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Publication Number: FHWA-HRT-07-021
Date: April 2007

Durability of Segmental Retaining Wall Blocks: Final Report

ANNEX: RECOMMENDED PROCEDURE FOR SURVEY OF INTERNAL TEMPERATURE DISTRIBUTION OF FREEZE-THAW CHAMBER

This section covers procedures for conducting a thermal survey of the freezer. The purpose is to characterize the internal temperature distribution of the freezing environment (consisting of the freezer and the specimens inside it) in terms of Temperature vs Time (T-t) and Standard Deviation vs Time (σ-t) functions. This survey can be treated as a pre-test mock up, and the information drawn from this survey (such as Reliability curves or R-curves) assist the planning and execution of eventual tests. As such, this survey must be conducted in an environment that reproduces the environment that will exist in actual tests.

Definitions

In reference to the freezer air cooling curve shown in Figure A.1, the following terms are defined:

  • Cold soak is the time period during which the air temperature is between -18 ± 5°C (0° ± 10°F), and ASTM C 1262 Clause 8.2.1 requires that cold soak be maintained for 4 to 5 hours.
  • Cooling ramp is the portion of the curve between the points at which the temperature starts falling until it reaches -13°C (0°F). Together, the cooling ramp and cold soak comprise what is shown as the Cooling branch of the curve.
  • Warm soak is the time period during which the air temperature is between 24 ± 5°C (75 ± 10°F); and ASTM C 1262 Clause 8.2.2 requires that warm soak be maintained for 2.5 to 96 hours.
  • Warming ramp is the portion of the curve between the end of cold soak and 19°C (65°F). Together, the warming ramp and warm soak comprise what is shown as the Warming Branch of the curve.

Figure A.1 Freezer air cooling curve definitions.
Figure A.1 Freezer air cooling curve definitions.

Initial planning

The overall goal of this initial planning is to identify as many variables as possible that will affect test conditions in actual tests and ensure that these conditions are reproduced during survey of the freezer. Variables that must be first identified include:

  • Freezer to be used
  • Size and shape of test containers. These may in turn depend on geometry of specimens to be tested.
  • Number of specimens to be tested.
  • Proposed arrangement of specimens in the freezer, which depends on various factors such as total number of specimens, shape of containers and available space or shelving units in the freezer. Also, the arrangement of specimens must also consider the ASTM C 1262 requirements that a minimum 13 mm (½ in) space separate specimens in the freezers.

Dummy specimens

Dummy specimens to be used for the freezer survey shall be of the same shape and mass as the actual test specimens that will be tested. Although specimens of the same SRW mix may not be necessary for the survey, it is important however that similar geometries be used. These specimens are to be placed in the same containers that will be used in the actual tests. Following this, the dummy specimens shall be placed in the freezer in the exact same arrangement as will be used in actual tests (specimen arrangement as determined from initial planning) and filled with the same volume of test solution (water or saline) as will be used in actual tests.

Temperature sensors

The temperature sensors to be used such as thermometers or thermocouples must be calibrated to improve the precision as well as accuracy of temperature measurements. Hance (2005) investigated thermocouple calibration in detail and determined that when uncalibrated type T thermocouples were used, any given measurement could be within ±1.3°C (2.3°F) of a reference thermometer at the 95 percent confidence level and within ±2.0°C (3.6°F) at the 99 percent confidence level. Calibration decreases the spread of values registered by the sensors and thus allows for more precise measurements of variations of temperatures within a freezer.

On a separate issue, since the T-t and σ-t characteristics are of interest, these temperature sensors must be connected to a data acquisition system capable of recording and storing multiple measurements over a specified time period (at 5-minute intervals or less). For this purpose, thermocouples connected to data acquisition computer are preferred, although other data logging alternatives may be used.

Placement of temperature sensors

As a general guide, temperature sensors shall be strategically placed in such manner that the recorded temperatures are representative of the conditions surrounding the specimens (note that it is this surrounding condition that needs to be as uniform as possible to reduce variability arising from freezer internal variation). Sensors shall therefore be placed on each shelf where specimens are located to capture variations at each of the different levels. Within each shelf, sensors shall also be placed around the perimeter of the specimen group, say at the corners of the shelf. In this manner, the sensors placed at each shelf level capture overall temperature variations in the vertical direction, while sensors placed within each shelf capture front-back and left-right variations. In addition, sensors shall also be placed in between specimens on each shelf to capture the conditions in this region. Examples of container and external temperature sensor placement on a given shelf of a freezer are shown in Figure A.2. Other considerations for external temperature sensor placement include:

  1. Ensuring that the sensors are not in contact with any other part of the freezer (e.g. wall or shelf) as it is the freezer air temperature that is sought. Thus, sensors shall be placed about 25 mm (1 in) off the shelf level, and
  2. Ensuring that the sensors are not in contact with the specimens, especially the bottom part of the container where the solution is, since the latent heat liberated by the solution during freezing can lead to misleading sensor measurements. Again, sensors shall be kept at least 25 mm (1 in) away from container surfaces.

In addition to these sensors, it is recommended that external temperature sensors be placed in the vicinity of the freezer internal (built-in) temperature sensors (specifically, the freezer sensor whose temperature is used by the freezer controller to run the cycle). This enables verifying the validity of the freezer's own sensors.

Figure A.2 Examples of container and sensor placement on freezer shelf.
Figure A.2 Examples of container and sensor placement on freezer shelf.

Cycles

It is recommended that at least 3 full freeze-thaw cycles be run to ensure consistency between cycles. For the survey, the duration of cooling ramp may be kept the same as that used in actual tests. However, the total length of the cooling branch in each cycle shall be at least equal to (length of cooling ramp + 5 hours), to ensure that data is collected for the entire cold soak period. From studies at Cornell University, the length of cooling ramp was about 1 hour for a chest freezer, < 2 hours for a Tenney freezer and up to 2.5 hours for a walk-in chamber loaded with 40 specimens. As such, the cooling branch for these freezers under the conditions tested would then need to be at least 6, 7 and 7.5 hours respectively. A trial run shall be carried out to determine this cooling ramp length. Temperature data shall be continuously collected either using a dedicated computer with data acquisition system or through other data loggers. Data shall be collected at intervals of not more than 5 minutes. The graphs shown throughout this annex were based on data collected at 1 minute intervals.

Data processing

The results for the various cycles collected shall be treated separately and independently. The cycles shall not be averaged together (i.e. Tlocation X = average (Tlocation X, cycle 1 + ...+ Tlocation X, cycle n), as this may mask any cycle-to-cycle variations. The various cycles shall be examined for cycle-to-cycle consistency, which is a requirement in ASTM C 1262 (Clause 5.1.1). For each cycle, the following steps shall then be performed:

  1. Plot graphs of the T-t, Tavg-t and σ-t.

    The T-t graph is simply the collection of Temperature vs. Time data for all available sensors.

    The Tavg-t graph is a plot of Average Temperature vs. Time where Tavg is the average temperature of all sensors at any given time.

    The σ-t graph is a plot of Standard Deviation vs. Time where σ is the temperature standard deviation of all sensors at any given time.

    Examples of these plots for measurements in a Tenney freezer are shown in Figure A.3.

  2. The T-t plots for all locations shall be scrutinized for any particular pattern in the spatial variation (i.e. Are locations near the fan colder? Are there any locations which did not get cold enough (i.e. stagnant locations)? How big is the temperature spread from front-back, left-right or top-down?) Knowledge of these types of variations may help decide the frequency and pattern of specimen rotation. For example, if front-back variations are observed to be more pronounced than left-right variations, it will then be necessary to rotate specimens more frequently in which front and back specimens are switched around every 10 cycles.

    Figure A.3 Sample T-t, T subscript avg -t and σ minus t graphs for Tenney freezer.
    Figure A.3 Sample T-t, Tavg-t and σ -t graphs for Tenney freezer.

  3. The Tavg-t and σ-t responses for the cooling branch shall then be modeled using best fit relationships. For the work conducted here, the software TableCurve 2D, version 4, from AISN Software Inc., copyright 1989-1996 was employed, and in general, it was determined that the exponential function best described the measured data for both T and σ. This relationship was of the form:

    T subscript avg equals a1 plus b1 exp parenthesis minus t over c1 (Equation A.1)

    and

    sigma equals a2 plus b2 exp parenthesis minus t over c2 (Equation A.2)

    Examples of curve fits for the graphs in Figure A.3 are shown in Figure A.4. For the Tavg-t graph, two separate fits were actually performed for the data before 2.9 hrs and for the data after 2.9 hrs. This is because the Tavg-t measurements performed in the Tenney freezer typically displayed a "kink" (in this particular case at 2.9 hrs) which prompted the use of two curves for the model. This bilinear response may not occur in other freezers as shown by the Tavg-t response for a walk-in freezer in Figure A.5 where a single curve fit was sufficient to model the entire range of interest (i.e. the cooling branch). In the σ-t response of the Tenney freezer (Figure A.4), data before about 0.3 hrs was truncated for the curve fit.

  4. Using these relationships, R-curves can then be constructed as follows[1]:

i.Select a trial length for the cooling branch, ttrial

ii. Compute t4 hr = ttrial - 4

iii. Compute t5 hr = ttrial - 5

iv. At t4 hr, compute Tavg (t4 hr) and σ (t4 hr) using Equations A.1 and A.2 respectively.

v. At t5 hr, compute Tavg (t5 hr) and σ (t5 hr) using Equations A.1 and A.2 respectively.

vi. From the values at t4 hr, compute Proportion of under cooled locations (PU) as follows:

x equals T subscript cold soak start minus T subscript avg parenthesis small t subscript 4 hr over sigma parentheses small t subscript 4 hr over sigma (Equation A.3)

where Tcold soak start is -13°C (10°F)

one over square root 2 pie exp parenthesis minus x superscript 2 over 2 bracket 0.436 over parenthesis one plus 0.333x minus 0.120 over parenthesis one plus 0.333x superscript 2 plus 0.937 over parenthesis one plus 0.333x superscript 3 (Equation A.4)

Figure A.4 Curve fits to T subscript avg -t and σ-t graphs of Figure A.3 for Tenney freezer.
Figure A.4 Curve fits to Tavg-t and σ-t graphs of Figure A.3 for Tenney freezer.

1 The concepts of reliability and methods of analysis were developed with the assistance of Prof. Mark Turnquist, School of Civil and Environmental Engineering, Cornell University, to whom the authors are grateful.

vii. From the values at t5 hr, compute Proportion of overcooled locations (PO) as follows:

z equals T subscript avg parenthesis t subscript 5 hr minus T subscript cold soak start over sigma parenthesis t subscript 5hr (Equation A.5)

where Tcold soak start is -13°C (10°F)

P subscript o equals one over square root 2 pie exp parenthesis minus z superscript 2 over 2 bracket 0.436 over parenthesis one plus 0.333z plus 0.120 over parenthesis one plus 0.333z superscript 2 plus 0.937 over parenthesis one plus 0.333z superscript 3 (Equation A.6)

Figure A.5 Curve fit to T<sub>avg</sub>-t response of walk-in freezer (single curve).
Figure A.5 Curve fit to Tavg-t response of walk-in freezer (single curve).

  • The total Proportion of non-compliant locations (PNC) is thus:

    (Equation A.7)

  • The Reliability (R) is then given by:

    (Equation A.8)

  • Repeat steps i to ix for various values of ttrial, and plot R versus ttrial. This curve is the R-curve which for the Tavg-t and σ-t graphs in Figures A.3 and A.4 is shown in Figure A.5.

EXAMPLE R-CURVE CALCULATIONS

The Tavg-t and σ-t response from the Tenney freezer shown in Figure A.3 will be used to illustrate the calculations of Reliability following the steps outlined above. The curves in Figure A.3 are modeled by exponential equations shown in Figure A.4.

i. Select ttrial = 6.0 hrs

ii. t4 hr = 6 - 4 = 2

iii. t5 hr = 6 - 5 = 1

iv. Using the curve fits equations,

[Equation A.9]

(Note that the curve fit to the region before 2.9 hrs was used in this case.)

[Equation A. 10]

v. Using the curve fits equations,

[Equation A.11]

(Note that the curve fit to the region before 2.9 hrs was used in this case.)

[Equation A.12]

From the values at t4 hr:

[Equation A.13]

[Equation A.14]

vi. From the values at t5 hr:

[Equation A.15]

[Equation A.16]

vii. PNC = 0.26 + 0 = 0.26

viii. R = (1 - 0.26) x 100 percent = 74 percent

ix. Repeating steps i to ix for various values of ttrial, the values in Table A.1 are obtained which are then used to plot R curve shown in Figure A.6.

Table A.1 R values for ttrial

ttrial (hr)

R ( Percent)

5.7

0

5.8

12

5.9

42

6.0

74

6.1

92

6.2

99

6.3

100

6.4

100

6.5

100

6.6

100

6.7

98

6.8

86

6.9

58

7.0

26


Figure A.6 Reliability (R) curve for the Tavg-t and σ-t graphs shown in Figure A.3.

Interpretation of R-curve

R-curves are guides to understand freezer behavior and to help plan cycle times. Figure A.6 shows an R-curve that is "flat topped." Actual freeze-thaw tests shall be run in the region where R is maximum, which for the curve in Figure A.6 would be in the "flat topped" region between 6.2 and 6.7 hours. It is generally recommended to operate the freezer in the middle of this "flat topped" region, i.e. about 6.4 to 6.5 hrs. Operating near the end of this "flat topped" zone, i.e. either at 6.2 or 6.7 hrs, is not advisable since fluctuations in freezer performance may cause R to suddenly drop. For example, if the freezer were set for 6.2 hrs cooling branch and a fluctuation in freezer performance resulted in the cooling branch ending prematurely by 10-minutes (0.2 hrs); R would drop from 99 to 74 percent.

When the results of a freezer survey indicate that certain variables need to be changed (e.g., reduce number of specimens or change freezer control program) to obtain higher R values, these changes must be improvised and be followed by another survey with the new set of conditions. The data acquired with the new set of conditions shall be analyzed in the manner described above and R-curves be produced to determine optimum cycle lengths.

The R-curve can also be used to determine the proportion of compliant locations had the cycle been operated using a different "control temperature." In the Tenney freezer used for the NCMA studies, the freezer internal sensor used to control the cycle length was located at the coldest measured location in the freezer. From the T-t graphs in Figure A.3, it is seen that the coldest location reached -13°C at 1.7 hrs. If cold soak were set for 4.0 hrs starting from this point, the cooling branch would only be 5.7 hrs long. In reference to Figure A.6, the corresponding R is about 0 percent. This means that all specimen locations in the freezer are under cooled (i.e. receive less than the minimum 4-hr cold soak required by ASTM C 1262).

Overall, freezer surveys shall precede actual freeze-thaw testing. While the information obtained from the surveys may assist planning actual tests, surveys shall be conducted in any of the following situations:

  • Changing specimen conditions including: a) changes in total specimen quantity (either by removing "failed" specimens or adding new test specimens), b) change of containers used or c) changes in the spatial arrangement of the specimens in the freezer.
  • Changing freezer conditions such as for maintenance or if the freezer is moved to a different environment (e.g. temperature controlled room or room with variable temperature conditions)

Even if none of the above changes occurred, there is no guarantee that cycles will be identical over say 100 cycles, and thus surveys shall also be periodically conducted. Preferably 5 cycles of every 25 cycles shall be surveyed to ensure that the performance is as expected or if not, that modifications in the programmed cycle length can be improvised. If possible, it is strongly recommended that dedicated temperature logging equipment be maintained for the duration of the actual freeze-thaw tests. In this manner, the actual cycles can be compared to the R-curves determined from the cycle data, thus ensuring that the actual performance is compliant with test standard requirements.

References

Hance, R.M., Studies of the Frost Resistance of Segmental Retaining Wall Units, Master's Thesis, School of Civil and Environmental Engineering, Cornell University, May 2005.

Fagerlund, G., "The Significance of Critical Degrees of Saturation at Freezing of Porous and Brittle Materials," ACI Special Publication, SP-47, American Concrete Institute, Detroit, MI, pp. 13-65, 1975.

Fagerlund, G., "An Introduction to RILEM Methods of Testing Resistance of Concrete to Freezing and Thawing and the International Cooperative Tests on the Critical Degree of Saturation Method," Materials and Structures, Vol. 10, No. 58, pp. 217-230, 1977.

Scherer, G.W. and Valenza II, J.J., "Mechanisms of Frost Damage," Materials Science of Concrete VII (eds. J. Skalny), The American Ceramic Society, 2005.

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