Evaluating Mechanical Properties of Earth Material During Intelligent Compaction (2020)

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60 Calibration of Numerical Models Introduction This chapter compares the measured field data with the responses obtained from the forward models with different levels of sophistication. It presents strategies for calibration of the forward models that simulate the pavement responses during mapping and discusses the process of deriving adjustment factors for the forward models to represent the field conditions more realistically. Structural Models Nazarian et al. (2014) indicated that direct estimation of field moduli using deflection- based NDT devices from laboratory-measured moduli was not appropriate, and that the lab and field moduli must be related through calibrated structural models. With that precedent, different response algorithms were developed and calibrated with the experimental results obtained from the laboratory tests and field measurements of the actual pavement sections. These models involved various levels of sophistication, as described in Chapter 3 and listed in Table 3-3. Evaluation and Calibration of Forward Models Table 5-1 presents information about the two construction sites that were used for field testing to support the evaluation of forward models. (Additional details are provided in Appendix G.) The data collected for this purpose consisted of the vertical displacements measured as a roller approached and moved away from embedded geophones (see Figure 5-1). Additional information included the laboratory properties of the geomaterials and field spot- test measurements. The data collected at Site 1 (Cleburne, Texas) was used to evaluate the pavement responses under several rollers with different operating features. Table 5-2 lists the properties of the layers at these two test sites. Table 5-2 also lists the averaged LWD moduli obtained on top of each layer as part of the spot-testing program conducted at the sites. In the case of the two-layer systems, the LWD moduli correspond to composite moduli of the top and bottom layers. The base moduli in Table 5-2 were backcalculated using the LWD measurements on top of the subgrade and base. Calibration of Forward Models under Stationary Vibration Three different manufacturers furnished rollers for the vibration measurements at Site 1. The specifications of these rollers are summarized in Table 5-3. As part of the analysis, all three C H A P T E R 5

Calibration of Numerical Models 61 Figure not to scale. 30 m30 m Figure 5-1. Data collection during vibratory moving condition. Site Location Layer Length of Test Section or Cell 1 Cleburne, TX Clayey subgrade on top of existing embankment 150 m (500 ft.) 2 MnROAD, MN Sandy (cells 185 and 186) and clayey (cells 188 and 189) subgrade* 70 m (225 ft.)* 300 mm (12 in.) thick unbound aggregate base on top of subgrade* *See Figure 4-3 for detailed information. Table 5-1. Field test sites for development of models. roller operators were directed to vibrate their rollers in a stationary position under various settings for very short periods. Figure 5-2(a) shows the vertical displacement time histories that were measured with two geophones embedded at depths of 0.6 m (24 in.) and 1.2 m (48 in.) during the stationary vibration of a roller at low frequency and high amplitude. Figure 5-2(b) shows the cor responding displacement time histories of the roller. The measured displacements in the stable region (after the roller ramped up to the desired setting and before the roller decelerated to no vibration) were averaged to obtain representative displacements for comparison with the FE models’ displace- ments. For simulations using the linear elastic models, the LWD modulus was used as input.

62 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction Site Location Layer Properties of Geomaterial Resilient Modulus (MR) Results (Modified MEPDG Model) In Situ Test k′1 k′2 k′3 MR ELWD Modulus* 1 Cleburne, TX Subgrade 269 0.54 -3.0 21 MPa(3.1 ksi) 41.8 MPa (6.1 ksi) -- 2 MnROAD Cell 185 Subgrade 335 1.6 -0.6 79 MPa(12 ksi) 29 MPa (4.3 ksi) -- Base 512 0.8 -0.1 129 MPa(19 ksi) 63 MPa (9 ksi) 117 MPa (17 ksi) Cell 186 Subgrade 335 1.6 -0.6 79 MPa(12 ksi) 36 MPa (5.2 ksi) -- Base 484 0.9 -0.1 126 MPa(18 ksi) 99 MPa (14 ksi) 193 MPa (28 ksi) Cell 188 Subgrade 649 0.6 -2.6 59 MPa(8.6 ksi) 43 MPa (6.2 ksi) -- Base 500 0.6 -0.1 98 MPa(14.2 ksi) 78 MPa (11.3 ksi) 138 MPa (20 ksi) Cell 189 Subgrade 649 0.6 -2.6 59 MPa(8.6 ksi) 26.3 MPa (3.8 ksi) -- Base 408 0.9 -0.1 118 MPa(17.1 ksi) 67 MPa (9.7 ksi) 134 MPa (19 ksi) *Base modulus backcalculated using LWD moduli measured on top of base and subgrade surface. Table 5-2. Geomaterial properties of test sections. Vendor/Manufacturer Model Width (m) Operating Weight (kN) Centrifugal Force (kN) Frequency (Hz) Caterpillar CS74B 2.1 157 166–332 23.3–28 Sakai SV540T 2.1 109 172–255 28.3–33.3 Hamm HD120 2.1 110 171–246 30–40 Table 5-3. Specifications of IC rollers used for calibration of forward models. 0.0 0.5 1.0 1.5 2.0 2.5 0 5 10 15 20 Su rf ac e D isp la ce m en t (m m ) Time (s) Accelerometer 1 Accelerometer 2 (b) 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 12 14 16 18 20 G eo ph on e M ea su re d D is pl ac em en t ( m m ) Time (s) (a) Geophone Depth 0.6 m (24 in.) 1.2 m (48 in.) Figure 5-2. Measured IC data during stationary vibratory test on top of embankment using Sakai roller operating under low frequency and high amplitude: (a) displacement measured by embedded geophones; (b) surface displacement calculated from mounted accelerometers.

Calibration of Numerical Models 63 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2 4 6 8 D ep th (m ) Displacement (mm) Field Data FE Model (a) Sakai SV540T High Amp., Low Freq. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2 4 6 8 D ep th (m ) Displacement (mm) Field Data FE Model (b) Sakai SV540T Low Amp., Low Freq. Figure 5-3. Vertical displacement at different depths as obtained from SSL FE model and field measurements during stationary vibratory tests on top of subgrade. Figure 5-3 compares the measured and simulated displacements under the vibratory roller at low and high amplitude settings. The two displacements show similar trends but with different amplitudes. Figure 5-4 compares the measured and simulated displacements during stationary tests with all three rollers under five different scenarios. Different roller manufacturers had different definitions for the low and high amplitude vibrations. The closeness of the measured and simu- lated data for each case is summarized in Table 5-4. The displacements from the SSL FE model are systematically about 2.6 times greater than those measured by geophones in the field, as shown in Figure 5-4(a). By introducing nonlinearity into the static stationary FE model (SSN), a better correlation between the measured field data and computed nonlinear SSN FE model is obtained, as judged by a higher R2 (0.74), and a lower SEE (0.17 mm), as seen in Figure 5-4(b); however, the slope of the regression line indicates a systematic difference of 5.5 times. These systematic differences can be attributed to the differences in the stress states and the compaction efforts achieved in the field and laboratory. To better represent the state of stress and compaction effort, parameter k ′1 in Equation 3-2 was recalculated by replacing the representative resilient modulus with the LWD modulus while maintaining the k ′2 and k ′3 to their corresponding values obtained from the laboratory resilient modulus tests. As shown in Figure 5-4(c), the simulated displacements are about 2.9 times greater than the measured ones. Figures 5-4(d) and 5-4(e) show that the introduction of vibratory conditions to the simulation only marginally impacted the outcomes. Calibration of Forward Models Under Moving Vibration The dataset consisting of accelerometer and geophone measurements collected under a moving vibratory roller at Site 2 is used as an example of this process. A Caterpillar CS74B roller with low amplitude and high frequency operating settings was used in this site and simulated for calibration purposes. (For additional specifications of the roller, see Table 5-3.) Single-Layer Systems. Figure 5-5(a) shows the measured vertical displacements as recorded by the embedded geophones over 30 m (100 ft.) during mapping of the clayey sub- grade of Cell 188. Figure 5-5(b) shows the corresponding surface displacements. Distance zero cor responds to the location of the embedded geophones. As seen in the figure, most of the appreciable vertical geophone deformations are limited to ±2 m (±6 ft.) of the embedded geophones.

64 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction y = 2.56x R² = 0.58 SEE = 0.36 0 3 6 9 12 15 0.0 0.5 1.0 1.5 2.0 SS L FE M od el D isp la ce m en t ( m m ) Geophone Measured Peak Vertical Displacement (mm) Line of Equality +/- 25% Uncertainty Bounds (a) SSL Model y = 5.50x R² = 0.74 SEE = 0.17 0 3 6 9 12 15 0.0 0.5 1.0 1.5 2.0 SS N F E M od el D isp la ce m en t ( m m ) Geophone Measured Peak Vertical Displacement (mm) Line of Equality +/- 25% Uncertainty Bounds (b) SSN Model y = 2.95x R² = 0.74 SEE = 0.17 0 3 6 9 12 15 0.0 0.5 1.0 1.5 2.0 SS N F E M od el D isp la ce m en t ( m m ) Geophone Measured Peak Vertical Displacement (mm) Line of Equality +/- 25% Uncertainty Bounds (c) SSN Model: k1′ recalculated y = 4.88x R² = 0.73 SEE = 0.17 0 3 6 9 12 15 0.0 0.5 1.0 1.5 2.0 V SN F E M od el D isp la ce m en t ( m m ) Geophone Measured Peak Vertical Displacement (mm) Line of Equality +/- 25% Uncertainty Bounds (d) VSN Model k1′ recalculated y = 2.60x R² = 0.75 SEE = 0.16 0 3 6 9 12 15 0.0 0.5 1.0 1.5 2.0 V SN F E M od el D isp la ce m en t ( m m ) Geophone Measured Peak Vertical Displacement (mm) Line of Equality +/- 25% Uncertainty Bounds (e) VSN Model: Figure 5-4. Relationship between geophone measurements during stationary tests for single-layer geosystem at Site 1 to their corresponding FE responses. Descriptive Correlation SSL FE Model SSN FE Model VSN FE Model Laboratory k′1* Recalculated k′1† Laboratory k′1* Recalculated k′1† Adjustment Factor, S 2.56 5.50 2.95 4.88 2.60 R2‡ 0.58 0.74 0.74 0.73 0.75 SEE‡ 0.36 0.17 0.17 0.17 0.16 * Nonlinear k′1 parameter determined from resilient modulus test as per AASHTO T-307. † Recalculated k′1 parameter using LWD modulus as resilient modulus in Equation (3-2). ‡ Coefficient of determination, R2, and standard error of the estimate, SEE. Table 5-4. Summary of relationships of measured field displacements for single-layer geosystem during stationary tests at Site 1 to FE model responses from various levels of sophistication.

Calibration of Numerical Models 65 0.0 0.2 0.4 0.6 0.8 1.0 -15 -10 -5 0 5 10 15 Distance of Geophone from IC Roller (m) 0.0 0.5 1.0 1.5 2.0 -15 -10 -5 0 5 10 15 Distance of Geophone from IC Roller (m) Geophone Depth 150 mm (6 in.) 600 mm (24 in.) (a) Embedded Geophones (b) Surface Displacement S ur fa ce D isp la ce m en t (m m ) G eo ph on e M ea su re d D isp la ce m en t ( m m ) Figure 5-5. Field measurements during proof mapping on top of clayey subgrade at Site 2. The displacements that were measured and simulated using a stationary static linear (SSL) condition are compared in Figure 5-6. The deflection basins resemble one another but show some shift in the magnitude. Table 5-5 presents the summary of the peak displacement measurements on top of the subgrade for cells 185, 186, 188, and 189 at Site 2. The displacements measured by the geophones embedded in the sandy subgrades are slightly larger than those obtained for the clayey subgrades. The influence depth of cells containing sandy material is thus slightly greater than the penetration depth observed in the clayey subgrade. 0 1 2 3 -2 -1 0 1 2 D isp la ce m en t ( m m ) Distance from Drum (m) Field Data FE Data (a) Geophone Depth: 150 mm (6 in.) 0 1 2 3 -2 -1 0 1 2 D isp la ce m en t ( m m ) Distance from Drum (m) Field Data FE Data (b) Geophone Depth: 600 mm (24 in.) Figure 5-6. Displacement basin at different depths as obtained from SSL FE model and field measurements during vibratory moving test on top of subgrade for Cell 188.

66 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction Table 5-6 summarizes the transfer functions between the measured and simulated displace- ments for several levels of sophistication of FE models for all four cells. The SSL FE model displacement responses were about 3.5 times greater than those measured in the field, with a weak correlation coefficient of determination of 0.48. The best relationships between the mea- sured and simulated results were obtained when the vibratory and nonlinear nature of the load was considered. Two-Layer Systems. The approach described in the previous section also was implemented for the two-layer (subgrade and base) systems. Figure 5-7(a) shows the example measure- ments of the embedded geophones at different depths for a pavement structure consisting of an unbound aggregate base layer on top of a clayey subgrade (Cell 188). The base layer atten uates the measured displacement of the embedded geophones in the subgrade. Figure 5-7(b) shows the surface displacements during the mapping of the base layer (Cell 188). When compared to the measurements on top of the subgrade that were seen in Figure 5-5(b), the measurements in Figure 5-7(b) are more variable, reflecting both the bouncing of the drum due to the stiffer base material and the skill of the operator, who tended to drive the roller faster than instructed. Figure 5-8 compares the displacement basins measured and simulated with SSL FE at the three different depths for Cell 188. As the roller moves farther away from the geophones, the displacements attenuated at a faster rate for the FE model in comparison to the field data. As was done for the single-layer systems, different FE scenarios were taken into consid- eration for the two-layer systems, including linear and nonlinear behaviors for the simulated geo materials under static and vibratory loading conditions. Table 5-7 summarizes the descriptive Embedded Geophone Depth Peak Vertical Displacement (mm) Sandy Subgrade Cell 185 Cell 186 Depth Surface 1.41 1.34 150 mm (6 in.) 0.75 0.70 600 mm (24 in.) 0.46 0.37 Clayey Subgrade Cell 188 Cell 189 Depth Surface 1.22 1.18 150 mm (6 in.) 0.59 0.26 600 mm (24 in.) 0.31 0.61 Table 5-5. Vertical displacement at different depths for cells 185, 186, 188, and 189 under moving vibration tests on top of subgrade at Site 2. Descriptive Correlation SSL FE Model SSN FE Model VSN FE Model Laboratory k′1* Recalculated k′1† Laboratory k′1* Recalculated k′1† Adjustment Factor, S 3.47 1.41 2.85 1.67 4.04 R2‡ 0.48 0.48 0.60 0.79 0.79 SEE‡ 0.53 0.08 0.44 0.13 0.41 * Nonlinear k′1 parameter determined from resilient modulus test as per AASHTO T-307. † Recalculated k′1 parameter using LWD modulus as resilient modulus in Equation (3-2). ‡ Coefficient of determination, R2, and standard error of the estimate (SEE). Table 5-6. Summary of relationships of measured field displacements for single-layer geosystem during moving tests at Site 2 as compared to FE model responses for various levels of sophistication.

Calibration of Numerical Models 67 statistics of the relationships for the vibratory moving IC tests that were performed on top of the base layer at Site 2. Considering the nonlinear behavior of the materials yields better relationships among the measured and simulated results. Detailed analyses and information, including the local relationships between the attempted FE scenarios and measured field data for the stationary and moving test protocols performed on top of single- and two-layer systems at Site 1 and Site 2 are provided in Appendix G. 0.0 0.5 1.0 1.5 2.0 -15 -10 -5 0 5 10 15 Distance of Geophone from IC Roller (m) (b) Surface Displacement S ur fa ce D is pl ac em en t (m m ) 0.0 0.1 0.2 0.3 0.4 -15 -10 -5 0 5 10 15 Distance of Geophone from IC Roller (m) Geophone Depth 150 mm (6 in.) 450 mm (18 in.) 900 mm (36 in.) (a) Embedded Geophones G eo ph on e M ea su re d D is pl ac em en t ( m ) Figure 5-7. Field measurements during proof mapping of base layer on top of clayey subgrade at Site 2. 0.0 0.5 1.0 1.5 2.0 -2 -1 0 1 2 D isp la ce m en t ( m m ) Distance from Drum (m) Field Data FE Model (a) Depth: 150 mm 0.0 0.5 1.0 1.5 2.0 -2 -1 0 1 2 D isp la ce m en t ( m m ) Distance from Drum (m) Field Data FE Model (b) Depth: 450 mm 0.0 0.5 1.0 1.5 2.0 -2 -1 0 1 2 D isp la ce m en t ( m m ) Distance from Drum (m) Field Data FE Model (c) Depth: 900 mm Figure 5-8. Displacement basin at different depths as obtained from SSL FE model and field measurements during vibratory moving test on top of base for Cell 188 at Site 2 (MnROAD).

68 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction Global Relationships Considering the results obtained from the two test sites on top of single- and two-layer geo- systems, this section aims to develop global relationships between the measured field data and the FE responses. Figure 5-9 compares the measured and simulated peak displacements directly under the roller at different depths, under both the stationary and moving conditions for the evaluated sites. The SSL FE model yields displacements that are globally about 2.85 times greater than the field measurements with significant scatter. These results concur with those found in NCHRP 10-84 (Nazarian et al. 2014) for spot tests. The scatter in the data can be attributed to the variability of the moisture content along the test sections. Figure 5-10(a) shows the global relationships of the nonlinear SSN FE model and the corresponding field data considering the laboratory-determined nonlinear k ′ parameters as model inputs. Two trends were observed for the measurements corresponding to Site 1 and Site 2 that can be attributed to the difference in compaction effort resulting in different states of stress. In that respect, resilient modulus tests of clayey subgrade materials yielded a nonlinear k ′1 parameter (the parameter associated to stiffness) at Site 1 that was lower in magnitude than the nonlinear k ′1 parameters obtained for Site 2. However, a higher averaged LWD modulus was reported for the subgrade at Site 1 compared to Site 2 (see Table 5-2). These differences can be attributed to the resilient modulus test, which cannot properly account for the compaction effort the geomaterials experience in the field, leading to different site-specific adjustment factors as shown in Figure 5-10(a). Descriptive Correlation SSL FE Model SSN FE Model VSN FE Model Laboratory k′1* Recalculated k′1† Laboratory k′1* Recalculated k′1† Adjustment Factor, S 5.11 3.19 5.06 3.55 5.84 R 2‡ 0.45 0.81 0.54 0.72 0.57 SEE‡ 0.26 0.08 0.36 0.16 0.58 * Nonlinear k′1 parameter determined from resilient modulus test as per AASHTO T-307. † Recalculated k′1 parameter using LWD modulus as resilient modulus in Equation (3-2). ‡ Coefficient of determination, R2, and standard error of the estimate (SEE). Table 5-7. Summary of the descriptive relationships of the measured field displacements for two-layer geosystem during moving tests at Site 2 as compared to the FE model responses for various levels of sophistication. y = 2.85x R² = 0.42 SEE = 0.47 mm 0 1 2 3 4 0.0 0.5 1.0 1.5 2.0 2.5 SS L FE M od el D isp la ce m en t ( m m ) Geophone-Measured Peak Vertical Displacement (mm) Cleburne, TX: Stationary Test, Embankment Cleburne, TX: Moving Test, Subgrade MnROAD, MN: Moving Test, Subgrade MnROAD, MN: Moving Test, Base Line of Equality Figure 5-9. Global relationship between field-measured displacements for vibratory rollers and SSL FE model displacements.

Calibration of Numerical Models 69 Figure 5-10. Global relationships between field geophone-measured displacements and their corresponding SSN FE model displacements with different input modeling approaches. y = 4.27x R² = 0.37 SEE = 0.97 mm 0 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 SS N F E M od el D isp la ce m en t ( m m ) Geophone-Measured Peak Vertical Displacement (mm) Cleburne, TX: Stationary Test, Embankment Cleburne, TX: Moving Test, Subgrade MnROAD, MN: Moving Test, Subgrade MnROAD, MN: Moving Test, Base Line of Equality Site 1 Dataset Site 4 Dataset (a) Laboratory k'1 y = 3.17x R² = 0.60 SEE = 0.42 0 1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 SS N F E M od el D isp la ce m en t ( m m ) Geophone-Measured Peak Vertical Displacement (mm) Cleburne, TX: Stationary Test, Embankment Cleburne, TX: Moving Test, Subgrade MnROAD, MN: Moving Test, Subgrade MnROAD, MN: Moving Test, Base Line of Equality (b) Recalculated k'1 To minimize this drawback, the LWD and laboratory results can be integrated so that the stress hardening and cohesiveness causing softening behaviors of the geomaterials under the loading can be quantified by nonlinear k ′2 and k ′3 parameters, respectively. The k ′1 parameter (associated with stiffness), on the other hand, can be more representative as compared to field conditions when it is adjusted by LWD measurements. As shown in Figure 5-10(b), this approach yields a more uniform global relationship with a higher R2 value and a lower SEE. The results in this case again confirm the findings of NCHRP 10-84 with spot-test devices. The developed global adjustment factors are necessary to accommodate the differences between field measurements and numerical analysis. These transfer functions can be incor- porated as part of the process to extract the mechanical properties of compacted geomaterials during proof mapping using robust inverse solvers that were developed based on the numerical pavement responses.