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â Implementation of roller-integrated compaction moni- toring technologies into earthwork specifications requires an understanding of relationships between roller MVs and soil compaction measurements. Previous studies (e.g., Floss et al. 1983; Samaras et al. 1991; Brandl & Adam 1997; White & Thompson 2008; Thompson & White 2008; White et al. 2008a, 2008b, 2008c) have documented relationships be- tween roller MVs and a variety of in situ soil properties but are generally limited to one roller measurement type and lim- ited soil and field conditions. This chapter presents results from a comprehensive evalu- ation of five roller-integrated compaction measurement systems, each with a unique MV (i.e., MDP, CMV D , E vib , k s , CCV) and 17 different soil types. The relationships presented here are divided into three material groups: nongranular sub- grade, granular subgrade, and granular subbase/base materi- als. MVs were obtained from CCC and IC rollers set up with smooth and pad foot drums on 60 controlled TBs. The beds varied in material types, moisture content, and underlying layer support conditions. Roller MVs were obtained for dif- ferent amplitude, frequency, and roller travel speed settings. The objectives of the evaluation were to (1) investigate simple linear relationships between roller MVs and various in situ point (spot-test) measurements, (2) identify key factors that influence these relationships, and (3) evaluate multiple re- gression relationships that consider variations in soil condi- tions and machine operation settings. A variety of conven- tional and mechanistic related in situ spot-test measurements (i.e., Î³ d , CBR, E LWD , E FWD , E V1 , E V2 , CIV, k SSG ) and laboratory M r test measurements were used in correlation analysis to MVs. In brief, results indicate that simple linear correlations be- tween roller MVs and in situ point measurements are possible for a compaction layer underlain by relatively homogeneous and stiff/stable supporting layer. Heterogeneous conditions in the underlying layers, however, can adversely affect the relationships. A multiple regression analysis approach is described in this chapter that includes parameter values to represent underlying layer conditions when statistically sig- nificant, to improve the correlations. E LWD , E V1 , E V2 , and E FWD measurements generally capture the variation in roller MVs better than Î³ d measurements. DCP tests are effective in de- tecting deeper âweakâ areas [at depths greater than 300 mm (1 ft)] that are commonly identified by roller MVs and not by compaction layer point measurements. High variability in soil properties across the drum width and soil moisture content contribute to scatter in relationships. Averaging mea- surements across the drum width and incorporating mois- ture content into multiple regression analysis, when statisti- cally significant, can help mitigate the scatter to some extent. Relatively constant machine operation settings are critical for calibration strips (i.e., constant amplitude, frequency, and travel speed), and correlations are generally better for low- amplitude settings [e.g., 0.7 to 1.1 mm (0.028 to 0.043 in)]. A field testing protocol to obtain reliable correlations during implementation/roller calibration testing and establishing target values from simple and multiple regression relation- ships are described in Chapters 7 and 8. An approach to relate M r to roller MVs using labora- tory-determined w-Î³ d -M r relationships is described in this chapter. Despite the challenges involved in relating field to laboratory measurements, encouraging relationships are observed between roller MVs and M r . Similar to relation- ships between MVs and compaction layer point measure- ments, correlations are possible for materials with relatively stiff/homogeneous subsurface conditions. Again, heteroge- neous underlying support conditions adversely affect cor- relations. These correlations can be improved by including parameter values that represent the underling layer condi- tions through multiple regression analysis. An approach to develop target values from the MV-M r relationship with respect to a targeted in situ moisture content range is pre- sented in Chapter 8. c h a p t e r 6 Relationships Between Roller Measurement Values and Point Measurements
0 6.1 Materials and Testing 6.1.1 materials A total of 17 different soils were evaluated as part of 60 TBs for the correlation study. The soils were divided into non- granular subgrade (13 TBs), granular subgrade (9 TBs), and granular subbase/base (38 TBs) materials, depending on their soil classification and location within the pavement founda- tion layers for each project (Table 6.1). Regression relation- ships presented later in this report are separated according to these general material groupings. Detailed TB information, including soil classification, preparation and construction, roller operations, and roller data maps are provided in Ap- pendix C. 6.1.2 Test Bed Construction and Testing Roller MVs and in situ point measurements (w-Î³ d , DCP- CBR, E LWD , E FWD , E V1 , E V2 , CIV 20-kg , k SSG ) were obtained from controlled TBs with varying plan dimensions [2.5 m Ã 30.0 m to 10 m Ã 65 m (8.2 ft Ã 98.4 ft to 33 ft Ã 213 ft)] to (1) evalu- ate empirical relationships between roller MVs and in situ point measurements and (2) investigate the effects of mois- ture content, amplitude, and underlying layer support con- ditions on compaction layer roller MVs. In situ point mea- surements were obtained at several locations at select roller passes to obtain measurements over a wide range of compac- tion conditions. Point measurements were obtained at one or three test locations over the drum width. When three tests were performed, the point measurements were averaged over the drum width for comparison to the roller MV, which is representative of an integrated response over the drum width. Laboratory M r tests were performed on âundisturbedâ Shelby tube samples collected from a compacted subgrade test bed (CO3), and the measurements were directly correlated to the roller MVs. M r tests were also performed on samples recon- stituted in the laboratory to obtain w-Î³ d -M r relationships for correlation to w-Î³ d -MV relationships. Nuclear moisture-density gauges (ASTM D6938) and drive cylinders (ASTM D2937) were used to determine in situ w-Î³ d . DCP tests (ASTM D6951) were performed to de- termine CBR profiles using CBR = 292/(DCPI)1.12 (ASTM D6951) relationship (measured as mm/blow). Zorn, Keros, and Dynatest LWD devices set up with 200- or 300-mm (8- or 12-in) plate diameters were used to determine E LWD (Zorn 2003, Dynatest 2004). A Dynatest falling weight deflectom- eter (FWD) device with 300-mm (12-in)-diameter plate was used to determine E FWD (Maryland TB locations only). FWD loads were obtained that targeted three contact stresses: 400 kPa, 500 kPa, and 650 kPa. E V1 and E V2 were determined using a 300-mm (12-in)-diameter plate at 100- to 200-kPa contact stress levels for nongranular and granular subgrade soils, and 200- to 400-kPa contact stress levels for granular base/sub- base soils. Poissonâs ratio Î½ = 0.4 was assumed for all soils, and shape factors f = Ï/2 for nongranular subgrade soils and f = 8/3 for granular subgrade/subbase/base soils were assumed in E LWD , E FWD , E V1 , and E V2 calculations. More details on testing methods are presented in Appendix A. table 6.1. Summary of test beds and material types used in correlation study. TB Number USCS (AASHTO)a Classification Material Group Roller Drum Configuration MN4âMN13 CL (A-6(5)) Nongranular subgrade Pad foot and smooth drum CO1âCO3 SC-SM (A-4(3)), CL (A-6(7)) MD2âMD5 SM (A-2-4) Granular subgrade Pad foot and smooth drum FL23 SP-SM (A-3) FL24 SM (A-3) FL25 SM (A-2-4), SP-SM (A-3) NC1âNC2 SM (A-2-4) MN17âMN39 SP-SM (A-1-b) Granular subbase/base Smooth drum CO6âCO15 GW-GM (A-1-a) CO16â20 SP-SM (A-1-a) MD6âMD14 SP-SM (A-1-a) FL19âFL20 SM (A-1-b) NC4 SP-SM (A-1-a) aUnited Soil Classification System (American Association of State Highway and Transportation Officials).
â 6.2 Simple Linear Regression Relationships Simple linear regression analysis involves developing a relationship between independent and dependent variables using an intercept and slope coefficient. This analysis has the advantage of being simple enough to perform on a hand cal- culator. For each linear univariate regression model, the coef- ficient of determination R2 provides a measure of how well the regression model describes the data. The linear correla- tion coefficient r used in the European specification options (see Chapter 2) is equivalent to R 2 . For reference, correla- tions considered acceptable per the European specification options meet the requirement of R2 â¥ 0.5. Although simple linear regression analysis is relatively straightforward, there are many factors that can affect the quality of the correlation between MVs and the various point measurement values. A list of these factors is provided to aid the reader in interpretation of the results. Multiple regression analysis was identified as one approach to overcome some of the factors that affect the simple linear regression relation- ships and is discussed later in this chapter. 6.2.1 analysis approach Simple linear regression relationships were developed by considering in situ point measurements as âtrueâ indepen- dent variables and roller MVs as dependent variables using the model shown in Equation 6.1, where b 0 = intercept, b 1 = slope, and Î± = point measurement value. Statistical sig- nificance of the independent variable was assessed based on p- and t-values. The selected criteria for identifying the sig- nificance of a parameter included p-value <0.05 = significant, <0.10 = possibly significant, >0.10 = not significant, and t- value <-2 or >+2 = significant. RollerMV 0 = +b b 1 Î± (6.1) 6.2.2 factors affecting Quality of regression relationships As with any regression analysis, it is important to identify factors that affect the quality of the regressions. Factors affect- ing regression relationships are broadly identified in Table 6.2 for the purpose of linking some of these factors to various TB conditions. This list was derived from linking TB conditions with correlation analysis but also from experiences gained from field tests as part of this study. Four examples described in the next section illustrate some of the TB conditions that led to development of Table 6.2. Heterogeneity in support conditions of layers underlying the compaction layer is one of the major factors that affect correlations between MVs and point measurements. This is largely due to differences in measurement depths between the roller and the point mea- surements (see Figure 6.1). As discussed in Chapter 4, roller MVs from 11- to 15-ton vibratory rollers can be representa- tive of conditions to depths of 1.0 to 1.2 m (3.3 to 3.9 ft). Use of underlying layer MVs and use of point measurements with comparable measurement influence depths are ways to overcome this obstacle. This approach is discussed in detail in the multiple regression analysis section. 6.2.3 examples of Simple linear regression analysis Below are discussions from select TB studies to highlight different aspects of simple linear regression analysis. Detailed information for all TB regression analyses is provided in Ap- pendix C. The examples present correlations of roller MVs to different in situ point measurements with homogeneous to heterogeneous support conditions and variable conditions across the drum and at different amplitude settings. These conditions represent some of the key aspects of regression analysis for all TBs summarized in Appendix C. 18.104.22.168â âExampleâ1:âTBâMN7(2) TB MN7(2) was constructed by scarifying an existing nongranular subgrade layer (classified as CL according to the USCS classification) to a depth of about 350 mm (14 in) using a soil reclaimer and by moisture conditioning to w = 13.0% to 14.5%. Plan dimensions of this TB were about 2.5 m Ã 120 m (8.2 ft Ã 394.0 ft). Twelve compaction passes were performed with a Caterpillar CS-563E vibratory pad foot roller with constant operation settings using nominal A = 0.80 mm (0.031 in), f = 33 Hz, and v = 4 km/h (2.5 mph). In table 6.2. Summary of factors affecting correlations between MVs and in situ point measurements. No. Factors Affecting Correlations 1 Heterogeneity in underlying-layer support conditions 2 High moisture content variation 3 Narrow range of measurements 4 Machine operation setting variation (e.g., amplitude, frequency, speed) and roller âjumpingâ 5 Nonuniform drum/soil contact conditions 6 Uncertainty in spatial pairing of point measurements and roller MVs (see Chapter 3) 7 Limited number of measurements 8 Not enough information to interpret the results 9 Intrinsic measurement errors associated with roller MVs and in situ point-test measurements (see Chapter 3)
situ point measurements (Î³ d , CBR, and E LWD-Z2 ) were obtained at roller passes 0, 1, 2, 4, and 8 at five test locations along the centerline of the roller path. DCP tests indicated that the layer below the compaction layer [from 350 to 700 mm below the surface (14.0 to 27.6 in)] was relatively homogeneous with CBR = 14 to 18. Figure 6.2 shows roller machine drive power (MDP) MVs as solid lines for roller passes 1, 2, 4, and 8 in comparison with in situ point measurements on the compaction layer. Com- paction growth curves for average roller MV and in situ point measurements with a hyperbolic fit are presented in Figure 6.3. The curves indicate that on average the roller MVs and in situ point measurements generally increased up to eight roller passes (note that a decrease in MDP indicates increas- ing compaction). Linear regression relationships were devel- oped based on spatially nearest point data (i.e., no averaging performed) as shown in Figure 6.3, producing correlations with R2 = 0.50 to 0.89. This example illustrates that with rela- tively homogeneous compaction layer and underlying layer support conditions, good correlations (R2 â¥ 0.5) are possible between MDP and in situ point measurements. 22.214.171.124â Exampleâ2:âTBâFL19B TB FL19B was constructed by placing a nominal 150-mm (5.9-in)-thick loose layer of granular base material (SM ac- cording to the USCS classification) over relatively stiff stabi- lized subgrade (E LWD-Z2 = 132 to 145 MPa). In situ moisture content of the base material was relatively consistent (w = 8.8% to 9.2%). Thirteen compaction passes were performed Figure 6.1. Illustration of differences in measurement depths for different measurements.
â with a Dynapac CA362 vibratory smooth drum roller at con- stant operation settings, with nominal A = 0.90 mm (0.035 in), f = 30 Hz, and v = 4.0 to 4.5 km/h (2.5 to 2.8 mph). In situ point measurements (Î³ d and E LWD-Z3 ) were obtained at five locations along the test bed after roller passes 1, 2, 3, 4, 8, and 12. Tests were conducted at three positions across the width of the drum lane at each point measurement location. Compaction growth curves for average roller MVs (CMV D ) and in situ point measurements with hyperbolic curves are presented in Figure 6.4. In situ point measurement data are presented separately for measurements along the center of the drum and measurements along the rear-wheel path. Different compaction trends were observed between center and wheel path measurements. On average, measurements along the center were about 1.1 to 1.6 times greater than measurements along the rear-wheel path (this observation should not be considered typical because at other sites simi- lar measurements showed higher measurements in the wheel path as opposed to the center of the drum). Linear regression relationships that were developed based on spatially nearest point data also are presented in Figure 6.4. Results are presented separately for the average of three measurements across the drum width and for one mea- surement at the drum center. Relationships for the average of three measurements showed significant improvement in correlations over one measurement at the center for Î³ d and E LWD from R2 < 0.5 to R2 > 0.8, while correlation to CBR was relatively high for both cases. Note that this example includes 5 of 30 data points with CMV D < 10. Chapters 2 and 3 showed that CMV < 10 is insensitive to soil stiffness due to the nature of the measurement. The inclusion of CMV D < 10 generally artificially increases R2 and its use is not recommended. Figure 6.2. Example 1: Comparison between roller MV and in situ point measurements.
Figure 6.3. Example 1: Average compaction curves of roller MV and in situ point measurements (top) and simple linear regression relationships between spatially nearest roller MV and in situ point measurements (bottom). 126.96.36.199â Exampleâ3:âTBâNC4B TB NC4B consisted of granular base material (SP-SM ac- cording to the USCS classification system) that was scarified in place using a motor grader to a depth of about 100 mm (4 in). In situ moisture content of the material was relatively constant (w = 3% to 4%). Compaction was performed using a Case SV212 vibratory smooth drum roller with 16 roller passes at constant settings with nominal A = 0.80 mm (0.031 in), f = 30 Hz, and v = 4.0 km/h (2.5 mph). In situ point measurements (Î³ d , E LWD-Z2 , and E LWD-D2 ) were obtained after 1, 2, 4, 8, and 16 roller passes at seven test locations, and DCP tests were performed after 16 roller passes. DCP tests were performed to a depth of about 400 to 850 mm (15.7 to 33.5 in). Three point measurements were performed across the drum lane at each location. Figure 6.5 shows roller MVs (k s ) as solid lines for 1, 2, 4, 8, and 16 roller passes in comparison with in situ point mea- surements. The in situ point measurements did not track well with variations in MVs. Compaction growth curves for av- erage roller MV and point measurements with a hyperbolic curve fit are presented in Figure 6.6. On average, roller MVs and point measurements showed limited increase in com- paction from pass 1 to pass 4 [k s from 15.5 to 18.0 MN/m, E LWD-Z2 from 40 to 52 MPa, E LWD-D2 from 65 to 72 MPa, and Î³ d from 19.3 to 20.5 kN/m3 (123.1 to 130.7 lb/ft3)]. Aver- age Î³ d increased to 20.9 kN/m3 (133.3 lb/ft3) after pass 16. The MV compaction curve showed evidence of what can be
â Figure 6.4. Example 2: Roller MV and in situ point measurement compaction curves (top) and simple linear re- gression relationships between MVs and in situ point measurements (bottom).
Figure 6.5. Example 3: Comparison MV and in situ point measurements. interpreted as decompaction and recompaction for passes 7 and higher. This is common for granular materials (e.g., White & Thompson 2008) and can often be overcome by alternating static and vibratory passes (see, e.g., Brandl & Adam 2000). Linear regression relationships between roller MVs and point measurements based on spatially nearest point data produced poor correlations (Figure 6.6). To further investigate the relationship between roller MVs and point measurement data, DCP tests are presented in Figure 6.7 along with pass 16 roller MVs. The CBR profiles showed a nonuniform subsurface layer below about 300.0 mm (11.8 in) from the surface. Average CBR calculated from depths of 300 to 600 mm (11.8 to 23.6 in) are plotted in comparison with roller MVs in Figure 6.8. CBR values from depths of 300 to 600 mm (11.8 to 23.6 in) tracked well with variations in roller MVs along the test bed. Regression rela- tionships between spatially nearest point roller MVs and CBR values produced a good correlation with R2 = 0.62. The results presented here indicate that roller MVs can be insensitive to thin compaction layers and can be strongly in- fluenced by underlying layers. This example also illustrates that in situ point measurements (e.g., Î³ d , E LWD ) may not cor- relate well with roller MVs when nonuniform subsurface conditions are evident at depths greater than the influence depth of the point measurements. In situ testing devices that provide information deeper than the compaction layer (e.g., DCP, FWD) can help interpret the vibratory roller MVs that are influenced by material to the measurement depth of 1 to 1.2 m (3.3 to 3.9 ft) as described in Chapter 4. 188.8.131.52â Exampleâ4:âTBsâMD6âMD9 TBs MD6âMD9 consisted of a nominal 150.0-mm (5.9- in)-thick layer of granular base material (SP-SM according to the USCS classification). The TBs were mapped using Dyna- pac CA362 and Bomag BW213-DH vibratory smooth drum rollers at a constant high-amplitude setting to assess the in- fluence of drum âjumpingâ on correlations. CMV D measure- ments were obtained at constant settings with nominal A = 2.40 mm (0.094 in), f = 30 Hz, and v = 4.0 km/h (2.5 mph). E vib measurements were obtained at constant settings with nominal A = 1.90 mm (0.075 in), f = 28 Hz, and v = 4.0 km/h (2.5 mph). Roller âjumpingâ was measured as bouncing value (BV) for CMV D and jump for E vib . Following mapping passes, E V1 measurements were obtained at 40 test locations across the test beds.
â Figure 6.6. Example 3: Compaction curves of average roller MV and in situ point measurements and simple lin- ear regression relationships. Relationships between roller MVs and corresponding âjumpingâ values are presented in Figure 6.9. Based on theo- retical simulations, Adam & Kopf (2004) and Anderegg (1998) found that accelerometer-based CMV, E vib , and k s MVs are af- fected by roller âjumping.â It was shown that with increasing ground stiffness the roller drum transitions to a jump mode, where the âjumpingâ values increase and the roller MVs de- crease. With further increase in ground stiffness, the roller MVs decrease to a minimum value and then increase again (see Chapter 2). The relationships presented in Figure 6.9 for roller MVs and âjumpingâ values show a similar feature. Linear regression relationships developed between roller MVs and E V1 measurements are also presented in Figure 6.9. Roller MVs at three test locations were identified as being out of trend for CMV D where BV > 10. Similarly, roller MVs at two test locations were found to be out of trend for E vib where jump = 2. Regression relationships improved after removing the out-of-trend points due to drum jumping (R2 = 0.29 to 0.72 for CMV D and 0.47 to 0.71 for E vib ). This example in- cludes 10 of 38 data points with CMV D < 10 that artificially increases R2. This example illustrates that it is important to remove roller MVs during drum âjumpingâ from the analysis. This is an issue, in particular, for stiff ground conditions when the machine is operated in the high-amplitude setting. Operating in the low-amplitude settings [e.g., A < 1.10 mm (0.043 in)] effectively eliminates jump mode. Further, AFC rollers auto- matically reduce vibration amplitude when jump mode is de- tected (although as discussed in Chapter 5, using AFC during quality control/quality assurance is not recommended).
Figure 6.7. Example 3: Comparison of pass 16 roller MVs with CBR profiles. Figure 6.8. Example 3: Simple linear regression rela- tionship between roller MV and CBR from depths of 300 to 600 mm (11.8 to 23.6 in). 6.2.4 Summary of Simple linear regression analysis Simple linear regression relationships between the various in situ point measurements and roller MVs for the referenced test beds with nongranular subgrade, granular subgrade, and granular subbase/base materials are summarized in Appen- dix C. The regression relationships are identified with possi- ble factor(s) (see Table 6.2) influencing the relationships (see notes on R2 values in Appendix C). For some cases with poor correlations, sufficient information was not available to iden- tify a factor. A summary of observed range of R2 values for dry unit weight, modulus (i.e., E LWD , E FWD , E V1 , E V2 ), and CBR measurements for different conditions is provided in Table 6.3. The R2 values resulted in a wide range that is attributed to various factors that affect the regression relationships (as identified in Table 6.2). The influence of some of these factors (i.e., soil moisture content, compaction layer lift thickness, underlying layer properties) and machine operation settings (A, f, v) were statistically analyzed using multiple regression analysis, as discussed in the following section. MVs are generally better correlated to compaction layer modulus measurements compared to dry unit weight and CBR measurements, especially where the underlying layer is
â Figure 6.9. Example 4: Influence of roller âjumpingâ on regression relationships, TBs MD6âMD9 (granular base material, USCS: SP-SM). 6.3 Multiple Linear Regression Analysis Use of multiple regression analysis to statistically assess the influence of variability in underlying layer soil conditions and variability in machine operation conditions is presented in this section. Multiple regression analysis is performed by incorporating variables of interest as independent variables into a general multiple linear regression model, as shown in Equation 6.2. The statistical significance of each variable is assessed based on p- and t-values. The selected criteria for identifying the significance of a parameter included p-value <0.05 = significant, <0.10 = possibly significant, >0.10 = not significant, and t-value <-2 or >+2 = significant. The p-value indicates the significance of a parameter, and the t-ratio value indicates the relative importance (i.e., the higher the absolute value, the greater the significance). table 6.3. observed range of R2 values from simple linear regression analysis with roller MVs. Material Modulusa CBR Î³ d Nongranular subgrade 0.1â0.7 0.1â0.7 0.0â0.6 Granular subgrade 0.3â0.7 0.0â0.4 0.1â0.5 Granular subbase/base 0.2â0.8 0.0â0.6 0.0â0.5 a Includes modulus obtained from LWD, FWD, and static PLT. heterogeneous. For TBs with relatively homogeneous mate- rial and subsurface conditions, MVs generally correlate well with dry unit weight, CBR, and modulus measurements.
90 RollerMV = + Ã + Ã + Ã + Ã + Ã + Ã b b b w b A b b b w 0 1 2 3 4 5 6 2 Î± Î² Î³ + Ã + Ãb f b v7 8 (6.2) where b 0 = intercept; b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 , and b 8 = regres- sion coefficients; A = amplitude (mm); Î± = point measure- ment value (Î³ d , E LWD , etc.); Î² = underlying layer roller MV or point measurement; Î³ = lift thickness (mm); f = vibration frequency (Hz); and v = velocity (km/h). For multiple regression analysis, the reported R2 values have been adjusted for the number of regression parameters, as shown in Eq. 6.3, where n = the number of data points and p = the number of regression parameters. The adjusted coefficient of determination R2 adj from multiple regression analysis may be compared with R2 from simple linear regres- sion analysis to assess which regression model best captures variation in the data. R R n n padj 2 =1 1 12â( â ) â â (6.3) Complications with collinearity should be avoided when performing multiple regression analysis. Collinearity refers to inclusion of two or more strongly related independent variables into a model to predict a dependent variable, which may result in misleading R2 adj values (Ott & Longnecker 2001). This is possible in the above-described model if, for example, underlying layer MV and point measurement values are in- cluded together. Collinearity in a model can be detected using variance inflation factors (VIF). VIF of the ith independent variable is defined as 1/(1 â R i 2), where R i 2 is the coefficient of determination for the regression of the ith independent variable on all other independent variables. Although there are no formal criteria on the acceptable magnitude of VIF, a common rule of thumb is that if VIF of the ith independent variable is <1/(1 â R2), where R2 is the coefficient of determi- nation of the univariate model, then it can be concluded that the variable is not contributing to collinearity (Freund et al. 2003). Example results of representative test beds where vibra- tion amplitude, soil moisture content, and underlying layer conditions affected the regression relationships are discussed below. The influence of moisture content and underlying layer properties was assessed in the analysis of all test beds for which measurements were available. Variability in soil moisture content and underlying layer conditions was inten- tionally introduced in the Colorado and Maryland test beds under controlled field conditions to study their influence on the relationships. Data obtained at different amplitude set- tings were combined to assess the influence of amplitude. This process was exercised for all test beds/layers, and sum- mary relationships are presented separately for nongranular subgrade, granular subgrade, and granular subbase/base ma- terials in Appendix C. At the end of this section, results from multiple sites and test beds are combined in an attempt to capture a wide range of variations to obtain relationships be- tween different roller MVs and modulus measurements (i.e., E LWD , E V1 , E V2 ). 6.3.1â âInfluenceâofâVibrationâAmplitudeâandâ Frequency Two examples are presented in the following discussion: Example 1 describes data with influence of vibration ampli- tude; Example 2 describes data with influence of vibration amplitude and frequency on roller MVs. 184.108.40.206â Exampleâ1:âTBsâMD6âMD9 Relationships between E vib and E V1 measurements obtained from TBs MD6âMD9 with granular base materials are pre- sented in Figure 6.10. E vib measurements were obtained at A = 1.9 and 0.7 mm (0.075 and 0.028 in) and constant f = 28 Hz and v = 4.0 km/h (2.5 mph) nominal settings. As described in Figure 6.9, the out-of-trend values due to roller âjumpingâ were not included in the analysis. For the multiple regression model to predict E vib , the inter- cept was not significant and the R2 adj = 0.66 (Table 6.4) was lower compared to simple linear regression relationships (R2 = 0.71 and 0.82). This is important to note because, although a parameter may be statistically significant in a multiple re- gression model, it may not always contribute to an improved model fit. In this case it is appropriate to interpret the rela- tionships between E vib and in situ point measurements sepa- rately for different amplitude settings, instead of combining the results. 220.127.116.11â âExampleâ2:âTBsâMN19,âMN20,âMN26,âFL20A,â FL20B,âFL23A,âFL23B,âandâFL25 Relationships between roller MVs (k s ) and E LWD-Z2 mea- surements obtained from TBs MN19, MN20, and MN26 and between roller MVs (k s ) and E LWD-Z3 measurements from TBs FL20A, FL20B, FL23A, FL23B, and FL25 are presented in Fig- ure 6.11. MN19, MN20, and MN26 consisted of granular base materials. FL20A and FL20B consisted of granular subbase, and FL23A, FL23B, and FL25 consisted of granular subgrade materials. The A and f settings in the beds varied from 0.3 to 1.7 mm (0.012 to 0.067 in) and 25 to 33 Hz, respectively. Set- tings in each bed are summarized in Figure 6.11. Simple linear regression relationships while treating data from each test bed separately are presented in the legends for Figure 6.11. For MN test beds, R2 varied from 0.0 to 0.6, and for FL test beds, R2 varied from 0.4 to 0.6. As shown in Figure
â 6.11, the relationships showed different trends, primarily due to differences in the A and f settings between the test beds. Multiple regression analysis was performed by combining data from different MN and FL test beds by incorporating the E LWD-Z2 , E LWD-Z3 , A, and f values as independent variables. The analysis results (see Table 6.5) indicate that both A and f are statistically significant parameters for both MN and FL test beds with R2 adj = 0.80 and 0.79, respectively, for the models. The resulting predicted MVs using the multiple regression equation are shown versus the actual MVs in Figure 6.11. The regression coefficient for frequency (b 7 ) is negative for MN test beds and positive for FL test beds. A negative coefficient suggests that increasing f causes a decrease in roller MV and vice versa for a positive coefficient. In contrast, the coefficient for amplitude (b 3 ) is positive for MN test beds and negative for FL test beds. This indicates that the frequency and ampli- tude dependency on roller MVs change with soil types and field conditions (see also Chapter 4). This example illustrates that an amplitude- and frequency- dependent regression model would be suitable for interpreta- tion of results for these site conditions and roller MVs. It is an interesting and encouraging finding that shows potential for analyzing measurements obtained in AFC mode and war- rants more research. 6.3.2 Influence of moisture Content Results obtained from TB MN11 are discussed to dem- onstrate the influence of moisture content on correlations between in situ point measurements and the MDP roller MV. The influence of moisture content on roller MVs for cohesive soils has been further documented by Thompson & White (2008). The test bed was constructed by placing a 375.0-mm (14.8-in)-thick loose lift of nongranular subgrade layer (CL according to the USCS soil classification system). Maximum dry unit weight and optimum moisture content as determined by the standard Proctor method were 16.95 table 6.4. Results of multiple regression analysis for influence of amplitudeâMD6âMD9. Model Term Estimate Std Error t-Ratio Prob > t (p-value) R2 adj VIF b 0 -14.67 9.28 -1.58 0.1183 â E vib = b 0 + b 1 E V1 + b 3 A b 1 2.72 0.23 12.02 < 0.001 0.66 1.00 b 3 16.10 5.77 2.79 0.0066 1.00 Note: Check for no collinearity: VIF < [1/(1 â R2)]. Figure 6.10. Influence of amplitude on Evib âTBs MD6âMD9 granular base material (USCS: SP-SM).
Figure 6.11. Influence of amplitude and frequency on roller MVs.
â kN/m3 (105.20 lb/ft3) and 16.4%, respectively. The test bed had plan dimensions of about 2.4 m Ã 90.0 m (7.9 ft Ã 295.3 ft) and was divided into three 30.0-m (98.4-ft)-long sections with target moisture contents of approximately -3%, 0%, and +3% of standard Proctor w opt . The subgrade layer was moisture conditioned using a water truck and mixed using a reclaimer. Vibratory compaction was performed with eight passes of a Caterpillar CS-563E vibratory pad foot roller at nominal constant settings of A = 0.80 mm (0.031 in), f = 33 Hz, and v = 4.0 km/h (2.5 mph). In situ point measurements (w, Î³ d , E LWD-K2 , CBR) were obtained at 15 test locations (five loca- tions in each moisture section) along the test bed. Tests were conducted after 1, 2, 4, and 8 roller passes. Figure 6.12 shows MDP as solid lines in comparison with in situ point measure- ments. Simple linear regression relationships between roller MDP and in situ point measurements were developed based on spatially nearest data, as presented in Figure 6.13. Regres- sion relationships produced R2 = 0.72, 0.50, and 0.57 for Î³ d , CBR, and E LWD-K2 measurements, respectively. Multiple regression analysis was performed by adding moisture content as an independent variable in predicting roller MDP. Results from the analysis are summarized in Table 6.6. Moisture was statistically significant in predicting MDP from Î³ d and E LWD-K2 measurements and was not significant for CBR measurements. The regression coefficient (b 2 ) for both measurements is positive, which indicates that increasing moisture content resulted in an increase in MDP (i.e., lower stiffness). Using the multiple regression models, relationships between predicted and actual roller MDP are presented in Figure 6.13. Correlations improved with R2 adj = 0.78 and 0.67 for predicting MDP from Î³ d and E LWD-K2 , respectively, by in- cluding moisture content as an independent variable. Generally, moisture content was not found to be statisti- cally significant in the regression analysis for most of the test bed studies. Factors contributing to this observation are (1) moisture content did not vary enough over the length of the test beds; (2) in situ point measurements typically only mea- sure moisture content to about 80 mm (3 in) below the sur- face, whereas the measurement influence depth of the roller is much larger; and (3) when correlating with elastic modulus- based in situ point measurements using multiple regression analysis, moisture content is collinear (i.e., highly correlated to in situ measurement). 6.3.3 results of multiple regression analysis The examples described above demonstrate the approach of applying multiple regression analysis to relate MVs with in situ point measurements. This same approach was exercised for results from all test beds listed in Table 6.1 to evaluate the influence of moisture content, underlying layer stiffness, lift thickness, amplitude, and frequency. If a variable was not sta- tistically significant or assessed as collinear (based on VIF), it was removed from the model. Multiple regression relationships for all test beds are summarized in Appendix C. A summary of the typical range of R2 adj values for modulus, CBR, and dry unit weight measurements for the three referenced material groups from multiple regression analysis is provided in Table 6.7. Where heterogeneous conditions were evident below the compaction layer, the underlying layer properties (MVs and point measurements) were often statistically significant in the multiple regression model. Regression relationships im- proved by incorporating the underlying layer properties. For some cases, when underlying layer properties are included in a multiple regression model, the compaction layer point measurements were found statistically not significant in the analysis. This is possible when MVs are more influenced by the underlying layer properties than the compaction layer properties. Moisture content was significant for two non- granular subgrade layer test beds and one granular base layer test bed. Lift thickness and w2 terms were not statistically sig- nificant. Amplitude variation was statistically significant for table 6.5. Results of multiple regression analysis for influence of amplitude and frequencyâMN19, MN20, MN26 and FL20A, FL20B, FL23A, FL23B, FL25. TB Model Term Estimate Std Error tâRatio Prob > t (p-value) R2 adj VIF MN19, 20, 26 k s = b 0 + b 1 E LWD-Z2 + b 3 A + b 7 f b 0 39.87 2.55 15.64 <0.0001 0.80 â b 1 0.23 0.02 9.33 <0.0001 1.07 b 3 6.85 0.51 13.36 <0.0001 1.11 b 7 -1.18 0.08 -13.94 <0.0001 1.08 FL20A/B23A/B, 25 k s = b 0 + b 1 E LWD-Z3 + b 3 A + b 7 f b 0 -40.86 6.91 -5.91 <0.0001 0.79 â b 1 0.12 0.02 5.81 <0.0001 2.53 b 3 -2.90 1.26 -2.30 0.0232 1.07 b 7 2.03 0.25 8.12 <0.0001 2.48 Note: Check for no collinearity: VIF should be <[1/(1 âR2)].
Figure 6.12. Roller MVs in comparison with in situ point measurements (TB MN11).
â Figure 6.13. Simple regression relationships between roller MVs and in situ point measurements (top) and mul- tiple regression relationships, including moisture content for predicting roller MVs (bottom). table 6.6. Results of multiple regression analysis for influence of moisture contentâtB MN11. Model Term Estimate Std Error t-Ratio Prob > t R2 adj VIF MDP = b 0 + b 1 Î³ d + b 2 w b 0 41.46 4.98 8.33 < 0.0001 0.78 â b 1 -2.68 0.26 -10.22 < 0.0001 1.26 b 2 0.43 0.13 3.27 0.0019 1.26 MDP = -b 0 + b 1 CBR + b 2 w b 0 9.03 3.67 2.46 0.0168 b 1 -0.99 0.19 -5.38 < 0.0001 âa âa b 2 0.26 0.22 1.23 0.2238 MDP = -b 0 + b 1 E LWD-K2 + b 2 w b 0 4.04 2.36 1.71 0.0928 â b 1 -0.28 0.036 -7.70 < 0.0001 0.67 1.19 b 2 0.57 0.15 3.79 0.0004 1.19 a Not statistically significant according to p < 0.10 and t < -2 or > +2. Note: Check for no collinearity: VIF should be < [1/(1 â R2)]. all cases where minimum amplitude variation of Â±0.30 mm (Â±0.012 in) was present in the data. Results from multiple sites and test beds (MD6, 7, 8, 9, 11, 12, 13, and 14; CO6, 7, 8, 11, 12, 13, 16, 17, and 18) were combined to capture a wide range of variations to obtain relationships between E vib and modulus measurements (i.e., E LWD , E V1 , E V2 ). Only test beds with underlying layer measure- ments were considered in this analysis. The influence of w, underlying layer properties (roller MV or point measure- ment), A, f, and v was assessed.
layer measurements and therefore were removed from the model. For all the test beds considered, the frequency varia- tion was within Â±2 Hz and the speed variation was 3.0 to 5.0 km/h (1.9 to 3.1 mph). For this variation, both f and v were not statistically significant. 6.4 Relationships Between Roller MV and Resilient Modulus Developing relationships between field and laboratory mechanistic parameters was an objective of this project and provided interesting results from an empirical perspective. A number of field studies over the past three decades have documented the challenges involved in developing these re- lationships (e.g., Anderson & Woods 1975, Rodhe & Scullion 1990, Daleiden et al. 1994, Nazarian et al. 1998). According to Anderson and Woods, primary factors that affect these rela- tionships include (1) sampling disturbance, (2) differences in the stress states between the laboratory specimen and in-place pavement material, (3) nonrepresentative materials, and (4) inherent errors in the field and laboratory test procedures. table 6.7. typical range of R2adj values for multiple linear regression analysis. Material Î³ d Modulusa CBR Nongranular subgrade 0.6â0.8 0.2â0.6 0.3â0.7 Granular subgrade â 0.5â0.7 â Granular subbase/base 0.4â0.8 0.6â0.9 0.4â0.8 aIncludes modulus obtained from LWD, FWD, and static PLT. Figure 6.14. Results of multiple regression analyses from MD and CO test beds from compaction layer ELWD-Z2 and vibration amplitude measurements and underlying layer ELWD-Z2 and roller MVs. Example results of multiple regression analysis combining Maryland and Colorado test beds for the E vib MV are pre- sented in Figure 6.14. Table 6.8 provides a summary of the complete analysis results. Results indicate that E LWD , E V1 , E V2 , and E FWD measurements correlate well with E vib . Amplitude was statistically significant for all cases, and underlying layer properties were significant for most cases. In some cases the underlying layer properties were collinear with compaction
â An attempt was made as part of this study to relate roller MVs to laboratory-determined M r . Laboratory M r tests were conducted on âundisturbedâ Shelby tube (ST) samples and reconstituted specimens. One confining and deviator stress combination was selected to correlate M r with roller MVs. For undisturbed ST samples, M r values at the selected stress condition were directly correlated with roller MVs at the sample location using simple linear regression analysis. For reconstituted laboratory samples, w-Î³ d -M r relationships were developed through multiple regression analysis, and the re- lationships were used to predict field M r values from in situ w-Î³ d point measurements. The predicted M r values were then empirically correlated to MVs. Further, the influence of vi- bration amplitude and underlying layer support conditions on compaction layer MVs were statistically assessed through multiple regression analysis. Laboratory and in situ test re- sults and analysis from TB MN10 are presented below, fol- lowed by a summary of results for other test beds. 6.4.1 TB mn10 nongranular Subgrade 18.104.22.168â SiteâandâMaterialâConditions This test bed was constructed by placing a nominal 425.0- mm (16.7-in)-thick layer of nongranular subgrade material (CL according to the USCS soil classification system). DCP tests indicated that the layer below the compaction layer was relatively homogenous with CBR = 14 to 18. Maximum dry unit weight and optimum moisture content as determined by the standard Proctor method were 16.95 kN/m3 (108.10 lb/ft3) and 16.4%, respectively. The test bed had plan dimen- sions of about 2.4 m Ã 86.0 m. The material was moisture conditioned by dividing the test bed into three sections to ap- proximately -3%, 0%, and +3% of standard Proctor w opt and mixed using a reclaimer. Compaction passes were performed using a Bomag BW213-DH pad foot roller. 22.214.171.124â âLaboratoryâTesting To develop w-Î³ d -M r relationships for the subgrade mate- rial, laboratory M r tests were performed on reconstituted laboratory-compacted specimens. Tests were conducted in general accordance with AASHTO T-307 standard procedure for Type 2 subgrade materials on 10 samples prepared at a selected range of w and Î³ d values. Samples were compacted using the static compaction method. Test procedure and de- tails regarding the resilient modulus test device are described in Appendix A. Average M r was calculated for each confining and deviator stress condition based on data from the last five cycles of a loading sequence. The test results were analyzed to fit the âuniversalâ model proposed by Witczak and Uzan (1988) shown in Equation 6.4. table 6.8. Results of multiple regression analyses combining multiple project sites and test beds. TB Model Term Estimate Std Error t-Ratio Prob > t (p=value) R2 adj VIFa MD6, 8, 9, 11, 12, 13, 14; CO6, 7, 11, 12, 16, 17 E vib = b 0 + b 1 E LWD-Z2 + b 3 A + b 4 E vib Ï n = 452 b 0 -4.21 4.66 -0.90 0.3663 0.52 â b 1 0.60 0.07 8.2 < 0.0001 1.26 b 3 10.63 2.31 4.59 < 0.0001 1.03 b 4 0.74 0.05 14.73 < 0.0001 1.28 MD6, 8, 9, 11, 12, 13, 14; CO6, 7, 11, 12, 16, 17 E vib = b 0 + b 1 E LWD-Z2 + b 3 A + b 4 E LWD-Z2 Ï n = 448 b 0 11.11 4.92 2.26 0.0243 0.41 â b 1 0.62 0.09 6.96 < 0.0001 1.16 b 3 7.25 2.56 2.84 0.0048 1.06 b 4 0.80 0.09 9.33 < 0.0001 1.10 MD8 E vib = b 0 + b 1 E LWD-Z3 + b 3 A + b 4 E vib Ï n = 18 b 0 -48.21 21.56 -2.24 0.0422 0.73 â b 1 0.94 0.22 4.22 0.0009 1.20 b 3 26.29 8.56 3.07 0.0083 1.00 b 4 1.32 0.54 2.43 0.0291 1.20 MD6, 8, 9, 11, 12, 13, 14 E vib = b 0 + b 1 E V1 + b 3 A n = 222 E V1 Ï not significant and collinear with E vib Ï b 0 -2.66 5.00 -0.53 0.59 0.61 â b 1 2.22 0.12 18.38 < 0.0001 1.00 b 3 13.20 3.14 4.20 < 0.0001 1.00 MD6, 8, 9, 11, 12, 13, 14 E vib = b 0 + b 1 E V2 + b 3 A + b 4 E vib Ï n = 111 E V2 Ï not significant b 0 -17.06 7.98 -2.14 0.0348 0.69 â b 1 0.43 0.06 6.93 < 0.0001 1.70 b 3 13.07 4.59 2.84 0.0053 1.00 b 4 0.65 0.10 6.22 < 0.0001 1.70 a Check for no collinearity: VIF should be < [1/(1 â R2)]. Ï = underlying layer measurement.
M k P P P k k r a a d a = ï£« ï£ï£¬ ï£¶ ï£¸ï£· ï£« ï£ï£¬ ï£¶ ï£¸ï£·1 2 3Î¸ Ï (6.4) where M r = resilient modulus; k 1 , k 2 , and k 3 = regression coef- ficients, typically with k 1 > 0, k 2 â¥ 0, and k 3 â¤ 0; Î¸ = sum of principal stresses (Ï 1 + Ï 2 + Ï 3 ); P a = atmospheric pressure, same units as M r and Î¸; and Ï d = deviator stress, same units as M r and Î¸. Results showing the effect of confining and deviator stresses on resilient modulus for four samples prepared at dif- ferent w and Î³ d are presented in Figure 6.15. Results show two commonly observed effects on fine-grained cohesive soils: (1) increasing w decreases M r and (2) increasing deviator stress decreases M r . Some differences with respect to these typical behaviors were observed in the results. For samples prepared dry of optimum (w opt â7.5%), confining stress affects the M r values more than deviator stress. Increasing confining stress tends to increase M r (up to about 1.5 times), whereas increas- ing deviator stress did not show a significant change in M r . On the other hand, as the moisture content increases (w opt + 2%), the confining stress only slightly affected M r while in- creasing deviator stress caused a decrease in M r (up to about two times). A summary of model coefficients (for Equation 6.4) for the different samples is provided in Table 6.9. The S5 and M5 samples with w > 20% experienced plastic strain Îµ p greater than 5% after the fifth sequence (note that S group represent samples compacted to target standard Proctor, and M group represent samples compacted to target modified Proctor w-Î³ d values), and therefore the model coefficients were not calcu- lated (AASHTO T-307 requires the test be terminated when a sample reaches Îµ p > 5%). The k 3 values shown in Table 6.9 on samples compacted to standard Proctor densities (S se- ries) show that k 3 decreased from about -0.24 to -0.60 with increasing w from w opt â7.5% to w opt + 6.5%. The smaller the k 3 value, the greater the influence of deviator stress, which Figure 6.15. Effect of Ïc and Ïd on compacted TB MN10 subgrade material at different target w-Î³d .
â M r (MPa) = b 0 + b 1 w + b 2 Î³ d (6.5) 126.96.36.199â âInâSituâTestingâandâRelationshipâBetweenâ RollerâMVâandâMr After the material was carefully moisture conditioned, the test bed was compacted using the Bomag vibratory pad foot roller with eight roller passes at constant operation settings with nominal A = 0.70 mm (0.028 in), f = 30 Hz, and v = 4.0 km/h (2.5 mph). In situ w-Î³ d point measurements were ob- tained on the compaction layer at 15 test locations (five loca- tions in each moisture section) along the test bed. Point mea- surements were obtained after 1, 2, 4, and 8 roller passes. Figure 6.17 shows w-Î³ d point measurements in comparison with MVs (E vib ) shown as solid lines. Note the conclusion in Chapter 3 that vibration-based MVs for pad foot rollers are not repeatable and should therefore not be used in practice without consideration of statistical averaging. Their use here is for illustration only. Results show that E vib measurements were spatially variable but generally increased from pass 1 to pass 2 and that in situ point measurement values increased with increasing passes. The multiple regression relationship developed for laboratory samples (Equation 6.5) was used to predict M r values for the in situ w-Î³ d point measurements. Since Equation 6.5 is valid only for the range of w-Î³ d of the laboratory samples, the in situ point measurements only close to the laboratory sample values were selected for M r predic- tion. Comparison of the predicted M r and E vib for the selected data is presented in Figure 6.18, which showed an acceptable correlation with R2 = 0.52. table 6.9. Summary of Mr model coefficients. Sample ID Dry Unit Weight (kN/m3) Moisture Content (%) Model Coefficientsa k 1 k 2 k 3 S1 16.1 8.9 675.4 0.45 -0.24 S2 16.8 11.9 706.7 0.00 -0.14 S3 17.4 16.2 431.5 0.17 -0.34 S4 16.8 18.5 149.6 0.35 -0.60 S5 15.7 22 âb âb â b M1 16.9 8.8 969.6 0.13 -0.11 M2 19.3 11.1 1,755.9 0.17 0.08 M3 18.3 13.6 952.6 -0.01 -0.04 M4 16.7 18 159.8 0.43 -0.50 M5 15.7 20.8 âb âb â b aWitczak & Uzan (1988) model. b Samples with permanent strain >5%. Figure 6.16. Relationship between w-Î³d and Mr at Ïd = 68.9 kPa and Ïc = 41.4 kPa. illustrates that the influence of deviator stress increases with increasing w for these samples. k 3 values generally increased with increasing density. The samples compacted to target standard Proctor densities exhibited consistently lower k 3 values compared to samples compacted to target modified Proctor densities. One sample (M3) yielded k 3 > 0, which sug- gests an increase in M r with increasing deviator stress. This behavior is common for granular materials but is not typical for fine-grained soils (Andrei et al. 2004). Near surface (z < 0.5 m) in situ deviator stresses under 11- to 15-ton vibratory roller compactors are considerably higher than the axial stresses applied in the laboratory M r test, whereas confining stresses are less (see Rinehart et al. 2009 and Chapter 4). To compare laboratory M r values with roller MVs, the maximum applied cyclic deviator stress and the confining stress condition of 68.9 kPa (10 psi) and 41.4 kPa (6 psi) from the M r test (following AASHTO T-307) were selected. Figure 6.16 shows the effect of w and Î³ d on M r for the subgrade material. Samples that produced Îµ p > 5% before reaching the selected stress condition [Ï d = 68.9 kPa (10 psi) and Ï c = 41.4 kPa (6 psi)] are highlighted in Figure 6.16. Multiple regression analysis was performed to predict M r (at the selected stress condition) as a function of w and Î³ d . The two samples with Îµ p > 5% were not included in the regres- sion analysis. The resulting multiple regression model from the analysis is presented in Equation 6.5, where b 0 = -593.33, b 1 = -10.86, and b 2 = 48.23 (for Ï d = 68.9 kPa and Ï c = 41.4 kPa), and shows strong correlations with R2 adj = 0.96. The re- gression coefficients for w (b 1 ) and Î³ d (b 2 ) were negative and positive, respectively, indicating that increasing moisture de- creases M r and increasing density increases M r .
00 Figure 6.17. Comparison of Evib and in situ compaction measurements. Figure 6.18. Simple linear regression relationship be- tween roller MV and predicted Mr . 6.4.2 Summary of relationships Between roller mvs and mr 188.8.131.52â âSimpleâLinearâRegressionâRelationshipsâ BetweenâRollerâMVsâandâMr A summary of laboratory determined w-Î³ d -M r multiple regression relationships for reconstituted and laboratory compacted nongranular subgrade, granular subgrade, and granular base materials is presented in Table 6.10. Shelby tube samples were obtained from a compacted nongranular subgrade layer for one test bed (CO3). w-Î³ d -M r relationships were developed only on materials with n â¥ 8 (following a gen- eral rule of thumb of a minimum four measurements per each variable). With the exception of FL23, all other materi- als showed good correlations with R2 adj = 0.6 to 1.0. M r test results along with the universal model coefficients k 1 , k 2 , and k 3 (see Equation 6.4) are presented in Appendix A. Simple linear regression relationships between predicted M r values at the selected stress condition for reconstituted samples (using the approach described in the example above) and roller MVs are presented in Table 6.11. The relationships produced R2 values of 0.0 to 0.6, with the majority at R2 < 0.5. Similar to the effect of underlying layer heterogeneity observed on simple linear regression relationships between
0â Î³ d point measurements and roller MVs, the relationships pre- sented here to M r are also affected. This is expected as the predicted M r values are based on the measured w-Î³ d point measurements. Multiple regression analysis was performed to further characterize the influence of underlying layers and amplitude in the following section. Further, relationships in Table 6.11 are presented separately for different nominal am- plitude settings. 184.108.40.206â âInfluenceâofâAmplitudeâandâUnderlyingâ LayerâSupportâConditionsâ Multiple regression analysis was performed to assess the influence of amplitude and underlying layer support condi- tions on compaction layer MVs, using the multiple linear regression model shown in Equation 6.2. Results from the analysis are summarized in Table 6.12, which shows that in- cluding underlying layer MVs in the regression model pro- duced improved correlations (e.g., R2 adj values for CO17 and CO18 from < 0.2 to > 0.5). For some cases, when underly- ing layer properties are included in the multiple regression model, the compaction layer point measurements were not statistically significant in the analysis (e.g., TBs MD6, 7, 8, 9). A similar finding was noted above in multiple regression analysis with in situ point measurements and is possible when MVs are more influenced by the underlying layer properties than the compaction layer properties. 220.127.116.11â Discussion Despite the challenges involved in relating field to labora- tory measurements, encouraging results were observed for some test beds. Results indicated that good correlations (with R2 or R2 adj > 0.5) are possible for test beds with relatively stiff/ homogeneous conditions below the compaction layer (e.g., MN10/11). Underlying layer variability contributed to poor correlations. Improved correlations are observed by factor- ing in the underling layer properties (using roller MVs on the underlying layer) through multiple regression analysis for some test beds. This observation is in line with findings for correlations between MVs and other in situ point measure- ments described earlier. 6.5 Summary and Conclusions Results obtained from evaluation of five roller-integrated compaction measurements (i.e., MDP, CMV D , E vib , k s , CCV) and 17 different soils were presented in this chapter. Relation- ships between roller MVs and a variety of in situ point mea- surements and laboratory-determined M r measurements via simple and multiple linear regression analysis were described. Results from a few select test beds were presented to highlight different aspects of the analysis and challenges involved in interpretation of the results. Results indicated that roller MV correlations are possible to in situ point measurements of dry unit weight, modulus via various devices, and CBR with simple linear regression analysis on test beds with homogeneous and relatively stiff underlying layer support conditions and MVs obtained under constant operation settings. Several factors can affect the quality of the regression relationship, including heterogeneous conditions in the underlying layers. Variability across the drum width also affected the correlations. Averaging point measurements across the drum width improved the correlations. table 6.10. Moistureâdry unit weightâMr relationships. Material TB USCS (AASHTO) n b 0 b 1 b 2 R2 adj Model: M r a = b 0 + b 1 w + b 2 Î³ d Nongranular subgrade MN10, 11 CL (A-6(5)) 8 -593.33 -10.86 48.23 0.95 CO3b CL (A-6(7)) 6 limited number of samples Granular subgrade MD2, 3, 4, 5 SM (A-2-4) 9 124.10 -7.56 0.03 0.83 FL23 SP-SM (A-3) 13 NS â NC2 SM (A-2-4) 16 -28.48 -1.17 4.12 0.94 Granular base CO17, 18 SP-SM (A-1-a) 9 -248.29 -5.14 20.95 0.62 MD2, 3, 4, 5 SM (A-2-4) 9 124.10 -7.56 0.03 0.83 MD6, 7, 8, 9, 11, 12, 13, 14 SP-SM (A-1-a) 10 -426.37 -30.09 32.19 0.57 FL19 SM (A-1-b) 5 limited number of samples NC4 SP-SM (A-1-a) 14 -512.01 -7.05 32.85 0.59 a For Ï d = 68.9 kPa and Ï c = 41.4 kPa. b Shelby tube samples.
0 table 6.11. Simple linear regression relationships between roller MVs and Mr. Material TB MV A (mm) n b 0 b 1 R2 Model: MV = b 0 + b 1 M r Nongranular subgrade MN10a E vib 0.70 22 35.65 0.18 0.52 MN11a MDP 0.80 22 6.47 -0.05 0.58 CO3b CMV D 0.80 6 3.73 0.07 0.43c Granular subgrade MD2,3, 4, 5a CMV D 0.50 28 NS â c Granular base CO17a E vib 0.70 33 -67.33 1.05 0.16d 1.90 11 56.5 0.47 0.17 d CO18a CMV D 0.90 33 -21.04 0.32 0.34 2.10 11 -16.90 0.37 0.46d MD6, 7, 8, 9a CCV 0.92 81 NS âd 2.19 18 NS âd CMV D 0.90 80 NS âd 2.10 37 NS âd E vib 0.70 70 NS âd 1.90 14 NS âd MD11, 12, 13, 14a CCV 0.92 20 NS âd 2.19 32 NS âd CMV D 0.90 42 -21.33 0.26 0.19d 2.10 26 -27.13 0.34 0.16d E vib 0.70 40 -52.14 0.72 0.29d 1.90 42 -133.05 1.37 0.22d NC4a E vib 0.70â1.10 35 -41.63 0.72 0.41d NC4a k s 0.80 35 NS âd a M r predicted from laboratory w-Î³ d -M r relationship; see Table 6.10. b M r of ST samples (Ï d = 68.9 kPa; Ï c = 41.4 kPa). c Narrow range of measurements and heterogeneous underlying layer. d Heterogeneous underlying layer. table 6.12. Multiple linear regression relationships between roller MV and laboratory Mrâgranular base materials. TB Model n b 0 b 1 b 3 b 4 R2 adj CO17 E vib = b 0 + b 1 M r a + b 3 A + b 4 E vib Ï 44 -98.78 0.85 30.15 0.54 0.52 CO18 CMV D = b 0 + b 1 M r a + b 3 A + b 4 CMVÏ 44 -24.63 0.23 0.50 8.17 0.75 cMD6, 7, 8, 9 CCV = b 0 + b 3 A + b 4 CCVÏ 168 -11.04 âb 12.58 0.92 0.41 CMV = b 0 + b 3 A + b 4 CMVÏ 274 -10.63 âb 5.77 4.95 0.59 E vib = b 0 + b 3 A + b 4 E vib Ï 216 4.58 âb 37.03 0.75 0.34 cMD11, 12, 13, 14 CCV = b 0 + b 3 A + b 4 CCV Ï 75 29.27 âb 13.42 3.20 0.49 CMV = b 0 + b 1 M r a + b 3 A + b 4 CMVÏ 68 -13.94 0.11 4.05 0.73 0.79 E vib = b 0 + b 1 M r a + b 3 A + b 4 E vib Ï 76 -49.51 0.37 3.22 1.07 0.75 a M r predicted from laboratory w-Î³ d - M r relationship, see Table 6.11. b M r not statistically significant based on p < 0.10 and t < -2 or >+2. c Ignored data with BV > 10 for CMV D and jump = 2 for E vib . Ï = underlying layer measurement.
0â For a few cases, including soil moisture content in multiple regression analysis improved the regression relationships. Vari- ations in machine vibration amplitude and frequency were also found to influence the regression relationships. Results from some test beds indicated that, although amplitude was statis- tically significant in multiple regression analysis, the quality of regression relationships was not (as identified as reduction in R2 adj values). This emphasizes the importance of constant machine operation settings during correlation and calibra- tion studies. A multiple regression model with amplitude and frequency as dependent variables was successful for a few test beds. This suggests the potential for analyzing IC measure- ments (obtained in AFC mode), although this topic warrants further research. Multiple regression analysis on in situ modu- lus data and roller MVs obtained from multiple sites and test beds produced good correlations when amplitude and under- lying layer measurements are incorporated in the analysis. An approach to empirically relate laboratory-determined M r for a select stress condition and roller MVs was presented. The M r values were predicted for in situ w-Î³ d point measure- ments using a w-Î³ d -M r relationship developed from labora- tory testing. Similar to other in situ point measurements, the relationships were possible for compaction layer material underlain by homogeneous and relatively stiff support con- ditions. Heterogeneous supporting layer conditions affected these relationships, and the relationships improved by in- cluding parameter values that represent the underlying layer conditions through multiple regression analysis.