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Publication Number: FHWA-HRT-08-057
Date: November 2008

Long-Term Pavement Performance Computed Parameter: Frost Penetration



The following outline the basis of the enhanced LTPP frost penetration methodology:


In the LTPP frost penetration analysis, the freezing isotherm was used to define a threshold temperature value differentiating between the freeze and no-freeze states of unbound pavement layers. The official definition of frost condition provided by the National Snow and Ice Data Center (NSIDC) is the condition which exists when the temperature of earth-bound objects falls below freezing (0 °C) (http://nsidc.org/cgi-in/words/letter.pl?F). However, based on the soil type and salinity, this temperature could have been depressed below 0 °C, making frost determination based on temperature alone questionable at low-freezing temperatures (0 °C to -1  °C). In such circumstances, changes in moisture and ER values were used to aid in freeze state determination. As soil temperature crosses over the freezing isotherm value, the following changes in moisture and ER values are expected:

Close examination of the LTPP data showed that no sites had strong or consistent evidence of the freezing isotherm being depressed below -1 °C. Based on these observations and considering the NSIDC frost definition presented at the beginning of this section, 0 °C was chosen as a default freezing isotherm for the analysis.

To account for the possibility that the freezing isotherm could be below 0 °C, a step was added to the analysis procedure that required a manual review and assignment of a freeze state based on conclusions from temperature, ER, and moisture trends analyses for the periods of time with temperatures between 0 °C and -1 °C. This provision allowed assignment of no-freeze or transitional conditions even when temperatures were below 0 °C.


Freeze-Thaw Processes

Frost forms in unbound pavement layers and subgrade when moisture is present in the soil and the temperature of the soil matrix falls below the freezing point of the contained water. When soil undergoes freezing or thawing, temperature stays constant at about the freezing/thawing point until the entire body of water is completely frozen or thawed. This physical process is known as the latent heat of fusion. The length of the constant temperature period varies with soil type, the amount of moisture in the soil, and the rate of change in air temperature. More saturated soils take longer to freeze. Granular materials are more likely to have a distinct freezing temperature, while fine-grained soils can have a considerable freezing range over which the soil water freezes.

In the spring, sunshine and warm air temperatures result in a top-down thawing of the pavement system. The water released by the melting ice can be trapped by deeper, still frozen material, creating saturated or supersaturated conditions that weaken the pavement structure. The thawing process can take from several weeks to several months, depending on the type of soil and the ease with which the excess water can drain back to the water table.

Freeze State Assignment

Close examination of daily thermistor readings in conjunction with the observation of ER and moisture trends were used to determine the freeze state of the unbound materials. The first-order approximation of the freeze state of the soil was determined by analyzing changes in subsurface temperatures with respect to the 0 °C freezing isotherm. For each site with subsurface temperature measurements, a frozen state of the soil was assigned for dates and depths with temperatures below 0 °C freezing isotherm. A no-freeze state was assigned to the soil for dates and depths with temperatures above 0 °C freezing isotherm.

Following this initial freeze state assignment, a more detailed analysis was conducted for the dates and depths with temperatures that fell in the range 0 ° to -1 °C. In this analysis, in addition to temperature readings, changes in ER and moisture values were analyzed over time and through the depths to determine the freeze state of the soil. If analysis of ER and moisture trends did not provide evidence supporting either transitional or no-freeze state, the freeze state previously assigned using the 0 °C freezing isotherm was not changed; otherwise, a new freeze state was assigned. Table 3 provides a summary of expected trends in temperature, moisture, and ER measurements to support assignment of different freeze state conditions.

Table 3. Freeze state characteristics.
Soil freeze state ER trend TDR trend Temperature trend Characterized by physical process
Frozen High Low Below freezing isotherm Pore water is solid frozen. Ice lenses formed in frost-heave susceptible soils
Unfrozen Low High Above freezing isotherm or above 0 °C Pore water is in a liquid state
Transitional Unstable Rapid change Around freezing isotherm Pore water is transitioning between liquid and solid state or partially frozen

Due to a limited availability of ER and moisture data for the dates of interest and sometimes due to inconclusive or unexplained ER and moisture trends, only a limited number of sites had the results of temperature-based freeze state prediction changed based on ER and moisture trend analysis, resulting in a limited number of transitional and no-freeze state assignments reported for temperatures at or below 0 °C.

In addition, for some of the  SMP I sites that had ER data available but no measured or predicted temperature and moisture data, freeze states were established based on the analysis of seasonal changes in ER trends. Freeze states were determined for the dates that corresponded to the historical winter months and had high ER values on a scale normalized from 0 to 1.


Thermodynamic modeling of the pavement structure was included in the LTPP frost penetration analysis for two reasons. First, it provided means for small amounts of missing subsurface temperature data to be accurately interpolated from the measured data. Second, thermodynamic modeling based on measured temperatures was used to aid in understanding the physical processes that took place in the field.

Thermodynamic modeling of the pavement structure was accomplished using EICM. The EICM's temperature auto-correction option was used in the analysis of LTPP data. Using this option, the EICM-predicted temperature values for each day were auto-corrected based on actual measured thermistor readings. The temperature profile for each SMP site was modeled on a daily basis, with the initial temperature profile being the previous day's temperature reading. If there were measured data for the following day, the EICM prediction were ignored. If measured temperature data were missing for the following day, temperature predictions considering all of the required inputs were made.

Prior to this daily auto-correction, the site was modeled and the inputs were calibrated to give an accurate set of predictions using the following procedure:

  1. Select model inputs for a specific site from the LTPP construction history, materials, and testing tables, along with the collected climatic data.
  2. Run the model.
  3. Compare these predictions to the actual measured values.
  4. Calibrate the model by varying the initial parameters so that the EICM predicted temperature profile exactly matches the known measured profile.

The secondary use of the EICM was to ensure that basic thermodynamic behavior was not violated in the course of determining frozen and thawed zones within the structure. For example, it is practically impossible for a soil to freeze to a depth of 2 m (6.56 ft) over a 24-hour period. The amount of heat released from freezing such a large quantity of water could not escape from the pavement or ground.

Cautionary Note

The thermodynamic modeling of subsurface pavement and soil layers can be an inexact science. Nonuniformity of materials, variable ground water tables, and other poorly defined inputs can cause considerable divergence between actual and predicted values. Careful modeling and selection of appropriate defaults can appreciably increase the prediction accuracy of thermodynamic programs but still will not yield accurate predictions for all cases. The auto-correction process is tedious and is based on the subjective analyst's judgment in selection of unknown input parameters. Furthermore, the EICM requires an extensive list of site-specific inputs. Not all of the required input parameters were available in the LTPP database, and those that were available were not available for all SMP sites.


The flowchart in figure 12 shows the step-by-step process used to determine freeze state and layers for unbound pavement layers and subgrade for each LTPP site included in this study.

This flowchart describes the sequence of events used in frost penetration analysis. The top block of boxes in the flowchart reads, "Preprocessing steps." Preprocessing steps include the following boxes connected by arrows from top to bottom: rectangle box, "Extract supporting LTPP data;" rectangle box, "Preprocess raw electrical resistivity, soil temperature and moisture data and prepare analysis database;" rectangle box, "Check for records missing soil temperature in the analysis database;" diamond box, "Temperature gap?" This diamond box has two arrows on it sides. The right arrow says, "No" and leads to a box located below the "Preprocessing steps" block called, "Open E-FROST program and upload preprocessed data." The left arrow says, "Yes" and leads to a box on the left side, outside of the "Preprocessing steps" block called, "Predict temperature using thermodynamic EICM model." "Predict temperature using thermodynamic EICM model" box has two arrows. The first arrow leads to a box called, "Add EICM predicted soil temperature to the analysis database." The second arrow leads to a box called, "Manually reinterpret freezing state conditions, based on trend plot and EICM analyses, as needed." A rectangle box labeled "Add EICM predicted soil temperature to the analysis database" is the last box in the "Preprocessing steps" block and leads to a box called, "Open EFROST program and upload preprocessed data." That box leads to a box below called, "For each LTPP SMP site use E-FROST to generate AutoFrost profile using 0 oC freezing isotherm."  Next, a set of steps is grouped in a block with a header that reads: "For each measurement depth, using E-FROST." This block contains three sequential steps identified by the following rectangular boxes: (1) Review temperature, ER, and moisture, trend plots to determine any transitional or non-freeze conditions for frozen layers identified on AutoFrost profile;  (2) Manually reinterpret freezing state conditions, based on trend plot and EICM analyses, as needed; (3) Generate frost penetration profiles. After this block, there are three more sequential steps identified by the following rectangular boxes: "Prepare SMP_FREEZE_STATE table;" "Compute frost penetration depth and prepare SMP_FROST_PENETRATION table;" and "Prepare submission data files." Two additional boxes are included on the flowchart to indicate quality control functions. The first box called, "Review and QC frost estimates" has an arrow pointing to indicate that this function should be performed before the "Prepare SMP_FREEZE_STATE table" action. The second box called, "QC generated tables" has an arrow indicating that this function should be performed before the "Prepare submission data files" action.

Figure 12. Chart. Frost depth and layers interpretation using E-FROST.

Additional Analysis Rules

Upon a detailed data review, it became apparent that not all of the data were available for every measurement date and depth, and some of the trends based on the in-situ data were difficult to interpret, leading to subjectivity in assignment of freeze states by the analyst. To minimize the subjectivity of the frost estimates and to provide uniformity of the analysis procedures, a set of guidelines was developed and followed by the data analyst.

During the data analysis phase, the following rules were followed when data were sparse or some of the measurements were ambiguous:

  1. For each date and measurement depth that had at least subsurface temperature or ER data available, freeze state estimates were conducted using methodology presented earlier in the report.
  2. If subsurface temperature measurements and ER data were missing for a portion of the winter season and there were sufficient LTPP data to estimate missing temperatures from EICM analysis, these estimated temperatures were used to evaluate freeze state. The source of the temperature in the SMP_FREEZE_STATE table was specified as estimated from EICM.
  3. For measurement depths and/or dates where no in-situ data and no EICM-predicted temperature values were available to predict the freeze state, no freeze state determinations were made, even though frozen depths were reported for surrounding depths and/or dates.
  4. For some SMP I sites that had ER data available but no measured or predicted temperature and moisture data, freeze states were determined based on the analysis of seasonal changes in ER trends. Freeze states were determined for the dates that corresponded to the historical winter months and have high ER values on normalized scale from 0 to 1.
  5. If, for a particular date and depth, the soil temperature was above 0 °C, the freeze state was reported as N-unfrozen.
  6. If, for a particular date and depth, the soil temperature was below -1 °C, the freeze state was reported as F-frozen.
  7. If, for a particular date and depth, the soil temperature was below 0 °C, the moisture values were low, and ER values were high, the freeze state was reported as F-frozen.
  8. If, for a particular date and depth, the soil temperature was below 0 °C, the moisture values were low, and no ER values were reported, the freeze state was reported as F-frozen.
  9. If, for a particular date and depth, the soil temperature was below 0 °C, the ER values were high, and no moisture values were reported, the freeze state was reported as F-frozen.
  10. In the absence of moisture and ER data or when ER and moisture trends are inconclusive, the freeze state was reported as F-frozen for temperatures less or equal 0 °C.
  11. If, for a particular depth, constant negative temperatures near 0 °C were observed over a few days, the freeze state was reported as T-transition and the following trends arose:

Data Normalization and Interpolation

To aid in the visual interpretation of the analysis results, electrical resistivity values were normalized on a scale from 0 to 1. Normalization was carried out for each analysis depth and construction event, which was identified by the change in the construction number. The following basic normalization formula was utilized:

Normalized_Measurement equals a difference between Actual_Measurement and Min_Of_Actual_Measurement divided by a difference between Max_Of_Actual_Measurement and Min_Of_Actual_Measurement.

Figure 13. Equation. Normalized measurement.


Normalized_Measurement = Normalized measurement

Actual_Measurement = Actual measurement

Min_Of_Actual_Measurement = Minimum actual measurement

Max_Of_Actual_Measurement = Maximum actual measurement

Extracted LTPP temperature and moisture content data were interpolated to ER analysis depths established in earlier LTPP frost penetration studies(3) using the following linear interpolation formula:

Interpolated_Measurement equals Upper_Measurement plus the product of the difference between Lower_Measurement and Upper_Measurement and X divided by L.

Figure 14. Equation. Interpolated measurement.


Interpolated_Measurement = Interpolated temperature or MC value

Upper_Measurement = Temperature at upper thermistor or MC for upper TDR sensor

Lower_Measurement = Temperature at lower thermistor or MC for lower TDR sensor

X = Distance from the ER analysis depth to the upper thermistor or TDR sensor

L = Distance between the two thermistors or TDR sensors


The results of data analysis were independently reviewed. During the review process, emphasis was placed on evaluating whether or not the results produced by the analyst followed the basic physical process of latent heat of fusion as described earlier in this chapter. In addition to reviewing the frost penetration profiles, trends in temperature, ER, and moisture changes were reviewed and correlated to evaluate the accuracy of analyst assigned freeze states.

Spatial and Temporal Checks

Frost penetration profiles were reviewed to evaluate the progression of frost penetration with time and depth and to check for any potential data gaps or presence of intermediate unfrozen layers. The following two checks were used to QC the initial freeze state assignments for all the cells in frost penetration plot except the boundary cells (boundary cells belong to the first frozen depth layer, the last frozen depth layer, the first and the last date with frost for each depth):

Spatial check for a given date is as follows:

Temporal check for a given depth is as follows:

Trend Reasonableness Check

ER, moisture, and temperature time-series plots were reviewed to evaluate reasonableness of ER and moisture changes with respect to temperature changes. The expected trends for ER and moisture changes are described as follows:

If and when the moisture and/or ER trends did not follow the expected trends described above, freeze assignment was based on temperature values with 0 °C used as freezing isotherm.

Analysis Results Database Checks

Finally, the results of the analysis compiled in the LTPP computed parameter tables were reviewed to assure data completeness, data integrity, and proper formatting.

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