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1
THE USE OF DYNAMIC CONE PENETROMETER TO PREDICT RESILIENT MODULUS OF SUBGRADE SOILS
Ananda Herath1, P.E., Ph.D., Member, ASCE, Louay N. Mohammad2, Ph.D., Member, ASCE, Kevin Gaspard3, P.E., Ravindra Gudishala4,
and Murad Y. Abu-Farsakh5, P.E., Ph.D.
ABSTRACT
The resilient modulus is used in the characterization of base and subgrade soils and in the design of pavement structures. The resilient modulus of subgrade soils can be estimated by using expensive and time-consuming laboratory test results or from overestimated backcalculated values from nondestructive test results. These limitations imply that the need of a simple and inexpensive insitu geotechnical test method to estimate the resilient modulus of subgrade soils. The dynamic cone penetration test is considered as a simple, rapid, and economical insitu test in geotechnical applications. However, the application of the dynamic cone penetration test in evaluating the resilient modulus of pavement subgrade soils is not well known.
The objective of this paper is to develop correlations to predict the resilient modulus of subgrade cohesive soils from the dynamic cone penetration test parameters, soil type, moisture content, and dry unit weight. Twelve laboratory-compacted large soil samples of two cohesive soil types and six test locations in two existing pavements were used to perform the dynamic cone penetration tests. Laboratory resilient modulus and soil property tests were also performed. The preliminary estimation models were developed for the prediction of the resilient modulus of subgrade soils from the dynamic cone penetration test parameters, moisture content, dry unit weight, and other soil properties. The models predicted separate data sets that were not used in their development, indicating the success of the application of the dynamic cone penetration test in evaluating the resilient modulus of pavement subgrade soils.
Keywords: Dynamic cone penetration, Resilient modulus, Repeated load triaxial test, Pavement subgrade soils
1 Postdoctoral Researcher, Louisiana Transportation Research Center, 4101 Gourrier Ave., Baton Rouge, LA 70808, Email: [email protected], Tel: 225-767-9128, Fax: 225-767-91082 Corresponding Author, Associate Professor, Louisiana Transportation Research Center and Dept. ofCivil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803,Email: [email protected], Tel: 225-767-9126, Fax: 225-767-91083 Research Engineer, Louisiana Transportation Research Center, 4101 Gourrier Ave, Baton Rouge, LA 70808, Email: [email protected], Tel: 225-767-91044 Graduate Research Assistant, Dept. of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, Email: [email protected], Tel: 225-767-91285 Research Assistant Professor, Louisiana Transportation Research Center, 4101 Gourrier Ave, Baton Rouge, LA 70808, Email: [email protected], Tel: 225-767-9147
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INTRODUCTION
The guide for design of pavement structures of the American Association of State Highway and Transportation Officials (AASHTO) recommends the use of resilient modulus (Mr) of subgrade soils as an important material property in characterizing pavements for their structural analysis and design (AASHTO 1993). The pavement subgrade resilient modulus can also be used as a measure of quality assurance and as a basis for pay factors in pavement construction. The resilient modulus of soils is influenced by many factors, such as soil type, moisture content, dry unit weight, and in-situ stresses (Fredlund et al 1977, Mohammad et al. 1994 and 1998, Titi et al. 2002).
The resilient modulus of subgrade soils can be estimated from the laboratory repeated load triaxial tests on soil samples. It can also be estimated from the empirical correlations with the soil properties or non-destructive test results. However, laboratory resilient modulus tests are expensive and time-consuming. Retrieving soil samples for the laboratory testing from the existing pavements is laborious and time-consuming. It also damages the pavement layers. Soil sampling is limited to a few locations along the pavement. This coring procedure is not enough to supply a subgrade resilient modulus profile along the pavement. Empirical correlations for the subgrade resilient modulus are based on soil static properties such as the California Bearing Ratio (CBR). Thus, they do not represent the dynamic response of pavement materials under moving vehicles. Nondestructive test results depend on backcalculation procedures and pavement layer thickness values. To overcome these disadvantages in the current subgrade resilient modulus estimation procedures, it is necessary to have an accurate and reliable insitu geotechnical test method to estimate the resilient modulus of subgrade soils. To meet the need for high quality, fast, economical, and reliable subgrade resilient modulus estimation procedure, the Louisiana Transportation Reseach Center (LTRC) has initiated the Dynamic Cone Penetration (DCP) test in pavement applications.
The DCP is a simple, fast, and economical in-situ geotechnical test that has widely been used in geotechnical investigations for a few decades (Kleyn, 1975). This device is designed for the estimation of the strength, pavement condition, and variability of granular bases and subgrade soils of existing pavements. The uses of the DCP in pavement engineering include identifying and estimating thickness values of weak spots, bases, subbases, and subgrades within an existing pavement. The DCP is also useful in monitoring the strength development of stabilized soils with time. Furthermore, this device is used for quality control/assurance in pavement construction by correlating the DCP penetration index (DCPI) to soil strength properties. The CBR of cohesive soils can be correlated to the DCPI (Scala, 1956). The DCPI and the elastic modulus (E) of soils can also be correlated (Webster et al., 1994). However, the use of the DCP as a tool in pavement engineering to estimate the resilient modulus of subgrade soils is not well established. This paper presents the results of laboratory and field DCP testing programs that were performed to investigate the applicability of the DCP test parameters in estimating the resilient
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moduli of subgrade cohesive soils. The laboratory DCP testing program was a part of another major project (Abu-Farsakh et al. 2002 and Seyman 2003) that evaluated the use of the DCP in quality control/assurance in geotechnical engineering. The laboratory experimental program consisted of DCP tests on two soils: Soil 1 and Soil 2 from the LTRC Pavement Research Facility (PRF) and disturbed soil sampling close to DCP test locations. In the laboratory DCP testing program, repeated load triaxial tests of the resilient modulus were performed on compacted soil samples. The field experimental program also consisted of DCP tests on two existing pavement sites (Soil 3 from the LA 347 and Soil 4 from the US 171) and undisturbed soil sampling close to DCP test locations. In the field DCP testing program, laboratory repeated load triaxial tests of the resilient modulus were performed on undisturbed core samples retrieved close to the DCP test locations. Soil property tests were also performed for material characterization. A statistical analysis was performed on the test results of the laboratory DCP testing program to develop correlations among the resilient modulus, dynamic cone penetration test parameters, moisture content, dry unit weight, and other soil properties of subgrade soils. The test results from the field DCP testing program (Soil 3 from the LA 347 and Soil 4 from the US 171) and a project (Soil 5) in Mississippi (George et al. 2000) were used to validate the proposed models.
OBJECTIVE AND SCOPE
The objective of this study was to develop estimation models to predict the resilient modulus of subgrade soils from the dynamic cone penetration test parameters and soil properties, such as moisture content, dry unit weight, and plasticity index (PI).
Twelve large soil samples of two soil types for twenty-four laboratory DCP tests and two pavement sites for six field DCP tests were studied. For each DCP test condition and soil type, a laboratory resilient modulus test was performed on a compacted or retrieved soil sample. Soil property tests were also performed.
MATERIALS AND SAMPLE PREPARATION
The DCP test was performed, according to the American Society for Testing and Materials (ASTM) test procedure D6951. The laboratory experimental program consisted of DCP, disturbed soil sampling close to the DCP test locations, repeated load triaxial Mr, and soil property tests. The moisture-unit weight relationship for the investigated soils was performed according to the AASHTO T 99-01 test procedure (standard Proctor curve). Two soils were considered in the laboratory study: Soil 1 and Soil 2 from the PRF (Table 1). Soil 1 and Soil 2 from the PRF were compacted at different moisture content and dry unit weight levels. All soil samples with 0.2m thick lifts for the laboratory DCP tests were compacted in large boxes of 1.5m by 0.9m by 0.6m (Seyman, 2003) using an electric jackhammer. A certain selected pattern of compaction was followed to achieve a uniformly compacted soil sample. The laboratory DCP tests were performed on twelve large soil samples (Seyman, 2003). In all the DCP tests, the depth for each drop of weight was recorded.
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Table 1. Properties of soils
Legend: * - George et al. (2000), NA - Not available, Opt. - OptimumSoil ID Soil 1 Soil 2 Soil 3 Soil 4 Soil5
Location PRF PRF LA 347 US 171
Mississippi*
Passing #200 (%)
65 91 93 77 68-98
Silt (0.074 to 0.002 mm) (%)
37 72 62 65 NA
Clay (less than 0.002 mm) (%)
28 19 31 12 NA
Plasticity index (PI)
15 6 27 12 4-26
Opt. water content (%)
13.1 18.5 20.2 12.0 NA
Max. dry unit weight (kN/m3)
18.5 16.5 14.8 18.9 NA
Unified Soil Classification System (USCS)
CL CL-ML CH CL NA
Soil classification (AASHTO)
A-6
A-4
A-7-6 A-6 A-6
For each soil sample, two DCP tests were performed to obtain an average DCPI profile. The average DCPI value of the DCP profile (excluding the first and last blows) of a soil layer was considered as the DCPI. The details of the sample preparation procedure are presented elsewhere (Seyman, 2003). In the laboratory DCP testing program, simulating the same moisture-unit weight conditions in the large test boxes, laboratory repeated load triaxial Mr tests were performed on compacted samples of soils obtained close to the DCP test locations. Disturbed soils were dried, pulverized, and sieved through the No. 4 sieve before they were mixed with water for soil compaction. The soil samples for the laboratory repeated load triaxial Mr tests were compacted in five layers using an impact compactor. The same moisture content and dry unit weight levels, used in the corresponding DCP tests, were selected in the laboratory soil sample compaction for the Mr tests. The 71.1 mm (diameter) by 142.2 mm (height) samples were compacted for the Mr in repeated loading triaxial tests.
The field experimental program also included DCP, undisturbed soil sampling close to the DCP test locations, repeated load triaxial resilient modulus, and soil property tests. Six field DCP tests were performed on two selected existing pavements in Louisiana (Soil 3 from the LA 347 and Soil 4 from the US 171 in Table 1). For each pavement, three DCP tests were performed. The distance between the two DCP locations was 2.0 m in each pavement. First, a 100 to 200 mm deep hole (diameter greater than 25 mm) was drilled through the top asphalt layer in the pavement. Then,
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the DCP test was performed through the rest of the layers in the pavement. The total depth of the DCP measurement was approximately 0.8 to 1.0 m. The average DCPI value of the DCP profile (excluding the first and last blows) of a soil layer wasconsidered as the DCPI. Simulating the same in-situ conditions in the field, laboratory repeated load triaxial tests of Mr were performed on undisturbed core samples retrieved close to the DCP test locations. Undisturbed core samples were cut and trimmed to the 71.1 mm (diameter) by 142.2 mm (height) sample size for the Mr
in repeated load triaxial tests.
Disturbed soil samples close to the DCP test locations from the large test boxes and the pavement sites were also obtained for the laboratory soil property tests. In accordance with the AASHTO and ASTM standard test procedures, soil property tests, such as moisture-unit weight, Atterberg limits, hydrometer, sieve analysis, and soil classification were performed. The soil properties of cohesive soils investigated in this study are presented in Table 1. Table 2 presents the test factorials.
Table 2. Test Factorial
Legend: γd - Dry unit weight, w - Moisture content, NA- Not available, * - Mississippi (George et al.,2000)
Soil ID SampleID
γd
(kN/m3)w
(%)Moisture level
L1 15.3 8.5 Dry of optimumL2 17.1 9.4 Dry of optimumL3 17.8 11 Dry of optimumL4 18.9 12.5 Dry of optimumL5 17.6 13.3 Wet of optimumL6 18.7 13.9 Wet of optimumL7 16.8 14.6 Wet of optimum
Soil 1
L8 15.8 20.9 Wet of optimumL9 16.1 15.6 Dry of optimumL10 16.7 18.5 OptimumL11 16.3 18.9 Wet of optimum
Soil 2
L12 16.1 20.1 Wet of optimum347-1 14.1 30.1 Wet of optimum347-2 14.1 30.1 Wet of optimumSoil 3347-3 13.1 32.8 Wet of optimum171-1 18.2 16.9 Wet of optimum171-2 17.0 20.4 Wet of optimumSoil 4171-3 15.5 17.9 Wet of optimum1349 18.4 14.1 NA1353 18.0 14.5 NA1591 18.6 14.6 NA1595 16.8 19.5 NA1598 17.3 17.9 NA
Soil 5*
1698 18.4 17.0 NA
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DESCRIPTION OF LABORATORY AND FIELD TESTS
Repeated Load Triaxial Test (Resilient Modulus Test)
The resilient modulus is experimentally determined by applying a repeated axial load on a soil sample that is mounted inside a triaxial cell. The resilient modulus in a repeated load test is defined as the ratio of the maximum deviator stress (σd) and the recoverable elastic strain (εr) as follows:
r
drM ε
σ= (1)
A new test procedure, Standard Method of Test for Determining the Resilient Modulus of Soils and Aggregate Materials, AASHTO T 307-99 (2003), was introduced by the AASHTO. The stress levels selected for the AASHTO T 307-99 resilient modulus test are based upon the location of the material sample within the pavement structure. The material sample size for the AASHTO T 307-99 resilient modulus test is based upon the type, gradation characteristics, and plastic limit of the material. A minimum confining pressure of 13.8 kPa (2 psi) was introduced in this test procedure. A contact stress of 10 percent of the maximum axial stress is also recommended in this test procedure.
Since this research study was initiated before the availability of the new test procedure, AASHTO T 307-99 (2003), the resilient modulus test in this study was conducted according to the AASHTO procedure T 294-94 “Resilient Modulus of Unbound Granular Base/Subbase Materials and Subgrade Soils” (AASHTO 1995). The samples were conditioned by applying one thousand repetitions of a specified deviator stress. The specimen was then subjected to different stress levels. The stress levels were selected to cover the expected in-service range that a pavement or subgrade material experiences under traffic loading. The resilient modulus at a specified stress level can be determined by interpolating the test results.
Dynamic Cone Penetration Test
The dynamic cone penetrometer (Figure 1), a portable instrument, consists of an 8 kg sliding hammer, anvil, pushing rod (diameter 16 mm), and steel cone tip. The cone tip angle is 60 degrees and its diameter is 20 mm. The diameter of the pushing rod is less than that of the cone base. This design assists in reducing the frictional forces along the wall of the cone penetrometer. The dynamic cone penetration test consists of pushing a conical tip, attached to the bottom of the pushing rod, into the soil layer and measuring the resistance to penetration. During the test, the hammer falls a distance of 575 mm vertically onto the anvil attached to the top of pushing rod and drives the cone tip into the soil layer. The penetration depth of DCP for each hammer drop (blow) is recorded. This measurement allows for the computation of the DCP penetration index (DCPI) in mm/blow. Two people are required to perform the test: one for lifting and dropping the hammer and another for measuring and recording the penetration depth for each blow.
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Figure 1. Dynamic cone penetrometer test
DISCUSSION OF RESULTS
The main focus of this study was to develop a model to predict the resilient modulus of cohesive soils from the dynamic cone penetration test data, soil types, moisture content, and dry unit-weight. However, there is concern regarding the similarities and differences in the DCP and laboratory repeated load resilient modulus tests that may affect the correlation of their test parameters in evaluating the resilient modulus of subgrade soils. The laboratory repeated load resilient modulus and DCP tests are dynamic tests. Both of them apply a peak load on the material tested and follow a rest period. The peak load and rest period in the laboratory repeated load resilient modulus test are predefined, whereas, in the DCP test, applied energy is predefined while a varying rest period is defined by the operator. Furthermore, the soil media fails in shear in the DCP test, while the soil sample does not fail in the laboratory resilient modulus test. Nevertheless, the DCP tests and laboratory repeated load resilient modulus tests were performed under the same moisture-unit weight conditions. Under the same environmental conditions, both DCP and laboratory repeated load resilient modulus parameters are controlled by the same soil variables. Despite some minor differences, there may be a correlation that exists among the DCP test parameters, subgrade soil resilient modulus, and soil properties.
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Prior to the model development, a field representative Mr value was defined and test results (Table 3) were analyzed to evaluate the effect of stress levels, moisture content, dry unit-weight, and soil types on the resilient and DCPI properties of cohesive soils. The influence of these variables on the Mr and DCPI of cohesive soils was considered in this research. Finally, a prediction model of the Mr of cohesive soils was developed and validated.
A Field Representative Resilient Modulus Value of Subgrade Soils
Selecting a field representative Mr value from the repeated load triaxial test results, such as those presented in Figure 2a, is a concern to many transportation engineers. To obtain this field representative Mr value, typical stresses on the top of the subgrade resulting from a standard single axle loading of 80 kN (18 kips) and a contact wheel pressure of 689 kPa (100 psi) were estimated using the ELSYM5 computer code for the analysis of linear-elastic pavement systems (Kopperman et al., 1986). A typical pavement selected for the stress analysis consisted of a 50 mm asphalt wearing course, 100 mm asphalt binder course, 200 mm granular base, and semi-infinite subgrade of silty clay. A typical vertical cyclic stress of about 42 kPa (6.1 psi) and a confining stress (including an insitu confining stress at 0.5 m in subgrade) of about 14 kPa (2.0 psi) were estimated on the subgrade under the traffic loading. A similar study in Mississippi showed that the standard single axle loading of 80 kN yielded a vertical cyclic stress of 37 kPa (5.4 psi) and a confining stress of 14 kPa (2 psi) on the top of the subgrade of a typical pavement, which consisted of a50 mm asphalt wearing course, 100 mm asphalt binder course, and 150 mm lime-treated subgrade (Rahim et al., 2004). As shown in Figure 2a, the change in the resilient modulus for deviator stress that is greater than 41.3 kPa (6 psi) is typically small. Thus the resilient modulus at a deviator stress of 41.3 kPa is frequently selected to represent the field condition. This also corresponds to the “resilient modulus at the break point” proposed by Thompson et al. (1979). The Asphalt Institute (1989) recommended the use of the subgrade resilient modulus at a deviator stress of 41.3 kPa (6 psi) and confining stress of 14 kPa (2 psi) for flexible pavement design.
Based on these stress estimations of the subgrade resulting from the traffic loading, an approximate field representative deviator stress of 41.3 kPa (6 psi) and a confining stress of 14 kPa (2 psi) were selected to interpolate the corresponding Mr value from the repeated load triaxial test results, such as those are presented in Figure 2a. The interpolated Mr was considered as the measured Mr from the laboratory repeated load triaxial test.
Behavior of Mr with Stress Levels and DCPI
A typical variation of the Mr of cohesive soils with its deviator stress and confining stress is shown in Figure 2a for sample L3. The Mr, at a constant deviator stress, increased as the confining pressure increased. This observation was due to the fact that as the confining pressure increased the stiffness of the cohesive soils increased
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Table 3. The DCP and Mr Test Results
Legend: γd - Dry unit weight, w - Moisture content, *- Excluded from the analysis, ** - Mississippi (George et al., 2000)
Soil ID SampleID
γd
(kN/m3)w
(%)PI
(%)DCPI
(mm/blow) Measured Mr (MPa)
L1 15.3 8.5 15 18.4 66.6L2 17.1 9.4 15 15.0 69.6L3 17.8 11 15 17.0 71.9L4 18.9 12.5 15 16.7 82.4L5 17.6 13.3 15 22.5 70.5L6 18.7 13.9 15 13.0 83.4L7 16.8 14.6 15 23.0 57.3
Soil 1
L8 15.8 20.9 15 36.0 38.8L9 16.1 15.6 6 18.8 67.1L10 16.7 18.5 6 29.0 42.6L11 16.3 18.9 6 26.1 48.4
Soil 2
L12 16.1 20.1 6 27.0 49.5347-1 14.1 30.1 27 13.5 82.4347-2 14.1 30.1 27 15.2 72.4
Soil 3
347-3 13.1 32.8 27 15.0 73.5171-1 18.2 16.9 12 14.3 91.4171-2 17.0 20.4 12 17.2 70.0
Soil 4
171-3* 15.5 17.9 12 6.54 64.21349 18.4 14.1 17 15.9 76.01353 18.0 14.5 17 11.7 106.01591 18.6 14.6 17 23.3 51.01595 16.8 19.5 23 63.7 44.01598 17.3 17.9 19 10.6 105.0
Soil 5**
1698 18.4 17.0 14 26.0 69.0
and dilatational properties of soils decreased. This observation confirms the stress and dilatational property dependent nature of the Mr. Figure 2b presents the variation of the Mr with DCPI values for the soil samples L1 to L12. According to Figure 2b, as the DCPI increases the Mr decreases. This implies that soil strength decreases as the DCPI increases. Furthermore, this implies that there may be a good correlation between the DCPI and Mr of cohesive soils.
Effect of Moisture Content on DCPI and Mr
Figure 3a presents the variation of the DCPI values with moisture content (w) for the soil samples L1 to L12. The coefficient of determination (R2) and square root of the mean square for error (RMSE) of the regression line are also presented in Figure 3a. In general, as shown in Figure 3a, as the w increases, the DCPI increases. This implies that soil strength decreases as the w increases. Figure 3b presents the variation of the Mr values with w for the soil samples L1 to L12. In general, as shown
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in Figure 3b, as the w increases, the Mr decreases. This implies that soil stiffness decreases as the w increases.
0 20 40 60 80
Deviator stress, σd (kPa)
0
20
40
60
80
100
120
140
160
180
200
Mr
(MP
a)
Confining stressσc =41.3 kPa
σc =20.7 kPa
σc =0.0 kPa
0 0.02 0.04 0.06 0.08 0.1(1/DCPI) (blow/mm)
0
50
100
150Soil 1 and Soil 2
γd = 17.8 kN/m3
w = 11.0 % σd = 41 kPa
R2 = 0.82RMSE = 6.6
(a) (b)
Figure 2. (a) A typical Mr test result (b) Variation of Mr with inverse of DCPI
8 12 16 20 24Moisture Content, w (%)
10
15
20
25
30
35
40
DC
PI
(mm
/blo
w)
Soil 1
Soil 2
0 5 10 15 20 25Moisture Content, w (%)
40
60
80
100
Mr
(MP
a)
Soil 1
Soil 2
R2 = 0.68RMSE = 4.01
R2 = 0.58RMSE = 10.05
(a) (b)
Figure 3. (a) DCPI versus moisture content (b) Mr versus moisture content
Effect of Dry Unit Weight on DCPI and Mr
Figure 4a presents the variation of the DCPI values with the dry unit weight (γd) for the soil samples L1 to L12. In general, as shown in Figure 4a, as the γd increases, the DCPI decreases. This implies that soil strength increases as the γd increases.
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Figure 4b presents the variation of the Mr values with the γd for the soil samples L1 to L12. In general, as shown in Figure 4b, as the γd increases, the Mr increases. This implies that soil stiffness increases as the γd increases.
12 14 16 18 20Dry Unit Weight, γd (kN/m3)
10
20
30
40
50
DC
PI
(mm
/Blo
w)
Soil 1 and Soil 2
12 14 16 18 20Dry Unit Weight, γd (kN/m3)
40
60
80
100
Mr
(MPa
)
Soil 1 and Soil 2
R2 = 0.32RMSE = 5.8
R2 = 0.51RMSE = 10.9
(a) (b)
Figure 4. (a) DCPI versus dry unit weight (b) Mr versus dry unit weight
Effect of Soil Type on DCPI and Mr
Figure 5a presents the variation of the DCPI values with the plasticity index (PI) for the soil samples L1 to L12. Although it was not well indicated in Figure 5a, it was observed that as the PI increased, the DCPI decreased. This observation implies that soil strength may increase as the PI increases. Figure 5b presents the variation of the Mr values with the PI for the soil samples L1 to L12. It was generally observed that as the PI increased, the Mr increased although this was not clearly evident in Figure 5b. This observation also implies that soil stiffness increases as the PI increases. However, no definitive conclusions could be drawn since the PI did not vary considerably in this study. With the exception of the PI, these observations may be attributed to the different clay and silt contents in Soil 1 and Soil 2. Soil 2 contains less clay (19 percent) and more silt (72 percent) than that of Soil 1 (70 percent clay and 23 percent silt). Percent fines in Soil 1 are higher than those in Soil 2 (Table 1). The higher percentages of fines in Soil 1 may result in a lower DCPI and higher Mr as compared to that of Soil 2. This is due to the fact that fines will occupy voids in the soil media. In general, the higher the percentages of fines that are present in the soils, the smaller the air void pockets are. The strength and stiffness increase in soils as the area of the pore size decreases.
THE MODEL DEVELOPMENT
Slopes of the regression lines in Figures 3a, 4a, and 5a are the opposite of the slopes of Figures 3b, 4b, and 5b respectively. This result implies that there may be a good correlation among the Mr, DCPI, and soil properties. Slopes of the regression lines in
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0 4 8 12 16PI
0
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20
30
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DC
PI
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w)
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0 4 8 12 16PI
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20
40
60
80
100
Mr
(MPa
)
Soil 1 and Soil 2
R2 = 0.14RMSE = 6.5
R2 = 0.27RMSE = 13.3
(a) (b)
Figure 5. (a) DCPI versus PI (b) Mr versus PI
Figures 3 to 5 and discussions in the preceding sections describing the test results also showed that the DCPI and Mr of cohesive soils are affected by moisture content, unit weight, and soil type. Therefore, an attempt was made in this study to account for those factors in the development of the Mr prediction models. A statistical analysis on the laboratory DCP, Mr, and soil property test results was performed using the Statistical Analysis System (SAS) program to develop models to predict the resilient modulus from the dynamic cone penetration test data, PI, w, and γd. The models were developed for fine-grained soils. The DCPI and Mr results from field test and literature were subsequently used to validate the models. The variables for the models were selected based on a parametric study. Considering the highest coefficient of determination (R2) and lowest square root of the mean square for error (RMSE), the variables and their combinations were selected for the models. These variables included Mr (MPa), DCPI (mm/blow), PI (%), γd (kN/m3), w (%), and clay content (clay) (%). The results of the parametric study are presented in Table 4. In the absence of uniform soil properties along a soil layer, a direct relationship between resilient modulus and DCPI is useful. A correlation among resilient modulus, soil properties, and DCPI may also be useful to understand the effect of soil properties on the DCPI predicted resilient modulus of subgrade soils. However, variations in moisture content, dry unit weight, and PI along the depth of a soil layer may pose a concern in using such a model based on soil properties. When the soil properties for a layer are found to be uniform or a profile of soil properties are available, a model based on soil properties may be used. Therefore, the following two models (hereafter referred as direct model and soil property model) are proposed to predict the Mr of cohesive soils based on the preliminary data considered in this study.
Direct model:
( )DCPIM r
24.92828.16 += (2)
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Soil property model:
( ) PIwDCPI
M dr 44.040.0
162.520 7362.0 +
+
= γ(3)
The SAS program performed the F-test of the regression analysis. The associated probability was designated as Pr> F or p-value. A small p-value implies that the model is significant in explaining the variation in the dependent variable. The p-value for the F-test was less than 0.0001 for both models. The R2 was 0.82 and the RMSE was 6.7 for the direct model, whereas R2 was 0.85 and the RMSE was 6.3 for the soil property model. These results indicate that both models are effective inpredicting the Mr of cohesive soils from the DCPI and soil properties. The results of the predicted versus the measured Mr for all samples are shown in Figure 6. These models were then used to predict the Mr of the field and literature DCP test results that were excluded in the development of the models.
Table 4. Selections of the Model Parameters
Legend: * - Excluded in the analysis because this model produces negative Mr for the DCPI values those are greater than 52.1 mm/blow.
Model parameters RMSE R2
DCPI
M r
1, 6.7 0.8224
PIwDCPI
M dr ,,
1,
7362.0
γ6.3 0.8516
clayPIwDCPI
M dr ,,,
1,
γ
7.0 0.8386
PIwDCPI
M dr ,,
1,
γ
7.7 0.7794
claywDCPI
M dr ,,
1,
γ
6.8 0.8294
clayPIDCPI
M r ,,1
,
6.6 0.8377
DCPIM r , * 5.8* 0.8598*
Verification of the Resilient Modulus Prediction Model
The preliminary Mr prediction models of cohesive soils from the DCP test results were developed based on the laboratory DCP, Mr, and soil property test results of cohesive soils. To validate the models, the Mr of the field DCP test results and Mr of the DCP project in Mississippi (George et al. 2000) were predicted and then
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compared to the measured results. The results of the predicted versus the measured Mr for these cohesive soils are shown in Figure 6.
0 40 80 120Measured-Mr (MPa)
0
40
80
120
Pred
icte
d-M
r(M
Pa)
Prediction of data excludedin modeling
Soil 3
Soil 4
Soil 5 (George et al., 2000)
Soil 1 and Soil 2
Prediction of data included in modeling
0 40 80 120Measured-Mr (MPa)
0
40
80
120
Pre
dict
ed-M
r(M
Pa)
Soil property model:
R2 = 0.85, RMSE = 6.3
Direct model:
R2 = 0.82, RMSE = 6.7
(a) (b)
Figure 6. Prediction of Mr for cohesive soils from the DCP results (a) using the direct model (b) using the soil property model
SUMMARY AND CONCLUSIONS
This paper presents the preliminary development of two models to predict the resilient modulus of cohesive soils from the dynamic cone penetration test results, moisture content, dry unit weight, and plasticity index of cohesive soils. Laboratory and field dynamic cone penetration testing programs were conducted on four cohesive soils. In addition, the resilient modulus tests were conducted on these cohesive soils using the repeated loading triaxial cell. Other laboratory tests were also conducted to determine the physical properties and compaction characteristics of soils. Next, results of the laboratory testing programs were analyzed and critically evaluated. Subsequently, two statistical models for predicting the resilient modulus were developed based on the laboratory test results of cohesive soils. These models correlate the resilient modulus to the dynamic cone penetration index and basic soil properties of the investigated soils. The prediction of the resilient modulus of two soils from the field DCP testing program and one soil from the literature (George et al. 2000), which were excluded in the model development and its comparison with
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the results of the laboratory repeated load triaxial resilient modulus measurements validated the models. A good agreement was observed between the predicted and measured values of the resilient modulus. The findings are summarized below:
• Two preliminary estimation models were developed. One model for the prediction of the resilient modulus of cohesive soils from the dynamic cone penetration index. The other model for the prediction of the resilient modulus of cohesive soils from the dynamic cone penetration index, moisture content, dry unit weight, and plasticity index of cohesive soils. The prediction of the separate data sets that were excluded in the development of models confirmed the validation of the models. The predicted resilient modulus values obtained from the proposed models corresponded well with the measured resilient modulus values from the repeated load triaxial test. The applicability of the dynamic cone penetration test results in predicting the resilient modulus of pavement subgrade cohesive soils was demonstrated.
• The proposed resilient modulus estimation models assist to implement the dynamic cone penetration test in evaluating pavement quality control/assurance procedures.
• The dynamic cone penetration test result is influenced by the moisture content, dry unit weight, and soil type. The dynamic cone penetration index increases with the increase in moisture content and it decreases with the increase in dry unit weight.
• The resilient modulus is also influenced by the moisture content, dry unit weight, and soil type. The resilient modulus decreases with the increase in moisture content and it increases with the increase in dry unit weight.
• Both dynamic cone penetration and resilient modulus test procedures follow a similar dynamic loading. They also follow a similar unloading and resting period with minor differences. When correlating test results, the soils for both tests are subjected to the same environmental variations regarding the moisture-unit weight variation and soil type. Despite some minor differences in both test procedures, the proposed correlations were successful.
ACKNOWLEDGEMENT
The Louisiana Department of Transportation and Development (LADOTD) and Federal Highway Administration (FHWA) through the Louisiana Transportation Research Center (LTRC) under contract numbers 02-4B and 03-3P sponsored this research work.
REFERENCES
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