Estimation of Key PCC, Base, Subbase, and Pavement Engineering Properties From Routine Tests and Physical Characteristics

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CHAPTER 3. LITERATURE REVIEW (2)

PREDICTION OF CHEMICALLY STABILIZED MATERIAL PROPERTIES

Several types of chemically stabilized materials are used under pavements as base courses, subbase courses, or treated subgrade. These include lean concrete, cement stabilized or treated aggregate, soil cement, lime-cement flyash, and lime-stabilized materials. Typically, the compressive strength of these materials is used for construction QA and modulus and flexural strength for pavement design. However, compressive strength testing is more common than resilient/elastic modulus testing and flexural strength testing. Industry groups and individual researchers have published several correlations to estimate chemically stabilized base elastic modulus and flexural strength from the compressive strength as shown in figure 29 through figure 32. The more common or feasible of these correlations are presented in figure 32. Resilient modulus (M_r) can be estimated conservatively as 20 percent of the unconfined compressive strength (q_u)_.⁽⁹⁵⁾

The LTPP database does not contain modulus test results for stabilized materials. Limited data were available for modulus tests of LCB layers, which were utilized for model development. Therefore, the discussion on stabilized materials in this report is brief.

 

Figure 29. Equation. E for lean concrete or cement treated aggregate.⁽⁹⁶⁾

Where:

E = Modulus of elasticity, psi.

f'_c = Compressive strength, psi tested in accordance with AASHTO T 22.⁽¹⁷⁾

 

Figure 30. Equation. E for soil cement.⁽⁹⁶⁾

 

Where:

E = Modulus of elasticity, psi.

q_u = Unconfined compressive strength, psi tested in accordance with ASTM D 1633.⁽⁹⁷⁾

 

Figure 31. Equation. E for lime-cement-flyash.⁽⁹⁸⁾

Where:

E = Modulus of elasticity, psi.

q_u = Unconfined compressive strength, psi tested in accordance with ASTM C 593.⁽⁹⁹⁾

 

Figure 32. Equation. M_r for lime-stabilized soils.⁽¹⁰⁰⁾

Where:

M_r = Resilient modulus, ksi.

q_u = Unconfined compressive strength, psi tested in accordance with ASTM D 5102.⁽¹⁰¹⁾

PREDICTION OF UNBOUND MATERIAL AND SOIL RESILIENT MODULUS

Overview

Resilient modulus of unbound materials and soils is a required input in most pavement design procedures. It has a significant effect on the computed pavement responses and, hence, pavement performance. Resilient modulus can be tested directly from the laboratory, backcalculated using nondestructive test data, or obtained through the use of correlations with other material strength and index properties such as the California bearing ratio (CBR), R-value, dynamic cone penetrometer (DCP) value, soil Atterberg limit and gradation properties, AASHTO soil class, etc.

As a result of extensive research into the characterization of resilient modulus characterization conducted over the past four decades, it is now widely recognized that resilient modulus exhibits stress-state dependency, material dependency, and moisture and temperature dependency. About 54 percent of State transportation departments use resilient modulus in routine pavement design.⁽¹⁰²⁾ Ideally, resilient modulus should be obtained from laboratory measurements; however, standard test procedures such as AASHTO T 307 and NCHRP 1-28A require substantial time and resources and are not used in routine engineering practice, especially beyond the design phase of the project.^(28,103)

Of the several approaches put forth to estimate resilient modulus in the laboratory for design purposes, the one that has gained considerable traction over time is using a universal constitutive model as proposed in NCHRP 1-28A (see figure 33).⁽¹⁰³⁾ The strength of this approach is that two of the resilient modulus dependencies, stress-state and material type, can be handled by this model form, which is an improvement over previously used discrete models for coarse- and fine-grained soils which require knowledge of material behavior prior to applying a function to characterize it.

The nonlinear elastic coefficients and exponents of the constitutive model are determined by using linear or nonlinear regression analyses to fit the model to laboratory generated resilient modulus test data.

 

Figure 33. Equation. M_r according to NCHRP Project 1-28A.⁽¹⁰³⁾

Where:

M_r = Resilient modulus, psi.

 = Bulk stress ()_.

 = Major principal stress.

 = Intermediate principal stress =  for M_r test on cylindrical specimen.

 = Minor principal stress/confining pressure.

_oct = Octahedral shear stress.

_oct =.

P_a = Normalizing stress (atmospheric pressure).

k₁, k₂, and k₃ = Regression constants (obtained by fitting M_r test data to this equation).

Resilient Modulus Prediction Models

There have been numerous attempts to estimate resilient modulus as a function of soil index or soil strength properties over time. One of the first studies of the resilient properties of soil with the objective of developing correlation equations for predicting resilient modulus from basic soil test data was conducted by Carmichael and Stuart.⁽¹⁰⁴⁾ They used the Highway Research Information Service (HRIS) database and developed two regression models, one for fine-grained soils and another for coarse-grained soils.⁽¹⁰⁴⁾ Regression models were developed for individual soil types according to the Unified Classification System (UCS). Variables used in the models for coarse-grained soils included moisture content and bulk stress. For fine-grained soils, plasticity index, confining, and deviatoric stresses were used as predictive variables.

Drumm et al. conducted a resilient modulus study of cohesive soils based on AASHTO soil classification.⁽¹⁰⁵⁾ They used deviator stress as the main model parameter. The model coefficients were derived as functions of liquid limit of soil, degree of saturation, and unconfined compressive strength.

Two resilient modulus regression models—one each for fine-grained and coarse-grained Mississippi soils—were developed by George.⁽¹⁰⁶⁾ Variables used to predict fine-grained soil resilient modulus included soil dry density, liquid limit, moisture content, and percentage passing the No. 200 sieve. Variables for the coarse-grained soil resilient modulus model included dry density, moisture content, and percentage passing the No. 200 sieve.

A potential benefit of estimating the resilient modulus from physical properties is that seasonal variations in resilient modulus can be estimated from seasonal changes in a material’s physical properties. A few of the models from phenomenological studies that relate resilient modulus to soil properties are presented in figure 34 to figure 48.

Other soil strength parameters have also been used to estimate resilient modulus. Due to its historical significance in pavement design, CBR is the most commonly used soil strength parameter for correlation. Direct correlations between resilient modulus and CBR are included in the MEPDG.⁽²⁾ Simple correlation equations were developed to predict resilient modulus from standard CBR by several researchers. (See references 107–110.) All these equations are purely empirical and do not depend on soil properties and stress state. Figure 49 through figure 58 present a list of correlations between resilient modulus and other strength parameters.

One should exercise caution in using these correlations because they may not produce the required input to the MEPDG. The resilient modulus input is required to be at optimum moisture content and density of the soil. Most of these correlations do not predict this resilient modulus at optimum moisture content.

The resilient modulus also has been correlated to indices determined from other test devices. A summary of correlations with in-place test methods is presented in figure 59 to figure 67.

 

Figure 34. Equation. M_r according to Jones and Witczak.⁽¹¹¹⁾

Figure 34 was developed for clay type A-7-6. The deviator stress is 6 psi, the confining pressure is 2 psi, and M_r is measured in ksi.

 

Figure 35. Equation. M_r according to Thompson and LaGrow.⁽¹¹²⁾

Figure 35 was developed for compacted subgrades. The additional moisture susceptibility correction factor is 0.7 for clay, silty clay, and silty clay loam; 1.5 for clay loam; and 2.1 for loam.

 

Figure 36. Equation. M_r according to Thompson and Robnett.⁽¹¹³⁾

Figure 36 was developed for fine-grained cohesive soils. The deviator stress is 6 psi, and there is no confinement.

 

Figure 37. Equation. M_r according to Carmichael and Stuart for fine subgrade soils containing clay and silts.⁽¹⁰⁴⁾

Figure 37 was developed for fine subgrade soils containing clay and silts. It was developed using the HRIS database for individual UCS soil types.

 

Figure 38. Equation. M_r according to Carmichael and Stuart for coarse granular soils and aggregate bases.⁽¹⁰⁴⁾

Figure 38 was created for coarse granular soils and aggregate bases. It was developed using the HRIS database for individual UCS soil types.

 

Figure 39. Equation. M_r according to Elliot et al. with deviator stress of 4 psi.⁽¹¹⁴⁾

Figure 39 was developed using cohesive subgrades.

 

Figure 40. Equation. M_r according to Elliot et al. with deviator stress of 8 psi.⁽¹¹⁴⁾

Figure 40 was developed using cohesive subgrades.

 

Figure 41. Equation. M_r according to Rahim for fine-grained soils.⁽¹¹⁵⁾

Figure 41 was developed using undisturbed field samples.

 

Figure 42. Equation. M_r according to Rahim for coarse-grained soils.⁽¹¹⁵⁾

Figure 42 was developed using undisturbed field samples.

 

Figure 43. Equation. M_r according to Farrar and Turner.⁽¹¹⁶⁾

Figure 43 was developed using 13 types of fine-grained soils.

 

Figure Figure 44. Equation. M_r according to Hudson et al.⁽¹¹⁷⁾

Figure 44 was developed using cohesive subgrade soil types A4 through A7-6.

 

Figure 45. Equation. M_r according to Li and Selig.⁽¹¹⁸⁾

Figure 45 was developed for cohesive soils.

 

Figure 46. Equation. M_r according to Gupta et al.⁽¹¹⁹⁾

Figure 46 was developed for cohesive soils. The valid for bulk stress is 83 kPa, and the octahedral shear stress is 19.3 kPa.

 

Figure 47. Equation. M_r according to Berg et al.⁽¹²⁰⁾

Figure 47 was developed using fine-grained and coarse-grained soils from the Minnesota Road Research Project test site; applicable only to cohesive soils.

 

Figure 48. Equation. M_r according to Pezo and Hudson.⁽¹²¹⁾

Figure 48 was developed for Texas subgrade data. It is valid for silty to clayey subgrades, and correction factors are provided.

The definitions of the terms used in figure 34 through figure 48 are as follows:

%CLAY = C = Clay content in percent.

%SILT = Silt content in percent.

%W = w = w_c = Moisture content.

_d = Deviation from the Standard Proctor maximum dry density in pounds per cubic foot.

w = Deviation from the optimum water content in percent.

_dr = Ratio of dry density to maximum dry density.

 =  = Confining stress.

 = Deviator stress.

 = Bulk stress.

 = Soil suction.

CH = 1 for CH type (clay and high plasticity) soil; 0 otherwise.

CLASS = Soil classification (e.g., soil type A7-6 use 7.6 in expression).

c_u = Uniformity coefficient.

f(S) = Normalized saturation by a unit saturation of 1 percent.

f() = Normalized octahedral shear stress by a unit stress of 1 psi.

F₀ = 9.8 ksi.

F₁ = Moisture content correction factor.

F₂ = Relative compaction correction factor.

F₃ = Soil plasticity correction factor.

F₄ = Age correction factor.

F₅ = Confining pressure correction factor.

F₆ = Deviator stress correction factor.

GR = 1 for gravelly soils (silty gravel, well-graded gravel, clay gravel, and poorly graded gravel); 0 otherwise.

LI = Liquidity index in percent.

LL = Liquid limit in percent.

MH = 1 for elastic silt type soil; 0 otherwise.

M_Ropt = Resilient modulus at optimum water content.

PI = Plasticity index.

PL = Plastic limit.

S = Degree of saturation in percent.

SM = 1 for silty sand type soil; 0 otherwise.

S200 = S₂₀₀ = P₂₀₀ = Percent material passing the No. 200 sieve.

w_opt = Optimum water content.

 

 

Figure 49. Equation. Correlation between M_r and CBR according to Heukelom and Klomp.⁽¹⁰⁷⁾

Figure 49 shows reasonable estimates for fine-grained soils with CBR less than or equal to 10.

 

Figure 50. Equation. Correlation between M_r and CBR according to Powell et al.⁽¹²²⁾

Figure 50 is currently included in the MEPDG.

 

Figure 51. Equation. Correlation between M_r and CBR according to George.⁽¹⁰⁶⁾

Figure 51 was developed for cohesionless soils and is recommended for medium clay sands.

 

Figure 52. Equation. Correlation between M_r and CBR according to the Asphalt Institute.⁽¹²³⁾

 

Figure 53. Equation. Correlation between M_r and R-value according to AASHTO.⁽¹²⁾

Where:

A = 772 to 1,155; recommended 1,000. B = 369 to 555; recommended 555.

 

Figure 54. Equation. Correlation between M_r and R-value according to Buu.⁽¹²⁴⁾

Figure 54 was developed for fine-grained soils. The deviator stress is 6 psi, the confinement stress is 2 psi, and the valid for R-value is greater than 20.

 

Figure 55. Equation. Correlation between M_r and R-value according to Yeh and Su.⁽¹¹⁰⁾

 

Figure 56. Equation. Correlation between M_r and R-value according to MEPDG.⁽²⁾

Figure 56 is currently included in the MEPDG. The R-value is between 2.3 and 11.

 

Figure 57. Equation. Correlation between M_r and unconfined compressive strength according to Thompson and Robnett.⁽¹¹³⁾

Figure 57 was developed assuming a bilinear M_r versus deviator stress behavior.

 

Figure 58. Equation. Correlation between M_r and shear strength according to Lee et al.⁽¹²⁵⁾

Figure 58 was developed for clayey subgrade soils and is valid for cohesive soils only where:

 a = Level of deviator stress. S_u,1% = Undrained shear strength at 1 percent axial strain.

 

Figure 59. Equation. Correlation between M_r and DCP test method according to Hassan.⁽¹²⁶⁾

Where DCPI is the DCP index in inches per blow.

 

Figure 60. Equation. Correlation between M_r and DCP test method according to Chen et al.⁽¹²⁷⁾

Figure 60 was developed for subgrade materials using backcalculated FWD modulus values. DCPI is in millimeters per blow.

 

Figure 61. Equation. Correlation between M_r and DCP test method for coarse-grained sandy soils according to George and Uddin.⁽¹²⁸⁾

For figure 61, DCPI is in millimeters per blow.

 

Figure 62. Equation. Correlation between M_r and DCP test method for fine-grained clays according to George and Uddin.⁽¹²⁸⁾

For figure 62, DCPI is in millimeters per blow.

 

Figure 63. Equation. Correlation between M_r and DCP test method according to Chen et al.⁽¹²⁹⁾

Figure 63 was developed for both base and subgrade soils materials. DCPI is in millimeters per blow.

 

Figure 64. Equation. Correlation between M_r and DCP test method, DCPI only according to Mohammad et al.⁽¹³⁰⁾

Figure 64 was developed for soil types A-4, A-6, A-7-5, and A-7-6. A field DCP test and laboratory test were correlated through statistical analysis. DCPI is in millimeters per blow.

Where:

_d = Dry unit weight in kN/m³. w = Water content in percent.

 

Figure 65. Equation. Correlation between M_r and DCP test method, DCPI, and soil properties according to Mohammad et al.⁽¹³⁰⁾

Figure 65 was developed for soil types A-4, A-6, A-7-5, and A-7-6. Field DCP test and laboratory test were correlated through statistical analysis. DCPI is in millimeters per blow.

Where:

_d = Dry unit weight in kN/m³. w = Water content in percent.

 

Figure 66. Equation. Correlation between M_r and CPT test method, in situ conditions according to Mohammad et al.⁽¹³¹⁾

Figure 66 was developed for silty clay and heavy clayey cohesive soils.

Where:

q_c = Tip resistance (MPa). f_s = Frictional resistance (MPa). u_t = Total pore pressure.

 

Figure 67. Equation. Correlation between M_r and CPT test method traffic loading conditions according to Mohammad et al.⁽¹³¹⁾

Figure 67 was developed for silty clay and heavy clayey cohesive soils.

Where:

 =  = Confining stress (kPa). _v = Vertical stress (kPa). w = Water content. _d = Dry unit weight (kN/m³). _w = Unit weight of water (kN/m³).

Recently, the resilient modulus has been predicted using a two-step approach. First, models to predict parameters k₁, k₂, and k₃ of the constitutive equation are developed. Next, the constitutive equation is used to estimate the resilient modulus. Von Quintus and Killingsworth, Dai and Zollars, and Santha developed prediction equations by regressing the coefficients of selected constitutive equations and relating them to soil physical properties.^(132–134) It was observed that the most influential parameters are moisture content, liquid limit, plasticity index, and percent passing the No. 200 sieve.

One of the most comprehensive reviews of the resilient modulus test data measured on pavement materials and soils was made in the LTPP program.⁽¹³⁵⁾ A total of 2,014 resilient modulus laboratory tests that passed all the QC checks of the LTPP database (i.e., level E data status, 2000 data release) were used in this review. The study verified that the response characteristics correlate to a form of the constitutive model presented in figure 33. The study correlated resilient modulus data to the physical properties of the materials and found that the physical properties that influenced the resilient modulus varied between the different materials and soils. No one physical property was highly correlated to the modulus. For example, the liquid limit, plasticity index, and the amount of material passing the smaller sieve sizes were found to be important for the lower strength unbound aggregate base/subbase materials, while the moisture content and density were important as related to higher strength materials. Furthermore, the amount of material passing the larger sieve sizes was important for the unbound aggregate base/subbase materials with larger MASs. It also was found that percent clay and test specimen moisture content or density were important for all soil groups, while percent silt was important for all soil groups except gravel. It was also found that to improve correlations, the sample locations (depth) had to be matched while comparing test results for the same test section or site. Based on the quality of correlations developed in this study, it was recommended that the results need to be verified and confirmed after all resilient modulus tests have been completed. Future model refinement was suggested with a more comprehensive dataset.

Appendix CC in the MEPDG presents a detailed discussion of moisture and temperature regime influences on resilient modulus.⁽²⁾ The values of the resilient moduli at any location and time within a given pavement structure are calculated in the MEPDG as a function of the soil moisture and freeze-thaw influences. The impact of temporal variations in moisture and temperature on resilient modulus are considered through the composite environmental adjustment factor, F_env. The Enhanced Integrated Climatic model (EICM) is integral to the MEPDG software (the publication by Larson and Dempsey deals with all environmental factors and provides soil moisture, suction, and temperature as a function of time, at any location in the unbound layers from which F_env can be determined).⁽¹³⁶⁾ This moisture prediction capability of the EICM was improved by Zapata and Houston.⁽¹³⁷⁾ The resilient modulus at any time or position within the pavement structure is then determined by multiplying the value at optimum with F_env ( i.e.,).

F_env is an adjustment factor, and M_ropt is the resilient modulus at optimum conditions (maximum dry density and optimum moisture content) at any state of stress. Variations of resilient modulus with stress and variations of modulus with environmental factors (i.e., moisture, density, and freeze-thaw conditions) are assumed to be independent.

Using the latest testing protocol to measure resilient modulus, AASHTO T 307, Titi et al. performed a comprehensive investigation to estimate the resilient modulus of various Wisconsin subgrade soils and develop basic models to estimate the resilient modulus from soil properties.^(28,138) Also, a laboratory testing program was conducted on common subgrade soils to characterize their physical properties. The resilient modulus constitutive equation was used to determine model factors k₁, k₂, and k₃. Titi et al. compared the predictive capability of these models with those developed by Yau and Von Quintus using LTPP data and concluded that the two sets of models did not agree.^(138,135) Differences in the test procedures, test equipment, sample preparation, and other conditions involved with development of the LTPP models and the models of this study were cited as potential factors for this lack of correlation. Key prediction models to estimate resilient modulus from soil properties are summarized below.

Regression Constant Estimates Based on Soil Properties

Prediction Model—Mississippi Materials

Based on the results of repeated triaxial load tests performed on 12 fine-grained and coarse-grained Mississippi subgrades, stress ratios were used in a bulk stress log-log model to describe their behavior. Subsequently, soil properties of the same materials were incorporated in the regression constants of the models. Then, the models were verified using a separate subset of nine different Mississippi subgrades with good correlation.^(106,139) The resulting equations and constants are shown in figure 68 through figure 73.

 

Figure 68. Equation. M_r of Mississippi materials for fine-grained soils.

 

Figure 69. Equation. k₁ of Mississippi materials for fine-grained soils.

 

Figure 70. Equation. k₂ of Mississippi materials for fine-grained soils.

 

Figure 71. Equation. M_r of Mississippi materials for coarse-grained soils.

 

Figure 72. Equation. k₁ of Mississippi materials for coarse-grained soils.

 

Figure 73. Equation. k₂ of Mississippi materials for coarse-grained soils.

The definitions of the parameters used in figure 68 through figure 73 are as follows:

P_a = Atmospheric pressure.

 = Deviator stress =  -_.

 = Major principal stresses.

 = Minor principal stresses.

 = Confining stress.

 = Ratio of dry density to maximum dry density.

LL = Liquid limit in percent.

w_c = Moisture content in percent.

w_cr = Ratio of moisture content to optimum moisture content.

#200 = Percent material passing the No. 200 sieve.

 = Bulk stress =  + +.

 = Intermediate principal stress.

c_u = Uniformity coefficient.

Prediction Model—Georgia Materials

The following equation was developed as a combination of the bulk and deviator stress models in an effort to improve the predicted response of resilient modulus test results by including both axial and shear effects.

 

Figure 74. Equation. M_r of Georgia materials.

Santha estimated values for the regression constants in terms of soil properties using a multiple correlation analysis.⁽¹³⁴⁾ The resulting constants for the analyzed Georgia granular soils are shown in figure 75 to figure 77.

 

 

Figure 75. Equation. k₁ of Georgia materials.

 

Figure 76. Equation. k₂ of Georgia materials.

 

Figure 77. Equation. k₃ of Georgia materials.

Where:

w_c = Moisture content.

w_opt = Optimum moisture content.

w_cratio = w_c /w_opt.

COMP = Degree of compaction.

SATU = Percent saturation.

%SILT = Silt content in percent.

%CLAY = Clay content in percent.

SW = Percent swell.

SH = Percent shrinkage.

CBR = California bearing ratio.

 = Dry density.

P₄₀ = Material passing No. 40 sieve in percent.

 

Prediction Model—Louisiana Materials

An equation similar to Uzan’s model using the octahedral normal stress instead of the bulk stress was used to study eight types of Louisiana soils.⁽¹⁴⁰⁾ Figure 79 shows the resilient modulus of Louisiana materials.

 

Figure 78. Equation. M_r of Louisiana materials.

Linear regression was then applied to estimate the values of the regression constants in terms of soil properties. The resulting equations are shown in figure 79 through figure 81.

 

Figure 79. Equation. k₁ of Louisiana materials.

 

Figure 80. Equation. k₂ of Louisiana materials.

 

Figure 81. Equation. k₃ of Louisiana materials.

Where:

_oct = Octahedral normal stress .

_oct = Octahedral shear stress .

w_c = Moisture content.

w_opt = Optimum moisture content.

w_cratio = w_c /w_opt.

LL = Liquid limit.

PL = Plastic limit.

%SILT = Silt content in percent.

%SAND = Sand content in percent.

 = Dry density in kN/m³.

 = Optimum density in kN/m³.

 

Prediction Model—LTPP Materials

Figure 82 has gained considerable acceptance over time and is the constitutive model using the same parameters as in figure 33 and proposed in NCHRP Project 1-28A.⁽¹⁰³⁾

 

Figure 82. Equation. M_r of LTPP materials.

The strength of this equation is its ability to handle two of the resilient modulus dependencies, stress-state and material type. Santha compared a log-log bulk stress model to figure 82 in modeling Georgia granular subgrade soils and concluded that the model presented in figure 82 provided a better representation of laboratory measurements of resilient modulus.⁽¹³⁴⁾

One of the most comprehensive validations of figure 82 using LTPP resilient modulus test data was performed by Yau and Von Quintus.⁽¹³⁵⁾ The authors first identified anomalous data, verified if the response characteristics correlated to the constitutive model presented in figure 82, subsequently explored the effect of material type and sampling technique, and performed a nonlinear regression analysis to establish relationships between the k regression constants in figure 82 and various material properties. The resulting regression equations for unbound and subgrade materials are presented in figure 83 through figure 115. The definitions of the variables used in the figures are as follows:

P_3/8 = Percent material passing ³/₈-inch sieve.

P₄ = Percent material passing No. 4 sieve.

P₄₀ = Percent material passing No. 40 sieve.

P₂₀₀ = Percent material passing No. 200 sieve.

%SILT = Silt content in percent.

%CLAY = Clay content in percent.

LL = Liquid limit in percent.

PI = Plasticity index.

W_opt = Optimum water content in percent.

W_s = Water content of the test specimen in percent

 = Maximum dry unit weight of soil in kg/m³.

 = Dry density of the test specimen in kg/m³.

 

Unbound Base and Subbase Materials

Figure 83 through figure 85 show equations for crushed stone (LTPP material code 303) as follows:

 

Figure 83. Equation. k₁ of LTPP materials—crushed stone.

 

Figure 84. Equation. k₂ of LTPP materials—crushed stone.

 

Figure 85. Equation. k₃ of LTPP materials—crushed stone.

 

Figure 86 through figure 88 show equations for crushed gravel (LTPP material code 304) as follows:

 

Figure 86. Equation. k₁ of LTPP materials—crushed gravel.

 

        

Figure 87. Equation. k₂ of LTPP materials—crushed gravel.

 

Figure 88. Equation. k₃ of LTPP materials—crushed gravel.

Figure 89 through figure 91 show equations for uncrushed gravel (LTPP material code 302) as follows:

 

Figure 89. Equation. k₁ of LTPP materials—uncrushed gravel.

 

Figure 90. Equation. k₂ of LTPP materials—uncrushed gravel.

 

Figure 91. Equation. k₃ of LTPP materials—uncrushed gravel.

Figure 92 through figure 94 show equations for sand (LTPP material code 306) as follows:

 

Figure 92. Equation. k₁ of LTPP materials—sand.

 

Figure 93. Equation. k₂ of LTPP materials—sand.

 

Figure 94. Equation. k₃ of LTPP materials—sand.

Figure 95 through figure 97 show equations for coarse-grained soil-aggregate mixture (LTPP material code 308) as follows:

 

Figure 95. Equation. k₁ of LTPP materials—coarse-grained soil-aggregate mixture.

 

Figure 96. Equation. k₂ of LTPP materials—coarse-grained soil-aggregate mixture.

 

Figure 97. Equation. k₃ of LTPP materials—coarse-grained soil-aggregate mixture.

Figure 98 through figure 100 show equations for fine-grained soil-aggregate mixture (LTPP material code 307) as follows:

 

Figure 98. Equation. k₁ of LTPP materials—fine-grained soil-aggregate mixture.

 

Figure 99. Equation. k₂ of LTPP materials—fine-grained soil-aggregate mixture.

 

Figure 100. Equation. k₃ of LTPP materials—fine-grained soil-aggregate mixture.

 

Figure 101 through figure 103 show equations for fine-grained soil (LTPP material code 309) as follows:

 

Figure 101. Equation. k₁ of LTPP materials—fine-grained soil.

 

Figure 102. Equation. k₂ of LTPP materials—fine-grained soil.

 

Figure 103. Equation. k₃ of LTPP materials—fine-grained soil.

Subgrade Soils

Figure 104 through figure 106 show equations for coarse-grained gravel soils as follows:

 

Figure 104. Equation. k₁ of LTPP materials—coarse-grained gravel soils.

 

Figure 105. Equation. k₂ of LTPP materials—coarse-grained gravel soils.

 

Figure 106. Equation. k₃ of LTPP materials—coarse-grained gravel soils.

Figure 107 through figure 109 show equations for coarse-grained sand soils as follows:

Figure 107. Equation. k₁ of LTPP materials—coarse-grained sand soils.

 

Figure 108. Equation. k₂ of LTPP materials—coarse-grained sand soils.

 

Figure 109. Equation. k₃ of LTPP materials—coarse-grained sand soils.

 

Figure 110 through figure 112 show equations for fine-grained silt soils as follows:

 

Figure 110. Equation. k₁ of LTPP materials—fine-grained silt soils.

 

Figure 111. Equation. k₂ of LTPP materials—fine-grained silt soils.

 

Figure 112. Equation. k₃ of LTPP materials—fine-grained silt soils.

Figure 113 through figure 115 show equations for fine-grained clay soils as follows:

 

Figure 113. Equation. k₁ of LTPP materials—fine-grained clay soils.

 

Figure 114. Equation. k₂ of LTPP materials—fine-grained clay soils.

 

Figure 115. Equation. k₃ of LTPP materials—fine-grained clay soils.

Prediction Model—Wisconsin Materials

Titi et al. evaluated the model presented in figure 82 using repeated triaxial test results performed on various Wisconsin subgrade soils and developed correlations between the model’s regression constants and soil properties.⁽¹³⁸⁾ Good results were achieved when the statistical analysis was performed for fine-grained and coarse-grained soils separately. Researchers also used the LTPP data to compare their correlations to those developed by Yau and Von Quintus.⁽¹³⁵⁾ It was discovered that the two sets of models did not agree. Differences in the test procedures, test equipment, sample preparation, and other conditions involved with development of the LTPP models versus the ones used in the study were cited as potential factors for this lack of agreement. The equations developed by Titi et al. are provided in figure 116 through figure 124.⁽¹³⁸⁾ The definitions of the terms used in the figures are as follows:

P₄ = Percent material passing No. 4 sieve.

P₄₀ = Percent material passing No. 40 sieve.

P₂₀₀ = Percent material passing No. 200 sieve.

%SAND = Sand content in percent.

%SILT = Silt content in percent.

%CLAY = Clay content in percent.

LL = Liquid limit.

PL = Plastic limit.

PI = Plasticity index.

LI = Liquidity index.

w = Water content.

w_opt = Optimum water content.

 = Dry unit weight.

 = Maximum dry unit weight.

Figure 116 through figure 118 show equations for fine-grained soils as follows:

 

Figure 116. Equation. k₁ of Wisconsin materials—fine-grained soils.

 

Figure 117. Equation. k₂ of Wisconsin materials—fine-grained soils.

 

Figure 118. Equation. k₃ of Wisconsin materials—fine-grained soils.

Figure 119 through figure 121 show equations for non-plastic coarse-grained soils as follows:

 

Figure 119. Equation. k₁ of Wisconsin materials—non-plastic coarse-grained soils.

 

Figure 120. Equation. k₂ of Wisconsin materials—non-plastic coarse-grained soils.

 

Figure 121. Equation. k₃ of Wisconsin materials—non-plastic coarse-grained soils.

Figure 122 through figure 124 show equations for plastic coarse-grained soils as follows:

 

Figure 122. Equation. k₁ of Wisconsin materials—plastic coarse-grained soils.

 

Figure 123. Equation. k₂ of Wisconsin materials—plastic coarse-grained soils.

 

Figure 124. Equation. k₃ of Wisconsin materials—plastic coarse-grained soils.