Equilibrium Matric Suctions in Subgrade Soils in Oklahoma Based on

Thornthwaite Moisture Index (TMI)

Er Yue1 and Rifat Bulut2

1Graduate Student, School of Civil and Environmental Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA 2Associate Professor, School of Civil and Environmental Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA; rifat.bulut@okstate.edu ABSTRACT: Climatic factors play a significant role in pavement design due to the impact of these parameters on pavement performance. Thornthwaite Moisture Index (TMI), a climatic parameter, is widely used in geotechnical engineering as well as other disciplines to evaluate the changes in moisture conditions in near surface soils in the unsaturated zone. This paper evaluates historical climatic data acquired from Mesonet weather stations across Oklahoma for pavement applications. Based on the TMI values calculated from the historical climatic data by applying three different models, contour maps have been created using ArcGIS software. This paper also builds the relationships between equilibrium suction and TMI values in subgrade soils, and compares the results among three TMI models. INTRODUCTION The Thornthwaite Moisture Index (TMI), originally developed by Thornthwaite in 1948, was determined by annual water surplus, water deficiency, and water need, which is used to classify the climate of a region (Thornthwaite 1948). The water surplus and deficiency can be determined using the maximum water storage of the soil by performing a water balance computation. In 1955, the original TMI equation was revised by Thornthwaite and Mather (1955). As a result of the revision, the modified TMI is only related to the precipitation and potential evapotranspiration at monthly intervals in evaluating the annual soil moisture balance. In addition to climatology, the TMI is also widely used in civil engineering, especially in the pavement design. Recently, the TMI has been modified further by Witczak et al. (2006) as part of the Enhanced Integrated Climatic Model (EICM) in the Mechanistic Empirical Pavement Design Guide (MEPDG), and correlations have been established between TMI and equilibrium suction at depth in the pavement profile. TMI is a simple climatic parameter and is easy to determine with, in many cases, readily available data from local weather stations. The parameter has the appeal of relevance to moisture conditions of a site, and thus, has been correlated with the depth

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of moisture active zone (depth to constant suction) and the equilibrium suction (Fityus et al. 1998). However, the review of literature indicates that there are discrepancies between the established correlations in the literature. It is believed that those differences are coming from the TMI calculation methods and to some extent from the local soil and weather conditions. The study area for this research paper is the state of Oklahoma. The historical climatic data, from 1994 to 2011, is obtained from the Oklahoma Mesonet. The Oklahoma Mesonet is a network designed to monitor the mesoscale weather events, which last from several minutes to several hours. The Oklahoma Mesonet contains 120 automated stations. Each of Oklahoma's 77 counties has at least one Mesonet station (The Oklahoma Mesonet 2011). In this research, 77 weather stations, one station in each of the 77 counties, have been selected. However, the climate boundaries are still based on the county boundaries because only one weather station is selected in each of the 77 counties in Oklahoma. Prior to the pavement design, climatic factors must be evaluated for which water balance at the ground surface is to be quantified. Among all the climatic factors, temperature and precipitation are two important components that affect TMI values, as well as pavement performance. BACKGROUND The original TMI given by Thornthwaite (1948) is based on an annual water balance calculation using records of long term climatic parameters such as precipitation, temperature, and estimated potential evapotranspiration. The moisture balance is determined in terms of precipitation, evaporation, water storage, deficit, and runoff. The water balance is computed by month. The process begins by calculating the difference between precipitation and corrected evaporation. If the difference is larger than zero, it is added into storage up to a maximum value. The amounts exceeding the maximum storage are considered as runoff. On the other hand, if the difference between the precipitation and corrected evaporation is less than zero, it is deducted from the storage up to zero. The amounts lower than zero are defined as deficit. A detailed analysis of the Thornthwaite (1948) method is given by McKeen and Johnson (1990). Later, Thornthwaite and Mather (1955) modified the original Thornthwaite (1948) equation by eliminating the water balance approach and reducing the amount of data required and computational effort in determining the climatic index. Recently, Witczak et al. (2006) offered a slightly different version of the Thornthwaite and Mather (1955) equation as part of a NCHRP research study for the Mechanistic Empirical Pavement Design Guide (MEPDG). These models are described in the following section. THORNTHWAITE MOISTURE INDEX Thornthwaite (1948) defined a moisture index (known as the Thornthwaite Moisture Index or TMI) as a relative measure indicating the wetness or dryness of a particular region. The TMI has been a popular and attractive parameter in the geotechnical engineering community due to the fact that the data required for its determination are usually readily available from local weather stations and it is based on a simple climatic model as compared to some of the rigorous models in the literature (Edris and Lytton 1976; McKeen and Johnson 1990). Thornthwaite (1948) equation is given as:

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100 60 ⁄ (1) where, D is the moisture deficit; R is the runoff; and PE is the net potential for evapotranspiration. TMI calculations are based on a period of one year with monthly values of precipitation, adjusted potential evapotranspiration, storage, runoff, and deficit by conducting a moisture balance approach. The calculation process requires the total monthly precipitation, average monthly temperature, initial and maximum water storage values, the day length correction factor, and the number of days for each month. The precipitation and temperature values can be obtained from the local weather stations. The maximum water storage is a function of the soil type and the initial water storage depends on the climate and site condition. The day length correction factor is a constant for a given month and location (latitude). Thornthwaite (1948) adopted a relatively simple model for the calculation of the adjusted potential evapotranspiration as compared to some of the sophisticated (yet complex in terms of the parameters involved) models available in the literature. The heat index for each month is determined using the mean monthly temperatures as follows:

0.2 . (2) where, hi is the monthly heat index and ti is the mean monthly temperature. The annual heat index is simply calculated by summing the monthly heat index values as:

∑ (3) where, Hy is the yearly heat index. The unadjusted potential evapotranspiration is then determined for each month as follows:

1.6 10 ⁄ (4) where, ei is the unadjusted potential evapotranspiration for a month with 30 days and a is a coefficient given by:

6.75 10 7.71 10 0.017921 0.49239 (5) The unadjusted potential evapotranspiration is then corrected for the location (latitude) and the number of days in the month as:

30⁄ (6) where, PEi is the adjusted potential evapotranspiration for the month i; di is the day length correction factor (provided in McKeen and Johnson 1990); and ni is the number of days in the month. A detailed explanation of the original TMI calculation process is given by McKeen and Johnson (1990) and Fityus et al. (1998). Equation 1 was later modified by Thornthwaite and Mather (1955) and is given as:

100 1⁄ (7)

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where, P is the annual precipitation. The potential evapotranspiration (PE) is determined using the same Thornthwaite (1948) model described above. As part of the NCHRP 1-40D research project for the development of the MEPDG, Witzack et al. (2006) modified Eq. 7 as follows:

75 1⁄ 10 (8) METHODOLOGY ArcGIS software is employed to create the contour maps of TMI showing its distribution across Oklahoma. ArcGIS is geographic software that is widely used in map creation and data management. Using geographic information system (GIS) database, the spatial analysis of data can be conducted to integrate other solutions and systems. GIS is playing an increasingly important role in Civil Engineering by supporting the infrastructure management. Contour maps consist of lines connecting points of equal value. In this research, the equal value means the value of TMI. The distribution of the lines shows how TMI values change throughout a certain area. By following the lines on a contour map, it is easy to identify which locations have the same TMI value. By considering the spacing between the lines, one can obtain a general idea of the gradation of the TMI values. To create the contour maps of TMI, the method of Inverse Distance Weighting (IDW) has been applied in ArcGIS. IDW is a type of interpolation with a known scattered set of points. This method calculates the values of the unknown points by using a weighted average of the values at the known points. By knowing TMI values for 77 points (e.g., representing the 77 counties of Oklahoma), the values to unknown points are calculated with a weighted average based on the available TMI values at the 77 known points. Russam and Coleman (1961) developed a correlation between the subgrade equilibrium suction and TMI. Based on their results, the suction beneath the pavement is related to the TMI as well as soil type. The soil suction tends to increase as TMI decreases and P200 increases. Witzack et al. (2006) applied statistical software to build a mathematical representation of TMI-P200/wPI subgrade model. For the subgrade soils, the common equation is given as (Witzack et al. 2006):

(9) where, h is measured matric suction, α, β, γ, and δ are constant obtained through the regression model and values are given in Table 2. ANALYSIS OF RESULTS

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TMI Contour Maps Figures 1, 2, and 3 show the TMI contour maps of Oklahoma using the three methods described earlier. The TMI values range from -50 to 20 in Figure 2 and from -30 to 25 in Figure 3. Based on the comparison of the values, the Witczak et al. (2006) method is more similar to the original TMI approach given by Thornthwaite (1948). Relationships between Suction and TMI Table 1 gives a number of TMI values selected from Figures 1, 2, and 3 representing different climatic regions in Oklahoma. The three TMI prediction models resulted in different TMI values for the same climatic regions in Oklahoma. However, Table 1 indicates that the differences between the original Thornthwaite (1948) and Witczak et al. (2006) methods are relatively small as compared the results based on the Thornthwaite and Mather (1955) method.

FIG. 1. TMI Contour Map Based on Thornthwaite (1948) Equation.

FIG. 2. TMI Contour Map Based on Thornthwaite and Mather (1955) Equation.

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FIG. 3. TMI Contour Map Based on Witczak et al. (2006) Equation. Table 1. Comparison of TMI Values Between Different Methods and Climatic Conditions

Weather Station Dry Climate

Equilibrium Climate

Wet Climate

BUFF HOLL MEDF ARD2 MIAM IDAB

Thornthwaite (1948) -19.6 -19.0 2.6 4.3 35.7 29.7 Thornthwaite and Mather (1955) -38.3 -33.5 -8.0 5.4 27.2 18.5 Witczak et al. (2006) -18.7 -15.1 4.0 10.8 33.6 23.6 Table 2 gives the regression constants for building the relationships between subgrade equilibrium suction and TMI (Witczak et al. 2006). Table 3 shows the results of matric suction computed using Equation 9 and the TMI values in Table 1. Figures 4 and 5 depict the relationships between matric suction and TMI for coarse and fine grain soils, respectively. Both Figure 4 and Figure 5 reflect that matric suction tends to increase as TMI decreases. For coarse-grained soils (P200=10), matric suctions are closer to each other for the 1948 and 2006 TMI models (Table 3). On the other hand, the 1955 TMI model predicts higher suctions when the climate becomes drier (e.g., more negative TMI values). All the three models predict the equilibrium matric suctions within close range as the climate becomes wetter (e.g., more positive TMI values) as shown in Table 3.

Table 2. Constants for TMI-P200/wPI Model for Subgrade Materials

α β γ δ

P200=10 0.3 419.07 133.45 15

wPI=50 0.3 1171.2 157.5 27.8

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Table 3. Matric Suction versus TMI for P200=10 and wPI=50

Station TMI Matric Suction for P200=10

(kPa) Matric Suction for wPI=50

(kPa) 1948 1955 2006 1948 1955 2006 1948 1955 2006

BUFF -19.6 -38.3 -18.7 16.40 29.04 16.07 1472.64 5558.21 1394.18

HOLL -19.0 -33.5 -15.1 16.18 24.36 14.85 1419.75 3802.38 1127.96

MEDF 2.6 -8.0 4.0 11.03 12.97 10.83 459.33 765.93 431.62

ARD2 4.3 5.4 10.8 10.79 10.64 9.98 425.97 406.05 324.11

MIAM 35.7 27.2 33.6 8.07 8.57 8.19 137.12 178.57 146.00

IDAB 29.7 18.5 23.6 8.41 9.23 8.83 164.74 241.23 201.43

FIG. 4. Matric Suction versus TMI for P200=10.

FIG. 5. Matric Suction versus TMI for wPI=50.

1

10

100

-60 -40 -20 0 20 40

Mat

ric

Su

ctio

n, k

Pa

TMI

P200=10

TMI (1948)TMI (1955)TMI (2006)

1

10

100

1000

10000

-60 -40 -20 0 20 40

Mat

ric

Su

ctio

n, k

Pa

TMI

wPI=50

TMI (1948)

TMI (1955)

TMI (2006)

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For fine-grained soils (wPI=50), matric suctions are much larger than the coarse-grained soils. However, unlike the matric suction trends observed for the coarse-grained soils, there is no particular and close trend between 1948 and 2006 TMI models for the fine-grained soils (Table 3). However, as compared to the predictions made by the 1955 TMI model, the 1948 and 2006 models predict relatively close matric suctions. Furthermore, when the matric suction values in Table 3 are plotted on a logarithmic scale (e.g., suction units of log kPa or pF) in Figures 4 and 5, the differences between the models disappear. CONCLUSIONS This research paper has evaluated historical climatic data from the Oklahoma Mesonet weather stations and calculated TMI across Oklahoma using three models. TMI values are also applied to calculate matric suction for the subgrade materials. The study shows the similarity and differences between three TMI models for predicting equilibrium matric suctions. The results of the study can be evaluated when determining the equilibrium suction boundary conditions in the new mechanistic pavement design guide software. ACKNOWLEDGMENTS The authors thank and acknowledge the support provided by the Oklahoma Transportation Center and the Oklahoma Department of Transportation. REFERENCES Edris, E.V. and Lytton, R.L. (1976). "Dynamic Properties of Subgrade Soils,

Including Environmental Effects." Research Report No. TTI-2-18-74-164-3, Texas Transportation Institute, College Station, Texas.

Fityus, S.G., Walsh, P.F., and Kleeman, P.W. (1998). "The Influence of Climate as Expressed by the Thornthwaite Index on the Design Depth of Moisture Change of Clay Soils in the Hunter Valley." Conference on Geotechnical Engineering and Engineering Geology in the Hunter Valley, Conference Publications, Springwood, Australia: 251-265.

McKeen, R.G. and Johnson, L.D. (1990). "Climate Controlled Soil Design Parameters for Mat Foundations." ASCE Journal of Geotechnical Engineering, Vol. 116 (7): 1073-1094.

Russam, K. and Coleman, J.D. (1961). "The Effect of Climatic Factors on Subgrade Moisture Conditions." Geotechnique, Vol. 11 (1): 22-28.

The Oklahoma Mesonet. (2011). http://www.mesonet.org/index.php/site/about Thornthwaite, C.W. (1948). "An Approach Toward A Rational Classification of

Climate." Geographical Review, Vol. 38 (1): 54-94. Thornthwaite, C.W. and Mather, J.R. (1955). "The Water Balance." Publ. Climatol.,

Laboratory of Climatology, Vol. 8 (1): 104 p. Witczak, M.W., Zapata, C.E., and Houston, W.N. (2006). "Models Incorporated into

the Current Enhanced Integrated Climatic Model for Used in Version 1.0 of the MEPDG." NCHRP 9-23 Project Report, Arizona State University, Tempe, Arizona.

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