DIANA Analysis of a Concrete Faced Rockfill Dam
Type In proceedings
Author Gerd-Jan Schreppers, Giovanna Lilliu
Year 2009 - 10th Benchmark Workshop on Numerical Analysis of Dams, ICOLD
Keywords CFRD, Cracking, 3D
Abstract
Several concrete faced rockfill dams in the world present cracks in the concrete face. In this paper the authors make an attempt to predict formation of cracks in one of such dams, the Mohale dam in Lesotho, South Africa. Foundation of the dam, dam body and the concrete slab are modelled in 3D. A Cam-clay plasticity model with hardening is adopted for the rockfill. Contact bewteen the concrete face and rockfill is modelled with contact elements, with a Coulomb friction material constitutive model. Interface elements are used to model the vertical joints among the 37 panels that form the concrete face. For the concrete face a total strain crack model in combination with crushing is adopted. In the analysis the different construction stages have been considered, as well as the different impoundment stages. The results shown in this paper are displacement and stresses in the rockfill and the concrete face, crack patterns and crack strains in the concrete face, and openings of the vertical joints.
1 Introduction
In CFRDs, settlements of the rockfill during and after construction can cause deformation and cracking of the concrete face. To prevent this, empirical rules have been formulated for controlling grading of the rockfill and compaction conditions. However, as higher and higher CFRDs are built in the world, numerical analysis is necessary to validate the empirical rules. Due to the complex physical mechanisms involved in the interaction of the different structural elements in a CFRD, and the need to consider 3D effects, there are not many comprehensive examples of numerical analysis of CFRDs. This has motivated the ICOLD Committee on Computational Aspects of Analysis and Design of Dams to propose the numerical analysis of a CFRD as one of the themes for the 10th Benchmark Workshop on Numerical Analysis of Dams [1]. Object of this benchmark is the Mohale dam in Lesotho, South-Africa. This is a 145 m high CFRD, with a crest length of 600 m, a concrete face surface of 73400 m2 and a total fill volume of approximately 7.5 million m3. The dam was built of basalt rockfill. After the reservoir was completely impounded, significant dam movements occurred and cracks developed in the concrete face, which caused leakage. Information provided in [1] is not sufficient for a quantitative comparison of numerical predictions and actual deformation and crack status in the Mohale dam. Nevertheless, this exercise has offered the authors the possibility to test the capability of the finite element package DIANA [2] to model the behaviour of CFRDs.
2 Modelling aspects
2.1 Finite Element Model
The finite element model of the dam body and the foundation is shown in Figure 1. The dam body is modelled with 4-node tetrahedral elements with 6 m edge size. This element size is chosen for limiting the number of degrees of freedom in the model. The total number of elements in the dam body is 184812, and the number of nodes is 36417. The foundation is modelled with 260900 elements, with 82321 nodes. The nodes at the outer and bottom surfaces of the foundation are constrained along the normal to the surface. Figure 2 shows the different construction stages of the dam body. The rock-fill phases are divided in a upstream half well-graded rockfill and a downstream half of poorly graded rockfill.
Figure 1. Finite element model of the dam body and foundation
The concrete slab is modelled with shell elements. The dam body has a complex shape, which cannot be easily meshed with a mapped mesh. For this reason, an automatic mesh generator has been used, which generates tetrahedral elements. However, quadrilateral elements are more suitable for modelling the concrete slab, as these elements account for the shear-stiffness in the slab more accurately. Furthermore, an element size smaller than 6 m is required in the concrete slab, for a more appropriate description of the failure behaviour of the slab. As a result, the quadrilateral mesh of the concrete slab, with 2.5 m element size, and the mesh of the rock fill are not compatible. Special contact elements that simulate the frictional interaction of rock fill and concrete slab are used to connect these two meshes. Line-shell interface elements between the concrete slab panels simulate the vertical joints. The concrete slab is constructed in two stages: in the first stage the concrete slab is casted up to a height of 100 m. Then a concrete beam is built at this height, for carrying paving equipment. The beam is modelled with beams elements with a cross section of 1 m2. In the second stage the slab is casted until 178 m height. The thickness of the shell elements varies from 0.30 m at the crest of the dam until 0.735 m at the foot. (1942 m). The mesh of the concrete slab is shown in Figure 3.
Figure 2. Construction stages of the dam body
Figure 3. Mesh of the concrete slab
2.2 Material properties
Settlement/load data from two experiments, respectively for poorly graded and well graded basalt were available for characterizing the material. It was assumed that the experiments were confined compression tests, and that the material follows the Cam-clay plasticity model, with exponential elastic behavior and explonential plastic hardening. The material parameters derived for the basalt are summarized in Table 1. Figure 4 compares the data from laboratory experiments with the results obtained from DIANA analysis.
Elastic harding parameter Poisson's ratio Preconsolidation stress Friction angle Plastic hardening parameter Pressure shift
Poorly Graded 0.002 0.2 0.2 MPa 30o 0.02 0.1 MPa
Well Graded 0.001 0.2 1.4 MPa 30o 0.01 0.7 MPa
Table 1. Material parameters of the basaltic rockfill
Figure 4. Calibration curves for the rockfill material
For the concrete slab a fixed total strain crack model with linear softening and Thorenfeld compressive failure is adopted. The material parameters corresponding to the C20, which were used for the concrete slab, are listed in Table 2. A higher Young's modulus has been used in order to account for the effect of steel reinforcement grids.
Young's modulus Poisson's ratio Tensile strength Compressive strength Ultimate crack strain
C20 40000 MPa 0.2 1.25 MPa 20 MPa 0.001
Table 2. Concrete material parameters
For the foundation it is assumed that this behaves linear elastically, with Young's modulus 5.0 GPa and Poisson's ratio 0.2. For the contact elements between rockfill and concrete slab cohesion and dilatancy are assumed null, and the friction angle is 400. A tensile strength of 0.5 MPa is assumed for the interface elements in the vertical joints.
2.3 Construction stages and loading
The analysis includes 16 phases. Phase 1 corresponds to the situation before construction of the dam. In this phase only the foundation element are activate elements in the analysis, and the only load considered is the own weight of the foundation. Starting from Phase 2 until Phase 6, the dam body is built as specified in Figure 2. In Phase 7, the concrete slab is casted up to a height of 100 m and the concrete beam is built. From Phase 8 until Phase 10 the construction of the dam body is completed. In Phase 11 the concrete slab is casted until the final height. From Phase 12 until Phase 16 the reservoir is impounded, and the water levels reach 85 m, 105 m, 120 m, 125 m and 138 m.
Figure 5. Results at the end of Phase 7
Figure 6. Results at the end of Phase 10
Figure 7. Results at the end of Phase 11
3 Results
The analysis was performed on a dual Intel Xeon X5550 LINUX system. The calculation time is about 3.5 hours. For sake of space, only part of the results for the analysis conducted assuming well graded rockfill and C20 concrete type are shown in this paper.
In Figure 5 are the results of Phase 7, when the first casting of the slab is completed. At the left is the geometry of the active part of the model, at the top right is the contour plot of the vertical stresses in the rock fill, at the bottom right is the crack plot in the concrete slab. But in this stage of the analysis hardly any cracks were found. The cracks are represented with discs laying on the crack surface. The different colours of the discs correspond to different crack strains. Red corresponds to a crack strain of larger then the ultimate crack strain 1•10-3, namely to a crack opening of 3.0 mm.
At the end of Phase 10, when the dam body has been completed, but only the lower half of the slab is present, cracks appear at the lateral ends of the concrete slab, as shown in Figure 6. The detail picture in the lower-right-hand of figure 6 shows the orientation of the cracks, which are mainly in vertical direction. These cracks are caused as result of the ongoing elevation of the rock-fill after the lower half of the concrete has already been put in place. As result of the ongoing elevation of the rockfill the slab is pushed downward, leading to tensile loading at the lateral ends and compressive horizontal stresses in the central part.
However, further cracking occurs in Phase 11, after the concrete slab has been completely casted, see Figure 7. In this phase the crack-strain in the lateral ends of the lower slab is reduced already (now blue, before green) as result of the load of the top-half of the slab.
In Phase 12, which corresponds to first impounding of the reservoir (water level 85 m), cracks form also at the base of the concrete slab, as consequence of the bending induced by the hydrostatic pressure.
At the end of the second impounding the water level is at the height of the concrete beam (Phase 13). In this phase a horizontal crack at the location of the beam is found, starting at the left-side of the slab and diagonal cracks parallel to the plinth in the lower slab were found. These crack patterns agree very well with observations. The principal stresses at the top-face in the slab in this stage are shown in the lower-left-hand picture of figure 8. Blue represent compressive stresses and red tensile stresses. The picture shows the high compressive stresses in lateral direction in the central part of the lower slab up to 18 MPa, where as the stresses in the upper slab are considerable lower, because the lower slab was already loaded at the time that the upper slab was constructed. The lower-right hand picture of figure 8 displays joint openings (red) and compactions (blue). In this phase the maximum joint opening is 0.5 cm.
During the sequent phases, cracks that have formed in the previous phase tend to close, and new discrete vertical cracks are initiated at the lateral ends of upper-slab when the reservoir is completely full.
Figure 8 and Figure 9 show the results in Phase 13 and Phase 16. The bottom right-hand pictures show the contour plots of the joints openings, and of their relative displacement normal to the concrete slab. Also the deformed shape of the concrete slab is shown. From the pictures of the vertical displacements the transition from well-graded rockfill (up-stream half of dam) and poorly graded rockfill (down-stream half of dam) can be recognized.
Figure 8. Results at the end of Phase 13
Figure 9. Results at the end of Phase 16
4 Conclusions
In this paper a concrete faced rockfill dam has been modeled in 3D and analyzed with the finite element package DIANA. Nonlinear compaction of the rockfill, effects of the construction stages, frictional slip between rock-fill and concrete slab, cracking and crushing of concrete, opening and out of plane slipping of the vertical joints are taken into account. The results of the numerical analysis show that the general deformation of and stresses in the dam can be well predicted with this model, as well as the most important observed crack-patterns. The analysis predicts strong lateral compaction stresses (18 MPa) in the lower half of the slab, which remain under the failure stress of 20 MPa and as a consequence the observed compressive failure in one of the central slabs was not predicted. When the compressive failure-stress of the concrete would be lower in practice then the applied value of 20 MPa, the model would be able to predict this compressive failure, leading to larger displacements and joint-openings.
References
[1] C. Marulanda and P. Anthiniac, Analysis of a Concrete Faced Rockfill Dam including Concrete Face Loading and Deformation, 10th Benchmark Workshop on Numerical Analysis of Dams, September 16-18, 2009, Paris, France. International Commission of Large Dams (ICOLD).
[2] DIANA User's Manual, Release 9.3.
1hwe
Type In proceedings
Author Gerd-Jan Schreppers, Giovanna Lilliu
Year 2009 - 10th Benchmark Workshop on Numerical Analysis of Dams, ICOLD
Keywords CFRD, Cracking, 3D
Abstract
Several concrete faced rockfill dams in the world present cracks in the concrete face. In this paper the authors make an attempt to predict formation of cracks in one of such dams, the Mohale dam in Lesotho, South Africa. Foundation of the dam, dam body and the concrete slab are modelled in 3D. A Cam-clay plasticity model with hardening is adopted for the rockfill. Contact bewteen the concrete face and rockfill is modelled with contact elements, with a Coulomb friction material constitutive model. Interface elements are used to model the vertical joints among the 37 panels that form the concrete face. For the concrete face a total strain crack model in combination with crushing is adopted. In the analysis the different construction stages have been considered, as well as the different impoundment stages. The results shown in this paper are displacement and stresses in the rockfill and the concrete face, crack patterns and crack strains in the concrete face, and openings of the vertical joints.
1 Introduction
In CFRDs, settlements of the rockfill during and after construction can cause deformation and cracking of the concrete face. To prevent this, empirical rules have been formulated for controlling grading of the rockfill and compaction conditions. However, as higher and higher CFRDs are built in the world, numerical analysis is necessary to validate the empirical rules. Due to the complex physical mechanisms involved in the interaction of the different structural elements in a CFRD, and the need to consider 3D effects, there are not many comprehensive examples of numerical analysis of CFRDs. This has motivated the ICOLD Committee on Computational Aspects of Analysis and Design of Dams to propose the numerical analysis of a CFRD as one of the themes for the 10th Benchmark Workshop on Numerical Analysis of Dams [1]. Object of this benchmark is the Mohale dam in Lesotho, South-Africa. This is a 145 m high CFRD, with a crest length of 600 m, a concrete face surface of 73400 m2 and a total fill volume of approximately 7.5 million m3. The dam was built of basalt rockfill. After the reservoir was completely impounded, significant dam movements occurred and cracks developed in the concrete face, which caused leakage. Information provided in [1] is not sufficient for a quantitative comparison of numerical predictions and actual deformation and crack status in the Mohale dam. Nevertheless, this exercise has offered the authors the possibility to test the capability of the finite element package DIANA [2] to model the behaviour of CFRDs.
2 Modelling aspects
2.1 Finite Element Model
The finite element model of the dam body and the foundation is shown in Figure 1. The dam body is modelled with 4-node tetrahedral elements with 6 m edge size. This element size is chosen for limiting the number of degrees of freedom in the model. The total number of elements in the dam body is 184812, and the number of nodes is 36417. The foundation is modelled with 260900 elements, with 82321 nodes. The nodes at the outer and bottom surfaces of the foundation are constrained along the normal to the surface. Figure 2 shows the different construction stages of the dam body. The rock-fill phases are divided in a upstream half well-graded rockfill and a downstream half of poorly graded rockfill.
Figure 1. Finite element model of the dam body and foundationThe concrete slab is modelled with shell elements. The dam body has a complex shape, which cannot be easily meshed with a mapped mesh. For this reason, an automatic mesh generator has been used, which generates tetrahedral elements. However, quadrilateral elements are more suitable for modelling the concrete slab, as these elements account for the shear-stiffness in the slab more accurately. Furthermore, an element size smaller than 6 m is required in the concrete slab, for a more appropriate description of the failure behaviour of the slab. As a result, the quadrilateral mesh of the concrete slab, with 2.5 m element size, and the mesh of the rock fill are not compatible. Special contact elements that simulate the frictional interaction of rock fill and concrete slab are used to connect these two meshes. Line-shell interface elements between the concrete slab panels simulate the vertical joints. The concrete slab is constructed in two stages: in the first stage the concrete slab is casted up to a height of 100 m. Then a concrete beam is built at this height, for carrying paving equipment. The beam is modelled with beams elements with a cross section of 1 m2. In the second stage the slab is casted until 178 m height. The thickness of the shell elements varies from 0.30 m at the crest of the dam until 0.735 m at the foot. (1942 m). The mesh of the concrete slab is shown in Figure 3.
Figure 2. Construction stages of the dam bodyFigure 3. Mesh of the concrete slab2.2 Material properties
Settlement/load data from two experiments, respectively for poorly graded and well graded basalt were available for characterizing the material. It was assumed that the experiments were confined compression tests, and that the material follows the Cam-clay plasticity model, with exponential elastic behavior and explonential plastic hardening. The material parameters derived for the basalt are summarized in Table 1. Figure 4 compares the data from laboratory experiments with the results obtained from DIANA analysis.
Elastic harding parameter Poisson's ratio Preconsolidation stress Friction angle Plastic hardening parameter Pressure shift
Poorly Graded 0.002 0.2 0.2 MPa 30o 0.02 0.1 MPa
Well Graded 0.001 0.2 1.4 MPa 30o 0.01 0.7 MPa
Table 1. Material parameters of the basaltic rockfill
Figure 4. Calibration curves for the rockfill materialFor the concrete slab a fixed total strain crack model with linear softening and Thorenfeld compressive failure is adopted. The material parameters corresponding to the C20, which were used for the concrete slab, are listed in Table 2. A higher Young's modulus has been used in order to account for the effect of steel reinforcement grids.
Young's modulus Poisson's ratio Tensile strength Compressive strength Ultimate crack strain
C20 40000 MPa 0.2 1.25 MPa 20 MPa 0.001
Table 2. Concrete material parameters
For the foundation it is assumed that this behaves linear elastically, with Young's modulus 5.0 GPa and Poisson's ratio 0.2. For the contact elements between rockfill and concrete slab cohesion and dilatancy are assumed null, and the friction angle is 400. A tensile strength of 0.5 MPa is assumed for the interface elements in the vertical joints.
2.3 Construction stages and loading
The analysis includes 16 phases. Phase 1 corresponds to the situation before construction of the dam. In this phase only the foundation element are activate elements in the analysis, and the only load considered is the own weight of the foundation. Starting from Phase 2 until Phase 6, the dam body is built as specified in Figure 2. In Phase 7, the concrete slab is casted up to a height of 100 m and the concrete beam is built. From Phase 8 until Phase 10 the construction of the dam body is completed. In Phase 11 the concrete slab is casted until the final height. From Phase 12 until Phase 16 the reservoir is impounded, and the water levels reach 85 m, 105 m, 120 m, 125 m and 138 m.
Figure 5. Results at the end of Phase 7
Figure 6. Results at the end of Phase 10
Figure 7. Results at the end of Phase 11
3 Results
The analysis was performed on a dual Intel Xeon X5550 LINUX system. The calculation time is about 3.5 hours. For sake of space, only part of the results for the analysis conducted assuming well graded rockfill and C20 concrete type are shown in this paper.
In Figure 5 are the results of Phase 7, when the first casting of the slab is completed. At the left is the geometry of the active part of the model, at the top right is the contour plot of the vertical stresses in the rock fill, at the bottom right is the crack plot in the concrete slab. But in this stage of the analysis hardly any cracks were found. The cracks are represented with discs laying on the crack surface. The different colours of the discs correspond to different crack strains. Red corresponds to a crack strain of larger then the ultimate crack strain 1•10-3, namely to a crack opening of 3.0 mm.
At the end of Phase 10, when the dam body has been completed, but only the lower half of the slab is present, cracks appear at the lateral ends of the concrete slab, as shown in Figure 6. The detail picture in the lower-right-hand of figure 6 shows the orientation of the cracks, which are mainly in vertical direction. These cracks are caused as result of the ongoing elevation of the rock-fill after the lower half of the concrete has already been put in place. As result of the ongoing elevation of the rockfill the slab is pushed downward, leading to tensile loading at the lateral ends and compressive horizontal stresses in the central part.
However, further cracking occurs in Phase 11, after the concrete slab has been completely casted, see Figure 7. In this phase the crack-strain in the lateral ends of the lower slab is reduced already (now blue, before green) as result of the load of the top-half of the slab.
In Phase 12, which corresponds to first impounding of the reservoir (water level 85 m), cracks form also at the base of the concrete slab, as consequence of the bending induced by the hydrostatic pressure.
At the end of the second impounding the water level is at the height of the concrete beam (Phase 13). In this phase a horizontal crack at the location of the beam is found, starting at the left-side of the slab and diagonal cracks parallel to the plinth in the lower slab were found. These crack patterns agree very well with observations. The principal stresses at the top-face in the slab in this stage are shown in the lower-left-hand picture of figure 8. Blue represent compressive stresses and red tensile stresses. The picture shows the high compressive stresses in lateral direction in the central part of the lower slab up to 18 MPa, where as the stresses in the upper slab are considerable lower, because the lower slab was already loaded at the time that the upper slab was constructed. The lower-right hand picture of figure 8 displays joint openings (red) and compactions (blue). In this phase the maximum joint opening is 0.5 cm.
During the sequent phases, cracks that have formed in the previous phase tend to close, and new discrete vertical cracks are initiated at the lateral ends of upper-slab when the reservoir is completely full.
Figure 8 and Figure 9 show the results in Phase 13 and Phase 16. The bottom right-hand pictures show the contour plots of the joints openings, and of their relative displacement normal to the concrete slab. Also the deformed shape of the concrete slab is shown. From the pictures of the vertical displacements the transition from well-graded rockfill (up-stream half of dam) and poorly graded rockfill (down-stream half of dam) can be recognized.
Figure 8. Results at the end of Phase 13
Figure 9. Results at the end of Phase 16
4 Conclusions
In this paper a concrete faced rockfill dam has been modeled in 3D and analyzed with the finite element package DIANA. Nonlinear compaction of the rockfill, effects of the construction stages, frictional slip between rock-fill and concrete slab, cracking and crushing of concrete, opening and out of plane slipping of the vertical joints are taken into account. The results of the numerical analysis show that the general deformation of and stresses in the dam can be well predicted with this model, as well as the most important observed crack-patterns. The analysis predicts strong lateral compaction stresses (18 MPa) in the lower half of the slab, which remain under the failure stress of 20 MPa and as a consequence the observed compressive failure in one of the central slabs was not predicted. When the compressive failure-stress of the concrete would be lower in practice then the applied value of 20 MPa, the model would be able to predict this compressive failure, leading to larger displacements and joint-openings.
References
[1] C. Marulanda and P. Anthiniac, Analysis of a Concrete Faced Rockfill Dam including Concrete Face Loading and Deformation, 10th Benchmark Workshop on Numerical Analysis of Dams, September 16-18, 2009, Paris, France. International Commission of Large Dams (ICOLD).
[2] DIANA User's Manual, Release 9.3.
1hwe
