RD-E: 4702 Splitting Tensile Test (Brazilian Test)
Using a splitting tensile test to calculate input for material LAW24.

A splitting tensile test is also known as a Brazilian test. It is a typical test used for concrete material characterization carried out using procedure adhering to ASTM D3967, “Standard Test Method for Splitting Tensile Strength of Intact Rock Core Specimens”. A load is applied to a concrete cylinder with its axis normal to the loading direction. A tensile stress develops in the center. The force is slowly increased until the specimen fails by an extension fracture along the loading plane. Then the tensile strength is computed from this force of failure.
The splitting tensile test aims to evaluate failure limits. It is difficult to apply uniaxial tension to a concrete specimen. Therefore, the tensile strength of the concrete material is determined by indirect test methods such as a Split Cylinder Test or even a Flexure Test. It should be noted that both methods give a higher value of tensile strength than the uniaxial tensile strength. This will be explained in the current example. This test will be modeled, and test results will be used for numerical calibration of the material law.
Options and Keywords Used
- Concrete material law (/MAT/LAW24 (CONC))
- Brick elements
- Solid property (/PROP/TYPE14 (SOLID))
- Boundary condition (/BCS)
- Imposed displacement (/IMPDISP)
Input Files
Model Description
Since this test is quasi-static, a concrete cylinder is crushed with slow velocity. It is the standard test, to evaluate the tensile strength of concrete. This test could be performed following IS:5816-1970.

- LL
- Cylinder length
- DD
- Diameter
- FmaxFmax
- Ultimate force that leads to failure causing the specimen to split into two halves
The Radioss concrete material LAW24 is designed to work with only a few mandatory parameters. The other parameters are optional. If the optional parameters are not entered default values are calculated using typical properties of concrete material.
- Direct Tensile Strength: ft=0.05fcft=0.05fc
- Biaxial Compression Strength: fb=1.2fcfb=1.2fc
- Confined Compression Strength (tri-axial test): f2=4.0fcf2=4.0fc
- Confined pressure: s0=1.25fcs0=1.25fc
Splitting Tensile Test

Experience provides that fstfst is related to loading force FF on the cylinder. This value is sometimes used as an estimation of the direct tensile strength ftft which is one of the input parameters. It can be observed that ft<fstft<fst.
- F
- Loading force
- D
- Cylinder diameter
- L
- Length
- d
- Position on the diameter
The loading path direction and stress state in this test are different than a typical uniaxial tensile test. The material in this test undergoes both compression and tension. Compression is due to the loading force over the cylinder, and tension is due to the Poisson effect.

Fusco suggested for conventional concrete buildings the relation ft=0.85fst but other authors found the relation ft=0.66fst. 4
Using the theoretical loading path from the elastic hypothesis with Han & Chen failure surface and the values for concrete:
ftfc=110; fbfc=s0fc=65; f2fc=4
This estimation is of course dependent on the failure envelope which is shaped by all 5 parameters. Changing their values will change the fstft ratio.
Rigid Walls
Rigid walls are used to model the plywood used in the test to apply the load. Nodes on the cylinder the width of the plywood are included as secondary nodes of the rigid wall. A high friction value is set to prevent the concrete cylinder from sliding.
Loading Pressure
A compressive load is created by applying displacements in opposite directions to both rigid walls using the imposed displacement option /IMPDISP. The imposed displacement uses a linear function large enough to split the cylinders in half.
Solid Properties
- qa =1e-20 and qb =1e-20
- Isolid = 24
- IHKT = 2
- All other property values use the default options
Material Data
Units: mm, ms, g, MPa
- Initial density = 0.0024 [gmm3]
- Concrete elasticity Young’s modulus Ec=61000 [MPa]
- Poisson’s ratio ν=0.17
- Concrete uniaxial compression strength from test fc=58 [MPa]
- Concrete uniaxial tension strength is 0.05 fc so the ratio is defined as ftfc=0.05
- All other parameters can be left as default in LAW24 because the default values are representative of generic concrete materials.
- D=150 mmL=300 mmFmax=280100 Nfst=2FmaxπLD=3.96MPa
- Tensile strength ft=1√2fst=1√2×3.96 with fc=58 ⇒ftfc=0.05
- Biaxial Compression Strength: fb=1.20fc by default.
- Confined Compression Strength (tri-axial test): f2=4.00fc by default
- Confined pressure: s0=1.25fc by default This leads to the following material card input file.
Results




Conclusion
The splitting tensile strength fst measured from the Brazilian test is bigger than the tensile strength ft from a direct tensile test ft<fst. Using LAW24 with mostly default values, the tensile strength ft is about 0.71 times the splitting tensile strength fst. Only the maximum force Fmax from the splitting tensile test and fc from a cube compression test are needed as input to LAW24.