1. SESSION 3
Subgrade
This module presents the concepts and methods of characterizing the subgrade for the purpose of concrete pavement design.
It also highlights some practical aspects of preparing a subgrade for construction.

2. The foundation upon which the pavement and base are constructed
Subgrade
The foundation upon which the pavement and base are constructed
Concrete slab }
Base
Embankment
The term “subgrade” is used commonly to refer to the foundation upon which the base and concrete layers are constructed.
The foundation consists of the natural soil at the site, possibly an embankment (fill) of improved material, and possibly a rigid layer (e.g., bedrock, hard clay) at a depth sufficiently shallow (within 3 m [10 ft]) that it may be significant.
Subgrade
Natural soil
Rigid layer

3. Objectives Characterize subgrade for concrete pavement design purposes
Select appropriate subgrade preparation methods
Identify subgrade remediation measures for protection against frost heave and soil swelling
The objectives of this module are to:
--Describe the concepts and methods of subgrade characterization for concrete pavement design purposes
--Describe subgrade preparation for construction purposes, including protection against frost heave and soil swelling.

4. Subgrade Models Dense liquid ( k ) model Real soil
Dense liquid (k) model of elastic soil response:
--deflection under the plate equals pressure divided by a k value (spring constant)
--deflection = 0 beyond edge of plate
--deflection is the same for rigid and flexible plates
--for a given pressure and deflection, k is independent of plate size
Elastic solid (E) model of elastic soil response:
--deflection depends on soil elastic modulus, plate size, and distance
--deflection basin is continuous and infinite
--rigid and flexible load plates produce different deflections
Between these two idealized extremes lies the elastic response of real soils (unbound sands, silts, and clays) of relatively low shear strength:
--plate punches down somewhat, producing a discontinuous deflection basin
--some surface deflection occurs beyond edge of load plate
--deflection = 0 at some finite distance
--for a given pressure and deflection, k varies with plate size
Real soil
Elastic solid ( E ) model

5. Soil Behavior Elastic response (k or E)
Plastic (permanent) deformation
Time-dependent response
Standardized tests have been developed to differentiate the elastic response from the plastic and time-dependent components
Both the dense liquid (k) and elastic solid (E) models attempt to describe the elastic portion of soil response. Real soils also exhibit plastic response (permanent deformation), and time-dependent response: slow dissipation of porewater pressures under sustained static loading results in larger deflections than rapid dynamic loading
Standardized plate bearing test methods were developed to differentiate the elastic response of soils to static loading from the plastic and time-dependent components.
Also, in real soils, deflection is a function of plate size for small plate sizes. This is because real soils do possess some (albeit low) shear strength, and with small plates, the shear resistance around the perimeter of the plate contributes significantly to the total resistance to deformation. As the plate size becomes larger (the perimeter-to-area ratio decreases), the k asymptotically approaches a value independent of plate size.

6. Static vs. Dynamic k
Static k: the elastic portion of a soil’s response to a static load
Dynamic k: the elastic response to a dynamic load
- a fast-moving wheel load
- an FWD load
These two terms are used a lot and it’s important to understand the difference between them. The static k is the elastic portion of soil response to static loading, as in a plate bearing test or under a load moving at creep speed. The dynamic k is the elastic portion of soil response to dynamic loading, as under a fast-moving wheel load or an FWD load impulse.
Both are elastic (that is, recoverable) but the dynamic k is higher than the static k, because under dynamic loading, porewater pressures cannot dissipate and permit further consolidation. This is especially true of fine-grained soils, although coarse-grained soils also exhibit higher dynamic k values than static k values.
The phenomenon of soil stiffness being greater under dynamic loading is explained by Terzhagi, for example. The idea of a higher k value being used to characterize this stiffer response goes back as far as Westergaard. It did not, however, become a practical concern in characterizing k value until deflection testing became common in recent decades.

7. K value steps, 1986/1993 AASHTO Guide
K of unprotected subgrade soil
Composite (top-of-the-base) k
Adjustment for rigid layer
Seasonal adjustment
Loss-of-support adjustment
These are the five steps in k value determination according to the 1986 AASHTO Guide. The differ in some significant ways from the k value methods which have been evolving since the time of Westergaard, the Arlington Road Tests, and the Corps of Engineers field studies.
--K for unprotected soil: the equation in the AASHTO Guide (k = Mr /19.4) is flawed and we do not recommend its use. We recommend instead the methods presented here and in the 1998 Supplement (correlations, backcalculation, or plate bearing tests).
--Composite k (from nomograph in 1986 AASHTO Guide, or its equations which we have put into the AASHTO Calculator spreadsheet): the composite k concept is not really valid. On the other hand, there’s no other way in the 1986/93 AASHTO method to reflect the potentially beneficial effect of a base on the performance of a concrete slab. The nomograph can produce unrealistically high k values in some cases. We recommend 190 MPa/m (700 psi/in) as the upper limit on static k value.
--Adjustment for rigid layer: conceptually okay, not a practical concern unless the rigid layer is within 3 m (10 ft) depth. More significant practical problem is that the 1986/93 method does not provide an additional adjustment for fill material on top of the natural soil.
--Seasonal adjustment: Conceptually okay, except one thing – the adjustment calculates a seasonally weighted annual average k value, but the AASHTO model for rigid pavements was derived for the AASHO Road Test springtime k value, not the weighted annual average.
--Loss-of-support adjustment: A serious conceptual flaw in the 1986/93 AASHTO design procedure, and if used, produces drastic reductions in k which are unwarranted. The AASHTO performance model is calibrated to the performance of AASHO Road Test pavements which experienced substantial loss of support. We strongly recommend against using any LOS factor other than 0.

8. K value steps, 1998 AASHTO Supplement
K value methods
correlation with soil type and properties
backcalculation
plate bearing tests
Adjustment for fill and/or rigid layer
Seasonal adjustment
These are the three steps in the determination of k value according to the 1998 AASHTO Supplement.
K value methods:
--correlations between soil k values and soil classes, CBR, density, degree of saturation. Note also, Dynamic Cone Penetrometer (DCP) correlates well to CBR for fine-grained soils (CBR less than 12).
--backcalculation from deflection tests on in-service pavements
--plate bearing tests
Adjustment for fill and/or rigid layer: Needed if k is estimated based on soil properties only, or if, for backcalculation and plate bearing test methods, the pavement being tested and pavement being designed are different in terms of (i) soil characteristics, (ii) fill height, and (iii) rigid layer depth.
Seasonal adjustment: determination of a damage-weighted annual average k value. The revised extended AASHTO model given in the 1998 Supplement is calibrated to this damage-weighted annual average k value for the AASHO Road Test site.

9. Plate Bearing Tests Direct measurement of static elastic k value
new alignment
on subgrade soil
on test embankment
existing alignment
remove slab and base
Photo of stacked plates positioned for plate bearing test. Loading plate is 760 mm (30 inches) diameter. Successively smaller plates are stacked on top to minimize plate bending, thus ensuring uniform deflections. Plate deflection is measured at 3 points around loading plate. A heavy load (e.g., water tank or heavy construction vehicle) is needed to produce sufficient deflection to determine the k value.
Plate load testing is the direct method of determining the static, elastic k value used in concrete pavement analysis and design. According to decades of testing by the Bureau of Public Roads and the Corps of Engineers, plate bearing test methods as standardized produce static k values which are consistent with the loading response of soils under full-size concrete slabs.
However, it is labor-intensive, time-consuming, and costly, and therefore rarely done today; instead, correlations are often drawn between k and other soil properties. Thus, most concrete pavement design procedures characterize the subgrade with a property that is rarely measured directly on soils in the field.

10. Plate Bearing Tests Repetitive loading test ASTM D 1195, AASHTO T221
k = slope of pressure to elastic deformation 760-mm (30 in) plate required
In a repetitive plate loading test, loads of increasing magnitude are slowly applied and slowly released, and the total and plastic deformations are measured each time. The elastic deformation is the total minus the plastic. The k value is defined as the average ratio of pressure to elastic deformation for the series of loads applied.
k = mean p / De
Plate pressure, p Dp De
Deflection, D

11. Plate Bearing Tests Nonrepetitive loading test
ASTM D 1196, AASHTO T222
k = pressure/deformation ratio at 1.25 mm (0.05 in)
760-mm (30 in) plate required
A nonrepetitive test takes less time than a repetitive test, but without going through an unloading cycle to determine the plastic deformation, how does one define the k value? Extensive testing by the Corps of Engineers established that the ratio of pressure to deflection at a deflection level of 1.25 mm [0.05 in] yields a k value consistent with that which would be obtained in a repetitive test.
However, sometimes in the literature you will come across references to defining k at a pressure of 68.9 kPa (10 psi) instead of 1.25 mm (0.05 in) deflection. Where did the idea of defining k at 68.9 kPa (10 psi) rather than 1.25 mm (0.05 in) come from? The PCA, when it conducted plate bearing tests on cement-treated bases in the 1960s. Since it was too difficult to produce a 1.25-mm (0.05-in) deflection on a cement-treated base with the available loading equipment, a pressure level of 68.9 kPa (10 psi) was selected as the defining criterion. This does not appear, however, in either the ASTM or AASHTO standard test methods.
k = p / D
Plate pressure, p
D = 1.25 mm (0.05 in)
Deflection, D

12. Correlation of k to Soil Properties
Soil Class Density CBR k
A-1-a, well graded
A-1-a, poorly graded
… … …
A-2-4 or 5, gravelly
A-2-4 or 5, sandy
… … … …
A-4, silt
A-4, mix
… … … …
Table 4 , page 13 in the Technical Digest presents the correlations of k to all soil classes, as well as soil descriptions, CBR ranges, and dry density ranges. This table summarizes the correlation recommendations of the Bureau of Public Roads, Corps of Engineers, Portland Cement Association, and the Zero-Maintenance design manual.
The bearing capacity of coarse-grained cohesionless soils (A-1 and A-3) is primarily a function of the shear modulus G, which is in turn a function of elastic modulus, Poisson’s ratio, void ratio, and all-around confining pressure. The bearing capacity of these materials is relatively insensitive to moisture variation.
Coarse-grained soils with high fines (the A-2s) are diverse in their gradation characteristics and difficult to characterize. Some are stress-hardening while others are stress-softening. The nature of the fines is not a good indicator of k value. Field data indicate that in terms of bearing capacity, A-2 soils tend to behave like A-1 or A-3 soils of comparable density.
The bearing capacity of fine-grained cohesive soils (A-4 through A-7) is strongly influenced by their degree of saturation, which is a function of the dry density, water content, and specific gravity. This is shown on the next slide.

13. Degree of Saturation Affects k of Fine-Grained Soils50
100
150
200
250 60 70 80 90
Degree of saturation (percent)
Subgrade k value (psi/in)
A-6
A-7-6
A-7-5
A-5
A-4
This figure shows the effect of degree of saturation on k value of fine-grained soils. There is a band of approximately kPa ( + 40 psi) around each line.

14. Dynamic Cone Penetrometer (DCP)
One increasingly popular method of determining subgrade soil properties is through the use of a dynamic (or drop) cone penetrometer (DCP). This device, which is used on in place soils, has a weight that is dropped, driving the rod (which is tipped with a metal cone) into the soil. The dropping of the weight is repeated, and the penetration of the device is measured using a graduated rod. The penetration rate (mm/blow) is then used in established correlations to determine the CBR of the subgrade. The CBR can then be used to estimate a static, elastic k-value. Automated DCPs are also now available.
Major advantages of this test is that it is done on in place soils, it can be performed relatively quickly and inexpensively, and it thus it can be used to provide more extensive testing on a project.

15. Backcalculation of k Falling Weight Deflectometer (FWD)
existing pavement
new alignment on similar soil
Photo of falling weight deflectometer, with load masses visible, and load plate and deflection sensors lifted up off the pavement. Briefly explain the testing sequence: lowering the plate and sensor bar, a small load drop to seat the plate, and then a series of loads applied by lifting the masses up to one or more heights and dropping them one ore more times. The load impulse is about milliseconds. All load and deflection data are recorded by computer, along with a distance measurement for stationing. Loads in the range of kN (5,650-15,750 lbs) are typical for highway testing. Heavyweight FWDs (for airport testing) can produce loads up to 250 kN (56,250 lbs).
Deflection measurement should be done on slabs which are uncracked, at least within the radius of the deflection basin measurements. Slab size corrections may be necessary for deflections measured on small or cracked slabs.

16. Backcalculation of k
Photo of FWD showing load plate and deflection sensors lowered onto pavement. Not visible is the sensor at the center of the load plate which measures the maximum deflection.

17.  Backcalculation of k Westergaard’s interior deflection equation:P
D = {  ( a /  ) }
k 2
 = radius of relative stiffness:
E h3
 =
12 ( 1 - 2 ) k
All k-value backcalculation equations and algorithms really boil down to this simple technique: using Westergaard’s equation for deflection (as a function of load, k, radius of relative stiffness, and load radius) and rearranging it to solve for k from a measured deflection.
To do this you need to know the measured deflection D, the load P, the load radius a, and the radius of relative stiffness. But you don’t need to know the slab modulus and thickness and subgrade k to know l, because, for a given load radius and sensor configuration, there is a unique relationship between the deflection basin AREA and the radius of relative stiffness.
AREA is the cross-sectional area of the deflection basin within the radii of the measured deflections (e.g., 0 to 36 inches), calculated by the trapezoidal rule, with all deflections normalized with respect to the maximum deflection to eliminate the effect of load level. AREA thus has dimensions of length, not area. See equation 1, page 15, Technical Digest.  4

18. Backcalculation of k Load, P radius, a Deflection, D
Figure 3, page 15 in the Technical Digest. This chart, which appears in the 1993 AASHTO Guide, is simply a graphical representation of Westergaard’s interior deflection equation, for a load level of 40 kN (9,000 lbs), a load radius of 150 mm (5.91 in) (the FWD load plate) and a sensor configuration of four sensors, at 0, 305, 610, and 914 mm (0, 12, 24, and 36 in) from the center of the load plate.
Variations on the main theme:
--AREA -  equations for other specific sensor configurations (SHRP, Air Force seven-sensor, outer AREAs excluding D0 , for AC-overlaid pavements and very thick slabs, etc.)
--Solutions using Westergaard’s edge and corner deflection equations
--Corrections for finite slab size
--Decomposition of the backcalculated E of the pavement into the component E values : concrete and base, or concrete and overlay
AREA = f (), for given sensor configuration

19. Adjustments to Backcalculated k Value
Slab size adjustment usually needed
Static k value needed for design:
approximately = dynamic k / 2
Different backcalculation equations for deflections measured on AC-overlaid PCC
Variations in embankment thickness and/or rigid layer depth affect k
Adjustments needed to backcalculated k results in order to obtain appropriate static k value for concrete pavement design:
--slab size adjustment
--divide dynamic k by two to obtain reasonable estimate of static k
--use appropriate backcalculation equations when testing on pavement with existing AC overlay
--adjust if necessary for design situation with embankment thickness and/or rigid layer depth significantly different than those of pavement tested

20. Embankment and/or Rigid Layer
Adjustment for embankment and/or rigid layer. Figure 2, page 14, Technical Digest. K may increase by factor of up to 2 when rigid layer is present at depth within 3 m (10 ft). At greater depths, no significant effect. Embankment adjustment depends on embankment thickness and embankment material, which is conveniently represented by its dry density.

21. Seasonal Adjustment 1998 AASHTO Supplement:
- seasonal movement of water table
- seasonal precipitation levels
- winter frost depths
- freeze-thaw cycles
- frost protection
1986/1993 AASHTO Guide
- annual average, or springtime?
Factors which the designer should consider when assigning k values to the distinct seasons of the year.
Should a seasonally adjusted k value be used in the 1986/1993 procedure, or the springtime k value? It’s an interesting philosophical point (the springtime value is probably more appropriate), but not a huge practical concern, because the procedure is not very sensitive to k value, at least for k values of 27 MPa/m (100 psi/in) or more.

22. Subgrade Preparation Foundation must provide: Assumed stiffness
Uniformity
Long-term stability
Stable construction platform
Has significant influence on smoothness
Typically achieved by monitoring density and moisture content during compaction
To ensure satisfactory concrete pavement performance, the subgrade must be prepared so as to provide the stiffness which was assumed in design, uniformity, long-term stability, and a stable platform for construction of the base and slab.
The uniformity of the foundation has a significant influence on the smoothness achieved in construction of the slab.
In the United States, these objectives are usually achieved by monitoring density and moisture content during compaction. Dynamic cone penetrometer (DCP) testing is also used sometimes. In some other countries, other methods such as small-plate testing and proof rolling are used.

23. Subgrade Improvement
Excavation and recompaction with moisture density control
Mechanical improvement (mixing in coarser material)
Excavation and replacement with select fill
Stabilization (with lime, cement, lime-flyash, asphalt)
Reinforcement with geosynthetics
Measures which can be employed to improve a subgrade to achieve the desired stiffness and stability, roughly in order of increasing cost.

24. Frost Heave Formation of ice lenses in frost-susceptible soils
- fine sands and silts
- low-plasticity clays
Both winter frost heave and subsequent spring thaw can cause pavement cracking
Soils freeze when freezing temperatures penetrate down into the pavement structure and encounter moisture in the unbound layers. Frost heave is a problem in areas with significant winter frost penetration, such as the northern United States. Silts are perhaps the most frost-susceptible soils because of their capacity to pull and hold water to considerable heights above the water table. Sands have much less suction potential because they are low in fines, and highly plastic clays, although fine-grained, have very low permeability (moisture movement is inhibited).
Both winter frost heave and subsequent settlement due to spring thaw can cause cracking.

25. Frost Protection
Replacing frost-susceptible soil with non-frost-susceptible within depth of frost penetration
Covering frost-susceptible soil with sufficient thickness of non-frost-susceptible soil
Factors to consider: drainage, change of grade, side slopes and ditches
Frost protection options: remove and replace, or cover, depending on grade restrictions. Cross-section features which will help drain the foundation will also help protect against frost damage.

26. Swelling Soils
Some clays and shales are susceptible to swelling (significant volume increase) when sufficient moisture is available, especially when an overburden pressure is removed
- southern and western US
- dry climates, low soil moisture contents
- pavement inhibits evaporation from soil
- excavation reduces overburden
Swelling causes heaving and cracking
Swelling is a natural response of consolidated clays to a reduction in applied pressure, when moisture is available to permit an increase in void ratio. Some clays and shales (layered sedimentary rock) are susceptible to to rather large volume changes. Soil swelling is particularly problem in the southern and western United States, where these soils are prevalent, and the climate is arid (so soil moisture contents are low).
A reduction in overburden pressure due to excavation, and/or an increase in soil moisture content, can cause soil swelling.

27. Swelling Protection
Avoid cut sections in soils with known swelling potential
Avoid overcompaction on dry side of optimum moisture content
Lime stabilization to adequate depth may be useful
Minimize moisture variation (moisture barriers or geomembranes may help)
Methods for attempting to control soil swelling are described here.

28. Collapsing Soils
Soils experiencing large decrease in volume with increases in water content
Treatment methods
Modest depths: compaction with rollers, wetting or inundation, and overexcavation and recompaction (with lime or cement)
Thicker deposits: ponding, flooding, dynamic compaction
Collapsing soils are soils with a large void content in the dry state, but undergo a very large decrease in volume if their water content increases significantly. Susceptible soils are loessial soils, weakly cemented sands and silts, and certain residual soils. Many collapsible soil deposits are associated with dry or semi-arid climates, while others are commonly found on flood plains.
Treatment methods for collapsible soils depend on the depth of the soil deposits:
--For modest depths, compaction with rollers, wetting or inundation, and overexcavation and recompaction, sometimes with lime or cement stabilization.
--For thicker deposits, ponding or flooding are ordinarily very effective, as is dynamic compaction.

29. Summary Foundation: soil, embankment, rigid layer
k value model works well for concrete pavements
Real soils exhibit some shear strength, elastic and plastic behavior, time-dependent response
Various methods for determining design k
Prepare subgrade to achieve stiffness, uniformity, long-term stability, stable construction platform, protection against frost and swelling
In summary: in this module we’ve described what makes up the foundation of a pavement, and how we characterize that foundation by a k value for the purpose of concrete pavement design. We recognize that real soils are not ideal dense liquids, but the dense liquid model suits our purposes far better than the elastic solid model.
We also described some practical considerations in preparing a subgrade so that it will provide the stiffness, stability, and uniform support desired: compaction and density control during construction, protection against frost heave, and protection against swelling.