ASSESSMENT OF CIRCULAR PRESTRESSING IMPACT ON CONDEEP PLATFORM STORAGE RESERVOIRS VIA MECHANICAL PRINCIPLES Текст научной статьи по специальности «Строительство и архитектура»

ТЕХНИЧЕСКИЕ НАУКИ. СТРОИТЕЛЬСТВО И АРХИТЕКТУРА

Научная статья УДК 624 : 69

ГРНТИ: 67 Строительство и архитектура

ВАК: 2.1.1 Строительные конструкции, здания и сооружения, 2.1.5 Строительные материалы и изделия, 2.1.9. Строительная механика DOI 10.51608/26867818_2023_4_29

ASSESSMENT OF CIRCULAR PRESTRESSING IMPACT ON CONDEEP PLATFORM STORAGE RESERVOIRS VIA MECHANICAL PRINCIPLES

© The Author(s) 2023 BASHIRZADE Seymur

Department of Civil Engineering, Akdeniz University

(Turkey, Antalya)

OZCAN Okan

Department of Civil Engineering, Akdeniz University

(Turkey, Antalya)

GARIBOV Rafail B.

Dr. of Technical, Prof., Advisor to RAACS

INO "IFCTE" (Tolyatti, Russia)

Abstract. The application of prestressed concrete to cylindrical structures is now recognized as one of the most cost-effective designs. Circular prestressing addresses the weaknesses of leakage and cracking that are common in traditional reinforced concrete tanks. It requires less maintenance, has superior fire resistance, and is a suitable substitute if the steel is costly. This study investigated the entire application of circular prestressed concrete Condeep platform supports and provided recommendations for a circular prestressing methodology.

Keywords: condeep platforms; circular prestressed; post-tensioned concrete; hollow concrete sections

For citation: Assessment of circular prestressing impact on condeep platform storage reservoirs via mechanical principles / S. Bashirzade, O. Ozcan, R.B. Garibov // Expert: theory and practice. 2023. № 4 (23). Pp. 29-35. (InRuss.). doi 10.51608/26867818 2023 4 29

ОЦЕНКА ВОЗДЕЙСТВИЯ КРУГЛОГО ПРЕДВАРИТЕЛЬНОГО НАТЯЖЕНИЯ НА РЕЗЕРВУАРЫ ХРАНЕНИЯ КОНДИП ПЛАТФОРМЫ С ПРИМЕНЕНИЕМ МЕХАНИЧЕСКИХ ПРИНЦИПОВ

© Авторы, 2023 ORCID 0000-0002-08706345

ORCID 0000-0001-99051657

БАШИРЗАДЕ Сеймур

Кафедра гражданского строительства, Акденизский университет

(Турция, Анталья)

ОЗДЖАН Окан

Кафедра гражданского строительства, Акденизский университет

(Турция, Анталья)

SPIN-код: 8718-9610 ORCID 0000-0001-95002874

ГАРИБОВ Рафаил Баширович

доктор технических наук, профессор, советник РААСН

АНО "ИССТЭ" (Тольятти, Россия, e-mail: srbashirzade@gmail.com)

Аннотация. Применение предварительно напряженного бетона в цилиндрических конструкциях в настоящее время признано одним из наиболее экономичных решений. Круговое предварительное напряжение устраняет недостатки, связанные с утечкой и растрескиванием, которые распространены в традиционных железобетонных резервуарах. Он требует меньше обслуживания, обладает повышенной огнестойкостью и является подходящей заменой, если сталь дорогая. В данном исследовании было рассмотрено применение круглого предварительно напряженного бетона для опор. Платформа СоМеер поддерживает методологию кольцевого предварительного напряжения и предоставляет рекомендации.

Ключевые слова: платформы Кондип; круглое предварительное напряжение; напряженный после натяжения бетон; полые бетонные секции

Introduction

Condeep platforms are large concrete structures that are used for offshore drilling and storage. The main support structure is a large concrete cylinder sunk into the seabed using a technique known as gravity-based structure (GBS) (Fig. 1). GBS involves the construction of a concrete cylinder on land, which is then towed to the site and sunk into place. The storage tanks on a Condeep platform were designed to withstand the weight of the stored liquid sand environmental conditions. The location of the storage tanks at the top of the platform has several benefits, such as easy access for maintenance and inspection, a reduction in the risk of contamination from seawater or other external sources, and the prevention of damage to the tanks from marine life or other environmental factors.

Cylinders are essential components used in a wide range of engineering applications to confine or resist liquids entering or exiting them. A Condeep platform storage tank is used to store various fluids, including water, liquid petroleum, petroleum products, and similar products. These storage tanks are built to endure high hydrostatic pressure, which is expected to be distributed equally within each layer but fluctuate vertically along the direction of the shell.

Researchers have investigated various aspects of their design and behavior to ensure the safe and reliable performance of these structures. Daftardar et al. (2017) presented an analytical solution for the calculation of the hoop tension in liquid storage cylindrical tanks. The authors used the classical bending theory to derive the formula and applied it to tanks with bottom-fixed and

top-free boundary conditions [1]. It is noteworthy that Timoshenko (1959) applied the solution of the radial deformation of a tank wall to a similar or superior equation for the deflection of a beam on an elastic foundation. In certain approaches, subgrade reaction coefficients are included in the equations [2]. Lui's dissertation (1960) comprehensively analyzed the design of circular prestressed concrete tanks and proposed a seldom used circular prestressed concrete tank approach in the United States. The study includes a dynamic analytica linvestigation, a detailed explanation of the proposed prestressing approach, and an illustration of the complete design procedure. Additionally, this study conducted a comparative evaluation of several commonly used circular prestressing methods to arrive at a final decision [3]. Pasternak (1932) also made a valuable contribution by presenting practical calculations for the design of folds and cylindrical shells that consider the bending moments [4]. Wills (1953) investigated the design and construction of prestressed concrete reservoirs and presented a case study of a 10,000-gallon tank [5].

Finally, Nwakonobi (2015) conducted a static analysis and design of laterised concrete cylindrical shells for farm storage, which provided insights into the behavior of such structures under different loads and soil conditions. The aforementioned studies collectively demonstrate the importance of understanding the behavior and design of cylindrical tanks and shells, as well as the significance of analyzing their responses to various loads and boundary conditions [6].

ЭКСПЕРТ:

ТЕОРИЯ И ПРАКТИКА

2023. № 4 (23)

EXPERT: THEORY AND PRACTICE

Fig .1. Condeep types offshore platform (Credit: energyfaculty)

This study investigated the influence of circular prestressing on the design of deep platform columns and storage tanks subjected to both internal and external hydrostatic pressures. Prestressing is a technique for increasing the strength and longevity of concrete constructions by compressing the material before subjecting it to external stress. We aimed to determine the appropriate prestressing force for Condeep platform columns and storage tanks under hydrostatic pressure, which is essential for a safe and effective operation.

Analytical modelling

It was considered that the thickness of the tank wall was relatively modest in relation to its height, and the thin cylindrical shell analysis concept was applied. The tank had a closed ring implementation. Moments and shear forces were observed mainly in the zy-plane and horizontal edges. The materia lwas considered to be elastic and isotropic, and the tangential force was constant (Fig. 2).

p„

M,

p*

M,

a) Force equilibrim

Force equilibrium refers to the state, in which all the forces acting on a body or system are balanced and there is no net force acting on it. For a system to be in force equilibrium, the sum of all the forces acting on it must be zero.

1. The concept of equilibrium in mechanics states that if an item does not accelerate in the vertical direction (along the z-axis), the total of all forces acting on it must equal zero.

^rFz = 0->

N..

!

- I Pzdz+C/(1)

2. Similarly, the concept of equilibrium in mechanics states that if an item does not accelerate radially, the total of all forces acting on it in the radial direction (perpendicular to the axis of rotation) must equal zero.

^ Fr = 0;

!

Tz4v6-9-V6:;< + T-T + p8-pB = 0

(2)

b) Compatibility equilibrium Compatibility equilibrium refers to the condition under which the deformation of a structure is compatible with the applied load. In other words, the deformation caused by an applied load should be consistent with the deformation capacity of the material. This requires that the structure not undergo any significant deformation, which can cause failure or instability.

£# =-{az-va>)

£Ф =Ë4°>- Vaz< = -

2n(R + w)- 2nR _ w 2nR = -~R

Vertical unit stress, also known as axial stress, is the vertical stress, whereas tangential unit stress, also known as circumferential stress, is the tangential or circumferential stress.

a# = --~{£z + VE4)a> = 1 + v£z<

1-v2

1-v2 A=1xt=t

The vertical load or force acting on a cylindrical structure, as determined by the axial stress, az, and the cross-sectional area, A

Et . .

Nz = az x A = --- + vsz)

Nz =

1-v2 Et /du

/du w\ {*i-VR)(3)

1-v2 Nz = -1 Pzdz + Ci = 0

du w

---v-=0 (4)

dz R

Fig . 2. Internal forces and displacements scheme in Condeep platform support sections and storage reservoir

Accordingly, for tangential or tension force: Et . .

T*=Y—^4£*+V£z)

т> —

Et

( w du\

Т> —

1 — v2 Et / w „ W\

U-R+v2R) =

Etw

R

■(6)

1-v2\ R ' ' R' c) Moment-curvature equilibrim This equilibrium refers to the balance between the moments and curvatures of an element: the moment-curvature relationship is typically derived from the stress-strain relationship of the material, and can be used to determine the strength and stiffness of the element.While studying a surface's curvature, it is critical to understand the many directions in which the curvature might occur. One example is parallel to the y-plane. The curvature is represented by the variable Kz, which is defined as the reciprocal of the radius of curvature in the zy plane, indicated by Rz.

l

z

It is also critical to evaluate the behavior of a complex surface while evaluating its curvature. The xy plane is one such plane, and its curvature is defined by variable Kx. It is defined as the reciprocal of Rx and the radius of curvature in the xy plane. However, in the case of a flat surface in the xy plane, the radius of curvature becomes infinite, resulting in Kx equal to zero.

ll x Rx *

By understanding how the curvature affects the strain in different directions, it can better predict how a material will deform or behave under various conditions and describe the relationship between the curvature-induced strain in a material and the radius of curvature in the zy and xy planes.

t t ez = t x Kz = —eY = txKY = — = 0

z z D Y Y D

Kz Kx

The relationships among stress, strain, and curvature can help determine the behavior of materials subjected to curvature-causing external pressures.

E . E

a# — ■

1 —V'

■ (£z + V£x) =

1 — V'

/ t t \R# Rx

E t

1—VkXK

a y — ■

1 —V'

■ (sx + v^) =

1 — v2

t t Rx R6

dd dw d2w

— —т~ @ = —= —T"T dz dz dz2

E ( d2w>

o, —

1 — v2

dz2

1 1 3

Mz — az-I — —t3

z zC 12

_ Et3 Mz = 12(1 —v2)

En —

d2w 'dz2 Et3

-s

= Ь°\ dz2 \

12(1—v2)

When we consider that it possesses flexural

stiffness,

d3w

Vy-—ED\ dZ3

(7)

We obtain the resulting equation by solving the (2) equilibrium equation.

d4w Etw

dz4

D 2

Pps +Ei_ — E± = о

D

(8)

When we consider in the flexural stiffness and simplify the equation, we obtain

Et

ß =

N

12(1 —v2)

(2R)2t2

Ed (2R)2ß4 '

Final state of equations; d4w Pi

1 ps

4 + 4ß4w — — — — — d z E'd E'D E'D R

(9)

Coefficient verification and modification

Because equation (9) is a heterogeneous differential equation, its solution can be viewed as a combination of general (wgen ) and specific (wsp ) solutions.

w - wgen + Wsp(10) d4w

+ 4ß4w — 0

dz4

w,

gen

— e1z(C1cosßz + C2sinßz)

+ e~1z(C3cosfiz + C4sin/3z) = 0 We may recalibrate the coefficients , C1 and C2 because H is several times bigger than t.

w — w,

gen

+ wsp — e 1z(C3cosßz + C4sinßz)

1 Pi d

ps

)

Ed EdRj internal pressure: P^ = C'y^H -

z)R(H)

External pressure: Pd = C'ydHR(12)

w = e~1z(C3cospz + C4sinfiz)

1 /C'yi(H-z)R C'ydHR p

1 ps

EdR

The coefficients C3 and C4 are determined from the bottom fixed supported condition.

1 iC'yi(H-z)R C'ydHR

4P4

Wz=0 -0 — Сз— —

ps

Ed — 0

Сз —

EDR, C'YîHR C'ydHR

ps

dw

— (z — 0) — dz

4ß4\ Ed Ed EdR

ßC3e~1z(cosßz + sinßz)

+ ßC4e~1z(cosßz — sinßz)

1 /C'yi(H — z)R C'ydHR — 4ß4'

ps

ëDDR

—0

dw

-(z — 0)—ß(C4 — C3) —

1 (C'YiHR\ — 4ß4\ Ed \

ill

ЭКСПЕРТ:

ТЕОРИЯ И ПРАКТИКА

2023. № 4 (23)

EXPERT: THEORY AND PRACTICE

dw I

— (z = 0) = (3¡C4

C'YíHR C'YaHR P,

4P4\ Ed 1 C'nHR

ED

1 (C'YiHR(1 -1Q 4B4\ ED ( B)

РрЛ) EdRJJ

= 0

C'YdHR P.

ps

w = e

-1#

4P4

c'yíhr c'ybhr p,

Ed EDR )

,s

+

Ed ED

1 (C'YiHR(i -1) 4Pd( ED ( p)

cosfiz

EdR,

1) - C'YaHR

P)

sinfîz

w =

e-Pz

WËd

,s

-ëdr

1 (c'yî(h-z)r c'ybhr p

,s

-ëdr ({(C,

+ (c'YíHr(1-j)-C'YaHR - ^pf) sin/3zj -(C'Yí(H-Z)R-C'YaHR

HR - C'ybHR - ) cosfiz R

1)

As a result, the ring tension and moment developed in the wall can be estimated using the following formula:

Etw _ Et\ e~1z

~=-~R}4l3dED

P@

ТФ=--

HR - c'ybhr

- -¡¡г) C0SPZ

+

(c'YiHR (1--)- C'YaHR

-Jppf)sinPz

(c'Yi(H - z)R - C'YaHR

Eq. (15) gives an equation for the circular prestressing force and is dependent on various parameters such as the Young's modulus of the wall material, the thickness of the wall, the radius of curvature, the depth of the wall, and other parameters such as the coefficients of pressure and the prestressing

force. This equation involves several terms with trigonometric and exponential functions, and can be used to estimate the circular prestressing force at different wall depths.

fd2w>

M# = -Er,

dz2

2P2Ed

(c'HRÍYí - Ya)

-jf)sínpz

+

(C'YiHR (1--)-C'YaHR (16)

Eq. (16) gives an equation for the moment, and is also dependent on parameters similar to Eq. (15). The formula involves second-order differentiation of the wall deflection with respect to depth and includes terms with trigonometric and exponential functions. This formula can be used to estimate the moment at various wall depths. As a case study, basic mechanical formulas (15) and (16) allow us to accurately evaluate the changes in tension (Fig. 3) and moments (Fig. 4) obtained by circular prest-ressing in a shell at a depth of 100 m. These data may be applied to best prepare the design of the Condeep structure and ensure that it can handle projected loads and environmental conditions.

Fig. 3. Tension force changing from the effect ofprestressing force

Fig. 4. Moment changing from the effect of prestressing force

4

The proper distribution of ring tension and prestressed force is essential for system analysis and performance. (Fig. 5) It affects the level of stress and strain experienced by the system and the failure mode of the system. If the forces are evenly distributed, the system may fail in a controlled manner, allowing appropriate mitigation measures to be taken. Therefore, it is important to prioritize an even distribution of these forces and ensure that they are properly balanced.

Prestress force

Fig . 5. The distribution of ring tension and prestress force along the length of structure for the displaced structure

Discussion and conclusion

For the constant-thickness case, the provided equations can be implemented with a low error rate. In a cylindrical tank, circular prestressing is used to generate pressure that opposes and balances the hydrostatic water pressure. Because the specified segment was submerged in water, the impact of the external liquid was sufficient to counterbalance the hydrostatic pressure within the structure of Condeep's multiple marine platforms. However, circular prestressing does not provide a significant advantage for Condeep-type platforms, as shown in Fig. (3) and (4), respectively. Instead, it adds stress to the reinforced concrete section by either "supporting" the external pressure or increasing the magnitude of the stresses. The impact of the circular prestressing force balances the moment produced by the external load when the prestressed concrete tank is full. This is the primary benefit of prestressing during concrete tank construction. When the tank was empty, only the bending effect of the circular prestressing wire occurred. In most cases, an empty tank represents the critical design condition. Hence, it is essential to investigate the tensile stresses induced by the prestressing forces. For instance, it may be advantageous to add conventional mild steel-reinforced bars to handle tensile loads, thereby resulting in partial prestressing.

Nomenclature:

Pz - Vertical pressure

T> -Tangential force or ring tension

P8 -internal forces

Pd —External force

R -Radius of Condeep supports

Pps -Prestressed force

Ed -flexural stiffness

C' - Impact factor

y8 - Density of liquid inside

Yd - Density of liquid outside

H -height of structure

V - Shear force

M -Bending moment

w - Radial displacement of structure

References

1. Anand Daftardar, Shirish Vichare, Jigisha Vashi. (2017): An Analytical Solution for Hoop Tension in Liquid Storage Cylindrical Tanks, International Journal of Engineering and Applied Sciences (IJEAS), pp. 99-104.

2. Timoshenko S.P., and Woinowsky-Krieger S. (1959), Theory of Plates and Shells, 2nd Edition, McGRAW-HILL, New York.

3. Liu, Chi-Yek. "A study of the complete design for circular prestressed concrete tank and its dynamic analysis." PhD diss., Virginia Tech, 1960.

4. Pasternak P. L. (1932), Practical Calculations for Folds and Cylindrical Shells Taking Bending Moments into Account, Stroitelny byulleten,

5. Wills, R. F. (1953). Prestressed concrete reservoirs. New Zealand Engineering, 8(2), 54-59.

6. Nwakonobi, T. U. (2015). Static Analysis and Design of Laterized Concrete Cylindrical Shells for Farm Storages (Doctoral dissertation).

7. Creasy, L. R. (1958). Prestressed Concrete Cylindrical Tanks. Proceedings of the Institution of Civil Engineers, 9(1), 87-114

8. Eremeev, V. V., & Zubov, L. M. (2017). Buckling of a two-layered circular plate with a prestressed layer. Mathematics and mechanics of solids, 22(4), 773-781.

9. Liu, C. F., & Chen, T. J. (2013). A simple and unified displacement field for three-dimensional vibration analysis of prestressed circular plates. Journal of Vibration and Control, 19(1), 120-129.

10. de Lana, J. A., Júnior, P. A. A. M., Magalhaes, C. A., Magalhaes, A. L. M. A., de Andrade Junior, A. C., & de Barros Ribeiro, M. S. (2021). Behavior study of prestressed concrete wind-turbine tower in circular cross-section. Engineering Structures, 227, 111403.

11. Pavel, F. (2021). Seismic risk assessment of on-ground circular reinforced concrete and prestressed concrete water tanks using stochastic ground motion simulations. Bulletin of Earthquake Engineering, 19, 161-178.

12. Zhang, H., Guo, Q. Q., & Xu, L. Y. (2023). Prediction of long-term prestress loss for prestressed concrete cylinder structures using machine learning. Engineering Structures, 279, 115577.

ЭКСПЕРТ: EXPERT:

теория и практика 2023. № 4 (23) theory and practice

Авторы заявляют об отсутствии конфликта интересов. Авторы сделали эквивалентный вклад в подготовку публикации.

Статья поступила в редакцию 01.08.2023; одобрена после рецензирования 27.10.2023; принята к публикации 27.10.2023.

The authors declare no conflicts of interests. The authors made an equivalent contribution to the preparation of the publication.

The article was submitted 01.08.2023; approved after reviewing 27.10.2023; accepted for publication 27.10.2023.