time domain reflectometry for measuring water- cement...

Yu, Drnevich and Olek, W-C Ratio by TDR, of 13 Fax: (765) 496-1364 Email: [email protected]

TIME DOMAIN REFLECTOMETRY FOR MEASURING WATER-CEMENT RATIO OF CONCRETE

Xiong Yu, Vincent P. Drnevich, and Jan Olek Post Doctoral Researcher, School of Civil Engineering, Purdue University, West Lafayette, IN, USA 47907-2051, [email protected] Professor, School of Civil Engineering, Purdue University, West Lafayette, IN 47907-2051, USA [email protected] (corresponding author) Associate Professor, School of Civil Engineering, Purdue University, West Lafayette, IN 47907-2051, USA [email protected] Abstract

Water-cement ratio is an important property for concrete strength and durability so getting reasonably accurate measurements of it for freshly mixed concrete is of great practical importance. The much larger dielectric constant of water compared with other ingredients in fresh concrete makes it strongly related to water content. On the other hand, the high ion content in the pore solution of the fresh concrete strongly affects the electrical conductivity. Time Domain Reflectometry (TDR) provides fast and accurate measurement of both dielectric constant and electrical conductivity. Simple calibration equations are proposed that relate water content to the dielectric constant and cement content to the electrical conductivity. Thus, TDR can measure both water content and cement content simultaneously, from which water-cement ratio can be calculated. Since both dielectric constant and electrical conductivity are somewhat temperature dependent, temperature compensation factors are required to adjust for temperature effects. The TDR system for this application is similar to that used for measurements in soils and consists of a TDR tester, cable and disposable, permanently inserted measurement spikes which penetrate approximately 135 mm into the surface of the fresh concrete. The concrete can be tested in place or in test specimens. In addition, a thermocouple is used to make temperature measurements in the curing concrete, which provides data for the temperature compensation factors. This paper presents the basic principles, testing system, and preliminary test results for use of TDR to determine water-cement ratios of the fresh concrete.


1. Introduction Water-cement ratio is an important design parameter for concrete. It influences the kinetics of hydration reactions and the quality of concrete microstructure. As a result, it determines many mechanical properties related to concrete service and durability, such as concrete strength1, bonding between concrete and rebars2, concrete permeability3 and resistance to sulfate attack4. The current field practice to estimate water-cement ratio is from batch mixture quantities, i.e., water-cement ratio is calculated from the amount of water and the amount of cement added to the mixture. The estimated results are not generally found accurate, as the quantities do not accurately account for factors such as moisture contained in aggregate or water added at the job site. A technique that can provide quick and accurate field measurement of water-cement ratio will significantly benefit the quality control and quality assurance of concrete.

Given the practical importance of water-cement ratio, many techniques have been proposed to measure this property. These generally involve measurement of water content and measurement of cement content. Field experiences indicate that accurate measurement of the water-cement ratio of fresh concrete is very difficult to achieve and currently there are no fast and reliable technologies available5. For example, the nuclear gauge, which is widely used for quality control of soil compaction, is found ill suited for field water-cement determination use due to its unsuitability for igneous aggregates, poor field performance with limestone aggregates, and extensive training and certification procedure for operators5. Popovics and Popovics6 proposed several approaches using ultrasonic testing. However, although the research unveiled some potential application of ultrasonic technology in fresh concrete characterization, none of the approaches produced satisfactory solution for the instantaneous determination of the water-cement ratio.

In this paper, Time Domain Reflectometry (TDR) is identified and proposed as an innovative tool for measuring water-cement ratio. It is shown that combined information of TDR measured dielectric constant, which is strongly related to water content, and electrical conductivity, which is strongly related to cement content, may be sufficient to measure water-cement ratio. The basics ideas and preliminary observations are summarized in this paper. 2. Theoretical Basis of Time Domain Reflectometry

This section provides a brief review of the theory behind TDR measurement and

presents its application to water and cement content determination. 2.1 Dielectric Constant and Electrical Conductivity from TDR

Time Domain Reflectometry (TDR) is an established technique in electrical engineering for locating discontinuities in electrical cables7. Previous research indicated that TDR was also a useful tool for characterizing material dielectric properties8. Since the pioneering work by Topp et al.9, TDR has been a topic of extensive research and is widely used in engineering practice. The applications include measuring soil water content, monitoring slope deformation, estimating field salinity conditions, etc.

A TDR system for field measurement generally includes a TDR device (which consists of pulse generator and sampler), a connection cable, and a measurement probe (Fig. 1). The pulse generator sends out pulse (which generally is a fast rising step pulse) and the


sampler records the response from the system. The typical TDR signal and information content for TDR measurement in a soil is shown in Fig. 2. In this figure, we can see a “peak” and a “valley”, which are caused by reflections and are characteristic of TDR signals measured in geomaterials. The “peak” is caused by the first reflection, which occurs when the electromagnetic pulse crosses the air/material interface. The “valley” is caused by the second reflection, which occurs when the electromagnetic pulse arrives at the end of measurement probe.

-1.25

-0.75

-0.25

0.25

0.75

1.25

0 1 2 3 4 5 6 7 8

Scaled Distance (m)

Rel

ativ

e V

olta

ge (V

)

−= 11

f

sb V

VC

EC2

=

p

aa L

LK

Apparent Length, La

-1.25

-0.75

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0.25

0.75

1.25

0 1 2 3 4 5 6 7 8

Scaled Distance (m)

Rel

ativ

e V

olta

ge (V

)

−= 11

f

sb V

VC

EC2

=

p

aa L

LK

-1.25

-0.75

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0.25

0.75

1.25

0 1 2 3 4 5 6 7 8

Scaled Distance (m)

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ativ

e V

olta

ge (V

)

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1.25

0 1 2 3 4 5 6 7 8

Scaled Distance (m)

Rel

ativ

e V

olta

ge (V

)

−= 11

f

sb V

VC

EC2

=

p

aa L

LK

Apparent Length, La

Fig. 2. Typical TDR signal and information content

Vf Vs/2

Campbell Scientific, TDR 100

Soil

50 ohms Coaxial Cable, 1.8 m long

Multiple Rod Probe (MRP) Head

66 mm

SpikesØ=9.5 mm

204

mm

Connection to computer serial port

Notebook computer


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Notebook computer

135.

2 m

m


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Notebook computer


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Notebook computer


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Notebook computer


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Soil



66 mm

SpikesØ=9.5 mm

204

mm


Notebook computer

135.

2 m

m

Fig. 1 Illustration of TDR System

1st reflection

2nd reflection

L p=1

35.2

mm

Energy loss by electrical conductivity


Dielectric constant and electrical conductivity are two pieces of important information that can be obtained from analysis of a TDR signal. Material dielectric constant is analogous to Young’s modulus in that it determines the wave speed (electromagnetic wave rather than stress wave). It can be determined from travel time analysis and is generally called apparent dielectric constant (denoted Ka in this paper). According to the theory9, Ka represents the real part of the frequency dependent dielectric permittivity. Equation (1) gives the mathematic expression for computing dielectric constant from TDR measurement.

2

aa

p

LKL

=

(1)

where pL is the length of the probe in the material and aL is the scaled horizontal distance between the two reflections (called apparent length, see Fig. 2).

The electrical conductivity (denoted ECb in this paper) causes attenuation of TDR signal and is another important piece of information that can be obtained from TDR waveforms. Different approaches can be used to obtain electrical conductivity from a TDR signal10,11. The approach based on analysis of the long-term response of a TDR system10 is used in this paper to determine electrical conductivity (Eq. (2)).

1 1sb

f

VECC V

= −

(2)

where sV is the source voltage, fV is the long term voltage level (a method to locate these two characteristic voltages are shown in Fig. 2, and C is a constant related to probe configuration, which can be obtained by calibration. For coaxially configured probes,

0

2

ln

p s

i

L RC

dd

π=

(3)

in which pL equals the length of probe in the material, sR the internal resistance of the pulse generator (typically 50 ohms), and do and di are the diameters of outer and inner coaxial conductors, respectively.

TDR measured dielectric constant is widely applied for measuring moisture content in a variety of materials and TDR measured electrical conductivity is widely used in agriculture science to estimate soil salinity and pore fluid electrical conductivity12,13,14. 2.2 Measuring Water Content by Time Domain Reflectometry Water plays an important role in concrete mixtures. It serves as a necessary agent for hydration reactions, in which free water molecules become chemically bound with cement particles. The amount of water involved in these reactions is typically only a fraction of the water added to the mixture. As the result, the major factor that controls the amount of water used in concrete is to provide a mixture that can be placed and is workable. Water in concrete mixtures comes from two main sources, i.e., water added during mixing process and the adsorbed water from aggregates. The moisture contents of coarse aggregates generally range from 0.5% to 2% and those of fine aggregates range from 2% to 6%, which can introduce significant amount of water into the concrete mixture. Currently, there is no effective approach for field measurement of water content in freshly placed concrete5.


TDR has been extensively applied to estimate the water content in soils from measurement of soil dielectric constant. The strong correlation between TDR-measured dielectric constant and the amount of water in soil is attributed to the much larger dielectric constant of free water (around 81 at room temperature) as compared with the dielectric constant of air (around 1) or soil solids (around 3 to 7). In freshly mixed concrete, where chemical reactions are just starting, the multiphase system resembles soil mixtures. The behavior of water in fresh concrete mixture resembles that in soils. As time goes on, more water becomes chemically bound by hydration reactions. Thus, the established TDR technology for soil water content measurement is a candidate for measuring the water content in concrete. One of the most popular equations used to relate TDR measured soil dielectric constant to volumetric water content is a third order polynomial called Topp’s equation9 (Eq. 4). It is currently widely used in field practice.

222436 103.51092.2105.5103.4 −−−− ×−×+×−×= aaa KKKθ (4) where Ka is dielectric constant, and θ is volumetric water content. A simplified square root type equation (Eq. (5)) was proposed later15 and was found to provide similar accuracy. aKb a +=θ (5)

Jones et al.15 recommend values of 1875.0,125.0 −== ab from a dielectric mixing model. Volumetric water contents (θ) in Eqs.(4) and (5) may be converted to gravimetric water contents (w) as conventionally used with soil and concrete by use of the relationship provided in Eq.(6) below:

d

wwρρθ= (6)

where dρ is the dry density of soil, wρ is density of water and w is the gravimetric water content.

Siddiqui and Drnevich16 and Siddiqui et al.17 related gravimetric water content and soil dry densities to soil dielectric constant using Eq. (7).

bwaK

d

wa +=ρρ (7)

where a and b are soil specific constants obtained from calibration tests. For rapid determination of water content of concrete using this equation, a batch sample can be obtained and put into a cylindrical mold of known volume, from which total density of concrete in the mold, tρ , can be determined. The relationship between total density and dry density is given by Eq. (8)

w

td +=

1ρ

ρ (8)

Substituting Eq. (8) into Eq. (7) and solving for the water content gives:

t

wa

t

wa

Kb

aKw

ρρ

ρρ

−

−= (9)

Equation (9), with appropriate values of a and b for concrete, can be used to obtain the free water content of concrete.


2.3 Relationship between TDR Measured Electrical Conductivity and Cement Content Electrical conductivity is another important piece of information that can be obtained from a TDR signal. For freshly mixed concrete, which consists of cement paste, sand, and coarse aggregate, the major contribution to electrical conductivity is from the cement paste. The conductivity in mixtures consisting of a highly conductive phase and low conductive phases has been investigated in previous research. This included studying of influence on electrical conductivity by the amount of carbon black added to two-phase composite materials18 and the percent graphite addition on a graphite-sand mixture19. Both works showed that bulk electrical conductivity was linearly dependent on the concentration of the highly conductive phase (defined as ratio of mass of high conductive phase to nonconductive solids). In addition, both works showed that once a conduction network of a highly conductive phase was formed in the mixture, conductivity was relatively independent of the amount of added water. Similar phenomena were observed in research that used bentonite to increase the seismic resistance capability of clean sand20. Figure 4 shows the TDR measured bulk electrical conductivity versus percent bentonite (defined as ratio of mass of bentonite versus mass of sand) using water with different salt additives. The plot indicates that there is a linear relationship between TDR electrical conductivity and percent bentonite content. The slope of this relationship is independent of a dispersant (sodium hexametaphosphate in this case), which only affects the intercept. In view of the similarity between fresh concrete mixtures and the mixtures investigated in previous research, a linear relationship is proposed between TDR-measured electrical conductivity of fresh concrete mixtures and cement content (defined as mass of cement to mass of sand plus aggregate) as shown in Eq. (10):

y = 13.254x + 143.38R2 = 0.9721

y = 14.167x + 34.513R2 = 0.9889

y = 12.078x - 0.893R2 = 0.97710

50

100

150

200

250

300

350

400

0 1 2 3 4 5 6Bentonite Content (%)

Elec

trica

l Con

duct

ivity

(mS/

m) Water and bentonite

Water and sodium hexametaphosphate

Water, sodium hexametaphosphate andbentonite

Fig. 3 Relationship between TDR measured electrical conductivity and bentonite content20


( )αβ

−= bECc 1(%) (10)

Where α (units of mS/m) is a constant related to the amount of chemical additives in fresh concrete; β is a property related to cement properties and aggregate geometry. For a given concrete mixture design, a group of calibration tests can be performed on samples with different cement contents to determine the calibration constants in Eq. (10). Amounts of water, sand, coarse aggregate, and the type and amount of admixtures used in calibration should be similar to those used in the field. 3. Experimental Study 3.1 TDR System Hardware and Software Configuration

Fig. 4. The TDR system used for this research Figure 4 shows the TDR system used in this study. The system uses a TDR100

tester by Campbell Scientific, Inc. The measurement sensor is made of four common spikes arranged in coaxial configuration (the spikes cost 20 cents each and can be obtained in most local hardware stores). Prior to testing, the spikes need to be cleaned to remove burrs and oil films. Before installing the sensor in the field or in a sampling mold, a plastic template is first placed on the surface of the fresh concrete. Spikes are pushed in through the predrilled holes in the plastic plate. The use of the plastic plate is to align the spikes and provide support for the weight of TDR measurement head. In this study, the net length of the portion of the spikes submerged in concrete was 135.2 mm (the length of spikes used can vary depending on need) and the distance between center spike and outer spike was 66 mm. This gave sufficiently large sampling volume, which was necessary to obtain accurate measurements in coarse grained mixtures such as concrete (ASTM D1556). Upon installation of the sensor, a measurement head was seated on the caps of the spikes, which was connected to Campbell Scientific TDR100 tester by a coaxial cable. A specially developed computer program was used to take data and obtain the initial dielectric constant and electrical conductivity. Multiple readings were taken and averaged to obtain improved


accuracy. This process took less than one minute. The monitoring module of the computer program was then activated, which automatically took TDR reading at specified time intervals to monitor the change of dielectric constant and electrical conductivity with time. A thermocouple wire was also installed to monitor the temperature with time, whether due to hydration reactions or changes in ambient temperature. 3.2 Concrete Properties

Two different concretes were studied in the preliminary research. Both used type I cement and one was obtained from the construction site at Purdue University Chemical Engineering building expansion project. The other was a self leveling concrete used in the strong floor of the newly built Bowen Civil Engineering High Performance Large Scale (HPLS) Laboratory at Purdue. The mixture proportions of the two concretes are shown in Table 1. The samples were obtained from field and put into standard 6’×12’’ plastic molds with volume of 6.107×10-3 m3. Additional samples were obtained to determine oven dry water content. Table 1: Mixture proportions and water-cement ratio from batch mix records

Gravel (kg/m3)

Sand (kg/m3)

Cement (kg/m3)

Water (kg/m3)

Water-Cement ratio

Chemical Engineering 1089 916 306 162 0.52 Bowen Lab 1101 916 336 161 0.48

3.3 Results and Analysis Measurement of Water Content in Fresh Concrete by TDR Water contents in concrete are computed from TDR-measured dielectric constant by Eq. (9). A temperature compensation factor (Eq. (11)) was applied before computing water content to compensate the effects of temperature on TDR-measured dielectric constant. More details of the temperature compensation factor can be found in Yu et al.21.

952.00019.01+⋅

=T

TCFbaK (11)

where T is temperature in °C. Physical interpretation as well as typical range of constants a and b for use in Eq. (9) are given by Drnevich et al.22, with a being predominantly dependent on dielectric properties of dry solid phases and b being mostly decided by pore fluid. Default values of a=1.0 and b=8.5 were recommended for use in soil and provided reasonably accuracy for various soil types22. In view of the fact that mixtures with highly conductive phases generally have much larger slopes (b values) than soils18,19, the values of constants a and b used in Eq.(9) for the concrete tested in this research were set to a=1.0 and b=14.5. A summary of measured water contents by TDR for the fresh concrete samples used in this study are shown in Table 2. There are several observations from this table. For both of these concretes, the oven dry water content is slightly larger than the water contents calculated from batch receipts (0.4% (for the Bowen Lab concrete) and 0.3% (for concrete at Chemical Engineering)). These are equivalent to aggregates moisture content of 0.6% and 0.8% respectively, which are at the lower end of typical moisture range of aggregates discussed above. It is expected that the effects of aggregate moisture could be much more pronounced in other situations.


For comparison purposes, volumetric water contents for these concretes were determined by Eqs. (4) and (5) and converted to gravimetric water contents by use of Eq. (6). From Table 2, we can see neither Topp’s equation (Eq.(4)) nor the simplified equation from dielectric mixing model (Eq.(5)), both of which are widely applied in soil moisture content measurement, gives satisfactory results of water content of concrete. This implies that although the fresh concrete mixtures resemble soil mixtures, the dielectric constant of the concrete mixture is different from soil. Use of Eq. (9) provides much better accuracy for water content measurement in concrete because it accounts for density and uses calibration parameters for concrete. Table 2: Water contents by TDR method

Concrete Source

Dry Density (kg/m3)

Oven Dry Water

Content (%)

Water Content from Batch

Weights (%)

Siddiqui-Drnevich Eq. (9)

(%)

Topp’s Eq. (4)

(%)

Simplified Eq. (5)

Bowen Lab

2041 7.4 7.0 7.5 16.9 15.8

Chemical Engrg.

2078 7.1 6.8 7.0 16.3 15.2

Monitoring of Change of Free Water Content in Concrete Water in concrete exists in two different types, i.e., free water and chemically bound water. These two types of water show significantly different dielectric behavior. It has been established that free water has relaxation frequency of around 18GHz while the relaxation frequency for bound water is within MHz range. (Relaxation frequency is a term that is analogous to resonant frequency for vibrating systems.) The TDR system used in this research has an effective frequency into the low gigahertz range23 and is more sensitive to the amount of free water than to bound water. Thus, it is a more direct indicator of amount of free water in concrete. This makes TDR-measured dielectric constant more instructive and easier to interpret compared with the system used by Beek et al.24, which measures dielectric behavior at 20MHz where the dielectric constant includes the combined effects of free water and bound water. The plots of TDR-measured dielectric constant with time are shown in Fig. 5 for both concretes. The dielectric constant consistently decreased with time (in contrast with the results by Beek et al.24, who measured increased dielectric constant during first day as a result of predominant effects of increasing amount of bound water). The TDR measured dielectric constant decreases at a high rate at the initial stage, which indicates the high intensity of hydration reactions. The rate of decrease becomes smaller with time, which reflects reduced intensity of hydration. The free water contents calculated using Siddiqui-Drnevich equation (Eq. (9)) are also plotted in this figure, which clearly shows the decreasing amount of free water in concrete with time. After 196 days, the free water content in concrete sample from Chemical Engineering site was around 3.0% and after 166 days that of Bowen Lab concrete sample was around 3.5%. The fact that TDR measurements can be easily automated makes it an attractive tool for monitoring the free water content in concrete.


0%

2%

4%

6%

8%

10%

0 5 10 15 20 25 30Time (day)

Free

Wat

er C

onte

nt

0

4

8

12

16

20

Die

lect

ric

Con

stan

t

Calculated Free Water Content by Eq.(9)TDR Measured Dielectric Constant

(a)

0%

2%

4%

6%

8%

10%

0 5 10 15 20 25 30

Time (day)

Free

Wat

er C

onte

nt

0

4

8

12

16

20

Die

lect

ric

Con

stan

tCalculated Free W ater Content by Eq. (9)

TDR Measured Dielectric Constant

(b)

Fig. 5 TDR monitored free water content in concrete: a) Bowen Lab concrete; b) Chemical

Engineering concrete Determination of Water-cement Ratio The TDR-measured water content can be combined with the information of cement content from batch receipts to make an estimate of water-cement ratio. The calculated water-cement ratio of concrete samples from chemical engineering site is 0.53 and that of Bowen Lab concrete is 0.52, which are slightly higher than calculated from batch receipts (by 0.1 and 0.4), respectively. As mentioned before, the moisture contents of aggregates in


these concretes are believed to be at the lower end of typical moisture content range. The resulting difference in water-cement ratio can be more significant for aggregates with higher water content or in situations where water is added at the job site. At this stage of the authors’ research, only TDR-measured dielectric constant is utilized in estimating the water-cement ratio. The amount of cement must be obtained from batch records. As discussed earlier, a preliminary theoretical framework has been established which will use TDR measured electrical conductivity to provide cement content using Eq. (10). The authors believe that incorporation of cement content from TDR- measured electrical conductivity will make the TDR technique more flexible and useful for concrete quality control. Investigations are being made to verify and refine the proposed approach. 4. Conclusions

Water-cement ratio is an important factor influencing concrete quality. Currently, there is no technology that can provide quick and reliable results for fresh concrete water-cement ratio measurement for field applications. Time Domain Reflectometry (TDR) is promising to be a useful and practical tool that can provide improved measurement of water-cement ratio. Research presented in this paper shows that by applying the established calibrations, TDR provides accurate measurement of free water content in freshly mixed concrete. Accurately measured water content combined with cement content from batch receipts provides better estimation of water-cement ratio than use of batch water because it accounts for adsorbed moisture in the aggregates. In addition to this, TDR-measured dielectric constant is a strong indicator of free water content in concrete and can be used for monitoring available free water with time. It also is suggested that the electrical conductivity by TDR can be used to measure cement content in a fresh concrete sample. Further verification and refinement should make TDR a very useful tool for concrete quality control.

5. Acknowledgements

The authors thank Study Advisory Committee member Mr. Peter Capon of Rieth-

Riley Construction Company for his encouragement to extend our research on soils to concrete. They also thank Wilhelm Construction Company, Inc. and Force Construction Company, Inc. for providing access to concrete specimens and sharing data. The authors also acknowledge help from Ms. Janet Lovell with the testing system. This work was supported by the Joint Transportation Research Program administered by the Indiana Department of Transportation and Purdue University. The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein, and do not necessarily reflect the official views or policies of the Federal Highway Administration and the Indiana Department of Transportation, nor do the contents constitute a standard, specification, or regulation. References

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