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Development of a geotechnical centrifuge in Hong Kong C.K. Shen, X.S. Li, C.W.W. Ng and P.A. Van Laak Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong B.L. Kutter University of California, Davis USA K. Cappel and R.C. Tauscher Team Corporation, USA ABSTRACT: An advanced 400g-ton geotechnical centrifuge is being developed for the Hong Kong University of Science and Technology (HKUST). The nominal 8-metre diameter beam centrifuge will be installed at HKUST in early 1998. A feature unique to this centrifuge is its capability to simulate dynamic problems in two horizontal directions using an in-flight bi-axial hydraulic shaker. For static tests, the centrifuge can be operated at up to 150g, whereas the bi-axial shaker is designed for shaking tests at up to 75g. 1 INTRODUCTION The decade of the 90s has witnessed a marked increase in centrifuge modelling of geotechnical structures for research and engineering practice. Centrifuge modelling constitutes a powerful tool for the study of many previously intractable geotechnical problems, and is useful for developing an understanding of the basic mechanical behaviour of large-scale geotechnical systems, both through direct physical analogy (similitude and scaling laws) and through verification and calibration of computer programs used for subsequent analysis of prototype systems. Centrifuge modelling also finds utility as a supplement to conventional design and analysis techniques. Significant progress has been made in recent years to improve the art and science of geotechnical centrifuge modelling. HKUST is developing its new centrifuge facility to take advantage of these recent advances in instrumentation and modelling techniques and, in an effort to contribute to the continuing evolution of centrifuge technology, has undertaken the development of a new bi-axial centrifuge shaker. With the intent of developing a state-of-the-art capability, the centrifuge has been designed to meet the following performance goals: - accommodation of large model containers to permit more detailed modelling and to make room for extensive instrumentation within the model, - provision for extensive on-arm instrumentation for detailed measurement of model parameters and simulation of field loading and construction processes, - improvement of earthquake loading simulation and the ability to generate bi-axial shaking in the plane perpendicular to the gravity field. The design and performance specifications for the HKUST centrifuge were conceived after taking these objectives into consideration. In this paper, a general description of the centrifuge facility along with specifications and details of the centrifuge and the bi-axial earthquake hydraulic shaker are given. Funding for the Geotechnical Centrifuge Facility was provided jointly by the Research Grant Council and by the University. The centrifuge and bi-axial shaker were designed and supplied by Team Corporation, Burlington Washington, USA. This company has many years of experience in servohydraulics and has participated in the development of several centrifuge shakers (Ketcham, 1991; Kutter, 1994; Van Laak, 1996). This facility is dedicated to serve not only the University but also the geotechnical community in Hong Kong and around the world. 2 THE CENTRIFUGE AT HKUST The centrifuge is installed in a new building, located a short distance from the main campus. The building houses the Geotechnical Centrifuge Facility (GCF) and the Wind and Wave Tunnel Facility (WWTF). For safety reasons, the centrifuge is housed underground in a circular chamber. A network of steel conduits is attached to the inner surface of the chamber wall, through which chilled water is circulated to cool the chamber as necessary during centrifuge operation. An elevation and floor plan of the centrifuge laboratory are shown in Figures 1 and 2. The centrifuge facility has a total of 255 m2 of office and general laboratory space. In the main laboratory area, a 20 tonne capacity overhead gantry crane is available to move the pre-cast concrete panels above the centrifuge enclosure and to load and unload the centrifuge model containers. The crane is also used to interchange the static platform and shaker when required. The unused platform or shaker is stored in a recess in the floor of the centrifuge enclosure. The centrifuge is monitored using CCTV cameras and microphones, and an intercom is used to communicate between the centrifuge chamber and control room during model checkout. The hydraulic power supply is located below the main laboratory area in a room adjacent to the centrifuge. Table 1 summaries some key specifications for the centrifuge. For static tests, the centrifuge can be operated at up to 150g whereas for dynamic tests, the bi-axial shaker is designed to operate at up to 75g. In total, three swinging platforms have been manufactured. Two platforms are identical and are designed for non-shaking tests. Each of these static platforms can accommodate a model of up to 1.5m x 1.5m x 1m in size and up to 40,000 N in weight. The third platform comprises the bi-axial shaker and associated structural supports, hydraulic manifolds and reaction mass. The shaker slip-table can accommodate payloads of up to 0.6m x 0.6m x 0.4m and up to 3000 N in weight. Due to the large mass of the dynamic platform, for static tests at higher than 75g the dynamic platform must be replaced with a static platform. 2.1 Main bearing and drive Figure 3 shows an elevation section of the centrifuge. The centrifuge arm is supported on a conventional shaft running in a pair of pre-loaded Timken tapered roller bearings. The centrifuge is driven by a hydraulic radial piston motor directly coupled to the lower end of the vertical drive shaft. This drive was selected because the torque applied to the end of the arm by tangential shaking greatly exceeds the required drive torque. A geared drive would be rapidly damaged by such an oscillating torque unless an expensive hydraulic clutch were provided to disconnect the gearbox during shaking. In order to prevent damage to the hydraulic motor and shaft coupling, oil flow to the drive motor is bypassed during the brief period in which the shaker is operated, in effect permitting the centrifuge to free-wheel. Upon completion of shaking, flow to the drive motor is re-established. The maximum permissible imbalance at 150g is 222 kN, corresponding to a weight imbalance of 149 kg. Balancing of the centrifuge is accomplished using weights of various sizes placed on the platform not used for carrying the model container. Careful bookkeeping is used to ensure the centrifuge is closely balanced to maintain stresses within Figure 1 Elevation view of the centrifuge facility at HKUST Table 1. Technical specifications for the centrifuge. Key item Specification Payload capacity 400 g-tons Arm radius 3.82 m to the centre of the swinging platform Maximum acceleration 150g Payload size 1.5mx1.5mx1m for static tests, 0.6mx0.6x0.4m for dynamic tests Figure 2 Plan view structural limits and to prolong bearing life. Strain gauges mounted on the centrifuge are used to monitor quasi-static structural loads arising from centrifugal forces and payload imbalance as well as dynamic loads during shaking. 2.2 Structural arm and mounting The base of the centrifuge is a tapered steel weldment used to transmit the static and dynamic loads from the rotating arm to the building foundation. The structural arm is a steel weldment rigidly attached to the main shaft. Its main function is to support the four tension straps and to transmit the drive torque from the main shaft to the platforms. The tension straps are fixed to the structural arm at one end only and are restrained against radial displacements by bearings placed along their length. With this arrangement, any unbalanced loads from the two swinging buckets are transmitted to the main shaft through the structural arm, while in the absence of unbalance forces (i.e. a perfectly balanced condition) the large centrifugal forces between the payload and the counterweight are transmitted entirely through the set of four tension straps, and the bending moment applied to the main shaft is zero. Apart from dynamic forces generated during shaking, the major bending moment on the main shaft is due to the imbalance forces. 2.3 Suspension of platforms To avoid deleterious material property changes and stress raisers, the highly stressed tension straps are machined from high strength steel without welding. The reliance on un-welded loadpaths is continued in the connection between the tension straps and the platforms: the swinging platform is carried by a multiplicity of high strength rods inserted through pivot blocks through which pass the trunnions at the ends of the tension straps. Each of these rods is loaded by no more than 13.3 kN, which gives a factor of safety of about 3 since the ultimate strength of each is over 40 kN. This structural sub- system is very tolerant of slight misalignment, such as that caused by small rotations of the platform structure. Four sets of 20 rods each are provided. To accommodate the requirement of tangential excitation of the shake table, the recoil of the platform requires an extra degree of freedom of rotation in the suspension, achieved by the insertion of a spherical joint between the pivot block in the main trunnion, and the two pairs of hinged blocks at the edges of the platform. Each platform is then allowed two degrees of rotational freedom, in the two orthogonal directions of shaker displacement. The dynamic moment transmitted from the shaker to the centrifuge arm is therefore determined by the sliding friction in the platform suspension pivots. All sliding surfaces are treated with a proprietary coating which results in a friction coefficient of 0.03. Figure 3 The HKUST 400 g-ton Centrifuge Since the tension rods are not suitable for transmission of the shear forces required to overcome pivot friction, they are encased in rectangular structural tubing members which are slideably attached to the pivot blocks, but not to the platform, so that they are not stressed in tension when the rods stretch under load. 2.4 Centrifuge Control System The centrifuge drive uses a variable volume pressure compensated pump driven by 200 hp electric motor. Pressurized oil from the main pump is circulated through the hydraulic radial piston motor in a closed hydraulic circuit. The volume flowrate of the oil in this circuit is controlled by a servovalve which controls the angle of the pump swashplate and determines the rotational speed of the centrifuge. The main drive pump for the centrifuge operates at a nominal pressure of 21 Mpa, while the pump used for powering the shaker and for controlling the drive pump swashplate operates at 35 Mpa. The hydraulic pumps for the centrifuge drive and shake table share a common reservoir and are located in the centrifuge power room (Fig. 1). An analog signal proportional to the desired rotational speed is applied to the servovalve in the high pressure hydraulic circuit attached to the main pump swashplate. In addition to modulating the flowrate of oil to the centrifuge drive motor, the swashplate angle also determines the oil pressure within the main drive circuit. Since the swashplate has a very high slew rate (with full travel achievable within a few milliseconds), the potential for over- pressurization of the main drive loop exists unless the entire hydraulic drive system is carefully controlled. In order to minimize the time required to reach a steady state, a shaped speed command rather than a linear ramp is used. This permits the speed to be increased quickly when the centrifuge is rotating slowly and the drag forces are small, and limits derivatives in speed under high drag conditions, preventing excessive operating torques and hydraulic pressures. Additionally, hydraulic pressure in the drive circuit is measured and used to attenuate the drive signal to prevent excessive pressure. A computer program is used to implement the control described above. Besides controlling the speed of the centrifuge, the computer is used to monitor operational parameters such as imbalance forces in the arm, temperature of the main bearings, hydraulic fluid temperature and pressure, and status of safety interlocks. The computer is also used to implement the sequence of valving operations required for operating the shaker system during shaking tests. Input data and measured parameters from each run are automatically logged to the computer hard disk to facilitate long-term monitoring of machine performance and scheduling of routine maintenance. 3. BI-AXIAL SHAKER ASSEMBLY The HKUST centrifuge incorporates a bi-axial hydraulic shaker, to be used for simulated seismic excitation. In consideration of the facts that earthquake motions are multi-directional in nature and that many uni-directional centrifuge earthquake simulators are already available, HKUST decided to develop a bi-axial shaker in order to simulate earthquake motions in two horizontal directions simultaneously. Because large shaking forces in two directions are possible with this shaker, development of the centrifuge and the shaker was carried out simultaneously, with the shaker designed as an integral part of the centrifuge. This integrated approach to the design was adopted in order to isolate the shaking forces from the centrifuge to as large an extent as possible, and led to the articulated suspension design described above. To facilitate installation and maintenance, and to permit operation of the centrifuge at accelerations greater than 75 g for static tests, the shake table and its bucket form a single assembly that is removable from the suspension arms and replaceable by an optional static bucket. With a payload weight of 3000N, the total moving weight (payload and shake table hardware) is about 10,000N. To optimize the dynamic behaviour of the in-flight shaker, a large reaction mass (4000 kg) has been incorporated into the design. The shake table is supported by hydrostatic self-aligning pad bearings. Compared with rubber shear pads, the hydrostatic bearings provide higher compressive stiffness. Rubber shear pads located underneath the slip table are only used to provide a nominal centering force to the table. The shaker utilizes two pairs of servo-actuators for each of the shaking directions (one pair in the tangential direction of the centrifuge rotation and the other in the direction of bucket swing-up). Each pair of actuators is located on opposite sides of the shaking platform and corresponding pairs are designed to act as a unit, applying identical forces to each side of the slip table. The motion of the slip table is then ostensibly a superposition of translations in the two orthogonal directions, with no rotations in the plane of shaking. Hydrostatic pad bearings are used between each actuator piston and the slip table. These bearings produce a low friction interface for motions of the slip table transverse to the piston axis, while providing a very stiff connection between the piston and slip table when loaded in the axial direction. The shake table receives oil from a 10 gpm, 35 Mpa variable volume pressure compensated pump. This pump supplies oil to the shaker through a 35 Mpa hydraulic rotary joint mounted near the top of the centrifuge. In order to provide enough pressure and flow to the shaker pistons, hydraulic fluid is stored in four 2.5 gallon pressure accumulators prior to shaking. Each actuator has a piston diameter of 7.6 cm so, for a peak pressure of 35 Mpa, each pair applies a force of 32,000 kgf per axis. For the moving mass of just under 1000 kg, this force yields 35 g of acceleration in each shaking direction, and for a typical seismic signal, a shaking duration of 2 seconds for each accumulator charging is achievable. Several key technical specifications of the shaker are listed in Table 2. Control of the shaker is complicated by the redundancy of actuators. Since four separate actuators are used to drive a slip table having only three degrees of freedom (translations in two directions plus rotation in the plane of shaking), one of the actuators is redundant, and measures must be taken to ensure that the commands to each actuator are consistent with the kinematic constraints; otherwise, the actuators will end up fighting each other, and the shaker performance will be compromised. To achieve the target shaking motions, a combined analog and digital control system is being implemented. The analog portion of the controller is used primarily to eliminate the actuator redundancy by using pressure feedback to attenuate actuator fighting. The analog control is also used to define the operating point (setpoint) of the system. The digital shaking control system is currently under development and is implemented using a Pentium Figure 4 The bi-axial shaker. Table 2. Technical specifications for the shaker. Key item Specification Shaking direction Two prototype horizontal directions Maximum shaking acceleration 35g Maximum shaking velocity 750 mm/sec Shaking frequency 0-350 Hz computer equipped with a high speed analog interface. The digital system itself has two functional layers. In the lower layer, the controller is designed based upon the assumption that the reaction mass of the shake table is fixed in reference to an inertial frame; in the upper layer, corrections will be made based upon the absolute acceleration of the platform itself. The lower layer is a real-time infinite impulse response controller implemented using an interrupt service routine. The parameters of this on-line closed-loop controller will be optimized by identifying the transfer functions of the shaker through a system identification procedure. The upper layer controller is essentially an open loop one that corrects the errors due to the vibrations of the platform and the centrifuge arm through an off-line iterative procedure. 4 SLIP RING AND ROTARY JOINT ASSEMBLY Rotary joint and slip ring assemblies are essential to the proper functioning of the centrifuge. They are used for transmitting electrical power, signals, compressible fluids such as air, water and oil to control various devices and acquire experimental data. Some specifications for the assemblies are given in Table 3. At HKUST, the two assemblies are stacked one above the other and mounted on the floor above the centrifuge chamber. This mounting arrangement minimises the effects of vibration and g-gradient from the centrifuge and the requirement of a higher headroom of the centrifuge chamber. This is an important consideration, since the geometry of the centrifuge chamber - radius and height - has a strong influence on the power consumption. Table 3. Specifications of slip ring and rotary joint assembly. Key item Specification Slip rings 32 for analog signals, 8 for analog return, 16 for power Co-axial cable channels 8 for video and high frequency equipment, 4 high quality for digital signals (computer network) Air ports 2 at 1400 kPa, 0.05 m3/min Water ports 2 at 2000 kPa, 40 liters/min 5 MODEL CONTAINERS Two model containers have been developed. One is a rectangular aluminum container, designed for static tests, having inside dimensions of 1270mm x 1245mm x 850mm, and incorporating an optional acrylic window. The container has been designed to limit average strains within the model to 0.025% during spinup. For dynamic tests, a laminar-type flexible walled container has been developed. This container is cylindrical in shape, with an inside diameter of 550mm and a height of 500mm. The container is constructed of fifty-two aluminum rings, with ball bearings used to provide the low-friction interface between adjacent rings. The laminar container has been designed to provide the necessary model boundary conditions for bi-directional shaking. 6 CLOSURE A b