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Publication Number: FHWA-HRT-12-030
Date: August 2012

 

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

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CHAPTER 6. SUMMARY AND FUTURE WORK

Summary

Material characterization has gained increasing importance in pavement engineering, mainly due to the development of analyses and design procedures that are capable of considering material properties to predict pavement performance. This becomes crucial not only in the initial design phase, but also in QA practices and in pavement management throughout the pavement service life. Materials behave differently depending on the material type (PCC materials, unbound fine-grained materials, unbound coarse-grained materials, etc.), the type of loading (loading under compression, under flexure, under thermal differentials, etc.), and the testing conditions (rate of loading, level of loading, etc). Therefore, materials are characterized by different properties to capture the behavior of the material under different conditions. Procedures like the MEPDG use various material property inputs to model pavement response and to predict pavement performance.

Consequently, there is a need for more information about material properties, which is addressed only to a limited extent in currently available resources. Reliable correlations between material parameters and index properties offer a cost-effective alternative and are equivalent to the level 2 MEPDG inputs. The LTPP database, which contains material property test results as well as material index properties, offers an opportunity to develop such correlations for PCC materials, stabilized materials, and unbound materials.(5) Furthermore, because these data come from real-world materials, workmanship, and construction practices instead of from controlled laboratory experiments, correlations developed from LTPP data can be considered suitable for use in pavement-related applications.

The MEPDG also requires certain design-related inputs, commonly called design feature inputs, which are influenced by material properties as well as climate and construction-related parameters. The deltaT values for JPCP and CRCP design are prime examples of design feature inputs. These inputs are not directly available from simple test results. In combination with the data available from the MEPDG calibration models, the LTPP database offers the potential to provide the much-needed guidance to estimate these inputs.

This study involved developing predictive models to estimate material and design parameters. The main objectives of this study were as follows:

 

A thorough review of the literature was performed to identify material properties for which predictive models would be required and to identify the index properties that have a significant impact on each material property of interest. This was followed by an evaluation of the data available in the LTPP database to assess the availability of data essential for developing these correlations. Based on the review of the database, the following material categories and material properties were selected for developing predictive relationships:

 

The LTPP database has an extensive record of material test results. Also, test data are available for SPS and GPS sections, which have distinctly different levels of detail for material index properties and cover different pavement age ranges. Therefore, multiple models were developed for each material property if suitable data were available. The data required to develop models under the rigid pavement design features category were obtained partly from the LTPP database and partly by conducting multiple analysis runs of the LTPP sections used in the calibration of the MEPDG distress models. All models were developed under rigorous statistical analysis procedures, and a uniform set of criteria was used across all models. The statistical significance was discussed in detail throughout the report.

The following is a summary of the models developed under this study, grouped by material type and material property.

PCC Materials

PCC Compressive Strength Models

Compressive Strength Model 1: 28-Day Cylinder Strength Model

fc,28d. f subscript c,28d equals 4,028.41841 minus 3,486.3501 times w/c plus 4.02511 times CMC.

Figure 265. Equation. Prediction model 1 for fc,28d.

Where:

fc,28d = 28-day compressive strength, psi.

w/c =   Water to cement ratio.

CMC = Cementitious materials content, lb/yd3.

Compressive Strength Model 2: Short-Term Cylinder Strength Model

f subscript c,t equals 6,358.60655 plus 3.53012 times CMC minus 34.24312 times w/c times uw plus 633.3489 times natural log open parenthesis t closed parenthesis.

Figure 266. Equation. Prediction model 2 for fc,t.

Where:

fc,t = Compressive strength at age t years, psi.

CMC = Cementitious materials content, lb/yd3.

w/c = Water to cement ratio.

uw = Unit weight, lb/ft3.

t = Short-term age, years.

Compressive Strength Model 3: Short-Term Core Strength Model

f subscript c,t equals 98.92962 plus 5.70412 times CMC plus 28.48527 times uw plus 2570.13151 times MAS times w/c minus 199.84664 times FM plus 611.30879 times natural log open parenthesis t closed parenthesis.

Figure 267. Equation. Prediction model 3 for fc,t.

Where:

fc,t = Compressive strength at age t years, psi.

CMC = Cementitious materials content, lb/yd3.

uw = Unit weight, lb/ft3.

MAS = Maximum aggregate size, inch.

w/c = Water to cement ratio.

FM = Fineness modulus of fine aggregate.

t = Short-term age, years.

Compressive Strength Model 4: All Ages Core Strength Model

f subscript c,t equals -6,022.44 minus 854.46 times w/c plus 4.8656 times CMC plus 68.5337 times uw plus 533.15 times natural log open parenthesis t closed parenthesis.

Figure 268. Equation. Prediction model 4 for fc,t.

Where:

fc,t = Compressive strength at age t years, psi.

w/c = Water to cement ratio.

CMC = Cementitious materials content, lb/yd3.

uw = Unit weight, lb/ft3.

t= Short-term age, years.

Compressive Strength Model 5: Long-Term Core Strength Model

f subscript c,LT equals -3,467.3508 plus 3.508 plus 3.63452 times CMC plus 0.42362 times uw squared.

Figure 269. Equation. Prediction model 5 for fc,LT.

Where:

fc, LT = Long-term compressive strength, psi.

CMC = Cementitious materials content, lb/yd3.

uw = Unit weight, lb/ft3.

PCC Flexural Strength Models

Flexural Strength Model 1: Flexural Strength Based on Compressive Strength

MR equals 22.7741 times f prime subscript c raised to the power of 0.4082.

Figure 270. Equation. Prediction model 6 for MR.

Where:

MR = Flexural strength, psi.

f'c,= Compressive strength determined at the same age, psi.

Flexural Strength Model 2: Flexural Strength Based on Age, Unit Weight, and w/c Ratio

MR subscript t equals 676.0159 minus 1,120.31 times w/c plus 4.1304 times uw plus 35.74627 times natural log times open parenthesis t closed parenthesis.

Figure 271. Equation. Prediction model 7 for MRt.

Where:

MRt = Flexural strength at age t years, psi.

w/c = water to cement ratio.

uw = Unit weight, lb/ft3.

t = Pavement age, years.

Flexural Strength Model 3: Flexural Strength Based on Age, Unit Weight, and CMC

MR subscript t equals 24.15063 plus 0.55579 times CMC plus 2.96376 times uw plus 35.54463 times natural log times open parenthesis t closed parenthesis.

Figure 272. Equation. Prediction model 8 for MRt.

Where:

MRt = Flexural strength at age t years, psi.

CMC = Cementitious materials content, lb/yd3.

uw = Unit weight, lb/ft3.

t = Pavement age, years.

PCC Elastic Modulus Models

Elastic Modulus Model 1: Model Based on Aggregate Type

E subscript c equals open parenthesis 4.499 times open parenthesis UW closed parenthesis raised to the power of 2.3481 times open parenthesis f prime c closed parenthesis raised to the power of 0.2429 closed parenthesis times D subscript agg.

Figure 273. Equation. Prediction model 9 for Ec.

Where:

Ec = PCC elastic modulus, psi.

uw = Unit weight, lb/ft3.

f'c = Compressive strength at same age, psi.

Dagg = Regressed constant depending on aggregate type as follows:

 

Elastic Modulus Model 2: Model Based on Age and Compressive Strength

E subscript c,t equals 59.0287 times open parenthesis f prime c subscript t closed parenthesis raised to the power of 1.3 times open parenthesis natural log open parenthesis t divided by 0.03 closed parenthesis, closed parenthesis raised to the power of -0.2118.

Figure 274. Equation. Prediction model 10 for Ec,t.

 

Where:

Ec,t = Elastic modulus at age t years f'ct = Compressive strength at age t years. t = Age at which modulus is determined, years.

Elastic Modulus Model 3: Model Based on Age and 28-day Compressive Strength

E subscript c,t equals 375.6 times open parenthesis f prime c subscript 28-day closed parenthesis raised to the power of 1.1 times open parenthesis natural log open parenthesis t divided by 0.03 closed parenthesis, closed parenthesis times 0.00524.

Figure 275. Equation. Prediction model 11 for Ec,t.

Where:

Ec,t = Elastic modulus at age t years.

F'c28-day = 28-day compressive strength.

t = Age at which modulus is determined, years.

PCC Indirect Tensile Strength Models

PCC Indirect Tensile Strength Model: Model Based on Compressive Strength

f subscript t equals 8.9068 times open parenthesis f prime c closed parenthesis raised to the power of 0.4785.

Figure 276. Equation. Prediction model 12 for ft.

Where:

ft = Indirect tensile strength of the PCC material. f'c= Compressive strength of the mix determined at the same age.

PCC CTE Models

CTE Model 1: CTE Based on Aggregate Type (Level 3 Equation for MEPDG)

Table 57. Model 13. CTE based on aggregate type.

Aggregate Type

Average From Data Used in Level 2 Model

Basalt

4.86

Chert

6.90

Diabase

5.13

Dolomite

5.79

Gabbro

5.28

Granite

5.71

Limestone

5.25

Quartzite

6.18

Andesite

5.33

Sandstone

6.33

 

CTE Model 2: CTE Based on Mix Volumetrics (Level 2 Equation for MEPDG)

CTE subscript PCC equals CTE subscript CA times V subscript CA plus 6.4514 times open parenthesis 1 minus V subscript CA closed parenthesis.

Figure 277. Equation. Prediction model 14 for CTEPCC.

Where:

CTEPCC = CTE of the PCC material, x10-6 inch/inch/°F.

VCA = Volumetric proportion of the coarse aggregate (value between zero and 0.6).

CTECA = Constant determined for each aggregate type as follows:

 

Rigid Pavement Design Features Models

deltaT—JPCP Design

DeltaT divided by inch equals 
-5.27805 minus 0.00794 times TR minus 0.0826 times SW plus 0.18632 times PCCTHK plus 0.01677 times uw plus 1.14008 times w/c plus 0.01784 times latitude.

Figure 278. Equation. Prediction model 15 for deltaT/inch.

Where:

deltaT/inch = Predicted gradient in JPCP slab, °F/inch.

TR = Difference between maximum and minimum temperature for the month of construction, °F.

SW = Slab width, ft.

PCCTHK = JPCP slab thickness, inch.

uw= Unit weight of PCC used in JPCP slab, lb/ft3.

 

w/c= Water to cement ratio.

latitude = Latitude of the project location, degrees.

deltaT—CRCP Design

DeltaT divided by inch equals 12.93007 minus 0.15101 times MaxTemp minus 0.10241 times MaxTempRange plus 3.279 times Chert plus 1.55013 times Granite plus 1.40009 times Limestone plus 2.01838 times Quarzite plus 0.11299 times PCCTHK.

Figure 279. Equation. Prediction model 16 for deltaT/inch.

Where:

deltaT/inch = Predicted gradient in CRCP slab, °F/inch.

MaxTemp = Maximum temperature for the month of construction, °F.

MaxTempRange = Maximum temperature range for the month of construction, °F.

PCCTHK = JPCP slab thickness, inch.

Chert =1 if PCC mix coarse aggregate is chert, or 0 if otherwise.

Granite = 1 if PCC mix coarse aggregate is granite, or 0 if otherwise.

Limestone = 1 if PCC mix coarse aggregate is limestone, or 0 if otherwise.

Quartzite = 1 if PCC mix coarse aggregate is quartzite, or 0 if otherwise.

Erosion for CRCP Design

There were no modifications to the existing MEPDG erosion model.

EI for JPCP Design

No model was developed for this parameter.

Stabilized Materials Models

LCB Elastic Modulus Model

E subscript LCB equals 58,156 times the square root of f prime subscript c,28d plus 716,886.

Figure 280. Equation. Prediction model 17 for ELCB.

Where:

ELCB = Elastic modulus of the LCB layer.

f'c, 28d = 28-day compressive strength of the LCB material.

 

Unbound Materials Models

Resilient Modulus of Unbound Materials

Resilient modulus will be determined using the following constitutive model:

M subscript r equals K subscript 1 times open parenthesis theta divided by P subscript a closed parenthesis raised to the power of k subscript 2 times open parenthesis tau subscript oct divided by P subscript a closed parenthesis raised to the power of k subscript 3.

Figure 281. Equation. Mr.

The constitutive model parameters are defined as follows:

k subscript equals 1,446.2 minus 4.56764 times PCTHALF plus 4.92 times LL minus 27.73 times OPTMOIST.

Figure 282. Equation. Prediction model 18 for k1.

k subscript 2 equals 0.45679 minus 0.00073376 times PCTNO80 minus 0.00269 times LL plus 0.00060555 times PCTGRVL plus 12.97 times D subscript 10.

Figure 283. Equation. Prediction model 19 for k2.

k subscript 3 equals -0.188 (for fine-grained soils) or -0.153 (for coarse-grained materials).

Figure 284. Equation. Prediction model 20 for k3.

Where:

PCTHALF = Percent passing 1/2-inch sieve.

LL = Liquid limit, percent.

OPTMOIST = Optimum moisture content, percent.

PCTNO80 = Percent passing No. 80 sieve.

PCTGRVL = Percent gravel fraction (0.078- to 2.36-inch size).

D10 = Maximum particle size of the smallest 10 percent of soil sample.

 

Future WORK

The models presented in this report, for most part, were developed from LTPP materials tables that are comprehensive and have been cleared through rigorous data screening and reviews (level E). The CTE values in the database are a relatively recent addition. Over the past year, some issues were identified with the accuracy of these data, and FHWA has made other efforts to correct the CTE test data. The CTE models developed in this study, therefore, need to be updated to reflect the recent changes.

Additionally, the deltaT models for JPCP and CRCP design are based on the calibration in the MEPDG version 1.0 software. The MEPDG rigid pavement models are being updated to account for changes in CTE values and to address software bugs identified since the release of version 1.0 in 2006. This version was completed in 2011. Therefore, the deltaT models presented here will not be applicable in the new version. These models will require updating. The procedures followed to develop these models are valid and can be used in a framework for future revisions.

 


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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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