Cracking Analysis of High Concrete Gravity Dams Under Floodwater and Seismic EffectsJIA Chao, LI Yafei School of Civil Engineering Shandong UniversityJinan, Chinajiachao@REN Qingwen School of Civil Engineering Hohai UniversityNanjing, Chinarenqw@Abstract—As economic develops, energy demand is also increasing. The development of hydroelectric energy has become one of the important measures to deal with energy crisis. In order to develop hydropower, many high concrete dams are being built or about to build in China. These dams are often operating at high water level and in high seismic intensity region. Accident due to the high concrete dam failure may cause serious harm to the economic development and the safety of the people, so it has an important significance to study the security and stability of high concrete dam under high water level and seismic. In the paper, Longtan high concrete dam was studied as an example, the strain softening characteristic of dam concrete is considered using linear softening curve, and a smear crack model is selected for the dam concrete crack. The seismic fracture response of concrete gravity dams is researched by considering the effects of dam-reservoir interaction for different case. Two dimensional seismic numeric analysis was performed by using Koyna earthquake acceleration-time records in 1976 Dam concrete cracking range and cracking law under different water level and seismic time was discussed, the over load method was also used in the paper. From research the positions which easy to generate cracks are pointed out. The research result can provide useful reference for dam structure design and safety operation.Keywords-concrete gravity damt; Longtan high RCC dam; cracking;waterloading; seismic; overloading; nonlinear FEAI.I NTRODUCTIONRecently, with the rapid development of West to East Power Transmission Project and Western Development of China, a few number of high concrete dams are being constructed or going to be constructed in west-south and west-north China. These dams are often very high, operating at high water head, and in a complex geological site and high-frequent earthquake areas. They may cause catastrophic consequences such as loss of life and property if the dams fail. So studying the stability and safety of the dam has important significance.Dam concrete is low tension materials; concrete structures are prone to develop cracks. Extensive research has been performed over the last decades into the fracture behavior of concrete. Kaplan [1] suggested fracture thesis into concrete cracking. The main methods of fracture are theoretical analysis, experimental research and numerical analysis. Numerical analysis is suitable the problems that have arbitrary geometry and boundary conditions, so it has been used abroad in concrete cracking. Concrete constitutive model and the crack model are the key technologies to be solved of using the finite element method.As is well known, concrete exhibits strain softening in tension, leading to a complete loss of strength. For the strain-softening curve, many scholars have proposed their views, such as: Hillerborg’s linear softening curve, Peterson’s bilinear softening curve, Kang and Lin’s segment softening curve and Jiang Jianjing’s and Reinhardt’s exponential softening curves [2]. The approaches used to model the cracks in the finite element method can be divided into two categories. The first method, usually named discrete crack approach, models the crack by separating the nodes belonging to crack flanks; another model is so-called smeared crack approach, where the properties of the material in the zone of cracking are modified to represent the physical discontinuity introduced in a system by cracks [3].It is well established that many operating concrete dams present internal zones of extensive cracking or micro-cracking.A well-known hydropower expert in China named Pan Jiazheng affirmed that” There is no one dam without cracks in it” [4]. The origin of cracking in concrete dams may be found in the phases of design, construction or in operation. The reasons for cracking may be fold: thermal variations due to internal or external sources, seismic actions, irregular settlements of the foundation, and internal chemical reactions during the setting, hardening and life of the concrete, etc [5]. There have been a few dams that failed because of concrete cracks: Tamworth in Australian; Kolnbrein in Austria; Koyna in India; Hsinfengkiang in China and Pacoima in USA. Many scholars have made a lot of research on concrete dam cracking: CHEN Jianyun, LIN Gao, LI Jing [6]carried out the static-dynamic cracking effects on the Xiaowan arch dam based on the nonlinear concrete constitutive relations, and compared with the corresponding linear analysis. The results show that the nonlinearity of concrete can not be ignored. PAN Jianwen ，WENG Jinting，ZHANG Chuhan [7] applied plastic damage model of concrete, and the softening behavior of tensile strain was considered, to analyze the cracking of Dagangshan arch dam under the action of extremely strong earthquake. The results show that the dam needs reinforcement.The cracks in concrete structures come through micro-cracks to extensional cracks. It has significance on highNational Program on Key Basic Research (973 Program)(2007CB714104)978-1-4244-4813-5/10/$25.00 ©2010 IEEEconcrete dam’s security and stability to study the formation anddevelopment of cracks in concrete dams. The southwest of china is the high-frequent earthquake area. The earthquake occurs in Wenchuan on May 12, 2008 with magnitude 8 has caused enormous losses of lives and property. If the dam in these regions fails, not only causes direct economic losses, but also enormous indirect damage. The seismic performance of the dam must be taken into account during desiring period. In this paper, by employing numerical model based on Longtan dam in China, the effects of cracking on flood water and seismic response of the concrete gravity dam are studied. The results can give reference to the dam reinforcement and operation period.II. THEORETICAL BASISA. Material Model and Yield Criterion The mechanical behaviors of concrete and rock under general conditions are very complex and highly nonlinear. The isotropy elastic-plastic method is selected to simulate both concrete and rock. In order to prescribe the different mechanical properties of concrete and rock, choose different yield criteria for them. The Buyukozuturk [8] criterion is adopted for concrete in this paper. The yield function is as below: 2221133σγσβ−++=J J J f (1) Buyukozuturk suggested that:3=β ，2.0=γ (2) The Drucker-Prager criterion is for rock, and its yield function used in this paper as the following [9]:321σα−+=J I f (3)where:φφα2sin 33sin +=，φφσ2sin 3cos 3+=C , c is the cohesion and Ф is the internal frictional angle of rock.The concrete material model including the strain softening behavior for tension is selected. Use Hillerborg’s linear softening curve [10] this paper and its anisotropic stiffness matrix of the softening phase and the stress-strain relationship under global coordinates are deduced in paper [11]. The constitutive model of concrete is show in Fig. 1.B. Cracking ModelSmeared cracking is a continue approach for fracture mechanics within the finite element. Since the advent of the smeared crack concept by Rashid [12], it has been refined byseveral researchers. The smeared cracking model uses the cracking strain to simulate the crack, and modifies the constitutive model when the concrete is softening [13]. So the results only show the cracking strain zone, we can’t see the crack directly. III. NUMERICAL EXAMPLES A. The parameters of the model and the materialThe Longtan dam is selected for the numerical examples. It is the highest gravity dam that has been constructed in China. The cross-section of the water retaining dam section and thematerial partition are shown in Fig. 2. The scope of thefoundation is 1.5 times of dam height upstream anddownstream, 1.7 times of dam height for foundation depth. Displacement constraint in foundation bottom and along riverconnecting rod in upper and down foundation. A plane strain finite element is adopted for the model, and it is constructedusing four-node isoparametric elements. The dam body usesfine grid blocks, and the rock foundation uses coarse grid blocks. The numerical model of the dam is show in Fig. 3. The model was divided into 8185 nodes, and 5997 elements for dam and 1885 elements for the foundation. The mechanical parameters for model are shown in table. 1.Figure 1. The constitutive model of concrete Figure 2 . The dam section and the material partiton Figure 3. Finite element model for the damTABLE I. T HE M ECHANICAL P ROPERTIES FOR THE M ATERIALSClass of MaterialsElastic Modulus (104MPa)Poisson’s RatioDensity (kg/m 3) Angle of Internal Friction （°）Cohesive Strength (MPa) Tensile Strength (MPa) Compression Strength (MPa)ConcreteCC1.96 0.1672.4 50 2.50 1.57 18.5R Ⅰ1.96 0.1632.4 50 2.16 1.57 18.5R Ⅱ 1.79 0.163 2.4 47 2.10 1.29 14.3R Ⅲ 1.54 0.163 2.4 45 1.97 0.97 9.8R Ⅳ1.96 0.1632.4 50 2.16 1.57 18.5Rock① 1.2 0.27 2.7 48 1.48 0.6 9② 1.1 0.27 2.7 45 1.2 0.5 9③ 1.6 0.27 2.7 56 2.45 1.2 23④1.5 0.272.7 50 1.63 0.7 18B. Cracking Analysisi Under Water Loading EffectsApplied loads include self-weight of the dam and the rock base and hydrostatic. The operation conditions with empty reservoir and water lever of 60m, 120m, 172m and 190m are calculated. The results show that there are cracks in the heel of the dam, the bottom of the galleries of the upstream, and around the grouting gallery of the downstream. The dam is safe because the cracking area is very small.In order to get the safety reserve of the dam, use bulk density-based gravity increase method to carry out the overloading calculates. Take K as the symbol of the overloading coefficient. Calculation is carried out under the normal water level (190m) when the coefficient K=2, 3. The distribution of cracks in the dam is shown in Fig. 4.The results show that cracks is firstly observed at the heel of the dam, and as the K increases, the crack region increase. The crack region extends from the heel to the downstream and the upper of the dam. In addition, the concrete around the gallery is prone to crack, too, especially the top left and lower right position of it.C. Cracking Analysis Under Water Loading and Seismic EffectsIn order to avoid the amplification of seismic waves because of the foundation’ mass, the mass-less base model is adopted. The dynamic interaction of dam-reservoir system is considered by the Westergaard added mass technique [14]. The equation to calculate the added mass is as the following:)(87m i i z H H −=ρ (4)the depth of the water, and z is the distance from the node to the water surface.The Rayleigh damping is adopted, of which α and β are calculated as following function [15]:⎪⎪⎩⎪⎪⎨⎧+=+=βωωαςβωωαςj j j i ii 22 (5)where ωi and ωj are the Characteristic frequency of the i and jorder modes. For numerical application, i=1, j=4 and the damping ratio of 0.05 are adopted. Two dimensional seismic analyses are performed by using the transverse and vertical acceleration components of 11 December 1967 Koyna earthquake records. The records of this ground motion are given in Fig. 5.Figure 5. The koyna accelerograms. (a) Transverse component and(b) vertical componentFigure 4.The Distribution of Cracks as the Overloading CoefficientThe results show the cracking strain distribution of each time. As the cracked elements can be closed and reopened at different times, the cracking strain becomes smaller or zero. Fig. 6 lists the cracking position and its extensions with time.Figure 6. Cracking extensions under water loading and seismic effectsIt can be conclude that the heel of the dam, the region near where the slop changes abruptly, the upstream dam surface elevation 160m, and the gallery’ around are prone to crack. As the time goes by, the cracks in the heel of the dam propagate from the heel to the toe, the cracks at the upstream face elevation 160m are initially in a horizontal region propagate deeper inside of the dam, and it can be form detached concrete block with the crack in the downstream neck. It can conclude that the dam has safe reservation under water loading and seismic effects because the cracks are not run – through.IV.CONCLUTIONSA computational model for the cracking analysis of high concrete dam is presented in this paper. The case in this study is Longtan concrete dam. The tensile softening character is considered using linear softening curve, and a smear crack model which includes the strain softening behavior is selected for the concrete. The dam-reservoir interaction is considered. The effects of cracking on flood water and seismic response of the dam are discussed.•During water filling, there are only small quantities of elements crack in the heel of the dam, the bottom ofthe galleries of the upstream, and around the groutinggallery of the downstream. The cracking regionextends from the heel to the downstream and the upperof the dam if the reservoir overloading.•Under water and earthquake loading, the heel of the dam, the location where the slope in upstream face ofthe dam changes, the upstream dam surface elevation134m, the downstream neck and the 160m elevationdam surface upstream. The cracks in the heel of thedam propagate from the heel to the toe. The cracks atthe upstream face elevation 160m are initially in ahorizontal region propagate deeper inside of the dam,and it can be form detached concrete block with thecrack in the downstream neck.•There are no run-through cracks in the dam, so the dam has safety reservation under water loading andseismic effects.•Cracks tend to initiate near stress concentrations in the dam, mainly at the heel, near the changes in the slop ofthe faces and the region around the gallery.Under hydrostatic pressure, overloading, and seismic effects, the positions that most easy to generate cracks and the law of crack propagation are gained, and it can provide reference for structure design and reinforcement.R EFERENCES[1]Kaplan M F. Crack propagation and the fracture ofconcrete[J].J.ACI.,1961,56(5):591-610[2]Jiang Jianjing, Lu Xinzheng, YeLieping. Finite element analysis ofconcrete structures [M].Beijing: Tsinghua University Press,2005.3(inChinese)[3]O.A. Pekau, Cui Yuzhu. 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