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Geotechnical Aspects of Pavements Reference Manual

Chapter 5.0 Geotechnical Inputs For Pavement Design (continued)

5.5 Thermo-Hydraulic Properties

Thermo-hydraulic material properties are required to evaluate the temperature and moisture conditions in a pavement system and their effects on the material behavior. Temperature has significant effects on the stiffness of asphalt concrete, and temperature gradients can induce thermal curling and stresses in rigid pavement slabs. Moisture content influences the stiffness and strength of unbound materials, and moisture gradients can induce warping of rigid pavement slabs. Combined temperature and moisture effects can cause detrimental freeze/thaw cycles in unbound materials.⁵

The empirical 1993 AASHTO Design Guide and the mechanistic-empirical NCHRP 1-37A design procedure have drastically different input requirements for thermo-hydraulic properties. The thermo-hydraulic design inputs in the 1993 AASHTO Guide are largely empirical coefficients grouped in the following categories:

• Drainage coefficients (for unbound layers)
• Swelling parameters (for expansive subgrade soils)
• Frost heave parameters (for frost-susceptible subgrade soils)

These empirical properties in the 1993 Guide often mix material property and climate factors. For example, drainage coefficients are functions of both climate-determined moisture conditions and material-related drainage quality.

The thermo-hydraulic properties required as input to the NCHRP 1-37A Design Guide tend to be more fundamental material properties. These include:

• Groundwater table depth
• Infiltration and drainage properties
• Physical properties
• Soil water characteristic curve
• Hydraulic conductivity (permeability)
• Thermal conductivity
• Heat capacity

These thermo-hydraulic properties are used in the mechanistic Enhanced Integrated Climate Model (EICM) along with climate inputs (discussed separately in Section 5.6) to predict temperature and moisture distributions in the pavement as functions of depth and time. Appendix D provides details on algorithms embedded in the EICM.

Because of the substantial differences in these thermo-hydraulic inputs to the two design methods, each design method is discussed separately in the following subsections.

5.5.1 1993 AASHTO Guide

The environment-related aspects in the 1993 AASHTO Design Guide are grouped into two general categories: drainage and subgrade swelling/frost heave. As described in Section 3.5.2 in Chapter 3, drainage is incorporated via adjustment to the unbound structural layer coefficients for flexible pavements or via a drainage factor in the design equation for rigid pavements. Swelling and/or frost heave, on the other hand, is incorporated via a partitioning of the total allowable serviceability loss ΔPSI; part of ΔPSI is allocated to environment-induced deterioration due to swelling and/or frost heave, and the remainder of ΔPSI is allocated to traffic-induced deterioration.

Drainage Coefficients

The 1993 AASHTO Guide provides guidance for the design of subsurface drainage systems and modifications to the flexible and rigid pavement design procedure to take advantage of improvements in performance due to good drainage. For flexible pavements, the benefits of drainage are incorporated into the structural number via empirical drainage coefficients:

(5.40)

SN = a₁D₁ + a₂D₂m₂ + a₃D₃m₃

in which m₂ and m₃ are the drainage coefficients for the base and subbase layers, respectively, and all other terms are as defined previously. Table 5-49 summarizes the recommended values for m_i in the 1993 AASHTO Guide as functions of qualitative descriptions of drainage quality and climate conditions.

For rigid pavements, the benefits of drainage are incorporated via an empirical drainage coefficient C_d in the rigid pavement design equation. Table 5-50 summarizes the recommended values for C_d in the 1993 AASHTO Guide as a function of qualitative descriptions of drainage quality and climate conditions.

Table 5-49. Recommended m_i values for modifying structural layer coefficients of untreated base and subbase materials in flexible pavements (AASHTO, 1993).

Quality of Drainage	Water Removed Within	Percent of Time Pavement is Exposed to Moisture Levels Approaching Saturation
		< 1%	1-5%	5-25%	> 25%
Excellent	2 hours	1.40-1.35	1.35-1.30	1.30-1.20	1.20
Good	1 day	1.35-1.25	1.25-1.15	1.15-1.00	1.00
Fair	1 week	1.25-1.15	1.15-1.05	1.00-0.80	0.80
Poor	1 month	1.05-0.80	1.05-0.80	0.80-0.60	0.60
Very Poor	no drainage	0.95-0.75	0.95-0.75	0.75-0.40	0.40

Table 5-50. Recommended values of drainage coefficient C_d values for rigid pavement design (AASHTO, 1993).

Quality of Drainage	Water Removed Within	Percent of Time Pavement is Exposed to Moisture Levels Approaching Saturation
		< 1%	1-5%	5-25%	> 25%
Excellent	2 hours	1.25-1.20	1.20-1.15	1.15-1.10	1.10
Good	1 day	1.20-1.15	1.15-1.10	1.10-1.00	1.00
Fair	1 week	1.15-1.10	1.10-1.00	1.00-0.90	0.90
Poor	1 month	1.10-1.00	1.00-0.90	0.90-0.80	0.80
Very Poor	no drainage	1.00-0.90	0.90-0.80	0.80-0.70	0.70

Swelling Parameters

The 1993 AASHTO Guide includes three empirical parameters for estimating potential serviceability loss due to swelling:

• Swell rate constant θ
• Potential vertical rise V_R
• Swell probability P_S

The swell rate constant θ is used to estimate the rate at which swelling will take place. It varies between 0.04 and 0.20, with higher values appropriate for soils exposed to a large moisture supply either due to high rainfall, poor drainage, or some other source. Figure 5-33 provides a nomograph for subjectively estimating the rate of subgrade soil swelling based upon qualitative descriptions of moisture supply and soil fabric. Little guidance beyond that in Figure 5-33 is provided in the 1993 Guide for estimating the values for moisture supply and soil fabric.

The potential vertical rise V_R is a measure of the vertical expansion that may occur in the subgrade soil under extreme swell conditions. Although it is possible to measure V_R from laboratory swell tests, this is not commonly done in practice. Instead, V_R is estimated using the chart in Figure 5-34 based on the soil's plasticity index, moisture condition, and overall thickness of the layer. The moisture condition is a subjective estimate of the difference between the in-situ moisture conditions during construction and moisture conditions at a later date.

The swell probability (P_S) is a measure of the proportion (percent) of the project length that is subject to swell. The probability of swelling at a given location is assumed to be 100% if the subgrade soil plasticity index is greater than 30 and the layer thickness is greater than 2 feet (or if V_R is greater than 0.20 inches). These criteria can be used to separate the project length into swelling and nonswelling sections, from which a length-averaged estimate of P_S can be determined.

These three swelling parameters are used in a nomograph (see Appendix C) along with the design life to determine the expected serviceability loss due to swelling ΔPSI_SW. However, it should be clear from the empirical and highly subjective procedures used to determine the input parameters that the predicted ΔPSI_SW will be only a very approximate estimate.

Figure 5-33. Nomograph for estimating swell rate constant (AASHTO, 1993).
Click here for text version of image

Notes: Low Moisture Supply Low rainfall Good drainage High Moisture Supply High rainfall Poor drainage Vicinity of culverts, bridge abutments, inlet leads Soil Fabric Conditions (self explanatory) Use of the Nonograph Select the appropriate moisture supply condition which may be somewhere between low and high (such as A). Select the appropriate soil fabric (such as B). This scale must be developed by each individual agency. Draw a straight line between the selected points (A to B). Read swell rate constant from diagonal axis (read 0.10).

Figure 5-34. Chart for estimating potential vertical rise of natural soils (AASHTO, 1993).

Notes: This figure is predicated upon the following assumptions: The subgrade soils for the thickness shown are all passing the No. 40 mesh sieve. The subgrade soil has a uniform moisture content and plasticity index throughout the layer thickness for the conditions shown. A surcharge pressure from 20 inches of overburden (± 10 inches will have no material effect). Calculations are required to determine VR for other surcharge pressures.

Frost Heave Parameters

The 1993 AASHTO Guide includes three empirical parameters for estimating potential serviceability loss due to frost heave:

• Frost heave rate φ
• Maximum potential serviceability loss ΔPSI_MAX
• Frost heave probability P_F

The frost heave rate φ is a measure of the rate of increase of frost heave in millimeters per day. The rate of frost heave depends on the type of subgrade material, in particular the percentage of fine-grained material. Figure 5-35 can be used to estimate the rate of frost heave based on the USCS class for the subgrade and the percentage of material finer than 0.02 mm.

The maximum potential serviceability loss ΔPSI_MAX due to frost heave is dependent on the quality of drainage and the depth of frost penetration. Figure 5-36 can be used to estimate the maximum potential serviceability loss due to these two factors. The drainage quality parameter in Figure 5-36 is the same as that used to define the drainage coefficients in Table 5-49 and Table 5-50. See Yoder and Witczak (1975) for methods for determining the depth of frost penetration.

The frost heave probability P_F is the designer's estimate of the percentage length of the project that will experience frost heave. This estimate will depend upon the extent of frost-susceptible subgrade material, moisture availability, drainage quality, number of freeze-thaw cycles during the year, and the depth of frost penetration. Past experience is valuable here, as there is no clear method for approximating the frost heave probability.

These three frost heave parameters are used in a nomograph (see Appendix C) along with the design life to determine the expected serviceability loss due to frost heave ΔPSI_FH. However, it should be clear from the empirical and highly subjective procedures used to determine the input parameters that the predicted ΔPSI_FH will be only a very approximate estimate.

Figure 5-35. Chart for estimating frost heave rate for subgrade soil (AASHTO, 1993).

Figure 5-36. Graph for estimating maximum serviceability loss due to frost heave (AASHTO, 1993).

5.5.2 NCHRP 1-37A Design Guide

The thermo-hydraulic properties required as input to the NCHRP 1-37A Design Guide can be grouped into the following categories:

• Groundwater depth
• Infiltration and drainage properties
• Physical/index properties
• Soil water characteristic curve
• Hydraulic conductivity (permeability)
• Thermal conductivity
• Heat capacity

Methods for determining the design inputs in each of these categories are described in the following subsections. In some cases, the design inputs are determined by direct measurement in the laboratory or the field. However, other design inputs (e.g., soil water characteristic curve) are much less commonly measured in geotechnical practice. Recognizing this, the NCHRP 1-37A project team expended substantial effort to develop robust correlations between these properties and other more conventional soil properties (e.g., gradation and plasticity). These correlations are also detailed in the following subsections as appropriate.

Groundwater Depth

The groundwater depth plays a significant role in the NCHRP 1-37A Design Guide predictions of moisture content distributions in the unbound pavement materials and thus on the seasonal resilient modulus values. The input value is intended to be the best estimate of the annual average groundwater depth. Groundwater depth can be determined from profile characterization borings during design (see Section 4.7.1) or estimated. The county soil reports produced by the National Resources Conservation Service can often be used to develop estimates of groundwater depth.

Infiltration and Drainage

Three input parameters related to infiltration and drainage are required in the NCHRP 1-37A design methodology:

• Amount of infiltration
• Pavement cross slope
• Drainage path length

Amount of Infiltration

The amount of infiltration will be a function of rainfall intensity and duration (determined from the climate inputs, see Section 5.6), pavement condition, shoulder type, and drainage features. The NCHRP 1-37A Design Guide qualitatively divides infiltration into four categories, as summarized in Table 5-51. These categories are used at all hierarchical input levels. The infiltration category is based upon shoulder type, generally the largest single source of moisture entry into the pavement structure, and edge drains, since these shorten the drainage path and provide a positive drainage outlet. Note that if a drainage layer is present in addition to edge drains, its influence is automatically accounted for within the EICM moisture calculations.

Table 5-51. Infiltration categories in the NCHRP 1-37A Design Guide (NCHRP 1-37A, 2004).

Infiltration Category	Conditions	% Precipitation Entering Pavement
None		0
Minor	This option is valid when tied and sealed concrete shoulders (rigid pavements), widened PCC lanes, or full-width AC paving (monolithic main lane and shoulder) are used or when an aggressive policy is pursued to keep the lane-shoulder joint sealed. This option is also applicable when edge drains are used.	10
Moderate	This option is valid for all other shoulder types, PCC restoration, and AC overlays over old and cracked existing pavements where reflection cracking will likely occur.	50
Extreme	Generally not used for new or reconstructed pavement levels.	100

Most designs and maintenance activities, especially for higher functional class pavements, should strive to achieve zero infiltration or reduce it to a minimum value. This can be done by proper design of surface drainage elements (cross slopes, side ditches, etc.), adopting construction practices that reduce infiltration (e.g., eliminating cold lane/shoulder joints, use of tied joints for PCC pavements, etc.), proactive routine maintenance activities (e.g., crack and joint sealing, surface treatments, etc.), and providing adequate subsurface drainage (e.g., drainage layers, edge drains). Chapter 7 provides more information on pavement drainage systems.

Pavement Cross Slope

The pavement cross slope is the slope of the surface perpendicular to the direction of traffic. This input is used in computing the drainage path length, as described in the next subsection.

Drainage Path Length

The drainage path length is the resultant of the cross and longitudinal slopes of the pavement. It is measured from the highest point in the pavement cross section to the drainage outlet. This input is used in the EICM's infiltration and drainage model to compute the time required to drain an unbound base or subbase layer from an initially wet condition.

The DRIP computer program (Mallela et al., 2002) can be used to compute the drainage path length based on pavement cross and longitudinal slopes, lane widths, edge drain trench widths (if applicable, and cross section crown and superelevation). The DRIP program is provided as part of the NCHRP 1-37A Design Guide software.

Physical Properties

Several physical properties are required for the internal calculations in the EICM. For unbound materials, these are:

• Specific gravity of solids G_s (see Table 5-10)
• Maximum dry unit weight γ_{d max} (see Table 5-13)
• Optimum gravimetric moisture content w_opt (see Table 5-13)

Table 5-52 describes the procedures to obtain these physical property inputs for hierarchical input levels 1 and 2 (level 3 inputs are not applicable for this input category). From these properties, all other necessary weight and volume properties required in the EICM can be computed. These include:

• Degree of saturation at optimum compaction (S_opt)
• Optimum volumetric moisture content (θ_opt)
• Saturated volumetric water content (θ_sat)

For rehabilitation designs only, the equilibrium or in-situ gravimetric water content is also a required input. NCHRP 1-37A recommends that this value be estimated from direct testing of bulk samples retrieved from the site, or through other appropriate means.

Although the material properties of the lower natural subgrade layers are important to the overall response of the pavement, a lower level of effort is generally sufficient to characterize these deeper layers as compared to the overlying compacted materials. Level 1 inputs are thus generally not necessary for in-situ subgrade materials. NCHRP 1-37A recommends that only gradation properties and Atterberg limits be measured for the in-situ subgrade materials.

Table 5-52. Physical properties for unbound materials required for EICM calculations (NCHRP 1-37A, 2004).

Material Property	Input Level	Description
Specific gravity, Gs	1	A direct measurement using AASHTO T100 (performed in conjunction with consolidation tests - T180 for bases or T 99 for other layers). See Table 5-10.
	2	Determined from P2001 and PI2 of the layer as below: Determine P200 and PI. Estimate Gs:(5.41) Gs = 0.041 ( P200 * PI )0.29 + 2.65
	3	Not applicable.
Optimum gravimetric water content, wopt, and maximum dry unit weight of solids, (γd)max	1	Typically, AASHTO T180 compaction test for base layers and AASHTO T99 compaction test for other layers. See Table 5-13.
	2	Estimated from D601, P2001 and PI2 of the layer following these steps: Determine PI, P200, and D60. Estimate Sopt:(5.42) Sopt = 6.752 ( P200 * PI )0.147 + 78 Estimate wopt: If P200 * PI > 0 (5.43) wopt = 1.3 ( P200 * PI )0.73 + 11 If P200 * PI = 0 (5.44) wopt (T99) = 8.6425 ( D60 )-0.1038 If layer is not a base course (5.45) wopt = wopt (T99) If layer is a base course (5.46) Δwopt = 0.0156 [ wopt (T99) ]2 - 0.1465 wopt (T99) + 0.9 (5.47) wopt = wopt (T99) - Δwopt Determine Gs using the level 2 procedure described in this table above. Compute (γd)max comp at optimum moisture and maximum compacted density: (5.48) γd max comp = Gs γwater   1 + wopt Gs   Sopt Determine (γd)max: If layer is a compacted material: (5.49) γd max = γd max comp If layer is a natural in-situ material: (5.50) γd max = 0.9 γd max comp
	3	Not applicable.

1. P₂₀₀ and D₆₀ can be obtained from a grain-size distribution test (AASHTO T 27)-see Table 5-19.
2. PI can be determined from an Atterberg limit test (AASHTO T 90)-see Table 5-21.

Soil Water Characteristic Curve

The soil water characteristic curve (SWCC) defines the relationship between water content and matric suction h for a given soil. Matric suction is defined as the difference between the pore air pressure u_a and pore water pressure u_w in a partially saturated soil:

(5.51)

h = ( u_a - u_w )

This relationship is usually plotted as the variation of water content (gravimetric w, volumetric θ, or degree of saturation S) vs. soil suction (Figure 5-37). The SWCC is one of the primary material inputs used in the EICM to compute moisture distributions with depth and time. Although the SWCC can be measured in the laboratory (e.g., see Fredlund and Rahardjo, 1993), this is quite uncommon and rather difficult. Instead, empirical models are used to express the SWCC in terms of other, more easily measurable parameters. The EICM algorithms in the NCHRP 1-37A analysis procedure are based on a SWCC model proposed by Fredlund and Xing (1994):

(5.52)

θw = C ( h ) ×

θsat

ln

EXP ( 1 ) +

h

bf

cf

af

(5.53)

C ( h ) =		1 -	ln		1 +	h
						hr
			ln		1 +	1.45 × 105
						hr

in which

h	=	matric suction (units of stress)
θsat	=	volumetric moisture content at saturation
af, bf, cf, and hr	=	model parameters (af, hr in units of stress)

Figure 5-37. Soil water characteristic curves (NCHRP 1-37A, 2004).

Table 5-53 summarizes the NCHRP 1-37A recommended approach for estimating the parameters of the SWCC at each of the three hierarchical input levels.

Table 5-53. Options for estimating the SWCC parameters (NCHRP 1-37A, 2004).

Input Level	Procedure to Determine SWCC parameters	Required Testing
1	Direct measurement of suction (h) in psi, and volumetric water content (θw) pairs of values. Direct measurement of optimum gravimetric water content, wopt and maximum dry unit weight, γd max. Direct measurement of the specific gravity of the solids, Gs. Compute (5.55) θopt = wopt γd max   γwater Compute (5.56) Sopt = θopt   1 - γd max   γwater Gs Compute (5.57) θsat = θopt   Sopt Using non-linear regression analysis, compute the SWCC model parameters af, bf, cf, and hr from Eqs. (5.52) and (5.53) and the (h, θw) pairs of values obtained in Step 1.	Pressure plate, filter paper, and/or Tempe cell testing. AASHTO T180 or T99 for γd max (see Table 5-13). AASHTO T100 for Gs (see Table 5-10).
2	Direct measurement of optimum gravimetric water content, wopt and maximum dry unit weight, γd max. Direct measurement of the specific gravity of the solids, Gs. Direct measurement of P200, D60, and PI. The EICM will then internally do the following: Calculate P200 * PI. Calculate θopt, Sopt, and θsat, as described for level 1. Determine the SWCC model parameters af, bf, cf, and hr in Eqs. (5.52) and (5.53) via correlations with P200, PI and D60. If P200 PI > 0 (5.58) af = 0.00364 ( P200 PI )3.35 + 4 ( P200 PI ) + 11 (psi)   6.895 (5.59) bf = -2.313 ( P200 PI )0.14 + 5   cf (5.60) cf = 0.0514 ( P200 PI )0.465 + 0.5 (5.61) hr = 32.44 e0.0186(P200 PI)   af If P200 PI = 0 (5.62) af = 0.8627 ( D60 )-0.751 (psi)   6.895 (5.63) bf = 7.5 (5.64) cf = 0.1772 ln( D60 ) + 0.7734 (5.65) hr = 1     af D60 + 9.7 e-4	AASHTO T180 or T99 for γd max (see Table 5-13). T100 for Gs (see Table 5-10). AASHTO T88 for P200 and D60 (see Table 5-19). AASTHO T90 for PI (see Table 5-21).
3	Direct measurement and input of P200, PI, and D60, after which the EICM uses correlations with P200PI and D60 to automatically generate the SWCC parameters for each soil as follows: Compute Gs, as outlined in Table 5-52 for level 2. Compute P200 * PI Estimate Sopt, wopt, and γd max, as shown Table 5-52 for level 2. Determine the SWCC model parameters af, bf, cf, and hr via correlations with P200PI and D60, as shown in this table for level 2.	AASHTO T88 for P200 and D60 (see Table 5-19). AASHTO T90 for PI (see Table 5-21).

Hydraulic Conductivity (Permeability)

Hydraulic conductivity (or permeability) k describes the ability of a material to conduct fluid (water). It is defined as the quantity of fluid flow through a unit area of soil under a unit pressure gradient. Hydraulic conductivity is one of the primary material inputs to the environment model in the NCHRP 1-37A analysis procedure, where it is used to determine the transient moisture profiles in unbound materials and to estimate their drainage characteristics.

The unsaturated flow algorithms in the EICM require a complete specification of the unsaturated hydraulic conductivity as a function of matric suction h. Although the unsaturated hydraulic conductivity vs. matric suction relationship can be measured in the laboratory (e.g., see Fredlund and Rahardjo, 1993), this is uncommon and difficult. At best, only the saturated hydraulic conductivity k_sat is measured in practice. Consequently, within the EICM an empirical model proposed by Fredlund et al. (1994) is used to express the unsaturated hydraulic conductivity k(h) vs. matric suction h relationship in terms of the Fredlund and Xing (1994) SWCC model, Eqs. (5.52) and (5.53). The k(h) model is expressed in terms of a relative hydraulic conductivity:

(5.54)

k_r ( h ) = k ( h ) / k_sat

Recommendations from NCHRP 1-37A for determining the k_sat value needed in Eq. (5.54) are summarized in Table 5-54. The Fredlund et al. (1994) model for k_r(h) is then expressed in integral form as:

(5.66)

kr ( h ) =	h	∫	hr	θ ( x ) - θ ( h )	θ′ ( x ) dx
				x2
	have	∫	hr	θ ( x ) - θs	θ′ ( x ) dx
				x2

in which:

θ(h)	=	volumetric water content as a function of matric suction, from the SWCC Eqs. (5.52) and (5.53)
θs	=	saturated volumetric water content
θ′(h)	=	derivative of the SWCC
x	=	dummy integration variable corresponding to water content
hr	=	matric suction corresponding to the residual water content (i.e., the water content below which a large increase in suction is required to remove additional water)
have	=	the air-entry matric suction (i.e., the suction where air starts to enter the largest pores in the soil)

The procedures described in Table 5-53 are used in the EICM to determine the SWCC via Eqs. (5.52) and (5.53), which in turn is then used to determine the unsaturated hydraulic conductivity via Eq. (5.66). These calculations are performed internally within the EICM software.

Table 5-54. Options for determining the saturated hydraulic conductivity for unbound materials (NCHRP 1-37A, 2004).

Material Property	Input Level	Description
Saturated hydraulic conductivity, ksat	1	Direct measurement using a permeability test (AASHTO T215) - see Table 5-55.
	2	Determined from P2001, D601, and PI2 of the layer as below: Determine P200PI = P200 * PI If 0 ≤ P200PI < 1 (5.67) ksat = 118.11 × 10[-1.1275(logD60+2)2+7.2816(logD60+2)-11.2891] Units: ft/hr Valid for D60 < 0.75 in If D60 > 0.75 in, set D60 = 0.75 mm If P200PI ≥ 1 (5.68) ksat = 118.11 × 10[0.0004(P200PI)2-0.0929(P200PI)-6.56] (ft/hr)
	3	Not applicable.

1. P₂₀₀ and D₆₀ can be obtained from a grain-size distribution test (Table 5-19)
2. PI can be determined from an Atterberg limit test (Table 5-21).

Table 5-55. Saturated hydraulic conductivity.

Description	Quantity of fluid flow through a unit area of soil under a unit pressure gradient.
Uses in Pavements	Used in the EICM for predicting distributions of moisture with depth and time in the NCHRP 1-37A Design Guide.
Laboratory Determination	AASHTO T 215; ASTM D 2434 (Granular Soils), ASTM D 5084 (All Soils). There are two basic standard types of test procedures to directly determine permeability: (1) the constant head test, normally used for coarse materials (Figure 5-38); and (2) the falling head test, normally used for clays (Figure 5-39). Undisturbed, remolded, or compacted samples can be used in both procedures.
Field Measurement	Pumping tests can be used to measure hydraulic conductivity in-situ.
Commentary	Both test procedures determine permeability of soils under specified conditions. The geotechnical engineer must establish which test conditions are representative of the problem under consideration. As with all other laboratory tests, the geotechnical engineer has to be aware of the limitations of this test. The process is sensitive to the presence of air or gases in the voids and in the permeant or water. Prior to the test, distilled, de aired water should be run through the specimen to remove as much of the air and gas as practical. It is a good practice to use de aired or distilled water at temperatures slightly higher than the temperature of the specimen. As the water permeates through the voids and cools, it will have a tendency to dissolve the air and some of the gases, thus removing them during this process. The result will be a more representative, albeit idealized, permeability value. The type of permeameter, (i.e., flexible wall ASTM D 5084 versus rigid ASTM D 2434 and AASHTO T215) may also affect the final results. For testing of fine grained low permeability soils, the use of flexible wall permeameters is recommended, which are essentially very similar to the triaxial test apparatus. When rigid wall units are used, the permeant may find a route at the sample permeameter interface. This will produce erroneous results. It should be emphasized that permeability is sensitive to viscosity. In computing permeability, correction factors for viscosity and temperatures must be applied. The temperature of the permeant and the laboratory should be kept constant during testing. Laboratory permeability tests produce reliable results under ideal conditions. Permeability of fine grained soils can also be computed from one dimensional consolidation test results, although these results are not as accurate as direct ksat measurements.
Typical Values	See Table 5-56 and Table 5-57. Saturated hydraulic conductivity for loose clean sands can also be estimated using the Hazen relationship: (5.69) ksat = C * D102 in which ksat is the saturated hydraulic conductivity in cm/sec; C is Hazen's coefficient ranging between 0.8 and 1.2 (a value of 1.0 is commonly used); and D10 is the effective particle size, defined as the largest particle diameter in the finest 10% fraction of the soil.

Figure 5-38. Schematic of a constant head permeameter (Coduto, 1999).

Figure 5-39. Schematic of a falling head permeameter (Coduto, 1999).

Table 5-56. Typical values of saturated hydraulic conductivity for soils (Coduto, 1999).

Soil Description	Hydraulic Conductivity k
	(cm/s)	(ft/s)
Clean gravel	1 - 100	3x10-2 - 3
Sand-gravel mixtures	10-2 - 10	3x10-4 - 0.3
Clean coarse sand	10-2 - 1	3x10-4 - 3x10-2
Fine sand	10-3 - 10-1	3x10-5 - 3x10-3
Silty sand	10-3 - 10-2	3x10-5 - 3x10-4
Clayey sand	10-4 - 10-2	3x10-6 - 3x10-4
Silt	10-8 - 10-3	3x10-10 - 3x10-5
Clay	10-10 - 10-6	3x10-12 - 3x10-8

Table 5-57. Typical values of saturated hydraulic conductivity for highway materials (Carter and Bentley, 1991).

Material	Hydraulic Conductivity k (m/s)*
Uniformly graded coarse aggregate	0.4 - 4x10-3
Well-graded aggregate without fines	4x10-3 - 4x10-5
Concrete sand, low dust content	7x10-4 - 7x10-6
Concrete sand, high dust content	7x10-6 - 7x10-8
Silty and clayey sands	10-7 - 10-9
Compacted silt	7x10-8 - 7x10-10
Compacted clay	< 10-9
Bituminous concrete**	4x10-5 - 4x10-8
Portland cement concrete	< 10-10

• *1 m/s = 3.25 ft/s
• **New pavements; values as low as 10^-10 have been reported for sealed, traffic-compacted highway pavements.

Thermal Conductivity

Thermal conductivity K is defined as the ability of a material to conduct heat. Typical units are BTU/ft-hr-°F or W/m-°K. Thermal conductivity is used in the EICM algorithms for the computation of temperature distributions with depth and time in the NCHRP 1-37A analysis methodology.

Table 5-58 outlines the NCHRP 1-37A recommended approach for characterizing the dry thermal conductivity K for unbound materials. Note that thermal conductivity is not commonly measured for unbound pavement materials, and consequently the level 3 inputs will be used for nearly all designs. The EICM automatically adjusts the dry thermal conductivity for the influence of moisture during the calculations.

Heat Capacity

Heat capacity Q is defined as the amount of heat required to raise by one degree the temperature of a unit mass of soil. Typical units are BTU/lb-°F or J/kg-°K. Heat capacity is used in the EICM algorithms for the computation of temperature distributions with depth and time in the NCHRP 1-37A analysis methodology.

Table 5-58 outlines the NCHRP 1-37A recommended approached for characterizing the dry heat capacity Q for unbound materials. Note that heat capacity is not commonly measured for unbound pavement materials, and consequently the level 3 inputs will be used for nearly all designs. The EICM automatically adjusts the dry heat capacity for the influence of moisture content during the calculations.

Table 5-58. Options for determining the dry thermal conductivity and heat capacity for unbound materials (NCHRP 1-37A, 2004).

Material Property	Input Level	Description
Dry Thermal Conductivity, K	1	Direct measurement (ASTM E 1952).
	2	Not applicable.
	3	Soil Type Range Recommended BTU/ft-hr-°F* A-1-a 0.22 - 0.44 0.30 A-1-b 0.22 - 0.44 0.27 A-2-4 0.22 - 0.24 0.23 A-2-5 0.22 - 0.24 0.23 A-2-6 0.20 - 0.23 0.22 A-2-7 0.16 - 0.23 0.20 A-3 0.25 - 0.40 0.30 A-4 0.17 - 0.23 0.22 A-5 0.17 - 0.23 0.19 A-6 0.16 - 0.22 0.18 A-7-5 0.09 - 0.17 0.13 A-7-6 0.09 - 0.17 0.12 Additional typical values are given in Table 5-59.
Dry Heat Capacity, Q	1	Direct measurement (ASTM D 2766).
	2	Not applicable.
	3	Typical values range from 0.17 to 0.20 BTU/lb-°F. Additional typical values are given in Table 5-59.

• *1 BTU/ft-hr-°F = 1.73 W/m-°K; 1 BTU/lb-°F = 4187 J/kg-°K

Table 5-59. Typical values for thermal conductivity and heat capacity of unbound materials (adapted from Sundberg, 1988).

Soil Type	Thermal Conductivity (W/m-°K)*	Heat Capacity (J/kg-°K)*
Clay with high clay content	0.85 - 1.1	1700 - 2050
Silty clay/silt	1.1 - 1.5	1650 - 1900
Silt	1.2 - 2.4	1400 - 1900
Sand, gravel below GWT	1.5 - 2.6 (1.6 - 2.0)	1450 - 1850 (1700)
Sand, gravel above GWT	0.4 - 1.1 (0.7 - 0.9)	700 - 1000 (800)
Till below GWT	1.5 - 2.5	1350 - 1700
Sandy till above GWT	0.6 - 1.8	750 - 1100
Peat below GWT	0.6	2300
Peat above GWT	0.2 - 0.5	400 - 1850

• *1 W/m-°K = 0.578 BTU/ft-hr-°F; 1 J/kg-°K = 2.388E-4 BTU/lb-°F

5.6 Environment/Climate Inputs

5.6.1 1993 AASHTO Guide

There are only four environmental inputs in the 1993 AASHTO Guide:

• Estimated seasonal variation of the subgrade resilient modulus M_R (Section 5.4.3)
• The category for the percentage of time that the unbound pavement materials are exposed to moisture conditions near saturation (Section 5.5.1)
• The qualitative description of moisture supply for expansive subgrades (Section 5.5.1)
• The depth of frost penetration (Section 5.5.1)

These environmental factors are intertwined with their associated material property inputs and have already been described in this chapter in the sections noted above.

5.6.2 NCHRP 1-37A Design Guide

Three sets of environmental inputs are required in the NCHRP 1-37A design methodology:

• Climate, defined in terms of histories of key weather parameters
• Groundwater depth
• Surface shortwave absorptivity

These parameters are the inputs/boundary conditions for the calculation of climate-specific temperature and moisture distributions with depth and time in the EICM (see Appendix D). These distributions, in turn, are used to determine seasonal moisture contents and freeze-thaw cycles for the unbound pavement materials.

Climate Inputs

The seasonal damage and distress accumulation algorithms in the NCHRP 1-37A design methodology require hourly history data for five weather parameters:

• Air temperature
• Precipitation
• Wind speed
• Percentage sunshine (used to define cloud cover)
• Relative humidity.

The NCHRP 1-37A Design Guide recommends that the weather inputs be obtained from weather stations located near the project site. At least 24 months of actual weather station data are required for the computations. The Design Guide software includes a database of appropriate weather histories from nearly 800 weather stations throughout the United States. This database is accessed by specifying the latitude, longitude, and elevation of the project site. The Design Guide software locates the six closest weather stations to the site; the user selects a subset of these to create a virtual project weather station via interpolation of the climatic data from the selected physical weather stations.

Specification of the weather inputs is identical at all the three hierarchical input levels in the NCHRP 1-37A Design Guide.

Groundwater Depth

The groundwater table depth is intended to be the best estimate of the annual average depth. Level 1 inputs are based on soil borings, while level 3 inputs are simple estimates of the annual or seasonal average values. A potential source for level 3 groundwater depth estimates is the county soil reports produced by the National Resources Conservation Service. There is no level 2 approach for this design input.

It is important to recognize that groundwater depth can play a significant role in the overall accuracy of the foundation/pavement moisture contents and, hence, the seasonal modulus values. This is explored further in Chapter 6. Every attempt should be made to characterize groundwater depth as accurately as possible.

Surface Shortwave Absorptivity

This last environmental input is a property of the AC or PCC surface layer. The dimensionless surface short wave absorptivity defines the fraction of available solar energy that is absorbed by the pavement surface. It depends on the composition, color, and texture of the surface layer. Generally speaking, lighter and more reflective surfaces tend to have lower short wave absorptivity.

The NCHRP 1-37A recommendations for estimating surface shortwave absorptivity at each hierarchical input level are as follows:

• Level 1-Determined via laboratory testing. However, although laboratory procedures exist for measuring shortwave absorptivity, there currently are no AASHTO protocols for this for paving materials.
• Level 2-Not applicable.
• Level 3-Default values as follows:
  • Weathered asphalt (gray) 0.80 - 0.90
  • Fresh asphalt (black) 0.90 - 0.98
  • Aged PCC layer 0.70 - 0.90

Given the lack of suitable laboratory testing standards, level 3 values will typically be used for this design input.

5.7 Development Of Design Inputs

Myth has it that an unknown structural engineer offered the following definition of his profession (Coduto, 2001):

"Structural engineering is the art and science of molding materials we do not fully understand into shapes we cannot precisely analyze to resist forces we cannot accurately predict, all in such a way that the society at large is given no reason to suspect the extent of our ignorance."

This definition applies even more emphatically to pavement engineering. In spite of our many technical advances, there are still great gaps in our understanding. Often the greatest uncertainties in an individual project are with site conditions and materials-the types and conditions of materials encountered along the highway alignment, their spatial, temporal, and inherent variability, and their complex behavior under repeated traffic loading and environmental cycles.

Site investigation and testing programs often generate large amounts of data that can be difficult to synthesize. Real soil profiles are nearly always very complex, so borings often do not correlate and results from different tests may differ enormously. The development of a simplified representation of the soils and geotechnical conditions at a project site requires much interpolation and extrapolation of data, combined with sound engineering judgment. But what is engineering judgment? Ralph Peck suggested several alternative definitions (Dunnicliff and Deere, 1984):

"To the engineering student, judgment often appears to be an ingredient said to be necessary for the solution of engineering problems, but one that the student can acquire only later in his career by some undefined process of absorption from his experience and his colleagues.

"To the engineering scientist, engineering judgment may appear to be a crutch used by practicing engineers as a poor substitute for sophisticated analytical procedures.

"To the practicing engineer, engineering judgment may too often be an impressive name for guessing rather than for rational thinking."

Perhaps Webster's New Collegiate Dictionary offers the definitive statement:

Judgment: The operation of the mind, involving comparison and discrimination, by which knowledge of values and relations is mentally formulated.

But when confronted with voluminous quantities of inconsistent-and often contradictory-information, how does the pavement engineer compare and discriminate? What tools (or tricks) of the trade are available? This is a difficult process to describe. However, some common techniques for determining design values from site exploration and other geotechnical data are as follows:

• Find and remove any obvious outliers in the data. Although there are statistical techniques for doing this (e.g., McCuen, 1993), in practice, detailed knowledge of the data plus engineering reasoning is usually sufficient for removing data outliers for cause. Table 5-60 summarizes some typical ranges of variability for pavement design inputs; additional information on measured variability of geotechnical parameters can be found in Baecher and Christian (2003). However, it is important that outliers (e.g., a single low stiffness value) not be arbitrarily removed without fully evaluating the data for an explanation. A local anomaly may exist in the field, for example, that requires remediation.
• Examine spatial (and in some cases, temporal) trends in the data. Look at both the subsurface stratagraphic profiles and plan view "map" of subsurface conditions. Refer to the 1993 AASHTO Design Guide for resolving spatial variations in pavement design data by defining homogeneous analysis units based on a "cumulative difference" approach (Figure 5-40). A separate set of design inputs can then be developed for each homogeneous analysis unit, reducing the variability of measured vs. design input values within each unit.
• Check whether the magnitudes and trends in the data pass the test of "engineering reasonableness" - e.g., are the values of the right order of magnitude? Are the trends in the data in the intuitively correct directions?
• Examine the internal consistency of the data - e.g., are the phase relationships by volume consistent with the phase relationships by weight?
• Use correlations among different types of data to strengthen data interpretation - e.g., statistical correlations between resilient modulus and CBR can be used to supplement a limited set of measured M_R values (although today, laboratory resilient modulus tests can often be performed more quickly and less expensively than laboratory CBR tests-see Table 5-61).
• Be clear on what is needed for a design value. The value of a material property used for specification purposes may be different from the value of that same material property when used for design. For example, a conservative value (mean plus one or two standard deviations) may be specified for the minimum compressive strength of a lime stabilized subgrade for construction quality control specifications; the mean value would be more appropriate for design applications where overall reliability (e.g., factor of safety) is considered explicitly, as is the case in both the AASHTO and NCHRP design procedures.
• Evaluate the sensitivity of the design to the inputs! This is perhaps the most important-and often the most overlooked-aspect of design. Evaluating sensitivity to design inputs can have several benefits. First, it will categorize which inputs are most important and which are less important to the design. There is no need to expend large effort determining the precise design values for inputs that have little impact on the final outcome. More resources can then be allocated to determining the inputs that have significant impact on the outcome once they have been identified. Second, design sensitivity analyses can indicate the potential consequences of incorrect judgments of the design inputs. For example, if the subgrade resilient modulus is underestimated by 50%, will this reduce the expected useful life of the pavement by 1 year or 10 years? How does the increased cost of reduced pavement life compare with the cost of additional exploration in order to establish the subgrade resilient modulus value more robustly?
• When in doubt run more tests (a single test is often worth a thousand guesses).

Figure 5-40. Variation of pavement response variable versus distance for given project (NCHRP 1-37A, 2004).

Table 5-60. Summary of typical pavement parameter variability (AASHTO, 1993).

Property	Standard Deviation
	Low	Average	High
Thickness (inches)
Portland cement concrete	0.1	0.3	0.5
Asphalt concrete	0.3	0.5	0.7
Cement treated base	0.5	0.6	0.7
Granular base	0.6	0.8	1.0
Granular subbase	1.0	1.2	1.5
Strength
CBR (%)
Subgrade (4 - 7)	0.5	1.0	2.0
Subgrade (7 - 13)	1.0	1.5	2.5
Subgrade (13 - 20)	2.5	4.0	6.0
Granular subbase (20 - 30)	5.0	8.0	12.0
Granular base (80+)	10.0	15.0	30.0
Percent compaction (%)
Embankment/subgrade	2.0	4.5	7.0
Subbase/base	2.0	2.8	3.5
Portland cement concrete properties
Air content (%)	0.6	1.0	1.5
Slump (inches)	0.6	1.0	1.4
28-day compressive strength (psi)	400	600	800
Asphalt concrete properties
Gradation (%)
3/4 or 1/2 inch	1.5	3.0	4.5
3/8 inch	2.5	4.0	6.0
No. 4	3.2	3.8	4.2
No. 40 or No. 50	1.3	1.5	1.7
No. 200	0.8	0.9	1.0
Asphalt content (%)	0.1	0.25	0.4
Percent compaction (%)	0.75	1.0	1.5
Marshall mix properties
Stability (lbs)	200	300	400
Flow (in./in.)	1.0	1.3	2.0
Air voids (%)	0.8	1.0	1.4
AC consistency
Pen @ 77°F	2	10	18
Viscosity @ 149°F (kilopoise)	2	25	100
	Coefficient of Variation (%)
	Low	Average	High
Pavement deflection	15	30	45

Table 5-61. Resilient modulus versus CBR testing for fine grained subgrade soil (Boudreau Engineering, 2004, personal communication).

Property	CBR	Resilient Modulus
Sample size required	60 lbs (27 kg)	5 lbs (2.3 kg)
Turnaround time	10 days	4 days
Data value	Empirical	Mechanistic
In-situ testing	Field test	Shelby tube - lab
Unit price	$365	$300

5.8 Exercises

Depending upon the number of groups in the class, one or more of the following exercises may be assigned.

5.8.1 1993 AASHTO Design Guide-Flexible Pavements

Small group exercise: Given the pavement information for the Main Highway in Appendix B, estimate appropriate material property inputs for the unbound materials in a flexible pavement structure as required for the 1993 AASHTO Design Guide. (A worksheet will be distributed to guide this exercise.)

5.8.2 1993 AASHTO Design Guide-Rigid Pavements

Small group exercise: Given the pavement information for the Main Highway in Appendix B, estimate appropriate material property inputs for the unbound materials in a rigid pavement structure as required by the 1993 AASHTO Design Guide. (A worksheet will be distributed to guide this exercise.)

5.9 References

• AASHTO (1972). AASHTO Interim Guide for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C.
• AASHTO (1986). Guide for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C.
• AASHTO (1993). AASHTO Guide for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C.
• AASHTO (2003). Standard Specifications for Transportation Materials and Methods of Sampling and Testing (23rd ed.), American Association of State Highway and Transportation Officials, Washington, D.C.
• Andrei, D. (1999). Development of a Harmonized Test Protocol for the Resilient Modulus of Unbound Materials Used in Pavement Design, Master of Science thesis, University of Maryland, College Park, MD.
• Andrei, D. (2003). Development of a Predictive Model for the Resilient Modulus of Unbound Materials, Ph.D. dissertation, Arizona State University, Tempe, AZ.
• Asphalt Institute (1982). "Research and Development of the Asphalt Institute's Thickness Design Manual, Ninth Edition," Research Report No. 82-2.
• Baecher, G.B., and Christian, J.T. (2003). Reliability and Statistics in Geotechnical Engineering, John Wiley and Sons, New York, NY.
• Barksdale, R.D., Alba, J., Khosla, P.N., Kim, R., Lambe, P.C. and Rahman, M.S. (1996). Laboratory Determination of Resilient Modulus for Flexible Pavement Design, Final Report, NCHRP Project 1-28, National Cooperative Highway Research Program, Transportation Research Board, National Research Council, Washington, D.C.
• Barksdale, R.D. (ed.) (2000). The Aggregate Handbook Plus Supplement, National Stone Association, Washington, D.C.
• Boudreau Engineering (2004) personal communication
• Burmister, D.M. (1943). "The Theory of Stresses and Displacements in Layered Systems and Applications to the Design of Airport Runways," Highway Research Board, Vol. 23, pp. 126-144.
• Carter, M., and Bentley, S.P. (1991). Correlations of Soil Properties, Pentech Press, London.
• Cheney, R.S., and Chassie, R.G. (1993). Soils and Foundations Workshop Manual. Federal Highway Administration, Washington, D.C.
• Coduto, D.P. (2001). Foundation Design Principles and Practices (2nd ed.), Prentice-Hall, Englewood Cliffs, NJ.
• Coduto, D.P. (1999). Geotechnical Engineering Principles and Practices, Prentice-Hall, Englewood Cliffs, NJ.
• Dunnicliff, D., and Deere, D.U. (1984). Judgment in Geotechnical Engineering: The Professional Legacy of Ralph B. Peck, John Wiley and Sons, New York, NY.
• Fredlund, D.G, and Rahardjo, H. (1993). Soil Mechanics for Unsaturated Soils, John Wiley and Sons, New York, NY.
• Fredlund, D.G., and Xing, A. (1994). "Equations for the Soil Water Characteristic Curve," Canadian Geotechnical Journal, Vol. 31, No. 4, pp. 521-532.
• Fredlund, D.G., Xing, A. and Huang, S. (1994). "Predicting the Permeability Function for Unsaturated Soils Using the Soil-Water Characteristic Curve," Canadian Geotechnical Journal, Vol 3., No. 4, pp. 533 - 546.
• Heukelom, W., and Klomp, A.J.G. (1962). "Dynamic Testing as a Means of Controlling Pavements During and After Construction," Proceedings, First International Conference on the Structural Design of Asphalt Pavements, Ann Arbor, MI.
• Holtz, W.G., and Gibbs, H.J. (1956). "Engineering Properties of Expansive Clays," Transactions ASCE, Vol. 121, pp. 641-677.
• Huang, Y.H. (1993). Pavement Design and Analysis, Prentice-Hall, Englewood Cliffs, NJ.
• LTTP (2003). Guide for Determining Design Resilient Modulus Values for Unbound Materials, interactive CD ROM (Version 1.1), Long Term Pavement Performance Program, Federal Highway Administration, U.S. Department of Transportation, Washington, D.C.
• Mallela, J., Larson, G.E., Wyatt, T., Hall, J.P. and Barker W. (2002). User's Guide for Drainage Requirements in Pavements - DRIP 2.0 Microcomputer Program, FHWA Contract No. DTFH61-00-F-00199, July.
• Mayne, P.W. and Kulhawy, F.H. (1982). "K_o-OCR Relationships in Soil," Journal of the Geotechnical Engineering Division, ASCE, Vol. 108, GT6, pp. 851-872.
• McCarthy, D.F. (2002). Essentials of Soil Mechanics and Foundations, 6th Edition, Prentice-Hall, Englewood Cliffs, NJ.
• McCuen, R.H. (1993). Microcomputer Applications in Statistical Hydrology, Prentice-Hall, Inc., Englewood Cliffs, NJ.
• Mohammad, L.N., Titi, H.H. and Herath, A. (2002). Effect of Moisture Content and Dry Unit Weight on the Resilient Modulus of Subgrade Soils Predicted by Cone Penetration Test, Report No. FHWA/LA.00/355, Federal Highway Administration, U.S. Department of Transportation, Washington, D.C.
• NAPA (1994). "Guidelines for Use of HMA Overlays to Rehabilitate PCC Pavements," Publication IS 117, National Asphalt Paving Association, Lanham, MD.
• NCHRP 1-37A (2004). Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures, Final Report, NCHRP Project 1-37A, Transportation Research Board, National Research Council, Washington, D.C.
• Peck, R.B., Hansen, W.E. and Thornburn, T.H. (1974). Foundation Engineering, Wiley.
• Saeed, A., Hall, J.W. and Barker, W. (2001). Performance-Related Tests of Aggregates for Use in Unbound Pavement Layers, NCHRP Report 453, Transportation Research Board, National Research Council, Washington, D.C.
• Seed, H.B., Chan, C.K. and Lee, C.E. (1963). "Resilience Characteristics of Subgrade Soils and Their Relation to Fatigue Failures in Asphalt Pavements," 1st International Conference on the Structural Design of Asphalt Pavements, Ann Arbor, MI.
• Seed, H.B., Chan, C.K. and Monismith, C.L. (1955). "Effects of Repeated Loading on the Strength and Deformation of Compacted Clay," HRB Proceedings, No. 34, pp. 541-558.
• Seed, H.B., and McNeill, R.L. (1956). "Soils Deformation in Normal Compression and Repeated Loading Tests," HRB Bulletin 141.
• Sowers, G.F. (1979). Introductory Soil Mechanics and Foundations, Macmillan, New York, NY.
• Sundberg, J. (1988) Thermal Properties of Soils and Rocks, Report No. 35, Swedish Geotechnical Institute, Linkoping, Sweden.
• Tseng, K. and Lytton, R. (1989). "Prediction of Permanent Deformation in Flexible Pavement Material," Implication of Aggregates in the Design, Construction, and Performance of Flexible Pavements, ASTM STP 1016, ASTM, pp. 154-172.
• U.S. Army Corps of Engineers (1953). "The Unified Soil Classification System," Technical Memorandum 3-357, Waterways Experiment Station, Vicksburg, MS.
• Van Til, C.J., McCullough, B.F., Vallerga, B.A. and Hicks, R.G. (1972). Evaluation of AASHTO Interim Guides for Design of Pavement Structures, NCHRP 128, Highway Research Board, Washington, D.C.
• Von Quintus, H.L. and Killingsworth, B. (1997a). Design Pamphlet for the Determination of Design Subgrade in Support of the 1993 AASHTO Guide for the Design of Pavement Structures, Report No. FHWA-RD-97-083, FHWA, Washington, D.C.
• Von Quintus, H.L. and Killingsworth, B. (1997b). Design Pamphlet for the Determination of Layered Elastic Moduli for Flexible Pavement Design in Support of the 1993 AASHTO Guide for the Design of Pavement Structures, Report No. FHWA-RD-97-077, Federal Highway Administration, Department of Transportation, Washington, DC.
• Von Quintus, H.L. and Killingsworth, B. (1998). Analysis Relating to Pavement Material Characterizations and Their Effects of Pavement Performance, Report No. FHWA-RD-97-085, Federal Highway Administration, Department of Transportation, Washington, DC.
• Witczak, M.W. (2004). Harmonized Test Methods for Laboratory Determination of Resilient Modulus for Flexible Pavement Design, NCHRP Project 1-28A Final Report, Transportation Research Board, National Research Council, Washington, D.C.
• Yoder, E.J., and Witczak, M.W. (1975). Principles of Pavement Design, John Wiley and Sons, New York, NY.

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Notes

1. Moisture and freeze/thaw are also important factors behind stripping of asphalt concrete, but this material phenomenon is beyond our scope. Return to Text

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