Compressive strength and Young’s Moduli of Concrete in Correlation to Ultrasonic Pulse Velocity

Nils Lange, winter semester, February 2017

The ultrasonic pulse velocity (UPV) in cement-based materials like concrete depends highly on its Young’s moduli. The dynamic Young’s module (E_dyn) can be found with the pulse velocity of the concrete specimen. There is a relation between the dynamic Young’s module and the compressive strength. Obviously, there should be a relation between the compressive strength and the pulse velocity, too. ^[1]

Determining the material properties such as E_dyn and the compressive strength with the UPV has several advantages. For instance, the material properties are directly determined on the construction component and not on a single test specimen. Moreover, the compressive strength can be determined quickly after placing concrete and the future compressive strength can be predicted. In addition to that, the ultrasonic velocity can be measured quickly and inexpensively compared to other testing methods.^[2] Furthermore, the use of non-destructive testing (NDT) benefits that the structure is not damaged.

This article will describe how to find the material properties of concrete using the UPV such as E_dyn, how it is related to the static Young’s module E_stat, and the compressive strength.

Basics

Ultrasound has typical frequencies (f) between 20 and 200 kHz. They spread in the velocity specific for every material. As already mentioned there are several material properties that are related to the wave velocity. The wave velocity can be evaluated as shown in Figure 1 by direct transmission or by indirect Transmission and respectively surface Transmission.

The Transmitter sends an impulse through the specimen. The impulse is received after a certain time (∆t) by the Receiver which has a certain distance (L) to the Transmitter. The velocity can be calculated with the ratio of L to ∆t.^[2]

$//<![CDATA[ \begin{array}{l}ν = \frac{L}{Δt}\qquad[m/s]\end{array} //]]>$

Determination of the dynamic Young’s module (E_dyn)

E_dyn can be evaluated in dependency of the bulk density ρ, the longitudinal wave velocity ν_L and the dynamic Poisson’s ratio (σ) by the following equation:

$//<![CDATA[ \begin{array}{l}E_{dyn} = ρ×ν_L^2×k\qquad[N/mm²]\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}k = \frac{(1-2σ)×(1+σ)}{1-σ}\qquad[-]\end{array} //]]>$

Poisson’s ratio can be determined by the ratio of the longitudinal wave velocity ν_L and the shear wave velocity ν_s as shown in the following equation:

$//<![CDATA[ \begin{array}{l}σ = \frac{1-2×(ν_S÷ν_L)^2}{2-2×(ν_S÷ν_L)^2}\qquad[-]\end{array} //]]>$

In civil engineering, it is only possible to determine the exact values of E_dyn in exceptional cases due to complex dimensions of the structures. It is much more advantageous to apply the method for comparison measurements. If there are constant testing conditions, especially in dimensions, the measurements are reproducible. ^[3][4]

Determination of the static Young’s module (E_stat)

It requires hard effort to measure the static Young’s Module (E_stat). Specimen preparation and testing takes a lot of time and the equipment costs are high whereas the measurement of the dynamic Young’s module (E_dyn) is much faster and less expensive. It would be beneficial to determine E_stat in dependency of E_dyn.

For typical loadings, the static Young’s Module (E_stat) is approximately five to ten percent smaller compared to the dynamic Young’s Module (E_dyn) due to higher stress in the concrete structure and a plastic deformation. If the compressive strength is increasing, the differences between E_stat and E_dyn are decreasing.

In literature, several formulas for calculatating E_stat in dependency of E_dyn are given. But they are only giving approximate values.^[5][6] E_stat can also be found after the determination of the regression line.^[4]

Determination of the dynamic shear module (G_dyn)

The dynamic shear module (G_dyn) can be determined in dependency of dynamic Young’s module (E_dyn) and dynamic Poisson’s ratio (σ) as shown in the following equation:

$//<![CDATA[ \begin{array}{l}G_{dyn} = \frac{E_{dyn}}{2×(1+σ)}\qquad[N/mm²]\end{array} //]]>$

Determination of the compressive strength

Many scientists have established an empirical correlation between compressive strength and UVP. In 2004 an exponential relationship had been found by Demirboga et al. and the equation most commonly used to determine the compressive strength S with the longitudinal wave velocity ν_L found by Trtnik et al. in 2009 is:

$//<![CDATA[ \begin{array}{l}S = a.exp⁡(b.ν_L)\end{array} //]]>$

a and b are empirical parameters that can be found by the least square method.^[1]

If the concrete compositions are not taken in account, the coefficients of determination R² will be low. There will not be any reliable result for practical purposes. Parameters such as the water-cement ratio, the type of cement, aggregate and other admixtures like fly ash and silica fume effect the pulse velocity and the compressive strength but not necessarily in the same way.^[1]

For structural elements with similar concrete mixes and are prepared under the same conditions, it is possible to establish a correlation between UPV and compressive strength. The first step is to determine the sections that have low, intermediate and fast pulse velocities. After that, drill cores with same diameters in those sections are obtained and will be used to measure the compressive strength and the pulse velocity. Finally, these values are entered in a diagram and the regression line is drawn. The compressive strength can then be calculated only by the UPV on different sections of the structural element.

This method proves advantageous compared to destructive testing methods because it causes less destruction and provides more significant results.

Nevertheless, it is difficult to transfer pulse velocities to compressive strength, if pulse velocities are not in the value range of the regression line.^[4]

Literature

1. T. H. Panzera: A. L. Christoforo; F. P. Cota; P. H. R. Borges and C. R. Bowen (2011). Ultrasonic Pulse Velocity,Evaluation of Cementitious Materials, Advances in Composite Materials - Analysis of Natural and Man-Made Materials, Dr. Pavla Tesinova (Ed.), ISBN: 978-953-307-449-8, InTech, Available from: http://www.intechopen.com/books/advances-in-composite-materials-analysis-of-natural-and-man-madematerials/ultrasonic-pulse-velocity-evaluation-of-cementitious-materials
2. A. Walther; M. Wilke, Zerstörungsfrei Ermittlung der Betondruckfestigkeit im Bestand mit kombinierten Prüfverfahren, Conference: Erhaltung von Bauwerken, Esslingen, 2015
3. N.K. Choudhari; Ashok Kumar; Yudhisther Kumar; Reeta Gupta, Evaluation of elastic moduli of concrete by ultrasonic velocity, Ultrasonics Section, National Physical Laboratory, New Delhi, 2002
4. C. Große, Einführung in die Zerstörungsfreie Prüfung im Ingenieurwesen Grundlagen und Anwendungsbeispiele, TU München, 2016
5. J, EIBL, Betonkalender, Teil II, Berlin, Ernst & Sohn, 1999
6. W. Erfurt, Erfassung von Gefügeveränderungen in Beton durch Anwendung zerstörungsfreier Prüfverfahren zur Einschätzung der Dauerhaftigkeit, Dissertation, F.A. Finger-Institut für Baustoffkunde Bauhaus-Universität Weimar, 2002