Shaking Table Test and Numerical Simulation On Seismic Behavior of a Receiver Tower in Concentrated Solar Power Plant Under Vertical Earthquake

The solar receiver tower is a new type of high-rise power generation structure, which has been constructed and applied in a small amount around the world in recent years. To understand its seismic behavior under vertical earthquakes, a 1/18 reduced scale model structure was designed and investigated by shaking table test. The El-Centro wave, Taft wave and Articial wave were input as the earthquake excitation. This paper summarized the results of the experimental work, which could provide an important theoretical basis for evaluating the seismic behavior of receiver tower under vertical earthquakes. The damage distribution, dynamic characteristics, acceleration responses, displacement responses and vertical seismic force were analyzed quantitatively. In addition, a numerical simulation model of the receiver tower was established, and nonlinear time-history analysis was then conducted by using the software ABAQUS. The results between the experimental test and the numerical simulation were compared and they were in good agreement. Both of experimental and numerical simulation results showed that the model structure was subjected to huge vertical seismic force in the middle part of concrete cylinder under vertical earthquakes with high PGA, which caused severe damage and should be paid more attention in seismic design. Despite the serious damage and complex earthquake responses, combined with experimental test and simulation results, the seismic behavior of structure under vertical earthquake is good and generally satisfactory.


Introduction
Solar energy has become a hot spot of current research because of its richness, safety and cleanliness (Lotfabadi et al. 2015). One of the signi cant uses of solar energy is power generation, which can effectively alleviate the global energy crisis (Azoumah et al. 2010). Tower-type concentrated solar power has the advantages of large capacity, low cost, small heat loss, and excellent power quality, therefore it has been gradually applied at home and abroad(Dominik et al. 2010; Zare et al. 2016;Ieva et al. 2020). The solar receiver tower is the core structure of concentrated solar power plant, which is not only a type of tower structure but also a high-rise industrial building. The shape of receiver tower looks like reinforced concrete chimney structure to some extent, but they are different in many aspects. First, the receiver tower consists of reinforced concrete cylinder and steel truss, it belongs to a vertical steel-concrete hybrid structure. The difference of material properties makes the stiffness of the connection part between steel structure and concrete cylinder suddenly change, which may cause serious whiplash effect in the top of tower. Next, in order to meet the power generation requirements, many platforms and power generation equipment are arranged inside the receiver tower, it makes the structure more complicated and more easily to be damaged or even collapse under earthquakes. On the other hand, as a lifeline project, the safety of receiver tower is higher than that of the common structure, so the design indexes such as displacement, inclination and settlement are strictly required (Behar et al. 2013).
In previous study, most of the researchers mainly focused on the seismic performance of high-rise tower structures under horizontal earthquakes (Zhang et  The earliest research on vertical ground motion began with the investigation and analysis of earthquake damage. The investigation of the Hanshin Earthquake in Japan in 1995 (Bruneau et al. 1998;Scawthorn et al. 1995) and the Turkish Earthquake in 1998 (Adalier et al. 2001; Sezen et al. 2003; Doğangün et al. 2003) showed that many structural damage and collapse were not caused by horizontal earthquake, but by vertical earthquake, which led to researchers paid more attention to the vertical seismic response of the structure once more. At rst, an orthogonal set of principal axes for earthquake ground motions (Penzien et al. 1974) was put forward, then the vertical ground motions and damage effects on structure were studied ( Lin et al. 1981 and Lin et al. 1982;Elnashai et al. 1996 andElnashai et al. 1997; Button et al. 2002;Elgamal et al. 2004), they con rmed that structural failure may be caused by direct tension or compression as well as due to the effect of vertical motion on shear and exural response. To take the vertical acceleration component in the current methods of seismic action into account and ll in the lack of seismic speci cation, the horizontal and vertical earthquakes were compared (Sarno et  , the results showed not only variance of the vertical ground motion, but also cross-covariance with the horizontal one should be considered in the near eld. The fracture phenomenon of a 180m RC chimney and a 45m brick chimney subjected to vertical seismic action by carrying out a shaking table test (Chen et al. 2005) were investigated and analyzed the test results by using wave theory. It indicated that the maximum vertical strain varied along the height of chimney with the increasing of seismic intensity, and the necessity of taking vertical seismic action into account in high-rise structure design was emphasized. A shaking table test (Jin et al. 2012) has been conducted to study the vertical seismic responses of a quayside container crane, and the modeling method about numerical simulation was put forward, the experimental results were compared with the numerical analysis and agreed fairly well. The shaking table test (Yu et al. 2014) of a largespan station hall was to carried out understand its dynamic response characteristics and yielding mechanism under different levels' vertical earthquake excitation. The studies mentioned above had provided precious information about vertical earthquake for this research, such as the test method and modeling method, but the tested structures were not tower structure, and their seismic responses were different. to study the seismic responses of the solar receiver tower under vertical earthquakes. In this paper, a high-rise steel-concrete hybrid model structure of solar receiver tower was selected to analyze the dynamic characteristics and seismic response by shaking table test and numerical simulation. A 1/18 reduced scale model structure was designed and investigated, the El-Centro wave, Taft wave and Arti cial wave were input as the earthquake excitation. This paper summarized the results of the experimental work and established the numerical simulation model of the receiver tower. The results between the experimental test and the numerical simulation were compared and they were in good agreement. This paper could provide important reference for evaluating the seismic behavior and the seismic design of receiver tower under vertical earthquakes.
2 Shake Table Test Setup   2.1 The prototype structure The prototype structure is a high-rise solar receiver tower located in a concentrated solar power plant, which has been used to power generation now ( Fig. 1(a)). The total height of the receiver tower is 243m, and it consists of the reinforced concrete cylinder (200m) and the steel truss (43m). The bottom diameter of the reinforced concrete cylinder is 23m and the top diameter is 20m. The elevation and section views are shown in Fig. 1(b).

Similarity design
The similarity ratios are one of the most important parameters in the shaking table test. In order to ensure the experimental results of the model structure accurately re ect the seismic performance of the prototype structure, the similarity ratios between the model structure and the prototype structure should be satis ed as much as possible. However, it is di cult to satisfy the similarity relationship of all physical quantities in a reduced scale model experiment. Generally, there are 3 controlling similarity ratios: length, stress, and acceleration in a shaking table test according the similarity law (Harris et al. 1983). The remaining similarity constants could be obtained according to quasi-dimensional analysis (Zhou et al. 2012). Considering the laboratory space and the capacity of the shaking table, the length similarity ratio is selected as 1/18; the lead powder microconcrete is used to replaced the ordinary concrete in the prototype structure, and its stress and elastic modulus are 1/3 of the prototype; the acceleration similarity ratio is decided to be 2.25 in order to avoid the insu cient inertia force. The rest of similarity ratios are calculated according to the quasi-dimensional analysis method, as shown in Table 1.

Materials
The scaled model structure is relatively small and can not be built using the materials in the prototype structure, so the lead powder micro-concrete, galvanized iron wire and red copper are selected to replace the ordinary concrete, rebar and steel in the prototype structure respectively. According to material experimental test, the material properties are obtained as summarized in Table 2. There is a certain error between the actual value and the design value of the stress and elastic modulus of the materials, but considering some in uence factors such as the special structure system, complex construction technology and the quality of the model, the similarity ratios of 1/3 of the stress and elastic modulus are acceptable in the test.

Design and construction of model structure
The simpli ed design of the model structure should follow the similarity law, and the scale design of the prototype structure should be carried out according to the similarity ratios, so that the test results can reckon the seismic performance of the prototype structure without much error. In fact, it is usually necessary to consider many factors such as the size of the test site and the construction environment, and then simplify or even ignore some secondary factors. The concrete cylinder of the model structure is designed based on the geometric similarity relationship, and the dimensions of the concrete cylinder are shown in Fig. 2 and Table 3. According to the similarity of bearing capacity , the simpli ed design of the longitudinal reinforcement and the circumferential reinforcement was carried out separately, it is summarized in Table 4 and shown in Fig. 3-4. The steel truss of prototype structure is simpli ed according to the equivalent lateral stiffness. The simpli ed copper truss structure and member types are displayed in Fig. 5-6.
The total height of the model structure is 13.980m (excluding 0.4m of the base), where the concrete cylinder is 11.290m and the copper truss is 3.1m (including the connection part). The total weight of the model structure is about 14.56t, which meets the requirement of the mass similarity ratio. The copper truss and the overall overview of the model are shown in Fig. 7-8.

Seismic waves and test conditions
The prototype structure is located in class site and 7 degree seismic forti cation. According to the selection requirements of the ground motions, combined with the Chinese speci cation( Code for seismic design of buildings GB 50009-2012 and Speci cation for seismic test of buildings JGJ/T 101-2015), at least 3 ground motions including two natural and one arti cial ground motions should be selected as the input seismic waves of the shaking table test. In this experimental test, two natural waves (El-Centro wave and Taft wave) were selected. The El-Centro wave: recorded from the Imperial Valley Earthquake (18, May, 1940). Taft wave: recorded from the Lincoln School Tunnel site in California during the Taft Earthquake (21, July, 1952). An arti cial wave was tted according to the response spectrum characteristics of the class site. The amplitude, frequency spectrum characteristics and duration time are the three main parameters of ground motion. All the waves for tests were corrected by the SeismoSignal software according to similarity principle. It is necessary to correct the amplitude, frequency and the duration time of these seismic waves so as to meet the similarity law. For example, the amplitude that also called the peak ground acceleration (PGA) in the test is equal to the peak value given by the Chinese speci cation multiplied by the acceleration similarity coe cient of 2.25. The input amplitude ratio of ground motion in different direction is 1 (X direction) : 0.85 (Y direction) : 0.65 (Z direction). All the seismic waves were well tted with the design response spectrum, Fig. 9-10 display the seismic waves and their acceleration response spectrum.
Before and after each loading condition, white noise (PGA = 0.030g) test was performed to study the dynamic characteristics of the model structure. The main research purpose of the paper is to study the seismic behavior of the receiver tower under vertical earthquake, therefore, in most conditions only Z direction seismic waves were input. In rare earthquake of 8 degree stage, three direction seismic waves were input in order to compare the vertical and horizontal earthquake response. The speci c test conditions are shown in Table 5.

Shaking table and measuring points
The shaking table test was carried out on the three directions earthquake simulation device in the Key Laboratory at Xi'an University of Architecture and Technology, Shaanxi Province, China. The parameters of the shake table are listed in Table 6. 33 acceleration sensors and 30 strain gauges were placed in the model structure in order to get the earthquake responses of the model conveniently. Fig .11 shows the layout of these measuring points.

Test phenomenon
The the PGA of 0.113g in Z direction: In the forti cation earthquake of 6 degree stage, El-Centro wave, Taft wave and Arti cial wave were input according to loading sequence. In the test process, the vibration of the whole model was very small, and no visible crack was found on the surface of the concrete cylinder, all the members of the copper structure did not buckle and no obvious deformation. The experimental phenomena showed that the model structure was in the elastic stage under forti cation earthquake of 6 degree.
The the PGA of 0.158g in Z direction: In the frequent earthquake of 8 degree stage, El-Centro wave, Taft wave and Arti cial wave were input according to loading sequence. The overall vibration of the model structure was obvious, some micro-cracks were formed on the surface of the concrete cylinder, and all the cracks appeared at the height of 0-2m, as shown in Fig. 12. Most of them were horizontal and several were diagonal, the length and width of every micro-crack was short and narrow, and all of the cracks were discontinuous. In the meanwhile, no visible local buckling or damage occurred in the copper structure. The white noise test showed that the vertical natural frequency of the model structure was attenuated slightly, but the reduction was small, which indicated the model structure was still in elastic stage, or may reach the edge of the elastic stage.
The the PGA of 0.225g in Z direction: In the forti cation earthquake of 7 degree stage, El-Centro wave, Taft wave and Arti cial wave were input according to loading sequence. The vertical amplitude of the model structure increased signi cantly, the vertical cracks appeared near the opening at the bottom of the model, and a series of cracks developed near 6-7m of the concrete cylinder, some of them extended to 300mm, as shown in Fig. 13. There was no obvious local buckling or damage occurred in the copper structure, which indicated the copper structure still kept good performance. The vertical natural frequency of the structure decreased further after white noise test, the results showed that the concrete cylinder may enter the elastic-plastic stage.
The the PGA of 0.900g in three directions (X: Y: Z= 1.00: 0.85: 065): In the rare earthquake of 8 degree stage, El-Centro wave, Taft wave and Arti cial wave were input according to loading sequence. Under the action of three-way seismic waves, the overall model shaked violently and the seismic responses were strong. The cracks at the 3m and 7m of the concrete cylinder continued to develop into horizontal circumferential cracks, the length and the width of the horizontal circumferential cracks were almost up to 3.5m and 0.8mm respectively (Fig. 14). Many new cracks appeared on the surface of the concrete cylinder due to the action of horizontal earthquake. In the copper structure, some columns and diagonal braces buckled, the overall stability reduced because of the buckling of members. But no visible deformation appeared in the horizontal beam, which meant the seismic responses of beam was small. By the white noise test, the natural frequency of model structure attenuated greatly, which indicated the stiffness of the model structure decreased at this time. Furthermore, the model did not collapse under high intensity earthquakes, it still remained bearing capacity.

Dynamic characteristics
Before and after each test stage, white noise test was carried out on the model structure to obtained the natural frequencies and damping ratios (Table 7) (1) and (2). The rst order mode factor can be obtained by normalizing the maximum displacement vector. Based on the mode factor, the rst-order mode shape in vertical is shown in Fig. 15. (1) (2) Where: k 0 is the initial stiffness of the model, and k is the stiffness at the end of each loading condition; m is the total mass ; f 0 is the initial natural frequency, and f is the natural frequency at the end of each loading condition.
The rst-order natural frequency in vertical of the model structure is relatively large, which is also in line with the general characteristics of high-rise structures: the vertical stiffness is signi cantly large, and the vertical vibration is close to high-frequency vibration (Li et al. 2011). With the increase of PGA, the vertical natural frequencies of the model structure gradually decreases. Before the PGA of 0.225g was input, the natural frequencies decreased slowly, and it begun to reduce quickly after the forti cation earthquake of 7 degree stage. The reason is that no damage occurred on the model structure or the damage was not severe before the PGA of 0.225g, while the damage became serious after the PGA of 0.225g was input. After the test, the vertical natural frequencies of rst three orders of the model structure reduced to 16.04 Hz, 17.38 Hz and 18.33 Hz respectively, which were decreased by 13.5%, 13.6% and 17.2% compared with the frequency before the test. The damping ratio increased gradually with the increase of PGA, especially after the input of the three dimensional seismic waves, the damping ratio increased from 0.045 to 0.096, which exceeded 0.005 that is damping ratio of RC structure de ned in Chinese speci cation (Load code for the design of building structures GB 50009-2012). Due to the damage of the model structure, the stiffness gradually decreased, and it decreased by 25.23% until the test was nished. Under the vertical earthquake, the vibration of the model structure is axial, it causes the vertical seismic force in model. The concrete cylinder is subjected to compression or even tensile stress, which results in horizontal circumferential cracks appear at the height of 3m and 7m, indicating that the two sections are dangerous part of the model structure.

Acceleration response
By analyzing the acceleration response at each measuring point of the model structure, the maximum acceleration at different heights under different PGA was obtained (Table 8). The acceleration ampli cation factors of the model structure under each working condition were further calculated by Equation (3), which is the ratio of the measured peak acceleration to the same direction peak acceleration at the base. It is an important indicator of the dynamic response of the model structure. (Fig. 16).
(3) Where: β i is the acceleration ampli cation factor at different height, a i, max is the maximum acceleration at measuring point, a 0, max is the maximum acceleration of the shaking table. Table 8 lists the maximum acceleration of model structure under different PGA. With the increase of PGA, the maximum acceleration also increase. Under the action of different PGA (0.113g, 0.158g, 0.225g, 0.900g), the average maximum acceleration are 0.401g, 0.519g, 0.713g and 1.979g, respectively.The receiver tower model consists of concrete cylinder and copper truss, but the acceleration responses of the two substructures are quite different. Under the same earthquake, the acceleration response of the copper structure is smaller than that of the concrete cylinder (Fig. 16), this is may attribute to the vertical whiplash effect that could reduce the acceleration response of copper structure.
The acceleration response of the concrete cylinder: Acceleration reaches the maximum value at the height of 2-8m under all seismic waves. Meanwhile the acceleration ampli cation factors under the arti cial waves are the largest among the three seismic waves, indicating that different types of seismic waves have different effects on the structural response. As the PGA of the input seismic waves gradually increase, there is no obvious change of the envelope diagrams of acceleration ampli cation factor, which has rarely been found in previous studies. As can be seen, β is the ratio of the PGA at measuring points to the PGA at the base, it is possible to present the same value under vertical earthquake. Under the PGA of 0.113g, 0.158g, 0.225g, all of the acceleration ampli cation factors are less than 1.0 at the height of 11m, while it is larger than 1.0 with the PGA of 0.900g. It shows that the acceleration response at the top of concrete cylinder is enhanced under the vertical earthquakes with high PGA. The acceleration response of copper structure: Under low seismic intensity, with the PGA increases, the acceleration ampli cation factors decreases, and it reduces to the minimum values when the PGA is 0.225g. But under high seismic intensity, for example, with the PGA of 0.900g, the acceleration ampli cation factor of the copper structure is close to that of the concrete cylinder, the reason may be that the arti cial mass on the copper structure increases the seismic response when subjected to vertical earthquakes with high value of PGA.
In term of the change rule of acceleration response, the two substructures are the same. That is, the acceleration response increases rst and then decreases gradually along the height, and the turning point of acceleration is located at the 2/3 height of the respective substructures, in which the acceleration response of concrete cylinder starts to decrease at the height of 8m, and the copper structure begins to decrease at the height of 12.5m. It indicates the range that from the height of 1/3 to 2/3 of each structure is the concentrated area of seismic response, which should be strengthened in seismic design.

Displacement response
Based on the second integration of the acceleration time history response measured by the acceleration sensor, the maximum displacement of the model structure at different height relative to the base under different levels of earthquakes can be obtained (Table 9). To analyse the displacement response better, the vertical displacement envelope diagrams are shown in Fig. 17.
Table. 9 and Fig. 17 show that with the increases of the PGA, the maximum displacement gradually increases, especially when the PGA is 0.900g, the displacement is almost twice compared with that of the PGA of 0.225g.
The displacement response of the model structure reaches its maximum at the height of 4m, and the maximum vertical displacement is 4.96mm under the arti cial wave. In view of the overall model, displacement response of concrete cylinder is larger than that of copper structure, and the displacement response is generally larger in the range from 4m to 7m, which shows that the displacement response of the model structure under vertical earthquake is mainly concentrated in the concrete cylinder. That may account for the severe damage of the model at the height of 3m and 7m, which is consistent with the test phenomenon. But generally speaking, the vertical displacement response of the model structure is always at a low level, indicating that the axial deformation of the model is not obvious under the vertical earthquakes. The displacement response of the connection part between copper structure and concrete cylinder is almost the same, which shows that the connection is reliable and the performance is good.
The displacement response characteristics of the concrete cylinder are similar to that of the acceleration responses, that is to say, the displacement response increases rst along the height and then decreases gradually. The displacement turning point is located at the 2/3 height of the concrete cylinder, and the displacement begins to decrease at 7m, illustrating the range of concentration area of the displacement response, which should be paid more attention. The vertical displacement of the copper structure is relatively small, and it is so tiny that can be neglected compared with the deformation ability of copper material.

Vertical seismic force
According to the acceleration response and structural mass distribution of the model structure, the vertical seismic force of the model structure under different levels of earthquakes is calculated. The speci c results are shown in Table 10, and the envelope diagram of the vertical seismic force is depicted in Fig. 18.   Fig. 18 shows the vertical seismic force increases with the increase of PGA. Under different PGA action, the maximum vertical seismic force occurs at the height of 2m. The main reason is that both of the acceleration and mass distribution are the largest at this position. It gradually decreases along the height and reduces to the minimum at the top of tower. Under the action of seismic waves with the PGA of 0.900g, the maximum vertical seismic force of the concrete cylinder at the height of 2m is 145.6kN, which is about 18 times compared with the maximum vertical seismic force of the copper structure whose maximum value is 7.8kN at the height of 12.5m. As shown in Fig. 18, the vertical seismic force of the model structure is mainly concentrated within the height of 2m-8m. This is because the vertical acceleration and mass distribution change along the model structure, causing the vertical seismic force to show the above-mentioned change trend. The damage of the concrete cylinder is also concentrated in this area, and the vertical seismic force is considered as the reason of structural failure.

Analysis Of Numerical Simulation
In order to verify the vertical earthquake responses of the shaking table test on the receiver tower model structure, a nite element model of the receiver tower was established with the widely used ABAQUS software. The S4R shell element and B31 beam elements were used in concrete cylinder and copper truss structure respectively. The constitutive relation of the lead powder concrete is shown in Fig. 19 (a) and (b) based on the Concrete Damage Plasticity Model. The ideal elastic-plastic model is used to de ne the copper members and galvanized wire, as shown in Fig. 19 (c). The parameters of the Concrete Damage Plasticity model and other material parameters are set in Table 11. The total nodes of the receiver tower nite element model are 6383, and the number of the elements is 6592, including 4288 B31 elements and 2304 S4R shell elements. Fig. 20 shows the whole receiver tower nite element model established in ABAQUS.

Dynamic characteristics of numerical model
The rst three natural frequencies of experimental and numerical model are summed up in Table 12. The rst natural frequency between experimental and numerical model are very close, their corresponding values are 18.55Hz and 19.06Hz respectively, the error is only 2.7%. Moreover, the errors of the second and third frequency between experimental and numerical model are 6.0% and 6.8% respectively. It shows that the experimental results are agree well with simulation results, which veri es the established numerical model could reproduce the earthquake responses of the receiver tower. Fig. 21 shows the rst vibration mode shape of the numerical model.

Time-history analysis of numerical model
The time-history analysis of numerical model was carried out with the three seismic waves that used in the shaking table test, and all the test conditions were also conducted in numerical model. Based on the experimental results, the earthquake responses under the arti cial wave are relatively large among the three seismic waves. Besides, there is limited to the article length. Therefore, only the earthquake responses under the arti cial wave with PGA of 0.158g and 0.900g are shown in this part.
The comparison of acceleration time-history curves between experimental and numerical simulation at the height of 4m are shown in Fig. 22. The difference of acceleration responses are minor, and the appearance time of peak acceleration is very close. It is indicated that the results of simulation are consistent with the experimental test. The errors of acceleration responses between experimental and numerical simulation are calculated, and the maximum errors of acceleration between experimental and numerical simulation with PGA of 0.158g and 0.900g are 6.1%, 14.7% respectively. Fig. 23 shows the comparison of vertical displacement time-history curves between experimental and numerical simulation at the height of 4m. With the PGA of 0.158g, the appearance time corresponding to the peak displacement of the simulation is slightly different with the experimental test, which is earlier than the experimental test. Whereas under the PGA of 0.900g, the appearance time of the peak displacement of the simulation coincides with the test. The peak displacement of the simulation is less than the test value under all conditions, which is considered to be the accumulated damage of the receiver tower in shaking table test and it does not be taken into consideration in the numerical simulation model. The maximum errors of vertical displacement between experimental and numerical simulation with PGA of 0.158g and 0.900g are 6.3%, 16.3% respectively.
The comparison of the time-history curves of vertical seismic force at the height of 2m under the three seismic waves with the PGA of 0.900g are shown in Fig. 24. The appearance time of peak value of time-history curves of simulation is highly consistent with the test value, while it can be seen that the peak vertical seismic force of simulation is slightly smaller than that of the experimental test. The average value of vertical seismic force under the arti cial wave is the largest among the three seismic waves. The maximum errors of vertical seismic force between experimental and numerical simulation are 11.1%. It is considered that time-history curves of simulation model basically coincides with the test model.

Damage patterns of numerical model
The result of numerical simulation model damage distribution is highly consistent with the test result, there is no observable damage under the PGA of 0.113g and little damage occurs under the PGA of 0.158g. In this paper, the damage distribution and stress nephogram of the numerical model with the PGA of 0.225g and 0.900g are presented in Fig. 25. It shows that the obvious damage rstly appears at the lower part and the middle section of the numerical model, with the PGA increases, the damage of the numerical model becomes severe. From Fig. 25(c), it can be seen that the damage in bottom, 3m and 7m of the numerical model, which coincides with the damage distribution of the test model and the damage in bottom of the model may be caused by the horizontal earthquake. The stress nephogram shows that the stress is relatively large below 8m, and the peak values appear at the damage area. Generally speaking, the numerical simulation agrees well with the experimental results.

Comparative Analysis Of Vertical And Horizontal Earthquake Action
The maximum horizontal and vertical acceleration are obtained under the action of seismic waves with the PGA of 0.900g (Fig. 26). It shows that the vertical acceleration of the concrete cylinder is much larger than that of the horizontal acceleration. C is de ned as the seismic action control coe cient, whose value is the ratio of horizontal shear force to vertical seismic force, as shown in Equation (4) and (5). When C is less than 1, vertical earthquakes play the control role in structural seismic responses, and the vertical earthquakes control effect decrease with the increase of C; whereas C is greater than 1, the horizontal earthquakes play the control role in structural seismic responses, and the horizontal earthquakes control effect increase with the increase of C. Table 13 shows the horizontal shear force of the model structure and the seismic action control coe cient C. As can be seen, in the range of 2m-8m of the concrete cylinder, the vertical seismic force is much larger than the horizontal shear force and the average value of the horizontal shear force is about 42.3% of the vertical seismic force, which indicates that the failure and damage at the middle position of the concrete cylinder is controlled by the vertical earthquakes. While at the base of the model structure, the steel-concrete connection part, and the copper structure, the average value of the horizontal seismic force is about 1.39 times to the vertical seismic force, demonstrating that and the horizontal seismic action de nitely plays the control role in these parts.
(4) (5) Where: C X , C Y is the seismic action control coe cient in X and Y direction; F X , F Y , F Z is the seismic force in X, Y, and Z direction.
In order to study the in uence of vertical seismic action on the structure, this paper uses nite element analysis to calculate the horizontal acceleration, horizontal displacement and bottom shear force of the model structure under the participation of vertical seismic. Compared with the seismic responses under horizontal seismic action, the seismic responses of the model structure under the XZ two-way earthquakes are greater than that of horizontal earthquakes, as shown in Table 14. The increment of those seismic responses under XZ two-way earthquakes are provided in Fig. 27.
When PGA is 0.225g, the top horizontal acceleration, displacement and bottom shear force of the model structure under XZ bidirectional earthquake action are increased by 2.20%, 11.30% and 2.50% respectively compared with those under single horizontal earthquake action. It shows that the vertical seismic action has a obvious in uence on the displacement of the structure. When PGA is 0.495g, the top horizontal acceleration, displacement and bottom shear force of the model structure under XZ bidirectional earthquake action are increased by 19.50%, 44.70%, and 9.30% respectively compared with those under single horizontal earthquake action. At this time, the structural responses generally increase, indicating that the in uence of vertical earthquakes on the structure is further strengthened, especially in terms of structural displacement and shear force. When PGA is 0.900g, the top horizontal acceleration, displacement and bottom shear force of the model structure under XZ bidirectional earthquake action are increased by 22.72%, 55.50%, and 20.10% respectively.
The in uence of vertical earthquake on the seismic response of the structure reaches the maximum, especially on the horizontal displacement. Therefore, the vertical earthquake action makes the structure more sensitive to the horizontal seismic action, and the vertical seismic action can not be neglected.

Conclusions
The solar receiver tower is a high-rise steel-concrete hybrid structure, which is also sensitive to vertical earthquake. To study its vertical earthquake responses and ensure its safety, shaking table test of a 1/18 scaled model structure was carried out, a series of vertical seismic waves were adopted to investigate the dynamic characteristics and seismic responses including acceleration and displacement. Moreover, a numerical simulation model of the receiver tower was established to verify the experimental results. The main conclusions of this paper were as follows: (1) Damage distribution: Vertical cracks appeared near the opening at the bottom of the model, and a series of cracks developed near 6-7m of the concrete cylinder under the action of vertical earthquakes with the PGA of 0.225g. The cracks developed rapidly due to the participation of horizontal earthquakes when the seismic waves with the PGA of 0.900g were input, horizontal circumferential cracks occurred at the height of 3m and 7m. The columns and diagonal braces of copper structure were subjected to large forces with the PGA of 0.900g, which caused buckling of members.
(2) Dynamic characteristics: The rst three vertical natural frequencies of the model structure were 18.55Hz, 20.12Hz and 22.14Hz, respectively. It showed that the vertical vibration was closed to the high-frequency vibration. With the increase of PGA, the vertical natural frequency decreased gradually, and the damping ratio increased that varied from 4.5-9.6%. In the meantime, the stiffness also reduced because of the damage in model structure, and it was almost decreased by 25.23%.
(3) Seismic responses: Under the vertical earthquake, the acceleration response at the height of 2-8m of the concrete cylinder was larger than any other parts of the model structure. The vertical displacement was also concentrated at the middle part, it reached peak value at the height of 4m, which was the mass center of the concrete cylinder. The seismic responses of the concrete cylinder were larger than that of copper structure, but they presented the same rule that seismic responses increased quickly and then decreased gradually along the height direction with the increase of PGA.
(4) Seismic forces: With the increase of PGA, the vertical seismic force also increased. In the range of 2m-8m of the model structure, the vertical seismic force was far greater than the horizontal shear force under the seismic waves with the PGA of 0.900g, while the horizontal shear force was larger than the vertical seismic force in other parts. The control coe cient of seismic action was calculated, which indicated that the vertical earthquake caused the damage of the concrete cylinder in the middle part, and the horizontal earthquake caused the damage of other parts.
(5) Numerical simulation: Time-history analysis of earthquake responses were conducted by the numerical model, the results of numerical simulation were highly consistent with the experimental test. It indicated that the numerical model and analysis method applied in this study were generally satisfactory.
(6) Seismic behavior: On one hand, under the action of rare earthquake of 8 degree, the severe damage occurred on the model, but the model structure did not collapse, which showed that the safety of the model structure could be guaranteed and the seismic behavior was good. On the other hand, since there was serious damage on the model, the impact of vertical earthquake should not be ignored.   Note: "6 degree, 7 degree,8 degree" represent the seismic intensity de ned by Chinese speci cation [44].      Longitudinal reinforcement con guration  Member types of copper structure    Cracks in concrete cylinder ( PGA=0.225g ) Figure 15 The rst-order mode shape in vertical Figure 16 Envelope diagrams of acceleration ampli cation factor of model structure Figure 17 Page 27/28

Declarations
Envelope diagrams of vertical displacement Figure 18 Envelope diagram of the vertical seismic force Figure 19 The constitutive relation of materials Figure 20 The whole receiver tower nite element model

Figure 21
The rst vertical mode shape The acceleration under different seismic waves with PGA of 0.900g

Figure 27
Increment of seismic responses under XZ earthquakes