Advances in Civil Engineering
Volume 2019 (2019), Article ID 1793601, 7 pages
https://doi.org/10.1155/2019/1793601

Research Article

Modeling the Resilient Modulus Variation of In Situ Soils due to Seasonal Moisture Content Variations

Kevin Gaspard,¹ Zhongjie Zhang,² Gavin Gautreau,³ Khalil Hanifa,⁴ Claudia E. Zapata,⁵ and Murad Abufarsakh⁶

¹Pavement Research Manager, Louisiana Transportation Research Center, 4101 Gourrier Ave., Baton Rouge, LA 70808, USA
²Pavement and Geotechnical Research Administrator, Louisiana Transportation Research Center, 4101 Gourrier Ave., Baton Rouge, LA 70808, USA
³Geotechnical Research Manager, Louisiana Transportation Research Center, 4101 Gourrier Ave., Baton Rouge, LA 70808, USA
⁴Geotechnical Research Engineer, Louisiana Transportation Research Center, 4101 Gourrier Ave., Baton Rouge, LA 70808, USA
⁵Associate Professor, Arizona State University, College Avenue Commons, P. O. Box 873005, Tempe, AZ 85287-3005, USA
⁶Professor, Louisiana State Universitsy, Louisiana Transportation Research Center, 4101 Gourrier Ave., Baton Rouge, LA 70808, USA

Correspondence should be addressed to Kevin Gaspard; doc.kevin1@gmail.com

Received 28 August 2018; Revised 23 November 2018; Accepted 20 December 2018; Published 26 March 2019

Academic Editor: Emilio García-Taengua

Copyright © 2019 Kevin Gaspard et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

LTRC is conducting a research project to determine the seasonal variation of subgrade resilient modulus (MR) in an effort to implement PavementME. One objective of that project, which is presented in this paper, was to locally calibrate the Enhanced Integrated Climate Model’s (EICM Fenv) curve for seasonal subgrade MR changes. Shelby tube sampling was conducted on six different roadways to a depth of approximately 7.92 m beneath the shoulder pavement’s base course. The AASHTO T-99 MR test method was used on all samples with an additional eight specimens being tested with NCHRP 1–28A MR test method. Four soils from Louisiana which were not from the six roadways were also tested and included in the analyses. Once the MR tests were completed and plotted, it was noticed that there was a rather large scatter (R² = −0.266) around the EICM Fenv curve. The authors hypothesized that this occurred due to the density differences between in situ and remolded specimens. Further analyses confirmed this hypothesis. LTRC developed a new method based on the EICM Fenv method to determine the relationship between changes in subgrade MR as a function of changes in moisture content with the in situ moisture content and MR used as the control. This method differs from the EICM Fenv in that the EICM Fenv uses optimum moisture content as the controlling parameter. The LTRC method can be used for design purposes as well as level 2 inputs into the EICM.

1. Introduction

In the last decades, it has been widely recognized by the pavement engineering community that environmental conditions have a significant effect on the performance of both flexible and rigid pavements [1–3]. External factors such as precipitation, temperature, wind speed, solar radiation, relative humidity, and depth to water table are environment parameters that impact pavement performance [4, 5]. On the other hand, internal factors, such as the susceptibility of the pavement materials to moisture and temperature changes, freeze-thaw damage, drainage of paving layers, and infiltration potential of the pavement, define the extent to which the pavement will react to the applied external environmental conditions [6–12]. For unbound materials (base course and subgrade) used in a pavement structure, the Mechanistic-Empirical Pavement Design Guide (MEPDG) [6–9], now called “PavementME,” has adopted the Enhanced Integrated Climatic Model (EICM Fenv) to address such susceptibility and determine the MR of unbound materials.

The EICM Fenv deals with all environmental factors and provides soil moisture, suction, and temperature as a function of time, at any location in the unbound layers from which the composite adjustment factor (Fenv) can be determined [6–9]. The resilient modulus MR at any time or position is then expressed as follows:

where and are in units of kilopascals (kPa) and Fenv is dimensionless.

The factor is an adjustment factor and is the resilient modulus at optimum moisture content and at any state of stress. It can be seen that the variation of the modulus with stress and the variation of the modulus with environmental factors (moisture, density, and freeze/thaw conditions) are uncoupled. Although this is not necessarily the case, several studies support the use of this assumption in predicting resilient modulus without “significant loss” in accuracy of prediction. The adjustment factor Fenv, being solely a function of the environmental factors, can then be computed by the EICM Fenv, without actually knowing MRopt. The model presented in equation (2) was developed from published models for usage in PavementME [6, 13–16]:

where  = resilient modulus ratio,  = minimum of log (), b = maximum of log (), = regression parameter, () = variation in the degree of saturation expressed in decimals, , and  = resilient modulus at the optimum moisture content. MR and MRopt are in units of kPa, and Fenv, a, b, and km are dimensionless.

Based on the available literature data, maximum modulus ratios of 2.5 for fine-grained materials and 2 for coarse-grained materials were adopted. The values of a, b, and km for coarse-grained and fine-grained materials are given in Table 1. Fine-grained soils refer to those with passing U.S. No. 200 sieve greater than 50 percent.

Table 1: Values of a, b, and km for coarse-grained and fine-grained materials.

Parameter
Coarse-grained materials
Fine-grained materials
Comments

A
−0.3123
−0.5934
Corresponding to modulus ratios of 2 and 2.5, respectively

B
0.3
0.4
Corresponding to modulus ratios of 2 and 2.5, respectively

km
6.8157
6.1324
Regression parameter

a, b, and km are dimensionless.

The graphical representation of the model is shown in Figure 1 for fine-grained and coarse-grained materials. The curves in Figure 1 will be hereafter referred to as “EICM Fenv curve(s).” It should be noted that these curves were formed based on samples that were acquired from the field and then remolded using standard proctor methods at varying degrees of moisture contents.

Figure 1: Effect of moisture changes on the resilient modulus.

LTRC is conducting a research project to determine the seasonal variation of subgrade resilient modulus MR in an effort to implement PavementME. One objective of that project, which is presented in this paper, was to locally calibrate the EICM Fenv curves for seasonal subgrade MR changes. Shelby tube sampling was conducted on six different roadways to a depth of approximately 7.92 m beneath the shoulder pavement’s base course as presented in Table 2. Sampling was conducted approximately 1.22 m from the edge of the outside lane on the shoulder so that traffic control would not be required on future assessments with devices such as the falling weight deflectometer (FWD). The AASHTO T-99 MR test method [17] was used on all samples with an additional eight specimens being tested with NCHRP 1–28A MR test method [18]. LTRC typically conducts all soil MR tests using the AASHTO T-99 MR test method. Testing from Shelby tube samples included standard classifications, moisture density curves from standard proctor methods, in situ densities, as well as the in situ MR. The in situ MR was used as the MR in MR/MRopt, whereas the MRopt was from the remolded sample at the optimum degree of saturation (Sopt) fabricated by molding the specimen with a compactive energy equivalent to standard proctor tests [19, 20].

Table 2: Project locations and soil information.

Route
Parish
Latitude
Longitude
Soil types
% passing range (1)
Plasticity index range

AASHTO
USCS

LA 1
Caddo
32.8466983
−93.983117
A-2-6, A-7-5, A-7-6
CL, CH
60–99
12–61

US 171
Desoto
32.213005
−93.836785
A-7-6, A-7-6
CH, CL
25–83
7–32

US 167
Jackson
32.4267917
−92.683188
A-7-4, A-7-6-8
CL
51–61
11–23

US 84
Concordia
31.6060933
−91.669885
A-6-7, A-6-8, A-7-6, A-7-5
CL, CH, OH
68–98
11–62

LA 13
Acadia
30.466195
−92.411847
A-6-14, A-7-6
CH, CL
93–98
20–35

US 61
Feliciana
30.90426
−91.342197
A-4-7, A-6-11, A-6-9
CL
83–93
10–12

Once the MR tests were completed and plotted, it was noticed that there was a rather large scatter around the EICM Fenv curve as presented in Figure 2. The results from 110 MR tests using the AASHTO T-99 test method were plotted on a graph with the EICM Fenv curve for fine-grained soils. One hundred ten tests equate to 55 points since two MR tests are required for each point plotted as presented in Figure 2. The results from eight NCHRP 1–28A tests (4 data points) were plotted on the graph. As with the AASHTO data, the NCHRP data were below the EICM Fenv curve. As evident from the figure, there was a very large scatter of points (R² = −0.266), with most below the Fenv EICM curve. This indicated that the EICM Fenv curve was not predicting the field MR/MRopt relationship well.

Figure 2: MEPDG curve for fine-grained soils with all points.

1.1. Scope and Objective

The objective of this paper was to explore the reason that the EICM Fenv curve did not predict the in situ MR/MRopt soil relationship appropriately and develop a method that more accurately predicts the in situ MR/MRopt soil relationship. This was accomplished by obtaining Shelby tube samples from six roadways in Louisiana as well as conducting tests on four soils from Louisiana which were not from those projects.

2. Methods and Materials

Further examining the data processing and analysis procedure, the authors discovered that this occurred for two primary reasons. First, the samples used to construct the curves in Figure 1 were from remolded samples constructed using standard proctor methods, not in situ undisturbed samples. Second, the in situ sample with its corresponding MR value was acquired from undisturbed (Shelby tube samples) and hence was not prepared using standard proctor compactive energy.

The EICM Fenv curve as outlined in Equation 2 and presented in Figure 1 was developed as generalized model fundamentally based on conditions found in the mechanically compacted embankment (Zone 1) as presented in Figure 3(a). Basically, an embankment is a composite soil structure whose purpose is to provide support to the overlying pavement layers (pavement and base course). Its height can vary from 1 to 10 m. The soils in Zone 1 are generally select materials with known properties [21]. Moisture-density curves are generally developed using standard proctor methods prior to their placement so that the values for maximum density at optimum moisture content can be determined as presented in Figure 3(b) [21]. Once these values are determined, quality control personnel conduct tests to monitor the moisture content and density of the mechanically compacted embankment. In Louisiana, the specifications require that the moisture content be within +/− two percent of optimum moisture content and the density be at least 95 percent of the density at optimum moisture content [21]. Devices such as a nuclear density gauge are generally used to determine the moisture content and density of the mechanically compacted material [21].

(a)

(b)

(c)

Figure 3: (a) Pavement embankment diagram, (b) moisture content-density relationship for mechanically compacted embankment, and (c) moisture content-density relationship for in situ subgrade.

In contrast to compacted soils in embankments, in situ subgrade soils (Zone 2) are in their natural condition and may or may not qualify as select material [21]. In this paper, the authors’ will only address the case where the soils in Zones 1 and 2 are of comparable types and densities. To attempt to address all combinations of soils within compacted embankments and subgrades would be impractical. The EICM Fenv curve (Equation (2)) represents changes in MR caused by the change of moisture content from the optimum moisture content (1OPT). The predominate subgrade soil types in Louisiana are clays and silts and they are generally near or at full saturation in regions beneath the embankment based upon LTRC’s experience as presented in Figure 3(c) [22]. With that being the case, the MR will be varying from the in situ density (2A) on the wet-side of optimum moisture content instead of from the optimum moisture content (1OPT). Because of that, LTRC has developed a model based upon changes from the in situ moisture content (2A) as presented in Figure 3(c).

The influence of soil compactive energy on the MR of granular soils has been studied by others [23–26]. Andrei studied the influence of compactive energy on the MR of soils using standard and modified compactive efforts [23]. The results indicated that different compactive efforts produced significant differences in MR. Rada conducted tests at 3 different compactive efforts on six aggregates: less than standard compaction, standard compaction, and modified compaction [24]. The R² value for the aggregates as a group was 0.61 and improved to 0.84 when the aggregates were evaluated independently. The following equation was developed from the results of the testing:

where , and = regression parameters and are dimensionless,  = degree of saturation in decimals, = percent compaction relative to the standard proctor method in decimals,  = bulk stress (kPa), and  = resilient modulus (kPa).

Cary and Zapata normalized equation (3) in order to create a refined model (equation (4)) in terms of 100 percent compaction and the degree of saturation at optimum moisture content [25, 26]. The values for C₁ and C₂ were obtained from tests conducted on 266 soil specimens. Cary and Zapata noted that all the specimens were from granular soils, and further tests should be conducted on an array of materials including fine-grain soils in order to refine equation (4) [25, 26]:

where , , ,  = degree of saturation,  = degree of saturation at the optimum moisture content, and = percent of compaction relative to the standard proctor energy.

3. Results and Analysis

The authors’ hypothesized that the large scatter of points around the EICM Fenv curve, as presented in Figure 2, existed due to significant differences in the dry densities from which the in situ MR and the remolded MR were determined. This hypothesis was tested first by plotting the (in situ dry density-optimum (opt.) dry density) versus (in situ moisture content-optimum moisture content) for each of the soils from the six projects used in the study. Figure 4 presents the data from the soils of one project. The authors theorized that data points whose dry density difference were within plus or minus 80 kg/m³ (at optimum moisture content) would better fit the EICM Fenv curve. The MR data were sorted based on that hypothesis, and Figure 5 presents the data. On a previous study, LTRC conducted MR tests on 4 soil types from Louisiana whose samples were molded using standard proctor compactive energy [19]. There were 15 data points available from the 4 soils. The soils had plasticity indices (PI) of 53, 26, 17, and 7. Those data were also plotted on Figure 5.

Figure 4: In situ moisture content-optimum moisture content versus in situ dry density-maximum dry density.

Figure 5: MEPDG curve for fine-grained soils with sorted points.

As presented in Figure 5, the scatter of the data (R² = −0.7865) was closer to the EICM Fenv curve in contrast to the data (R² = −0.266) in Figure 2. The authors’ hypothesis that data from points whose dry densities were within plus or minus 80 kg/m³ would be closer to the EICM curves was validated. Three significant points can be inferred from this. First, when the density of in situ field samples is within plus or minus 80 kg/m³ of the sample remolded using standard proctor compactive energy, one can expect the ratios (MR/MRopt) plotted in Figure 1 to be reasonably similar. Second, the EICM Fenv curve may not adequately represent the changes in MR that occur in the field due to the fact that the curve was created with data from remolded samples, not field specimens. Finally, samples remolded using standard proctor compactive energy follow a similar trend to the EICM Fenv curve.

LTRC developed a procedure based upon the EICM Fenv procedure, except that instead of using the optimum moisture content as the control, the in situ or field moisture content was used as the control. To illustrate, Figure 6(a) presents the moisture-density curve relationship used to develop the EICM Fenv method. According to the NCHRP 1–28A protocol, samples are molded with standard proctor compactive energy at various moisture contents so that the maximum density and optimum moisture content is established. Resilient modulus tests were conducted at optimum moisture content and at moisture contents above and below optimum moisture content. Using the relationships shown in Figure 1, the value for S − Sopt and its corresponding MR/MRopt is plotted and fitted with a nonlinear regression curve as presented in equation (2). In this case, conditions (S and MR) at optimum moisture content are used as the control in which to gauge changes in MR as a function of changes in soil moisture.

(a)

(b)

Figure 6: Moisture-density curves for (a) EICM Fenv method and (b) LTRC method.

In Louisiana, testing conducted by LTRC to date has indicated that the degree of saturation (S) beneath pavements generally ranges from 80 to 100 percent, with most being above 90 percent. Therefore, seasonal changes will vary from the in situ moisture content and not from the optimum condition. Figure 6(b) conceptually illustrates LTRC’s process on a moisture density curve using standard proctor compactive energy.

Points A to F were obtained by allowing the specimens to dry out in a room with controlled relative humidity, in this case 50 percent. The drying times for points A to F were 1, 2, 24, 48, and 72 hours, respectively. Resilient modulus tests were performed on the specimens at the time they were removed from the 50 percent relative humidity controlled room and outliers were removed. The in situ moisture content sample was tested at the time of molding.

The soil used to create the curve presented in Figure 7 had a PI of 26, optimum moisture content of 15.8 percent, maximum dry density of 1746 kg/m³, and classified as an A-6 material under the AASHTO designation. It was molded at 20.6 percent moisture content with corresponding densities and MR values of 1616.3 kg/m³ and 11.72 MPa, respectively. An exponential curve provided the best fit (R² = −0.9875) to the data, as presented in equation (5). This curve values differ from the EICM Fenv curve values in several ways. The ratio was approximately 7.1 at −70 (S − Scontrol) based upon the exponential curve while the MEPDG MR/MRopt ratio was approximately 2.5 at −70 (S − Scontrol). The magnitude difference (7.1 versus 2.5) exists because the EICM Fenv value is based on the difference from optimum degree of saturation while the LTRC method is based on the difference from the in situ degree of saturation, which is usually between 80 and 100 percent in Louisiana. It is possible to have (S − Sopt) values greater than zero with the EICM Fenv method but not with the LTRC method. This is because the LTRC method begins at or near maximum saturation (80 to 100 percent) from which samples are dried and then tested while the EICM Fenv method allows for samples to be prepared and tested at saturation contents both above and below the saturation percent at optimum moisture content as presented in Figures 6(a) and 6(b).

Figure 7: LTRC temporal MR curve.

The procedures to construct LTRC’s MR curves are as follows:

(1)Obtain Shelby tube samples at the desired location(s) and depth(s).(2)Perform soil classification, determine in situ density and moisture content, construct moisture/density curves, and determine in situ MR on the soils obtained from the sampling.(3)Mold the desired number of specimens at the in situ or field moisture content or degree of saturation (Sfield) for the purpose of performing MR testing using standard proctor compactive energy.(4)Place the untested samples in a 50 percent relative humidity room. Perform a MR test on one sample immediately after it is prepared. The MR result becomes the and its moisture content (degree of saturation) becomes Scontrol. Record its density as well.(5)Remove specimens from the 50 percent relative humidity room at desired moisture contents and conduct MR tests. Record both the density and moisture content of the specimen at the time of testing.(6)Develop an versus S − Scontrol curve from the data as presented in Figure 7.

where  = resilient modulus,  = resilient modulus at the control moisture content condition,  = degree of saturation, and  = degree of saturation at control moisture content condition.

The authors’ acknowledge that this procedure does not exactly mimic field density or MR conditions. It would be impractical if not impossible to attempt to determine the compactive energy required using a laboratory method to obtain the actual measured in situ density with its corresponding moisture content. Even if such a methodology were developed, it would have to be varied for every sample obtained, which negates its usability as a practical tool. It is the authors’ opinion though, that the LTRC curve method is a viable tool for the purposes of pavement design if family of curves were developed for different soil types. Such a feat was accomplished by Cary and Zapata [26]. Additionally, the LTRC curve method could not practically replace the EICM Fenv curve method due to the countless variations of subgrade densities and strengths.

LTRC plans to create a family of curves for clays, silts, and granular soils from Louisiana. Values from these curves will be used for design purposes and as level 2 inputs into the EICM Fenv when changes of moisture contents in the field are known. LTRC also plans to conduct a statewide project to obtain the typical changes in moisture contents beneath pavement structures. Once this is complete, a design guide will be prepared using the data obtained.

4. Conclusions

LTRC collected Shelby tube samples from six different roadways in Louisiana. Resilient modulus tests were conducted on the specimens at in situ moisture content and were also remolded at optimum moisture content using standard proctor compactive energy. Those data were plotted on the EICM Fenv curve and the results indicated that the data did not adequately fit (R² = −0.266) the curve. When the data were resorted to discover which points from the field were within 80 kg/m³ of remolded specimens at optimum moisture content, it was evident that those points closely matched (R² = −0.7865) the EICM Fenv curve. Resilient modulus data from four additional Louisiana soils, all remolded in the laboratory, were also plotted on the EICM Fenv curve. Those data closely matched the EICM Fenv curve.

LTRC developed a new method based on the EICM Fenv method to determine the relationship between changes in subgrade MR as a function of changes in moisture content with respect to the in situ moisture content and MR used as control values. This method differs from the EICM Fenv in that the EICM Fenv uses optimum moisture content as the controlling parameter. The LTRC method can be used for design purposes and level 2 inputs into the MEPDG EICM Fenv. LTRC plans to build a family of curves using its method for soils typically found beneath pavements in Louisiana and conduct a statewide research project to determine the variation of moisture content beneath pavements.

Data Availability

The data in this article were taken in part from an ongoing research project. The figures contain the data points that were used to make them.

Disclosure

This manuscript was presented at the Transportation Research Board 97th Annual meeting. The manuscript was not published by the TRB but they did publish an extended abstract, which differs from the one in this document.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The contents of this paper/article were funded by the Louisiana Transportation Research Center (LTRC) as part of the normal employment activities of the authors. The authors wish to thank LTRC for providing the resources necessary for the project. The assistance of the LTRC research staff members Mitch Terrell, Shawn Elisar, Patrick Frazier, and Renee Crosse is noteworthy.

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