Rockfill materials and foundation continuously interact with each other during lifetime of the rockfill dams. This 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. The 3D finite difference model of this dam is modelled using FLAC3D software that is based on the finite difference method. The concrete slab, rockfill materials, foundation, and reservoir water are separately created for the 3D interaction analyses. A WIPP-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.
The 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. These important water structures have a great importance for the continuation of the human life and vital needs of people. The 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 [[
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. The importance of estimating the hydrodynamic pressure on rigid dams was examined by him in 1933 [[
The Ilısu Dam is the part of the Southeastern Anatolian Project (GAP), and it is currently the largest hydropower project in Turkey. This huge water structure was completed in the year 2017. The 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
This 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. This 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.
Material properties of Ilısu Dam body [
Characteristics Specific weight (g/cm3) Unit weight (g/cm3) Porosity (%) Water content (%) Air content (%) Material content (%) 2B 2.74 2.23 18.61 4.05 14.56 81.39 3A 2.68 1.99 25.75 7.78 17.97 74.25 3B 3.01 2.25 25.25 1.50 23.75 74.75
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. The 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. The 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. The 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. This viscoplastic model was rarely used to simulate the viscoplastic creep analyses of the water structures in the literature [[
In FLAC3D, the interaction condition is represented defining a normal stiffness value and a shear stiffness 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 different element methods, for either side of the interface [[
The 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(
Normal and shear stiffnesses (kn and ks) are not easily measured or well-known parameters. Many methods of estimating joint stiffness 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 infilling material. These methods are explained in detail as shown below.
Normal stiffness and shear stiffness 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. The following relation applies for uniaxial-loaded rock which contains a single set of uniformly spaced joints oriented normally to the direction of loading:(
The same expression can be used to derive a relation for the joint shear stiffness as follows:(
Several expressions have been derived for two- and three-dimensional characterizations and multiple joint sets [[
Another approach for estimating joint stiffness assumes that a joint has an infill material with known elastic properties. The stiffness of a joint can be evaluated from the thickness and modulus of the infilling material by the following equation:(
The 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. The viscoplastic strain rate and viscoelastic components are presumed to act in series. The viscoelastic constitutive law corresponds to the Burger model (the Kelvin and Maxwell components), and the plastic constitutive law corresponds to the Mohr–Coulomb model and the burger model. The symbols Sij and eij are used to denote deviatoric stress and strain components [[
The 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:(
The Kelvin model is expressed as follows:(
The Mohr–Coulomb model is expressed as follows:(
The Maxwell model is expressed as follows:(
In turn, the volumetric behaviour is given by(
Shear yielding:(
Tension yielding:(
Shear failure:(
Tension failure:(
Viscoplasticity can model by combining the viscoelastic WIPP model with the Drucker–Prager plasticity model. The 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. The shear yield function for the Drucker–Prager model is(
The plastic potential function in shear, gs, is similar to the yield function, with the substitution of qψ for qφ as a material property that controls dilation:(
If the yield condition fs=0 is met, the following flow rules apply:(
In elastic/plastic formulation, these equations are solved simultaneously with the condition fs=0, and the condition is that the sum of elastic and plastic strain rates must equal the applied strain rate. The 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. The tensile yield surface is(
Using an approach similar to that used for shear yield, the strain rates for tensile yield are:(
When both creep and plastic flows occur, it is assumed that the associated strain rates act “in series”:(
In contrast to the creep-only model, the volumetric response of the viscoplastic model is not uncoupled from the deviatoric behaviour unless qψ=0 [[
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. This interaction condition is provided defining the interface elements between the dam body and foundation while modelling these dams. The 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 [[
Normal and shear stiffness parameters for numerical analyses.
Case Stiffness (kn and ks) (Pa/m) 1 0 2 101 3 102 4 103 5 104 6 105 7 5 × 105 8 106 9 5 × 106 10 107 11 5 × 107 12 108 13 5 × 108 14 109 15 5 × 109 16 1010 17 5 × 1010 18 1011 19 5 × 1011 20 1012
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. These 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 (kn and ks), 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.
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. These 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 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. This result clearly indicates the effect 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 stiffness value (kn and ks=0). In addition, it is clearly seen that when the stiffness parameters (kn and ks) are increased from 0 to 10
After the most critical stiffness parameters are determined for interaction analyses of the rockfill dams, time-dependent viscoplastic analyses are performed for next 35 years of the Ilısu Dam. In the numerical analyses, kn and ks stiffness values are taken into account as 10
Horizontal displacements for the rockfill dams generally take place due to the effect of the hydrostatic pressure. These displacements disrupt the stability and functionality of the rockfill dams in time. For this reason, observing of the horizontal displacements for Ilısu Dam is vitally important in order to obtain more 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). These 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 effect 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 defined between the dam body and the foundation clearly altered the horizontal displacement behaviour of the Ilısu Dam. When the horizontal displacements for 4 different 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) 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 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. These results clearly mean that no matter how much the stiffness values are changed between 10
After determining the most critical stiffness values for horizontal displacement behaviour of the rockfill dams, these critical stiffness parameters (kn and ks) are defined to FLAC3D software using fish codes. In the numerical analyses, shear (ks) and normal (kn) stiffness parameters are considered as 10
In this section, the effect of the interaction parameters on the principal stress behaviour of the Ilısu Dam is examined in detail. The 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. This result obviously shows the effect of the hydrostatic pressure on the time-dependent viscoplastic behaviour of the Ilısu Dam. When examining 4 different points that are selected on the dam surface (Figure 8), the maximum and minimum principal stresses are observed at Point 2 and Point 4, respectively (Figures 16(b) and 16(d)). This important conclusion means that when considering the hydrostatic pressure effect, the maximum principal stresses take place at approximately middle of the dam body surface. When comparing 20 different interaction conditions, large stress changes are observed between Case 1 and Case 12 (Figure 16). In other words, if the stiffness parameters are selected between 0 and 10
After the most critical stiffness range is determined for the principal stress behaviour of the Ilısu Dam, creep analyses are performed considering this critical range. Normal and shear stiffness values are selected as 10
In this paper, the effect of the dam body and foundation interaction on the time-dependent viscoplastic behaviour of the Ilısu Dam is examined in detail. The three-dimensional finite difference model of the Ilısu Dam is modelled using special fish codes, and it is created according to the original dam project. The special material models are used for rockfill and foundation materials in the creep analyses. These material models were rarely used for creep analyses of the rockfill dams, previously. Thus, this study is very important in terms of evaluating the effect of the different material models on the viscoplastic behaviour of the CFR dams. 20 different interaction parameters (normal and shear stiffnesses) are used between the dam body and foundation for the interaction analyses of Ilısu CFR dam. Therefore, totally 20 various interaction analyses are performed for the empty and full reservoir conditions of the dam. The effect of these interaction conditions on the viscoplastic behaviour of the Ilısu Dam is evaluated as below:
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
1 Gou Q., Pei L., Zhou Z., Chen J., Yao F., Response surface and genetic method for deformation back analysis for high core rockfill dams, Computers and Geotechnics, 2016, 74, 132, 140, 10.1016/j.compgeo.2016.01.001, 2-s2.0-84955480361
- 2 Zhang G., Zhang J. M., Numerical modelling of soil-structure interface of a concrete face rockfill dam, Computers and Geotechnics, 2009, 36, 5, 762, 772, 10.1016/j.compgeo.2009.01.002, 2-s2.0-64849100535
- 3 Qu Y., Zou D., Kong X., Xu B., A novel interface element with asymmetric nodes and its application on concrete-faced rockfill dam, Computers and Geotechnics, 2017, 85, 103, 116, 10.1016/j.compgeo.2016.12.013, 2-s2.0-85007473722
- 4 Westergaard H. M., Water pressures on dams during earthquakes, Transactions of the American Society of Civil Engineers, 1933, 98, 2, 418, 433
- 5 Gazetas G., Dobry R., Tassoulas J., Vertical response of arbitrarily shaped embedded foundations, Journal of Geotechnical Engineering, 1985, 111, 6, 750, 771, 10.1061/(asce)0733-9410(1985)111:6(
750 ), 2-s2.0-0022076381 - 6 Gazetas G., Tassoulas J., Horizontal stiffness of arbitrarily shaped embedded foundations, Journal of Geotechnical Engineering, 1987, 113, 5, 440, 457, 10.1061/(asce)0733-9410(1987)113:5(
440 ), 2-s2.0-0023346194 - 7 Fan K., Gazetas G., Kaynia A., Kausel E., Ahmad S., Kinematic seismic response of single piles and pile groups, Journal of Geotechnical Engineering, 1991, 117, 12, 1860, 1879, 10.1061/(asce)0733-9410(1991)117:12(1860), 2-s2.0-0026370887
- 8 Luco J. E., A simply model for structural control including soil-structure interaction effects, Earthquake Engineering and Structural Dynamics, 1998, 27, 3, 225, 242, 10.1002/(sici)1096-9845(199803)27:3<225::aid-eqe713>3.0.co;2-s
- 9 Militano G., Rajapakse R. K. N. D., Dynamic response of a pile in a multi-layered soil to transient torsional and axial loading, Géotechnique, 1999, 49, 1, 91, 109, 10.1680/geot.1999.49.1.91, 2-s2.0-0033081188
- 10 Anonymous, Progress at current major CFRD projects, International Journal on Hydropower and Dams, 2003, 10, 4, 79, 87
- 11 Gens A., Carol I., Alonso E. E., An interface element formulation for the analysis of soil-reinforcement interaction, Computers and Geotechnics, 1988, 15, 7, 133, 151
- 12 Plesha M. E., Hutson R. W., Dowding C. H., Determination of asperity damage parameters for constitutive models of discontinuities, International Journal of Numerical Analytical Methods Geomechanics, 1991, 15, 4, 289, 294, 10.1002/nag.1610150406, 2-s2.0-0025920352
- 13 Justo J. L., Segovia F., Jaramillo A., Three dimensional joint elements applied to concrete-faced dams, International Journal of Numerical Analytical Methods Geomechanics, 1995, 19, 9, 615, 636, 10.1002/nag.1610190903, 2-s2.0-0029500189
- 14 Soydemir C., Kjaernsli B., Deformation of membrane-faced rockfill dams, Proceedings of the 7th European Conference Soil Mechanics and Foundation Engineering, September 1979, Brighton, England, 120, 126
- 15 Clements R. P., Post-construction deformation of rockfill dams, Journal of Geotechnical Engineering, 1984, 110, 7, 821, 840, 10.1061/(asce)0733-9410(1984)110:7(
821 ), 2-s2.0-0021464511 - 16 Kovacevic N., Potts D. M., Vaughan P. R., Finite element analysis of a rockfill dam, Proceedings of the 8th International Conference on Computer Methods and Advances in Geomechanics, May 1994, Morgantown, WV, USA, 2459, 2464
- 17 Duncan J. M., State of the art: limit equilibrium and finite element analysis of slopes, Journal of Geotechnical Engineering, 1996, 122, 7, 577, 595, 10.1061/(asce)0733-9410(1996)122:7(
577 ) - 18 Zhan B., Wang J. G., Shi R., Time-dependent deformation in high concrete-faced rockfill dam and separation between concrete face slab and cushion layer, Computers and Geotechnics, 2004, 31, 7, 559, 573, 10.1016/j.compgeo.2004.07.004, 2-s2.0-11344258930
- 19 DSI, General Directorate of State Hydraulic Works, 2018, Ankara, Turkey, Regional Directorate
- 20 Zou L., Wang S., Lai X., Creep model for unsaturated soils in sliding zone of Qianjiangping landslide, Journal of Rock Mechanics and Geotechnical Engineering, 2013, 5, 2, 162, 167, 10.1016/j.jrmge.2013.03.001, 2-s2.0-84925288532
- 21 Itasca Consulting Group, Inc., FLAC Version 5 User Manual, 2002, Minneapolis, MN, USA, Itasca Consulting Group, Inc.
- 22 Li G. C, Desai C. S., Stress and seepage analysis of earthen dams, Journal of Geotechnical Engineering, 1983, 109, 7, 946, 960, 10.1061/(asce)0733-9410(1983)109:7(
946 ), 2-s2.0-0020610987 - 23 Cundall P. A., Hart R. D., Numerical modeling of discontinua, Engineering Computations, 1992, 9, 2, 101, 113, 10.1108/eb023851, 2-s2.0-0026851050
- 24 Fossum A. F., Effective elastic properties for a randomly jointed rock mass, International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1985, 22, 6, 467, 470, 10.1016/0148-9062(
85 )90011-7, 2-s2.0-0022192983 - 25 Gerrard C. M., Equivalent elastic moduli of a rock mass consisting of orthorhombic layers, International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1982, 19, 1, 9, 14, 10.1016/0148-9062(
82 )90705-7, 2-s2.0-0019999680 - 26 Gerrard C. M., Elastic models of rock masses having one, two and three sets of joints, International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1982, 19, 1, 15, 23, 10.1016/0148-9062(
82 )90706-9, 2-s2.0-0019999678 - 27 Singh B., Continuum characterization of jointed rock masses: part I—the constitutive equations, International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1973, 10, 4, 311, 335, 10.1016/0148-9062(
73 )90041-7, 2-s2.0-0015648720 - 28 Kulhawy F. H., Stress deformation properties of rock and rock discontinuities, Engineering Geology, 1975, 9, 4, 327, 350, 10.1016/0013-7952(
75 )90014-9, 2-s2.0-0016622543 - 29 Rosso R. S., A comparison of joint stiffness measurements in direct shear, triaxial compression, and in situ, International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1976, 13, 6, 167, 172, 10.1016/0148-9062(
76 )91282-1, 2-s2.0-0016961685 - 30 Shariatmadar H., Mirhaj A., Dam-reservoir-foundation interaction effects on the modal characteristic of concrete gravity dams, Structural Engineering and Mechanics, 2011, 38, 1, 65, 79, 10.12989/sem.2011.38.1.065, 2-s2.0-79953304265
PHOTO (COLOR): The location and view of Ilısu Dam.
PHOTO (COLOR): (a) The typical cross section of Ilısu Dam. (b) Change in the dam body depth along crest axis [
PHOTO (COLOR): 3D finite difference model of Ilısu Dam.
PHOTO (COLOR): Maximum settlements on the dam body for different mesh widths.
PHOTO (COLOR): An interface condition between A and B sides.
PHOTO (COLOR): Solution algorithm for three-dimensional numerical analyses.
PHOTO (COLOR): Settlements for selected 4 points on the dam body surface: (a) Point 1, (b) Point 2, (c) Point 3, and (d) Point 4.
PHOTO (COLOR): Selected points on the dam body surface.
PHOTO (COLOR): Vertical displacements (m) for the empty reservoir condition of the Ilısu Dam after 35 years.
PHOTO (COLOR): Vertical displacements for the full reservoir condition of the Ilısu Dam after 35 years.
PHOTO (COLOR): Time-dependent vertical displacements for the full reservoir condition during 35 years.
PHOTO (COLOR): Horizontal displacements for selected 4 points on the dam body surface: (a) Point 1, (b) Point 2, (c) Point 3, and (d) Point 4.
PHOTO (COLOR): Horizontal displacements for the empty reservoir condition of the Ilısu Dam after 35 years.
PHOTO (COLOR): Horizontal displacements for the full reservoir condition of the Ilısu Dam after 35 years.
PHOTO (COLOR): Time-dependent horizontal displacements for the full reservoir condition during 35 years.
PHOTO (COLOR): Principal stresses for selected 4 points on the dam body surface: (a) Point 1, (b) Point 2, (c) Point 3, and (d) Point 4.
PHOTO (COLOR): Principal stresses for the empty reservoir condition of the Ilısu Dam for next 35 years.
PHOTO (COLOR): Principal stresses for the full reservoir condition of the Ilısu Dam for next 35 years.
PHOTO (COLOR): Time-dependent principal stresses for the full reservoir condition during 35 years.
By Memduh Karalar and Murat Çavuşli