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1. Underlying standards
When designing structural systems for nuclear power plants in Europe, the verifications of stability and serviceability for purpose must be conducted based on Eurocode standards with the semi-probabilistic partial safety concept. Eurocode standard principles are therefore followed in the specific rules for nuclear power plants, consisting of the KTA rules and DIN standards. KTA status report KTA-GS-78 and the corresponding new DIN 25449 are of fundamental importance here.
KTA status report KTA-GS-78 provides recommendations to be used in the partial safety concept required for designing building structures in Europe. These recommendations, which focus particularly on categories of requirements specific to nuclear power plants relate to both reinforced and pre-stressed concrete and to steelwork. The new DIN 25449, which is guided by the recommendations of KTA status report KTA GS-78, includes specific definitions of specific extraordinary actions involved in nuclear power plants and details of proofs and design concepts for concrete, reinforced and pre-stressed concrete structural members.
Apart from KTA status report KTA-GS-78 and DIN 25449 with their fundamental design requirements, KTA 2201.3 and DIN 25459 should also be mentioned.
KTA 2201.3 gives details on designing nuclear power plant structures to withstand earthquake effects and DIN 25459 governs designing containments, covering possible containment variants - reinforced concrete and pre-stressed containments with liners.
2. Partial safety concept
2.1 General notes
When considering the partial safety concept, the various ultimate limit states (ULS) and serviceability limit states (SLS) must be verified: that is to say, the actions Ed must not exceed the structural resistance Rd to be considered in each case. For these limit conditions, following DIN 1055-100, we distinguish between a number of effects:
- independent constant actions Gk
- independent actions of pre-stressing Pk
- dominant independent variable actions Qk1
- other independent variable actions Qki (i>1)
- extraordinary actions Ad
- effects due to earthquakes AEd
When designing nuclear power plants, the effects designated as external or internal actions can be assigned to the group of 'extraordinary actions' or 'earthquake actions'. These are pre-given as design values, so that implicitly a partial safety factor is given a value of 1.0 and the design basis earthquake to KTA 2201.1 is given a weighting factor g1 to DIN 1055-100 and the importance factor to DIN 4149 is taken as 1.00. All other effects are to be stated as characteristic values.
To obtain the reference values for these actions, we need to examine different combinations to DIN 1055-100. We distinguish between design situations, as follows:
Ultimate limit state
- Permanent and temporary design situation
- Extraordinary design situation
- Design situation due to earthquake
[eqn. 1- 6]
Serviceability limit states
- Rare (characteristic) combination:
- Frequent combination:
- Quasi-permanent combination:
2.2 Partial safety factors and combination factors for actions
Partial safety factors g of effects may be assumed to DIN 1045-1. Recommended coefficients of combinations factors c to KTA-GS-78 and DIN 25449 are stated in Table 6.1.
2.3 Partial safety factors for structural resistance
For verifications of the serviceability limit states, the partial safety factors for the resistance are generally to be taken as 1.00.
Table 1 Reference values for partial safety factors and combined coefficients
The partial safety factors to determine the structural resistance of the ultimate limit states depend on the design situation (permanent and temporary, extraordinary) of the building materials used (concrete, concrete steel, pre-stressed steel, construction steel) and the demands on the structure or structural member in question.
Safety-related structural members are subject to different requirements under these effects. Factors to be taken into account here include:
- Chances of their occurring during working life
- Repair options available
- Limiting the extent of the damage, such that the structural members remain fit for use and system components remain intact and operational.
With these aspects in mind, requirements when designing structural components of nuclear installations are divided into three requirement categories, A1, A2 and A3.
These are defined irrespective of the building materials involved as shown in Table 1.
Requirement category A1
Those combinations of physical effects corresponding to the permanent and temporary design situations in accordance with DIN 1055-100 will be assigned to requirement category A1. The partial safety factors specified in DIN 1045-1 for the load-bearing capacity regarding permanent and temporary design situations will be assigned to these combinations.
Requirement category A2
Following the method described in DIN 1055-100, those combinations of physical effects that comprise extreme design situations, which must be assumed to occur several times during service life, are assigned to requirement category A2. It must be ensured that the building elements designed accordingly are continuously useable after occurrence of these combinations. In regard to the stability or functional safety of plant components, additional requirements may have to be specified for individual locations (e.g. limit values for deformations and crack widths).
Requirement category A3
Combinations of physical effects comprising extreme design situations with a low probability of occurrence (internal or external events,_10_4 per year) which must be assumed to occur once during service life will be assigned to requirement category A3.
The forming of large cracks and permanent deformations is permitted, provided, these are not prohibited for safety-related reasons. In regard to the stability or functional safety of plant components, additional requirements may have to be specified for individual locations (e.g. limit values for deformations and crack widths) that go beyond the minimum requirements with regard to the load-bearing capacity.
Partial safety factors of structural strength for structural components of concrete, reinforced concrete and pre-stressed concrete in requirement categories A1, A2 and A3 to KTA-GS-78 and DIN 25449 are shown in Table 6.2. Table 6.3 Table 6.2 Partial safety factors for structural members of concrete, reinforced and pre-stressed concrete (ULS) contains the partial safety factors for structural members of steel as recommended in KTA-GS-78.
Table 3 Partial safety factors for steel members (ULS)
3. Design instructions for concrete, reinforced and pre-stressed concrete structures
3.1 Strength parameters
In principle, the strength parameters for concrete, reinforced and pre-stressed concrete, including limits of ultimate limit strains to be observed, must be taken as per DIN 1045 1. Further details specific to nuclear power plants can be found in DIN 25449.
To determine the design values, the characteristic strength parameters must be divided by the partial safety factor gM in each case. Concrete compression strength fc must be divided by gc and the strength of concrete steel and pre-stressing steel (concrete steel:
yield stress fyk and tensile strength ftk, pre-stressing steel: yield point fp 0.1k and tensile strength fpk)must be divided by gS, using the partial safety factors as shown in Table 2 for the proofs in ULS depending on the category of requirements concerned.
For concrete compression strength, the influence of long-term effects and the influences on design-relevant concrete characteristics, such as the effects of load duration, curing and loading speed, must be taken into account. In certain justified cases, variations from the design-relevant characteristics of concrete as a construction material from the characteristics on which DIN 1045-1 is based may be used (deviations from design values). This applies in particular to the concrete getting stronger as it cures in long-standing reinforced concrete structures and the increase in strength of concrete stressed in multiple axes or high expansion rates and the influence on the ultimate limit strains of concrete.
3.2 Shear force
Verifications of shear resistance of reinforced or pre-stressed concrete members must be conducted to DIN 25449. The verifications are based on the method in accordance with DIN 1045-1, having regard to the different requirement categories, A1, A2 and A3. Shear force reinforcement will be necessary if, in a cross-section, the design value of the acting shear force VEd is greater than the design value of the shear force VRd, ct a structural member can withstand without shear force reinforcement, i.e. if:
VEd > VRd;ct (eqn.7)
The design value VRd,ct considers the different requirement categories A1, A2 and A3 by a factor cd, which is to be taken as 1.0 for A1, 1.15 for A2 and 1.50 for A3. This makes the reference value:
Where bw is the smallest cross-sectional width within the tension area of the cross-section [mm] cd is the pre-factor reflecting the requirement category d is the static effective depth of the flexural reinforcement in the cross-section [mm] fck is the characteristic value of the concrete compression strength [N/mm^2] rl is the longitudinal reinforcement ratio in the tension area scd is the design value of the axial concrete stress at the height of the center of gravity of the cross-section where scd = NEd Ac < fctk;0;05
Shear force design of structural members that are subject to bending stresses must be carried out based on a truss system in which the angle of the strut of the truss must be limited and the shear force reinforcement must be proven as VEd _VRd, sy and VEd _VRd, max. The maximum angle of the strut and the design value of the shear force which can be absorbed, limited by the strength of the shear force reinforcement VRd, sy and the design value of the maximum shear force VRD, max that can be absorbed to DIN1045-1 must be complied with in accordance with requirement categories A1, A2 and A3.
3.3 Punching shear
As with the verifications for shear resistance, punching shear verifications for reinforced and pre-stressed concrete structures in nuclear installations must be conducted to DIN 25449. Under these verifications, which are also based on DIN 1045-1, punching shear reinforcement is required if, along the critical circular section to DIN 1045-1, the shear force vEd to be absorbed per unit of length is greater than the shear resistance vRd, i.e. if:
vEd > vRd;ct (eq.10)
Shear resistance vRd,ct is obtained from DIN 1045-1. Like VRd,ct,vRd,ct reflects the different requirement categories A1, A2 and A3 by a factor.
To find the punching shear reinforcement required, we distinguish between:
- structural members subject to indirect effects of action, as covered in DIN1045-1 (e.g. supports in slabs or foundations), and
- structural members subject to direct effects of actions, as they occur in nuclear engineering construction as structural members subject to extraordinary actions in requirement categories A2 or A3, such as airplane crash or jet forces.
Fig. 1 Punching shear cone (area of direct effects of actions)
The reinforcement of structural members subject to indirect effects of actions must be obtained to DIN 1045-1. Should no more precise calculation and design procedure be used, the reinforcement required for structural members subject to direct effects of actions may be calculated in accordance with DIN 25449, which is based on DIN 1045 1 and additional experimental studies. The upper bound vRd,max to DIN 1045-1, which is intended to prevent the concrete cover palling at column faces, is irrelevant here, although the concrete strut resistance must be verified to ensure that the stirrup reinforcement is activated, i.e.
VEd _ VRd;max = 0:25 _ fcd _ uload _ d (eq.11)
Where fcd is the design value of concrete compression strength [N/mm^2]; fcd =fck/gc (gc in Table 2) uload is the circumference of the load area Aload (equivalent circle with radius Rload; see Figure 1) d is the static effective depth of the flexural reinforcement of the side facing away from the load in the cross-section considered In calculating the punching shear reinforcement, the decisive shear force VEd is taken as the maximum load resulting on the load area Aload. The verification may assume as the failure figure a punching shear cone with an effective surface area Acw = p _ ðr 2 ex _ r 2 inÞ and angle of inclination of the punching shear cone _r (generally cot _r =1.25) (Figure 1).
For the reinforcement, it must be shown that the relationship VEd _ VRd;sy (eq.12) is satisfied.
The design value for the required shear force reinforcement VRd,sy consists of a contribution of concrete load-bearing VRd,c (with the contribution of longitudinal reinforcement) and a contribution of punching shear reinforcement, i.e.
(eq.13)
Where Asw is the effective cross-sectional area of the vertical punching shear reinforcement in area Acw asw is the effective cross-sectional area of the punching shear reinforcement asw =Asw/Acw Acw is the effective projection area of the punching shear cone; Acw =p _ (r 2 ex _ r 2 in) fck is the characteristic concrete compression strength fck _35 [N/mm^2] uex is the circumference for rex (uex =2 _ p _ rex) ftd is the design value of the tensile strength of the concrete steel; ftd =ftk/gs (gs in Table 6.2) k
_ (average useful height in mm) cd
Prefactor reflecting requirement category rl
Degree of longitudinal reinforcement in tension area
4. Design instructions for steel components
The current steelwork standards (DIN 18800-1 and/or DIN EN 1993-1-1) with the new partial safety factor have only been reflected in KTA rules for steel structures to a limited extent to date: so KTA status report KTA-GS-78 advises relating steelwork load cases H, HZ, HS1, HS2 and HS3, and requirement categories A1, A2 and A3.
Table 4 Assigning steelwork load cases to requirement categories
How steelwork structures are designed depends on which KTA rule is to be used for the structure in question: so verifications may be required either by the global safety concept or the partial safety concept.
Fundamentally, the design procedures in DIN 18800-1may be used (Table 5). Stability verifications must also be considered here, such that either with beam structures the limits of slenderness must be observed in all cross-sections, or with plates and shell structures buckling safety must be verified to DIN 18800-3 or DIN 18800-4.
The plastic-plastic design procedure, as shown in Table 5, reflects the plastic hinge analysis as a simplified method. More precise design procedures, such as using non linear calculation methods reflecting realistic steel material laws, may also be used.
When using plastic cross-section or system reserves, the design criteria in Table 6.5 must be observed.
Table 5 Design procedures to DIN 18800-1
5. Particularities of containment design
5.1 Requirements of containments
The containment (safety container or enclosure) in the reactor building of a nuclear power plant is the essential structural barrier involved in containing radioactive substances safely (cf. Sections 2.5 and 4.2). The verifications required for this barrier are:
- bearing capacity
- serviceability in the sense of functional ability
- integrity (gas-tightness)
Bearing capacity and serviceability for use can be combined as a single overall concept, structural integrity. The structural integrity of a containment is tested once it has been made, while gas-tightness is tested regularly every three to five years.
The verifications must take account of the actions when operated as intended (normal and abnormal operation) and those of incidents (cf. Section 2.5). Containment design is governed in particular by the possibility of a loss of coolant accident, with its high pressure of the order of 0.5MPa accompanied by temperatures of approx. 150 C.
5.2 Reactor containment of steel
Except for two blocks at Gundremmingen nuclear power plant, all containments in Germany are made of steel. The containments of the more recent German PWR plants (Convoy and pre-Convoy plants) consist of a steel sphere 56m in diameter with walls 30-40mm thick. These dimensions are based on a design pressure in the range 4-5 bar overpressure at a design temperature of approx. 150 C. The guideline values for the maximum permitted leakage rate are 0.25-0.50% per day.
Steel containments are designed in accordance with KTA rules. KTA 3401 covers materials, design conditions, design, production and testing. The material that KTA 3401.1 requires is 15MnNi 63 steel, whose mechanical characteristics, with a yield point of 330-370N/mm^2 and a tensile strength of 490-630N/mm^2 are comparable with those of construction steel S355.
Design is governed by KTA 3401.2, and is based on permitted stresses, departing from the partial safety concept. Permitted stresses are defined for four stress levels and the various stress categories, allowing for how steel characteristics change at high temperatures. A loss of coolant accident as the dominant verification demand of the containment is put in the operating stress level and hence not regarded as a failure case.
Stability studies are also required to cover the possibility of a partial vacuum arising in the containment. The pressure tests here assume a partial vacuum of 45mbar and a partial vacuum of 5-30mbar in normal operation.
5.3 Pre-stressed concrete containments with steel liners
Not all structural sections are pre-stressed, even in pre-stressed concrete containments.
Pressurized water reactors have cylindrical containments with cupolas on top. The cylinder walls and cupola are pre-stressed, the base slab is not. Boiling water reactors, on the other hand, have flat cylindrical covers; only the cylinder walls being pre stressed. Pre-stressing increases the containment's serviceability, i.e. it keeps deformation and cracking low; but the cross-section of the concrete cannot be over-pressed completely, to ensure integrity in problem areas such as transitions between structural sections or around openings, so today's pre-stressed concrete containments are fitted with steel liners to guarantee their integrity. One example of a pre-stressed concrete containment with a steel liner is EPR containment.
The steel liner is anchored to the concrete structure via headed studs and/or steel profiles to give a composite steel-concrete structure. To avoid affecting the pre stressing, the steel liner is made of thin plate, t=6mm, for example. When verifying the structural strength of a containment, the steel liner is only taken into account if its effects are adverse.
Pre-stressing the concrete structure induces a compressive strain in the steel liner. Pre stressing also induces a time- and stress-based concrete creep which devolves the stresses involved and puts an additional compressive strain on the steel liner. The liner also expands under the influence of dissipation of the heat of hydration and as the concrete shrinks and also under the effects of operating conditions and in incident cases. The verification of liner integrity is obtained by limiting the liner strains and the action effects of the connectors.
Pre-stressed concrete containments with steel liners can be designed using DIN 25459.
5.4 Reinforced concrete containments with steel liners
With reinforced concrete containments with steel liners, the reinforced concrete structure ensures the structural integrity, and the steel liner the gas-tightness. A reinforced concrete containment is about as strong as a pre-stressed concrete one if the stressing steel is replaced with the concrete steel in proportion to their respective yield stresses. With the massive concrete cross-sections usually found in building nuclear power plants, this can be done without further ado.
The steel liner is anchored to the concrete structure via headed studs and/or steel sections so that a steel composite construction exists once it is completed with this concept; but the expansion of the steel liner and stresses on the laminate are less critical, as there is no pre-stressing. The reinforced concrete structure also enables a thicker steel liner to be used. Increasing the inherent rigidity of the steel liner makes it easier to install, and improves its strength and hence its integrity. As with a pre-stressed concrete containment, the design can be based on DIN 25459. The steel laminate effect must be considered in particular here, especially if using relatively thick steel liners, as with the non-pre-stressed containment of the KERENA BWR reactor model (steel liner t=10mm).