Numerical Modeling and Analysis of Concrete Slabs in Interaction with Subsoil
Abstract
:1. Introduction
2. Parametric Study and Basic Computational Model
2.1. Experiment—Reinforced Concrete Slab
2.2. Experiment for Reinforced Concrete Slab—Numerical Modeling
2.3. Result of Parametric Study
3. Fiber-Reinforced Concrete Slabs
3.1. Experiments
3.2. Numerical Analysis of Fiber-Reinforced Concrete Slabs on Subsoil
4. Discussion
5. Recommendations for Numerical Modeling of Slabs in Interaction with Subsoil
- (1)
- Current computer technology and numerical methods make it possible to solve the problem using three-dimensional computational models with linear and non-linear solutions.
- (2)
- The chosen finite element method is suitable, and a linear isoparametric eight-node finite element with eight integration points is recommended. The use of tetrahedral finite elements in a non-linear solution can reduce the quality of the solution with respect to the principle of implementation of physical non-linearity. The use of more advanced isoparametric elements also leads to a significant increase in computational complexity.
- (3)
- The size of the finite elements must be chosen appropriately with regard to the dimensions of the structure. Setting the mesh along the thickness of the slab with at least eight finite elements is important for the accuracy of the calculation.
- (4)
- In the case of a linear calculation, the results of deformations are more significantly affected by the subsoil deformation modulus than the stiffness of conventional concrete and the size of finite elements.
- (5)
- The boundary conditions of the computational model must account for the actual geological profile. With greater depth of the model, there are also greater deformations. However, the computational model should not be deeper than the active depth (space) of the subsoil.
- (6)
- Suitable boundary conditions for the subsoil model are for the bottom surface, vertical support uz = 0, and the walls ux = 0 or uy = 0.
- (7)
- For modeling, it is appropriate to use the interface in the fixed contact or interface contact. Such use removes the need for there to be a common finite element mesh. The use of the contact interface significantly increases the requirements for computational complexity and knowledge of input parameters. Contact interface parameters have mixed properties. Some have a physical nature and some are more influenced by the specific geometry of the model. The parameter selection is an iterative process; the model must respect the actual behavior of the structure.
- (8)
- In the case of failure of conventional or fiber-reinforced concrete, it is necessary to use a non-linear solution, where the failure of the cross-section of the slab significantly affects the total deformation.
- (9)
- For the accuracy of the non-linear calculation, the choice of input parameters for conventional or fiber-reinforced concrete is important. The tensile strength of concrete determines the initial formation and development of cracks. During further loading, knowledge of tensile softening or fracture energy is required.
- (10)
- For concrete of ordinary strength classes and composition, it is advantageous to follow the recommendations in Model Codes 1990 or 2020. For fracture energy, it is appropriate to use VOS 1983 from the ATENA theoretical manual [26].
- (11)
- It is more difficult to determine the parameters for fiber-reinforced concrete. There are several approaches to modeling fiber-reinforced concrete and determining constitutive relationships. The basic methods include modeling of concrete and fiber separately [77], the approach presented in this study of using effective values of tensile strength and fracture energy, the definition of tensile softening [2,27], and the approximation of the tensile softening function [1]. When determining the parameters, it is appropriate to proceed from a detailed laboratory program. The basic parameters can be determined similarly to conventional concrete. Specialized tests are then the bending test and the tensile test. It is also appropriate to take into account the stochastic nature [27,78] of the parameters in the resulting parameters.
- (12)
- In the case of a known overall load-bearing capacity of a structure, it is possible to use the Newton–Raphson method. If it is necessary to determine the total load capacity, the descending branch of the calculation must use the arc-length method or the Newton–Rapson method with deformation load. It is also possible to combine methods but as a consequence, the calculation becomes complicated. The proven number of iterations was 30. The loading step should ideally be 1/20 or 1/50 of the total load capacity.
- (13)
- For a non-linear calculation, it is important to check that the experimental failure mechanism is the same.
- (14)
- A balanced compromise should be found between the requirements of the experimental program, laboratory tests, and computational complexity in order to obtain the appropriate value of the knowledge.
6. Conclusions
- The analysis of a slab in interaction with subsoil is a complex task, where conventional concrete, reinforced concrete, and fiber-reinforced concrete slabs behave differently.
- Damage and deformations to fiber-reinforced concrete slabs depend on the dosage of the fibers.
- The influence of the parameters of the subsoil (subsoil deformation modulus and depth of subsoil) increases with a higher load and damage to the slabs.
- In this study, the subsoil deformation modulus had a more significant effect on deformations than the depth of the subsoil.
- Accuracy of the input parameters for the material model is important for analysis and calculations. Individual variants can differ significantly, especially for fiber-reinforced concrete. It is necessary to appropriately identify the tensile strength and fracture energy, which are different from the values for conventional concrete.
- For the solved type of soil–structure interaction task detailed in this study, it is appropriate to use a three-dimensional computational model and non-linear analysis.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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C (MPa) | fcoef | ften (MPa) | Knn (MN/m3) | Ktt (MN/m3) | Knn,min (MN/m3) | Ktt,min (MN/m3) |
---|---|---|---|---|---|---|
1.0 | 0.1 | 0.3 | 2.0 × 108 | 2.0 × 108 | 2.0 × 105 | 2.0 × 105 |
Deformation Modulus of the Subsoil (MPa) | Load (kN) | Subsoil of Depth (m) | ||
---|---|---|---|---|
2 | 4 | 6 | ||
12.5 | 150 | 2.92 | 3.57 | 4.08 |
300 | 8.60 | 9.90 | 10.91 | |
450 | 14.25 | 16.19 | 17.73 | |
600 | 22.40 | 25.30 | 26.25 | |
750 | 35.91 | 38.33 | 40.02 | |
22.5 | 150 | 1.80 | 2.15 | 2.43 |
300 | 5.28 | 6.00 | 6.57 | |
450 | 9.00 | 10.10 | 10.96 | |
600 | 12.62 | 14.10 | 15.23 | |
750 | 17.07 | 18.92 | 20.48 | |
32.5 | 150 | 1.37 | 1.61 | 1.81 |
300 | 3.92 | 4.44 | 4.82 | |
450 | 6.71 | 7.50 | 8.08 | |
600 | 9.47 | 10.52 | 11.29 | |
750 | 12.32 | 13.62 | 14.60 |
Fibers (kg/m3)|(%) | Average Compressive Strength Cylinder|Cube (MPa) | Average Split Tensile Strength (MPa) | Bending Tensile Strength (MPa) | |||
---|---|---|---|---|---|---|
Type of Test | ||||||
3B500 | 3B600 | 4B600 | 4B500 | |||
0|0 | 20.03|25.11 | 2.10 | 3.02 | 2.89 | 2.55 | 2.85 |
25|0.32 | 29.28|34.96 | 2.96 | 4.04 | 3.81 | 3.10 | 3.76 |
50|0.64 | 25.27|31.65 | 3.12 | 4.41 | 4.24 | 3.56 | 4.06 |
75|0.96 | 24.90|27.87 | 3.17 | 4.72 | 5.16 | 4.35 | 4.95 |
Input Parameter | Unit | Marker of Slab|Fibers (%) | |||
---|---|---|---|---|---|
G01|0 | G02|0.32 | G03|0.64 | G01|0.96 | ||
Modulus of elasticity | GPa | 19.51 | 19.51 | 19.51 | 19.51 |
Compression strength | MPa | 21.34 | 29.71 | 26.90 | 23.69 |
Poisson’s ratio | - | 0.2 | 0.2 | 0.2 | 0.2 |
Tension strength | MPa | 1.89 | 2.66 | 2.81 | 2.85 |
Fracture energy | N/m | 47 | 225 | 1100 | 2500 |
Fixed crack | - | 1 | 1 | 1 | 1 |
Maximum aggregate size | mm | 16 | 16 | 16 | 16 |
Reduction coefficient Fc, red | - | 0.8 | 1 | 1 | 1 |
Shear factor | - | 20 | 20 | 20 | 20 |
Fracture energy | N/m | 47 | 225 | 1100 | 2500 |
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Cajka, R.; Marcalikova, Z.; Bilek, V.; Sucharda, O. Numerical Modeling and Analysis of Concrete Slabs in Interaction with Subsoil. Sustainability 2020, 12, 9868. https://doi.org/10.3390/su12239868
Cajka R, Marcalikova Z, Bilek V, Sucharda O. Numerical Modeling and Analysis of Concrete Slabs in Interaction with Subsoil. Sustainability. 2020; 12(23):9868. https://doi.org/10.3390/su12239868
Chicago/Turabian StyleCajka, Radim, Zuzana Marcalikova, Vlastimil Bilek, and Oldrich Sucharda. 2020. "Numerical Modeling and Analysis of Concrete Slabs in Interaction with Subsoil" Sustainability 12, no. 23: 9868. https://doi.org/10.3390/su12239868