2_ECI_175_READER_1-25

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1 University of California, Davis Department of Civil and Environmental Engineering ECI 175 Geotechnical Earthquake Engineering READER By Professor: Katerina Ziotopoulou, PhD, PE Fall Quarter 2023

2 ECI 175 – Geotechnical Earthquake Engineering Ground Motions Reading 1. Ground Motions Primer 2020 (in Canvas) – mandatory 2. Kramer Sections 2.1 – 2.5, 2.9.2.5 (ref) 3. Kramer Sections 3.1, 3.3, 4.4.1.2 (ref) 4. Kramer Sections 5.1 – 5.4 (but information is spotty there so best to reference these notes) Objectives of this topic: 1. Understand how tectonic earthquakes are generated and what seismic waves are produced in the process. 2. Describe fault types and fault rupture. 3. Describe fault rupture qualitatively in terms of intensities and quantitatively in terms of magnitudes. 4. Understand that different seismic waves are generated as a direct consequence of fault rupture and quantify wave velocities. 5. Be able to discuss basic principles of wave propagation including reflection and refraction at material interfaces. 6. Describe ground motions in terms of accelerations, velocities, and displacements as well as their response spectra. 7. Discuss the form of GMPEs and use them to obtain ground motion parameters. 8. Understand and describe what a PSHA is in the context of decision making. Context within Class

3 Tectonic Plates, Faults, and Earthquake Occurence Internal structure of earth Relative Masses: Oceans: 1/5000, Crust 1/250, Mantle = 2/3, Core 1/3 How are earthquakes generated? Whole-mantle convection (Wikipedia, 2023) Mantle convection: The Earth's surface lithosphere rides atop the asthenosphere & the two form the components of the upper mantle. The lithosphere is divided into several tectonic plates that are continuously being created or consumed at plate boundaries¨ _______________________________________________________________aka the earth is a patchwork of large mobile, oceanic and continental regions of solid rock called plates, floating on softer rock.

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4 Tectonic movement in time The earth is a very dynamic environment:

5 Preliminary determination of epicenters: 358,214 events from 1963 to 1998 Activity 1 : Let’s see some earthquakes being recorded https://ds.iris.edu/ieb https://ds.iris.edu/seismon https://www.usgs.gov/programs/earthquake-hazards/earthquakes Seismicity of a region: Earthquakes occur because: i. Relative movement of plates forces interactions at boundaries … ii. Plates comprised of rock and soil which are strong materials with tensile and frictional components … iii. Plates move steadily, resulting in build-up stresses … iv. Eventually energy stored exceeds soil/rock strength, relative motion occurs to release energy → earthquake! v. Types of plate interactions:

6 Types of faults:

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7 Fault Descriptors Intensity Scales Intensity is a qualitative (a FEELING) measure of the strength of shaking at a location. Depends on: i. energy released, ii. distance from the fault rupture iii. “directivity” iv. “site effects” v. quality of construction and vi. sensitivity of the observer (See Modified Mercali Intensity MMI)

8 Most common qualitative scale is Modified Mercali Intensity (MMI) scale. MMI values are subjective and dependent on building stock, population, and other factors. Magnitude Scales: Richter Local Magnitude ➢ is the log 10 of the maximum amplitude (in micrometers) recorded on a Wood-Anderson seismometer located 100 km from the epicenter of an earthquake. Note assumed relation between distance and S-P time. ➢ Familiar to public, but not particularly useful for engineering purposes.

9 Moment Magnitude, Mw (MOST COMMON – only one that does not saturate a high levels) Seismic Moment: Represents the elastic strain energy released by the earthquake: Moment Magnitude M W ○ Standard Form: ○ Inverse From:

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10 Magnitude versus fault characteristics

11 Earthquake Recurrence: How frequently can a Magnitude be expected? We want to know the relative frequency of different earthquake magnitudes. Gutenberg-Richter (1944) relation aka the exponential model ○ where  m = mean annual rate of exceedance for an earthquake of magnitude m, and the parameters a and b are determined by fitting the historic seismicity data. ○ The sum of seismic moment releases from all expected earthquakes per year must be balanced with the rate of seismic moment build-up, which is estimated from the geologic slip rate. ○ Other recurrence models account for geologic constraints on the maximum magnitude or the occurrence of characteristic magnitudes ….

12 Strong Motion Networks ▪ Array of Strong Motion measurement stations installed around the world ▪ California o ~900 stations ▪ 650 ground-response ▪ 70 buildings ▪ 20 dams ▪ 60 bridges ▪ Coordinated network to automatically record, transmit, process, check, and distribute data ▪ Enable rapid response output like ShakeMap https://www.conservation.ca.gov/cgs/smip/ https://www.strongmotioncenter.org/stationmap_worldwide/all_stations.php Others: K-NET, KiK-net of Japan ( https://www.kyoshin.bosai.go.jp/ ) etc.

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13 Wave Propagation https://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

14 Compression Wave (P-wave) Shear Wave (S-wave)

15 Surface Wave (Rayleigh wave) Surface Wave (Love wave)

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16 Wave Speeds ▪ Body waves depend on moduli and density: ▪ Saturated soil has an equivalent Poisson's ratio close to 0.5 in undrained loading ▪ ▪ V R is almost equal to the V s of the soil to a depth of about 1 to 1.5 x the wavelength: ▪ If V S increases with depth, then V R increases as the frequency 𝑓 decreases (wavelength l increases) ▪ Recall 𝜆 = 𝑉 𝑆 / 𝑓 ▪ Love waves only develop if V S increases with depth. Activity 2 Suppose a horizontally-polarized shear wave (SH) is transmitted from one borehole to another borehole. The two borings are 5-m apart. Accelerometers at the same depth in the two borings record the wave passage. The recorded wave can be approximated as a single harmonic wave with a frequency of 500 Hz and amplitude of 0.001g. The wave takes 24 ms to travel between the accelerometers. The soil's total unit weight is 19 kN/m 3 . What is the shear modulus of the soil?

17 Wave Velocity Measurements Wave velocity measured using: ▪ ____________________ techniques (need a boring): downhole, crosshole, seismic CPT, … ▪ ____________________ techniques (no holes): surface waves, reflection/refraction surveys, … ▪ Downhole JUST as an example (not the best test though but easiest for explaining concepts): Graphics courtesy Brady Cox (2020)

18 Resolution depends on quality of signals Different sources (strikes) and sensors (geophones) [what you hit is what you get]

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19 Beware of artifacts & errors Time-averaged shear wave velocity for the upper 30 m of a soil deposit, V S30 V S 30 , the time-averaged shear-wave velocity ( V S ) in the upper 30 meters, is a key index adopted by the earthquake engineering community to account for seismic site conditions. https://earthquake.usgs.gov/data/vs30/us/ Activity 3 What’s the V S30 for the profile above?

20 Activity 4 If you measure a P-wave and an S-wave arrival at a seismic station can you figure out how far the source is? How many stations with such recordings do you need to precisely identify the earthquake source? Wave reflection and refraction Reflected and refracted waves resulting from incident: (a) P wave, (b) SV wave, and (c) SH wave:

21 Practical Implication Activity 4: Wave refraction near the surface Typically, the shallower a layer, the lower its shear wave velocity (softer) and vice versa. What does this mean for the refraction of an incident SH-wave ray path through a series of surficial layers? e.g. the layered deposit of Problem 5.8 (Kramer 1996). Let’s zoom out now:

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22 Metrics of Ground Motions Acceleration, Velocity, Displacement…. time histories The Single Degree of Freedom (SDOF) Oscillator

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23 Response Spectra Response spectrum for a motion is a plot of how the peak response of a single-degree-of-freedom (SDOF) oscillator varies with the oscillator's fundamental period and damping ratio. Response spectra are revealing the _____________ Equation of motion for a SDOF oscillator (e.g., a mass on a spring) is: Undamped natural period and damping ratio (fraction of critical damping) are:

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