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

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70 Extraction of Mechanical Properties Introduction To extract mechanical properties in a practical manner, a robust backcalculation technique that does not require excessive processing time is needed. This chapter reports on the research team’s efforts to develop procedure(s) to extract the mechanical properties of geomaterials during mapping of the compacted layers on a real-time basis. Selecting the Backcalculation Process The extraction of mechanical properties of layered materials can be performed directly using ICMVs captured during the mapping process or indirectly using a reliable inverse solver that incorporates ICMVs in the estimation of soil properties. The following sections describe each of the two approaches. Estimation of Stiffness As was discussed in Chapter 4, the layer stiffness can be extracted directly from the force imposed by the drum and the deflection at that location. Force-displacement loops are created by plotting the time-varying contact force versus drum displacement (see Figures 4-16 and 4-17). However, the calculation of stiffness can be simplified by obtaining the ratio of the complex amplitudes of the force and displacement records in the frequency domain at the roller’s operating frequency. This process allowed the development of maps of the surface deflections and the stiffness of geomaterials (see Figure 4-18). Backcalculation of Modulus Due to the nonlinear behavior of the unbound geomaterials, the modulus of a layer varies spatially and with depth. To gauge the quality of the pavement, it is desirable to use a represen- tative modulus for the layer. The moduli at half-depth of the base and at 300 mm (12 in.) into the subgrade were considered as their representative properties. For the single-layer geosystems (subgrade), the layer stiffness can be extracted directly at each spatial location by dividing the known force of the roller by the corresponding deflection. For a multi-layer geosystem, this process would provide a composite stiffness. For developing inverse models for the backcalculation of the moduli of the subgrade and base layers, a set of machine-learning techniques was implemented. GP and ANN methods were used for that purpose. A training dataset that consisted of 2,200 single-layer and 4,400 two-layer geosystems with different base thicknesses was used to develop a predictive function using the C H A P T E R 6

Extraction of Mechanical Properties 71 GP method for symbolic regression. To arrive at the optimal predictive function using the GP approach, the inputs considered were: • The nonlinear k ′ parameters of the subgrade, ki′s; • The surface displacement, d1, measured on top of the subgrade; • The base nonlinear parameters, ki′b and layer thickness, h; and • The surface displacements, d2, recorded on top of the base layer. These inputs yielded relationships for the subgrade, ESUBG, and the base modulus, EBASE, as follows: , (6-1)1E f k dSUBG i s( )= ′ and , , , , . (6-2)1 2E f k k h d dBASE i s i b( )= ′ ′ To build the models for a roller commonly used in the field (with operating features as shown in Table 3-1), the moduli at their representative locations were obtained from the SSN FE model and used as target values. The following equation provided the best predictive modulus of subgrade from the GP method: , (6-3)1 1 2 3 2 4 3 5 6 2 7 2 2 1 3 E C k C C k C k C C k e C k d SUBG s s s s k ss( )= ′ + + ′ + ′ + + ′ − ′ ( )′ where C1 = 0.0191, C2 = 136, C3 = 107, C4 = 45.9, C5 = 38.1, C6 = 40.5, and C7 = 9.9. The GP method was then applied to the training dataset, and the resulting predictions of subgrade moduli were compared to subgrade moduli obtained using the SSN FE model with the same dataset. As seen in Figure 6-1, Equation 6-3 provided a reasonable estimate of the subgrade moduli generated by the SSN FE model. Following a similar process, the best equation for predicting the base modulus took the following form: , (6-4)1 1 2 1 2 3 1 3 2 1 1 1 3 4 1 E C k C h k k C k k d h k k k k C hk BASE b b b b b b s b b b( ) ( ) = ′ + − ′ ′ + ′ ′ + ′ + ′ − ′ ′ + ′ where C1 = 0.108, C2 = 2.97 × 103, C3 = 1.42 × 103, and C4 = 0.0098.

72 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction Applying Equation 6-4 to the training dataset, the resulting base modulus predictions were again compared to those determined using the SSN FE model. As seen in Figure 6-2, the base modulus can be predicted favorably using the proposed equation. The ANN-based method involved an input layer that, at the most complex level, included nine predictor independent variables: the nonlinear k ′ parameters of the base and the subgrade; base thickness h; surface displacements d1 and d2, corresponding to the top of the subgrade and the base layer, respectively; and an output layer that included the values predicted by the network. When the ANN method was applied to the dataset, the resulting predictions of subgrade moduli were compared to the subgrade moduli determined using the FE model, yielding the results shown in Figure 6-3 and Figure 6-4. After comparing the results of the GP method with those from the ANN method, a decision was made to continue with the ANN-based method. Using the ANN method, more complex inverse solvers can be developed to predict the output more precisely; however, more complex inverse solvers would require more laboratory efforts to determine the needed input variables. Based on the available input parameters from IC field operation and laboratory test results, two backcalculation scenarios were proposed for predicting ESUBG and five scenarios were proposed for EBASE. The scenarios and their corresponding input parameters are listed in Table 6-1. y = 0.98x R² = 0.99 SEE = 6.3 MPa 0 100 200 300 400 0 50 100 150 200 250 300 350 400 SSN FE Model-Determined Subgrade Modulus (MPa) Line of Equality +/- 20% Error Line G P- Pr ed ic te d Su bg ra de M od ul us (M Pa ) Figure 6-1. Comparison of GP-predicted subgrade modulus to SSN FE model- determined subgrade modulus using data set aside for validation. y = 0.90x R² = 0.94 SEE = 68.2 MPa 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 SSN FE Model-Determined Base Modulus (MPa) Line of Equality 20% Error Line G P- Pr ed ic te d Ba se M od ul us (M Pa ) Figure 6-2. Comparison of GP-predicted base modulus versus SSN FE model- determined base modulus using data set aside for validation.

Extraction of Mechanical Properties 73 R² = 0.99 SEE = 4.58 MPa 0 50 100 150 200 250 300 0 100 200 300 A N N -P re di ct ed Su bg ra de M od ul us (M Pa ) FE-Determined Subgrade Modulus (MPa) Line of Equality +/- 20% Uncertainty Bounds (b) Scenario 2 R² = 0.99 SEE = 4.95 MPa 0 50 100 150 200 250 300 0 100 200 300 FE-Determined Subgrade Modulus (MPa) Line of Equality +/- 20% Uncertainty Bounds (a) Scenario 1 A N N -P re di ct ed Su bg ra de M od ul us (M Pa ) Figure 6-3. Comparing ANN-predicted versus FE-determined subgrade moduli with different input scenarios. R² = 0.99 SEE = 8.4 MPa 0 100 200 300 0 100 200 300 A N N -P re di ct ed M od ul us (M Pa ) FE-Determined Modulus (MPa) +/- 20% Uncertainty Bounds (a) Scenario 6 R² = 0.99 SEE = 6.7 MPa 0 100 200 300 0 100 200 300 FE-Determined Modulus (MPa) +/- 20% Uncertainty Bounds (b) Scenario 7 A N N -P re di ct ed M od ul us (M Pa ) Figure 6-4. Comparison of ANN-predicted versus FE-determined base modulus using ANN with different input scenarios. Geosystem Scenario Input Parameters* Target Single-Layer 1 h, k′1 s, k′2s, k′3s, d1 Subgrade Modulus ESUBG2 h, k′1s, k′2s, k′3s, d1, MRSUBG-Rep Two-Layer 3 h, k′2b, k′3b, d2, d1 Base Modulus EBASE 4 h, k′2b, k′3b, d2, ESUBG 5 h, k′2b, k′3b, d2, MRSUBG-Rep 6 h, k′1b-back, k′2b, k′3b, d2, d1 7 h, k′1s-back, k′2s, k′3s, k′1b-back, k′2b, k′3b, d2, d1 * ESUBG input values in Scenario 4 for two-layer systems is the modulus of subgrade determined at 300 mm (12 in.) from the top of the subgrade as obtained from nonlinear FE analysis; MRSUBG-Rep is the resilient modulus of subgrade material calculated from NCHRP 1-28A representative stresses; and k′1-back is the backcalculated k′1 value using the LWD modulus ELWD of the corresponding layer in Equation 3-2, following the model from Ooi et al. (2004). Table 6-1. Feasible backcalculation scenarios based on available IC field and laboratory data.

74 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction More detailed information regarding different levels of sophistication of the FE models used during the backcalculation process can be found in Appendix F. Figure 6-3 shows the results obtained from the trained algorithms to backcalculate subgrade modulus for the proposed Scenarios 1 and 2. The results show that both scenarios can predict the subgrade modulus quite accurately. Scenario 1 was preferred because of its simplicity. In contrast to the single-layer systems, the backcalculation of the modulus of the base layer requires additional input parameters. The results of the trained algorithms for Scenarios 3 through 5 were not as promising, as is discussed in Appendix F. Scenarios 6 and 7 were proven viable, as is shown in Figure 6-4. Evaluation and Calibration of Inverse Models The displacement measurements acquired during the proof mapping of the MnROAD test sections (Site 2) and the nonlinear k ′ parameters obtained from the resilient modulus test as per AASHTO T-307 were used for evaluating the proposed inverse scenarios/architectures. Table 6-2 lists the inputs used for the evaluation of the inverse solver scenarios using data from the four pavement sections built at MnROAD. Prior to feeding the input displacements d1 and d2 into the inverse solver, the field-measured displacements were calibrated using a global adjustment factor f = 3.2, which was obtained for the SSN models using the process discussed in Chapter 5. The extracted moduli of single- and two-layer systems obtained from the inverse scenarios were compared with the corresponding LWD measurements for cells 185, 186, 188, and 189, as seen in Figure 6-5: • Scenarios 1 and 2 yielded promising results for the single-layer systems as most of the samples fall within the 20% uncertainty bounds. • Scenario 1 is optimal for extracting the modulus of subgrade materials because it requires fewer input parameters than Scenario 2. • Scenarios 6 and 7 both predicted the base modulus with reasonable accuracy. • Scenario 6 is recommended as the most optimized inverse solver for extracting the base modulus because it is less complicated and requires fewer input parameters and less laboratory efforts than Scenario 7. As observed in Figures 6-5(c) and 6-5(d), the extracted moduli of the top (base) layer from Scenarios 6 and 7 are about 1.2 and 1.1 times the backcalculated LWD moduli, respectively. MnROAD Cells Base Thickness h (mm) Nonlinear Parameters for Subgrade Layer * Nonlinear Parameters for Base Layer* Modulus of Subgrade* Surface Displacement on Top of k′1s-back k′2s k′3s k′1b-back k′2b k′3b ESUBG (MPa) MRSUBG (MPa) Base d2 (mm) Subgrade d1 (mm) 185 300 123 1.60 -0.60 467 0.80 -0.10 29 79 1.36 1.41 186 300 152 1.60 -0.60 722 0.90 -0.10 36 79 1.29 1.34 188 300 462 0.60 -2.60 709 0.60 -0.10 43 60 0.99 1.22 189 300 283 0.60 -2.60 470 0.90 -0.10 26 60 1.25 1.18 *ESUBG is the subgrade modulus, in this case using the LWD modulus determined on top of subgrade; MRSUBG is the resilient modulus of subgrade material as obtained from resilient modulus test as per AASHTO T-307; and k′1-back is the backcalculated k′1 value using the LWD modulus ELWD of the corresponding layer in Equation 3-2, following the model from Ooi et al. (2004). Table 6-2. Summary of predictor variables measured for Site 2 (MnROAD).

Extraction of Mechanical Properties 75 The difference between the field measurements and the extracted values can be attributed to the global adjustment factor acquired during the calibration process that was discussed in Chapter 5. The prediction can be thus improved by developing local adjustment factors for single- and two-layer systems distinctly. Extracting Modulus Using ANN Inverse Solvers (Approach 1) The dataset obtained during the field evaluations conducted at the MnROAD site was used to evaluate the developed inverse solvers for extracting subgrade and base moduli. Figure 6-6 summarizes the steps of the proposed approach. The inputs to the inverse solvers are the material properties (nonlinear parameters and layer thicknesses), drum dimensions and weight, and surface deflection measurements of the drum. The roller-induced surface displacement is obtained from the mapping process using the average drum displacement in each sublot. The nonlinear parameters k ′2 and k ′3 are obtained from resilient modulus tests conducted in the laboratory at the optimum moisture content. The nonlinear k ′1 parameter is adjusted using y = 1.02x SEE = 5.9 MPa 0 25 50 75 0 25 50 75 Ex tr ac te d Su bg ra de M od ul us (M Pa ) ELWD-SUBG (MPa) ELWD-SUBG Line of Equality +/- 20% Uncertainty Bounds (a) Scenario 1: y = 1.02x SEE = 9.6 MPa 0 25 50 75 0 25 50 75 Ex tr ac te d Su bg ra de M od ul us (M Pa ) Line of Equality +/- 20% Uncertainty Bounds ELWD-SUBG (MPa) ELWD-SUBG (b) Scenario 2: y = 1.14x R² = 0.91 SEE = 11.9 MPa 0 100 200 300 400 0 100 200 300 400 Ex tr ac te d Ba se M od ul us (M Pa ) Line of Equality +/- 20% Uncertainty Bounds Backcalculated ELWD-BASE (MPa) (d) Scenario 7: ELWD-BASE y = 1.23x R² = 0.92 SEE = 10.1 MPa 0 100 200 300 400 0 100 200 300 400 Backcalculated ELWD-BASE (MPa) Line of Equality +/- 20% Uncertainty Bounds (c) Scenario 6: ELWD-BASE Ex tr ac te d Ba se M od ul us (M Pa ) Figure 6-5. Comparison of extracted subgrade and base modulus obtained from four proposed scenarios with corresponding backcalculated modulus.

76 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction the LWD modulus after conducting LWD tests at the sublots. The next section describes an evaluation of this process as used for both single-layer and two-layer systems. Single-Layer System Figure 6-7 shows the moisture-adjusted nonlinear parameters k ′2 and k ′3 at the time of compaction of the clayey subgrade in the sublots corresponding to cells 188 and 189. The non- linear parameters were estimated using a best-fit regression curve through the variations of the relevant parameters from the resilient modulus tests with moisture content. The adjustment process also was applied to the nonlinear parameters for sandy subgrade samples from cells 185 and 186 (not shown). Nonlinear parameter k ′1 was adjusted using the LWD modulus obtained along the test section on each sublot. Figure 6-8 compares the modulus of each sublot as predicted by the inverse solver and compared to the corresponding sublot’s LWD modulus, ELWD. Figure 6-8 provides comparisons for both the sandy subgrade materials (cells 185 and 186) and the clayey subgrade materials Figure 6-6. Flowchart for extracting modulus of unbound materials using ANN inverse solvers. y = -0.015x2 + 0.13x - 0.98 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0 5 10 15 20 N on lin ea r Pa ra m et er k ' 3 N on lin ea r Pa ra m et er k ' 2 Moisture Content—NDG (%) Lab Data Cell 188 Cell 189 y = 0.018x2 - 0.38x + 2.44 2.5 0.0 0.5 1.0 1.5 2.0 3.0 0 5 10 15 20 Moisture Content—NDG (%) Lab Data Cell 188 Cell 189 (a) Variation of k'2 (b) Variation of k'3 Figure 6-7. Adjustment of parameters k’2 and k’3 using moisture correction for clayey subgrade (cells 188 and 189).

Extraction of Mechanical Properties 77 (cells 188 and 189). As shown by Figure 6-8, the inverse solver can predict the modulus of subgrade with reasonable accuracy. Two-Layer System Similar to the subgrade, the nonlinear parameters of the base layers were adjusted for moisture for each sublot. The nonlinear parameters were interpolated and, in some cases, extrapolated using regression lines similar to those shown in Figure 6-7. The base moduli were backcalculated using the LWD measurements on top of the base and corresponding measurements on top of the subgrade using a layered-elastic program through an iterative process. The nonlinear parameters, in conjunction with the roller-surface deflections on top of the subgrade and base layers, were used as inputs to the inverse solver for extract- ing the base modulus. The extracted base moduli compared well with the corresponding LWD base moduli, as judged by the number of cases that fall within the ±25% uncertainty bounds (see Figure 6-9). y = 1.11x R² = 0.61 SEE = 5.43 MPa 0 50 100 150 0 30 60 90 120 150 LWD Subgrade Modulus (MPa) Sandy Subgrade: Cells 185 & 186 Clayey Subgrade: Cells 188 & 189 Line of Equality +/- 25% Uncertainty Bounds Ex tr ac te d M od ul us (M Pa ) Figure 6-8. Comparison of extracted subgrade moduli obtained from inverse solver with corresponding measured moduli for each of the sublots (cells 185, 186, 188, and 189). y = 0.98x R² = 0.62 SEE = 52.4 MPa 0 100 200 300 400 500 600 0 100 200 300 400 500 600 LWD Base Modulus (MPa) Base on Top of Sandy Subgrade Base on Top of Clayey Subgrade Line of Equality +/- 25% Uncertainty Bounds Ex tr ac te d Ba se M od ul us (M Pa ) Figure 6-9. Comparison of extracted subgrade moduli obtained from inverse solver with corresponding measured moduli for each of the sublots.

78 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction The extracted base moduli compared well with the corresponding LWD base moduli as judged by the number of cases that fall within the ±25% uncertainty bounds. Retrieving Modulus Using Dynamic Drum Force (Approach 2) A more practical approach for determining the modulus of single-layer and two-layer systems was developed using the drum force, Fd, determined from the accelerometers measuring the drum’s inertia. Using the dynamic drum force does not require laboratory resilient modulus and field LWD testing. The expectation was that the impact of the variability of the compacted geomaterial properties would be less significant toward the calculation of the geomaterial’s modulus if the more uniform areas of the lot were identified and considered for the local calibration process. Illustrated in Figure 6-10, the dynamic drum force approach consisted of four steps: 1. Upon completion of the mapping process, generate color-coded maps of (a) the dynamic drum force, (b) CMVs, and (c) coefficient of variation (COV) of the CMVs. 2. To obtain optimal results, choose at least five sublots with a COV of CMV less than or equal to 25%. 3. Obtain a site-specific local calibration factor between the LWD modulus and the drum force of the sublots selected in Step 2. 4. Estimate the moduli using the measured dynamic forces adjusted with the established site-specific calibration factor. Evaluation of Approach to Determine Modulus Using the Drum Force Figure 6-11 illustrates the process used to retrieve the moduli of the sandy subgrade of MnROAD Cell 186. Figure 6-11(a) shows the mapping of the sublot’s representative CMVs, Figure 6-10. Flowchart for estimation of moduli of unbound materials using dynamic drum force.

Extraction of Mechanical Properties 79 y = 0.19x R² = 0.63 0 20 40 60 80 100 150 200 250 300 Drum Force (kN) Cell 186 (b) Step II: Identifying Sublots (c) Step III: Developing Local Transfer Function LW D M od ul us (M Pa ) (a) Step 1: Mapping Process Figure 6-11. Process of retrieving modulus using dynamic force for sandy subgrade at MnRoad (Cell 186).

80 Evaluating Mechanical Properties of Earth Material During Intelligent Compaction COV of CMV, and drum force. Five sublots with COV of the CMVs less than or equal to 25% were selected for conducting LWD tests, as seen in Figure 6-11(b). The drum forces and LWD moduli from the selected sublots were used to develop a local calibration factor, as shown in Figure 6-11(c). The moduli of all sublots were then calculated by multiplying the adjustment factor by the corresponding drum forces. Figure 6-12 compares the retrieved and LWD moduli for all sublots of the subgrade sections evaluated at MnROAD (cells 185, 186, 188, and 189). Figure 6-12(a) shows the results of this approach, excluding the condition imposed to the variability of CMV measurements (i.e., uniformity of the proof-mapped section) discussed above. Figure 6-12(b) compares the LWD and retrieved moduli by considering the condition of selecting the sublots with COV of the CMVs less than or equal to 25% to develop the adjustment factor. Identifying sublots exhibiting more uniformity in their CMV measurements significantly reduces the uncertainty of the calculated moduli as obtained from the drum force. As seen in Figure 6-12(b), data points tend to fall closer to the line of equality. y = 0.65x 0 25 50 75 100 0 25 50 75 100 LWD Modulus (MPa) Cell 185: Sandy Subgrade Cell 186: Sandy Subgrade Cell 188: Clayey Subgrade Cell 189: Clayey Subgrade Line of Equality +/- 70% Uncertainty Bounds (a) All Sublots Considered R et ri ev ed M od ul us (M Pa ) y = 0.93x 0 25 50 75 0 25 50 75 LWD Modulus (MPa) Cell 185: Sandy Subgrade Cell 186: Sandy Subgrade Cell 188: Clayey Subgrade Cell 189: Clayey Subgrade Line of Equality +/- 25% Uncertainty Bounds (b) Sublots with COV of CMV ≤ 25% R et ri ev ed M od ul us (M Pa ) Figure 6-12. Relationship between retrieved modulus and LWD modulus for sandy and clayey subgrade sections at MnROAD using (a) all sublots and (b) sublots with COV of CMVs less than or equal to 25%.