1、 The Determination of Soft Subgrade Modulus for Airport Pavement Rehabilitation via Backcalculation of Falling Weight Deflectometer Data Michael A. Mooney, M. ASCE, William Bong, 2 and Gerald A. Miller, t M. ASCE Abstract The integrity of existing highway and airfield pavement is increasingly being
2、evaluated based on the analysis of falling weight deflectometer (FWD) deflection basin data. Measured deflection bowls are matched to deflection bowls computed from multi-layered elastic analysis; the resulting “backcalculated“ layer moduli are sometimes blindly used to forge pavement rehabilitation
3、 design decisions. However, as has been clearly documented in the literature, the static analysis of dynamic phenomena and the existence or lack of a near surface rigid layer dramatically affects the backcalculated moduli, particularly the subgrade moduli. This paper presents a detailed investigatio
4、n of soft subgrade moduli via backcalculation from FWD data, triaxial testing, and pressuremeter testing. FWD testing was conducted and data was collected at more than 80 locations along a 1200 m general aviation flexible runway pavement. Deflections were significant, reaching 1.9 mm for an applied
5、stress of 700 kPa. Layer moduli were determined using the widely accepted and Strategic Highway Research Program-recommended MODULUS backcalculation program. For comparison, the subgrade modulus was determined using the pavement pressuremeter and laboratory triaxial testing. Both the pressuremeter a
6、nd the triaxial test results revealed very soft subgrade soil with moduli ranging from 5 to 47 MPa. Conversely, moduli backcalculated from FWD tests varied considerably depending on the depth to bedrock. Using the shallow depth to bedrock estimated by MODULUS, backcalculated subgrade moduli ranged f
7、rom 25 to 60 MPa, however, using the actual depth to bedrock measured through site investigation, backcalculated subgrade moduli ranged from 65 to 180 MPa. Assistant Professor, Civil Engineering A-6 according to AASHTO) is fairly uniform along the length of the pavement and with depth; the plastic l
8、imit is approximately 20 and the liquid limit is 35. The natural water content (wn) remains near 20% both spatially and with depth, with the exception at a depth of approximately 1 m, where w, approaches 30% in some areas. The SPT test results are shown in Figure 3. The reduced N-values near a depth
9、 of 1 m are consistent with higher water contents at this depth and convey the existence of a soft soil. Figure 2. Profile of Natural Water Content and Atterberg Limits 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING SPT N-value 0 5 10 15 I I I I B3 A B4 B5 B6 -P,I B7 20 F
10、igure 3. Standard Penetration Test Results The pre-bored pressuremeter test (PMT), used herein to measure subgrade modulus, consists of lowering a cylindrical probe into a pre-bored hole and inflating the probe while measuring the changes in volume and pressure. A small-diameter pressuremeter was sp
11、ecifically developed for use in pavements (Briaud and Shields 1981), and more recently, a testing procedure was developed for use in design of airport pavements (Cosentino and Briaud 1989). The use of the pressuremeter allows for relatively rapid direct testing of each pavement layer and is less exp
12、ensive than obtaining undisturbed samples and subjecting them to triaxial testing. A primary disadvantage is the necessity of drilling a hole to deploy the test, which causes some unknown degree of disturbance to the surrounding soil. The pavement pressuremeter was conducted at four locations as ide
13、ntified in Fig. 1, between depths of 0.75 m and 1.0 m. Each hole was carefully hand-angered to produce a borehole with a diameter slightly larger than the probe diameter (33 mm). For three of the four tests conducted, the probe had to be pushed gently to fit into the borehole because the wet clay te
14、nded to squeeze slightly as the auger was withdrawn. Thus, some disturbance was inevitable. Pressuremeter testing was conducted using stress control procedures according to ASTM Standard D 4719, which involves incrementing the pressure and recording the change in probe volume. Because the possibilit
15、y for testing in aggregate base existed, a rubber membrane with steel sheathing was used. The membrane was relatively stiff, requiring a membrane correction of approximately 350 kPa at full expansion. 6 PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING Triaxial compression tests were carried out on four
16、100-mm diameter Shelby tube samples extruded from test boring 6 (see Figure 1). The samples were extracted from depths of 0.6 m, 0.7 m, 1 m, and 1. I m (24, 24-30, 36-42, and 42-48 in). Each partially saturated sample was subjected to an isotropic confinining stress consistent with the depth of extr
17、action (see Table 2) prior to axial compression. Each specimen was compressed at an axial strain rate of 15%/hr. FWD testing was carried out at 80 locations. A 53 kN (12,000 lbf) force was applied; geophones were placed at 0, 0.2, 0.3, 0.6, 0.9, 1.2, and 1.8 m to measure surface deflections. The MOD
18、ULUS software program (Uzan et a1.1988) was adopted to backcalculate layer moduli, Results The pressuremeter results are shown in Figure 4 and computed subgrade modulus values are presented in Table 1. Initial modulus values (Einitial) were calculated using the initial straight-line portion of the P
19、MT curves, while reload values (Eretoaa) were calculated using the reload portion of the PMT unload-reload loop. The actual data points and fust-order regression lines used in these calculations are shown in Figure 4. Modulus values were calculated using the equation developed by Baguelin et al. (19
20、78) for the expansion of an infinitely long cylindrical cavity in an elastic material and assuming a Poissons ratio of 0.33. Initial modulus values are lower than reload modulus values primarily due to the greater influence of disturbance during initial loading (Briaud and Shields 1981) and because
21、the mean stress during reloading was higher than the initial loading (Briaud and Shields 1981). While Eloaa is less susceptible to the influence of soil disturbance around the borehole, it is more sensitive to the accuracy of the volume measuring equipment, system compressibility, and membrane corre
22、ctions because smaller volume changes occur during reloading. This can be seen in results of PMT- 3 where initial points on the reloading curve are not usable because of the barely perceptible changes in volume that occurred with the first two reloading pressure increments. Pressuremeter Test Einiti
23、al (MPa) Ereload (MPa) PMT-1 4.28 26.9 PMT-2 2.48 17.3 PMT-3 20.1 58.1 PMT-4 4.57 47.3 Table 1: Summary of Modulus Values from Pressuremeter Test Results PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING 7 1200 I000 800 600 %- t 400 200 o iooo o 800 600 400 . / /I / I / I / I / I / 1 / I i i/ ) I I t I 5
24、0 100 150 PMT- 1 _a.-e PMT-3 20o 9 PMT Data / PMT-2 / ., o PMT Data for Ei,i,l and E=k,a a / / sl . . / - 1 Order Regression Lines / / / / / / / / / i , i i I / PMT-4 I / I / I / I / / / / I 50 100 150 200 250 Corrected Volume (cm 3) Figure 4. Pressuremeter Expansion Curves Four undisturbed Shelby t
25、ube subgrade samples were obtained from Boring 6 (see Figure 1) at depths of 0.6 m, 0.7 m, 1 m, and 1.1 m (24, 24-30, 36-42, and 42-48 in). Note that the subgrade begins at a depth of 0.3 m. The partially saturated samples were isotropically consolidated to stress states consistent with geostatic co
26、nditions, and subjected to triaxial compression in accordance with ASTM D4767 (see Table 2). A multilayered linear elastic analysis was performed using the Kenlayer computer program (Huang 1992) to estimate deviator stress induced by the 53 kN FWD load. These deviator stress magnitudes (see Table 2)
27、 were applied during triaxial compression testing at an axial strain rate of 15%/hr; each specimen was subjected to one unload-reload cycle. The deviator stress-axial strain behavior of each specimen is shown in Figure 5. The secant modulus was determined during initial loading and during the unload
28、-reload cycle of each test; these results are summarized in Table 2. The initial moduli were computed at strains corresponding to the deviator stress in Table 2. The test results clearly indicate a very soft subgrade soil. Due to sample disturbance and handling, the initial secant modulus is lower t
29、han the unload-reload modulus for each specimen. As illustrated by the results in Table 2, the soil softens with depth. This finding is likely a result of increasing water content with depth. For example, in boring B-6, w, increases from 20% at a depth of 0.5 m to 30% at a depth of 1.1 m (see Fig. 2
30、). 8 PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING 160 140 120 , 100 80 “ 60 40 20 0 0.0 ,.t j 9 i / i/st1 “/ TXC 1 TXC 2 TXC 3 TXC 4 /. ,., o m L , i , , 1.0 2.0 3.0 4.0 5.0 Axial Strain (%) Figure 5. Triaxial Compression Test Results Test Depth (m) 6c (kPa) TXC1 0.46-0.61 14 TXC2 0.61-0.76 18 TXC3
31、0.91-1.07 21 TXC4 1.07-1.22 24 d (kPa)“ Einitial (MPa) Eu-l (MPa) 49 6.3 20 31 13 28 20 2.8 9.8 11 2.8 5.6 * Determined from Kenlayer multilayered elastic analysis Table 2: Summary of Triaxial Compression Test Data Falling Weight Deflectometer The magnitude and location of center plate deflections i
32、nduced by the 53 kN FWD load are illustrated in Figure 6; deflection bowls for each location are shown in Figure 7. Great care was exercised to avoid visible cracks intersecting the radius of geopbones during FWD testing. Numerous boring logs to depths approaching 4.5 m revealed a lean clay subgrade
33、 soil with no bedrock present. A boring record less than PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING 9 Figure 6. Center Deflections for 53 kN Falling Weight Deflectometer Tests Figure 7. Summary of Measured Deflection Basins 10 PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING 800-m from the runway pave
34、ment revealed bedrock at a depth of 13 m. The non-zero deflections at the outer radial locations of each FWD deflection basin corroborate the lack of shallow bedrock. Layer thickness magnitudes, ascertained from numerous coring and DCP correlations and used in MODULUS backcalculation, included 130 m
35、m of AC and 200 mm of granular base course. The MODULUS backcalculation program estimates the depth to a rigid layer by extrapolating the deflection vs. inverse of the radial offset (I/r) curve to the intercept of zero deflection and t/r axis (Rohde and Scullion 1990). For uniformly distributed load
36、 acting over a multilayered system, Rohde and Scullion (1990) developed a set of regression equations relating the depth to bedrock (Db,) with the zero deflection vs. l/r intercept and basin shape factors surface curvature index, base damage index and base curvature index. The surface curvature inde
37、x, base damage index and base curvature index are defined as the differences between surface deflections at 0 m and 0.3 m, 0.3 m and 0.6 m, and 0.6 m and 0.9 m, respectively. MODULUS uses these regression equations to estimate the depth to a rigid layer. The average Db computed by MODULUS from the 8
38、0 FWD tests was 1.24 m; the standard deviation was 0.24 m. These computed values of Db are significantly less than the actual Db (estimated to be approximately 13 m). A stiffer subgrade layer beneath the very soft subgrade layer may have caused the shallow estimation of Dbr. The SPT data illustrated
39、 in Figure 3 reveals N values of 15-20 blows/ft at depths of 1.5-2.5 m as compared with N values of 2-5 blows/ft in the upper subgrade. Adopting an empirical correlation between N value and modulus, E (kPa) = 300(N+6) from Bowles (1996), the modulus for the N = 20 blows/ft soil equals 8 MPa while th
40、e modulus for the N=3 material equals 3 MPa. While N values of 15-20 blows/ft do not correlate to a “stiff layer, when comparing to the overlying soft subgrade, the modulus is greater by a factor of more than two. Note, however, that the correlation of SPT N-value to modulus is inexact and further c
41、omplicated by the near-surface partially saturated nature of the soil. Unfortunately, DCP test results to a depth of only 1 m did not permit further analysis of a stiffer subgrade layer. An alternative accepted technique to determine Dbr involves minimizing the root mean square error (RMSE) between
42、measured and theoretical deflections (Chou 1989). Here, a trial and error approach was adopted wherein MODULUS was performed for an array of Dbr values until the RMSE was minimized. The mean Dbr required to minimize the RMSE was 2.9 m, a value that lies between the 1.24 m average Dbr computed by MOD
43、ULUS and the measured 13 m. The impact of using various Dbr values is evidenced by the backcalculated moduli and in the theoretical deflection basins that “match“ the measured deflection basin. The backcalculation results from three representative tests (1, 41, 74) are summarized in Table 3. The nea
44、r surface estimation of Dbr results in a significantly lower subgrade modulus than the modulus backcalculated when the actual Dbr is used. This is explained in Figure 8 by the deflection bowls of tests 1, 41, and 74. The shallow estimation of Dbr forces the theoretical deflections at outer radial lo
45、cations to be significantly less than the measured deflections. The small outer theoretical PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING 11 0 0.2 . 0.4 1 0.6 0.8 radial distance (m) 0 0.4 0.8 1.2 1.6 2 f +measured ._ + theoretical Modulus 5.1 Dbr (1.5 m) / I ical using actual Dbr (6 m) -*- theoretic
46、al using RMS Dbr (2.3 m) 0 0.2 “ 0.4 0.6 0.8 1.2 1.4 radial distance (m) 0 0.4 0.8 1.2 1.6 2 FWD Test 41 + theoreticdl Modulus 5.1 Dbr (1.5 m) / i - + theoretical using actual Dbr (6 m) + theoretical using RMS Dbr (2 m) 0 - o.2 g 0.4 0.6 - o.8 radial distance (m) 0 0.4 0.8 1.2 1.6 2 . measured a the
47、oretical Modulus 5.1 Dbr (1.4 m) b“ J + theoretical using actual Dbr (6 m) , theoretical using RMS Dbr (1.8 m) Figure 8. Measured and Computed Deflection Basins for Tests 1, 41, and 74 12 PAVEMENT SUBGRADE AND NONDESTRUCTIVE TESTING deflections, however, are considered significant in the presence of
48、 a near surface stiff layer, and thus, the backcalculated subgrade modulus is low. Using the actual Dbr, the theoretical deflections at outer radial locations adequately match those measured. Given the significant thickness of the subgrade layer, the subgrade modulus required to produce such deflect
49、ions is much greater than that backcalculated in the presence of a near surface rigid layer. The backcalculated subgrade moduli using Dbr = 2.9 m are lower than those backcalculated when the measured Dbr is used yet greater than those backcalculated when the l/r method D values are used. Additionally, the outer deflections predicted by the RMSE approach were less than the measured deflections (see Figure 8). Note that the actual Db i
