1 Nonlinear Static Analysis of Shuibuya Dam in China World s Highest CFRD Ye Zhu School of Hydraulic Engineering, Dalian University of Technology, Dalian, Dalian Liaoning, , China Lu Lu The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning, , China ABSTRACT Since there are lots of technical problems in high CFRD, it is necessary to figure out how dams move under high stress. Shubuya CFRD is the highest CFRD in the world. It is the representative of high concrete face rocfill dam. This paper presents the results of simulations on Shuibuya CFRD. During numerical modeling, the paper selects Duncan E-B model as the elastic constitutive model of rocfill; selects Goodman element to simulate the contact relationship between the concrete slab and the cushion, and the peripheral joints between the concrete slab and the plinth. The simulation of the dam loads steps is almost as the same as the actual situation. The relevance of the model seems acceptable, It is significant for further numerical analysis of high CFRD. Ediror s note: CFRD: Concrete Faced Rocfill Dam. KEYWORDS: CFRD, Nonlinear Static Calculation, Prototype observation data, Duncan E-B model, Goodman element. INTRODUCTION Concrete faced rocfill dam (CFRD) is developing very fast these years. The symposium Decade of CFRD in China was convened in It shows that people has already formed dam technologies through accumulating experience from dam design, construction and operation. However there are still ey technologies especially when dams are higher than 180m, need to be further studied, such as engineering properties, constitutive model of rocfill, parameter selection etc. The use of rocfill as a construction material of CFRDs started during the second half of the nineteenth century with the building of timber-faced mining dams in California . Since then, during construction and operation of large rocfill dams in the twentieth century, a large number of field observations concerning rocfill behavior have been collected, as a result studies about CFRDs numerical simulation can be compared and verified. This paper simulates Shuibuya CFRD during construction and initial impounding, and compares with the prototype observation data. Shuibuya CFRD was constructed in Badong City in Hubei Province, China, The crest elevation is 409 m, the normal water level of the reservoir is 400 m, the maximum dam height is 233 m, the upstream dam and the downstream slope is 1:1.4. The maximum cross-section and
2 Vol. 21 , Bund construction process of the Shuibuya CFRD is shown in Fig.1, the solid lines represent the material partition, and the dotted lines represent the construction partition. Figure 1: Dam material partition and the construction schedule This paper combines with the experiences of predecessors, and uses three-dimensional nonlinear FEM [2,3] to obtain the stress and movement of the rocfill zone, the face slab deformation and stress distribution, relative deformation of slab joints and peripheral joints. NUMERICAL SIMULATION FEM model The FEM model grid of the entire dam comprises mainly eight nodes of hexahedral elements, partly using prism elements for the boundary zone. FEM model grid and the maximum cross-section of Shuibuya CFRD are shown in Figure 2. The loading process of the FEM model is in accordance with the actual construction schedule. Figure 2: FEM model grid (left) and the maximum cross-section (right) Material model and parameters Constitutive model of rocfill As a support structure of the dam, rocfill usually studied can be modelled with the continuum hypothesis, because most geomaterials are composed of a large quantity of particles whose size is negligible compared to the size of the structure. Mostly linear elastic and nonlinear elastic models have been used to characterize the behavior of rocfill materials. Hyperbolic models are often adopted to depict the behavior of rocfill
3 Vol. 21 , Bund materials . Recently, the elastoplastic constitutive model based on disturbed state concept has been used for characterization of the behavior of a roc and rocfill material . This paper selects Duncan E-B model  as the constitutive model of the rocfill. It is a nonlinear elastic hyperbolic model with a large quantity of using experiences and is easily to be realized in the procedure. n σ R ( )( ) 2 f σ1 σ3 1 sinf Tangent modulus of elasticity: 3 Et = Kpa 1 p a 2ccosf+ 2σ3sinf (1) Tangent Bul modulus: m σ3 t = bp a B K a p (2) In which R f = Damage ratio; K= Cardinal number of tangent modulus; n = Tangent modulus Index; P a = Unit pressure; c = Cohesion of material; ϕ = Angle of internal friction; K =Dimensionless bul modulus; m = Dimensionless modulus index number; σ 1 = b Axial stress; σ 3 = Confining pressure; σ3 For coarse-grained soil, if c = 0, ϕ = ϕ 0 Δϕlg (3) Pa In which ϕ 0 = ϕ when σ 3 = Pa ; ϕ = Parameter of ϕ which decreases withσ 3 ; According to IWHR triaxial test results, Duncan E-B model parameters of Shuibuya rocfill material are shown in Table 1. Table 1: Duncan E-B model parameters of Shuibuya rocfill material Filler ρ ϕ ( ) d 0 Δϕ 0 ( ) K n R f K b m Cushion Transition material Main rocfill Secondary rocfill Constitutive model of concrete face slab The dam uses patchwor of reinforced concrete slabs as seepage control structure. The operation of the dam is affected by the stress and deformation of slabs. Concrete face slabs are undergoing pressure along three inds of directions: the dam axis direction, the upstream slope direction and normal direction of hydraulic pressure. There are same features of concrete: (a)the tensile strength and compressive strength is basically same, when concrete undergoing one-way loads; (b)concrete compressive strength undergoing double-way pressure is 1.25 times the value of undergoing one-way pressure; (c)when concrete undergoing double-way tension, the strength is the same as undergoing one-way tension; (d)the relation curve between the stress and strain of concrete is not linear when it undergoing complex stress; (e)when concrete undergoing both pressure and tension, the strength decreases significantly. Jiang proposed that as long as the concrete has not been destroyed , the linear elastic model can be used. But if the deformation is larger, the linear elastic model should be used piecewise.
4 Vol. 21 , Bund This paper uses piecewise linear elastic model to simulate concrete face slab, and uses linear elastic model to simulate the plinth. The initial value of concrete elastic modulus is MPa, Poisson's ratio γ = Constitutive model of contact materials The difference of material stiffness between concrete face slab and the cushion is huge, so it is important to select a appropriate contact element in order to calculate the slab deformation and stress distribution more reasonable. This paper selects Goodman element  to simulate the contact surface for simplicity. σ τ τ y yx yy yx Δu Δu yy = 0 0 Δu (4) yx Under the condition of linear elastic hypothesis, shear stress is proportional to the relative displacement, and the scale factor which is called the tangential stiffness of contact surface, is defined as: ij yx n 2 1 σ y R f τ yx = 1ρ wg 1 Pa (5) c + σ ytanδ n 2 1 σ y R fsτ = 1ρ wg 1 (6) Pa c + σ ytanδ In which yx, = Tangential shear stiffness modulus of the contact surface. The first and the second subscript represent normal direction and stress direction respectively; σ y = The normal stress of contact surface; ρ w = The density of water; g = Acceleration of gravity; K1,n1, R fs and δ = The parameter of the model, they can be determined by direct shear test. The units of the stiffness coefficient is KPa/m.The normal stiffness becomes large when the contact surface was undergoing pressure, and it becomes smaller when the contact surface was undergoing tension. In this paper c = 0, δ = 36.6, K 1 = 4800, n = 0.56, R f = Constitutive model of joint material The joint of CFRDs comprises peripheral joint and slab joint. Generally rocfill dam has three water stops: On the top of the face slab, using flexible or non-sticy filler; At the bottom of the face slab, using copper water stop; In the middle of the slab, using asphalt plan embeded joint to stop water. This paper selects Goodman element to simulate the joint element. σ τ τ z zy zx zx zx zz 0 0 Δu zz = 0 zy 0 Δu zy (7) 0 0 Δu Under the condition of small strain, here gives the stiffness relationships:
5 Vol. 21 , Bund zz = 650a b zy = 225a zx = 608a b In which a = The number of the copper water stops; b = The number of the others. (8) (9) (10) THE CALCULATE RESULTS OF FEM Crest settlement and face deformation are two parameters commonly used to quantify the deformation characteristics and performance of CFRDs. More attention was paid to the calculation of these two parameters. The stress and movement of rocfill The movement and stress in the maximum cross-section of the dam is shown in Figure 3~5. The maximum stress and displacement value is shown in Table 2. Table 2: The maximum stress and displacement value in the maximum cross-section Woring conditions Construction Initial impounding Upstream Downstream Displacement Settlement ( cm ) Left side of the abutment Right side of the abutment Stress( MPa ) Major principal stress Minor principal stress Figure 3: Horizontal displacement:construction (left) initial impounding (right)(cm) Figure 4: Settlement i: construction (left) initial impounding (right) (cm)
6 Vol. 21 , Bund Figure 5: Major principal stress: construction (left) initial impounding (left)(10kpa) During completion, the largest settlement occurred in the middle of the dam, 1/2 dam high. The horizontal displacement to upstream and downstream is divided by the dam axis. Downstream displacement value is greater than that of upstream. During initial impounding, displacement in most dam areas is deflected to the downstream direction, influenced by water pressure. The largest displacement occurred at the downstream side of the dam axis, 1/2 dam high. The stress and deformation of face slab The deformation and stress of the concrete face slab is shown in Figure 6~8. The maximum stress and deformation value of the slab is shown in Table 3. Table 3: The maximum stress and deformation of the slab Woring conditions Construction Initial impounding The deflection(cm) Stress( MPa) Dam axial direction Slab slope direction Tensile Compressive Tensile Compressive Figure 6: The deformation of the face slab: construction (left) initial impounding (right) DEFORMATION Deformation value is positive if it is downward perpendicular to the upstream side. Concrete face slab deformations typically are greatest near the upper part of the slope and near the toe as a result of crest settlement and toe bulging, respectively, during construction, and near the mid slope during initial impoundment . Based on measured deformation distributions,
7 Vol. 21 , Bund CFRD face slab deformation patterns can be characterized as a D-shaped distribution  with the maximum deformation near the center of the face slab(e.g., Foz do Areia Dam) or a B-shaped distribution  with large deflections at the center of the face slab and near the top part of the slab(e.g., Cetana Dam). Here the face slab deformation patterns can be characterized as a B-shaped distribution during construction and a D-shaped distribution during initial impounding. The maximum value of the deformation occurred near the center of the face slab during initial impoundment. The maximum deformation value is 65.70cm Figure 7: Stress in slab slope direction(left), dam axial direction(right),10kpa The face slab stress The face slab stress is positive if it is compressive. In the slab slope direction: It is basically compressive during construction, maximum value is 4.50Mpa. The tensile stress occurred on both sides of the abutment, also the dam crest, the value is small. Stress value in middle became larger during initial impounding. Tensile stress occurred at edge, the value is larger compared to construction; In dam axial direction: during construction, compression stress occurred in middle, slab was undergoing tension at edge and top. During initial impounding, compression stress value became larger in middle, tensile stress on both sides of abutment increased. Slab stress mainly depends on the movement of the dam body and the effect of hydraulic pressure, also influenced by the contact surface. As these special parts can t be simulated well at present, slab stress is now given for reference only, and it still needs to be macro-controlled. Relative displacement of joint The maximum relative displacement value of joint is shown in Table 4. Table 4: The maximum relative displacement of joint Woring condition Construction Initial impounding Peripheral joint(cm) Slab joint(cm) Tangential Vertical Dam axial Compression Tension
8 Vol. 21 , Bund Peripheral joint During initial impounding, the joint was basically tensioned, Overall the value of the tensile joint during construction is less than it during initial impounding. Slab joint During construction, there is basically no relative displacement on the top. The distribution of the joint relative displacement during initial impounding is basically the same as it during construction. The relative displacement value was increased. The largest compression joint occurred at the left side of the abutment, 1/3 dam high. COMPARED WITH ACTUAL DAM Shuibuya dam safety monitoring based on topographic, geologic conditions of the dam site, construction of the dam structure and characteristics of the design layout. There are 5 measuring lines setting on the maximum dam section, elevation of 235m, 265m, 300m, 335m and 370m. The deformation was monitored at the in situ measurement points as shown in Figure 8. In this figure, SV01-(1~38) refer to settlement instruments, SE01-(1~38) refer to horizontal-displacement instruments. design flood level parapet wall top of the slab nomal water level SE ~ WS SV ~38 dead water level SE ~35 WS SV ~35 SE ~ WS SV ~ SE ~22 WS SV ~22 SE01-1-1~ WS SV01-1-1~ Figure 8: Layout of in situ instrument measurement scheme Figure 9~13 present the settlement and horizontal displacement process lines of those five levels. Displacement is positive if the dam moving downstream. Given by The Damming Technique Of Shuibuya CFRD. The project was supported by national engineering technology research center of dam safety.
9 Vol. 21 , Bund Figure 9: Settlement (left) and horizontal displacement(right) process lines (235 m) Figure 10: Settlement (left) and horizontal displacement(right) process lines (265 m) Figure 11: Settlement (left) and horizontal displacement(right) process lines (300 m) Figure 12: Settlement (left) and horizontal displacement(right) process lines (340 m)
10 Vol. 21 , Bund Figure 13: Settlement (left) and horizontal displacement(right) process lines (370 m) It is generally believed settlement is more reliable in the prototype observation results. This paper collects dam settlement observation data before January 2007, when the dam was completed, rheological deformation had not occurred, gives the measured settlement distribution in maximum cross-section of the dam, as shown in Figure Figure 14: Actual dam (solid blac line), simulation (dotted red line)(cm) The relevance of the model seems acceptable, considering that the settlement values obtained in the simulations are in the same order of magnitude as the actual dam. CONCLUSION The paper simulates Shuibuya CFRD during construction and initial impounding, and compares the result with the actual dam, especially during construction. The relevance of the model seems acceptable, Due to the boundary is more complex, the processing of the simulation need to be improved. The results obtained in this paper can also be used as the foundation of the further study such as creep, etc. ACKNOWLEDGEMENTS This research was supported by the National Science Foundation of China (Grant No ) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No ). These financial supports are gratefully acnowledged. REFERENCES 1. Penman, A. D. M. (1992). Rocfill for embanment dams. Raul J. Marsal Volume (eds E. Ovando, G. Auvinet, W. Paniagua & J. DõĀaz),
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