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

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 5. MODEL DEVELOPMENT (4)

Compressive Strength Model 1: 28-Day Cylinder Strength Model

The data used for this model included SPS sections that had 28-day cylinder test results. The data included 42 sets of results after averaging the 28-day cylinder strength for each site and for each mix design.

All material properties discussed in the section, Data Used in PCC Models, in chapter 5 of this report were evaluated to verify if they co-vary with the predicted variable. The first statistical procedure was a C_p analysis wherein various submodels were considered for fit using ANOVA, and the resulting C_p and R² values are provided at the end of the SAS^® analysis. The results are listed by SAS^® in order of the resulting C_p value. Also provided in the results are the number of variables (regressors) used in each model and a listing of the variables. The C_p analysis results are shown in table 16 for the 28-day cylinder strength model.

The C_p analysis summary indicates that 42 observations were read. There were missing data for certain PCC mix parameters. For example, the amount of coarse aggregate in the mix design and the amount of fine aggregate in mix design were missing in 13 cases, while the information on admixtures was missing in 21 cases. A summary indicates that only 21 observations had values for all variables considered in the model. Using a subset of 21 datasets, the potential prediction models created produced the R² values as listed in the table. The model form used for the analysis was as follows:

Figure 132. Equation. f_c model form.

Where:

A₀ = Model intercept determined through the regression.

A₁ through A_n = Regression coefficients.

x₁ through x_n = Parameters included in each submodel.

These results do not imply that all models listed in table 16 are feasible models. C_p and R², as explained earlier, do not indicate whether the parameters included in the model, or submodel in this case, are significant, exhibit multicollinearity, or physically explain the trend. Each submodel suggested by the C_p analysis needs to be further evaluated and verified individually.

Table 16. C_p selection method for 28-day cylinder compressive strength model.

Number of Parameters in Model	*C_p*	R²	Variables in Model
4	1.0058	0.8184	w_c cementitious Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	1.2802	0.8143	cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
2	1.5747	0.7493	cementitious Coarse_Aggregate_Mix_Design
3	1.807	0.7761	cementitious Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	1.8277	0.806	w_c MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
3	1.8478	0.7755	w_c cementitious Coarse_Aggregate_Mix_Design
3	2.0836	0.7719	cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design
5	2.2057	0.8305	w_c cementitious FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
3	2.3622	0.7677	w_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	2.4771	0.7962	cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	2.4789	0.8264	cementitious FM AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	2.5453	0.7952	w_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
3	2.5577	0.7647	cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design
5	2.7348	0.8225	w_c cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	2.9597	0.8191	w_c cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	2.9672	0.819	w_c cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	2.97	0.819	w_c cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	2.9955	0.8186	cementitious AVG_UNIT_WT2 AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	3.0046	0.8185	cementitious AVG_UNIT_WT AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	3.04	0.8179	w_c MASm15pct_W_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	3.1679	0.7857	cementitious FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	3.2171	0.8152	cementitious MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
3	3.4873	0.7507	cementitious FM Coarse_Aggregate_Mix_Design
5	3.4917	0.8111	AVG_UNIT_WT2 MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	3.4928	0.8111	w_c AVG_UNIT_WT2 MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	3.4971	0.811	w_c AVG_UNIT_WT MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	3.5058	0.8109	cementitious MASm15pct_W_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
5	3.5095	0.8108	AVG_UNIT_WT MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
2	3.5215	0.7199	w_c cementitious
5	3.5431	0.8103	w_c MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
3	3.5548	0.7496	cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design
3	3.5574	0.7496	cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design
4	3.6023	0.7792	FM AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
3	3.6744	0.7478	AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
2	3.711	0.717	cementitious MASm15pct_W_c
4	3.7405	0.7771	w_c cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design
4	3.7435	0.777	cementitious AVG_UNIT_WT2 AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design
4	3.7458	0.777	MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	3.7472	0.777	w_c cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design
4	3.7504	0.7769	w_c cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design
4	3.757	0.7768	cementitious AVG_UNIT_WT AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design
4	3.7817	0.7765	w_c cementitious FM Coarse_Aggregate_Mix_Design
4	3.8069	0.7761	cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	3.807	0.7761	cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
4	3.8079	0.7761	w_c cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design
2	3.9079	0.7141	cementitious AVG_UNIT_WT_W_c
4	4.0157	0.7729	cementitious FM AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design
4	4.034	0.7726	w_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design
6	4.0832	0.8324	w_c cementitious MASm15pct_W_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

Table 17 to table 20 show examples of submodels evaluated in the selection of the optimized model for the prediction of 28-day compressive strength of PCC cylinders. This procedure typically involves an iterative process and specifically evaluates the following aspects:

Is it reasonable to assume that the variables selected for the submodel are readily available for use at the intended stage of a project?
- For the 28-day compressive strength value to be used by a designer at an initial design stage, information regarding the unit weight is perhaps not available. The unit weight is dependent on the consolidation achieved in the field. However, it could be available from field tests during the QA stage or to determine opening time or for long-term strength estimates.
Do the regressed coefficients for the selected parameters explain the trends expected based on literature review and engineering knowledge?
- Verify the absolute value and the sign (plus or minus) of the coefficient.
Is the inclusion of the parameter significant to the prediction model (i.e., is the predictive ability of the model negatively affected by the inclusion of a given parameter)?
- Verify if the p-value is less than 0.05 for a 95 percent confidence level.
Does the parameter have an interaction effect with another parameter in the model?
- Verify if VIF is below 5 (or 10 in exceptional cases).
Is the model showing reasonable sensitivity to each parameter?
- Verify using sensitivity analyses.

Page Owner: Office of Research, Development, and Technology, Office of Infrastructure, RDT

Topics: research, infrastructure, pavements and materials
Keywords: research, infrastructure, pavements and materials, Pavements, LTPP, material properties, MEPDG, prediction model, Index properties
TRT Terms: research, facilities, transportation, highway facilities, roads, parts of roads, pavements
Scheduled Update: Archive - No Update needed

This page last modified on 09/14/2012

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

CHAPTER 5. MODEL DEVELOPMENT (4)

Compressive Strength Model 1: 28-Day Cylinder Strength Model

Figure 132. Equation. fc model form.

Table 16. Cp selection method for 28-day cylinder compressive strength model.

Figure 132. Equation. f_c model form.

Table 16. C_p selection method for 28-day cylinder compressive strength model.