JP2002090230A - Technique for evaluating behavior of tensile-stress- bearing mass concrete - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technique for evaluating the behavior of tensile-stress- bearing mass concrete capable of reevaluating the behavior of a structure of mass concrete by a highly accurate material model and substantially reducing the number of reinforcing bars. SOLUTION: The technique for evaluating the behavior of tensile-stress- bearing mass concrete includes a procedure for analytically evaluating the behavior of the mass concrete by an RC(reinforced concrete) non-linear FEM(finite element method).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for evaluating the behavior of mass concrete which bears tensile stress in mass concrete of a huge structure such as concrete around an underground power plant.

[0002]

2. Description of the Related Art In general, various external forces such as the body's own weight, water pressure in a casing and generator load act on a concrete portion around a generator in an underground power plant, and a temperature stress caused by concrete hydration heat during construction. And thermal stress generated by the heat generated by the generator during operation. Conventionally, to design the concrete part around this generator, the allowable stress method based on the linear FEM (finite element method) using the structure as an elastic body has been applied. As a result of the burden of the reinforcing bars, there is a problem that the reinforcing bars are excessively arranged, and the excessive amount of the reinforcing bars naturally causes disadvantages in terms of material costs, work costs, delivery dates, and the like. Similarly, mass concrete of a huge structure other than the concrete surrounding the generator also has excessive reinforcement and causes problems, but no effective technology has been proposed to solve the problem.

[0003]

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method of evaluating the behavior of a mass concrete structure by applying a non-linear FEM using a highly accurate material model to the behavior of a structure made of mass concrete and permitting cracks. Aim.

[0004]

In order to achieve the above object, the present invention has the following arrangement. That is, according to the present invention, the behavior of mass concrete is controlled by RC (Reinforc).
ed collect) Nonlinear FEM (finite element method)
This is a method for evaluating the behavior of mass concrete bearing tensile stress, characterized by including a procedure of analytically evaluating the concrete. It is also a design systematization that compares the analysis results with the performance required for each part. In addition, for mass concrete of a huge structure, this is a method for evaluating cracks based on nonlinear FEM in consideration of stepwise construction. Further, this is a method of calculating an equivalent temperature distribution for reproducing a temperature stress generated at the time of stepwise construction.

[0005] As a result of the inventor's intensive studies, concrete structures originally tend to exhibit significant non-linearity even at low load levels. It has been found that it can be reduced. The present invention has been made based on such a viewpoint, and the behavior of mass concrete is described as RC.
Analytical evaluation by non-linear FEM allows the behavior of a structure, which was conventionally treated as an elastic body, to be re-evaluated with a high-precision material model, and by taking into account the balance with the performance required for the structure. There is potential for significant cost savings. In the present invention, by including a procedure for comparing the analysis result with the performance required for each part of the structural system, it is possible to significantly reduce the amount of reinforcing bars. Further, in the present invention, regarding the mass concrete of the huge structure,
Casting mass concrete by lift division, that is,
By including a procedure for evaluating a crack based on a non-linear FEM in consideration of stepwise construction, it is possible to appropriately capture behavior during construction. Further, in the present invention, by including a procedure of calculating an equivalent temperature distribution for reproducing a temperature stress generated at the time of stepwise construction, it is possible to evaluate the effect of the construction temperature by using a non-linear FEM.
As described above, a non-linear FEM in which various loads including the construction temperature are considered is performed, and an evaluation system capable of checking performance based on information such as principal stress and crack damage obtained from this analysis can be realized.

[0006]

Embodiments of the present invention will be described below with reference to the drawings. The embodiment exemplifies an underground power plant as an example of a giant concrete structure, and implements the present invention for the purpose of obtaining basic data for rationalizing the design of a filled concrete part of the power plant. .

FIG. 1 is an explanatory view of the entire structure of an example of an underground power plant. As shown in FIG. 1, the inside of the slab, the side wall, and the temporary wall surrounded by the concrete 10 is filled with the filled concrete portion 14, and the periphery of the draft portion of the generator is also filled with the concrete 16. In addition, 12 is a generator room of the part of the room surrounded by the slab and the wall, 17a is a main transformer room, and 17b is an assembly room. FIG. 2 is a three-dimensional model of the filling concrete portion 14, and FIG. 3 is an axisymmetric model of the filling concrete portion 14. As shown in FIGS. 2 and 3, in the filled concrete portion 14, the upper vibration isolating stay 18, the stator foundation and the lower vibration isolating stay 20, the lower bracket 22, and the casing accommodating portion 24 where internal water pressure is generated from the upper portion. Mainly composed.

[I] Analytical Study by Nonlinear FEM FEM (Finite Element Method) analysis in consideration of nonlinearity of RC (Reinforced Concrete) structures is performed by a computer (for example, "Reinforced Concrete" by H. Okamura and K. Maekawa) Non-linear Analysis and Constitutive Rule "(published by Gihodo Shuppan Co., Ltd. in 1991)).

[1] Content of Study Analytical Model An example of the analytical model is shown in FIG. 3 described above. In this model, the assumed underground power plant has an axisymmetric structure having a height of 21 m and a radius of about 16 m (in FIG. Is indicated by CL), and is roughly composed of a temporary wall portion 10 and a concrete filling portion 14 for supporting a casing steel pipe of a generator and a water turbine. The elements in the model in this case are 8-node isoparametric elements, and are RC elements based on the elasto-plastic fracture model. In the element division, especially around the casing, a radial shape was used up to a range of about 50 cm from the casing steel pipe in consideration of the flow of the main stress at the time of internal water pressure action. Further, the temporary wall portion was divided into two in the cross-section height direction.
The casing steel pipe was assumed to have a thickness of 80 mm, and in the case where the steel pipe was modeled, this was used as an elastic element. Since the boundary condition and the load condition were set as parameters to be studied, they will be described in detail later in and.

Investigation case In the investigation case, factors that are important in conducting rationalization investigation, such as the amount of reinforcing steel and concrete strength of the filled concrete part, the element type and boundary conditions of the analysis model (casing steel pipe boundary conditions, etc.). Is a parameter, and by changing these parameters,
We mainly evaluated how the deformation of the structure or the damage such as cracks and rebar yield change. A total of 15 cases were studied (CASE 1 to 15), and the analysis conditions in each case were as shown in FIG. The details of the individual parameters considered in each study case are described below.

Boundary conditions The underground power plant has rocks on its side and bottom.
Therefore, also in the analysis model, the rocky portion, that is, the side and bottom of the model were fixed. However, CASE
Regarding No. 15, in order to examine whether the temperature stress (during operation) is mainly generated by external restraint or internal restraint, the entire model was pin-roller supported, and the model was designed to eliminate the influence of external restraint as much as possible. . Next, it is considered that the end (the turbine side) of the casing steel pipe is considerably firmly constrained by the speed ring. On the other hand, in the conventional design, the analysis is performed with this end being a free condition. When a high internal water pressure acts, it is expected that the effect of the internal water pressure on the filled concrete portion will greatly change depending on the boundary conditions at this portion. Therefore, in this case, the case of the free condition and the fixed condition is set using the boundary condition of the casing end as a parameter. As shown in FIG. 3, the three types of boundary conditions that have been set are as follows: fixation of rock attachment portion A (CASE1 to CASE3), fixation of rock attachment portion + casing end B fixation (CASE4 to CASE14), vertical roller C and pin D is a pin roller support (CASE 15) on the side wall of the temporary wall 10.

Load conditions The loads considered in this analysis are the body's own weight, the water pressure in the casing,
Generator load (vertical and horizontal), anti-vibration stay reaction force, temperature load during operation. For the temperature load due to the heat of hydration of concrete during construction,
The model is updated according to the placement of each lift, or the elastic modulus of concrete is taken into account in consideration of the difference in material age for each lift. Figure 5 shows the load diagram and temperature distribution during operation.
And FIG. First, the water pressure inside the casing is 80kg
f / cm ² , which corresponds to an underground power plant with a large effective head. In addition, in CASE10 and CASE11 in which the casing steel pipe is not modeled, the internal water pressure burden of concrete is set to 50% of the total internal water pressure, and is 40 kgf / cm ² in the present analysis, similarly to the design of the existing point. Generator load horizontal 7 kgf / cm ^2, a vertical 20kgf
/ cm ² and the anti-vibration stay reaction force is 13 kgf / cm ² . In the sequential incremental analysis, these loads are given by load control. The design considers two types of temperature load during operation, the summer temperature distribution and the winter temperature distribution. In this study, the summer temperature was considered. This is a temperature distribution in which the difference between the water temperature in the casing and the concrete temperature is larger than in winter, and the tensile stress around the casing is dominant. For temperature distribution, steady heat conduction analysis was separately performed, and the calculated temperature distribution was used for nonlinear stress analysis. The material constants used in the heat conduction analysis are as shown in FIG.

Reinforcement In the design of a conventional underground power plant, a particular problem is the amount of reinforcing steel which seems to be an excess of the concrete filling around the generator. This is because the stress generated in the structure is calculated by elastic analysis, so the rebar arrangement was determined by the allowable stress method without taking into account the mechanical properties such as the tensile stress of concrete and the adhesion between the reinforcing steel and the concrete. caused by. Therefore, when considering rationalization of design, it is necessary to determine how much reduction in the amount of rebar in a structure can be expected by analysis taking into account the nonlinearity and mechanical properties of the material. In this study, the amount of hoop reinforcement around the casing with a particularly large amount of reinforcement was used as a parameter, and the amount of reinforcement was D32 x 6 steps / 150 (2 per unit volume).
A case of 00 kgf / cm ³ ) was set as the case of the maximum amount of reinforcing steel, and a total of three cases, a half of D32 × 3 steps３２150 and a case of unreinforced concrete, were set. At that time, the amount of reinforcing steel in the filled concrete part excluding the surroundings of the casing was 0.6% (150 kgf / c) in all directions.
and m ³ equivalent), the whole in packed concrete unit only in a case where the casing around the unreinforced concrete was unreinforced concrete. The temporary wall is also modeled using RC elements.
Reinforcement ratio in all cases except the CASE13 of elastic analysis was 0.4% in each direction (100 kgf / cm ³ equivalent).

Material Property Values The material property values used in the analysis are shown in FIG. At this time, the concrete strength of the hollow portion was used as a parameter for studying design rationalization. Specifically, f'c = 210 kgf / cm ² as a standard concrete strength, and f′c = 135 kgf / cm ² and 180 kg as a case assuming that the unit cement amount of concrete is reduced.
f / cm ² , f'c = 282 kg as an actual measurement value of the existing point
f / cm ² was set. In addition, the tensile strength is calculated by the following equation.

(Equation 1) On the other hand, the concrete strength of the temporary wall is f′c = 240 kgf / cm ² in all cases.

[2] Results of study Comparison of behaviors due to differences in the amount of reinforcing bars (casing end free
(Conditions) Here, the filling is performed under the condition that the casing end is not restrained.
Comparison of cases with the amount of reinforcing bar in the cleat part as a parameter
went. The following three cases compared the analysis results.
is there. CASE1: Hoop around casing D32 × 6 steps
相当 150 equivalent Filled parts other than around the casing Rebar ratio 0.6% (r,
(Z, θ directions) CASE 2: Hoop streak around casing 32 × 3 steps
150 equivalent Filled portion other than around the casing Rebar ratio 0.6% (r,
(Z, θ directions) CASE3: Filled part is all plain concrete Comparison of deformation and crack in analysis results
Is shown in FIG. In the deformed view, the thin line is before deformation and the thick line is after deformation.
Show. The length of the crack shown in the figure is
Represents the level of distortion in the cross direction, the maximum shown on the left shoulder
Value strain (ε _nmax) Is the maximum value of cracked orthogonal strain.
You.

When the end of the casing is free as shown in the analysis results here, the casing steel pipe exhibits a deforming property such that it can be spread up and down by the internal water pressure. Therefore, the upper part of the casing steel pipe should originally exhibit a vertical displacement such as sinking due to a vertically downward generator load (20 kgf / cm ² ), but the entire mass concrete above the casing steel pipe is pushed up by the internal water pressure. That is, the vertical displacement is almost canceled and is close to 0 (except for CASE3). In addition, the tensile strain of concrete tends to concentrate on the outside of the casing (the right side of the casing in the drawing) as the casing is expanded, which can be confirmed by a crack diagram. Comparing the difference in behavior due to the difference in the amount of reinforcing bars, the degree of deformation and damage is almost the same in CASE1 and CASE2, even though the amount of reinforcing bars around the casing of CASE2 is の of that in CASE1.
At this time, since the direction of the maximum principal stress <tensile> around the casing was the tangential direction of the casing, cracks occurred radially, and the range was approximately from 50 cm to 100 cm. Next, when the filled concrete portion is made of unreinforced concrete (CASE 3), the behavior is significantly different from those of the other two cases. When loaded under the condition of plain concrete, the strain is localized at a stretch on the right side of the casing where tensile stress is concentrated, and the cracks have reached near the temporary wall. Therefore, the vertical displacement of the structure above the casing is larger than in other cases. Such localization of strain is caused by the total internal water pressure of 8 in the process of sequential incremental analysis.
It occurs when 0% is loaded (the other loads are also 80%), and the state of crack propagation at that time is shown in FIG. For reference, FIG. 11 shows the main stress state immediately before the localization. The tensile stress at the portion where cracks occur at a stretch in the next step is 16 k for ft = 20 kgf / cm ² .
gf / cm ² , which is the largest value as compared with peripheral elements. Note that, in this analysis, no crack occurred in any case except around the casing, and it is understood that the water pressure in the casing is the most dominant load condition in designing the filled concrete portion.

Comparison of behaviors due to differences in the amount of reinforcing steel
Fixing conditions of the ring end>
Considering fixed conditions, the amount of reinforcing steel in
A comparison was made between the cases with parameters. The comparison case is
These are the following three cases. CASE4: Hoop streak around casing 32 x 6 steps
Equivalent to 150 0.6% (r, z,
θ direction) CASE5: Hoop streak around the casing D32 x 3 steps
Equivalent to 150 0.6% (r, z,
(θ direction) CASE6: Filled portion is all plain concrete.
As shown in FIG. In the deformed view, the thin line is before deformation and the thick line is after deformation.
Show. The length of the crack shown in the figure is
Represents the level of distortion in the cross direction, the maximum shown on the left shoulder
Value strain (ε _nmax) Is the maximum value of cracked orthogonal strain.
You.

When the casing end is fixed as shown in the analysis results, the casing exhibits the property of spreading the casing relatively evenly due to the internal water pressure, and the casing end described in the previous study is free. (CASE1-CA
In SE2), the behavior is significantly different from the case where the casing steel pipe exhibited a deformable property such that the casing steel pipe was pushed up and down. In addition, even in the case where all the filling portions are made of unreinforced concrete, localization of strain does not occur, and the damage range is not so different from the model assuming a large amount of reinforcing steel. In this analysis, cracks that occurred radially were approximately 50 mm from the steel pipe.
cm up to 10 cm, even in cracked areas
It was less than 0 cm. From this, it was found that the water pressure in the casing was borne by the entire concrete around the casing, and the stress was not concentrated at one place but was evenly distributed in a limited range. Next, in order to investigate the influence of the boundary condition on the generator side, FIG. 13 shows the principal stress diagram (C R1) of CASE 1 with the casing end free and CASE 4 with the casing fixed.
C, the principal stress for equivalent rigidity). As is clear from the figure, in CASE1, a large amount of compressive stress due to internal water pressure is generated in a wide range in the vertical direction of the casing.
On the other hand, the tensile stress is relatively large on the right side of the casing. On the other hand, in CASE4, the stress distribution is relatively uniform around the casing, and the influence range of the internal water pressure is CASE1.
It can be seen that the range is narrower than that of. In the case where the casing end is fixed, a displacement such as sinking due to a vertically downward generator load (20 kgf / cm ² ) is shown at the generator installation position (for example, corresponding to the position of reference numeral 20 in FIG. 3). The displacement amount at this time is about 0.4 mm regardless of the amount of reinforcing steel in the filled concrete portion. This also indicates that the influence of the casing water pressure is very small at the generator installation position. In each case, no crack occurred except around the casing. The vertical displacement of the slab on the top floor of the temporary wall (upward)
Is considered to be due to the expansion of the structure because the generator temperature is as high as 40-C among the operating temperatures.

Influence of Concrete Strength The results of analysis using the concrete strength of the filled concrete part as a parameter were compared. The comparison cases are the following four cases. CASE 7: f′c = 135 kgf / cm ² , ft = 15
kgf / cm ² CASE 8: f′c = 180 kgf / cm ² , ft = 18
^{kgf / cm 2 CASE6: f'c =} 210kgf / cm 2, ft = 20
^{kgf / cm 2 CASE9: f'c =} 282kgf / cm 2, ft = 25
FIG. 14 shows a comparison between the deformation diagram and the crack diagram among the results of the kgf / cm ² analysis. In the deformed view, the thin line shows the state before deformation, and the thick line shows the state after deformation. The length of the crack shown in the figure represents the strain level in the direction orthogonal to the crack, and the maximum strain (ε _nmax ) shown on the left shoulder is the maximum value of the orthogonal strain. According to the deformation diagram, the difference in deformation due to the difference in concrete strength is not remarkable, and the four cases show almost the same behavior. However, the vertical displacement of the generator installation position is C
ASE7 is 0.5 mm and CASE9 is 0.3 mm, which decreases as the concrete strength increases.
As for the crack range, the damage range tends to slightly increase in cases where the concrete strength is low, but it can be said that the difference in the degree of damage due to the difference in concrete strength is small in the range of the parameters in this case. Therefore,
When the boundary condition of the casing end is fixed, it is considered possible to reduce the amount of unit cement in concrete to some extent and to use low-strength concrete.

[II] Rationalization Study The operation and effect of the method of the embodiment will be described in terms of rationalization. Here, based on the results of the parameter studies conducted mainly in the analytical study using FEM in [I] above, the design of the underfilled concrete section of the underground power plant was considered from the viewpoint of reducing the amount of reinforcing steel and cement in the underfilled concrete section. The rationalization of was considered.

Reduction of the amount of reinforcing bars When the range of the generated cracks is evaluated from the result of the nonlinear analysis of the RC structure, as shown in FIG. 12, in the analysis in which the boundary condition of the casing end is a fixed condition, Even in the case where the middle filling portion set as an example in which the design was rationalized extremely was made of unreinforced concrete, the range of the crack was less than 1 m from the casing steel pipe. The maximum value of the cracked orthogonal strain generated at this time is 2
It is on the order of 00 to 300 μ, and the crack width estimated from this degree of strain is not considered to be a particular problem in securing the casing pipe support function required for the filling portion. In addition, in the upper part of the stuffed concrete (around the barrel) where the generator is installed, the compressive stress is predominant mainly due to the vertical load of the generator, and there is no case where cracks are generated due to the tensile stress. Therefore, regarding the concrete around the barrel, it can be determined from the analysis that the support function of the generator is not lost even in a state close to the plain concrete.

From the examination results, when the strain calculated by the nonlinear analysis and the estimated crack width are used as evaluation criteria, the range in which reinforcement by reinforcing steel is necessary to control the crack is the area around the casing in the mass concrete part. Can be expected to be limited to a narrow range. Therefore,
For the filled concrete part, a considerable reduction in the amount of reinforcing steel can be expected from the current situation. In the above analysis, as an example of extreme rationalization, we set a case with unfilled concrete as the filling part, but for example, as a more realistic rationalization plan,
We tentatively calculated the effect of cost reduction assuming that the amount of reinforcing steel in the middle-filled concrete part was about the critical reinforcing steel ratio. The limit rebar ratio in this case is a rebar ratio set as in the following equation. First, the amount of reinforcing steel required for the middle concrete section of an existing underground power plant is around 2 casings on average.
00kgf / cm ³ , 90 ~
It is 150 kgf / cm ³ and the average of all parts is about 145 kgf / cm ³ . Therefore, since the volume of the filled concrete portion is about 4500 m ³ , a reinforcing bar of about 650,000 kgf is required in total. On the other hand, when the same calculation is performed with the limiting rebar ratio <0.57% × 3 directions>, the rebar amount is estimated to be about 135 kgf / cm ^3, and the total necessary rebar amount is 607,500 kgf.
(135 kgf / cm ³ × 4500 m ³ ), which can be rationalized by about 7% in terms of ratio. In the portion of the existing structure where the amount of reinforcing steel of the filling concrete is the smallest, the reinforcing steel ratio in one direction is 0.38%, which is, for example, a value corresponding to D19 ＠ 300 × 300. If this amount of rebar is applied to the entire filling concrete, the total amount of rebar is approximately 405,000.
kgf (90 kgf / cm ³ × 4500 m ³ ), and in this case, the amount of reinforcing bars is reduced by almost 40%. However, considering that the analysis suggests that the function can be maintained even with unreinforced concrete, it is considered to be a rationalization plan that can be expected sufficiently. FIG. 15 summarizes the above examination results.

(Equation 2)

As another improvement for rationalization, in the current design, the necessary reinforcing bar amount of the hoop bar around the casing is
It can be pointed out that the calculation is performed by a method of adding the required reinforcing bar amounts in the r direction and the z direction of the element. Regarding this, considering that the main stress direction when the internal water pressure which is the most dominant load to the generated stress around the casing is applied is almost the hoop streak direction, the design using the main stress It is thought that it is also possible to reduce the amount of rebar by doing. By the way, according to the result of this elasticity analysis, the maximum principal stress of the concrete around the casing (tensile principal stress) is 86.5 kgf / cm ² at the maximum, the hoop is 50 cm from the casing, and the yield strength of the reinforcing bar is 3500 k.
Assuming gf / cm ² , the required amount of rebar per meter in depth in that range is 122 cm ² , which can be dealt with by arranging D29 @ 150 in three stages. On the other hand, when the reinforcement is arranged based on the conventional design method, the required amount of rebar in the r direction (x direction) and the z direction (y direction) obtained by the following equation is added, and in this analysis, σ _r = -12.7kg
f / cm ² , σ _z = 0.4 kgf / cm ² , τ _rz = 92.4
kgf / cm ² , the required rebar amount in the same range is 2
82 cm ² , and it is necessary to arrange D32Ｄ150 in 5 to 6 steps.

(Equation 3)

Reduction of Unit Cement Amount FIG. 14 shows a comparison of analysis results when the concrete strength of the filled concrete portion is changed in the range of f′c = 135 kgf / cm ^{2 to} 282 kgf / cm ^2. As a result, it was confirmed that even if the concrete strength was reduced to some extent, the deformation and damage did not change significantly. This is due to the fact that the compressive stress is predominant in the filled concrete part except around the casing, and the stress level is sufficiently smaller than the compressive strength of the concrete. Therefore, we studied rationalization of the design by reducing the unit cement amount within a range that does not impair the quality of concrete. Unit cement in concrete is 300k
gf / m ³ , and the water / cement ratio W / C is about 55%. As a result, the uniaxial compressive strength of the concrete f'c
Is 282 kgf / cm ² as an actually measured value. Increasing the unit water content in the concrete mix causes increased drying shrinkage. Therefore, the ratio of water / cement W / C is increased to 65% which is allowed in the concrete standard specification without changing the unit water amount, and the rationalization is examined. Unit water content in concrete than 300kgf / m ³ × 55% 1
It is required to be 65 kgf / m ³ . W / C without changing this value
To make 65%, the unit cement amount becomes 254 kgf / m ³ from 165/65%. That is, about 46 kgf
/ m ³ of cement can be reduced, and the volume of the filled concrete part is about 4500 m ³ ,
The amount of cement of 000 kgf (46 kgf / m ³ × 4500 m ³ ) can be reduced. The concrete compressive strength at this time also depends on the type of aggregate and the like, but can generally be estimated to be approximately 200 kgf / cm ² . In addition, even when the same examination is performed on the case where the water / cement ratio W / C = 60%, a reduction in the amount of cement of about 112,000 kgf can be expected. The above results are summarized in FIG. However, in the case of mass concrete, it is necessary to pay attention to the fact that W / C increases and drying shrinkage increases.

(III) Advancement of nonlinear analysis (introduction of thermal stress during construction) Since the concrete filling around the generator of the underground power plant structure is treated as mass concrete, the concrete hydration heat generated during construction causes It is necessary to consider temperature stress. In order to control the generation of residual stress due to heat of hydration in the construction process of a mass concrete structure, it is common to divide the filled concrete part into a plurality of lifts and perform stepwise construction. Therefore, it is necessary to carry out the stage construction analysis taking into account the construction process and to calculate the thermal stress in the design, and this requires not only the stepwise updating of the model as an analysis method, but also the It is essential to change the heat transfer conditions and the material age of each lift each time. However, at present, it is very difficult to integrate a nonlinear analysis and a heat conduction analysis that considers stepwise construction. Here, as a method for dealing with such a problem, a method of calculating the thermal stress during construction without using sequential analysis in consideration of stepwise construction was studied.

(1) Calculation method of thermal stress during construction In RC nonlinear analysis, it is difficult to calculate thermal stress during construction by sequential analysis in consideration of step construction, so that the following step analysis of thermal stress during construction is performed as shown below. We proposed a method to reproduce without doing. This is a method of calculating the temperature distribution that can reproduce the temperature stress during construction remaining in the structure when the temperature becomes steady without performing the heat conduction analysis considering the stage construction, and applying this directly to the nonlinear analysis It is. The procedure is described below.

First, a residual stress in a steady state which is generated at the stage of construction is calculated by a thermal stress analysis based on a heat conduction analysis and an elasticity analysis. The analysis model and material properties at this time are as shown in FIG. 3 and FIG. 17, and an axisymmetric element is used. In addition, about the elastic modulus of concrete, 1/4 of the initial elastic modulus was used as a value in consideration of the reduction in rigidity due to cracks. Was calculated based on the following theory. The strain that reproduces the final stress distribution at the time of construction is the strain generated by internal or external constraints that contributes to the stress itself, and the strain corresponding to the expansion or contraction (irrespective of the stress) generated by temperature. It is expressed by the following equation by assuming that they are added.

(Equation 4)

Based on Equation 4, the equivalent temperature increment ΔT to be obtained
It is considered that the stress can be reproduced by performing a linear temperature stress analysis in which the equivalent temperature distribution is input by performing the inverse calculation.

(2) Result of Calculation of Temperature Distribution FIG. 18 shows the result of heat conduction analysis (temperature distribution) by sequential analysis.
And FIG. Further, in the final analysis step in FIG. 19, that is, in the results of the thermal stress analysis corresponding to the steady state (day 181), the maximum principal stress (tensile side), the minimum principal stress (compression side) and the principal stress arrow diagram 20 to FIG. 22 are shown in FIGS. FIG. 24 shows a result of calculating an equivalent temperature distribution (ΔT) from the residual stress in the final step of the analysis (181 days upon completion) by using the above strain equation.

Next, in order to confirm the reproducibility of the temperature stress during construction when the obtained equivalent temperature distribution was applied, a thermal stress analysis was performed again using this temperature distribution. The maximum principal stress (tensile side) and the minimum principal stress (compression side) of the stress distribution obtained by this analysis are shown in FIGS. 25 and 26, and the principal stress arrow diagram is shown in FIG. At this time, the stress distribution of the sequential analysis performed earlier is also shown for comparison. Focusing on the maximum principal stress that affects the cracks in concrete, in the sequential analysis (FIG. 25 (b)) in consideration of the stepwise construction, the value around the casing is slightly larger, and the value is up to 15 kgf / cm ^2.
It is. The other parts have a tensile stress of about ^{2 to} 8 kgf / cm ² . On the other hand, in the analysis using the equivalent temperature distribution (FIG. 25 (a)), the stress level is ² to 10 kgf / cm ^{2 as} a whole, including around the casing, and it is almost consistent with the result of the sequential analysis. I understand. However, the contact with the temporary wall of the top lift or the bottom lift
somewhat shows a larger value from kgf / cm ² and 18 kgf / cm ² at maximum. This is thought to be due to the fact that the external constraint due to the temporary wall is large and a shear component is actually included. However, it is also considered that this method calculates the equivalent temperature while ignoring the shear component.

(3) Non-linear analysis using equivalent temperature distribution 1) Analysis conditions Here, an equivalent temperature distribution that reproduces the temperature stress during construction calculated in (2) was applied to the non-linear analysis and analysis was performed. The analysis model of the non-linear analysis uses an axially symmetric element and is a model shown in FIG. In addition, the physical properties of the material
7 is the same as that shown in FIG. The reinforcing bars around the casing are arranged in three steps of D32 (pitch in the depth direction of 150 mm) for the reinforcing concrete around the casing, and the remaining portions are 0.6% in the r, z, and θ directions. The loads used in the study, including the temperature load during construction, are as follows.
These details are shown in FIGS. 5 and 6 described above.

Temperature analysis during construction Temperature during operation Frame weight of the body Water pressure in the casing Generator weight Self-vibration stay Reaction force The above analysis case is referred to as CASE1, and an analysis model CASE2 that does not consider only the temperature load during construction was performed. From the comparison between the two, the effect of the temperature load during construction on the structure was examined.

2) Analysis Results FIG. 28 shows a crack diagram among the analysis results when only the temperature load during construction is considered. As shown in the figure, cracks have occurred in the entire filling portion, and the order of the cracks is as fine as about 100 μm. However, at the junction with the temporary wall at the top of the filling, the order of the cracks is 1500 μm because of the large constraint of the temporary wall. It was decided that this would not be a problem because it had expired. In FIG. 25 (a), a stress sufficient to cause cracking is not generated and does not always agree with the present analysis result, but this is due to drying shrinkage and self-shrinkage during construction in elasticity analysis. This is because the elastic modulus was previously reduced to 1/4 in consideration of the cracks that occurred, that is, it could be said that the nonlinear analysis could directly evaluate the crack without manipulating the material properties.

Next, FIG. 29 to FIG. 32 show the results of CASE 1 in which both the temperature at the time of construction and other external forces (including own weight) are taken into consideration and the results of CASE 2 in which the temperature at the time of construction is not taken into account only by other external forces. Show. FIG. 30 shows cracks in both cases, and FIG. 31 shows an enlarged view around the casing steel pipe. In CASE2, cracks occurred only in a narrow area around the casing. Cracks have occurred in the entire filling part due to the influence of the above. The crack around the casing is 200 to 600 μm at maximum in CASE2, but is 1200 μm at maximum in CASE1 because the temperature during construction is taken into account. However, in this analysis, the rigidity of the speed ring was not taken into account, and the boundary condition on the left side of the casing steel pipe was free, so the casing steel pipe was greatly expanded and the surrounding cracks became remarkable. Since deformation of the casing is suppressed by this, it is considered that cracking is reduced if the effect is considered. As described above, when the influence of the thermal stress generated at the time of construction is analytically evaluated, it is possible to predict that cracks are generated in the hollow portion of the structure although it is minute. Therefore, sufficient attention must be paid to this point even in the case of rationalization in design, and the setting of the performance required for the structure and the limit value for the crack which is expected to occur will be a future subject.

In the above-described embodiment, the present invention is applied to a concrete filled with a generator. However, the present invention can be applied to other large-scale concrete structures.

[0036]

As described above, since the present invention is constructed as described above, the behavior of mass concrete is analytically evaluated by RC non-linear FEM, so that the structure conventionally designed by elastic analysis is used. By re-evaluating the actual behavior of an object with a non-linear FEM incorporating a high-accuracy material model, and taking into account the balance with the performance required for the structure, significant cost reduction can be achieved.

[Brief description of the drawings]

FIG. 1 is an overall structural explanatory view of an example of an underground power plant according to an embodiment of the present invention.

FIG. 2 is a three-dimensional three-dimensional model of the filling concrete part 14;

FIG. 3 is an explanatory diagram of an axially symmetric model of a concrete filling portion.

FIG. 4 is an explanatory diagram of each case (CASE 1 to 15) studied.

FIG. 5 is a load diagram of the model.

FIG. 6 is an explanatory diagram of an operating temperature distribution.

FIG. 7 is an explanatory diagram of material constants used for heat conduction analysis.

FIG. 8 is an explanatory diagram of material property values.

FIG. 9 is a comparative explanatory diagram of a behavior due to a difference in the amount of rebar in the hollow portion of CASE1 to CASE3.

FIG. 10 is an explanatory diagram of a crack propagation process.

FIG. 11 is a diagram illustrating the progress of cracks.

FIG. 12 is a comparative explanatory diagram of behavior due to a difference in the amount of rebar in the filling portion of CASE4 to CASE6.

FIG. 13 is an explanatory diagram of main stresses in CASE1 in which a casing end is free and CASE4 in which a casing is fixed.

FIG. 14 is a comparative explanatory diagram of behavior due to a difference in the amount of rebar in the filling portion of CASE7 to CASE9.

FIG. 15 is an explanatory diagram of a result of a rationalization study of the reduction of the amount of reinforcing bars in the filled concrete portion.

FIG. 16 is an explanatory diagram of a result of a rationalization study on reduction of the amount of cement in the filled concrete portion.

FIG. 17 is an explanatory diagram of material property values and material constants for analysis in calculating a working temperature stress.

FIG. 18 is a heat conduction analysis result (first lift to fourth lift).
FIG.

FIG. 19 is an explanatory diagram of a heat conduction analysis result (fifth lift to completion).

FIG. 20 is a maximum principal stress diagram at the time of completion.

FIG. 21 is a minimum principal stress diagram upon completion.

FIG. 22 is a principal stress arrow diagram at the time of completion.

FIG. 23 is a modified view upon completion.

FIG. 24 is an explanatory diagram of an equivalent temperature distribution.

FIG. 25 is a maximum principal stress diagram obtained from an equivalent temperature distribution.

FIG. 26 is a minimum principal stress diagram obtained from an equivalent temperature distribution.

FIG. 27 is a principal stress arrow diagram obtained from a temperature distribution.

FIG. 28 is an explanatory diagram of behavior based on only a temperature load during construction.

FIG. 29 is a modified view.

FIG. 30 is an explanatory diagram of cracks.

FIG. 31 is an explanatory diagram of cracks.

FIG. 32 is a main stress diagram.

[Explanation of symbols]

 10 Slab / side wall / temporary wall concrete section 14 Filled concrete section 24 Internal water pressure

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Toshihiro Koyama 3-3-1 Higashi-Ueno, Taito-ku, Tokyo Inside TEPCO Design Co., Ltd. (72) Inventor Masanobu Adachi 3-3-1, Higashi-Ueno, Taito-ku, Tokyo Tokyo Electric Power Design Co., Ltd. (72) Inventor Atsushi Yamatani 3-3-3 Higashi Ueno, Taito-ku, Tokyo Tokyo Electric Power Co., Ltd. (72) Inventor Shigeyoshi Nambu 1-3-1, Uchisaiwaicho, Chiyoda-ku, Tokyo Tokyo Electric Power Company Inside (72) Inventor Sadayoshi Kato 3-3-1 Higashi-Ueno, Taito-ku, Tokyo Tokyo Electric Engineering Co., Ltd. (72) Keiichi Iizuka 3-3-1, Higashi-Ueno, Taito-ku, Tokyo Tokyo Electric Design Co., Ltd. Company F-term (reference) 2D047 AB01

Claims (4)

[Claims] 1. The behavior of mass concrete is determined by RC nonlinear F
A method for evaluating the behavior of mass concrete bearing tensile stress, comprising a procedure of analytically evaluating by EM. 2. The method for evaluating the behavior of mass concrete according to claim 1, further comprising a step of comparing the analysis result with the performance required for each part. 3. The mass concrete bearing a tensile stress according to claim 1, wherein the mass concrete of the huge structure includes a step of evaluating a crack based on a non-linear FEM in consideration of stepwise construction. Behavior evaluation method. 4. The method for evaluating behavior of mass concrete bearing tensile stress according to claim 1 or 2, further comprising a step of calculating an equivalent temperature distribution for reproducing temperature stress generated at the time of stepwise construction. .