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Unitized concept for earthquake-resistant nuclear power plants
NUCLEAR I.NGINEERING AND DESIGN 21 119721406-420. NORTIt-IIOLLAND PUBLIStIING (7OMPANY
UNITIZED
CONCEPT FOR
EARTHQUAKE-RESISTANT
NUCLEAR
POWER PLANTS
J. F1NKE and M.S. LIN Kaiser Engineers, Oakland, CaliJbrnia 94604, USA
Received 29 October 1971
This paper discusses a unitized concept for an earthquake-resistant nuclear power plant which can withstand major earthquake shaking and fault slips without releasing radioactive material into the atmosphere. A 1000 MWe pressurized water reactor power plant of recent design is adapted to a unitized concept, and cost studies are made for the incremental cost. 1. Introduction The prevalence of earthquakes in the United States and the increasing demand for nuclear power plants lead to the possibility that within a decade or two, one or more nuclear power plants will be subjected to a strong earthquake. This study investigates the feasibility and comparative costs of a unitized concept for earthquake resistant nuclear power plants. The unitized concept permits nuclear power plants to withstand major seismic events, which may cause a ground displacement of up to six feet and ground acceleration of up to 1.0 g. Even if such seismic events should combine with a loss-ofcoolant accident (LOCA) resulting from a primary sys tern rupture, a public hazard would not be created beyond that acceptable by AEC standards. A set of seismic events corresponding to the proof earthquake loading for Uniform Building Code (UBC) zones I, I1, and 11I, has been postulated, and a commercial 1000 MWe pressurized water reactor power plant of recent design [1] at seismic zone 1 is modified to Kaiser Engineers' unitized plant concept to withstand these seismic events. The modifications to this conventionally designed reactor plant, which allow it to withstand the postulated seismic events considered in this study, were principally in the area of the reactor containment and auxiliary structures, and provision for a self-sustaining safety system. A lumped-mass modal analysis [2 4] was perfor-
med to define the seismic response forces for design of the unitized structure and its equipment anchors. The average-acceleration-spectrum curves for the El Centro, California, 1940 earthquake were scaled up to the magnitudes of the postulated maximum free field disturbance. A finite element analysis [5, 6] was performed for investigation of secondary stress, stress concentrations, and structure-foundation interaction. The unitized plant was designed to minimize the dynamic effects of the s t r u c t u r e - f o u n d a t i o n interaction; however, the analytical methods used in this design analysis could be modified to include the effects of s t r u c t u r e - f o u n d a t i o n interaction [7]. The methods used in this design analysis are standard met hods and are not repeated in this paper. Two types of structures: one of reinforced concrete and the other of partial prestressed concrete, on three types of sites (artificial off-shore island, alluvium site, rock site) have been considered for cost study. Discussions on the structural features, faulting effects and foundation-structure interaction, and dynamic effects and failure mechanism of the unitized plant are presented in this paper.
2. Unitized concept The unitized concept envisions placing the reactor and all critical equipment and facilities for safe shut-
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
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407
Y FORCE :)9,081 K
MASS 13,461 K
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10,973 K
15,090 K
I 9,B78 K
13,61 I K
23,493 K
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30,500 K
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~ t~ I
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SEISMIC RESPONSE FORCES
Fig. 1. The unitized concept for a typical 1000 MWe plant. down (class 1 structures) of the reactor on a single rigid foundation to form an integral structure capable of withstanding extreme seismic events which includes a sizable earth faulting under the unitized plant. Fig. 1 illustrates the unitized concept for a typical 1000 MWe plant. The plant is separated into three distinct areas, i.e., containment vessel, peripheral structure and foundation mat, within a circular concrete structure 215 ft high by 230 ft in diameter. The central containment vessel, which has an airtight liner, has an inside diameter of 135 ft and contains the reactor, reactor coolant system, steam generators, and manipulator crane. The vessel's ventilation system maintains a normal operating environment of 120 ° F at atmospheric pressure. The peripheral structure, contains all the support equipment and safety related systems of the reactor. Here are housed the reactor control and protection system, as well as the emergency diesel generators and diesel fuel storage tanks with a combined capacity of 100 000 gallons. Other equipment arranged on three floors of the peripheral structure includes the primary water storage tanks (150 000 gallons), decay heat removal system, radiation monitoring sys-
tern, process instrumentation and controls, chemical and volume control systems, emergency core cooling systems, waste holdup and disposal system, spent fuel handling and storage area, and the plant storage and maintenance shops. The rigid foundation mat, some 30 ft deep and of the same diameter as the peripheral structure, is designed primarily for support of a class I structure under earth faulting conditions, although it also accommodates storage for refueling water (300 000 gallons) and condensate water (1 200 000 gallons). The main feature of the unitized concept is that the power plant is completely self-supporting for orderly prevention of nuclear excursions, and safe containment of any radioactive material resulting from the most unfavorable conditions which combines primary coolant system rupture with severance of normal power supply, service water and secondary coolant piping due to earth faulting. In addition to the safety systems provided in the reference plant, the unitized plant includes additional safety provisions of special equipment supports required to accommodate the postulated extreme seismic events and self-supporting safety systems.
408
J. Finke and MS. Lin, Earthquake-resistant nuclear power plants
3. Structural design considerations 3. I. Design basis eartquakes This design study is based on the requirements that the unitized plant must be capable of stopping the chain reaction, maintaining the integrity of the outer containment vessel, and providing continued operation of the emergency cooling system, including required emergency power supply, its fuel supply, and power lines. Each of the above requirements is considered with respect to three seismic events: 1.1 -ft displacement in any direction and 0.3-g maximum horizontal ground acceleration. 2.3-ft displacement in any direction and 0.6-g maximum horizontal ground acceleration. 3.6-ft displacement in any direction and 1.0-g maxinmm horizontal ground acceleration. In considering each of these events, a vertical component of two-thirds the horizontal acceleration is assumed to accompany the horizontal forces; the vibration spectrum is assumed to be a typical one for large motion earthquakes, such as Hausner's average spectrum o f the 1940 El Centro earthquake scaled in amplitude to provide the specified maximum ground acceleration. The stipulated seismic events are hypothetical extreme conditions and are considered proof-earthquake loading for UBC zones I, II and III, respectively, and the structures are required to withstand these loading only once in their service lifetime. Consequently, the stresses in the materials at these high levels of loading are allowed to approach the yield strength o f the materials, these values being above typical design code limits. Corresponding to each of the stipulated three proof earthquakes in this study is an earthquake of lower magnitude, which structures are capable of withstanding when combined with a LOCA and remain within range of normal allowable code stress limits. This loading is referred to as a design earthquake, and its magnitude is normally set by design criteria at a value which reflects the seismic history of a given selected site. No appreciable structural damage is to be allowed at this level of loading, and no long term disruption of operation is to be expected. The proof-earthquake approach to the design, therefore assumes an extreme hypothetical maximum
Table l l.oad parameters for contaimnent vessel Dead load
As established by design
Live load
As based on area usage
Operating thermal
120° F
Operating pressure
0 psig
Test pressure
LOCA pressure X 1.15 = 54 psig
LOCA pressure
47 psig
LOCA temperature
290°F
Proof load acceleration
0.3 g horizontal - 0.2 g vertical 0.6 g horizontal - 0.4 g vertical 1.0 g horizontal - 0.67 g vertical
Proof load horizontal faulting Ground displacement: 1 ft, 3 ft, 6 ft Proof load vertical faulting
Ground displacement: 1 ft, 3 ft, 6ft
Tsunami
50-foot run up aoove mean level at a beach, with site assumed at an elevation 20 feet above sea level.
loading case. This affords the design a margin of strength over a design earthquake, which considers only an earthquake that could reasonably be expected. This is analogous to applying a higher factor of safety to allowable stresses when designing for loads resulting from a specified design earthquake. 3.2. Load and site conditions Design of the containment vessel is based on the load parameters shown in table 1. Table 2 prese.nts the load combinations with the corresponding allowable principal stresses for both the containment vessel and foundation structure. Load combinations for the peripheral structure are given in table 3. Three types of sites, each with homogeneous soil material, were considered in this study: an artificial offshore island, an alluvium site, and a rock site. For structural design of the reactor plant it was assumed that the soil charecteristics for the artificial island would be similar to those of alluvium, a highly con-
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
409
Table 2 Load combinations and allowable stresses for containment vessel and foundation structure. Allowable stresses Load case no.
Load combination
Concrete
Reinforcing steel
Prestressing steel
Testing dead + live loads + test pressure
0.45 fc
0.67 Jy
0.6 is' or 0.8 t~,
equivalent AC1 318
equivalent ACI 318
equivalent ACI 318
0.60 )'c
0.67 fy
0.6 f~ or 0.8fy
0.76 fc
0.9 jy
0.6 f s or 0.S f y
0.76 )'c
0.9 fy
0.6 .fs' or 0.8 fy
equivalent ACI 318
equivalent ACI 318
equivalent AC1318
Normal operation dead + live loads + operating pressure + steady state thermal + wind
, Normal operation + design earthquake 0.6 g proof load earthquake + LOCA dead + live loads + LOCA pressure + LOCA thermal + 0.6 g proof acceleration + proof faulting 1.0 g proof load earthquake + LOCA dead + live loads + LOCA pressure + LOCA thermal + 1.0 g proof acceleration + proof faulting Tsunami dead + live loads + operating pressure + Tsunami
solidated gravelly sand. The rock site is representative of a m o u n t a i n o u s , coastal area. It is also assumed that all sites are located in a zone o f high seismicity, similar to that found in the coastal regions o f California where the postulated design seismic loading w o u l d most likely occur. All sites, however, are located outside an area where landslides occur. The shape and p r o p o r t i o n o f the f o u n d a t i o n structure are such that usual allowable soil bearing pressure criteria need not be a design consideration. Soil failure is precluded because o f the large area o f soil con-
finement under the structure. The chief p r o b l e m is with earth faulting, and a c o m p l e t e description of h o w the soil and structure behave under these conditions is given in a later section o f this paper.
4. Structural design characteristics Two design schemes were investigated for this study: conventionally reinforced concrete and partially prestressed concrete. Designs are conceptual
410
J. Finke and M.S, Lin, Earthquake-resistant nuclear power plants
Table 3 Load combinations and allowable stresses for peripheral structure, Load case no. Load combination Load factor 1
testing
ACI 318
2
normal operation dead + live loads
ACI 318
normal operation + design earthquake
ACI 318
normal operation + 0.6 g proof load earthquake
1.0
normal operation + 1.0 g proof load earthquake
1.0
Tsunami
ACI 318
3
6
only and no attempt was made at optimization; schemes were investigated to establish feasibility and approximate estimates of cost. Concrete was selected as the primary structural element for the containment vessel; it is also used in the reference plant. Construction materials of various elements of the unitized structure are shown in fig. 2. Since design of reinforced concrete pressure vessels is not directly covered by any current design codes, such as ACI or ASME, allowable stresses for the containment vessel must be based on equivalent codes, stress levels, established precendent, good engineering practice, and theory substantiated by material testing.
containn]ent vessel wall. One scheme uses vertical prestressing, while the other uses conventional vertical reinforcing bars as principal reinforcement. Both schemes use hoop reinforcing bars to counteract pressure and shear stresses. The Test pressure loading case controls the design of the upper portion of the cylinder while seismic loading, combined with LOCA effects, controls the design in the lower elevations and the base. The wall was assumed to be diagonally cracked under seismic loading plus LOCA pressure with the shear loads being carried by the horizontal reinforcing. The validity of this assumption should be verified by the model test. Membrane theory was used to determine the primary stresses. A finite element analysis was used to determine combined primary and secondary stresses, stress concentrations, and soil reaction forces due to static axisymmetric loads. Reinforcing bars were used for secondary reinforcement for both the prestressed and conventionally reinforced schemes. 4.3. Foundation structure
Both reinforced and prestressed concrete concepts were considered for design of the foundation structure. Its design is based on a rigid concept, to minimize deflection of the superstructure and relative displacement between equipment anchors.
DOME-REINFORCEDCONCRETE
4.1. Dome
The dome is designed as a reinforced concrete pressure vessel with the test pressure loading case (54 psig) controlling the design. Allowable stresses for this loading were maintained within the equivalent ACI code, since this is a known loading that could be placed on the structure and would allow engineering analysis of cracking width and spacing. Concrete cracking must be kept at a minimum in order ro protect the integrity o f the liner plate.
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Fig. 2. Unitized plant cross section construction materials.
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
4.4. Interior structure The interior structure was not revised from the configuration used for the reference plant, except for the addition of more reinforcement penetrating the liner plate to the perimeter wall for seismic resistance, and the revision of the steam generator and pressur,izer supports to inhibit the dynamic forces while still allowing free expansion. In this study, individual pieces of equipment were not examined for seismic effects. General provisions, however, are made in design of the unitized plant for hardening of equipment anchors, tie-downs and locking devices for movable objects. 4.5. Peripheral structure The structural scheme for the peripheral structure uses reinforced concrete floors supported by the containment vessel walls and exterior columns. The floors are rigidly connected to the containment vessel cylinder wall to minimize the relative displacement between individual floors and equipment anchors. The containment cylinder wall is designed for the seismic inertia forces of the peripheral structure and the secondary moments due to the restraining of the floor system.
5. Potential faulting effects 5.1. Vertical faulting The most unusual feature of the class 1 design criteria, which sets it apart from criteria used in conventional seismic investigations, is the large ground displacement that must be accommodated without sustaining excessive stresses or deflections in either the plant structure or the equipment. The displacement criterion alone however is not sufficient to analyze the dynamic loading condition imposed on the structure. In the case of vertical faulting under the structure, the time history of the vertical displacement is required to determine the impact forces and deceleration experienced by the structure. For the purpose of establishing feasibility of design the vertical displacement is assumed to occur in one step 2 at an acceleration of + 5- g. Considering the massive proportions of the unitized structure and the anticipated stiffness of the surcharged foundation material (alluvium or rock),
411
no appreciable energy absorbing capability was credited to either the structure or the soil foundation. In order to limit the impact effects resulting from sudden vertical displacement, a circumferential belt of shock absorbing material is provided at the bottom of the foundation structure. The material proposed should have sufficient thickness and adequate elastoplastic characteristics to limit the impact effects to values less than the postfaulting loading condition assumed in design of the foundation structure (figs. 3, 4). Due to the immense stiffness of the foundation structure even minor vertical displacements (say greater than 6 in) of the foundation material can create the simple beam or cantilever configuration which governs design of the foundation structure. Consequently, all vertical displacements considered impose the same design forces within the foundation structure.
5.2. Horizontal faulting The phenomenon of horizontal faulting appears to have less influence on structural design of the unitized plant than does vertical faulting. The ground accelerations associated with this horizontal displacement can reasonable be expected not to exceed the proof-load earthquake levels stipulated in the design criteria. A fault occurring directly beneath the structure might tend to spin the entire structure. Spin effects were not investigated in this study because they are expected to be limited due to the confinement of the structure by the soil. In the unitized concept, a considerable portion of the foundation structure rests below finish grade, and large passive earth pressures can be exerted on the structure when horizontal faulting occurs. When embedded to a depth of 30 ft in an alluvium site, the foundation structure can withstand a maximum of 150 000 psf of this additional pressure, which is within safe limits for an alluvium site, since maximum pressure that can be transmitted by alluvium soil is less than this value. On the other hand, the foundation structure cannot be economically designed to resist the passive forces if enbedded in rock. This passive pressure may be avoided by providing an isolation space at least greater than the anticipated horizontal displacement. The surface of the excavation can be sealed by a compression-ring reinforced concrete retaining wall
~1 2
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Fig. 3. The earth faulting raises the left side of the structure, leaving the central protion of the structure no longer in contact witl7 the ground.
to control rock spalling. A uniform layer of sand, with a thickness equal to one half the anticipated ground displacement or minimum of 2 It, is provided underneath the foundation structure to act as a buffer in addition to the circumferential shock absobing ring. This sand layer serves to protect the foundation structure from highly concentrated rock reaction and ensures that the foundation structure and shock absorbing ring foundation as designed.
6. Projected soil-structure interaction The interaction between soil and the structure varies for different sites and seismic conditions, as discussed below. 6.1. A l l u v i u m a n d island site
Under non-seismic conditions the dead-plus-liveload soil pressure distribution may be expected to be rather uniform based on anticipated behavior of the subsoil. A uniform soil pressure of 8.5 ksf was calculated. A more precise soil pressure distribution
for a plant on alluvium or on an artificial island site may be readily calculated to any desired degree of accuracy consistant with the reliability in establishing soil properties. An iteration process of finite element analysis would be employed in such a calculation, using moduli of elasticity of the subsoil as an iteration parameter, During an earthquake, the most serious faulting may be expected to occur close to the edge of the foundation structure with the ground on one side (say, left side) moving upward relative to the ground on the other, accompanied by ground acceleration directed to the left. This condition is shown in fig. 3. In this case, the earth faulting raises the left side of structure, leaving the central portion of the structure no longer in contact with the ground. Support of the structure may be described as a simple support. At the onset of vertical ground faulting, soil pressure redistribution occurs by decreasing the pressure at the central portion of the foundation structure and increasing the pressure at opposite edges. As soon as the soil pressure at the edge of the foundation exceeds the yield strength of the shock absorbing ring
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
(say 60 000 p/ft2), the shock absorbing ring crushes and spreads the forces to a wider area over the foundation structure while absorbing shock energy. This crushing of the shock absorbing ring serves three purposes: it absorbs shock energy and reduces the vertical seismic acceleration and impact forces; it spreads the concentrated forces over a wider area to avoid a prohibitive shear stress problem on the foundation structure design; and it reduces the dynamic response amplification of the vertical acceleration due to the damping achieved by deformation of the shock absorbing ring. If the horizontal inertia force is greater than the resultant of ultimate passive soil pressure, the soil at the right side of the foundation structure fails by shear. The location of the fault line and the sense of the horizontal acceleration in fig. 3 are oriented for evaluation of the positive bending moment on the foundation structure. Should the fault line occur closer to the left edge of the structure, the subsoil on the left fails by shear as well as by crushing of the shock absorbing ring, and the simple support condition might not be
413
realized. Should the fault line occur closer to the center of the foundation structure, the span of the simple support is reduced, thus reducing the magnitude of positive moment. Reversal or cancellation of the horizontal acceleration also results in a reduction of the positive bending moment. 6.2. R o c k site The calculated foundation pressure underneath the structure during non-seismic conditions showed substantial fluctuations (from five times the average to a fraction of the average value), reflecting the flexibility of the foundation structure and effect of the large cutouts in the neutral zone. This foundation pressure distribution was determined by a preliminary finite element analysis in which the subsoil was considered to be a rigid rock foundation. A theoretically exact pressure distribution can also be obtained by an iteration process in which mechanical properties of the subsoil, shock absorbing ring and buffer zone of sand are considered the iteration parameters.
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Fig. 4. Major fault conditions associated with a rock site; a) simple support type, with no passive soil pressure; b) overhanging of the plant created by a drop of ground.
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
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There are two major fault conditions associated with a rock site. The simple support type, as shown in fig. 4 (a), is essentially identical to that shown in fig. 3, except the passive soil pressure does not exist. The sand layer in the center of the foundation structure serves as buffer zone to avoid prohibitive concentrated stress and also provides easy displacement to insure the structures' behavior as a simple beam. Although not considered in the analysis, this sand layer can potentially serve as a bond breaker to limit the magnitude of the horizontal acceleration transmitted to the structure. Fig. 4 (b) shows the overhanging situation created when the ground on one side of the fault line under the plant foundation drops. The structure is conservatively designed for an overhanging moment (negative moment) assuming the fault line occurs at a distance of one-third the diameter from the edge of the foundation, with the maximum horizontal acceleration directed to yield the maximum value of the negative moment. If the fault line is closer to the center of the structure, the overhanging configuration would not be possible unless the maximum horizontal acceleration acts in the reverse direction to counteract the overturning effects. In such a case, when the horizontal acceleration reverses, the structure overturns, and there is an enormous amount of potential and kinetic energy converted to impact energy. The shock absorbing ring is designed to absorb this energy by plastic deformation. Optimum material for the shock absorbing ring has yet to be determined and the credible acceleration accompanying the postulated maximum ground faulting must be carefully reviewed in the future.
7. Structural action and modes of faillure 7.1. Structural analysis As the cost study points out later, the partially prestressed concrete scheme is more economical than the conventionally reinforced concept. It is also more consistent with the rigid unitized design concept. Furthermore, cracking in vicinity of the storage tanks in the neutral zone of the foundation structure can be minimized through prestressing. Consequently, the discussion within this section is confined to prestressed concrete scheme.
Lumped-mass modal analysis was peiTormed to define the seismic response forces. The E1 Centro, California, 1940 earthquake average-acceleration spectrum curves [8, 9] were linerarly scaled upwards for the ground acceleration postulated in the design criteria. The modal idealization is shown in fig. 1. The axisymmetric structural analysis for static loading was performed using the finite element method employing IBM 360 digital computer. The total structure is idealized as an axisymmetrical finite element model containing 543 quadrilateral elements and 666 modal points. The five loading conditions shown in fig. 5 were investigated. Results of the finite element analysis indicate that the structure can withstand all five loading conditions without excessive stress or deformations. Also illustrated in fig. 5 are the critical concrete stresses in the containment vessel and foundation structure. Excepts at the juncture of the dome, no concrete stress exceeds 221 000 p/ft 2 (1 530 psi) in compression and 70 000 p/ft 2 (490 psi) in tension. Therefore, the secondary reinforcement in the containment vessel and the foundation structure is not governed by stress requirements but by load distribution and local crack distribution. The dome and peripheral structure are designed to withstand all design loads including a proof-load earthquake. Seismic forces are excluded from the five loading conditions studies in the finite element analysis. For extreme loading conditions combining seismic forces and LOCA pressure; stresses are allowed to approach yielding, which tend to relax the self-equilibrating secondary stress and stress concentrations. Therefore, as long as sufficient strength is provided in the structure for the primary forces on the structure under extreme loading, the integrity of the structure is assured. Since the mechanism of stress redistribution on the prestressed foundation structure is somewhat different from foundations for conventional structures, a detailed description of its pertinent features follows. 7.2. Forces at transfer o f hoop prestress The hoop prestress is designed to withstand either the test pressure or the LOCA pressure, combined with a positive or negative seismic moment. At the transfer prestress the resultant forces Tu and T1, of I the hoops correspond to the values of 0.6 f s , and
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
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they are almost balanced by the resultant compressive stress in the foundation structure across any vertical section cut through the center of the structure. The upper hoop prestress produces a twodimensional hydrostatic state of stress of approximately 100 000 p/ft 2 (700 psi) on the top flange, and about 40 000 to 100 000 p/ft 2 (270 to 700 psi) on the bottom flange of the foundation structure. The variation of the concrete prestress in the bottom flange reflects the irregular cutouts in that portion. 7. 3. Stress redistributions and failure mode due to positive moments
TUI: 112,850 K TLr : 233~000 K CI : TL.r+ TUI:345,SSOK 4" MULT : ] l T x IOGKI : 1.37M
t
TENSION B OlAGONAL
c Fig. 6. a) Foundation structure at (+M) max. b) failure by ÷M; c) foundation at (+M) ultimate.
As a result of ground faulting underneath the foundation structure, there is a possibility of forming a condition of the foundation structure analogous to that of a simply supported beam. This condition was shown earlier in fig. 3 for the alluvium site and fig. 4 (a) for the rock site. Due to the weight of the structure and seismic acceleration, a large positive moment is developed in the foundation structure. Although the magnitude of the positive moment is a function of the magnitude of the maximum ground acceleration, the relationship is not necessarily in direct proportion. Damping effects play an important role in determination of seismic response forces. In a reinforced concrete structure damping increases as a cracking increases and reduces the response forces in an exponential order. An increase in cracking can be anticipated under severe seismic and LOCA loadings, since stresses are allowed to approach yielding. Therefore, the use of higher damping factors is justified for greater magnitudes of ground acceleration. In the dynamic analysis, damping factors of 3% and 5% were used for the cases of 0.6 g and 1.0 g maximum accelerations ,respectively. The maximum positive moment was obtained by combining the maximum ground accelerations with the fault line located at the most critical location. When subject to this moment, and the consequent strain, the lower hoop prestress force, T1, increases from the value corresponding to effective prestress of ~-f~ = 160 000 psi to the value corresponding to 0.8 f~ = 192 000 psi, while the forces, Tu, in the upper hoops remain essentially the same. This condition is illustrated in fig. 6 (a). Compressive stress redistribution takes place on the foundation structure, and the
4 18
J. Finke and M.S. Lin. Earthquake-resistant nuclear power plants
top flange is stressed to 4 195 psi maximum, which is .t near the yield stress 0 . 8 5 0 / c = 4 250 psi. The compressive stress decreases linearly to zero toward the bottom, and may subject the b o t t o m fibers o f the foundation structure to some tensile cracking. The maximum concrete strain due to the maximum positive moment is E = 0.001. and although the b o t t o m of the foundation structure may crack, the mild steel liner plate of the storage tanks can safely stand this strain. The positive moment is counteracted by the internal moment through an upward shift of the resultant compression force across the entire cross section of the foundation structure. The ultimate positive moment capacity of the structure is evaluated assuming T 1 = TI', which is the resultant tensile forces of the hoop prestress stretched to f~ = 240 000 psi, the rein.. forcing steel in the foundation structure stressed to [y = 60 000 psi. The concrete stress block is idealized as rectangular at 0.85 f c stress. The magnitude of this ultimate positive m o m e n t is found to be 1.37 times the positive moment, which means that the foundation structure has 37% reserve strength beyond the most critical load combination in the design criteria. At this ultimate load condition it may be postulated that the b o t t o m flange experiences a strain, e = 0.003, and potentially may develop a single crack width of Wr -- 4 in., which would cause liner failure. This con-
TUI% 1691000t( TLI: 1471600K CII : 316,600K ¥' : Tua~.TLIb:II.SxlO6KI
dition is illustrated in fig. 6 (b). The cracking is gradual. however, and the hi-strength steel reinforcenrent wil distribute this crack into numerous small cracks on the lower portion of the foundation structure, as shown fig. 6 (c). As plastic deformation occurs on the top flange, numerous fine shear cracks appear on the top flange and adjacent containment cylinder wall. Also, due to the stress concentration sustained during earth faulting impact, the concrete protective cover over the reinforcement in the containment vessel and the top flange juncture may spall. With proper detailing of the joint reinforcement for ductility, the spalling of the concrete protective cover should not endanger the integrity of the structure. 7.4. Stress redistribution and failure m o d e due to negative m o m e n t s
The case of negative moment exists when ground faulting occurs underneath the foundation structure by a sudden drop of one side, creating a overhang. (shown earlier as fig. 4b). For this case, spalling of the concrete protective cover over the reinforcing steel is not anticipated, and the mechanism o f stress redistribution is just the reverse of the case for positive moment. The most serious negative moment occurs when the fault is centered under the foundation causing a temporary imbalance of the struc-
b
TUI
[
"~ PLASTICOEFORHATION 0.115f~ 'iAIUIILT-~'~
~
~.L
Fig. 7. a) Foundation structure at (-M) ult.; b)failure by -M.
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
ture. (This condition is illustrated in fig. 7 a). The ultimate negative moment capacity during this time, however, is also 1.37 times the maximum negative moment, which leaves the same margin of reserve strength in the design. Nevertheless, failure by negative moment may produce a larger tension crack on the top flange and the adjacent containment vessel wall, as shown in fig. 7 b. These cracks may only exist momentarily because in the next instant the structure tips to create a reversal of loading. If joint detailing provides for ductility in the juncture of the top flange and the containment vessel, the probability of tearing the containment liner plate is slight and the integrity of the unitized structure is reasonably assured.
419
Table 4 Class 1 structures construction cost comparison. Unitized plant Reference Description plant Foundation
Reinforced Partialprestressed concrete concrete 0.6g 1.0g 0.6g 1,0g
5.8
49.5
55.7 46.7
50.0
Containment 70.0
78.0
79.3
72.3
77.5
Peripheral structure
21.0
32.5
33.0
34.0
34.5
Subtotal
96.8
160.0
8. Cost studies
Excavation 3.2 total
2.2
Preliminary cost estimates were prepared to compare additional costs of the proposed unitized plant designed for high seismic loading and a conventional reactor plant designed for low or non-seismic conditions. The estimates are comparative only and do not include all elements of nuclear power plant costs; for example, the costs of the turbine generator plant and its structures and buildings, as well as the cost of the nuclear steam supply system, were excluded. Cost of the excluded items should not vary significantly between plants designed for areas of high seismic activity and those designed for conventional sites. All estimates, including those for the reference plant, were prepared assuming location on sites in southern California. Construction costs for structures and foundations are estimated for plants located on both alluvium and on rock. Cost a plant constructed on an artificial island is approximately the same as that estimated for a plant located on alluvium except for the added cost of transporting men, materials and equipment to the site. Estimates for the unitized plant are further broken down by earthquake magnitude and construction scheme (reinforced versus prestressed concrete). These estimates, summarized in table 4, represent the cost of structures and foundations relative to the cost of the reference plant, which is given as 100.00. The greatest increase in cost for the unitized concept
subtotal
168.0 153.0 162.0
Alluvium site 2.0
2.0
2.0
100.0 162.0 170.0 155.0 164.0
Rock site Excavation 7.4 total Total
104.0
9.4 169.0
9.4
9.4
9.4
177.0 162.0 171.0
is for the foundation structure. This is to be expected considering the magnitude of the loading resulting from earth faulting. The incremental cost difference of the foundation for various ground accelerations is small compared with the total plant cost, and the size of earth fault has no effect within the range of faults studied. Smaller cost increases result from high ground accelerations for the containment vessel and peripheral structure. The cost increase to employ the unitized concept for the reactor plant is estimated at $ 5 million to $ 10 million, an increase in overall plant costs of less than 5%. An estimate was also made of the direct cost of the decay heat removal system and special equipment supports required to accommodate the postulated extreme seismic events. These costs are summarized in table 5.
420
J. f i n k e and M.S. Lin, Earthquake-resistapzt nuclear power plants
Table 5 Unitized plant incremental equipment and support cost summary.
Description
0.6 g
1.0 g
Primary equipment supports
~ 150 000
~ 200 000
100 000
150 000
Other equipment supports Decay heat removal system (cooling tower) Subtotal
to $ 600 000 greater than in alluvium. For the unitized concept there is no apparent cost advantage in locating the plant on an artificial island. 5. Although this study reviewed only major elements o f the design to establish feasibility, the concept appears to offer a workable solution to problems associated with severe earthquakes.
Acknowledgement
400 000
500 000
650 000
850 000
9. Conclusions The major conclusions resulting from this study and development of a unitized reactor plant are: 1. It appears feasible that a reactor plant, meeting the stipulated LOCA and seismic requirements, can be designed and constructed using a unitized concept. 2. The 0.6.-g proof, 0.3-g design earthquake criterion appears reasonable for locating the plant in areas corresponding to UBC (Uniform Building Code) zone II. The 1.0-g proof, 0.5-g design earthquake criterion appears reasonable for locating the plant in an area of high seismicity corresponding to UBC zone III. The structure can be upgraded to suit higher magnitude design earthquakes at a small differential cost increase if dictated by site conditions. 3. Design of the foundation structure is governed by ground displacement of the p r o o f earthquake, and it remains essentially the same for all the vertical and horizontal displacements investigated. 4. Rough estimates indicate that the cost increase for a unitized structure over a conventional plant will be approximately $ 5 to $ 1 0 million. This is an increase in total facility cost o f less than 5%. The study also indicates that the cost of founding the structure in rock will be approximately $ 500 000
This study is part of a broad continuing research and development program on earthquake problems of nuclear reactors sponsored by the U.S. Atomic Energy Commission through the Oak Ridge National Laboratory. This particular study was performed under Subcontract No. 2963 with Union Carbide Corporation Nuclear Division, Oak Ridge, Tennessee; U.S. Atomic Energy Commission Contract No. W-7405- eng-26, Oak Ridge Operations Office.
References [1] Indian Point Nuclear Generating Unit No. 3 Preliminary Safety Analysis Report, Vol. 1, 2 and 3, Consolidated Edison Company of New York, Inc. [2] Blume, Newmark and Corning, Design of Multistory Reinforced Concrete Building for Earthquake Motion, Portland Cement Association, 1961. [3] Norris, Hansen, Holley, et al., Structural Design for l for Dynamic Loads, John Wiley and Sons (1959). [4] E.L. Wilson, Symbolic Matrix Interpretation System 1BM-7094 Computer Program, University of California (August 1963). [5] E.L. Wilson, Structural Analysis of Axisymmetric Solids, AIAA Journal, 3, 12 (1965). [6] O.C. Zienkiewicz and G.S. Holister, Stress Analysis, John Wiley and Sons, (1965). [7] C.A. Miller, and C.J. Costantino, Structure-Foundation Interaction of a Nuclear Power Plant With A Seismic Disturbance. Nuclear Engineering and Design 14 (1970) 332. [8] R.A. Eppley, Earthquake History of the United States, Pamphlet No. 41-1, U.S. Coast and Geodetic Survey (1960). [9] Nuclear Reactors and Earthquakes, TID-7024, Lockheed Aircraft Corporation and Holmes and Narver, Inc. for USAEC (1963).
UNITIZED
CONCEPT FOR
EARTHQUAKE-RESISTANT
NUCLEAR
POWER PLANTS
J. F1NKE and M.S. LIN Kaiser Engineers, Oakland, CaliJbrnia 94604, USA
Received 29 October 1971
This paper discusses a unitized concept for an earthquake-resistant nuclear power plant which can withstand major earthquake shaking and fault slips without releasing radioactive material into the atmosphere. A 1000 MWe pressurized water reactor power plant of recent design is adapted to a unitized concept, and cost studies are made for the incremental cost. 1. Introduction The prevalence of earthquakes in the United States and the increasing demand for nuclear power plants lead to the possibility that within a decade or two, one or more nuclear power plants will be subjected to a strong earthquake. This study investigates the feasibility and comparative costs of a unitized concept for earthquake resistant nuclear power plants. The unitized concept permits nuclear power plants to withstand major seismic events, which may cause a ground displacement of up to six feet and ground acceleration of up to 1.0 g. Even if such seismic events should combine with a loss-ofcoolant accident (LOCA) resulting from a primary sys tern rupture, a public hazard would not be created beyond that acceptable by AEC standards. A set of seismic events corresponding to the proof earthquake loading for Uniform Building Code (UBC) zones I, I1, and 11I, has been postulated, and a commercial 1000 MWe pressurized water reactor power plant of recent design [1] at seismic zone 1 is modified to Kaiser Engineers' unitized plant concept to withstand these seismic events. The modifications to this conventionally designed reactor plant, which allow it to withstand the postulated seismic events considered in this study, were principally in the area of the reactor containment and auxiliary structures, and provision for a self-sustaining safety system. A lumped-mass modal analysis [2 4] was perfor-
med to define the seismic response forces for design of the unitized structure and its equipment anchors. The average-acceleration-spectrum curves for the El Centro, California, 1940 earthquake were scaled up to the magnitudes of the postulated maximum free field disturbance. A finite element analysis [5, 6] was performed for investigation of secondary stress, stress concentrations, and structure-foundation interaction. The unitized plant was designed to minimize the dynamic effects of the s t r u c t u r e - f o u n d a t i o n interaction; however, the analytical methods used in this design analysis could be modified to include the effects of s t r u c t u r e - f o u n d a t i o n interaction [7]. The methods used in this design analysis are standard met hods and are not repeated in this paper. Two types of structures: one of reinforced concrete and the other of partial prestressed concrete, on three types of sites (artificial off-shore island, alluvium site, rock site) have been considered for cost study. Discussions on the structural features, faulting effects and foundation-structure interaction, and dynamic effects and failure mechanism of the unitized plant are presented in this paper.
2. Unitized concept The unitized concept envisions placing the reactor and all critical equipment and facilities for safe shut-
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
/
407
Y FORCE :)9,081 K
MASS 13,461 K
I$,BB2K
10,973 K
15,090 K
I 9,B78 K
13,61 I K
23,493 K
18,559.~K
50,4(;7 K
30,500 K
i61~000K
/
\ PRESTREBSINB CABLES
~ t~ I
BOTTEEBFTO LPA N B [ ~ ~
0.6G TM 3%DAMPING
TU
TL
T~
SEISMIC RESPONSE FORCES
Fig. 1. The unitized concept for a typical 1000 MWe plant. down (class 1 structures) of the reactor on a single rigid foundation to form an integral structure capable of withstanding extreme seismic events which includes a sizable earth faulting under the unitized plant. Fig. 1 illustrates the unitized concept for a typical 1000 MWe plant. The plant is separated into three distinct areas, i.e., containment vessel, peripheral structure and foundation mat, within a circular concrete structure 215 ft high by 230 ft in diameter. The central containment vessel, which has an airtight liner, has an inside diameter of 135 ft and contains the reactor, reactor coolant system, steam generators, and manipulator crane. The vessel's ventilation system maintains a normal operating environment of 120 ° F at atmospheric pressure. The peripheral structure, contains all the support equipment and safety related systems of the reactor. Here are housed the reactor control and protection system, as well as the emergency diesel generators and diesel fuel storage tanks with a combined capacity of 100 000 gallons. Other equipment arranged on three floors of the peripheral structure includes the primary water storage tanks (150 000 gallons), decay heat removal system, radiation monitoring sys-
tern, process instrumentation and controls, chemical and volume control systems, emergency core cooling systems, waste holdup and disposal system, spent fuel handling and storage area, and the plant storage and maintenance shops. The rigid foundation mat, some 30 ft deep and of the same diameter as the peripheral structure, is designed primarily for support of a class I structure under earth faulting conditions, although it also accommodates storage for refueling water (300 000 gallons) and condensate water (1 200 000 gallons). The main feature of the unitized concept is that the power plant is completely self-supporting for orderly prevention of nuclear excursions, and safe containment of any radioactive material resulting from the most unfavorable conditions which combines primary coolant system rupture with severance of normal power supply, service water and secondary coolant piping due to earth faulting. In addition to the safety systems provided in the reference plant, the unitized plant includes additional safety provisions of special equipment supports required to accommodate the postulated extreme seismic events and self-supporting safety systems.
408
J. Finke and MS. Lin, Earthquake-resistant nuclear power plants
3. Structural design considerations 3. I. Design basis eartquakes This design study is based on the requirements that the unitized plant must be capable of stopping the chain reaction, maintaining the integrity of the outer containment vessel, and providing continued operation of the emergency cooling system, including required emergency power supply, its fuel supply, and power lines. Each of the above requirements is considered with respect to three seismic events: 1.1 -ft displacement in any direction and 0.3-g maximum horizontal ground acceleration. 2.3-ft displacement in any direction and 0.6-g maximum horizontal ground acceleration. 3.6-ft displacement in any direction and 1.0-g maxinmm horizontal ground acceleration. In considering each of these events, a vertical component of two-thirds the horizontal acceleration is assumed to accompany the horizontal forces; the vibration spectrum is assumed to be a typical one for large motion earthquakes, such as Hausner's average spectrum o f the 1940 El Centro earthquake scaled in amplitude to provide the specified maximum ground acceleration. The stipulated seismic events are hypothetical extreme conditions and are considered proof-earthquake loading for UBC zones I, II and III, respectively, and the structures are required to withstand these loading only once in their service lifetime. Consequently, the stresses in the materials at these high levels of loading are allowed to approach the yield strength o f the materials, these values being above typical design code limits. Corresponding to each of the stipulated three proof earthquakes in this study is an earthquake of lower magnitude, which structures are capable of withstanding when combined with a LOCA and remain within range of normal allowable code stress limits. This loading is referred to as a design earthquake, and its magnitude is normally set by design criteria at a value which reflects the seismic history of a given selected site. No appreciable structural damage is to be allowed at this level of loading, and no long term disruption of operation is to be expected. The proof-earthquake approach to the design, therefore assumes an extreme hypothetical maximum
Table l l.oad parameters for contaimnent vessel Dead load
As established by design
Live load
As based on area usage
Operating thermal
120° F
Operating pressure
0 psig
Test pressure
LOCA pressure X 1.15 = 54 psig
LOCA pressure
47 psig
LOCA temperature
290°F
Proof load acceleration
0.3 g horizontal - 0.2 g vertical 0.6 g horizontal - 0.4 g vertical 1.0 g horizontal - 0.67 g vertical
Proof load horizontal faulting Ground displacement: 1 ft, 3 ft, 6 ft Proof load vertical faulting
Ground displacement: 1 ft, 3 ft, 6ft
Tsunami
50-foot run up aoove mean level at a beach, with site assumed at an elevation 20 feet above sea level.
loading case. This affords the design a margin of strength over a design earthquake, which considers only an earthquake that could reasonably be expected. This is analogous to applying a higher factor of safety to allowable stresses when designing for loads resulting from a specified design earthquake. 3.2. Load and site conditions Design of the containment vessel is based on the load parameters shown in table 1. Table 2 prese.nts the load combinations with the corresponding allowable principal stresses for both the containment vessel and foundation structure. Load combinations for the peripheral structure are given in table 3. Three types of sites, each with homogeneous soil material, were considered in this study: an artificial offshore island, an alluvium site, and a rock site. For structural design of the reactor plant it was assumed that the soil charecteristics for the artificial island would be similar to those of alluvium, a highly con-
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
409
Table 2 Load combinations and allowable stresses for containment vessel and foundation structure. Allowable stresses Load case no.
Load combination
Concrete
Reinforcing steel
Prestressing steel
Testing dead + live loads + test pressure
0.45 fc
0.67 Jy
0.6 is' or 0.8 t~,
equivalent AC1 318
equivalent ACI 318
equivalent ACI 318
0.60 )'c
0.67 fy
0.6 f~ or 0.8fy
0.76 fc
0.9 jy
0.6 f s or 0.S f y
0.76 )'c
0.9 fy
0.6 .fs' or 0.8 fy
equivalent ACI 318
equivalent ACI 318
equivalent AC1318
Normal operation dead + live loads + operating pressure + steady state thermal + wind
, Normal operation + design earthquake 0.6 g proof load earthquake + LOCA dead + live loads + LOCA pressure + LOCA thermal + 0.6 g proof acceleration + proof faulting 1.0 g proof load earthquake + LOCA dead + live loads + LOCA pressure + LOCA thermal + 1.0 g proof acceleration + proof faulting Tsunami dead + live loads + operating pressure + Tsunami
solidated gravelly sand. The rock site is representative of a m o u n t a i n o u s , coastal area. It is also assumed that all sites are located in a zone o f high seismicity, similar to that found in the coastal regions o f California where the postulated design seismic loading w o u l d most likely occur. All sites, however, are located outside an area where landslides occur. The shape and p r o p o r t i o n o f the f o u n d a t i o n structure are such that usual allowable soil bearing pressure criteria need not be a design consideration. Soil failure is precluded because o f the large area o f soil con-
finement under the structure. The chief p r o b l e m is with earth faulting, and a c o m p l e t e description of h o w the soil and structure behave under these conditions is given in a later section o f this paper.
4. Structural design characteristics Two design schemes were investigated for this study: conventionally reinforced concrete and partially prestressed concrete. Designs are conceptual
410
J. Finke and M.S, Lin, Earthquake-resistant nuclear power plants
Table 3 Load combinations and allowable stresses for peripheral structure, Load case no. Load combination Load factor 1
testing
ACI 318
2
normal operation dead + live loads
ACI 318
normal operation + design earthquake
ACI 318
normal operation + 0.6 g proof load earthquake
1.0
normal operation + 1.0 g proof load earthquake
1.0
Tsunami
ACI 318
3
6
only and no attempt was made at optimization; schemes were investigated to establish feasibility and approximate estimates of cost. Concrete was selected as the primary structural element for the containment vessel; it is also used in the reference plant. Construction materials of various elements of the unitized structure are shown in fig. 2. Since design of reinforced concrete pressure vessels is not directly covered by any current design codes, such as ACI or ASME, allowable stresses for the containment vessel must be based on equivalent codes, stress levels, established precendent, good engineering practice, and theory substantiated by material testing.
containn]ent vessel wall. One scheme uses vertical prestressing, while the other uses conventional vertical reinforcing bars as principal reinforcement. Both schemes use hoop reinforcing bars to counteract pressure and shear stresses. The Test pressure loading case controls the design of the upper portion of the cylinder while seismic loading, combined with LOCA effects, controls the design in the lower elevations and the base. The wall was assumed to be diagonally cracked under seismic loading plus LOCA pressure with the shear loads being carried by the horizontal reinforcing. The validity of this assumption should be verified by the model test. Membrane theory was used to determine the primary stresses. A finite element analysis was used to determine combined primary and secondary stresses, stress concentrations, and soil reaction forces due to static axisymmetric loads. Reinforcing bars were used for secondary reinforcement for both the prestressed and conventionally reinforced schemes. 4.3. Foundation structure
Both reinforced and prestressed concrete concepts were considered for design of the foundation structure. Its design is based on a rigid concept, to minimize deflection of the superstructure and relative displacement between equipment anchors.
DOME-REINFORCEDCONCRETE
4.1. Dome
The dome is designed as a reinforced concrete pressure vessel with the test pressure loading case (54 psig) controlling the design. Allowable stresses for this loading were maintained within the equivalent ACI code, since this is a known loading that could be placed on the structure and would allow engineering analysis of cracking width and spacing. Concrete cracking must be kept at a minimum in order ro protect the integrity o f the liner plate.
IL--III IL< _ II ~
-
III] 1-g°.72':
i ~,,~ i
OUNDATIOIIMATERIAL. RENIFOIICIEDCOIICRETE
~..~::~---D--
m~
Ek~RGyABSORBING COIIC~.TIE
4.2. Cylinder walls
Two preliminary designs were investigated for the
Fig. 2. Unitized plant cross section construction materials.
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
4.4. Interior structure The interior structure was not revised from the configuration used for the reference plant, except for the addition of more reinforcement penetrating the liner plate to the perimeter wall for seismic resistance, and the revision of the steam generator and pressur,izer supports to inhibit the dynamic forces while still allowing free expansion. In this study, individual pieces of equipment were not examined for seismic effects. General provisions, however, are made in design of the unitized plant for hardening of equipment anchors, tie-downs and locking devices for movable objects. 4.5. Peripheral structure The structural scheme for the peripheral structure uses reinforced concrete floors supported by the containment vessel walls and exterior columns. The floors are rigidly connected to the containment vessel cylinder wall to minimize the relative displacement between individual floors and equipment anchors. The containment cylinder wall is designed for the seismic inertia forces of the peripheral structure and the secondary moments due to the restraining of the floor system.
5. Potential faulting effects 5.1. Vertical faulting The most unusual feature of the class 1 design criteria, which sets it apart from criteria used in conventional seismic investigations, is the large ground displacement that must be accommodated without sustaining excessive stresses or deflections in either the plant structure or the equipment. The displacement criterion alone however is not sufficient to analyze the dynamic loading condition imposed on the structure. In the case of vertical faulting under the structure, the time history of the vertical displacement is required to determine the impact forces and deceleration experienced by the structure. For the purpose of establishing feasibility of design the vertical displacement is assumed to occur in one step 2 at an acceleration of + 5- g. Considering the massive proportions of the unitized structure and the anticipated stiffness of the surcharged foundation material (alluvium or rock),
411
no appreciable energy absorbing capability was credited to either the structure or the soil foundation. In order to limit the impact effects resulting from sudden vertical displacement, a circumferential belt of shock absorbing material is provided at the bottom of the foundation structure. The material proposed should have sufficient thickness and adequate elastoplastic characteristics to limit the impact effects to values less than the postfaulting loading condition assumed in design of the foundation structure (figs. 3, 4). Due to the immense stiffness of the foundation structure even minor vertical displacements (say greater than 6 in) of the foundation material can create the simple beam or cantilever configuration which governs design of the foundation structure. Consequently, all vertical displacements considered impose the same design forces within the foundation structure.
5.2. Horizontal faulting The phenomenon of horizontal faulting appears to have less influence on structural design of the unitized plant than does vertical faulting. The ground accelerations associated with this horizontal displacement can reasonable be expected not to exceed the proof-load earthquake levels stipulated in the design criteria. A fault occurring directly beneath the structure might tend to spin the entire structure. Spin effects were not investigated in this study because they are expected to be limited due to the confinement of the structure by the soil. In the unitized concept, a considerable portion of the foundation structure rests below finish grade, and large passive earth pressures can be exerted on the structure when horizontal faulting occurs. When embedded to a depth of 30 ft in an alluvium site, the foundation structure can withstand a maximum of 150 000 psf of this additional pressure, which is within safe limits for an alluvium site, since maximum pressure that can be transmitted by alluvium soil is less than this value. On the other hand, the foundation structure cannot be economically designed to resist the passive forces if enbedded in rock. This passive pressure may be avoided by providing an isolation space at least greater than the anticipated horizontal displacement. The surface of the excavation can be sealed by a compression-ring reinforced concrete retaining wall
~1 2
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
,
\
i
\ .
xx I lu--~ i l u unn~
SHOCK ABSORBING RING \
PLANE
60 KSF
ABSORBING
RL=gI.oOOK-~
M IHORIZONTAL X. GROUND kCCELERATION
.
RR
FAULT LINE
Fig. 3. The earth faulting raises the left side of the structure, leaving the central protion of the structure no longer in contact witl7 the ground.
to control rock spalling. A uniform layer of sand, with a thickness equal to one half the anticipated ground displacement or minimum of 2 It, is provided underneath the foundation structure to act as a buffer in addition to the circumferential shock absobing ring. This sand layer serves to protect the foundation structure from highly concentrated rock reaction and ensures that the foundation structure and shock absorbing ring foundation as designed.
6. Projected soil-structure interaction The interaction between soil and the structure varies for different sites and seismic conditions, as discussed below. 6.1. A l l u v i u m a n d island site
Under non-seismic conditions the dead-plus-liveload soil pressure distribution may be expected to be rather uniform based on anticipated behavior of the subsoil. A uniform soil pressure of 8.5 ksf was calculated. A more precise soil pressure distribution
for a plant on alluvium or on an artificial island site may be readily calculated to any desired degree of accuracy consistant with the reliability in establishing soil properties. An iteration process of finite element analysis would be employed in such a calculation, using moduli of elasticity of the subsoil as an iteration parameter, During an earthquake, the most serious faulting may be expected to occur close to the edge of the foundation structure with the ground on one side (say, left side) moving upward relative to the ground on the other, accompanied by ground acceleration directed to the left. This condition is shown in fig. 3. In this case, the earth faulting raises the left side of structure, leaving the central portion of the structure no longer in contact with the ground. Support of the structure may be described as a simple support. At the onset of vertical ground faulting, soil pressure redistribution occurs by decreasing the pressure at the central portion of the foundation structure and increasing the pressure at opposite edges. As soon as the soil pressure at the edge of the foundation exceeds the yield strength of the shock absorbing ring
J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
(say 60 000 p/ft2), the shock absorbing ring crushes and spreads the forces to a wider area over the foundation structure while absorbing shock energy. This crushing of the shock absorbing ring serves three purposes: it absorbs shock energy and reduces the vertical seismic acceleration and impact forces; it spreads the concentrated forces over a wider area to avoid a prohibitive shear stress problem on the foundation structure design; and it reduces the dynamic response amplification of the vertical acceleration due to the damping achieved by deformation of the shock absorbing ring. If the horizontal inertia force is greater than the resultant of ultimate passive soil pressure, the soil at the right side of the foundation structure fails by shear. The location of the fault line and the sense of the horizontal acceleration in fig. 3 are oriented for evaluation of the positive bending moment on the foundation structure. Should the fault line occur closer to the left edge of the structure, the subsoil on the left fails by shear as well as by crushing of the shock absorbing ring, and the simple support condition might not be
413
realized. Should the fault line occur closer to the center of the foundation structure, the span of the simple support is reduced, thus reducing the magnitude of positive moment. Reversal or cancellation of the horizontal acceleration also results in a reduction of the positive bending moment. 6.2. R o c k site The calculated foundation pressure underneath the structure during non-seismic conditions showed substantial fluctuations (from five times the average to a fraction of the average value), reflecting the flexibility of the foundation structure and effect of the large cutouts in the neutral zone. This foundation pressure distribution was determined by a preliminary finite element analysis in which the subsoil was considered to be a rigid rock foundation. A theoretically exact pressure distribution can also be obtained by an iteration process in which mechanical properties of the subsoil, shock absorbing ring and buffer zone of sand are considered the iteration parameters.
'\ !
b
~ T
T
60KSF 60
GROUNO JkCCELERITIONIR'~ U~''~'~'~F'~LT " LINE
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J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
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J. Finke and M.S, Lin, Earthquake-resistant nuelear power plants
There are two major fault conditions associated with a rock site. The simple support type, as shown in fig. 4 (a), is essentially identical to that shown in fig. 3, except the passive soil pressure does not exist. The sand layer in the center of the foundation structure serves as buffer zone to avoid prohibitive concentrated stress and also provides easy displacement to insure the structures' behavior as a simple beam. Although not considered in the analysis, this sand layer can potentially serve as a bond breaker to limit the magnitude of the horizontal acceleration transmitted to the structure. Fig. 4 (b) shows the overhanging situation created when the ground on one side of the fault line under the plant foundation drops. The structure is conservatively designed for an overhanging moment (negative moment) assuming the fault line occurs at a distance of one-third the diameter from the edge of the foundation, with the maximum horizontal acceleration directed to yield the maximum value of the negative moment. If the fault line is closer to the center of the structure, the overhanging configuration would not be possible unless the maximum horizontal acceleration acts in the reverse direction to counteract the overturning effects. In such a case, when the horizontal acceleration reverses, the structure overturns, and there is an enormous amount of potential and kinetic energy converted to impact energy. The shock absorbing ring is designed to absorb this energy by plastic deformation. Optimum material for the shock absorbing ring has yet to be determined and the credible acceleration accompanying the postulated maximum ground faulting must be carefully reviewed in the future.
7. Structural action and modes of faillure 7.1. Structural analysis As the cost study points out later, the partially prestressed concrete scheme is more economical than the conventionally reinforced concept. It is also more consistent with the rigid unitized design concept. Furthermore, cracking in vicinity of the storage tanks in the neutral zone of the foundation structure can be minimized through prestressing. Consequently, the discussion within this section is confined to prestressed concrete scheme.
Lumped-mass modal analysis was peiTormed to define the seismic response forces. The E1 Centro, California, 1940 earthquake average-acceleration spectrum curves [8, 9] were linerarly scaled upwards for the ground acceleration postulated in the design criteria. The modal idealization is shown in fig. 1. The axisymmetric structural analysis for static loading was performed using the finite element method employing IBM 360 digital computer. The total structure is idealized as an axisymmetrical finite element model containing 543 quadrilateral elements and 666 modal points. The five loading conditions shown in fig. 5 were investigated. Results of the finite element analysis indicate that the structure can withstand all five loading conditions without excessive stress or deformations. Also illustrated in fig. 5 are the critical concrete stresses in the containment vessel and foundation structure. Excepts at the juncture of the dome, no concrete stress exceeds 221 000 p/ft 2 (1 530 psi) in compression and 70 000 p/ft 2 (490 psi) in tension. Therefore, the secondary reinforcement in the containment vessel and the foundation structure is not governed by stress requirements but by load distribution and local crack distribution. The dome and peripheral structure are designed to withstand all design loads including a proof-load earthquake. Seismic forces are excluded from the five loading conditions studies in the finite element analysis. For extreme loading conditions combining seismic forces and LOCA pressure; stresses are allowed to approach yielding, which tend to relax the self-equilibrating secondary stress and stress concentrations. Therefore, as long as sufficient strength is provided in the structure for the primary forces on the structure under extreme loading, the integrity of the structure is assured. Since the mechanism of stress redistribution on the prestressed foundation structure is somewhat different from foundations for conventional structures, a detailed description of its pertinent features follows. 7.2. Forces at transfer o f hoop prestress The hoop prestress is designed to withstand either the test pressure or the LOCA pressure, combined with a positive or negative seismic moment. At the transfer prestress the resultant forces Tu and T1, of I the hoops correspond to the values of 0.6 f s , and
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they are almost balanced by the resultant compressive stress in the foundation structure across any vertical section cut through the center of the structure. The upper hoop prestress produces a twodimensional hydrostatic state of stress of approximately 100 000 p/ft 2 (700 psi) on the top flange, and about 40 000 to 100 000 p/ft 2 (270 to 700 psi) on the bottom flange of the foundation structure. The variation of the concrete prestress in the bottom flange reflects the irregular cutouts in that portion. 7. 3. Stress redistributions and failure mode due to positive moments
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As a result of ground faulting underneath the foundation structure, there is a possibility of forming a condition of the foundation structure analogous to that of a simply supported beam. This condition was shown earlier in fig. 3 for the alluvium site and fig. 4 (a) for the rock site. Due to the weight of the structure and seismic acceleration, a large positive moment is developed in the foundation structure. Although the magnitude of the positive moment is a function of the magnitude of the maximum ground acceleration, the relationship is not necessarily in direct proportion. Damping effects play an important role in determination of seismic response forces. In a reinforced concrete structure damping increases as a cracking increases and reduces the response forces in an exponential order. An increase in cracking can be anticipated under severe seismic and LOCA loadings, since stresses are allowed to approach yielding. Therefore, the use of higher damping factors is justified for greater magnitudes of ground acceleration. In the dynamic analysis, damping factors of 3% and 5% were used for the cases of 0.6 g and 1.0 g maximum accelerations ,respectively. The maximum positive moment was obtained by combining the maximum ground accelerations with the fault line located at the most critical location. When subject to this moment, and the consequent strain, the lower hoop prestress force, T1, increases from the value corresponding to effective prestress of ~-f~ = 160 000 psi to the value corresponding to 0.8 f~ = 192 000 psi, while the forces, Tu, in the upper hoops remain essentially the same. This condition is illustrated in fig. 6 (a). Compressive stress redistribution takes place on the foundation structure, and the
4 18
J. Finke and M.S. Lin. Earthquake-resistant nuclear power plants
top flange is stressed to 4 195 psi maximum, which is .t near the yield stress 0 . 8 5 0 / c = 4 250 psi. The compressive stress decreases linearly to zero toward the bottom, and may subject the b o t t o m fibers o f the foundation structure to some tensile cracking. The maximum concrete strain due to the maximum positive moment is E = 0.001. and although the b o t t o m of the foundation structure may crack, the mild steel liner plate of the storage tanks can safely stand this strain. The positive moment is counteracted by the internal moment through an upward shift of the resultant compression force across the entire cross section of the foundation structure. The ultimate positive moment capacity of the structure is evaluated assuming T 1 = TI', which is the resultant tensile forces of the hoop prestress stretched to f~ = 240 000 psi, the rein.. forcing steel in the foundation structure stressed to [y = 60 000 psi. The concrete stress block is idealized as rectangular at 0.85 f c stress. The magnitude of this ultimate positive m o m e n t is found to be 1.37 times the positive moment, which means that the foundation structure has 37% reserve strength beyond the most critical load combination in the design criteria. At this ultimate load condition it may be postulated that the b o t t o m flange experiences a strain, e = 0.003, and potentially may develop a single crack width of Wr -- 4 in., which would cause liner failure. This con-
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dition is illustrated in fig. 6 (b). The cracking is gradual. however, and the hi-strength steel reinforcenrent wil distribute this crack into numerous small cracks on the lower portion of the foundation structure, as shown fig. 6 (c). As plastic deformation occurs on the top flange, numerous fine shear cracks appear on the top flange and adjacent containment cylinder wall. Also, due to the stress concentration sustained during earth faulting impact, the concrete protective cover over the reinforcement in the containment vessel and the top flange juncture may spall. With proper detailing of the joint reinforcement for ductility, the spalling of the concrete protective cover should not endanger the integrity of the structure. 7.4. Stress redistribution and failure m o d e due to negative m o m e n t s
The case of negative moment exists when ground faulting occurs underneath the foundation structure by a sudden drop of one side, creating a overhang. (shown earlier as fig. 4b). For this case, spalling of the concrete protective cover over the reinforcing steel is not anticipated, and the mechanism o f stress redistribution is just the reverse of the case for positive moment. The most serious negative moment occurs when the fault is centered under the foundation causing a temporary imbalance of the struc-
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J. Finke and M.S. Lin, Earthquake-resistant nuclear power plants
ture. (This condition is illustrated in fig. 7 a). The ultimate negative moment capacity during this time, however, is also 1.37 times the maximum negative moment, which leaves the same margin of reserve strength in the design. Nevertheless, failure by negative moment may produce a larger tension crack on the top flange and the adjacent containment vessel wall, as shown in fig. 7 b. These cracks may only exist momentarily because in the next instant the structure tips to create a reversal of loading. If joint detailing provides for ductility in the juncture of the top flange and the containment vessel, the probability of tearing the containment liner plate is slight and the integrity of the unitized structure is reasonably assured.
419
Table 4 Class 1 structures construction cost comparison. Unitized plant Reference Description plant Foundation
Reinforced Partialprestressed concrete concrete 0.6g 1.0g 0.6g 1,0g
5.8
49.5
55.7 46.7
50.0
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78.0
79.3
72.3
77.5
Peripheral structure
21.0
32.5
33.0
34.0
34.5
Subtotal
96.8
160.0
8. Cost studies
Excavation 3.2 total
2.2
Preliminary cost estimates were prepared to compare additional costs of the proposed unitized plant designed for high seismic loading and a conventional reactor plant designed for low or non-seismic conditions. The estimates are comparative only and do not include all elements of nuclear power plant costs; for example, the costs of the turbine generator plant and its structures and buildings, as well as the cost of the nuclear steam supply system, were excluded. Cost of the excluded items should not vary significantly between plants designed for areas of high seismic activity and those designed for conventional sites. All estimates, including those for the reference plant, were prepared assuming location on sites in southern California. Construction costs for structures and foundations are estimated for plants located on both alluvium and on rock. Cost a plant constructed on an artificial island is approximately the same as that estimated for a plant located on alluvium except for the added cost of transporting men, materials and equipment to the site. Estimates for the unitized plant are further broken down by earthquake magnitude and construction scheme (reinforced versus prestressed concrete). These estimates, summarized in table 4, represent the cost of structures and foundations relative to the cost of the reference plant, which is given as 100.00. The greatest increase in cost for the unitized concept
subtotal
168.0 153.0 162.0
Alluvium site 2.0
2.0
2.0
100.0 162.0 170.0 155.0 164.0
Rock site Excavation 7.4 total Total
104.0
9.4 169.0
9.4
9.4
9.4
177.0 162.0 171.0
is for the foundation structure. This is to be expected considering the magnitude of the loading resulting from earth faulting. The incremental cost difference of the foundation for various ground accelerations is small compared with the total plant cost, and the size of earth fault has no effect within the range of faults studied. Smaller cost increases result from high ground accelerations for the containment vessel and peripheral structure. The cost increase to employ the unitized concept for the reactor plant is estimated at $ 5 million to $ 10 million, an increase in overall plant costs of less than 5%. An estimate was also made of the direct cost of the decay heat removal system and special equipment supports required to accommodate the postulated extreme seismic events. These costs are summarized in table 5.
420
J. f i n k e and M.S. Lin, Earthquake-resistapzt nuclear power plants
Table 5 Unitized plant incremental equipment and support cost summary.
Description
0.6 g
1.0 g
Primary equipment supports
~ 150 000
~ 200 000
100 000
150 000
Other equipment supports Decay heat removal system (cooling tower) Subtotal
to $ 600 000 greater than in alluvium. For the unitized concept there is no apparent cost advantage in locating the plant on an artificial island. 5. Although this study reviewed only major elements o f the design to establish feasibility, the concept appears to offer a workable solution to problems associated with severe earthquakes.
Acknowledgement
400 000
500 000
650 000
850 000
9. Conclusions The major conclusions resulting from this study and development of a unitized reactor plant are: 1. It appears feasible that a reactor plant, meeting the stipulated LOCA and seismic requirements, can be designed and constructed using a unitized concept. 2. The 0.6.-g proof, 0.3-g design earthquake criterion appears reasonable for locating the plant in areas corresponding to UBC (Uniform Building Code) zone II. The 1.0-g proof, 0.5-g design earthquake criterion appears reasonable for locating the plant in an area of high seismicity corresponding to UBC zone III. The structure can be upgraded to suit higher magnitude design earthquakes at a small differential cost increase if dictated by site conditions. 3. Design of the foundation structure is governed by ground displacement of the p r o o f earthquake, and it remains essentially the same for all the vertical and horizontal displacements investigated. 4. Rough estimates indicate that the cost increase for a unitized structure over a conventional plant will be approximately $ 5 to $ 1 0 million. This is an increase in total facility cost o f less than 5%. The study also indicates that the cost of founding the structure in rock will be approximately $ 500 000
This study is part of a broad continuing research and development program on earthquake problems of nuclear reactors sponsored by the U.S. Atomic Energy Commission through the Oak Ridge National Laboratory. This particular study was performed under Subcontract No. 2963 with Union Carbide Corporation Nuclear Division, Oak Ridge, Tennessee; U.S. Atomic Energy Commission Contract No. W-7405- eng-26, Oak Ridge Operations Office.
References [1] Indian Point Nuclear Generating Unit No. 3 Preliminary Safety Analysis Report, Vol. 1, 2 and 3, Consolidated Edison Company of New York, Inc. [2] Blume, Newmark and Corning, Design of Multistory Reinforced Concrete Building for Earthquake Motion, Portland Cement Association, 1961. [3] Norris, Hansen, Holley, et al., Structural Design for l for Dynamic Loads, John Wiley and Sons (1959). [4] E.L. Wilson, Symbolic Matrix Interpretation System 1BM-7094 Computer Program, University of California (August 1963). [5] E.L. Wilson, Structural Analysis of Axisymmetric Solids, AIAA Journal, 3, 12 (1965). [6] O.C. Zienkiewicz and G.S. Holister, Stress Analysis, John Wiley and Sons, (1965). [7] C.A. Miller, and C.J. Costantino, Structure-Foundation Interaction of a Nuclear Power Plant With A Seismic Disturbance. Nuclear Engineering and Design 14 (1970) 332. [8] R.A. Eppley, Earthquake History of the United States, Pamphlet No. 41-1, U.S. Coast and Geodetic Survey (1960). [9] Nuclear Reactors and Earthquakes, TID-7024, Lockheed Aircraft Corporation and Holmes and Narver, Inc. for USAEC (1963).