shaking table 0f

development of the shaking table and array system technology in china

Chun-hua Gao, Xiao-bo Yuan, "Development of the Shaking Table and Array System Technology in China", Advances in Civil Engineering, vol. 2019, Article ID 8167684, 10 pages, 2019.

Shaking table is important experimental equipment to carry out antiseismic research. Research, conclusion, comparison, and analysis concerning the developmental history, constructional situation, performance index, control algorithm, and experimental technique of the internal shaking table were reviewed and compared. Such functional parameters as internal shaking tables table-board size, bearing capacity, working frequency, and maximum acceleration were given. Shaking tables constructional status quo and developmental trend were concluded. The advantages and disadvantages of different control algorithms were contrastively analyzed. Typical shaking table test, array system tests, and experimental simulation materials were induced and contrasted. Internal existing shaking table and array system tests structural type, reduced scale, and model-material selection were provided. Analysis and exposition about the developmental tendency of shaking tables enlargement, multiple shaking tables array, full digitalization, and network control were made. The developmental direction, comparison of technical features, and relevant research status quo of shaking table with high-performance were offered. The result can be reference for domestic or overseas shaking tables design and type selection, control technique, and research on experimental technique.

At present, the structural seismic research methods include the pseudostatic test, pseudodynamic test, and shaking table test. The test method of the shaking table test can recreate the structural response and seismic oscillation in the lab accurately and reproduce the whole process of seismic oscillation effect or artificial effect in real time. The development of shaking table provides an accurate and effective way to study structural elastic-plastic seismic response [13].

Japan and the United States are the first two countries to establish shaking tables in the world. And, China initially built a shaking table in 1960 [1] when Institute of Engineering Mechanics, Chinese Academy of Sciences, built one-way horizontal vibration [47] with a specimen size of 12m3.3m. So far in China, there are a lot of shaking tables [1]; some were made in China, some were systematically remodeled from imported parts, and some were totally imported. In recent years, many scholars [8, 9] and Wang et al. [2] conducted abundant research on the development and control technology of Chinas shaking tables and also got some research achievements. However, such results are mostly summaries of the test technologies or control technologies of shaking table [10], while there are few summaries concerning the construction history and usage of domestic shaking tables. This paper makes a comprehensive summary of the development and application of domestic shaking tables and array test technologies in terms of the development, control technology, test application, and development trend of shaking table and array system based on current collected information, so as to provide some reference and basis for the construction and development of domestic shaking table.

The development of shaking table in China came relatively late [1, 3, 1114]. It can be roughly divided into four stages. In 1960s, the mechanical shaking table was the main stream with a working frequency of 1Hz40Hz, of which the characteristics of the specimens in low segment are difficult to be controlled [2, 10, 11]. Electrohydraulic shaking table was then rapidly developed with its high frequency. In 1966, departments of machinery and electronics collaborated with each other to build Chinas first exclusive shaking table for national system of defense in three years [2, 10, 13]. Thereafter, many domestic colleges and universities as well as scientific research institutes also begun to conduct researches. For example, Tongji University brought in the 4m4m two-horizontal dimensional identically dynamic electrohydraulic shaking table developed by American MTS, which has been transformed into three- to six-degree-of-freedom identically dynamic shaking table [1]. At the beginning of the 70s, the research on shaking table in China was continuously carried out and quickly developed. Our country also started to develop one-way electrohydraulic servo shaking table but rarely hooked into multiaxis shaking table [1520]. And, foreign shaking tables were introduced only when the test was demanding, so the introduction quantity of shaking tables was sharply decreased. Domestic institutes that conduct researches on shaking table mainly include China Academy of Building Research, Xian Jiaotong University, HIT (Harbin Institute of Technology), Institute of Engineering Mechanics, and Tianshui Hongshan Testing Machine Co., Ltd. [21, 22]. The shaking table construction situation in China is shown in Table 1.

The work frequency of electrohydraulic shaking table in the early stage of our country was about 50Hz. At present, at home and abroad, the work frequency of high-thrust shaking table with over 50t can reach more than 1000Hz. For instance, the work frequency of Y2T.10c shaking table developed by 303 Research Institute of China Aviation Industry Corporation is as high as 1000Hz, and the wide band random vibration control precision is 2.0dB [23] within the frequency range of 20Hz1000Hz.

In 2006, Beijing University of Technology built a nine-sub-building block array system with a size of 1m1m, which along with the original 3m3m single-array system composed the 10-subarray system, which can be used to constitute testing systems with any several subarray systems and many optional positions; at the end of 2006, Institute of Electro-Hydraulic Servo Simulation and Test System of Harbin Institute of Technology (HIT) developed successfully the first domestic multiaxis independent intellectual property rights (the hydraulic vibration test system with shaking table system is shown in Figure 1) and got identification, which changed the history of depending on importing shaking tables [24]. In 2012, Jiangsu Suzhou Dongling Vibration Test Instrument Co., Ltd. successfully developed the worlds largest single electromagnetic shaking table test system ( with a thrust of 50 tons.

With the 9-subarray system of Beijing University of Technology as an example, this paper introduces the construction situation of shaking table array system. In 2003, The State University of New York built the first set of two-subarray systems. In the same year, the University of Nevada-Reno built the three-subarray system with three movable two-direction shaking tables. The size of the table and the maximum bearing capacity of the shaking table are introduced. The array system (shown in Figure 3) is suitable for experimental research on spindly space structure.

In 2004, Chongqing Jiaotong Institute of our country completed the constitution of the two-subarray system with a specimen size of 6m3m, of which one is fixed and the other is movable (shown in Figure 4). And, in 2008, National Key Laboratory of Bridge Dynamics was established.

In 2011, Beijing University of Technology began to prepare to construct nine-subarray system (shown in Figure 5) and has built 12 sets of actuator building block array systems till 2006, which was increased to 16 sets in 2009 and is now the array system with the largest number of single-array system in the world. Each single shaking table is composed by mesa, 5 connecting rods, a vibrator, and a base. The array system can be made into various combinations by 16 sets of vibrators and connecting rods to conduct varied shaking table array tests with different layouts and forms. The performance indicators of nine-subarray system are shown in Table 2. The system uses four piston pumps to offer oil. The rated oil supply pressure of the seismic simulated shaking table system is the same as the maximum oil supply pressure. In addition to 4 oil pumps, the system also has energy storage to supplement the oil supply when the oil supply of the oil supply pump is insufficient.

There are two main types of traditional shaking table control technology: one is PID control based on displacement control and the other is three-parameter feedback control (also known as the three-state feedback control) synthesized by the displacement, velocity, and acceleration [25]. It is essential for feedback theory to adjust the system after making the right measurement and comparison. In 1950, the PID control method mainly composed of unit P proportion, integral unit I, and differential unit D was developed. The traditional PID control method is simple in control algorithm, good in stability, and high in reliability and thus has been widely applied in the practical engineering. The PID control method is especially suitable for deterministic control system. Yet, as the target signal of shaking table is acceleration signal, high-frequency control performance is poorer when the displacement PID control is adopted, while the mesa cannot be located if acceleration PID is used. Meanwhile, in the process of control, nonlinear behavior exists in every specimen; thus, the effect of traditional PID control is not ideal due to the large waveform distortion [24, 2629]. As the structure sets higher requirement for control accuracy, three-parameter feedback control synthesized by the displacement, velocity, and acceleration was put forward in 1970s (the control principle is shown in Figure 6), which makes up for the narrow frequency band and the inability to realize acceleration control of single displacement control. Acceleration feedback can improve the system damping, and velocity feedback can improve the oil column resonance frequency. Adopting the displacement to control low frequency, speed to control midfrequency, and acceleration to control high frequency plays an important role in improving the dynamic behavior and bandwidth of the system. The introduction of three-parameter control technology greatly improved the playback accuracy of seismic time history, but due to the complexity of transfer function in the system, the correlation of input and output waveform is still not high. Power spectrum emersion control algorithm modifies drive spectrum utilizing system impedance and the deviation of the reference spectrum and the control spectrum, so as to get a relative high consistency of response spectrum and reference spectrum of the system [30, 31]. Power spectrum retrieval principle diagram is shown in Figure 7. This method belongs to the nonparametric method, which has nothing to do with any model parameters. But the matching degree of estimated power spectral density and real power spectral density is very low, so it is an estimation method with low resolution.

Another kind of the parametric estimation method, using the parameterized model, can give a much higher frequency resolution than period gram methods. The power spectrum control method based on the parameter model has high resolution and can improve the system control convergence speed and power spectrum estimation precision, yet it is sensitive to noise with higher computation requirements. Therefore, in the vibration test control, it has not reached practical stage [32].

The traditional control algorithm is based on the linear model of vibration table and specimen [33], and the parameters in the process of test are assumed unchanged, but the actual test object is very complex. The components experience elastic-plastic phase and then the failure stage in the process of the test, and the parameters that were assumed to be unchanged turn out to have been changed in the process of test. The change of the parameters influences the accuracy of the input seismic signal, which is the biggest defect in the traditional control technology. From the 1970s to 80s, intelligent control is a new theory and technology with strong control ability and great fault tolerance. The introduction of the adaptive control improved the robustness and control precision of the system, such as adaptive harmonic control theory (AHC), adaptive inverse function control theory (AIC), and the minimum control algorithm (MCS) [34]. At present, the fuzzy control algorithm of the structure control attracted the attention of more and more scholars with its advantages of powerful knowledge expression ability, simple operational method, and the adoption of fuzzy language to describe the dynamic characteristics of the system. As early as 1996, some scholars abroad has carried out the induction and comparison of structural seismic control methods and summarized the advantages and disadvantages of various control methods, particularly expounding that the fuzzy control and neural network control algorithm could better solve the problem of nonlinear. The application of domestic intelligent control algorithm in the engineering structure control is relatively late. In 2000, Ou [29] and other scholars proposed the control algorithm which can realize fuzzy control according to the control rules and fuzzy subset, which greatly improved the practicability and efficiency of fuzzy control algorithm.

Most of the fuzzy control rules are established based on experience, leading to great difficulty in structure control. In view of this, Wang and Ou [35], in 2001, put forward the method of extraction, optimization, and generation of fuzzy control rules with the basis of structural vibration fuzzy modeling and genetic algorithm. Qu and Qiu [36] came up with a kind of active feed forward control method based on adaptive fuzzy logic system method, which better solved the nonlinear control problems of reference signal and external interference in the feedforward control. Wang [30] for flexible structure completed the application of the fuzzy PID control method in the structural vibration and conducted the active control experimental verification of beam vibration.

The efficiency of fuzzy control depends on the selection of function parameters and the establishment of the fuzzy control rules. Therefore, the adaptive fuzzy control is of great research significance for the nonlinear structure system. Because of the functions of self-adaptation and self-study of artificial neural network, the application of neural network in seismic control in civil engineering began in the 60s, which adopts a simple neural network controller to control the movement of the inverted pendulum, and achieved good effect. In 2003, Mo and Sun [31] implemented numerical simulation of active vibration control on the beam vibration control model by using genetic algorithm with the minimum energy storage structure as the goal, compared with the exhaustive method, and achieved good control effect. Chen and Gu [37] carried out simulation research on the application of frequency adaptive control algorithm based on the least square method in the domain of vibration control, and the simulation got the damping effect of about 50db. Li and Mao [38] achieved evolutionary adaptive filtering algorithm with strong instantaneity and applied it into the vibration control of structures to conduct simulation calculation based on genetic algorithm and moving least mean square algorithm of transient step, and the simulation obtained the damping effect of about 30db.

To solve the limit bearing capacity of shaking table for large structure test, scholars from all over the world conducted a wide variety of researches. The combination of substructure technique and shaking table test is an effective way to solve this problem [39]. Hybrid vibration test divides the structure into test substructure and numerical substructure. Test substructure is the complex part in experiment on shaking table, while numerical substructure is the simple part to carry out numerically simulation. Test substructure can carry out full-scale or large-scale model test, avoiding the influence of the size limit of shaking table with large-scale structure, and thus was widely used in the study of the engineering seismic test. The domestic researchers Chen and Bai [33] implemented preliminary exploration into structural seismic hybrid test technique on account of the condensation technology. In 2008, Chen and Bai [33] also embarked on the hybrid vibration test on the hybrid structural system of commercial and residential buildings, of which the bottom commercial district was put into a full-scale experiment on shaking table and other parts were involved in numerical simulation.

In 2007, Mr. Wu Bin from Harbin Institute of Technology applied the center difference method into the change of the acceleration calculation formula in hybrid real-time test which takes consideration of the quality of test substructure and analyzed the stability of the algorithm. The test results show that the stability of the center difference method in real-time substructure application is poorer than that of the standardized center difference method. Such scholars as Yang [40] in the same year made the numerical simulation analysis on the shaking test substructure test, and the analysis results show that the integral step change is sensitive to the influence of experimental stability. At the same time, he verified the validity of the theoretical research results.

In recent years, the structural styles of shaking table test research were developed from masonry structure, frame structure, tube structure to bridge structure, structures with the consideration of some isolation and damping measures, and structural foundation interaction experiment. The application of shaking table tests on the structure seismic resistance made it possible to establish structure nonlinear model with various structural styles [2]. Many shaking table tests have been carried out in recent years in China, which, according to the testing purpose, can be roughly divided into three categories: the first type is to determine structural earthquake-resistance performance as the test purpose; the second type is to determine the dynamic characteristics of structure, obtain such dynamic parameters as the natural vibration period and damping of structure, seek for weak parts of the structure damage, and provide the basis for super high-rise and supergage designs; the third type is to verify the applicability of certain measure or design theory in the structure. This paper drew a conclusion of typical shaking table tests in recent years in terms of building types, model dimensions, and so on (shown in Table 3).

Shaking table experiment diversifies the structural styles in experiment, makes it possible to establish the nonlinear damage model, and provides a reliable basis for all kinds of structures to establish the corresponding destruction specification. But large span structure tests on bridges, pipes, aqueduct, transmission lines, and so on may produce traveling wave effect under the action of earthquake due to large span, and a single shaking table will not be able to simulate the real response of the whole structure under seismic action. Array system can better solve these problems. For example, the State University of New York-Buffalo did damper damping effect research on Greek Antiliweng Bridge using 2-subarray system; conducted shaking table array test research on two continuous steel plate girder bridge and concrete girder bridge by using the 3-subarray system of University of Nevada. Many domestic scholars also carried out shaking table array test research on different structures of array systems. For instance, in 2008, Gao Wenjun made shaking table array test research of organic glass model on Chongqing Chaotianmen Bridge with the 2-subarray system of Chongqing Traffic Academy; conducted a multipoint shaking table array test research on concrete-filled steel tubes arch bridge with the 9-subarray system in Beijing University of Technology.

According to the size of mesa, shaking tables can be divided into large, medium, and small ones; in general, specimen size less than 2m2m for the small, 6m6m for the medium, and over 10m10m for the large. Due to the size limitation of a small seismic simulation vibration table, it can only do small-scale tests, and there is a certain gap with the prototype test. In the seismic simulation vibration table test of scale model, all parameters are required to meet the similarity principle, but it is difficult to do in practical engineering. For some important structures, especially the important parts of large structures, to accurately reflect the dynamic characteristics of the structure, within the permitted scope of the condition of capital, it is necessary to increase the specimen size and the maximum load as much as possible to eliminate the size effect of the model, so the large full-scale test must be the development trend of shaking table. China Academy of Building Research developed a shaking table with a mesa dimension of 6.1m6.1m and the maximum model load of 80t.

Due to the great investment, high maintenance cost, and test fees as well as long production cycle of large-scale shaking table, infinite increase in size of shaking table is obviously unreasonable, and likewise, it is not possible to fully meet the actual requirements only by increasing the size of shaking table. For large-span structure tests on bridges, pipes, aqueduct, transmission line, and so on array systems composed of many sets of small shaking table can be adopted. Shaking table array can either conduct a single test or make seismic resistance test on the structure of large-scale, multidimensional, multipoint ground motion input with varied combinations according to various needs. Therefore, the array system composed of many sets of small shaking tables must be the development trend of shaking table.

In terms of control mode, power spectral density control was mostly adopted before 1975. After 1975, Huang Haohua and other scholars used the time-history playback control to finish the seismic wave control research in a broad band. In the mid-1990s, digital control and analog control are widely used in the shaking table control, of which digital control is mainly applied in the system signal and compensation and the analog control is the basis for the control, whose control mode is complicated in operation with too much manual adjustment. After 1990s, Fang Zhong and other scholars developed a full digital control technology which has been widely used in the hydraulic servo control system with the rapid development of digital technology. Other than the valve control device and feedback sensor which adopt analog circuits, the rest utilize digital software to fulfill implementation. This control method can make up for some flaws in the analog control with simple test operation, being able to improve the accuracy, reliability, and stability of the system. Full digital control is the inevitable development trend of hydraulic servo system control.

With the appearance of slender and shaped structures and the application of new materials in building engineering, the seismic test methods of structures are put forward with higher and higher requirements. To meet the requirements of actual engineering and seismic research, scholars from all over the world are active in exploration and attempt and put forward some new testing methods. In recent years, countries around the world greatly invest in seismic research. From 2000 to 2004, the United States Science Foundation Committee spent eighty million dollars of research funding on the NEES plan; Europe established a collaborative research system European Network to Reduce Earthquake Risk (ENSRM); South Korea established a virtual structure laboratory using grid technology, which includes the wind tunnel, the shaking table, and other scientific research equipment. Furthermore, Internet ISEE Earthquake Engineering Simulation System in Taiwan of China was the earthquake engineering research platform developed by National Earthquake Engineering Research Center of Taiwan, China, with the Internet. The platform not only allows several laboratories to interconnect each other to implement large-scale shaking table test but also permits different laboratory researchers around the world to observe the test simultaneously and synchronously.

In China, Hunan University firstly put forward the structure network synergy test research and cooperated with Vision Technology Co., Ltd in 2000 to develop the network structure laboratory (NetSLab is shown in Figure 8). The main module and interface are shown in Figure 8. Thereafter, Hunan University cooperated with Harbin Institute of Technology to accomplish secondary development to establish the network collaborative hybrid test system and conducted a structure remote collaborative test along with Tsinghua University, Harbin Institute of Technology. Three domestic universities firstly completed remote collaboration pseudodynamic test, which is shown in Figure 9.

This paper drew a conclusion of the construction, history, and status quo as well as application and research of shaking table and array. The main conclusions are as follows:(i)On account of factors of actual application demand and economy, the size of the shaking table is between 1m and Xm, among which 3m6m are the majority. For large span structures such as bridges and pipes many sets of small array mode of vibration table can be used.(ii)Shaking table mesa acceleration and speed are about and 80cm/s, respectively. Through statistics, the remarkable frequency of previous ground motion records is mainly within 0.1Hz30Hz, and the frequency range of medium shaking table should be in 0Hz50Hz according to the requirements of the similar rule. Moreover, tests with special requirements need to be above 100Hz.(iii)With the appearance of slender and shaped structures and the application of new materials in building engineering, the seismic test methods of structures are put forward with higher and higher requirements.

The authors acknowledge the support from the Science and Technology Breakthrough Project of the Science and Technology Department of Henan Province ( 9), the Key Scientific Research Projects in He Nan Province (No. 18B560009), and Nanhu Scholars Program for Young Scholars of XYNU in China. The authors thank Xin Yang Normal University School of Architecture and Civil Engineering Laboratory and would also like to thank teachers and students of the team for collecting data.

Copyright 2019 Chun-hua Gao and Xiao-bo Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

shaking table test on the seismic responses of a slope reinforced by prestressed anchor cables and double-row antisliding piles

Zuo-ju Wu, Zhi-jia Wang, Jun-wei Bi, Xiao Fu, Yong Yao, "Shaking Table Test on the Seismic Responses of a Slope Reinforced by Prestressed Anchor Cables and Double-Row Antisliding Piles", Shock and Vibration, vol. 2021, Article ID 9952380, 13 pages, 2021.

The combined retaining structure has gradually received considerable attention in the slope engineering, due to its good reinforcement effects. However, most of the published research studies were focused on the seismic responses of the single-formal supporting structure only. The investigations of dynamic responses of the combined retaining structures are scarce, and the current seismic design is conducted mainly based on experiences. In this work, a series of large-scale shaking table tests were conducted to investigate the seismic responses of the combined retaining structures (i.e., prestressed anchor cables and double-row antisliding piles) and the reinforced slope under seismic excitations, including amplification effect of internal and surface acceleration of the reinforced slope, distribution and change of prestress of the anchor cable, dynamic response of soil pressure behind the antislide pile, and horizontal displacement of the reinforced slope surface. Test results show that, supported by the reinforcement of composite support system, the slope with the multilayer weak sliding surface can experience strong ground motion of 0.9g. The load of the antisliding pile has reached 80% of its bearing capacity, and the load of the anchor cable has reached 75.0% of its bearing capacity. When the seismic intensity reaches 0.5g, the slope surface has an obvious downward trend, which will make the corresponding soil pressure suddenly increase after the antislide pile. At the potential sliding zone, the axial force of the anchor cable will increase suddenly under the action of earthquake; after the earthquake, the initial prestress of the anchor cable will be lost, with the loss range of 17.0%23.0%. These test results would provide an important reference for the further study of the seismic performance of such composite support structure.

There are many mountains in Southwest China, so there are many slopes. Particularly, most slope projects in Sichuan Province are located in the areas with high seismic intensity. When strong earthquakes occur, these supporting structures (such as anchor cables and antisliding piles) are often damaged [13]. Therefore, the seismic research of the slope-supporting structure is of great significance.

As an important mean to study the seismic performance of supporting structures, the shaking table test has been developing rapidly in the past decade. Lai et al. [4] conducted shaking table tests to research the seismic responses of a slope reinforced by double-row antisliding piles, which indicates that the double-row antisliding piles could effectively resist the combination of tension and shear during earthquake. Jiang et al. [5] performed a series of shaking table model tests of the slope supported by anchor cables to deeply study the responses and characteristics of the reinforced slope under earthquake action. Ye et al. [6] investigated the seismic behavior of a slope reinforced by prestressed anchor cables through the shaking table test, in which the antislip mechanism of the prestressed anchor cables is well analyzed. Lin et al. [7] conducted experimental and numerical investigations and researched the seismic behavior of an anchoring frame beam under earthquakes. Through model tests, Zheng et al. [8] investigated the seismic-induced damage and deformation patterns of a rock slope reinforced by prestressed cables. Xu et al. [9] conducted a shaking table test to determine the load transfer mechanism and dynamic response characteristics of a slope supported by adaptive anchor cables. Ma et al. [10] used the shaking table test to study the distribution and variation of the dynamic soil pressures acting on supporting structures, including the antisliding pile and the prestressed anchor slab-pile wall. Through a series of shaking table tests, Ding et al. [11] investigated the seismic behavior and performance of the slopes reinforced by concrete-canvas and composite reinforcement. Zhou et al. [12] analyzed the seismic damages of road slopes in Wenchuan earthquake and pointed out that the prestressed anchor cable and antisliding pile have good earthquake resistance performance. Currently, the combined retaining structures are more and more widely applied, especially for large-scale slope and landslide projects. Lin et al. [13] performed shaking table tests and investigated the dynamic responses of a slope which is reinforced by prestressed anchor cables and single-row antisliding piles. More recently, Fan et al. [14] conducted experimental investigations to study the dynamic behavior of a slope reinforced by double-row antisliding piles and prestressed anchor cables under Wenchuan seismic excitations.

The above studies mainly focus on the seismic response of the single-formal support structure. However, the dynamic response of the slope reinforced by the composite support structure under earthquake action is very limited. Moreover, investigations related to the seismic responses of the slope reinforced by prestressed anchor cables and double-row antisliding piles are rather scarce, and the corresponding design method for such combined retaining structure is still unclear. Therefore, further in-depth study on the dynamic responses of prestressed anchor cables and double-row antisliding piles under the earthquake loadings must be available to improve the current seismic design.

To address these issues, a series of large-scale shaking table tests were conducted to investigate the seismic responses of a slope reinforced by prestressed anchor cables and double-row antisliding piles. Some meaningful conclusions and recommendations are obtained based on the analysis of test results.

Figure 1 shows the prototype slope that is located in Sichuan, China. The height and width of the slope are about 150.00m and 325.00m, respectively, and the elevation of the slope toe is 606.00m. A typical cross section for the shaking table test is selected, as shown in Figure 2. According to the site exploration, the slip bed of the prototype slope mainly formed in intact celadon shale, and the sliding mass mainly consists of the highly weathered shale and Quaternary alluvial deposit. There are two slip surfaces inside the slope, which the potential sliding zones consist of the silty clay with minor gravels. The parameters of the prototype slope are listed in Table 1. In reference to Seismic Ground Motion Parameters Zonation Map of China [15], the seismic design intensity of the prototype site is 7.00. Therefore, taking consideration of the significance of the prototype slope, the effects of seismic loadings should not be neglected. According to the results of stability analyses, the safety factor of the prototype slope under earthquakes is 1.03, and the value of which under the pseudostatic conditions is 0.90. The peak ground acceleration and seismic influence coefficient in the horizontal direction are 0.15g and 0.24, respectively. The calculations show that the residual sliding force of prototype slopes is extremely large; thus, the original design of single-row antisliding piles and prestressed anchor cables could not meet the needs of stability. Therefore, the slope is designed to be reinforced by prestressed anchor cables and double-row antisliding piles.

The shaking table facility used for the tests allows input of three directions of earthquake records with independent control. The shaking table has 6 degrees of freedom, including 3 degrees of translation and 3 degrees of rotation, and the dimensions of which are 6.0m by 6.0m. At full load, the maximum acceleration could reach 1.0g in the horizontal direction and 0.8g in the vertical direction. The maximum displacements of the shaking table in the horizontal and vertical direction are 150.0mm and 100.0mm, respectively, and the loading frequency range of which is 0.1Hz80.0Hz. Additionally, a data acquisition system with 128 channels is adopted, which the maximum error can be controlled within 5.0%.

According to the scaling laws, three controlling parameters were selected, which are the dimension L, density , and acceleration a, respectively. Limited by the dimensions and bearing capacity of the shaking table facility, the similar constants of dimension (CL), density (C), and acceleration (Ca) were set to be CL=100.0, C=1.0, and Ca=1.0 for this shaking table test, leading to the model slope height of 200.0cm. Based on the Buckingham theorem [16], the similarity ratios of other parameters for this model test could be obtained, as illustrated in Table 2, and the detailed derivation of which could be found in Ref. [17].

The slope model was placed in a rigid box container with waterproof treatment which fixed on the shaking table, and the dimensions of the box are 325.0cm150.0cm250.0cm (lengthwidthheight), as shown in Figure 3. The slope model was built layer by layer, in which the height of each layer is 20.0cm. Based on the required thickness and density of each layer, similar materials with a certain quality would be placed into the model box and then compacted to the desired thickness. After each layer was compacted, the cutting ring method was applied to ensure whether the unit weight meets the requirements or not. For the potential sliding zones, the similar materials were obtained from the prototype slope and remodeled for the shaking table tests. After the test model was built, the slope model is saturated through the pipes preinstalled in the model slope. Additionally, for each component of the model slope, samples were collected, and soil mechanics tests (i.e., cutting ring method, resonant column test, direct shear test, uniaxial compression test, and triaxial test) were performed to obtain the physical parameters. The mechanical parameters of the test model are presented in Table 3.

After the model slope was completed, the prestressed anchor cables and double-row antisliding piles were used to reinforce the slope through the reserved holes. Considered to be rigid, the antisliding piles were made of concrete with a section of 2.0cm by 3.0cm, and the bending deformation of which were ignored in this work. As shown in Figure 4, a row of antisliding piles labeled the Pile A were installed at the waist of the model slope, and the other row of piles named the Pile B were located at the slope toe. The height of the Pile A and B are 20.0cm and 16.0cm, respectively. Due to the limitation of the model size, it is difficult to install too many rows of prestressed anchor cables in the mode slope. It should be pointed out, in this work, the adjacent six rows of prestressed anchor cables are merged to be one row. Therefore, three rows of prestressed anchor cables numbered 1#, 2#, and 3# were installed above the Pile A, as can be seen in Figure 4; the other four rows were installed between the Pile A and B, which were numbered with 4#, 5#, 6#, and 7#.

For the prestressed anchor cables, as presented in Figure 5(a), the construction holes were reserved using PVC pipes with diameter of 8.0cm. The prefabricated anchor cables were inserted into the reserved holes. Then, with pulling the PVC pipes out, the reserved holes were filled with sand simultaneously. The depth of sand was determined by the designed length of the anchorage segment of the anchor cable. In this shaking table test, the length of the anchorage segment is 8.0cm. The cable material is steel with the diameter of 2.0cm. The inclined angle of the prestressed anchor cable is set to 20.0. According to the designed pulling resistance and the similarity ratio, the filled sand in reserved holes was manually compacted for a given number of times, which was determined by the previous compaction test in the laboratory, as presented in Figure 5(d). The prestress of the anchor cable was applied by rotating the nut on the screw which was fixed on the lattice beam, and the applied prestress was close to real-time values measured by the axial force monitoring. It should be noted that utilizing the sand to fill the reserved holes does not seem to match the in situ field situation. However, by controlling and monitoring the prestress strictly, the specific physical significance of anchor cables in this shaking table test agrees well with that in the in situ field situation. In addition, to attenuate the wave reflection from the steel box during shaking, the expanded polystyrene boards with a thickness of 10.0cm were placed between the slope model and test box [18, 19].

As shown in Figure 4, a total of 14 three-dimensional accelerometers were installed inside the model slope and on the slope surface to measure accelerations in the horizontal and vertical directions. For the horizontal direction, the sensitivity of accelerometers is 173.46mv/g, which is 192.08mv/g in the vertical direction. To measure the displacements on the slope surface, six laser displacement meters with the range of 30.00cm were installed at different locations throughout the slope height, and the sensitivity of which was 33.33mv/mm. For the prestressed anchor cables, as shown in Figure 5(b), axial force sensors installed at the tension segment were employed to measure the axial force. The sensitivity of the axial force sensor was 1.50mv/v. Additionally, the dynamic earth pressure acting on the back of antisliding piles was measured by the earth pressure cells with the measuring range of 0.00MPa0.80MPa. As illustrated in Figure 5(c), five earth pressure cells were installed on the Pile B and numbered with 1#5#; the other five ones for the Pile A were numbered with 6#10#.

All the abovementioned sensors are new, and calibration of which was conducted before the shaking table test. Moreover, to attenuate the boundary effect on the test results, all the earth pressure cells and axial force sensors were installed on the middle column of antisliding piles and prestressed anchor cables, and all the accelerometers and laser displacement meters were also installed in the middle section.

The seismic loading used in this shaking table test was the El Centro earthquake record which has been widely used in the earthquake engineering. Two simultaneous loading directions of seismic excitations were applied in this shaking table test, namely, the X and Z direction, for which the corresponding time histories of the input seismic motions can be seen in Figure 6. Based on the similarity criteria, the input earthquake records were compressed in the time axis with a compression ratio of 10.00 (the similarity ratio of Time t). Six different horizontal peak accelerations of the input seismic loadings (i.e., 0.15g, 0.30g, 0.40g, 0.50g, 0.70g, and 0.90g) were selected. As highlighted in Refs. [2022], the vertical peak acceleration is generally two-thirds of the horizontal peak acceleration. Additionally, before the excitation of the El Centro earthquake record, the model was scanned by the 0.05g white noise. The loading sequence of the shaking table tests is listed in Table 4.

The slope would have obvious nonlinear responses under strong seismic motions [23]. According to Ref. [24], the acceleration amplification behavior of the prototype slope could be well revealed by the shaking table test. In this study, the baseline corrected and band-pass filtered are adopted to the measured signals before calculating amplification factors. The peak values of horizontal accelerations are obtained by taking the maximum absolute values from the acceleration time histories.

In this section, the ratio of the peak horizontal acceleration obtained on the slope surface or inside the slope to that collected by A14 is defined as the amplification factor. Figure 7 presents the variations of the amplification factor of horizontal acceleration on the slope surface and inside the slope. As shown in Figure 7(a), comparing with the slope mass above the Pile A, the amplification factors on the slope surface between the Pile A and B are smaller. This indicates that the existence of the Pile A weakens the seismic responses of the slope effectively. However, for the slope mass above 1# anchor cable, the acceleration amplification factor increases rapidly along the slope height because of the reason that this part of the slope is not reinforced by any supporting structures. Based on the above analysis, the prestressed anchor cables and double-row antisliding piles could effectively reduce the dynamic responses of the slope surface under earthquakes. It can be seen from Figure 7(b) that the amplification factor of horizontal acceleration inside the slope increases generally with the slope height, whereas the acceleration amplification factor decreases when the seismic waves pass through the potential sliding zone from the bottom to the top. It indicates that some of the energy carried by earthquake waves could be dissipated by the potential sliding zone.

To research the seismic responses of prestressed anchor cables, the axial force of each anchor cable was measured, and the initial values of which before each excitation are listed in Table 5. For 2# prestressed anchor cable, the time histories of the axial force under the El Centro seismic loading with different amplitudes are plotted in Figure 8. From the figure, the variations of axial forces are similar to the time history of the input excitation (in Figure 6). The peak values of axial force occur at around the same time for that of the input earthquake motion. In this work, to well discuss the seismic responses of the prestressed anchor cables, the peak values and residual values of the axial force are analyzed separately.

Figure 9 shows that the peak values of the axial force of prestressed anchor cables increase with the amplitudes of the input seismic loadings, especially when the input amplitude is larger than 0.5g. It indicates that the performance of the anchor cable is taken full advantage when the amplitude of excitation is greater than 0.5g. As presented in Figure 4, seven rows of prestressed anchor cables can be divided into two parts by the Pile A. The maximum increment of the axial force occurs in 2# prestressed anchor cable. The increment of the peak axial force of 1# anchor cable is larger than that of 3# anchor cable, especially when the input amplitude of seismic motion is larger than 0.4g. It indicates that stronger dynamic responses occur on the upper part of the slope. Under earthquake loadings, the sliding force is firstly undertaken by the anchor cables located in the upper part of the slope, and the rest of which is undertaken by other anchor cables. For the prestressed anchor cables located between the Pile A and B, the increment of the peak axial force increases generally with the slope height. However, the increment of the peak axial force in 7# anchor cable is larger than 5# and 6# anchor cables and smaller than 4# anchor cable. This is due to that, with a shorter free segment, the seismic responses of the axial force of 7# anchor cable are mainly influenced by the anchor cable length.

To further reveal the relationship between the initial axial force and the variation of axial force during shaking, the notation is defined in this section as the increase rate of axial force, which is expressed as follows:where A1 is the initial axial force of the anchor cable and A2 denotes the peak value of axial force during earthquake loadings.

The increase rates of the axial force of anchor cables under the El Centro earthquake motions with different amplitudes are depicted in Figure 10. It can be seen from the figure that, under 0.50g, 0.70g, and 0.90g seismic excitations, the increase rates of axial force for 2# anchor cable are 2.49, 4.22, and 6.79, respectively, which is the maximum among the prestressed anchor cables. For the other anchor cables, the increase rates are smaller than 2.00 when the amplitude of earthquake loading is not larger than 0.70g, and in the range of 0.833.30 under 0.90g seismic motions. In reference to the current seismic design method, the safety factor of the calculation of the section area for the prestressed anchor cable is 2.20, in which only static condition is considered. It can be highlighted that the performance of the prestressed anchor cable under dynamic conditions should be taken into consideration in the seismic design.

The occurrence time of the peak axial force for seven prestressed anchor cables under different excitations is shown in Figure 11. To ensure the integrity of the data collected in the shaking table tests, the data acquisition starts some time before the input of each excitation. Therefore, it is meaningless to compare the occurrence time of the peak axial force with time history of the input El Centro seismic motion, and the comparison of the occurrence time of peak axial force between different prestressed anchor cables would be discussed in this work. It can be seen from Figure 11 that the most anchor cables get their peak vibration values almost at the same time under each seismic excitation, which indicates that all the prestressed anchor cables work together during shaking. However, under 0.15g earthquake motion, the occurrence time of the peak axial force for the anchor cables located in the upper part of the slope is somewhat earlier than those in the lower part. This is mainly because that the slope mass is compacted during the seismic excitations, which affects the propagation of the earthquake wave in the slope.

For the seismic design of the prestressed anchor cable, the prestress loss and the residual value of axial force after earthquake are of great significance. In this work, the notation is defined as the changing rate of axial force, which is expressed asin which A1 is the initial axial force of the anchor cable and A3 denotes the residual value of axial force after each seismic excitation.

The changing rates of axial force for each anchor cable under seismic excitations are presented in Figure 12. When subjected to 0.15g seismic motions, the loss of prestress for 1#, 2#, and 3# anchor cables are 11.00%, 16.00%, and 22.00%, respectively. Under the excitations with amplitudes in the range of 0.30g0.70g, the prestress of 1# anchor cable is lost by 4.00% approximately, and by 21.00% under 0.90g seismic motion. Both for 2# and 3# anchor cables, the prestress increases under 0.30g0.90g seismic excitations. The maximum increment of prestress in 2# anchor cable is about 10.00%, which is greater than that in 3# anchor cable. The loss of prestress for 4#, 5#, and 6# anchor cables are 21.00%, 23.00%, and 19.00% under 0.15g earthquake excitation, whereas there is almost no prestress loss in 7# anchor cable. When subjected to 0.30g excitation, the residual axial forces of prestressed anchor cables between the Pile A and B are mainly identical with the initial values. In addition, under the seismic motions with other amplitudes, the prestress of these four anchor cables increases about 10.00%. According to the analysis above, since the maximum of prestress loss is about 23.00% in this test, it is suggested that the initial axial force of the prestressed anchor cable could be raised by 1.201.30 times in the seismic design.

The test results show that the axial forces of the prestressed anchor cables in different slope areas are significantly different. It indicates that, for the current seismic design method, all the prestressed anchor cables are assumed to sustain the same load is inaccurate and uneconomic. In practice, the failure of one anchor cable can cause the failures of adjacent ones because of the chain reaction, which could lead to the slope failure. Therefore, the seismic response differences between anchor cables located in different areas should be fully taken into consideration in the seismic design. Additionally, to ensure the reliability of the prestressed anchor cables and the slope stability, specific design considerations should be adopted in the areas with different geological conditions.

The lateral earth pressures acting on the back of the antisliding Pile A and B under the excitations of El Centro earthquakes are shown in Figure 13. It should be noted that the lateral earth pressure plotted in Figure 13 is the dynamic earth, and the static pressure is not considered in this section. Both for the Pile A and B, the lateral earth pressure increases with the increasing input amplitude. Comparing with the Pile A, the lateral earth pressure acting on the back of the Pile B is much greater, especially for the location with relative height of 0.17 and 0.50. Under the excitations with the amplitude of 0.15g and 0.30g, the distribution curves of earth pressure acting on the Pile A are similar to the Pile B. However, when the input amplitude becomes larger than 0.50g, the lateral earth pressure acting on the Pile A decreases first and then increases along the height, and the minimum of which occurs near the location with relative height of 0.67. It can be seen from Figure 14(b), for the Pile A, the earth pressure acting on the pile toe is larger than that acting on the pile top. As highlighted in Reference [25], the earth pressure measured behind the piles can be equivalent to the earth pressure used in the traditional pseudostatic design, due to the piles are assumed to be rigid. Hence, the major cause of this phenomenon is that the plastic strain happens in the surrounding soil near the top and toe of the pile under strong earthquake motions. Note that, comparing with the soils, the model piles in this test are of infinite strength and stiffness, leading to rigid rotation and translation of piles during seismic loading. In addition, the difference of the distribution of earth pressure between the Pile A and B is mainly contributed that the Pile B is embedded much deeper than the Pile A and behaving nearly as a fixed pile.

For the seismic responses of double-row antisliding piles, few studies were related to the load-sharing ratio. The ratios between the peak lateral earth pressure acting on the back of the Pile B and A are depicted in Figure 14. It can be seen from the figure that the ratios change mainly in the range of 2.05.0, implying that there is a large difference on the load-sharing ratios between the Pile A and B. The earth pressure acting on the back of the Pile B is much larger than that of the Pile A. As highlighted in Refs. [15, 26], the seismic design intensity scale of most areas in China is not larger than 9.0, and the corresponding design acceleration of which is smaller than 0.4g. The test results in this work have an important practical significance for China and also can provide a reference for other countries and regions in the world.

The horizontal displacements on the slope surface were measured by the laser displacement meters located at different locations throughout the slope height. In this work, the horizontal displacement towards the slope is defined as negative and that away from the slope is defined as positive. In Figure 15, the peak horizontal displacements during seismic excitations and the postearthquake permanent displacements are presented. The figure shows that, when the input amplitude is not larger than 0.50g, the permanent lateral displacements on the slope surface are small which indicates that the reinforced slope is of good overall stability. The peak displacement and permanent displacement on the slope surface increase with the increasing amplitude of the input seismic motions. The slope could be divided into two parts by the Pile A, and the horizontal displacements on the slope surface both for the upper and lower parts of the slope increase with the elevation. Additionally, it should be noted that the negative permanent displacements on the slope surface occur under 0.15g El Centro earthquake motion. It is mainly because of that the slope mass is compacted somewhat under the dual actions of seismic motion and retaining structures, and this phenomenon is in accordance with the prestress loss of anchor cables under 0.15g seismic motion.

According to the test results, several conclusions can be drawn:(1)Comparing with the unreinforced part of the slope, the value and the increase rate of the acceleration amplification factor can be effectively controlled by the reinforcements of prestressed anchor cables and double-row antisliding piles, especially for the slope mass between the Pile A and B.(2)The maximum of prestress loss is 23.00%. When subjected 0.30g0.90g excitations, the maximum increment of axial force is 15.00%. It can be highlighted that the initial prestress of the anchor cable is suggested to be raised by 1.201.30 times in the seismic design for the slope with high requirements of deformation control.(3)The lateral earth pressures acting on the back of the Pile A and B increase with the increasing amplitude of the input seismic motions. Comparing with the Pile B located at the slope toe, the earthquake loading undertaken by the Pile A located at the slope waist is obviously smaller, and the load-sharing ratios between the Pile A and B mainly changed in the range of 2.05.0.(4)Under the seismic excitations, especially the input amplitude not larger than 0.5g, the lateral displacements on the slope surface can be controlled by the combined retaining structures well. It can be concluded that, reinforced by prestressed anchor cables and double-row antisliding piles, the slope would have a good overall stability.

This work was supported by the National Natural Science Foundation of China (Grant no. 51808466) and Young Talents Science and Technology Innovation Project of Hainan Association for Science and Technology (QCXM201807).

Copyright 2021 Zuo-ju Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

structural straightening with tension braces using aftershocks shaking table study - sciencedirect

Strengthening buildings with tension braces in the direction of residual displacement can straighten them during aftershocks.Using a buckling brace decreased residual drift by 65% on average and it did not push the frame in the opposite direction.Using a ratcheting brace changed residual drift 260% on average implying that it pushed the frame in the opposite direction.A gapping brace also changed the residual drift 150% on average.

Straightening of a two story low damage half scale steel structure with residual drift is investigated by shake table testing. A straight structure was initially subjected to a strong shake, so that it had residual displacements after the shaking stopped. Then, several methods were applied to the structure to evaluate their effectiveness in straightening the structure naturally using aftershocks. It was found that when the frame with no brace (NB) was subjected to additional shaking with the same record, residual displacements decreased by 15% on average. Use of a buckling brace (BB) decreased the residual drift by 65% on average and it did not push the frame in the opposite direction. While application of a ratcheting brace (RB) or a gapping brace (GB) led to an average increase of residual displacements by 160% and 50% in the opposite direction respectively. A numerical model developed captured the responses well.

multi-point shaking table test of a long tunnel subjected to non-uniform seismic loadings | springerlink

A 40-m long test was conducted to estimate the seismic performance of the tunnel of the Hong KongZhuhaiMacau Bridge project under non-uniform earthquake loadings. The test used twelve connected model boxes, a synthetic model soil and a scaled model tunnel. The model boxes included four active boxes, which were fixed to four isolated shaking tables that worked as excitation sources, and eight inactive boxes, which were passively excited by the active boxes through connections. The soil at the tunnel location was simulated with a mixture of sawdust and sand with mass proportion 1:2.5, that yielded dynamic properties analogous to those of the in situ soil. The tunnel model, at a 1/60 scale, was composed of 98 sections, each with dimensions 600375170mm, that were made of aluminum, which best approximated the target response of the actual tunnel, given the size of the model, geometry and scaled engineering properties required. In the tests, a non-uniform seismic excitation was provided by imposing the seismic wave to the active model boxes with a time lag equal to the time that would take a seismic wave to travel from one active box to the next along the axis of the tunnel. The test started with the assembly of the tunnel sections and installation of transducers on the tunnel at critical locations. After placement of the soil and the tunnel, the seismic loadings were applied through the active boxes. The test results showed that the acceleration response of the tunnel was larger than that of the surrounding soil. It was also found that the deformation of the tunnel joints under non-uniform excitation was larger than under uniform excitation, to the extent that it could jeopardize the safety of the tunnel had it been designed solely using the uniform excitation. The results of the experiments clearly showed that the effects of non-uniform seismic excitation should be considered for the seismic design of long tunnels.

Huo HB, Bobet A, Fernandez G, Ramirez J (2005) Load transfer mechanisms between underground structure and surrounding ground: Evaluation of the failure of the Daikai Station. J Geotech Geoenviron Engg 131:15221533

The research has been supported by the National Natural Science Foundation of China (51678438, 51478343), the Shanghai Rising-Star Program (17QC1400500) and the Shanghai Committee of Science and Technology (16DZ1200302, 16DZ1201904). The authors acknowledge the support from the Fundamental Research Funds for the Central Universities, the National Basic Research Program of China (2015CB057902), the Shanghai Municipal Engineering Design Institute (K2017J019) and the State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology (SKLGDUEK1723).

Yu, H., Yan, X., Bobet, A. et al. Multi-point shaking table test of a long tunnel subjected to non-uniform seismic loadings. Bull Earthquake Eng 16, 10411059 (2018).