Earthquakes and Seismic Ground Motion

1.1  Origin of Earthquake 2079 Bhadra2080 Bhadra

1.1.1  What is an Earthquake?

Earthquake is the sudden shaking or trembling of the earth's surface caused by the rapid release of strain energy accumulated in elastically strained rocks of the earth's crust. The released energy radiates in all directions from its source in the form of seismic waves, and when these waves reach the ground surface they set the ground — and everything standing on it — into motion.

1.1.2  Source of an Earthquake — Focus and Epicentre

• Focus (Hypocentre) — the point inside the earth where the rupture begins and from where the seismic energy is first released. This is the source of the earthquake.
• Epicentre — the point on the ground surface vertically above the focus. Shaking is generally strongest here.
• Focal depth — the vertical depth of the focus below the epicentre.
• Epicentral distance — horizontal distance from the epicentre to the site; hypocentral distance is the slant distance from the focus to the site.
• Fault — a fracture (crack) in the earth's crust along which the two sides have moved relative to each other, parallel to the fracture surface.

Classification by focal depth

About 90% of earthquake foci are shallower than 100 km, large earthquakes are mostly at less than 60 km depth, and no earthquake occurs deeper than about 700 km because below that the rock is too ductile to store elastic strain.

1.1.3  Causes of Earthquakes

1.1.4  Interior of the Earth

Understanding why plates move needs a quick look at the earth's layers, because it is the temperature difference between the core and crust that drives convection in the mantle and therefore plate motion.

The rigid outermost shell — the crust plus the uppermost mantle, about 80–100 km thick — is called the lithosphere, and it is broken into the tectonic plates.

1.1.5  Theory of Plate Tectonics

Proposed in the 1960s and developed from Alfred Wegener's 1915 theory of continental drift, plate tectonics is the unifying theory that explains the formation and deformation of the earth's surface. According to it the lithosphere is divided into about 12 major plates that float on the plastic upper mantle and move relative to one another at a few centimetres per year. Earthquakes, volcanoes and mountain ranges are concentrated at the boundaries of these plates.

Evidence for continental drift

• Matching coastlines (South America and Africa fit like jigsaw pieces).
• Matching mountain ranges across the Atlantic (Appalachians – Caledonides).
• Matching rock types and radiometric rock ages on facing coasts.
• Matching glacial deposits of ~300 million years ago in now-tropical continents.
• Matching fossils — e.g. Mesosaurus, a freshwater reptile, found on both sides of the Atlantic.

Types of plate boundary

1.1.6  Elastic Rebound Theory 2079 Bhadra, Q1a

Proposed by H. F. Reid after studying the 1906 San Francisco earthquake, the elastic rebound theory is the standard explanation of how an earthquake is generated:

Foreshocks and aftershocks

• Foreshocks — smaller earthquakes that precede the main shock by days or sometimes years, as the rock progressively fails.
• Aftershocks — smaller earthquakes that follow the main shock as the crust readjusts to the new stress state. They are the biggest danger to already-cracked masonry buildings, which is why damaged buildings must be shored immediately.
• Whether a tremor was a foreshock or an aftershock is only known after the main shock has occurred.

1.1.7  Faults and Fault Types

A fault is a fracture in the crust along which the two blocks have moved relative to each other. The block resting above the inclined fault plane is the hanging wall and the one below is the footwall. The orientation of a fault is described by its strike (compass direction of the fault line on the surface) and its dip (angle of the fault plane from horizontal).

1.1.8  Origin of Earthquakes in the Himalayas 2079 Bhadra, Q1a

The Himalaya is the classic continent–continent convergent margin:

1. About 225 million years ago the Indian plate, carrying the Indian landmass, separated from Gondwanaland and began drifting northwards at roughly 10 cm per year, with the intervening Tethys oceanic crust subducting beneath the Eurasian plate.
2. Around 55 million years ago the Tethys closed and India collided with Asia. Because both are continental crust of about the same low density, neither could subduct beneath the other.
3. The only way the collision pressure could be relieved was by crustal thickening and thrusting upward, contorting the collision zone and raising the Himalayan range. This is why the Himalaya has great earthquakes but no volcanoes.
4. Convergence continues today at about 2 cm/yr (India–Eurasia ~4–5 cm/yr, of which about 2 cm/yr is absorbed across the Himalaya). Nepal therefore shortens by roughly 2 m per century.
5. This shortening is taken up on a system of north-dipping thrust faults that all sole into one gently north-dipping detachment, the Main Himalayan Thrust (MHT):
   • MFT — Main Frontal Thrust (southernmost, active, at the Terai–Siwalik front)
   • MBT — Main Boundary Thrust (Siwalik–Lesser Himalaya)
   • MCT — Main Central Thrust (Lesser–Higher Himalaya)
   • STDS — South Tibetan Detachment System (northernmost, normal fault)
6. The shallow part of the MHT is locked by friction between earthquakes. Strain accumulates for decades to centuries and is then released suddenly as a great earthquake — exactly the elastic rebound mechanism. The 2015 Gorkha earthquake (M_w 7.8) was a rupture of the locked MHT that propagated eastward from Barpak, Gorkha, at a focal depth of about 15 km.

1.1.9  Factors Influencing the Shaking at a Location 2080 Bhadra, Q1a

The severity of shaking at a particular site is not governed by magnitude alone. It is best remembered under three headings — source, path and site:

1.2  Seismic Waves, Earthquake Ground Motion, Magnitude and Intensity 2078 Bhadra2079 Bhadra

1.2.1  Sequence of Events

1.2.2  Seismic Waves

The energy released at the focus travels through and over the earth as seismic waves. They are of two broad classes:

(A) Body waves — travel through the earth's interior

(B) Surface waves — travel along or just below the ground surface

Surface waves are generated when the body waves reach the free surface. They decay more slowly with distance than body waves, so at large epicentral distances the surface waves dominate the record. In general, high-frequency body waves shake low-rise (stiff) buildings more, while low-frequency surface waves shake tall (flexible) buildings more. Whenever a P or S wave is reflected or refracted at an interface, part of its energy is converted into the other wave type.

1.2.3  Recording and Locating an Earthquake

• A seismograph records ground motion using a mass with such large inertia that it stays effectively at rest while the frame and ground move around it; the relative movement is recorded.
• The record it produces is a seismogram, showing the P, S and surface wave arrivals.
• A strong-motion accelerograph records three orthogonal components of ground acceleration (two horizontal — usually N–S and E–W — and one vertical) and is the instrument used for engineering design data.

Locating the epicentre. Because the P wave is faster than the S wave, the time gap between the P and S arrivals increases with distance from the epicentre. Each station converts its S–P time interval into a distance D and draws a circle of radius D around itself on a map. Three or more stations are required; the single point where the three circles intersect is the epicentre (triangulation). About 95% of major earthquakes occur within a few narrow belts that mark the plate boundaries.

1.2.4  Earthquake Ground Motion Parameters

An accelerogram can be integrated once to obtain the ground velocity time history and twice to obtain the ground displacement time history. Three quantities describe the destructiveness of the record:

PGA varies enormously over a few kilometres because of ground type, so a moderate earthquake on soft soil can produce a larger PGA than a bigger earthquake on rock. The spatial variation is plotted as a shake map. In each record the peaks of the two horizontal components (H1, H2) and the vertical component (V) are reported; the peak horizontal ground acceleration is taken as the larger component, the mean of the two, or their vector sum.

1.2.5  Magnitude 2078 Bhadra2079 Bhadra

Magnitude is a quantitative, instrumental measure of the size of an earthquake — that is, of the total energy released at the source. It is a single number for a given earthquake, independent of where it is measured.

(a) Richter scale (local magnitude, M_L)

• Devised by Charles F. Richter in 1935. It is based on the logarithm (base 10) of the maximum trace amplitude recorded by a standard Wood–Anderson seismograph, corrected to a standard epicentral distance of 100 km.
• Because it is logarithmic, an increase of one unit of magnitude means 10 times larger wave amplitude and about 31.6 (≈32) times more energy released.
• Hence an M7.7 earthquake releases about 31 times the energy of an M6.7, and about 31×31 ≈ 1000 times that of an M5.7.
• The scale is open-ended and can be negative for very small tremors, but it saturates — it does not adequately distinguish the size of very large earthquakes (above about M7).

(b) Moment magnitude (M_w)

Derived from the seismic moment M₀ = µ A D, where µ is the rigidity of the rock, A the ruptured fault area and D the average slip. Because it is calculated from the physical size of the rupture rather than from one instrument trace, it does not saturate and is the scale now used for all large earthquakes — the 2015 Gorkha earthquake is quoted as M_w 7.8.

1.2.6  Intensity

Intensity is a qualitative, observational measure of the actual effects of an earthquake at a particular place — on people, objects, buildings and the ground. Because the effects change from place to place, one earthquake has many intensity values but only one magnitude. Intensity is highest near the epicentre and decreases outward; lines joining points of equal intensity are called isoseismals, and their map is used to identify the epicentre of historic (pre-instrumental) earthquakes and to prepare seismic hazard maps.

The scale used is the Modified Mercalli Intensity (MMI) scale, which has 12 grades written in Roman numerals I to XII. Other scales in use are the MSK-64 (Europe, also 12 grades) and the JMA scale (Japan).

1.2.7  Comparison of Magnitude (Richter) and Intensity (MMI) 2079 Bhadra, Q1b

Approximate correlation between Richter magnitude and MMI

1.3  Occurrence of Earthquakes; Loss and Damages

1.3.1  Where do Earthquakes Occur?

Earthquakes are not scattered at random. About 95% of all major earthquakes occur in a few narrow belts that coincide with the boundaries of the tectonic plates:

• Circum-Pacific belt (“Ring of Fire”) — about 80% of all earthquakes; associated with subduction around the Pacific.
• Alpide (Mediterranean–Himalayan) belt — about 15%; runs from the Mediterranean through Iran and the Himalaya to Indonesia. Nepal lies in this belt.
• Mid-oceanic ridge belt — the remaining ~5%; shallow and mostly moderate earthquakes.
• A small number of intraplate earthquakes occur far from any boundary.

1.3.2  Seismic Hazards

Ground shaking is the primary hazard, and it is what causes all the others:

1.3.3  Factors Governing the Extent of Damage

Damage is a site-specific parameter — it depends not only on the size of the earthquake but on:

1. The distance between the source (focus/hypocentre) and the site.
2. The magnitude of the earthquake — the amount of energy released.
3. The type of soil or rock at the site — unconsolidated materials amplify shaking far more than rock, and fine-grained sensitive soils may lose strength altogether by liquefaction.
4. The nature of the structures — their period, mass, stiffness, ductility, configuration, material and construction quality. Timber is flexible and performs well; earthen and unreinforced masonry construction is highly vulnerable.
5. The duration of shaking and the number of load reversals.
6. Time of day, population density and preparedness — which govern the human loss for a given physical damage.

1.3.4  Major Historic Earthquakes of the World

1.3.5  Earthquake History of Nepal

1.4  Time History, Frequency Spectra and Response Spectra of Earthquake Force

1.4.1  Accelerogram and Time History

The most direct description of an earthquake motion in the time domain is the accelerogram, recorded by a strong-motion accelerograph. It records three orthogonal components of ground acceleration — two horizontal and one vertical — at a given location.

• From a single accelerogram we can read directly the peak ground acceleration, the duration and (after processing) the frequency content of the shaking.
• Integrating the acceleration record once gives the ground velocity time history, and integrating again gives the ground displacement time history.
• Nepal's own records — for example the Kantipath record of the 2015 Gorkha earthquake — are used as input for time-history analysis of buildings in the Kathmandu Valley.

Time-history analysis

Time-history analysis evaluates the linear or nonlinear dynamic response of a structure to a loading that varies with time. The dynamic equilibrium equation is solved step by step:

It is solved either by modal superposition or by direct integration. Direct integration is sensitive to the time-step size, which must be reduced until the results stop changing. It is the most sophisticated and most expensive level of analysis, and is reserved for irregular, very tall or critically important structures.

1.4.2  Frequency Spectra

• An earthquake record is not a single sine wave — it is the sum of a large number of harmonic components of different frequencies. The frequency spectrum shows how much energy is carried at each frequency.
• The frequency at which the amplitude is largest is the predominant frequency (its inverse being the predominant period) of the ground motion.
• Longer wavelength → smaller frequency; shorter wavelength → larger frequency.
• Engineering use: if the predominant period of the ground motion is close to the fundamental natural period of the building, resonance occurs and the response is greatly magnified. Soft deep soils have long predominant periods and therefore endanger tall flexible buildings; rock sites have short predominant periods and endanger low, stiff buildings such as ordinary masonry houses.

1.4.3  Response Spectra

How it is constructed

1. Take a set of SDOF oscillators (a mass on a spring) with natural periods covering, say, 0 to 4 seconds, all with the same damping ratio — conventionally 5% of critical damping.
2. Apply the same recorded ground acceleration time history to the base of every oscillator.
3. Carry out a time-history analysis of each oscillator and note only the single maximum absolute response reached during the shaking.
4. Plot those maxima against the corresponding natural periods. The resulting curve is the response spectrum of that ground motion.

Key points about response spectra

• For a transient input such as an earthquake, the peak response is reported. For a steady-state periodic input the steady-state response is reported, and in that case damping must be present or the response would be infinite.
• The ground response spectrum is the spectrum computed from a record measured at the free surface of the ground. If the natural frequency of a structure is known, its peak response can simply be read off this curve — this is the basis of the seismic force calculation in almost every building code.
• Response spectra can also handle multi-degree-of-freedom systems: modal analysis gives the modes, the peak response of each mode is read from the spectrum, and the modal responses are combined, typically by the SRSS (square root of the sum of the squares) rule when the modal frequencies are well separated (CQC is used when they are close).
• Because phase information is lost in forming the spectrum, the combined result differs from a direct time-history result.
• Main limitation: response spectra are universally valid only for linear systems. They can be generated for nonlinear systems but are then applicable only to systems with the same nonlinearity, and the results cannot be directly combined for multi-mode response.
• Resonance case study: in the 1985 Mexico City earthquake the oscillation period of the deep soft lake-bed deposits matched the natural period of mid-rise concrete buildings; those buildings were destroyed while shorter (stiffer) and taller (more flexible) buildings suffered far less damage.
• George W. Housner began publishing response spectra at Caltech in 1941; Newmark and Hall later developed the idealised spectrum (EERI Monograph, 1982) that became the modern design response spectrum.

Design response spectrum in codes

A code spectrum is a smoothed, idealised envelope of many recorded spectra, given for each soil type and a nominal 5% damping. In IS 1893 (Part 1) it appears as the average response acceleration coefficient S_a/g, plotted against the fundamental period T for hard, medium and soft soil. The design horizontal seismic coefficient and base shear then follow:

For a moment-resisting frame with brick infill panels IS 1893 gives T_a = 0.09 h/√d, and without infill T_a = 0.075 h^0.75. Detailed application to masonry buildings, and the NBC 105 equivalents, are covered in Chapter 4.

1.4.4  Methods of Seismic Analysis — Summary

1.5  Effects of Earthquake on Building 2081 Bhadra

1.5.1  Nature of Earthquake Force — Earthquake as a Lateral Force 2081 Bhadra, Q1a

An earthquake does not apply a force to a building in the way that wind or a live load does. The ground simply moves; the building is dragged along with it, and the force is generated inside the building itself:

Why a lateral force develops

1. When the ground shakes, the foundation of the building moves with the ground.
2. The mass of the roof and floors, by inertia (Newton's first law), resists this motion and tends to stay where it was, so the upper part lags behind the base.
3. This relative displacement between the base and the mass distorts the walls and columns and sets up internal forces in them.
4. Because the ground reverses direction many times a second, the building swings back and forth and the lateral force reverses in sign for every cycle — unlike gravity load, which is one-directional.
5. If the building were perfectly rigid, every point would move exactly with the ground and the inertia force would simply be m × PGA. Real buildings are flexible, so different parts move by different amounts and the force depends on the building's own dynamic properties as well.

Flow of the inertia force — the seismic load path

The inertia force is generated wherever there is mass, and it must be carried to the ground through a continuous and complete load path. In a masonry building it is:

• Walls parallel to the direction of shaking act as shear walls and carry the force efficiently by in-plane shear — they are strong and stiff in that direction.
• Walls perpendicular to the shaking are loaded out-of-plane, i.e. as vertical slabs spanning between floor and roof. Unreinforced masonry is very weak in this mode and overturns — this is the classic cause of collapse of Nepali masonry houses.
• If any link in the path is missing or discontinuous (no band, no wall-to-roof anchorage, no corner interlocking), the building loses box action and the walls fail individually.

Horizontal versus vertical shaking

• Ground shaking has three components; the two horizontal components generally govern design, because buildings are designed with a large factor of safety against vertical (gravity) load but have little inherent resistance to horizontal load.
• The vertical component is normally taken as about two-thirds of the horizontal, and is important for cantilevers, long spans and for masonry, where it momentarily reduces the compressive pre-load and hence the frictional shear capacity of the wall.
• Because vertical inertia force adds to and subtracts from gravity load, the axial force in piers fluctuates — combined with overturning this is why piers must be checked for the increase in axial load (Chapter 4).

1.5.2  Earthquake Force Parameters 2081 Bhadra, Q1b

The magnitude of the seismic force that a building must resist depends on three families of parameters — those of the ground motion, those of the structure, and the code coefficients that combine them.

(A) Ground motion parameters

(B) Structural parameters

(C) Code parameters (IS 1893 / NBC 105)

These are simply the design shorthand for the parameters above: the zone factor Z (regional seismicity), the importance factor I (consequence of failure), the response reduction factor R (ductility and redundancy), the soil/site factor and the spectral acceleration coefficient S_a/g (period and soil). Together they give A_h and hence the design base shear V_B = A_hW, as set out in §1.4.3.

1.5.3  Effects of Earthquake on Buildings

The deformation imposed by the ground produces the following effects, which for masonry appear as characteristic damage patterns:

1.5.4  Seismic Design Philosophy

Designing a building to remain undamaged in the strongest possible shaking is prohibitively expensive, while ignoring earthquake effects leads to disaster. The accepted philosophy therefore lies between the two extremes:

In other words, damage is unavoidable and is deliberately permitted; the engineer's task is to control where the damage occurs and keep it to an acceptable level at a reasonable cost — much like an electrical fuse, some pre-determined parts are allowed to yield in a ductile way so that the rest survives. This is the basis of capacity design.

1.5.5  The Four Virtues of an Earthquake-Resistant Building

Principles of ductility: avoid shear failure, avoid compression failure, ensure continuity, and confine the critical regions where plastic hinges may form. Configuration-related parameters to check are: load path, geometry, redundancy, weak storey, soft storey, vertical discontinuities, mass irregularity, torsion and short columns.

End of Chapter 1 – Earthquakes and Seismic Ground Motion