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

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


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][2][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][7][8][9][10][11][12].For unbound materials (base course and subgrade) used in a pavement structure, the Mechanistic-Empirical Pavement Design Guide (MEPDG) [6][7][8][9], now called "PavementME," has adopted the Enhanced Integrated Climatic Model (EICM F env ) to address such susceptibility and determine the M R of unbound materials.
e EICM F env 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 (F env ) can be determined [6][7][8][9].e resilient modulus M R at any time or position is then expressed as follows: where M R and M R opt are in units of kilopascals (kPa) and F env is dimensionless.e factor F env is an adjustment factor and M R opt 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 "signi cant loss" in accuracy of prediction.
e adjustment factor F env , being solely a function of the environmental factors, can then be computed by the EICM F env , without actually knowing M R opt .e model presented in equation ( 2) was developed from published models for usage in Pave-mentME [6,[13][14][15][16]: , k m regression parameter, (S − S opt ) variation in the degree of saturation expressed in decimals, M R F env × M R opt , and M R opt resilient modulus at the optimum moisture content.M R and M R opt are in units of kPa, and F env , a, b, and k m are dimensionless.
Based on the available literature data, maximum modulus ratios of 2.5 for ne-grained materials and 2 for coarsegrained materials were adopted.e values of a, b, and k m for coarse-grained and ne-grained materials are given in Table 1.Fine-grained soils refer to those with passing U.S. No. 200 sieve greater than 50 percent.
e graphical representation of the model is shown in Figure 1 for ne-grained and coarse-grained materials.e curves in Figure 1 will be hereafter referred to as "EICM F env curve(s)."It should be noted that these curves were formed based on samples that were acquired from the eld and then remolded using standard proctor methods at varying degrees of moisture contents.
LTRC is conducting a research project to determine the seasonal variation of subgrade resilient modulus M R in an e ort to implement PavementME.One objective of that project, which is presented in this paper, was to locally calibrate the EICM F env curves for seasonal subgrade M R 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 tra c control would not be required on future assessments with devices such as the falling weight de ectometer (FWD).e AASHTO T-99 M R test method [17] was used on all samples with an additional eight specimens being tested with NCHRP 1-28A M R test method [18].LTRC typically conducts all soil M R tests using the AASHTO T-99 M R test method.Testing from Shelby tube samples included standard classi cations, moisture density curves from standard proctor methods, in situ densities, as well as the in situ M R .
e in situ M R was used as the M R in M R /M R opt , whereas the M R opt was from the remolded sample at the optimum degree of saturation (S opt ) fabricated by molding the specimen with a compactive energy equivalent to standard proctor tests [19,20].
Once the M R tests were completed and plotted, it was noticed that there was a rather large scatter around the EICM F env curve as presented in Figure 2. e results from 110 M R tests using the AASHTO T-99 test method were plotted on a graph with the EICM F env curve for ne-grained soils.One hundred ten tests equate to 55 points since two M R tests are required for each point plotted as presented in Figure 2. e 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 F env curve.As evident from the gure, there was a very large scatter of points (R 2 −0.266), with most below the F env EICM curve.
is indicated that the EICM F env curve was not predicting the eld M R /M R opt relationship well.e objective of this paper was to explore the reason that the EICM F env curve did not predict the in situ M R /M R opt soil relationship appropriately and develop a method that more accurately predicts the in situ M R /M R opt soil relationship.
is 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.

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 M R value was acquired from undisturbed (Shelby tube samples) and hence was not prepared using standard proctor compactive energy.
e EICM F env 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. e 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 speci cations require that the moisture content be within  Advances in Civil Engineering +/− 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].
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.
e EICM F env curve (Equation ( 2)) represents changes in M R caused by the change of moisture content from the optimum moisture content (1OPT).
e 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 M R will be varying from the in situ density (2A) on the wetside of optimum 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).
e influence of soil compactive energy on the M R of granular soils has been studied by others [23][24][25][26].Andrei studied the influence of compactive energy on the M R of soils using standard and modified compactive efforts [23].
e results indicated that different compactive efforts produced significant differences in M R .Rada conducted tests at 3 different compactive efforts on six aggregates: less than standard compaction, standard compaction, and modified compaction [24].e R 2 value for the aggregates as a group was 0.61 and improved to 0.84 when the aggregates were evaluated independently.
e following equation was developed from the results of the testing: where C 0 , C 1 , C 2 , and C 3 � regression parameters and are dimensionless, S � degree of saturation in decimals, PC � percent compaction relative to the standard proctor method in decimals, θ � bulk stress (kPa), and M R � 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].e values for C 1 and C 2 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 03223, S � degree of saturation, S opt � degree of saturation at the optimum moisture content, and PC � percent of compaction relative to the standard proctor energy.

Results and Analysis
e authors' hypothesized that the large scatter of points around the EICM F env curve, as presented in Figure 2, existed due to significant differences in the dry densities from which the in situ M R and the remolded M R were determined. is 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.e authors theorized that data points whose dry density difference were within plus or minus 80 kg/m 3 (at optimum moisture content) would better fit the EICM F env curve.e M R data were sorted based on that hypothesis, and Figure 5 presents the data.On a previous study, LTRC conducted M R tests on 4 soil types from Louisiana whose samples were molded using standard proctor compactive energy [19].ere were 15 data points available from the 4 soils.
As presented in Figure 5, the scatter of the data (R 2 � −0.7865) was closer to the EICM F env curve in contrast to the data (R 2 � −0.266) in Figure 2. e authors' hypothesis that data from points whose dry densities were within plus or minus 80 kg/m 3 would be closer to the EICM curves was validated.ree significant points can be inferred from this.First, when the density of in situ field samples is within plus or minus 80 kg/m 3 of the sample remolded using standard proctor compactive energy, one can expect the ratios (M R / M R opt ) plotted in Figure 1 to be reasonably similar.Second, the EICM F env curve may not adequately represent the changes in M R 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 F env curve.
LTRC developed a procedure based upon the EICM F env 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 F env 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 − S opt and its corresponding M R /M R opt is plotted and fitted with a nonlinear regression curve as presented in equation (2).In this case, conditions (S and M R ) at optimum moisture content are used as the control in which to gauge changes in M R as a function of changes in soil moisture.
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.erefore, seasonal changes will vary 4 Advances in Civil Engineering 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.e 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.
e in situ moisture content sample was tested at the time of molding.
e 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/m 3 , and classi ed as an A-6 material under the AASHTO designation.It was molded at 20.6 percent moisture content with corresponding densities and M R values of 1616.3 kg/m 3 and 11.72 MPa, respectively.An exponential curve provided the best t (R 2 −0.9875) to the data, as presented in equation (5). is curve values di er from the EICM F env curve values in several ways.e M R /M R Control ratio was approximately 7.1 at −70 (S − S control ) based upon the exponential curve while the MEPDG M R /M R opt ratio was approximately 2.5 at −70 (S − S control ).e magnitude di erence (7.1 versus 2.5) exists the EICM F env value is based on the di erence from optimum degree of saturation while the LTRC method is based on the di erence from the in situ degree of saturation, which is usually between 80 and 100 percent in Louisiana.It is possible to have (S − S opt ) values greater than zero with the EICM F env method but not with the LTRC method.is 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 F env 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 e procedures to construct LTRC's M R curves are as follows: (1) Obtain Shelby tube samples at the desired location(s) and depth(s).(2) Perform soil classi cation, determine in situ density and moisture content, construct moisture/density curves, and determine in situ M R on the soils obtained from the sampling.(3) Mold the desired number of specimens at the in situ or eld moisture content or degree of saturation (S eld ) for the purpose of performing M R testing using standard proctor compactive energy.(4) Place the untested samples in a 50 percent relative humidity room.Perform a M R test on one sample immediately after it is prepared.e M R result becomes the M R control and its moisture content (degree of saturation) becomes S control .Record its density as well.(5) Remove specimens from the 50 percent relative humidity room at desired moisture contents and conduct M R tests.Record both the density and moisture content of the specimen at the time of testing.( 6) Develop an M R /M R Control versus S − S control curve from the data as presented in Figure 7.
where M R resilient modulus, M R control resilient modulus at the control moisture content condition, S degree of saturation, and S control degree of saturation at control moisture content condition.Advances in Civil Engineering e authors' acknowledge that this procedure does not exactly mimic eld density or M R 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 di erent soil types.Such a feat was accomplished by Cary and Zapata [26].Additionally, the LTRC curve method could not practically replace the EICM F env 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 F env when changes of moisture contents in the eld 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.

Conclusions
LTRC collected Shelby tube samples from six di erent 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.
ose data were plotted on the EICM F env curve and the results indicated that the data did not adequately t (R 2 −0.266) the curve.When the data were resorted to discover which points from the eld were within 80 kg/m 3 of remolded specimens at optimum moisture content, it was evident that those points closely matched (R 2 −0.7865) the EICM F env curve.Resilient modulus data from four additional Louisiana soils, all remolded in the laboratory, were also plotted on the EICM F env curve.ose data closely matched the EICM F env curve.
LTRC developed a new method based on the EICM F env method to determine the relationship between changes in subgrade M R as a function of changes in moisture content with respect to the in situ moisture content and M R used as control values.is method di ers from the EICM F env in that the EICM F env uses optimum moisture content as the controlling parameter.e LTRC method can be used for design purposes and level 2 inputs into the MEPDG EICM F env .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.

Figure 1 : 2 Advances in Civil Engineering 1 . 1 .
Figure 1: E ect of moisture changes on the resilient modulus.

Figure 3 :
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.

3 )Figure 4 :Figure 5 :
Figure 4: In situ moisture content-optimum moisture content versus in situ dry density-maximum dry density.

Table 1 :
Values of a, b, and k m for coarse-grained and ne-grained materials.
a, b, and k m are dimensionless.

Table 2 :
Project locations and soil information.
Figure 2: MEPDG curve for ne-grained soils with all points.