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Seismic Loads
Scrivener Publishing
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Publishers at Scrivener
Martin Scrivener([email protected])
Phillip Carmical ([email protected])
Seismic Loads
Victor M. Lyatkher
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Library of Congr ess Cataloging-in-Publication Data:
ISBN 978-1-118-94624-4
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
v
Contents
Preface vii
1 Statement of the Problem 11.1 General Scheme of Estimation of Seismic Stability 31.2 Seismic Hazard 111.3 Variation of Seismic Hazard 151.4 Seismic Loads 20
2 Th e Defi nition of Seismic Actions 292.1 Th e Probability of Loads During the Earthquake of
a Given Intensity 322.2 Recognition of Earthquake Foci 532.3 Th e Calculation of Seism Caused by Movement in
the Earthquake Focus 612.4 Physics of Focus and Control of Seismicity 822.5 Seismic Forces for a Fixed Position and Energy of
the Earthquake Source 99
3 Th e Infl uence of Topography and Soil Conditions. Secondary Processes 1133.1 Infl uence of the Canyons 1133.2 Dynamics of Water-Saturated Soil Equivalent
Single-Phase Environment 1173.3 Dynamics of Water-Saturated Soil as Multiphase
Medium 1213.4 Th e Real Estimates of the Property of Soils 145
3.4.1 Mathematical Formulation of the Problem 1473.4.2 Examples of Calculations 152
3.5 Landslides and Mudfl ows 1583.6 Waves on the Water 162
vi Contents
4 Example of Determination of Seismic Loads on the Object in an Area of High Seismicity 1674.1 Assessment of Seismotectonics and Choice of
Calculation of Seismicity 1674.2 Th e Parameters of Impacts 1714.3 Selection of Unique 1794.4 Numerical Models of the Focus 1834.5 Th e Infl uence of the Shape of the Canyon 189
5 Examples of Determination of Seismic Eff ects on Objects in Areas of Low Seismicity 1955.1 Preliminary Analysis 1955.2 Assessment of Seismic Risk on Seismological Data 2015.3 Tectonic Structure of the Area 2055.4 Recognition of Seismically Active Nodes’
Morphostructure 2125.5 Th e Types of Computational Seismic Eff ects 2255.6 Analog Modeling of Seismic Eff ects 2335.7 Mathematical Modeling of Seismic Eff ects 237
6 Stability of Structures During Earthquakes 2476.1 Stability of Concrete Dams 2486.2 Vibration and Strength Reserves of the High Dams 278
6.2.1 Stability and Final Displacements of the Dam 2826.2.2 Stress and Strain of the Dam 2876.2.3 Character and Form of Dam Failure 292
6.3 Th e Reliability of Groundwater Dams 2966.4 Th e Stability of Underground Structures 3336.5 Seismic Eff ects Caused by Missing Floods Th rough
the Waterworks 3406.5.1 Th e Vibration of the Dam 3456.5.2 Soil Vibration Outside of the Dam 3526.5.3 Vibration Houses 3566.5.4 Results and Recomendation 360
Conclusion 362
References 365Index 375
vii
Preface
Tectonic mobility of the earth’s crust makes all construction and, in General, all life on Earth associated with some risk of seismic impacts. In some areas (seismic) this risk is greater, in others (aseismic) - less. Existing maps of seismic zoning and building codes of the diff erent countries, to some extent, evaluate and regulate this risk is usually in an implicit form. Seismic risk for a single object or group of objects is determined primarily by seismic impact.
A comprehensive description of the seismic action may be given only on a probabilistic basis and in the General case is very bulky and quite uncer-tain. However, for a variety of structures or systems that meet fairly simple models of behavior during earthquakes, a General description of the seis-mic action is not required. For prediction of the status of such facilities or systems may be suffi cient to defi ne one or more common parameters of seismic impact. Th us, it makes sense to search for OPTIMAL parameters of infl uence, in which OPTIMALITY is understood as the greatest ease when suffi cient information.
Th is book contains a description of several models of job seismic eff ects and examples of implementation of these models at specifi c sites.
Th e main results obtained by the author and his colleagues during the work in the Research Sector (now JSC NIIAS) of Institute Hydroproject (Moscow) at 1968-2010 years. Th e names of the main participants of the works listed in the references joint publications. All these people the author is eternally grateful.
Work on the dynamics of water-saturated soil at 1974 received Award of the Indian Society of Earthquake Technology, Roorkee, India; research on the seismic stability of large dams in 1984 awarded the prize of the Council of Ministers of the USSR.
1Statement of the Problem
The description of loads on mass civil or industrial buildings can belimited to the consideration of the impacts and consequences on theaverage over the ensemble of objects and similar events on-site. Theresulting gradation effects on INTENSITY (seismic scale scores and seis-mic intensity) includes not only the mechanical parameters of themotion of the ground during earthquakes, as reflected in the testimonyof certified devices, but also the condition of the facilities after theearthquake, changing landscapes, people's reactions, and animals.Gradation of earthquakes may be different, seemingly unrelated to
the earthquake, and characterize mechanical parameters according to amodel of the phenomenon. It is clear that depending on the adoptedmodel will change the form and content classification information. Forexample, in the simplest focal model input parameters are the ENERGY(magnitude M and class K are proportional to the logarithm of theenergy of the earthquake source), geographic coordinates, and depth offocus. These parameters can be interpreted in terms of mechanics andserve as a basis for a mathematical model of seismic movements. The
1
representation of the environment, two or three phase system, is verysignificant.Any volume statistical information about seismic impacts that meet a
certain score or magnitude (plus length and depth) can be significantlydifferent for structures of different levels of responsibility. For mass civiland industrial buildings, construction regulations in many countriesallow job seismic effects that match a specific seismicity (one factor seis-micity) with the sense of mean-square acceleration, oscillations of theearth's surface (in fractions of the acceleration of gravity), and theensemble averaged data related to earthquakes fixed macro seismicintensity.Similarly, sets and spectral properties of earthquakes are averaged for
all of the observed effects. This approach, suggesting some variationdegree (measure) fracture within one macro seismic area, bulk plants,apparently, can be considered acceptable.The situation is different when considering seismic effects on struc-
tures, the destruction of which should be considered a catastrophe on anational or even international scale. Here, risk assessment must be spe-cific and accurate. These objects include, nuclear power plants and largehydraulic and hydropower plants with large reservoirs. The design ofsuch facilities in areas of seismic activity is a challenging task.This task is complicated when the question of the earthquake pertains
to existing structures. On the one hand, in this case, it becomes possible toobtain reliable data on the dynamic properties of the object. However, seis-mic evaluation and engineering conclusions, in this case, should be partic-ularly reasonable, as changes in the structures are very complex, veryexpensive, or even impossible. Meanwhile, the problem in recent years hasbecome relevant due to changes in the map of seismic zoning of Russia.For example, according to the normative documents in force for the periodof design and construction of the Volga (Volgograd) HPP district, place-ment was considered virtually aseismic (five points or less). In accordancewith the new map of general seismic zoning of the territory of Russia GSZ-97, included in new edition Russian standard (SNiP 11-7-81* M, 2002), inthe region of the Volga, the hydroelectric power station assumes the possi-bility of occurrence of earthquakes with the intensity of shock in sevenpoints on the MSK-64 scale with the repetition of such events one time infive thousand years. The increase in the background level of seismicity, upto seven points, requires estimates of the seismic safety of the main struc-tures of hydroelectric power stations to take into account the existing regu-latory documents. During engineering surveys for waterworks, similar
2 SEISMIC LOADS
works on the main site structures were carried out and organized the miss-ing studies that were conducted in two areas:
� recording and analysis of vibrations of soils andstructures at the microseism and/or seismic events(earthquakes, explosions, etc) to determine instrumentalmethods and system response at the base of the dam onweak seismic effects (micro seismiczoning),
� recording and analysis of vibrations of soils andstructures at the maximum vibration modes caused bythe fluctuations of water fight spillway of the dam duringthe flood passage.
Research, in the first direction, relied on recording extremely weak,quasi-stationary signals. On the contrary, the second research directionhas studied the strongest signals caused by vibration of the water fightunder the action of a stream of water. The conducted work comple-ments each other. The same situation occurs on many other importantand dangerous objects, which sometimes were designed and built with-out due consideration of seismic effects. Their reliability must be care-fully checked.Modern concepts of seismology and engineering are detailed and
reflected in a comprehensive “International Handbook of Earthquakeand Engineering Seismology” edited by renowned experts W.Lee, H.Kanamori, P. Jennings, and C.Kisslinger. My book complements thispublication and is an important choice discussing seismic loads onstructures with different measure of responsibility in areas with differentfrequency of occurrence of earthquakes, as well as specific problems ofthe dynamics of water-saturated soil and seismic stability of hydraulicstructures.
1.1 General Scheme of Estimation of SeismicStability
In the description of seismic effects on mass civil or industrial buildings,seeking to maximize the simplicity of the parameters characterizing theimpact response and the condition of the facilities on average, the stateof buildings after the earthquake, the behavior and emotions of people,and the response of the animals were important characteristics in the
STATEMENT OF THE PROBLEM 3
drafting of the first version of the scale of seismic intensity proposed byMercalli and adapted Richter (C. F. Richter, 1956 [37]) – Table 1.1.Later, on that basis, a more full scale was created, including quantita-
tive characteristics of seismic motions [4, 16, 116, 139].In the current construction standards of many countries, the seismic
action is defined by the ratio of seismicity, multiplied by the weight ofthe structural element to obtain the estimated inertial forces, summedwith other active forces. The value of this ratio depends on the seismic-ity of the area, properties of soil foundation construction, constructionmaterial, and the frequency of natural oscillations. All these features aretaken into account in the form correction factors that are multiplied bythe source seismicity coefficient corresponding to the calculated seismic-ity of the site location of the facility. As shown by statistical analysis ofinstrumental data, this factor, for example, in modern the norms ofRussia, has the sense of the maximum acceleration values of the Earth'ssurface (in fractions of the acceleration of gravity) averaged over ensem-bles of accelerogram earthquakes with fixed intensity seven, eight, ornine points on the international scale (MSK) (respectively one hundred,two hundred and four hundred cm/s2). When the intensities of earth-quakes are smaller than seven points, the design cannot need bechecked and, if the intensity is greater than nine points, building is notrecommended.In some countries (and in the old norms of the USSR), the coefficient
of seismicity sense of the RMS accelerations of the Earth's surface aver-aged over the ensemble earthquakes, the consequences of whichbelonged to the same point intensity.Dynamic properties of the structure and range of influence are
accounted for by the coefficient, depending on the frequency and damp-ing of oscillations of the considered element. The magnitude of thedynamic factor reaches 2.2÷2.5 for periods of natural oscillations from0.4 to 1 sec, and is less than 1 during periods of natural oscillations ofgreater than 1.5÷2.5 sec. Detailed guidance, available in the modernnorms, essentially reflects the results of statistical processing of the so-called action spectra of the earthquakes discussed in paragraph 2.2books.For critical structures, for example, retaining structure class one
standards, Russia is allowed to perform additional calculations on theaction properly selected accelerogram (seismograms, velocigrams). Inthis approach, the actual earthquake resistance of structures is essen-tially dependent on the local characteristics of soil foundationstructures.
4 SEISMIC LOADS
Table 1.1 The Mercalli Earthquake Intensity Scale (Adapted from C. F.Richter, 1956)
I. Not felt. Some objects may sway.
II. Felt by some people at rest and on upper floors.
III. Felt by most people indoors but may not be recognized. Hangingobjects swing.
IV. Felt by everyone indoors but still may not be recognized. Windows,doors rattle; wood structures creak. Standing autos rock. Dishesrattle.
V. Felt and recognized by everyone indoors, most outdoors. Sleeperswake. Doors swing, windows rattle. Pendulum clocks affected.Liquids may spill. Unstable objects upset.
VI. Felt by everyone; many frightened, walk unsteadily. Weak plasterand masonry (like adobe) crack. Windows break. Crockery broken.Furniture moved. Trees shaken visibly, rustle.
VII. Difficult to stand. Noticed by auto drivers. Weak chimneys break atroofline. Architectural ornaments fall. Unreinforced masonrydamaged. Concrete ditches damaged. Waves on ponds, watermuddied. Small slides on sand banks. Furniture broken. Hangingobjects quiver.
VIII. People thrown down, frightened. Masonry damaged or collapsedunless of resistant design. Elevated structures, tanks, twist or fall.Unbolted frame houses move on foundations. Springs and wellschange. Wet ground cracked. Auto steering affected. Tree branchesbroken.
IX. Panic. Reinforced masonry destroyed or seriously damaged.Foundations damaged. Unbolted frame houses shifted offfoundations, frames damaged. Reservoirs seriously damaged.Underground pipes broken. Cracks in ground. Ejection of sand orwater from soft ground.
X. Panic. Most structures and foundations ruined. Dams seriouslydamaged. Railroads slightly bent. Large landslides. Water thrown onbanks of rivers. Sand and mud shifted horizontally.
XI. Panic. General destruction of buildings. Pipelines unusable. Railroadsgreatly bent.
XII. Damage nearly total. Rock masses displaced. Lines of sight distorted.Objects thrown in air.
STATEMENT OF THE PROBLEM 5
The actual life of structures, their ability to plastically deform, andthe validity of the partial destruction during strong earthquakes are alltaken into account by the system coefficients, generalizing researchexperience, the design construction, and partially exploitation massstructures. This approach, suggesting some variation degree (measure)fracture within one macro seismic area for conventional mass structures,seems logical. The situation is different when considering seismic effectson objects, the destruction of which causes economic and social conse-quences, which is not commensurate with the price of the objects in thecondition of normal. The probability of such events should be evaluatedwith high accuracy and, of course, must be controlled low. The choiceof impact for such a facility should be carried out in several stages, cor-responding generally to the gradual increase of information about thelocation of the object.The first phase reference is notions of local geological conditions.
This is enough information to build estimates based on statistics ofinstrumental data, classified according to macro seismic intensity (mod-ern MSK scale).The next step clarifies the possible shape and position of earthquakes,
their mechanism, the geological structure of the district structures, androck properties on the propagation of seismic waves from the earth-quake source. On this basis, a possible new round of forecast impactsusing more fractional statistics and poorer ensembles instrumental data,classified according to the magnitude or seismic moment, hypocentraldistance, soils, and the mechanism of the focus. Here are mechanicalmodels of earthquake focus and the environment, transmitting impact.Based on this, already quite extensive information is possibly consideredin the regulatory management seismic activity of the area.At all stages in-depth study of local peculiarities of soil oundation
construction, water, and gas regime is carried out to largely define theseismic action.The principal feature of the calculations for existing facilities is the
possibility of direct use of data field observations on the most dangeroussections (elements) of structures. These results determine their naturalfrequencies based on measurements of the spectra of vibrations andcomparative evaluation intensity vibrations of different parts of thestructures under similar impact. This allows you to specify the estimatedseismicity for different parts of the object having a large length. As anexample, Figures 1.1 and 1.2 show the increment of seismic intensity
6 SEISMIC LOADS
42
so
il d
am
41
so
il d
am
Sp
illw
ay d
am
Po
we
r h
ou
se
40
so
il d
am
Figure 1.1 Diagram of the increment of seismic intensity on the X-component of seis-mic vibrations in the frequency range 1-2 Hz (top) and 2-4 Hz (bottom). The triangles(red) are seismic stations (observation points), signature (blue) bottom stations are thenumber of observation points, signature (red) top stations are the increment intensityaccording to the microseisms.
40 soil dam
Distance, 100 m
Ch
an
ge
se
ism
icit
y
ΔI
Power houseSpillway dam
41 soil dam
fault42 soil dam
Figure 1.2 Change the increment of seismic intensity for the frequency range 1-2 Hzin the X-, Y- and Z-components along the profile. Dark gray - X-component, lightgray- Y-component, and black - Z-component. The arrow indicates the location of theVolgograd reset.
STATEMENT OF THE PROBLEM 7
for structures of pressure front of the Volgograd hydroelectric powerstation.On these figures, it is seen that the greatest attention should be paid
to:For concrete dams – middle sections of the dam,For the building of hydroelectric power station - contiguity to the
dirt dam 40.For an earth dam 40 – section 300 m from the powerhouse,For an earth dam 41 – section 500 m from the spillway of the dam,For an earth dam 42 – section 500 m from the dam 41.These surveys, conducted by a standard method and standard equip-
ment, are a necessary element in assessing the seismic stability of thecurrent responsible entity. Specified in this example, the cross-sections’different geological characteristics of the base (Figure1.3) are reflected inthe spectral properties of the relevant sections of concrete structuresand sections of underground dams.Selected sites have data about the spectral densities of the vibrations
caused by the flood passage. The normalized spectral density, s(ω) (orsimply spectra, sec), associated with the normalized autocorrelationfunction, r(�), is the Fourier transform -
sðωÞ ¼ 1=pð
rð�Þ Cos ω� d�; ð1:1Þ
Right bank40302010
0102030405060708090
100110120130140150160
Soil
ΠC60 ΠC55 ΠC50 ΠC45 ΠC40 ΠC35 ΠC30 ΠC25 ΠC20 ΠC15 ΠC10 ΠC5 ΠC0
Power
house
Spillway
dam
Soil
m
80
07
00
60
05
00
40
03
00
20
01
00
0
Soil
Figure 1.3 The model for the structure of the substrate structures of the Volgogradhydroelectric power station. Field investigations conducted under the guidance of A.I.Savich and G.L. Mazhbits.
8 SEISMIC LOADS
rð�Þ ¼ 2ð
sðωÞ Cos ω� dω; ð1:2Þ
rx(�) = <[(x(t) – <x>)(x(t + �) – <x>)]>/(x0)2, here < > – averaged oper-ation, x0 – RMS of x.
0 1 2 3Frequency, Hz
S x, S
S υ, S
4 5 6
0.100
1
2
1
2
0.080
0.060
0.040
0.020
00.100
0.080
0.060
0.040
0.020
0
Figure 1.4 The normalized spectra(sec) of the horizontal vibrations (displacement andvelocity) of the center section base 7 of the Volgograd dam from the re-recordingresults (lines 1and 2) of the same mode, skipping flood of 2003. The flow through thedam 12000 m3/s. The spectrum maximum at a frequency of 1.45 Hz. You can see theinfluence of the low-frequency part of the spectrum of hydrodynamic effects.
0 1 2 3Frequency, Hz
S z, S
4 5
1
20.080
0.120
0.160
0.200
0.040
Figure 1.5 Spectra of vertical displacements of the center (line 1) and saddle points(line 2) of section base 7 when skipping consumption 12000 m3/s through the dam.The maximum of the spectra at a frequency of 1.44 Hz.
STATEMENT OF THE PROBLEM 9
The integrals are calculated in the limits from zero to infinity, thedimension of the spectral density of sec. Formula 1.2 is used for controlcalculations according to Formula 1.1.Figure 1.4 and 1.5 are examples showing the spectra normalized by
the standard vertical and horizontal vibrations of section seven of thespillway dam Volgograd hydroelectric station at the normal level of theupstream (+30.0 m) and a relatively high level downstream (–3.40 m,the flow through the hydro system 25950 m3/s, depth over the waterfight 12.6 m). These spectra make it possible to determine the frequencyof natural oscillations of the system in horizontal direction 1.44and 2.16 1.88 Hz and in the vertical direction is 0.62 (only in the oftunnels), 1.38 and 1.88 Hz.Analysis of cross-correlations of movements of different points of the
cross section of the section and of the trajectories of individual pointsindicates the presence of all three forms of movement of the dam as arigid body on an elastic foundation: vertical (mostly), horizontal, androtational. The lowest frequency reflects the hydrodynamic loads associ-ated with the hydraulic jump over a water fight. Frequency 1.44 (period0.694 sec) for horizontal and 1.38 Hz (period annual production of0.725 sec) for vertical vibrations are taken into account in determiningthe coefficients of dynamic b.Another approach is to directly use the results of in-situ measure-
ments of the spectra of fluctuations in the water under the excitation ofvibrations of a dam’s seismic vibrations coming from the water fight,and, in the middle of summer, for a total of micro seismic background.The next stage is the calculation of the stability of the structures withthe application of inertial forces specified in the form of additional staticregulatory burden for each of the mode shapes. Groundwater dams areparticularly important to further study the stress strain state with theproperties of the soil; its compression or decompression. These proc-esses, in the framework of the stability calculations, are not considered,although, in many cases, they determine the state of soil dams duringearthquakes. The issue of seismic soil compaction of the real, existingstructures can be solved using special techniques, the theoretical founda-tions of which are given in Chapter 3.Seismic stress components are calculated by the application based
structure forces, which, in the absence of structures, would cause thosemovements that are selected or assigned as parameters to the seismicaction. This scheme is the essence of the theorem of the author aboutthe definition of seismic effects [98, page 171]. According to this theo-rem, seismic excitation can be represented by a system of forces applied
10 SEISMIC LOADS
to the base of the dam, which, in the absence of the dam, causes seismicsurface deformation of the footprint of the dam and is equal to thespecified seismic movements. In the application of these forces, themotion of the base of the dam may differ significantly from the move-ment trace of the dam in its absence; that is. will be distortion of theinput seismic motion under the influence of structures. The communi-cation source and the resulting movements in weak earthquakes lineartask can be expressed via the impulse transient function and the rela-tionship of the spectra of these movements through the complex trans-fer function of the system. The theorem remains true also in case ofstrong earthquakes, when under the action of applied seismic forces arelarge deformations, for example, partial or complete destruction of thestructure.A consequence of the theorem is the nonuniqueness possible job seis-
mic effects. The proof uses only the uniqueness property operators, link-ing movement in the field, limited to some hypothetical surface, S, withthe effects set on this surface. On this surface, S is not required to setthe volume force; here can be supplied kinematic conditions providingspecified motion in the selected area in the initial conditions. On thesurface, can be combined kinematic and dynamic effects so that theyare most easily where the parameters associated with the source field ofthe motion environment. In particular, seismic impact can be definedon the surface, S, of the jump of displacements �u and leap stress ��,equal to just offsets u0 and stresses �0 on this surface in the originalmotion. More detailed consideration of the assignment of the seismicaction and the proof of formulated theorem is given in Chapter 1.4.
1.2 Seismic Hazard
Seismic hazard assessment and subsequent determination of seismiceffects on important facilities requires the following source data:
1. The intensity of seismic effects for the location of facilities(points MSK or MM), indicating the probability(frequency) of occurrence of these effects in format mapsof general seismic zoning (medium soil), detailed seismiczoning, and micro zoning, taking into account thereal properties of soil foundation. Collectively, thisinformation is reflected on the maps of seismicity inpoints on the seismic scale (corresponding to different
STATEMENT OF THE PROBLEM 11
recurrence periods) or on maps’ shaking territories (theterm of Y. V. Riznichenko [130]).
2. Structures of the first class of solidity will need thefollowing materials research:
� characteristic structural-tectonic setting and seismicregime of the area within a radius of fifty to onehundred km;
� the bounds of the main seismogenic zones anddescription of available seismic characteristics(maximum magnitude, the depth of the focuses, theirmechanism, spatial location, frequency of earthquakesin different areas, a complete catalog of seismic events,purified from pseudo seismics data type explosions,collapses, etc.) and engineering-geological conditions ofthe site; and
� the bounds of the possible zones of occurrence ofresidual deformations in case of strong earthquakes,the contours of the mountain masses rock that canlose stability and fall into the reservoir, and data aboutchanges in the seismic regime under the influence ofreservoir;
3. Data geodynamic observations, the parameters of theseismic waves from different angles appropriate tothe facilities, and information about the speeds ofdisplacement of the Earth's surface;
4. Paleoseismological data obtained aerospace survey andmore young, opening breaks;
5. Data magnetometric and gravimetric filming;6. Records of movements of the Earth's surface andstructures during earthquakes;
7. Topographic data;8. Map of lineaments and faults; and9. Results recognition of seismogenic nodes of a differentclass.
This data, in many cases, is lacking in the necessary volume. Quali-fied collection and screening of the source material is a serious problemfor specialists of different profile. For example, the analysis of the seis-mic events in the Volzhskiy (Volgograd) region hydro system showed
12 SEISMIC LOADS
that during the whole period of observation there was no earthquake,which could cause, on site of the main structures, a shaking intensity offive points or higher. The number of earthquakes that occurred on theterritory, within a radius of approximately four hundred kilometersfrom the site of the main structures, present in different directories aresmall. It was found that a considerable part of them belong to the exog-enous category associated with landslide processes are widely developedon the banks of the Volga. In addition, the published directories andexplosions should be excluded when compiling a specified source direc-tory. Creating a correct catalog of earthquakes in the area of the objectunder study is the first and most important task, which can be vulner-able to criticism.For areas with rare frequency of occurrences of earthquakes, the
important results are formalized with methodology morpho structuralzoning, which allows the determination of the hierarchical block struc-ture of the region and the establishment of the location of the morphostructural units: the earth's crust, characterized by increased tectonicactivity. There is a training program for the recognition algorithm forearthquake-prone sites on the basis of seismological information for aspecific region.Thus, the recognition sites of the Volga region and the surrounding
areas, learning algorithm “Kora-3”, were carried out on the basis of thedata about known earthquakes of the Russian platform, the magnitudewhich does not exceed five. Therefore, the potential of the detected seis-mic nodes should be assessed within the observed magnitudes.Most earthquake-prone sites of the Volga region and adjacent areas,
established as a result of this formal zoning (OCR), are located on thelineaments of the first rank, who share the largest blocks of the earth'scrust (macro blocks). On the lineament of the first rank, traced alongthe valley R. Volga, all nodes on the segment of the Volga from NizhnyNovgorod to the Samara reservoir are recognized as earthquake-prone.On the site of the Volga from Samara to the area South of Kamishin,seismic nodes are not installed. Nodes located on the stretch of theVolga River, upstream of Volgograd and including the district of Volgo-grad, were recognized as earthquake-prone.The criteria of high seismicity for magnitude 6.5, installed for recog-
nition for the nodes of the Pamir and Tien Shan, showed that none ofthe nodes of the Volga do not match. Therefore, it was possible to con-clude that the potential earthquake-prone nodes identified in the Volgaregion are not greater than magnitude five. The depth of earthquakefoci on the Russian plain does not exceed twenty kilometers, while the
STATEMENT OF THE PROBLEM 13
vast majority of earthquakes occur at depths of ten to fifteen kilometers.Hence, it was concluded that the probable depth of the hypocenters ofpossible earthquakes in the Volgograd fault, when the magnitude is fiveis ten (plus or minus five) kilometers, and the magnitude is 5.5 is atleast fifteen kilometers. This gave the basis for clarifying the maximumpossible seismic risk of the waterworks at the level of seven points onthe MSK scale, made it possible to construct a mechanical model of theseismic action, and give a specific forecast of the possible seismicmovements.Seismic hazard may be remote from focal zones. The Volgograd
dams were considered potential seismogenic structures that could serveas sources of influence from the “far zone”. The nearest of them isCherkessia (part of the zone of the North Caucasus fault of the Alpine-Mediterranean belt). If an earthquake with a magnitude of seven to 7.5is in this zone, the intensity of shaking at the site of the main water-works facilities can reach three to four points on soils category II seis-mic properties, taking into account cross major tectonic structures.This causes a stronger attenuation of seismic waves whose intensityshould not exceed two to three points GMT. The Krasnovodsk area,with the highest seismic potential, is held at twelve hundred kilometersto the southeast of the site of the waterworks. If an earthquake withmagnitude 8.2 in this zone, the intensity of shaking at the site of themain waterworks facilities can reach five points on soils II categoryseismic properties, taking into account cross major tectonic structures,causing a stronger attenuation of seismic waves from three to fourpoints MSK.Seismic hazard, in the final result set or macroseismic intensity, indi-
cates possible frequency or magnitude of possible focus (foci) earth-quakes with an indication of position and repeatability. Determinationof seismic effects is the main, final stage of work on the assessment ofseismic hazard. In general, the estimated seismic impact refers to theparameters of the seismic motion of the ground. It is possible to neph-rogram the basis of the object with a given probability that has notexceeded at a fixed time (e.g. per year), a set (ensemble) of seismicrecords accelerogram, and action spectra corresponding to theseparameters.Work on seismic hazard assessment ends with the definition:A - settlement intensity (intensities) effects, and/orB - parameters of ground motion modelling settlement records,seismic vibrations, action spectra, Fourier spectra, and the duration
of the oscillations.
14 SEISMIC LOADS
1.3 Variation of Seismic Hazard
Seismic ground mode, at the interval of one hundred years, is not sta-tionary (Figure 1.6), but may be associated with the regime of solaractivity, characterized by the smoothed length of the solar cycle [64].Figure 1.7 shows the length of the solar cycle for the previous one
hundred years, defined by highs and lows in the number of sunspots.The schema definitions of these periods is shown in Figure 1.8.The comparison of Figure 1.6 and 1.7 shows that the greater the
length of the solar cycle, the more the average interval between strongearthquakes and a less chance of earthquakes with fixed intensity in thecurrent year or the next period, compared with an estimated service lifeof structures. Found links provide a basis for forecasting changes in theseismic regime of the Earth according to the Sun. This was proposed bya special scheme for smoothing data on solar cycles. It was proposed touse one-sided, unbalanced filters, smoothing only the information thatis known up to the current time. The simplest filter of this type is filter1-2, which includes the processing of only the last two solar cycles.Figure 1.9 shows the length of the solar cycles, averaged by filter 1-2,separately for the lengths of the cycles in the highs and lows of wolfnumbers with subsequent averaging and attribution to the end of thelast cycle (median date between the last maximum and minimum wolfnumbers):
<Li>k ¼ ½Li�1 þ 2Li�k=3 k ¼ M; m<Li> ¼ ½<Li>M þ <Li>m� =2<ti> ¼ ½tiM þ tim� =2
ð1:3Þ
Here, averaged, the smoothed length of the solar cycle, <Li>, refers tothe average time, <ti>, of the end of solar cycle maxima and minimaWolf numbers. The same point applies to the averaged eleven yearbasis, the interval between earthquakes with a magnitude of not lessthan seven. The regression is the straight line connecting a certain speci-fied way the average length of the solar cycle, Ts = <Li >, and the aver-age interval, Te, between strong earthquakes, has formed (Figure 1.10):
Te ¼ 0:79 þ 0:21ðTs – 10:7Þ ð1:4ÞHere, for the interval between earthquakes, measured in months, and
the length of the solar cycle, in years, the standard deviation is:
STATEMENT OF THE PROBLEM 15
Te0 ¼ 0:21 month ¼ 0:0176 year
Ts0 ¼ 0:741 year:
40
30
20
10
01900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Calendar time, year
Th
e n
um
be
r o
f e
art
hq
ua
ke
s p
er
ye
ar
Figure 1.6 The number of earthquakes per year with magnitude more or equal to sevenin the last one hundred years. Data by year - end current year.
13
12
11
10
91900 1950
10.77 y
2000Time, years
Le
ng
th o
f th
e c
ycl
e, y
ea
rs
Figure 1.7 Unfiltered sunspot cycle length. 1880–1998. Triangles derived from epochsof sunspot maximal. Circles from epochs of minimal.
16 SEISMIC LOADS
The correlation coefficient, r, equals 0.734, when homogeneous units(years) equation (1.4a) has the form:
Te ¼ 0:0658 þ 0:0175ðTs – 10:7Þ: ð1:4aÞThe assumption that there is a five year lag in the Earth's response
does not decrease the scatter in the results and slightly reduces the cor-relation to 0.691. As is shown in Figure 1.7, the variations in the solaractivity exhibit a quasi-periodic component with a period of about sixtyto one hundred years. The inferred correlation between the solar activityand recurrence of strong earthquakes indicates that even local character-istics of seismicity, determined from statistical data over a limited time
250
200
150
100
50
0
250
200
150
100
50
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
1800 1810 1820 1830 1840 1850 1860
Lmi tmi
LMitMi
1870 1880 1890 1900
Su
nsp
ot
nu
mb
er
Su
nsp
ot
nu
mb
er
Figure 1.8 Annual Sunspot Numbers from 1800 to 1998 years. Individual sunspotlength maximum (LMi) and minimum (Lmi) epochs – (tMi) and (tmi) respectively.
STATEMENT OF THE PROBLEM 17
interval, can vary in time with approximately the same periodicity asthe smoothed lengths of solar cycles. The study of Solar-Terrestrial rela-tions in a new production turns out to be useful for prediction of seis-mic ground mode. Variations of solar activity are observed with aquasi-periodic component over a period of about sixty to one hundredyears. A correlation was found between solar activity and the frequencyof strong earthquakes that allows the assertation that the local charac-teristics of seismicity are defined as inevitable for a limited time. Statisti-cal material may change over time with approximately the samefrequency as the smoothed length of solar cycles [64]. Using this output,you can try to give a heuristic prediction of solar and seismic activity ofthe Earth for the next one hundred years (Figure 1.11).This forecast should, in particular, increase the total seismic activity
and risk in the period 2020 plus or minus 10 g and decreased risk after2040 g. The results were obtained by the author in 1999. Data aboutsolar cycles accumulates so slowly that, over the past 15 years, therehave been only two points that fell within the confidence intervals inFigure 1.10. Information about earthquakes became significantly moreeach year and took place from eleven to twenty-four strong earthquakes.The average interval between strong earthquakes in this period wasabout 0.8 of the month; therefore, the real danger was slightly less thanexpected in the forecast.The patterns found for the Earth as a whole may be, with some the
approach, extended to the local characteristics of the seismic regime. Infact, if we denote by the symbol pxydΩ, the likelihood of the presence ofat least one earthquake per year, with magnitude not less than seven,
1.2
0.6
01900 1950 2000
1
2
13
12
11
10
9
Calendar time, year
Solar cycle, yearsEarthquake recurrence
interval, months
Figure 1.9 The smoothed filter 1-2, average length of solar activity cycles (1) and aver-aged eleven year-old base intervals (2) between earthquakes with magnitude more orequal to seven, in the 20th century.
18 SEISMIC LOADS
on-site dΩ with coordinates x and y, then the probability of p in suchsituations on Earth will be determined by the integral over the entiresurface of the earth:
p ¼ 1=Te ¼ð
pxydΩ ð1:5Þ
In the left and right hand side of Equation 1.5, astronomical timeenters only as a parameter; therefore, it is natural to imagine its impact
1.2
0.6
09 10 11 12 13
Solar cycle, years
Earthquake recurrence interval, month
Figure 1.10 The average recurrence interval, Te, of M > 7 earthquakes versus the aver-age solar cycle length smoothed with the 1-2 filter. The solid line is formula (1.4). TheRMS deviation is shown by broken lines.
1.2
0.6
01900 1950 2000 2025 2050 2075
1
2
13
12
11
10
9
Calendar time, year
Solar cycle, years
Interval between earthquakes,
months
Figure 1.11 Gray dots and black dots after 2000 – heuristic prediction. 1 is a smoothedlength of solar cycles, 2 – the average interval between the strongest earthquakes.
STATEMENT OF THE PROBLEM 19
to some multiplicative factor, k� , is the same for the Earth as a wholeand for its individual sections:
k� ¼ ð1=TeÞ=<1=Te> ð1:6ÞHere, angle brackets average on the time interval normal for seismo-
logical analysis (103–104 years). In fact, the parameter, k� , given as apositive, definite function of the smoothed length of the solar cycle, Ts,is calculated according to Equation 1.7:
k� ¼ 3:762= ðTs – 6:94Þ: ð1:7ÞFor the previous one hundred years, smoothed length of the solar
cycle has changed from 9.8 to 12.5 years, which corresponds to thechange, k� , from 1.32 to 0.68. Such factors would enter into the calcula-tions of the probability of the magnitude of strong earthquakes or shak-ing options in the respective periods. The last cycle ending in 1997, hada length of 10 years, which means k�equals 1.23.The probability of a strong earthquake in the next one hundred years
would be slightly higher than the average for the century.
1.4 Seismic Loads
Calculations of seismic loads correspond to the ideology and requiredbuilding codes in force in the Russian Federation, as well as the codesof the countries formed after the breakup of the USSR, and the USA,Mexico, Italy, Greece, India, Japan, China, and several other countries.The initial data for calculations can and should be seismological infor-mation and the reliability requirements contained in these codes andshould be transformed into the appropriate parameters used below. Cal-culated seismic loads are assumed to be short acting (averaging fromfive to twenty seconds) when implementing the rare event of a strongearthquake. In this regard, the design scheme should be chosen to themaximum extent possible to consider the provisions of the bearingcapacity of structures and their elements. Seismic impact is considered,in conjunction with other types of random effects, to be taken with theprovision of fifty percent over the estimated lifetime of the structure.Deterministic load is accepted by the scheme in special combinations.The parameters of strength and stability that characterize properties’
materials, structures, grounds, or contact zones should be accepted by
20 SEISMIC LOADS
