A new ecological underground group tank with inner steel plate lining for edible oil: Full-scale test and numerical simulation

Abstract

Underground group tanks (UGTs) for edible oil offer benefits in land conservation, ecological sustainability, and oil quality preservation. However, ensuring their structural integrity is a critical concern. This study investigates the mechanical behavior and stability of tank walls with inner steel plate lining in the empty tank, employing both full-scale tests and numerical simulations. Parameters such as internal forces, circumferential deformation, and wall stability under earth pressure were comprehensively examined. Findings reveal that the circumferential internal forces in walls proximal to the junction are more influenced by the junction and adjacent tank walls than those in walls located further away. The numerical results deviate by only 7.7% and 13.3% from the experimental results, verifying the efficacy and accuracy of the numerical model employed. Additionally, it was determined that for tank walls with heights below 5 m, the internal force can be computed using retaining wall force calculations; for greater heights, arch action force calculations are more suitable. Based on stability analysis, a formula for assessing the stability of double-layer, heterogeneous material group tank walls under earth pressure is introduced. It is advised that the thickness of the concrete tank wall should exceed 150 mm to ensure structural stability. These findings offer valuable insights into the rational design of UGTs.

Graphical abstract

Keywords

underground group tanks / full-scale test / numerical simulation / mechanical properties / stability

1 Introduction

The escalating global population has spurred a dramatic increase in the demand for edible oil. In 2022, China reported an oilseed output of 67.49 Mt [1], indicating the growing need for storage tanks for edible oil. At present, above-ground steel tanks dominate the storage landscape. However, underground tanks offer notable benefits, including enhanced cold storage capabilities, reduced land use, energy efficiency, and optimal preservation of oil quality, making them a more desirable choice for edible oil storage [2].

A tank, being a characteristically thin-walled structure, is susceptible to buckling failure due to internal radial pressure and external horizontal loads, thus emphasizing the paramount importance of its structural safety. For above-ground steel tanks, numerical simulations have been performed to investigate the buckling performance of walls and the foundation stress behaviors under wind loads [3–5]. In contrast, underground tanks present a tri-phase mechanical environment comprising soil, structure, and liquid, which complicates their structural and mechanical performance. Related studies focused on the stability and reliability of underground steel tanks subjected to earth pressure and overhead dynamic loads, resulting in more rational design guidelines [6,7]. In parallel, initiatives [8] using lightweight aggregate concrete to seal steel tanks aimed to counteract corrosion have promoted the evolution of underground steel–concrete storage tanks. Subsequent research on steel plate–concrete composite structures highlighted enhanced mechanical properties due to mutual constraints [9,10], proving their suitability for underground applications.

Distinct from an underground single tank, underground group tanks (UGTs) do not require isolated equipment space for oil access due to interconnecting junctions. Consequently, this paper proposes a novel steel plate–concrete UGTs composite design. The UGTs configuration comprises four cylindrical tanks, interconnected via junctions, as depicted in Fig.1.

The large stiffness of these junctions alters the circumferential force, vertical force, and load distribution in UGTs compared to a single independent tank. Typically, as UGTs’ height increases, wall arching effects become evident, yet the underlying mechanism remains unclear. This special structure also finds relevance in ground-reinforced concrete group silos. Findings indicated the inappropriateness of single silo standards for group silo designs, stressing the significance of position considerations [11]. Moreover, design forces for group silos under internal pressure have been recommended [12]. However, in unoccupied UGTs, walls endure radial external pressures from adjacent soil, differentiating them from ground group silos. At this time, tank walls undergo compression, raising concerns over bending stability. The presence of junctions causes non-uniform vertical and circumferential forces along the wall, with complexities intensifying near the junctions. Consequently, conventional internal force and stability computation methodologies are unsuitable when applied to UGTs walls.

For similar structures, numerous studies have delved into the mechanical properties, stability, and waterproofing characteristics of underground structures. Research on underground shafts has investigated the impact of different lateral pressure coefficients on silo wall deformation and failure mechanisms [13]. Additionally, a model rooted in catastrophe theory has been proposed to address vertical stability concerns [14]. In the realm of underground silos, solutions such as polypropylene plastic–concrete walls [15–17] and novel waterproof joints [18] have been recommended to address waterproofing issues. Moreover, thorough testing of the mechanical properties of vertical joints has been carried out [19], resulting in the derivation of critical pressure values for prefabricated steel–concrete silo walls through an equivalent principle [20]. Similarly, in subway stations, the application of finite element analysis (FEA) software has facilitated the examination of mechanical [21,22], alongside discussions on damage development laws and failure evolution mechanisms [21]. Research efforts on tunnel segments have focused on analyzing the mechanical behavior of segments [23] and joints [24,25] under bending loads, as well as investigating stress distribution in supporting structures [26]. Moreover, investigations into the excavation stability of adjacent tunnels [27] and the properties of structural waterproof materials [28] have yielded invaluable insights for design and construction practices. Nonetheless, the structural forms and force conditions of these structures diverge from UGTs, making direct application of their analytical results unsuitable. Hence, an in-depth examination of the mechanical properties and stability parameters of UGTs is necessary.

In this study, we conducted a comprehensive full-scale test and analysis of UGTs, and subsequently established a corresponding numerical model. Variations in internal forces and displacements along the wall height due to earth pressure were investigated, alongside the exploration of the influence of diverse parameters on wall stability. The discussion ends with recommendations for internal force computations for UGTs of varying wall heights. A marked observation highlights that the thickness of the concrete tank wall must exceed 150 mm to ensure optimal wall stability.

2 Experimental program

2.1 Test overview

The research object was the cast-in-place UGTs located at Hangzhou’s Renhe Grain Depot, depicted in Fig.2(a). This UGTs consisted of four tangentially oriented cylinders composed of steel plates and concrete. The upper section of the UGTs was composed of internal steel plates and upstand beams. As illustrated in Fig.2(b), the steel plate–concrete composite tank wall consisted of concrete, internal steel plates, and steel bars. These internal steel plates were welded, serving multiple roles, including structural reinforcement, waterproofing, and formwork functionality. The UGTs’ base comprised internal steel plates paired with a concrete bottom. Central to the UGTs layout is a star tank, designated for equipment storage, as demonstrated in Fig.2(c).

2.2 Layout of measuring points

Given the structure’s perfect symmetry, half of the UGTs sufficed for testing purposes, as presented in Fig.2(c). The measuring point arrangement is shown below.

Earth pressure gauges were arranged vertically on the external wall surface, as depicted in Fig.3. Designations for these points followed the format E-V-C, where “V” denotes the vertical points in three layers, and “C” represents the circumferential points in three columns.

The steel bar gauges were positioned along both the inner and outer circumferential steel bars within the concrete tank wall, as depicted in Fig.4. These points were labeled as S_O-V-C and S_I-V-C, where “S_O” signifies points on the outer circumferential steel bar, “S_I” indicates those on the inner circumferential steel bar, “V” represents the vertical points in three layers, and “C” refers to the circumferential points in six columns.

2.3 Test loading

As illustrated in Fig.5, the steel bar gauges were welded when the steel bars were tied. Stress measurements were conducted before the backfilling, serving as initial data benchmarks. The installation of earth pressure gauges, depicted in Fig.6, also preceded the backfilling process. Subsequent to the embedding of both steel bars and earth pressure gauges, data were systematically obtained in phases based on the on-site construction progression and specific UGTs process requirements.

A working condition correlating to a backfill height of 3.20 × 10³ mm was selected for data acquisition and analysis according to the construction procedure. It’s important to note that the UGTs were empty during this period. Tab.1 presents the test results of the earth pressure gauges, while Tab.2 shows the findings from the steel bar gauges. Note that the stress values listed in the tables were derived by substituting the frequency modulus into the formula provided by the factory, a computation using data from both the earth pressure and steel bar gauges.

2.4 Results and analysis

2.4.1 External earth pressure

An obvious increment in earth pressure was observed with the height increases, a trend that conforms to the classical earth pressure theory, as presented in Fig.7. The test mean values (\overline{E}) surpassed the magnitudes of static soil pressure (E_0) and active soil pressure (E_{\mathrm{a}}), yet remained inferior to the magnitudes of passive soil pressure (E_{\mathrm{p}}). Adoption of the passive earth pressure method was advocated for lateral pressure calculations during structural analysis. This methodology considers the influence of adverse elements, such as uneven backfilling and ground overloading, on the lateral pressure generated on the wall throughout the construction phase [29].

2.4.2 Outer circumferential steel bar stress

Upon reaching a backfill height of 3.20 × 10³ mm, stress measurements of the outer circumferential steel bar are depicted in Fig.8. It can be observed that the compressive stress initially increases as the height increases, reaching a peak at 1.70 × 10³ mm from the UGTs base, and subsequently decreasing gradually with further increases in height.

An examination of the figure indicates the variable stress dynamics of the circumferential steel bar at a height of 0.70 × 10³ mm, particularly close to the junction. Initial stress reduction is succeeded by an increase, which then stabilizes away from the junction. The maximum compressive stress, measured at 1.87 MPa, is located at the 150° circumferential orientation. Compared with the 70° circumferential angle, compressive stresses at 80°, 90°, 120°, 150°, and 180° have increased by −3.4%, −4.6%, 2.3%, 6.9%, and 6.9%, respectively. For wall heights of 1.70 × 10³ mm and 2.70 × 10³ mm, the compressive stress initially rises, reaching a peak at the 80° ring position close to the junction, subsequently maintaining stability further away. It is noteworthy that the maximum stress at these heights surpasses the 0.70 × 10³ mm height counterpart.

Such results imply that buoyancy generates shearing forces and bending moments, counteracting the earth pressure direction at the UGTs base. This leads to a unique stress profile in the outer circumferential steel bar, which initially elevates and then recedes, deviating from the earth pressure’s distribution. The adverse impacts of neighboring tank walls, junctions, and earth pressure are the greatest near the junction, meriting special design consideration.

2.4.3 Inner circumferential steel bar stress

Fig.9 presents the stress profile for the inner circumferential steel bar. The data display a steady increase in stress corresponding to the wall height, with a pronounced peak at 1.70 × 10³ mm from the UGTs base.

It shows a pattern where the compressive stress in the inner circumferential steel bar at a wall height of 0.70 × 10³ mm intensifies with increasing distance from the junction, peaking in areas away from it. Compared with the 70° circumferential position, compressive stresses in the circumferential positions of 80°, 90°, 120°, 150°, and 180° have surged by 95.7%, 127.1%, 184.3%, 202.9%, and 202.9%, respectively. As for the wall heights of 1.70 × 10³ and 2.70 × 10³ mm, the compressive stress in the inner circumferential steel bar exhibits a consistent increase, peaking at the 120° circumferential direction.

It is found that compared with the outer counterpart, at the same angle, the inner circumferential steel bar is subjected to a weaker constraint from the junction. The circumferential internal forces in walls near the junction are more influenced by both the junction and adjacent tank walls than those in walls located further away. This stress state differs from that of a single independent tank.

3 Numerical analysis

3.1 Model establishment

For a numerical representation of the UGTs, the ABAQUS software was utilized. The C3D8R element is applied for the concrete tank wall and the bottom plate. The S4R element and the T3D2 element are used to the internal steel plate and the steel bar, respectively. Hexahedral cells structured the meshes for the tank wall and base plate, whereas the internal steel plate and steel bar meshes were more fluid, founded on quadrilateral cells. This study used a validated mesh size, with a specific mesh size of 80 mm, as shown in Fig.10. An “Embedded Region” feature connected the steel bar and the concrete tank wall, while the internal steel plate and concrete wall were bound together using the “Tie” functionality. The same “Tie” method was employed to link the UGTs wall with the roof internal steel plate, the roof internal steel plate with the roof concrete plate, and the UGTs wall with the bottom plate’s rigid body. This study primarily focused on analyzing the stress and deformation characteristics of the UGTs in the elastic stage. The strength grade of the concrete was C30 with an elastic modulus of 30000 MPa and the Poisson’s ratio of 0.2. The elastic modulus of the steel bar and internal steel plate was 206000 MPa, with the Poisson’s ratio of 0.3.

A comprehensive understanding of UGTs’ mechanical properties necessitated the consideration of the surrounding soil, mainly for its loading effect without factoring in its potential constraining impact on the tank wall. However, the confining effect of the soil beneath the base plate was incorporated. The UGTs’ bottom plate was subjected to both displacement and rotational constraints in the X, Y, and Z dimensions. Notably, the UGTs’ upper section remained free from constraints. In UGTs, the primary load on the tank wall was exerted by the backfill. A triangular load was applied to the outside of the tank wall to simulate the earth pressure under test conditions. Based on the linear regression analysis of the average pressure at the same heights, the expression for the lateral pressure exerted on the tank wall was obtained as follows:

(1)E=-23.76h+86970,

where E represents earth pressure (unit: Pa), and h represents tank wall height (unit: mm).

3.2 Model verification

Upon reaching a backfill height of 3.20 × 10³ mm, a comparative analysis between the experimental stress measurements for inner and outer circumferential steel bars at the heights of 0.70 × 10³, 1.70 × 10³, and 2.70 × 10³ mm, and their numerical counterparts was undertaken, as illustrated in Fig.11.

According to Fig.11(a), the stress value of the outer circumferential steel bars in the numerical simulation agrees with the experimental findings. For the wall height of 0.70 × 10³ mm, the stress value on the outer circumferential steel bar first drops, then ascends near the junction, subsequently reaching a plateau in the part away from the junction. For the 1.70 × 10³ and 2.70 × 10³ mm wall heights, the stress values initially rise and subsequently decrease close to the junction, and show an ensuing growth in the position away from the junction. The peak discrepancy between the simulated and empirical values is 7.7%.

From Fig.11(b), an agreement is observed in the stress values of the inner circumferential steel bars between the numerical simulations and the full-scale tests. Specifically, for wall heights of 0.70 × 10³, 1.70 × 10³, and 2.70 × 10³ mm, there is an initial surge in stress values close to the junction, which then stabilizes in the position near the junction. A maximum deviation of 13.3% between simulated and experimental values suggests an ideal simulation accuracy.

The noted disparities can be attributed to a few factors. First, the inevitable heterogeneity of the backfill soil is introduced during the backfilling phase, leading to creep in the tank wall under the influence of earth pressure. Secondly, simplifications were made during the establishment of the numerical model. For instance, in the simulation, a “Tie” constraint was employed between the internal steel plate and the concrete tank wall, whereas the actual test setup saw the internal steel plate affixed to the concrete tank wall using welded studs.

In essence, the numerical simulations align closely with experimental data, proving the feasibility of the numerical simulation. The results offer significant evidence to support the subsequent analysis of how correlation parameters affect the mechanical performance and stability of UGTs.

4 Stress analysis of tank walls with varying heights

Using the validated UGTs model, UGTs with varying heights were constructed to explore how height influences the mechanical properties and displacement of the tank wall in the empty tank. Concurrently, to attenuate the impacts of constraints and wall height on internal forces, midpoints of these models were individually investigated.

4.1 Stress analysis of steel bars

Fig.12(a) and Fig.12(b) illustrate the stress curves of both the outer and inner circumferential steel bars around the wall's perimeter. Notably, the presence of the junction leads to geometric discontinuity and stress concentration in the tank wall subjected to earth pressure. This leads to abrupt stress inflection points, with the abruptness increasing with the wall height. Fig.12(c) and Fig.12(d) emphasize that both outer and inner vertical steel bars experience lesser abrupt stress changes at the junction compared to their circumferential counterparts.

The presence of the junction results in a stress change of the steel bar relatively complex at the circumferential position from 0° to 70°. Therefore, this paper mainly analyzes the stress distribution of the steel bar from 80° to 180° in the circumferential direction. Fig.12 suggests that for a wall height of 4 × 10³ mm, the peak stress in the circumferential steel bars is reduced compared to the vertical steel bars on both the outside and inside of the tank wall at the circumferential position from 80° to 180°. Furthermore, the ratios of the average stress in the circumferential steel bar to the vertical steel bar on the outer and inner sides of the tank wall at the circumferential position from 80° to 180° are 0.91 and 0.93, respectively. Predominantly, both the internal and external sections of the UGTs wall at the circumferential position from 80° to 180° exhibit vertical stresses, mirroring stress profiles typically seen in retaining walls. This observation suggests that the internal forces of the tank wall at the circumferential position from 80° to 180° can be estimated using methods traditionally reserved for computing the internal forces of retaining walls.

From Fig.12, it becomes evident that for a wall height of 5 × 10³ mm, the peak stress exhibited by the circumferential steel bars exceeds that of the vertical steel bars on both the wall’s external and internal sides at the circumferential position from 80° to 180°. Additionally, the ratio of the average stress between the circumferential and vertical steel bars stands at 1.83 and 1.51 on the exterior and interior of the wall at the circumferential position from 80° to 180°, respectively. At this time, the inside and outside of the UGTs wall at the circumferential position from 80° to 180° predominantly experience circumferential forces, and as the wall height surpasses 5 × 10³ mm, circumferential forces come into play. Thus, the force behavior of the UGTs wall at the circumferential position from 80° to 180° starts to resemble that of an arch, implying that internal force calculations can be benchmarked against arch-based computational methods.

The findings demonstrate that at diminished wall heights, arch action of the tank wall at the circumferential position from 80° to 180° is absent and the force is majorly vertical. However, as the wall height exceeds 5 × 10³ mm, to enhance the wall’s vertical stiffness, forces are transferred to both ends of the wall along an arch. Consequently, vertical forces decrease, giving way to an elevation in circumferential forces which then manifest as circumferential steel bar forces.

4.2 Stress analysis of concrete tank wall

4.2.1 Stress analysis

Fig.13 elucidates how stress in the concrete wall varies circumferentially with increasing wall height.

The observations from Fig.13 highlight that, within the star tank section, there is a gradual decline in tensile stress around the wall's circumference. For a wall height of 12 × 10³ mm, this tensile stress surpasses the limit, suggesting that the optimal wall height should be capped below 12 × 10³ mm. The presence of the junction leads to geometric discontinuity and stress concentration in the tank wall subjected to earth pressure. These factors contribute to abrupt stress inflections, and the slope of these inflections increases with wall height. Near the junction, the predominant stress is compressive in nature, and its magnitude first increases, then decreases, and eventually stabilizes in the position far away from the junction. The most pronounced stress values emerge near the junction, emphasizing the need for special design consideration in this region.

4.2.2 Displacement analysis

Fig.14 showcases the circumferential displacements for varying wall heights.

Notably, across different wall heights, there is a consistent trend in the circumferential displacements of the UGTs. These displacements decrease in the segments of the star tank and the junction. The position near the junction witnesses complicated displacement patterns due to force complexities, reaching a maximum displacement of −6 mm at the wall’s midpoint. Moreover, it tends to stabilize in the position away from the junction. This aligns with the concrete tank wall's stress distribution.

Conclusively, the concrete wall's internal force escalates with the wall height. The junction alters the force distribution within the concrete tank wall, with the peak internal force occurring at the 80° circumferential position. Parts far away from the junction are relatively insulated from these alterations.

4.3 Stress analysis of internal steel plates

4.3.1 Stress analysis

Fig.15(a) provides a visual representation of the circumferential stress across the internal steel plate. The internal steel plate cooperates with the concrete, sharing the load. The stress pattern of the internal steel plate mirrors that of the inner circumferential steel bar. Specifically, it first decreases, then increases at the star tank, interrupted by sudden stress shifts at the junction’s ends. Both the highest tensile and compressive stresses emerge at the junction’s ends and rise as the tank wall height increases. The circumferential stress, in proximity to the junction, first descends and then escalates, achieving stability in the position away from the junction. Analysis of the stress curve reveals a sudden change at the junction, primarily attributed to the geometric discontinuity and stress concentration of the tank wall at this position.

Fig.15(b) shows the vertical stress curve across the internal steel plate. The primary source of stress in the star tank section is attributed to internal deformation, resulting in relatively lower stress levels in this area. The most pronounced stresses manifest at the junction’s two ends, which are much larger than the stresses at the junction’s midpoint. Furthermore, the stress values are closer in the position away from the junction. Through the analysis of the stress curve, it is found that the stress at the junction has a sudden change, which is mainly attributable to geometric discontinuity in the steel plate concrete composite tank wall at this position.

The presence of the junction resulted in relatively complex stress variations in the circumferential position from 0° to 70°. Therefore, this paper mainly analyzes the stress distribution of the internal plate from 80° to 180° in the circumferential direction. Fig.15 suggests that at a wall height of 4 × 10³ mm, the peak vertical stress in the internal steel plate at the circumferential position from 80° to 180° surpasses its circumferential counterpart. The circumferential stress’s average stands at 0.63 times the vertical stress, emphasizing that stresses primarily propagate vertically, similar to those in the retaining walls.

However, as the wall height reaches 5 × 10³ mm, the peak circumferential stress in the internal steel plate at the circumferential position from 80° to 180° exceeds the vertical stress. On average, circumferential stress is 1.45 times that of vertical stress. With the wall height progression, arch effects emerge, directing forces on the internal steel plate circumferentially. For wall heights exceeding 5 × 10³ mm, the internal steel plate’s force dynamics resemble those of 5 m-high UGTs.

These insights suggest that for wall heights below 5 × 10³ mm, the composite wall’s internal force calculations at the circumferential position from 80° to 180° should be based on the retaining wall. Conversely, for heights surpassing 5 × 10³ mm, the arch-based method is more suitable.

4.3.2 Displacement analysis

Fig.16 presents how the internal steel plate’s circumferential displacements vary with its height. The data suggest that the internal steel plate’s maximal displacement, which lies at the wall’s midpoint, rises with escalating wall heights. The displacement pattern of the internal steel plate aligns with that of the concrete tank wall, peaking near the junction at −6 mm.

In summary, the internal steel plate’s deformations synchronize with those of the concrete tank wall. This coordinated deformation requires heightened design attention, especially at the composite wall’s midpoint, where is subjected to considerable displacements.

5 Eigenvalue buckling analysis

The stability of a “cylindrical thin shell”—a tank with a wall thickness-to-radius ratio less than 1/20 [30]—under external pressures, elastic stability calculations are usually required. This is due to the characteristic tendency of such structures to reach instability before strength failure. The design recommendations made in Section 4 are based on the assumption that UGTs will not undergo failure under the influence of earth pressure. In light of this, the present section conducts an in-depth stability assessment of the tank wall under the most unfavorable conditions.

5.1 Numerical simulation results

Assuming the UGTs are built using the reverse construction method, the most unfavorable condition occurs when the tank wall is fully constructed while its upper and bottom sections are not. Under these conditions, the wall endures earth pressure but lacks constraints at its upper and bottom, allowing only radial movement [20].

Based on the 4 m-high UGTs model, 40 numerical models are developed. Given the negligible impact of reinforcement on the wall’s overall stability in the elastic analysis [31], it is excluded. The eigenvalue buckling analysis is used to analyze the stability of the tank wall in 4 m-high UGTs. The buckling load of the structure is 1.2675 MPa greater than the earth pressure. Therefore, when the height of the wall is 4 × 10³ mm, the UGTs remain stable under earth pressure. The first-order buckling mode is “elliptical,” as shown in Fig.17. This method is employed to analyze wall buckling for varying design parameters. These parameters include the wall height, internal steel plate thickness, concrete tank wall thickness, concrete’s elastic modulus, and inner diameter (r). The buckling modes of all models are observed to be “elliptical” as shown in Fig.17. Hence, this paper primarily focuses on analyzing the buckling loads of all models and comparing them with the earth pressure. Fig.18 to 22 depict the buckling load curves for each model.

In scenarios where only the wall height varies, Fig.18 reveals that buckling load decreases with increasing wall height under the least favorable conditions. Yet, this decline is minor in magnitude. The lowest value recorded is 1.26 MPa, which significantly surpasses earth pressure. This verifies the findings from Section 4, asserting that UGTs remain stable under earth pressures for wall heights spanning 4 to 12 m. Across this height spectrum, the change in buckling load is a mere 0.4%, signifying a negligible impact of height on wall stability.

When varying the internal steel plate thickness (t_2) of the composite tank wall, Fig.19 indicates that wall stability increases with thickness. Specifically, compared to a wall with a 5 mm thick internal steel plate, walls with thicknesses of 10, 15, 20, 25, 30, 35, and 40 mm exhibit increased buckling loads by 21.4%, 39.1%, 53.6%, 66.0%, 76.7%, 85.7%, and 94.3%, respectively. Thus, thicker internal steel plates promise enhanced wall stability.

Upon applying the control variable method, both t_2 and the concrete tank wall (t_1) are adjusted. Fig.20 shows that, with a constant internal steel plate thickness, the wall’s buckling load escalates with an increase in the concrete tank wall thickness. A thicker concrete proportion in the composite wall significantly improves its stability. A critical observation is that when the concrete tank wall thickness is just 150 mm, the wall’s buckling load drops below earth pressure.

As the inner diameter (6.778–7.625 mm) of the tank wall changes, a distinct alteration in the thickness-to-diameter ratio (t/r) of the tank wall becomes evident, as demonstrated in Fig.21. It is obvious from the figure that increasing the inner diameter while maintaining a consistent composite tank wall thickness, results in a reduced buckling load. When the ratio of the internal steel plate thickness to the concrete thickness is held constant, a progressive increase in the composite tank wall thickness causes the buckling load to rise. Fig.22 highlights the change when only the concrete strength is altered. It is clear that the wall stability linearly escalates with rising concrete strength.

These findings emphasize that the wall stability is enhanced by augmentations in the concrete tank wall thickness, the internal steel plate thickness, the overall wall thickness, and the concrete strength. Conversely, growth in the wall height and the tank’s inner diameter incrementally undermines the wall stability. Consequently, it is imperative that the thickness of the concrete tank wall never drops below 150 mm.

5.2 Theoretical calculation of composited tank wall buckling load

Considering that UGTs comprise four cylinders tangentially connected, the wall is understood as being constituted of several cylinders. Existing literature [32,33] provides a formula for determining the buckling load of a ring exposed to uniform pressure:

(2)q_{\mathrm{c}\mathrm{r}}=\frac{3EI}{R^3},

where R is the inner radius of a single wall in a UGTs.

Under the most unfavorable working conditions, the UGTs is exclusively under the influence of earth pressure. Relying on equivalent stiffness [20] and numerical simulations, Eq. (3) is suggested for calculating the buckling load for a four-circle tangent group tank wall, possessing a dual-layer heterogeneous material and exposed to external pressure, considering wall heights spanning from 4 to 12 m. Fig.23 offers a diagrammatic representation of the composite section.

(3)q_{\mathrm{c}\mathrm{r}}=\frac{5.31\times \left(E_1{I}_1+E_2{I}_2\right)}{{\left[R+t-0.5\times \left(-E_1{t}^2+E_{1}2t{t}_2-E_1{t_2}^2-E_{2}2t{t}_2+E_2{t_2}^2\right)/(-E_{1}t+E_1{t}_2-E_2{t}_2)\right]}^3},

where t is the wall thickness, E_1 and E_2 are the elastic moduli of two materials, respectively, I_1 and I_2 are the inertia moments of the sections of two materials against the neutral axis of the composite section, respectively.

To validate the formula’s efficacy, its calculation results are compared with the simulation numerical results derived by altering the internal steel plate thickness (5–40 mm), the concrete thickness (175–325 mm), the concrete strength (C20–C50), and the tank wall’s inner diameter (6.778–7.625 mm), as illustrated in Fig.24-Fig.27.

The depicted results imply that, regardless of changes to these design parameters, the disparity between the outcomes from the proposed formula and the numerical simulations remains within 16.3%. Therefore, the theoretically derived formula in this paper offers an accurate prediction for the buckling load of a four-circle tangent group tank wall with a dual-layer heterogeneous material subjected to earth pressure.

5.3 Parameter sensitivity analysis

Employing the buckling load of the specimen as the dependent variable, and incorporating factors like the wall height, internal steel plate thickness, concrete tank wall thickness, concrete strength, and the single tank’s inner diameter as independent variables, a comprehensive multiple linear regression analysis was conducted (Tab.3).

The subsequent significance analysis has two crucial insights. First, the thicknesses of the internal steel plate and the concrete tank wall significantly impact the buckling load (). Secondly, the concrete’s elastic modulus presents a significant influence on the wall’s buckling load (). Delving into the standardized coefficients (Beta), the values for parameters such as the tank wall height, internal steel plate thickness, concrete thickness, concrete strength, and single tank’s inner diameter are −0.032, 0.595, 0.863, 0.162, and −0.099, respectively. These figures imply that the internal steel plate thickness, concrete thickness, and concrete strength have the most profound positive influence on the wall’s buckling load. Conversely, the tank wall height and inner diameter exert a negative influence.

Therefore, the specimen’s stability can be improved by increasing the thicknesses of the internal steel plate and concrete. The concrete thickness has a greater impact on the buckling load than the internal steel plate thickness.

6 Conclusions

This study investigated the characteristics of a novel UGTs with an internal steel plate lining designed for edible oil storage. Comprehensive analyses were conducted, including full-scale tests and numerical simulations. To begin with, the experimental study helped us grasp the internal circumferential force characteristics within the concrete tank wall of UGTs. Secondly, a numerical model was employed to examine and discuss the internal forces and circumferential deformations of the walls at various heights. Lastly, the LANB method was utilized to investigate the key parameters influencing the wall stability. The findings of this study offer valuable guidance and reference for the engineering design of UGTs. The primary conclusions are as follows.

1) Based on full-scale tests, it is evident that the most substantial circumferential stresses in the wall manifest in the middle section. This region requires special attention in design processes. Furthermore, the stresses near the junction predominantly arise from the wall junction and the neighboring tank wall. Conversely, areas far away from the wall junction mainly experience stresses from earth pressure.

2) The developed numerical model is verified by field test results. The comparative analysis highlighted the maximum deviations of 7.7% and 13.3%, respectively. This close alignment implies the numerical model’s accuracy and reliability.

3) Analyzing varying parameters revealed that for wall heights below 5 × 10³ mm, the primary force experienced by the wall is vertical. In these scenarios, it is appropriate to employ retaining wall force calculations. For walls exceeding this height, forces transition along the arch to the wall's ends, necessitating the use of arch force calculations.

4) The stability analysis showed the superior stability attributes of the new UGTs. Based on this result, a formula was devised to evaluate the stability of dual-layer heterogeneous material group tank walls. A crucial design recommendation stemming from the stability analysis is that the thickness of the concrete tank wall should not be less than 150 mm to ensure optimal structural integrity.

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