Due Date: Tuesday January 27, 2009CIE 619 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING II Spring 2009 1/4 DEPARTMENT OF CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING CIE 619 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING II Spring 2009 ASSIGNMENT No. 1 Due Date: Tuesday January 27, 2009 Problem 1 Figure 1 shows an earthquake record obtained from a station in Southern California. The record was obtained with an instrument having a static amplification factor of 7180. The nominal properties of the rock in the region can be estimated as: Young’s modulus: 140,000 MPa Poisson’s ratio: 0.28 Specific weight: 27 kN/m3 Figure 1 - Earthquake record from a station in Southern California. Note: The interval between two horizontal lines is 1 mm. a) Compute the distance between the station and the focal point of the earthquake. b) Determine the local magnitude, ML, of this earthquake.CIE 619 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING II Spring 2009 2/4 Problem 2 Read verses 14:3 to 14:5 of the book of Zachariah in the bible (OLD TESTAMENT) and interpret the geological phenomenon described. You need to write the verses in your solution. Problem 3 Compute the maximum energy transferable to seismic waves from the rock fall on Mount Huascaran during the May 31, 1970 earthquake in Peru. Fifty (50) millions cubic meters (m3) of rock fell from a height of 1 km. Estimate the equivalent surface wave magnitude, Ms, of this event? d e 010 = a-BAML.maxProblem 4 Figure 2 shows the locations of the 38 seismological stations on rock sites triggered by the October 17, 1989 Loma Prieta earthquake that occurred on the San Andreas Fault south of San Francisco. Table 1 lists the peak ground horizontal accelerations recorded at these stations. The local Richter magnitude scale of this earthquake is ML = 7.1. The earthquake was centered 16 km north-east of Santa Cruz at a focal depth of 18.5 km. a) Using only the peak ground horizontal acceleration values recorded by the 38 stations, construct an attenuation relation for the region of the simple form: where amax = peak ground horizontal acceleration (g) ML = Richter’s local magnitude d = hypocentral distance (km) A, B = constants obtained from a least square regression on the logarithmic form of the attenuation relation b) Assuming that the natural logarithm of the peak ground acceleration follows a normal distribution (i.e. log-normal distribution on amax), plot the variation of the standard deviation of ln amax (maxln aσ) with hypo-central distance. Base your estimate by binning the recorded data in increments of 20 km. What constant value of maxln aσwould you recommend to use with the attenuation relationship that you have constructed in a)? c) Based on the result obtained in b), compute the probability that a ML = 7.3 earthquake on the San Andreas Fault cause a peak acceleration greater than 0.2 g at a rock site 100 km from the hypocenter? Tabl e 1 - Index of seismological stations. No on Fig. 2 Name of station amax (g) 1 Anderson Dam 0.26 2 San Jose Interchange 0.18 3 Cherry Fl at Reser vo i r 0.09 4 Sunnyvale 0.22 5 Hollister Airport 0.29CIE 619 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING II Spring 2009 3/4 No on Fig. 2 Name of station amax (g) 6 Palo Alto VA 0.38 7 Hollister City Hall 0.25 8 Cal aver as Reser vo i r 0.13 9 Hollister, SAGO 0.06 10 Stanford, SLAC 0.29 11 M enl o Park VA 0.27 12 Fremont 0.20 13 Crystal Springs Reservoir 0.12 14 Sunol 0.10 15 Redwood City 0.28 16 Foster City 0.12 17 Del V all e Dam 0.06 18 L i ver mor e V A 0.06 19 Bear V al l ey no 12 0.17 20 APEEL 2E, Hayward 0.16 21 Bear V al l ey no 5 0.07 22 Hayw ard Ci ty Hall 0.10 23 Dublin 0.09 24 Bear V al l ey no 10 0.13 25 Bear V al l ey no 7 0.06 26 S.F., 1295 Shaf ter 0.11 27 S. F. State Uni ve r si ty 0.14 28 S.F., 575 Market 0.13 29 S.F., 600 Montgomery 0.18 30 Emeryville 0.26 31 Ber keley, Str awber r y Canyo n 0.08 32 Ber keley, Havi l and Hal l 0.06 33 Berkeley, 2168 Shattuck 0.11 34 San Fr ancisco VA 0.16 35 S.F., Golden Gate Bridge 0.24 36 Richmond 0.11 37 M arti nez V A 0.07 38 Larkspur 0.14CIE 619 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING II Spring 2009 4/4 Figure 2 -Seismological stations triggered by the October 17, 1989 Loma Prieta earthquake. Station Problem 5 Tabl e 2 pr esents the maxi mum tr ace amplitudes obtained on a Wood-Anderson seismograph during an earthquake in Southern California. Evaluate the local magnitude based on these recorded values. Assume that both horizontal components for each station are in phase. Tabl e 2 - Trace amplitudes on a Wood-Anderson seismograph. Maximum trace amplitude (mm) Epicentral distance (km) Nor th-south component East -west component 1 8.4 6.0 114 2 7.9 8.5 179 3 24.5 30.0 90 4 8.1 7.0