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英文原文 Title: Digitally controlled simple shear apparatus for dynamic soil testing Author: Duku, Pendo M, Fugro West Stewart, Jonathan P, University of California, Los Angeles Venugopal, Ravi, Sysendes, Inc. Publication Date: 01-01-2007 Series: UC Los Angeles Previously Published Works Publication Info: UC Los Angeles Previously Published Works, UC Los Angeles Additional Info: Copyright 2007, ASTM, http://journalsip.astm.org/ Original Citation: Duku, P.M., Stewart, J.P., Whang, D.H., Venugopal, R. (2007). “Digitally controlled simple shear apparatus for dynamic soil testing,” Geotech. Testing Journal, ASTM, 30 (5), 368-377. Digitally Controlled Simple Shear Apparatus for Dynamic Soil Testing ABSTRACT:We describe the characteristics of a simple shear apparatus capable of applying realistic multidirectional earthquake loading to soil specimens. This device, herein termed the Digitally Controlled Simple Shear (DC-SS) apparatus, incorporates features such as servohydraulic actuation and true digital control to overcome control limitations of some previous dynamic soil testing machines. The device is shown to be capable of reproducing sinusoidal and broadband command signals across a wide range of frequencies and amplitudes, although the device has limited control capabilities for very small command displacements (less than approximately 0.005 mm). The small deformation limitation results from noise introduced to the control system from analog-to-digital conversion of feedback signals.We demonstrate that bidirectional command signals can be accurately imparted with minimal cross coupling, which results from an innovative multiple-input, multiple-output digital control system. The capabilities of the device are demonstrated with a series of broadband tests on unsaturated soil specimens subjected to uni- and bidirectional excitation. KEYWORDS: digital control, simple shear, dynamic soil testing, multidirectional loading Introduction Direct simple shear apparatuses have been utilized successfully formany years to characterize static and dynamic soil properties. Thismethod of testing is often preferred when it is desirable for thespecimen to experience a smooth and continuous rotation of theprincipal stress directions during shear. Initial stresses can be applied to simulate at-rest field conditions when wire reinforcedmembranes are utilized that minimize lateral distortion of thesample (i.e., the NGI-type configuration, Bjerrum and Landva1966). Perhaps the most common application of simple shear testing has been for the simulation of vertical (or nearly vertical) shearwave propagation through a soil column. Advantages and limitations of simple shear tests relative to other types of laboratory tests have been described elsewhere and are not repeated here (e.g., Lucks et al. 1972; Shen et al. 1978; Saada et al. 1982; Vucetic and Lacasse 1982; Budhu 1985; Bhatia et al. 1985; Amer et al. 1987; Airey and Wood 1987; Budhu and Britto 1987; Boulanger et al. 1993). Most simple shear apparatuses operate in a single horizontal direction and apply harmonic loading at frequencies which are typically slower than dynamic processes such as earthquake shaking (e.g., Tatsuoka and Silver 1981; Doroudian and Vucetic 1995; Lefebvre and Pfender 1996; Riemer and Seed 1997; Kusakabe et al. 1999; Hazirbaba and Rathje 2004). While there are always approximations involved in applying soil properties measured in the laboratory to field conditions, the inability of existing devices to provide rapid, multidirectional loading introduces further errors of unknown significance when laboratory-measured soil properties are used in engineering simulations. A number of simple shear apparatuses have been developed to investigate soil response to multidirectional loading (e.g., Ishihara and Yamazaki 1980; Boulanger et al. 1993; DeGroot et al. 1996). The University of California, Berkeley bidirectional cyclic simple shear (UCB-2D) device is noteworthy since it significantly reduced mechanical compliance issues that caused relative top/base cap rocking in earlier devices (e.g., Ishihara and Yamazaki 1980; Ishihara and Nagase 1988). Another significant feature of the UCB-2D device is chamber pressure control, which facilitates back pressure saturation . The principal limitation of the UCB-2D device, and earlier devices, is their inability to apply earthquake-like broadband loading at rapid displacement rates. This limitation also exists for most unidirectional simple shear devices. The reasons for this are twofold :(1) pneumatic loading systems use a compressible fluid (i.e., air) which introduces significant errors to the feedback loop at high frequencies; and (2) digitally-supervised analog controllers were employed which effectively limit the processing speed and sophistication of the control algorithms. Of course, shaking table and centrifuge experiments are capable of applying multidirectional earthquake-like loading to soil models (i.e., Pyke et al. 1975;Jafarzadeh andYanagisawa 1998; Kutter 1995;Wilson et al. 2004).However, direct measurements of the soil element response (e.g.,shear stress-shear strain relationships, volumetric strain, and porewater pressure) in these types of experiments requires dense instrumentationarrays that can affect the response they are intended to measure, which in turn complicates data interpretation (e.g., Elgamal et al. 2005). The capability of applying, with a reliable degree of control, multidirectional loading across a wide range of frequencies to soil elements in the laboratory is critical to advancing our fundamental understanding of dynamic soil properties. For example, broadband loading capabilities are needed to investigate rate effects on soil properties, which are known to be significant for clays (e.g., Lefebvre and Pfender 1996; Sheahan et al. 1996). Moreover, the effect of shear rate and 2D loading on pore pressure generation or volume change behavior, or both, is less well understood and requires further investigation for some soil types.To meet these research needs, a digitally-controlled simple shear device with capabilities for chamber pressure control and multidirectional excitation has been developed. This device, herein termed the Digitally-Controlled Simple Shear (DC-SS) apparatus incorporates features such as servohydraulic actuation and true digital control to overcome the limitations of previous dynamic soil testing machines. The result is a truly unique simple shear apparatus with the capability to apply broadband (earthquake-like) displacement demands on soil specimens in two directions and with minimal cross coupling between the horizontal motions. In this paper, we describe this device and its capabilities for dynamic soil testing. Physical Description of DC-SS Device The mechanical design of the DC-SS device was developed using the UCB-2D device as a prototype (Boulanger et al. 1993). The DC-SS device was designed to retain the main features of the UCB-2D device such as inclusion of cell pressure for purposes of back pressure saturation, limited mechanical compliance with respect to simple shear boundary conditions (e.g., top and base platen “rocking”), and bidirectional loading capability. In addition to these features, the DC-SS device incorporates several design improvements relative to the UCB-2D device including: _i_ the use of a tri-post frame with high performance track bearings (which accommodate vertical displacements of the top cap) to further reduce rocking; _ii_ a servohydraulic control system to allow for high frequency loading; and _iii_ a dual axis load cell to obtain post-friction shear load measurements. Figure 1 shows the general assembly of the DC-SS apparatus. Photographs of the DC-SS device are shown in Fig. 2. The DC-SS device was designed to test cylindrical soil specimens with a diameter of 10.2 cm or less. The specimen is located between relatively rigid bottom and top caps (Fig. 1, Fig. 2(b)) and is typically confined by a wire reinforced membrane. As shown in Fig. 2(c), the horizontal (top and bottom) faces of the specimen are confined by the caps, which contain fine porous stones epoxied into a recess covering the entire face of the cap except for a retaining lip of aluminum around the edge. These caps provide a “frictional” surface while allowing for drainage into the porous stones if the stones are unsaturated (the stones can be saturated for undrained tests). The top cap/specimen/bottom cap stack is positioned between the top and bottom adapter plates shown in Fig. 1. The bottom cap fits into a recess within the bottom adapter plate. The top adapter plate is gently lowered such that a recess within the top adapter plate fits snugly over the top cap. The top and bottom caps are held tightly on their respective adapter plates by three set screws on each plate. Once the specimen is secured between the two adapter plates, three LVDTs equally spaced around the specimen are mounted on the top adapter plate and fixed to the plate by set screws. The specimen is then consolidated by a vertical stress and is ready for shear loading. Above the top adapter plate is a vertical table, which in turn is attached to a vertical load cell (Fig. 1). Vertical loads are transferred to the specimen through the vertical table, which is attached to three equally spaced linear slides. Each of the three linear slides is attached to a separate post, which effectively precludes lateral movements and rocking of the vertical table (and hence, practically speaking, the specimen as well). This tri-post frame is a significant improvement over the UCB-2D device, which employed a cantilever system (vertical table attached to a pair of track bearings along the same wall). Loads are applied to the vertical table by a pneumatic actuator mounted outside the main frame. An important feature of the DC-SS device that was retained from the UCB-2D device is its bidirectional loading capability. Horizontal shear loads are applied at the base of the specimen through two independently controlled horizontal tables. The bottom horizontal table is mounted on linear slides attached to the main frame of the apparatus, and this table is free to move in only one horizontal direction. The upper horizontal table is also mounted on linear slides such that the movement of the upper table is exactly perpendicular to the lower table. The two horizontal tables can be controlled to produce net resultant movements of the bottom adapter plate in any horizontal direction. Loads are applied to the lower horizontal table by threaded rods that are attached to an actuator that can apply tension and compression. There is a tensioncapable roller connection between the upper table and its actuator to accommodate perpendicular displacements of the lower table. The loads applied to the tables are measured by loadcells mounted between the actuators and the tables. The loads measured by the loadcells are not identical to those imparted to the specimen due to friction in the linear slides. The magnitude of the frictional load within the system was characterized and observed to be quite small (approximately 2.2 N). The significance of this frictional load is dependent on what type of testing is desired. This frictional load will produce inaccuracies of approximately 0.3 kPa (for a10.2-cm diameter specimen), which represents a negligible percentage of the shear stress for most applications. However, if very low stress measurements are needed, post-friction shear stresses can be measured by using a dual-axis loadcell. The dual-axis loadcell fits in between the top adapter plate and the vertical table, a space which is otherwise occupied by a spacer block. The dual-axis loadcell is capable of measuring both the vertical and shear loads simultaneously with minimal cross talk between these channels. However, the presence of the dual-axis loadcell introduces system compliance (i.e., rocking and vertical deformations) that may be significant at medium to large strains. Therefore, most tests are performed without the dual-axis loadcell in place. Three LVDTs (linear variable differential transducers), mounted between the top and bottom adapter plates, are used to measure the vertical specimen deformations. These locations of LVDTs minimize errors due to mechanical compliance. The three LVDTs are used so that relative rocking of the specimen in either direction of loading can be measured. Data from the three LVDTs are averaged to define specimen height during a test. Horizontal deformations are measured by two LVDTs mounted to the horizontal tables in orthogonal directions. The DC-SS device operates under “strain-control” conditions, meaning that table displacements are controlled and the actuator forces required to achieve those displacements are measured. The motions that can be imparted to the tables are limited by different aspects of the control system for different frequency bands. At low frequencies （f≤0.24Hz）, the limiting factor is the peak actuator displacement （Umax=51 mm）. At intermediate frequencies (0.24Hz≤f≤15Hz) the limiting factor is the flow rate capacity of the servo-valve (_Qmax=158 cm3/s). At frequencies (f<15 )Hz, the limiting factor is the pressure capacity of the hydraulic pump (Pmax=21 MPa)_. For the case of harmonic control signals, these quantities can be related to the peak table motions as follows: Ut=Dsinwt≤Umax (1) Utdx=Dwcos(wt)≤Qmax/A (2) U(t)dx2=-Dw2sin(wt)≤PmaxA/m (3) where U(t) and its derivatives describe the table displacement, velocity, and acceleration, A is the cross-sectional area of the actuator( 20.3 cm2), m is the table mass( 5.7 kg), and _ is the frequency of table motion (in radians/s). The corresponding peak values of displacement, velocity, and acceleration are given in Fig. 3. The control system is capable of producing any motion that lies below the limit lines in Fig. 3 . DC-SS Control System As illustrated in Fig. 4, the digital control system for the DC-SS device serves two purposes. The first is to provide control signals to direct drive servovalves that drive hydraulic actuators for each axis (direct drive servovalves have an onboard controller that corrects tracking errors in the control signal before driving the hydraulic actuators). The second purpose is to acquire data from the LVDTs and loadcells. The physical device referred to here as DC-SS was originally developed with a PC-based digitally-supervised analog control system. This control system used a PID (Proportional- Integral-Derivative) control algorithm that ran within a Windows? operating system. The principal problem with that control system was latency in the processing of feedback signals from instruments (such as an LVDT) and the generation of command signals. This limited the ability of the device to accurately replicate some command signals. These problems were especially acute for loading functions involving fast velocities and 2D shaking. The system was successfully used in previous testing (e.g., Whang et al. 2004; Whang et al. 2005), although those applications involved unidirectional shaking and a 1.0 Hz loading frequency, so control problems associated with the PC-based system were not significant. The control system for the present device uses a system referred to as hard real-time digital control. The principal difference from PC-based digital control is that the control functions are implemented on the controller board as opposed to a PC operating system. This enables guaranteed sampling frequencies for the internal feedback loop of 5 kHz using displacement feedback from the horizontal LVDTs,whereas PC-based digitally-supervised analog control systems typically cannot reliably execute the computations required for complex control at feedback sampling frequencies higher than 200 Hz, depending on the processor clock speed, control algorithm sophistication, number of background processes handled by the PC operating system, etc. The digital control system utilizes two dSPACE DS1104 controller boards. Each board contains a PowerPC 603e processor, four 16-bit 2 _s analog-to-digital (A/D) converters, four 12-bit 800 ns A/D converters and eight 16 -bit 10 _s digital-to-analog (D/A) converters, in addition to other input/output ports. The two boards are mounted in PCI slots in a host PC but run their own real-time kernel (i.e., an operating system specifically tailored for control functions) independent of the host PC’s operating system. A PID control algorithm was implemented for both PC-based and hard real time digital control. This is referred to subsequently as the “PID controller”. Gains for the PID controller are tuned by trial-and-error for optimal performance using a step function command signal. The output of the PID controller is a digital voltage command that is sent to a Moog voltage amplifier via one of the D/A channels on the dSPACE board. The voltage amplifier, in turn, sends a voltage drive signal to the appropriate actuator servovalve. As illustrated in Fig. 5(a), PID control of the two axes are independent, and hence the control system as a whole is unable to compensate one axis on the motion along the second axis). In order to minimize cross-coupling effects, the digital control system was enhanced by introducing a multiple-input multipleoutput (MIMO) control algorithm that interfaces with the PID controllers. As illustrated in Fig. 5(b), this controller uses LVDT feedback from both axes and generates a compensated command signal for each of the PID controllers, taking into account cross-coupling effects. The controller is designed and implemented as a discretetime state space system using the LQG (Linear-Quadratic- Gaussian) optimal control method (Franklin et al. 1990). This method requires the estimation of four empirical quantities that reflect system properties. This is accomplished using the N4SID system identification algorithm (Van Overschee and De Moor 1995). System identification algorithms operate on input-output data sequences; the data used for this purpose were two uncorrelated random inputs (generated by the PID controllers) and the corresponding LVDT output signals. The combination of the MIMO control algorithm and the two PID controllers is referred to subsequently as the “MIMO-PID” controller. The DC-SS device is configured so that the MIMO algorithm can be turned on or off. Hence, either PID or MIMO-PID digital control of experiments is possible. Data acquisition capabilities for either mode are summarized below: ? Input motion time step: no practical lower limit; ? Number of input motion data points: no practical upper limit; ? Feedback sampling frequency (i.e., the internal frequency for the feedback loop): 5 kHz; ? Data logging frequency: upper bound is 5 kHz, can be downsampled as needed. DC-SS System Performance To evaluate the performance of the DC-SS system (i.e., controller, pump, actuators, and servo-valves), both harmonic and broadband earthquake input motions were specified to the PID controller and the MIMO-PID controller and the resulting feedback signals were measured. Unidirectional tests were performed to evaluate the performance of each axis independently, and to provide baseline results for evaluating interaction effects. Bidirectional loading was performed to evaluate cross-coupling between axes. Acknowledgments The development of the DC-SS device was supported by a CAREER grant from the National Science Foundation to the second author (NSF Award No. 9733113), the Henry Samueli School of Engineering and Applied Science at UCLA, and the U.S. Geological Survey, National Earthquake Hazards Reduction Program, Award Nos. 1434-HG-98-GR-00037 and 05HQGR0050