2  Subgrade

Although a pavement's wearing course is most prominent, the success or failure of a pavement is more often than not dependent upon the underlying subgrade (see Figures 4.1 and 4.2) - the material upon which the pavement structure is built.  Subgrades be composed of a wide range of materials although some are much better than others.  This subsection discusses a few of the aspects of subgrade materials that make them either desirable or undesirable and the typical tests used to characterize subgrades.

Figure 4.1: Subgrade Preparation	Figure 4.2: Subgrade Failure Crack

2.1 Subgrade Performance

A subgrade’s performance generally depends on three of its basic characteristics (all of which are interrelated):

1. Load bearing capacity.  The subgrade must be able to support loads transmitted from the pavement structure.  This load bearing capacity is often affected by degree of compaction, moisture content, and soil type.  A subgrade that can support a high amount of loading without excessive deformation is considered good. 
2. Moisture content.  Moisture tends to affect a number of subgrade properties including load bearing capacity, shrinkage and swelling.  Moisture content can be influenced by a number of things such as drainage, groundwater table elevation, infiltration, or pavement porosity (which can be assisted by cracks in the pavement).  Generally, excessively wet subgrades will deform excessively under load.
3. Shrinkage and/or swelling.  Some soils shrink or swell depending upon their moisture content.  Additionally, soils with excessive fines content may be susceptible to frost heave in northern climates.  Shrinkage, swelling and frost heave will tend to deform and crack any pavement type constructed over them.

Poor subgrade should be avoided if possible, but when it is necessary to build over weak soils there are several methods available to improve subgrade performance:

• Removal and replacement (over-excavation).  Poor subgrade soil can simply be removed and replaced with high quality fill.  Although this is simple in concept, it can be expensive.  Table 4.1 shows typical over-excavation depths recommended by the Colorado Asphalt Pavement Association (CAPA).

Table 4.1: Over-Excavation Recommendations (from CAPA, 2000)

Table 4.2: Some Stabilization Recommendations (from CAPA, 2000)

In sum, subgrade characteristics and performance are influential in pavement structural design.  Characteristics such as load bearing capacity, moisture content and expansiveness will influence not only structural design but also long-term performance and cost.

2.2  Stiffness/Strength Tests

Subgrade materials are typically characterized by their resistance to deformation under load, which can be either a measure of their strength (the stress needed to break or rupture a material) or stiffness (the relationship between stress and strain in the elastic range or how well a material is able to return to its original shape and size after being stressed).  In general, the more resistant to deformation a subgrade is, the more load it can support before reaching a critical deformation value.  Three basic subgrade stiffness/strength characterizations are commonly used in the U.S.: California Bearing Ratio (CBR), Resistance Value (R-value) and elastic (resilient) modulus.  Although there are other factors involved when evaluating subgrade materials (such as swell in the case of certain clays), stiffness is the most common characterization and thus CBR, R-value and resilient modulus are discussed here.

2.2.1  California Bearing Ratio (CBR)

The California Bearing Ratio (CBR) test is a simple strength test that compares the bearing capacity of a material with that of a well-graded crushed stone (thus, a high quality crushed stone material should have a CBR @ 100%).  It is primarily intended for, but not limited to, evaluating the strength of cohesive materials having maximum particle sizes less than 19 mm (0.75 in.) (AASHTO, 2000).  It was developed by the California Division of Highways around 1930 and was subsequently adopted by numerous states, counties, U.S. federal agencies and internationally.  As a result, most agency and commercial geotechnical laboratories in the U.S. are equipped to perform CBR tests.

The basic CBR test involves applying load to a small penetration piston at a rate of 1.3 mm (0.05") per minute and recording the total load at penetrations ranging from 0.64 mm (0.025 in.) up to 7.62 mm (0.300 in.).  Figure 4.3 is a sketch of a typical CBR sample.

Figure 4.3: CBR Sample

Values obtained are inserted into the following equation to obtain a CBR value:

Table 4.3 shows some typical CBR ranges.

Table 4.3: Typical CBR Ranges

Standard CBR test methods are:

2.2.2  Resistance Value (R-value)

The Resistance Value (R-value) test is a material stiffness test.  The test procedure expresses a material's resistance to deformation as a function of the ratio of transmitted lateral pressure to applied vertical pressure.  It is essentially a modified triaxial compression test.  Materials tested are assigned an R-value.

The R-value test was developed by F.N. Hveem and R.M. Carmany of the California Division of Highways and first reported in the late 1940's.  During this time rutting (or shoving) in the wheel tracks was a primary concern and the R-value test was developed as an improvement on the CBR test.  Presently, the R-value is used mostly by State Highway Agencies (SHAs) on the west coast of the U.S.

The test procedure to determine R-value requires that the laboratory prepared samples are fabricated to a moisture and density condition representative of the worst possible in situ condition of a compacted subgrade.  The R-value is calculated from the ratio of the applied vertical pressure to the developed lateral pressure and is essentially a measure of the material's resistance to plastic flow.  The testing apparatus used in the R-value test is called a stabilometer (identical to the one used in Hveem HMA mix design) and is represented schematically in Figure 4.4.

Values obtained from the stabilometer are inserted into the following equation to obtain an R-value:

Some typical R-values are:

• Well-graded (dense gradation) crushed stone base course: 80+

• MH silts: 15-30

Standard R-Value test methods are:

• AASHTO T 190 and ASTM D 2844: Resistance R-Value and Expansion Pressure of Compacted Soils

2.2.3  Resilient Modulus

The Resilient Modulus (M_R) is a subgrade material stiffness test.  A material's resilient modulus is actually an estimate of its modulus of elasticity (E).  While the modulus of elasticity is stress divided by strain (e.g., the slope of the Figure 4.5 plot within the linear elastic range) for a slowly applied load, resilient modulus is stress divided by strain for rapidly applied loads – like those experienced by pavements.  This subsection discusses:

• Elastic modulus and its relationship with resilient modulus
• Nomenclature and symbols
• Stress sensitivity of moduli
• Typical values
• The triaxial resilient modulus test
• Elastic modulus correlations

  .  Although they measure the same stress-strain relationship, the load application rates are different, thus resilient modulus is considered an estimate of elastic modulus. 

2.2.3.1  Elastic Modulus

Elastic modulus is sometimes called Young's modulus after Thomas Young who published the concept back in 1807.  An elastic modulus (E) can be determined for any solid material and represents a constant ratio of stress and strain (a stiffness):

A material is elastic if it is able to return to its original shape or size immediately after being stretched or squeezed.  Almost all materials are elastic to some degree as long as the applied load does not cause it to deform permanently.  Thus, the "flexibility" of any object or structure depends on its elastic modulus and geometric shape. 

The modulus of elasticity for a material is basically the slope of its stress-strain plot within the elastic range (as shown in Figure 4.5).  Figure 4.6 shows a stress versus strain curve for steel.  The initial straight-line portion of the curve is the elastic range for the steel.  If the material is loaded to any value of stress in this part of the curve, it will return to its original shape.  Thus, the modulus of elasticity is the slope of this part of the curve and is equal to about 207,000 MPa (30,000,000 psi) for steel.  It is important to remember that a measure of a material's modulus of elasticity is not a measure of strength.  Strength is the stress needed to break or rupture a material (as illustrated in Figure 4.5), whereas elasticity is a measure of how well a material returns to its original shape and size.

Figure 4.5: Stress-Strain Plot Showing the Elastic Range

Figure 4.6: Example Stress-Strain Plot for Steel

2.2.3.2  Nomenclature and Symbols

The nomenclature and symbols from the 1993 AASHTO Guide is generally used in referring to pavement moduli. For example:

2.2.3.3  Stress Sensitivity of Moduli

Changes in stress can have a large impact on resilient modulus. "Typical" relationships are shown in Figures 4.7 and 4.8.

Figure 4.7: Resilient Modulus vs. Bulk Stress for Unstabilized Coarse Grained Materials

Figure 4.8: Resilient Modulus vs. Deviator Stress for Unstabilized Fine Grained Materials

2.2.3.4 Typical Values

Tables 4.4 shows typical values of modulus of elasticity for various materials.

Table 4.4: Typical Modulus of Elasticity Values for Various Materials

2.2.3.5  Triaxial Resilient Modulus Test

There are two fundamental approaches to estimating elastic moduli – laboratory tests and field deflection data/backcalculation.  This section discusses laboratory tests.  Of the laboratory tests, two are noted:

• Diametral resilient modulus.  This test is typically used on HMA and is covered in Module 5, Section 6, HMA Performance Tests.  
• Triaxial resilient modulus.  This test is typically used on unbound materials such as soil and aggregate and is covered here.

In a triaxial resilient modulus test a repeated axial cyclic stress of fixed magnitude, load duration and cyclic duration is applied to a cylindrical test specimen.  While the specimen is subjected to this dynamic cyclic stress, it is also subjected to a static confining stress provided by a triaxial pressure chamber.  The total resilient (recoverable) axial deformation response of the specimen is measured (see Figure 4.9) and used to calculate the resilient modulus using the following equation:

The standard triaxial resilient modulus test is:

• AASHTO T 292: Resilient Modulus of Subgrade Soils and Untreated Base/Subbase Materials

2.2.4  Strength/Stiffness Correlations

A widely used empirical relationship developed by Heukelom and Klomp (1962) and used in the 1993 AASHTO Guide is:

E_SG (or M_R) = (1500) (CBR)

This equation is restricted to fine grained materials with soaked CBR values of 10 or less.  Like all such correlations, it should be used with caution.

The proposed new AASHTO Design Guide will likely use the following relationship:

M_R = 2555 x CBR^0.64

The 1993 AASHTO Guide offers the following correlation equation between R-value and elastic modulus for fine-grained soils with R-values less than or equal to 20.

E_SG (or M_R) = 1,000 + (555)(R-value)

2.3  Modulus of Subgrade Reaction (k)

The modulus of subgrade reaction (k) is used as a primary input for rigid pavement design.  It estimates the support of the layers below a rigid pavement surface course (the PCC slab).  The k-value can be determined by field tests or by correlation with other tests. There is no direct laboratory procedure for determining k-value. 

The modulus of subgrade reaction came about because work done by Westergaard during the 1920s developed the k-value as a spring constant to model the support beneath the slab (see Figure 4.10).

Figure 4.10: Modulus of Subgrade Reaction (k)

The reactive pressure to resist a load is thus proportional to the spring deflection (which is a representation of slab deflection) and k (see Figure 4.11):

Figure 4.11: Relation of Load, Deflection and Modulus of Subgrade Reaction (k)

The value of k is in terms of MPa/m (pounds per square inch per inch of deflection, or pounds per cubic inch - pci) and ranges from about 13.5 MPa/m (50 pci) for weak support, to over 270 MPa/m (1000 pci) for strong support.  Typically, the modulus of subgrade reaction is estimated from other strength/stiffness tests, however, in situ values can be measured using the plate bearing test.

Figure 4.12: Plate Load Test Schematic
	Figure 4.13: Plate Load Test

The 1993 AASHTO Guide offers the following relationship between k-values from a plate bearing test and resilient modulus (M_R):

The standard plate bearing test is:

2.4  Summary

Subgrade properties are essential pavement design parameters.  Materials typically encountered in subgrades are characterized by their strength and their resistance to deformation under load (stiffness).  In the U.S. the CBR, R-value and resilient modulus are commonly used to characterize subgrade materials.  Although each method is useful, the resilient modulus is most consistent with other disciplines and is gaining widespread use in pavement design.  The modulus of subgrade reaction (k) is the subgrade characterization used in rigid pavement design.  It can be estimated from CBR, R-value or elastic modulus, or calculated from field tests like the plate bearing test.