The shaking table is a gravity beneficiation equipment for selecting fine materials, such as the tin, tungsten, gold and silver, lead, zinc, antimony, bismuth, iron, manganese, ferrotitanium and coal, etc.
The shaking table is a gravity beneficiation equipment for selecting fine materials. When the gold shaking table in action, the effective particle size range of metal ore is 3~O. 019 mm. While it processes the coal, the upper limit granularity is 10mm. The outstanding advantage of the shaker is that the sorting precision is high, and high-grade concentrate or waste tailings can be obtained by one sorting, and multiple products can be taken out at the same time. Besides, the shaking table is easy to adjust.
Mining gold shaking table is a common mineral processing equipment for sorting fine ore. When the metal ore is processed, the effective particle size range is 3~O. 019 mm, the upper limit particle size can be up to 10 mm when coal is selected. The outstanding advantage of 6-S shaker is the high precision of sorting. High-grade concentrate or waste tailings can be obtained by one selection, and multiple products can be taken at the same time. The flat 6-S shaker is easy to handle and easy to adjust. The main disadvantage is that the equipment covers a large area and the processing capacity per unit of the factory area is low.
Shaking table is widely used in many industries, and can be used for rough selection and sweeping of materials. Its main materials are various metals and heavy metal materials such as gold, silver, zinc, tungsten, iron, manganese, lead, coal, etc. The size of coarse sand is 2-0.5mm, and the fine sand is 0.5-0.074mm. The effective recycling range of shaking table is 2-0.22mm when processing the tungsten, tin and other metal ore materials.
The gold shaking table is made up of table surface, main frame, transmission device and motor. Moreover, the gold shaking table will be armed with the water filling chute, feeding chute and engine base.
The motor of the shaking table drives the crankshaft to rotate the rocker through the belt and then moves up and down. When the rocker moves downward, the mineral material enters through the mining channel on the inclined surface. Shaker sink provides lateral impact water.
The material with different specific gravity, particle size, and density flushed with rinsing and will be selected and output from the concentrate mouth of shaking table, and the tailings mouth. Thus, the processed ore is the high-quality concentrate. However, because of the replacement of mining gold shaking table, FTM Machinery, as the gold shaking table supplier, had improved a lot in term of its throughput and accuracy.
4.After checking the installation connections, the empty shaking table runs for 1-2 hours to check whether the bed surface is running smoothly, whether the connection is loose, shaking or sliding, whether the lubrication is good, and 2whether the lateral slope adjustment is flexible and stable.
6.If there is no problem with empty shaking table, you can put the ore there. according to the ore transportation and zoning on the shanking table surface, adjusting the ore concentration and concentration, stroke, cross slope and flushing water volume, etc.
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 .
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  when Institute of Engineering Mechanics, Chinese Academy of Sciences, built one-way horizontal vibration  with a specimen size of 12m3.3m. So far in China, there are a lot of shaking tables ; 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.  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 , 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 . 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 . 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  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 . 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 . 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 .
The traditional control algorithm is based on the linear model of vibration table and specimen , 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) . 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  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 , 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  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  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  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  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  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 . 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  implemented preliminary exploration into structural seismic hybrid test technique on account of the condensation technology. In 2008, Chen and Bai  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  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 . 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.
A Gold Shaking Table are basically low-capacity machines used as last step in the gold upgrading process. Theshakingtable is a thin film, shear flow process equipment, that separatesparticlegrains of its feed material based on thedifferences in their specific gravity, density, size and shape. Mineral rich particles, from light to heavy and fine to coarse will be sorted by net effective weight. Finely crushed or ground ore material goes as feed mixed with water to form a pulp (mud) andfed as slurry of an average about 2025% of solids by weight onto the highest point of the table deck. The gold tables deck hasa reciprocal movement along its main axis that is given using a vibrator or an eccentric head motion. The table surface is manufactured and fitted with several tapered strips called riffles or grooves, often made with of yellow pine (way back in time that is), low-density polythene or aluminum surfacing.Shaking tables and other thin film separating plant recover finely divided gold under conditions of subcritical laminar and supercritical laminar regimes of flow, which may occur only where there is a very thin depth of fluid.
Agold shaking tables riffles taper downwards in elevation in the direction the gold (and all heavies), precious metals concentrate discharge end of the table. This facilitates the ease with which mineral particles can move transversal to the tables axis or shaker-line, therefore helpingseparation over the complete tablelength. Riffle heights and pattern designs are selected based on the desired and required duty/function expected.
Preparing several size fractions for tabling is usually achieved in a hydrosizer. Ifgold is present in both coarse and finely divided sizings at least three, or perhapsfour separate size fractions must be treated, each under a different set of operatingconditions. Tables operate most efficiently with a closely sized feed. The slurry fansout across a smooth section of the surface until it reaches the riffles. The lighterand very fine particles are washed over the riffles and moved along the riffles by thereciprocating motion imparted to the deck while the heavier particles are held back. The concentrates of heavy mineral and gold are discharged over the end of thedeck. Tailings are washed over the lower edge and a middlings fraction is taken offbetween the lower edge of the concentrate strip and the higher edge of the tailingstrip.
Wash water usage is dependent upon the particle diameter and varies from aslow as 0.7 m/t/h of solids for slime decks, up to 56 m/t/h for coarse solidsseparation. Coarse fractions are usually treated at feed rates of up to 1 t/h using approximately 15 to 20 mm stroke lengths at around 280 rpm (Wilfley table data). Thestroke lengths of finer fractions are reduced to 915 mm with increased speeds ofup to 325 rpm but, because of the corresponding lower film, thickness capacitiesmay fall to around 0.25 t/h. The inclination of the deck is adjusted during operationusing a hand-operated tilting device. It is important following each adjustment toallow the table operation to settle down before making a fresh adjustment. The correct inclination is reached when the ribbon of concentrates is clearly defined andremains steady.
The extreme sensitivity of water depths and corresponding current depths to obtain F = 1, and the use of stationary tables as primary concentrating units, was probably the main reason for the consistently low (R.E. 6065%) gold recoveries of early dredgers. For such table types, the fluid forces are applied to the stream-beds as a whole and ripples form, which keep the sand in orbital motion and provide for the denser particles to sink to the bed. Deposition is most favoured by anti-dune conditions produced by free-surface flow at or near the supercritical state. Such bed forms are in phase with the water surface and are produced in the rapid flow conditions of Froude Number F = 1. In this state of flow, the bed forms of the upper flow regime are stable. Below F = 1 the flow is tranquil and shear forces are reduced. In reviewing recovery distributions of certaindredgers it wasnoted that some coarse gold reported with the tailing after passing through two stages of tabling and that fine gold did not concentrate noticeably down the line.
I consider the gold shaker table to be a shaking sluice box OR self cleaning sluice as they both essentially are classifiers used as heavy gold concentrating devices. Apart from nuggets; generally the valuable minerals like heavy precious metals like platinumandpalladium thatcan berecovered by tables and sluices, are found in one size range (generally the finest) and the waste minerals in another. On agold sluice, large particles (gravel) travel by sliding and rolling over the riffles, with finer particles travelling by saltation. Sand travels by a combination of modes described earlier with some saltation over the riffles.Very fine particles are maintained in suspension by turbulent and inter-particle collision.
Riffles function properly only if in the space between them and the slurry is sufficiently live (turbulent) to reject the lighter particles, but not so lively that the gold cannot settle. On a gold shaker table, those particles are allowed to settle as they will get transported to the other end by the vibrating/shaking back-and-forth motion. Lower grade, light pieces, will be able to escape the table a the riffles becomes shorter along the tables length.Once the particle has started to move, the coefficient of friction changes to a dynamic coefficient of friction. In fact, because the fluid push on the particles is larger at the top of the particle than at the bottom, the particle rolls, largely according to the shape of the particle and according to the speed. At low speeds, the effective friction is the relatively large coefficient of dynamic sliding friction, and at high speeds it is the lower coefficient of rolling friction. The change probably takes place partly continuously and partly discontinuously. As a first approximation, the dynamic coefficient of friction may, however, be regarded as constant.
In a sluice box, the settling of heavy minerals between the riffles requires frequent stirring to prevent the riffle spaces from blinding. This also disturbs the gold, which then moves progressively down-sluice. Frequent clean-ups are needed to avoid excessive loss. Boxes may be used in parallel to avoid loss of production time. One box is kept in operation while cleaning up in the other.
Effect of Deck Roughness: The foregoing analysis is based on the postulate that the deck is perfectly smooth. If the deck is rough, i.e., if it has at its surface some recesses capable of partly shielding fine particles from the rub of the fluid, the slope required to move the particles by either rolling or sliding will be increased. At the same time such an effect, while present also for large particles, may be so much smaller for them as to be imperceptible. The relationship of critical angle to size obtained above will therefore not hold for rough surfaces. The problem is analytically complex and it is nevertheless a problem that might well be explored further if a full insight is desired into the mechanism of flowing-film concentration.
Adjustments are provided in all tables for the amount of wash water, the cross tilt, the speed, and the length of the stroke. The speed of the table ranges usually from 180 to 270 strokes per minute, and the strokes are from 1/2 to 1 1/2 long.
Variations in character of feed require variations in operation. The operators duty is to take care of them by adjusting the tilt, the wash water, and the position of the splitters that control discharge of table into concentrate, middling, and tailing launders. One man may look after 10 to 100 tables, depending upon the regularity of the feed and the difficulty of the task assigned to the table.
A coarse feed can be treated in larger amounts than a fine feed. It would seem that the treatable tonnage increases at least as the square of the average size (theory indicates that it increases as the cube of the particle size).
A roughing operation is preferably conducted on a fully riffled deck. These decks have a greater capacity because the particles are treated throughout the deck in the form of a teetering suspension many particles deep instead of as a restive layer one particle deep. Such decks do not provide flowing-film concentration but some sort of jigging. On the other hand, a cleaning operation is preferably performed on a partly riffled deck.
It is clear that minerals of different specific gravity must be present the greater the spread in specific gravity between minerals, the greater the capacity since that sort of condition permits crowding without considerable penalty.
The effect of locked particles on capacity of tables should also be recognized. These particles behave in a fashion intermediate between that of pure particles of their constituent minerals. It is as if a three-product separation were sought in which one of the products would guide-in specific gravity between the two other.
Table capacity may be as high as 200 tons per 24 hr. on a fully riffled deck 4 by 12 ft. treating minus 3-mm. sulphide ore having a specific gravity of about 3.0 (roughing duty), or 500 tons per 24 hr. But table capacity may be as low as 5 tons per 24 hr., or even less, for fine ore (minus 0.3 mm.) if there is only a small specific-gravity differential between minerals.
Operating a shaking table is cheap as power requirement per table are typically low. Most of the energy is expended to move the deck, which must therefore be as light as is consistent with rigidity. Laboratory gold shaking table testingreport.
There are a few steps that need to be taken in order to get yourgold shaker table to work efficiently. The first step that aspiring gold miners must take would be to make sure that all four corners of the table are level from forward to back. It is very important to anchor the bolts so that the shaking of the gold goes to the table and not through the frame. After you begin running your table, you may need to adjust your table from side to side to maintain an even flow of materials on both sides of the table.
A gold shaker table contains a water access point where you can fill it with clean water, which can be seen right under the control area. Alternatively you can directly fill the tank of the shaker table with clean water. The water access point allows you to connect a clean water system through a garden hose. The valve that is right behind the tank is then turned off and the pump system is not running during the process of running fresh water. When clean washing water is distributed at the top of the table at right angles, particles are moved diagonally across the deck and separate from each other according to their size and density. During the fast shaking process, you will gradually begin to see the separation of materials. For example, when you have dirt and rocks that contain materials like lead, sulfides and gold, because of the varying weights of these different materials, you will see these materials venture off in different directions on the shaker table. The lead and the sulfides will be carried over to the right side of the table while the pure gold will be carried over to the far left side of the table.
There is one term to remember when professional gold miners describe the actions of a gold shaker table. When professional gold miners say that small particles of gold are being carried through the grooves, they are referring to the ripples that you can plainly see on the shaker table. When they say that there is an overflow of materials like Black Pyrrhotite, White Quartz, silver and gold on the grooves, then this is a good thing.
When materials are washed by the clean water they are supposed to drop into 3 hoppers/launders underneath the table. There is a centre launderthat will gather the purest portions of gold while the two outside launders will gather some gold, though not as much.
It is crucial to remember to plug the cable of your shaker table into a GFCI (Ground Fault Circuit Interrupter) outlet. Most shaker tables will not work if they are plugged into any other kind of outlet.
In aPercussion Gold Shaker Table,the work of keeping the pulp in a state of agitation, done by the rakes or brushes in the German and Cornish buddies described above, is affected by sudden blows or bumps imparted sideways or endways to the table. The table is made of wood or sheet metal, the surface being either smooth or riffled.
End-bump tables are hung by chains or in some similar manner, so as to be capable of limited movement, and receive a number of blows delivered on the upper end. These blows are given by cams acting through rods, or else the table is pushed forward against the action of strong springs by cams on a revolving shaft, and then being suddenly released is thrown back violently by the springs against a fixed horizontal beam. The movement of the pulp depends on the inertia of the particles, which are thrown backward up the inclined table by the blow given to the table, the amount of movement varying with their mass, and depending, therefore, both on their size and density. The vibrations produced by the percussion also perform the work of the rakes in destroying the cohesion between the particles, and a stream of water washes them down. The result is that the larger and heavier particles may be made to travel up the table in the direction in which theyare thrown by the blow, by regulating the quantity of water, while the smaller and lighter particles are carried down. These machines yield only two classes of material, headings and tailings. One such machine, the Gilpin County Gilt Edge Concentrator was devised in Colorado, and has displaced the blanket sluices atalmost all the mills at Blackhawk. It consists (Fig. 46) essentially of a cast-iron or copper table, 7 feet long and 3 feet wide, divided into two equal sections by a 4-inch square bumping-beam. The table has raised edges, and its inclination is about 4 inches in 5 feet at its lower end, the remaining 1 feet at the head having a somewhat steeper grade. The table is hung by iron rods to an iron frame, the length of the rods being altered by screw threads, so as to regulate the inclination to the required amount. A shaft with double cams, A, making 65 revolutions per minute, enables 130 blows per minute to be given to the table in the following manner; onbeing released by the cam, the table is forced forward by the strong spring, B, so that its head strikes against the solid beam,C, which is firmly united to the rest of the frame.
The pulp coming from the copper plates is fed on to the table near its upper end by a distributing box, D, and is spread out and kept in agitation by the rapid blows. Thesulphides settle to the bottom of the pulp, and are thrown forward by the shock, and eventually discharged over the head of the table at the left hand of the figure, while the gangue is carried down by the water and discharged at the other end. One machine is enough to concentrate the pulp from five stamps. If the table consists of amalgamated copper plates, it is of some use for catching free gold also, treating about 8 cwts. of ore per hour. This machine is not so effective in saving slimed pyrites as the Wilfley table or the vanners.
Gold shaker tables are environmentally friendly (chemical free) for recovering pure gold as they can play an important part in reducing the use of mercury by gold miners. With gold shaker tables miners dont need to resort to mercury amalgamation or cyanide to recover gold. The filter will constantly need to be removed and cleaned as it will get dirty even after using the table a few times.
Miners can design and construct a basic shaking table out of cheap materials that are affordable in local stores, including a drive mechanism that contains bicycle gears, chains and rubber bands that are made from car tire inner tubes. The drive mechanism for a gold shaker table can be a hand crank or it can contain parts of a motorcycle frame and engine. If one prefers to use a motor for his or her table, either an electric motor or a motor that runs on diesel fuel would be the ideal options.
It is important to keep in mind that there is no one specific way to create your own gold shaker table system. Many professional gold mining organizations will create tables of different shapes and sizes to cater to the needs of their customers. Some shaker table systems will feature machines that can crush hard rocks, which are referred to as jaw crushers. The speeds of shaker table systems will vary as they can shake from hundreds to thousands of pounds of materials per hour.
The laminar shear boxes (LSBs) are commonly preferred for geotechnical physical modeling over the fixed wall boxes; the latter may suffer from problems associated with wave reflection. This paper mainly describes the seismic response of a uniform layer of loose saturated and dry sands in rigid and flexible boundary conditions. A lightweight LSB was recently designed and fabricated by the authors for physical modeling of geotechnical earthquake engineering problems. To investigate the boundary effect on the seismic response of level ground, a series of shaking table tests were conducted with both LSB and rigid wall containers in identical conditions. The seismic performance of the free-field ground in the experiments is evaluated in terms of time histories, shear stressstrain hysteresis loop, and dynamic soil properties. The dynamic movements of all layers in the LSB, captured by image processing techniques, are compared with that of the rigid end-wall condition. The results demonstrate that acceleration and settlement of the ground surface are highly affected by artificial boundaries in both dry and saturated sands. It is shown that the hysteresis loops estimated from the LSB tests are more compatible with the cyclic behavior of sands, compared with those of the rigid box tests.
Bhattacharya S, Lombardi D, Dihoru L, Dietz MS, Crewe AJ, Taylor CA (2012) Model container design for soil-structure interaction studies. In: Role of seismic testing facilities in performance-based earthquake engineering. Springer, Dordrecht, pp 135158
Jafarian Y, Ghorbani A, Salamatpoor S, Salamatpoor S (2013) Monotonic triaxial experiments to evaluate steady-state and liquefaction susceptibility of Babolsar sand. J Zhejiang Univ Sci A 14(10):739750
Iai S, Sugano T (1999) Soil-structure interaction studies through shaking table tests. In: International society for soil mechanics and geotechnical engineering, second international conference on earthquake geotechnical engineering, vol 3. A A Balkema, Lisbon, pp 927940
This study was done as a part of project No. 6321 in International Institute of Earthquake Engineering and Seismology (IIEES). The authors would like to thank the image processing team of IIEES, including Dr. Hossein Jahankhah, Dr. Mohammad Ali Goudarzi and Mr. Mohammad Kabiri, who performed all the steps of image processing in this project.
Jafarian, Y., Taghavizade, H., Rouhi, S. et al. Shaking Table Experiments to Evaluate the Boundary Effects on Seismic Response of Saturated and Dry Sands in Level Ground Condition. Int J Civ Eng 18, 783795 (2020). https://doi.org/10.1007/s40999-019-00485-4
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The damping characteristics of soil-structure interaction (SSI) system were investigated.Identification method of SSI damping system was firstly developed.A collaborative mechanism between soil and structure was observed after small excitation.The interface of energy transfer soil-structure interaction system was observed to be integral.SSI system can be viewed as approximately classical damping system.
Soil-structure interaction (SSI) system is composed of soil and structure that are two materials with quite different damping behaviors and it is regarded as non-classical damping system in conventional concept. Based on the analysis of motion state of SSI system, the paper presents the damping characteristic of SSI system via shaking table test. The results of transfer function, acceleration response time histories and equivalent viscous damping ratio and so on indicate that under certain conditions, SSI system shows approximate classical damping characteristic. In practical projects, dynamical analysis of SSI system can be viewed as approximately classical damping system once the synergistic effect of soil is considered.
Xuelei Cheng, Chunyi Cui, Zongguang Sun, Jinhong Xia, Guangbing Wang, "Shaking Table Test and Numerical Verification for Free Ground Seismic Response of Saturated Soft Soil", Mathematical Problems in Engineering, vol. 2018, Article ID 3416315, 14 pages, 2018. https://doi.org/10.1155/2018/3416315
This paper investigates shaking table test (1g) and numerical simulation (fully coupled) of vertically propagating shear waves for saturated soft free field. A large-scale shaking table model test was performed to study seismic response characteristics of saturated soft soil free field. According to test results of seismic response features of free field system in saturated soft soil, the free field nonlinearity fully coupled numerical model of dynamical effective stress of saturated soft soil was established using OpenSEES, based on the u-p formulations of dynamic consolidation equation as well as effective stress solution method for saturated two-phase media. The numerical simulation of the free field seismic response of saturated soft soil under various test conditions was performed and the calculated results were compared with the shaking table test results. The results show the following. With the increase of input ground motion intensity, the characteristic frequency of the saturated soft free ground decreases and the damping ratio increases gradually. The saturated soft soil ground has short period filtering and long period amplification effect on the horizontal input seismic loads. The failure foundation takes on the isolation and shock absorption under strong ground motions. The peak pore pressure ratio of the saturated soft soil ground is located in the shallow buried soil layer, and with the increase of the input ground motion intensity, the advantage of dynamic pore pressure ratio in this area is gradually weakened. The numerical simulation results are consistent with the results of the shaking table test. This fully coupled effective stress numerical method can reasonably simulate the seismic response characteristics of free field in saturated soft soil, which lay the foundation for other more complex parameter extrapolation models of saturated soft soil sites. This research can provide the necessary technical experience for experimental study on non-free field.
Soft soil is widely distributed in China. As numerous studies suggest, soft ground can cause greater seismic damage of underground structures. For instance, Dakai subway station was destroyed in 1995 Hanshin earthquake, which consumed 10 billion yen to repair [1, 2] (Kawashima, 2000; Hashash, 2001). The design standards for underground structure in soft ground are behind that of the liquefiable sand ground, which only gives some qualitative and general provisions  (Yamashita, 2012). Therefore, there is a lack of more in-depth and systematic research, and more extensive and intensive studies are still needed on seismic disaster mechanism in saturated soft soil foundation.
Generally, theoretical analysis method, numerical simulation method, and model test method are three major research methods in seismic responses of underground structure. Plenty of theoretical results have not been validated since the complexity of soft soil. Therefore, it is difficult to guide engineering design. Since shaking table test has no Coriolis effect, it is an effective method to study the seismic response of free field. Model test should be necessarily performed to verify the results of theoretical research. Some scholars have studied the seismic responses of underground structures embedded in soft soil sites. Turan  (2009) investigates seismic soil-structure interaction of building with embedded basement stories founded in unsaturated clayey sons by small shaking table test. Chen et al. [5, 6] (2010, 2012) conduct on scaled utility tunnel models embedded in unsaturated clay soil of Shanghai with and without construction joints under nonuniform input earthquake wave excitation by a series of shaking table tests and numerical simulation method. Chen et al.  (2015) investigate the damage mechanisms of a subway structure in soft soil while experiencing strong ground motions by shaking table test. Chen et al.  (2016) investigate the effect of pulse-like ground motion on a multistory subway station embedded in unsaturated soft soil with a series of shaking table tests. Further, Wang et al.  (2013) investigate the dynamic through-soil interaction between underground station and nearby pile supported structure on viscous-elastic soil layer under vertically incident S wave with numerical method. Zhuang et al.  (2015) estimate the earthquake damage of a large subway station built in soft ground with the total stress numerical simulation method. Huang et al.  (2017) investigate the nonlinear responses of the tunnels within surface normal fault ground under obliquely incident P waves based on the total stress numerical simulation method. The above research is important to understand the seismic response of underground structure embedded in soft ground. From the research of shaking table test performed, underground structure is mostly embedded in unsaturated soft soil, and the numerical simulation methods are mostly based on the total stress analysis methods. The total stress method can not consider the effect of pore pressure, which is inconsistent with the real situation. It is necessary to consider the influence of pore pressure in soft soil sites with the dynamic effective stress method  (Chen, 2011). The shaking table test has been rarely performed for saturated soft ground and the seismic response numerical simulation of saturated soft ground has been also rarely analyzed with test verification. Besides, in order to further consider the coupling effect of pore pressure and soil skeleton in the seismic dynamic response analysis of underground structures embedded in soft soil, Zhou et al.  (2004) carry out soft soil indoor dynamic test and adopted the two-dimensional decoupling finite element effective stress dynamic response analysis based on Hardin dynamic viscoelastic model. Azadi et al.  (2010), based on the decoupling two-dimensional effective stress dynamic finite element method, discuss the influence rule of large deformation of the site on the dynamic deformation of shallow buried underground structures, while the decoupling effective stress dynamic calculation method based on the pore pressure stress (strain) model has certain limitation for describing the deformation characteristics of pore pressure and soil skeleton under seismic loads  (Schrefler, 2001; Luan, 2009; Ghassemi, 2010). The fully coupled effective stress dynamic calculation method should be applied in seismic dynamic response analysis of the underground structure embedded in saturated soft soil ground.
The study on the seismic response characteristics of free ground is the premise of underground structure embedded in soft soil. In this regard, a large-scale shaking table test was performed to study seismic response characteristics of saturated soft free field ground. The nonlinearity coupled numerical model of dynamical effective stress of saturated soft free foundation was established using OpenSEES, based on the u-p formulations of dynamic consolidation equation and effective stress solution method for saturated two-phase media. And the test results are compared with the numerical simulation results to verify the accuracy of this numerical simulation method.
Shaking table test of saturated soft free field was performed in the Key Laboratory of Urban Security and Disaster Engineering in Beijing University of Technology. The table is sized as 3m6m in plane. The maximum acceleration of shaking table is 1g with full load (10 tons), in which g denotes the acceleration resulting from gravity in m/s2. The frequency of input wave ranges from 0.1Hz to 50Hz. The maximum displacement of shaking reaches up to 125mm.
The box is 2.50m long (x) 1.40m width (y) 1.38m height (z) in overall dimension, as shown in Figure 1. It encompasses 14 steel frames stacked on box, numbered as No. 1-14 from bottom to top. Each frame is made of steel pipe with a rectangular cross-section size of 80mm 80mm 3mm (width height thickness). Damping coefficient reaches up to 200 Ns/m, and spring stiffness coefficient reaches up to 2250 N/m. The interlayer distance is 20mm between steel pipes. The natural frequency of the empty box is 1.28Hz. The natural frequency of the model box filled with saturated soft soil is 8.85Hz. The natural frequency of the empty box is different from the model natural frequency of the filled box model with saturated soft soil. Therefore, the resonance phenomenon cannot occur in this experiment.
In accordance with Bukinghan theorem, the shear wave velocity, density, and (gravity) acceleration are selected as the basic physical quantity for soil similar ratio, and the specific similarities are listed in Table 1. The similarity constant is the ratio between the model physical quantity and the prototype physical quantity.
The soft clay was from Beijing, which should be dried and cleared before testing. The soil was placed into the shear box layer by layer and each layer was with the thickness of 20cm. At the same time, soil samples were measured to ensure the soil density of each layer valued the same. After paving each layer of soil, the surface of soil was leveled with a wooden board. The model soil was enabled to stand 72h to make the model soil fully consolidated. The average temperature is 30C, and the average relative humidity is 70% in the laboratory in Beijing in August. In order to fully saturate and consolidate the model foundation, the surface of model foundation was covered with a layer water of 5cm thickness and covered with plastic paper for moisturizing. The surface water should be drained before test. Table 2 lists the test result of soil properties.
Table 3 lists the type of sensors. The sensor layout of the primary observation section and subobservation section as presented in Figure 2. The flexible chain sensor placement technique was used in this experiment to increase the packing efficiency of soil model and to avoid the sensor deflection and shift in traditional sensor embedding method, as presented in Figure 3. It is necessary to pay attention to the waterproof of accelerometers. In this test, the plexiglass box was used to waterproof the accelerometers, as shown in Figure 3(a). It required 34 acquisition channels in total in this shaking table test.
Since the soft soil is impermeable, a few test cases can make the model foundation as close to the natural earthquake process as possible. The experiments were performed in horizontal excitation with a total of 11 test cases. Table 4 lists the test cases. Kobe (N-S) and EL-Centro (N-S) were selected for input acceleration and waveform, respectively, as presented in Figure 4. Earthquake details are listed in Table 5. Before the test, the soil model was previbrated with small amplitude white noise to make the soil denser. Besides, model soil was vibrated by inputting small amplitude white noise to monitor dynamic characteristics of the model system before the next test case. Each test case was carried after excess pore pressure dissipated. By inputting sine wave with the frequency close to natural frequency of model system, the model system dynamic characteristics and boundary effect were monitored.
Figure 5 presents the time history comparisons of feature points acceleration between model midline and boundary. Figure 6 presents the time history comparisons of feature points dynamic pore pressure ratio between model midline and boundary. The seismic responses of measured points at the same depth are basically equal. The design of laminar shear model box is reasonable. Thus, the boundary effects can be ignored in this test.
The response of the soil surface after the corresponding shaking test is presented in Figure 7. The dynamic response of the model was slight under a small excitation, and a small amount of water overflows at the boundary of the box. As input ground motion increases progressively, the dynamic response of the model increases, and the settlement of the model surface also increases progressively. The amount of water on soil surface increases progressively too. The water surface overflows and vibrates with a light wave-like movement. The depth of water layer is nearly 0.5cm as all the cases of test were completed. Cumulative settlement displacement of model ground surface under different excitation levels is listed in Table 6. The settlement of model soil surface increases with the increase of the acceleration amplitude. The settlement of soil around the boundary is not significantly different from the surface center, showing similar seismic characteristics. The settlement of model surface center accumulates to 0.55cm as all shaking table test cases were completed.
Table 7 lists the characteristic frequency and damping ratios of model system. The initial characteristic frequency of model system reaches 8.85Hz, and the damping ratio reaches 3.6%. As the input acceleration amplitude increases, the characteristic frequency of model system decreases, and the damping ratio increases progressively. The characteristic frequency decreases to 25% of the initial value, and the damping ratio is 1.8 times the initial damping ratio as the test cases have been completed.
In brief, the dynamic responses suggest that the characteristics frequency of model system decreases, and the damping ratio increases as input acceleration amplitude increases. This phenomenon is attributed to the rise of dynamic pore pressure, the decrease of dynamic shear strength, and dynamic shear modulus of soft soil.
Acceleration amplification factor refers to the PGA (Peak Ground Acceleration) ratio of peak acceleration response at the measuring point to the peak input acceleration at the shaking table. Figure 8 presents the acceleration responses of midline measuring point under different shaking table test cases. The peak acceleration of Kobe decreases and then increases progressively when the acceleration propagates upward along the midline from the shaking table. The maximum PGA amplification factor of soils under small deformation conditions results from minor earthquakes input. Yet the PGA amplification coefficient at each measuring point along the soil depth decreases correspondingly with the increase of input acceleration amplitude. The same seismic characteristics are also presented by input EL-Centro waves, whereas the PGA amplification factor compared with input Kobe wave cases take on some differences. As this result suggests, the spectral components of the input seismic wave impact the acceleration to some extent.
Figure 9 presents the acceleration response spectrum of measuring points under different excitation conditions, following the parabolic interpolation spectrum construction method. With the increase of input ground motion, the characteristic period of acceleration spectrum increases increasingly, agglomeration amplification effect of the short period weakens progressively, and agglomeration amplification effect of the long period increases progressively.
The amplification effect of the soil layer is associated with soil properties, earthquake intensity, as well as earthquake spectrum information. The saturated soft soil layer primarily plays an amplification role under the action of small or moderate earthquakes. The softening degree of the foundation progressively increases as the input acceleration amplitude increases. Under the energy consumption of soil, the high-frequency filtering and the low-frequency amplification effects increase evidently, and the model foundation shows the isolation and shock absorption. The effects of high-frequency filtering and long period amplification are presented in saturated soft soil.
According to the principle of effective stress, the dynamic pore pressure ratio is computed as the ratio of excess pore pressure to initial effective vertical stress. Figure 10 presents the peak value of pore pressure ratio along model midline under different excitation conditions.
The soft soil is impermeable as soft clay particles are finer, and bonding interactions are strong between the particles. Accordingly, pore pressure ratio is below 0.25, which is at a low level. The peak pore pressure ratio of the saturated soft soil ground is located in the shallow buried soil layer, and, with the increase of the input ground motion intensity, the advantage of dynamic pore pressure ratio in this area is gradually weakened. At the identical input acceleration amplitude, Kobe waves, and EL waves are different in the pore pressure ratio. The pore pressure ratio and frequency information of acceleration are indicated to be associated. As the input acceleration amplitude increases, pore pressure ratio of corresponding measuring points increases, and the difference decreases progressively between shallow soils and deeper soils. It is difficult for the pore pressure dissipation as the saturated soil is impermeable. It is more significant effect to pore pressure ratio of the deeper soils under potent earthquake.
Saturated two-phase medium matrix numerical equation here is given as follows :where denotes total mass matrix; represents displacement vector; refers to strain-displacement matrix, , which is associated with strain and displacement increments; denotes effective stress increments; represents soil-water coupled discrete gradient operators; refers to pore pressure vector; denotes compression coefficient matrix; is permeability coefficient matrix; and represent soil-water mixture boundary conditions of body force and liquid phase boundary conditions of body force, respectively.
where denotes deviatoric stress tensor; represents the yield surface numbered, ; refers to the total number of yield surfaces; and represent the center and radius of the yield surface, respectively; and denotes the cube root of two times that of yield surface radius. .
PressureIndependMultiYield material counts as an elastic-plastic material where plasticity merely presents in the deviatoric stress-strain response. The volumetric stress-strain response is linear-elastic and independent of the deviatoric response. This material is introduced to simulate monotonic or cyclic response of materials, and these shear behaviors are insensitive to the confinement variation.
Yield surface motion direction tensor is expressed in the following:where denotes the second-order deviatoric stress tensor, the deviatoric stress tensor at the intersection of the yield surface fm+1 and fm; and represent yield surface center of and , respectively.
The site soil is simulated using 4-noded quadUP elements. These elements have three degrees of freedom per node: two for displacements and one for pore pressure. These elements can be used to model coupled pore pressure displacement analysis following the u-p formulation. In this model, the continuum material models, referred to as nDMaterial, are used to simulate the mechanical behavior of clay, and they are attached to continuum elements. The soft soil constitutive calculation parameters are listed in Table 8  (Mckenna, 2009).
Figure 11 presents the model grid of finite element method. The bottom of the model is fixed in such a way that no movement is allowed on the vertical and horizontal direction. The pore pressure is allowed to fluctuate freely, which means that there is no drainage on the bottom. The pore does not allow to fluctuate freely in surface, which means that there is drainage on the model surface. The displacements of the model on the sides at the level of clay are periodic conditions: each side has the same displacement with the other side. That is, both sides of the model are set as the tied boundary. In the OpenSEES program, the behavior of the laminar box can be modeled by adopting tied node feature. This feature allows the horizontal and vertical displacement at the two boundaries with the identical value. The stress-strain behavior of the material model for saturated soil could simulate the hysteresis damping to a certain extent.
The viscous effect of the pore fluid also incorporates damping. Yet the plastic hysteresis would not be able to capture the full damping of the soils in the low strain range. The soil is very large in damping at a small confining pressure, which is difficult to simulate by adopting the stress-strain relationship. Thus, a 5% viscous damping of Raleigh type was involved in the dynamic analysis for the soft soil . Hilber-Hughes-Taylor method was used for time integration algorithms in soil dynamics. It is an implicit method considering energy dissipation and second-order accuracy (which is not possible following the regular Newmark method), and this method can be unconditionally stable in terms of the choices of input parameters.
The actual input acceleration and the target acceleration are different in the shaking table test. Thus, the output acceleration of the shaking table is selected as the ground motion input for numerical simulation. Turn on the gravity and solve problems in the static case to use elastic material for the entire model. It is performed by solving a coupled transient analysis with time-steps. The large time-steps (dt=5 105 s) are employed to ensure analysis to be drained, and any initial excess pore pressures have been dissipated. After the elastic steps, the material is switched to an elastoplastic state, and a similar large time-step is performed when all the initial transients and excess pore pressures have been dissipated. After the elastoplastic gravity step, the analysis object is destroyed, and the time is reset to zero. The dynamic analysis is then executed. The test to judge when convergence has been achieved is based on increments of energy. This is a good criterion in an elastoplastic problem where increments of displacement can be really large during yielding. The constraint handler is set as the transformation handler, after recommendations from the creators of the quadUP elements when one is applying pore pressure boundary conditions. The algorithm selected is a KrylovNewton algorithm. It is a robust and simple algorithm with asymptotically quadratic rate of convergence. The system used is a ProfileSPD. The Jacobian matrix of frictional materials is not symmetric but in many situations ignoring the nonsymmetric elements can help improve performance without significant differences in the results. All numerical calculation results are extracted and visualized using the interface program of GID with MATLAB.
The numerical verification is mostly based on the peak comparison of the dynamic response index or only the qualitative comparison of the time history response. For the aim to the quantitative evaluation of the accuracy of the numerical simulation results, the root mean square error (RMSE) is used to measure the difference between the shaking table test and the numerical calculation results, and the consistency analysis between them is also carried out.
In particular, the root mean square error is only reliability estimate of a set of measured data, rather than the actual error of the two or the error range. It reflects the extent to which the dynamic response results of numerical simulation deviates from the test results. According to the Gaussian theory of random error, when the root mean square error of measured values is , then the random error has a probability of 68.3% in (-, ). The smaller the RSME value, the lower the error and the better the consistency, which means that the numerical simulation accuracy is higher.
Table 9 lists the acquired subsidence of both experimental results and numerical simulation. Ground surface settlement of test is nearly 30% greater than that in numerical method, because PressureIndependMultiYield material is an elastic-plastic material in which plasticity exhibits only the deviatoric stress-strain response, and the volumetric stress-strain is linear-elastic and is independent of the deviatoric response. This material is implemented to simulate monotonic or cyclic response of materials whose shear behavior is insensitive to the confinement change, which is attributed to the shaking additive effect.
Figure 12 presents the time history comparison of acceleration response between shaking table test and corresponding numerical simulation results. Figure 13 presents the comparison of acceleration response at feature points between shaking table test and corresponding numerical simulation results. As illustrated in Figures 12 and 13, the RMSE of acceleration time history is 0.2879ms2 and 0.3721ms2 for W1-3F and W1-5F, respectively, in K2 case, and the RMSE of acceleration time history is 0.4074ms2 and 0.5468ms2 for W1-3F and W1-5F, respectively, in EL2 case, while the RMSE of acceleration response spectrum is 0.1000ms2 and 0.1301ms2 for W1-3F and W1-5F, respectively, and the RMSE of acceleration response spectrum is 0.1507ms2 and 0.1032ms2 for W1-3F and W1-5F, respectively. Both the experimental results and the numerical simulation results are well consistent with K2 case regardless of the time history or the Fourier spectrum of acceleration responses, while it is not consistency for low period in EL2 case; specifically, the predominant period (0.14s) of measuring point acceleration is greater than that in the test result (0.24Hz) in EL2 case. The shape of both errors has better consistency though both errors are confined in 40%. The consistency of acceleration response between numerical results and test results is also associated with the spectrum characteristics of input ground motions.
Figure 14 presents the time history comparison of pore pressure ratio between the shaking table test and numerical results. The numerical results of time history of pore pressure ratio are well consistent with the test results under different excitation conditions. Negative pore pressure phenomenon occurs around piezometer resulting from dilatancy of soft soil under input ground motion.
Figure 15 presents the peak response contours of pore pressure ratio under different excitation conditions. The peak value of pore pressure ratio in shallow soil is greater than that in the deeper soil, and these results are consistent with those of the literature  (Gao, 2011). The RMSE of pore pressure ratio is 0.0290 and 0.0238 for W1-7F and W1-9F, respectively, in K2 case, and the RMSE of pore pressure ratio is 0.0324 and 0.0294 for W1-7F and W1-9F, respectively, in EL2 case. The peak response contours of pore pressure ratio of free field in soft soil are associated with the frequency spectrum characteristics of the input ground motion, whereas the variation results of them are similar.
The comparison is presented merely between the shaking table test and the numerical simulation under the 0.2g ground motion. Also, the test results of other shaking table test case and corresponding numerical simulation results are found with good consistency. It is noteworthy that soft soil is homogenous in model test, whereas the soil of project site is sophisticated in geological conditions with heterogeneous, inclined, or underground structure embedded. Thus, it is easy to flow for soft soil and damage of the underground structure because of the uneven deformation resulting from soil softening.
The regularity of the macroscopic phenomena of test, the dynamic characteristics of the model system, the acceleration responses, and the dynamic pore pressure (ratio) responses are analyzed in this paper from the shaking table test results of the saturated soft soil free field. Also, the comparison between the test results and the numerical simulation results is anatomized. The reliability of the numerical simulation method is analyzed by the quantitative evaluation of the root mean square error. The results are presented in the following.
The characteristic frequency of the model system decreases progressively, whereas damping ratio increases increasingly with the increase of ground motion acceleration and the number of vibrations. The initial characteristic frequency and damping ratio are quite different compared with the end of the shaking table test.
The seismic wave propagates in the model ground and the acceleration response spectrum amplitude of the short period components decreases while the acceleration response spectrum amplitude of the long period components increases from the bottom to the top of the ground. The PGA amplification factor is amplified along the soil layer to the surface under small or moderate ground motions. The failure of the foundation model takes on the isolation and shock absorption under strong ground motions.
The peak value of pore pressure ratio is at a low level in saturated soft ground. The peak pore pressure ratio of the saturated soft soil ground is located in the shallow buried soil layer, and, with the increase of the input ground motion intensity, the advantage of dynamic pore pressure ratio in this area is gradually weakened. It is more significant effect to pore pressure ratio of the deeper soils under potent earthquake.
The full coupled effective stress numerical simulation method and the shaking table model test results are in good agreement with each other regardless of displacement, acceleration, and pore pressure. This also suggests that it is reliable to further build other more sophisticated prototype site conditions.
Copyright 2018 Xuelei Cheng 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.