Evaluation of Liquefaction Potential in Saturated Sand Under Different

Journal of Marine Science and Engineering

Article Evaluation of Liquefaction Potential in Saturated Sand under Diﬀerent Drainage Boundary Conditions—An Energy Approach

Chang-Rui Yao 1,2 , Bo Wang 1,2,* , Zhi-Qiang Liu 1,2, Hao Fan 3, Fang-Hao Sun 1,2 and Xin-Hao Chang 1

1 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China; [email protected] (C.-R.Y.); [email protected] (Z.-Q.L.); [email protected] (F.-H.S.); [email protected] (X.-H.C.) 2 State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China 3 Track Maintenance Division in Xuzhou of Shanghai Bureau Group Limited Company of China Railway, Xuzhou 221116, China; [email protected] * Correspondence: [email protected]

Received: 1 October 2019; Accepted: 30 October 2019; Published: 12 November 2019

Abstract: Drainage conditions are supposed to have significant influence on sand liquefaction behavior. An infiltration device was utilized in cyclic triaxial tests to reproduce different drainage conditions by altering dry density of the within silt. Permeability coefficient ratio (kp) was utilized for quantifying the drainage boundary effect. Cyclic triaxial tests were conducted on saturated Fujian standard sand samples. Test results were used to evaluate the liquefaction potential by using the energy approach. It can be concluded that, if kp increases slightly bigger than zero, excess pore water pressure (EPWP) will respond more fiercely, and the dissipated energy that triggers sand liquefaction will be less. By considering kp, an energy-based database was built by taking kp into consideration and different neural network (NN) models were constructed to predict liquefaction potential by energy approaches accurately under different drainage boundary conditions. It was suggested that the neuro-fuzzy (NF)-based NN model has more satisfactory performance.

Keywords: cyclic triaxial tests; sand liquefaction; drainage condition; energy approach; neural network

1. Introduction Earthquakes and associated aftershocks may cause liquefaction in sand sediments, which can cause substantial damage—for example, excessive settlement and tilt of foundations, bearing capacity failure, failure of offshore embankment, and slope engineering [1,2]. Drainage conditions refer to permeability of soil sediments, drainage path, and drainage boundary conditions. Soil sediments used to be supposed at an undrained state in an earthquake, because the liquefaction occurred rapidly and pore water pressure can hardly dissipate in a short duration of loading. However, it is inferred that the drainage condition is not critically undrained with longer duration of earthquake loading, larger permeability of sand sediments, and better drainage boundary condition. Furthermore, the soil elements adjacent to the drainage boundary are considered under different drainage conditions. Then, some of the excess pore water pressure (EPWP) generated during seismic loading is being dissipated simultaneously. Thus, the effect of different drainage conditions is hard to control and quantify. It is necessary to study the influence that drainage effect exerts on soil liquefaction characteristics.

J. Mar. Sci. Eng. 2019, 7, 411; doi:10.3390/jmse7110411 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2019, 7, 411 2 of 15

Several research studies have been carried out to investigate the liquefaction potential and EPWP response in sand sediments under different drainage conditions [3–7]. Ohara and Yamamoto [3] carried out a series of shaking table tests. The drainage boundary condition was controlled by a valve. Then, a parameter that reflected the rate of drain was introduced to quantify the drainage effect. Their study provided an original thought to investigate drainage effect. Yamamoto et al. [5] developed the test scheme and conducted a series of cyclic triaxial tests. The drainage boundary condition under seismic loading was reproduced by employing a triaxial apparatus with a valve to precisely measure the amount of squeezed water. In addition, the pore pressure was measured at the top and bottom of sand samples to make sure no hydraulic gradient is within the specimen. They introduced parameters to consider the drainage effect, which is a function of soil permeability coefficient, the length of drainage path, and the loading frequency. Their study shows that soil samples under partial drained conditions can resist liquefaction better than those under undrained conditions. Adamidis and Madabhushi [7] conducted two dynamic centrifuge tests. The drainage of a part of a soil sample was enclosed in a chamber that was constructed by different materials. Conclusions were drawn that the material property of drainage boundaries influenced the response of EPWP evidently. Evaluation of liquefaction potential in saturated sands is an important topic among liquefaction research. A dissipated strain energy concept is introduced to analyze soil liquefaction characteristics as an alternative analysis approach. Dissipated energy density (W) represents the energy that soil particles consume in the process of reorganization under seismic loading per unit volume in soil. Capacity energy (Wliq) is denoted as the W that achieves liquefaction and has been identified as a representative indicator in the evaluation liquefaction potential [8–12]. When the test soil mechanical parameters are provided, the Wliq can be predicted by employing different neural network (NN) models [11,13–16]. Baziar and Jafarian [11] collected data from other energy-based researches [17–20] and built a database. Considering the initial density parameters such as relative density (Dr, %), initial effective mean confining pressure (σ’m0, kPa), grains size distribution parameters mean grain size (D50, mm), coefficient of uniformity (Cu), and coefficient of curvature (Cc), and individual parameter non-plastic fines contents (FC, %), a multilayer perceptron (MLP)-based NN model was proposed by Baziar and Jafarian [11] to predict Wliq. The parameters aforementioned were set as input parameters and Wliq was set as a target parameter. The training result of the model indicated that D50 and Cu seemed to be sufficient to represent the characteristics of grains size distribution, and the prediction of FC was disputable since the complex nonlinear relationship between FC and Wliq need further study. Cabalar et al. [15] built a neuro-fuzzy (NF)-based NN model with the same database. The result showed that the NF-based model had high accuracy, and the relationship among input and output parameters was obvious. However, this energy-based liquefaction potential evaluation research did not consider the effect of drainage boundaries. By the infiltration device installed in the triaxial apparatus, cyclic tests were conducted on Fujian standard saturated sand to explore the effect of drainage conditions. Toevaluate sand liquefaction potential, an energy-based database was built, and different NN models were constructed.

2. Cyclic Triaxial Tests with Simulated Drainage Boundary

2.1. Basic Concepts and Realization of Diﬀerent Drainage Conditions

The drainage condition of soil element is illustrated in Figure1, where ki = permeability coefficient of the soil at the drainage path; k0 = permeability coefficient of the soil element; and u = excess pore water pressure. It is assumed that the resistance of permeability at the drain is zero, and the EPWP here is zero. Thus, the water head difference among analyzed specimens and the drain mainly descends at the drainage path. In addition, there is another assumption in this research: only one plane of the drainage boundary is taken into consideration as shown in Figure1. The influence of other planes remains to be explored by applying biaxial dynamic loading [21,22]. By controlling ki, the permeability of the drainage path can be simulated. ki = 0 represents the undrained state. Therefore, the in-situ drainage condition under seismic loading theoretically is able to be reproduced by regulating a drainage system. J. Mar. Sci. Eng. 2019, 7, 411 3 of 15 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 3 of 15

Figure 1. Assumed drainage conditions of soil element. Figure 1. Assumed drainage conditions of soil element. The simplified illustration of the employed triaxial apparatus is shown in Figure 2. To reproduce TheThe simplified simplified illustration illustration of of the the employed employed triaxialtriaxial apparatus apparatus is shownis shown in Figurein Figure2. To 2. reproduce To reproduce differentdifferent drainage drainage conditions, conditions, an an in infiltrationfiltration devicedevice connectingconnecting a flowmetera flowmeter was was installed installed onto onto the the top oftop specimen of specimen to tocontrol control permeability permeability of of the silt.silt. TheThe infiltration infiltration device device can can retain retain soil soil and and free thefree the draineddrained water. water. More More detail detail waswas mentioned mentioned by Wangby Wang et al. [et23 ].al. Note [23] that. Note the dithatfference the indifference cross sections in cross sectionsbetween between the infiltration the infiltration device and device the drain and pipethe drain results pipe in no results head loss, in no considering head loss, the considering hypothesis the hypothesisthat the EPWPthat the is zeroEPWP at theis zero drain at pipe. the drain The valve pipe. at The the bottom valve at is closed,the bottom and the is closed valve at, and the top the is valve at theopen top during is open a test.during With a thetest. designed With the infiltration designed device, infiltration the cyclic device, triaxial the equipment cyclic triaxial can conduct equipment tests under the replicated drainage boundary conditions. can conduct tests under the replicated drainage boundary conditions.

Figure 2. Schematic of the infiltration device in cyclic triaxial equipment. Figure 2. Schematic of the infiltration device in cyclic triaxial equipment. The positionFigure of drainage 2. Schematic path of in the the infiltration infiltration device device in wascyclic illustrated triaxial equipmen in Figuret. 2; tests were The position of drainage path in the infiltration device was illustrated in Figure 2; tests were carriedThe position out to calibrate of drainage the permeability path in the of siltinfiltration layer with device varied was dry density.illustrated Then, ink pFigurewas introduced 2; tests were carried out to calibrate the permeability of silt layer with varied dry density. Then, kp was introduced carriedto represent out to calibrate the effect the of the permeability drainage boundary of silt layer condition with considering varied dry permeability density. Then, of the kp soilwas element, introduced to representwhich is shown the effect as of the drainage boundary condition considering permeability of the soil k element, which is shown as k = i . (1) p k k 0 ki kp= i . (1). kp can represent the silt with different density,kp which= k0. is only appropriate for silt and sand used in this (1). k0 research. The result of calibration was depicted in Figure3. There is a strong negative correlation p kp can represent the silt with different density, which3 is only appropriate for silt and sand used in this k canbetween representkp and theρ dsilt. When withρ differentd is larger density, than 1.3 gwhich/cm , theis onlykp descends appropriate more slowly.for silt Itand is suggested sand used the in this research.permeability The result resistance of calibration of infiltration was device depicted develops in Figure mostly when3. There the densityis a strong reaches negative a certain correlation value. 3 between kp and ρ . When ρ is than 1.3 g/cm3, the kp descends more slowly. It is suggested the In addition,kp kp d= 0 representsd the larger undrained state. With thep calibration test results, the response of a between and ρd. When ρd is larger than 1.3 g/cm , the k descends more slowly. It is suggested the permeabilitysoil element resistance adjacent toof a infiltration soil layer of arbitrarydevice develops permeability mostly can be when predicted. the density reaches a certain value. In addition, kp = 0 represents the undrained state. With the calibration test results, the response value. In addition, kp = 0 represents the undrained state. With the calibration test results, the response of a soil element adjacent to a soil layer of arbitrary permeability can be predicted.

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Figure 3. Relationship between kp and ρd of silt in the inﬁltration device. Figure 3. Relationship between kp and ρ of silt in the infiltration device. d 2.2. Sand Properties and Experiment Conditions 2.2. Sand Properties and Experiment Conditions Fujian standard sand was employed in the tests. Some important parameters of the sand are listed inFujian Table1 .standard The average sand relative was density employed before in consolidation the tests. Some ( Dr0 ,important %) of specimens parameters were controlled of the sand to are listed50.0% in approximately,Table 1. The and average the average relative relative density density before post consolidation consolidation (Dr, %)(D wasr0, %) 48.7%. of specimens The fractal were dimension of sand particles may be an influential parameter and need further investigation [24]. controlled to 50.0% approximately, and the average relative density post consolidation (Dr, %) was The specimens were constituted by the water pluviation because this method can ensure the uniformity 48.7%. The fractal dimension of sand particles may be an influential parameter and need further of relative density of specimens [25]. Then, the specimens were saturated by applying back pressure of investigation [24]. The specimens were constituted by the water pluviation because this method can 500 kPa until the B value surpassed 0.95. The dense silt layer in the infiltration device may cause the ensureapplied the back uniformity pressure of much relative higher density than common of spec value.imens [25]. Then, the specimens were saturated by applying back pressure of 500 kPa until the B value surpassed 0.95. The dense silt layer in the infiltration device may cause theTable applied 1. Properties back ofpressureFujian standard much sand.higher than common value.

emax e Cu Cc D (mm) Tablemin 1. Properties of Fujian standard sand. 50 0.848 0.597 5.6 0.45 0.63 emax emin Cu Cc D50 (mm) The employed cyclic triaxial0.848 apparatus 0.597 is electric5.6 0.45 servo-type. 0.63 With the flowmeter fitted to the infiltration device, the amount of water drained out of soil can be measured. Considering high permeabilityThe employed of the cyclic saturated triaxial sand apparatus specimens, theis electric EPWP isservo-type. assumed to With equally-redistributed the flowmeter rapidlyfitted to the infiltrationunder the device, stress condition the amount in short of time water intervals. drained Thus, out this of studysoil measuredcan be measured. the pore water Considering pressure high permeabilityat the bottom of ofthe specimen saturated to representsand specimens, the whole the element EPWP approximately. is assumed to equally-redistributed rapidly under the stress condition in short time intervals. Thus, this study measured the pore water pressure Table 2. Cyclic triaxial tests series at different boundary drainage states. at the bottom of specimen to represent the whole element approximately.

The cyclic triaxialTest No. tests seriesDr were(%) performedσ’0 (kPa) accordingσd (kPa)to ASTM D5311/D5311M-13,kp Standards Test Method for Load1 Controlled Cy 48.7clic Triaxial 200Strength of Soil 50 [26]. The scheme 0 of test series was concluded in Table 2.2 The tests were 48.7 conducted 200 under isotropic 50 consolidation 0.107 with 200 kPa initial 3𝜎 48.7 200 50 0.119 effect confining pressure4 ( ) and 48.7the top valve was 200 unbolted and 50 connected 0.132 to the infiltration device; then, the specimen was5 applied 48.7a cyclic loading. 200 The applied 50 loading was 0.17 a sinusoidal wave with 6 48.7 200 50 0.54 amplitude (𝜎) of 50 kPa. The tests were stress-controlled with loading frequency of 1.0Hz. Initial 7 48.7 200 50 0.68 liquefaction is obvious8 to observe 48.7 herein and approp 200riate to be 50 the liquefaction 0.84 criterion. Two stress parameters were shown to present the traditional triaxial test results: deviator stress: q = σ1-σ3, average effective principal stress, p’= (𝜎+2𝜎)/3. The cyclic triaxial tests series were performed according to ASTM D5311/D5311M-13, Standards Test Method for Load Controlled Cyclic Triaxial Strength of Soil [26]. The scheme of test series was concluded Table 2. Cyclic triaxial tests series at different boundary drainage states. in Table2. The tests were conducted under isotropic consolidation with 200 kPa initial e ﬀect conﬁning

pressure (σ0) and the top valveTest No. was unboltedDr(%) andσ'0(kPa) connected σd(kPa) to the inﬁltrationkp device; then, the 1 48.7 200 50 0 2 48.7 200 50 0.107 3 48.7 200 50 0.119 4 48.7 200 50 0.132 5 48.7 200 50 0.17

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J. Mar. Sci. Eng. 2019, 7, 411 6 48.7 200 50 0.54 5 of 15 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 5 of 15 7 48.7 200 50 0.68 8 48.7 200 50 0.84 specimen was applied a cyclic6 loading. 48.7 The applied200 loading was50 a sinusoidal0.54 wave with amplitude (σd) of 50 kPa. The tests were stress-controlled7 48.7 with200 loading frequency50 0.68 of 1.0Hz. Initial liquefaction 3. Test Results and Analysis is obvious to observe herein and8 appropriate48.7 to be200 the liquefaction50 criterion.0.84 Two stress parameters were shown to present the traditional triaxial test results: deviator stress: q = σ σ , average effective 1− 3 3.1. Preliminaryprincipal stress, Resultsp = σ +2σ )/3. 3. Test Results and 0Analysis10 30 Figure 4 and Figure 5 showed the liquefaction behavior characteristics of test results conducted 3. Test Results and Analysis under3.1. Preliminary a certain drainageResults condition (kp = 0.17). Time histories of axial deviator stress (q), axial strain (εa), and EPWP were plotted in Figure 4 at the same time scale. Stress path and stress–strain curves 3.1.Figure Preliminary 4 and Figure Results 5 showed the liquefaction behavior characteristics of test results conducted were plotted in Figure 5. As pore pressure in the sand specimen accumulated under cyclic loading, under a Figurescertain4 drainage and5 showed condition the liquefaction (kp = 0.17). behavior Time characteristicshistories of axial of test deviator results conductedstress (q), underaxial strain the effective confining stress decreased. Then, the deformation resistance ability of specimen (εa), aand certain EPWP drainage were conditionplotted in ( kFigurep = 0.17). 4 at Time the historiessame time of axialscale. deviator Stress path stress and (q), stress axial strain–strain (ε acurves), decreased. Then, EPWP increased to and initial liquefaction achieved, accompanied by a sudden wereand plotted EPWP in were Figure plotted 5. As in Figurepore pressure4 at the same in the time sand scale. specimen Stress path accumulated and stress–strain under curves cyclic were loading, increaseplotted in the in Figureq and5 ε.a. As Cyclic pore pressuremobility′ inbehavior the sand was specimen also displayed, accumulated leading under to cyclic a near loading, zero effective the the effective confining stress decreased.𝜎𝜎0 Then, the deformation resistance ability of specimen stresse ffstateective with confining a typical stress “butterfly” decreased. stress Then, path the deformation as illustrated resistance in Figure ability 5(a). of The specimen hysteresis decreased. loops of decreased. Then, EPWP increased to and initial liquefaction achieved, accompanied by a sudden specimenThen, were EPWP plotted increased in Figure to σ0 and 5( initialb), and liquefaction the first few achieved, circles accompaniedof loops are byindiscernible. a sudden increase As the in axial increase in the q and εa. Cyclic mobility′ behavior was also displayed, leading to a near zero effective strainthe increased,q and εa. Cyclicthe shape mobility of the behavior loops𝜎𝜎 0demonstrated was also displayed, a nonlinear leading tohysteresis a near zero stress effective–strain stress behavior. state stresswith state a typical with “butterfly”a typical “butterfly” stress path asstress illustrated path as in Figureillustrated5a. The in hysteresis Figure 5(a). loops The of specimenhysteresis were loops of specimenplotted were in Figure plotted5b, and in Figure the first 5( fewb), circlesand the of first loops few are circles indiscernible. of loops As are the indiscernible. axial strain increased, As the axial strainthe increased, shape of the the loops shape demonstrated of the loops a nonlineardemonstrated hysteresis a nonlinear stress–strain hysteresis behavior. stress–strain behavior.

Figure 4. Time–histories of test results with kp = 0.17.

(a) (b)

FigureFigure 5. Test 5. Test result result (k (pk p= =0.17)0.17) of of (a (a)) s stresstress path; ((bb)) stress–strain stress–strain curves. curves.

Comparing with the aforementioned test results in Figure 5, stress path and stress–strain curves of an unliquefied condition(a) (kp = 0.84) were plotted in Figure 6 to discriminate(b) different patterns of soil liquefaction behavior characteristics. Both curves in Figure 6 are indiscernible; the variation of

Figure 5. Test result (kp = 0.17) of (a) stress path; (b) stress–strain curves.

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J. Mar. Sci.Comparing Eng. 2019, 7 with, x FOR the PEER aforementioned REVIEW test results in Figure5, stress path and stress–strain curves6 of 15 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 6 of 15 of an unliqueﬁed condition (kp = 0.84) were plotted in Figure6 to discriminate di ﬀerent patterns of soil stressliquefaction and strain behavior are in characteristics.a narrow scale, Both and curvesno sudden in Figure increase6 are occurred. indiscernible; The thevalue variation of ’ under of stress cyclic stress and strain are in a narrow scale, and no sudden increase occurred. The value of ’ under cyclic loadingand strain rema areins in a a relative narrow scale,high level, and no which sudden means increase that occurred. the pore Thewater value dissipated of p under rapidly cyclic with loading a good loading remains a relative high level, which means that the pore water dissipated0 rapidly𝑝𝑝 with a good drainageremains aboundary relative high condition. level, which Thus, means the ability that the to pore resist water deformation dissipated rapidlymostly withremains a good𝑝𝑝 under drainage a good drainage boundary condition. Thus, the ability to resist deformation mostly remains under a good drainageboundary boundary condition. condition. Thus, the Note ability that to resistthe polylines deformation in Figure mostly 6(a) remains resulted under from a good the fact drainage that the drainage boundary condition. Note that the polylines in Figure 6(a) resulted from the fact that the amountboundary of condition.water that Note passed that thethrough polylines the in drainage Figure6a resultedboundary from under the fact cyclic that theloading amount was of not amount of water that passed through the drainage boundary under cyclic loading was not proportionalwater that passed to the throughdeviator the stress. drainage boundary under cyclic loading was not proportional to the proportionaldeviator stress. to the deviator stress.

(a) (b) (a) (b) Figure 6. Test result (kp = 0.84) of (a) stress path; (b) stress–strain curves. FigureFigure 6. 6.TestTest result result (k (pk p= =0.84)0.84) of of (a ()a s)tress stress path; path; ( (bb)) stress stress–strain–strain curves. The EPWP response time–history was provided in Figure 7. N refers to the loading cycles. Two TheThe EPWP EPWP response response time time–history–history w wasas provided provided in in Figure Figure 77.. N refers toto thethe loadingloading cycles. cycles. Two Two groups were divided by whether liquefaction achieved. The response regularity of EPWP and the groupsgroups were were divided divided by by whether whether liquefaction liquefaction achieved. achieved. The The response response regularity ofof EPWPEPWP and and the the influenceinﬂuence of of kkp phavehave been been discussed discussed [[24]24].. influence of kp have been discussed [24].

(a) (b) (a) (b) Figure 7.7.Time–history Time–history of of excess excess pore pore water water pressure pressure (EPWP): (EPWP) (a) liquefied: (a) liquefied group; (group;b) unliquefied (b) unliquefied group. Figure 7. Time–history of excess pore water pressure (EPWP): (a) liquefied group; (b) unliquefied group. Drainage boundary conditions have a stronggroup.influence on the liquefaction behavior of sand specimens.Drainage In boundary Figure8, schematic conditions diagrams have a were strong plotted influence based on thethe observationliquefaction in behavior each group of tosand illustrateDrainage a probable boundary cause conditions of the sand have liquefaction a strong under influence different on drainagethe liquefaction boundary behavior conditions. of Thesand specimens. In Figure 8, schematic diagrams were plotted based on the observation in each group to specimenmechanisms. In ofFigure how the8, schematic drainage boundary diagrams influences were plotted the liquefied based on specimen the observa is discussed:tion in cycliceach group loading to illustrate a probable cause of the sand liquefaction under different drainage boundary conditions. illustrateacts on a the probable sand element cause of under the disandfferent liquefaction drainage boundaries.under different The sanddrainage particles boundary werecondensed conditions. The mechanism of how the drainage boundary influences the liquefied specimen is discussed: cyclic Thefrom mechanism the bottom of how of specimens the drainage under boundary the effect influences of loading the and liquefied gravity. Thespecimen condensing is discussed: of sand c andyclic loading acts on the sand element under different drainage boundaries. The sand particles were loadingseismic acts loading on the both sand cause element a process under of upward different seepage, drainage which boundar accumulatesies. The thepore sand water particles at the were top. condensed from the bottom of specimens under the effect of loading and gravity. The condensing of condensed from the bottom of specimens under the effect of loading and gravity. The condensing of sand and seismic loading both cause a process of upward seepage, which accumulates the pore water sand and seismic loading both cause a process of upward seepage, which accumulates the pore water at the top. The poor drainage boundary condition may induce the sand more susceptible to liquefy at the top. The poor drainage boundary condition may induce the sand more susceptible to liquefy at a localized zone. The more significant of the seepage effect will make pore water response more at a localized zone. The more significant of the seepage effect will make pore water response more fiercely. fiercely.

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J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 7 of 15 The poor drainage boundary condition may induce the sand more susceptible to liquefy at a localized J. Mar.zone. Sci. The Eng. more2019, 7 significant, x FOR PEER of REVIEW the seepage effect will make pore water response more fiercely. 7 of 15

(a) (b)

Figure 8. The schematic( diagramsa) for phenomena under different drainage(b) conditions: (a) liquefied group;FigureFigure (b 8.) u 8.ThenliquefiedThe schematic schematic group diagrams diagrams. for for phenomena phenomena underunder didifferentfferent drainage drainage conditions: conditions (a: )(a liquefied) liquefied group;group; (b ()b u)nliquefied unliquefied group group.. 3.2. Liquefaction Potential Evaluation 3.2. Liquefaction Potential Evaluation 3.2. Liquefaction Potential Evaluation 3.2.1.3.2.1. Energy Energy-Based-Based Analysis Analysis and and Database Database Building Building 3.2.1. Energy-Based Analysis and Database Building As FigureAs Figure 9 depicted,9 depicted, in in cyclic cyclic triaxial triaxial tests, W can bebe calculated calculated using using trapezoidal trapezoidal rule rule results results as as followfollows:s:As Figure 9 depicted, in cyclic triaxial tests, W can be calculated using trapezoidal rule results as n 1 follows: X− n 1 =W = (q i+1+qi)(εi+1 εi), (2) W i=1 (qi+1 qi)( − ), (3) = n i=1 1 + W i−=1 (qi+1 qi)( ), (3) 𝑖𝑖+1 𝑖𝑖 where n = number of total loading cycles;∑ − qi = deviatoric stress in the ith cycle; a,i = axial strain in the where n = number of total loading cycles; qi = deviatoric𝜀𝜀𝑖𝑖+1 − stress𝜀𝜀𝑖𝑖 in the ith cycle; εa,i = axial strain in where n = number of total loading cycles;∑ qi = deviatoric𝜀𝜀 −stress𝜀𝜀 in the ith cycle; a,i = axial strain in the ith cyclethe ith; and cycle; the and stored the stored energy energy is denoted is denoted as as WWs. sPhysically,. Physically, W representsrepresents the the energy energy inside inside sand sand ith cycle; and the stored energy is denoted as Ws. Physically, W represents theε energy inside sand sedimentssediments that that need need to be to bedissipated dissipated and and indirectly indirectly reflectsreflects the the friction friction of of sand sand particles εparticles and and the extentthe extent sediments that need to be dissipated and indirectly reflects the friction of sand particles and the extent that thatthe sand the sand skeleton skeleton breaks breaks down. down. Thus, Thus, employing employing WWas as an an indicator indicator for for liquefaction liquefaction evaluation evaluation is is that the sand skeleton breaks down. Thus, employing W as an indicator for liquefaction evaluation is rationalrational because because the the energy energy approach approach accounts accounts for bothboth seismically seismically induced induced stress stress and and strain. strain. rational because the energy approach accounts for both seismically induced stress and strain.

Figure 9. Energy density and hysteresis loop modiﬁed after Yang and Pan [12]. FigureFigure 9. 9. Energy Energy density density and and hysteresishysteresis loop modifiedmodified after after Yang Yang and and Pan Pan [12] [12]. . In the liquefied group, test results were analyzed by an energy approach. An example (kp = 0.17) In the liquefied group, test results were analyzed by an energy approach. An example ( kp = 0.17) wasIn the plotted liquefied in Figure group, 10. Time-history test results ofwereW and analyzed the calculated by anW energyliq were approach. shown, which An isexample a typical ( curve kp = 0.17) was plotted in Figure 10. Time-history of W and the calculated Wliq were shown, which is a typical was ofplotted stress-controlled in Figure test 10. results. Time-history The majority of W of and the strainthe calculated energy was W dissipatedliq were shown, in the last which several is cycles a typical curvecurve of of stress stress-controlled-controlled test test results. results. TheThe mmajority of thethe strainstrain energyenergy was was dissipated dissipated in in the the last last several cycles close to liquefaction occurrence. It has been proved that both the stress- and strain- several cycles close to liquefaction occurrence. It has been proved that both the stress- and strain- controlled cyclic triaxial undrained tests have similar EPWP generation results analyzed by an energy controlled cyclic triaxial undrained tests have similar EPWP generation results analyzed by an energy approach [27]. approach [27].

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J. Mar.close Sci. Eng. to liquefaction 2019, 7, x FOR occurrence. PEER REVIEW It has been proved that both the stress- and strain- controlled cyclic8 of 15 triaxial undrained tests have similar EPWP generation results analyzed by an energy approach [27].

Figure 10. Time–history of W with kp of 0.17.

In the unliquefied group,Figure different 10. Time–history drainage of Wconditionswith kp of0.17. showed evident influence on the behavior of W. As shown in Figure 11, W would rise to a peak value and then decreased, which is Figure 10. Time–history of W with kp of 0.17. differentIn with the unliquefied the cyclic rising group, curve different in drainageFigure 10 conditions of liquefied showed group evidents. Then, influence the peak on the value behavior of W was of W. As shown in Figure 11, W would rise to a peak value and then decreased, which is different denotedIn the as Wunliquefiedmax. Considering group, the different physical drainage meaning, conditionsthe trend thatshowed W decreases evident circularly influence indicates on the with the cyclic rising curve in Figure 10 of liquefied groups. Then, the peak value of W was denoted behaviorthat the structure of W. As of shown soil is in repaired Figure or11, densified, W would rather rise to than a peak being value damaged and then or brokendecreased, down which in case is as Wmax. Considering the physical meaning, the trend that W decreases circularly indicates that the of good drainage boundary conditions. differentstructure with of the soil cyclic is repaired rising or curve densified, in Figure rather 10 than of beingliquefied damaged group ors. broken Then, downthe peak in case value of goodof W was denoteddrainage as W boundarymax. Considering conditions. the physical meaning, the trend that W decreases circularly indicates that the structure of soil is repaired or densified, rather than being damaged or broken down in case of good drainage boundary conditions.

Figure 11. Time–history of W with kp of 0.54.

Figure 11. Time–history of W with kp of 0.54. To numerically investigate how the drainage effect influenced W, the generalized W (Wg) are defined including both Wliq and Wmax. The relationship between Wg and kp was shown in Figure 12. It is To numerically investigate how the drainage effect influenced W, the generalized W (Wg) are indicated that Wliq and Wmax can be correlated through parameter kp. The function is shown as follows: defined including both Wliq and Wmax. The relationship between Wg and kp was shown in Figure 12. It Figure 11. Time–history of W with kp of 0.54. 6.6kp is indicated that Wliq and Wmax can be correlatedWg =5391.3e through− . parameter kp. The function is shown (3) as followTos: numerically investigate how the drainage effect influenced W, the generalized W (Wg) are The liquefaction probability of a certain ground condition can be evaluated by considering drainage defined including both Wliq and Wmax. The relationship-6.6k between Wg and kp was shown in Figure 12. It boundary conditions. The evaluation systemWg=5391.3 basede onp. sand liquefaction behavior characteristics (4) is indicated that Wliq and Wmax can be correlated through parameter kp. The function is shown as is concluded: the eﬀect of drainage boundary condition can be quantiﬁed to the corresponding kp followaccordings: to the permeability of soil. It can be discriminated whether the sand specimen will achieve

liquefaction based on the value of k . The probability-6.6kp of liquefaction occurring is high, if the k p Wg=5391.3e . p (4) represents that the sand is under bad drainage boundary conditions. The Wliq can be roughly predicted by Equation (3).

J. Mar. Sci. Eng. 2019, 7, 411 9 of 15

The energy-based database was developed by taking in new test results [8,9,12,28], and these tests were undrained with kp = 0. Whether before or post consolidation, relative density is almost the same for saturated sand under undrained conditions. While the data from research focused on drainage conditions are shown in Table3. To analyze these test results with di fferent drainage effects quantifying parameters by an energy approach, the different parameters were converted into J. kMar.p uniformly. Sci. Eng. 2019 The, 7 hysteresis, x FOR PEER loop REVIEW curves were reconstituted based on the provided stress and strain 9 of 15 time-histories; then, the corresponding Wliq can be calculated.

Figure 12. Relationship between generalized Wg and kp. Figure 12. Relationship between generalized Wg and kp. Table 3. Summary of sand liquefaction potential under diﬀerent drainage boundary conditions using an energy approach. The liquefaction probability of a certain ground condition can be evaluated by considering 3 drainageσ’m0 (kPa) boundary Dconditionr0 (%) s. The kevaluationp systemCu based Don50 (mm)sand liquefactionWliq (J/m ) behavior characteristics is concluded:Niigata thesand, effect cyclic of triaxial drainage tests, Umeharaboundary et al. condition (1985) can be quantified to the corresponding100 kp accor 45.8ding to the permeability 0.108 of soil. 1.9 It can be discriminated 0.32 whether 271 the sand Toyura sand, cyclic triaxial tests, Yamamoto et al. (2009) specimen will achieve liquefaction based on the value of kp. The probability of liquefaction occurring 200 49.9 0.03 1.2 0.2 3494 is high, 100if the kp represents 91.5 that the sand 0.03 is under bad drainage 1.2 boundary 0.2 conditions. 2797 The Wliq can be roughly predicted by EquationFujian (4).standard sand, cyclic triaxial tests, this study The200 energy-based 50.0database was developed 0 by taking 5.6 in new test 0.63 results [8,9,12,28] 5067 , and these 200 50.0 0.107 5.6 0.63 3402 tests were200 undrained with 50.0 kp = 0. Whether 0.119 before or post 5.6 consolidation 0.63, relative density 2119 is almost the same for200 saturated sand 50.0 under undrained 0.132 condition 5.6s. While the data 0.63 from research 2706 focused on drainage200 conditions are 50.0 shown in Table 0.17 3. To analyze these 5.6 test results 0.63 with different 2191drainage effects Toyura sand, centrifuge tests, Ohara and Yamamoto (1982) quantifying parameters by an energy approach, the different parameters were converted into kp 9.4 48.7 0 1.6 0.27 84 uniformly.9.4 The hysteresis 53.6 loop curves 0.08 were reconstituted 1.6 based on 0.27the provided stress 67 and strain time-histories; then, the corresponding Wliq can be calculated.

For example, Figures 13 and 14 illustrate the procedure of Wliq calculation in a centrifuge test Table 3. Summary of sand liquefaction potential under different drainage boundary conditions using under diﬀerent drainage conditions performed by Ohara and Yamamoto [3]. In Figure 13, the shear stressan time–history energy approach. was reconstructed based on the recorded acceleration time–history within the zones

between the accelerometersσ'm0 (kPa) by a techniqueDr0 (%) [29],k andp theC shearu D strain50 (mm) time–history Wliq (J/m was3) shown together. The technique can evaluateNiigata the shear sand, stress cyclic curve triaxial according tests, toUmehara acceleration et al. curve (1985) based on shear beam theory and was depicted as 100 45.8 0.108 1.9 0.32 271 τ = ρha , (4) Toyura sand, cyclic triaxialmax tests,max Yamamoto et al. (2009) where ρ is the mass density200 of sand49.9 and assumed0.03 20001.2 kg/m3,0.2h is the depth3494 of liquefaction zone, and amax is the peak acceleration.100 The91.5 technique 0.03 has1.2 been proved0.2 eﬀective2797 [9,11 ,30]. In Figure 14, reconstructed shear stress–strainFujian standard loops were sand, shown cyclic for calculation triaxial tests, of W thisliq and study recalculated parameters σ’m0 and kp were also provided.200 In anisotropically50.0 0consolidated 5.6 tests,0.63 the parameter5067 σ’m0 was calculated as follows: 200 50.0 0.107 5.6 0.63 3402 200 50.0 0.119 5.6 0.63 2119 200 50.0 0.132 5.6 0.63 2706 200 50.0 0.17 5.6 0.63 2191 Toyura sand, centrifuge tests, Ohara and Yamamoto (1982) 9.4 48.7 0 1.6 0.27 84 9.4 53.6 0.08 1.6 0.27 67

For example, Figure 13 and Figure 14 illustrate the procedure of Wliq calculation in a centrifuge test under different drainage conditions performed by Ohara and Yamamoto [3]. In Figure 13, the shear stress time–history was reconstructed based on the recorded acceleration time–history within the zones between the accelerometers by a technique [29], and the shear strain time–history was

J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 10 of 15 shown together. The technique can evaluate the shear stress curve according to acceleration curve J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 10 of 15 based on shear beam theory and was depicted as shown together. The technique can evaluate the shear stress curve according to acceleration curve τmax=ρhamax, (8) based on shear beam theory and was depicted as where ρ is the mass density of sand and assumed 2000kg/m3, h is the depth of liquefaction zone, and amax is the peak acceleration. The techniqueτmax= ρhashamax been, proved effective [9,11,30]. In Figure (8)14, wreconstructedhere ρ is the massshear density stress –ofstrain sand andloops assumed were shown2000kg/m for3, hcalculation is the depth of of liquefactionWliq and recalculated zone, and m0 p m0 aparametersmax is the peakσ' andacceleration. k were also The provided. technique In anisotropicallyhas been proved consolidated effective [9,11,30]tests, the. parameterIn Figure σ14,' reconstructedwas calculated shearas follow stresss: –strain loops were shown for calculation of Wliq and recalculated parameters σ'm0 and kp were also provided. In anisotropically(1+2K ) consolidated tests, the parameter σ'm0 J. Mar. Sci. Eng. 2019, 7, 411 = 0 , 10 of 15 (9) ′ 3 was calculated as follows: ′ 𝜎𝜎𝑣𝑣0 𝑚𝑚0 where σ'v0 is the initial vertical effective stress𝜎𝜎 acting on the specimen and K0 is the at-rest lateral earth ((1++2K0) =σv0 0 1 2K, 0 (9) pressure coefficient and is assumed as σ10 for= saturated′ 3 sand., The drainage parameter was converted (5) m0′ 𝜎𝜎𝑣𝑣0 3 p i 𝑚𝑚0 t wintohere k :σ based'v0 is the on initial Darcy’s vertical law, effectivek can be stressconverted𝜎𝜎 acting by on parameter the specimen v that and employed K0 is the atin- resttheir lateral research earth to where σ’v0 is the initial vertical effective stress acting on the specimen and K0 is the at-rest lateral earth quantify drainage effect, and k0 has also been shown. pressurepressure coefficient coefficient and and is is assumed assumed asas 11 for for saturated saturated sand. sand. The The drainage drainage parameter parameter was convertedwas converted intointo kp: kbasedp: based on on Darcy’s Darcy’s law, law, kkii cancan be convertedconverted by by parameter parametervt thatvt that employed employed in their in their research research to to quantifyquantify drainage drainage effect, effect, and and k0 hashas also beenbeen shown. shown.

Figure 13. Average shear stress and strain time–history curves.

Figure 13. Average shear stress and strain time–history curves. Figure 13. Average shear stress and strain time–history curves.

Figure 14. Reconstructed average shear stress–strain curves. Figure 14. Reconstructed average shear stress–strain curves. With all the research mentioned above, the corresponding database of 217 test results was built containingWith all inputthe research parameters, mentioned such as initialabove, eff theective corresponding mean confining database pressure of (σ ’217m0, kPa),test resultsDr0, kp, wasCu, built Reconstructed3 average shear stress–strain curves. and Cc and target parameterFigure W14.liq (J/m ). Since the complex nonlinear relationship remains disputable containing input parameters, such as initial effective mean confining pressure (σ'm0, kPa), Dr0, kp, Cu, between FC and Wliq [11,15,28], only the data with FC = 0 were chosen to build the database. and WithCc and all target the research parameter mentioned Wliq (J/m 3above,). Since the the corresponding complex nonlinear database relationship of 217 test remains results disputable was built liq containingbetween3.2.2. MLP-Based FC input and Wparameters, and [11, NF-Based15,28] such, only NN as Modelthe initial data effective with FC mean = 0 were confining chosen pressure to build the(σ'm0 database., kPa), D r0, kp, Cu, 3 and Cc andThe performancetarget parameter of a widely Wliq (J/m used). model Since was the shown. complex Multiple-linear nonlinear relationship regression (MLR) remains is a sort disputable of 3.3.2. MLP-Based and NF-Based NN Model betweena statistic FCmodel, and W inliq which[11,15 di,28]fferent, only parameters the data exertwith the FC influence = 0 were on chosen the dependent to build variable the database. of function through linear regression. It used to be primary option in W prediction to obtain approximations of liq 3.3.2.the MLP relations-Based between and NF variables-Based for NN its Model convenience and high-efficiency [11,13,31,32]. The MLR-based model previously developed by Baziar and Jafarian [11] was employed on the new database as

LogW =2.1028+0.004566σ0m +0.005685Dr +0.001821FC 0.02868Cu+2.0214D . (6) liq 0 0 − 50 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 11 of 15

The performance of a widely used model was shown. Multiple-linear regression (MLR) is a sort of a statistic model, in which different parameters exert the influence on the dependent variable of function through linear regression. It used to be primary option in Wliq prediction to obtain approximations of the relations between variables for its convenience and high-efficiency [11,13,31,32]. The MLR-based model previously developed by Baziar and Jafarian [11] was employed on the new database as

LogWliq=2.1028+0.004566σ'm0+0.005685Dr0+0.001821FC 0.02868Cu+2.0214D50 . (10) J. Mar. Sci. Eng. 2019, 7, 411 11 of 15 In terms of Figure 15 and the corresponding parameters such− as correlation coefficients (R2), root mean square error (RMSE), and mean absolute error (MAE), the MLR-based model did not predict In terms of Figure 15 and the corresponding parameters such as correlation coefficients (R2), root the Wliq with a good degree of accuracy. Values of the Wliq in tests under different drainage conditions mean square error (RMSE), and mean absolute error (MAE), the MLR-based model did not predict the appear to be overestimated as marked. It can be indicated that kp is an influential parameter and the Wliq with a good degree of accuracy. Values of the Wliq in tests under different drainage conditions necessityappear for to bedeveloping overestimated a model as marked. of better It canperformance be indicated is that obvious.kp is an influential parameter and the necessity for developing a model of better performance is obvious.

Figure 15. Prediction performance of an multiple-linear regression (MLR)-based model. Figure 15. Prediction performance of an multiple-linear regression (MLR)-based model. NN practitioners can handle sophisticated problems and the complexity of NN models can beNN varied practitioners simply by can altering handle the sophisticated network architecture problems [33]. and As forthe architecture complexity of of NNs, NN multilayermodels can be variedperceptron simply (MLP) by altering and neuro-fuzzy the network (NF) are architecture different kind [33] feedforward. As for (FF)architecture NNs [34]. of MLP NNs, is the multilayer most basic kind NN. It is adaptive and widely applied. The NF-based NN is based on an integration of NNs perceptron (MLP) and neuro-fuzzy (NF) are different kind feedforward (FF) NNs [34]. MLP is the and fuzzy logic, which means a complex fuzzy system is designed to obtain the learning capability most basic kind NN. It is adaptive and widely applied. The NF-based NN is based on an integration of networks. NF-based models offer the advantages of both fields and have provided more accurate of NNsresults and than fuzzy a simple logic, NN which model means in many a complex prediction fuzzy applications system [is34 ].designed Moreover, to theobtain relationship the learning capabilitybetween of input networks. parameters NF-based can be models illustrated offer by the a visual advantages perception of both figure fields in an and NF-based have model.provided more accurateWith results the newthan parameter a simplek pNNtaken model into account, in many the performanceprediction applications of two sort of [34] NNs. mentionedMoreover, the relationshipabove are between supposed input to be diparametersfferent in W canliq prediction. be illustrated The MLP-basedby a visual and perception NF-based figure NN models in an NF were-based model.both constructed on the new database and the proceedings were concluded: WithIn the data new division parameter aspects, k bothp taken NN into models account, chose the the performance random approach of two and sort the dataof NNs group mentioned can abovebe are divided supposed into training, to be different testing, and in W validationliq prediction. data setsThe [MLP35]. Testing-based dataand willNF- bebased also NN used models to train were boththe constructed network and on the the division new database of it can and be omitted. the proceedings Validation were data willconcluded: be used to check whether the model performs well. In architecture design aspects, both NN models are feedforward (FF) and back In data division aspects, both NN models chose the random approach and the data group can be propagation (BP), which means that the direction of calculation is from input parameters to target divided into training, testing, and validation data sets [35]. Testing data will be also used to train the parameters, and the calculated error will be distributed back forward to calibrate the networks till the networkmodel and meets the the division criterion of set it at can beginning. be omitted. In structure Validation aspects, data the neuros will be number used into the check hidden-layer whether the modelof anperforms MLP-based well. NN In architecture model is 5, which design is theaspects, same both as the NN number models of are input feedforward parameters (FF) [33], and and back propagationthe number (BP of), membership which means functions that the (MFs) direction is 3, which of calculation can represent is thefrom results input well parameters enough and to istarget parameterless computationally-consuming.s, and the calculated error will be distributed back forward to calibrate the networks till the modelOther meets main the features criterion of theset twoat beginning. kind NN models In structure are listed aspects, in Table the4. neuros number in the hidden- layer of an MLP-based NN model is 5, which is the same as the number of input parameters [33], and Table 4. Different features between MLP-based and NF-based NN models. the number of membership functions (MFs) is 3, which can represent the results well enough and is less computationally-consumiNFng. MLP Other Fuzzymain Inferencefeatures System of the Type two kind NN Sugeno models are listed Training in Table function 4. Trainlm Input membership function type Triangular Adaption learning function Learngdm Output membership function type Linear Transfer function Tansig Performance criterion Epochs Performance criterion MSE J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 12 of 15

J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 12 of 15 Table 4. Different features between MLP-based and NF-based NN models.

Table 4. DifferentNF features between MLP-based and NF-based MLPNN models . Fuzzy Inference SystemNF Type Sugeno Training functionMLP Trainlm InputFuzzy membership Inference S ystemfunction Type type TriangularSugeno AdaptionTraining learning function function LearngdmTrainlm OutputInput membership membership function function type type TriangularLinear AdaptionTransfer learning function function LearngdmTansig OutputPerformance membership criterion function type EpochsLinear PerformanceTransfer function criterion TansigMSE Performance criterion Epochs Performance criterion MSE J. Mar.The Sci. training Eng. 2019 results, 7, 411 of the MLP-based and NF-based NN models were given in Figure12 16. of 15The accuracyThe trainingof the models results was of theverified MLP -bybased validation and NF sets-based, and NN the models results were plottedgiven in in Figure Figure 16. 17. The By 2 accuracycomparison of theof Rmodels, RMSE, was and verified MAE, bythe validation accuracy ofsets an, andMLP the-based results model were is plotted slightly in better Figure than 17. theBy The training results of the MLP-based and NF-based NN models were given in Figure 16. NF-based model.2 However, it has a data point whose error is about 30%. It may result from the fact comparisonThe accuracy of R of, theRMSE, models and was MAE, veriﬁed the accuracy by validation of an sets, MLP and-based the results model were is slightly plotted better in Figure than 17 the. that the data were collected from the centrifuge test, in which the stress condition is uncertain and NFBy-based comparison model. ofHowever,R2, RMSE, it andhas MAE,a data the point accuracy whose of error an MLP-based is about 30%. model It is may slightly result better from than the the fact needs to be calculated according to the acceleration time–history. In the NF-based model, errors of thatNF-based the data model. were collected However, from it has the a data centrifuge point whose test, in error which is about the stress 30%. Itcondition may result is fromuncertain the fact and all data are less than 20%. For the centrifuge test data, performance of NF-based model is better than needthats to the be data calculated were collected according from to the the centrifuge acceleration test, time in which–history the. stressIn the condition NF-based is model, uncertain errors and of an MLP-based model. Compared with the prediction performance of an MLR-based model shown in all needsdata are to beless calculated than 20%. according For the tocentrifuge the acceleration test data, time–history. performance In theof NF NF-based-based model,model is errors better of than all Figure 15, both NN models perform better than MLR-based models (R2 an dataMLP are-based less thanmodel. 20%. Compared For the centrifuge with the testprediction data, performance performance of of NF-based an MLR= 0.231, model-based RMSE is model better = 0.474, shown than MAE an in Figure= 0.303MLP-based 15,). The both capacity model. NN modelsCompared energy perform of witha certain better the prediction kindthan MLRsand performance -specimenbased model under ofs an (R MLR-based2different = 0.231, RMSEdrainage model = 0.474, shown boundary MAE in =conditions 0.303Figure). The15 ,can both capacity be NN evaluated models energy perform byof imputinga certain better kind thansoil mechanical MLR-basedsand specimen modelsparameter under (R2 s=different to0.231, the RMSEdeveloped drainage= 0.474, boundaryNF MAE-based conditionsmodel= 0.303). with can Theaccuracy be capacity evaluated of about energy by 80%. ofimputing a certain soil kind mechanical sand specimen parameter unders di toﬀerent the developed drainage boundary NF-based modelconditions with accuracy can be evaluated of about by 80%. imputing soil mechanical parameters to the developed NF-based model with accuracy of about 80%.

(a) (b)

Figure 16.(a) Training results (a) MLP-based model; (b) NF-based (NNb) model. FigureFigure 16. 16. TrainingTraining results results (a (a) )MLP MLP-based-based model model;; ((bb)) NF-basedNF-based NN NN model. model.

(a) (b)

FigureFigure( a17.)17. ValidationValidation results results ( (aa)) MLP MLP-based-based model;model; ((bb)) NF-basedNF-based(b) NN NN model. model.

As elucidatedFigure in 17. Figure Validation 18, a visual results perception (a) MLP-based figure model was; provided (b) NF-based by an NN NF-based model. NN model to As elucidated in Figure 18, a visual perception figure was provided by an NF-based NN model analyze the influence of input parameters on the Wliq prediction. It can be concluded that the drainage to analyzeAs elucidated the influence in Figure of input18, a visual parameters perception on the figure Wliq wasprediction. provided It bycan an be NF concluded-based NN that model the condition effect on Wliq will increase as σ’m0 increases. When other soil parameters are constant, Wliq to willanalyze increase the asinfluence drainage of conditions input parameters get worse slightlyon the W (k liqdecreases) prediction. as It well can as beσ’ concludedincreases. that These the p m0 results are in agreement with the observed phenomena in cyclic triaxial tests (as shown in Figure8);

when kp increases, sand will achieve liquefaction with less dissipated energy density, and the loading cycling number for liquefaction will be less. J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 13 of 15 drainage condition effect on Wliq will increase as σ'm0 increases. When other soil parameters are constant, Wliq will increase as drainage conditions get worse slightly (kp decreases) as well as σ'm0 increases. These results are in agreement with the observed phenomena in cyclic triaxial tests (as shown in Figure 8); when kp increases, sand will achieve liquefaction with less dissipated energy J. Mar. Sci. Eng. 2019, 7, 411 13 of 15 density, and the loading cycling number for liquefaction will be less.

Figure 18. Nonlinear mapping for liquefaction potential: kp vs. σ’m0 (kPa).

Figure 18. Nonlinear mapping for liquefaction potential: kp vs. σ'm0 (kPa). 4. Conclusions 4. ConclusionsThe study was to exploit the influence of different drainage boundary conditions on the liquefaction behavior characteristics of saturated sand. The infiltration device was utilized to simulate drainage The study was to exploit the influence of different drainage boundary conditions on the boundary effects. The parameter k was introduced to quantify drainage boundary effects. Cyclic liquefaction behavior characteristics pof saturated sand. The infiltration device was utilized to simulate triaxial tests were carried out to assess the drainage effect on the liquefaction behavior characteristics. drainage boundary effects. The parameter kp was introduced to quantify drainage boundary effects. Test results were analyzed by the energy approach. Different NN models were constructed to evaluate Cyclic triaxial tests were carried out to assess the drainage effect on the liquefaction behavior liquefaction potential. The main conclusions were drawn as follows: characteristics. Test results were analyzed by the energy approach. Different NN models were constructed(1) The test to results evaluate indicate liquefaction that the potential. drainage boundaryThe main evidentlyconclusions aff ectwere the drawn EPWP as response follows regularity.: 1)The The sand test specimens results indicate will not that achieve the liquefactiondrainage boundary under cyclic evidently loading affect as drainage the EPWP ability response is good regularity. The sand specimens will not achieve liquefaction under cyclic loading as drainage (0.54 kp 1.0). Otherwise, the specimens will liquefy under poor drainage boundary conditions ability≤ is≤ good (0.54 ≤ kp ≤ 1.0). Otherwise, the specimens will liquefy under poor drainage (0 kp 0.17). Analyzed by an energy approach, it results from the fact that the sample consumes ≤ ≤ lessboundary capacity condition energy ass the (0 ≤ drainage kp ≤ 0.17). boundary Analyzed alerts by an better. energy It isapproach, assumed it that result a seepages from the in sandfact causedthat the by thesample partial consumes drainage less boundary capacity condition energy resultsas the indra poreinage water boundary accumulating alerts better. and EPWP It is increasesassumed rapidly that a inseepage a liquefied in sand group. caused by the partial drainage boundary condition results in pore water accumulating and EPWP increases rapidly in a liquefied group. (2) A technique was employed to calculate Wliq from the stress–strain curves of other research. After 2)gathering A technique data andwas conversionemployed to of thecalculate drainage Wliq efromffect quantifyingthe stress–strain parameter curves from of other drainage research. effect After gathering data and conversion of the drainage effect quantifying parameter from research, a database considering kp was built for Wliq prediction. drainage effect research, a database considering kp was built for Wliq prediction. (3) The traditional statistical model and different NN models were constructed for Wliq prediction. 3) The traditional statistical model and different NN models were constructed for Wliq Results indicate that an NF-based NN model has better performance and the accuracy rate of prediction. Results indicate that an NF-based NN model has better performance and the capacity energy assessment under different drainage is about 80%. The visual perception figure accuracy rate of capacity energy assessment under different drainage is about 80%. The provided by an NF-based model suggests that the dense specimen will consume more capacity visual perception figure provided by an NF-based model suggests that the dense specimen energy (as Dr0 increases). will consume more capacity energy (as Dr0 increases).

Author Contributions: Data curation, Z.-Q.L.; Formal analysis, X.-H.C.; Investigation, H.F.; Methodology, F.-H. Author Contributions: Data curation, Z.-Q.L.; Formal analysis, X.-H.C.; Investigation, H.F.; Methodology, F.-H.S.; S;Resources, Resources, B.W.; B.W Supervision,.; Supervision, B.W.; B.W Writing—original.; Writing—original draft, draft, C.-R.Y.; C.-R.Y Writing—review.; Writing—review and and editing, editing, C.-R.Y. C.-R.Y. Funding:Funding: TheThe authors authors are grateful are grateful for the forsupport the from support the Fundamental from the Fundamental Research Funds Research for the Funds Central for Universities the Central ofUniversities China (Grant of ChinaNo. 2013QNB22), (Grant No. 2013QNB22),the National Science the National Foundation Science of Foundation China (Grant of No. China 51408595), (Grant No. the 51408595),Scientific Researchthe Scientific Starting Research Foundation Starting for Foundation Returned forOverseas Returned Chinese Overseas Scholars, Chinese Ministry Scholars, of Education, Ministry of China Education, (Grant China No. ((Grant2015)1098). No. (2015)1098). Acknowledgments: This study was supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 2013QNB22), the National Science Foundation of China (Grant No. 51408595), the Scientific Research Starting Foundation for Returned Overseas Chinese Scholars, Ministry of Education, China (Grant No. (2015)1098), and the support is gratefully acknowledged. Conflicts of Interest: The authors declare no conflict of interest. J. Mar. Sci. Eng. 2019, 7, 411 14 of 15

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