Seismic Loads

By Victor M. Lyatkher

Earthquakes are a way of life on Earth, and, whether you live in an area that is often affected by earthquakes or not, every building, every road, every bridge, and, in fact, almost everything constructed by humans in which we walk, sleep, live, sit, or visit, has to be constructed to withstand an earthquake, by following local, regional, or national codes, laws, and regulations. Further to this, the science and engineering behind these constructions go further than what is mandated by government as a part of their practice. All construction, and, in general, all life on Earth, has some risk of seismic impacts.

A comprehensive description of any seismic action may be given only on a probabilistic basis and, in general, is very bulky and quite uncertain. However, for a variety of structures or systems that meet fairly simple models of behavior during earthquakes, a general description of the seismic action is not required, for prediction of the status of such facilities or systems may be sufficient to define one or more common parameters of seismic impact. Thus, it makes sense to search for optimal parameters of influence in which optimality is understood with the greatest ease with sufficient information.

This book contains a description of several models of seismic effects and examples of implementation of these models at specific sites.  Using this information, scientists and engineers can design structures that are stronger, safer, and longer-lasting. It is a must-have for any scientist, engineer, or student working in or researching seismic loads and constructions with a view toward withstanding seismic activity.

• Language: English
• Publisher: Wiley
• Release date: Dec 3, 2015
• ISBN: 9781118946251

Book preview

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 different 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 uncertain. However, for a variety of structures or systems that meet fairly simple models of behavior during earthquakes, a General description of the seismic action is not required. For prediction of the status of such facilities or systems may be sufficient to define one or more common parameters of seismic impact. Thus, it makes sense to search for OPTIMAL parameters of influence, in which OPTIMALITY is understood as the greatest ease when sufficient information.

This book contains a description of several models of job seismic effects and examples of implementation of these models at specific sites.

The 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. The 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.

Chapter 1

Statement of the Problem

The description of loads on mass civil or industrial buildings can be limited to the consideration of the impacts and consequences on the average over the ensemble of objects and similar events on-site. The resulting gradation effects on INTENSITY (seismic scale scores and seismic intensity) includes not only the mechanical parameters of the motion of the ground during earthquakes, as reflected in the testimony of certified devices, but also the condition of the facilities after the earthquake, changing landscapes, people’s reactions, and animals.

Gradation of earthquakes may be different, seemingly unrelated to the earthquake, and characterize mechanical parameters according to a model of the phenomenon. It is clear that depending on the adopted model will change the form and content classification information. For example, in the simplest focal model input parameters are the ENERGY (magnitude M and class K are proportional to the logarithm of the energy of the earthquake source), geographic coordinates, and depth of focus. These parameters can be interpreted in terms of mechanics and serve as a basis for a mathematical model of seismic movements. The representation of the environment, two or three phase system, is very significant.

Any volume statistical information about seismic impacts that meet a certain score or magnitude (plus length and depth) can be significantly different for structures of different levels of responsibility. For mass civil and industrial buildings, construction regulations in many countries allow job seismic effects that match a specific seismicity (one factor seismicity) with the sense of mean-square acceleration, oscillations of the earth’s surface (in fractions of the acceleration of gravity), and the ensemble averaged data related to earthquakes fixed macro seismic intensity.

Similarly, sets and spectral properties of earthquakes are averaged for all of the observed effects. This approach, suggesting some variation degree (measure) fracture within one macro seismic area, bulk plants, apparently, can be considered acceptable.

The situation is different when considering seismic effects on structures, the destruction of which should be considered a catastrophe on a national or even international scale. Here, risk assessment must be specific and accurate. These objects include, nuclear power plants and large hydraulic and hydropower plants with large reservoirs. The design of such 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 to obtain reliable data on the dynamic properties of the object. However, seismic evaluation and engineering conclusions, in this case, should be particularly reasonable, as changes in the structures are very complex, very expensive, or even impossible. Meanwhile, the problem in recent years has become relevant due to changes in the map of seismic zoning of Russia. For example, according to the normative documents in force for the period of design and construction of the Volga (Volgograd) HPP district, placement was considered virtually aseismic (five points or less). In accordance with 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), in the region of the Volga, the hydroelectric power station assumes the possibility of occurrence of earthquakes with the intensity of shock in seven points on the MSK-64 scale with the repetition of such events one time in five thousand years. The increase in the background level of seismicity, up to seven points, requires estimates of the seismic safety of the main structures of hydroelectric power stations to take into account the existing regulatory documents. During engineering surveys for waterworks, similar works on the main site structures were carried out and organized the missing studies that were conducted in two areas:

recording and analysis of vibrations of soils and structures at the microseism and/or seismic events (earthquakes, explosions, etc) to determine instrumental methods and system response at the base of the dam on weak seismic effects (micro seismiczoning),

recording and analysis of vibrations of soils and structures at the maximum vibration modes caused by the fluctuations of water fight spillway of the dam during the flood passage.

Research, in the first direction, relied on recording extremely weak, quasi-stationary signals. On the contrary, the second research direction has studied the strongest signals caused by vibration of the water fight under the action of a stream of water. The conducted work complements each other. The same situation occurs on many other important and dangerous objects, which sometimes were designed and built without due consideration of seismic effects. Their reliability must be carefully checked.

Modern concepts of seismology and engineering are detailed and reflected in a comprehensive International Handbook of Earthquake and Engineering Seismology edited by renowned experts W. Lee, H. Kanamori, P. Jennings, and C. Kisslinger. My book complements this publication and is an important choice discussing seismic loads on structures with different measure of responsibility in areas with different frequency of occurrence of earthquakes, as well as specific problems of the dynamics of water-saturated soil and seismic stability of hydraulic structures.

1.1 General Scheme of Estimation of Seismic Stability

In the description of seismic effects on mass civil or industrial buildings, seeking to maximize the simplicity of the parameters characterizing the impact response and the condition of the facilities on average, the state of buildings after the earthquake, the behavior and emotions of people, and the response of the animals were important characteristics in the drafting of the first version of the scale of seismic intensity proposed by Mercalli and adapted Richter (C. F. Richter, 1956 [37]) – Table 1.1.

Table 1.1 The Mercalli Earthquake Intensity Scale (Adapted from C. F. Richter, 1956)

Later, on that basis, a more full scale was created, including quantitative 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 of the structural element to obtain the estimated inertial forces, summed with other active forces. The value of this ratio depends on the seismicity of the area, properties of soil foundation construction, construction material, and the frequency of natural oscillations. All these features are taken into account in the form correction factors that are multiplied by the source seismicity coefficient corresponding to the calculated seismicity of the site location of the facility. As shown by statistical analysis of instrumental data, this factor, for example, in modern the norms of Russia, has the sense of the maximum acceleration values of the Earth’s surface (in fractions of the acceleration of gravity) averaged over ensembles of accelerogram earthquakes with fixed intensity seven, eight, or nine points on the international scale (MSK) (respectively one hundred, two hundred and four hundred cm/s²). When the intensities of earthquakes are smaller than seven points, the design cannot need be checked and, if the intensity is greater than nine points, building is not recommended.

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 averaged over the ensemble earthquakes, the consequences of which belonged 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 damping of oscillations of the considered element. The magnitude of the dynamic factor reaches 2.2÷2.5 for periods of natural oscillations from 0.4 to 1 sec, and is less than 1 during periods of natural oscillations of greater than 1.5÷2.5 sec. Detailed guidance, available in the modern norms, essentially reflects the results of statistical processing of the so-called action spectra of the earthquakes discussed in paragraph 2.2 books.

For critical structures, for example, retaining structure class one standards, Russia is allowed to perform additional calculations on the action properly selected accelerogram (seismograms, velocigrams). In this approach, the actual earthquake resistance of structures is essentially dependent on the local characteristics of soil foundation structures.

The actual life of structures, their ability to plastically deform, and the validity of the partial destruction during strong earthquakes are all taken into account by the system coefficients, generalizing research experience, the design construction, and partially exploitation mass structures. 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 effects on objects, the destruction of which causes economic and social consequences, which is not commensurate with the price of the objects in the condition of normal. The probability of such events should be evaluated with high accuracy and, of course, must be controlled low. The choice of impact for such a facility should be carried out in several stages, corresponding generally to the gradual increase of information about the location of the object.

The first phase reference is notions of local geological conditions. This is enough information to build estimates based on statistics of instrumental data, classified according to macro seismic intensity (modern MSK scale).

The next step clarifies the possible shape and position of earthquakes, their mechanism, the geological structure of the district structures, and rock properties on the propagation of seismic waves from the earthquake source. On this basis, a possible new round of forecast impacts using more fractional statistics and poorer ensembles instrumental data, classified according to the magnitude or seismic moment, hypocentral distance, soils, and the mechanism of the focus. Here are mechanical models of earthquake focus and the environment, transmitting impact. Based on this, already quite extensive information is possibly considered in 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 the seismic action.

The principal feature of the calculations for existing facilities is the possibility of direct use of data field observations on the most dangerous sections (elements) of structures. These results determine their natural frequencies based on measurements of the spectra of vibrations and comparative evaluation intensity vibrations of different parts of the structures under similar impact. This allows you to specify the estimated seismicity for different parts of the object having a large length. As an example, Figures 1.1 and 1.2 show the increment of seismic intensity for structures of pressure front of the Volgograd hydroelectric power station.

Figure 1.1 Diagram of the increment of seismic intensity on the X-component of seismic 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 the number of observation points, signature (red) top stations are the increment intensity according to the microseisms.

Figure 1.2 Change the increment of seismic intensity for the frequency range 1-2 Hz in the X-, Y- and Z-components along the profile. Dark gray - X-component, light gray- Y-component, and black - Z-component. The arrow indicates the location of the Volgograd reset.

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 equipment, are a necessary element in assessing the seismic stability of the current responsible entity. Specified in this example, the cross-sections’ different geological characteristics of the base (Figure 1.3) are reflected in the spectral properties of the relevant sections of concrete structures and sections of underground dams.

Figure 1.3 The model for the structure of the substrate structures of the Volgograd hydroelectric power station. Field investigations conducted under the guidance of A.I. Savich and G.L. Mazhbits.

Selected sites have data about the spectral densities of the vibrations caused by the flood passage. The normalized spectral density, s(ω) (or simply spectra, sec), associated with the normalized autocorrelation function, r(τ), is the Fourier transform -

(1.1)

equation

(1.2)

equation

rx(τ) = <[(x(t) − <x>)(x(t + τ) − <x>)]>/(x′)², here < > – averaged operation, x′ – RMS of x.

The integrals are calculated in the limits from zero to infinity, the dimension of the spectral density of sec. Formula 1.2 is used for control calculations 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 the spillway dam Volgograd hydroelectric station at the normal level of the upstream (+30.0 m) and a relatively high level downstream (–3.40 m, the flow through the hydro system 25950 m³/s, depth over the water fight 12.6 m). These spectra make it possible to determine the frequency of natural oscillations of the system in horizontal direction 1.44 and 2.16 1.88 Hz and in the vertical direction is 0.62 (only in the of tunnels), 1.38 and 1.88 Hz.

Figure 1.4 The normalized spectra(sec) of the horizontal vibrations (displacement and velocity) of the center section base 7 of the Volgograd dam from the re-recording results (lines 1and 2) of the same mode, skipping flood of 2003. The flow through the dam 12000 m³/s. The spectrum maximum at a frequency of 1.45 Hz. You can see the influence of the low-frequency part of the spectrum of hydrodynamic effects.

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.

Analysis of cross-correlations of movements of different points of the cross section of the section and of the trajectories of individual points indicates the presence of all three forms of movement of the dam as a rigid body on an elastic foundation: vertical (mostly), horizontal, and rotational. The lowest frequency reflects the hydrodynamic loads associated with the hydraulic jump over a water fight. Frequency 1.44 (period 0.694 sec) for horizontal and 1.38 Hz (period annual production of 0.725 sec) for vertical vibrations are taken into account in determining the coefficients of dynamic β.

Another approach is to directly use the results of in-situ measurements of the spectra of fluctuations in the water under the excitation of vibrations 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 with the application of inertial forces specified in the form of additional static regulatory burden for each of the mode shapes. Groundwater dams are particularly important to further study the stress strain state with the properties of the soil; its compression or decompression. These processes, in the framework of the stability calculations, are not considered, although, in many cases, they determine the state of soil dams during earthquakes. The issue of seismic soil compaction of the real, existing structures can be solved using special techniques, the theoretical foundations 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 those movements that are selected or assigned as parameters to the seismic action. This scheme is the essence of the theorem of the author about the definition of seismic effects [98, page 171]. According to this theorem, seismic excitation can be represented by a system of forces applied to the base of the dam, which, in the absence of the dam, causes seismic surface deformation of the footprint of the dam and is equal to the specified seismic movements. In the application of these forces, the motion of the base of the dam may differ significantly from the movement trace of the dam in its absence; that is. will be distortion of the input seismic motion under the influence of structures. The communication source and the resulting movements in weak earthquakes linear task can be expressed via the impulse transient function and the relationship of the spectra of these movements through the complex transfer function of the system. The theorem remains true also in case of strong earthquakes, when under the action of applied seismic forces are large deformations, for example, partial or complete destruction of the structure.

A consequence of the theorem is the nonuniqueness possible job seismic effects. The proof uses only the uniqueness property operators, linking movement in the field, limited to some hypothetical surface, S, with the effects set on this surface. On this surface, S is not required to set the volume force; here can be supplied kinematic conditions providing specified motion in the selected area in the initial conditions. On the surface, can be combined kinematic and dynamic effects so that they are most easily where the parameters associated with the source field of the motion environment. In particular, seismic impact can be defined on the surface, S, of the jump of displacements Δu and leap stress Δσ, equal to just offsets u0 and stresses σ0 on this surface in the original motion. More detailed consideration of the assignment of the seismic action and the proof of formulated theorem is given in Chapter 1.4.

1.2 Seismic Hazard

Seismic hazard assessment and subsequent determination of seismic effects 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 maps of general seismic zoning (medium soil), detailed seismic zoning, and micro zoning, taking into account the real properties of soil foundation. Collectively, this information is reflected on the maps of seismicity in points on the seismic scale (corresponding to different recurrence periods) or on maps’ shaking territories (the term of Y. V. Riznichenko [130]).

2. Structures of the first class of solidity will need the following materials research:

characteristic structural-tectonic setting and seismic regime of the area within a radius of fifty to one hundred km;

the bounds of the main seismogenic zones and description of available seismic characteristics (maximum magnitude, the depth of the focuses, their mechanism, spatial location, frequency of earthquakes in different areas, a complete catalog of seismic events, purified from pseudo seismics data type explosions, collapses, etc.) and engineering-geological conditions of the site; and

the bounds of the possible zones of occurrence of residual deformations in case of strong earthquakes, the contours of the mountain masses rock that can lose stability and fall into the reservoir, and data about changes in the seismic regime under the influence of reservoir;

3. Data geodynamic observations, the parameters of the seismic waves from different angles appropriate to the facilities, and information about the speeds of displacement of the Earth’s surface;

4. Paleoseismological data obtained aerospace survey and more young, opening breaks;

5. Data magnetometric and gravimetric filming;

6. Records of movements of the Earth’s surface and structures during earthquakes;

7. Topographic data;

8. Map of lineaments and faults; and

9. Results recognition of seismogenic nodes of a different class.

This data, in many cases, is lacking in the necessary volume. Qualified collection and screening of the source material is a serious problem for specialists of different profile. For example, the analysis of the seismic events in the Volzhskiy (Volgograd) region hydro system showed that during the whole period of observation there was no earthquake, which could cause, on site of the main structures, a shaking intensity of five points or higher. The number of earthquakes that occurred on the territory, within a radius of approximately four hundred kilometers from the site of the main structures, present in different directories are small. It was found that a considerable part of them belong to the exogenous category associated with landslide processes are widely developed on the banks of the Volga. In addition, the published directories and explosions should be excluded when compiling a specified source directory. Creating a correct catalog of earthquakes in the area of the object under study is the first and most important task, which can be vulnerable to criticism.

For areas with rare frequency of occurrences of earthquakes, the important results are formalized with methodology morpho structural zoning, which allows the determination of the hierarchical block structure of the region and the establishment of the location of the morpho structural units: the earth’s crust, characterized by increased tectonic activity. There is a training program for the recognition algorithm for earthquake-prone sites on the basis of seismological information for a specific region.

Thus, the recognition sites of the Volga region and the surrounding areas, learning algorithm Kora-3, were carried out on the basis of the data about known earthquakes of the Russian platform, the magnitude which does not exceed five. Therefore, the potential of the detected seismic 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 the lineaments of the first rank, who share the largest blocks of the earth’s crust (macro blocks). On the lineament of the first rank, traced along the valley R. Volga, all nodes on the segment of the Volga from Nizhny Novgorod 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 the Volga River, upstream of Volgograd and including the district of Volgograd, were recognized as earthquake-prone.

The criteria of high seismicity for magnitude 6.5, installed for recognition for the nodes of the Pamir and Tien Shan, showed that none of the nodes of the Volga do not match. Therefore, it was possible to conclude that the potential earthquake-prone nodes identified in the Volga region are not greater than magnitude five. The depth of earthquake foci on the Russian plain does not exceed twenty kilometers, while the vast majority of earthquakes occur at depths of ten to fifteen kilometers. Hence, it was concluded that the probable depth of the hypocenters of possible earthquakes in the Volgograd fault, when the magnitude is five is ten (plus or minus five) kilometers, and the magnitude is 5.5 is at least fifteen kilometers. This gave the basis for clarifying the maximum possible seismic risk of the waterworks at the level of seven points on the MSK scale, made it possible to construct a mechanical model of the seismic action, and give a specific forecast of the possible seismic movements.

Seismic hazard may be remote from focal zones. The Volgograd dams were considered potential seismogenic structures that could serve as sources of influence from the far zone. The nearest of them is Cherkessia (part of the zone of the North Caucasus fault of the Alpine-Mediterranean belt). If an earthquake with a magnitude of seven to 7.5 is in this zone, the intensity of shaking at the site of the main waterworks facilities can reach three to four points on soils category II seismic properties, taking into account cross major tectonic structures. This causes a stronger attenuation of seismic waves whose intensity should not exceed two to three points GMT. The Krasnovodsk area, with the highest seismic potential, is held at twelve hundred kilometers to the southeast of the site of the waterworks. If an earthquake with magnitude 8.2 in this zone, the intensity of shaking at the site of the main waterworks facilities can reach five points on soils II category seismic properties, taking into account cross major tectonic structures, causing a stronger attenuation of seismic waves from three to four points MSK.

Seismic hazard, in the final result set or macroseismic intensity, indicates possible frequency or magnitude of possible focus (foci) earthquakes with an indication of position and repeatability. Determination of seismic effects is the main, final stage of work on the assessment of seismic hazard. In general, the estimated seismic impact refers to the parameters of the seismic motion of the ground. It is possible to nephrogram the basis of the object with a given probability that has not exceeded at a fixed time (e.g. per year), a set (ensemble) of seismic records accelerogram, and action spectra corresponding to these parameters.

Work on seismic hazard assessment ends with the definition:

A - settlement intensity (intensities) effects, and/or

B - parameters of ground motion modelling settlement records,

seismic vibrations, action spectra, Fourier spectra, and the duration of the oscillations.

1.3 Variation of Seismic Hazard

Seismic ground mode, at the interval of one hundred years, is not stationary (Figure 1.6), but may be