A genetic-based model to predict maximum lateral …scientiairanica.sharif.edu/article_2097_4a0746c5c9d2a... · · 2018-04-27foundation of adjacent structure, density, Young's modulus,

Scientia Iranica A (2016) 23(1), 54{65

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringwww.scientiairanica.com

A genetic-based model to predict maximum lateraldisplacement of retaining wall in granular soil

A. Joharia;�, A.A. Javadib and H. Naja�c

a. Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran.b. Computational Geomechanics Group, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter,

UK.c. Department of Civil Engineering, Bushehr Graduate Azad University, Bushehr, Iran.

Received 19 February 2014; accepted 13 September 2015

KEYWORDSRetaining wall;Lateral displacement;Gene expressionprogramming;Soil-structureinteraction.

Abstract. Retaining walls are one of the most common geotechnical structures.Horizontal displacement at the top of the retaining wall is an important parameter indesign of retaining structures because of serviceability of the wall and adjacent structures.In this research, the Gene Expression Programming (GEP) is used for developing a modelto predict this design parameter of retaining wall. The input parameters of the modelconsist of e�ective period of adjacent structure, horizontal and rocking sti�ness of thefoundation of adjacent structure, density, Young's modulus, and friction angle of granularsoil as well as the thickness and height of retaining wall. The output of the model ismaximum lateral displacement of retaining wall. A database including 240 cases, createdfrom 3D �nite element modeling of a soil-retaining wall with an adjacent steel structuremodeled as surcharge, is employed to develop the model. Comparison of the GEP-basedmodel predictions with the simulated data indicates a very good performance and abilityof the developed models in predicting maximum lateral displacement of retaining walls.Sensitivity and parametric analyses are conducted to verify the results. It is shown that soildensity is the most in uential parameter in the maximum lateral displacement of retainingwall.© 2016 Sharif University of Technology. All rights reserved.

1. Introduction

Excavation adjacent to structures is a common geotech-nical engineering practice in urban areas. Severalretaining structures, such as soldier pile, soil nailing,retaining wall, and bored pile, are designed by geotech-nical engineers for supporting the walls of excavation.A safe and economical design requires adequate knowl-edge about di�erent aspects of behavior of retainingstructures, such as their deformation. For this purpose,3D numerical modeling of soil-retaining structures canbe useful for better understanding of these behav-

*. Corresponding author. Mobile: +98 9173144386E-mail address: [email protected] (A. Johari)

iors. In this research, 3D �nite element modelingof soil-retaining walls (as the most common retainingstructures) is used for predicting the maximum lateraldisplacement of this type of structures.

There have been many attempts to model thebehavior of retaining walls in 2D and 3D includingor neglecting the soil-retaining structure interactione�ects. The existing methods can be categorizedinto numerical, analytical, experimental, and arti�cialintelligence methods. Many research works in thesecategories are summarized in the following:

Numerical method: The �rst systematic numericalmethod to analyze the Soil Structure Interaction (SSI)of retaining wall behavior was presented by Clough and

A. Johari et al./Scientia Iranica, Transactions A: Civil Engineering 23 (2016) 54{65 55

Duncan [1,2] and Duncan and Clough [3] by the �niteelement method. These investigators used a hyperbolicconstitutive relationship to model the behavior of aback�ll, and extended it to model the behavior of thewall-to-soil interfaces. They observed the importanceof modeling the di�erent stages of construction of thewall and placement of the back�ll in the SSI analysis.Ebeling et al. [4] performed a comparison between re-sults from conventional equilibrium and �nite elementanalyses of several hypothetical gravity walls foundedon rock. Their analyses were performed considering thestages of the back�ll placement incorporated in Cloughand Duncan [2]. They concluded that the magnitudeof the downdrag force is signi�cantly a�ected by theconcrete-to-back�ll and rock-to-back�ll shear sti�nessvalues. Goh [5] performed �nite element analyses toinvestigate the e�ects of subsoil sti�ness, wall sti�ness,and wall roughness on the lateral earth pressure forconcrete cantilever retaining walls, and proposed amodi�ed earth pressure distribution.

Using an explicit �nite di�erence code, Ben-mebarek et al. [6] investigated the increase in thepassive earth pressures due to the decrease in the wallbreadth in a 3D model. Ebeling et al. [7] and Ebelinget al. [8] presented the results of extensive SSI analysisfor the soil founded Red River Lock and Dam No. 1.A reinforced soil berm was recommended, among otheralternatives, as a solution to the problems induced bysiltation of the lock. They also noted that conventionalequilibrium analyses are inadequate for the design ofthis type of structure.

Experimental method: Ebeling et al. [9] performedexperimental analysis on several gravity walls foundedon rock. They found that conventional equilibriumanalyses are very conservative because they do notaccount for the stabilizing e�ect of the downdrag forcesgenerated by the settlement of the back�ll. Huangand Luo [10] arranged several experiments on cantileverwall models to investigate the behavior of soil-retainingwalls on deformable foundations. They found that themeasured values of the coe�cient of lateral pressureincreased signi�cantly with a decrease in subgradesti�ness.

Analytical method: Filz and Duncan [11] presenteda theory to quantify the downdrag force on the backof nonmoving retaining walls. Filz et al. [12] presenteda simpli�ed method for incorporating downdrag forcesin conventional analyses of nonmoving retaining walls.Caltabianoa et al. [13] investigated the static andseismic sliding limit equilibrium conditions of retainingwalls. Ghanbari and Taheri [14] used an analyticalmethod for calculating active earth pressure in rein-forced retaining walls subject to a line surcharge. Contiand Viggiani [15] developed a new limit equilibrium

method for the pseudostatic design of embedded can-tilevered retaining walls.

Arti�cial intelligence method: Yildiz et al. [16] de-veloped an arti�cial neural network model for predict-ing the total lateral thrust and its point of applicationon rigid retaining walls due to �nite surface strip loads.

Gene expression programming [17] is a branchof arti�cial intelligence and a recent extension toGenetic Programming (GP) that develops computerprograms of di�erent sizes and shapes encoded in linearchromosomes of a �xed length. The main advantage ofthe GP-based approaches over the regression and othersoft computing techniques is their ability to generateprediction equations without assuming the prior formof the existing relationship. There have been somescienti�c e�orts directed at applying GEP to a numberof civil engineering problems (e.g. [18-27]). The mainobjectives of this paper are to:

- Investigate the feasibility of using gene expressionprogramming to �nd the relationship between max-imum lateral displacements of retaining wall withsti�ness of adjacent structure, horizontal and rockingsti�ness of foundation of adjacent structure, density,Young's modulus, and friction angle of granular soilas well as the thickness and height of retaining wall;

- Assess and evaluate the prediction capabilities of theGEP-based model using 3D �nite element modelingdata, not exposed to the model during its develop-ment;

- Carry out sensitivity analysis and parametric studyusing the developed GEP model.

2. Gene expression programming

Gene expression programming is an evolutionary algo-rithm for learning the most �t computer programs bymeans of arti�cial evolution. It incorporates both thesimple, linear chromosomes of �xed length similar toGenetic Algorithms (GA) and the rami�ed structuresof di�erent sizes and shapes similar to the parse treesof genetic programming [28].

Its behavior forms a metaphor of the processesof evolution in nature. GEP, similar to GA and GP,initializes a population that compounds the randommembers known as chromosomes. Afterwards, �tnessof each chromosome is evaluated with respect to a tar-get value. The principle of Darwinian natural selectionis used to select and reproduce \�tter" programs. Theprocess continues until a best solution for that problemis reached.

In GEP application, the chromosome can haveone or more genes. The gene contains two types ofinformation. The �rst type is stored in the head ofthe gene containing the information which is used in

56 A. Johari et al./Scientia Iranica, Transactions A: Civil Engineering 23 (2016) 54{65

producing the overall GEP model. The head containssome of the functions from the pre-selected functionset `F' along with some terminals from the terminal set`T'. The second type is stored in the tail and containsonly terminals. The tail contains information thatcan be used in generating future GEP models. Thearrangement of functions and terminals in head andtail of a GEP gene is called its structural architecture.Gens can be linked to each other by plus, minus,product, and division. Plus linking function usuallyproduces better �tness. It is only in recent yearsthat GEP has found its applications in geotechnicalengineering [18-27].

3. Finite element modeling

To develop a database including SSI e�ects, several 3Dsoil-retaining wall structures with surcharge adjacentto the excavation were modeled using the Finite Ele-ment (FE) software, ABAQUS. The ABAQUS modelwas validated against Plaxis and hand calculations fora number of simple retaining structures. Below a briefintroduction is given to the modeling procedure:

- Surcharge: Two 6-storey and 8-storey steel struc-tures, with a plan shown in Figure 1, were selectedand modeled as the non-uniform surcharge adjacentto the excavation. The modeled structures hadrigid connections and a mat foundation with 1.0 mthickness. The structures were designed by ETABSfor gravity loading. As ABAQUS is not a designing

Figure 1. Plan of the structures used in �nite elementmodeling.

Figure 2. Comparison of vertical reactions of the 6-storeysteel structure determined by ABAQUS and ETABS(without considering SSI).

software, the structures with �xed bases were �rstdesigned by ETABS and then used in ABAQUSmodeling. The structures were also analyzed inABAQUS and comparison of vertical reactions fromETABS and ABAQUS was made for veri�cation ofthe ABAQUS model. Figure 2 shows this comparisonfor the 6-storey structure.

The positions of structural elements (e.g. thespan of columns) and their sti�ness can changethe distribution of the surcharge (the stresses underfoundation). To include this e�ect, the e�ectiveperiod of structure was calculated based on the designcode FEMA 450 [29] and included in GEP modelingas an input parameter. These parameters for alladjacent structures are given in Table 1. The e�ectiveperiod is de�ned as:

~T = T

s1 +

KKy

�1 +

Ky�h2

K�

�; (1)

where:

Table 1. Basic adjacent structure e�ective periodadopted for developing GEP Model.

Type ofstructure

Soil type ~T (sec)

6-story

A 0.8157B 0.7903C 0.7740D 0.7626E 0.7543F 0.7478

8-story

A 1.0599B 1.0186C 0.9919D 0.9733E 0.9595F 0.9498


�K = 4�2�WgT 2 ; (2)

Ky = KT :2G(1 + v)pBL = KTE

pBL; (3)

K� = K�

�GBL2

1� v�

= K�

�EBL2

2(1� v2)

�; (4)

~T E�ective period;T The fundamental period of the

structure;�K The sti�ness of the �xed-base

structure;�W The e�ective gravity load of the

structure, which shall be taken as0.7W;

W The weight of structure with �xedbase;

�h The e�ective height of the structure,which shall be taken as 0.7 times thetotal height;

Ky The lateral sti�ness of the foundation;K� The rocking sti�ness of the foundation;K�;KT The coe�cients that can be de�ned

using speci�c curves in FEMA 450;g Acceleration due to gravity;G Shear modulus;v Passion ratio;B Width of foundation;L Length of foundation;E Young's modulus.

- Soils: Six granular soils with their properties, suchas density, Young's modulus, and friction angle thatwere used in this modeling, are shown in Table 2.They are sorted from weaker to stronger soil (A to F)in this table. The Mohr-Coulomb model was selectedto describe the soil behavior.

Table 2. Basic soil properties adopted for developingGEP Model.

Soil Property

type � E �(kg/m3) (kN/m2) (deg.)

A 1700 40000 32B 1800 52000 34C 1900 64000 36D 2000 76000 38E 2100 88000 40F 2200 100000 42

Figure 3. Global modeling by ABAQUS.

Table 3. Basic wall characteristics adopted for developingGEP Model.

h (m) t (m)

3.0 0.254.0 0.305.0 0.356.0 0.40

0.45

- Retaining wall: For retaining the wall of exca-vation, a wall connected to the adjacent founda-tion was used (see Figure 3). The height of theretaining wall is always 1.0 m less than the depthof excavation because of the 1.0 m thickness of thefoundation. Table 3 shows the basic characteristicsof the retaining wall in the �nite element modeling.Di�erent components of the FE model are shown inFigure 4.

Figure 5 shows typical results of modeling forlateral deformation of the retaining wall. Figure 6shows the vertical foundation deformation. Figure 7shows the horizontal displacement of the retaining wallin di�erent soils. It can be seen that the lateraldisplacement decreases as the strength of the soilincreases (from A to F). Figure 8 demonstrates thehorizontal displacement of the retaining wall for alllengths of walls in di�erent soils. It is clear that thelateral displacement decreases as the strength of thesoil increases (from A to F).

4. Database

A database consisting of the results of 240 three-dimensional �nite element models of soil-retaining wallsystems with an adjacent steel structure modeled assurcharge was used to train and test the GEP model.Usually, 70 to 80% of database is used for training whilethe remaining 30 to 20% of data is used for testing


Figure 4. The components of the FE model.

Table 4. Basic range for input and output model parameters.

Parameters Range

Input

SoilDensity (ton/m3) 17.0-22.0

Young's modulus (kN/m2) 40000-100000

Friction angle (degree) 32.0-42.0

Adjacent structure E�ective period (sec) 0.7478-1.0599

Retaining wallHeight (m) 3.0-6.0

Thickness (m) 0.25-0.45

Output Retaining wall Maximum horizontal lateraldisplacement (mm)

0.332-35.59

Figure 5. Lateral retaining wall deformation (m).Excavation h = 6 m, thickness of wall = 0.25 m, andsurcharge = 6-storey structure.

the model. In this study, the results from 180 �niteelement models (%75 of total data) were employedto train the GEP model to determine the maximumlateral displacement of retaining wall. The model wasfurther tested using the remaining 60 data sets (%25of total data) that were not seen by the GEP in themodel development process. Table 4 indicates therange of basic input and output parameters adoptedfor this study. It should be noted that, like allempirical models, GEP performs best in interpretationrather than extrapolation; thus, the extreme values ofthe data used are included in the training set. Fornormalization, each component of the data set was


Figure 6. Foundation deformation (m). Excavationh = 6 m, thickness of wall = 0.25 m, and surcharge =6-storey structure.

Figure 7. Horizontal displacement with respect to theheight of retaining wall.

Figure 8. Horizontal displacement with respect to thelength of retaining wall.

normalized to lie in an interval of [0,1] using a max-min approach.

5. GEP modeling for predicting maximumlateral displacement of retaining wall

A GEP software package, GeneXproTools 4.0 [30] wasused in this study to perform symbolic regression to

�nd a relationship for maximum lateral displacementof retaining wall. Six independent parameters, namelysti�ness of adjacent structure, horizontal and rockingsti�ness of foundation of adjacent structure, density,Young's modulus, and friction angle of granular soil,thickness and height of retaining wall, were selectedas the input terminals. The output terminal was themaximum lateral displacement of retaining wall.

A large number of generations were needed to�nd a relationship with minimum error. To �ndthe optimum formulation, �ve functions, namely plus,minus, product, division, and power were used. Duringthe evolution process, these functions are selected toimprove the �tness of the solution. The selection ofthe best relationship was based on simplicity and itsrelevance to the nature of the problem, thus ensuringa simple and e�cient �nal GEP model. De�ning thechromosome structure requires the speci�cation of themaximum number of genes per chromosome as well asthe size of the gene. The size of gene is the maximumnumber of functions and terminals that can be storedin the head and the tail of the gene. It is normallycontrolled by its head size and the complexity of theproblem. The results showed that the model performedbetter when the addition (+) was used as a linkingfunction.

The evolution process was continued until nosigni�cant changes were noticed in the model statistics(�tness value and R2) and a formula with the shortestpossible length was developed. In this research, fordeveloping the model, a performance analysis for set-ting GEP parameters and the model development wascarried out. These stages are described below.

5.1. Performance analysisTo set the model parameters, a performance analysiswas undertaken. In GEP, values of the parameters havesigni�cant in uence on the �tness of the output model.These include the number of chromosomes, numberof genes, gene's head size, and the rate of geneticoperators. This approach involved using di�erentsettings and conducting runs in steps. During eachstep, runs were carried out and the values of one ofthe above-mentioned parameters were varied, whereasthe values of the other parameters were kept constant.The runs were stopped after a hundred generations,which were found su�cient to evaluate �tness of theoutput. At the end of each run, the Mean SquaredErrors (MSE) for both training and testing sets wererecorded in order to identify the values that give theleast MSE. When the output had the same error indi�erent generations for the training data set, thegeneration with lower error was selected for the testingdata set. Typical results of performance analysis fordeveloping maximum horizontal displacement model ofwall are shown in Figures 9 and 10.


Figure 9. E�ect of number of chromosomes on theperformance of the GEP model (selected value = 20chromosomes).

Figure 10. E�ect of mutation rate on the performance ofthe GEP model (selected value = 0.025).

In the �rst step, the number of chromosomes wasdetermined. Figure 9 shows that the model had thebest performance when the number of chromosomeswas 20. This value corresponds to the least MSE forthe training sets. Figures 10 present the in uenceof the rates of the genetic operator, mutation on theperformance of the GEP model. It can be seen thatthe GEP model performs best when mutation and generecombination rates are 0.05. The �nal parametersinvolved in the GEP predictive algorithm are shownin Table 5.

Table 5. Input parameters used for the GEP models.

Parameters Achieved functions,values, and rates

Linking function Addition (+)

Function set +;�;�;�, power

Number of chromosomes 20

Number of genes 5

Gene head size 7

Recombination rate 0.2

Mutation rate 0.025

Figure 11. Variation of error measured during trainingand testing generations.

5.2. Model developmentAfter �nding the best GEP setting parameters, theshort, simple, and most accurate model (optimumformulation) was obtained by conducting several runsusing these parameters. For this purpose, the chromo-somes corresponding to the formulation with minimumerror was compared with the actual test results. Inthis process, the performance was also checked usingsum of absolute di�erences between the predicted andactual values of the maximum lateral displacement.The average relative error is de�ned as:

Average relative absolute error =

1N

NXi=1

��Ai � PiAi

�� 100: (5)

Iterations continued until this error measure did notdecrease appreciably. Figure 11 indicates the variationof average relative absolute error during the best modeldevelopment for maximum horizontal displacement.The training error of the model dropped from 6.92in the �rst generation to about 0.10 after 100,000generations and, in testing, the error dropped from 6.34to about 0.12 in the same number of generations.

As mentioned earlier, one of the advantages ofthe GEP technique is that the relationship betweenthe inputs and corresponding output is automaticallyconstructed in the Expression Trees (ET). In thisresearch, the appropriate ETs (ET1 to ET4) that arelinked to each other with addition to produce the �nalmodel are presented in Figure 12 for the maximumlateral displacement.

The trees are easily formulated into a mathe-matical equation for maximum lateral displacement asfollows:

Umax = �� 0:187:h1:5 +h1:33

t+ 1:032 + tan(�)� E

+ (t+ E � 5:064)4 � 0:000275: ~T ; (6)


Figure 12. Expression Tree (ET) of the developed GEPmode.

where:Umax Maximum horizontal displacement of

retaining wall;� Soil density;h Height of retaining walls;t Thickness of retaining walls;� Friction angle;E Young's modulus;~T E�ective period.

6. Results and discussion

Eq. (6) was used to predict the maximum lateraldisplacement of retaining wall for all 180 cases of thetraining set and 60 cases in the testing set. Figures 13and 14 compare the predicted maximum horizontaldisplacements of retaining wall with the actual datafor training and testing cases. The results show agood correlation between the predictions made usingthe GEP formulation and the actual data both formodeling and testing data sets. In these �gures, thecorrelation coe�cient R2 is used to compare the results,given by:

R2 = 1�nPi=1

(Ai � Pi)2

nPi=1

�Ai � �Ai

�2 ; (7)

where Ai and Pi are, respectively, the actual andpredicted output values for the ith output; �Ai is the

Figure 13. Actual versus predicted maximum horizontaldisplacement for training data, R2 = 0:982.

Figure 14. Actual versus predicted maximum horizontaldisplacement for testing data, R2 = 0:984.

average of the actual outputs; and n is the number ofdata points.

6.1. Sensitivity analysisTo evaluate the model's response to changes in inputparameters, a sensitivity analysis was carried out. Forthis purpose, all input parameters (the friction angle(�), Young's modulus (E), density ( ), e�ective periodof adjacent structure ( ~T ), height (h), and thickness (t)of retaining wall) were considered. To evaluate thein uence of each input parameter on the maximumlateral displacement of retaining wall, the mean value ofthe input parameter was increased approximately 20%while the ranges of the other input parameters werekept constant. The results are given in Table 6. In thistable, negative change means reduction and positive


Table 6. The change in retaining wall designing parameters corresponding to 20% increase in the mean value of the inputparameters.

Parameter Frictionangle

Young'smodulus

Soildensity

Height ofretaining wall

Thickness ofretaining wall

E�ectiveperiod

Maximum horizontaldisplacement

-17.06 -24.35 35.60 23.57 -14.56 11.48

means increase in the maximum lateral displacementof retaining wall. It is shown that the maximum lateraldisplacement of retaining wall decreases with increasein friction angle, Young's modulus, and thickness ofretaining wall. Furthermore, Table 6 shows that withan increase in density, e�ective period and height ofretaining wall and the maximum lateral displacementof wall decrease. This table shows that the soil densityplays an important role in determining the maximumlateral displacement of retaining wall.

6.2. Parametric analysisFor further veri�cation of the proposed GEP models,a parametric analysis was performed. The main goalwas to �nd how each parameter a�ects the maximumlateral displacement of retaining wall. Figures 15 to 20present the predicted values for the maximum lateraldisplacement as a function of each parameter whereothers were constant. For this purpose, a data set withthe following characteristics was selected for trainingand testing as given in Table 7.

The results of the parametric analysis indicate

Figure 15. Parametric analysis of output model withrespect to friction angle.

Figure 16. Parametric analysis of output model withrespect to Young's modulus.

Figure 17. Parametric analysis of output model withrespect to soil density.

that, as expected, the maximum lateral displacementof retaining wall continuously increases with increasingsoil density, height of retaining wall, and e�ectiveperiod of adjacent structure. The maximum lateraldisplacement of retaining wall decreases when the

Table 7. Selected data from training and testing data sets for parametric analysis.

ParameterFriction

angle(degree)

Young'smodulus(kN/m2)

Soildensity

(ton/m3)

Height ofretainingwall (m)

Thickness ofretainingwall (m)

E�ectiveperiod(sec)

Training 36.0 640 19.0 0.30 6 0.774Testing 40.0 880 21.0 0.35 6 1.0186


Figure 18. Parametric analysis of output model withrespect to height of retaining wall.

Figure 19. Parametric analysis of output model withrespect to thickness of retaining wall.

friction angle, Young's modulus of soil, and thicknessof retaining wall increase.

7. Conclusion

A model was proposed based on GEP to estimatethe maximum lateral deformation of a retaining wall.The input parameters of the model include periodof adjacent structure, horizontal and rocking sti�nessof foundation of adjacent structure, density, Young'smodulus, and friction angle of granular soil as wellas the thickness and height of retaining wall. Adatabase comprising 240 cases was developed usingthree dimensional �nite element modeling of a soil-retaining wall system, with an adjacent steel structuremodeled as surcharge. The database was used to trainand test the GEP model. The predictions of the modelindicated a good accuracy both for the results used inthe training and those used in testing. The results of

Figure 20. Parametric analysis of output model withrespect to e�ective period.

the model predictions were compared to the actual testdata and indicated its good performance for predictionof the maximum lateral displacement of retaining wall.Sensitivity analysis showed that soil density is the mostin uential parameter in the maximum lateral displace-ment of retaining wall. Furthermore, a parametricanalysis showed an acceptable trend for the model withchanging the input parameters.

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Biographies

Ali Johari is Assistant Professor at Shiraz Universityof Technology, Civil and Environmental EngineeringDepartment, where he has been a faculty member since2009. He received his BSc, MSc and PhD degrees fromShiraz University in 1995, 1999, and 2006, respectively.In 2008, he was a Post-Doctoral researcher at ExeterUniversity, where he is currently a member of researchsta� in Computational Geomechanics Group. His mainareas of research interests are in probabilistic analysisand reliability assessment, application of intelligentsystems in geotechnical engineering and unsaturatedsoil mechanics. He has also advised and supervisednumerous geotechnical projects.


Akbar Javadi obtained his BS and MS degrees fromTabriz University, Iran, and a PhD degree from Brad-ford University, UK, where he is Associate Professorof Geotechnical and Geoenvironmental Engineeringand Head of the Computational Geomechanics Group.He teaches geotechnical courses at undergraduate andgraduate levels, and has also supervised over 20 PhDstudents and 3 postdoctoral researchers. He is a mem-ber of the British Geotechnical Society, member of theInternational Society of Soil Mechanics and Geotech-nical Engineering (ISSMGE), graduate member of theInstitution of Civil Engineers, and committee member

of the UK Association of Computational Mechanics inEngineering (ACME). The results of his research havebeen presented in over 250 publications in internationaljournals, book chapters, conference proceedings, andresearch reports.

Hadi Naja� was graduate student in GeotechnicalEngineering. His research area is study on conventionalsoil retaining systems using �nite element method,laterally loaded piles and arti�cial intelligence meth-ods. At present, he is actively involved in geotechnicalengineering projects and research.

Documents

A genetic-based model to predict maximum lateral …scientiairanica.sharif.edu/article_2097_4a0746c5c9d2a... · · 2018-04-27foundation of adjacent structure, density, Young's modulus,