Lecture#15

2. Lecture#15 CE-312 Engineering Geology and Seismology Instructor: Dr Amjad Naseer Department of Civil Engineering N-W.F.P University of Engineering and Technology, Peshawar

3. Outlines of the Presentation • Ground Motion Parameters • Amplitude, Frequency and Duration

4. Ground Motion Parameters • Ground motion parameters are essential for describing the important characteristics of strong ground motion in compact, quantitative form. • Amplitude, Frequency and Duration 4

5. (A) Amplitude Parameters • Amplitude Parameters: • The most common way of describing a ground motion is with a time history. The motion parameter may be acceleration, velocity, or displacement, or all three may be displayed. Typically, only one of these quantities is measured directly with the others computed form it by integration and/or differentiation. 5

6. (a) Peak Acceleration • The most commonly used measure of the amplitude of a particular ground motion is the peak horizontal acceleration (PHA). The PHA for a given component of motion is simply the largest (absolute) value of horizontal acceleration obtained from the accelerogram of that component. 6

7. (a) Peak Acceleration Horizontal accelerations have commonly been used to describe ground motions because of their natural relationship to inertial forces; indeed, the largest dynamic forces induced in certain type of structures (that is very stiff structures) are closely related to the PHA. 7

8. (a) Peak Acceleration • The PHA can also be correlated to earthquake intensity. Although this correlation is far from precise, it can be very useful for estimation of PHA when only intensity information is available, as in the cases of earthquakes that occurred before strong motion instruments were available (pre-instrumental earthquakes). A number of intensity-acceleration relationships have been proposed. 8

9. (a) Peak Acceleration • Vertical acceleration have received less attention in earthquake engineering than the horizontal acceleration, primarily because the margins of safety against gravity-induced static vertical forces in constructed works usually provide adequate resistance to dynamic forces induced by vertical accelation during earthquakes. For engineering purposes, the peak vertical acceleration (PVA) is often assumed to be two third of PHA. 9

10. (a) Peak Acceleration • Ground motions with high peak accelerations are usually, but not always, more destructive than motions with lower peak accelerations. Very high peak accelerations that last for only a very short period of time may cause little damage to many types of structures. A number of earthquakes have produced peak acceleration in excess of 0.5 g but caused no significant damage to structures because the peak accelerations occurred at very high frequency and the duration of the earthquake was not long. Although peak acceleration is a very useful parameter, it provides no information on the frequency content or duration of the motion; consequently, it must be supplemented by additional information to characterize a ground motion accurately. 10

11. (b) Peak Velocity Peak Velocity: The peak horizontal velocity (PHV) is another useful parameters for characterizations of ground motion amplitude. Since the velocity is less sensitive to the higher-frequency components of the ground motion, the PHV is more likely than the PHA to characterize ground motion amplitude accurately at intermediate-frequencies. For structures or facilities that are sensitive to loading in this intermediate frequency range (for example, tall or flexible buildings, bridges, etc), the PHV may provide a much more accurate indication of the potential for damage than the PHA. 11

12. (c) Peak Displacement Peak Displacement: Peak displacements are generally associated with the lower-fequency components of an earthquake motion. They are, often difficult to determine accurately due to signal processing errors in the filtering and integration of accelerograms and due to long-period noise. As a result, peak displacement is less commonly used as a measure of ground motion than is peak acceleration or peak velocity. 12

13. (B) Frequency Content Frequency Content Parameters: Dynamic response of buildings, bridges, slopes or soil deposit is very sensitive to the frequency at which they are loaded. Earthquake produces complicated loading with components of motion that span a broad range of frequencies. The frequency content describes how the amplitude of a ground motion is distributed among different frequencies. Since the frequency content of an earthquake motion will strongly influence the effects of that motion, characterization of the motion cannot be complete without consideration of its frequency content. 13

14. (C) Duration Duration: The duration of strong ground motion can have a strong influence on earthquake damage. Many physical processes, such as the degradation of stiffness and strength of certain types of structure and the buildup of porewater pressures in loose, saturated sands, are sensitive to the number of load or stress reversals that occure during an earthquake. A motion of short duration may not produce enough load reversals for damaging response to build up in a structure, even if the amplitude of the motion is high. On the other hand, a motion with moderate amplitude but long duration can produce enough load reversals to cause substantial damage. 14

15. (C) Duration The duration of a strong ground motion is related to the time required for release of accumlagted strain energy by rupture along the fault. As the length or area of fault rupture increase, the time required for rupture increase. As a result, the duration of strong motion increases with increasing earthquake magnitude. While this relationship has been supported empirical evidence for many years, advances in source mjuechanism modeling, have provided theoretical support indicated that 15

16. Response Spectra RESPONSE SPECTRA The response spectrum is the most important characterisation of seismic ground-motion in earthquake engineering and forms the basis for most design. This chapter introduces the concept of the response spectrum and the particular influence that certain features of the earthquake can have on have on its shape and amplitude. 16

17. Response Spectra Definition of the elastic response spectrum A single-degree-of-freedom (SDOF) system is a mechanical system with mass, m, that provides inertia, and stiff, k, that provides a restoring force, whose deformation can be fully described by a single coordinate. The natural period of vibration of such an SDOF system, T, is given by the following equation: Real systems do not vibrate indefinitely when they are perturbed because of the dissipation of energy by damping. The damping is usually expressed as a proportion of critical damping, which is the level of damping that will restore a system to its at rest position without vibrations. For reinforced concrete structures it is usually assumed that the damping can be taken as 5% of critical. 17

18. Response Spectra Real systems do not vibrate indefinitely when they are perturbed because of the dissipation of energy by damping. The damping is usually expressed as a proportion of critical damping, which is the level of damping that will restore a system to its at rest position without vibrations. For reinforced concrete structures it is usually assumed that the damping can be taken as 5% of critical. 18

19. Response Spectra If a series of SDOF systems with a given level of structural damping are all subjected to an acceleration time-history acting at their base, each mass will respond differently according to its natural period and the relationship between this period and the frequency content of the ground motion. The maximum absolute value of the response of each SDOF oscillator can be calculated and plotted against the corresponding value of period, T. The resulting plot, called a response spectrum, shows the maximum response that an SDOF system will experience when subjected to the ground motion represented by that particular accelerogram. This is illustrated in figure on the last slide. The response spectrum reflects the characteristics of the earthquake that generated the motion and the nature of the recording site. 19

20. Response Spectra Figure 2. Elastic response spectra of absolute acceleration of the four accelerograms shown in Figure 9.8. 1 – Peru 1974, 2 – Yugoslavia 1979, 3 – Romania 1977, 4 – Mexico 1985 20

21. Response Spectra Three different spectra can be defined according to how the response of each SDOF is measured: relative displacement, relative velocity or absolute acceleration. At zero period the spectra of relative displacement and relative velocity are equal to zero since for an infinitely rigid SDOF there is no vibration. At zero period the relative acceleration is also zero and the absolute acceleration is equal to the maximum acceleration of the ground. This is a very important point to grasp: the response spectrum of absolute acceleration anchors at PGA, as can be appreciated from fig.2: despite their very significant differences, all of the spectra converge to 0.18g at the period T=0. 21