numerical analysis and back calculation for embankment dam

Scientia Iranica A (2021) 28(5), 2519{2533

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

Numerical analysis and back calculation forembankment dam based on monitoring results (Casestudy: Iran-Lurestan Rudbar)

V. Ghiasia;�, F. Heidaria, and H. Behzadinezhadb

a. Department of Civil Engineering, University of Malayer, Hamadan, P.O. Box 65719-95863, Iran.b. Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran.

Received 11 June 2020; received in revised form 5 February 2021; accepted 15 March 2021

KEYWORDSBack calculation;Monitoring;Instrumentation;FLAC 2D;Rudbar rock�ll dam.

Abstract. The present study aims to compare the results obtained from monitoring withthose from numerical modeling in order to signi�cantly facilitate the stability analysis forembankment dams. In addition to making a comparison between these analyses, which arethe precise instrument results, this study validates the outcome of numerical analysis, thusforming a basis for carrying out back analysis to obtain accurate geotechnical parameters.Rudbar Lurestan dam was selected as the case study and the results of its instrumentationwere processed and analyzed. The model was established in a static state at the time ofconstruction. FLAC 2D V7 software was employed for modeling, and simulation was doneusing Mohr-Coulomb behavioral model and the initial parameters of the material (obtainedfrom the laboratory). Then, upon completing the modeling at the end of constructionand performing the initial impounding, the results of back calculation give us the �nalparameters of the materials. The consistency between the results of these analyses anddesign assumptions and instrumentation results was evaluated. The observations show thatthere is good agreement between the monitoring results of the modeling and, also, the �nalparameters obtained from the back calculation point to an increase in most parameters.

© 2021 Sharif University of Technology. All rights reserved.

1. Introduction

Earth and rock�ll dams are important colossal struc-tures. The initial materials used in construction ofthese dams include natural materials such as earth orrock. The behavior of these dams cannot be predictedin a well-de�ned and speci�c framework due to several

*. Corresponding author. Tel./Fax: 00988143213210E-mail addresses: [email protected] (V. Ghiasi);[email protected] (F. Heidari);[email protected] (H. Behzadinezhad)

doi: 10.24200/sci.2021.56159.4579

reasons such as their three-phase nature (soil, water,and air) and soil properties of materials. In addition,due to the high costs of dam construction and theirsusceptibility to heavy damages due to their insecu-rity, it is essential that the stability and monitoringof the dams during construction, impounding, andexploitation be closely managed. In addition, it is quiteimportant to design and model the dams accurately. Inthe case of �nding a behavioral model with realistic pa-rameters, which is also consistent with the instrumentalresults, using a model able to study the dam behaviorin di�erent sections where the instrumentation is notinstalled or damaged is necessary. Given that someproblems may occur over the course of impounding

2520 V. Ghiasi et al./Scientia Iranica, Transactions A: Civil Engineering 28 (2021) 2519{2533

or exploitation, with proper modeling of the plan,dam safety can be ensured against accidents such ashydraulic failure and arching ratio. In this respect,the actual geotechnical parameters of the dam bodycan be obtained during construction, impounding, andoperation.

Monitoring operations and studying the processof data changes obtained from the instrumentationused in the dams in many cases can prevent furtherdestruction by predicting the occurrence of lateraland linear cracks, arching, hydraulic failure, and highstress, thus reducing possible damages to downstreamof the dam. Therefore, taking control of dam behaviorduring construction, impounding, and exploitation isessential. In recent decades, dam sustainability hasdrawn engineers' attention.

One of the recommendations of the InternationalCommission on Large Dams is to constantly control thesafety and sustainability of dams during constructionand exploitation [1]. The dams can be modi�ed basedon displacement monitoring data and penetration as-sessments. Park and Oh [2] discussed dam modi�cationusing low-pressure injection method. To reduce theimpact of rock falls and protect the structures such asreinforced concrete, stone vents, retaining walls, andrigid and exible dams, dams are widely constructedin mountainous areas [3,4]. Statistical informationillustrates that earth dams are exposed to destructionmore than concrete dams, and more than 50% of earthdam destructions or damages occur at the time ofconstruction and during initial impounding [5]. Theobservation data of embankment dam displacementcan obviously re ect the actual service behavior of thedam [6]. In the implementation of constructive andgeotechnical projects, monitoring and surveying of theconstruction and structures are done with importantobjectives: construction control, warning against anyimminent failure, quality assurance, validation of newtheories, resolving of legal and judicial matters asquickly as possible, veri�cation of long-term implemen-tation and stability [7], and application of di�erenttypes of geotechnical instrumentation as one of themost commonly used methods for the monitoring ofgeotechnical structures, especially in earth dams [8].Researchers in the �elds of engineering and economymaintain that in many cases of dam constructionprojects around the world, rock-�ll dams with a claycore are so impervious that they are considered tobe the best choice for the ultimate design [9]. Mostdam failures experience a process of quantitative toqualitative changes [10].

Mahinrousta et al. [11] evaluated the linear behav-ior of rock �ll materials using numerical analysis andlaboratory test results. Strain hardening and softeningmodel in the FLAC software were modi�ed based onthe data provided by laboratory examinations in order

to estimate the failure phenomenon resulting from thesettlement in the earth and rock�ll dams at the timeof ooding. The obtained results helped engineersbetter predict the nonlinear behavior of the failurephenomenon from the result of the settlement in theupstream crust.

The pore water pressure, stresses, and settlementare the main parameters for the stability analysis ofearth and rock�ll dams [12], as investigated in thisstudy. Beiranvand and Komasi [13] analyzed the porewater pressure on the Eyvashan earth and rock�lldams in the initial impounding using two Plaxis andGeostudio software products. In addition, according tothe data recorded by the instrumentation installed inthe dam, there is no unexpected leakage phenomenonin this dam.

Dam safety monitoring as an essential task in riskmanagement guarantees the normal operation of theseinfrastructure. Proper modeling and analysis of thestructural responses under the given loads and ambientconditions as well as verifying the measured data withsimulated ones are all essential tasks in dam safetymonitoring. Seepage control is one of these tasks indam surveillance, especially for earth dams [14]. Wanget al. [15] established a monitoring model to analyze thelong-term trend and short-term uctuation of a gravitydam seepage behavior, for which the support vectormachine is used as a baseline model for prediction. Guoet al. [16] presented an analytical method for predictingthe pore water pressure inside embankment dams.

Taham dam was numerically modeled using Plaxissoftware [17]. The values obtained from the modelingin the pore water pressure parameter were in goodagreement; however, in case of stress, slight di�erenceswere observed.

In [18], the results of instrumentation and nu-merical analyses in the Siah Sang embankment damwere analyzed, indicating good agreement with theaforementioned results.

Implementation of back analysis in geotechnicalengineering has been signi�cantly expanded and widelyrecognized as a powerful tool for evaluating �eld-measurement information. Among the most importantreasons behind the popularity of back analysis amongengineers are lack of laboratory restriction and insidetests and a complete description of soil pro�les [19].In 2008, Gikas and Sakellariou made a comparisonbetween the various horizontal shapes obtained frommonitoring the dam and the back numerical analysis ofthe earth dam. This dam was modeled using Z soil soft-ware and Finite Element Method (FEN). Movementswere measured at di�erent stages of construction andexploitation of the dam. The settlement behavior ofthe Shuibuya dam at the time of construction, initialimpounding, and after two years of exploitation wasinvestigated. They also performed a two-dimensional

V. Ghiasi et al./Scientia Iranica, Transactions A: Civil Engineering 28 (2021) 2519{2533 2521

numerical analysis using FEM and compared the re-sults of the measured settlement using the instrumen-tation. Furthermore, they performed the back analysisusing Hybrid General Algorithms (HGAs) [20]. Theresults indicated that this method could successfullycontrol dam deformation. In addition, the results ofsettlement showed that after initial impounding, whilethe reservoir volume increased, the value of settlementdecreased and tended to be �xed over time [21]. Fromback analysis in Geotechnical projects, studying thetype of stability of slopes and correction methods ofinstability can be mentioned [22], analyzing types oftunnel, caverns and galleries stability [19], and also thecalibration of models [23], analyzing, and estimationof probability of fracture expansion and its e�ect onthe safety of concrete dams [24], analyzing earth androck �ll dams during all stages of construction andcompletion of construction [25]. The back analysis wasused as a suitable method for selecting the foundationand loan sources [26]. Rashidi and Haeri investigateda method based on the back analysis performed on theGavoshan dam in Kurdistan and obtained the actualparameters at the end of construction [27]. In 2017,Wen et al. evaluated measurement results obtainedfrom a detailed deformation-monitoring system. Intheir study, the results of the numerical analyses andmeasurements were compared and then, the results ofgeodetic measurement were con�rmed through numer-ical analyses [28].

Pramthawee et al. performed time-dependentanalysis of a high rock�ll dam. They compared the3D �nite element analyses with and without creep ina rock�ll dam with in-situ measurements. In addition,measurement results were veri�ed by numerical analy-ses [29].

Evaluation and control of the stability of earthlydams are of signi�cance mainly due to the occurrencepossibility of some phenomena such as settlement, hy-draulic failure, leakage, and pore water pressure. Dammonitoring is a method for evaluating dam behaviorin di�erent states of construction, impounding, andexploitation. Numerical modeling is one of the methodsof the analysis and control of earth and rock�ll dams.A comparison between the monitoring and numericalmodeling facilitates the stability analysis of these dams.A comparison between the results of this analysis andthe real-world data indicates that they both yield thesame instrumentation results and, consequently, vali-date the outcome of numerical analysis, thus forminga basis for performing back analysis to obtain precisegeotechnical parameters. In this regard, the presentstudy aims to extract the �nal parameters throughapplying back analysis method to earth and rock�lldams to predict their performance. Therefore, stabilityanalysis was carried out, indicating that monitoring ofearth and rock�ll dams is essential; however, no study

has investigated Lurestan-Rudbar dam so far. Hence,this study addressed this case study.

2. Main features of Rudbar dam

Rudbar dam, located 90 km away from Aligudarz,Lurestan Province, Iran, is situated on Dez River(Figure 1). This dam was constructed for severalmain reasons such as providing required water foragricultural use, producing electricity-watery energy(986 GW/year), reducing the cost of thermal powerdepreciation, and controlling the oodwater. To eval-uate the behavior of Rudbar dam, di�erent types ofinstrumentation including piezometers, measuring cellsof the total pressure of the soil mass, and inclinometerswere installed in three sections along the body ofRudbar-Lurestan dam that consists of several partsincluding the clay core, �lter and transition zones,pebble shell, and upstream body slope protective layer(Rip Rap). The dam core consists of GC material withthe maximum particle size of 75 mm as well as a �ltermaterial that comprises a �ne-grained part with themaximum size of 20 mm and a coarse-grained part withthe maximum size of 50 mm. Moreover, the particlesizes of the transition zone or drain and dam crust are20 and 120 cm, respectively.

The core of the dam is protected by two-layer�lters and a transitive drain in both upstream anddownstream of the dam. The dam crust contains twoparts: transitive crust or drain and rock�ll crust. Thetransitive crust lies between the �lter and shell rock�ll.The outer part of the rock�ll uppermost crust is alsoprotected by a beaching layer. With respect to earthheight, type of foundation, and depth of the valley, themost frequently installed instrumentation is in the C5-5section, which is the most important and critical damsection in terms of maximum settlement, pore waterpressure, and total stress. The critical section as well asdi�erent levels and zones of di�erent parts are depictedin Figure 2. As shown in Figure 3, construction of Rud-bar dam began in October 2011, the last layer of theembankment (for 24 months) �nished in October 2017,and its initial impounding began in June and lasteduntil the next ten months, April 2017. The technicalcharacteristics of Rudbar dam are presented in Table 1.

3. Properties of materials and numericalmodeling

Rudbar dam was modeled using FLAC 2D softwarebased on the di�erence method. Mohr-Coulomb elasto-plastic model is a behavioral model used in the core,�lters, upstream, and downstream.

3.1. Properties of materialsThe properties of the materials used in numerical


Figure 1. Location and view of the body of Rudbar dam.

Figure 2. The critical section, di�erent levels, and zones of di�erent parts of Rudbar dam.

modeling were extracted from laboratory experimentsof soil mechanic in a �ne and coarse materials of thedam. Table 2 presents the initial values of the Mohr-Coulomb model parameters including elastic modulus(E), Poisson ratio (�), friction of soil (C), frictionangle (�), dilation angel and stress ( ), and hydraulicconductivity (k) in di�erent conditions for di�erentdam areas. As the inputs to the software, these valueswere used for initial calculations.

3.2. Back analysisMachine learning methods and data mining are othertechniques employed in this study. With their greatcapability to handle the nonlinear database, machinelearning methods have been proven powerful in dam en-gineering. Inverse analysis is one of these methods [30{32]. Back analysis is an e�ective tool for investigatingand modifying soil parameters. The obtained resultsfrom this analysis can be used for project evaluation,


Figure 3. Construction and impounding periods ofRudbar dam.

Table 1. Technical characteristics of the Rudbar dam andits reservoir [25].

Dam detail Value

Height from bed to crestLargest cross-section

153 m

Width of the dam crest 15 mLength of the dam crest 185 mDam crest elevation a.s.l 1765 mNormal water level a.s.l 1756 mArea of reservoir length 20 kmDam body material volume 4:596� 106 m3

Volume reservoir 228� 106 m3

and their designs that are similar in structure canalso be improved [33]. Back analysis of data frominstrumentation and monitoring of dams at the timeof construction and operation, in addition to almostsure evaluation of geotechnical parameters, determinesthe stability status of the structure. In general, backanalysis is a method for predicting the parametersgoverning a system by analyzing the output behaviorof that system. Overall, back analysis methods areclassi�ed in two inverse and direct types [34].

Generally, to conduct a back analysis, two stepsare required. First, in the stress analysis method,the numerical methods are employed to determine the

stress, strain, and displacement distribution for theproblem in question. Second, an appropriate algorithmof optimization is employed that can minimize thedi�erence between the values measured in situ andthe data obtained from the stress analysis [35]. Thisdi�erence is expressed in the form of an error function.In this paper, a direct displacement-based method wasutilized. One of the great advantages of the directdisplacement method is its easy application to non-linear problems and elastoplastic materials. Althoughthis method requires much time for computation and agreat deal of repetition in computing, it is still widelyused in geotechnical engineering [36]. In general, thereare three di�erent algorithms for direct back analysis:the invert method, multivariate method, and alternat-ing univariate methods [37]. In the univariate method,only one parameter at each step changes and the otherparameters will remain constant. In the next step,after optimizing one parameter, another parameter ischanged, while the other parameters are kept constant.This process continues until all optimal values of allparameters are obtained. In the multivariate method,unlike the invert method, parameter optimization isperformed simultaneously. Therefore, the model withthe least error is considered as the optimal model,and the parameters corresponding to it are calledthe optimal parameters. The alternating univariatemethod is the extended form of the univariate methodwith enhanced functions. In this method, upon �ndingthe optimal values of the parameters according tothe invert method, all parameters are simultaneouslychanged. Simultaneous change of parameters continuesuntil the target function reaches the desired value.

In other words, the back analysis can be describedas obtaining the initial parameters when conductingsoil mechanics experiments on the borrow materials.These materials are transported to the site of the damand crushed into layers with certain thickness untilreaching a certain density. This is the reason why itis necessary to obtain the actual parameters of thematerials when they are in the dam body using theinstrumentation and back analysis results. In thisrespect, the main input parameters to the software

Table 2. List of properties of materials for numerical analysis (primary parameters) [25].

Materialdescriptions

k(cm/s)

�� C(kPa)

(kN/m3) E(MPa)

� �Sat Dry

Core 1� 10�7 25 50 23.4 21.5 35 0 0.35

Filter 3 5� 10�4 39 0 21.9 19 70 7{10 0.33

Filter 2 5� 10�2 39 0 22.2 19.5 70 7{10 0.30

Drain 1 45 0 23.2 21 70 7{10 0.25

Shell upstream 1� 10�1 45 0 23.5 21.5 70 3{5 0.25

Downstream 1� 10�1 45 0 23.2 21 70 3{5 0.25


Figure 4. Solution algorithms for back analysis.

must be changed according to the actual dam behaviorobtained from the information of instrumentation tothe extent that the actual behavior of the dam iscreated in the model. The solution process algorithmis illustrated in Figure 4.

Due to the availability of the displacement valuesmeasured by the tube of the de ectometer installed inthe dam body, the displacement-based direct back anal-ysis method was employed for back analysis of Rudbardam to determine the optimal material parameters.This method functions based on the optimization ofthe mechanical parameters of the materials through thetrial-and-error method. To this end, the error function(Eq. (1)) was written in the FISH programming lan-guage in order to minimize the di�erence between thedisplacements measured by the de ectometers tubesand those calculated by numerical modeling.

2 (P ) =

vuut 1n

nXi=1

�umi (p)� ui

ui

�2

; (1)

where n is the number of measurement points, i =1; 2; � � � ; n; ui and umi (p) are the measured and calcu-lated values of the displacements, respectively, throughnumerical analysis at the corresponding points. Thevalue of ui(p) depends on the unknown parametersof the model that are aggregated in the vector P .Before performing the back analysis, it is recommendedthat the results of the instrumentation be processedand the incorrect displacements caused by error ofreading or improper performance of instrumentationbe removed. In conventional analysis, a mechanicalmodel capable of introducing the mechanical behaviorof a structure is taken into consideration. Then, thevalues of mechanical constants are determined using�eld and laboratory experiments. Based on the rela-tionship between the values of the back analysis, the�eld measurements (instrumentation), and methods fordesign and execution, it can be concluded that backanalysis is completely di�erent from the conventionalanalysis.

It is assumed that a typical analysis of a mechan-


Figure 5. Typical analysis and back analysis.

ical model can introduce the mechanical behavior ofa structure. Then, the values of mechanical constantsare determined using �eld experiments and laboratorytests. The input data of the typical analysis, presentedin Figure 5, are employed to calculate settlementvalues, pore water pressure, and stress.

3.3. Numerical analysis and modelingRudbar dam was modeled using FLAC 2D software,which is based on the �nite di�erence method. In ad-dition, Mohr-Coulomb elastoplastic behavioral modelwas used to investigate the materials used in the body.As one of the most well-known soil behavioral models,this model contains most of the basic soil parameterssuch as plastic and elastic that make it suitable formodeling most soil behavioral modes. In this respect,this model has been employed in a number of researchesdue to its simplicity and non-requirement for multipleparameters.

The parameters used in this behavioral modelinclude cohesion (C), friction angle (�), elastic modulus(E), Poisson's ratio (�), unit weight ( ), and coe�cientof permeability (k). Table 2 represents initial values ofthe mentioned parameters.

There is a criterion in the Mohr-Coulomb behav-ioral model that de�nes the boundary between elasticand plastic deformations, and the behavior of materialsafter entering the plastic zone is quite di�erent fromthat before crossing this boundary. In this behavioralmodel, the failure envelope is obtained by the well-known Mohr-Coulomb criterion, which is a functionof shear failure (fs), considering the tensile failurecriterion (ft). The failure level of fs and ft is obtainedthrough Eqs. (2){(4), as shown in the following:

fs = �1 � �3N� + 2CpN�; (2)

ft = �1 � �3: (3)

N� can be measured as in the following:

N� =1 + sin�1� sin�

; (4)

where C is the adhesion, � is the angle of internalfriction, and �1 and �3 are the tensile strengths.

Figure 6. Mesh generation of Rudbar dam body at thecritical cross-section.

The parameters of the Mohr-Coulomb behavioralmodel are � and C, which are related to the plasticmechanism of the model, as well as E and �, which arerelated to the elastic mechanism of the model. Theseparameters are determined by ordinary and commonexperiments such as triaxial tests. A simulation of adrained triaxial test with the Mohr-Coulomb modelreveals that the behavior of the model before the failureis controlled by E and � parameters, and the maximumshear strength is controlled by � and C parameters.

Rudbar dam was modeled in 31 layers, and theheight of each layer was 5 m. An element grid of97 � 31 was used for modeling the dam body. In the�rst step, the quadrilateral elements with four nodeswith a length-to-width ratio of approximately 1 wereconsidered in producing the mesh. After designingthe total grid of the dam body, extra elements wereremoved, and the optimal mesh model of the criticalsection was obtained based on Figure 6. In the secondstep, after creating the dam model geometry, theboundary and initial conditions were applied to themodel so that the lateral boundaries could be displaced,and at the lower boundary, the horizontal and verticaldisplacements were assumed to be zero.

In the third step, for bedded modeling and in-vestigating both consolidation phenomenon and porewater pressure on the dam, �rst, the timing plan of thedam construction was determined based on the actualtime of dam body embankment that took more than1440 days. Then, the total required construction timewas given to the software for each of the 31 layers ofthe body. Next, the �rst layer of the dam body wascreated, and by performing mechanical computational


steps, the unbalanced force reached zero. Followed bythis step, all layers of the dam body were constructed,and construction of the dam in the model softwarewas simulated and then, impoundment of Rudbar damat seven stages, each stage with the height of 20 m(which lasted for 10 months), was modeled. Themaximum water stage in the reservoir was recordedas 141 m. To simulate the dam impoundment, themechanical force resulting from the weight of thereservoir water was applied to the upstream crust andthen, the corresponding hydrostatic pressure of thereservoir water was applied to the same area and themodel was run until the allotted time.

It should be noted that due to the very lowpermeability of the rock bed and construction of aconcrete slab under the core as well as the partialsettlement at the time of construction (7 cm), themodeling of foundation was ignored.

4. Results and discussion

In this section, �rst, the contours obtained from mod-eling the pore water pressure, vertical and horizontalstress at the end of construction and impounding arepresented in Figures 7{12.

4.1. Pore water pressureWith regard to embankment dams, monitoring the porewater pressure gains signi�cance since it is the main

Figure 7. Pore water pressure at the end of construction(body height 155 m) (unit: Pa).

Figure 8. Pore water pressure at steady-state (unit: Pa).

Figure 9. Vertical stress construction at 155 m height(unit: Pa).

Figure 10. Vertical stress of initial impounding tonormal levels (unit: Pa).

Figure 11. Settlement construction at 155 m height(unit: m).

Figure 12. Settlement initial impounding to normallevels (unit: m).

indicator of internal erosion and seepage problems thatplays a signi�cant role in the stability of geotechnicalworks [38].

Installed piezometers at the core of the Rudbardam were placed at six di�erent levels. This studyemphasizes the most acute pore water pressure or themost pore water pressure recorded by piezometers atthe core of the dam located at 1615 m. The electricalpiezometers installed at this level consist of 7 piezome-ters where piezometer EP16 and EP19 are obstructedand their results are not available. Figure 13(a) showsthe pore water pressure diagram of electric piezometersat a level of 1615 m. As shown earlier, as the heightof the dam increases, the pore water pressure alsoincreases. Another signi�cant note is that at the timeof construction, the middle piezometers of the coredam record much more water pressure than lateralpiezometers due to greater water pressure at the middleof the core than the lateral section of the core.

4.2. Comparison of pore water pressuremeasured by instrumentation with anumerical model

In this study, because of the highest pore waterpressure recorded at the bottom of the core, i.e.,Level 1615 m is recorded by the instrumentation, thecomparison between instrumentation results and thenumerical modeling is made at this level. A comparisonbetween the pore water pressure measured by the


Figure 13. Pore water pressure changes at the time of construction (a) and comparison of the pore water pressuremeasured by instrumentation and numerical model at the end of construction (b) at level of 1615 m.

Figure 14. (a) Total vertical stress of core dam at the time of construction. (b) Changes in the total vertical stress atlevel of 1615 m.

instrumentation and the numerical model at the end ofthe dam body construction is shown in Figure 13(b).

As given in Figure 13(b), the maximum pore wa-ter pressure values for instrumentation are determinedas 736 kPa and 780 kPa at the end of constructionand in the numerical modeling, respectively. Goodagreement exists between the results. The numericalanalysis and instrumentation suggest that the maxi-mum pore water pressure occurs at the center of thecore, while the minimum pressure during constructionand end of construction is recorded in upstream anddownstream of the core.

4.3. Total vertical stressManometers that measure total stress (vertical andhorizontal) were installed at the core of the dam at �vedi�erent levels with three clusters that measure the soilpressure in three directions: vertical, horizontal, and inaccordance with the core axis. This study focuses onthe most critical level in the dam body, the 1615 mlevel where PC1, PC2, and PC3 pressure cells areinstalled at this level and the following measurements

of these pressure cells are presented. Pressure cells thathave been horizontally installed, measure stress in thevertical direction (�Y ); those that are parallel to thedam axis measure stress along the X-axis (�X), andthose that have been vertically installed on the damaxis measure stress along the Z-axis (�Z).

Figure 14(a) shows the measurement of totalvertical stress at the core of the dam at the end ofconstruction at di�erent embankment levels. As canbe seen, the vertical stress at the center of the core ishigher than that on the lateral side and by increasingthe height of the dam embankment, vertical stressincreases.

Figure 14(b) shows changes to pressure cells atthe end of construction and impounding at a level of1615 m.

4.4. Comparison of the total vertical stressmeasured by the instrumentation with thenumerical model

Considering that the highest vertical stress is recordedat the bottom of the core, i.e., the level 1615 m by


Figure 15. Comparing the total vertical stress measured by the instrumentation and numerical modeling at the end ofconstruction (a) and at the end of impounding (b) at level of 1615 m.

Figure 16. Changes in the total vertical stress measured by instrumentation and numerical model in the pressure cellsPC1, PC2, PC3 at level of 1615 m.

the instrumentation, a comparison between the instru-mentation results and numerical model is performed atthis level. Figure 15(a) shows the veri�cation of thevertical stress measured by the instrumentation andthe numerical model at the end of construction. Themaximum vertical stress of instrumentation at the endof construction and in the numerical model is obtainedas 2530 kPa and 2442 kPa, respectively. Figure 15(a)points to the good convergence. Accordingly, themaximum vertical stress occurs at the center of thecore, and the results of the numerical model and

instrumentation indicate that the least stress occursin the upstream of the core during construction anddownstream of the core at the end of construction.

In this research paper, the vertical stress ofimpounding stage is presented. Figure 15(b) shows acomparison between the results of instrumentation andthe numerical model. Figure 16 presents the verticalstress variations of PC1, PC2, and PC3 cell pressuresderived from a numerical model and instrumentationduring construction and impounding.

According to Figure 16(a), there is a slight di�er-


ence between the instrumentation and the numericalmodel, because there is less density around the cell thanother parts of the core to prevent damage. Therefore,the rigidity of other parts is greater than that of thesurrounding of the cell, but changes in the cell pressurePC2 and PC3 are in good agreement, as shown earlier.

4.5. Evaluation of arching ratioWhen the arching ratio is larger, arching does notoccur many times in that location. However, whenthe arching ratio is smaller, arching occurs quite alot in that location. Increase in the arching ratiovalue reduces the soil core pressure with respect tothe hydrostatic pressure, resulting in cracks appearingon the core. This phenomenon is known as hydraulicfailure [39]. Eq. (5) shows the existing relation for thearching ratio:

Ar =ruRu

=�pc :h

; (5)

where is the unit weight column of soil above theinstrumentation, h the height of the soil column abovethe instrumentation, and �pc the total stress measuredby instrumentation.

In Figure 17(a), the arching ratio at the end ofconstruction and impounding is shown at level 1615 m.As it is known, at the end of construction, the lowestarching ratio was recorded 0.53 at upstream of thecore, while at the end of the initial impounding, thehighest increase was observed at upstream of the core;this �nding points to the e�ect of impounding on thearching ratio.

4.6. Comparison of arching ratio of theinstrumentation with the numerical model

The comparison of arching ratios in Figure 17(b) showsthat the maximum and minimum of the arching ratioobtained from numerical modeling are 0.68 and 0.59,respectively.

After initial impounding, it should be investigatedwhether the hydraulic failure phenomenon has occurred

in the dam body or not. One solution is to obtainthe arching ratio. After impounding, due to the waterpressure on the upstream of the dam, the arching ratiomust be checked because if the value of this ratio issmall at the end of the construction, the possibility ofarching to occur is very high. Of course, in Rudbardam, the lowest value of arching ratio was 0.53 at theend of construction and it reached 0.59 in impounding,which not only not declined but also increased.

4.7. SettlementAt Rudbar dam, three inclinometers (settlement tubes)are installed at the upstream center of the core anddownstream, which measure the settlement in thesesections. Figure 18 shows the settlement changes onthe core (IN2) at nine intervals and di�erent heightsat the time of construction and initial impounding ofthe dam. Per o�cial notice, the dam construction wascompleted in October 2012; the maximum settlementwas 137.5 cm which occurred at the core of the damin this period. The initial impounding began in March2016 and in this period, the maximum settlement inthe dam was recorded as 156.9 cm on the inclinometerscritical sections.

Figure 18. Core settlement obtained from IN2 alongwith dam height at di�erent times.

Figure 17. The arching ratio of core of the dam at the end of construction and initial impounding; comparison of thearching ratio measured by instrumentation and numerical model at the end of construction at level of 1615 m.


Figure 19. Comparison of the core settlement obtained from instrumentation and numerical model at the end ofconstruction and initial impounding.

Table 3. Final parameters in the back analysis (actual parameters).

Materialdescriptions

k(cm/s)

�� C(kPa)

(kN/m3) E(MPa)

�Sat Dry

Core 1� 10�13 28 50 23.5 21.5 43 0 0.37Filter 3 5� 10�10 40 0 21.9 20 70 9 0.37Filter 2 5� 10�8 40 0 22.2 20.5 70 9 0.30Drain 1� 10�3 46 0 23.2 22 70 9 0.37Upstream 1� 10�3 46 0 23.5 22.5 70 5 0.25Downstream 1� 10�13 46 0 23.2 22 70 5 0.25

4.8. Comparison of settlements obtained frominstrumentation measurements andnumerical model

One of the parameters for stability analysis of earth androck�ll dams is the experience of settlement in earthrock�ll dams during construction [24]. Figure 19 makesa comparison concerning the settlement occurring atthe center of the core at the end of construction (a)and initial impounding (b). The maximum settle-ment recorded by the instrumentation and modelingat the end of the construction was as 137.5 cm and146/5 cm, respectively. The mentioned settlement afterthe impounding in instrumentation and modeling wasobtained as 156.9 cm and 147.8 cm, respectively.

4.9. Results of back analysisIn order to validate and verify such parameters as porewater pressure and vertical and horizontal stresses, theactual geotechnical parameters of the dam body wereobtained using the back analysis method. Table 3presents the values of the �nal parameters obtainedfrom the back analysis.

4.10. Comparison of actual geotechnicalparameters obtained from back analysiswith initial parameters

Table 3 gives the �nal parameters obtained by backanalysis and some parameters were presented as a bar

graph in this paper. Figure 20(a) shows Poisson's ratioand Figure 20(b) shows the friction angle in di�erentdam conditions. Figure 20(a) of the core, Filter 3, anddrain experienced an increase in the �nal condition,while no change or variation was detected in the otherparts. However, in Figure 20(b), all of the dam sectionschanged in the �nal condition.

Figure 20(c) shows the dry unit weight of the corethat remains constant, while all the other parts increasein the �nal condition.

5. Conclusion

The main objectives of the present study are as follows:

(a) Providing a general assessment of the performanceof the dam at the time of construction and initialimpounding using the data obtained from theinstrumentation of the Rudbar rock�ll earthendam;

(b) Reaching actual geotechnical parameters in thebody of the Rudbar dam at the end of theconstruction through the back analysis method.

The results of the present study are as follows:

1. The highest settlement rate for Rudbar dam wasobserved at the core and height of 85 m from the oor. Rudbar dam experienced 87% of its total


Figure 20. Comparison of Poison's ratio, friction angle, and dry unit weight in the initial conditions obtained from theback analysis (�nal).

settlement at the end of construction. In addition,the maximum settlement in this dam at the end ofconstruction was 1.37 m, which was less than 1% ofthe dam height. In comparison with the settlementin other dams, such as Alavian dam with the heightof 80 m and settlement of 1.30 m (about 1.6% of thebody height) and Gavoshan dam with the height of123 m and settlement of 2.7 m (about 2.1% of thebody height), the settlement of the Rudbar damwas acceptable;

2. The maximum pore water pressure was observed atthe center of the core at the end of the constructionwhile the lateral part of the core did not toleratethe pressure much. At the impounding stage, themaximum pore water pressure was recorded in theupstream of the dam, mainly because of its vicinityto the upstream of the core;

3. The dam was constructed of 31 layers and theimpounding was appropriate in seven states. Ofnote, the assumption of fewer layers existing at thetime of construction would change the results ofpore water pressure due to the thick layers placedand their sudden weight addition. Placing layerswith the thickness more than 8 m would causeextra pore water pressure at the initial stage ofconstruction. In this regard, to analyze the earthand rock�ll dams, it is suggested that the number

of layers be considered in accordance with thethickness of 5 m;

4. Arching ratio was one of the criteria used for con-trolling hydraulic failure in earth rock�ll dams. Thearching ratio of the critical level of the Rudbar dambody was 0.53{1.6 which was in good agreementwith the arching ratios observed in large damssuch as Asvatvan (Norway), Karkheh, and Ardakdams with the arching ratios of 0.33{0.9, 0.47{0.75, and 0.63, respectively. After impounding theRudbar dam, the arching ratio rate increased andthe arching decreased;

5. According to the results, the back analysis methodwas a suitable method for determining the actualparameters of earth and rock�ll dams;

6. Based on the evaluation results of instrumentationsystem of the Rudbar dam body, it can be con-cluded that both the instrumentation system andthe measuring equipment of this dam quantitativelyand qualitatively enjoyed good health to continuemeasuring and recording the instrumentation data;

7. According to the values obtained from back analy-sis, the utmost change was observed in the dry unitweight parameter, and all the parameters followeda constant or increasing trend.

Generally, in case one does not apply back analysisfor the geotechnical parameters of the dam, there will


be no real assessment or understanding of the actualgeotechnical parameters of the dam body. However,this study could present a proper view of the actualgeotechnical parameters of the Rudbar dam body.

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Biographies

Vahed Ghiasi is an Assistant Professor of Geotechni-cal Engineering on Malayer University. His research in-terests are tunnel engineering, foundation engineering,soil mechanics, slope stability, and dam engineering.He has presented and published more than 100 papersin various international conferences and journals.

Farzad Heidari received his BSc degree in Civil En-gineering from University of Jahad Khuzestan and hisMSc degree in Civil Engineering from Malayer Univer-sity. His research interests include numerical analysis,monitoring and instrumentation, computational me-chanics and geomechanics, dam, and geotechnical andtunnel Engineering. He has presented and publishedseveral papers in various international conferences andjournals.

Hossein Behzadinezhad graduated from IsfahanUniversity of Technology in 2010 in the �eld of rockmechanics engineering (MSc). He has more than 10years of executive experience in the �elds of under-ground and open cuts, implementation of consolidationand maintenance system, and instrumentation andmonitoring. He is currently working as the managerleading the stability control of the body of RudbarDam in Lorestan (Iran Water & Power ResourcesDevelopment Co).

numerical analysis and back calculation for embankment dam

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