Study of Rupture Directivity in a Foam Rubber Physical Model

Transcription

1 Progress Report Task 1D01 Study of Rupture Directivity in a Foam Rubber Physical Model Rasool Anooshehpoor and James N. Brune University of Nevada, Reno Seismological Laboratory (MS/174) Reno, Nevada (775) rasool@seismo.unr.edu, brune@seismo.unr.edu

2 Introduction The main objective of this project is to use foam rubber modeling experiments to provide constraints on parameters that control rupture dynamic, especially forward directivity effects. Different parameterizations used in the existing numerical models lead to substantially different predictions of ground motion. Foam rubber scale models of earthquake (Brune et al., 1993) provide a means for better understanding of the physical parameters that control near-field ground motions during earthquakes. Physical models of faulting are guaranteed to obey static and dynamic mechanical laws and thus can be used to gain insight into possible physical processes involved. Of course, there are inherent problems of scaling laboratory models to the real earth. Such models can nonetheless provide important insight and constraints on numerical and theoretical models. Foam rubber models have been used in a number of studies as analogs of earthquake ruptures. Foam rubber is very flexible, i.e., it has a low rigidity, making it easy to produce large strains and particle motions. Since foam rubber is light, relatively large models can be constructed, enabling the scale of dynamic phenomena to be enlarged. This allows dynamic features to be more easily observed and recorded using relatively simple electronic devices. Foam-rubber models automatically assure that motions are physically realistic (no singularities or unreasonably specified slips). Description of Model The strike-slip model consists of two large blocks of foam rubber, one driven horizontally past another by a hydraulic piston. The lower block is glued to a sheet of plywood that is in turn bolted to the concrete floor (Figs. 1-2). The upper block and the attached rigid box are supported by four steel pipes equipped with scaffolding jacks. Normal force at the contact (fault) is provided by some fraction of the weight of the upper block (~3000 N) and is varied by lowering or raising the jacks. Shear force is provided by a hydraulic piston, which is placed between a concrete wall and the upper block's frame. As the upper block is forced to slide over the lower block, the strain in the blocks increases until the stress at the interface exceeds the frictional resistance and a stick-slip event occurs over the entire fault plane. Successive events usually cause about the same amount of average slip (1 cm) between the blocks; but the pattern of slip can vary markedly, with the rupture initiating at different points and propagating in different directions. If the driving displacement is steady, the characteristic events repeat more or less regularly until the upper block has slipped about 20 centimeters, corresponding to about 20 characteristic events with some additional smaller events. At this point, the stress is removed and the upper block lifted and moved back to the starting position for repeat of the procedure. Near the point of shear failure events can be caused to nucleate at different points by slightly raising one or more of the jacks. 2

3 Instrumentation Position-Sensing Detectors: Displacement at the foam surface is measured by a telescopic, 2- axis, position-sensing detector, which is focused on a small light emitting diode (LED) embedded in the foam. The Dual Axis Super Linear Position Sensor (DLS10, manufactured by the United Detector Technology Sensors, Inc.), is a square of photovoltaic material, 1 cm on a side. The sensor locates the centroid of a light spot (image of the embedded LED) projected upon it, and provides continuous output as the light spot moves from the null point to either direction along each of the two perpendicular axes. The output of the position-sensing detector depends on the location as well as the intensity of the bright spot. Therefore, it is necessary to calibrate detectors before and after each experimental run (The position detectors have a built-in calibrating mechanism.). The resolution of the DLS10 sensors is limited only by the intensity of the light source and the signal resolving circuitry. In our experiments, the resolution is better than 0.01~cm. Ultra-light Accelerometers: Due to foam rubber s low density and high elasticity, particle accelerations in a stressed foam rubber model of earthquakes can exceed several hundred (the acceleration due to gravity). Slips of the order of 1 cm can take place in a few milliseconds, resulting in very large accelerations at high frequencies. In order to measure these accelerations, accelerometers with a high dynamic range and low mass (to minimize the mass loading effects) are needed. We use ultra-light ENDEVCO Model 25A accelerometers. The Model 25A, has a mass of 0.2 gm, a dynamic range of 1000 g, and a flat response from about 1 hz to about 20 khz. In order to further reduce the mass loading effects, each accelerometer is mounted on a styrofoam disk, 3.8 cm in diameter, before inserting them in the foam; the 3 mm thick styrofoam disk (with the same density as the foam rubber used in the model, but far more rigid) distributes the accelerometer's mass over a larger area (about 50 times larger). Data Acquisition System: The data acquisition system consists of a PC with a 330 khz analog-todigital converter (Microstar, DAP1200e/6). Particle motions during stick-slip events at 32 sites were digitized at the rate of 5000 samples-per-second and recorded on the PC. Experimental Results We used two configurations (A and B) to instrument the lower block of the model. In Configuration A, we used 32 miniature accelerometers along four profiles (Fig. 3). Eleven sensors were embedded on the fault plane at two different depths to record the fault parallel accelerations (Profiles 1 and 2). The other 21 sensors were placed on the free surface. Ten pairs were embedded along profiles 3 and 4 (parallel to the fault trace) and one at a larger distance from the fault. Table 1 lists the location, orientation and sensitivity of each sensor. In Configuration B (Fig. 4), we used 26 accelerometers and 6 position sensors. The position sensors were placed on the free surface, along the fault trace. Table 2 lists the location, orientation and sensitivity of each sensor. 3

4 We recorded 31 events in configuration A and 26 events in configuration B. The corrected data are at in subdirectories config-a and config-b. The format of the ASCII files is explained in file ch_order. The accelerations are in units of g, and the displacements in mm. Figs. 5 and 6 show two events recorded in configurations A and B, respectively. The numbers next to each trace corresponds to channel numbers listed in Tables 1 and, as well as Figs In Fig. 5, all 32 traces are accelerations; in Fig. 6, traces 1 through 26 are accelerations and displacements. In both cases the events nucleated near the left-hand-side of the fault plane (Fig. 3) and propagated toward the right-hand-side, producing strong forward directivity effect. The directivity effect is better displayed in Fig. 7, where the acceleration time histories in Fig. 5 are re-plotted along the four profiles shown in Fig. 3. The fault-normal components along profiles 3 and 4 show simple directivity pulses that increase in amplitude with time. The reflections off the model boundaries arrive later. Plots in Fig. 8 are similar to those in Fig. 7, except for the rupture propagating in the opposite direction. 4

5 Table1: Sensor location, orientation and sensitivity for each channel are listed below. Channel Coordinates Accelerometer Sensitivity Sensor Number X (cm) Y (cm) Z (cm) S/N (Counts/g) Orientation BK FP CT FP AB FP CT FP AB FP CT FP CT FP CT FP CW FP CW FP BK FN CT FN AB FN CT FN BK FN CT FN CT FN CT FN AC FN CW FN BK FP CT FP AC FP AC FP AC FP AC FP AB FP AC FP BK FP AB FP BK FP BK FN

6 Table2: Sensor location, orientation and sensitivity for each channel are listed below. Channel Coordinates Accelerometer Sensitivity Sensor Number X (cm) Y (cm) Z (cm) (S/N) (Counts/g) Orientation BK FP CT FP AB FP CT FP AB FP CT FP CT FP CT FP CW FP CW FP BK FN CT FN AB FN CT FN BK FN CT FN CT FN CT FN AC FN CW FN BK FP CT FP AC FP AC FP AC FP BK FP Displacement Sensor Sensitivity (counts/mm) LED 1920 FP LED 1920 FP LED 1920 FP LED 1920 FP LED 1920 FP LED 1920 FP

7 Figure 1: A photograph of a foam rubber model of strike-slip faulting is shown here.

8 F Rigid Box Roller Hinge Jack A B Floor Figure 2: Diagram of a foam rubber model of earthquakes is displayed. The upper block is driven over the lower block by a hydraulic piston. F

9 Configuration A 2 1 y x z Lower Block 50 cm Accelerometer, Fault Normal Accelerometer, Figure 3: Sensors in the lower block are labeled according to the channel numbers listed in Table 1.

10 Configuration B y x z Lower Block 50 cm Accelerometer, Fault Normal Accelerometer, Displacement Sensor, Figure 4: Sensors in the lower block are labeled according to the channel numbers listed in Table 2.

11 Figure 5: Acceleration time histories of a stick-slip event recorded at locations shown in Fig. 3 are plotted here.

12 Figure 6: Acceleration and displacement time histories of a stick-slip event recorded at locations shown in Fig. 4 are plotted here.

13 Profile 1 Profile 2 Profile 3 Fault Normal Profile 4 Fault Normal Figure 7: The traces in Fig. 5 are re-plotted here to better display the rupture directivity effect.

14 Profile 1 Profile 2 Profile 3 Fault Normal Profile 4 Fault Normal Figure 8: The rupture propagation direction is opposite to that of the event shown in Fig. 7.