# Assessment of Adequate Margin to Liquefaction for Nuclear Power Plants.

1. IntroductionAccording to generally accepted design requirements of nuclear power plants (NPPs), the design shall provide for an adequate margin to protect items ultimately necessary to prevent an early radioactive release or a large radioactive release in the event of levels of natural hazards exceeding those considered for design basis [1]. It should be demonstrated that those values of the parameters of natural hazards will highly probable not be reached, for which the sudden loss of capability of the mentioned above items would occur, which would result in abrupt and severe change of the plant condition. The design has to guaranty that a severely abnormal plant behaviour could not be caused by plant response to a small deviation of magnitude of external events. This abrupt change to severe plant condition is termed as 'cliff-edge-effect'.

An essential question is how large the margin should be to be accepted as adequate for complying with above requirements. According to the regulations, best-estimate approach can be adopted for the evaluation of this margin [2]. In case of earthquake, the High-Confidence-of-Low-Probability-of-Failure (HCLPF) could be the measure of the seismic margin [3-5]. In the U.S. for new plants, a HCLPF capacity of at least 1.67 times the design basis peak ground acceleration (PGA) is required to be demonstrated [6]. In the European practice, a margin exceeding by 40% the design basis PGA has tobe justified [7]. These acceptance criteria are based on the conservatism of the established nuclear design standards and justified by extensive studies.

The catastrophe at the Fukushima Daiichi Nuclear Power Plant caused by the Great Tohoku earthquake followed by a huge tsunami on 11th of March 2011 revealed the fundamental experience that the plants designed in compliance with nuclear standards can withstand effects of the vibratory ground motion due to disastrous earthquake exceeding several times the design basis one [8 ] but may fail due to effects of phenomena accompanying or generated by the earthquakes. Liquefaction is one of those secondary effects of beyond-design basis earthquakes that should be investigated and evaluated for nuclear power plants (NPPs) at soil sites (see [9-12]). In case of new plant, if the potential for soil liquefaction is recognized, the site shall be qualified for unacceptable, unless proven engineering solutions are available for the soil improvement [12]. For screening out the hazard, the factor of safety to the liquefaction (FSL) due to design basis earthquake (DBE) is applied, which should be calculated by conservative methods (see [10]).

In case of operating at soil sites NPPs, reevaluation of the liquefaction hazard can be subject of periodic safety review or a focused review, as it has been done at several NPPs after Fukushima accident.

Liquefaction hazard has been considered with some extent for 41 operating NPPs at soil sites in the U.S. [13]. Basic finding of these analyses was that the liquefaction is generally not a safety issue. However, if it is the case, liquefaction could be an essential contributor to the core damage. Similar conclusion was made on the basis of seismic PSA for Paks NPP [14].

Contrary to the margin with respect to the earthquake vibratory motion, the margin with respect to liquefaction and the issue of potential liquefaction caused by beyond-design basis earthquakes are not sufficiently investigated up to now. How to define the margin to liquefaction and how large should be the margin to be sufficient are open questions and actual research tasks. Even the question has not been answered, whether an earthquake characterised by 1.4 or 1.67 times the design basis peak ground acceleration, vibratory effects of which the plant can withstand thanks to seismic margin, will not induce liquefaction at soil sites and loss safety functions.

In the paper, a procedure has been developed for evaluation of the margin to liquefaction, assuming that an earthquake happens, with maximum horizontal acceleration (PGA) 1.67 (or 1.4) times larger than that of the DBE. This earthquake will be denoted further as margin earthquake. The procedure is based on the recent research publications on the liquefaction phenomenon and on the investigations of the author, which are devoted to the application of these research results for resolving of the liquefaction related safety issues of nuclear power plants. These publications are thoroughly referenced in the paper.

The applicability of the procedure is demonstrated in the paper via case study with site characteristics approximately similar to those for the site of Paks Nuclear Power Plant in Hungary. For the case study, the probability for liquefaction due to margin earthquake is evaluated and compared to the probability of liquefaction due to the design basis earthquake. The question is answered, whether this margin earthquake could cause liquefaction with subsequent loss of function of structures, systems, and components (SSCs) that are necessary to avoid the severe plant conditions and the cliff-edge-effect. Criteria for probability for screening and acceptable probabilistic margin to liquefaction are proposed. Reactor building settlement due to margin earthquake is also assessed.

2. The Example

The case considered in the paper is rather similar to the case of Paks NPP, Hungary, where the earthquake hazard as well as the liquefaction hazard was completely neglected in the design. During operation the site seismicity had been reevaluated, and the seismic design basis has been defined as a [10.sup.-4]/a event with PGA, [a.sub.max] = 0.25 g. Deaggregation of the [10.sup.-4]/a seismic hazard shows that the dominating source is a nearby shallow earthquake with magnitude 5.8- 6.0. The plant was upgraded to the new DBE that required great effort [15]. The return period of the liquefaction was found slightly larger than 10000 years [16]. In spite of this, the liquefaction is considered as beyond-design basis event. The liquefaction hazard and the response of the Paks NPP to the liquefaction have been thoroughly investigated during last ten years [17-21].

In the example created on the basis of case of Paks NPP, the main reactor building is considered. The foundation level is about 8.0 m depth. The ~2 m thick liquefiable soil layer is assumed to be beneath the 150 m x 80 m large base-mat; the average ground-water level is about the base-mat level at ~8.0 m depth. The height to width ratio of the building is ~0.5, and the foundation contact pressure is ~400 kPa. It is assumed for the simplicity that the fines content is FS [??] 35%, and the average SPT in the layer beneath foundation is [([N.sub.1]).sub.60] [approximately equal to] 20.

3. Probability of Liquefaction due to Design Basis Earthquake

3.1. Screening Criterion. Complying with [9], let us assume that the probability of the liquefaction hazard due to DBE is negligible, a core damage or early large release of radioactive substances practically excluded.

First of all, the criterion for negligibility should be quantified.

The probabilistic safety criterion for the early large releases of radioactive substances can be used for measure of the negligibility, which is equal to [10.sup.-6]/a. Let us assume in a conservative way that the cliff-edge-effect will appear, if the soil is liquefied. It means that the probability distribution for loss of required functions for avoiding the severe accident is a step-function: H([FS.sub.L] [less than or equal to] 1) = 1 and H([FS.sub.L] > 1) = 0.

Liquefaction due to design basis earthquake can be screened out, if the probability of liquefaction due to DBE is minimum one order of magnitude less than the early large release criterion is. (In this case the core damage due to liquefaction can also be avoided with high assurance.) The design basis earthquake is selected with [10.sup.-4]/a annual exceedance probability level. It means that the probability for liquefaction due to DBE should be less than [10.sup.-3]. These considerations are generally applicable for screening out the liquefaction hazard from the design basis with high assurance.

3.2. Evaluation of the Probability of Liquefaction for Design Basis Case. Using the procedure for the evaluation of liquefaction developed by Cetin et al. [22] the probability of liquefaction, [P.sub.L], can be expressed as

[mathematical expression not reproducible] (1)

where [PHI] is the standard normal cumulative distribution function, [([N.sub.1]).sub.60] is the corrected SPT resistance, FC is the fines content in percent, [M.sub.w] is the moment magnitude, [[sigma]'.sub.vo] is the initial vertical effective stress, and [p.sub.a] is atmospheric pressure in same units as [[sigma]'.sub.vo]; [[sigma].sub.[epsilon]] is the measure of the estimated model and parameter uncertainty; and [[theta].sub.1]-[[theta].sub.6] are model coefficients obtained by regression. In (1) the cyclic stress ratio, CSR, should be calculated via (2), but without accounting for the magnitude scaling factor, MSF. This is indicated as [CSR.sub.eq].

The CSR is

CSR = 0.65[[a.sub.max]/g] x [[[sigma].sub.vo]/[[sigma]'.sub.vo]] x [[r.sub.d]/MSF] (2)

where [a.sub.max] is the peak ground surface acceleration equal to 0.25 g; g is the acceleration of gravity in same units as [a.sub.max]; [[sigma].sub.vo] is the initial vertical total stress; [[sigma]'.sub.vo] is the initial vertical effective stress; [r.sub.d] is the depth reduction factor.

If the probability of the liquefaction due to DBE should be less than 0.001, i.e., [P.sub.L] [less than or equal to] 0.001 than the argument of [PHI](x) shall be x [less than or equal to] -3.091. Thus, the corresponding cyclic resistance ratio will be as

[mathematical expression not reproducible]. (3)

For the soil data, (1) gives CSR ~ 0.09. From (2) the resistance ratio that corresponds to the [P.sub.L] [less than or equal to] 0.001 will be CRR ~ 0.13; i.e., the requirement for DBE induced liquefaction probability to be [P.sub.L] [less than or equal to] 0.001 is fulfilled.

The evaluation can be performed via method published in [23, 24]. According to this, the probability for liquefaction can be calculated as

[mathematical expression not reproducible] (4)

Here, [([N.sub.1]).sub.60,cs] is the blow-count modified for clean sand, and [[beta].sub.0] - [[beta].sub.3] are constants, defined by Bayesian update on a large database of case histories [22].

In this case the numerical result is slightly more conservative, [P.sub.L] [approximately equal to] 0.004.

The [P.sub.L] can be calculated by similar to [23] method published in [25]. The result will be very close to those obtained by (4).

The cyclic resistance ratio given by (3) can be crosschecked by the method of [26, 27]

[CRR.sub.7.5] = [1/(34 - [([N.sub.1]).sub.60])] + [[([N.sub.1]).sub.60]/135] + [50/[[10[([N.sub.1]).sub.60] + 45].sup.2]] - [1/200] (5)

In this particular example, (5) gives CRR = 0.2154 and [FS.sub.L] [approximately equal to] 2.4.

It should be mentioned that several correlations have been published for calculation of [P.sub.L]. For example, according to [25] the probability of liquefaction can also be calculated and the required condition [P.sub.L] [less than or equal to] 0.001 can be checked as follows:

[P.sub.L] = 1/[1 + [([FS.sub.L]/0.783).sup.6.63]] [less than or equal to] 0.001 (6)

The condition expressed by (6) is valid, if factor of safety is already [FS.sub.L] [approximately equal to] 2.2. According to [25], the probability of liquefaction is less than 15%, and the liquefaction incidence is improbable, if the safety factor is over 1.15.

Considering the results for [FS.sub.L] obtained by (1)-(4) and (6), it can be concluded that for the screening out the liquefaction from the design basis, a factor of safety [FS.sub.L] [??] 2.2 should be justified for the site.

4. Probability of Liquefaction due to Margin Earthquake

4.1. Acceptance Criteria for the Probability of Liquefaction due to Margin Earthquake. Before performing the calculations of probability of liquefaction for the margin earthquake the acceptance criteria for the probability of liquefaction should be defined.

It is proposed to adopt the concept for seismic margin developed in Section 1.3 of the ASCE/SEI 43-05 [28]. According to this the probability of unacceptable performance should be less than about a 10% for a ground motion equal to 150% of the DBE ground motion.

Adopting this concept, the probability of liquefaction is accepted, if it is less than 10% for the case of margin earthquake with 1.67 (1.4) times of the design basis PGA.

For the justification of the proposed criterion, the annual probability of exceedance of the margin earthquake should be estimated. For this purpose, results of the probabilistic seismic hazard assessment should be used, i.e., the hazard curves and deaggregation of the seismic hazard.

Approximation of the annual exceedance probability of the margin earthquake can be done via median hazard curve. In the case considered, the annual rate of exceedance for 1.67 x [a.sub.max] is [10.sup.-5]/a, while the annual rate of 1.4 x [a.sub.max] is approximately 2 x [10.sup.-5]/a. (These are the real values for the Paks site). In the given case, if the margin earthquake with 1.67 x [a.sub.max] will cause liquefaction with probability less than 0.1, the acceptance criterion for avoiding early large release ([less than or equal to] [10.sup.-6]/a) will also be fulfilled. It is obvious that annual probability of the margin earthquake depends on the slope of the hazard curve, which can be measured by increase of PGA versus decreasing the annual probability of exceedance with one order of magnitude, similar as in ASCE/SEI 43-05 [28]. In the case considered, the slope of the hazard curve is rather steep.

4.2. Evaluation of the Probability of Liquefaction due to Margin Earthquake. Let us calculate the [P.sub.L] for the parameters of the margin earthquake for the case considered, where [a.sub.max,M] = 1.67 x [a.sub.max] = 0.42g (or [a.sub.max,M] = 14 x [a.sub.max] = 0.35g).

Calculation via (1) results in [P.sub.L] ~ 0.2 with CSR ~ 0.22 and the resistance for ensuring [P.sub.L] [less than or equal to] 0.1 should be CRR ~ 0.19. Consequently, for the case of margin earthquake with 1.67 x [a.sub.max], the onset of liquefaction in the critical layer below the foundation mat could not be excluded with high assurance. However, the beyond-design basis events should be treated in best-estimate manner [1]. Thus, the result [P.sub.L] ~ 0.2 also can be matter of consideration and further acceptance. A positive conclusion can be supported by less conservative calculations, for example, via (6), which results in [P.sub.L] [approximately equal to] 0.07 for the case with [a.sub.max,M] = 1.67 x [a.sub.max].

In the case of [a.sub.max,M] = 1.4 x [a.sub.max], and using (1), the liquefaction can be practicallyneglected, since the probability of liquefaction is [P.sub.L] ~ 0.05. It can be concluded that the margin earthquake with [a.sub.max,M] = 1.4 x [a.sub.max] is practically harmless from the point of view of loss of required functions due to liquefaction.

It has to be mentioned that a probabilistic liquefaction hazard assessment has been made for the Paks site applying methodologies [29, 30] (see in [16-20, 31]). The real site soil conditions at Paks are a little different from those used in the above case study. For the real site conditions, [FS.sub.L] varies between 0.4 and 0.8 below of annual rate of exceedance [10.sup.-4], and for all soil layers beneath the base-mat, although the peak ground acceleration in the calculations was rather moderate. This finding complies with other observations. For example, as it shown in [30], the liquefaction potential index, [I.sup.*.sub.LP] can exceed the critical values of 5 and 15 even if the maximum horizontal acceleration is rather low. Consequently, it is advised to perform the first estimation of the margin to liquefaction via (1)-(4). If the criterion in Section 4.1 could not be met with application of (1)-(4), further analysis with appropriate and less conservative correlations (for example, (6)) could resolve the issue.

5. Assessment of the Margin for Settlement of Reactor Building

The liquefaction due to margin earthquake does not mean that the plant will unavoidably loose the functions that are ultimately necessary to prevent early large releases. Experience shows that the building relative settlement could be a proper damage measure that is caused by uneven consolidation settlement due to heterogeneous soil layering [20, 21].

According to a most recent publication [32], the settlement, S, can be approximated by an equation having form of

ln S = [f.sub.soil] + [f.sub.found] + [f.sub.str] + [s.sub.0]ln (CAV), (7)

where [f.sub.soil], [f.sub.found] and [f.sub.str] are the contribution to settlement related to soil, foundation, and structure, respectively, [s.sub.0] is constant, and [[s.sub.0] ln(CAV)] represent the contribution of the earthquake expressed in terms of cumulative absolute velocity (CAV) as intensity parameter. [f.sub.soil], [f.sub.found] and [f.sub.str] are week functions of the CAV; therefore, their dependence on the CAV can be neglected.

The ration of the settlement caused by margin earthquake, SM, to the settlement due to design basis earthquake, [S.sub.DBE], will be

ln[[S.sub.M]/[S.sub.DBE]] = [s.sub.0]ln([CAV.sub.M]/[CAV.sub.DB]) (8)

The CAV is proportional to the product of strong motion duration and average energy of the strong motion acceleration time history a(t) [33]. Thus, the CAV can be considered as product of two random variables, the duration of strong motion T, and the mean of absolute value of ground acceleration time history, E{[absolute value of a(t)]}:

CAV = [[integral].sup.T.sub.0][absolute value of a(t)]dt [congruent to] T x E {[absolute value of a(t)]} (9)

Generally, the variables T and E{[absolute value of a(t)]} are not independent as the moment magnitude, [M.sub.w], and the maximum horizontal acceleration, [a.sub.max], are not. Here, these variables are calculated via marginal distributions.

As it shown in [33], the CAV reflects the main physical properties of the cyclic load due to earthquake excitation and can be expressed as a product of duration and the average number of load cycles in form:

CAV [approximately equal to] 2[1/[[omega].sub.c]] x N x [A.sub.c], (10)

where [[omega].sub.c] is the median frequency of the power spectral density function of the acceleration time history, a(t), [A.sub.c] is the mean amplitude.

The CAV is an adequate indicator of accumulating effects of liquefaction since it is reflecting the main features of pore pressure accumulation phenomena [34] as well as the ratcheting-type settlement phenomena that are depending on the number of cycles and amplitude of cyclic motion. The higher the mean frequency of the excitation is, the less will be the possibility of a damage, which corresponds to the observations.

For [A.sub.c], the relationship [A.sub.c] [approximately equal to] 0.65 x [a.sub.max] can be accepted. The approximate number ofload cycles of the earthquake can be defined on the basis of [35, 36]. Detailed investigations have been published in [37]. Further, it can be assumed that mean frequencies are approximately equal in design basis and margin earthquakes. The ratio of CAV values for the margin earthquake [CAV.sub.M] to the design basis earthquake [CAV.sub.DBE] will be

[CAV.sub.M]/[CAV.sub.DBE] = 1.67[[N.sub.M]/[N.sub.DBE]] ~ 1.67 x 1.1 [congruent to] 1.84 (11)

and the ratio of corresponding settlements

[S.sub.M]/[S.sub.DBE] = exp[[s.sub.0]ln([CAV.sub.M]/[CAV.sub.DBE])] ~ 1.35, (12)

where [s.sub.0] = 0.4973 have been used in accordance with [32].

Consequently, the settlement due to margin earthquake is about 35% higher than those due to design basis earthquake, if (a rather improbable) liquefaction would occur at DBE. In (12), the [CAV.sub.M] and [CAV.sub.DBE] correspond to liquefaction cases with very differing annual probabilities, as it has been shown in Sections 3 and 4 above.

As it is shown in [30], the annual rate for liquefaction potential index, [I.sup.*.sub.LP], shows a degressive character, having a cut-off above certain [I.sup.*.sub.LP], although [a.sub.max] is increasing monotonous with decreasing of annual rate. It means that the settlement should have also a cut-off value that depends on the soil conditions, depth and thickness of liquefiable layers.

In critical cases, final conclusion on the loss of required plant functions can be made on the basis of detailed analysis of both the liquefaction hazard and response of the structure. Sophisticated hazard analysis can even result in lower annual probability for liquefaction. There are examples, where the annual probability of liquefaction was found approximately an order of magnitude less than the annual rate of exceedance of [a.sub.max] of the causal earthquake (see [30]). A sophisticated plant response analysis can demonstrate that the plant can withstand the effects of the liquefaction. For detailed evaluation of the plant response, the ultimate acceptable condition should be defined for the SSCs needed for avoiding/managing severe accidents. In case of some SSCs, the ASCE/SEI 43-05 [28] LS-B condition (moderate permanent distortions) can be allowed (LS condition as per FEMA 365 [38]). For some SSCs, the large permanent distortions could also be accepted (LS-A condition ASCE/SEI 43-05 or NC as per FEMA 365). These conditions can be evaluated, for example, applying ASCE 41-13 [39] or EUROCODE 8, Part 3 [40]. Decision on the allowable condition of SSCs can be made on the basis of probabilistic and deterministic accident analyses. This type of analysis has been performed for Paks NNP [20].

6. Summary

For nuclear power plants, adequate margin should be demonstrated for avoiding/managing the severe accidents in case of beyond-design basis earthquake. Compliance with this requirement does not mean that a beyond-design basis earthquake cannot cause liquefaction, even if the liquefaction hazard is negligible under design basis conditions. Analysis of the probability of liquefaction for beyond-design basis "margin earthquake" for realistic site-plant parameters demonstrated the safety relevance of the issue.

The paper provides basic thoughts how to interpret the margin to liquefaction and outline a procedure for the evaluation of the margin. The site-plant conditions have to be accounted for, while adopting the method for particular NPP.

First step for performing the analysis of the issue is to define the criterion for screening out the liquefaction from the design basis. In the paper, the probabilistic criterion has been derived from the safety requirement for the acceptable level of the probability of early large release of radioactive substances. For screening out the liquefaction from the design basis, annual probability of liquefaction should be one order of magnitude less than what is acceptable for the large early releases.

The correlation developed by Cetin et al. [22] has been applied for calculation of the probability of liquefaction due to design basis earthquake. As an alternative to this correlation, correlation given in [25] has also be applied. Based on the calculations, a factor of safety to liquefaction [FS.sub.L] [??] 2.2 is proposed for the criterion of screening out the liquefaction from the design basis.

For the assessment of liquefaction hazard due to margin earthquake with PGA 1.67 (1.4) times larger than the design basis, an acceptance criterion has been defined. It is proposed to demonstrate that the probability of liquefaction is less than 10% in the case of margin earthquake. This condition will ensure the compliance with the probabilistic safety criterion for early large release, even if the liquefaction would cause cliff-edge effect.

In the studied case, the condition [P.sub.L] [less than or equal to] 0.1 is not fulfilled if [P.sub.L] is calculated via correlation of Cetin et al. In similar situations, conservatism of the data and used correlations should be analysed and removed, since the beyond-design basis hazards should be treated in best-estimate way. Use of several correlations for calculation of [P.sub.L] could be considered, for example, the correlation given by (6). However, it is advised to perform the first estimation of the probability of liquefaction via (1)-(4). If the criterion [P.sub.L] [less than or equal to] 0.1 could not be met, further analysis with appropriate correlations may resolve the issue.

Main effect of the liquefaction is the differential building settlement and differential movement between buildings and connected pipelines, cables. In the paper, a quick method is demonstrated for approximate definition of the building settlement for the case, if the margin earthquake will cause liquefaction. In critical cases, detailed analysis of the plant response to liquefaction should be performed for justification of the plant capability to withstand beyond-design basis liquefaction effects. For these evaluations, the acceptable ultimate condition of structures, systems, and components of the plant should be defined on the basis of analysis of accident sequences.

Comprehensive conclusion on the sufficiency of the value for the margin to liquefaction, and on the evaluation methodology, should be achieved in the future and should be based on consensus of experts, similar as it similar as it has happened in case of development of requirements of seismic margin for NPPs.

https://doi.org/10.1155/2018/3740762

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The author declares no conflicts of interest.

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[39] ASCE 41-13 Seismic Evaluation and Retrofit of Existing Buildings, American Society of Civil Engineers, 2013.

[40] "EN 1998-3 EUROCODE 8: Design of structures for earthquake resistance--Part 3: Assessment and retrofitting of buildings," https://law.resource.org/pub/eu/eurocode/en.1998.3.2005.pdf, 2005.

Tamas Janos Katona (ID)

University of Pecs, Boszorkany ut2, 7624 Pecs, Hungary

Correspondence should be addressed to Tamas Janos Katona; katona.tamas.janos@mik.pte.hu

Received 18 June 2018; Revised 31 July 2018; Accepted 5 August 2018; Published 2 September 2018

Academic Editor: Eugenijus Uspuras

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Title Annotation: | Research Article |
---|---|

Author: | Katona, Tamas Janos |

Publication: | Science and Technology of Nuclear Installations |

Date: | Jan 1, 2018 |

Words: | 5517 |

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