gold shaker tables

gold shaker tables

Overflow from the grinding millruns over GoldShaker Tables which are flat and smooth and made of a fibrous wood known as yolombo. They are arranged in series much the same as blanket or amalgamation plate tables. The grain of the wood in the deck runs with the flow of pulp, and a sharp-pointed tool is used to scratch its surface in a crosshatched pattern. The fibrous wood stands up along the scratches and forms an ideal trap for free gold. Twice a day the tables are cleaned and the high-grade concentrate is amalgamated by hand in a wooden batea or gold pan.

During the early days of operation referred to, nine wooden mills totaling 66 stamps, one ten-stamp California-type stamp mill, and three sand-leaching cyanide plants were in operation. Use of this equipment was discontinued.

The gravity concentrators used in gold and silver milling plants are usually of the bumping-table or the endless-belt (Vanner) type. The former consists of a riffled deck carried on a supporting mechanism that permits adjustment of slide slope and connected to a head mechanism that imparts a rapid reciprocating motion in a direction parallel to the riffles. A cross flow of water is provided by means of launder or other type distributors mounted along the upper side of the deck. The feed enters just ahead of the water supply, concentrate is taken off at the lower end of the table, and tailings overflow the lower side (see Figs. 42and 43). A. M. Gaudin in Principles of Mineral Dressing, 1939, hasin Chap. XIII made a comprehensive mathematical analysis of the principles involved in flowing film concentration and tabling. On p. 294 Gaudin states:

The flowing film concentrators that are known as shaking tables utilize other principles besides those discussed so far (stationary tables). Shaking tables are provided with a reciprocating motion at right angles to the flowing fluid film and directed horizontally. This reciprocating motion of the table deck has an asymmetrical acceleration, the net effect of which is to cause intermittent travel of solids resting on the table. This is one of the auxiliary principles utilized in shaking tables.

Another auxiliary principle derives from the use of riffles which disturb the viscous flow of the fluid across the deck and substitute for it a fluid composed of one top layer flowing more or less by viscous flow and an eddying bottom layer.

They are responsible for the increased capacity of riffled decks over smooth ones. This is realized when it is considered that a smooth deck treats a bed one particle deep and a riffled deck treats a teetering suspension of particles often many particles deep. Each trough between successive riffles is a place where hindered settling and consolidated trickling occur.

The capacity of tables varies widely between a maximum of, perhaps. 200 tons per 24 hr. in coarse roughing operations to 5 to 10 tons per 24 hr, on very fine feeds. Around 10 mesh is about the upper practical size offeed, while only incomplete recoveries are made in the 200 to 325 mesh range. Finer material is lost on all but very low-capacity slime tables.

The endless-belt or Vanner type of table was developed for the purpose of recovering the fine mineral particles lost in ordinary table operation. With a feed range of minus 65 to 100 mesh, particles as fine as 10 to 20 microns are recovered, but the capacity of such tables is only 1 to 3 tons per 24 hr., and the vanner is now practically obsolete.

Tables can be operated on either classified (sized) or unclassified feed. The use of an unsized feed, particularly in roughing operations, as at Hollinger, is common practice, but it is generally recognized that preliminary sizing of the feed with each sized band going to a separate table is the more efficient practice.

A. W. Fahrenwald concludes that preliminary classification, particularly if classifiers of the hydraulic types are used, gives increased recovery, a higher grade concentrate, greater table capacity, and less middling for regrind; in other words, classification enables a table to do its best work.

development of the shaking table and array system technology in china

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. https://doi.org/10.1155/2019/8167684

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 (http://www.cnki.net/kcms/detail/11.2068.TU.20130124.1608.001.html) 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.

shaker dining room & kitchen tables by countryside amish furniture

shaker dining room & kitchen tables by countryside amish furniture

Our Shaker style tables are handcrafted for kitchen and dining room with hand-applied stains or two-tone finishes, expansion potential, and various shapes, and sizes. Shaker dining room tables, made from solid wood, are often characterized by sleek, simple designs and tapered legs.

Handmade in USA by expert Amish craftsmen, Countrysides Shaker kitchen tables range in size and hardwood specie availability. Defined by their simple, hardwood construction and classic tapered legs, Shaker dining tables are an easy fit in nearly any interior design scheme. At Countryside Amish Furniture, our Shaker tables are made from sustainably-harvested real wood. Your family will take pride in the high quality Amish craftsmanship and superior Shaker design details.

2021 Countryside Amish Furniture. All rights reserved. While we make every effort to provide accurate information, typographical errors in product descriptions, availability or pricing may occur. In this event, Countryside Amish Furniture reserves the right to correct any issues and contact you prior to processing your order.

dining table sets for 4 - ikea

dining table sets for 4 - ikea

At IKEA, we believe that no matter the size of your home, having a place to gather with your loved ones before and after each day is very important. For smaller homes, we have a great selection of dining sets with 4 chairs in many shapes and sizes to fit even the most unique spaces. Our 4-seater dining sets also come in different finishes and price points to make it easier for families to come together without breaking the bank.

reports of unexplained shaking rattles south florida residents on friday cbs miami

reports of unexplained shaking rattles south florida residents on friday cbs miami

The City of Weston even posted a tweet that reads, In regard to the rumbling that people in Weston felt just earlier. There was NO explosion in #Weston. There are reports this was felt in several counties. We do not have definitive information on what caused it at this time.

In regard to the rumbling that people in Weston felt just earlier. There was NO explosion in #Weston. There are reports this was felt in several counties. We do not have definitive information on what caused it at this time.

A CBS4 viewer said in an email her sliding glass doors and windows shook violently. Im in West Kendall. Friends as faar south as marathon and Islamorada felt it and as far north as Davie and Lauderhill.

The United States Geological Survey is not reporting any activity in South Florida, however, there was a strong 5.9 magnitude earthquake in Guatemalas capital Friday morning. The U.S. Geological Service said the earthquakes epicenter was located just off Guatemalas Pacific coast 3 miles south-southwest of Champerico. The USGS has not linked the earthquake in Guatemala to the what people felt in South Florida.

But one of the most notable events in Miami took place nearly one year ago. It was Jan. 28, 2020 when buildings in Miami had to be evacuated after a magnitude 7.7 earthquake rattled off the coast of Jamaica and was felt along the east coast of South Florida.

shaking hands (hand tremors): 14 causes and treatments

shaking hands (hand tremors): 14 causes and treatments

If an underlying condition, such as hyperthyroidism, is responsible for the tremor, it will usually get better when a person receives treatment. If a tremor is a side effect, it will often go away when a person switches medications.

This can improve muscle control, functioning, and strength while enhancing coordination and balance. An occupational therapist can help people living with tremors to continue to engage in daily activities.

DBS requires a doctor to place a small generator under the skin in the upper chest. It sends electrical signals to electrodes implanted in the thalamus, which is the part of the brain that coordinates and controls some involuntary movements.

shaking table tests for seismic response of oblique overlapped tunnel

shaking table tests for seismic response of oblique overlapped tunnel

Hao Lei, Honggang Wu, Tianwen Lai, "Shaking Table Tests for Seismic Response of Oblique Overlapped Tunnel", Shock and Vibration, vol. 2021, Article ID 8816755, 19 pages, 2021. https://doi.org/10.1155/2021/8816755

To study the dynamic response and spectrum characteristics of the three-dimensional crossing tunnel under the action of seismic load, we established a 1/50 downscale model based on a typical of the oblique overlapped tunnel and conducted a series of shaking table tests. Through examining the recorded dynamic responses (acceleration and dynamic strain measured at different locations in model tunnels), we found that the seismic response of the crown was the largest at the central section, and the invert of the tunnels was exactly opposite to the crown, which presented a parabolic distribution, and we inferred that the damage within the model may be mainly concentrated on the crown of the tunnels. Additionally, the dynamic strain showed obvious nonlinear and nonstationary characteristics under the action of different degrees of seismic intensities. Different from a single tunnel, the acceleration superposition effect appears in the cross section of two tunnels because of the spatial effect of overlapping tunnels, resulting in the obvious seismic response in the cross section. Meanwhile, we also found that the 1st dominant frequency (0.16.26Hz) seismic wave played a leading role in the process of tunnel slope failure. Furthermore, the analysis of the acceleration response spectrum also showed that the surrounding rock mass has an amplification effect on low-frequency seismic waves. These results help us better understand the features of the dynamic responses and also provide evidence to reinforce the overlapped tunnels against earthquakes.

In general, owing to the constraints of the surrounding rock, it is considered that the dynamic response of tunnel and underground engineering under earthquake is quite different from that of other structures. However, with the occurrence of many large earthquakes, a large number of tunnel structures have been damaged to varying degrees, and many scholars also have different opinions on the dynamic response of tunnel engineering under seismic loads [13]. Nowadays, lots of overlapped tunnels are inevitable in practical engineering, such as highway tunnel-railway tunnel, highway tunnel-highway tunnel, railway tunnel-railway tunnel, and subway [46]. Owing to the complexity of the overlapped tunnel, its damage and earthquake resistance under the action of seismic loading have become the key issues.

In recent years, scholars mainly focused on field investigation, theoretical analysis, numerical simulation, and model test for the seismic response of underground structures in the past. Among these means, theoretical analysis and numerical simulation are the most widely used. For instance, Gazetas et al., Parra-Montesinos et al., Anastasopoulos et al., and Andreotti et al. [710] carried out theoretical analysis in the mechanical behavior of underground structures subjected to earthquake loading. They not only described the development of appropriate ground motion parameters, including peak accelerations and velocities, target response spectrum, and ground motion time history but also proposed that the seismic design loads of underground structures are characterized in terms of the deformations and strains imposed on the structure by the surrounding ground, often due to the interaction between the two [11, 12]. These theories all provide references for the seismic dynamic response design of underground structures.

Different numerical approaches have been reported in the technical literature, for the investigation of tunnel dynamic response, for design, or for back-calculation of the dynamic test results in field or in the laboratory [1315]. In the dynamic analysis approach, seismic dynamic response of the tunnel is conducted using numerical analysis tools such as finite element or finite difference methods. For instance, Khoshnoudian et al. and Ding et al. [16, 17] carried out the numerical simulation for large-scale seismic response analysis of the tunnel by taking account of nonlinear material behavior such as soil, nonreflecting boundary definition, and soil-tunnel interaction and provided relevant data and references for the aseismic design of underground structures. Additionally, it was reported by Sun and Dias [18, 19] that the stress redistribution caused by the tunneling process has an important effect on the seismic forces in the lining, and numerical results revealed that the target damping ratios and the damping determination approaches have an important influence on the tunnel dynamic response analyses.

Shaking table tests can directly reflect the deformations and failure mechanisms of tunnels under vibrations and are therefore an important means for studying the seismic dynamic response and instability failure mechanisms of tunnels [20, 21]. The seismic performance of the rectangular tunnel under different excitations was studied, and the isolation mechanism of the damping layer was also discussed based on the centrifuge tests by Cilingir et al. and Chen et al. [22, 23]. In addition, it has been found that the sudden change of stiffness or cross section would cause stress concentration in the shaking table test of the immersed tunnel under nonuniform excitation [2426]. The shaking table tests were also conducted by Moss and Crosariol and Chen et al. et al. [2729] for the overlapped subway tunnel, which found that the peak strain and damage degree on both sides of the tunnel model structure were distributed in the form of S along with the height. Furthermore, Kutter et al. Tsinidis et al., Zhao et al, and Wu et al. [3033] not only conducted the shaking table tests of the subway but also used numerical simulation to verify the accuracy and rationality of the model. Zhang at al. [34] described discrepant responses between the cross passage and the twin tunnels by acceleration data. In the past study of the seismic performance of tunnel structures, researchers mainly focused on the dynamic response of single-line tunnels and subway tunnels. However, there are few shaking table tests on the overlapped tunnel, and no systematic research results have been obtained.

In this paper, the design of shaking table model tests for the overlapped tunnel is well first presented. Then, the peak acceleration and dynamic strain on the overlapped tunnels are discussed, and the specific section and measured point are analyzed in detail. Then, the wavelet packet is used to analyze the energy and spectrum of the invert of the upper-span tunnel and the crown of the under-crossing tunnel. Finally, a series of conclusions about the seismic response and seismic characteristics of the overlapped tunnel are drawn, which can provide a reference for the seismic design of such an overlapped tunnel.

The Pandaoling tunnel is located in Zhenxing District, Dandong City, Liaoning Province, with a total length of 4870m and a diameter of 7m, which is a single-track tunnel with a buried depth of about 17106m. The Strawberry ditch tunnel No. 1 is located in Strawberry ditch village, Dandong City, Liaoning Province, with a total length of 3205m and a diameter of 10m, which is also a single hole double line tunnel with a maximum buried depth of about 105m. The Strawberry ditch tunnel No. 1 spans the Pandaoling tunnel at DK250+865915. Further, the height difference of the rail surface at the intersection is 14.19m, and the net structure distance is 4.24m. The terrain position of the overlapping tunnel and the site position of tunnels are shown in Figure 1.

The rock formations in the cross section of the tunnel are mainly Proterozoic Sinian mixed granite, with relatively simple lithology, and the rock masses are gray-white. In addition, we used the TRT6000 advanced geological detector to forecast the geological conditions in the cross-affected zone, as shown in Figure 2. Within the mapping range, the blue range indicates that the geological structure of the section is weak, while the yellow range indicates that the geological structure of the section is hard. We found that surrounding rock was mainly composed of mixed granite with different weathering degrees with developed joint fissures, where it had VS (shear wave velocity) of 1000m/sec and Vp (pressure wave velocity) of 2600m/sec. Although the rock mass was relatively broken and there were surrounding rock cavities in some areas, no large-scale unfavorable geological structure had been discovered.

According to the relevant Chinese codes, the surrounding rock condition was set to the classification of grade IV, and the site area was in the area of the basic seismic intensity of grade VII. Owing to the poor nature of the surrounding rock in the area where the tunnel is located and the particularity of the overlapped tunnel, the tunnel may be severely damaged when an earthquake occurs and the traffic line may be paralyzed. Therefore, it is necessary to carry out the corresponding seismic response model test for the tunnel group in this area.

In this shaking table tests, the tunnel buried depth, section size, and shaking table size are considered comprehensively. Additionally, the design of the test model is reasonable and meets the geometric similarity to the greatest extent [35]. The similarity ratios of key controlling factors based on the Buckingham- theorem are summarized in Table 1. The similarity ratio of length CL, Youngs modulus CE, and density C are predetermined as 1/50, 1/30, and 1/1, respectively.

For example, according to the similarity relationship, it can be deduced that the diameter of the tunnel section is 20cm and the thickness of primary lining is 0.5cm and secondary lining is 1cm. As a summary, the properties of surrounding rock similar material and lining similar materials are tabulated in Table 2. Their counterparts in the engineering prototype, which were collected from the design document of the tunnel, are also listed in Table 2 for comparison.

Through the above similar relationship and considering the economics and feasibility of the actual material, the main materials used in this test are cement, coarse sand, water, and soil. Taking grade IV surrounding rock as an example, the orthogonal test design method, direct shear test, and triaxial test were used to determine similar material parameters. It is noted that the effectiveness of using these mixed materials to simulate the surrounding rock has been validated by the former study [36, 37]. To improve efficiency, only a single parameter was changed at a time and a total of 5 sets of ratio experiments were designed. The specific ratio and its mechanical parameters are shown in Table 3.

According to the above tests and similar relations, the proportion of similar materials in surrounding rock was finally determined. The surrounding rock of the prototype was simulated by a similar material, which was blended by cement, coarse, sand, soil, and water, with their mass mixture ratios of 0.5%: 12%: 5%: 2%. In the test, the thickness of the primary and second lining (0.5cm and 1cm) of the tunnel model was small, which was regarded as the whole structure (lining structure). Moreover, the lining structure similar material was made up of gypsum, quartz sand, and water by their mass mixing ratio of 10%, 15%, and 20%. The model of the tunnel and lining structure is shown in Figure 3.

To simultaneously analyze the response of the overlapped tunnels with different crossing forms, the model was set up with left and right sides, and the left side was the orthogonal type and the right side was the oblique type, respectively. This study mainly focused on the right oblique overlapped tunnel, and the response of the overlapped tunnel on the left will be described in other articles.

The tests were performed in combination with the servo-driven seismic simulation shake table system of the Lanzhou Institute of Seismology of the China Earthquake Administration. The laboratory adopts VPS-600ES-2 bidirectional (X direction, Z direction, and XZ direction) shaking table; the size of the vibration table is 46m, the maximum load is 25t, the working frequency is 0.150.0Hz, and the maximum displacement is 250mm in the X direction, 100mm in the Z direction, and 150mm in the XZ direction [38, 39].

The size of the model box is 2.80m in length1.40m in width1.80m in height, which both sides are composed of U-shaped steel plates and plexiglass. Considering the influence of rigid model box boundary effect, we dealt with the model box boundary. The boundary of the model box perpendicular to the horizontal excitation direction can generate shock reflection of the seismic wave, which makes the wave propagation quite different. The 5cm thick polystyrene foam board was adhered to the inner wall of the model box, which was treated as a flexible boundary. Additionally, the seismic wave is input from the bottom of the model box, so there should be no relative sliding between the model soil and the bottom plate of the box. A layer of 5cm thick gravel soil was laid on the bottom plate of the model box to increase the friction force. The particle size of the gravel was about 2cm, and the bottom plate was treated as a friction boundary. Furthermore, a smaller polystyrene foam ring was adhered to the tunnel portal, which was treated as a sliding boundary to prevent the tunnel structure from being affected by the vibration of the box. The model layout is shown in Figure 4.

This paper mainly studied the dynamic response characteristics of the affected section, surrounding rock, and slope body of the overlapped tunnel on the right side of the model box. Therefore, a total of 16 accelerometers were mainly arranged in the crown and invert axis of the tunnel, the cross-influence section of the two tunnels, and the inside of the slope body. Apart from this, 8 dynamic strain gauges were pasted on the outside of the two tunnels, respectively. The accelerometers are three-phase capacitive with a sensitivity of 680mV/g in the horizontal direction, 680mV/g in the X direction, 680mV/g in the Z direction, and 2g in range. The size of each accelerometer is 13mm15mm8mm. The dynamic strain gauges have a sensitive grid size of 9.8mm3.0mm and a base size of 15.5mm5.0mm, with a sensitivity coefficient of 2.02.20 and a temperature range of 3080C. The central cross section of the upper-span and under-crossing tunnels was set to I and I, respectively, and the two sides of the affected section 30cm away from the central cross section were marked as II, III, II, and III, respectively. The layout of the accelerometers and dynamic strain gauges is shown in Figure 5, where the accelerometers SA2, SA5, XA2, XA5, and PA1-PA4 were set on the central cross section and the dynamic strain gauges ZS2, ZS5, ZS7, and ZS8 (ZX2, ZX5, ZX7,and ZX8) were set on the central cross section I (I) as well. Additionally, accelerometers and dynamic strain gauges were only set on the crown and invert of the affected sections II and III (II and III).

During the loading process, sine waves, EL-Centro, and WenChuan (WC) waves were inputted in horizontal (X) and horizontal-vertical (XZ) direction, respectively, as shown in Figure 6(a). The seismic waves selected as input ground motions in the shaking table tests were sine wave and EL-Centro wave and were inputted in X direction in this paper. The EL-Centro earthquake record (Imperial Valley earthquake (Mw 6.9) in Southeastern California, USA) is the first strong earthquake record obtained by humans with a maximum acceleration exceeding 300 gal. Additionally, another important reason for choosing to load seismic waves is that the response spectrum of the EL-Centro seismic wave is in good agreement with the design response spectrum of Chinese seismic code (Code for seismic design of buildings GB50011-2010). Some previous studies [40, 41] have shown that horizontal earthquakes were the main cause of tunnel structural damage and landslides. Therefore, this paper only analyzed the dynamic response of one-way horizontal input seismic waves.

Moreover, if the time compression ratio of the seismic wave is less than 1:3.16 in the shaking table test, it will cause the seismic wave spectral components to be too complex and produce distortion, which will lead to adverse effects on the acquisition and processing of test data [42]. In this test of the manuscript, the time similarity ratio is 1:9.129, less than 1:1.316. Considering these factors, the seismic waves in the test were not compressed in time similarity ratio, and the original wave of the EL-Centro wave was input during the shaking table test. When the input peak value of acceleration is 0.1g, the acceleration time-history curve of the EL-Centro wave at the measuring point tabletop of the shaking table is shown in Figure 7(a). The sampling interval is T=0.0013s, the peak acceleration is 0.982m/s2, and the main vibration duration is about 23s65s, a total of 42s. The Fourier spectrum of the EL-Centro wave is shown in Figure 7(b), the predominant frequency is 1.02.5Hz, the maximum amplitude is about 0.019, and the amplitude of the seismic wave above 20Hz is almost zero.

The peak acceleration of ground motion along the engineering prototype site area is 0.15g, and the characteristic period of the ground motion response spectrum is 0.35s, which belongs to the basic earthquake intensity zone of grade VII. To meet the seismic design requirements of frequent, fortified, and rare earthquakes of the prototype area, the peak values of input waves were 0.1, 0.2, 0.3, and 0.4g, respectively. Additionally, to explore the failure mode of the tunnel model under extreme earthquakes, 0.6g was designed and loaded, as presented in Figure 6(b). Therefore, by inputting the designed seismic wave, all kinds of failure modes and dynamic response of the overlapped tunnel model are analyzed comprehensively under different seismic loads. Furthermore, to test the dynamic characteristics of the system and study the damage of the system with the input seismic, the sine-sweep (with the PGA of 0.05g) was inputted when the amplitude of input seismic was changed.

To compare the different dynamic response of the acceleration of the tunnel crown and invert under the same cases, the upper and lower horizontal axes were set as different section positions, while the left and right longitudinal axes were set as peak acceleration (Figure 8).

It can be seen from Figure 8 that the distribution and change of the peak acceleration of the upper-span tunnel show a certain regularity; that is, with the increase in the PGA, the peak acceleration at each measured point increases accordingly. For the crown of the upper-span tunnel, the peak acceleration is the largest at the section-I in the center of the intersection, and the peak acceleration values at the section-II and section-III on both sides of the affected section are almost equal, which is approximate parabola distribution. On the other hand, for the invert of the upper-span tunnel, the peak acceleration at the measured point SA5 significantly decreases, and their magnitudes are as follows: section-II

As the cross section is the key study object, the time history of acceleration at the invert (SA5) of section-I in the center of the intersection under different cases was also analyzed, as shown in Figure 9. When the PGA of 0.1, 0.2, 0.3, 0.4, and 0.6g seismic waves were inputted, the peak accelerations were 0.95, 1.78, 2.39, 3.06, and 4.57m/s2, respectively, and the peak acceleration basically occurred within 2040s after loading. Furthermore, the growth rate of peak acceleration is slow in the range of 0.10.3g, while it changes greatly in the range of 0.40.6g, which indicates that the invert of the upper-span tunnel is more sensitive to the high intensity seismic wave.

To more clearly illustrate the changing trend of crown and invert of the upper-span tunnel under different cases, we define the peak acceleration ratio (), as shown in equation (1), which is the ratio of the peak acceleration of each measured point under other cases (Case25) to the peak acceleration with the PGA of 0.1g. It can be seen from the above that with the PGA of 0.1g, the peak acceleration of the crown (invert) of section-I, II, and III is 2.33, 0.84, and 0.79m/s2 (0.95, 1.36, and 0.83m/s2), respectively. The results are shown in Figure 10. The peak acceleration of each section at the crown is more sensitive to the change of input cases, while the change of each section at the invert is more stable. Moreover, the acceleration magnification effect is smaller before 0.20.4g, and is 2.55 at the maximum, while has a sharp increase after 0.4g, which reaches 5.01 at the maximum. In particular, the dynamic response of acceleration at the SA2 of the crown does not change significantly with the different input seismic amplitude, while the seismic response of acceleration at the invert (SA5) has a noticeable transformation.where i denotes different cases, i=2, 3, 4, and 5 and j denotes different measured points, j=1, 2, 3, 4, 5, and 6. For example, is the peak acceleration of measured point SA1 in Case 1 (with the PGA of 0.1g).

The results illustrate that the peak values of strain under different cases show basically the same law when different amplitude seismic waves are inputted. With the increase in the input seismic amplitude, the peak strain of each measured point increases, and the envelope of the peak strain gradually spreads out. As for the Cases 1 and 2, the peak strain at each measured point is crown (ZS2)>side walls (ZS8 and ZS7)>invert (ZS5). However, the peak strain at each measured point is side walls>crown>invert when the inputted seismic wave amplitude is large (Case 35). The reason for this is that the displacement of the invert at the cross section of the upper-span tunnel is limited by the surrounding rock mass owing to the influence of the under-crossing tunnel. Further, on both sides of the side walls, the strain is relatively increased because of the small limit of the surrounding rock.

We also define the peak strain ratio (), as shown in equation (2), which is the ratio of the peak strain of each measured point under other cases (Case 25) to the peak strain with the PGA of 0.1g. Based on the peak value of each measured point in Case 1 (the PGA of 0.1g), Figure 12 presents the amplification factor of each case. It is implied that the maximum generated by the side wall is 13.16, which indicates that the side wall of the upper-span tunnel is the most sensitive to the seismic load response, followed by the crown, and the invert is the least obvious. Since the inputting direction is the direction of the cross section, the side wall of the tunnel is first subjected to seismic loading, and the effect is the strongest at this time. In addition, owing to the shallow depth of the crown of the tunnel, the absorption of the seismic waves by the surrounding rock is not obvious, and the soil body squeezes the tunnel to produce a large displacement, resulting in a large strain response. It is noted that this kind of view has also been presented in some former studies [43, 44].where i denotes different cases, i=2, 3, 4, 5 and j denotes different measured points, j=2, 5, 7, 8. For example, is the peak strain of measured point ZS2 in Case 1 (with the PGA of 0.1g).

The peak value of the acceleration of the crown and the invert of the under-crossing tunnel is also analyzed in Figure 13. For the crown of the under-crossing tunnel, the peak acceleration at the intersection section-I (XA2) is the largest, followed by the section-III(XA3) in the affected section, and the acceleration peak at the section-II (XA1) is the smallest, respectively. It is clear that the distribution of acceleration response at different sections is approximate parabola under the same case. However, the peak acceleration at the XA5 in section I is the smallest and at the XA4 and XA6 on both sides of the affected section are basically equal, which shows an approximate linear distribution. Additionally, it can also be seen that under different cases, the peak acceleration of the crown of the under-crossing tunnel is less than the invert, and the fluctuation of the peak acceleration of each cross section crown is not obvious. This is the reason why the crown is inclined to become a potential seismic damage area, which is very easy to cause damage to the model of the upper-span tunnel.

The time history of acceleration at the crown (XA2) of section-I in the center of the intersection under different cases is analyzed, as shown in Figure 14. It can also be seen from the time history that with the increase in the amplitude of the inputted EL-Centro wave, the acceleration response at the crown of the under-crossing tunnel changes smoothly. The peak acceleration is 4.04, 3.94, 4.02, 4.12, and 4.20m/s2 when the PGA is 0.1, 0.2, 0.3, 0.4, and 0.6g seismic waves, respectively, and the peak acceleration basically occurs within 2040s after loading. Different from the invert of the upper-span tunnel, the seismic response at the crown of the under-crossing tunnel is larger all the time, and its proportion is about 1, which indicates that the seismic response of the crown does not change significantly with the amplitude of seismic waves.

We also use to denote the changing trend of crown and invert of the under-crossing tunnel, here. With the PGA of 0.1g, the peak acceleration of the crown (invert) of the section-I, II, and III is 3.94, 0.94, and 0.78m/s2 (0.77, 0.93, and 0.90m/s2), respectively. From Figure 15, it can be seen that owing to the existence of the upper-span tunnel, the peak acceleration at the cross section I has little change, and the hovers around 1.0 under various cases. Further, the peak accelerations of the other measured points of each section are sensitive to the change of the seismic waves. The acceleration amplification effect has a small increase with the PGA of 0.20.4g, and the maximum is 2.70, while the shows a sharp increase with the PGA of 0.40.6g, which reaches 5.50.

The circumferential strain of the central section (section-I) of the under-crossing tunnel in different cases is summarized in Figure 16. Under low shaking intensity (Case 1 and Case 2), the peak strain of each measured point increases with the increase in the loading cases, and the envelope of the peak strain is basically the same as the upper-span tunnel, which is side walls (ZX8 and ZX7)>crown (ZX2)>invert (ZX5). When the inputted seismic wave amplitude is 0.3g, the peak strain envelope migrates to the right-side wall, and the maximum value of 27.53 appears in the crown, which is 54.3% of the upper-span tunnel. When the inputted seismic wave amplitude is large (0.4g and 0.6g), the envelope of peak strain gradually develops along the flat direction, indicating that when the seismic intensity is large, the response of the side wall is the strongest. However, the maximum strain on the side wall of the under-crossing tunnel is much smaller than that of the upper-span tunnel, which is only 11.1% of its peak strain. The surrounding rock absorbs part of the seismic waves because of the large burial depth of the tunnel.

Figure 17 also presents of each case based on the PGA of 0.1g (Case 1). The is approximately teardrop-shaped, and the maximum generated by the crown is 1.42, which indicates that the crown of the under-crossing tunnel is the most sensitive to the seismic load response, followed by the side walls, and the invert is the smallest. This rule also shows that with the increase in seismic intensity, there may be greater deformation at the crown of the under-crossing tunnel, while the invert is relatively stable.

Comparing the peak values of the circumferential strain of the upper-span tunnel and the under-crossing tunnel, it can be found that when the seismic intensity is small, the peak strains of the two crossing tunnels are basically the same. However, when the seismic intensity is high, the strain peak value of the upper-span tunnel is far greater than that of the under-crossing tunnel. The percentage of peak strain value of each measured point of the under-crossing tunnel to that of the upper-span tunnel is 11.1% for the side walls, 54% for the crown, and 62% for the invert. It is well known that owing to the interaction between the central sections of the tunnels, the existence of the upper-span tunnel weakens the dynamic response of the earthquake to the under-crossing tunnel. The same conclusion was reached in the studies of Sun et al. and Zhang et al. [45, 46].

To compare the similarities and differences of the acceleration response of the tunnel inside and outside the slope body, the location along the vertical centerline of the tunnel intersection, that is, the PA1-4 measured points inside the slope body are analyzed.

Form Figure 18, the acceleration amplification effect is not obvious with the PGA of 0.10.3g, while the acceleration amplification effect is more obvious along the elevation with the PGA of 0.4g and 0.6g. Taking P4 measured point as an example under the cases of 0.4g and 0.6g, it can be concluded that the acceleration amplification factors of P2 and P1 measured points are 1.05 and 1.22; 1.07 and 1.32, respectively; that is, the acceleration amplification factor is smaller at the bottom of the slope and larger at the top of the slope.

Generally, with the decrease in tunnel buried depth, the acceleration in surrounding rock and soil has amplification effect for a single tunnel, and the acceleration amplification coefficient gradually increases with the decrease in buried depth. However, the peak accelerations at all measured points inside the slope body (except for the measured point PA3 at the center of the intersection of the two tunnels) have an amplification effect along the elevation for the overlapped tunnel. Specifically, the peak acceleration of PA3 at the cross center is significantly greater than other parts of the slope under the same case. Owing to the reflection and refraction of the seismic wave between two tunnels, the superposition effect of acceleration will be produced in space. Therefore, the dynamic response of acceleration can provide necessary theoretical reference for seismic design of the overlapped tunnel.

Wavelet packet analysis can perform time-frequency localization and frequency band uniformization on signals with characteristics of short duration and nonstationary [47, 48]. In this section, the wavelet packet transform is used to decompose the acceleration signals of the invert (the upper-span tunnel) and the crown (the under-crossing tunnel), respectively. Furthermore, the eigenvalues of signal energy in each frequency band after decomposition are extracted so that the frequency band which has the main effect on different measured points in the invert and the crown of tunnels can be determined quantitatively.

According to the principle of wavelet packet decomposition, the seismic waves can be decomposed at the infinite level when wavelet packet decomposition is adopted, but in the actual decomposition process, too low or too high decomposition layers are not conducive to the analysis of seismic waves [49]. When the number of decomposition layers is too low, the extraction effect of seismic wave information cannot reach the ideal level, while when the number of decomposition layers is too high, a false frequency phenomenon may occur and a higher resolution cannot be guaranteed. Moreover, with the increase in the number of decomposition layers, the number of computations increases, which results in the slow processing speed.

In this shaking table test, the sampling time interval of the seismic wave signal is 0.02s, then the sampling frequency is 50Hz, and the duration of the ground motion signal is generally 1020s, so the signal degree LS is about 29210. By substituting LS into equation (3), it can be concluded that the number of decomposition layers k of wavelet packet is between 0 and 9. Considering the resolution and frequency bandwidth comprehensively, this paper believes that when the number of decomposition layers is 3, it can meet the analysis requirements.

According to the Shannon sampling theorem [51], the Nyquist frequency is 0.150Hz. When 8-layer wavelet packet decomposition is performed on the collected signal, there are 23=8 wavelet packets in total. Therefore, the width of each frequency band is 50/8=6.25Hz, and the corresponding minimum frequency band is 0.16.26Hz. Taking the eight frequency bands (0.150Hz) as the object of analysis, the corresponding frequency range of each frequency band is shown in Table 4.

Moreover, the wavelet functions used in wavelet analysis are various, and the effect of selecting different wavelet functions on signal processing will be different. The Daubechies (db wavelet) function in the wavelet function has good approximate symmetry, smoothness, and tight support, which has obvious advantages in the analysis of seismic and other unstable signals. The db wavelet function can be divided into db1db10 wavelet bases according to the coefficient N. In the current application, the most used are db3, db5, and db8. In this paper, db3 is selected as the wavelet basis function of this shaking table test.

The MATLAB program is used to extract the energy characteristic values of measured points SA5 and XA2 in the above frequency bands under the seismic wave action of Case 15. Further, the data in the program are used to make the acceleration energy ratio of each measured point of the tunnels in each frequency band, as shown in Figure 19.

Form Figure 19(a), it is implied that under the action of EL seismic waves in the cases, the acceleration energy characteristic value at the invert of the upper-span tunnel (SA5) reaches the maximum value in the 1st dominant frequency (0.16.26Hz). Additionally, the energy in the1st dominant frequency band at the invert accounts for more than 94% of the total energy, indicating that the main frequency band that affects the acceleration response at the invert is the 1st dominant frequency band. With the increase in inputted seismic wave amplitude, the proportion of energy in the 1st dominant frequency band frequency band increases, while the proportion of the 2nd to 8th dominant frequency bands (6.2650Hz) decreases.

The energy characteristic values at the crown of the under-crossing tunnel (XA2) in each frequency band have a very significant regularity. Figure 19(b) illustrates that the energy in the 1st dominant frequency band at XA2 accounts for more than 97% of the total energy, indicating that the main frequency band that affects the acceleration response at the crown is the 1st dominant frequency (0.16.26Hz).

By comparing the energy ratio, we found that under the same cases, the energy proportion of the invert of the under-crossing tunnel in the 1st dominant frequency band is greater than that of the crown of the upper-span tunnel. Owing to the superposition effect of acceleration, the energy at the crown of the under-crossing tunnel increases, which is also the part of the tunnel structure that is easy to be damaged in earthquake. It is shown that the low-frequency component plays a leading role in the tunnel failure process of the seismic load. Moreover, before the seismic wave propagates from the soil to the concrete, the low-frequency components will change dramatically due to the complex refraction and reflection relationship between the soil and the concrete interface.

Generally, the monitoring data are usually the acceleration time-history curves of different measuring points after the shaking table model test. However, the spectrum characteristics of seismic waves cannot be accurately expressed from the original monitoring data. Therefore, it is necessary to introduce the seismic wave response spectrum to analyze the seismic wave characteristics which have an impact on the damage mode and development process of the tunnel and surrounding rock. The seismic response spectrum (including displacement spectrum, acceleration spectrum, and velocity spectrum) mainly reflects the impact of earthquake on the structure and can characterize the natural frequency (period) of the structure, which is widely used in the process of evaluating the dynamic response of the structure [38, 52].

The response spectrum is established on the basis of the vibration of the single particle system, which represents the characteristics of the influence of seismic waves on the structure represented by the single particle system. In the dynamic response spectrum analysis, the surrounding rock mass material at the location of the measuring point in the model can be regarded as a rigid body element. Thus, the dynamic response spectrum obtained can represent the curves of the maximum displacement response, velocity response, and acceleration response with the particle period in the given seismic wave excitation process of the rock and soil mass element at different positions of the tunnel, which has more engineering significance.

To study the variation law of the acceleration response spectrum of the cross tunnel in different surrounding rock positions, the acceleration measurement points of cross section with the peak acceleration of 0.15g (low earthquake), 0.4g (moderate earthquake), and 0.6g (strong earthquake) seismic wave are selected as the research object for response spectrum analysis. The measuring points are crown and invert of the upper-span tunnel (SA2 and SA5), intersection center of slope (PA3), and crown and invert of the under-crossing tunnel (XA2 and XA5), and the vertical distances from the measuring points to the bottom of the slope are 0.63m, 0.43m, 0.39m, 0.35m, and 0.15m, respectively. It should be noted that the acceleration response spectrum calculation process used a 5% damping ratio commonly used in engineering to carry out, and the response spectrum curve was smoothed by the Origin software so as to express the predominant period of the acceleration response spectrum more clearly.

It can be obtained that the shape of the acceleration response spectrum of each measuring point is basically the same, with obvious peak characteristics. In the short period part (T=0.020.30s), the response spectrum distribution curve of each measuring point has obvious amplification effect along the elevation (except for PA3 intersection center of slope). The reason for this phenomenon is analyzed owing to the refraction and reflection of seismic waves between tunnels, which will produce a superposition effect of the response spectrum in space, resulting in the abnormal increase in acceleration spectrum amplitude of PA3. However, in the remaining long period part (low-frequency part), the amplification effect of the response spectrum along the elevation is not obvious. With the increase in the predominant period, the amplitude of the response spectrum decreases. When the predominant period is 2s, the amplitude of the acceleration response spectrum is basically 0.

Moreover, Figure 20(a) presents the predominant period corresponding to the peak value of the response spectrum of SA2 is concentrated at T=0.10s, which is earlier than other measurement points, and its corresponding predominant frequency is 10Hz. The reason is that under the action of 0.1g seismic waves, slight damage may occur at the crown of the upper-span tunnel, which leads to a large difference in response spectrum amplitude between SA2 and other measuring points. It is seen that the SA2 also showed the phenomenon of forward migration of the predominant period when 0.4g seismic wave loading in Figure 20(b), which shows that under the loading of low and moderate earthquakes, the crown of the upper-span tunnel will be the earliest and prone to damage. At the same time, the maximum amplitude acceleration response spectrum of PA3 when 0.2g loaded is 9.30m/s2, which is 4.11 times larger than the 2.26m/s2 when 0.1g loaded. With the increase in the peak value of the input wave, the predominant period of the acceleration response spectrum of each measuring point has increased; that is, the predominant frequency has decreased, indicating that the nonlinear characteristics of the slope have become more obvious. Taking PA3 as an example, the input seismic wave increases from 0.1g to 0.4g to 0.6g, and its predominant period (predominant frequency) is 0.20s, 0.22s, and 0.24s (5Hz, 4.54Hz, and 4.17Hz), respectively. Furthermore, the surrounding rock mass has an amplification effect on low-frequency seismic waves.

In order to examine the distribution and variation of the acceleration and dynamic strain of the oblique overlapped tunnel during earthquakes, a series of shaking table model tests were carried out, which were the inputted EL-Centro wave in the horizontal with the PGA of 0.10.6g. Based on the recorded data, as well as observations on the post-test behaviors of the model, we analyzed features of the acceleration and dynamic strain of the upper-span and the under-crossing tunnels, as well as the main factors resulting in the changes. At the same time, the wavelet packet was used to study the acceleration energy ratio of the invert (the upper-span tunnel) and the crown (the under-crossing tunnel). Some conclusions are summarized as follows:(1)The peak acceleration of the crown of the upper-span and the under-crossing tunnels is the largest at the central section (I and I) which is the key part of the tunnel structure that be paid attention to in the antiseismic process, and the seismic response of sections on both sides of the affected section is basically the same. However, the peak acceleration of the invert of the tunnels is exactly opposite to the crown, which presents a parabolic distribution. This kind of variation of acceleration dynamic response provides evidence for the practical design of the overlapped tunnel during the earthquake.(2)When the tunnels were subjected to shaking with low seismic intensities (with the PGA of 0.1g and 0.2g), the hoop peak strains of the two tunnels are basically stable, and the failure modes of the two tunnels are in the form of transmission evolution from crown to side walls to invert. Additionally, the strain in the upper-span tunnel is much larger than that in the under-crossing tunnel under the moderate and high shaking intensity (with the PGA of 0.3g0.6g), whose the peak strains of the upper-span tunnel are side walls>crown>invert and crown>side walls>invert for the under-crossing tunnel.(3)Different from the single tunnel, because of the spatial effect of overlapping tunnel, the acceleration superposition effect appears in the intersection section of two tunnels, which leads to the obvious seismic response in the cross section. The peak acceleration inside the slope body has an amplification effect along the elevation except for cross section. Further, the acceleration amplification factor gradually decreases with the increase in the buried depth of the measured points.(4)The low-frequency component (0.16.26Hz) seismic wave plays a leading role in the process of tunnel slope failure, and owing to the superposition effect of acceleration, the energy proportion of the invert of the under-crossing tunnel in the 1st dominant frequency band is greater than that of the crown of the upper-span tunnel. With the increase in the peak value of the input wave, the predominant frequency has decreased, indicating that the nonlinear characteristics of the slope have become more obvious. Furthermore, the surrounding rock mass has an amplification effect on low-frequency seismic waves.

The research was supported by the National Key R&D Program of China (2018YFC1504903) and the Science and Technology Development Project of China Railway Nine Bureau Group Co., Ltd. Dalian Branch (KJ-2019-01). The authors gratefully acknowledge the support from the Key Laboratory of Loess Earthquake Engineering, CEA.

Copyright 2021 Hao Lei 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.

failure mechanism of steel arch trusses: shaking table testing and fem analysis - sciencedirect

failure mechanism of steel arch trusses: shaking table testing and fem analysis - sciencedirect

A series of shaking table tests based on a platform canopy were conducted.A finite-element model of the prototype structure was established.The cumulative damage effect was considered using the ABAQUS User Subroutines.Three types of lateral bracings were chose to analyze the effect on failure mode.The results obtained from the FEM are compared with the experimental measurements.

To study the failure mechanism of steel arch truss structures that are subjected to severe earthquakes, a series of shaking table tests were conducted, and the results are discussed in this paper. Furthermore, the effect of bracing forms on the structure failure mode and the cumulative damage effects on the member internal forces were evaluated using the Finite Element Method (FEM). The results from the numerical model are compared with the experimental measurements in terms of displacement, acceleration, steel strain and amplification factor of the structural model. The comparison shows that the numerical results are significantly consistent with the experimental measurements. Under severe earthquakes, structural cumulative damage and plastic deformation increased, whereas the structure stiffness declined, which leads to structural failure. The failure load of the structure was 0.81.0g, and in-plane anti-symmetric deformation was found in the main trusses after loading. The maximum strain in the test model is larger than those in the cumulative damage model and the ideal elasto-plastic model by 715% and 826%, respectively. Increasing the number of rigid tied bars slightly enhances the stiffness of the main truss, whereas using cross diagonal bracings enhances the stiffness of the main truss by 2.9 times.

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