The 3rd National Graduate Conference (NatGrad2015), Universiti Tenaga Nasional, Putrajaya Campus, 8-9 April 2015.
APPLICATION OF 2D AND 3D FINITE ELEMENT MODELLING OF GRAVITY DAMS UNDER SEISMIC LOADING Khaled Ghaedi Department of Civil Engineering, University of Malaya, 50603, Malaysia. Email:
[email protected] Ahad Javanmardi Department of Civil Engineering, University of Malaya, 50603, Malaysia. Email:
[email protected] Meisam Gordan Department of Civil Engineering, University of Malaya, 50603, Malaysia. Email:
[email protected] Hamed Khatibi Department of Civil Engineering, University of Malaya, 50603, Malaysia. Email:
[email protected] Abdollah Mohammadi Department of Civil Engineering, Universiti Tenaga National, Malaysia. Email:
[email protected]
Abstract—The Finite Element Modelling (FEM) is widely used in various type of analysis by numerous researchers and engineers worldwide. In present study, a challenge is made to consider dams under seismic loading deliberating hydrostatic effect of reservoir water using nonlinear dynamic analysis. Therefore, it tries to take deepest section of dams in 2 and 3 dimensions to show the effect of FE modelling during analysis. For this aim, Kinta Roller Compacted Concrete (RCC) gravity dam in Malaysia has been selected as case study and the bidirectional Koyna earthquake accelerations, 1967 are imposed to the dam. The outcomes show that the dam response is almost similar in terms of displacement and damage analysis under seismic loading, however, the stress responses are not same for different aforementioned models. Keywords— FEM, Seismic analysis, Earthquake, RCC Dam
1 Introductio
The FE modelling technique is implementing for different structures including dams. Dams are one of most important structures that have to analyze in secure manners. Present paper tries to show the effect of 2D and 3D FE modelling on dams’ structure. A numerous researchers have been considered various aspects of dams’ analyses however, it seems the comparison of the FEM application in 2D and 3D has been ignored. For instance, a especial 3D Finite Element (TDFE) program was developed in order to analyze the Concrete Arch Dams (CAD) and seismic response. The program includes two kinds of continuum mechanics non-linear (CMNL) methods such as Elasto-Plastic and Non-Orthogonal smeared-crack models. The development introduced initially crack with high accuracy of a model [1]. A study on non-linear seismicresponse of concrete gravity dams was done. Dams were
subjected to both near-fault and far-fault movement of the ground with dam-reservoir- foundation interaction considering sediment [2]. The solution for engineering problems to use fracture mechanics, crack modeling, damping implementation, and computational algorithm were discussed. The development of the crack-embedded elements obtained an analogy with the computational plasticity for dynamic study of crack propagation in concrete. The analogy enabled engineers to apply the return-mapping algorithm as computational plasticity for the nonlinear dynamic analysis of crack propagation in concrete [3]. The Size effects law Applicability which result from linear elastic failure mechanics to gravity dams. A comparison was made between the estimates, based on the overall strength and fracture mechanism by means of simplified limit state approach, cohesive crack methods, and from equivalent elastic analyses. [4]. The presented work proposed the strange role to stabilize crack development for conventional structural dimensions in construction of dams. A numerical pattern based on non-linear crack band theory introduced to inspect the 2D seismic fracture response of concrete dams. Moreover, Finite Element remesh technique presented for the crack front by changing the edge pairs of the crack elements candidates to be corresponding to principal tensile stresses for better adapt the crack development in concrete [5]. The concrete gravity dams’ response of the seismic fracture reviewed after considering the effects of the interaction between dam and reservoir. A co-axial-rotating crack model (CRCM) that contains the strain softening factor selected for concrete materials and the effect of cracking on the concrete gravity dam under seismic loading was discussed [6]. A study used the FEM and employed the IDCE (incremental displacement constraint equation) modeling to handle all types of motions of cracks. Some calculations revealed i.e. occurrence of jumping and rocking, coupling between peak
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The 3rd National Graduate Conference (NatGrad2015), Universiti Tenaga Nasional, Putrajaya Campus, 8-9 April 2015.
rocking direction and the residual sliding direction and the big damping effect of multiple cracks on the peak residual sliding [7]. The temperature distribution simulated by means of TDFERMM (3D-finite-element relocating mesh method), for 3rd grader roller compacted-concrete, (TGRCC) dam with dissimilar materials and thicknesses of impassable layer, considering the conventional concrete, grader enrich concrete (GEVRCC) and 2nd grader roller compacted concrete, (SGRCC) during the period of construction. The computed results demonstrated that different kinds of impervious layer will not have any impact on the dam temperature distribution [8]. A model for dynamic contact between two surfaces broken apart with a crack and simulation of effect of the earthquakeresistant reinforcement on the cracked dam were developed [9]. The effects of different sizes and shapes of galleries inside dams was investigated and obtained results showed the galleries have significant influences on the dam bodies in terms of cracking, stresses, displacements and accelerations [10]. A gravity dam was built in Portugal with height of 52 m by means of roller compacted concrete (RCC) technique and a seismic acceleration was applied. With a method i.e. using program EAGD-84, vertical and horizontal accelerations of the seismic activity, allowing Maximum Expectable Earthquake (MEE) and Base Design Earthquake was considered. The obtained results showed the nodal crest displacements and the stress at chosen elements, to evaluate the structural safety of the RCC dam [11].
Figure 1: 2D FEM
Through review of the literature it seems lack of investigation of the 2D and 3D gravity dam modeling is felled. In this paper, an attempt is done to show the difference percentage of the 2D and 3D modeling of non-arch dams can approximately be negligible. For this aim, Kinta dam located in Malaysia is chosen as a case study. Meantime, a bidirectional earthquake excitation is applied to models using Finite Element (FE) software, Abaqus.
2 Finite Element Model and Material Properties
To conduct the seismic analysis, a model of the dam is done by means of FE software, Abaqus. 2D and 3D isoparametric elements with four and 8 nodes is implemented to discretization of the Kinta dam. The details of discretization can be seen in table 1.
Figure 2: 3D FEM The used material properties for dam body is indicated in Table 2 [12]. Table 2: Used material properties
Table 1: Finite element discretization Block
Nodes
Elements
Dam (2D)
609
560
Dam (3D)
6061
5040
The Finite Element Model (FEM) and geometric section of the dam in 2D and water level state is shown in Figure 1.Meanwhile, the 3D FEM of the dam is shown in Figure 2 as well.
Material properties
RCC Dam
Young modulus (N/m2)
0.23E+ 11
Poisson ratio v
0.2
Mass density
2386
Compressive (Mpa)
20
Tensile strength (Mpa)
2
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strength
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The 3rd National Graduate Conference (NatGrad2015), Universiti Tenaga Nasional, Putrajaya Campus, 8-9 April 2015.
Dynamic strength (Mpa)
Tensile
2.5
Allowable strength (Mpa)
tensile
3.2
3 Loading 3.1 Seismic Loading
In this study the bidirectional acceleration of the Koyna earthquake (India, 1967) is applied to the dam. The earthquake components in horizontal and vertical direction are shown in Figure 3.
Figure 5: Top and Bottom Nodal Displacement in 3D modelling As shown in Figure 4 and 5, the nodal displacement values of the dam for top and bottom nodes at upstream face are close to each other. The horizontal displacement of the dam for top and bottom nodes in 2D and 3D modelling is 4.83 cm, 2.09 cm, 5.47 cm and 2.09 cm. Thus, the difference of values between two modeling can surely be negligible. Regarding the relative displacement of the dam crest it can be seen that the maximum value is 3.95 cm and 4.61 cm for 2D and 3D modelling respectively. As values indicated, the difference of 16.7% is occurred for relative displacement for 3D modelling in compared to 2D modelling. The state of the relative displacement of the dam crest is indicated in Figure 6 and 7.
(a) Horizontal Component
(b) Vertical Component Figure 3: Koyna excitations (India, 1967)
4 Results and Discussions
Figure 6: Relative Displacement in 2D
4.1 Displacement Responses
The nodal displacement of the crest and bottom nodes of the dam at the upstream face is depicts in Figure 4 and Figure 5 for 2D and 3D modelling respectively.
Figure 4: Top and Bottom Nodal Displacement in 2D modelling
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Figure 7: Relative Displacement in 3D
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The 3rd National Graduate Conference (NatGrad2015), Universiti Tenaga Nasional, Putrajaya Campus, 8-9 April 2015. 4.2 Crack Tendency
The crack propagation of the dam body is occurred at the same zone for both 2D and 3D FE modelling. These patterns are indicated in figure 8 and 9 for 2D and 3D FE modelling. However, the severity of the damage level in 2D modelling appears more in compare to 3D modelling specially at the heel elements. The intensity of damage is due to the hydrostatic reservoir effect which has been applied to the dam.
From above Figures, it is noticeably obvious that the tensile damage occurred of the dam appears in the bottom zone (heel elements) and middle areas. For both cases the crack tendency develops in same level from upstream face to downstream face in horizontal direction. 4.3 Stress on Dam
The maximum stress contour lines for Kinta RCC dam in 2D and 3D model are illustrated Through Figure 10 to Figure 12. As indicated in these figures, the maximum stress for the 2D dam is 2.161 Mpa, whereas, this value is 2.469 Mpa while 3D model is considered. The 14.25% difference is obvious when that the modelling is taken change from 2D to 3D. The other point is that, the pattern of maximum principal stress of the dam for 3D model is not similar in both sides of the dam. Taking a look at Figure 11 and 12 shows this variety very well.
Figure 8: Crack Propagation of the Dam in 2D Modelling
Figure 10: Max. Principal Stress for 2D model
Figure 11: Max. Principal Stress for 3D model Figure 9: Crack Propagation of the Dam in 3D Modelling
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References [1]
R. Espandar and V. Lotfi, “Comparison of nonorthogonal smeared crack and plasticity models for dynamic analysis of concrete arch dams,” Comput. Struct., vol. 81, no. 14, pp. 1461–1474, Jun. 2003.
[2]
M. Akköse and E. Şimşek, “Non-linear seismic response of concrete gravity dams to near-fault ground motions including dam-water-sediment-foundation interaction,” Appl. Math. Model., vol. 34, no. 11, pp. 3685–3700, Nov. 2010.
[3]
H. Horii and S.-C. Chen, “Computational fracture analysis of concrete gravity dams by crack-embedded elements––toward an engineering evaluation of seismic safety,” Eng. Fract. Mech., vol. 70, no. 7–8, pp. 1029–1045, May 2003.
[4]
G. Bolzon, “Size effects in concrete gravity dams: a comparative study,” Eng. Fract. Mech., vol. 71, no. 13–14, pp. 1891–1906, Sep. 2004.
[5]
W. Guanglun, O. A. Pekau, Z. Chuhan, and W. Shaomin, “Seismic fracture analysis of concrete gravity dams based on nonlinear fracture mechanics,” Eng. Fract. Mech., vol. 65, 2000.
[6]
Y. Calayir and M. Karaton, “Seismic fracture analysis of concrete gravity dams including dam–reservoir interaction,” Comput. Struct., vol. 83, no. 19–20, pp. 1595–1606, Jul. 2005.
[7]
X. Zhu and O. a. Pekau, “Seismic behavior of concrete gravity dams with penetrated cracks and equivalent impact damping,” Eng. Struct., vol. 29, no. 3, pp. 336– 345, Mar. 2007.
[8]
H. Xie and Y. Chen, “Determination of the type and thickness for impervious layer in RCC dam,” Adv. Eng. Softw., vol. 36, no. 8, pp. 561–566, Aug. 2005.
[9]
S. Jiang, C. Du, and Y. Hong, “Failure analysis of a cracked concrete gravity dam under earthquake,” Eng. Fail. Anal., vol. 33, pp. 265–280, Oct. 2013.
[10]
K. Ghaedi, M. Jameel, Z. Ibrahim, and P. Khanzaei, “Seismic analysis of roller compacted concrete (RCC) dams considering effect of sizes and shapes of galleries,” KSCE J. Civ. Eng., vol. 19, no. 4, pp. 1–12, 2015.
[11]
G. Monteiro and R. C. Barros, “SEISMIC ANALYSIS OF A ROLLER COMPACTED CONCRETE GRAVITY DAM IN PORTUGAL,” in World Conference on Earthquake Engineering, 2008.
[12]
GHD, “Study of restrictions on RCC temperature, Stage 2 development of Ipoh water supply,” 2002.
Figure 12: Max. Principal Stress for 3D model at Other Side 5 Conclusion
In this paper an effort is done to assess the seismic response of dams using 2D and 3D FE modelling. For this purpose, Kinta dam located in Malaysia has been chosen and nonlinear time history analysis has been conducted. The obtained results has been presented in terms of top and bottom nodal and relative displacement, tensile crack pattern and maximum principal stress. Consequently, the following conclusions can be written:
Nodal displacement values of the topmost and lowest node of the dam are close in 2D and 3D modelling, however, the relative displacement of the dam in 3D is 16.7% greater than when the dam is modelled in 2D.
The crack propagation of Kinta dam in 2D and 3D FE modelling appears at the heel and middle zone of the dam.
The trend of cracking occurs in same level from upstream to downstream face in both 2D and 3D FE modelling.
The severity of the crack propagation of the dam in heel zone for 2D model is higher, nevertheless, in middle zone this intensity seems more for 3D model.
The value for maximum principal stress for 3D model is larger than 2D model by 14.25%.
It is obviously clear that the contour lines of stress is different in both sides of the dam for 3D model.
Based on presented discussion and conclusions, it recommends to analyze dams in 3D model to reach accurate results.
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The 3rd National Graduate Conference (NatGrad2015), Universiti Tenaga Nasional, Putrajaya Campus, 8-9 April 2015.
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