Novel prefabricated joints for underground silos with steel cavity and concrete-filled cavity: Axial compression tests and numerical simulations

Design of specimens and joints

Based on the structural configuration shown in Fig 1 and the provisions of the Code for Design of Composite Structures [39], the prefabricated composite silo wall segments and their corresponding joint configurations were designed. Although the prototype wall is curved, curved specimens require specialized loading equipment and make it difficult to satisfy the desired boundary conditions. Therefore, to ensure that the stress state remained representative of the prototype while facilitating laboratory testing, flat specimens were adopted in place of the curved wall segments. A total of four prefabricated wall segments were fabricated. Two segments were connected through a single joint to form one test specimen, resulting in two full-scale specimens. Both specimens had identical geometric dimensions, with a total length of 2200 mm, a width of 1000 mm, and a thickness of 310 mm. The inner layer of prefabricated blocks consisted of a 10 mm thick steel plate, while the outer layer was composed of 300 mm thick concrete. The inner steel plate was connected to the precast concrete block by means of headed studs. The steel grade was Q355, and the concrete strength grade was C40. The geometric dimension and the three-dimensional configuration of the specimen are shown in Fig 2.

Based on the construction characteristics of underground silos, two types of joints were designed, namely the steel cavity (SC) joint and the concrete-filled cavity (CFC) joint. The SC joint is a dry-type connection consisting of two bound steel plates, an external waterproof steel plate, and an internal waterproof steel plate. The bound steel plates were designed with an inclined configuration to facilitate top-down construction and the integrated implementation of foundation pit support [34]. All three components have an equal thickness of 16 mm and are connected together by welds. The external and internal waterproof steel plates are 240 mm and 200 mm long, respectively. The CFC joint adopts a combined dry-wet connection method. Based on the configuration of the SC joint, the cavity is filled with C25 micro-expansive concrete. In this study, the prefabricated steel-plate concrete specimens assembled with the SC joint and the CFC joint are referred to as PSC-SC and PSC-CFC, respectively. The schematic diagram of the structure of the two joints is shown in Fig 3.

Specimen fabrication and material property testing

As shown in Fig 4 a and Fig 4b, the specimen fabrication process involves the processing of steel components, the pouring and curing of concrete, the joint treatment and the overall assembly of prefabricated blocks. The steel components were fabricated in batches by a structural steel manufacturer in accordance with standardized procedures. The prefabricated concrete blocks were cast using commercially available C40 concrete in batches. Adequate compaction was achieved using a vibrating rod, and the top surface was manually leveled upon completion of the casting. After 28 days of standard curing and joint treatment, the prefabricated blocks were assembled.

As shown in Fig 4d, standard steel specimens fabricated from the same material as the test specimens were subjected to tensile tests using a universal testing machine. The testing machine has a maximum load capacity of 600 kN and a load measurement resolution of 1/20,000. The measured mechanical properties of steel plates are presented in Table 1. Additionally, standard concrete compressive strength cubes with dimensions of 150 × 150 × 150 mm were cast in accordance with the Code for Design of Concrete Structures (GB 50010) [40]. The compression tests were conducted using an automatic compression testing machine (JYE-2000A), as illustrated in Fig 4c, and the resulting concrete strength values are summarized in Table 2.

Experimental method

The loading configuration for the axial compression test is shown in Fig 5. The loading device comprised an electro-hydraulic servo loading system (YAJ-12000) with a maximum loading capacity of 1200 t. As shown in Fig 5b, a restraint was installed to prevent misalignment of the specimen during loading. The data acquisition system adopted the DH3816N data logger, with each unit providing 60 channels. Displacement measurements were conducted using the YHD-50 displacement gauge, which had a measurement accuracy of 0.01 mm. Steel and concrete strain gauges were installed on the corresponding materials to measure strain.

To investigate the strength and stiffness of silo wall joints under axial pressure, displacement and strain measurement points were arranged on both sides of specimens. As illustrated in Fig 6, PSC-SC and PSC-CFC had an identical layout of displacement and strain gauges. The total axial deformation of the specimen was obtained by subtracting the average displacement of gauges on the top bearing plate (YW9-YW10, YW19-YW20) from the average displacement of those on the bottom loading plate (YW1-YW2, YW11-YW12).

According to the Standard for Test Methods of Concrete Structures (GB/T 50152) [41], the loading process was divided into two stages: pre-loading and formal loading. During the pre-loading stage, the applied load was limited to no more than 15% of the specimen's predicted bearing capacity determined by finite element analysis. This stage aimed to ensure the proper functioning of the loading system and measurement devices, as well as to ensure reliable contact at the support and loading interfaces. In the formal loading stage, a load-controlled approach was adopted, and each loading increment was set to 10% of the predicted ultimate bearing capacity. Upon reaching 70% of this predicted capacity, the loading method was switched to displacement control, with a displacement increment of 0.5 mm per step and a loading rate of 0.002 mm/s. The loading process continued until either significant yielding occurred at the joints or the specimen’s bearing capacity dropped to 85% of the predicted ultimate capacity. Each loading level was held for 5 minutes to ensure data stability.

Axial force-displacement relationship of PSC-SC and PSC-CFC

• (1)

  Axial load-displacement relationship of PSC-SC

The displacement curve of the PSC-SC under axial pressure and the failure mode are shown in Fig 7. It is evident that the failure is primarily governed by the damage of the external waterproof steel plate at the joint, and the whole compression deformation process of PSC-SC can be divided into three stages: the elastic stage (O₁-A₁), the elasto-plastic stage (A₁-B₁), and the buckling stage (B₁-C₁). The deformation characteristics of each stage are investigated as follows.

Elastic stage (O₁-A₁): The load-deformation curve of PSC-SC is a straight line with a certain slope, and the compressive stiffness reaches the maximum value in this stage. At the same time, no cracks are observed in the precast concrete blocks, and the connection between the concrete and the inner steel plate via shear studs remains intact. Both the steel plates and welds at the joint remain undamaged, and no lateral buckling deformation is observed in either the internal or external waterproof steel plate.

Elasto-plastic stage (A₁-B₁): The total axial compression displacement of PSC-SC increases at an accelerating rate, accompanied by a gradual reduction in compressive stiffness. After reaching the peak load B₁, lateral deflection begins to develop in the external waterproof steel plate (Fig 7b), whereas the remainder of the specimen remains intact.

Buckling stage (B₁-C₁): As the total axial compression deformation continues to increase, the lateral deflection of the external waterproof steel plate markedly enlarges. However, the precast concrete blocks, the inner steel plates, and the internal waterproof steel plates at the joint remain undamaged, with their stress states still in the elastic range.

• (2)

  Axial load-displacement relationship of PSC-CFC

As illustrated in Fig 8a, the failure mode of PSC-CFC is primarily manifested as the crushing of precast concrete blocks, and the stress deformation process can also be divided into three stages: the elastic stage (O₂-A₂), the elasto-plastic stage (A₂-B₂), and the softening stage (B₂-C₂).

Elastic stage (O₂-A₂): At this initial stage, no cracks are observed in either the precast concrete blocks or the joint concrete. The connection between the precast concrete and the inner steel plate via shear studs remains intact. The internal and external waterproof steel plates and welds at the joint remain intact, with no signs of lateral buckling deformation observed.

Elasto-plastic stage (A₂-B₂): As shown in Fig 8b, cracks gradually develop in the precast concrete blocks. As loading continued, the cracks extended progressively toward both ends, and their widths also gradually increased. Debonding is observed at the ends between the precast concrete block and the inner steel plate. However, at the peak load B₂ (10004 kN), the internal and external waterproof steel plates, as well as the welds remain intact, and no cracks are observed in the concrete at the joint.

Softening stage (B₂-C₂): After the peak load, as the total axial compression deformation continues to increase, both the depth and width of the cracks in the prefabricated concrete blocks increase continuously, while the debonding between the upper prefabricated concrete block and the inner steel plate progressively propagate downward. When the C₂ point is reached, the specimen cannot continue to carry and stop loading.

Axial load-strain relationships of PSC-SC and PSC-CFC

• (1)

  Axial load-strain relationship of PSC-SC

Based on the experimentally measured strain data, the axial load-strain curves for PSC-SC are shown in Fig 9. It can be seen that both the concrete-side and steel-side measurement points initially exhibit compressive strains aside from a few outliers. As the load increases, strains on both sides generally increase linearly during the early loading phase. A noticeable inflection point appears in the load-strain curve at an axial load of approximately 6230 kN, where a sudden increase in strain is observed on the steel plate side. At this time, lateral buckling deformation occurs in the external waterproof steel plate at the joint, and the specimen begins to exhibit global arching deformation.

After the load exceeds the peak value, the arching deformation of PSC-SC intensifies further. As shown in Fig 9b, the proportion of the load borne by the steel plate side increases significantly, with its strain rising rapidly in response to the load. The opposite phenomenon observed at measurement point SC1 may be attributed to the influence of the specimen's end. In contrast, it can be seen from Fig 9a that the strain on the concrete side decreases rapidly with increasing load. By the end of loading, tensile strain is observed at measurement points near both ends of the concrete side (CC2, CC5, CC13, and CC17). This phenomenon is mainly due to the pronounced arch-shaped deformation of the specimen. During this process, the limiting angle steels at the top and bottom ends impose lateral constraints on the concrete ends, leading to a tendency for localized tensile stress to develop in these regions.

• (2)

  Axial load-strain relationship of PSC-CFC

For PSC-CFC, it can be seen from Fig 10a that when the axial load reaches 8760 kN, the load-strain curve of the concrete has an inflection point, and the strain increases at an accelerating rate. As shown in Fig 10b, except for the measuring point on the internal waterproof steel plate at the joint, the strain curves at the other locations on the steel plate side also exhibit inflection points. However, the rate of strain increase tends to slow down. In comparison, the strain variation on the external waterproof steel plate is smaller than that on the internal one (Fig 10c). At this time, axial cracks are generated in the prefabricated block near the joint, which reduces the effective compressive area of the concrete, and the upper prefabricated block and the inner steel plate begin to peel off. As the proportion of load carried by the concrete increases, the strain growth rate on the concrete side increases accordingly, while that on the steel-plate side decreases. The internal and external waterproof steel plates, as well as the joint concrete, remain intact and are still in the elastic stage. After peak load, the cracks in the precast block concrete further develop, and the peeling of the upper precast block concrete and the inner steel plate further extend. As a result, the strain on the concrete side continues to increase but the strain on the steel plate side continues to decrease as the load gradually decreases. Owing to the concrete infill in the joint cavity, which significantly enhances the joint stiffness, the load-strain curve of the internal waterproof steel plate remains approximately linear up to the peak load. After the peak load, the strain returns approximately along the original path. The lateral deflection deformation of the external waterproof steel plate is also small.

Constitutive models of materials

The concrete constitutive model is based on the concrete plastic damage model proposed by Lubliner et al. [42] and subsequently modified by Lee et al. [43] in 1998. The model assumes that the elastic behavior of materials is linearly elastic and isotropic. The inelastic behavior of concrete under uniaxial tension and compression is described by introducing damage factor. The elastic modulus E_c of concrete is calculated by the following formula:

where, f_cu represents the compressive strength of the concrete cube.

The damage variables are used to describe and quantify the extent and progression of damage in concrete due to tensile cracking and compressive crushing. The calculation method follows the approach proposed by Sidoroff [44]:

where, σ_c denotes the stress in the concrete, and ε_c represents the strain in the concrete.

In addition, only the cubic specimens cast simultaneously with the test specimens are subjected to compressive tests. The conversion formula between the cubic compressive strength fcu and the prism compressive strength fc used in the concrete constitutive model is expressed as:

The stress-strain relationship of the steel material adopts a bilinear model [45], in which the stress-strain curve is uniquely defined, facilitating numerical convergence during analysis. The material properties of the steel are based on the experimental results (Table 1), with an elastic modulus of E_a = 2.06 × 10⁶ MPa and a poisson’s ratio of 0.3.

Establishment of finite element model

The finite element model is developed based on the actual dimensions of the specimens. The component models include concrete, steel plates, shear studs, and welds. The finite element models of PSC-SC and PSC-CFC are shown in Fig 11. The C3D8R elements are adopted for all solid components. The PSC-SC and PSC-CFC models consist of approximately 146,000 and 156,000 elements, respectively. The mesh size of the precast concrete block is 25 × 21.4 × 50 mm, while that of the inner steel plate is 25 × 10 × 50 mm. The shear studs are embedded into the concrete using the embedded constraint method, and are rigidly connected to the steel plates. The interaction between the steel plates and concrete is modeled using contact elements. In the tangential direction, a coulomb friction model is adopted with a friction coefficient μ = 0.6 [46]. In the normal direction, ‘hard contact’ is used to simulate the contact behavior.

Grid division and boundary condition setup

Structured meshing is employed for all structural components to generate regular, low-distortion elements. A uniform mesh size is used for most regions of the model, with local refinement introduced in areas prone to stress concentrations or geometric discontinuities, particularly around the joint. A mesh independence study is conducted using different mesh densities. Under the same axial compressive load, the maximum displacement of the specimen is selected as the evaluation index. When the relative difference in the maximum displacement between two successive mesh densities is less than 1%, the numerical results are considered to be mesh-independent. Based on this criterion, the final mesh configuration adopted in this study is shown in Fig 12. In the model, loading is applied through displacement control on the loading end surface. The boundary condition settings mainly include two aspects. Firstly, on the loading face, the displacement constraints in the X and Y directions and the rotation constraints are applied to all nodes. Secondly, displacement constraints in the X, Y, and Z directions, along with rotational constraints about the X and Y axes, are imposed on all nodes on the fixed end face.

Numerical simulation results and analysis

Joint parameters of PSC-SC

For the PSC-SC, both the experimental results and finite element analysis indicate that the failure is caused by large lateral buckling and instability of the external waterproof steel plate. Therefore, the joint design parameters for PSC-SC primarily focus on the effects of the connection length l and thickness d of the external waterproof steel plate. Table 5 presents the selected values of the joint design parameters and the corresponding key results. Using the finite element model PSC-SC-l240 as the baseline model, each comparative model modifies a single parameter while keeping all other parameters constant. The resulting load-deformation curves for the various finite element models are shown in Fig 16.

• (1)

  Connection length of external waterproof steel plate

As shown in Fig 16a, with the increase in the connection length of the external waterproof steel plate, the displacement in the elastic stage and the initial stiffness of the finite element model remain nearly unchanged, whereas the peak load exhibits a gradual reduction. When the connection length increases from 160 mm to 240 mm, the elastic stage displacement remains constant at 1.90 mm, and the peak load obtained from the finite element analysis decreases by 6.56% and 1.15%, respectively. Moreover, the shorter the connection length of the external waterproof steel plate, the more fully the specimen develops plasticity. The displacements in the elastic-plastic stage for connection lengths of 160 mm, 200 mm, and 240 mm are 2.24 mm, 0.44 mm, and 0.22 mm, respectively. It can be seen that the connection length of the external waterproof steel plate has little influence on the elastic stage of the specimen but significantly affects its plastic development and peak load.

• (2)

  Thickness of external waterproof steel plate

As shown in Fig 16b, an increase in the thickness of the external waterproof steel plate has a negligible effect on the initial stiffness of finite element models. The displacement in the elastic stage increases significantly when the thickness increases from 10 mm to 16 mm, while no change is observed between 16 mm and 20 mm thickness. This indicates that once the thickness of the external water-stop steel plate reaches a certain level, further increases have minimal impact on both the elastic stage displacement and the initial stiffness. As the thickness increases from 10 mm to 16 mm and then to 20 mm, the peak load obtained from the finite element analysis increases by 53.00% and 9.42%, respectively. Therefore, when designing the silo wall joints, the thickness of the external waterproof steel plate should neither be too small nor too large. If the thickness is too small, it significantly reduces the peak load-bearing capacity of the silo wall specimen. Conversely, an excessively large thickness offers only limited improvement in the elastic-stage displacement and peak load, resulting in unnecessary material consumption. Therefore, the steel plate thickness should be reasonably selected to balance structural performance and cost-effectiveness.

Joint parameters of PSC-CFC

Due to the filling of concrete in the joint cavity, the compressive strength of the CFC joint of the specimen is significantly improved, and the crushing failure of the precast block concrete occurs before the joint. Therefore, the design parameters of PSC-CFC can be regarded as the strength of the concrete at the joint. To investigate the compressive bearing capacity of the joint, the materials of the prefabricated blocks in the finite element model are assumed to be linear elastic. The outside bound steel plate, internal and external waterproof steel plates, and joint concrete are modeled as elastic-plastic materials. Table 6 lists the design parameter values and main results. The load-deformation curves obtained from the finite element model are shown in Fig 17.

As shown in Fig 17, with the increase in joint concrete strength, the elastic-stage displacement, initial stiffness, and peak load of the finite element model all exhibit corresponding improvements. As the joint concrete strength increases from 30 MPa to 40 MPa and then to 50 MPa, the peak load obtained from the finite element analysis increases by only 3.77% and 3.63%, respectively, indicating that the influence of concrete strength on the compressive capacity becomes relatively limited within the investigated strength range. However, compared with the compressive load-carrying capacity of the SC joint, that of the CFC joint increases by more than seven times. Among the investigated design modifications, concrete infilling of the joint cavity is the most effective approach for enhancing the compressive capacity of the joint, compared with increasing the waterproof steel plate thickness or reducing its connection length. Therefore, for the proposed CFC joint under axial compression and within the investigated concrete strength range (30–50 MPa), the use of excessively high-strength infill concrete is not necessary, since only marginal improvements in the peak load are achieved.