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Numerical analysis and experimental research on the vibration performance of concrete vibration table in PC components

  • DeFang Zou , ZiHan He , XueFei Cheng and WenDa Yu EMAIL logo
Published/Copyright: September 30, 2024
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Science and Engineering of Composite Materials
From the journal Science and Engineering of Composite Materials Volume 31 Issue 1

Abstract

Vibration table is the key equipment to realize high efficiency and high quality forming and compacting of concrete in prefabricated component (PC) production line, and its performance directly affects the shape quality and compressive strength of PC components. However, the operating parameters of the vibration table are difficult to match the rheology of the concrete during the construction process, which directly leads to a low molding efficiency or unqualified shape quality in the case of slab-type components. Therefore, it is crucial to accurately describe the concrete flow behavior during vibration to improve the construction performance and compaction effect. In this work, the coupled theory of computational fluid dynamics and discrete element is used to study the concrete vibration and compacting characteristics, and the influence of process parameters on vibration performance is analyzed in order to realize the adjustment and optimization of key parameters. First, the concrete solid-liquid two-phase model parameters are calibrated by V-shaped funnel experiments and slump experiments. Then, based on the simulation results, the homogeneity and compactness of concrete are discussed using the segmented sieving method and the slicing method, and the indexes for evaluating the working performance of the vibration table are proposed. Finally, the relationship between vibration frequency (20–30 Hz), vibration amplitude (3–4 mm), and vibration time (15–35 s) and concrete vibration compaction characteristics is investigated to provide a theoretical basis for improving the molding efficiency and mold quality of PC components.

Keywords: vibration table; prefabricated component; computational fluid dynamics; concrete homogeneity; concrete compactness

1 Introduction

With the development of prefabricated construction, higher requirements have been put forward for the demand and quality of prefabricated concrete (PC) components. As a key equipment in the molding process of PC components, vibration table is mainly used for filling and compacting freshly mixed concrete, and its performance directly affects the molding quality and production cost of PC components [1]. During the vibration molding process, there is a certain degree of matching relationship between the set parameters of the equipment and the concrete state properties to ensure the maximum working performance of the equipment. If the vibration table process parameters are not set reasonably, the concrete material in the mold will often have uneven local accumulation, bubble retention, or even deposition of segregation [2]. Generally speaking, the homogeneity and compactness of concrete poured into the mold are closely related to the mechanical properties of PC components. The occurrence of the above situation will result in the surface flatness and compressive strength of concrete components not meeting the construction standards. Research has shown that when the compactness of concrete is increased by 1%, the compressive strength of concrete products can be increased by about 4% [3]. Therefore, using the homogeneity and compactness of concrete stacking as key indicators to evaluate the performance of the vibration table, matching or optimizing equipment process parameters based on the concrete state properties, is of great significance for improving the working performance of the vibration table and reducing construction costs.

At present, researchers have conducted a series of studies on the rheological characteristics of concrete during transportation and compaction processes using rheological theory, and experimental and numerical simulation methods. Zhu and Cao [4] discussed the effects of working time and amplitude on the rheological behavior of concrete under vibration based on the theory of viscosity, and obtained a theoretical model to describe the constitutive relationship of concrete. The results indicated that under a constant shear strain rate, the yield stress decreased with increasing vibration time, while the apparent viscosity increased instead. Navarrete and Lopez [5] studied the relationship between concrete segregation phenomena based on rheological theory and obtained a theoretical discriminant inequality to discriminate the occurrence of segregation reactions. At the same time, based on the research results, the effects of factors such as aggregate size, compactness, slurry viscosity, and vibration energy on the segregation behavior of concrete under vibration conditions, both individually and in combination, were discussed. Wünsch [6] studied the settlement of a sphere in a viscous plastic fluid under vibration, and the results showed that settlement motion can only occur when the vertical force applied to the sphere causes the kinetic energy of settlement to exceed the viscous plastic resistance. Safawi et al. [7] used the segmented aggregate screening method to characterize the degree of concrete segregation and discussed the mapping relationship between vibration time and amplitude on material segregation behavior. From the above analysis, it can be seen that the analysis of the rheological behavior of concrete during construction based on traditional rheological theory lacks reliable experimental verification. Meanwhile, there is also a certain degree of error in the relevant prediction results, making it difficult to directly apply them to practical engineering. In order to address the shortcomings of theoretical methods in analyzing the rheological properties of concrete, some scholars have adopted experimental methods to analyze the rheological laws of materials during the vibration process based on experimental results. For example, Gao et al. [8] discussed the effect of vibration amplitude and vibration time on the rheological properties of concrete based on experiments for the relatively poor vibration effect caused by the mismatch between vibration process parameters and concrete properties. The results indicated that simply increasing the vibration amplitude or prolonging the vibration time could lead to severe segregation of concrete, and plastic bonding was the key factor in solving the segregation problem during the vibration process. Zhang et al. [9] also used experimental methods to study the effect of vibration parameters on the segregation behavior of concrete. The results showed that the segregation behavior of concrete increased with the increase in vibration amplitude and vibration time. When the vibration amplitude is larger, the segregation of concrete with higher plastic viscosity is greater. When the vibration time is longer, the segregation of concrete with lower yield stress is greater. Petrou et al. [10] used the radioactive element labeling method to obtain real-time images of aggregate settlement during the vibration process. They believed that the type of vibration applied (frequency, amplitude, geometric shape of the vibrator, etc.), vibration mode, and vibration duration were all important factors affecting the rheological properties of concrete during the vibration process. As can be seen from the above literature, the experimental methods are used to analyze the influence of vibration process parameters on vibration performance and concrete rheological properties, and the research results are reliable. However, these methods are difficult to visually describe the movement mechanism and behavior of concrete aggregates, mortar, and bubbles during the vibration process at a microscopic scale. Meanwhile, due to the typical regional physical property differences of concrete raw materials, research results based on experimental data analysis are difficult to be widely applied.

With the development of computer technology, a numerical simulation method for visualizing modeling of concrete materials, analyzing the motion behavior of aggregate particles or flow fields, namely, the discrete element method and computational fluid dynamics method, has been widely adopted by scholars [11,12]. Based on numerical simulation methods, researchers have studied the effects of operating parameters (vibration frequency, pumping pressure, conveying speed, etc.) on work performance during the construction process, such as concrete conveying volume, homogeneity, and compactness [13,14]. The relevant research conclusions provide important theoretical basis for improving the production quality of concrete products and reducing construction costs. Liao et al. [15] used the Hertz Mindlin with JKR model to establish a concrete simulation model to simulate the working mechanism of a spiral mixer. The results showed that the numerical simulation predictions were very close to the experimental results. Sebastien Remond and Pizette [16] proposed a new DEM model for describing concrete based on discrete element theory, which is a composite particle aggregate consisting of concentric spherical layers of mortar wrapped around spherical hard particles of crushed stone aggregate. This model can relatively accurately describe the macroscopic flow behavior of concrete. Tan et al. [17] and Deng et al. [18] used discrete element theory to conduct a detailed analysis of the flow behavior of concrete during transportation and mixing processes. The results indicated that using the DEM simulation method could reliably obtain the flow patterns of concrete during the construction process. Some scholars used computational fluid dynamics method to consider fresh concrete as a non-Newtonian fluid model for numerical simulation analysis. For example, Cui et al. [19] considered concrete as a Bingham fluid model to simulate the macroscopic flow behavior during the collapse experiment process. By comparing with the experimental results, it is known that the CFD method can reliably describe the flow characteristics of concrete. Sassi et al. [20] considered fresh concrete as a Bingham model within the framework of computational fluid dynamics to simulate the macroscopic flow behavior of L-box. Research has found that the yield stress and plastic viscosity of concrete can be important indicators for evaluating its rheological properties. However, from the above literature, simply using the discrete element method or computational fluid dynamics method to establish a theoretical model of concrete is difficult to fully solve the complex particle flow problems that exist in the construction process, such as pressure drop, aggregate deposition, and segregation behavior during concrete pumping.

To further analyze the complex flow problems involved in the construction process, scholars have adopted the DEM-CFD coupling method to establish a concrete theoretical model for problem research. For example, Blaisa et al. and Tamburini et al. [21,22] analyzed the force distribution of solid particles in concrete mixing tanks using a solid-liquid two-phase flow model. It was found that although the solid-liquid two-phase flow model can simulate the gravel and mortar in concrete wall, this method still cannot accurately describe the problems of bubble rise and fusion in actual concrete during vibration. Krishnya et al. [23] used a coupling method to consider the concrete as a solid-liquid-gas three-phase flow model, studied the dynamic interaction relationship between various media during the concrete flow process, and analyzed the complex motion problems of bubbles, crushed stones, and mortar during construction. Therefore, the discerete element method-computational fluid dynamics (DEM-CFD) coupling method can effectively analyze the interaction relationship between particles and fluid motion, and can accurately simulate the motion process of material particles in the fluid. Meanwhile, this method can more accurately predict the trajectory, velocity, and interaction forces of particles in the fluid, thereby more accurately predicting the settling, suspension, and transportation of particles in the fluid. When using the DEM-CFD coupling method to establish a concrete theoretical model, solid-liquid gas multiphase flow has more advantages in solving complex flow problems in terms of ability and accuracy compared to solid-liquid two-phase flow. The aim of this study is to establish an accurate solid-liquid-gas multiphase flow theory model that describes the rheological behavior of concrete, analyze the influence of process parameters of the vibration table on its performance, and provide a theoretical basis for optimizing process parameters. First, based on the DEM-CFD coupling theory, a concrete solid-liquid-gas three-phase flow model is established, and the contact parameters of the theoretical model are determined according to the standard performance test of concrete. Then, numerical simulations are conducted on the medium motion law and aggregate settlement behavior during the concrete vibration process, and the predicted results are experimentally verified. Finally, based on a combination of numerical simulation and experiments, the influence of vibration process parameters (vibration frequency, amplitude, and vibration time) on work performance is explored, such as material compactness, stacking homogeneity, and bubble discharge. The research results of this study can provide effective methods and theoretical basis for improving the performance indicators of the vibration table and reducing construction costs.

2 Numerical model of concrete vibration table

2.1 DEM-CFD model of concrete

Concrete, as a composite material, is mainly composed of materials such as mortar, crushed stone, and admixtures. During the flow process, the shear stress does not follow a linear relationship with the movement rate, which satisfies the characteristics of non-Newtonian fluids [24]. In addition to the raw materials mentioned above, the mixing process of concrete also includes bubbles between the material particles. Therefore, the Bingham model is used to simulate liquid phase mortar and gas phase bubbles. This study describes concrete as solid spherical particles based on discrete element theory, and couples concrete with gas-liquid phase media for trajectory calculation. The theoretical model structure of concrete DEM-CFD is shown in Figure 1, the algorithm flow is shown in Figure 2, and the detailed calculation equations are given here.

Figure 1 The discrete element models for a concrete mixture. (a) Single-phase element, (b) separate single-phase element, and (c) three-phase element.
Figure 1

The discrete element models for a concrete mixture. (a) Single-phase element, (b) separate single-phase element, and (c) three-phase element.

Figure 2 Flowchart of the DEM-CFD algorithm [25].
Figure 2

Flowchart of the DEM-CFD algorithm [25].

The flow behavior of gas and liquid phases in the theoretical model of concrete is calculated using the continuity equation and momentum conservation equation. Among them, based on the flow characteristics of concrete, the mortar is assumed to be an incompressible fluid and isothermal flow, under the condition that the Navier–Stokes equation is satisfied. The equations are as follows [26]:

The continuity equation:

(1) ∂ u ∂ x + ∂ v ∂ y + ∂ w ∂ z = 0 .

The momentum conservation equation

(2) ρ ∂ u ∂ t + ρ ( u ⋅ ∇ ) u = ∇ ⋅ ( − p + μ [ ∇ u + ( ∇ u ) T ] ) ρ ∂ v ∂ t + ρ ( v ⋅ ∇ ) v = ∇ ⋅ ( − p + μ [ ∇ v + ( ∇ v ) T ] ) + ρ g ρ ∂ w ∂ t + ρ ( w ⋅ ∇ ) w = ∇ ⋅ ( − p + μ [ ∇ w + ( ∇ w ) T ] ) ,

where p is the pressure of the fluid; u, v, and w are the velocity components in the x, y, and z directions, respectively; ρ and μ are the density and dynamic viscosity of the fluid, respectively; and g is the gravitational acceleration.

The Bingham model belongs to a typical non-Newtonian fluid, and its rheological parameters include plastic viscosity and yield stress [26]. It is mainly used to describe mortar and air bubbles, and its model equation is as follows:

(3) τ = τ 0 + μ 0 γ ̇ ,

where τ is the shear stress (Pa); τ 0 is the yield stress (Pa); μ 0 is the plastic viscosity (Pa s); γ ̇ is the shear rate (1/s). Among them, the shear rate is calculated using the following formula:

(4) γ ̇ = 2 S : S S = 1 2 [ ∇ u + ( ∇ u ) T ] ,

where S represents the strain tensor, S:S represents the dot product of the strain tensor S with itself. According to Tattersall [27], it has been found that the state of mortar during vibration changes from Bingham fluid to pseudoplastic fluid with almost zero yield stress. The shear rate and shear stress variation of mortar under both vibration and non-vibration modes are shown in Figure 3. The horizontal axis represents the rotor torque, the vertical axis represents the rotor speed, the solid line represents the vibration curve, and the dashed line represents the vibration curve. When the shear rate is low, the mortar is approximately a Newtonian fluid. As the shear rate increases, the relationship with shear stress becomes a power function. The expression for shear stress is as follows:

(5) τ v τ s = C 2 ⋅ ( C 3 γ • ) C 4 x max • ,

where τ v is the shear stress of cement mortar under vibration (Pa); τ s is the shear stress of cement mortar without vibration (Pa); C 2 is the dimensionless constant of cement mortar; C 3 is the constant of cement mortar (s); and C 4 is the constant of cement mortar (s/m).

Figure 3 Shear rate–shear stress curves of mortar under vibration and no vibration [28]. (a) Power function, (b) intersection, and (c) linearity.
Figure 3

Shear rate–shear stress curves of mortar under vibration and no vibration [28]. (a) Power function, (b) intersection, and (c) linearity.

When the yield stress of concrete approaches zero, the apparent viscosity becomes the determining factor for the settlement resistance of concrete aggregates.

Figure 4 shows the relationship curve between vibration amplitude and the ratio of rheometer operating torque to speed (1/S). As shown in the figure, with the increase of vibration amplitude, the 1/S value actually decreases, that is, the viscosity of the mortar decreases. When the vibration frequency is higher, 1/S is smaller and the viscosity of the mortar is higher. The slope S is inversely proportional to the mortar viscosity η v, which is converted into an expression for the mortar viscosity under vibration using the formula

(6) η v = η 0 ⋅ [ 1 − e − k A 1 ( f − f 0 ) ] − 1 ,

where η v is the low shear rate Newtonian fluid viscosity of the mortar under vibration (Pa); η 0 is the lower critical value of the mortar viscosity under vibration (Pa s); k is a constant greater than 0 controlled by the adaptation ratio (s/m); and f 0 is a constant greater than 0 controlled by the adaptation ratio (Hz).

Figure 4 The relation curve of 1/S with vibration frequency and amplitude [28].
Figure 4

The relation curve of 1/S with vibration frequency and amplitude [28].

The Reynolds number of the mortar flow field is given below:

(7) Re = 2 ρ b U R η p ,

where Re is the Reynolds number; ρ b is the density of the mortar (kg/m3); U is the flow velocity (m/s); and R is the radius of the aggregate (m).

For fresh concrete, the calculated value of Re is 0.02 (less than 1) when the physical property parameters are ρ b = 2,500 kg/m3, R = 0.01 m, η p = 10 Pa s, and U = 0.004 m/s, respectively, so the resistance to crushed aggregate can be calculated by

(8) F b = 6 π η U R ,

where F b is the resistance of the aggregate to the cement paste (N) and η is the Newtonian fluid viscosity (Pa s).

Due to the fact that mortar is also a solid-liquid mixture rather than a pure liquid phase, the plastic viscosity of its Newtonian fluid needs to be transformed into the plastic viscosity of Bingham fluid when calculating resistance. The modified resistance coefficient calculation formula is

(9) C S = F 6 π η p U t R ,

where C s is the Stokes drag coefficient; F is the sum of the settling force (N); U t is the critical settling velocity of the aggregate (m/s), i.e., the settling velocity under the equilibrium state of power and drag (m/s).

During the vibration process of concrete, determining whether the aggregate has settled can be expressed using the yield stress parameter Y g [18] as follows:

(10) Y g = 2 π τ 0 R 2 F ,

where τ 0 is the yield stress of concrete (Pa).

Normally, a mortar layer is wrapped around the crushed stone aggregate, as shown in Figure 5. Under the continuous action of excitation force, the mortar and crushed stone aggregate particles of concrete will undergo sliding motion. When the shear stress on the mortar is greater than the yield stress, flow deformation occurs; otherwise, it appears as a solid state in clusters.

Figure 5 Aggregate settlement and surrounding mortar state [6].
Figure 5

Aggregate settlement and surrounding mortar state [6].

The gravel solid phase particles follow Newton’s second law during motion and the expression for the motion behavior is:

(11) m p d v d t = F d + F g ,

where m p is the mass of the gravel (kg); v is the velocity of the gravel (m/s); F d is the resistance of the fluid to the gravel (N); and F g is the gravity of the gravel (N).

The expression for the resistance of the mortar fluid to the crushed aggregate is given below:

(12) F d = 1 τ p m p ( u − v ) ,

(13) τ p = ρ p d p 2 18 μ .

where ρ p is the density of the gravel (kg/m3); d p is the diameter of the gravel (mm); u is the velocity of the fluid (m/s); and μ is the dynamic viscosity of the fluid (N·s/m2).

The segregation behavior of crushed stone aggregates is affected by gravity, and its gravity expression is

(14) F g = m p g ,

where g is the acceleration of gravity, assumed to be 9.8 m/s2.

2.2 Three-dimensional model of vibration table

To analyze the working performance of the concrete vibration table, SolidWorks software is used to establish a three-dimensional model of the vibration table, as shown in Figure 6. As shown in the figure, the vibration table mainly includes a vibration table top, four vibration spring components, an eccentric vibration motor, and a base. The research content of this study does not consider the influence of the installation position of the vibration motor on the vibration performance. Therefore, a vibration motor is selected for the experimental platform and installed in the center area of the table.

Figure 6 Concrete vibration table model.
Figure 6

Concrete vibration table model.

The excitation methods of eccentric vibration motors are divided into two categories: vertical vibration and horizontal swing vibration. When the vibration table carries out vertical vibration, its vibration direction (sine wave) is parallel to the direction of concrete material deposition movement, so it has a significant impact on material deposition movement and a weak impact on horizontal paving movement. When the direction of material movement is the same as the amplitude and acceleration of vibration, the vibration motor undergoes periodic harmonic motion [18], and its amplitude F 2 can be expressed as follows:

(15) F 2 = 4 3 π μ ⁎ μ R 3 ρ m f 2 A 2 K ,

where μ is Lamés’ constant; μ * is the correction for μ in the case of elastic-viscoplastic bodies; A 2 is the aggregate response amplitude (m); and K is the complexity function.

In addition, the response amplitude of the material is positively correlated with the vibration amplitude of the vibration table, which has a significant effect on the packing density (compactness) of the material. The yield stress Y g during continuous vibration is expressed as follows:

(16) Y g = 2 π τ 0 R 2 F = 2 π τ 0 R 2 F 1 + F 2 ⋅ sin ( 2 π f t ) .

3 Parameter determination of the model

3.1 Material properties

Concrete raw materials mainly include cement, fine sand, crushed stone, coarse aggregate, and water-reducing agent, which are measured as a percentage of the mass of the material during the trial mixing process, and the detailed material composition and content are shown in Table 1. The fine sand is river sand with apparent density 2,490 kg/m3 and fineness modulus 2.5. The crushed coarse aggregate (CA) was selected from limestone with grain size gradation of 9.5–19 mm and bulk density of 2,450 kg/m3. Add high-performance polycarboxylate superplasticizer to adjust the material and workability during the mixing and stirring process. Among them, the specific gravity of the water reducer is 0.8, the water reduction rate is 28%, the solid content is 25%, and the pH value is 6.3.

Table 1

Composition and content of fresh concrete

Materials Cement Fly ash River sand Coarse aggregate Water Superplasticizer
Concrete 1 (kg/m3) 500 40 678 1,170 202 8

According to the concrete material preparation standard, the above raw materials are put into the horizontal mixer for mixing, and the detailed mixing steps are shown in Figure 7. In the preparation process, the influence of human factors on the workability of concrete is ignored.

Figure 7 Fresh mix concrete mixing and experimental process.
Figure 7

Fresh mix concrete mixing and experimental process.

3.2 Methods and results

3.2.1 Model parameter

The theoretical model of concrete mainly consists of coarse aggregate particles, mortar fluid, and bubbles. The ratio of coarse aggregate, mortar, and bubbles is 1:1.15:0.35. Customize a particle factory on the vibration table mold to randomly generate particles and fluid materials in proportion. For numerical models of coarse gravel particles, physical parameters such as particle size, shape, density, friction coefficient, and bonding coefficient have important effects on simulating the flow and compaction of concrete [13]. In this work, the physical property parameters of gravel particles determined in the literature by Yu et al. [14] are selected for the simulation setup. For the parameters of mortar fluid mainly including plastic viscosity and yield stress, this work calibrates the data results based on standard performance experiments (V-box, U-box, J-ring).

3.2.2 Experimental verification

Slump test is a testing method that characterizes the flowability of concrete, mainly measuring the vertical slump and horizontal expansion. Due to its simple operation, compact device, and short experimental period, this experiment has been widely used in the construction field by researchers. The slump and expansion measurement equipment and key dimensional data are shown in Figure 8.

Figure 8 Slump experimental device. (a) Slump cylinder object and (b) corresponding size.
Figure 8

Slump experimental device. (a) Slump cylinder object and (b) corresponding size.

In order to verify the physical parameters of the concrete theoretical model, the numerical simulation and experimental results of the slump experiment were compared, as shown in Figure 9. The height ratios of concrete 1 simulation and experiment are 0.58 and 0.47, respectively. The simulation and experimental results of concrete slump and expansion are 192, 174 and 468, 485 mm, respectively. It can be seen that the established concrete theoretical model and physical parameters can accurately describe the macroscopic flow process of concrete.

Figure 9 Slump experiment and simulation results 1 comparison. (a) Experimental results and (b) simulation results.
Figure 9

Slump experiment and simulation results 1 comparison. (a) Experimental results and (b) simulation results.

The V-shaped funnel experiment is mainly used to measure the rheological properties of concrete, and to verify the accuracy of rheological parameters by comparing the emptying time of concrete through the V-shaped funnel. The V-shaped funnel equipment and key dimensional parameters are shown in Figure 10.

Figure 10 V-funnel experimental device. (a) V-shaped funnel and (b) corresponding size.
Figure 10

V-funnel experimental device. (a) V-shaped funnel and (b) corresponding size.

In numerical simulation, define the boundary conditions for fresh concrete entering and exiting the V-shaped funnel. When t = 0, fill the fresh concrete into the V-shaped funnel and randomly generate concrete particles with uniform distribution. Make the fresh concrete flow out of the V-shaped funnel under its own gravity, bonding force, and friction force. The flow of fresh concrete in a V-shaped funnel at certain times is shown in Figure 11.

Figure 11 V-shaped funnel flow simulation process.
Figure 11

V-shaped funnel flow simulation process.

Six sets of fresh concrete with different plastic viscosity and yield stress are designed, and the simulation results were compared with experimental results, as shown in Figure 12. From Figure 12, it can be seen that the simulation results of the fifth and sixth groups are closest to the experimental results, while the simulation results of the other groups have smaller rheological parameters than the experimental results. Therefore, the plastic viscosity of the fresh concrete simulation 1 is 124 Pa s, and the yield stress value is 508 Pa.

Figure 12 Comparison of V-shaped funnel simulation and experimental results.
Figure 12

Comparison of V-shaped funnel simulation and experimental results.

4 Operating conditions and evaluation indicators

4.1 Operating conditions

Before numerical simulation, it is necessary to set the initial values and boundary conditions of the concrete. The filling height of the concrete is 150 mm, and the total number of concrete particles is about 7,500. The vibration amplitude of the vibration table is 1 mm, and the vibration frequencies are set to 20, 30, and 40 Hz, respectively, with a vibration time of 25 s. The physical field is set as the coupling of turbulence and Euler model, with a time step of range 0, 0.02, and 25.

4.2 Evaluation indicators

In order to evaluate the influence of process parameters on the performance of the vibration table, this study selects concrete homogeneity, concrete compactness, and rebound value as quantitative indicators. For the concrete homogeneity, the segmented screening method is used to measure the proportion of coarse aggregate in the same volume. By calculating the relative error value of the proportion of coarse aggregate, its homogeneity can be determined. In the experimental measurement process, the filling domain is uniformly divided into three layers and it is assumed that the aggregate is uniformly distributed (ideally, the proportion of coarse aggregate is 33%). The measurement process is shown in Figure 13. The formula for calculating the relative error value of coarse aggregate is:

(17) N 1 = max ( 1 − N i / N A ) × 100 % ,

where N 1 is the relative error value of concrete homogeneity; N i is the actual percentage of coarse aggregate in different layers in the mold; and N A is the percentage of coarse aggregate in the ideal case of different layers.

Figure 13 Experimental steps of segmented screening method.
Figure 13

Experimental steps of segmented screening method.

Concrete compactness is mainly characterized by the porosity of the material during the stacking process, i.e., the ratio of the volume of air bubbles contained in the material to the volume of concrete. The smaller the porosity value during the concrete stacking process, the better the compaction effect; otherwise, the less ideal the compaction effect. This study describes the compaction effect of concrete by collecting concrete from different layers and calculating the porosity of materials. The experimental steps are shown in Figure 14, using a high-resolution imaging instrument to observe the accumulation of concrete before and after processing, and using Image Pro Plus image processing technology to calculate the changes in concrete porosity. In order to fully analyze the compactness of concrete stacking, the relative error value N 2 of compactness is used for quantitative analysis, and the expression is

(18) N 2 = max ( 1 − N t / N b ) ( 1 − N t / N m ) × 100%,

where N t is the compactness of the concrete at the top of the mold, N m is the compactness of the concrete at the center of the mold, and N b is the compactness of the concrete at the bottom of the mold.

Figure 14 Experimental steps of concrete pore observation.
Figure 14

Experimental steps of concrete pore observation.

The compressive strength of concrete is an important indicator for evaluating the quality of concrete cast after vibration, and the compressive strength is mainly measured by rebounders or presses. In this study, JGT-A rebound tester is used to measure the rebound value of concrete and then calculate the compressive strength, the measuring device is shown in Figure 15.

Figure 15 JGT-A rebound meter.
Figure 15

JGT-A rebound meter.

According to the Technical Specification for Testing the Compressive Strength of Concrete by the Rebound Method [27], the rebound value of the concrete specimen block should be uniformly distributed. In this study, the concrete specimen block with 28 days of curing is selected for the experiment, and the net distance between the measuring points is taken as 20 mm.Three locations at the top, bottom, and center of the concrete specimen, respectively, and 16 measurement points at each location are taken for the experiment, and the measurement scheme is shown in Figure 16. The rebound values are converted to compressive strength according to the experimental specification using the conversion formula

(19) f cu c = 0.034488 R m 1.94 × 10 − 10 , 173 d m ,

where f cu c is the strength conversion value of the concrete measuring range (MPa); R m is the concrete rebound value of the measuring range; and d m is the average carbonation depth value of the concrete in the measuring range (mm).

Figure 16 Rebound value measuring point scheme. (a) Concrete top measuring point scheme and (b) measuring point scheme of concrete middle.
Figure 16

Rebound value measuring point scheme. (a) Concrete top measuring point scheme and (b) measuring point scheme of concrete middle.

Similarly, the rebound values at each measurement point were statistically analyzed for the relative error N 3 using the expression

(20) N 3 = max ( 1 − R t / R b ) ( 1 − R t / R m ) × 100 % ,

where R t is the rebound value of the upper region of the concrete; R m is the rebound value of the middle region of the concrete; and R b is the rebound value of the lower region of the concrete. It can be seen from Equation (20) that the larger the value of N 3, the larger the difference in concrete rebound value and the larger the difference in concrete strength.

5 Results and discussion

In this section, the error method is used to discuss the changes in the homogeneity, compactness, and rebound value of concrete on a concrete vibration table under different vibration frequencies, amplitudes, and times. The vibration effect was evaluated by porosity calculation of bubbles on concrete slices in both simulation and experimental ways. In order to eliminate experimental errors and ensure the repeatability of the method, the experimental results are determined by the average value of multiple concrete experiments.

5.1 Effect of frequency on vibration performance

Figure 17 shows the simulation and experimental results of concrete 1 under different vibration frequencies, where the large white particles are concrete crushed stones, the small white particles are bubbles in the concrete, and the pink liquid is concrete mortar. As shown in Figure 17, with the increase in vibration frequency (0–40 Hz), the bubble overflow is more obvious, and the simulation and test trends are the same. When the vibration frequency is 40 Hz, the bubble overflow of concrete is more obvious, but the degree of concrete segregation is also increasing. Therefore, for the vibration process of concrete, the selected vibration frequency should be as close as possible to the natural vibration frequency of the aggregates inside the concrete, so that resonance occurs and the ideal vibration compaction effect can be achieved.

Figure 17 Simulation results of concrete 1 under different vibration frequencies. (a) No vibration, (b) 20 Hz, (c) 30 Hz, and (d) 40 Hz.
Figure 17

Simulation results of concrete 1 under different vibration frequencies. (a) No vibration, (b) 20 Hz, (c) 30 Hz, and (d) 40 Hz.

Figure 18 shows the changes in the homogeneity and relative error values of concrete 1 with height when there is no vibration and when there is vibration. When there is vibration, the vibration amplitude is 1.5 mm, the vibration time is 20 s, and the frequencies are 20, 30, and 40 Hz, respectively. The concrete is divided into three parts along the pouring direction, namely, the top area, the middle area, and the bottom area. From Figure 18, it can be seen that the homogeneity of concrete under vibration decreases with the increase in concrete height. Among them, the homogeneity of the top area of concrete is the lowest, and the relative error value of homogeneity between concrete 1 simulation and experiment is the highest at 3.3%. The experimental results are consistent with the simulation results. The minimum relative error value of simulated homogeneity for concrete with a vibration frequency of 30 Hz is 16%. Therefore, when the vibration frequency is 30 Hz, the distribution of aggregates in various areas of the concrete is the most uniform.

Figure 18 Homogeneity and error value of concrete 1.
Figure 18

Homogeneity and error value of concrete 1.

Figure 19 shows the changes in the compactness and relative error values of concrete 1 with height when there is no vibration and when there is vibration. For the case with vibration, the vibration amplitude is 1.5 mm, the vibration time is 20 s, and the frequencies are 20, 30, and 40 Hz, respectively. From Figure 19, it can be seen that the compactness of each region of the concrete increases, with the simulated compactness of the bottom region of concrete 1 with a vibration frequency of 40 Hz reaching a maximum of 96.7%, and the simulated compactness of the bottom region of concrete with a vibration frequency of 20 Hz reaching a minimum of 96.2%. Among them, the compactness of the middle and bottom regions of concrete with a vibration frequency of 40 Hz is the best, but the compactness of the top and middle regions of concrete increases slowly.

Figure 19 Compactness and error value of concrete 1.
Figure 19

Compactness and error value of concrete 1.

Figure 20 shows the changes in the rebound values and relative error values of concrete 1 with height when there is no vibration and when there is vibration. For the case with vibration, the vibration amplitude is 1.5 mm, the vibration time is 20 s, and the frequencies are 20, 30, and 40 Hz, respectively. From Figure 20, it can be seen that the rebound values in each area of Concrete 1 are within the range of 39–45.7. The rebound values from the top area to the bottom area of concrete 1 gradually increase, i.e., the compressive strength of concrete gradually increases. The difference in rebound values between the top and bottom areas of Concrete 1 is above 1.9. The maximum relative error between the simulated and experimental rebound values of concrete 1 is 3.6%, and the experimental results are consistent with the simulation results. The relative error value of the simulated rebound value of concrete with a vibration frequency of 30 Hz is the lowest at 9.7%. Therefore, when the vibration frequency is 30 Hz, the rebound value of each area of the concrete is better.

Figure 20 Concrete 1 rebound value and error comparison.
Figure 20

Concrete 1 rebound value and error comparison.

5.2 Effect of vibration amplitude on vibratory performance

Figure 21 shows the simulation and experimental results of concrete 1 under different vibration amplitudes, with a high degree of agreement. Figure 22 shows the changes in the homogeneity and relative error values of concrete 1 with height when there is no vibration and when there is vibration. When there is vibration, the vibration frequency is 20 Hz, the vibration time is 20 s, and the amplitude is 2, 3, and 4 mm, respectively. From Figure 22, it can be seen that the compactness of concrete under vibration decreases with the increase in concrete height. The highest homogeneity in the top area of concrete 1 is 30.2% with a vibration amplitude of 2 mm. The lowest homogeneity in the top area of concrete 1 with a vibration amplitude of 4 mm is 28.2%, both lower than the average compactness of 33%. The homogeneity of the middle area of concrete 1 varies between 34.2 and 35.1%, while the bottom area of concrete 1 varies between 35.6 and 36.7%. The maximum relative error value of homogeneity between concrete 1 simulation and experiment is 7.6%, and the experimental results are consistent with the simulation results. The minimum relative error value of the simulated homogeneity for concrete with a vibration amplitude of 3 mm is 14%. Therefore, when the vibration amplitude is 3 mm, the distribution of aggregates in various areas of the concrete is the most uniform.

Figure 21 Simulation results of concrete 1 under different vibration amplitudes. (a) Not vibrating, (b) 2 mm, (c) 3 mm, and (d) 4 mm.
Figure 21

Simulation results of concrete 1 under different vibration amplitudes. (a) Not vibrating, (b) 2 mm, (c) 3 mm, and (d) 4 mm.

Figure 22 Homogeneity and error value of concrete 1.
Figure 22

Homogeneity and error value of concrete 1.

Figure 23 shows the changes in the compactness and relative error values of concrete 1 with height when there is no vibration and when there is vibration. When there is vibration, the vibration frequency is 20 Hz, the vibration time is 20 s, and the amplitude is 2, 3, and 4 mm, respectively. When the vibration amplitude of concrete 1 is 4 mm, the compactness of the bottom area of concrete is the highest at 95.8%, and the compactness of the bottom area of concrete with a vibration amplitude of 2 mm is the lowest at 94.9%. The compactness of the middle area of concrete varies from 93.6 to 94.5%. The maximum relative error between the compactness of concrete 1 simulation and experiment is 5.3%, and the experimental results correspond to the simulation results. The minimum relative error value of simulated compactness for concrete with a vibration amplitude of 3 mm is 22.1%. The compactness of each area of concrete with a vibration amplitude of 3 mm is better, and the relative error value of homogeneity is the lowest.

Figure 23 Compactness and error value of concrete 1.
Figure 23

Compactness and error value of concrete 1.

Figure 24 shows the changes in the rebound values and relative error values of concrete 1 with height when there is no vibration and when there is vibration. For the case with vibration, the vibration frequency is 20 Hz, the vibration time is 20 s, and the amplitude is 2, 3, and 4 mm, respectively. The rebound values of each area of concrete 1 are within the range of 39–45.2, and the difference in rebound values between the top and bottom of concrete 1 is more than 1.6. The maximum relative error between the simulated and experimental rebound values of concrete 1 is 5.6%, and the experimental results are consistent with the simulation results. The minimum relative error value of the simulated rebound value for concrete with a vibration amplitude of 3 mm is 10.8%. When the vibration amplitude is 3 mm, the difference in rebound values among different areas of concrete is relatively low.

Figure 24 Concrete 1 rebound value and error comparison.
Figure 24

Concrete 1 rebound value and error comparison.

5.3 Effect of vibration time on vibration performance

Figure 25 shows the simulation and experimental results of concrete 1 under different vibration times, with a high degree of agreement. Figure 26 shows the changes in the homogeneity and relative error values of concrete 1 with height for no vibration case and vibration case with a vibration frequency of 25 Hz and a vibration amplitude of 2.5 mm. From Figure 26, it can be seen that under vibration, the concrete crushed stone gradually layers with time. Among them, when the vibration time is 35 s, the simulated homogeneity of the bottom area of concrete 1 is the highest at 37.2%, the simulated homogeneity of the top area of concrete 1 is the lowest at 28%, and the relative error value of the homogeneity of concrete 1 is the highest at 17.3%. This indicates that excessive vibration time can lead to obvious layering of concrete due to excessive vibration. When the vibration time is 15 s, the highest simulated homogeneity in the bottom area of concrete 1 is 35.2%, the lowest simulated homogeneity in the top area of concrete 1 is 30.3%, and the maximum relative error value of homogeneity in concrete 1 is 13%. It can be inferred from the relative error value of the homogeneity of concrete that the homogeneity of concrete aggregates gradually decreases with time.

Figure 25 Simulation results of concrete 1 under different vibration time. (a) Not vibrating, (b) 15 s, (c) 25 s, and (d) 35 s.
Figure 25

Simulation results of concrete 1 under different vibration time. (a) Not vibrating, (b) 15 s, (c) 25 s, and (d) 35 s.

Figure 26 Homogeneity and error value of concrete 1.
Figure 26

Homogeneity and error value of concrete 1.

Figure 27 shows the variation in compactness and relative error values with vibration time for concrete 1 without vibration and with a vibration frequency of 25 Hz and a vibration amplitude of 2.5 mm. From Figure 27, it can be seen that the compactness of vibrated concrete is higher than that of unvibrated concrete, and as the vibration time increases, the relative error values between the layers of concrete also increase. Among them, when the vibration time is 35 s, the highest compactness simulated in the bottom area of concrete 1 is 96.2%. When the vibration time is 15 s, the lowest compactness simulated in the bottom area of concrete 1 is 94.7%, and there is no significant change in the compactness range of the middle area of concrete 1 from 92.7 to 94.5%. The maximum relative error value between the simulated and experimental compactness of concrete 1 is 4.8%, and the lowest relative error value of the simulated compactness of concrete 1 with a vibration time of 15 s is 13.4%. Therefore, the compactness of each area of concrete with a vibration time of 15 s is better, and the relative error value of homogeneity is the lowest.

Figure 27 Compactness and error value of concrete 1.
Figure 27

Compactness and error value of concrete 1.

Figure 28 shows the variation in rebound value and relative error value with vibration time for concrete 1 without vibration and with a vibration frequency of 25 Hz and a vibration amplitude of 2.5 mm. In Figure 28, the rebound values of each area of concrete 1 range from 39.1 to 44.5, and the difference in rebound values between the top and bottom of concrete 1 is above 1.1. The maximum relative error between the simulated and experimental rebound values of concrete 1 is 7.8%. The lowest relative error value of the simulated rebound value of concrete 1 with a vibration time of 15 s is 6.8%, and the lowest relative error value of the simulated rebound value with a vibration time of 15 s is 5.9%. Therefore, when the vibration time is 15 s, the difference between the compactness of concrete and the average compactness is the smallest, and the relative error value of the rebound value is the smallest.

Figure 28 Concrete 1 rebound value and error comparison.
Figure 28

Concrete 1 rebound value and error comparison.

6 Conclusion

This study establishes a fresh concrete model obtained by coupling the multiphase flow model, Bingham model, and discrete phase model with the liquid phase flow equation. The model and its rheological parameters are validated through V-shaped funnel experiments and slump experiments. Based on the verified concrete vibration table model, the influence of vibration process factors on the vibration performance of the concrete vibration table is discussed, and the main conclusions are as follows:

  1. The concrete V-shaped funnel and slump experiments are effective methods for measuring the material parameters of concrete and the physical parameters of the multiphase flow model of fresh concrete. The verification process and time sequence have a significant impact on the measurement accuracy.

  2. Due to the opacity of concrete, the use of segmented screening and slicing methods plays a decisive role in measuring experimental parameters of concrete. At the same time, using multiphase flow methods to simulate fresh concrete can serve as a method for visualizing aggregate movement.

  3. Within the vibration frequency range of 20–40 Hz, the increase in vibration frequency can improve the compactness of concrete. Within a vibration amplitude of 2–4 mm, the increase in amplitude can increase the compactness of concrete particles, but excessive amplitude can lead to particle layering and a decrease in concrete strength. Within a vibration time of 15–35 s, the increase in vibration time will increase the compactness of concrete, but excessive time will lead to a decrease in the relative error value of concrete homogeneity.

Next we will prepare a combination of experiments and simulations, using concrete calibration experiments to verify the curing process of concrete as time increases, and consider the concrete bond coefficients as a function of time during the simulation process to perform analogue simulations of concrete curing. Follow-up research will be carried out on how to improve the vibration effect by optimizing the vibration method and exploring the influence of variables on pores distribution.

Acknowledgements

The authors are grateful for the laboratory provided by the School of Mechanical Engineering of Shenyang Jianzhu University, and thank the reviewers for their valuable comments that improved the manuscript.

  1. Funding information: This work was funded by the Liaoning province Department of Education fund article (JYTMS20231604) and (LJKMZ20220923).

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and consented to its submission to the journal, reviewed all the results and approved the final version of the manuscript. DFZ designed the research approach and proposed solutions. WDY designed the experimental plan. ZHH wrote the article. XFC processed the data.

  3. Conflict of interest: Authors state no conflict of interest.

  4. Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-05-26
Revised: 2024-07-31
Accepted: 2024-08-21
Published Online: 2024-09-30

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/secm-2024-0038
Keywords for this article
vibration table; prefabricated component; computational fluid dynamics; concrete homogeneity; concrete compactness
Creative Commons
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