Usgs Seismic Design Tool Sea

Design procedures for tall buildings with dynamic modification devices

Alberto Lago , ... Antony Wood , in Damping Technologies for Tall Buildings, 2019

5.5.3.2.1 Seismic hazard level

Seismic hazard due to ground shaking can be defined as acceleration response spectra or ground motion acceleration histories specified based upon a probabilistic or a deterministic analysis ( ASCE, 2013). This hazard may depend upon the location of the building with respect to faults, the regional and site-specific geologic and geotechnical features, and the specified seismic hazard levels. Different seismic hazard level can be defined (ASCE, 2013) and relative 5% damped acceleration response spectrum for short period ( $T_s=0.2\text{second}$ ), $S_S$ , and long period ( $T_1=1\text{second}$ ), $S_1$ , in the maximum direction of horizontal response, can be determined as follows:

•

Basic safety earthquake-2 (BSE-2N). It is equivalent to MCE_R to be used for the BPON standards. Therefore, it is computed using values of $S_S$ and $S_1$ taken from the MCE_R spectral response acceleration contour maps (ASCE, 2017a).

•

Basic safety earthquake-1 (BSE-1N). Defined as two-thirds of the BSE-2N useful for the BPON standards. Therefore, it is estimated using two-thirds of the $S_S$ and $S_1$ values obtained for the BSE-2N seismic hazard level.

•

Basic safety earthquake-1 (BSE-1E). It is equivalent to a seismic hazard with a 20% probability of exceedance in 50 years (lower than the BSE-1N). It is computed using values from approved 20%/50-year maximum-direction spectral response acceleration contour maps ( $S_S$ and $S_1$ ). Values for BSE-1E are not required to be greater than those achieved for BSE-1N.

•

Basic safety earthquake-2 (BSE-2E). It is considered as a seismic hazard with a 5% probability of exceedance in 50 years (lower than the BSE-2N). It is computed using values from approved 5%/50-year maximum-direction spectral response acceleration contour maps ( $S_S$ and $S_1$ ). Values for BSE-2E are not required to be greater than those obtained for BSE-2N.

In addition to the above-mentioned procedures, it is also possible to specify the acceleration response spectra with the use of site-specific procedure. This is based on the geologic, seismologic, and soil characteristics associated with the building site. Reader may refer to Section 2.4.2 of ASCE 41-13 (ASCE, 2013) and also Section 5.2.1.1 for more details.

Independent ground motion acceleration histories with magnitude, fault distances, and source mechanisms can be chosen for the BSE-1N, BSE-2N, BSE-1E, or BSE-2E seismic hazard levels. At least three data sets of ground motion acceleration, for site seismic hazard, should be used for the RHA, where each one includes two horizontal components. In case the vertical motion is important, two horizontal components and one vertical component of at least three records should be selected and scaled. It is recommended to refer to Section 2.4.2.2 of ASCE 41-13 (ASCE, 2013) or to Section 16.2 of FEMA P-1050 (FEMA, 2015) for a more detailed discussion (as well as Section 5.2.1.1). The required number of ground motion pairs (N) is listed in Table 5.29 depending on the building site distance from the active fault. These limiting numbers are for POs of existing buildings (e.g., BPOE).

Table 5.29. Required Number of Ground Motion Acceleration Records and Method of Response Analysis (ASCE, 2013)

Building Site Distance From Active Fault (km)	Method of Calculating Responses	Limiting Number of Earthquake Record Pairs (N)
$\>5$	Average	$N\ge 10$
$\>5$	Maximum	$3\le N\le 9$
$\le 5$	Average	$N\ge 10$
$\le 5$	Maximum	$3\le N\le 9$

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Probabilistic seismic hazard analysis of civil infrastructure

G.M. Atkinson , K. Goda , in Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems, 2013

1.2.3 Current issues in modern PSHA

PSHA results are sensitive to model components/assumptions. Therefore, any seismic hazard assessment should be scrutinised by testing various cases regarding key model components. For many applications, the choice and weighting of the GMPEs, including the assigned aleatory uncertainty, are the most critical of the input parameters. This should not be surprising, as the GMPEs control the ground motions at the site for every earthquake considered; however, the GMPEs and their uncertainty often do not receive sufficient scrutiny in PSHA. Moreover, as discussed in Section 1.4, common practices regarding the use of multiple GMPEs to represent epistemic uncertainty, along with the use of regression statistics to define aleatory uncertainty, should be improved. Another significant impact is the spatio-temporal characterisation of seismic activities and seismotectonic features, which controls the rates of seismicity in and around the site (Beauval et al., 2006; Atkinson and Goda, 2011). These characterisations may be particularly uncertain in low-to-moderate seismicity regions. Other less critical issues requiring careful consideration include ensuring internally-consistent definitions for various variables in PSHA, such as magnitude, distance, and orientation of ground motion parameters.

To illustrate some of the above-mentioned issues, GMPEs used for assessing seismic hazard in western Canada are compared in Fig. 1.6 (see Atkinson and Goda, 2011, for more details). Figure 1.6 shows significant differences of the predicted SA at 0.2   s for the interface and inslab events; attenuation characteristics over distance differ significantly and variability is large at short-distance range (where empirical data are scarce). These differences are caused by several factors, such as different ground motion datasets, adopted functional forms, and employed approaches (e.g. regression analysis of empirical data versus simulation of ground motions). Uncertainties are particularly large when ground motions are required for types of seismic events that have not yet been recorded (e.g. Cascadia subduction events) and when empirical data coverage is poor in the magnitude–distance ranges of engineering interest (e.g. as is often the case in low-seismicity regions, where instrumentation tends to provide only sparse coverage).

1.6. Comparison of several GMPEs for western Canada: (a) crustal events, (b) inslab events, and (c) interface events.

(see Atkinson and Goda (2011) for details)

It should be emphasised that the controlling factors for PSHA results depend significantly on location, site condition, and probability level of interest. Thus it is important to conduct a full range of sensitivity analyses as a part of PSHA. A sensitivity analysis may be even more important than an uncertainty analysis, in that it provides insight into the critical assumptions that drive the results. Note that the effects of changing seismicity models and GMPEs on seismic hazard estimates are inter-connected; for instance, a change of spatial distribution of seismic activities affects scenario characteristics and their contributions to the overall hazard, and thus the impact of alternative GMPEs may depend on the seismicity model characteristics.

There are several pending issues to be addressed/incorporated in the PSHA methodology (this is not a comprehensive list): (i) characterisation of regional site amplification factors using a proxy measure beyond V _S30 (Hunter et al., 2010; Cadet et al., 2011), (ii) improvement of GMPEs (including better characterisation of magnitude scaling for both small and large events, and more comprehensive treatment of regional site effects), and (iii) quantification of epistemic uncertainty. To improve the prediction accuracy of site effects, the fundamental frequency of a site can be employed, which renders supplementary information in addition to near surface average shear wave velocity. Such an additional measure tends to reduce variability associated with GMPEs (Cadet et al., 2011), thus resulting in reduction of overall uncertainty in PSHA. A challenging issue is the appropriate treatment of epistemic uncertainty. Epistemic uncertainty, by definition, stems from incomplete knowledge/understanding of the subject matter. Therefore, it is not trivial to confidently capture epistemic uncertainty, and events or their consequences may not be foreseen (e.g. as in the tragic 11 March 2011 M _w9.0 Tohoku earthquake). Modelling of epistemic uncertainty requires a synthesis of theories and available data from various fields, and imagination to blend model components to evaluate possible scenarios.

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Assessing seismic risks for new and existing buildings using performance-based earthquake engineering (PBEE) methodology

T.Y. Yang , in Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems, 2013

Conduct seismic hazard analysis and ground motion record selection

A conventional seismic hazard analysis is conducted, taking into account the site and the basic dynamic characteristics of the building. One outcome of the seismic hazard analysis is a hazard curve that quantifies expected ground motion intensity measures as a function of exceedance probability considered in the PBEE analysis of the building. The hazard curve and engineering judgment are used to identify several discrete hazard levels for which the performance of the building will be further examined. Another outcome of the seismic hazard analysis is a suite of ground motions representing the seismicity of the site at different seismic hazard levels. For example, a suite of ground motion records representing the seismic hazard with a 10% probability of exceedance in 50 years at the site may be provided. A typical suite comprises several ground motions with their intensity scaled to the level implied by the seismic hazard. The motions may be further divided into subclasses by record type, such as near-field or far-field ground motions.

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Central and South America

P. Moya Rojas , in Geothermal Power Generation, 2016

23.1.2.3 Seismic hazard

A seismic hazard refers to the statistical likelihood of a seismic event (earthquake) occurring in a given geographic area. The seismic hazard of any area is used to assess the risk to buildings (standard, larger, and infrastructure), land use, and overall insurance rates. From Fig. 23.4, most of the countries in Central America with geothermal potential also rank greater than 4.0   m/s² on the seismic hazard scale. The accelerations are greater close to the Pacific Coast, where they can reach values close to 4.8   m/s² in some regions of Guatemala, Nicaragua and Costa Rica. The greatest value can be observed in Costa Rica (9.8   m/s²). Clearly, the probability that an earthquake might occur is very high.

Figure 23.4. Earthquake hazard map for Central America [5].

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Natural Hazard Characterization

G. Lanzano , ... E. Salzano , in Natech Risk Assessment and Management, 2017

5.2.1.2 Probabilistic Seismic Hazard Analysis

PSHA is a probability-based framework to evaluate the seismic hazard ( Baker, 2008; Kramer, 1996). According to Baker (2008), PSHA is composed of the five steps described in Fig. 5.1. This approach aims to identify the annual rate of exceeding a given ground-motion intensity by considering all possible earthquakes and the associated ground motions together with their occurrence probabilities, thereby avoiding the definition of a worst-case ground-motion intensity which is not without difficulty.

Figure 5.1. Schematic of the Five Basic Steps in Probabilistic Seismic Hazard Analysis According to Baker (2008)

(A) Identify earthquake sources, (B) characterize the distribution of earthquake magnitudes from each source, (C) characterize the distribution of source-to-site distances from each source, (D) predict the resulting distribution of ground motion intensity, (E) combine information from A–D to calculate the annual rate of exceeding a given ground motion intensity.

For Natech risk analysis it is important to know the ground shaking at a hazardous site. In order to predict the ground motion, the distance distribution from earthquakes to the site of interest needs to be modeled. Baker (2008) notes that for a given earthquake source, an equal occurrence probability is generally assumed at any location on the fault. If locations are uniformly distributed, the distribution of source-to-site distances by using the geometry of the source is straightforward.

For any earthquake, if IM is the ground-motion intensity measure of interest (such as PGA), the natural logarithm of IM is normally distributed. Hence, at any distance r from the earthquake source with magnitude m, the probability of exceeding any PGA level x can be evaluated by using the corresponding mean and standard deviation σ:

(5.6) $P\left(IM>x\left|m,r\right.\right)=1-\Phi \left(\frac{\ln x-\overline{\ln IM}}{{\sigma }_{\ln IM}}\right)$

where Φ is the standard normal cumulative distribution function (Baker, 2008). Considering the number of possible sources, n _sources, we can then integrate over all considered magnitudes and distances in order to obtain λ (IM > x), that is, the rate of exceeding IM:

(5.7) $\lambda (IM>x)=\sum _{i=1}^{n_{\text{sources}}}\lambda (M_i>m_{\min })\underset{m_{\min }}{\overset{m_{\max }}{\int }}\underset{0}{\overset{r_{\max }}{\int }}P(IM>x|m,r)f_{{\text{M}}_i}(m)f_{{\text{R}}_i}(r)drdm$

where λ (M _i > m _min) is the rate of occurrence of earthquakes greater than m _min from the source i, and f _M(m) and f _R(r) are the probability density functions (PDFs) for magnitude and distance.

Occasionally, the results of a PSHA are expressed in terms of return periods of exceedance, that is, the reciprocal of the rate of occurrence, or as probabilities of exceeding a given ground-motion intensity within a specific time window for a given rate of exceedance. The latter is calculated under the assumption that the probability distribution of time between earthquakes is Poissonian. The probability of observing at least one event in a period of time t is therefore equal to (Baker, 2008):

(5.8) $P_{(\text{at}\text{least}\text{one}\text{event}\text{in}\text{time}t)}=1-e^{-\lambda t}\approx \lambda t\text{,}$

where λ is the rate of event occurrence as defined earlier. For an exhaustive discussion of PSHA the reader is referred to Baker (2008) and Kramer (1996).

For design applications, there has emerged a convention to consider the probability of a ground-motion level within a given design life (T _L) of a structure in question [t = T _L in Eq. (5.8)]. Hence for a given probability and design life, the seismic hazard can also be expressed in terms of the return period T _R given by:

(5.9) $T_{\text{R}}=\frac{-T_{\text{L}}}{\text{ln}\left(1-P\right)}$

It is common to see seismic hazard defined in terms of P and T _L in the current codes and provisions, for example, in Eurocode 8 (CEN, 2004).

For some critical structures, such as nuclear power plants, the design ground motion may be more commonly expressed as an annual probability or frequency of being exceeded (i.e., T _L = 1 year). Under International Atomic Energy Association regulations (IAEA, 2003), a typical design criterion for critical elements of a nuclear power station is a ground motion with an annual probability of being exceeded of 10⁻⁴. Using Eqs. (5.8) and (5.9), this corresponds to approximately a 1% probability of being exceeded in 100 years (or a 0.5% probability of being exceeded in 50 years).

More generally, the performance-based seismic design (PBSD) formalizes the approach of citing multiple objectives for structures to withstand minor or more frequent levels of shaking with only nonstructural damage, while also ensuring life-safety and the avoidance of collapse under severe shaking (ATC, 1978). These objectives define the limit states, which describe the maximum extent of damage expected to the structure for a given level of ground motion.

Although there are different definitions of limit states, a 475-year return period (corresponding to P = 10% in T _L = 50 years) is commonly adopted as a basis for ensuring "life-safety." However, several codes have recently begun to adopt 2475 years (corresponding to P = 2% in T _L = 50 years) as the return period for the no-collapse criterion, even though it is subsequently rescaled to incorporate an assumed inherent margin of safety against collapse (NBCC, 2005; NEHRP, 2003). Longer return periods may be considered for critical structures, but this kind of analysis would require that uncertainties be treated carefully.

The 2009 revision to the NEHRP Provisions introduces a new conceptual approach for the definition of the input seismic action (NEHRP, 2009). The seismic input (maximum considered earthquake) is modified by a risk coefficient (for both short and long periods) which is derived from a probabilistic formulation of the likelihood of collapse (Luco et al., 2007). These modifications change the definition of seismic input to ensure a more uniform level of collapse prevention.

For most applications, the hazard is described in terms of a single parameter, that is, the value of the reference PGA on type A ground, which corresponds to rock or other rock-like geological formations. As an example, Fig. 5.2 shows the European Seismic Hazard Map (ESHM) which illustrates the probability to exceed a level of ground shaking in terms of the PGA in a 50-year period. The illustrated levels of shaking are expected to be exceeded with a 10% probability in 50 years, which corresponds to a return period T _R of 475 years.

Figure 5.2. European Seismic Hazard Map in Terms of Exceeding a Peak Ground Acceleration (PGA) With a Probability of 10% in 50 Years

©SHARE project, http://www.share-eu.org/

European legislation (CEN, 2004) prescribes the use of zones for which the reference PGA hazard on a "rock" site (a _g) is assumed uniform. Many seismic codes are moving away from this particular practice, choosing instead to define the hazard directly for the site under consideration (NEHRP, 2003, 2009; NTC, 2008; NBCC, 2005), or allowing for interpolation between contour levels of uniform hazard.

As an example and to give an order of size of the acceleration levels in Europe, for a medium-high seismicity area like Italy four seismic zones are defined (OPCM, 2003) according to the value of the maximum horizontal peak ground acceleration a _g whose probability of exceedance is 10% in 50 years (Table 5.1). Subsequently, in the new Italian Building Code (NTC, 2008) the Italian Hazard Map (called MPS04) was defined for each single location and is therefore site specific.

Table 5.1. Seismic Zonation in Italy According to the OPCM (2003)

Seismic Zone	Ground Acceleration (g) With Probability of Exceedance Equal to 10% in 50 Years (a g)	Acceleration (g) of the Elastic Response Spectrum (a g) at period T = 0
1	>0.25	0.35
2	>0.15–0.25	0.25
3	0.05–0.15	0.15
4	<0.05	0.05

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Seismic risk management of insurance losses using extreme value theory and copula

K. Goda , J. Ren , in Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems, 2013

28.3.1 Seismic hazard analysis and generation of spatially correlated seismic intensities

Probabilistic seismic hazard analysis offers a rational framework to describe elastic seismic demand in terms of peak ground motions and response spectra, and addresses key uncertainties and dependence in earthquake occurrence (both temporal and spatial), earthquake magnitude, rupture characteristics, and ground motion intensities (see Chapter 1). The typical outputs are given by seismic hazard curves and seismic hazard deaggregation. For Canada, details of the national seismic hazard maps, which form the basis of seismic design provisions of the current National Building Code of Canada (NBCC2005), were given by Adams and Halchuk (2003). In this study, an updated seismic hazard model for western Canada (Goda et al., 2010; Atkinson and Goda, 2011) is used to reflect newly available seismo-logical information and models. The key improvements include: (i) conversion of different magnitude scales into a uniform moment magnitude scale in the earthquake catalogue; (ii) re-evaluations of magnitude–recurrence relations for different earthquake sources based on a longer and homogeneous catalogue up to the end of 2008; (iii) use of newer ground motion prediction equations with proper distance measure conversions (note that this enables more flexible adjustment for different site conditions using the average shear wave velocity in the uppermost 30   m V _S30); and (iv) consideration of probabilistic mega-thrust Cascadia scenario events (that can be as large as M _w9.0 earthquake, similar to the 2011 Tohoku earthquake in size). Overall, adoption of the updated seismic hazard model instead of the NBCC2005 model decreases uniform hazard ordinates at short vibration periods (0.1–0.5   s) by 10–30% for the 2% probability of exceedance in 50years (i.e. seismic deign level for the majority of structures in Canada), whereas uniform hazard ordinates at long vibration periods (2.0–3.0s) are similar for the two models. (These changes are specific to soft-to-firm soil sites in Vancouver at the 2% probability of exceedance in 50 years; see Goda et al., 2010, and Atkinson and Goda, 2011, for details.)

The seismic damage assessment of multiple buildings requires the estimation of simultaneous seismic effects at multiple building locations. This is beyond the capability of conventional ground motion prediction equations, because they have been developed for a single site. To enable the application of existing ground motion models to multiple sites, their correlation structures need to be characterised (Goda and Hong, 2008). Consider spectral accelerations at two sites i and j, SA_ik(T_i) and SA_jk(T_j), due to the kth seismic event in a synthetic earthquake catalogue; the two sites are separated by a distance Δ _ij (km), and T_i and T_j represent vibration periods of linear elastic single-degree-of-freedom oscillators at sites i and j, respectively. Using a suitable ground motion prediction model, SA_ik (T_i ) and SA_jk (T_j ) are characterised by:

[28.11a] ${\log }_{10}S{A}_{ik}(T_i)=f(M_{w,k},R_{ik},{\lambda }_{ik},T_i)+{\eta }_k(T_i)+{\epsilon }_{ik}(T_i),$

[28.11b] ${\log }_{10}S{A}_{jk}(T_j)=f(M_{w,k},R_{jk},{\lambda }_{jk},T_j)+{\eta }_k(T_j)+{\epsilon }_{jk}(T_j),$

and

[28.11c] ${\rho }_T({\text{Δ}}_{ij},T_i,T_j)={\rho }_{\eta }(T_i,T_j)\frac{{\sigma }_{\eta }(T_i){\sigma }_{\eta }(T_j)}{{\sigma }_T(T_i){\sigma }_T(T_j)}+{\rho }_{\epsilon }({\text{Δ}}_{ij},T_i,T_j)\frac{{\sigma }_{\epsilon }(T_i){\sigma }_{\epsilon }(T_j)}{{\sigma }_T(T_i){\sigma }_T(T_j)},$

where f(M _w, R, λ, T) is the median prediction equation as functions of the moment magnitude M _w, distance R (typically, closest distance from station to rupture plane), and additional explanatory variables λ; η(T) is the interevent residual with zero mean and standard deviation σ_η (T); and ε(T) is the intra-event residual with zero mean and standard deviation σ_ε (T). η(T) and ε(T) are assumed to be independent and normally distributed, and the total standard deviation σ_T (T) therefore equals ${[{\sigma }_{\eta }^2(T)+{\sigma }_{\epsilon }^2]}^{0.5}$ . In Equation [28.11c], ρ_T(Δ _ij , T_i , T_j) is the correlation coefficient between η_k (T_i )+ε_ik (T_i ) and η_k (T_j ) + ε_jk (T_j ); ρ_η (T_i, T_j ) is the inter-event correlation coefficient between η _k(T_j ) and η _k(T_j ); and ρ_ε(Δ_ij,T_i,T_j) is the intra-event correlation coefficient between ε _ik(T _i) and ε _jk(T _j). The inter-event residual is calculated as the overall deviation of spectral accelerations at multiple recording stations from a median prediction equation for a given seismic event, whereas the intra-event residual is evaluated as the deviation of spectral acceleration at a particular site from the event-based spectral acceleration. These correlations can be evaluated by statistical analysis of regression residuals (Goda and Hong, 2008; Goda and Atkinson, 2009, 2010).

Two spatial correlation models of seismic effects (i.e. ρ_η(T_i, T_j ) and ρ_ε (Δ_ij , T_i, T_j ) in Equation [28.11c]) are adopted in this study: the GH08 model (Goda and Hong, 2008) for shallow crustal earthquakes in North America, and the GA09 model (Goda and Atkinson, 2009, 2010) for Japanese earthquakes. The GH08 model may be suitable for shallow crustal earthquakes in western Canada, as it is based on statistical analysis of strong ground motion records from the PEER-NGA database (http://peer.berkeley.edu/nga/index.html), while the GA09 model may be applicable to in-slab and interface earthquakes in the Cascadia subduction zone, because many GMPEs for subduction earthquakes have been developed by including ground motion records from the K-NET and KiK-net databases (http://www.kyoshin.bosai.go.jp/). The details of the correlation models can be found in Goda and Hong (2008) and Goda and Atkinson (2009, 2010). Generally, the GA09 model predicts higher correlation than the GH08 model for the same separation distance, and the decay of the correlation coefficient as a function of separation distance is more gradual for the GA09 model than the GH08 model.

The above-mentioned analysis is carried out based on Monte Carlo simulation (see Chapter 1). Initially, earthquake occurrence models, seismic source zones, and magnitude-recurrence relations are used to produce a synthetic earthquake catalogue (see Panel 1 in Fig. 28.1). Then, by using suitable ground motion models and spatial correlation models of peak ground motions and response spectra, simultaneous seismic effects at different locations are generated for each seismic event (see Panel 2 in Fig. 28.1). These two steps generate probabilistic estimates of elastic seismic demands at multiple sites for many seismic events over a certain period (i.e. multiple seismic intensity maps). This information is used as input in seismic vulnerability analysis.

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Assessment of Rockburst Risk

Shili Qiu , ... Xia-Ting Feng , in Rockburst, 2018

11.3.1 Formulation of the Problem

The probabilistic seismic hazard is a potential possibility of the occurrence of ground motion caused by seismicity, expressed in the form of likelihoods. This possibility results from probabilistic properties of the seismic source ( source), propagation of seismic waves from the source to a receiver (path), and receiving site (site). The hazard can be quantified in terms of any ground motion parameter of interest or any set of such parameters. However, the seismic risk, which is the probability of loss due to a seismic event, is primarily related to amplitude parameters of ground motion. Therefore the seismic hazard is usually quantified in terms of the amplitude parameters: peak accelerations (horizontal PHA, vertical PVA), peak velocities (horizontal PHV, vertical PVV) and the like, which are sometimes related to specific frequencies (i.e., in terms of the spectral amplitude that is the response spectrum amplitude for a given frequency). Mining-induced seismic sources are in general weak as compared to tectonic earthquakes, and the associating ground motion contains a considerable portion of higher-frequency components that weakly affect surface objects. For this reason the hazard linked to mining seismicity is often expressed by the peak ground motion amplitudes from a specified, low frequency band (e.g., from up to 10   Hz). Farther on, the probabilistic seismic hazard assessment (PSHA) problem will be linked to the ground motion amplitude parameter, but its extension to other motion parameters is also possible.

The classic PSHA problem has been formulated for multifault tectonic seismicity (e.g., Cornell, 1968; Cornell & Toro, 1992; Reiter, 1991), which is stationary; that is, its probabilistic properties do not change over time. If amp(x ₀, y ₀) is the value of the ground motion amplitude parameter at point (x ₀, y ₀) at the surface, the PSHA problem can be formulated by

(11.3.1) $R\left(a\left(x_0,y_0\right),D\right)=Pr\left[amp\left(x_0,y_0\right)\ge a\left(x_0,y_0)\mathrm{in}D\mathrm{time}\mathrm{units}\right)\right]=p$

where R(a(x ₀, y ₀), D) is the exceedance probability function of a; that is, the probability that amp at (x ₀, y ₀) will exceed a in the time period D. The objective is to find a for the prescribed values of p, (x ₀, y ₀) and D. For stationary seismicity and given p, a(x ₀, y ₀) depends only on the time period length, D, during which the point (x ₀, y ₀) is exposed to seismic influences, and not on the location of this time period on the absolute time axis.

Mining seismicity differs from natural stationary seismic processes in many aspects of which two, the most important for the PSHA problem formulation, are transience and time variability in the time perspective of humans. The transience means that the seismically active sections of the mining rockmass are not permanently active. Seismicity of these sections is correlated in time and space with the activity of mining works carried out in these volumes (e.g., Lasocki, 2008; Orlecka-Sikora & Lasocki, 2002). The seismicity does not occur before the works begin, and it does not continue indefinitely long after the works terminate. The time-variability of seismicity, linked to a specific mine section, results from the variability in time of the mining factors that induce seismicity, like the location of works in combination with the heterogeneity of the rockmass, mining rate, etc. (e.g., Lasocki, 1993a, 2008). These time effects are discussed in Section 11.3.4 and illustrated in Figs. 11.3.3 and 11.3.4.

Due to the transience of mining seismicity, the exceedance probability function, R, must be attached to a specified period of time [D ₁, D ₁  + D], where D ₁ is the beginning and D ₁  + D is the end of the time period for which the hazard is assessed. The PSHA solution, a, refers also exclusively to [D ₁, D ₁  + D]. The PSHA problem reformulated for the seismicity induced by mining reads:

(11.3.2) $R\left(a\left(x_0,y_0\right),D_1,D\right)=Pr\left[amp\left(x_0,y_0\right)\ge a\left(x_0,y_0)\mathrm{in}\left[D_1,D_1+D\right]\mathrm{time}\mathrm{period}\right)\right]=p$

The time-variability of seismicity implies dependence on time of the probabilistic functions describing the seismic process, which are components of Pr[•] in Eq. (11.3.2).

In the engineering seismology of natural earthquakes, the seismic hazard is often quantified by a maximum credible amplitude of ground motion for a specified time period T rather than by the amplitude value, whose exceedance probability is determined by Eq. (11.3.1). The maximum credible amplitude is the amplitude value, whose mean return period is T. The maximum credible amplitude and the amplitude from Eq. (11.3.1), a(x ₀, y ₀), are strictly related formally and can be calculated one from another. However, in mining engineering seismology the interpretation of a is always straightforward because it is linked to the period of interest [D ₁, D ₁  + D], whereas the maximum credible amplitude is meaningful only when T is less than or equal to D. For this reason, we use a here.

Eq. (11.3.2) refers to one seismically active area or seismic zone, whose activity is described by the source probabilistic functions, which are presented below. To assess the impact of more than one seismic zone, we aggregate the probabilities (Eq. 11.3.2) of individual zones. Let R _k (a(x ₀, y ₀), D ₁, D) be the exceedance probability of a(x ₀, y ₀) in the time period [D ₁, D ₁  + D], resulting from the activity of the seismic zone k. Let be L active zones, k  =   1,…,L in that time period. The PSHA problem, accounting for these L zones, reads:

(11.3.3) $R\left(a\left(x_0,y_0\right),D_1,D\right)=1-{\displaystyle \prod _{k=1}^L\left[1-R_k\left(a\left(x_0,y_0\right),D_1,D\right)\right]}=p$

and its solution is again a(x ₀, y ₀), given p, D ₁, D. Note that none from L zones must be active throughout the whole period [D ₁, D ₁  + D]. In the extreme case, we could take into account also a zone, which is not active in this period at all; however, R for such a zone is zero and hence does not add anything in Eq. (11.3.3).

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Seismic risk assessment for oil and gas pipelines

D.G. Honegger , D. Wijewickreme , in Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems, 2013

25.4 Types of seismic hazard

In addition to the loadings under operational conditions, potential loads on buried pipelines from seismically induced hazards are of importance to assessing the performance of pipeline systems.

The typically seismic hazards to pipelines include:

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wave propagation;

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permanent ground deformation hazards:

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differential movements at topographic discontinuities or faults,

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slope failures,

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liquefaction-induced permanent ground deformations;

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volcanic hazards;

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tsunami inundation.

25.4.1 Wave propagation

Seismic wave propagation is a ground motion phenomenon that relates to the passage of body waves, including compression waves and shear waves, radially from the source of earthquake energy release (hypocenter) into the surrounding rock and soil medium. Compression waves cause compressive and tensile strains in the ground in a radial direction away from the hypo-center. Shear waves cause shear strains in the ground perpendicular to these radial lines. When the compression waves and shear waves are reflected by interaction with the ground surface, surface waves (Love waves and Rayleigh waves) are generated. Except at large distances from the epicenter, the amplitudes of surface waves are much less than body waves. An earthquake at its source generates only compression and shear waves, and propagation of its radiated waves can be evaluated using ray theory (Pujol, 2003). Since the amplitude of shear waves is significantly larger than compression waves and thus generates greater strains in a pipeline, the examination of wave propagation can be limited to the effects of shear waves. Also, the strongest component of ground shaking in strong motion instrument records used to derive attenuation relationships is typically from shear waves (Bolt and Abrahamson, 2003).

A pipeline buried in soil that is subject to the passage of these seismic waves will incur longitudinal and bending strains as it conforms to the associated ground strains. In most cases, these strains are relatively small, and welded pipelines in good condition typically do not incur damage. Propagating seismic waves also give rise to hoop membrane strains and shearing strains in buried pipelines, but these strains are small and may be neglected.

25.4.2 Permanent ground deformation

Earthquake-induced permanent ground deformations have been recognized as one of the major causes of system damage and associated service disruption to lifeline facilities during past earthquakes (Hamada and O'Rourke, 1992). Essentially, large soil loads arising from permanent ground movements can lead to potentially unacceptable strains in the pipelines. Extensive research has been focused in the last few decades to investigate the response of the pipes under permanent ground deformations. Common causes of permanent ground displacement are related to surface fault displacement, liquefaction-induced lateral spreading and flow slides, slope instability and landslides, and ground subsidence.

Ground movements at fault crossings

Pipelines crossing faults can be subjected to displacements ranging from a few centimeters to several meters. In addition to the lateral movements significant vertical movements can occur in the crossings involving reverse-thrust faults. Large ground movements at the Trans-Alaska Pipeline crossing of the Denali fault near Glennallen, Alaska, during the 2002 M7.9 Denali fault earthquake is a classic example of the type of ground movements expected at fault crossings.

Liquefaction-induced ground movements

In saturated loose or soft granular soils, liquefaction occurs when the shear strains induced due to seismic shaking cause transient pore water pressures to increase in the soil mass. As a result, intergranular contact stresses will reduce to negligible levels. In this transient state, the soil mass is subject to significant reduction in shear strength and behaves essentially as a viscous fluid that could deform or flow under gravitational or inertia forces. Areas susceptible to liquefaction could undergo significant vertical and lateral movements even in gently sloping terrain. The extent of permanent ground displacements is expected to increase with the increasing amplitude of earthquake accelerations and with the duration of seismic shaking. The extent of ground movements can be classified as: flowslides (more than ~5   m), lateral spreading flowslides (~5   m to ~0.3   m), and ground oscillation (less than ~0.3   m). In addition to liquefaction-induced ground movements, flotation and soil uplift could also be identified as another potential concern in relation to the reduction in soil strength associated with liquefaction. This would be of particular concern if the pipe trench backfill materials are poorly compacted and susceptible to liquefaction.

Liquefaction can produce overall volume changes in the liquefied soil mass that take place due to the dissipation of earthquake-shear-induced excess pore water pressures. The volume changes manifest in the field as post-liquefaction settlements, and they may occur both during and after earthquake shaking. The adverse impacts of these settlements on the performance of structural foundations and linear lifelines (such as buried pipelines and bridges) have been well recognized (Tokimatsu and Seed, 1987; Wijewickreme and Sanin, 2010).

Ground movements due to landslides

Significant ground movements could occur due to landslides triggered (without soil liquefaction) during earthquake shaking. This would become a concern in areas of steep terrain and saturated slopes with soft soils, or in areas where there is ongoing relatively slow moving landslide activity.

25.4.3 Volcanic hazards

In terms of volcanic hazards, exposure to the hazard is generally related to the type and nature of the volcano (e.g. impact of volcanic hazards tends to be greater for andesitic volcanoes than for basaltic volcanoes) and to the proximity to the volcano edifice, as well as to whether it is on a drainage that emanates from the edifice. The potential volcanic hazards that may be present along the pipeline routes include tephra (ash) fall, pyroclastic flow/surge, blast surge, lava flow, mud flow, debris flow, ground deformations, and volcanic earthquakes.

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Seismology and Earthquake Effects for Engineers

Mohiuddin Ali Khan Ph.D., P.E., C. Eng., M.I.C.E. (London) , in Earthquake-Resistant Structures, 2013

2.7 Seismology-Related Hazards

Most large earthquakes occur in long fault zones around the margin of Pacific Ocean. The zones that ring the Pacific are subdivided by geologic irregularities into smaller fault segments, each rupturing individually. Friction controls the movement of tectonic plates at a fault. The lower the friction, the weaker the fault and the easier it displaces. Medium friction produces small earthquakes. High friction produces a fault that will slip, occasionally generating large earthquakes. The USGS and many state geological surveys have produced maps of these major active faults, all of which have ruptured within last 11,000 years.

Seismic risk assessment has traditionally involved peak ground acceleration (PGA), velocity, and displacement as functions of frequency or period. For example, using a set of assumptions about fault mechanics and rate of stress accumulation, the USGS predicted that an earthquake of about 6.0 magnitude would occur in Parkfield, California, between 1988 and 1992. Although this quake did not materialize until 2004, long after the prediction window had expired, estimating an earthquake using a dense network of instrumentation was a significant accomplishment and gave new insights on the mechanics of fault rupture.

2.7.1 Probabilistic Seismic Hazard Analysis

Definition: A seismic hazard is the probability of occurrence of a particular earthquake characteristic such as PGA. Based on geological and seismological studies, probabilistic seismic hazard analysis (PSHA) estimates the likelihood of a hazard, considering the uncertainties in magnitude and the location of earthquakes and their resulting ground motions that are likely to affect a particular site. For statistical reasons, risk involves probabilistic values that are greater than expected.

2.7.2 USGS and UN Global Seismic Hazard Assessment Programs

The USGS and its partners in the multi-agency National Earthquake Hazard Reduction Program (NEHRP) are working to improve monitoring and reporting capabilities via the USGS Advanced National Seismic System (ANSS). Another project, the UN Global Seismic Hazard Assessment Program (GSHAP), a demonstration project of the UN/International Decade of Natural Disaster Reduction initiative, was carried out from 1992 through 1998. The GSHAP Global Seismic Hazard Map joins GSHAP regional maps to depict global seismic hazards as PGAs with a 4% chance of exceedance in 50 years, corresponding to a return period of 475 years. Exceedance refers to a range of values to be exceeded.

Landslide Hazard Maps

The USGS and the California Geological Survey (CGS) have prepared landslide hazard zone maps indicating areas where slope, soil type, and seismic risk could trigger landslides. Because downslope slides can undermine foundations and cut off utilities and access, rendering a structure nonoperational and structurally unsafe, construction in the Landslide Hazard Zone requires assessment by a geotechnical engineer.

2.7.3 Shake Maps and Response Spectra

Definition: A shake map is useful in seismic zoning. This technology is rapidly evolving as new advances in communications, earthquake science, and user needs drive improvements. Shake maps have become a valuable tool for emergency response, public information, loss estimation, earthquake planning, and post-earthquake engineering and scientific analyses.

Use of GIS: The USGS ShakeMap program produces a computer-generated representation of ground shaking. It represents a major advance for scientific and engineering purposes (see http://earthquake.usgs.gov/shakemap). Automatically generated shaking and intensity maps combine instrumental measurements of shaking with information about local geology and earthquake location and magnitude to estimate shaking variations throughout a geographic area. The results are rapidly available online in a variety of map formats, including geographic information system (GIS) coverage.

Site Response Spectra

Structures with different periods or frequency responses react in widely differing ways to the same earthquake ground motion; conversely, any structure acts differently during different events. Thus, for design purposes the site response spectrum represents a structure's range of responses to ground motion of different frequencies for the peak accelerations.

Definition: A site response spectrum graph plots the maximum response values of acceleration, velocity, and displacement against period and frequency. It enables the engineer to identify the resonant frequencies at which a structure undergoes peak accelerations. According to NEHRP (1997), structural design might be adjusted to ensure that the building period does not coincide with the site period of maximum response.

Structural Response Methods

Besides the site response spectrum, other methods of evaluating structural response are step-by-step integration, equivalent lateral force, and soil–structure interaction. Depending on seismic intensity, structural response is evaluated by different mathematical methods. Methods specifically for the evaluation of buildings and bridges include base isolation and energy dissipation.

Objectives: Engineers and building code developers use site response evaluation methods to improve the safety of new and existing structures, thereby reducing ultimate risk. New design codes ensure that new structures are built with sufficient resistance to lateral forces and sufficient flexibility of movement.

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Seismic Design for Buildings

Mohiuddin Ali Khan Ph.D., P.E., C. Eng., M.I.C.E. (London) , in Earthquake-Resistant Structures, 2013

10.4.2 Effective Peak Acceleration

The USGS 2008 seismic hazard maps identify effective peak acceleration (EPA), (based on seismology of the area) which reflects light, moderate, and severe shaking risks as a percentage of the acceleration of gravity that can be expected in an area. Seismic codes use EPA calculations to proportion member sizes of buildings to resist resulting seismic shear forces and bending moments and prevent damage.

Two Hazard Levels: One approach to satisfying basic safety objectives using EPA maps is to evaluate a structural design according to two levels of shaking hazard: the functional evaluation event (FEE) and the safety evaluation event (SEE). If a structure meets FEE following an inspection, immediate operation is allowed and minimal damage is permissible. This hazard level has a 10% probability of exceedance in 50 years (i.e., a return period of approximately 500 years). For SEE, significant disruption to service is permissible as is significant damage. This level has a corresponding 2% probability of exceedance in 50 years (amounting to return period of approximately 2,500 years).

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Usgs Seismic Design Tool Sea

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