CHARACTERIZATION OF A TWO-LAYER SOIL SYSTEM USING A LIGHTWEIGHT DEFLECTOMETER WITH RADIAL SENSORS Paper #

Transcription

1 CHARACTERIZATION OF A TWO-LAYER SOIL SYSTEM USING A LIGHTWEIGHT DEFLECTOMETER WITH RADIAL SENSORS Paper # By Christopher T. Senseney, P.E., Maj, USAF (Corresponding Author) Ph.D. Student Division of Engineering Colorado School of Mines 1610 Illinois Street Golden, CO Ph: (303) F: (303) csensene@mines.edu Michael A. Mooney, Ph.D., P.E. Associate Professor Division of Engineering Colorado School of Mines 1610 Illinois Street Golden, CO Ph: (303) F: (303) mooney@mines.edu Word Count: Abstract = 0218 Text = 4710 Tables (4 x 250) = 1000 Figures (6 x 250) = 1500 Total = 7428 Re-submitted on November 10, 2009 for presentation and publication by Transportation Research Board, 88 th Annual Meeting, January 2010, Washington, D.C.

2 Senseney, C.T. & Mooney, M.A ABSTRACT Non-destructive tests to estimate stiffness modulus, such as the light weight deflectometer (LWD), have experienced increased popularity, but very little research has been performed to evaluate the LWD with radial sensors. Results are presented from LWD testing with radial sensors that measured the deflection bowl on one- and two-layer field test beds consisting of unbound materials. LWD testing produced a measureable deflection bowl on medium stiffness granular materials to a radial sensor spacing of 750 mm (30 in). When limited to a stiff over soft layered system, the LWD with radial sensors demonstrated the ability to accurately backcalculate layered moduli. Backcalculated moduli closely matched laboratory determined moduli from triaxial testing at a similar stress state as in the field. The measurement depth for the LWD with radial sensors was found to be 1.8 times plate diameter versus the measurement depth of conventional LWD testing of 1.0 to 1.5 times plate diameter. The LWD with radial sensors was able to measure deeper than conventional LWD testing because the radial geophones measure vertical surface deflections caused almost entirely by deeper material. As compared to other configurations, the 300 and 600 mm (12 and 24 in) radial sensor configuration is recommended for unbound materials because it produced the most accurate moduli backcalculation results and captures deflections critical to the backcalculation process. INTRODUCTION The light weight deflectometer (LWD) was developed to estimate the in-situ stiffness modulus of soils. The device can be used for quality control/quality assurance and structural evaluation of compacted earthwork and pavement construction. Over the past decade or more, resilient modulus, analogous to stiffness modulus, was established as the primary input parameter for characterizing subgrade, subbase and base materials for highway pavement design in the United States. As a result, non-destructive tests to estimate stiffness modulus, such as the LWD, have experienced increased popularity [1-5]. Conventional LWD testing uses deflection measured from a center geophone or accelerometer coupled with static, linear-elastic half space theory to calculate one stiffness modulus for the composite soil system. LWD manufacturers have recently begun offering an LWD with radial geophones. This evolution suggests that layered soil systems may be characterized in a similar method as the falling weight deflectometer (FWD). If so, a significant advancement would be achieved because earthwork is often layered. The modulus obtained from conventional LWD testing represents the composite modulus of the layers within the influence depth rather than the true modulus of the tested layer [6]. Very little research has been performed to evaluate the LWD with radial sensors. To the authors knowledge there is just one published study presenting actual LWD radial deflection results [7] and no published studies of backcalculated moduli from radial sensors. This paper presents results from LWD testing that employed radial sensors to measure the deflection bowl of one- and two-layer soil systems. Layer moduli were then backcalculated based on measured deflections. The objectives of this paper are to: (1) verify the LWD produces a deflection bowl on unbound materials and describe the nature of the deflection bowl on oneand two-layer systems, (2) assess the capability of LWD with two radial sensors to accurately characterize moduli of known two-layer stratigraphies (limited to stiff over soft), (3) evaluate measurement depth of LWD with two radial sensors and show how and why it is different than

3 Senseney, C.T. & Mooney, M.A conventional LWD testing, and (4) evaluate the influence of radial sensor spacing on backcalculation. BACKGROUND LWD Characteristics The LWD is a portable device that applies an impulse load from a drop weight impacting a circular plate resting on the ground. The LWD consists of a circular load plate (150 mm, 200 mm or 300mm diameter), housing, urethane dampers, guide rod, drop weight and geophone sensors (Figure 1a). During testing the drop weight releases from a variable height, slides down the guide rod and applies a dynamic force impulse to the load plate lasting ms. Surface deflections (through integration of velocity) are measured from a geophone mounted in the center of the load plate and from up to two radial geophones mounted on a support bar resting on the soil. Applied force (P) is measured with a force transducer mounted within the housing. In conventional LWD testing, the maximum deflection measured by the center geophone (d 0 ) and maximum measured P are coupled with homogeneous, isotropic, static linear-elastic half space theory to calculate a conventional LWD modulus (E vd or E LWD ) that follows as: E LWD 2 ( 1 ν ) A P = (1) ad π 0 where ν is the Poisson s ratio of the soil, A is the contact stress distribution parameter (A = 2 for a uniform stress distribution, π/2 for an inverse parabolic distribution, 8/3 for a parabolic distribution) and a is the plate radius. The user has the option to input values for ν and A. The LWD is designed for an impact force and load plate diameter to deliver an average contact stress of 100 to 200 kpa (14.5 to 29 psi) on the soil surface. This stress range mimics the approximate stress level on a typical subgrade, subbase or base course due to vehicle loading on the pavement surface [8]. Two commercial LWD devices that employ radial geophone sensors are the Prima 100 and Dynatest LWD produced by Grontmij - Carl Bro Pavement Consultants and Dynatest International, respectively. Results from testing with the Prima 100 (Fig. 2b) along with backcalculated moduli from Dynatest s LWDmod program are presented in this study. The Prima 100 utilizes seismic velocity transducer geophones with a resolution of 1 µm and a frequency range of 0.2 to 300 Hz [9].

4 Senseney, C.T. & Mooney, M.A FIGURE 1 (a) Schematic of LWD, (b) picture of Prima 100 LWD. Forward-calculation and Backcalculation Dynatest s LWDmod program forward-calculates deflections using Odemark s layer transformation approach together with Boussinesq s equations. The basic assumption of Odemark s layer transformation is that the layered structure can be transformed into an equivalent uniform, semi-infinite material, to which Boussinesq s equations may be applied to calculate deflections. Two critical assumptions of the Odemark-Boussinesq method are: (1) layer thicknesses should be more than one-half the radius of the loading plate, and (2) moduli should decrease with each descending layer by at least a factor of two [10]. Accurate backcalculation with the Odemark-Boussinesq method is limited to pavement profiles with stiff layers over soft layers. Using Odemark s layer tranformation, a two-layer linear elastic system may be transformed to a semi-infinite space provided that layer one is replaced by an equivalent thickness (h e ) of material having the properties of the semi-infinite space. Assuming the Poisson s ratio is the same for all layers, the transformed equivalent thickness may be determined as: E 1 h 3 e = fh1 (2) E2 where h 1 is the thickness of the top layer, E 1 and E 2 are the moduli of the top and bottom layer respectively, and f is a correction factor for better agreement with exact values [11]. A significant advantage of the Odemark-Boussinesq method is the ability to accommodate for the stress dependent non-linearity in dynamic deflection testing by incorporating a non-linear relation for the subgrade modulus. The universal non-linear model for resilient modulus (M r ) that reflects stress dependence [12] is given by: k2 k3 M = k p q (3) r 1 where p is the mean normal stress ( 3), q is the deviator stress, and k 1, k 2 and k 3 are best fit parameters determined by laboratory data. The k 3 value is negative, typically in the

5 Senseney, C.T. & Mooney, M.A range of 0 to -0.2 for granular materials and 0 to -0.6 for cohesive materials [12]. As k 3 becomes more negative, a material exhibits greater stress softening behavior where the modulus decreases with increasing deviator stress. Dynamic deflection testing, e.g. FWD and LWD testing, produces a non-linear effect in a stress softening subgrade, where the subgrade stress levels beneath the outer sensors are much lower than subgrade stress levels for the inner sensors. The apparent subgrade modulus measured by outer sensor locations is therefore higher than the apparent subgrade modulus measured by the inner sensors [13]. The variation of modulus with radial distance due to dynamic deflection testing is similar to that given by k 3 part of Equation 3. To this end, the non-linear subgrade modulus (E 2 ) for use in Odemark-Boussinesq calculations [14] is expressed in the form: E σ 1 2 = C p a n where σ 1 is the major principle stress from external loading, p a is atmospheric pressure, and C and n are constants. As is the case with k 3, a material exhibits greater stress softening behavior as n becomes more negative. A material is considered linear elastic when n = 0. LWDmod uses a Odemark-Boussinesq static analysis to forward-calculate deflections. First, apparent subgrade moduli E(r) are determined from a Boussinesq equation (Equation 5) for loading on a homogeneous, isotropic, linear elastic half-space where d r is the measured deflection at distance r, and P is a point load representing the uniformly distributed load of the LWD. At a radial distance beyond one diameter from the center of the load, a point load produces approximately the same surface deflections as a distributed load [15]. Next, the nonlinearity constant n is calculated (Equation 6) where E(r 1 ) and E(r 2 ) are the apparent subgrade moduli determined from radial sensors at r 1 and r 2. The n value is essentially a measure of subgrade non-linearity as E(r 2 ) will be greater than E(r 1 ) when testing on a non-linear subgrade due to a lower stress state at r 2. Then, Odemark s transformation is modified to accommodate a non-linear subgrade in which the equivalent thickness of layer one (h e,1 ) is calculated (Equation 7) as follows: 2 (1 ν ) P E( r) = (5) πrd r E( r 1) log E( r2 ) n = (6) r 2 2log r1 (4)

6 Senseney, C.T. & Mooney, M.A h e,1 = f h 3 1 E1 3P C(1 2n) 2 p π a n 1 3 2n where f is an correction factor (= 1.05 for a 2-layer system with n -0.4, = 1.0 for n > -0.4) [16]. Then, stresses are calculated with Boussinesq s equations on the transformed system and are used to calculate E 2 (Equation 4). Finally, deflections are calculated as the sum of the compression in the transformed layer one, plus the deflection at the top of the subgrade. The compression of the transformed layer one is the difference between deflections at the top and the bottom of the transformed layer one. The deflection at the top the subgrade is calculated using E 2. The calculated deflections are compared with measured deflections and assumed moduli are adjusted in an iterative procedure until calculated and measured deflection bowls reach an acceptable match [13]. Field Test Beds Two field test beds were constructed to investigate the ability of the LWD with radial geophones to characterize layered stratigraphies. Figure 2 summarizes the geometry of test bed one (TB1) and test bed two (TB2). TB1 was 4 m (13 ft) long and 2.5 m (8 ft) wide and TB2 was 4 m (13 ft) long and 2 m (6.6 ft) wide. TB1 was designed as a homogeneous, medium stiffness soil profile with in-situ material excavated to a depth of 1500 mm (60 in) and subsequently filled with medium stiff sand (SW-SM) compacted with a vibratory plate in 150 mm (6 in) lifts. TB2 was designed as a medium stiffness soil over soft soil profile with in-situ soft clay (CL) excavated to a depth of 600 mm (24 in) and filled with SW-SM compacted with a vibratory plate in 75 mm (3 in) lifts. Great care was taken to ensure vertical homogeneity of both test beds with quality assurance testing conducted every 150 mm (6 in). LWD testing was conducted at two locations in each test bed, herein referred to as TB1-1, TB1-2, TB2-1 and TB2-2. (7) FIGURE 2 Test bed schematics for (a) homogeneous stiff sand profile (TB1); (b) medium stiff sand over soft clay profile (TB2).

7 Senseney, C.T. & Mooney, M.A Soil properties are summarized in Table 1. Average dry density, moisture content, DCP penetration rate and surface seismic modulus were obtained from in-situ quality assurance testing with the sand cone, DCP and surface seismic. The seismic modulus was determined from multichannel analysis of surface wave (MASW) testing utilizing an instrumented hammer to generate surface waves which were measured at 0.1 m (4 in) intervals along a 1 m (39 in) array. MASW based methods typically produce moduli greater than moduli determined from conventional methods due to the low strains associated with MASW testing [16]. In the laboratory, the triaxial secant modulus was determined from a consolidated, drained triaxial test using 150 mm (6 in) tall, 70 mm (2.8 in) diameter samples. TABLE 1 Summary of soil properties from TB1 and TB2 parameter Medium stiffness sand Soft clay USCS classification SW-SM CL AASHTO Classification A-1-b A-6 Liquid limit N/A 17 Plasticity index N/A 11 Average dry density 1988 kg/m 3 (124 pcf) 1890 kg/m 3 (118 pcf) Average moisture content 3.5% 17% Average DCP penetration rate 7 mm/blow 22 mm/blow Average low strain seismic modulus 263 MPa (38,000 psi) 48 MPa (7000 psi) Triaxial secant modulus 63 MPa (9100 psi) 9 MPa (1300 psi) Testing using the Prima 100 LWD with a 300 mm load plate and radial sensors was conduced on both test beds. The test protocol consisted of testing on two points with three initial 10 kg (22 lb) pre-load drops. Measurements were then taken using 10 kg drop weights for 3 drops with radial sensor spacing (r) at 300/600 mm (12/24 in), followed by 3 drops with r = 450/750 mm (18/30 in). The same protocol was then used for 15 kg (33 lb) and 20 kg (44 lb) drop weights. Testing was first conducted on the surface of TB1 to establish a baseline modulus for the medium stiff sand. Then, testing was conducted on each 75 mm (3 in) lift of medium stiff sand in TB2 in order to assess the capability of LWD to characterize a known two-layer system with increasing depth of a medium stiff soil over a soft subgrade. Results from 10 kg and 15 kg drop weight loading are presented in the following section; results from 20 kg loading are not presented. It was determined that the LWD is not robust enough to support the 20 kg drop weight because the device jumps and rocks during loading with such a heavy weight. Because of the rocking motion, data from 20 kg loading was inconsistent and deemed unreliable, especially deflection data from the center geophone. RESULTS Radial Deflections LWD testing on medium stiffness granular soil produced a measureable deflection bowl to a radial sensor spacing (r) of 750 mm. For both test beds, a decrease in surface deflection with increasing radial sensor spacing was evident with the rate of decay dependent on soil modulus and layering. Measured deflections on points 1 and 2 were nearly identical for both test beds; therefore, only results from TB1-1 and TB2-1 are presented. Measured deflections on the

8 Senseney, C.T. & Mooney, M.A homogeneous SW-SM profile of TB1-1 are presented in Figure 3a for r = 300/600 mm with 10 kg and 15 kg loading. TB1-1 deflections indicated a gradual rate of decay with an increase in radius. The change in deflection from r = 0 to r = 150 mm radial spacing is constant and equal to d 0 because the plate is assumed to be rigid. Deflections for the two-layer profile, TB2-1, are presented in Figure 4a and 4b for r = 300/450/600/750 mm with 10 kg loading. The deflections on TB2 with 15 kg loading are not presented here since the contours of the 15 kg deflection bowls were similar to the contours of the 10 kg deflection bowls. Because the LWD is limited to two radial sensors per measurement, measurements on TB2 were recorded for r = 300/600 mm, followed by measurements for r = 450/750 mm. TB2-1 deflections exhibited a steep rate of decay from r = 150 to r = 450 mm at shallow h 1 of 240 mm, 310 mm, 385 mm (9 in, 12 in, 15 in). The steep decrease is an indication of weak CL material below layer one that caused high deflections at the center geophone, followed by significant decreases in deflections with an increase in radius. As h 1 increased, measured deflections decayed at a more gradual rate and began to match the 10 kg measured deflections from TB1-1. Measured deflections indicate that TB1 was representative of a homogenous, isotropic, linear elastic half-space. This is supported by the Boussinesq equation for deflection on the surface a homogenous, isotropic, linear elastic half-space (see Equation 5). With an assumed modulus of 63 MPa, Equation 5 was used to calculate the theoretical radial deflections presented in conjunction with measured deflections in Figures 3a, 4a and 4b. The theoretical deflections between r = 150 and 300 mm are labeled invalid because the assumption of P (Equation 5) representing a uniformly distributed load is only valid one diameter and beyond from the center of the load. Equation 1 was used to generate the theoretical deflections between r = 0 and 150 mm (Figures 3a, 4a and 4b) with a modulus of 63 MPa and A = 2. Assuming the load plate is perfectly rigid, theoretical deflections beneath the 150 mm radius plate are equal. Measured radial deflections from TB1 showed good correlation with theoretical radial deflections. Figures 3b, 4c and 4d show apparent subgrade moduli E(r) calculated at radial distances based on measured deflections. If a given test bed was an ideal homogeneous, isotropic, linear elastic halfspace all the moduli would be the same. In fact, the calculated E(r) in Figure 3b closely match the assumed theoretical modulus of 63 MPa, indicating TB1 is nearly homogeneous.

9 Senseney, C.T. & Mooney, M.A FIGURE 3 (a) TB1-1 deflections at radial distances for 10 kg and 15 kg; (b) TB1-1 moduli at radial distances for 10 kg and 15 kg. Measured deflections indicate TB2 with h 1 < 400 mm (16 in) was not representative of a homogeneous, isotropic, linear elastic halfspace. Figure 4a shows that measured deflections with h 1 < 400 mm do not match theoretical deflections. A mismatch was expected because TB2 was vertically heterogeneous with E 1 = (5-7)E 2. As h 1 increased, the degree of homogeneity measured by the LWD in TB2 increased (Figure 4b). At an h 1 = 620 mm (24 in), measured deflections converge on the theoretical deflection bowl. Also, Figure 4c shows that calculated E(r) do not match the assumed theoretical modulus of 63 MPa at h 1 < 400 mm, while Figure 4d shows that calculated E(r) start to converge on the assumed theoretical modulus of 63 MPa at h 1 > 400 mm.

10 Senseney, C.T. & Mooney, M.A FIGURE 4 TB2-1 deflections at radial distances for 10 kg and (a) h 1 = 240 mm, 310 mm, 385 mm; and (b) h 1 = 460 mm, 535 mm, 620 mm; TB2-1 moduli at radial distances for the same h 1 thicknesses (c-d). Backcalculation Results Moduli were backcalculated from measured deflections and compared to laboratory triaxial moduli with the caveat that stress levels in the lab do not necessarily represent those experienced in the field owing to the varying stress state with depth. For this study, the comparison soil moduli for layer one and two (E 1 and E 2 ) were estimated to be 63 MPa and 9 MPa based on consolidated, drained triaxial testing. The triaxial E 1 and E 2 were dependent on the mean normal stress of the chamber (p) and applied deviator stress (q) as evidenced in Equation 3. When E 1 was measured during triaxial testing of the SW-SM material, mean p and q were 38 kpa (5.5 psi) and 24 kpa (3.5 psi). When E 2 was measured during triaxial testing of the CL material, mean p and q were 34 kpa (4.9 psi) and 12 kpa (1.7 psi). A separate study measured in-situ stresses generated by LWD loading on a test bed with 470 mm (18.5 in) of SP-SM sand over a CL subgrade [17]. Table 2 presents measured stresses from that study where p and q were calculated assuming an at rest earth pressure coefficient (K o ) of 0.5 and where,. Table 2 suggests that p and q from the SW-SM triaxial test correspond to stresses at a depth of approximately 200 mm (8 in) from LWD loading. According to Equation 3, the

11 Senseney, C.T. & Mooney, M.A comparison E 1 would be larger if derived from a lower stress state than the stress state observed at 200 mm. Table 2 also suggests that the p and q from the CL triaxial test correspond to stresses at a depth of approximately 250 mm (10 in). Again, the comparison E 2 would be larger if derived from a lower stress state than the stress state observed at 250 mm. TABLE 2 In-situ stresses from LWD loading where, depth (mm) (kpa) p (kpa) q (kpa) LWDmod demonstrated the ability to accurately characterize the moduli and nonlinearity of the stiff over soft layered system in TB2. Backcalculation results from TB2-1 are presented in Table 3 where measured deflections are shown for r = 0, 300 and 600 mm along with the backcalculated deflections from LWDmod. LWDmod attempts to minimize the root mean square (RMS) of the absolute difference between measured and backcalculated deflections. E 1 and E 2 are the backcalculated moduli for layer one and layer two respectively. Percent error represents the percent discrepancy from the comparison moduli. C and n (Equation 4) are the non-linear subgrade modulus constants. E LWD (Equation 1) is also provided. The most accurate moduli backcalculation results were generated in a range of h 1 = 385 mm (15 in) to h 1 = 535 mm (21 in). The soft clay of layer two caused underestimation of E 1 at shallow h 1. At deep h 1, it is proposed in the next section that the LWD with radial sensors has reached the depth of influence or measurement depth, resulting in an overestimation of E 2. The value of n increases with increasing h 1, indicating the radial sensors measure more of the non-linear CL at shallow h 1 and measure more of the linear SM-SW at deep h 1.

12 Senseney, C.T. & Mooney, M.A TABLE 3 TB2-1 Backcalculation results for 10 kg and 15 kg parameter h 1 = 245 mm 310 mm 385 mm 460 mm 535 mm 620 mm 10 kg d 0 (measured) (mm) d 300 (measured) (mm) d 600 (measured) (mm) d 0 (back) (mm) d 300 (back) (mm) d 600 (back) (mm) RMS (%) E 1 (MPa) [% error] 23 [63.5] 32 [49.2] 67 [-6.4] 61 [3.2] 60 [4.8] 56 [11.1] E 2 (MPa) [% error] 6 [33.3] 7 [22.2] 10 [-11.1] 15 [-66.7] 37 [-311.1] 77 [-755.6] C (MPa) n E LWD (MPa) kg d 0 (measured) (mm) d 300 (measured) (mm) d 600 (measured) (mm) d 0 (back) (mm) d 300 (back) (mm) d 600 (back) (mm) RMS (%) E 1 (MPa) [% error] 23 [63.5] 33 [47.6] 60 [4.8] 59 [6.35) 60 [4.76] 60 [4.76] E 2 (MPa) [% error] 5 [44.4] 7 [22.2] 9 [0.0] 12 [-33.3] 29 [-222.2] 71 [-688.9] C (MPa) n E LWD (MPa) Measurement Depth The measurement depth of the LWD with radial sensors was found to be greater than the measurement depth of conventional LWD testing. In conventional LWD testing, the depth of influence or measurement depth reflected in E LWD has been shown to range from 1.0 to 1.5 times the plate diameter (for a = 200 and 300 mm) [6, 8, 17]. An inspection of the E LWD data for TB2 (Table 3) and the corresponding d 0 data (Figure 5) suggest the E LWD and d 0 plateau at h 1 = 385 mm for 10 kg and at h 1 = 460 mm for 15 kg. These measurement depths (1.2a for 10 kg and 1.5a for 15 kg) are consistent with those found in previous studies. The measurement depth for LWD with radial sensors was found to be 535 mm or 1.8a for both 10 kg and 15 kg. Beyond the depth of 1.8a at h 1 = 620 mm, measured deflections from TB2 for r = 300 and 600 mm match measured deflections from the homogeneous SW-SM profile in TB1 for r = 300 and 600 mm. The matching deflections indicate that the radial sensors no longer measured the CL layer two and only measured the SW-SM layer one. In addition, n = 0 at h 1 = 620 mm, indicating the radial sensors are only measuring the linear SW-SM material. Interestingly, radial deflections did not plateau in this study (Figure 5). However, it is proposed that radial deflections would plateau at

13 Senseney, C.T. & Mooney, M.A h 1 > 620 mm because measured deflections at h 1 = 620 mm match theoretical deflections of a homogeneous, isotropic, linear elastic halfspace with E = 63 MPa (Figure 4b) FIGURE 5 TB2-1 deflection versus h 1 for (a) 10 kg and (b) 15 kg. The LWD with radial sensors was able to measure deeper than conventional LWD testing because the radial geophones measure vertical surface deflections caused almost entirely by deeper material. For a homogeneous, isotropic, linear elastic halfspace, the vertical deflection at z = r is approximately equal to the vertical deflection at r [15]. Figure 6 displays deflection (d z ) versus depth based on Boussinesq analysis (Equation 8) 2 1 (8) where E = 63 MPa, ν = 0.35, r is the radial offset and z is the depth. Figure 6 indicates that d z is representative of material deformation below the 45º line because there is little change in deflection from the surface to the 45º line. The 45º angle would be shallower for the layered system is this study, however, the same principles apply. For the materials in this study, the sand below the outer geophones is not affected by the LWD-induced stress, so the sand does not experience deformation. The clay below the outer geophones is affected by the LWD-induced stress that is spread through the sand. The clay deforms due to this stress and the geophones measure the deflection at the surface.

14 Senseney, C.T. & Mooney, M.A FIGURE 6 Vertical deflection versus depth for r = 0, 300 and 600 mm on a homogeneous, isotropic, linear elastic halfspace. Radial Sensor Spacing As compared to other configurations, the r = 300/600 geophone configuration produced the most accurate moduli backcalculation results and this configuration captures deflections critical to the backcalculation process on unbound materials. Results from two h 1 thicknesses (Table 4) show that the r = 300/600 exhibits the lowest percent error. More importantly, r = 300/600 characterizes the non-linearity of the CL layer two with the largest n value. Previously presented results (Table 2) indicated the CL layer is highly non-linear. An r = 300 mm is the recommended radial spacing for the inner sensor. For backcalculation on unbound materials, the inner sensor is critical because it captures the steepness of the deflection bowl. In the Odemark- Boussinesq method with a 300 mm load plate, a sensor could not be placed any closer than r = 300 mm because the point load assumption is only valid beyond a radial distance of one diameter. Due to the 1 µm resolution of the geophone, an r = 600 mm is the recommended spacing for the outer sensor. The smallest deflection measurement recorded in this study was 13 µm, measured by the r = 750 mm sensor, which is starting to approach an unacceptable signal to noise ratio of 10 percent. The smallest deflection measurement recorded by the r = 600 mm sensor was 22 µm, well within an acceptable signal to noise ratio.

15 Senseney, C.T. & Mooney, M.A TABLE 4 TB2-1 backcalculation results by radial sensor configuration for 10 kg and h 1 = 385 mm and 460 mm CONCLUSIONS radial sensor spacing (mm) parameter 300/ / / /750 h 1 = 385 mm E 1 (MPa) [% error] 67 [6.3] 65 [(3.2] 71 [12.7] 62 [-1.6] E 2 (MPa) [% error] 10 [11.1] 14 [55.6] 11 [22.2] 23 [155.6] C (MPa) n h 1 = 460 mm E 1 (MPa) [% error] 61 [-3.2] 51 [-19] 55 [-12.7] 56 [-11.1] E 2 (MPa) [% error] 15 [66.7] 22 [144.4] 17 [88.9] 18 [100] C (MPa) n LWD testing with a 300 mm diameter load plate on medium stiffness granular materials produced a measureable deflection bowl to a radial sensor spacing of 750 mm. The measured deflection bowl may be investigated to determine the degree to which a soil system is homogeneous, isotropic and linear elastic. The measured deflection bowl on TB1 indicated the one-layer, medium stiff sand profile was homogeneous, isotropic and linear elastic. The measured deflection bowl on TB2 at h 1 < 400 mm indicated the twolayer stiff over soft profile was not homogeneous, isotropic and linear elastic. 2. When limited to a stiff over soft layered system, the LWD with radial sensors demonstrated the ability to accurately backcalculate layered moduli. Backcalculated moduli closely matched laboratory determined moduli from triaxial testing at a similar stress state as in the field. The companion LWDmod program found the clay subgrade in the two-layer profile to be highly non-linear. 3. The measurement depth for the LWD with radial sensors was found to be 1.8 times plate diameter versus the measurement depth of conventional LWD testing of 1.0 to 1.5 times plate diameter. The LWD with radial sensors was able to measure deeper than conventional LWD testing because the radial geophones measure vertical surface deflections caused almost entirely by deeper material. 4. As compared to other configurations, the r = 300/600 mm geophone configuration is recommended for unbound materials because it produced the most accurate moduli backcalculation results and captures deflections critical to the backcalculation process. Acknowledgements The authors thank the Air Force Research Lab for funding this study. John Siekmeier (MnDOT) and Roger Surdahl (FHWA) are acknowledged for providing testing equipment critical to this study. The authors also thank Gabriel Bazi, Norman Facas and Caleb Rudkin for helping to analyze and process LWD data.

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