STIFFNESS CHARACTERISTICS OF THE GROUND BASE AND THERMAL STRESS STATE OF MASSIVE CONCRETE SLABS DURING THE CONSTRUCTION PERIOD Текст научной статьи по специальности «Строительство и архитектура»

Original article

УДК 691.32 + 691.328.1 + 691.335 + 624.042.5 ГРНТИ: 67 Строительство. Архитектура

ВАК: 2.1.1 Строительные конструкции, здания и сооружения; 2.1.6 Строительные материалы и изделия;

2.1.9. Строительная механика

doi:10.51608/26867818_2023_2_48

STIFFNESS CHARACTERISTICS OF THE GROUND BASE AND THERMAL STRESS STATE OF MASSIVE CONCRETE SLABS

DURING THE CONSTRUCTION PERIOD

© Authors 2023 SPIN: 7890-9506 ORCID: 0000-0003-3420-9518 Scopus ID:57189362370

IVANOV Ernest Nikolaevich

PhD Candidate

Peter the Great St. Petersburg Polytechnic University (Russia, Saint-Petersburg, email: 79602615868@yandex.ru)

SPIN: 8120-8541

ORCID: 0000-0002-3752-1219

Scopus ID: 23019786200

SEMENOV Kirill Vladimirovich

assistant professor

Peter the Great St. Petersburg Polytechnic University (Russia, Saint-Petersburg, email: kvsemenov@bk.ruJ

SPIN: 9322-5097 Scopus ID:57194429853

MANOVITSKYI Sergei Sergeevich

lead structural engineer LLC «N-Systems»

(Russia, Saint-Petersburg, email: sergeimanovitsky@mail.ru)

SPIN: 3782-6138 Scopus ID:5720507378

MAKEEVA Aleksandra Vasilevna

PhD Candidate

Peter the Great St. Petersburg Polytechnic University (Russia, Saint-Petersburg, email: nicealexa@mail.ru)

SPIN: 6369-9061

ORCID: 0000-0002-7661-4071

Scopus ID:57197806433

KULESHIN Aleksey Sergeevich

BIM-manager

Semren & Mansson - Bureau of Architecture (Russia, St. Petersburg, email: alex_kulesh4@mail.ru)

Abstract. Thermal stressed state of massive concrete and reinforced concrete structures during the building period is characterized by the risk of large tensile stresses that can lead to the temperature cracks and affect the whole structure integrity. For the crack resistant constructions, such defects are unacceptable. The concrete hardening process is accompanied by a large amount of heat release due to the cement hydration reaction. The most dangerous cases are those, which cause the nonuniform temperature distribution over the body of the block. Significant gradients can lead to stresses exceeding the stresses from operational loads. On top of that, there are factors also affecting the thermal stress state such as ambient temperature fluctuations, solar radiation, the block cooling velocity, initial and boundary conditions, the stiffness of the basement. The last factor is the subject of research reflected in the current work.

The article found that ignoring the ground base deformation characteristics may lead to a significant crack resistance overesti-mation during the design of concrete curing measures. By the calculation, the direct dependence between concrete cracking in the foundation slab and the basement stiffness was revealed: the larger stiffness, the more intensive crack propagation. It is shown that the influence degree depends on the construction thickness: there is the decrease of sensitivity with the larger block thickness, when the thing concreting block is more susceptible to this effect.

Keywords: thermal stresses; thermal cracks; massive concrete constructions; thermal stress analysis; temperature; hydration; early-age concrete; building period

For citation: Ivanov E.N., Semenov K.V., Manovitskyi S.S., Makeeva A.V., Kuleshin A.S. Stiffness characteristics of the ground base and thermal stress state of massive concrete slabs during the construction period // Expert: theory and practice. 2023. № 2 (21). Pp. 48-52. (InRuss.). doi:10.51608/26867818_2023_2_48.

il

2023. № 2 (21)

Научная статья

ХАРАКТЕРИСТИКИ ЖЁСТКОСТИ ОСНОВАНИЯ И ТЕРМОНАПРЯЖЁННОЕ СОСТОЯНИЕ МАССИВНЫХ БЕТОННЫХ ПЛИТ В СТРОИТЕЛЬНЫЙ ПЕРИОД

© Авторы SPIN: 7890-9506 ORCID: 0000-0003-3420-9518 Scopus ID:57189362370

ИВАНОВ Эрнест Николаевич

аспирант

Санкт-Петербургский политехнический университет Петра Великого (Россия, Санкт-Петербург, email: 79602615868@yandex.ru)

SPIN: 8120-8541

ORCID: 0000-0002-3752-1219

Scopus ID: 23019786200

СЕМЁНОВ Кирилл Владимирович

доцент

Санкт-Петербургский политехнический университет Петра Великого (Россия, Санкт-Петербург, email: kvsemenov@bk.ru)

SPIN: 9322-5097 Scopus ID:57194429853

МАНОВИЦКИИ Сергей Сергеевич

ведущий инженер-конструктор ООО «N-Systems»

(Россия, Санкт-Петербург, ул. Оптиков, д. 4, email: sergeimanovitsky@mail.ru)

SPIN: 3782-6138 Scopus ID:5720507378

МАКЕЕВА Александра Васильевна

аспирант

Санкт-Петербургский политехнический университет Петра Великого (Россия, Санкт-Петербург, email: nicealexa@mail.ru)

SPIN: 6369-9061

ORCID: 0000-0002-7661-4071

Scopus ID:57197806433

КУЛЁШИН Алексей Сергеевич

BIM-менеджер

Semren & Mansson - Архитектурное бюро

(Россия, Санкт-Петербург, Набережная канала Грибоедова, д.6/2, литера А, пом. 9Н, email: alex_kulesh4@mail.ru)

Аннот ация.Термонапряжённое состояние массивных бетонных и железобетонных конструкций в строительный период характеризуется риском появления больших растягивающих напряжений и, как следствие, температурных трещин, нарушающих целостность конструкции. Данные дефекты для трещиностойких конструкций недопустимы. Процесс твердения бетона сопровождается выделением большого количества теплоты в результате реакции гидратации цемента. Наиболее опасны случаи неравномерного распределения температур по телу блока. Значительные градиенты могут привести к напряжениям, превышающим напряжения от эксплуатационных нагрузок. Также на термонапряжённое состояние оказывают влияние колебания температуры окружающей среды, солнечная радиация, скорость остывания блока, начальные и граничные условия, жёсткость основания. Последний фактор является предметом исследования, отражённого в данной работе.

В статье установлено, что игнорирование деформативных характеристик основания может привести к существенной переоценке трещиностойкости при проектировании мер по уходу за бетоном. Расчётным путём выявлена прямая зависимость распределения трещин в фундаментной плите от жёсткости основания: чем больше жёсткость, тем более интенсивно трещинообразование. Показано, что степень влияния зависит от толщины конструкции: при большей толщине блока, наблюдается снижение его чувствительности, в то время как блок с меньшей толщиной более подвержен воздействию данного эффекта.

Ключевые слова:температурные напряжения; температурное трещины; массивные бетонные конструкции; расчёт термонапряжённого состояния; температура; гидратация; молодой бетон; строительный период

Для цитирования: Характеристики жёсткости основания и термонапряжённое состояние массивных бетонных плит в строительный период / Э.Н. Иванов, К.В. Семёнов, С.С. Мановицкий, А.В. Макеева, А.С. Кулёшин // Эксперт: теория и практика. 2023. № 2 (21). С. 48-52. doi:10.51608/26867818_2023_2_48.

Introduction

Hardening of massive concrete and reinforced concrete structures is accompanied by a larger amount of heat liberation due to the exothermic reaction of cement hydration. As a result of non-uniform cooling of the structure, the thermal cracks may develop [1-7]. Such fractures are unacceptable in crack resistant constructions.

There are factors influencing the thermal stress state of massive concrete and reinforced concrete structures such as initial conditions (thermal gradient between concrete mixture and ambient, temperature), boundary conditions (presence/absence of insulation), temperature fluctuations of ambient, cement activity, solar radiation [8, 9].

Currently, thermal stressed state calculations taking in account the ground base stiffness characteristics are not spread. The basement is not modeled but just substituted by rigid constraints of the bottom surface of the concreting block that may lead to non-realistic temperature and stress distributions [2-5, 10, 11].

In engineering practice, the soil stiffness consideration plays a significant role. It allows forming the appropriate measures for concrete curing based on the right thermal crack resistance estimation. The direct dependence between concrete cracking in the foundation slab and the basement stiffness is revealed in this research.

(fig. 1). In order to estimate the basement stiffness effect quantitatively, the required insulation thickness was selected for each design situation to meet the crack resistance criterion.

Material of heat insulation is polystyrene with coefficient of heat conductivity A = 0,038 W/mx°C. Air and initial basement temperature are 20oC, concrete mix temperature is 25oC.

ЩШШШШШШШШ.

Fig. 1. Fragment of a cross section of the gateway

The slab is fully height concreted. Concrete mixture is poured on the concrete bedding. Structure properties are represented in table 1.

Table 1 - Slab parameters_

N Name Material Thickness, m

1 Ground base variable -

2 Concrete bedding concrete B12.5 0.5

3 Wate rproofing technoelast -

4 Foundation slab concrete B30 variable

Materials and Methods

Thermal-stress analysis of massive concrete and reinforced concrete structures during the building period consists of three tasks:

1. thermal field determination

2. stress determination

3. crack resistance verification

The 1st task is based on the solution of thermal conductivity homogeneous differential equation [1213]. The result of this step provides the thermal field distribution across the concreting block. The 2nd one includes stress evaluation via deformations generated from the specified temperatures. Finally, the special check according to P.I. Vasil'ev's design criteria is made, which allows to reveal the crack propagation in the construction [14].

Thermal-stress state analysis is performed with the TERM program invented in the Civil Engineering Institute of Peter the Great St. Petersburg Polytechnic University [15]. All calculations are done providing creep and hardening temperature influence on the thermal-physical and strain characteristics of concrete [16-18].

The ground base stiffness influence on the thermal stress state of a massive foundation slab is established on the consideration of several calculation cases with different basement materials and foundation thickness (table 1, 2). The foundation slab of the Nizhny Novgorod hydroelectric complex of inland water transport of the Russian Federation was taken as the design object

Characteristics of the main parameters for each design situation are represented in table 2.

Table 2 - Design parameters

N Subfounda-tion material Elasticity modulus (E), MPa Thickness of the slab, m

4.2 3 1.5

1 Gran it 50000 + + +

2 Limestone 25000 + + +

3 Mild clay 25 + + +

NOTE "+" - means that parameter is combined in the design situation.

The following thermal-physical characteristics are accepted for the concrete B30:

- thermal conductivity coefficient: Ab = 2.67 W/(mxoC)

- specific heat capacity: cb = 1.0 kJ/(kgxoC). Results

Thickness 4.2 m

The calculation of the thermal stressed state of a foundation slab with a thickness of 4.2 m was carried

2023. № 2 (21)

out for three values of basement stiffness (table 2). The required thickness of the thermal insulation was selected in each case.

The dependence of the thermal stresses on the age of concrete is shown in the graph (Fig. 2).

Time, days

Fig. 2. Change in stresses of the center slab for each basement rigidity value

According to the graph, the maximum compressive stresses develop in the core of the slab with foundation basement made with granite then limestone and mild clay (on a 1/1.2/1.6 ratio). On the 22nd day, compression is replaced by stretching. The block center with the limestone base and mild clay was compressed throughout the entire base period.

The required thickness of thermal insulation on the slab surface of block on the granite basement, limestone and mild clay respectively: 0.2 cm, 0.5 cm, 1.3 cm. Thickness 3 m

The calculation of the thermal stressed state of a foundation slab with a thickness of 3 m was carried out for three values of basement stiffness (table 2). The required thickness of thermal insulation was selected in each case.

The dependence of temperature stresses on the age of concrete is shown in the graph (Fig. 3).

4

V N \ 4 и г 1 i 1 I 1 ) 1 j 1 I 1 J i J 1 > : j 'i

s — 1?

\

—-

Time, clays

-Granit -Limestone -Mildclav

Fig. 3. Change in stresses of the center slab for each basement rigidity value

According to the graph, the maximum compressive stresses develop in the core of the slab with foundation basement made with granite then limestone and mild clay (on a 1/1.2/1.9 ratio). On the 12th day compression is replaced by stretching. The block center with limestone base is stretched on the 13th day, with mild clay on the 16th day. The maximum tensile stresses ratio

in the core during the reference period is respectively 1/1.4/4.3.

The required thickness of thermal insulation on the slab surface of block on the granite basement, limestone and mild clay respectively: 1.2 cm, 0.2 cm, 1.1 cm. Thickness 1.5 m

The calculation of the thermal stressed state of a foundation slab with a thickness of 1.5 m was carried out for three values of basement stiffness (table 2). The required thickness of thermal insulation was selected in each case.

The dependence of temperature stresses on the age of concrete is shown in the graph (Fig. 4).

Time, days

-Granit -Limestone -Mild clay-

Fig. 4. Change in stresses of the center slab for each basement rigidity value

According to the graph, the maximum compressive stresses develop in the core of the slab with foundation basement made with granite then limestone and mild clay (on a 1/1.1/2.7 ratio). On the 4th day compression is replaced by stretching. The maximum tensile stresses ratio in the core during the reference period is respectively 1/1.2/3.3.

The required thickness of thermal insulation on the slab surface of the block on the mild clay basement is 0.4 cm. In other cases, it is not possible to select the thermal insulation: cracks appear with any thermal insulation.

Discussion

The calculation results of thermal crack resistance for slabs with the heights of 4.2 m, 3 m and 1.5 m are represented in table 3.

Table 3 - The foundation slab crack resistance calculation results

Insulation thickness, Tensile stresses, 101

Slab cm, provided the base- N/mm2, provided the

thick- ment is basement is

ness, m Granit Limestone Mild clay Granit Limestone Mild clay

4.2 0.2 0.5 1.3 - - -

3 1.2 0.2 1.1 26 18.5 6

1.5 - - 0.4 50 41 15

According to table 3, the stiffer basement with the smallest slab thickness (granite, slab thickness 1.5 m, tensile stresses 5 N/mm2) has the greatest impact on the distribution of thermal stresses in the core; the smallest impact is observed for the weakest basement and the thickest slab (mild clay, slab thickness 4.2 m, no tensile stresses). Such an effect is explained by the occurrence of large reactions in the base with its greater stiffness and less bearing capacity of concrete massive, when the foundation thickness decreases (Fig. 2, 3, 4).

The distribution of the required thermal insulation thickness for all design situations does not fully correlate with the stress values in the block core. This fact may be explained by increasing the ground base stiffness effect on the block's surface layers due to decreasing its thickness. In that case, it is recommended to concrete a slab with 3 m thickness on a limestone base, where thermal insulation is almost not required. Thus, there is a certain balance, when the crack resistance criterion of P.I. Vasil'ev is nearly complied.

Conclusion

1. The stiffness of the massive foundation basement should be taken into account in the calculation of thermal stress state during the construction period.

2. The influence of the basement stiffness is greater, when the ratio of basement stiffness to foundation stiffness is bigger, and should be evaluated by calculations.

3. Thermal insulation as a control measure of cracks elimination could be used in situations, where the structure is less sensitive to the basement strain characteristics, i.e. has a greater thickness. Otherwise, a combination of measures to regulate the hardening regimes will be required, e.g. pre-cooling of the concrete mixture before concreting, pipe cooling, etc.

4. Further research may be performed in the direction of comparing the effect of different soil models such as linear elastic, elasto-plastic, visco-elastic and others.

References

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The authors declare no conflicts of interests. The authors made an equivalent contribution to the preparation of the publication. The article was submitted 19.02.2023; approved after reviewing 30.03.2023; accepted for publication 15.05.2023.

Авторы заявляют об отсутствии конфликта интересов. Авторы сделали эквивалентный вклад в подготовку публикации. Статья поступила в редакцию 19.02.2023; одобрена после рецензирования 30.03.2023; принята к публикации 15.05.2023.