The dynamic modulus of elasticity of concrete is an important parameter for evaluating the stiffness, internal condition, and durability of concrete. Unlike static modulus testing, which measures deformation under gradually applied mechanical loading, dynamic modulus testing evaluates the response of a concrete specimen to vibration, typically by measuring its resonant frequency.

The resonance method is particularly useful for monitoring concrete subjected to freeze-thaw cycles, chemical attack, weathering, and other durability conditions. Changes in resonant frequency can be sensitive to internal defects such as microcracks and pores, making dynamic modulus testing a useful method for evaluating changes in concrete performance.

1. What Is the Dynamic Modulus of Elasticity of Concrete?

The dynamic modulus of elasticity describes the stiffness of concrete when it is subjected to dynamic or vibratory loading. It is commonly determined from the resonant frequency of a concrete specimen together with its mass, dimensions, density, and applicable calculation factors.

Because dynamic testing involves very small strains, it generally does not cause significant permanent damage to the specimen. The dynamic modulus obtained by the resonance method is normally higher than the static modulus determined by conventional stress-strain testing.

Dynamic modulus testing is therefore useful not only for determining the dynamic stiffness of concrete but also for monitoring changes in the internal condition of concrete during durability testing.

2. What Standard Is Used to Determine the Dynamic Modulus of Concrete?

One important international reference standard is ASTM C215-19, Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Resonant Frequencies of Concrete Specimens.

ASTM C215 covers the measurement of the fundamental transverse, longitudinal, and torsional resonant frequencies of concrete prisms and cylinders. These measurements can be used to calculate the dynamic Young's modulus, dynamic shear modulus, and dynamic Poisson's ratio.

The standard is also useful for monitoring changes in concrete properties during weathering and durability testing. When performing dynamic modulus testing, specimen dimensions, shape, moisture condition, and vibration mode should be properly controlled because these factors can affect the measured results.

3. How Does the Resonance Method Work?

The basic principle of the resonance method is to excite a concrete specimen and determine its natural or resonant frequency.

When the excitation frequency approaches the natural frequency of the specimen, the vibration response reaches a maximum. This frequency is identified as the resonant frequency.

Depending on the test configuration, the specimen can be evaluated using:

Transverse resonance;

Longitudinal resonance;

Torsional resonance.

After the resonant frequency is determined, it is combined with the specimen's physical properties and the appropriate calculation formula to obtain the dynamic modulus of elasticity.

The resonance method is particularly useful for durability studies because repeated measurements can be performed on the same specimen to monitor changes in its dynamic properties.

4. How Is the Dynamic Modulus of Concrete Calculated?

The calculation depends on the specimen geometry and the selected vibration mode. In general, the dynamic modulus is related to the square of the resonant frequency, the density of the specimen, and an appropriate geometric or correction factor.

A simplified relationship can be expressed as:

Dynamic Modulus ∝ Density × Resonant Frequency² × Correction Factor

Therefore, accurate measurement of the resonant frequency is essential for obtaining reliable dynamic modulus results.

For a typical test, the operator records the specimen's dimensions and mass, determines its resonant frequency, and then uses the applicable calculation procedure to obtain the dynamic modulus.

ASTM C215 provides specific calculation procedures for different specimen configurations and resonance modes. The resulting values should be compared only when the testing conditions and calculation methods are consistent.

5. How to Perform a Concrete Dynamic Modulus Test?

A typical resonance-based test includes the following steps:

Step 1: Prepare the specimen

Prepare a concrete prism or cylinder according to the applicable testing requirements. Record its dimensions, mass, age, curing condition, and moisture condition.

Step 2: Place the specimen

Place the specimen on suitable supports according to the selected vibration mode. Proper support conditions are important because they can influence the measured resonant frequency.

Step 3: Apply dynamic excitation

Excite the specimen using the appropriate excitation system. Depending on the equipment and testing method, forced vibration or impact excitation may be used.

Step 4: Measure the resonant frequency

Determine the frequency at which the specimen produces its maximum vibration response.

Step 5: Calculate the dynamic modulus

Use the measured resonant frequency together with the specimen's mass, dimensions, density, and applicable correction factors to calculate the dynamic modulus of elasticity.

Step 6: Record and analyze the results

Record the test results and compare them with initial measurements or measurements obtained after durability exposure.

6. How Is Dynamic Modulus Used to Evaluate Concrete Durability?

One of the most important applications of dynamic modulus testing is evaluating the deterioration of concrete during freeze-thaw cycles.

Repeated freezing and thawing can cause internal stresses and microcracking in concrete. As internal damage increases, the stiffness and vibration characteristics of the specimen may change, resulting in a reduction in resonant frequency and dynamic modulus.

For durability studies, the Relative Dynamic Modulus (RDM) is often used to monitor changes in concrete performance.

A commonly used relationship is:

RDM = (fₙ / f₀)² × 100%

where:

 • fₙ = resonant frequency after a specified number of exposure or freeze-thaw cycles

 • f₀ = initial resonant frequency before exposure

A decreasing relative dynamic modulus generally indicates progressive internal deterioration of the concrete specimen.

This makes dynamic modulus testing particularly useful for assessing the durability of concrete exposed to repeated freeze-thaw cycles and other environmental conditions.

7. What Is the Difference Between Dynamic and Static Modulus of Concrete?

Dynamic and static modulus tests evaluate concrete under different loading conditions and provide different types of material information.

The dynamic modulus of elasticity is commonly determined using a resonance-based method. The specimen is subjected to dynamic excitation, and its resonant frequency is measured. Because the deformation involved is very small, the test can be used repeatedly to monitor changes in a specimen without causing significant permanent deformation.

The static modulus of elasticity, on the other hand, is generally determined from the stress-strain relationship of concrete under mechanical loading. ASTM C469/C469M is a commonly referenced standard for determining the static modulus of elasticity and Poisson's ratio of concrete in compression.

The dynamic modulus is generally higher than the static modulus. The difference can be influenced by factors such as strain level, loading frequency, moisture condition, concrete composition, specimen condition, and internal microcracking.

Therefore, dynamic and static modulus values should not be directly substituted for one another. The appropriate value should be selected according to the purpose of the test and the applicable testing standard.

Conclusion

The dynamic modulus of elasticity of concrete can be determined by measuring the resonant frequency of a concrete specimen and applying the appropriate calculation procedure based on the specimen's physical properties and vibration mode.

The resonance method provides a practical way to evaluate concrete dynamic stiffness and monitor changes in its internal condition. It is particularly useful for freeze-thaw testing, durability evaluation, and monitoring concrete deterioration.

By repeatedly measuring the resonant frequency and dynamic modulus of the same specimen, laboratories can identify changes in concrete properties during durability testing and obtain useful information about its long-term performance.

The TD50082-5 Concrete Dynamic Modulus of Elasticity Tester is designed for automatic frequency measurement, data processing, and dynamic modulus calculation. It provides an efficient laboratory solution for evaluating the dynamic properties and durability-related changes of concrete and other suitable materials.

Reference Standard: ASTM C215-19