Skip to contentUnited States Department of Transportation - Federal Highway Administration FHWA Home
Research Home   |   Pavements Home
Report
This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-HRT-08-035
Date: March 2008

LTPP Computed Parameter: Moisture Content

Chapter 2. Background and Literature Review

Environmental factors such as moisture content, temperature gradient, and depth of frost penetration have a significant effect on pavement performance. Understanding the effect of these factors on performance is crucial to the optimal design of pavement structures and involves consideration of not only seasonal variations but also changes throughout the day.

To provide a means for studying the contribution of environmental factors on pavement structures, SMP was initiated within LTPP. This program was designed to provide (1) the means to link pavement response data obtained at random points in time relative to critical design conditions, (2) the means to validate models for relationships between environmental conditions and in situ structural properties of pavement materials, and (3) expanded knowledge of the magnitude and impact of the changes involved. To accomplish this, SMP sites were instrumented with the equipment in table 1.

Table 1. Instrumentation for SMP.([3])
Instruments Measurement
TDR (time domain reflectometry) Moisture content of subsurface
Thermistor sensors Pavement temperature gradients and air temperature
Electrical resistivity probes Depth of frost/thaw
Piezometer Depth of ground water table
Tipping-bucket rain gauge Precipitation

The design of SMP was a two-tiered approach including the core experiment and supplemental studies. The core experiment included 64 LTPP test sections selected by the categories listed in table 2. An additional six test sections were included as supplemental studies to the original SMP experimental design. To capture seasonal and diurnal changes, pavement response data were collected more frequently than routine LTPP monitoring. The supplemental studies were carried out in response to highway agencies' desire to collect data on LTPP test sections not included in the core sites.

Table 2. SMP core experiment sectioning category. (3)
Pavement type - Flexible-thin asphalt concrete (AC) surface (<127 mm (5 inches))
- Flexible-thick AC surface (>127 mm (5 inches))
- Rigid-jointed plain concrete
- Rigid-jointed reinforced concrete
Subgrade soil - Fine grained - Coarse grained
Environment - Wet-freeze - Wet-no freeze - Dry-freeze - Dry-no freeze

Overview of Time Domain Reflectometry (TDR)

The collection of TDR waveforms from subsurface materials is of particular interest in this study. Although the importance of in situ moisture content of subsurface layers in pavement structures has been well recognized, moisture measurement has sometimes been difficult because of the limitations of existing measurement and computational methods.

Figure 1. Diagram. TDR probe for SMP. Top view and side view schematic of TDR probes installed at LTPP-SMP sites.
Figure 1. Diagram. TDR probe for SMP. (3)

The TDR method was selected for use in the SMP core experiment. TDR equipment was originally developed for measuring electromagnetic wave travel times to detect breaks or shorts in electrical conductors and subsequently was adapted to collect sufficient data to allow for soil moisture to be estimated. The TDR system records an electromagnetic waveform that can be analyzed as it is transmitted and reflected to characterize the nature of objects that reflect the waves. The waveform pulse is transmitted along a coaxial metallic cable shielded by a waveguide at a velocity that is influenced by the dielectric constant (e) of material surrounding the conductors. This dielectric constant is a dimensionless ratio of a material's dielectric permittivity to the permittivity of free space. Changes in the dielectric constant of the surrounding material occur as its moisture content or conductivity (the reciprocal of resistance) changes. Signal reflectivity also varies (from 1 to -1) as a function of the degree of open to short circuitry, respectively, and exists in the wave reflections as evidenced by slope changes in the return wave pulse recorded by the TDR readout unit. A full short circuit eliminates any additional return signals, while varying degrees of an open circuit results in a variety of return signals.(3)

The Federal Highway Administration (FHWA) TDR moisture probe is shown in figure 1. The coaxial lead cable (signal lead) is connected to the center of the three stainless steel rods, which are inserted horizontally into the soil at the point of monitoring. The cable's outer shield is connected to the outer rods, which serve as the waveguide. The recorded TDR signal rises to a peak (initial inflection point), as the electromagnetic wave enters the probe rods, followed by a fall in the return signal to a second inflection point as the wave hits the end of the probes as illustrated in figure 2. The distance between the first inflection point (point Dl) and final inflection point (point D2) is known as the "apparent" length of the probe, La. (3)

Ten TDR probes were used to measure in situ moisture content of pavement sublayers at SMP test sections that were placed in one hole located in the outer wheel path. ([4]) At most sites, the TDR installation hole was located at approximately 0.76 m (2.5 ft) from the outside edge of the white stripe and at least 1.2 m (4 ft) away from joints and/or cracks to avoid unrepresentative surface moisture infiltration. Figure 3 provides a schematic of the instrumentation.

Figure 2. Graph. Typical TDR signal.  This line graph shows a typical TDR signal.  Distance is on the horizontal axis and rho is on the vertical axis.  Inflection points are labeled on the graph.  Apparent length is labeled on the graph as the distance between inflection points.
Figure 2. Graph. Typical TDR signal.(3)

Figure 3. Diagram. Illustration of instrumentation installation.  Schematic of the equipment layout and installation at LTPP-SMP sites.
Figure 3. Diagram. Illustration of instrumentation installation.

The TDR probes were placed at specified depths as the type of sublayer and its thickness varied. If the top granular base (or subbase) layer was greater than 305 mm (12 in), the first TDR probe was placed 152 mm (6 in) below the surface layer and/or bottom of the lowest stabilized layer; otherwise, the probe was placed at mid depth of the top granular base (or subbase) layer. The next seven TDR probes were placed at 152 mm (6 in) intervals and the last two probes were placed at 305 mm (12 in) intervals. (3)

Interpretation of TDR Trace

The waveform obtained from the TDR sensor must be analyzed to determine in situ soil parameters. Existing procedures for the interpretation of TDR data have included determining the apparent length (La ) so as to compute the dielectric constant and the VMC for the material surrounding the TDR probe.

The initial inflection point (D1) is located where the signal enters the probe rods while the final inflection point (D2) occurs at the end of the probes. Both are displayed in the TDR readout device. The distance between Point D1 and D2 is the La value used to determine the dielectric constant of surrounding material. The La value can be determined using a variety of methods. Klemunes studied ways to find the most accurate methodology to determine the La value of the TDR signal response.([5]) The study investigated and compared five methods: (1) Method of Tangents, (2) Method of Peaks, (3) Method of Diverging Lines, (4) Alternate Method of Tangents, and (5) the Campbell Scientific Method.

Differences among the methods are centered on the procedure of locating the initial and final inflection points of the TDR trace. From the study, the method of tangents was found to be the most accurate while the least accurate methods are the alternate method of tangents and the method of diverging lines.

The method of tangents employs the tangent lines at the local values of the TDR traces to isolate the inflection points. D1 is located at the intersection of the horizontal and negatively sloped tangents (i.e., local maximum) of the TDR trace, and D2 is located at the intersection of the horizontal and positively sloped tangents (i.e., local minimum) as shown in figure 4(a). However, the method cannot be applied to very dry or partially frozen soils, so the method of peaks is used for those soil type situations.([6]) In the Method of Peaks, D1 is determined by locating the intersection of the tangents drawn on both sides of the initial inflection point, and D2 is at the intersection of the tangents drawn of both sides of the final inflection point, as shown in figure 4(b).

Figure 4. Graph. Illustration of trace interpretation methods.  The graphs show the method of tangents and the method of peaks to determine the inflection points of TDR trace. Distance is on the horizontal axis and rho is on the vertical axis.  Initial and final inflection points determined by tangent method and peaks method are labeled on graph (a) and graph (b), respectively.
Figure 4. Graph. Illustration of trace interpretation methods. (5, 6)

Previous Computation Methodology of Dielectric Constant

An electromagnetic signal is transmitted along the TDR probe. When the signal reaches the end of the probe, it is reflected back to the data acquisition unit and the reflected signal is recorded. The velocity of this reflected electromagnetic wave in the probe depends on the dielectric constant and magnetic permeability of the surrounding material (relative to the speed of light in a vacuum) and is given in equation 1 as: ([7])

Equation 1.  Equation.  c equals c sub 0 multiplied by the product of 1 divided by the square root of the product of epsilon multiplied by mu. (1)

Where:

c= velocity of electromagnetic wave,
e= dielectric constant, (approximately 1.0 for air, 80 for water, and 3-5 for dry soil)
m= relative magnetic permeability of the soil
C0= speed of light in vacuum

Assuming the effects of ferromagnetic components in soils are not significant, the magnetic permeability of soil can be set to unity (m = 1). (8) By substituting the velocity of electromagnetic wave with the travel time and the length of probe (c = 2L/Dt), the dielectric constant is:

Equation 2.  Equation.  epsilon equals the squared product of delta t multiplied by c sub 0 divided by the product of 2 multiplied by L. (2)

Where:

Dt= the travel time of the TDR signal
L= actual length of TDR probe

The travel time of the signal is also dependent on the dielectric constant, which includes signal propagation in the soil-moisture mixture; hence, the apparent probe length can be determined by the travel time of the signal if it were propagating at the speed of light:

Equation 3.  Equation. L sub a equals the product of delta t multiplied by c sub 0 divided by 2. (3)

Therefore, the dielectric constant of soil can be expressed as the ratio of apparent length to actual length of TDR probe from equations 2 and 3:

Equation 4.  Equation. epsilon equals the squared product of L sub a divided by L. (4)

Where:

La= apparent length of probe, m

The dielectric constant can be determined with the phase velocity considering the propagation as follows: (5)

Equation 5.  Equation.  epsilon equals the squared product of L sub a divided by the product of L multiplied by V sub p, which equals the squared product of the subtraction of D sub 1 from D sub 2 divided by the product of L multiplied V sub p. (5)

Where:

L= actual length of TDR probe, 0.203 m (8 inches) for FHWA probes
Vp = phase velocity setting on TDR cable tester (usually 0.99); this is the ratio of the actual propagation velocity to the speed of light.

In short, the dielectric constant is derived from the relationship between the speed of light and the wave velocity (delayed due to wave propagation caused by the dielectric properties of the soil surrounding the TDR probe).

Previous Methodology for Determination of In Situ Volumetric Moisture Content

The methods currently used to determine soil VMC from dielectric constants are mainly based on empirical approaches:

(1) Topp's equation

(2) Klemunes' model

(3) Third-order polynomial Ka - soil gradation model

Topp's equation employs empirical regression functions to relate the dielectric constant to the VMC.([8]) The third-order polynomial function developed by Topp is widely used for calculating moisture content of soil materials. Topp's equation can be applied to all types of soils but is inaccurate for certain scenarios: (1,8)

Equation 6.  Equation.  theta equals the product of the following: minus 5.3 plus 2.923 times epsilon minus 0.055 times squared epsilon plus 0.00043 times cubic epsilon. (6)

Where:

?= volumetric moisture content (%)

Klemunes developed calibrated mixing models for soil samples obtained from 28 LTPP sites. (5, 6) TDR traces were obtained from the soil samples prepared at various combinations of moisture content and compaction levels. The moisture content and dry density of each combination was determined by laboratory testing after the TDR trace was obtained. A total of 415 data points were obtained; however, outliers and TDR traces that were impossible to interpret were removed from the dataset. Consequently, 397 data points were available and used to develop Klemunes' moisture models, which employ a hierarchal methodology (i.e., level 1 to level 4) relative to the level of information available and the desired accuracy.

At level 1, the moisture content would be determined without any information about the properties of the soil, such as coarse-/fine-grained or American Association of State Highway and Transportation Officials (AASHTO) classification. Therefore, level 1 has the lowest explained variance and the highest standard error. At level 2, moisture content is determined on the basis of the soil being identified as either coarse- or fine-grained. The accuracy of this level is better than that of level 1. At level 3, the VMC is based on the AASHTO soil classification, accounting for the soil's gradation and the characteristics of fraction passing No. 40.

The most accurate level of Klemunes' model is level 4 since this involves testing the soil at various moisture and density levels in the laboratory and correlating the results with the TDR recordings. Accordingly, a calibration curve is developed for a range of VMC expected in the field. The following equation is used to predict the VMC for each of the four levels. Table 3 provides the specific regression coefficients for each level.

Equation 7.  Equation.  percentage of theta equals the product of the following: 5 times L sub a minus 1 minus B sub 0 times gamma sub d divided by the product of G sub s multiplied by gamma sub w, end of sum, that sum divided by B sub 1. (7)

Where:

?d ,?w= unit weight of the soil and water
Gs= specific gravity of the soil
B0, B1= regression coefficients
Table 3. Coefficient for mixing model. (5, 6)
Level Soil Type B0 B1
Level 1 All-type 1.41 7.98
Level 2 Coarse 1.06 9.30
  Fine 1.50 7.56
Level 3 A-1-b 1.43 7.69
  A-2-4 1.00 9.57
  A-3 1.11 9.02
  A-4 1.77 6.25
  A-6 -1.56 12.26
  A-7-5 1.04 8.49
  A-7-6 1.02 10.31
Level 4 Determined based on a site-specific calibration

As part of the third-order polynomial Ka -soil gradation approach, four models were developed for the VMC computation. The first three models take the third-order polynomial Ka model based on soil type while the fourth model applies to only fine-gradation soils and incorporates the contribution of the gradation into the model. (1) A computer program entitled MOISTER incorporates all four of the third-order polynomial Ka models to determine the VMC of soil, the method of tangents, and the method of peaks to determine the apparent length (and dielectric constant) of the TDR trace.

The third-order polynomial Ka models were developed based on the regression of dielectric constants and VMC from the dataset obtained in Klemunes' study. The coarse-grained soil has a different trend compared with fine- grained soil, but both of them show a third-order polynomial functional form. Hence, in order to provide a more accurate model, data for coarse-grained soil and fine-grained soil were modeled separately. The models are valid only within the dielectric constant range or the inference space that was used to develop the model. (1) The three empirical regression equations developed using the dielectric constant as the sole independent variable are given below with the regression coefficients shown in table 4.

Equation 8.  Equation.  percentage of theta equals the product of the following: a sub 0 plus a sub 1 times epsilon plus a sub 2 times square epsilon plus a sub 3 times cubic epsilon.(8)

Where:

e= dielectric constant
a0, a1, a2, a3 = regression coefficients
Table 4. Third order polynomial Ka-soil model parameters. (1)
Model type a0 a1 a2 a3
Coarse-Ka model -5.7875 3.41763 -0.13117 0.00231
Fine-Ka model 0.4756 2.75634 -0.061667 0.000476
All soil-Ka model -0.8120 2.38682 -0.04427 0.000292

To refine the regression model and to increase the R2 for fine-grained soil, another model was developed using gradation, plastic limit, and liquid limit as independent variables. Equation 9 provides the VMC model for fine-grained soil with variables: (1)

Equation 9.  Equation.  percentage of theta equals the product of the following: a sub 0 plus a sub 1 times epsilon plus a sub 2 times squared epsilon plus a sub 3 times cubic epsilon plus a sub 4 times G11 underscore 2 plus a sub 5 times G1 underscore 2 plus a sub 6 times No4 plus a sub 7 times No10 plus a sub 8 times No200 plus a sub 9 times PL plus a sub 10 times LL. (9)

Where:

?= volumetric moisture content
e= dielectric constant
a0, a1,¼, a 10 = regression coefficients (see table 5)

This model was used for computing the VMC for the fine-grained soils where gradation and other parameters were available and within the inference region of the model. Table 5 shows the descriptions, values, and inference ranges of these variables.

Table 5. Refined third order polynomial Ka-soil model parameters. (1)
Variable Description Coef. Value Inference Range
Interceptao1761.78
KaDielectic constanta12.91453 - 58.4
Ka2a2-0.07674
Ka3a30.000722
G11_2%passing 1 ½-sievea4-19.664999 - 100
G1_2%passing ½-sievea54.366797 - 100
No4%passing No.4 sievea6-5.151690 - 100
No10%passing No.10 sievea72.773784 - 100
No200%passing No.200 sievea80.0605712.6 - 94.6
PLPlastic limita9-0.20570 - 45
LLLiquid limita100.102310 - 69

The four models are selected based on the dielectric constant and properties of soil to calculate moisture content. The flow chart of the model selection scheme is shown in figure 5.

Figure 5.  Flowchart. Volumetric moisture model selection process.  Flowchart depicts the process for selecting a model to calculate moisture content.  First, if the dielectric constant is less than 1.5 or larger than 58.4 then check the data or flag as outlier, but if not, determine what soil type is.  For coarse-grained soils, if the dielectric constant is less than 24.8 then use the coarse Ka model, but if not, use the all soil Ka model.  For fine-grained soils, if the dielectric constant is less than 3, use the all soil Ka model, but if it is larger than 3, check whether the soil satisfies the inference range or not.  If the soil is within the range then use the fine gradation model, but if not then use fine Ka model."
Figure 5. Flowchart. Volumetric moisture model selection process. ([9])

Calculation of Gravimetric Moisture Content

VMC can be converted to a gravimetric basis using volume and weight relationships. The volume relationships used for soil solid-moisture-air mixture are degree of saturation, void ratio, and porosity as shown below: ([10])

Equation 10. Equation. S equals the product of V sub w divided by V sub v. (10)

Equation 11. Equation.  e equals the product of V sub v divided by V sub s, which equals n divided by the subtract of n from 1. (11)

Equation 12. Equation.  n equals the product of V sub v divided by V, which equals e divided by the sum of 1 and e. (12)

Where:

S= degree of saturation
e= void ratio
n = porosity
Vs= volume of soil solids (cm3)
Vw= volume of water (cm3)
Vv= volume of void (cm3)
V= total volume of mixture (cm3)

The weight relationship can be represented by moisture content and unit weight:

Equation 13.  Equation. w equals the product of W sub w divided by W sub s. (13)

Equation 14.  Equation. gamma equals the product of W divided by V. (14)

Where:

w = gravimetric moisture content (%)

? = unit weight (g/cm3)

Ww = weight of water (g)

Ws = weight of solids (g)

W = total weight of mixture (g)

To calculate gravimetric moisture content, a relationship among moisture content and unit weight can be derived from a volume of soil mixture in which the volume of the soil solids is set to 1 as shown in figure 6. The volume of water can be defined as:

Equation 15.  Equation. V sub w equals the product of W sub w divided by gamma sub w, which equals the product of w multiplied G sub s. (15)

Where:

?w= unit weight of water (g/cm3)
Gs= specific gravity of solids

The dry density of soil can be written as:

Equation 16.  Equation. gamma sub d equals the product of W sub s divided by V, which equals the product of G sub s multiplied by gamma sub w divided by the sum of 1 and e. (16)

Where:

?d= dry unit weight of soil (or soil dry density, g/cm3)

Equation 17.  Equation. S equals the product of V sub w divided by V sub v, which equals the product of w multiplied by G sub s divided by e. (17)

Figure 6. Diagram.  Soil mixture with volume of soil solids equal to 1.  The diagram of soil mixture shows a relationship of moisture content and unit weight of soil mixture in which the volume of soil solids is set to 1.
Figure 6. Diagram.  Soil mixture with volume of soil solids equal to 1.  The diagram of soil mixture shows a relationship of moisture content and unit weight of soil mixture in which the volume of soil solids is set to 1.
Figure 6. Diagram. Soil mixture with volume of soil solids equal to 1.

Thus, the gravimetric moisture content can be expressed in terms of the unit weight of water, unit weight of solids, and VMC by combining equations 16 and 17:

Equation 18.  Equation. w equals the product of S multiplied by e divided by G sub s, which equals the product of v sub w divided by V multiplied by the product of gamma sub w divided by gamma sub d, which equals the product of theta multiplied gamma sub w divided by gamma sub d. (18)

Where:

?= volumetric moisture content (%)

Equation 18 is used to convert soil moisture from a volume to a weight basis as needed in pavement engineering applications. Reasonably accurate in situ dry density estimates of material surrounding the TDR sensors must be made for moisture conversion. During installation, field moisture measurements were performed on the material placed around TDR probes with additional material samples retained for laboratory analyses. (3)

 

< PreviousContentsNext >>

The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
FHWA
United States Department of Transportation - Federal Highway Administration