(to be published in "journal of nuclear engineering and
design", NorthHolland,
THE Design AND ANALYSIS OF TIANWAN NPP REACTOR CONTAINMENT ACCORDING TO DESIGN BASIS AND BEYOND DESIGN BASIS CONDITION
Pentti Varpasuo[1]
ABSTRACT
This paper reports the design of VVER91
type Tianwan nuclear power plant in
In the first part of the paper the
development of the instructure response spectra without any reduction of the
model size neither by condensation methods or component mode synthesis methods
is presented.
In the second part of the paper the concrete and tendon stresses were checked against the ASME allowances for all load combinations stipulated by ASME. Also the required amounts of longitudinal and transversal reinforcement were calculated as maximums from all investigated load combinations according to stipulations of ASME. The reinforcement amounts were depicted in color maps giving the needed longitudinal reinforcement crosssection area in square millimeters per meters width in both surfaces of the shell and in to mutually perpendicular directions and the needed transversal reinforcement in square millimeters per unit area of the shell.
In the third part of the paper the beyond design basis analysis of the inner containment shell is presented. The design pressure for the containment building was 5 bars of absolute pressure. As the safeguard against higher pressures because of direct containment heating in severe accidents the ultimate load carrying capacity of containment had to be evaluated.
The analysis consisted of the determination of the average cracking pattern in the containment shell for 7 bars absolute pressure load. The approach for the analysis was to use the same global 3D model for the containment shell as the one used in the design. The extension of the analysis was that all material nonlinearities were taken into account excluding direct analysis of concrete cracking. The concrete shell elements were modeled using orthotropic elastoplastic material properties having different stiffness in compression and tension. In compression the element stiffness was the stiffness of concrete evaluated from Youngfs modulus, Poisson ratio and shell thickness. In tension the element responded with stiffness that consisted of the stiffness of reinforcement in hoop and vertical directions. The tensile strength of concrete was neglected. The tendons were depicted with elastoplastic material properties that were evaluated from the measured stressstrain properties of tendons.
The results of the ultimate strength analysis were the strain plots for the containment shell for various pressure values. On the basis of calculated strains the average crack widths and crack distances were calculated and the overall containment leak amounts were evaluated.
The purpose of the reactor containment building is to protect the environment against leakage of the primary circuit and to protect the environment against direct radiation of the primary circuit. On the other hand the purpose of the building is to protect the primary circuit against external hazardous events.
The task in this assignment was to perform the final design of a dry prestressed concrete containment structure for a pressurized water reactor. The structure under consideration is a double containment. The inner containment is a prestressed concrete structure consisting of a flat base mat, a cylindrical shell, and a hemispherical dome. The outer containment is a reinforced concrete structure consisting of a cylindrical shell with a flat top dome.
In this design task, the final detailed design of the inner containment under the criteria given by the ACI 35995 Code [[1]] was carried out. The material characteristics of concrete and reinforcing steel were derived according to the Russian standard for concrete and reinforced concrete structures [[2]]. The work was performed in several stages as follows:
1. Initial proportioning of the containment using a rational design approach developed basic prestressing and reinforcement requirements, and thickness of the concrete structure. The prestressing requirements were given by the type, number, and spacing of the tendons. The thickness of the cylinder wall and dome was chosen to be 120 cm and 100 cm, respectively. Finite element analysis of the containment shell was also performed during this initial phase and base slab design analysis as well as the development of floor response spectra for the reactor building were also carried out during the initial phase of design and analysis.
2. Evaluation of the final prestressing forces was based on specific prestressing system, final layout of all containment penetrations and corresponding tendon duct routing. The forces were calculated for the initial prestress and for the end of the design lifetime after 40 years.
3. Finite element analysis and design was made for the prestressed concrete containment shell, excluding the base slab, which has been designed in the previous design task. However, in the integral finite element model to analyse the load effects to the inner containment shell, also the foundation soil, base slab, outer containment, internal structures with main equipment and the prestressing tendons were included in the calculation model. In this phase the reinforcement requirements were developed and the capacity of the tendons was verified.
4. Local finite element model was developed for the buttress area to establish the reinforcement requirements near the anchors of the horizontal tendons.
5. Analysis and design of the steel liner plate and the supporting structures of the polar crane and accumulator tanks of emergency core cooling system.
6. The task in the beyond design basis analysis is to investigate the state of Tianwan plant containment in 7 bar absolute internal pressure condition and to establish the deformations and average cracking at containment shell.
The 5 % bedrock field ground spectra according to HAF 0101 [[3], 1992 ] were adopted for targets for ground motion simulation. The horizontal ground motion spectrum was anchored to 0.2g and the vertical ground motion spectrum was anchored to 0.1g [[4], 1989]. In the following Table 1 the spectral ordinates as functions of frequency are given in tabular form.
Horizontal spectrum 

Frequency,
Hz 
0.25 
3.3 
14.3 
25 
33.3 
50 
Horizontal
acceleration, g 
0.062 
0.610 
0.538 
0.346 
0.2 
0.2 
Vertical spectrum 

Frequency,
Hz 
0.25 
4 
14.3 
25 
33.3 
50 
Vertical
acceleration, g 
0.084 
0.262 
0.294 
0.182 
0.1 
0.1 
Table 1 Design ground response spectra
The reactor building consists of the outer containment, the inner containment, the internal structures and the base slab with the tendon gallery. The outer containment is a conventionally reinforced shell structure that consists of a cylinder part and a flat dome. The outer diameter of the cylinder is 51.2 m and the top of the dome is at level +74.20. The thickness of the outer containment is 0.6 m both in the cylinder part and dome.
The inner containment is a prestressed concrete shell structure that consists of a cylindrical part and a hemispherical dome. The inner surface of the containment is covered with a 6 mm thick carbon steel plate to secure the tightness. The inside diameter of the cylinder is 44.0 m. The height of the cylinder part is 41.2 m and the top of the dome is at level +71.60. The thickness of the cylinder and dome are 1.2 m and 1.0 m respectively.
The prestressing of the inner containment will be performed by means of the Freyssinet posttensioning system. The tendons are divided into two horizontal and two vertical sets. The horizontal tendons in the cylinder and dome will be going around the whole 360 degrees so, that the anchorage is in turn on the opposite sides of the containment. The vertical tendons are inverted Ushaped tendons and they are divided into two groups of tendons at 90 degrees to each other. The base slab is utilized for the anchorage of the vertical tendons.
The internal structures are conventionally reinforced concrete structures that consist of a reactor pit, pools for fuel handling and reactor internals service, vertical walls and columns and intermediate floors at levels +16.00, +22.50 and +34.00. The internal structures are isolated by a clearance of 100 mm from the cylinder wall of the internal containment. The thickness of the internal structures varies from 0.2 m to 2.6 m and the median value is 1.2 m.
Both the outer and inner containments and the internal structures are based on a round concrete base slab, which is founded directly on the bedrock. The base slab is a conventionally reinforced massive concrete structure that is divided into two layers by the base liner. The both containments are supported on the lower part of the base slab and the internal structures are supported on the upper part of the base slab. In the centre region of the upper part of the base slab there is a big tooth that is in a hole of the lower part of the base slab. The aim of the tooth is to prevent sliding between the two layers of the base slab under seismic conditions.
The top of the upper part of the base slab is at level +8.00 and the bottom of the lower part of the base slab is at level +4.00. The thickness of the lower base slab is 3.0 m except in the centre region 1.0 m. The thickness of the upper base slab is about 0.8 m in the outer region and about 2.8 m / 1.8 m in the centre region. The diameter of the base slab is 51.2 m.
The ringshaped tendon gallery is situated under the base slab and centred under the inner containment. The base slab of the tendon gallery is at level +0.80 and this is the lowest floor in the reactor building. The thickness of the base slab of the tendon gallery is about 1.0 m and the thickness of the outer and inner walls are 0.6 m and 1.02.0 m respectively. The view of the reactor building model is given in the Figure 2. The colors in Figure 2 depict the thicknesses of various concrete structures. The red color means the thick end of color spectrum and blue color the thin end of spectrum. Thicknesses vary from 0.2 m to 3 m.
The grade of concrete for the design of the reactor building is B25 according to Russian concrete classification given in building code [[5], 1985], except in the inner containment where the grade of concrete is B45. AIII hot rolled ribbed bars according to Russian code [5,1985] were considered for principal reinforcement. Prestressing tendons are Freyssinet type tendons consisting of 55 strands of 15.7 mm nominal diameter, made of high strength steel SUPER St 1630/1860. Nominal crosssection area of a tendon is 8250 mm^{2} and nominal mass per metre is 65 kg/m. Modulus of elasticity is 199000 MN/m^{2} and coefficient of thermal expansion is 1.0~10^{5} /‹C.
The following strength and elastic characteristics for weakweathered metamorphic rock are used in the developing of finite element model:
· static elasticity
modulus E_{o}
= 37300 MPa,
· dynamic elasticity
modulus E
= 45500 MPa,
· weight density
r = 26.4 kN/m^{3},
· speed of longitudinal
waves
V_{p} = 4640 m/s,
· Poissonfs ratio n = 0.24,
· shear modulus G
= 14800 MPa.
The frequency independent spring and damper constants were calculated according to elastic halfspace theory following the recommendations given in reference [ [6],1986] and [[7] , 1985] for circular shape foundation slab.
The FEM models used in the sequence of analyses carried out during the design effort did form a set that increased in sharpness of resolution and in the accuracy of material modeling as the dseig task advanced.
The general FEM – model for analysing the
overall response on the reactor building and for developing the instructure
response spectra is described first. Fournoded quadrilateral shell elements
capable to take also transverse shear forces into account were used to model
the structure. Each node in the model has six degrees of freedom, a translation
in the X, Y and Zdirections and rotations around these directions. A
3Dmodel was created for the whole reactor building. The 3Dmodel consists of
the outer containment, the inner containment, the internal structures and the
base slab with the tendon gallery. The FEMmodel was formed along centre lines
of the concrete structures. The number of shell elements used to describe the
concrete walls and floors is 21994. The columns in the internal structures were
described by 48 beam elements. The properties of the elements were determined
according to the concrete material properties and the nominal dimensions of the
structures. The main components
were described by point mass elements. In this way, the weight of these
components was taken into account both in static and dynamic analyses. Water in
the pools of the internal structures was also modelled by point mass
elements.The prestressing tendons in the inner containment were described by
16072 bar elements. The tendons were placed in their real places giving offsets
for the bar elements. The vertical tendons are placed on the centre line in the
cylinder. In the dome the vertical tendon group 1 is placed a little outside of
the centre line and the group 2 a little inside of the centre line. The
horizontal hoop tendons are offset 0.36 m outside of the centre line in the cylinder
and 0.30 m outside of the centre line in the dome. In the vicinity of the
equipment hatch opening every second hoop tendon is bent 0.5...0.8 m into
inward direction. The equivalent drop of temperature representing the
prestressing forces in tendons varies from 364.3 to 716.7 ‹C, which
corresponds to stress varying from 725 to 1426 MN/m^{2}. The
boundary conditions for the 3Dmodel were described by spring elements in
static analysis and by spring and damper elements in dynamic analysis. All the
nodes against the rock were connected to springs and dampers and the other end
of the spring and damper elements were connected to one nodal point having a
big mass representing the ground and situated below the building. The ground
accelerations were input to that node in the seismic analyses, but in other
analysis that node was fixed in all six directions. The spring and damping
constants were calculated so that they represent the properties of the rock. The righthanded
Cartesian global coordinate system was used in this study. The origin of the
coordinate system is on the vertical axis of the reactor vessel at the
elevation +0.00. The X and Yaxes are in the horizontal plane and the Zaxis
is vertical. The Xaxis is to the direction of the refuelling pool. The Yaxis
is normal to the Xaxis according to the right hand rule so that the Zaxis
points upwards. The local coordinate systems of the shell elements determines
the positive and negative directions of stress resultants and reinforcements
are evaluated in the local coordinate system. The local x and yaxes are
located in the plane defined by the nodal points of the shell element. The
xaxis is always normal to the yaxis. The zaxis is normal to the xyplane
according to the right hand rule. The bottom surface of a shell element is in
the side of negative zaxis and the top surface is in the side of positive
zaxis.
For the second phase of the containment analysis and proportioning the more refined FEM – model was developed. The model was created for the whole reactor building, but the refining of the mesh was done only for inner containment shell.. The model includes the outer containment, the inner containment, the internal structures and the base slab with the tendon gallery. The model was formed along centre lines of the concrete structures. The number of shell elements used to describe the concrete walls and floors is 22825. The columns in the internal structures were described by 48 beam elements. The properties of the elements were determined according to the concrete material properties and the nominal dimensions of the structures.
For third phase of the analysis studying beyond design condition of the reactor containment the same FEM – model as in phase two was utilized. The only difference between phases two and three was that in phase three the nonlinear material properties were taken into account. The FEM models used in three different phases of analysis are depicted in Figures 2 and 3.
The isotropic material
of the concrete of grade B45 is described using the stressstrain relationship
presented in Figure 1 and Table 2. The reinforcement has been taking into
account by giving the concrete corresponding amount of tension strength.
Figure 1 Nonlinear stressstrain relationship of the concrete of grade B45
Figure 2 Finite element model of the reactor building in the first phase of analysis
Figure 3 Finite element model of the reactor building in the second and third phases of analysis
Strain,
10^{3} 
1000 
2.0 
1.5 
1.0 
0.5 
0.0 
1.95 
1000 
Stress,
MPa 
37.5 
37.5 
35.5 
28.0 
14.5 
0.0 
2.613 
2.613 
Table 2 Nonlinear stressstrain relationship of the concrete of grade B45
In the first phase of analysis the earthquake excitation was applied to a big mass representing the base excitation applied to the model to obtain the desired time history response of reactor building. The big mass was connected by springs and dampers to the base elevation of the structure. The eigenvalues and modes were calculated by the Lanczos method. All modes below 50 Hz were used in the modal transient analysis to solve the displacement, velocity and acceleration histories. Damping of structures was determined by the equivalent viscous damping and the damping value was 5 % for all modes. Solution timespan was selected to be 20 seconds with an increment of 5 ms between each calculation point. Duration of the design earthquake was 15 seconds. The acceleration response spectra were calculated using four different damping values, 0.5, 2, 5 and 10 % of critical damping, at the following 73 frequencies: 0.2, 0.3, 0.4, ... , 3.0, 3.15, 3.3, 3.45, 3.6, 3.8, 4.0, 4.2, 4.4, 4.7, 5.0, 5.3, 5.661, 6.0, 6.25, 6.5, 6.75, 7.0, 7.3, 7.6, 8.0, 8.5, 9.0, ... , 13.0, 13.565, 14.0, 14.5, 15.0, 15.801, 17.0, 18.5, 20, 24, 27.238, 31.127, 33, 40 and 50 Hz. The response spectra were determined at points near the centre of the concrete floors of the internal structures and base slab and at two extra points both in the inner and outer containment. At each point, the spectra were evaluated in the global X, Y and Zdirections. The calculated acceleration responses are in units of m/s^{2}. The results of the response spectra calculations in global X – direction for the elevation of +22.5 are depicted in Figure 4.
The prestressing of the containment will be performed by means of
the posttensioning system. The tendons are divided into two horizontal and two
vertical sets. The horizontal tendons in the cylinder and dome will be going
around the whole 360 degrees so, that the anchorage is in turn on the opposite
sides of the containment. Two buttresses at 120 and 300 degrees are used for
the anchorage of the horizontal tendons. The vertical tendons are inverted
Ushaped tendons and they are divided into two groups of tendons at 90 degrees
to each other. The base slab is utilized for the anchorage of the vertical
tendons.
The containment shell has a large number of
penetrations. The majority of these, with a diameter between 20 cm and 50 cm,
allow for the passage of electrical circuits and piping through the containment
wall. The penetrations for the main process pipes, ventilation and electrical
circuits have a diameter between 50 cm and 120 cm. The largest penetrations for
the equipment hatch (diameter 742 cm), personnel air lock (diameter 273 cm),
and auxiliary personnel air lock (diameter 273 cm) provide access for personnel
and equipment. Other attached structures and equipment of the containment shell
are the liner plate and the supporting structures of the polar crane and
accumulator tanks of the emergency core cooling system.
General view of the posttensioning tendon system is given in Figure 5. As can seen from Figures 5 the containment shell penetrations are arranged in two main bands. The first band is situated in the lower part of the shell and the largest penetrations in this band are containment sump drain pipes and auxiliary personnel airlock. The second band is situated on the upper part of the containment shell above the main operation deck and biggest penetrations and openings in this band are the material air lock, personnel air lock . In between these two horizontal bands are the main steam and main feed water penetrations. The bands form clear weak zones in the containment shell, where the prestress losses concentrate and there the requirements for mild reinforcement amounts are the highest. These are also the areas, where the high values of deformations and pronounced cracking are to be expected in the beyond design basis investigations of the containments shell.
Figure 4 Floor response spectra in Xdirection for elevation +22.5
Figure 5 Plot from the plant layout model depicting the posttensioning tendon system
The design loads applied to the inner containment of the reactor building and the principle to combine the design loads followed the ACI 35995 Code [1].
The dead load of the reinforced and prestressed concrete structures was calculated by multiplying the volume of the concrete with the weight density of 25 kN/m^{3}. The influence of the additional surface concrete of thickness 60 mm was added using equivalent uniformly distributed load 1.5 kN/m^{2} on each intermediate concrete floor. On the roof the additional uniformly distributed load is 2.5 kN/m^{2}. The dead load of the prestressing tendons and the steel structures was calculated using the weight density of 77 kN/m^{3}.
Component 
Code 
Level 
Number 
Mass, t 
Reactor block with water 
JAA10 
+14.10 
1 
913.0 
Reactor support frame and insulation 

+14.70 
1 
172.0 
Bubbler tank with water 
JEG10 
+16.00 
1 
34.4 
Primary coolant pump unit 
JEB 
+22.50 
4 
177.0 
Steam generator with water 
JEA 
+22.50 
4 
568.0 
Pressurizer with water 
JEF 
+22.50 
1 
269.5 
ECCS tank with water 
JNG 
+34.00 
4 
129.1 
Refuelling machine 

+34.00 
1 
46.0 
Polar crane 

+47.90 
1 
385.0 
Table 3 Mass of the main components
Penetration 
Code 
Level 
Number 
Mass, t 
Personnel air lock + bush (1) 
JMF10/20 
+11.8/+35.1 
2 
45.0 + 5.0 
Material air lock + bush (1) 
JME10 
+37.00 
1 
120.0+40.0 
Recirculation sump 
JNG 
+6.55 
4 
4.6 
Cooling water pipe 
LAB 
+18.80 
4 
4.0 
Steam pipe 
LBA 
+25.50 
4 
5.6 
Electric, high voltage 
JEB 
+29.0...+31.0 
8 
1.5 
Emergency filtered ventilation 
JMQ 
+32.15 
1 
3.6 
Ventilation 
KLD 
+37.20 
2 
2.5 
Table 4 Mass of the main penetrations
Mass of the main components given in Table 3 and mass of the main penetrations (the steel parts poured into concrete) given in Table 4 was included in the dead load.
For the prestressing forces of the tendons two separate cases were analysed: prestress immediately after prestressing work and prestress at the end of the design lifetime i.e. after 40 years.
The polar crane load is the only live load. The maximum loads on the polar crane are the lifts of the steam generator and reactor pressure vessel. The design load value is 405 t in the vertical direction, 4~32 t in the radial direction and 4~6 t in the circumferential direction. The load was put in front of the material opening that is the load location at the beginning of the maximum lift.
In normal conditions the temperature of air inside the inner containment varies from +20 ‹C to +40 ‹C and in the calculations were used the most probable value of +25 ‹C. The temperature between the inner and outer containment and in the tendon gallery is +20 ‹C. The temperature of outside air is +2.4 ‹C, which is the mean temperature in winter. The temperature of ground is +10 ‹C. According to these conditions calculated outer and inner surface temperatures of the concrete structures are +5.6 ‹C and +16.8 ‹C for the outer containment, +20.6 ‹C and +24.4 ‹C for the inner containment and +10.0 ‹C and +24.4 ‹C for the base slab. The calculation has been made in stationary conditions using thermal conductivity of 2.04 W/‹C/m for concrete and heat transfer coefficient of 12 W/‹C/m^{2} both for outer and inner surface. The reference temperature of the concrete structures is +7.0 ‹C calculated from the winter and summer mean outside temperatures +2.4 ‹C and +25.2 ‹C.
The pipe reaction forces of the main steam and cooling water pipes during normal operation conditions are given in Table 5. The forces presented are the total values during normal operation conditions including both mechanical and thermal loads.
Pipe Code 
F_{x }(kN) 
F_{y }(kN) 
F_{z }(kN) 
M_{x }(kNm) 
M_{y }(kNm) 
M_{z }(kNm) 
LBA10 
50 
16 
28 
62 
192 
141 
LBA20 
111 
23 
66 
46 
8 
34 
LBA30 
88 
24 
122 
57 
617 
22 
LBA40 
120 
54 
17 
49 
32 
161 
LAB10 
25 
29 
12 
6 
10 
19 
LAB20 
36 
1 
44 
1 
86 
2 
LAB30 
23 
1 
4 
0 
11 
3 
LAB40 
59 
5 
32 
6 
39 
43 
Table 5 Pipe reactions during normal conditions in the global coordinate directions
The external pressure load is a result from
malfunction of the sprinkler system. The maximum value of the underpressure
inside the inner containment is 21 kPa.
The test pressure is applied during the structural integrity testing. The value of the overpressure inside the inner containment in the test conditions is 15 percent bigger than the design pressure i.e. 1.15 ~ 0.40 MPa.
The following sections describe the loads generated by the Safe Shutdown Earthquake (SSE). The SSE loads are specified in subsection 2. For the Operating Basis Earthquake (OBE) the generated time histories and corresponding response spectra should be multiplied by 0.5.
In extreme conditions the design temperature of air is +150 ‹C inside the inner containment. In the design accident situation the temperature will rise very quickly from +50 ‹C up to +150 ‹C, stay unchanged about 12 hours and decrease back to normal. Because the phenomenon is quite fast, it is supposed, that the air temperature between the inner and outer containment and in the tendon gallery is +20 ‹C. The temperature of outside air is +2.4 ‹C, which is the mean value in winter. The extreme temperature of 18.0 ‹C in winter was not examined, because it is not critical for the inner containment that is the main interest of this calculation. The temperature of ground is +10 ‹C. The reference temperature of the concrete structures is +7.0 ^{o}C calculated from the winter and summer mean outside temperatures +2.4 ‹C and +25.2 ‹C. Transient thermal analyses were made using one dimensional heat transfer models for the containment wall, dome and base slab to evaluate the temperatures during extreme conditions.
The design pressure load generated by the design basis accident (DBA) is 0.40 MPa overpressure inside the inner containment.
The pipe reactions from thermal conditions generated by the design basis accident (DBA) are almost the same as from the normal operation conditions and so the values given in the Table 5 can be used. The reaction loads generated by ruptured high energy pipes during DBA at containment penetration areas were evaluated by multiplying the design pipe pressure by the pipe cross sectional area. The dynamic effects of the reaction loads were taken into account by assuming that the time history curve of the transient reaction loads is the Heaviside step function. The design value of the pipe break reaction load is 4090 kN for the LBA steam pipes and 2700 kN for the LAB cooling water pipes. The maximum amplitudes of the pipe reaction forces from the safe shutdown earthquake (SSE) are given in Table 6. The forces presented must be added to the values during normal operation conditions.
Pipe Code 
F_{x }(kN) 
F_{y }(kN) 
F_{z }(kN) 
M_{x }(kNm) 
M_{y }(kNm) 
M_{z }(kNm) 
LBA10 
430 
63 
108 
144 
180 
118 
LBA20 
542 
62 
136 
20 
199 
116 
LBA30 
579 
299 
252 
96 
905 
1376 
LBA40 
463 
59 
71 
117 
185 
260 
LAB10 
47 
69 
71 
27 
48 
47 
LAB20 
26 
6 
10 
2 
16 
9 
LAB30 
47 
10 
68 
38 
172 
22 
LAB40 
110 
66 
21 
46 
28 
139 
Table 6 Pipe reactions from safe shutdown earthquake in the global coordinate directions
The principle to combine the design loads of the inner containment of the reactor building followed the ACI 35995 Code [1]. Load combinations for the service and factored loads are given in Tables 7 and 8, respectively.
Category 
No 
1 
2 
3 
4 
5 

D 
1 
Dead load 
1.0 
1.0 
1.0 
1.0 
1.0 
F_{1} 
2 
Prestress after prestressing 
1.0 
1.0 
1.0 
 
 
F_{2} 
3 
Prestress after 40 years 
 
 
 
1.0 
1.0 
L 
4 
Polar crane load 
 
1.0 
 
 
1.0 
T_{t} 
5 
Test temperature (= T_{o}) 
 
 
1.0 
 
 
T_{o} 
6 
1.0 
1.0 
 
1.0 
1.0 

T_{a} 
7 
Accident temperature 
 
 
 
 
 
P_{n} 
8 
External pressure (= 0.0525 P_{a}) 
1.0 
 
 
1.0 
 
P_{t} 
9 
Test pressure (= 1.15 P_{a}) 
 
 
1.0 
 
 
P_{a} 
10 
Accident pressure 
 
 
 
 
 
E_{o} 
11 
Operating earthquake (= 0.5 E_{ss}) 
 
 
 
 
 
E_{ss} 
12 
Safe shutdown earthquake 
 
 
 
 
 
R_{o} 
13 
Pipe reactions during operation 
1.0 
1.0 
 
1.0 
1.0 
R_{a} 
14 
Pipe reactions, accident (= R_{o}) 
 
 
 
 
 
R_{r} 
15 
Pipe break reaction 
 
 
 
 
 
R_{ss} 
16 
Pipe reactions from earthquake 
 
 
 
 
 
Table 7 Load combinations for service loads
Category 
No 
1 
2 
3 
4 
5 

D 
1 
Dead load 
1.0 
1.0 
1.0 
1.0 
1.0 
F_{1} 
2 
Prestress after prestressing 
1.0 
 
 
 
 
F_{2} 
3 
Prestress after 40 years 
 
1.0 
1.0 
1.0 
1.0 
L 
4 
Polar crane load 
 
 
 
 
 
T_{t} 
5 
Test temperature (= T_{o}) 
 
 
 
 
 
T_{o} 
6 
 
 
1.0 
 
 

T_{a} 
7 
Accident temperature 
1.0 
1.0 
 
1.0 
1.0 
P_{n} 
8 
External pressure (= 0.0525 P_{a}) 
 
 
1.0 
 
 
P_{t} 
9 
Test pressure (= 1.15 P_{a}) 
 
 
 
 
 
P_{a} 
10 
Accident pressure 
1.5 
1.5 
 
1.25 
1.0 
E_{o} 
11 
Operating earthquake (= 0.5 E_{ss}) 
 
 
 
1.25 
 
E_{ss} 
12 
Safe shutdown earthquake 
 
 
1.0 
 
1.0 
R_{o} 
13 
Pipe reactions during operation 
 
 
1.0 
 
 
R_{a} 
14 
Pipe reactions, accident (= R_{o}) 
1.0 
1.0 
 
1.0 
1.0 
R_{r} 
15 
Pipe break reaction 
 
 
 
 
1.0 
R_{ss} 
16 
Pipe reactions from earthquake 
 
 
1.0 
 
1.0 
Table 8 Load combination for factored loads
Maximum values of displacements for the inner containment of the reactor building model are presented in Table 9. The Table includes the ten basic static load cases (load numbers 110), four static load combinations (load numbers 1114) and also the components of the dynamic displacements from earthquake load (load numbers 1517).
Load 
Basic load case or load 
Displacement, mm 
1 
Dead load 
3.4 
2 
Prestress after prestressing 
12.2 
3 
Prestress after 40 years 
11.2 
4 
Polar crane load 
0.5 
5 
Normal conditions temperature 
10.1 
6 
Extreme conditions temperature 
33.6 
7 
Accident pressure 
12.0 
8 
Pipe reactions during operation 
0.1 
9 
Pipe break reaction 
2.8 
10 
Pipe reactions from earthquake 
0.4 
11 
Normal operation 
14.5 
12 
Normal operation after 40 years 
13.7 
13 
Design basis accident 
6.7 
14 
Design basis accident after 40 years 
7.4 
15 
Earthquake, Xdisplacement at top 
13.6 
16 
Earthquake, Ydisplacement at top 
12.0 
17 
Earthquake, Zdisplacement at top 
1.0 
Table 9 Maximum values of total displacements for the inner containment
The displacement time history (m)
for the load case 15 are depicted in Figure 6.
Figure 6 Displacement time history for the top of the containment for seismic load
The dead load of the reinforced and prestressed concrete structures was calculated by multiplying the volume of the concrete with the weight density of 25 kN/m^{3}. The influence of the additional surface concrete of thickness 60 mm was added using equivalent uniformly distributed load 1.5 kN/m^{2} on each intermediate concrete floor. On the roof the additional uniformly distributed load is 2.5 kN/m^{2}. The dead load of the prestressing tendons and the steel structures was calculated using the weight density of 77 kN/m^{3}. The prestressing forces of the tendons were calculated by taking into account all losses in tendon forces. Two separate cases were analysed: prestress immediately after prestressing work and prestress at the end of the design lifetime i.e. after 40 years. Stresses are presented separately for four groups of tendons described in Table 10. The extreme values of these stresses are collected in Table 3. In this analysis only the prestress after 40 years was used.
Group name 
Description 
Horizontal tendons group 1 
Horizontal tendons
anchored in buttress at 120^{o} 
Horizontal tendons group 2 
Horizontal tendons
anchored in buttress at 300^{o} 
Vertical tendons group 1 
Vertical tendons
in direction of 30^{o} 
Vertical tendons group 2 
Vertical tendons
in direction of 120^{o} 
Table 10 Group names of the tendons

Horizontal tendons, MPa 
Vertical tendons, Mpa 


Group 1 
Group 2 
Group 1 
Group 2 
After prestressing, maximum 
1452 
1452 
1413 
1413 
After prestressing, minimum 
603 
649 
740 
672 
After 40 years, maximum 
1347 
1347 
1315 
1315 
After 40 years, minimum 
540 
583 
674 
610 
Table 11 Extreme values of axial stresses of the tendons without elastic losses
The design pressure load generated
by the design basis accident (DBA) is 0.40 MPa overpressure inside the inner
containment. In this analysis the internal overpressure of 0.60 MPa was used.
Two static analyses were made using the aforementioned loads. In the linear analysis all the loads were applied at the same time. In the nonlinear analysis the internal pressure was increased in small steps, however, the total load is the same as in the linear analysis.
Category 
No 
Linear analysis 
Nonlinear analysis 

D 
1 
Dead load 
1.0 
1.0 
F 
2 
Prestress after 40
years 
1.0 
1.0 
P 
3 
Internal pressure 
1.0 
1.0 
Table 12 Analysed load combinations
Maximum and minimum principal strains at inner and outer surface of the inner containment are collected in Table 13. The strains were evaluated in the centre point of each shell element. Common values of the strains are less than half of the extreme values. Distribution of the linear and nonlinear strains is quite similar in compression zones but different in tension zones, which is a direct consequence of the different stressstrain curves.
Load 
Strain 
Maximum principal strain, 10^{6} 
Minimum principal strain, 10^{6} 

combination 
component 
Inner surface 
Outer surface 
Inner surface 
Outer surface 
Linear 
Maximum 
290 
502 
75 
130 
analysis 
Minimum 
90 
107 
740 
372 
Nonlinear 
Maximum 
1900 
2220 
501 
850 
analysis 
Minimum 
175 
165 
1070 
683 
Table 13 Extreme values of strains for the inner containment
The distribution of principal strains in the outer surface of the
containment shell is shown in Figure
7.
Figure 7 Distribution of the maximum principal strain in the outer surface of the containment shell for 7 bar absolute internal pressure
In the nonlinear analysis the concrete structures are more compressed than in the linear analysis, which is a consequence of the different stressstrain curves. Common values of the stresses are less than half of the extreme values. Distribution of the linear and nonlinear stresses is quite similar in compression zones but different in tension zones. The extreme values of concrete stresses are collected in Table 14. The stresses were evaluated in the centre point of each shell element.
Load 
Stress 
Maximum principal stress, Mpa 
Minimum principal stress, MPa 

combination 
component 
Inner surface 
Outer surface 
Inner surface 
Outer surface 
Linear 
Maximum 
8.77 
14.68 
2.87 
5.11 
analysis 
Minimum 
4.01 
3.93 
21.67 
11.15 
Nonlinear 
Maximum 
7.29 
4.93 
0.87 
1.58 
analysis 
Minimum 
7.13 
6.13 
29.33 
20.05 
Table 14 Extreme values of concrete stresses for the inner containment
In the nonlinear analysis the tendon stresses are a somewhat higher than in the linear analysis, because tension forces are partly transferred from concrete to the tendons. The tendon stresses are well below the yield strength of 1630 MPa and so the linear material model for the prestressing steel is adequate. The extreme values of the tendon stresses are collected in Table 15. The stresses were evaluated in the centre point of each bar element.
Load 
Stress 
Horizontal tendons, MPa 
Vertical tendons, MPa 

combination 

Group 1 
Group 2 
Group 1 
Group 2 
Linear 
Maximum 
1414 
1413 
1331 
1332 
analysis 
Minimum 
582 
616 
691 
628 
Nonlinear 
Maximum 
1427 
1443 
1393 
1445 
analysis 
Minimum 
600 
624 
730 
657 
Table 15 Extreme values of axial stresses of the tendons
The paper presented the three phases of the response and stress and strain analysis of the reactor building and the containment shell of the Tianwan nuclear power plant for the design basis and beyond the design basis conditions.
In the first phase of the analysis the base slab proportioning and the instructure spectra for earthquake excitation were developed.
In the second phase of the analysis the proportioning of the inner containment shell and the determination of the mild reinforcement amounts in the shell were calculated.
In the third phase of the of the analysis the beyond design
condition for internal pressure value of 7 bars of absolute pressure was
investigated. The load combination used for the investigation was internal
pressure combined with dead load and prestress after the losses of 40 years operational life of the plant.
The elastoplastic behavior of the concrete material as well as prestressing
tendons were taken into account in the analysis. The load was increased to
final in ten equally large load steps.
The obtained
results show large increase in the extreme fiber tensile strains in the
containment wall because of nonlinear behavior of the materials. The increases
in tendon strains and tendon stresses were only minor because of the nonlinear
behavior of the materials.
This analysis
was only the first step in the integrity assessment of the containment shell
for the beyond design basis loading situations. In the second step of
containment ultimate strength analysis the reinforced concrete model based on
smeared crack concept has to be adopted. This step requires developing of the
new element model for containment shell. The prestressing tendons and
reinforcing bars have to be modeled on individual bar basis using
elastoplastic material properties for steel. Concrete should be modeled with
the aid of measured stressstrain curve and crushing strength on the
compression side and with the aid measured rupture strain in the tension side.
The cracking status has to be monitored in each integration point during the
loading sequence of the finite element model. The cracks can open and close but
never heal. The open cracks should have shear resistance parallel to crack
surface because of aggregate interlock effect. The aim of the second step of
the beyond the the design basis strength analysis is to load containment until
failure and the result is the ultimate failure pressure of containment.
[[1]] ACI 35995 (ASME Boiler and Pressure Vessel Code, Section III, Division 2), Code for Concrete Reactor Vessels and Containments, New York, 1995.
[[3]] Safety Guide on Earthquakes and Associated Topics in Relation to NPP Siting, HAF0101. Approved jointly by NNSB and SSB. A Collection of Safety Guides for NPP, NNSB. Law Publisher of China, 1992.
[[4]] Normi proektirovanija sejsmostojkih atomnih stancij. PiN AE G500687. (Code for design of seismically resistant nuclear power plants), Gosatomenergonadzor SSSR. M.: Energoatomizdat, 1989.
[[5]] SNiP 2.03.0184. Betonnie i zchelezobetonnie konstuktsii. (Code for concrete and reinforced concrete constructions),M. Gosstroi SSSR. 1985.