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					A.Kubaneishvili,…                                                            Energyonline №1(2), 2010


            PRE-STRESSED IRON CONCRETE BODY OF NUCLEAR
                       POWER PLANT REACTOR

                             A. Kubaneishvili, M.Kalabegishvili

Construction of high pressure pre-stressed iron concrete body is described. An issue of body creation is
decided experimentally and theoretically.
High pressure body is an iron concrete structure of a cylinder shape made of coaxially located external
and internal envelopes with the clearance between them. Cement slurry is pumped into the clearance.
Internal envelope at this moment squeezes and the external one – expands. Pressure is brought to
necessary preliminary concrete reduction of the internal envelope considering all the losses as a result of
which the canals with mixed pre-stressed reinforcement are filled with slurry.
Theoretical estimations for the construction are run by attracting the body of mathematics of finite
elements.

Key words: pre-stressed iron concrete, reactor body of nuclear power plants, high pressures, protecting
envelope, concrete reduction, high pressure capacity.

    INTRODUCTION
     In the design and construction of high-pressure structures considerable attention is given to the
development of protective shells. The strength of the protective shell should be adequate to
withstand emergency stresses and temperatures, provided that reasonable safety is ensured and
leakage speed does not exceed the estimated value.
     The frames of present-day high-pressure vessels are generally made of prestressed reinforced
concrete, the inner surfaces being clad with steel [1]. Impenetrability and plasticity of this type of
lining make the structure air-tight. While enjoying all the advantages of prestressed reinforced
concrete (high degree of reliability and resistance to cracking; better resistance to seismic loads and
impacts from flying objects etc.), the shells have some serious drawbacks, such as: the use of
heavy-duty reinforcing curvilinear elements (twisted ropes, bundled bars) with tension augmented
up to 49...98⋅105N to ensure compressive prestressing of cylindrical frame, duct building for tendon
laying-out, placement of heavy-duty steel arrangements on the outer side of reactor, which,
including assembly operations and curvilinear tendon jacking, makes up 2/3 of the total cost of the
frame [2].
     Hydraulic pressure tunnels have composite lining constituting two-layer structures, with the
outer ring withstanding external pressure and the inner ring designed to resist intrinsic water
pressure. Hydroproject has suggested two-layer lining for pressure tunnel lining in soft rocks, its
outer ring being subject to compressive stressing by the action of rock pressure and the inner ring
thus getting also compressed. Between the outer and the inner rings of the lining provision is made
for bitumen compound to prevent the two concrete rings from bonding [3].
     A number of suggestions have been advanced on effecting the inner ring compressive stressing
through the injection of cement mortar into the gap between the inner and the outer rings [4].
     In this case the injected cement mortar under pressure will stretch the outer lining and
compress the inner one in the process.
     The composite lining proposed by Georgian Research Institute of Power Engineering and
Power Structures consists of outer monolithic concrete and inner ferrogunite ring. There is a 5-8 cm
thick circular gap which, unlike the above-mentioned gaps, undergoes filling with expanding
alunite cement mortar that provides on hardening compressive prestressing of the entire ferrogunite
ring. Such a design is employed at Inguri waterpower plant (Georgia) pressure tunnel sections with
inner diameter coming up to 9,5 m at internal water pressure of 15 Mpa [5].
A.Kubaneishvili,…                                                         Energyonline №1(2), 2010

     The same principles form the basis for the prestressing of high-pressure vessel frames. The gap
may at times be injected by cement or similar mortar [6] and at other times by some fluid [7].
     In the high-pressure frame proposed by Georgian Research Institute of Power Engineering and
Power Structures the gap between concrete cylindrical shells is divided into separate air-tight
sections by circular elements, one of the sections being filled with fluid under pressure and the
adjacent section with the straining cement mortar [8].
     It is to be noted that the water pressure in the gap of above-mentioned structures should be
maintained constant, for in the event of leakage or water pressure drop one may face the possibility
of structural collapse.
     Application of cement mortar is followed by shrinkage after hardening as well as intensive
creep with time, which leads to the substantial loss in prestressing. Furthermore, in cylindrical high-
pressure frames the steel prestressing takes place in the wall, the floor and the roof independently of
one another.
     The work seeks to develop a new design of a prestressed reinforced concrete high-pressure
frame with improved reliability and performance characteristics that will make it possible to device
emergency double-protection shell and all-round simultaneous compressive stressing technology
(the wall as well as the roof and the floor) allowing to eliminate the need for expensive equipment,
providing the desired magnitude of compressive stressing and structure operation within elasticity
stage as well as the reduction in temperature gradient and permeability.
     The work implementation will make it possible to device a high-pressure frame, its safety and
reliability resulting from the following peculiarities:
     • The replacement of the traditional and labor-consuming technology for individual
prestressing of structural elements by the technology of simultaneous compressive prestressing of
the wall, floor and the roof in one go.
     • The magnitude of the inner shell, the roof and the floor compressive stressing exceeds the
design values thus ensuring their operation within elasticity limits.
     • The stress level in concrete is being taken making provision for the damping character of
strain-creep.
     • Main deformations, connected with prolonged processes (shrinking, creeping) take place
during the first month after the frame fabrication and compressive prestressin, i.e. before putting it
into service, which enables to detect unforeseen defects at that stage.
     • Considerable difference between crack formation and frame destruction bringing about
gradual further development of deformations and crack opening in the outer shell in the event of
increased loads, helps to detect and localize cracks and defects long before the exhaustion of the
frame carrying capacity.
     • Model testing and taking account of various factors in the process of calculation will ensure
high reliability of the results obtained.
     • Concrete characteristics included in the calculations are taken for monoaxial loading, which
provides additional margin of safety with three-dimensional nature of the frame stressed state.
     The issues concerning the development of a new design of high-pressure vessel frame have
been solved both experimentally and theoretically. The theoretical study of the structure has been
carried out using the finite-element method.




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A.Kubaneishvili,…                                                          Energyonline №1(2), 2010

    1. A NEW DESIGN OF HIGH-PRESSURE PRESTRESSED
       REINFORCED CONCRETE BODY
      The high-pressure frame (Fig.1.1) is a reinforced concrete vessel of cylindrical shape built of
coaxially set outer 1 and inner 2 shells with a gap 3 in between, prefilled with loose material of
specific granulation 4. The floor 5 as well as the roof 6 of the frame is a circular reinforced concrete
plate rigidly fitted to the inner shell 2, and connected through the compensator, say, triple-hook
rubber 7, with the outer shell. They are reinforced by bent prestressed tendons 8 placed in specially
designed ducts and uniformly distributed throughout the frame, and securely fixed in the lower and
upper parts of the outer shell 1 with special grippers 9.
      The intercrossing prestressed tendons laid in pairs (abcd and a'b'c'd') (Fig.1.2), placed within a
square (aa' ee') inscribed in the circle of the roof and the floor, contain a curvilinear stretch shaped
as a semicirle (bcd and b'c'd') and tangent line portions orthoganal to it (correspondingly ba, de and
b'a', d'e'). In this case, the angle β between the tendons and the radial movement u of the circle is an
optimal one and accordingly the prestress level in the reinforcement is at its maximum.
      The above-mentioned pair is symmetrical in bend about abscissa axis (Fig.1.2). The most
effective zone of roof and floor compressive prestressing manifests itself with points b and b'
brought into coincidence with each other.




                                Fig. 1.1. A design of high-pressure body




    Fig. 1.2. A layout of one pair of prestressed         Fig.1. 3. A layout of the distribution of
                       tendons                                   prestressed tendons pairs




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A.Kubaneishvili,…                                                         Energyonline №1(2), 2010

     The number of tendon pairs (Fig.1.3) is assigned subject to the condition of frame strength as
well as the condition of compressive prestressing of concrete. The said tendon pairs are being laid
uniformly in a circle by the turning of the corresponding axes of symmetry (x1-x1; x2-x2 etc.)
through angle α.
     In the course of cement grout injection into gap 3 the inner shell 2 will undergo compressive
stressing, whereas the outer shell 1 will undergo tension, moving away from the centre along the
radius and in so doing stretching out the roof and floor tendons anchored in the upper and lower
parts of the outer shell. Jacking leads to all-round compressive prestressing of concrete zone
confined between each pair of symmetrically placed tendons (the crosshatched region in Fig.1.2).
     Cement grout is injected into the gap untill full saturation of intergranular space is achieved.
Thereupon the stress is increased to the desired level of compressive prestressing of the inner shell
concrete, with regard for all losses, following which the ducts with prestressed steel bars are filled
with cement grout.

    2. AN ANALYSIS OF HIGH-PRESSURE BODY
     The developed design of a high-pressure body is a system of "cylinder-anchor". By "anchor"
the point of prestressed tendon fixing on the external surface of the outer cylinder is meant.
     In the analysis of the structure by finite elements method, spacial isoparametric elements are
taken in the form of hexahedron and pentahedron with 20-15 nodes, respectively (Fig.2.1).
     In the points of tendon anchorage on the external surface of the outer cylinder, additional rod
elements are taken (Fig.2.2 and 2.4) with rigidity corresponding to the rigidity of the reinforcing
bars.
     The analysis involves three stages.
     At the first stage the structure is considered to be monolithic (a unified whole), and internal
pressure Pint analysis is being performed. Tangential and longitudinal stresses are determined on the
external and internal surfaces of the cylinder, respectively.
     At the second stage the structure is divided into external open and internal closed cylindrical
shells and the required pressure is achieved in the gap in between. The stressed and strained state of
the shell under the action of pressure is determined and the dimensions of their sections are defined
more accurately, when needed. The maximum tangential stress σθ, generated in the inner cylinder
shell under the external action of pressure Pg can be determined by the methods of variation relying
on the condition of its crack resistance
                                           σ θ = σ int − R bt ,
                                                   θ                                             (2.1)
       int
with σ θ being tangential stress on the inner serface under the action of internal pressure defined
on the first stage of analysis; Rbt - design concrete resistance to axial tension.
     In the outer shell, under the action of pressure P3 in steelbar anchoring points (vessel floor and
roof), reactive stresses are induced by steel stretching out.
     In the intercrossing prestressed tendons placed in pairs and causing compressive stressing of a
plate (roof and floor), under the action of pressure Pg on the linear section, tensile stresses are
               a
generated N 0 (fig.2.3) varying along the length of a circular contour embracing the plate zone; The
said stresses may be calculated from
                                        N α = N a ⋅ e −μα ,
                                          a
                                                0                                                (2.2)
with μ - the coefficient of friction of the reinforcing bars on duct material; α - polar coordinate
         π
0≤α≤       .
         2


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A.Kubaneishvili,…                                                        Energyonline №1(2), 2010




  Fig.2.1. Finite-element scheme of the body:        Fig. 2.2.A scheme of the reinforcement of model
                1 –outer cylinder;                   roof and floor plates with two pairs of stressed
           2 – inner cylinder; 3 - gap                tendons available: 1 – prestressed tendons; 2 –
                                                                     additional bar




Fig. 2.3. A diagram of the distribution of normal   Fig. 2.4. A scheme of the reinforcement of model
 q a and tangential q a stresses, induced by the
   σα                 τα
                                                         roof and floor plates with four pairs of
                                                       prestressing steel available: 1 – prestressed
        stretchening-out of tendons σ a
                                      0                         tendons; 2 – additional bar




   Radial load on the plate transferred by the stressed reinforcing bars will be (fig.2.3)




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A.Kubaneishvili,…                                                            Energyonline №1(2), 2010


                                                         Na
                                               q a ,α
                                                 σ      = α,                                        (2.3)
                                                          R
with R - the radius of plate compressive stressing zone.
    Furthermore, the side surface of the plate is under the action of radial load corresponding to
pressure Pg in the gap. Its total magnitude will be
                                                      a
                                           q σ, α = q σ, α + Pg .                                   (2.4)
    Tangential load from stressed reinforcing steel on plate cylindrical surface can be determined
from
                                            q a, α = σ a i − σ a i +1 .
                                              τ        α       α                                    (2.5)
       a
with σ α i - determined with regard for formula (2.2).

    The total radial and tangential loads can be determined from the condition of superposition:
                                                [                    ]                   ⎫
                                                n

                                  ∑   q σ,α = ∑ (q σ,α i + q σ,α n − i +1 ) + Pg ⎪
                                              i =1
                                                      a         a
                                                                                         ⎪
                                                          n                              ⎬ .   (2.6)
                                           ∑ q τ , α = ∑ (q τ , α i + q τ , α n − i +1 ) ⎪
                                                        i =1
                                                             a            a              ⎪
                                                                                         ⎭

    In the third stage, the three-layer structure, as in the first stage, is considered as a unified whole
and is analized for the action of the inner pressure with due regard for its prestress.

    Design stresses in the sections of the structure can be determined from the expression
                                             {σ}={σ0}+{σP},                                (2.7)
with {σ0} - stresses from structure prestressing; {σP} - stresses generated by the action of inner
pressure Pint.

    The vector of nodal forces in the elements may be written as
                                             {Fσ } = − ∫ [ N]{q σ,α }dv⎫
                                                       v                ⎪
                                                                        ⎬,                          (2.8)
                                             {Fθ } = − ∫ [ N]{q τ,α }dv ⎪
                                                       v                ⎭
with [N] - the matrix of form function.

    The block diagram for the analysis of the structure following finite element method is
displayed in fig.2.5.




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A.Kubaneishvili,…                                                   Energyonline №1(2), 2010




                    Fig. 2.5. Block diagram for the analysis of body disain




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A.Kubaneishvili,…                                                        Energyonline №1(2), 2010

    EXAMPLE
     Initial data.
     Geometric dimensions:
     model height – 690 mm; a gap between the shells of the compound wall – 10 mm; the thickness
of shell walls – 14 mm; outer shell – an open cylinder with an outer diameter – 490 mm; inner shell
– a closed cylinder with firmly fixed roof and floor 56 mm in thickness and external diameter of
442 mm.
     Model material – plexiglass; ultimate strength R=74,5 Mpa, modulus of elasticity E=3560
Mpa; Poisson's coefficient μ=0,33, coefficient of friction on metal K=0,37.
     In the medium layer of the roof and floor are placed mutually perpendicular two pairs of
curvilinear wire adjoining a square inscribed in the circumference of the roof and floor and
anchored on the external surface of model wall.
     The reinforcement layout is represented in fig. 2.2.
     The diameter of the wire – 1,7 mm, ultimate strength Rs =1870 Mpa. The modulus of elasticity
E=20⋅104 Mpa.
     The pressure in the gap of the compound wall is produced at the expense of the energy of the
expanding cement and comes up in a radial direction on the outer shell, to 0,095 Mpa and on the
inner shell – to 0,078 Mpa. Along the generatrixes of cylindrical shells pressure values are 1,0 and
1,4 Mpa, respectively.
     Theoretical investigations of the model were conducted with three-dimensional model
following the finite element method (FEM), with the condition of symmetry taken into account. The
total number of nodes and isoparametric elements added up to 1821 and 317, respectively.
     As a force factor, allowance was made for the action of reinforcement anchores' reaction
forces, occuring due to cement expansion in the gap, on the outer cylindrical shell and along the
circular contour of the plate (roof and floor). The reactive forces of two pairs of anchors (placed at
right angles) applied to the circular surface of the plate, are assumed with due account for stress
distribution pattern ascertained by (2.2). The anchors were simulated by bar elements.
     The stress sheet obtained with above-mentioned forces acting at various vertical sections for
the symmetrical half of the model are represented in fig. 2.6...2.14. The pattern of tangential stress
distribution in two vertical sections of model wall passing through reinforcing bar anchor as well as
outside it is represented in fig. 2.6...2.8.
     It can be seen from fig.2.6 that tangential stresses on the external surface of the cylinder
occuring due to prestress are developing in a linear fashion throughout the height of the section,
while in the zone of tendon anchoring (fig.2.7) they are concentrated locally (fig.2.15-2.18). Similar
stresses on the internal surface of the cylinder in the section passing through the anchor as well as
outside it, as may be expected, are identical, that is, the anchor has no effect at all (fig.2.8).
     A sharp increase observed in the stress sheet occasioned by internal pressure (fig.2.6...2.8) in
the zone of plate-to-cylinder wall connection is produced by the influence of nodal (joint) moment.
     Fig.2.13 and 2.14 provide the pattern of distribution for longitudinal stresses throughout
cylinder heights at model prestressing as well as under the action of internal pressure. As might be
expected, as long as there is no contact with the plate, they remain unchanged, the changes occuring
in the said stresses in the zone of the plate are associated with the magnitude of the internal
pressure.
     If there were hydrostatic pressure in model gap, with its magnitude corresponding to the mean
value of expanding-cement-produced radial pressure taken in the analysis, 0,0865 MPa, the
longitudinal tensile stresses occuring in cylinder walls would be equal to 0,03 MPa, that is, 40 times
smaller.




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                                                                                                                                  A.Kubaneishvili,…




    Fig. 2.6. Tangential Stresses on the external cylindrical surface of the model (Vertical section with no anchors available)
                                                                                                                                  Energyonline №1(2), 2010




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     Fig. 2.7. Tangential Stresses on the external cylindrical surface of the model (Vertical section through anchors)
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     Fig. 2.8. Tangential Stresses on the intemal cylindrical surface of the model (Vertical section with no anchors available)
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A.Kubaneishvili,…                                                   Energyonline №1(2), 2010




         Fig. 2.9. Stresses on the external surface of the model plate under prestressing



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A.Kubaneishvili,…                                                 Energyonline №1(2), 2010




           Fig. 2.10. Stresses on the mid-plane of the model plate under prestressing




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A.Kubaneishvili,…                                                  Energyonline №1(2), 2010




        Fig. 2.11. Stresses on the internal surface of the model plate under prestressing




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A.Kubaneishvili,…                                           Energyonline №1(2), 2010




                    Fig. 2.12. Total stress in the model Plate




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                                                                                                                                    A.Kubaneishvili,…




     Fig. 2.13. Longitudinal Stress on the external cylindrical surface of the model (Vertical section with no anchors available)
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                                                                                         A.Kubaneishvili,…




     Fig. 2.14. Longitudinal Stresses on the internal cylindrical surface of the model
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A.Kubaneishvili,…                                                   Energyonline №1(2), 2010




     Fig. 2.15. Tangential stress field on the extended external surface of the outer cylinder




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A.Kubaneishvili,…                                                   Energyonline №1(2), 2010




    Fig. 2.16. Longitudinal stress field on the extended external surface of the outer cylinder




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A.Kubaneishvili,…                                                    Energyonline №1(2), 2010




     Fig. 2.17. Tangential stress field on the extended internall surface of the outer cylinder




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A.Kubaneishvili,…                                                   Energyonline №1(2), 2010




    Fig. 2.18. Longitudinal stress field on the extended internal surface of the outer cylinder




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A.Kubaneishvili,…                                                    Energyonline №1(2), 2010




            Fig. 2.19. Stress field on the external surface of the plate (floor & roof)
                                      a) radial; b) tangential




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A.Kubaneishvili,…                                                    Energyonline №1(2), 2010




            Fig. 2.20. Stress field on the internal surface of the plate (floor & roof)
                                      a) radial; b) tangential




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                                                                                                         A.Kubaneishvili,…




     Fig. 2.21. Tangential Stresses on theexternal cylindrical surface of the model under prestressing
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A.Kubaneishvili,…                                                  Energyonline №1(2), 2010




        Fig. 2.22. Tangential stress field on the exntended surface of the outer cylinder




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A.Kubaneishvili,…                                                  Energyonline №1(2), 2010




        Fig. 2.23. Stresses on the external surface of the model plate under prestressing



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A.Kubaneishvili,…                                                 Energyonline №1(2), 2010




           Fig. 2.24. Stresses on the mid-plane of the model plate under prestressing



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A.Kubaneishvili,…                                                  Energyonline №1(2), 2010




        Fig. 2.25. Stresses on the internal surface of the model plate under prestressing



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A.Kubaneishvili,…                                                        Energyonline №1(2), 2010

     In fig. 2.9...2.11 are represented the sheets of radial and tangential stresses occuring on the
upper and lower surfaces as well as in the mid-layer of the plate in vertical sections passing through
the anchor and also outside it under model prestressing, while in fig.2.12 - at internal pressure of
P=0,4 MPa. The same figure also includes total stresses.
     The sharp increases in stresses as well as changes in sign at plate-inner cylinder contact zone
are caused by the influence of model gap expanding cement - produced moment acting along the
circular contour of the plate (fig.2.19 and 2.20).


                                        REFERENCY

    1. Prestressed reinforced concrete. By the materials of FJP. Moscow. Stroyizdat. 1986.
    2. Burron R.E.D. Prestessing tend systems – S.I.Taylor Woodron Construction // Conf. of
prestressed concrete pressure vessels, Westminster, 1967, p.22, pp.251-257.
    3. V.M.Mostkov, V.A.Orlov et all. Underground hydraulic-engineering structures. Moscow.
Higher School. 1986
    4. Patent of the Federative Republic of Germany №1484379, cl..84а 9/06.
    5. Author's certificate of the USSR №1137798А, cl. Е02В9/06.
    6. Patent of France №1344260, cl. Е04Н 7/20.
    7. Patent of the Federative Republic of Germany №1185362, cl. 37 F 3/01.
    8. Author's certificate of the USSR №768920, cl. Е04Н 7/00.




АRCHIL KUBANEISHVILI. Doctor of Technical Sciences, Professor, Georgian Research
Institute of Power Engineering and Power Structures,
0171, Georgia, str. Kostava, 70.
Теl.: +995(32) 38-67-98; Моb.: +995 99 939496
E-mail: SPTC.Centre@gmail.com




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