Influence of construction interfaces on dynamic characteristics of
Transcription
Influence of construction interfaces on dynamic characteristics of
J. Cent. South Univ. (2015) 22: 1521−1535 DOI: 10.1007/s11771-015-2669-5 Influence of construction interfaces on dynamic characteristics of roller compacted concrete dams GU Chong-shi(顾冲时)1, 2, 3, WANG Shao-wei(王少伟)1, 2, 3, BAO Teng-fei(包腾飞)1, 2, 3 1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China; 2. National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Hohai University, Nanjing 210098, China; 3. College of Water-Conservancy and Hydropower, Hohai University, Nanjing 210098, China © Central South University Press and Springer-Verlag Berlin Heidelberg 2015 Abstract: To study the influence of construction interfaces on dynamic characteristics of roller compacted concrete dams (RCCDs), mechanical properties of construction interfaces are firstly analyzed. Then, the viscous-spring artificial boundary (VSAB) is adopted to simulate the radiation damping of their infinite foundations, and based on the Marc software, a simplified seismic motion input method is presented by the equivalent nodal loads. Finally, based on the practical engineering of a RCC gravity dam, effects of radiation damping and construction interfaces on the dynamic characteristics of dams are investigated in detail. Analysis results show that dynamic response of the RCC gravity dam significantly reduces about 25% when the radiation damping of infinite foundation is considered. Hot interfaces and the normal cold interfaces have little influence on the dynamic response of the RCC gravity dam. However, nonlinear fracture along the cold interfaces at the dam heel will occur under the designed earthquake if the cold interfaces are combined poorly. Therefore, to avoid the fractures along the construction interfaces under the potential super earthquakes, combination quality of the RCC layers should be significantly ensured. Key words: roller compacted concrete dam; construction interface; nonlinear fracture; radiation damping; viscous-spring artificial boundary; dynamic response 1 Introduction The construction technique of roller compacted concrete dam (RCCD) has been rapidly developed in the last 30 years. It is widely applied for its rapidness. With the implementation of the National West to East Power Transmission Project, a large number of high dams are constructed or under construction in western China. During this process, RCCD is more frequently adopted by designers to shorten the construction period, especially the RCC gravity dams. There are 49 RCCDs in China with the dam height more than 100 m, and 36 of them are gravity dams [1]. While all these RCCDs are gravity dams if the dam height exceeds 150 m, such as Longtan (Hmax=217 m, the highest RCCD in the world at present), Huangdeng (Hmax=202 m), Guangzhao (Hmax=201 m) and Guanyinyan RCC gravity dam (Hmax=168 m). The special mountain valleys in western China provide advantageous topographic conditions for the construction of these high dams. However, dam safety becomes an important issue in the western area due to the complicated geological conditions as well as strong earthquakes of high frequency. The recent immense earthquake in Wenchuan of the Sichuan province on May 12, 2008 in China, its huge destructive force reminds us that more attention should be paid to the seismic safety of dams. A large number of construction interfaces exist in dam bodies due to the construction technology of thin roller compaction layers of the RCCDs. Under the effects of material property, local weather condition, construction machinery and management, and some other construction influencing factors, these construction interfaces perform as effect zones with actual thickness and gradually changed mechanical properties [2−3]. What’s more, the disappearance or poor quality of embedment between two adjacent concreting lifts always results in a reduced bond strength of construction interfaces, and the bigger maximum size of concrete Foundation item: Projects(20120094110005, 20120094130003) supported by the Research Fund for the Doctoral Program of Higher Education of China; Projects(51379068, 51139001, 51279052, 51209077, 51179066) supported by the National Natural Science Foundation of China; Project(NCET-11-0628) supported by the Program for New Century Excellent Talents in University, China; Projects(201201038, 201101013) supported by the Public Welfare Industry Research Special Fund Project of Ministry of Water Resources of China Received date: 2013−12−09; Accepted date: 2014−04−10 Corresponding author: WANG Shao-wei, PhD; Tel: +86−25−83786957; E-mail: [email protected] J. Cent. South Univ. (2015) 22: 1521−1535 1522 aggregates, the lower bond strength [4]. Therefore, nonlinear fracture may occur along these interfaces under strong earthquakes. However, seismic failure mechanisms are more frequently focused on normal concrete dams [5−7], and RCCDs are similarly treated in which effects of the construction interfaces are ignored [8−10]. So, it is more useful to study the mechanical property of construction interface and its influence on the seismic failure mechanism of RCCDs. The key problem in studying the seismic failure mechanism of the RCCDs under the influence of construction interfaces by the finite element method (FEM) is the acquisition of real dynamic responses of dams. Dam seismic response analysis is actually a simulation of seismic waves propagating in the open system composed by dam body and its infinite foundation. Under the effects of seismic waves, dam vibration occurs, at the same time dam body will serve as a scattering source to radiate energies to external foundation during earthquakes, namely the radiation damping of infinite foundations. Research results [11] show that compared with the massless foundation input model which does not consider the radiation damping, seismic response of dam bodies in displacement and stress are significantly reduced when using the viscous-spring artificial boundary (VSAB) to model the influence of radiation damping of infinite foundations. The reduction amplitude ranges between 10% and 65%, and the higher the foundation flexibility, the bigger the reduction amplitude. The commonly used seismic input model at present is the massless foundation model proposed by CLOUGH [12] who just took the elasticity of dam foundation into account, while the inertia effects are ignored. Meanwhile, the massless foundation input model is established on the finite foundation, so the radiation of seismic energies to the external infinite foundations cannot be simulated. Based on the numerical simulation technology of FEM, wave differential equations and physical boundary conditions are dispersed in temporal and spatial domain, and virtual artificial boundaries are established on the periphery of the computational domain to insure that the scattered waves caused by dam body can successfully propagate out of the finite domain without reflection. These artificial boundaries are viscous boundary [13], VSAB [14−17], and artificial transmission boundary [18]. Especially the VSAB, which not only overcomes the problem of instability at low frequency and the inability of simulating the elastic recovery of infinite foundations in the viscous boundary, but also there is no need to increase a large number of boundary elements. In addition, the seismic waves in VSAB can be translated into equivalent nodal loads at the intercepted boundaries, which can be easily realized in FEM. In this work, to study the influence of construction interfaces on the dynamic characteristics of the RCCDs, mechanical properties of the RCC construction interfaces are firstly analyzed. Then, according to the convention of dam FE mesh in dynamic analyses, the equivalent nodal loads of seismic waves at the intercepted boundaries of the VSAB input model are respectively deduced, and a simplified seismic motion input method is presented on the basis of the Marc software. Based on the combination of these two, a dynamic nonlinear fracture analysis model for the RCCDs is established, in which the radiation damping of infinite foundations and the construction interfaces are both considered. Finally, based on the practical engineering of a RCC gravity dam, effects of radiation damping and construction interfaces on the dynamic response are investigated in detail, and some conclusions are drawn. 2 Mechanical properties construction interfaces of RCC The biggest difference between the RCCDs and the normal concrete dams is that the former are made up of super-stiff concretes. Thin roller compaction layers by large rolling equipments are conducted during the dam filling, so a large number of slightly smooth construction interfaces are formed in this process. Combination quality of the compacted layers is affected by these interfaces more or less; especially, the poor combination quality will threaten the integrity of the RCCDs. From the construction process of the RCCDs, these construction interfaces can be divided into two types, namely hot construction interfaces and cold construction interfaces, which are determined by the interval time of two adjacent RCC layers. Figure 1 shows the typical structure model of RCC layers, in which B represents the thickness of RCC layers and ba denotes the thickness of effect zones. Fig. 1 Structure model of RCC layers 2.1 Hot construction interface RCCDs are commonly constructed by the technology of thin roller compaction layers, and the completed layer thickness is defined as 30 cm in Chinese J. Cent. South Univ. (2015) 22: 1521−1535 1523 design specification. Research results show that combinations between RCC layers are in good quality if the upper RCC layers are poured in normal conditions before the initial setting of the lower RCC layers, and the mechanical properties of the interface effect zones change slightly, so these interfaces are defined as the hot construction interfaces [19]. Meanwhile, effect zones of hot interfaces can be regarded the same as the RCC noumena as isotropic medium due to their thin thickness. However, back analysis results of mechanical parameters of the RCCDs show that elastic modulus of the interface effect zones is a little smaller than that of the RCC noumena [20], so RCCs are layered structures consisting of two isotropic mediums. Compared with the aftermentioned so-called cold construction interface, hot interfaces have a higher bond strength so that the potential interface fracture under strong earthquakes may firstly occur along the cold construction interfaces. Therefore, to reduce the total number of FE meshes and also take the mechanical properties of hot interfaces into account, these hot interfaces are equivalently reflected by the relevant RCC noumena, and the layered structures are converted into the transversely isotropic bodies [21]. In the global coordinate system, the transversely isotropic surface is assumed parallel to the xOy coordinate surface, and z axis is perpendicular to the interface. According to the theories of composite material mechanics, and based on the limit conditions of static equilibrium and deformation compatibility, the layered structures can be converted into the transversely isotropic body. Calculation models of series structure and parallel structure used for determining the equivalent elastic parameters of RCCs are shown in Fig. 2. For example, as for the elastic modulus of E1 (in the direction perpendicular to the interface), the series structure model in Fig. 2(a) should be used, and the limit conditions are: z az (1 ) cz and z az cz . The five used equivalent elastic parameters for RCCs in the model of transversely isotropic body are deduced as follows: E1 Ec (1 ) Ea (1) Ea Ec Ea (1 ) Ec (2) E2 u1 Ec c (1 ) Ea a Ec (1 ) Ea (3) u2 Ea Ec [ c (1 ) a ] [ Ea (1 ) Ec ][ Ec (1 ) Ea ] (4) G2 Ga Gc Ga (1 ) Gc (5) where E1, μ1 and E2, μ2 are elastic modulus and Poisson ratio in directions of parallel and perpendicular to the interface, respectively; G2 is the plane shear modulus perpendicular to the interface; β=(k−1)ba/[kbc+(k−1)ba] (k is the number of roller compaction layers). Then, the elasticity matrix D corresponding to the stress−strain relationship of RCCs is expressed as follows: C1 C 2 C D 3 0 0 0 C3 C3 0 0 0 0 C3 0 0 0 C4 0 0 0 0 C5 0 0 0 0 C6 0 C1 E1 where C3 E1 C2 C1 2 m ; (1 n 2 2 ) ; (1 1 )m C4 E2 0 0 0 0 0 C6 (6) C2 E1 1 n2 2 ; (1 1 )m 1 1 E1 ; C5 ; C6=G2; m 2(1 1 ) n=E1/ E2; m 1 1 2n 22 . Fig. 2 Equivalent calculation models of RCC layers: (a) Series model; (b) Parallel model 2.2 Cold construction interface RCCDs are compacted by the intermittent construction technology. Long time interval between the continuous concreting lifts (usually 3.0 m every placing lift) is designed to satisfy the temperature control and some other field operations. The interval time is usually a few days, which exceeds the initial setting time of RCC, so the cold construction interfaces are formed in this period. Layer face treatments, such as interface roughening and laying mortar cushion, are implemented before the next concreting lift. However, bond strength of the cold construction interfaces is obviously reduced due to the disappearance or poor quality of embedment between two adjacent concreting lifts, so that the adjacent concreting lifts cannot be completely combined. Therefore, dam safety is seriously threatened by the reciprocating phenomenon of cracking, closing and sliding along the cold construction interfaces under strong earthquakes. Nonlinear fracture may occur along these interfaces under strong earthquakes if the cold construction interfaces are treated badly, so both the plastic deformation and the fracture along the cold construction interfaces should be considered when studying the influence of the RCC interfaces on the seismic failure 1524 mechanism of the RCCDs, namely, yield criterion and failure criterion are both needed in the dynamic response analyses of the RCCDs. Instead of assuming the development of cracks’ location and direction, the actual concrete cracks are converted to the relevant elements in FEM simulation by the smeared crack model [22]. In this model, the damaged concretes are regarded as anisotropic materials if the maximum principal stress at the integral points exceeds the concrete tensile strength, and the constitutive relationships are adjusted to reflect the degradation of mechanical properties caused by cracking. Hence, the smeared crack model is adopted in this work to represent the nonlinear fracture along the cold construction interfaces. The stress−strain relationship is shown in Fig. 3. Tensile softening property is presented when the maximum principal stress comes up to the concrete tensile strength. Linear softening is adopted in this work, the softening modulus is determined to be about 1/10 of the original elastic modulus, and the transfer coefficient of the residual shear force after cracking is defined as 0.1. The reloading rigidity under cyclic loads keeps the same as the original, and the closed cracks are assumed to have the complete compressive bearing capacity during the reciprocating process of opening and closing. Fig. 3 Stress-strain diagram of concrete J. Cent. South Univ. (2015) 22: 1521−1535 Drucker-Prager yield criterion is commonly used for concretes and rock materials as it can yield a smooth failure surface and is determined corresponding to the hydrostatic stress. Therefore, the Drucker-Prager yield criterion is combined with the smeared crack model to represent the nonlinear deformation of RCCs, especially the nonlinear fracture along the cold construction interfaces. 3 Mechanism and realization of seismic motion input by VSAB 3.1 Foundation of VSAB In order to simulate the scattered waves propagating out of the finite domain without reflection, shunt-wound spring−damper components are set in the intercepted finite domain to absorb the seismic energies carried by the scattered waves in the VSAB. Figure 4 shows the sketch of transverse section of gravity dam−foundation system with the concentrated VSAB. According to the different realization methods, VSAB can be divided into two forms, namely, the consistent VSAB [14] and the concentrated VSAB [15]. The former VSAB is more complex due to its realization method of adding anisotropic viscous-spring boundary elements at the intercepted boundaries, and it is more difficult to deal with the stiffness matrix and the damping matrix for boundary elements; while the concentrated VSAB is widely used for its clear mechanical concepts. Sketch of the isolated body of spring−damper components used in the concentrated VSAB is shown in Fig. 5. Three pairs of spring−damper components are added to every node of the artificial boundaries, in which two pairs work in the tangential direction and one is in the normal direction. One end of the spring−damper components is connected with the artificial boundary nodes, and the other one is fixed in three directions. In Fig. 4 Sketch map of transverse section of gravity dam−foundation system with concentrated viscous−spring artificial boundary J. Cent. South Univ. (2015) 22: 1521−1535 1525 addition, seismic motion input in the concentrated VSAB can be accurately realized by translating the earthquake motion into the equivalent nodal loads acting on the artificial boundaries, in which displacement field and stress field at the intercepted boundaries should be precisely kept as the same as the seismic free-field. Fig. 5 Sketch map of isolated body of spring−damper components The key problem of establishing the concentrated VSAB is the determination of the spring stiffness and the damping coefficient. Published research results show that it is more consistent in the damping coefficient. However, due to different type assumptions of the scattered waves (plane wave or spherical wave), large differences exist in the equivalent calculation of the spring stiffness. As for the hydraulic dams, the spherical wave assumption is more in accordance with the actual situation due to the anisotropy of dam foundations as well as the uneven slope surfaces. Based on the theory of spherical elastic wave, LIU et al [15] deduced the spring stiffness coefficients and the damping coefficients of the concentrated VSAB in three-dimensional space. Tangential direction: K BT n 2G n Ai , CBT cs Ai R i 1 i 1 (7) Normal direction: K BN n 4G n Ai , CBN cp Ai R i 1 i 1 (8) where KBN and KBT are the normal and tangential stiffness coefficients, respectively; CBN and CBT are the normal and tangential damping coefficients, respectively; G and ρ are the medium’s shear modulus and mass density, respectively; R is the distance from the scattered wave source to the artificial boundary point. However, due to the uneven slope surfaces, the scattered waves are not conducted by a point source during the propagation of seismic waves in the dam-foundation system. Here, the scattered wave source is assumed to be located at the center of the interface between dam and foundation for simplicity, and R for all points on the same straight boundary surface is similarly determined as the shortest distance from the assumed scattered wave source to the boundary surface. cs and cp are wave velocities of the S wave and P wave, respectively. The dam-foundation system is isolated from the infinite rock domain by the VSABs, and energies of the out-going scattered waves caused by dam body and slopes are absorbed by the boundary located springs and dampers. To satisfy the original seismic free-field, the mechanism of seismic motion input is determined by the conditions of displacement continuity and internal force equilibrium at the interface of artificial boundaries. The simulated seismic motion is inputted at the bottom of the near-field foundation in the VSABs. While in the seismic risk evaluation of the practical engineering project areas, the proposed seismic motion represented by the peak acceleration is the maximum horizontal ground motion on the flat free surface of the half-space isotropic rock foundations [23]. Due to the inertia effects caused by the mass of the simulated rock foundations, seismic motions are enlarged during the propagation from deep bedrock to land surface. Therefore, the designed free-surface seismic motion should be converted into the incident wave propagated from deep bedrocks. Taking the reflection of the free-surface into account, the commonly used method by researchers at present is that the amplitude of the free-field incident wave is determined to be half of the peak value of the designed free surface seismic motion. 3.2 Equivalent nodal loads of seismic motion in VSAB input model The free-field stress and displacement are denoted as σ Bff ( x, y, z , t ) and U Bff ( x, y, z , t ) [u ( x, y, z , t ) v( x, y, z , t ) w( x, y, z , t )], respectively; where w is the normal displacement, and u and v are tangential displacements. Hence, in order to accurately simulate the seismic motion, the stress field and displacement field created by the equivalent nodal loads should satisfy the following conditions: σ σ Bff ( x, y, z, t ) U U Bff ( x, y, z , t ) (9) (10) According to the mechanical model of the spring−damper components in the VSAB, to satisfy the conditions of Eqs. (9) and (10), equivalent nodal loads applied to the artificial boundaries are composed of three parts [16]. The first two parts are used in removing the effects that the spring-damper components work on the seismic motion input, namely, to offset the spring force and damping force caused by the motion of boundary nodes accompanied with the ground seismic motion. The third one is the free-field stress on the boundary surface J. Cent. South Univ. (2015) 22: 1521−1535 1526 created by the free-field motion. Therefore, the equivalent nodal loads exerted on the boundary node i can be expressed as FBi K BU Bff C BU Bff σ Bff nABi (11) where U Bff and U Bff are the free-field displacement and velocity at the boundary node i, respectively; ABi is the influence area of node i; n=[l m n]T is the outward normal direction cosine of the selected artificial boundary; KB and CB are 3×3 diagonal matrixes consisting of the spring and damping coefficients, respectively; σ Bff is the free-field stress tensor at node i. KB, CB and σ Bff are represented as follows: 0 0 K BT KB 0 K BT 0 0 0 K BN 0 0 CBT C B 0 CBT 0 0 0 CBN σ Bff xx xy xz analyses, the incident seismic wave at the bottom of the near-field foundation can be represented by three components, namely, seismic waves at the stream, cross-stream and vertical directions, respectively. In the global coordinate system, the aforementioned directions are respectively denoted as the x, y and z axes. The corresponding time histories of displacement of the input seismic waves are denoted as u0(t), v0(t) and w0(t), in which u0(t), v0(t) are transverse waves and w0(t) is the longitudinal wave. Based on the wave theory, the seismic free-field at node i is stacked by the incident wave and the reflected wave as follows: U Bff l 2L l ) u0 (t ) u0 (t cs cs u l 2L l ) v v0 (t ) v0 (t cs cs w 2L l l w0 (t ) w0 (t ) cp c p (12) U Bff l 2L l ) u0 (t ) u0 (t cs cs u 2L l l v v0 (t ) v0 (t ) cs cs w l 2L l w 0 (t ) w 0 (t ) cp cp (13) yx zx yy yz zy zz As for the half-space problems, the free-field consists of two parts, namely, the seismic incident wave and the reflected wave caused by the free surface of homogeneous elastic semi-infinite space. Therefore, the free-field in half-space should be firstly determined before calculating the boundary equivalent nodal loads of the seismic motion. Reflection sketch of the seismic wave is shown in Fig. 6. The free-field at node i at any time t is stacked by the bottom incident wave and the top reflected wave. As for arch dams, obvious differences of elevation are shown on the valley surfaces. Here, to simplify the auxiliary pre-treatment, the free surface can be simply defined at a reasonable elevation between the maximum and the minimum elevation of dams. According to the commonly used component representation method of seismic wave in hydrodynamic Fig. 6 Reflection sketch of seismic wave Components of the free-field stress on the surface of the bottom artificial boundary are the normal stress ( zz ) caused by the longitudinal wave, and the shear stresses ( zx and zy ) caused by the transverse waves in the stream and cross-stream directions, respectively. w w c 2p zz ( 2G ) z z u u cs2 zx G x x v 2 v zy G y cs y (14) where λ and G are the medium’s Lame constants, which also determine the wave velocity of S wave and P wave. According to the wave theory, the differential equation can be deduced as p( x, t ) x (1 c) (p( x, t ) t ), where p(x, t) is the wave displacement equation and c is the wave velocity. As for the free-field, the incident wave and the reflected wave propagate in the opposite direction, namely (cs, cp) and (−cs, −cp), respectively. Substituting Eqs. (7), (8) and (12) to (14) into Eq. (11), and taking the outward normal direction of the bottom artificial boundary n=[0 0 −1] and l=0 into account, the equivalent nodal loads at the bottom artificial boundary are expressed as follows: J. Cent. South Univ. (2015) 22: 1521−1535 2L FBx K BT u0 (t ) u0 (t ) 2CBT u0 (t ) cs 2L FBy K BT v0 (t ) v0 (t ) 2CBT v0 (t ) cs F K w (t ) w (t 2 L ) 2C w (t ) BN 0 0 BN 0 Bz c p 1527 (15) Mechanism of calculating the equivalent nodal loads at the lateral artificial boundaries (four intercepted surfaces) is similar to that of the bottom. Differences are mainly focused on the varied distance from the lateral boundary nodes to the bottom surface, so different time intervals between the incident wave and the reflected wave appear in the lateral artificial boundaries. In addition, directions of the spring-damper components in the global coordinate system should be carefully dealt with due to their different coefficients in the normal and tangential directions, and also the directions of the free-field stress. 3.3 Realization of VSAB based on Marc software The realization of the VSAB contains two steps. Firstly, the normal and tangential spring−damper components should be set at the boundaries of the intercepted finite domain. Then, the seismic motion is simulated by exerting the equivalent nodal loads at the artificial boundaries. To establish the spring−damper components, one end of the spring−damper components is fixed on the discrete boundary nodes of the FE mesh, and the other one is fixed on the external constrained nodes one to one corresponding to the discrete boundary nodes and added in advance. According to the node number of the spring−damper components and the FE mesh, the spring−damper components addition subroutine (based on the FORTRAN platform) for the VSAB has been created, and the spring stiffness coefficients and the damping coefficients are calculated according to Eqs. (7) and (8). Finally, based on the commonly used FEM Marc software, the spring-damper components are added in the Marc input file by the key word “Springs”. According to the relationship between the global coordinate system and the surface direction of the artificial boundaries, equivalent nodal loads at the bottom and lateral artificial boundaries are respectively calculated and exerted by Marc’s user subroutine of Forcdt [24]. Thus, the concentrated VSAB and its relevant equivalent nodal load input model has been fully realized. 4 Dynamic response analyses of a RCC gravity dam A RCC gravity dam is located in the west of China with the maximum dam height of 85.0 m. The width at the crest is 8.0 m, all dam sections are designed with a vertical upstream dam surface, and the downstream dam surface is at a gradient of 1:0.75. The designed ground motion is determined by the exceeding probability of 10%, and the corresponding horizontal peak acceleration represented at the land surface is 0.154 g. The typical No. 7 water retaining dam section with the maximum dam height is dynamically analyzed as an example. The FEM model and the sketch of the VSAB are shown in Fig. 7, in which every symbol of the screw between the external fixed node and the interrupted boundary contains three pairs of spring−damper components: two pairs work in the tangential direction and one pair in the normal direction. The range of the FEM model is about two times the maximum dam height in the upstream, downstream and downward directions according to the dam heel and dam toe. The damfoundation system is discretized into eight-node and six-node solid elements with 17740 elements and 23070 nodes, in which 936 fixed nodes are added around the bottom and lateral artificial boundaries as the fixed ends of the spring−damper components. According to the current Chinese specifications for seismic design of hydraulic structures DL5073−2000 [25], the cross-stream seismic can be ignored in the dynamic analysis of single gravity dam section, so normal constraints are applied to the cross-stream lateral boundaries. Static material properties of the dam−foundation system are listed in Table 1. The dynamic modulus and strength of concretes are taken as 1.3 times the corresponding static parameters, respectively. A normal concrete cushion with the thickness of 1.0 m is poured above the foundation plane. For seepage control, normal concretes and the second grade RCCs are consecutively poured on the dam upstream surface, and the thickness of these impermeable concretes are 1.0 m and 4.0 m, respectively. Other parts are mainly constructed by the three grade RCCs. Thicknesses of the compacted layer and its effect zone are 30.0 cm and 2.0 cm, respectively, and the concreting lifts are about 3.0 m in height. To better analyze the influence of the construction interfaces and the radiation damping of infinite foundations on the dynamic response of the RCC gravity dam, only the seismic load is considered in this work. Time histories of displacement, velocity and acceleration of the input horizontal seismic wave at the ground surface are shown in Fig. 8. The vertical peak acceleration is 2/3 of the horizontal value, and the cross-stream seismic is not considered. The dynamic dam−water interaction is modeled by the added mass assumption [26] as follows: pw ( h ) 7 ah w H 0 h 8 (16) J. Cent. South Univ. (2015) 22: 1521−1535 1528 Fig. 7 Dam-foundation FEM model: (a) FEM model; (b) Sketch of VSAB Table 1 Static material properties of RCC gravity dam Strength/MPa Material Modulus/GPa Poisson ratio Mass density/ (kN·m−3) Tensile Compressive Normal concrete 19.6 0.167 24.0 1.60 18.5 Noumenon of RCC I (three grade) 17.9 0.163 24.0 1.32 14.3 Noumenon of RCC II (second grade) 19.6 0.163 24.0 1.60 18.5 Interface of RCC I (three grade) 13.0 0.3 24.0 1.0 14.3 Interface of RCC II (second grade) 15.0 0.3 24.0 1.2 18.5 Dam foundation 9.0 0.24 26.2 — — Notes: Strengths of the hot construction interfaces are the same as the RCC noumena; the bond strength parameters of cohesion force (c) and friction angle (φ) used in the Drucker-Prager yield criterion are equivalently calculated by ft and fc as c=0.5(fc·ft)1/2, φ=arcsin[(fc−ft)/ (fc+ft)]; the cohesion force and the friction angle of the foundation rocks are 1.3 MPa and 48 °, respectively. Fig. 8 Time histories of input seismic wave: (a) Acceleration; (b) Velocity; (c) Displacement J. Cent. South Univ. (2015) 22: 1521−1535 1529 where pw(h) is the hydrodynamic pressure acting on the dam upstream surface at the water depth of h; ah is the designed seismic peek ground acceleration in the horizontal direction; ρw is the water density; H0 is the water depth related to the normal reservoir water level. 4.1 Influence of radiation damping on dynamic response of RCC gravity dam To study the influence of the radiation damping of infinite foundations on the dynamic response of the RCC gravity dam, dynamic analyses are performed by input models of the massless foundation and the VSAB, respectively. Here, the RCC construction interface and the nonlinear deformation are both not considered. In the massless foundation input model, the mass density of the foundation rocks is defined as zero, and the damping ratio of the dam-foundation system is determined as 5% according to the hydraulic specification of DL5073− 2000 [25]. The Rayleigh damping is adopted in this work, in which the damping matrix is expressed as follows [27]: [C ] [ M ] [ K ] (17) where [M] and [K] are the mass matrix and the stiffness matrix, respectively; α and β are damping parameters. According to the Rayleigh damping, α and β are determined by ξ=0.5α/ωi+0.5βωi. Hence, α and β are gradually changed with the circular frequency ωi under a constant damping ratio ξ. However, α and β are commonly assumed to be constant in the sensitive frequency domain of dams, and these two parameters are cooperatively calculated by the upper and lower limits of the sensitive frequency domain [28]. In this work, the sensitive domain is determined from the first to the tenth frequency, namely 2.023 Hz to 24.066 Hz for the selected RCC gravity dam section. Corresponding to a 5% damping ratio, α=1.1725 and β=6.1×10−4. For comparison analyses, the stream displacement at dam crest in this work is denoted by the relative displacement corresponding to dam heel, and the positive value represents the downstream direction displacement; otherwise, it is towards the upstream direction. Figures 9 and 10 show the time histories of displacement along river at the dam crest and the maximum principal stress at the dam heel, respectively. The envelope diagrams of the maximum principal stress are shown in Fig. 11. It can be seen that dynamic response of the dam body reduces obviously in the VSAB input model. The peak displacements along river at the dam crest are 28.24 mm and 21.21 mm for the massless foundation model and the VSAB input model, respectively. The peak maximum principal stresses at dam heel are 4.85 MPa and 3.99 MPa. It can be seen that both of the peak values are reduced by about 25% in the VSAB input model. As for the envelope value of the maximum principal stress of dam body, it reduces obviously on the upstream dam surface when the radiation damping is considered, especially for the region of dam heel commonly considered the tensile stress control area. The reduction of the dynamic response in the VSAB input model can better reflect the radiation of seismic energies to the infinite foundations, which is modeled by the energy absorption action of the spring-damper components. Fig. 9 Time history of displacement along river at dam crest Fig. 10 Time history of maximum principal stress at dam heel 4.2 Influence of construction interfaces on dynamic response of RCC gravity dam 4.2.1 Influence of hot construction interfaces Based on the mechanical property analyses of the hot construction interfaces of the RCCDs in section 2.1, two FEM models are established to study the influence of the hot interfaces on the dynamic response of the RCC gravity dam, in which no interface is considered in model 1, while the hot interfaces are represented by the transversely isotropic dam materials in model 2. Radiation damping of the infinite foundation is modeled by the VSAB in two models. Natural frequencies of the RCC gravity dam are shown in Table 2, and Fig. 12 shows the comparison of time histories of displacement along river at the dam crest. It can be seen that natural frequencies are slightly reduced when the hot construction interfaces are J. Cent. South Univ. (2015) 22: 1521−1535 1530 Fig. 11 Envelope diagrams of maximum principal stress of dam body: (a) Massless foundation model; (b) VSAB input model Table 2 Natural frequency of RCC gravity dam Model Natural frequency/Hz 1 2.023 4.002 5.352 8.971 13.436 16.105 18.337 20.893 22.752 24.066 2 2.016 3.996 5.319 8.917 13.338 15.945 18.191 20.678 22.554 23.869 Fig. 12 Time history of displacement along river at dam crest represented by the transversely isotropic dam materials in model 2. Dynamic responses of dam body at any time are almost the same in both models, and the peak displacements at dam crest in the stream direction are 21.21 mm and 21.56 mm, respectively. Therefore, it can be concluded that the hot construction interfaces have little influence on the seismic response of the RCC gravity dam, so the hot interfaces can be ignored for simplification. 4.2.2 Influence of cold construction interfaces The poor bond strength of the cold construction interfaces is mainly caused by the disappearance or poor quality of the embedment between two adjacent concreting lifts. Nonlinear fracture along these cold construction interfaces maybe occurs under strong earthquakes, and is also accompanied with reciprocating phenomenon of cracking, closing and sliding, which makes the dynamic response of the RCCDs more complicate than that of the normal concrete dams. Therefore, the cold construction interfaces should be seriously considered in the seismic safety evaluation of the RCCDs. Aiming at the property of the lower bond strength, dynamic nonlinear fracture analysis model for the RCCDs is established with the thickness cold construction interfaces, and different reduction ratios for the bond strength of the cold interfaces are adopted to reflect the combination quality of the compacted layers. Therefore, to study the influence of the bond strength of the cold construction interfaces on the dynamic response of the RCC gravity dam, five computation cases are performed based on the VSAB model and its equivalent nodal load input method. The aforementioned smeared crack model in section 2.2 is used for all dam concretes, and the nonlinear deformation of foundation rocks is determined by the Drucker-Prager yield criterion. Performance of the cold construction interfaces and the peak dynamic response of each case are shown in Table 3. J. Cent. South Univ. (2015) 22: 1521−1535 1531 Without considering the construction interfaces, time histories of displacement along river at the dam crest in the linear elastic model and the smeared crack model are comparatively shown in Fig. 13. It can be seen that dynamic response of dam body obviously reduces when the nonlinear deformation is considered in the smeared crack model. The peak displacement along river at the dam crest reduces from 21.21 mm (−25.97 mm) to 16.15 mm (−17.98 mm), with a reduction amplitude of about 25%. The envelope diagrams of the maximum principal stress in these two constitutive models also comparatively show a obvious reduction amplitude. The reduced dynamic response is mainly caused by the seismic energy consumption in the development of plastic deformation and fracture, so the nonlinear deformation should be considered to obtain the real dynamic response of the RCCDs. Dynamic responses of case 1 and case 2 are comparatively shown in Figs. 14−16. It can be seen that although the bond strength of the normal cold interfaces is reduced at certain amplitude compared with the RCC noumena, normal cold construction interfaces have little influence on the dynamic response of the RCC gravity dam. Envelope values of the maximum and minimum Fig. 13 Time history of displacement along river at dam crest without construction interfaces Fig. 14 Time history of displacement along river at dam crest with construction interfaces or not Table 3 Computation cases and peak dynamic response Tensile strength Maximum Displacement reduction ratio principal Case Interface along river at of cold stress at dam dam crest/mm interface heel/MPa Case 1 × / 16.15 (−17.98) 1.26 Case 2 √ 1.0 15.87 (−18.12) 1.14 Case 3 √ 0.8 14.95 (−18.86) 1.05 Case 4 √ 0.7 14.61 (−22.01) 1.01 Case 5 √ 0.6 Non-convergence Notes: “×” means no cold interfaces; “√” means that cold interfaces are considered in this case. Fig. 15 Envelope diagrams of the maximum principal stress of dam body with construction interfaces or not: (a) Case 1; (b) Case 2 1532 J. Cent. South Univ. (2015) 22: 1521−1535 Fig. 16 Envelope diagrams of the minimum principal stress of dam body with construction interfaces or not: (a) Case 1; (b) Case 2 principal stress are only slightly changed on the downstream surface of the dam body. As for the tensile stress control area of the dam heel, there is almost no difference. Under the designed earthquake, no cracking appears in case 1, and smaller cracking areas appear at the dam heel when the normal cold construction interfaces are considered in case 2. However, dam safety is not likely to be seriously threatened by these cracks due to their shallow depth. Under different tensile strengths of the cold interfaces, time histories of displacement along river at the dam crest and the equivalent cracking strain at the first RCC layer of the dam heel are shown in Figs.17 and 18, respectively. It can be seen that dynamic responses of the RCC gravity dam in cases 2, 3 and 4 are almost the same at the early stage of earthquake, which indicates that dam deformation is mainly in the stage of linear Fig. 17 Time history of displacement along river at dam crest under different tensile strengths of cold construction interfaces Fig. 18 Time history of equivalent cracking strain at first RCC layer of dam heel under different tensile strengths of cold construction interfaces elasticity. With the intensification of the seismic motion, plastic yielding and fracture appear successively, and a slightly reduced peak displacement is represented. Smeared cracks begin to appear when the maximum principal stress exceeds the tensile strength of the concrete, resulting in a decline of the integral rigidity of the RCC dam body, especially under a large reduction ratio of the tensile strength of the cold construction interfaces. The enlarged cracking areas at the dam heel promote the development of residual deformation towards the upstream direction. Figure 18 also shows the reciprocating opening and closing process of the smeared cracks at the dam heel, so the dynamic nonlinear fracture of concrete can be perfectly simulated by the smeared crack model. Plastic yielding and cracking firstly appear at the dam heel and on downstream dam surface where the J. Cent. South Univ. (2015) 22: 1521−1535 envelop values of the principal stress are higher, and the nonlinear deformation areas gradually extend to inside dam body. Therefore, with the reduction of the tensile strength of the RCC interfaces, it can be seen from Figs. 15 and 19 that envelope values of the maximum principal stress reduce on the dam surface and increase inside dam body. The envelope diagrams of the minimum principal stress of dam under different tensile strengths of cold 1533 construction interfaces are shown in Fig. 20. Cracking processes are shown in Fig. 21. It can be seen that the lower tensile strength of the RCC interfaces is, the earlier the cracking occurs and the bigger the cracking areas are; the cracking areas are all at the dam heel and the foundation gallery. Meanwhile, the enlarged cracking areas also result in an increased envelop value of the compressive stress at the dam toe which can be concluded from Figs. 16 to 20. Fig. 19 Envelope diagrams of the maximum principal stress of dam under different tensile strengths of cold construction interfaces: (a) Case 3; (b) Case 4 Fig. 20 Envelope diagrams of the minimum principal stress of dam under different tensile strengths of cold construction interfaces: (a) Case 3; (b) Case 4 J. Cent. South Univ. (2015) 22: 1521−1535 1534 Fig. 21 Sketch map of equivalent cracking strain of RCC dam body: (a) Case 2 (t=9.52 s); (b) Case 2 (the last); (c) Case 3 (t=9.48 s); (d) Case 3 (t=9.52 s); (e) Case 3 (t=17.30 s); (f) Case 4 (t=5.86 s); (g) Case 4 (t=9.56 s); (h) Case 4 (t=17.32 s) 5 Conclusions 1) To study the influence of construction interfaces on the dynamic characteristics of the RCCDs, mechanical properties of construction interfaces are firstly analyzed, and according to their causes of formation, these interfaces are divided into two categories, namely, hot interface and cold interface, which are respectively represented by the transversely isotropic body and the smeared crack model in the dynamic analysis. 2) The VSAB seismic input model is adopted to simulate the radiation damping of dam infinite foundations. The equivalent nodal loads of seismic waves at the intercepted boundaries of the VSAB input model are respectively deduced, and a simplified seismic motion input method is presented on the basis of the Marc software. 3) The effects of radiation damping and construction interfaces on the dynamic characteristics of a RCC gravity dam are investigated at last. Research results show that the dynamic responses of the RCC gravity dam both reduce by about 25% when the radiation damping of infinite foundation and the nonlinear deformation of dam body are respectively considered. Under the designed earthquake, no cracking occurs in the assumed RCC gravity dam model without interfaces. As for the interfaces model, almost no influence is conducted by the hot construction interfaces, and the normal cold interfaces show a little influence on the dynamic response of the RCC gravity dam and a smaller cracking area at the dam heel. 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