 1 0.92 Yes 6 82.08 0.066 57.57 0.072 0.165 0.079 4 0.35 7 0.017 25 0.2 0.88 1.1 1 0.92 Yes 8.9 159.8 0.043 142.12 0.049 0.693 0.087 20 0.22 6.7 0.019 43 0.302 0.97 1 1 1.13 Yes 7.9 129.6 0.194 66.05 0.169 0.13 0.2 8.4 0.19 7.3 0.015 67 0.104 0.94 1 1 0.83 Yes 7.9 143.2 0.137 88.63 0.121 0.24 0.2 19.3 0.13 7.4 5 0.2 0.94 1 1 1.21 No 2.7 44.57 0.28 22.52 0.257 0.12 0.2 4.6 0.348 6.7 5 0.2 0.71 1 1 1 Yes 5 84.97 0.206 44.91 0.185 0.1 0.2 8.8 0.318 6.7 0 0 0.84 1 1 1.09 No 3.7 60.52 0.162 32.09 0.156 0.24 0.2 8.8 0.42 7.4 0 0 0.77 1 1 1 Yes 3.7 58.83 0.217 36.28 0.164 0.12 0.2 3.7 0.189 6.7 10 0.2 0.77 1 1 1.09 No 5.5 97.24 0.069 52.15 0.089 0.35 0.2 18.1 0.088 8 0.011 20 0.15 0.86 1 1 1 Yes 2.5 35.74 0.089 30.84 0.113 0.18 0.111 10.9 0.202 6.7 0.019 30 0.167 0.69 1 1 1.05 No 5.7 94.84 0.108 38.48 0.153 0.116 0.155 8.9 0.079 7.7 0.013 3 0.333 0.87 1 1 1.22 Yes 2.9 45.74 0.238 25.71 0.207 0.2 0.2 5.6 0.143 7.9 20 0.15 0.72 1 1 1.17 Yes 8.5 155.1 0.15 120.82 0.102 0.4 0.1 19.7 0.142 6.9 0.016 20 0.25 0.95 1 1 1.22 No 7.7 146.5 0.24 94.08 0.192 0.34 0.029 5.7 0.246 6.9 0.016 20 0.25 0.93 1 1 1.22 Yes 4.7 84.15 0.096 40.83 0.196 0.19 0.105 21 0.024 6.7 0.019 18 0.167 0.83 1 1 1.05 No 3.5 61.66 0.206 38.13 0.171 0.22 0.2 19.7 0.157 8 0.011 5 0.6 0.76 1 1 1 No 4.5 72.31 0.118 40.16 0.118 0.13 0.2 9.5 0.263 8 0.011 12 0.25 0.81 1 1 1 Yes 4.5 65.59 0.117 41.08 0.102 0.09 0.278 4.5 0.778 6.2 0.023 75 0.133 0.81 1 1 1.05 No 7.2 127.4 0.156 78.84 0.126 0.25 0.1 20 0.205 7.6 19 0.105 0.92 1 1 0.65 Yes 3.5 53.41 0.065 48.51 0.053 0.28 0.2 11 0.245 7.4 5 0.4 0.76 1 1 1 Yes 2 30.93 0.257 16.28 0.256 0.2 0.3 1.8 0.333 8 27 0.111 0.64 1 1 1.17 Yes 3 49.72 0.12 29.14 0.126 0.32 0.2 15.5 0.31 7.4 4 0.25 0.73 1 1 1.12 No 4.6 68.04 0.099 57.01 0.1 0.14 0.093 4.6 0.717 7 0.017 30 0.233 0.82 1.1 1 0.92 No 2.4 41.9 0.223 26.96 0.188 0.225 0.111 14.4 0.153 7.9 5 0.4 0.68 1 1 1.21 No 2.6 41.67 0.181 28.44 0.144 0.32 0.2 5.2 0.385 7.4 4 0.25 0.7 1 1 1 Yes 5.7 94.84 0.108 38.48 0.153 0.213 0.141 8.9 0.079 7.8 3 0.333 0.87 1 1 1.22 Yes 6 87.58 0.066 63.07 0.067 0.13 0.1 4 0.35 7 0.017 25 0.12 0.88 1.1 1 0.92 Yes 4.5 75.4 0.089 60.7 0.069 0.5 0.2 29.4 0.139 8 0.011 10 0.2 0.81 1 1 1 No 4.2 66.67 0.115 54.66 0.142 0.28 0.2 13.2 0.424 7.4 0 0 0.8 1 1 1.21 No 3.6 57.38 0.18 39.24 0.13 0.12 0.2 2 0.4 6.7 60 0.083 0.77 1 1 1 No 5.3 81.54 0.073 70.93 0.086 0.45 0.1 3.4 0.265 6.6 55 0.091 0.85 1 1 1.13 Yes 6.6 96.57 0.071 87.5 0.085 0.46 0.109 10.2 0.363 7 0.017 27 0.185 0.9 1 1 1.13 Yes 6 101.6 0.093 63.9 0.084 0.24 0.2 21 0.09 7.4 0 0.88 1 1 1.12 No 3.3 51.47 0.188 33.55 0.142 0.09 0.256 5.9 0.288 5.9 0.025 31 0.097 0.75 1 1 1.05 No 4.5 65.59 0.117 41.08 0.102 0.17 0.118 4.5 0.778 5.9 0.025 75 0.133 0.81 1 1 1.05 Yes 7.5 123.1 0.226 53.4 0.23 0.227 0.154 7.6 0.224 7.7 0.013 1 1 0.93 1 1 1.22 Yes 4.2 66.08 0.131 51.14 0.091 0.13 0.077 6.4 0.516 6.5 0.02 92 0.109 0.8 1 1 1.05 No 4.7 72.78 0.147 35.43 0.148 0.1 0.05 7.8 0.449 6.2 0.023 40 0.075 0.83 1 1 1.05 No 3.6 57.38 0.18 39.24 0.13 0.24 0.2 2 0.4 7.4 60 0.083 0.77 1 1 1 Yes 9.2 158.3 0.056 77.4 0.085 0.15 0.2 13.1 0.229 7.1 0 0 0.97 1 1 1.22 No 9.5 174.8 0.17 130.65 0.119 0.4 0.1 30.2 0.235 6.9 0.016 20 0.25 0.98 1 1 1.22 No 3 49.07 0.118 22.22 0.139 0.12 0.2 7 0.229 6.7 12 0.167 0.73 1 1 1 No 4.5 76.85 0.124 55.93 0.097 0.24 0.2 11.9 0.227 7.4 26 0.192 0.82 1 1 1.09 No 2.5 39.27 0.092 34.37 0.078 0.24 0.104 17.9 0.173 7 0.017 1 2 0.69 1 1 1 No 3.4 54.08 0.172 37.9 0.225 0.47 0.106 10.6 0.302 6.5 0.02 37 0.135 0.76 1 1 1.13 No 4.1 68.41 0.205 45.87 0.15 0.27 0.093 15 0.22 7 0.017 1 2 0.79 1 1 1 No 3.5 53.57 0.169 36.9 0.125 0.29 0.086 6.1 0.557 7 0.017 2 1 0.76 1 1 1 Yes 5.2 85.16 0.123 42.66 0.146 0.16 0.15 7.9 0.177 7.5 0.015 8 0.25 0.85 1 1 1.09 Yes 6 82.08 0.119 57.57 0.084 0.15 0.087 3.9 0.487 7 0.017 50 0.1 0.88 1.1 1 0.92 Yes 5.5 104.4 0.155 71.52 0.122 0.225 0.111 25.5 0.067 7.9 5 0.4 0.86 1 1 1.21 No 3.5 54.98 0.153 37.83 0.118 0.25 0.22 9.7 0.227 7.7 0.013 1 1 0.76 1 1 1.22 Yes 4.5 73.01 0.15 53.9 0.103 0.24 0.104 15.7 0.204 7 0.017 1 2 0.82 1 1 1 Yes 3.7 60.52 0.162 32.09 0.156 0.12 0.2 8.8 0.42 6.7 0 0 0.77 1 1 1 No 6.5 123.3 0.051 113.51 0.087 0.24 0.1 37 0.038 7 0.017 7 0.286 0.9 1.2 1 0.92 No 7.5 122.3 0.124 57.72 0.152 0.16 0.15 9.4 0.16 7.5 0.015 8 0.25 0.93 1 1 1.09 Yes 11.4 210.5 0.225 136.98 0.171 0.34 0.118 11.6 0.31 6.9 0.016 20 0.25 1 1 1 1.22 Yes 5.2 88.44 0.119 71.78 0.081 0.4 0.125 20.7 0.454 6.9 0.016 18 0.222 0.85 1 1 1.22 No 7 117.4 0.108 63.66 0.119 0.2 0.2 12.4 0.056 7.3 0.015 48 0.104 0.91 1 1 1 Yes 4.2 66.08 0.142 51.14 0.179 0.19 0.132 6.4 0.516 5.9 0.025 92 0.109 0.8 1 1 1.05 Yes 3.5 56 0.199 32.48 0.166 0.22 0.2 5.9 0.136 8 0.011 3 0.667 0.76 1 1 1 Yes 4.7 82.08 0.128 35.52 0.165 0.25 0.16 8.5 0.247 6.9 0.016 20 0.35 0.83 1 1 1.22 Yes 2.7 44.57 0.28 22.52 0.257 0.32 0.2 4.1 0.39 7.4 5 0.2 0.71 1 1 1 Yes 8.2 131.4 0.031 95.58 0.046 0.2 0.075 9 0.233 7.4 20 0.15 0.95 1 1 0.75 Yes 7.9 130.5 0.137 61.06 0.161 0.16 0.15 8.8 0.25 7.5 0.015 8 0.25 0.94 1 1 1.09 Yes 4.2 66.08 0.131 51.14 0.091 0.174 0.115 6.4 0.516 6.7 0.019 92 0.109 0.8 1 1 1.05 No 4.2 69.32 0.26 37.46 0.215 0.2 0.2 4.8 0.583 7.7 0.013 15 0.267 0.8 1 1 1.22 Yes 7.5 131.4 0.082 70.63 0.106 0.24 0.2 20.5 0.215 7.4 17 0.176 0.93 1 1 1.12 No 9.9 183.8 0.139 115.18 0.115 0.34 0.118 9.5 0.137 6.9 0.016 20 0.25 1 1 1 1.22 Yes 1.1 15.47 0.243 8.14 0.378 0.16 0.281 5.8 0.241 6.5 0.02 80 0.125 0.5 1 1 1.05 Yes 3.3 51.47 0.188 33.55 0.142 0.51 0.098 5.9 0.288 6.5 0.02 31 0.097 0.75 1 1 1.05 Yes 6 108.3 0.066 61.46 0.077 0.18 0.15 30 0.097 7.5 0.015 0 0 0.88 1 1 1.21 No 4.9 85.81 0.181 59.83 0.13 0.25 0.1 34.2 0.216 7.6 19 0.105 0.84 1 1 0.65 No 4.2 69.61 0.149 51.85 0.107 0.14 0.171 6 0.483 6.7 10 0.2 0.8 1 1 1.09 No 2.9 49.88 0.163 39.1 0.169 0.156 0.128 26.4 0.394 6.7 0.019 25 0.16 0.72 1 1 1.13 No 4.2 71.87 0.067 40.01 0.095 0.2 0.2 10.4 0.538 8 0.011 5 0.6 0.8 1 1 1 Yes 1.1 15.47 0.243 8.14 0.378 0.19 0.105 5.8 0.241 6.7 0.019 80 0.125 0.5 1 1 1.05 No 6.2 117.8 0.048 85.96 0.057 0.25 0.04 6 0.65 7 0.017 8 0.375 0.89 1.1 1 0.92 Yes 3.7 61.59 0.214 24.99 0.231 0.16 0.15 3.9 0.179 7.5 0.015 10 0.3 0.77 1 1 1.09 Yes 7.9 141.6 0.053 98 0.054 0.4 0.125 25.9 0.193 6.9 0.016 2 0.5 0.94 1 1 1.22 No 4.7 72.78 0.148 35.43 0.249 0.23 0.087 7.8 0.449 5.9 0.025 40 0.075 0.83 1 1 1.05 Yes 5.9 91.33 0.119 74.9 0.114 0.14 0.171 9 0.2 6.7 5 0.6 0.88 1 1 1 No 12.1 165.6 0.187 78.98 0.155 0.135 0.111 13 0.269 7.5 3 0.333 1 1 1 0.75 No 4.5 73.95 0.153 33.27 0.176 0.12 0.183 7.7 0.091 7.1 0 0 0.81 1 1 1.22 Yes 7 115.4 0.084 92.84 0.062 0.41 0.122 20 0.165 7 0.017 13 0.154 0.91 1 1 1.13 Yes 9.1 129 0.238 54.35 0.213 0.135 0.111 4.3 0.302 7.5 3 0.333 0.97 1 1 0.75 Yes 6.5 98.26 0.086 82.58 0.063 0.46 0.109 9 0.1 7 0.017 15 0.133 0.9 1 1 1.13 Yes 4.5 65.59 0.117 41.08 0.102 0.2 0.2 4.5 0.778 6.6 0.02 75 0.133 0.81 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.14 0.2 9 0.233 6.7 20 0.15 0.74 1 1 1.09 No 7.5 135.6 0.119 80.04 0.108 0.18 0.15 17.5 0.063 7.5 0.015 8 0.25 0.93 1 1 1.21 No 4.7 80.68 0.066 37.36 0.105 0.17 0.118 21 0.024 5.9 0.025 18 0.167 0.83 1 1 1.05 No 9.2 172.4 0.045 120 0.048 0.51 0.118 24.4 0.123 6.7 0.019 25 0.2 0.97 1 1 1.13 Yes 4.2 133.4 0.122 105.94 0.072 0.2 0.2 23.3 0.094 7.4 10 0.2 0.8 1 1 1.21 No 4.2 69.32 0.26 37.46 0.215 0.15 0.2 4.8 0.583 7.1 15 0.267 0.8 1 1 1.22 No 4 65.91 0.183 32.15 0.211 0.225 0.111 4.5 0.156 7.9 5 0.4 0.79 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.24 0.2 4.3 0.581 7.4 10 0.2 0.73 1 1 1 Yes 4.5 65.59 0.118 41.08 0.104 0.18 0.106 4.5 0.778 6.5 0.02 75 0.133 0.81 1 1 1.05 Yes 3.3 53.17 0.224 32.21 0.175 0.4 0.3 3.6 0.278 7.3 0 0 0.75 1 1 1.17 Yes 4.7 72.78 0.147 35.43 0.148 0.18 0.028 7.8 0.449 6.6 0.02 40 0.075 0.83 1 1 1.05 Yes 3.5 53.06 0.157 38.2 0.123 0.2 0.3 6 0.333 8 13 0.077 0.76 1 1 1.17 Yes 1.7 26.7 0.15 19.35 0.166 0.25 0.1 6.5 0.062 7 0.017 35 0.143 0.61 1 1 1 Yes 6 86.4 0.12 66.79 0.078 0.42 0.119 8 0.45 7 0.017 22 0.136 0.88 1 1 1.13 Yes 4.2 65.12 0.154 47.19 0.114 0.2 0.3 1.5 0.4 8 25 0.12 0.8 1 1 1.17 Yes 3.9 61.38 0.144 46.19 0.183 0.24 0.104 10.2 0.039 7 0.017 3 0.333 0.79 1 1 1 Yes 6 86.01 0.091 71.3 0.145 0.37 0.135 9 0.244 7 0.017 8 0.25 0.88 1 1 1.13 Yes 5 81.53 0.076 38.4 0.114 0.16 0.15 4.4 0.364 7.5 0.015 0 0 0.84 1 1 1.09 Yes 20.4 383.9 0.04 198.66 0.065 0.4 0.1 8.5 0.259 8 − 10 0.3 1 1 1 1.22 Yes 7.5 140 0.071 95.86 0.068 0.25 0.04 12 0.425 7 0.017 10 0.1 0.93 1.1 1 0.92 Yes 7.5 137.9 0.168 103.54 0.117 0.4 0.125 14.5 0.407 6.9 0.016 25 0.2 0.93 1 1 1.22 Yes 3.4 54.08 0.179 37.9 0.235 0.13 0.154 10.6 0.302 6.7 0.019 37 0.135 0.76 1 1 1.13 No 14.4 238.5 0.044 105.28 0.074 0.095 0.011 3.6 0.167 6.1 27 0.037 1 1 1 1.09 No 4.5 73.95 0.153 33.27 0.176 0.278 0.144 7.7 0.091 7.7 0.013 0 0 0.81 1 1 1.22 Yes 8.7 152.6 0.056 101.11 0.058 0.4 0.125 11 0.236 6.9 0.016 2 0.5 0.96 1 1 1.22 Yes 2.5 35.74 0.075 30.84 0.099 0.16 0.125 10.9 0.183 5.9 0.025 30 0.167 0.69 1 1 1.05 No 6.5 106.4 0.142 67.22 0.119 0.18 0.15 12 0.25 7.5 0.015 0 0 0.9 1 1 1.09 No 4.2 71.34 0.158 53.42 0.112 0.24 0.2 9.6 0.448 7.4 3 0.333 0.8 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.12 0.2 4.3 0.581 6.7 10 0.2 0.73 1 1 1 No 2.5 35.74 0.079 30.84 0.102 0.16 0.119 10.9 0.202 6.5 0.02 30 0.167 0.69 1 1 1.05 No 2.4 39.26 0.182 27.31 0.144 0.2 0.075 13.9 0.007 7.4 4 0.375 0.68 1 1 0.75 No 3.2 47.09 0.157 32.88 0.266 0.47 0.106 2.7 0.815 6.5 0.02 29 0.155 0.74 1 1 1.13 Yes 4.2 71.34 0.158 53.42 0.112 0.14 0.2 9.6 0.448 6.7 3 0.333 0.8 1 1 1.09 No 6.2 94.92 0.072 84.47 0.077 0.45 0.1 7.2 0.333 6.6 50 0.1 0.89 1 1 1.13 Yes 5 84.97 0.206 44.91 0.185 0.2 0.2 8.8 0.318 7.4 0 0 0.84 1 1 1.09 Yes 3.2 47.09 0.166 32.88 0.276 0.15 0.133 2.7 0.815 6.7 0.019 29 0.155 0.74 1 1 1.13 No 11.6 181.8 0.052 133.22 0.05 0.2 0.075 11.4 0.14 7.4 20 0.15 1 1 1 0.75 Yes 7.9 132.2 0.197 90.83 0.143 0.35 0.3 16.1 0.155 7.3 4 0.25 0.94 1 1 1.3 Yes 8.5 124.5 0.068 70.58 0.077 0.41 0.122 18.5 0.151 7 0.017 20 0.15 0.95 1 1 1.13 Yes 8.3 104.3 0.186 63.97 0.121 0.135 0.111 14.9 0.154 7.5 3 0.333 0.95 1 1 0.75 No 4.7 83.3 0.095 47.19 0.101 0.2 0.2 9.8 0.204 8 0.011 12 0.25 0.83 1 1 1 Yes 3.5 53.41 0.065 48.51 0.053 0.14 0.2 11 0.209 6.7 5 0.4 0.76 1 1 1 No 2.9 45.61 0.107 38.14 0.085 0.2 0.075 15.2 0.026 7.4 3 0.333 0.72 1 1 0.75 No 4.2 68.93 0.221 41.97 0.202 0.18 0.056 6 0.55 7 0.017 20 0.2 0.8 1.1 1 1.13 Yes 5.9 91.33 0.119 74.9 0.114 0.24 0.2 9 0.444 7.4 5 0.6 0.88 1 1 1 Yes 2.4 38.18 0.093 27.02 0.113 0.12 0.2 11.5 0.191 6.7 7 0.143 0.68 1 1 1.12 No 1.1 15.47 0.243 8.14 0.378 0.17 0.118 5.8 0.241 5.9 0.025 80 0.125 0.5 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.24 0.2 9 0.256 7.4 20 0.15 0.74 1 1 1.09 Yes 13.5 240.2 0.045 141.19 0.058 0.4 0.125 5.8 0.483 6.9 0.016 18 0.222 1 1 1 1.22 Yes 6.5 119.9 0.037 88.49 0.045 0.4 0.1 9.5 0.074 6.7 0.019 37 0.135 0.9 1 1 1.13 Yes 6.1 111.1 0.043 80.23 0.085 0.22 0.045 12.6 0.246 7 0.017 3 0.333 0.88 1.1 1 0.92 Yes 7.5 121.3 0.14 62.7 0.13 0.2 0.2 10.3 0.32 7.3 0.015 5 0.4 0.93 1 1 1 Yes 3.4 54.08 0.17 37.9 0.124 0.26 0.096 10.5 0.067 7 0.017 2 1 0.76 1 1 1 Yes 2.9 49.88 0.163 39.1 0.169 0.47 0.106 26.4 0.394 6.5 0.02 25 0.16 0.72 1 1 1.13 No 2.6 41.67 0.181 28.44 0.144 0.12 0.2 5.2 0.385 6.7 4 0.25 0.7 1 1 1 No 3.3 51.47 0.188 33.55 0.142 0.16 0.125 5.9 0.288 6.7 0.019 31 0.097 0.75 1 1 1.05 No Mean depth (m) . Mean σv (kPa) . COV σv . Mean |$\sigma^\prime_v$|(kPa) . COV |$\sigma^\prime_v$| . Mean amax (g) . COV . Mean Nm . COV Nm . Mean Mw . COV Mw . Mean FC (%) . COV FC . CR . CS . CB . CE . Liquefied? . 4.2 69.61 0.149 51.85 0.107 0.24 0.2 6 0.333 7.4 10 0.2 0.8 1 1 1.09 Yes 5.2 89.15 0.085 57.29 0.084 0.4 0.1 11.7 0.248 8 2 0.5 0.85 1 1 1.22 Yes 3 49.07 0.118 22.22 0.139 0.24 0.2 7 0.229 7.4 12 0.167 0.73 1 1 1 Yes 4.5 73.26 0.078 46.37 0.08 0.2 0.075 6 0.017 7.4 50 0.1 0.82 1 1 0.75 Yes 3.7 58.83 0.217 36.28 0.164 0.2 0.2 3.7 0.189 7.4 10 0.2 0.77 1 1 1.09 Yes 4.7 72.78 0.157 35.43 0.189 0.17 0.265 7.8 0.449 6.5 0.02 40 0.075 0.83 1 1 1.05 No 6 102.7 0.123 67.73 0.103 0.24 0.2 9.9 0.424 7.4 10 0.2 0.88 1 1 1.09 No 9.9 184.6 0.179 135.57 0.126 0.4 0.1 17.5 0.154 6.9 0.016 20 0.25 1 1 1 1.22 No 3.5 53.89 0.057 44.04 0.073 0.26 0.096 13 0.238 7 0.017 3 0.333 0.76 1 1 1 Yes 8.5 137.8 0.105 69.39 0.109 0.1 0.2 9.5 0.158 7.3 0.015 5 0.4 0.95 1 1 1 Yes 5.5 90 0.095 45.05 0.109 0.095 0.011 4.6 0.087 6.1 13 0.077 0.86 1 1 1.09 No 11.4 211 0.054 116.24 0.068 0.18 0.15 24.7 0.121 7.5 0.015 8 0.25 1 1 1 1.21 No 6.2 112.6 0.04 93.48 0.044 0.54 0.074 10.3 0.155 6.7 0.019 38 0.605 0.89 1 1 1.13 Yes 3.2 52.82 0.133 30.77 0.137 0.09 0.2 2.7 0.556 7.5 0.015 5 0.4 0.74 1 1 1.22 Yes 10.7 200.1 0.106 110.44 0.106 0.4 0.1 26 0.096 8 0 0 1 1 1 1.22 No 2.4 38.18 0.093 27.02 0.113 0.24 0.2 11.5 0.191 7.4 7 0.143 0.68 1 1 1.12 Yes 6.5 117.4 0.036 83.12 0.053 0.22 0.045 13 0.315 7 0.017 5 0.2 0.9 1.1 1 0.92 Yes 6 82.08 0.066 57.57 0.072 0.165 0.079 4 0.35 7 0.017 25 0.2 0.88 1.1 1 0.92 Yes 8.9 159.8 0.043 142.12 0.049 0.693 0.087 20 0.22 6.7 0.019 43 0.302 0.97 1 1 1.13 Yes 7.9 129.6 0.194 66.05 0.169 0.13 0.2 8.4 0.19 7.3 0.015 67 0.104 0.94 1 1 0.83 Yes 7.9 143.2 0.137 88.63 0.121 0.24 0.2 19.3 0.13 7.4 5 0.2 0.94 1 1 1.21 No 2.7 44.57 0.28 22.52 0.257 0.12 0.2 4.6 0.348 6.7 5 0.2 0.71 1 1 1 Yes 5 84.97 0.206 44.91 0.185 0.1 0.2 8.8 0.318 6.7 0 0 0.84 1 1 1.09 No 3.7 60.52 0.162 32.09 0.156 0.24 0.2 8.8 0.42 7.4 0 0 0.77 1 1 1 Yes 3.7 58.83 0.217 36.28 0.164 0.12 0.2 3.7 0.189 6.7 10 0.2 0.77 1 1 1.09 No 5.5 97.24 0.069 52.15 0.089 0.35 0.2 18.1 0.088 8 0.011 20 0.15 0.86 1 1 1 Yes 2.5 35.74 0.089 30.84 0.113 0.18 0.111 10.9 0.202 6.7 0.019 30 0.167 0.69 1 1 1.05 No 5.7 94.84 0.108 38.48 0.153 0.116 0.155 8.9 0.079 7.7 0.013 3 0.333 0.87 1 1 1.22 Yes 2.9 45.74 0.238 25.71 0.207 0.2 0.2 5.6 0.143 7.9 20 0.15 0.72 1 1 1.17 Yes 8.5 155.1 0.15 120.82 0.102 0.4 0.1 19.7 0.142 6.9 0.016 20 0.25 0.95 1 1 1.22 No 7.7 146.5 0.24 94.08 0.192 0.34 0.029 5.7 0.246 6.9 0.016 20 0.25 0.93 1 1 1.22 Yes 4.7 84.15 0.096 40.83 0.196 0.19 0.105 21 0.024 6.7 0.019 18 0.167 0.83 1 1 1.05 No 3.5 61.66 0.206 38.13 0.171 0.22 0.2 19.7 0.157 8 0.011 5 0.6 0.76 1 1 1 No 4.5 72.31 0.118 40.16 0.118 0.13 0.2 9.5 0.263 8 0.011 12 0.25 0.81 1 1 1 Yes 4.5 65.59 0.117 41.08 0.102 0.09 0.278 4.5 0.778 6.2 0.023 75 0.133 0.81 1 1 1.05 No 7.2 127.4 0.156 78.84 0.126 0.25 0.1 20 0.205 7.6 19 0.105 0.92 1 1 0.65 Yes 3.5 53.41 0.065 48.51 0.053 0.28 0.2 11 0.245 7.4 5 0.4 0.76 1 1 1 Yes 2 30.93 0.257 16.28 0.256 0.2 0.3 1.8 0.333 8 27 0.111 0.64 1 1 1.17 Yes 3 49.72 0.12 29.14 0.126 0.32 0.2 15.5 0.31 7.4 4 0.25 0.73 1 1 1.12 No 4.6 68.04 0.099 57.01 0.1 0.14 0.093 4.6 0.717 7 0.017 30 0.233 0.82 1.1 1 0.92 No 2.4 41.9 0.223 26.96 0.188 0.225 0.111 14.4 0.153 7.9 5 0.4 0.68 1 1 1.21 No 2.6 41.67 0.181 28.44 0.144 0.32 0.2 5.2 0.385 7.4 4 0.25 0.7 1 1 1 Yes 5.7 94.84 0.108 38.48 0.153 0.213 0.141 8.9 0.079 7.8 3 0.333 0.87 1 1 1.22 Yes 6 87.58 0.066 63.07 0.067 0.13 0.1 4 0.35 7 0.017 25 0.12 0.88 1.1 1 0.92 Yes 4.5 75.4 0.089 60.7 0.069 0.5 0.2 29.4 0.139 8 0.011 10 0.2 0.81 1 1 1 No 4.2 66.67 0.115 54.66 0.142 0.28 0.2 13.2 0.424 7.4 0 0 0.8 1 1 1.21 No 3.6 57.38 0.18 39.24 0.13 0.12 0.2 2 0.4 6.7 60 0.083 0.77 1 1 1 No 5.3 81.54 0.073 70.93 0.086 0.45 0.1 3.4 0.265 6.6 55 0.091 0.85 1 1 1.13 Yes 6.6 96.57 0.071 87.5 0.085 0.46 0.109 10.2 0.363 7 0.017 27 0.185 0.9 1 1 1.13 Yes 6 101.6 0.093 63.9 0.084 0.24 0.2 21 0.09 7.4 0 0.88 1 1 1.12 No 3.3 51.47 0.188 33.55 0.142 0.09 0.256 5.9 0.288 5.9 0.025 31 0.097 0.75 1 1 1.05 No 4.5 65.59 0.117 41.08 0.102 0.17 0.118 4.5 0.778 5.9 0.025 75 0.133 0.81 1 1 1.05 Yes 7.5 123.1 0.226 53.4 0.23 0.227 0.154 7.6 0.224 7.7 0.013 1 1 0.93 1 1 1.22 Yes 4.2 66.08 0.131 51.14 0.091 0.13 0.077 6.4 0.516 6.5 0.02 92 0.109 0.8 1 1 1.05 No 4.7 72.78 0.147 35.43 0.148 0.1 0.05 7.8 0.449 6.2 0.023 40 0.075 0.83 1 1 1.05 No 3.6 57.38 0.18 39.24 0.13 0.24 0.2 2 0.4 7.4 60 0.083 0.77 1 1 1 Yes 9.2 158.3 0.056 77.4 0.085 0.15 0.2 13.1 0.229 7.1 0 0 0.97 1 1 1.22 No 9.5 174.8 0.17 130.65 0.119 0.4 0.1 30.2 0.235 6.9 0.016 20 0.25 0.98 1 1 1.22 No 3 49.07 0.118 22.22 0.139 0.12 0.2 7 0.229 6.7 12 0.167 0.73 1 1 1 No 4.5 76.85 0.124 55.93 0.097 0.24 0.2 11.9 0.227 7.4 26 0.192 0.82 1 1 1.09 No 2.5 39.27 0.092 34.37 0.078 0.24 0.104 17.9 0.173 7 0.017 1 2 0.69 1 1 1 No 3.4 54.08 0.172 37.9 0.225 0.47 0.106 10.6 0.302 6.5 0.02 37 0.135 0.76 1 1 1.13 No 4.1 68.41 0.205 45.87 0.15 0.27 0.093 15 0.22 7 0.017 1 2 0.79 1 1 1 No 3.5 53.57 0.169 36.9 0.125 0.29 0.086 6.1 0.557 7 0.017 2 1 0.76 1 1 1 Yes 5.2 85.16 0.123 42.66 0.146 0.16 0.15 7.9 0.177 7.5 0.015 8 0.25 0.85 1 1 1.09 Yes 6 82.08 0.119 57.57 0.084 0.15 0.087 3.9 0.487 7 0.017 50 0.1 0.88 1.1 1 0.92 Yes 5.5 104.4 0.155 71.52 0.122 0.225 0.111 25.5 0.067 7.9 5 0.4 0.86 1 1 1.21 No 3.5 54.98 0.153 37.83 0.118 0.25 0.22 9.7 0.227 7.7 0.013 1 1 0.76 1 1 1.22 Yes 4.5 73.01 0.15 53.9 0.103 0.24 0.104 15.7 0.204 7 0.017 1 2 0.82 1 1 1 Yes 3.7 60.52 0.162 32.09 0.156 0.12 0.2 8.8 0.42 6.7 0 0 0.77 1 1 1 No 6.5 123.3 0.051 113.51 0.087 0.24 0.1 37 0.038 7 0.017 7 0.286 0.9 1.2 1 0.92 No 7.5 122.3 0.124 57.72 0.152 0.16 0.15 9.4 0.16 7.5 0.015 8 0.25 0.93 1 1 1.09 Yes 11.4 210.5 0.225 136.98 0.171 0.34 0.118 11.6 0.31 6.9 0.016 20 0.25 1 1 1 1.22 Yes 5.2 88.44 0.119 71.78 0.081 0.4 0.125 20.7 0.454 6.9 0.016 18 0.222 0.85 1 1 1.22 No 7 117.4 0.108 63.66 0.119 0.2 0.2 12.4 0.056 7.3 0.015 48 0.104 0.91 1 1 1 Yes 4.2 66.08 0.142 51.14 0.179 0.19 0.132 6.4 0.516 5.9 0.025 92 0.109 0.8 1 1 1.05 Yes 3.5 56 0.199 32.48 0.166 0.22 0.2 5.9 0.136 8 0.011 3 0.667 0.76 1 1 1 Yes 4.7 82.08 0.128 35.52 0.165 0.25 0.16 8.5 0.247 6.9 0.016 20 0.35 0.83 1 1 1.22 Yes 2.7 44.57 0.28 22.52 0.257 0.32 0.2 4.1 0.39 7.4 5 0.2 0.71 1 1 1 Yes 8.2 131.4 0.031 95.58 0.046 0.2 0.075 9 0.233 7.4 20 0.15 0.95 1 1 0.75 Yes 7.9 130.5 0.137 61.06 0.161 0.16 0.15 8.8 0.25 7.5 0.015 8 0.25 0.94 1 1 1.09 Yes 4.2 66.08 0.131 51.14 0.091 0.174 0.115 6.4 0.516 6.7 0.019 92 0.109 0.8 1 1 1.05 No 4.2 69.32 0.26 37.46 0.215 0.2 0.2 4.8 0.583 7.7 0.013 15 0.267 0.8 1 1 1.22 Yes 7.5 131.4 0.082 70.63 0.106 0.24 0.2 20.5 0.215 7.4 17 0.176 0.93 1 1 1.12 No 9.9 183.8 0.139 115.18 0.115 0.34 0.118 9.5 0.137 6.9 0.016 20 0.25 1 1 1 1.22 Yes 1.1 15.47 0.243 8.14 0.378 0.16 0.281 5.8 0.241 6.5 0.02 80 0.125 0.5 1 1 1.05 Yes 3.3 51.47 0.188 33.55 0.142 0.51 0.098 5.9 0.288 6.5 0.02 31 0.097 0.75 1 1 1.05 Yes 6 108.3 0.066 61.46 0.077 0.18 0.15 30 0.097 7.5 0.015 0 0 0.88 1 1 1.21 No 4.9 85.81 0.181 59.83 0.13 0.25 0.1 34.2 0.216 7.6 19 0.105 0.84 1 1 0.65 No 4.2 69.61 0.149 51.85 0.107 0.14 0.171 6 0.483 6.7 10 0.2 0.8 1 1 1.09 No 2.9 49.88 0.163 39.1 0.169 0.156 0.128 26.4 0.394 6.7 0.019 25 0.16 0.72 1 1 1.13 No 4.2 71.87 0.067 40.01 0.095 0.2 0.2 10.4 0.538 8 0.011 5 0.6 0.8 1 1 1 Yes 1.1 15.47 0.243 8.14 0.378 0.19 0.105 5.8 0.241 6.7 0.019 80 0.125 0.5 1 1 1.05 No 6.2 117.8 0.048 85.96 0.057 0.25 0.04 6 0.65 7 0.017 8 0.375 0.89 1.1 1 0.92 Yes 3.7 61.59 0.214 24.99 0.231 0.16 0.15 3.9 0.179 7.5 0.015 10 0.3 0.77 1 1 1.09 Yes 7.9 141.6 0.053 98 0.054 0.4 0.125 25.9 0.193 6.9 0.016 2 0.5 0.94 1 1 1.22 No 4.7 72.78 0.148 35.43 0.249 0.23 0.087 7.8 0.449 5.9 0.025 40 0.075 0.83 1 1 1.05 Yes 5.9 91.33 0.119 74.9 0.114 0.14 0.171 9 0.2 6.7 5 0.6 0.88 1 1 1 No 12.1 165.6 0.187 78.98 0.155 0.135 0.111 13 0.269 7.5 3 0.333 1 1 1 0.75 No 4.5 73.95 0.153 33.27 0.176 0.12 0.183 7.7 0.091 7.1 0 0 0.81 1 1 1.22 Yes 7 115.4 0.084 92.84 0.062 0.41 0.122 20 0.165 7 0.017 13 0.154 0.91 1 1 1.13 Yes 9.1 129 0.238 54.35 0.213 0.135 0.111 4.3 0.302 7.5 3 0.333 0.97 1 1 0.75 Yes 6.5 98.26 0.086 82.58 0.063 0.46 0.109 9 0.1 7 0.017 15 0.133 0.9 1 1 1.13 Yes 4.5 65.59 0.117 41.08 0.102 0.2 0.2 4.5 0.778 6.6 0.02 75 0.133 0.81 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.14 0.2 9 0.233 6.7 20 0.15 0.74 1 1 1.09 No 7.5 135.6 0.119 80.04 0.108 0.18 0.15 17.5 0.063 7.5 0.015 8 0.25 0.93 1 1 1.21 No 4.7 80.68 0.066 37.36 0.105 0.17 0.118 21 0.024 5.9 0.025 18 0.167 0.83 1 1 1.05 No 9.2 172.4 0.045 120 0.048 0.51 0.118 24.4 0.123 6.7 0.019 25 0.2 0.97 1 1 1.13 Yes 4.2 133.4 0.122 105.94 0.072 0.2 0.2 23.3 0.094 7.4 10 0.2 0.8 1 1 1.21 No 4.2 69.32 0.26 37.46 0.215 0.15 0.2 4.8 0.583 7.1 15 0.267 0.8 1 1 1.22 No 4 65.91 0.183 32.15 0.211 0.225 0.111 4.5 0.156 7.9 5 0.4 0.79 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.24 0.2 4.3 0.581 7.4 10 0.2 0.73 1 1 1 Yes 4.5 65.59 0.118 41.08 0.104 0.18 0.106 4.5 0.778 6.5 0.02 75 0.133 0.81 1 1 1.05 Yes 3.3 53.17 0.224 32.21 0.175 0.4 0.3 3.6 0.278 7.3 0 0 0.75 1 1 1.17 Yes 4.7 72.78 0.147 35.43 0.148 0.18 0.028 7.8 0.449 6.6 0.02 40 0.075 0.83 1 1 1.05 Yes 3.5 53.06 0.157 38.2 0.123 0.2 0.3 6 0.333 8 13 0.077 0.76 1 1 1.17 Yes 1.7 26.7 0.15 19.35 0.166 0.25 0.1 6.5 0.062 7 0.017 35 0.143 0.61 1 1 1 Yes 6 86.4 0.12 66.79 0.078 0.42 0.119 8 0.45 7 0.017 22 0.136 0.88 1 1 1.13 Yes 4.2 65.12 0.154 47.19 0.114 0.2 0.3 1.5 0.4 8 25 0.12 0.8 1 1 1.17 Yes 3.9 61.38 0.144 46.19 0.183 0.24 0.104 10.2 0.039 7 0.017 3 0.333 0.79 1 1 1 Yes 6 86.01 0.091 71.3 0.145 0.37 0.135 9 0.244 7 0.017 8 0.25 0.88 1 1 1.13 Yes 5 81.53 0.076 38.4 0.114 0.16 0.15 4.4 0.364 7.5 0.015 0 0 0.84 1 1 1.09 Yes 20.4 383.9 0.04 198.66 0.065 0.4 0.1 8.5 0.259 8 − 10 0.3 1 1 1 1.22 Yes 7.5 140 0.071 95.86 0.068 0.25 0.04 12 0.425 7 0.017 10 0.1 0.93 1.1 1 0.92 Yes 7.5 137.9 0.168 103.54 0.117 0.4 0.125 14.5 0.407 6.9 0.016 25 0.2 0.93 1 1 1.22 Yes 3.4 54.08 0.179 37.9 0.235 0.13 0.154 10.6 0.302 6.7 0.019 37 0.135 0.76 1 1 1.13 No 14.4 238.5 0.044 105.28 0.074 0.095 0.011 3.6 0.167 6.1 27 0.037 1 1 1 1.09 No 4.5 73.95 0.153 33.27 0.176 0.278 0.144 7.7 0.091 7.7 0.013 0 0 0.81 1 1 1.22 Yes 8.7 152.6 0.056 101.11 0.058 0.4 0.125 11 0.236 6.9 0.016 2 0.5 0.96 1 1 1.22 Yes 2.5 35.74 0.075 30.84 0.099 0.16 0.125 10.9 0.183 5.9 0.025 30 0.167 0.69 1 1 1.05 No 6.5 106.4 0.142 67.22 0.119 0.18 0.15 12 0.25 7.5 0.015 0 0 0.9 1 1 1.09 No 4.2 71.34 0.158 53.42 0.112 0.24 0.2 9.6 0.448 7.4 3 0.333 0.8 1 1 1.09 Yes 3 47.6 0.144 34.39 0.115 0.12 0.2 4.3 0.581 6.7 10 0.2 0.73 1 1 1 No 2.5 35.74 0.079 30.84 0.102 0.16 0.119 10.9 0.202 6.5 0.02 30 0.167 0.69 1 1 1.05 No 2.4 39.26 0.182 27.31 0.144 0.2 0.075 13.9 0.007 7.4 4 0.375 0.68 1 1 0.75 No 3.2 47.09 0.157 32.88 0.266 0.47 0.106 2.7 0.815 6.5 0.02 29 0.155 0.74 1 1 1.13 Yes 4.2 71.34 0.158 53.42 0.112 0.14 0.2 9.6 0.448 6.7 3 0.333 0.8 1 1 1.09 No 6.2 94.92 0.072 84.47 0.077 0.45 0.1 7.2 0.333 6.6 50 0.1 0.89 1 1 1.13 Yes 5 84.97 0.206 44.91 0.185 0.2 0.2 8.8 0.318 7.4 0 0 0.84 1 1 1.09 Yes 3.2 47.09 0.166 32.88 0.276 0.15 0.133 2.7 0.815 6.7 0.019 29 0.155 0.74 1 1 1.13 No 11.6 181.8 0.052 133.22 0.05 0.2 0.075 11.4 0.14 7.4 20 0.15 1 1 1 0.75 Yes 7.9 132.2 0.197 90.83 0.143 0.35 0.3 16.1 0.155 7.3 4 0.25 0.94 1 1 1.3 Yes 8.5 124.5 0.068 70.58 0.077 0.41 0.122 18.5 0.151 7 0.017 20 0.15 0.95 1 1 1.13 Yes 8.3 104.3 0.186 63.97 0.121 0.135 0.111 14.9 0.154 7.5 3 0.333 0.95 1 1 0.75 No 4.7 83.3 0.095 47.19 0.101 0.2 0.2 9.8 0.204 8 0.011 12 0.25 0.83 1 1 1 Yes 3.5 53.41 0.065 48.51 0.053 0.14 0.2 11 0.209 6.7 5 0.4 0.76 1 1 1 No 2.9 45.61 0.107 38.14 0.085 0.2 0.075 15.2 0.026 7.4 3 0.333 0.72 1 1 0.75 No 4.2 68.93 0.221 41.97 0.202 0.18 0.056 6 0.55 7 0.017 20 0.2 0.8 1.1 1 1.13 Yes 5.9 91.33 0.119 74.9 0.114 0.24 0.2 9 0.444 7.4 5 0.6 0.88 1 1 1 Yes 2.4 38.18 0.093 27.02 0.113 0.12 0.2 11.5 0.191 6.7 7 0.143 0.68 1 1 1.12 No 1.1 15.47 0.243 8.14 0.378 0.17 0.118 5.8 0.241 5.9 0.025 80 0.125 0.5 1 1 1.05 No 3.2 52.33 0.089 44.37 0.08 0.24 0.2 9 0.256 7.4 20 0.15 0.74 1 1 1.09 Yes 13.5 240.2 0.045 141.19 0.058 0.4 0.125 5.8 0.483 6.9 0.016 18 0.222 1 1 1 1.22 Yes 6.5 119.9 0.037 88.49 0.045 0.4 0.1 9.5 0.074 6.7 0.019 37 0.135 0.9 1 1 1.13 Yes 6.1 111.1 0.043 80.23 0.085 0.22 0.045 12.6 0.246 7 0.017 3 0.333 0.88 1.1 1 0.92 Yes 7.5 121.3 0.14 62.7 0.13 0.2 0.2 10.3 0.32 7.3 0.015 5 0.4 0.93 1 1 1 Yes 3.4 54.08 0.17 37.9 0.124 0.26 0.096 10.5 0.067 7 0.017 2 1 0.76 1 1 1 Yes 2.9 49.88 0.163 39.1 0.169 0.47 0.106 26.4 0.394 6.5 0.02 25 0.16 0.72 1 1 1.13 No 2.6 41.67 0.181 28.44 0.144 0.12 0.2 5.2 0.385 6.7 4 0.25 0.7 1 1 1 No 3.3 51.47 0.188 33.55 0.142 0.16 0.125 5.9 0.288 6.7 0.019 31 0.097 0.75 1 1 1.05 No Open in new tab © The Author(s) 2020. Published by Oxford University Press on behalf of the Society for Computational Design and Engineering. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - Computer-aided SPT-based reliability model for probability of liquefaction using hybrid PSO and GA
JF - Journal of Computational Design and Engineering
DO - 10.1093/jcde/qwaa011
DA - 2020-02-01
UR - https://www.deepdyve.com/lp/oxford-university-press/computer-aided-spt-based-reliability-model-for-probability-of-Swu3Au9hUw
SP - 107
EP - 127
VL - 7
IS - 1
DP - DeepDyve
ER -