Effect Of Soil Structure Interaction On The Seismic .
Proceedings of the 2016 24th International Conference on Nuclear EngineeringICONE24June 26-30, 2016, Charlotte, North CarolinaICONE24-60714EFFECT OF SOIL STRUCTURE INTERACTION ON THE SEISMIC FRAGILITY OF ANUCLEAR REACTOR BUILDINGSamer El-Bahey, Ph.D, P.ESenior Seismic EngineerStevenson & AssociatesPhoenix, AZ, USAYasser Alzeni, Ph.DAssociate ProfessorAlexandria UniversityAlexandria, EgyptABSTRACTdifferent elevations. Computations taking into accountthe SSI effects are then performed using the subtractionmethod accounting for inertial interactions by usingfrequency dependent foundation impedance functionsdepicting the flexibility of the foundation as well as thedamping associated with foundation-soil interaction.Kinematic interactions are also taken into account in theSSI analysis by using frequency dependent transferfunctions relating the free-field motion to the motion thatwould occur at the foundation level as the presence offoundation elements in soil causes foundation motions todeviate from free-field motions as a result of groundmotion incoherence and foundation embedment.Comparing the results of the seismic responseanalyses, the effects of the SSI is quantified on theoverall seismic risk and the SSI margin is calculated. Afamily of realistic seismic fragility curves of the structureare then developed using common industry safety factors(capacity, ductility, response, and strength factors), andalso variability estimates for randomness and uncertainty.Realistic fragility estimates for structures directlyenhances the component fragilities from which enhancedvalues of Core Damage Frequency (CDF) and LargeEnergy Release Frequency (LERF) are quantified as afinal S-PRA deliverable.In recent years, the nuclear industry and the NuclearRegulatory Commission (NRC) have made a tremendouseffort to assess the safety of nuclear power plants asadvances in seismology have led to the perception thatthe potential earthquake hazard in the United States maybe higher than originally assumed. The SeismicProbabilistic Risk Assessment (S-PRA) is a systematicapproach used in the nuclear power plants in the U.S. torealistically quantify the seismic risk as by performing anS-PRA, the dominant contributors to seismic risk andcore damage can be identified. The assessment ofcomponent fragility is a crucial task in the S-PRA andbecause of the conservatism in the design processimposed by stringent codes and regulations for safetyrelated structures, structures and safety related items arecapable of withstanding earthquakes larger than the SafeShutdown Earthquake (SSE). One major aspect ofconservatism in the design is neglecting the effect ofSoil-Structure-Interaction (SSI), from which conservativeestimates of In-Structure Response Spectra (ISRS) arecalculated resulting in conservative seismic demands forplant equipment.In this paper, a typical Reactor Building is chosen fora case study by discretizing the building into a lumpedmass stick model (LMSM) taking into account modeleccentricities and concrete cracking for higher demand.The model is first analyzed for a fixed base conditionusing the free field ground motion imposed at thefoundation level from which ISRS are calculated atINTRODUCTIONSeismic Probabilistic Risk Assessment (S-PRA)studies have been performed in many of the US Nuclear PowerPlants over the last two decades. The S-PRAs were initiallyperformed to answer safety concerns in heavily populated areas,1Copyright 2016 by ASME
then evolved to satisfy the NRC’s request for informationregarding severe accident vulnerabilities in Generic Letter 8820, Supplement 4 [1]. The NRC encourages the use of PRA formaking risk informed decisions and has developed a RiskInformed Regulation Implementation Plan [2] and associatedregulatory guides. Most of the initial S-PRAs performed in theUS in the 1980s, contained a level of uncertainty arising fromthe seismic hazard and uncertainty in the fragilities of structure,systems and components (SSCs) which resulted in the spread ofthe level of uncertainty in the calculated Core DamageFrequency (CDF).Following the March 2011 Great Tahoku Earthquake andits catastrophic consequences on the Fukushima Daiichi NPP, itwas clear that relying on uncertainties in the design could leadto catastrophic consequences. From which, the NuclearRegulatory Commission (NRC) established a Near Term TaskForce (NTTF) to conduct a systematic review of NRCprocesses and regulations and to determine if the agency shouldmake additional improvements to its regulatory system. TheNTTF developed a set of recommendations intended to clarifyand strengthen the regulatory framework for protection againstnatural phenomena. Subsequently, the NRC issued a 50.54(f)letter on March 12, 2012 requesting information to assure thatthese recommendations are addressed by all U.S. nuclear powerplants. The 50.54(f) letter requests that licensees and holders ofconstruction permits under 10 CFR Part 50 reevaluate theseismic hazards at their sites against present-day NRCrequirements and guidance.Advances in characterizing earthquake source, travel path,and local site effects have led to the perception that thepotential free field earthquake hazard in the United States maybe higher than originally assumed. The effect of SSI is yet still amajor uncertainty in the seismic design of nuclear power plants.Direct Analysis: where the soil and superstructure areincluded in the same finite element model and analyzed as onesystem. This could be performed using multiple SSI softwarelike FLUSH by representing the soil as a continuum along withfoundation elements. The direct analysis method is rarely usedin practice due to the computational complexity.Substructure Approach: where the structure is initiallyanalyzed having a fixed-base, from which the dynamiccharacteristics of the structure are calculated including themodal frequencies, Eigen vectors, and Eigen values. Thekinematic effects are then addressed using frequency dependenttransfer functions relating the free-field motion to thefoundation input motion (FIM) taking into account the soilcolumn properties. The inertial interactions are then addressedby calculating frequency dependent impedance functions torepresent the stiffness and damping of the soil-foundationinterface depending on the soil column properties. Thesuperposition inherent in a substructure approach requires anassumption of linear soil and structure behavior, although inpractice this requirement is often followed only in anequivalent-linear sense.SEIMSIC FRAGILITY ANALYSIS METHODOLOGYThe seismic fragility of a structure or equipment is definedas the conditional probability of its failure at a given value ofacceleration (i.e., peak ground acceleration or peak spectralacceleration at different frequencies). The objective of afragility evaluation is to estimate the capacity of a givencomponent relative to a ground acceleration parameter. Themethodology for evaluating seismic fragilities of structures andequipment is documented in the PRA Procedures Guide [3] andis more specifically described for application to NPPs in theEPRI Methodology for Developing Seismic Fragilities [4].Fragility curves for an element corresponding to aparticular failure mode can be expressed in terms of the bestestimate of the median ground acceleration capacity, Am, andtwo random variables lognormally distributed with logarithmicstandard deviations for randomness, βR, and uncertainty, βU. Atany peak ground acceleration value, a, the fragility, Pf, at anynon-exceedance probability level, Q, can be represented by asubjective probability density function [5] and [6].SOIL-STRUCTURE INTERACTION OVERVIEWThe ground motion observed by any structure is differentthan the free field motion due to the following interactions: Inertial Interaction: Inertia developed in the structure dueto its own vibrations gives rise to base shear and moment,which generates displacements and rotations of the foundationrelative to the free-field due to the flexibility of the soilfoundation system. This added flexibility affects the buildingfrequency by shifting it towards the flexible range The systemoverall damping is also affected by the added displacements asenergy dissipation via radiation damping and hysteretic soildamping rises affecting the overall system damping. Kinematic Interaction: The presence of stiff foundationelements at or below the ground surface cause foundationmotions to deviate from free-field motions as a result of groundmotion incoherence, wave inclination, or foundationembedment.Commonly used methods for capturing the SSI effects areeither: ln(a / Am ) u 1 (Q) pf R (1)where Ф(.) is the standard Gaussian cumulative distributionfunction. Per the equation above, probability functions ofdiscrete values of non-exceedance probability level (Q) such as5%, 50%, 95% can be developed resulting in a family offragility curves for different failure modes of structures orequipment.Fragility can also be represented in terms of totalvariability, βC, as follows:2Copyright 2016 by ASME
1a P( A a ) ln( ) Am C(2) C R2 U2(3)Computing fragility curves for different confidence levelsrequires values of βR and βU. Using the composite variability,βC, value of 0.4, Ref. [9] proposed a methodology to estimate βRif βC is known:3(6) R C4From which, βU can be estimated using Eqn. (3).Alternatively, it has been suggested per Ref.’s [9] and [10].thatin lieu of determining βR and βU explicitly, it is usuallyconservative to assume that the sum (βR βU ) is 0.7–0.8.where;Seismic capacities of SSCs, could be represented by a HighConfidence, Low Probability of Failure (HCLPF). The HCLPFcapacity value is defined as the ground accelerationcorresponding to a 5% probability of failure (P f 0.05) on the95% confidence of non-exceedance curve calculated per Eqn. 1,or a 1% probability of failure (P f 0.01) on the mean fragilitycurve calculated per Eqn. 3. The HCLPF capacities equationscan then be rearranged into the following equations:AHCLPF Am e 1.645( R U )AHCLPF Am e 2.326( C )FRAGILITY PARAMETERS CALCULATIONIn estimating fragility parameters, it is convenient to usethe factor of safety method [6]. This method works in terms ofan intermediate random variable called the factor of safety. Thefactor of safety, F, on ground acceleration capacity above areference level earthquake specified for design; e.g., the safeshutdown earthquake level specified for design, ASSE, is definedbelow [11]:(4)(5)A FASSEHYBRID METHODThe fragility methodology of estimating the median, Am andβR and βU described requires the median factors of safety fordifferent variables affecting the response and capacity to beestimated as well as their logarithmic standard deviations. In theU.S. nuclear industry, seismic margin assessments have beendone for a number of nuclear power plants. Seismic margin isdefined as the HCLPF capacity of the plant safe shutdownsystems relative to the design basis or safe shutdown earthquake(DBE or SSE). The HCLPF capacity of the weakest linkcomponent in the safe shutdown path is considered the plantlevel HCLPF capacity. The HCLPF capacities are calculatedusing a deterministic procedure called ConservativeDeterministic Failure Margin (CDFM) method which isextensively described in Ref. [7]. In order to simplify theseismic PRA, a hybrid method is suggested in Ref.’s [4] and [8].The main feature of this method is the development of seismicfragility using the HCLPF capacity. First, the HCLPF capacityof the component is determined using the CDFM method. Next,the logarithmic standard deviation, βC, is estimated usingprocedures described in Ref. [4]. For structures, βC typicallyranges from 0.3 to 0.5 with a recommended value of 0.4 for aconservative estimate [4]. The median capacity is calculatedusing Eqn. (5) and an approximate mean fragility curve for thecomponent is thereby obtained. Reference [4] furtherrecommends that this approximate fragility method initially beused for each component in the systems analysis to identify thedominant contributors to the seismic risk (e.g., core damagefrequency). For the few components that dominate the seismicrisk, more accurate fragility parameter values should bedeveloped and a new quantification done to obtain a moreaccurate mean core damage frequency and to confirm that thedominant contributors have not changed.(7)where; A is the actual ground motion capacity. Forstructures, the factor of safety is typically modeled as theproduct of three random variables:F FS Fµ FSR(8)where; The strength factor, FS , represents the ratio ofultimate to the stress calculated for ASSE. The inelastic energyabsorption factor (ductility factor), Fµ, accounts for the fact thatan earthquake represents a limited energy source and manystructures or equipment items are capable of absorbingsubstantial amounts of energy beyond yield without loss-offunction. The structure response factor, FSR, is based onrecognition that in the design analyses, structural response wascomputed using specific deterministic response parameters forthe structure.The structure response factor, FSR, is modeled as a productof factors influencing the response variability as follows:FSR FSA FGMI F FM FMC FEC FSSI(9)where; FSA, is the spectral shape factor, FGMI, is the groundmotion incoherence factor, Fδ, is the damping factor, FM, is themodeling factor, FMC, is the mode combination factor, FEC, isthe earthquake component factor, and FSSI, is the soil-structureinteraction factor.Depending on the analysis procedure, many of these factorsare directly accounted for in the analysis. Generic data are alsoavailable in literature for these factors if not taken into accountby direct analysis [5] and [6].3Copyright 2016 by ASME
REACTOR BUILDINGThe chosen Reactor Building is a Seismic Category Istructure consisting of two basic parts: the containment shell(CS) and internal structure (IS). The Reactor Building isdesigned to be structurally independent of any other buildingwith a minimum 3 inch isolation gap. Additionally, the shell andinternal structure are designed to be structurally independent ofeach other however supported on a common base mat.The containment shell consists of a 140 feet (insidediameter) right cylindrical wall 4 feet in thickness closed on topby a hemispherical dome 3 feet in thickness. The wall, dome,and internal structures are supported on a circular base slab 10feet in thickness with a central cavity and instrumentationtunnel. The containment shell is constructed of concrete andpre-stressed by post-tensioned tendons in the cylindrical walland dome. The base slab is constructed of conventionallyreinforced concrete. The interior face of the containment waslined with 1/4" thick steel plates welded to form a leak-tightbarrier.The Internal Structure includes the following majorcomponents: Primary shield wall and reactor cavity, Secondaryshield walls, Refueling canal walls, Operating and intermediatefloors, Equipment supports (including the reactor, steamgenerators, reactor coolant pumps, pressurizer, and polar crane),Service platforms, Simplified head assembly with Reactormissile shield, Polar crane support system.Shield structures are constructed of reinforced concrete.Floors are constructed of reinforced concrete or steel grating,both on structural steel framing. Support is provided by thewalls of the refueling pool, the secondary shield walls, and thereactor building shell, which allows for differential movementbetween the shell and internal structure. The Refueling canalwalls are constructed of reinforced concrete at a minimum 4feet in thickness and lined with 1/4" stainless steel plateswelded to supporting beams.The internal structures are isolated from the shell by meansof an isolation gap to minimize interaction. Where connectionsare used to vertically support structural steel floor framing ofthe internal structure to the shell, independent horizontalmovement is allowed.North American Rift System (CNARS). At least four MMI VIIearthquakes have been associated with the Nemaha Uplift(Manhattan, 1867; Eastern Nebraska, 1877; Manhattan, 1906;Tecumseh, 1935).SITE-SPECIFIC GROUND MOTIONIn accordance with the 50.54(f) letter and following theguidance in the SPID [12], a probabilistic seismic hazardanalysis (PSHA) was completed in a separate effort using therecently developed Central and Eastern United States SeismicSource Characterization (CEUS-SSC) for Nuclear Facilities(CEUS-SSC, 2012) together with the updated EPRI GroundMotion Model (GMM) for the CEUS [13]. For the PSHA, alower-bound moment magnitude of 5.0 was used, as specified inthe 50.54(t) letter. Information pertaining to the HazardConsistent Strain-Compatible Properties for upper bound, UB,best estimate, BE, and lower bound, LB, soil cases are obtainedfrom the PSHA and used herein.The site-specific ground motion considered herein is basedon the new 100,000 year return period earthquake UHRSdeveloped as part of the PSHA effort. Artificial time historiescorresponding to the UHRS are generated herein using theStevenson and Associates SpectraSA software using randomseeds for two horizontal and one vertical time histories at 5%damping and shown in Figure 1. Comparison between theUHRS and the response spectrum generated from the artificialtime histories are presented in Figure 2. The fit and envelopingrequirements of Ref. [14] Section 3.7.1 Option 1 Approach 2are applied. This is not specifically required for an S-PRA butserves to ensure resulting time histories are suitable without anydeficiencies of power across the frequency range of interest.SOIL PROPERTIESThe site PSHA gives the best estimation (median) of thevalues of the relevant large strain soil properties, together withlower bound values and upper bound values at 10-5 UHRS. Thedata obtained from the PSHA and that given by the plant USARreport are used to build the soil profile at the location of theReactor Building.The soil profile is modeled up to a depth of 259 ft. where ahard rock layer (dense limestone) is present. A sensitivity studywas carried considering depth up to 500 ft, it was found thatconsidering layers below depth of 259 ft (dense limestone, shaleand sand stone) does not have a significant effect on theresponse of the structure. Accordingly the depth of the soilprofile for the three soil cases was taken to be 259 ft.SITE CONDITIONS AND SEISMISITYThe chosen site is located in an area with surface bedrockconsisting of alternating layers of Pennsylvanian age shales,limestones, sandstones, and a few thin coal seams. Residualsoils ranging in thickness from 0 to 16 feet have been developedon the Pennsylvanian strata. Quaternary alluvium, whichreaches a thickness of approximately 25 feet, is present in thetributary valleys, and scattered Tertiary age deposits of clayeygravel cap some of the higher hills in the site area.The chosen site is located in a seismically stable region ofthe central United States. The nearest shocks have hadintensities no greater than Modified Mercalli Intensity (MMI)III. The major zone of seismicity in the region surrounding thesite is associated with the Nemaha Uplift and adjacent Central4Copyright 2016 by ASME
Figure 1.Figure 2.Artificial Time Histories Corresponding to the UHRSComparison between the UHRS and the Response Spectrum Generated From the Artificial Time HistoriesVPub VsublThe Poisson’s ratio was calculated based on the shear wavevelocities values for BE, LB, and UB and the compressionwave velocities from the USAR. The top of the soil profile is atthe grade level, and soil properties were calculated as follows:The low strain Poisson’s ratio, νl, that is the same for BE,LB, and UB, is calculated based on values of the best estimateshear wave velocity at low strain, Vsbel, and the compressionwave velocity based on low strain, Vpbe , as follows:2 l 22 l 12 beh V1 2 sbeh V pbe V2 2 sbel V pbe uph V 1 2 subh V pub 2 Vsubh 2 2 V pub (10) 2 (13)2Using low strain shear LB and UB velocity values, thestrain independent upper, Vpub, and lower bounds, Vplb, forcompression wave velocities were calculated as follows:VPlb Vslbl(12)High strain Poisson’s ratios, νbeh, νubh, and νlbh, for BE, UB,and LB can then be calculated using high strain shear wavevelocities respectively as follows:2 V 1 2 sbel V pbe l 2 Vsbel 2 2 V pbe 2 l 22 l 1(14)(11)5Copyright 2016 by ASME
stiffness parameters for these elements were incorporated perthe guidance of ASCE 4-13 Table 3-1 [15]2 lbh V 1 2 slbh V plb 2 Vslbh 2 2 V plb (15)High strain soil properties for the best estimate, soil case ispresented in Table 1.Table 1.LayerThickness (ft)555555666664666318181818181818181812Soil Properties, Best Estimate, used in 270.0047270.0047270.004851Shear 91Figure 3. Reactor Building Fixed Base LumpedMass Stick ModelCONCRETE CRACKINGCracking assessment was performed on the CS and the ISto determine whether the major concrete elements crack underthe 1E-5 UHRS loading from which adjustments to buildingstiffness are necessary to obtain realistic building responses.The review level cracking at each floor was determined byscaling the design basis shear stresses and comparing to thecracking threshold of 3 fc/ per ASCE 4-13 [15]. Significantcracking below El. 2051’ in the East-West direction was found,from which stiffness adjustments were applied to bothhorizontal directions as the shell is cylindrical by using aneffective shear area and an effective area moment of inertia ofelements to be equal to 50% of their nominal values.STRUCTURAL MODEL DESCRITIZATIONThe Reactor Building is composed of four structures: theNuclear Steam Supply System (NSSS), the Internal Structure(IS), Reactor Vessel (RV), and the Containment Shell (CS).These four structures share the same foundation; however, theCS is considered as an independent structure, whereas theNSSS and RV are coupled with the IS.A fixed base lumped mass stick model was constructedusing GT-STUDL software as shown in Figure 3 for one planeof symmetry using beams representing the containment wallsabove the ground surface as well as the internal walls, reactorinternals, and floors. Spring elements with displacement androtational stiffnesses were also used to model the lateralsupports for the reactor vessel and the steam generator.Concrete stick elements were anticipated to be significantlycracked at the review level earthquake (RLE). Reductions inSSI ANALYSISThe EKSSI computer programs used herein for SSIanalysis were developed by Professor Eduardo Kausel of theMassachusetts Institute of Technology (MIT), and verified byStevenson and Associates (S&A). The EKSSI software packageincludes multiple modules. The following two modules wereused for the current analysis. The SUPELM program modulecomputes the frequency-dependent dynamic impedance of the6Copyright 2016 by ASME
24th26th34th36.1138.8946.33Horizontal Y Direction4.2511.818.6532.4436.1639.32Vertical . The foundation is assumed to be rigid andcylindrical in shape, which is reasonable. SUPELM can alsocompute transfer functions allowing for the determination oftime histories at the bottom of the foundation using theSUPELM KININT module. The EKSSI program moduleprovides the frequency domain solution, including SSI effects,to a dynamically-loaded structure that is supported on compliantsoil. The EKSSI program performs the SSI analysis bycombining the building model and the foundation impedancematrix, subjecting the combined model to input accelerationtime histories, and determining the response at required nodes.Fixed-base modal properties for the Reactor Building andthe Internal Structure are calculated using GT-STRUDLsoftware. The UHRS time histories applicable to the free fieldsurface are calculated using SPECTRASA software.Impedance functions for the substrata are calculated usingSUPELM. The transfer functions are used by the KININTmodule to generate time histories at the foundation bottom.The structural model and the foundation impedancefunctions are combined in EKSSI to form the soil-structureinteraction model. The models are then analyzed in EKSSI usingthe input time histories. Resultant response time histories arecalculated separately in the X, Y, and Z directions at all levelsof interest. Structural inherent damping was considered at 5%accounting for cracked pre-stressed containment wall.Figure 4 shows a comparison between the foundation baseISRS resulting from the SSI and the FB analyses and thehorizontal UHRS input. It can be seen that the UHRS inputexactly matches the FB analysis ISRS as expected. However, asignificant reduction is observed in the high frequency regiondue to the SSI effect. No significant effect was observed at thelow frequency region below 3 Hz. This is due to that the seismicinput has a high frequency content above 3Hz as shown in thepower amplitude function in Figure 5. A ZPA of 0.363g isobserved for the envelope SSI ISRS compared to 0.6g for theFB ISRS.SEISMIC RESPONSE ANALYSISTwo analyses are conducted on the finite elements model,namely SSI and Fixed-base analyses. The SSI analysis examinesthe soil-structure system using the substructure method andcomputes the floor response spectra associated with the SSIeffects at various elevations of the structure. The fixed-basecondition analyzes the same model but neglects the SSI effects.The in-structure response spectra outputs of these two analysesare compared and used to calculate the family of fragility curvesfor both cases from which the effect of the SSI could bequantified.Structural inherent damping was considered at 5% takinginto account the non-linear effects for cracked pre-stressedcontainment wall.The vibration properties of the model are summarized inTable 2 for the two horizontal and the vertical directions. Thefundamental frequency of the CS was observed at the lowfrequency range at 4.25Hz, however the fundamental frequencyof the IS was observed at the high frequency range at 15.83 Hz.Figure 4.Comparison between the Foundation BaseSSI ISRS , FB , and The Horizontal UHRS InputTable 17.7Vibration Properties of the ModelFrequencyMass Contribution(Hz)(%)Horizontal X Direction4.2527.311.87.215.831131.936.67Copyright 2016 by ASME
Figure 5.Figure 7.Fourier Amplitude of the Ground MotionSignificant ZPA reductions are expected for floors withhigher fundamental frequencies mainly in the IS, however lesssignificant benefit from the SSI is expected in floors with lowfundamental frequencies as in the CS. Figure 6 shows the Xdirection ISRS comparison for the top of CS floor at elevation2206’-6”, and Figure 7 shows the ISRS comparison for the topof IS floor at elevation 2083’-6”.Horizontal Direction Comparison betweenSSI and FB at top of IS at Elev. 2083’-6”Figure 8 and Figure 9 shows plots depicting the modelnodes and the associated ZPA for both the CS and the ISrespectively, a representation of the FSSI is also represented inthe plots as:FSSI Figure 6.Horizontal Direction Comparison betweenSSI and FB at top of CS at Elev. 2206’-6”Figure 8.8ZPAFBZPASSI(16)Containment Shell Nodal ZPA’scomparisonCopyright 2016 by ASME
An average quantification of the FSSI factor can becalculated assuming all other factors are not changed betweenthe two cases as: AHCLPF FBFSSI A HCLPF SSIFigure 9. (17)An average value of FSSI 1.6 was calculated, this is in lieuwith the range of median values observed for the SSI effect inliterature [5] and [6].The overall fragility curves are computed and plotted forfive confidence levels and a mean fragility curve in. Figure 10and Figure 11 for SSI and Fixed base analysis respectively.Median acceleration values and HCLPF values are presented inTable 3 for the fixed base and the SSI fragility analyses.Internal Structure Nodal ZPA’scomparisonTable 3.AccelerationAHCLPF Am A95 A84 A16 A05 It can be seen that the upper portions of the CS exhibits theleast benefit from the SSI with a minimum FSSI factor of 1.26observed at model point 2, this is due to the low fundamentalfrequency compared to the high frequency content of theseismic input. The maximum FSSI factor observed was at the topof the IS and equal to 4.62, the steam generator also exhibitsmajor SSI benefit as its fundamental frequency is also in therigid range. Median Acceleration Values and HCLPFβC 0.4 βR 0.3Fixed Base0.47g1.18g0.77g0.91g1.53g1.81gβU 0.26SSI0.74g1.87g1.22g1.44g2.43g2.87gIn order to illustrate the effects of SSI on the total fragilitycurves, fixed-base fragility curves are compared to the SSIfragility curves. Figure 12 compares the mean and 50%confidence level fragility curves of SSI with those of the fixedbase condition.FRAGILITY ANALYSISEvaluation of the Reactor Building design basiscalculations revealed that the foundation bearing pressure is thecritical failure mode with the least seismic design margin. TheCDFM method is adopted h
regulatory guides. Most of the initial S-PRAs performed in the . US in the 1980s, contained a level of uncertainty arising from . the seismic hazard and uncertainty in the frag. ilities of structure, systems and components (SSCs) which resulted in the spread of . the level of unc
3 Objectives of Soil Mechanics To perform the Engineering soil surveys. To develop rational soil sampling devices and soil sampling methods. To develop suitable soil testing devices and soil testing methods. To collect and classify soils and their physical properties on the basis of fundamental knowledge of soil mechanics. To investigate the physical properties of soil and
practice to ignore soil structure interaction (SSI) effects, simply by treating structures as if they are rigidly based, regardless of the soil condition. However, to evaluate the seismic response of a structure at a given site the dynamic properties of the combined soil
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