CC BY
33doi: 10.18720/MCE.69.5
Deformation of concrete creep in the thermal stress state calculation of massive concrete and reinforced concrete structures
Деформации ползучести бетона в расчетах термонапряженного состояния массивных бетонных и железобетонных конструкций
I.A. Korotchenko,
E.N. Ivanov,
S.S. Manovitsky,
V.A. Borisova,
K.V. Semenov,
Yu.G. Barabanshchikov,
Peter the Great St. Petersburg Polytechnic
University, St. Petersburg, Russia
Key words: massive concrete structures; reinforced concrete; cement setting temperature; thermal stressed state; thermal cracking resistance
студент И.А. Коротченко, студент Э.Н. Иванов, студент С.С. Мановицкий, студент В.А. Борисова, канд. техн. наук, доцент К.В. Семенов, д-р техн. наук, профессор Ю.Г. Барабанщиков, Санкт-Петербургский политехнический университет Петра Великого, г. Санкт-Петербург, Россия
Ключевые слова: массивные железобетонные конструкции; железобетон; нарастание температуры смеси; термонапряженное состояние; трещиностойкость
Abstract. In the article the thermal stress state of the reinforced concrete foundation of a nuclear power plant during the building period are analyzed. The calculation results of thermal stressed state in massive foundation slabs with and without concrete creep is given. The article also provides a comparative selection of insulation to ensure crack resistance of the foundation plate with and without creep. Authors found that calculation of the problem at elastic definition leads to substantial over the tensile stresses and the elongation deformations on the surface of the slab for the point of time to create maximum of heat dissipation. Not taking into account concrete creep deformation in the problems of crack control for concrete and reinforced concrete massive structures in the building period leads to substantial increasing of required thickness of heat insulation.
Аннотация. В статье проведен анализ термонапряженного состояния железобетонного фундамента атомной электростанции в период строительства. Представлены результаты расчета теплового напряженного состояния в массивных фундаментных плитах с учетом и без ползучести бетона. Проведен сравнительный выбор изоляции для обеспечения трещиностойкости фундаментной плиты с учетом ползучести и без. Авторами было установлено, что расчет задачи в упругой постановке приводит к существенным переоценкам растягивающих напряжений и деформаций удлинения на поверхности плиты в момент для создания максимального тепловыделения. Показано, что не учет деформаций ползучести бетона в задачах обеспечения трещиностойкости бетонных и железобетонных массивов в строительный период приводит к значительному увеличению требуемой толщины необходимой теплоизоляции.
Introduction
The point of over research is the calculation of thermal fields which based on the heat equation solution as well as thermal stresses definition [1-13], linked with calculation of cracking resistance of NPP reactor base slab in construction period. A change in the thermal state of such structures occurs due to the heat liberation from cement hydration during the concrete hardening process, as well as outside temperature fluctuations, solar exposure, various technological factors, etc. Emerging thermal stresses may cause damage to the structural integrity [14-33].
Due to a number of technological and manufacturing reasons, it is preferable to concrete massive foundation mats and other massive structures as a single block of equal height. However, it causes a considerable heat rise in the mass concrete as the result of an exothermic reaction during the concrete hardening. Consequently, the irregular temperature distribution arises along with the block height, which leads to the dangerous tensile strain first on the surface of the foundation slab and then in its central zones. In this regard, the winter period is especially unfavorable for construction [1, 3, 28].
Lowering the thermal field irregularity inside the block by raising its surface temperature prevents high tensile strain in the winter period. Both heat enclosure and an insulation layer on the concrete block are used in order to prevent high tensile strain [1, 3, 21, 26]. A peripheral concrete electric cable with or without minimum thermal protection is usually used as a more efficient and expensive measure.
The regulation process of the hardening concrete thermal effect requires preliminary thermal protection calculations or the electric heating management depending on the environmental conditions, thermal field inside the block and other factors. The papers [1, 29-31] deal with issues of safe replacement of passive thermal protection and lists the calculation results of electric-mode heating of massive concrete structures in the strict formulation (taking into account the influence of the hardening temperature on the thermal and deformation characteristics of concrete).
Calculation of thermal stressed state of massive concrete structures in the building period and value of cracking resistance are hard enough with a practice and engineering point of view. Some researchers close to solution of these problems in a simplified variant. In on nearly every methods, used in a practice calculations at the present time not be taken account hardening temperature influence on the heat dissipation process.[20, 24, 26] and its deformation characteristics.[14, 15, 19]. The research papers [19, 20, 24] have not taken account deformation of concrete creep, but solve to thermoelastic problem.
The purpose of this article is rationale for allowance deformation of concrete creep in the calculation of the NPP reactor base slab thermal stressed state. Calculations of thermal stressed state and cracking resistance taken account the temperature influence on a concrete characteristic.
This paper demonstrates calculation of the foundation mat thermal stressed state with the help of TERM software developed by the staff of the Structural Mechanics and Building Structures department of the Institute of Civil Engineering at the Peter the Great St.Petersburg Polytechnic University [18, 21].Considering horizontal mats sizes significantly exceed their height, we can study a one-dimensional structural model for the mat central part with the reasonable degree of accuracy. In this model, stress and temperature are functions of the vertical coordinate space. In order to estimate the cracking resistance of the foundation mat, we would use the deformation criterion suggested by P.I. Vasiliev [24]. According to this criterion, concrete elongation deformations, determined in view of the concrete creep factor and variable deformation modulus, should not exceed the ultimate concrete elongation.
Methods
Consider B35 foundation slab 2 m high with the cement consumption of 340 kg/m3 constructed in winter (Fig.1). The foundation slab is supported by the concrete bedding layer B12.5 with the grade foundation. Thermal and physical characteristics of the concrete B40 are defined by the concrete thermal conductivity A = 2.67 W/(m0C) and thermal capacity c = 1.0 kJ/(kg0C).
/ \
Mat Foundation B 3 5 1
, Waterproofing / \ layer Concrete bedding layer B12.5 I
Grade foundation
Figure 1. The structural model of the foundation slab
As demonstrated in [14], the instantaneous elastic deformation modulus of concrete is:
— Emax(l e
(1)
E„
where max = 34500 MPa is the limit value of deformation of concrete B35 [15, 16]; a = - 0.37, y = 0.72 - are functional dependency parameters; t - the current time.
Consideration of creep deformation in the paper is based on straight line inherited theory of aging. The equation between stress and deformation are defined by the P.I. Vasiliev recommendation [24]:
where a(y,t) - normal stresses in concrete ;
£n(y,t,T) - deformation induced normal stresses; E(y,T) - elastic deformation modulus of concrete; R(y,t,T) - function of relaxation; t - the current time; t - applied force moment.
The relaxation function in the fixed value is of the form:
R(t,T) — A(l - e-Pja) + (B1 + Die-PTa)e-yi(t-T^ + (B2 + D^^e-^-), where functional dependency parameters are as follows:
(2)
(3)
A = 0.7; B1 = 0.2; D1 = 0.4; B2 = 0.1; D2 = 0.3; a = 0.67; p = 3.61x10-6 c-1; Y1 = 1.17x10-5 c-1; Y2 = 2.33x10"7 c-1.
The heat dissipation process follows the I.D. Zaporozhets equation [19]. The equation parameters I.D. Zaporozhets gets from experimental evidence on concrete heat dissipation.
The heat dissipation process and deformation characteristics depend on the concrete hardening temperature. Registration of such influence goes by adjustment time hypothesis in which a real time is exchanged to adjustment time, which is a function of hardening temperature. The temperature function is of the form:
(4)
(T1-T2) fT —2 s ,
where £ is the characteristic temperature difference.
The following technological specifications of concrete pouring were taken into account: inside the heat enclosure, the concrete mix is poured as a single 2.0 m high block with the inside heat enclosure temperature is 5 °C and surface concrete temperature is 15 °C. After concreting the surface is covered with insulation, which thickness is determined by the cracking prevention condition.
Results
Evaluation of thermal stressed state with a fixed thickness of thermal insulation
Calculations of this paragraph provide for the same thickness of thermal insulation layer for concrete creep and without concrete creep. Fig. 2 shows graphs of variation in time the thermal stresses in the control points of the base slab. Dash line on the graph is response a thermal stresses determined with concrete creep. Solid line is the thermal stresses in the elastic problem definition.
Fig 2. Dependency graph of stresses in the center and on the upper surface of the slab depends on time without concrete creep (solid line) and with concrete creep (dash line)
Analyze of a results show us the following:
1. Character of changing thermal stresses with time is the same in a both cases.
2. The maximum stresses in the elastic problem definition for exothermal heating moment (4 days) is: tensile on the surface of the slab is 4.6 MPa, compressive in the center of the slab is 1.8 MPa;
3. Similarly in the case of concrete creep: tensile stresses on the surface is 2.8 MPa, compressive in the center is 1.1 MPa.
In such a way, problem solution in the thermoelastic definition leads to increase of tensile stresses on the surface to 1.8 MPa (or to 40 %), but compressive tensile to 0.7 MPa (or to 39 %).
Figure 3 shows graphs of changing of stretching deformation on the surface slab in the time for the thermoelastic problem and problem in the strict definition.
Figure 3. Dependency the relative elongation stresses on the surface of the slab in the time without concrete creep and with concrete creep
Analyze of a results show us:
1. Character of the relative elongation deformation is the same in a both cases.
2. The maximum of the relative elongation deformations in the elastic problem definition for exothermal heating moment (4 days) is 24*10-5;
3. Similarly in the case of concrete creep is 16*10-5;
In such a way, problem solution in the thermoelastic definition leads to increase of the relative elongation deformation on the surface of the slab to 8*10-5 (or to 33 %).
Selection of the required insulation thickness
Calculation is performed for the thermal insulation of foam polystyrene density 40 kg/m3, with a coefficient of heat conductivity: A = 0.030 W/m*0C.
For the problem in thermoelastic definition the required thickness of insulation layer is 13 cm. The maximum tensile stresses on the surface of the slab occur on the 4-th day and being 2.1 MPa with modulus of deformation is 33317 MPa. The corresponding relative elongation deformation is 6.3 * 10-5 with their limit value is 6.5 * 10-5.
For the problem in the strict definition the required thickness of insulation layer is 3 cm. The maximum tensile stresses on the surface of the slab occur on the 4-th day and being 1.7 MPa with modulus of deformation is 32366 MPa. The corresponding relative elongation deformation is 5.3 * 10-5 with their limit value is 6.5 * 10-5.
In such a way, the concrete creep accounting in the thermal stress stated of massive concrete structures leads to substantial saving of the thermal insulating material: in this case an economy is 70 %.
Discussion
According to studies, the calculation of the problem in an elastic formulation leads to a significant overestimation of stresses. And in the neglect of creep strain there are problems with the definition of rational thickness of heat insulation from the technical and economic points of view.
According to the work [5-10, 12, 14] energy efficiency and the economic benefit from the application of technical solutions is crucial in modern construction. Therefore, we can recommend using in the calculation of the inelastic formulation of the problem, which turns out to be more advantageous and profitable. And also take into account creep deformation, which give more accurate results [1, 2, 4, 21, 23, 27].
Conclusions
1. Calculation of the problem thermal stressed state of massive concrete and reinforced concrete structures in the building period at elastic definition leads to substantial over the tensile stresses (to 40 %) and the elongation deformations (to 33 %) on the surface of the slab for the point of time to create maximum of heat dissipation.
2. Not accounting concrete creep deformation in the problem of crack control for concrete and reinforced concrete massive structures in the building period leads to substantial increasing of required thickness of heat insulation (to 70 %).
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Ivan Korotchenko,
+7(911)7537423; saenko84@yandex.ru Ernest Ivanov,
+7(960)2615868; ivanov-efimov.e@yandex.ru Sergey Manovitsky,
+7(981)9803734; sergeimanovitsky@mail.ru Victoria Borisova,
+7(921)7718791; vi4ko93@mail.ru Kirill Semenov,
+7(921)7811957; kvsemenov@bk.ru
Yuriy Barabanshchikov, +7(812)5341286; ugb@mail.ru
Иван Алексеевич Коротченко,
+7(911)7537423;
эл. почта: saenko84@yandex.ru
Эрнест Николаевич Иванов, +7(960)2615868;
эл. почта: ivanov-efimov.e@yandex.ru
Сергей СергеевичМановицкий, +7(981)9803734;
эл. почта: sergeimanovitsky@mail.ru
Виктория Александровна Борисова,
+7(921)7718791;
эл. почта: vi4ko93@mail.ru
Кирилл Владимирович Семенов, +7(921)7811957; эл. почта: kvsemenov@bk.ru
Юрий Германович Барабанщиков, +7(812)5341286; эл. почта: ugb@mail.ru
© Korotchenko I.A.,Ivanov E.N.,Manovitsky S.S.,Borisova V.A.,Semenov K.V.,Barabanshchikov Yu.G., 2017
