Design Earthquake Parameters for Engineering Projects Manish Shrikhande Department of Earthquake Engineering Indian Institute of Technology Roorkee Roorkee–247667. INDIA

Introduction The design earthquake parameters refer to the estimates of design earthquake ground motions that are used to estimate the seismic response of a given structure, or facility. These design parameters can be obtained either directly from the standard codes of practice for earthquake resistant design,1 or conducting a site-specific study for the determination of relevant design earthquake parameters. The recommendations of the standard codes of practices are applicable only for the design of ordinary structures and for important structures, such as, large scale hydroelectric projects it is recommended that a site-specific study for the estimation of seismic design parameters be carried out in accordance with the requirements of International Commission on Large Dams (ICOLD). The need for a site-specific study for each major project has been emphatically stated in the ICOLD Bulletin 72:2 The use of meaningful seismic parameters is necessary to perform a satisfactory evaluation of the earthquake safety of dams. These Guidelines are intended to help the Engineer and Project Manager to select seismic evaluation parameters for dam projects, based on requirements mandated by the project location and its associated seismic hazard, the design selected, and the risk of the completed structure. Appropriate seismic evaluation is not a substitute for, but will complement the use of sound design, high quality materials, effective construction control procedures, and continuous surveillance and monitoring of the completed structure. It should be emphasized that, regardless of the seismic parameters and methods of analysis selected, the final evaluation of the seismic safety of the dam usually depends on engineering judgement and previous experience with similar structures (evaluating and taking into consideration newly developed research methods and newly obtained research results), keeping in mind that each completed structure and its immediate environment form a unique system that is not duplicated elsewhere. 1 2

such as, IS-1893:(2002) Indian Standard Criteria for Earthquake Resistant Design of Structures ICOLD Bulletin 72: Selecting Seismic Paramters for Large Dams: Guidelines, 1989

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The estimation of design earthquake parameters at a site requires inputs from diverse fields— making it a challenging inter-disciplinary exercise in churning of vast amount of information to produce a set of legible and meaningful parameters. Specifically information is required regarding geology of the region, historical seismicity, seismotectonics, etc. In the following, we start with a discussion of inputs required for a seismic hazard analysis and then outline a deterministic method of evaluation of seismic hazard at a site. The probabilistic approach for seismic hazard assessment is still under development and it is difficult to interpret the results in the backdrop of a host of assumptions, whose validity may be questionable, involved in developing the probabilistic framework.

Background Earthquake—as the name suggests—refers to a phenomenon associated with shaking/movement of the ground resulting from a sudden release of energy. An earthquake occurs when stress, building up within rocks of the earth’s crust,is released in a sudden jolt. Rocks crack and slip past one-another causing the ground to vibrate. The slippage emits large amounts of energy in the form of waves that travel through the interior of the earth and across the surface. Cracks along which rocks slip are called faults; these may break through the ground surface, or remain deep within the earth. San Andreas fault, which stretches for more than 900 km along the coast of California, is shown in Figure 1. This fault lies along the boundary between the Pacific Plate and the North American tectonic plate. Activities of this fault have caused some of the major earthquakes in the United States, such as the 1906 San Francisco earthquake (magnitude 8.3, killed 700 people Figure 1: San Andreas and left 250,000 people homeless). The study of earthquake pheFault, California, U.S.A. nomenon can be viewed from two perspectives: pure geophysical point of view and the engineering approach primarily concerned with the safety of man-made facilities during earthquakes. The physics of the earthquake process is not of much importance as compared to the estimation of design forces expected during a future earthquake. A complete specification of design (future) earthquake motion comprises information on: (i) severity of shaking, (ii) spectral distribution of of the energy of seismic waves, and (iii) duration of strong shaking. In order to have a conservative estimate of future earthquake ground motions, it is of vital importance to gather data on past history of seismicity of the region. In particular, information is obtained from the following sources of data: (i) historical seismicity, (ii) instrumental records of ground motions during past earthquakes, and (iii) geological data for region.

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Historical Seismicity The compilation of historical seismicity is an important first step in the evaluation of seismic hazard in a region. It helps to identify the seismicity patterns of a region, and provides a basis for estimating the possible future earthquake motion at the site considered. The lack of historical seismicity data should, however, not be construed as a basis for region being considered as aseismic. The compilation should include information about all past earthquakes occuring within a circle of radius 300 km around the project site. The following data should be provided (when available) for each event: epicenter location, magnitude (or, epicentral intensity), data and time of occurrence, focal depth, focal mechanism, felt area, accompanying surface effects, intensity of ground motion induced at the project site (known, or estimated), relibility and source of data.3

Geological Studies Since earthquakes are caused by the propagation of elastic waves through the strata the local geological characteristics of the region greatly influence the nature of earthquake ground motion. Moreover, it is important to explore the possibility of secondary geological hazards, such as landslides, being triggered by an earthquake in the region. Local geologic data should include information on type, thickness, stability characteristics of rock units and soil deposits, orientation of lineaments, dip and strike of faults, etc. in the region. Key Fault Parameters The key fault parameters that appear most significant include: rate of strain release, or fault slip rate; amount of fault displacement in each event; length (and area) of fault rupture; earthquake size and earthquake recurrence interval. Slip Rate: The geologic slip rate provides a measure of the average rate of deformation on a fault (measured in mm/Year). The slip rate is estimated by dividing the amount of cumulative displacement, measured from displaced geologic or geomorphic features, by the estimated age of the geological material or feature. The geologic slip rate is an average value over a geologic time period, and reliable to the extent that the strain accumulation and release over this time period has been uniform and responding to the same tectonic stress environment. Generally, prominent and highly active faults have a much higher slip rate than minor faults. Moreover, a range of values for the slip rate have to be considered for a fault in any application in view of the inherent uncertainties in estimation of fault movements. Earthquake Size: The magnitude of an earthquake is related to the total energy released by the earthquake at the source irrespective of the place of observation. Originally, it was 3

ICOLD Bulletin 72, op. cit.

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Figure 2: Relation between moment magnitude and various magnitude scales [after, Heaton et al. (1986)] empirically related to the maximum amplitude of seismic ground motion recorded on a particular type of instrument. There have been several definitions for magnitude scales depending on the type and period of wave being observed. A more physically meaningful measure based on the seismic moment has been in use since last 25 years, or so. Seismic moment, in dyne-cm, is defined by Mo = µAf D

(1)

where, Mo is the seismic moment in dyne-cm, µ is the shear modulus of the material along the fault plane, Af is the area in cm2 of the fault plane underrgoing slip, and D, in cm, is the average displacement over the slip surface. The magnitude scale based on the seismic moment generated during an earthquake is now universally used as a measure of the size of earthquake. The moment magnitude (Mw ), as it is called, is related to the seismic moment by the relation4 2 Mw = [log Mo − 16.1] (2) 3 Figure 2 shows a comparison of moment magnitude with other magnitude scales.5 While all magnitude scales exhibit a saturation level—when the ruptures fault dimension exceeds the wavelength of the seismic waves that are used in measuring the magnitude—the moment magnitude does not saturate as it is derived from seismic moment as opposed to an amplitude of a ground motion record. 4 Hanks, T.C. and Kanamori, H. A moment magnitude scale. Journal of Geophysical Research, 84:2348–2350, 1979. 5 Heaton, T., Tajimi, F. and Mori, A. Estimating ground motions using recorded accelerograms Surveys in Geophysics 8:25–83, 1986.

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Figure 3: Gutenberg-Richter recurrence models: (a) Historical seismicity data for the period 1900–1980 along the south central segment of the San Andreas fault; the box in the figure represents range of recurrence for M=7.5–8.0, based on geologic data; (b) Characteristic earthquake recurrence model for south central segment of San Andreas fault. Earthquake Recurrence Interval: A key element in seismic hazard assessment is estimating recurrence intervals for various magnitude earthquakes. The most widely used relation to approximate occurrence of earthquakes during a given time period is given as6 log N (m) = a − bm

(3)

where, N (m) is the number of earthquakes with magnitude greater than or equal to m within a specified duration (generally assumed to be one year), 10a is the total number of earthquakes with magnitude greater than zero and b is the slope of a linear fit to the regional seismicity data. This relation is derived with the assumption of spatial and temporal independence of all earthquakes—a Poisson process model. The slope b, based on regional historical seismicity records, typically ranges from 0.6 to about 1.1. Plots of frequency of occurrence versus magnitude can be prepared for small to moderate earthquakes and extrapolations to larger magnitudes can provide estimates of the mean rate of occurrence of larger magnitude earthquakes. This technique has limitations, however, because it is based on regional seismicity, and often cannot result in reliable recurrence intervals for specific faults. Discrepancies between earthquake recurrence intervals based on historical seismicity and recurrence intervals based on geologic data are common when applied to a specific fault, as shown in Fig. 3(a). In order to circumvent this difficulty, a characteristic earthquake model has been proposed.7 This model uses the 6 Gutenberg, B. and Richter, C.F. Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34:185–188, 1944. 7 Schwartz, D.P. and Coppersmith, K.J. Fault behaviour and characteristic earthquakes from the Wasatch

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historical seismicity data to derive the b-value of Gutenberg-Richter relation for low-tointermediate earthquake magnitudes. For maximum magnitude earthquake, the recurrence is evaluated from geologic data based on estimation of average slip rate on a fault and the seismic moment derived therefrom. The recurrence between the intermediate and the maximum magnitude is derived using a Gutenberg-Richter relation but having a slope much smaller than the slope used for the low-to-intermediate magnitude range. The characteristic recurrence model for south central segment of the San Andreas fault is shown in Fig. 3(b).

Estimation of Seismic Hazard Geological and seismological studies can define fault length, fault width, amount of displacement per event, and slip rate for potential earthquake sources. Estimation of potential of a seismic source (fault) in a region to generate an earthquake depends on estimation of these key fault parameters. Several regression relations exist which relate these parameters to the earthquake magnitude. Selection of a maximum magnitude for each source is ultimately a judgement that incorporates understanding of specific fault characteristics, the regional tectonic environment, similarity to other faults in the region, and data on regional seismicity. Some of the relations used for this purpose are:8 Mw = 5.08 + 1.16 log(SRL)

Mw = 4.38 + 1.49 log(RLD)

Mw = 4.07 + 0.98 log(RA)

Mw = 6.69 + 0.74 log(MD) Mw = 6.93 + 0.82 log(AD)

(4)

where, Mw is the moment magnitude, SRL is surface rupture length in km, RLD is subsurface rupture length in km, RA is rupture area in km2 , MD is maximum surface displacement in m, and AD is average surface displacement in m. Most of the times, however, such detailed information is not available for most of the seismogenic features in region. In such cases, the historical seismicity data is used to plot the epicenters of past earthquakes on a map showing all seismogenic features in the region. The past events are associated to different seismogenic features in the region based on proximity of the epicenter to the known seismogenic feature. In case an event can not be conclusively assigned to any specific feature, it is known as a floating earthquake and is associated will all surounding seismogenic features. The maximum magnitude of the earthquake thus assigned to each of the seisogenic feature in the range is then arbitrarily increased by 0.5 unit to get an estimation of maximum earthquake magnitude on each of the seismogenic feature in the region. This increase in magnitude value is to account for the incompleteness of seismicity catalogue. This assigned hypothetical maximum magnitude and San Andreas faults. Journal of Geophysical Research, 89:5681–5698, 1984. 8 Wells, D.L. and Coppersmith, K.J. New empirical relationships among magnitude, rupture length, rupture width, rupture area and surface displacement. Bulletin of the Seismological Society of America, 84:974–1002, 1994.

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is termed as maximum considered earthquake (MCE) for the specific fault. The effect of this hypothetical maximum earthquake occurring on distant faults at the project site is expressed in terms of peak ground motion parameters (acceleration, velocity and displacements) with the use of attenuation relationships. Several such relationships have been derived for different parts of the world and for different seismo-tectonic environment. One such relation is:9 a = 5600 exp(0.8ML )/(R + 40)2 v = 32 exp(ML )/(R + 25)2 v2 d = (1 + 200R−0.6 ) a

(5)

where, a is peak ground acceleration (PGA) in cm/s2 , v is peak ground velocity (PGV) in cm/s and d is peak ground displacement (PGD) in cm, R is hypocentral distance in km, and ML is the Richter (local) magnitude. The coefficients 40 and 25 are empirical constants to account for the volume of lithospheric rock that participates in releasing the stored energy. These relations indicate more rapid attenuation of high frequency components of ground motions.

Response Spectra Earthquake engineers prefer to report interaction between ground acceleration and structural systems through response spectrum. It reflects frequency content, amplitude of ground motion and effect of subsequent filtering by the structure. Acceleration spectrum is a plot of natural period of vibration of a single degree of freedom (SDOF) oscillator with a specific value of damping versus peak absolute acceleration of oscillator mass when subjected to a base acceleration equal to the earthquake accelerogram (i.e., ground acceleration). The value of the spectral acceleration at zero periods, known as zero period acceleration (ZPA), is the PGA because oscillator is composed of infinitely stiff linear spring. The relative displacement response spectrum asymptotically approaches maximum ground displacement for highly flexible structure. This implies that the mass remains stationary for all practical purposes and only the ground moves as the linear elastic SDOF system is composed of spring with negligible stiffness. In between the two extremes period, the value of spectral acceleration at a particular period is a constant multiplier, known as amplification factor, of peak ground acceleration. The amplification factor at short-period increases with increase of period and reaches a maximum at the sub soil period and then it decreases with increase of period in general. The amplification factor for rocky site condition is higher than that of alluvium site condition at short-periods and vice-verse at long-periods. The amplification factor reduces with increase of hypocentral distance from the site and peak amplification occurs at higher period. 9

Esteva, L. and Villaverde, R. Seismic risk design spectra and structural reliability. In Proceedings of the Fifth World Conference on Earthquake Engineering, Rome, 2586–2596, 1974.

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Figure 4: Design Spectra recommended by Newmark et al. (1973) for 1 g PGA,at 84.1 percentile Table 1: Ground Motion Parameters after Mohraz (1976)

Site Condition Rock Alluvium underlain by rock < 9 m deep Alluvium underlain by rock between 9-61 m deep Alluvium

Larger Horizontal v/a ad/v 2 v d v/a (m/s)/g m/s mm (m/s)/g 0.686 6.9 0.686 330.0 0.787

Vertical ad/v 2 v d m/s mm 7.6 0.787 480.0

0.940

5.2

0.940 467.0

0.940

8.5

0.940 765.0

0.838 1.295

5.6 4.3

0.838 401.0 1.295 734.0

0.838 1.295

9.1 5.0

0.838 650.0 1.295 856.0

Design Spectrum The design response spectrum is a smooth response spectrum specifying level of seismic resistance required for design. Thus the design spectrum is a specification of the required strength of structure. The strength is frequency dependent and also dependent on maximum velocity, maximum displacement and maximum acceleration in various ranges of frequencies. Three straight lines bound the general shape of the smooth spectra on a logarithmic tripartite graph as shown in Fig. 4. At low frequency range the spectral displacement Sd = maximum ground displacement d; and in the high frequency range, the spectral acceleration Sa = maximum ground acceleration a. As we proceed from low to high frequency, there exist five different regions. These are

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1. a transition from maximum ground displacement to amplified spectral displacement, 2. amplified displacement ∈ (0.015, 0.3] Hz., 3. amplified velocity ∈ (0.3, 1.8] Hz., 4. amplified acceleration ∈ (1.8, 6.0] Hz. and 5. a transition from amplified spectral acceleration to ground acceleration at 33.0 Hz.

Table 2: Amplification factors (5% damping) for larger Horizontal (1976) Percentile Site Condition 50 84.1 50 84.1 Displacement Velocity Rock 1.83 2.71 1.28 1.90 Alluvium underlain by rock < 9 m deep 2.53 3.30 1.33 2.09 Alluvium underlain by rock between 9-61 m deep 1.85 2.73 1.47 2.19 Alluvium 2.07 2.78 1.44 2.08

Component after Mohraz

50 84.1 Acceleration 1.98 2.82 2.60

3.38

2.29 2.01

2.94 2.58

Table 3: Site Design Coefficient after Mohraz (1976) Coefficients Site Category Displacement Velocity Acceleration Rock 0.50 0.50 1.05 Alluvium underlain by rock 0.75 0.75 1.20

The design spectrum can be obtained from maximum ground velocity, displacement and acceleration if the amplifications are known. Table 2 gives the amplification factors for larger horizontal component of earthquake. Newmark et al. proposed10 transition from amplified ground acceleration to ground acceleration begin at 6 Hz. for all damping values and end at 40, 30, 17 and 9 Hz, for critical damping ratio 0.5, 2.0, 5.0 and 10.0 percent, respectively. Corresponding to l g ZPA, the peak ground velocity is 122 cm/s and displacement is 91 cm for alluvial soil, and 58 cm/s and 30 cm for the rock. The measure of width of the spectrum is ad/v 2 = 6 for both type of spectra. Figure 4 shows the spectrum for alluvial soil recommended by Newmark et al. for l g ZPA. Figure 5 shows the 84.1 percentile, (i.e. mean + one standard deviation) 5% critical damping spectra for the horizontal component of earthquake motion by 10

Newmark, N.M., Blume, J.A. and Kapoor, K.K. Seismic design spectra for nuclear power plants, Journal of Power Division, ASCE, 99(02):873–889, 1973.

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Figure 5: Design Spectra recommended by Seed for 5% damping at 84.1 percentile

Seed et al.11 Mohraz12 studied three components of ground motion. The mean value of the ratio of smaller and larger horizontal component (RS) is 0.83 and that of vertical and larger horizontal component (RV) is 0.48. 84.1 percentile values are RS = 0.98 and RV = 0.65 which indicates that both horizontal component are almost equal and vertical component is approximately 2/3 of horizontal component. Figure 6 shows average spectra normalized to l g ZPA for 2% critical damping. Tables 1–3 give the ground motion parameter, amplification factor for alluvium and site design spectra coefficients proposed. Given the PGA is a, using Tables 1–3, 50 or 84.1 percentile horizontal design response spectrum can be obtained. The spectral values are Sd = factor ×d, Sv = factor ×v and Sa = factor ×a where d, v and a are PGD, PGV and PGA respectively from Table 1. From Table 2, design spectrum value can be obtained as site coefficients × design spectrum value for alluvium site. According to the geological condition of site, taking averaged spectral acceleration as a guide, the spectral acceleration of each faults are drawn. An envelope, of all these spectral acceleration of various causative faults for a particular site, is called acceleration spectrum of MCE . The acceleration spectrum corresponding to DBE is obtained by multiplying a fraction less than equal to half to the spectral acceleration of MCE . The spectral acceleration for DBE is used for working stress design and that of MCE is used for ultimate design. 11 Seed, H.B., Ugas, C. and Lysmer, J. Site dependent spectra for earthquake resistant design. Bulletin of the Seismological Society of America, 66:221–243, 1976. 12 Mohraz, B. A study of earthquake response spectra for different geologic condition. Bulletin of the Seismological Society of America, 66:915–932, 1976.

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Figure 6: Average Design Spectra recommended by Mohraz for 2% damping

Strong Motion Duration The duration of strong shaking (Ts ) at a site is an important aspect of design ground motion characterisation. Several relations relating the strong motion duration to earthquake magnitude, source-to-site distance, and site conditions have been proposed on the basis of analyses of recorded motions during past earthquakes. One such relation is13 Ts = −4.88s + 2.33M + 0.149R

(6)

where, s (= 2,1, and 0 for rock, firm and soft soil, respectively) is a site characterisation parameter, M represents the earthquake magnitude, and R is the epicentral distance.

13 Trifunac, M.D. and Brady, A.G. A study on the duration of strong motion. Bulletin of the Seismological Society of America, 65:581–626, 1975.

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