Effect of Normal and Shear Interaction Stiffnesses on Three-Dimensional Viscoplastic Creep Behaviour of a CFR Dam

Rockfill materials and foundation continuously interact with each other during lifetime of the rockfill dams. +is interaction condition alters the viscoplastic behaviour of these dams in time. For this reason, examination of the time-dependent viscoplastic interaction analyses is vital important for monitoring and evaluating of the future and safety of the rockfill dams. In this study, it is observed how the time-dependent displacement and stress behaviour of a concrete-faced rockfill (CFR) dam change by the effect of the normal and shear interaction spring stiffness parameters. Ilısu Dam that is the longest concrete-faced rockfill dam in the world now and has been completed in the year 2017 is selected for the three-dimensional (3D) creep analyses.+e 3D finite differencemodel of this dam is modelled using FLAC3D software that is based on the finite difference method. +e concrete slab, rockfill materials, foundation, and reservoir water are separately created for the 3D interaction analyses. AWIPP-creep viscoplastic material model and a burger-creep viscoplastic material model that are special material models for the creep analyses of rockfill dams are used for concrete slab and for rockfill materials and foundation, respectively. Totally 20 different interaction parameters (normal and shear stiffnesses) are separately defined between the rockfill materials and the foundation to represent the interaction condition. According to numerical analyses, the effect of these various interaction parameters on the viscoplastic behaviour of the Ilısu Dam is evaluated for the empty and full reservoir conditions. As a consequence, the most critical normal and shear stiffnesses’ range for creep analyses of the rockfill dams is determined. Afterwards, the long-term viscoplastic interaction behaviour of Ilısu Dam is examined during 35 years considering this important stiffness values. Settlements, horizontal displacements, and principal stresses are evaluated for both reservoir conditions, and these results are compared with each other in detail.


Introduction
e concrete-faced rockfill dam (CFRD) is a major type of the rockfill dams, and it consists of transition, cushion, main rockfill, and secondary rockfill zones.In recent times, the construction of CFRDs has increased in many countries in the world due to their adaptability to topography and geology, and short construction period, using locally available materials and cost effectiveness.
ese important water structures have a great importance for the continuation of the human life and vital needs of people.e deformation-stress behaviour of these huge structures should be monitored continuously due to the large deformations and stresses can occur in the dam body by the effect of the hydrostatic pressure in time.Control of these deformations and stresses is one of the most important technical and scientific problems for the CFRDs, and numerical simulation is an effective approach for these problems [1].During lifetime of the CFRDs, rockfill materials consistently interact with the foundation [2].erefore, while the behaviour of rockfill dams is monitored and analysed, this interaction behaviour should not be ignored.Simulation of the interaction condition is obtained defining interface elements between two discrete surfaces while performing numerical simulation.e construction of interface elements is a necessary and efficient technique for the transition between the foundation and rockfill, simplifying the modelling process and increasing the efficiency and accuracy of the computation [3].
Dam body and foundation interaction studies have started many years ago.Westergaard is one of the most important pioneers of these studies.He proposed one of the earliest results of the dam-foundation interaction, under external load effects.e importance of estimating the hydrodynamic pressure on rigid dams was examined by him in 1933 [4].In the following years, many numerical techniques were developed to describe foundation-dam interaction.
ese techniques can be classified into the three categories.In the first type, interface regards simply as a surface of soil.So, the analytic or numerical solutions can be derived for the relationship between the corresponding foundation-structure displacement and foundation pressure against the structure under specific conditions.In this type of method, the foundation must be considered as an ideal material which is an oversimplification of the nonlinear behaviour of the concrete-faced rockfill dams.e second type is based on the contact mechanics.Many algorithms have been developed to analyse structure-foundation interaction (e.g., Lagrange methods and penalty function methods).
is type can represent the discontinuity behaviour of the interface between the rigid structure bodies or continuums.However, creating a model, which can describe the complex behaviour of the interface, is very difficult for this type.e third type is the interface element.It has been widely used in the interaction analysis of the foundation-structure systems.For this type, an element can model the discontinuity between the foundation and neighbouring structure at the interface within a continuum-based numerical method (e.g., finite difference method and finite element method) [5][6][7][8][9].e interface elements that are defined between the dam body and foundation are very thin and intensively constrained by the structure, and the interface elements usually take into account the three components.ese components are one stress component normal to the interface and two shear stress components tangential to the interface [10][11][12][13].Afterwards, an important interaction technique was proposed in 1979 to predict the settlement of concrete-faced rockfill dams during 10 years [14].is prediction technique was edited in 1984 [15], and this process has provided significant contributions to the literature.en, investigators were contributed to developments in interaction analysis and deformation behaviours of the CFRDs [16,17].An interaction analysis method was proposed for timedependent interaction analysis of CFRDs.It was revealed that whether the deformation of the CFR dam body is nonlinear or time dependent [18].ere are very few literatures related to time-dependent viscoplastic analysis of CFRDs considering interaction conditions between dam body and foundation.So, it is aimed at filling these important lacks in this study.
e effect of various interface element parameters (normal and shear stiffnesses) on the long-term viscoplastic behaviour of Ilısu CFR dam using special material models is examined.According to the analysis results, stiffness value range for creep analyses of the CFR dams is suggested and the deficiencies in the literature have been largely eliminated.

Ilısu Dam and Mechanical Properties of Rockfill Materials.
e Ilısu Dam is the part of the Southeastern Anatolian Project (GAP), and it is currently the largest hydropower project in Turkey. is huge water structure was completed in the year 2017.e project area is located between Siirt, Batman, and Diyarbakır provinces, and it was built in the boundaries of the Ilısu village.Ilısu Dam's location is shown in detail in Figure 1.
Ilısu Dam that is the longest concrete-faced rockfill dam in the world has 1775 m crest length.Moreover, this structure is one of the largest rockfill dams in the world now.44 million•m 3 filling material is used for constructing of the dam body.3 diversion tunnels with a diameter of 12 m and length of 1 km and 3 power tunnels with a diameter of 11 m are constructed in the project.Dam's precipitation area is 35509 km 2 .e crest width is 8 m, and the dam body height is 130 m. e lake volume is 10.4 billion•m 3 .Maximum water elevation is 526.82 m, and the reservoir area is 318.5 km 2 .
e dam generates 3.833 GWh power per year in average.e slopes of the upstream and downstream are 1 : 1.4, and the slopes of the rockfill zones and transition zones are 2 : 1.5.e most critical section and depth changes of the dam body are presented in detail in Figure 2.
is dam was built as a concrete-faced rockfill dam, and it was constructed using different rockfill materials.While constructing the dam, rockfill materials were compacted by sheepsfoot rollers. is water construction has 3 different filling materials such as basalt (3B), limestone (3A), and bedding zone (2B) and a concrete slab that was constructed on the surface of the dam body to provide impermeability.All materials have different mechanical properties, and mechanical properties of the materials are selected from the laboratory experiments for interaction analyses as given in Table 1.

Finite Difference Model of Ilısu Dam.
Ilısu Dam that is one of the most important rockfill dams in Turkey is selected for the three-dimensional creep analyses in this study.It is modelled using FLAC3D software to examine the time-dependent viscoplastic behaviour of the dam.
e details of the 3D finite difference model are shown in Figure 3.
While modelling this water structure, the concrete slab, rockfill materials, and foundation are modelled as the original project of the Ilısu Dam. e finite difference model of Ilısu Dam has 5 different sections and 4 different blocks.Details of sections and blocks are shown in Figure 3.After the dam body is modelled, the foundation is modelled in detail.It is extended toward downstream and the valley side as much as dam height.Also, it is extended three times of the dam height at upstream side of the dam.Finally, the height of the foundation is considered as much as the dam height.Total 1304547 finite difference elements are used in the 3D finite difference model.Special material models are taken into account for the numerical analyses.e burger-creep viscoplastic model is characterized with visco-elastoplastic deviatoric behaviour and elastoplastic volumetric behaviour.Its plastic constitutive laws correspond to the Mohr-Coulomb material model.is viscoplastic model was rarely used to simulate the viscoplastic creep analyses of the water structures in the literature [20].So, rockfill materials 2 Advances in Civil Engineering and foundation are taken into account in this study.e Drucker-Prager material model is widely used for frictional materials such as concrete.is material model is the most compatible with the WIPP-reference creep law because both models are formulated with the second invariant of the deviatoric stress tensor [21].
us, the    Advances in Civil Engineering WIPP-creep viscoplastic model is taken into account for concrete slab.While de ning these material models to FLAC3D, the sh codes which are specially de ned to FLAC3D software are used.Interface elements are de ned between dam body and foundation to provide the interaction.Totally 20 di erent interaction parameters are used in the time-dependent numerical analyses.Finally, the reservoir water is modelled for the full reservoir water height (130 m), and the e ect of the leakage on the behaviour of the dam is taken into account for all time-dependent analyses [22].e boundary movements of the 3D model must be restricted before the 3D model is analysed.So, the movement of the bottom of the foundation is restricted in three directions (x, y, and z).Moreover, the movement of the side surfaces of the model is allowed only in the vertical direction (z), and it is restricted in the horizontal directions (x, y). e Ilısu Dam has a great number of elements and nodes.So, the creating and meshing of the 3D model took a long time.
Many problems are encountered during viscoplastic numerical analyses because the three-dimensional nite difference model of the Ilısu Dam has a great number of elements and nodes.For this reason, the nite di erence mesh is changed several times, and a new mesh is created so that the correct result can be achieved.Totally 6 di erent mesh widths are tried for 3D analyses.ese mesh widths are 50 m, 40 m, 30 m, 20 m, 15 m, and 10 m, respectively.It is clearly seen that when mesh range is selected less than 15 meters, the settlements on the Ilısu Dam surface do not change (Figure 4).So, the mesh width is selected 15 m for numerical analyses.

eoretical Background of the Interaction between Discrete
Surfaces.In FLAC3D, the interaction condition is represented de ning a normal sti ness value and a shear sti ness value between two discrete planes (e.g., dam and foundation) as seen in Figure 5. FLAC3D uses a contact logic which is similar in nature to that used in the di erent element methods, for either side of the interface [23].As seen in Figure 5, gridpoint N is checked for contact on the segment between grid points M and P. If contact is detected, the normal vector (n) is computed for the contact gridpoint (N).In addition, a length (L) is de ned for the contact at N along the interface.is length is equal to half of the distance to the nearest gridpoint to the left of N, irrespective of whether the neighbouring gridpoint is on the same side of the interface or on the opposite side of N. In this way, the entire interface is divided into contiguous segments, each controlled by a gridpoint.During each time step, the velocity is determined as seen at Equation (1).Since the units of velocity are displacement per time step, the calculation of the time step has been scaled to unity to speed convergence.e incremental displacement for any given time step is e incremental relative displacement vector at the contact point is resolved into the normal and shear directions, and total normal and shear forces are determined by where the unit of k n and k s is calculated.Normal and shear sti nesses (k n and k s ) are not easily measured or well-known parameters.Many methods of estimating joint sti ness have been derived in the past.Two important methods are generally used in the numerical analyses.One of them is based on the deformation properties of the rock mass, and second one is adopted from the properties of the joint in lling material.ese methods are explained in detail as shown below.

Calculation of Normal and Shear Sti nesses considering
Rock ll Properties.Normal sti ness and shear sti ness values can be calculated from joint structure in the jointed rock mass and information on the deformability and the deformability of the intact rock.If the jointed rock mass is presumed to have the same deformational response as an equivalent elastic continuum, relations can be derived between jointed rock properties and equivalent continuum properties.e following relation applies for uniaxial-loaded rock which contains a single set of uniformly spaced joints oriented normally to the direction of loading: where E m is the rock mass modulus, E i is the intact rock modulus, k n is the joint normal sti ness, and L is the mean joint spacing.Equation ( 3) can be rearranged to obtain the joint normal sti ness as given in the following equation: e same expression can be used to derive a relation for the joint shear sti ness as follows: where G m is the rock mass shear modulus, G i is the intact rock shear modulus, and k s is the joint shear sti ness.e equivalent continuum assumption, when extended to three orthogonal joint sets, provides the following relations: Several expressions have been derived for two-and three-dimensional characterizations and multiple joint sets [24][25][26][27].

Calculation of Normal and Shear considering Joint In ll
Properties.Another approach for estimating joint sti ness assumes that a joint has an in ll material with known elastic properties.e sti ness of a joint can be evaluated from the thickness and modulus of the in lling material by the following equation: where k n is the joint normal sti ness, k s is the joint shear sti ness, E 0 is Young's modulus of the in ll material, G 0 is the shear modulus of the in ll material, and h is the joint thickness or opening.

e Burger-Creep Viscoplastic Material
Model. e burger-creep viscoplastic model that is a special model for time-dependent creep analysis is characterized with an elastoplastic volumetric behaviour and a visco-elastoplastic deviatoric behaviour.e viscoplastic strain rate and viscoelastic components are presumed to act in series.

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where e Kelvin, Maxwell, and plastic contributions are labeled using the superscripts K, M, and p, respectively.With those conventions, the model deviatoric behaviour may be described by the following relations.
Strain rate partitioning: e Kelvin model is expressed as follows: e Mohr-Coulomb model is expressed as follows: e Maxwell model is expressed as follows: In turn, the volumetric behaviour is given by where the properties K and G are the bulk and shear moduli and η is the dynamic viscosity (kinematic viscosity times mass density).e Mohr-Coulomb yield envelope is a composite of shear and tensile criteria.e yield criterion is f � 0, and in the principal axes formulation, the following formulation is obtained.
Shear yielding: Tension yielding: where C is the material cohesion, φ is the friction, N φ � (1 + sin φ)/(1 − sin φ), σ t is the tensile strength, and σ 1 and σ 3 are the minimum and maximum principal stresses (compression negative).e potential function g has the following form.
Shear failure: Tension failure: where ψ is the material dilation and N φ � (1 + sin ψ)/ (1 − sin ψ).Finally, λ * is a parameter that is nonzero during plastic flow only, which is determined by application of the plastic yield condition f � 0 [21].

WIPP-Creep
where f s � 0 at yield and σ 0 � σ kk /3, and τ �� J 2  τ, where J 2 is the second invariant of the deviatoric stress tensor; the parameters q φ and k φ are the material properties: where τ may be related to the stress magnitude, σ: e plastic potential function in shear, g s , is similar to the yield function, with the substitution of q ψ for q φ as a material property that controls dilation: If the yield condition f s � 0 is met, the following flow rules apply: where λ is a multiplier (not a material property) to be determined from the requirement that the final stress tensor must satisfy the yield condition.e superscript p denotes "plastic" and d denotes "deviatoric." In elastic/plastic formulation, these equations are solved simultaneously with the condition f s � 0, and the condition is that the sum of elastic and plastic strain rates must equal the applied strain rate.
e Drucker-Prager model also contains a tensile yield surface, with a composite decision function used near the intersection of the shear and tensile yield functions.e tensile yield surface is where σ t is the tensile yield strength.e associated plastic potential function is 6

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Using an approach similar to that used for shear yield, the strain rates for tensile yield are: where λ is determined from the condition that f t � 0. Note that the tensile strength cannot be greater than the value of mean stress at which f s becomes zero.
When both creep and plastic flows occur, it is assumed that the associated strain rates act "in series": where the terms represent elastic, viscous, and plastic strain rates, respectively.We first treat the case of shear yield f s > 0: In contrast to the creep-only model, the volumetric response of the viscoplastic model is not uncoupled from the deviatoric behaviour unless q ψ � 0 [21].

Numerical Results
Rockfill and foundation materials have different mechanical properties, and these materials interact during the dam's lifetime.So, the examination of the dam body-foundation interaction is very important for the evaluation of the safety and future of the rockfill dams. is interaction condition is provided defining the interface elements between the dam body and foundation while modelling these dams.e mechanical parameters of the interface elements are variable for each dam, and the most important parameters for interaction analyses are the normal and shear spring stiffnesses.Effect of these stiffness parameters on the nonlinear behaviour of the structures was examined by very few investigators [28,29].ey proposed that values of the normal and shear stiffnesses for rock joints typically can range roughly from 10 to 100 MPa/m for joints with soft clay infilling and to over 100 GPa/m for tight joints in granite and basalt.So, mechanical parameters of the interface elements are considered for this range in this study.Mechanical behaviour of the normal and shear spring stiffnesses is explained in Section 2. ese stiffness parameters depend on the elasticity modulus and shear modulus of the materials.us, the elasticity modulus and shear modulus are assumed as the variables in the numerical analyses.As a consequence, various stiffness values are obtained for each variable (Table 1).Special fish codes are used while defining normal and shear stiffness parameters to FLAC3D software.e effect of these variable parameters on the viscoplastic behaviour of the dam is examined for empty and full reservoir conditions in this section.Totally 20 different normal and shear stiffness parameters are used for both reservoir conditions in the numerical analyses as shown Table 2.
Solution algorithm for 3D interaction analyses is shown in Figure 6.According to numerical results, the maximum settlements, maximum horizontal displacements, and maximum principal stresses during lifetime of the dam are examined considering 20 different interaction situations.ese results are compared graphically for empty and full reservoir conditions.After the most critical stiffness values for the interaction analyses of the rockfill dams are determined, time-dependent viscoplastic analyses of the Ilısu Dam are performed using these critical stiffness values (k n and k s ), and it is observed that how the interaction behaviour of the Ilısu Dam will change in the future by the effect of normal and shear stiffnesses.

Vertical Displacements.
Monitoring of the dam's settlement behaviour is one of the most important factors for assessing the future and safety of these water structures, and it provides a warning system for abnormal behaviour of the dams.In this section, time-dependent settlement behaviour of the Ilısu rockfill dam is monitored for empty and full reservoir conditions considering various interaction parameters (normal-shear spring stiffnesses) between the dam body and foundation (Figure 7). 4 different significant points are selected from the dam surface to better evaluate the effect of the normal and shear spring stiffnesses on the behaviour of the dam.ese critical points are shown in Figure 8.
According to the numerical analyses, viscoplastic behaviour of the Ilısu Dam changes by the effect of changing normal-shear stiffness parameters for empty and full reservoir conditions.When the full and empty reservoir conditions are compared, more vertical displacements are observed for the full reservoir condition.For the full reservoir condition, the maximum and minimum settlements are observed on Point 3 and Point 1, respectively (Figure 7).In other words, the maximum settlement occurs on the Advances in Civil Engineering approximately middle of the dam surface.But, when the empty reservoir condition of the dam is investigated, maximum settlements occurred at the crest point of the dam. is result clearly indicates the e ect of the hydrostatic pressure on the viscoplastic settlement behaviour of the Ilısu Dam.When examining Figure 7, the maximum settlement took place for the smallest sti ness value (k n and k s 0).In addition, it is clearly seen that when the sti ness parameters (k n and k s ) are increased from 0 to 10 12 Pa/m for numerical analyses, the vertical displacement values obviously diminish for both reservoir conditions. is result clearly shows that how the sti ness values alter the time-dependent behaviour of the Ilısu Dam.According to Figure 7, the settlements changed continuously until a certain sti ness value, and any signi cant settlement changes were not observed for larger sti ness values than this value.In other words, when normal and shear sti ness parameters are selected between 10 8 Pa/m and 10 12 Pa/m, the settlement behaviour of the Ilısu Dam obviously does not change.However, if smaller sti ness than 10 8 Pa/m is chosen for interaction analyses, settlements on the dam body surface increase.is result provides a very important proposal for new dam design.When considering the average settlements of the rock ll dams during its lifetime, it can be understood that the sti ness values can be selected between 10 6 Pa/m and 10 8 Pa/m for interaction analyses of rock ll dams. is result provides very important information for modelling these dams.
After the most critical sti ness parameters are determined for interaction analyses of the rock ll dams, timedependent viscoplastic analyses are performed for next 35 years of the Ilısu Dam.In the numerical analyses, k n and k s sti ness values are taken into account as 10 8 Pa/m.Vertical displacement results are shown for the empty reservoir condition of the Ilısu Dam in Figure 9.According to the numerical results, maximum settlement took place at the crest point of the dam and approximately 37.3 cm settlement is observed on this point.In addition, 25 cm and 10 cm vertical displacements occurred at the middle and bottom of the dam body surface, respectively.e dam body is divided into two parts from the midpoint of the center to better examine the behaviour changes in the dam body, and it is clearly seen that the vertical displacements decreased from the crest to the bottom of the dam.Hydrostatic pressure is an important factor for evaluating of the settlement behaviour [30].So, e ect of the hydrostatic pressure and water owing on the dam behaviour are examined for the full reservoir condition.First, all displacements and principal stresses, which are obtained from the empty reservoir condition of the dam, are set to zero in order to exclude the stresses and deformations.
en, reservoir water is modelled considering full reservoir height (130 m).According to the numerical results for the full reservoir condition, maximum settlement occurred at approximately middle of the dam body surface, and about 116 cm vertical displacement is observed at this point (Figure 10).Moreover, when the settlements of 4 points on the dam body surface are examined during 35 years, it is seen that the largest settlement is observed at Point 3 and the smallest settlement occurred at Point 1 (Figure 11).ough any settlement did not take place on the surface of the foundation for the empty reservoir condition,   Advances in Civil Engineering information about its stability and future.Numerical results for various interaction conditions between dam body and foundation are shown graphically in this section (Figure 12).ese graphs are created taking into account the maximum horizontal displacements that may occur during Ilısu Dam's life.Ilısu Dam is examined for two reservoir conditions to better seen the e ect of the hydrostatic pressure.When comparing the empty and full reservoir conditions of the dam, more horizontal displacements are observed for the full reservoir condition as seen in Figure 12.According to the numerical analyses, the interface elements that are de ned between the dam body and the foundation clearly altered the horizontal displacement behaviour of the Ilısu Dam.When the horizontal displacements for 4 di erent points on the dam body surface (Figure 8) are investigated, it is obviously seen that maximum and minimum horizontal displacements took place on Point 2 and Point 1, respectively (Figures 12(a 12(a) and 12(c)).Moreover, when 20 different interaction conditions are compared with each other, large horizontal displacement changes occurred between Case 1 and Case 12.However, very small displacement changes are obtained between Case 12 and Case 20. ese results clearly mean that no matter how much the sti ness values are changed between 10 8 Pa/m and 10 12 Pa/m, large horizontal displacement changes are not observed on the Ilısu Dam body for this sti ness range.But, it is seen from Figure 12 that the creep behaviour of the Ilısu Dam obviously changes for smaller sti ness values than 10 8 Pa/m.When considering these numerical results, it is understood that the sti ness parameters have a great e ect on the horizontal displacement behaviour of the rock ll dams. is information will be a guide for designing and modelling the rock ll dam.
After determining the most critical sti ness values for horizontal displacement behaviour of the rock ll dams, these critical sti ness parameters (k n and k s ) are de ned to FLAC3D software using sh codes.In the numerical   Advances in Civil Engineering examined, large displacement changes are observed between the empty and full reservoir conditions.For the empty reservoir condition, very small horizontal displacements occurred on the dam body surface because external loads did not expose to the dam as seen in Figure 13.However, viscoplastic behaviour of the Ilısu Dam clearly changed by e ect of the hydrostatic pressure.More displacements are obtained for the full reservoir condition compared with the empty condition, and 83 cm maximum horizontal displacement is observed at the middle of the dam body surface as seen in Figure 14.When 4 critical points (Figure 8) on the dam body surface are examined, maximum and minimum displacement values took place at Point 2 and Point 1, respectively (Figure 15).Moreover, it is understood that large horizontal displacement changes will take place in the dam body surface from the year 2017 to 2040.But, displacement changes will decrease after the year 2040. is result provides very important information about future of the Ilısu Dam.

Principal Stresses.
In this section, the e ect of the interaction parameters on the principal stress behaviour of the Ilısu Dam is examined in detail.e numerical results are presented graphically in Figure 16.Graphs are created considering the maximum principal stress values that may take place during dam's lifetime.Generally, it is clearly understood from the numerical graphs that the principal stress values for the full reservoir condition are larger than   those for the empty reservoir condition.is result obviously shows the e ect of the hydrostatic pressure on the time-dependent viscoplastic behaviour of the Ilısu Dam.
When examining 4 di erent points that are selected on the dam surface (Figure 8), the maximum and minimum principal stresses are observed at Point 2 and Point 4, is important conclusion means that when considering the hydrostatic pressure e ect, the maximum principal stresses take place at approximately middle of the dam body surface.When comparing 20 di erent interaction conditions, large stress changes are observed between Case 1 and Case 12 (Figure 16).In other words, if the sti ness parameters are selected between 0 and 10 8 Pa/m for the interaction analyses of the rock ll dams, great principal stress changes occur on the dam body surface for this sti ness range.However, when these parameters are chosen as greater value than 10 8 Pa/m, no large stress changes are observed on the dam body surface (Figure 16).According to these results, it is understood that the most critical normal and shear sti ness parameters are 10 8 Pa/m for principal stress analyses of the rock ll dams.
is result provides very important support for modelling and analysing these dams.
After the most critical sti ness range is determined for the principal stress behaviour of the Ilısu Dam, creep analyses are performed considering this critical range.Normal and shear sti ness values are selected as 10 8 Pa/m in the numerical analyses.Time-dependent results are presented in Figures 17-19.Ilısu Dam is examined for 2 di erent reservoir conditions to better observe the e ect of the hydrostatic pressure on the viscoplastic behaviour of the dam.For the empty reservoir condition, any principal stresses are not observed on the dam body surface, and the stresses increased from the crest to the foundation surface (Figure 17).e 3D dam model is divided into two halves to better see principal stress changes in the dam body.When investigating the split half condition of the Ilısu Dam, approximately 4.61 MPa maximum principal stress is observed at the bottom of the 3D model.In addition, 2.5 MPa principal stress took place at the bottom of the dam body as seen in Figure 17.As soon as the reservoir water interacted with the dam body surface, principal stress behaviour of the Ilısu Dam obviously changed.More principal stresses occurred for the full reservoir condition compared with the empty reservoir condition (Figure 18).For the full reservoir condition, maximum principal stress is 6.78 MPa, and it is observed at the bottom of the foundation.Approximately 1.4 MPa principal stress is obtained on the surface of the foundation, and 2 MPa principal stresses occurred at the middle of the dam body.When examining 4 di erent points on the dam body surface, the maximum and minimum stresses that may occur on the dam body surface during 35 years are observed at Point 2 and Point 4, respectively (Figure 19). is result indicates the e ect of the hydrostatic pressure on the Ilısu Dam principal stress behaviour.

Conclusion
In this paper, the e ect of the dam body and foundation interaction on the time-dependent viscoplastic behaviour of the Ilısu Dam is examined in detail.
e threedimensional nite di erence model of the Ilısu Dam is modelled using special sh codes, and it is created according to the original dam project.e special material models are used for rock ll and foundation materials in the creep analyses.ese material models were rarely used for creep analyses of the rock ll dams, previously.us, this study is very important in terms of evaluating the e ect of the di erent material models on the viscoplastic behaviour of the CFR dams.20 di erent interaction parameters (normal and shear sti nesses) are used between the dam body and foundation for the interaction analyses of Ilısu CFR dam.erefore, totally 20 various interaction analyses are performed for the empty and full reservoir conditions of the dam.
e e ect of these interaction conditions on the viscoplastic behaviour of the Ilısu Dam is evaluated as below: (i) According to the numerical results, it is clearly understood that the hydrostatic water pressure (ii) When examining the vertical displacements on the dam body surface that may occur from the year 2017 to 2052, 0.37 m maximum settlement is observed at the crest of the dam body for the empty reservoir condition.However, as soon as the reservoir water contacts the dam body surface, the settlement behaviour of the Ilısu Dam clearly changes.1.16 m maximum settlement value is obtained at the approximately middle of the dam body surface for the full reservoir condition.is result obviously indicates the e ect of the reservoir water pressure on the creep behaviour of the Ilısu Dam.(iii) For the empty reservoir condition, very small horizontal displacements are observed on the dam body surface because hydrostatic pressure did not contact the dam body surface.But, horizontal displacements obviously increased on the dam body surface by the e ect of the hydrostatic water pressure.0.83 m maximum horizontal displacement is observed at the approximately middle of the dam body surface for the full reservoir condition.(iv) According to the stress analyses, any principal stress value is not observed at the dam body surface for the empty reservoir condition of the dam.But, approximately 2 MPa principal stress value is acquired on the dam body for the full reservoir condition.

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(v) According to the interaction analyses, it is clearly seen that the most critical shear and normal stiffness values are 10 8 Pa/m for creep analyses of the CFR dams.When the stiffness parameters (normal and shear stiffnesses) that are defined between dam body and foundation is selected between 0 and 10 8 Pa/m in the interaction analyses, large changes are observed in the time dependent viscoplastic behaviour of the CFR dams.Moreover, if these parameters are chosen as larger than 10 8 Pa/m in the creep analyses, small changes are observed in the viscoplastic behaviour of these dams.When considering the average settlement values of the rockfill dams during its lifetime, it can be understood that the normal and shear stiffness values can be selected between 10 6 Pa/m and 10 8 Pa/m for interaction analyses of rockfill dams. is conclusion is very important for modelling and analysing the CFR dams.(vi) It is clearly seen from this study, normal and shear spring stiffness parameters are very important for evaluating the creep behaviour of the rockfill dams.So, these parameters should not be ignored in the time-dependent interaction analyses of CFR dams.

Figure 1 :
Figure 1: e location and view of Ilısu Dam.

Figure 2 :
Figure 2: (a) e typical cross section of Ilısu Dam.(b) Change in the dam body depth along crest axis [19].

Figure 5 :
Figure 5: An interface condition between A and B sides.

Figure 8 :
Figure 8: Selected points on the dam body surface.
) and 12(b)).In addition, less displacements are observed on Point 4 (crest point of the dam) compared with Point 2 and Point 3 (Figures

- 1 .Figure 10 :
Figure 10: Vertical displacements for the full reservoir condition of the Ilısu Dam after 35 years.

Figure 11 :Figure 12 :
Figure 11: Time-dependent vertical displacements for the full reservoir condition during 35 years.

Figure 13 :
Figure 13: Horizontal displacements for the empty reservoir condition of the Ilısu Dam after 35 years.

Figure 14 :
Figure 14: Horizontal displacements for the full reservoir condition of the Ilısu Dam after 35 years.

Figure 15 :Figure 16 :
Figure 15: Time-dependent horizontal displacements for the full reservoir condition during 35 years.

Figure 17 :
Figure 17: Principal stresses for the empty reservoir condition of the Ilısu Dam for next 35 years.

Figure 18 :Figure 19 :
Figure 18: Principal stresses for the full reservoir condition of the Ilısu Dam for next 35 years.
Viscoplastic Material Model.Viscoplasticity can model by combining the viscoelastic WIPP model with the Drucker-Prager plasticity model.e Drucker-Prager model is the most compatible with the WIPP-reference creep law because both models are formulated in terms of the second invariant of the deviatoric stress tensor.e shear yield function for the Drucker-Prager model is

Table 2 :
Normal and shear stiffness parameters for numerical analyses.