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â Relationship Between Roller-Based stiffness and in situ Response c h a p t e r 4 This chapter explores the relationship between roller- measured stiffness and in situ stress-strain-modulus be- havior. Numerous vertically homogeneous embankments and layered subgrade/subbase/base TBs were instrumented with stress and strain sensors at multiple levels to capture in situ behavior during static and vibratory roller passes. Three smooth drum vibratory rollers were operated over the TBs: Ammann AC110, Bomag BW213, and Sakai SV510 with in- dependent instrumentation (see Table 4.1). The three dis- tinct force delivery approaches employed by the three rollers were summarized in Chapter 2. This chapter describes how current stiffness-based vibratory roller measurement values (MVs; i.e., E vib , k s ) are related to in situ soil response in verti- cally homogeneous and layered structures. From a mechan- ics perspective, this chapter explains the vibration amplitude dependence of roller MVs and measurement depth of the instrumented roller. This chapter also discusses the sensitiv- ity of roller-measured stiffness to thin lifts (e.g., base over subbase/subgrade). A detailed, more technical presentation of this investigation and the results is provided in Rinehart & Mooney (2009a, 2009b), Rinehart et al. (2008, 2009), and Mooney & Rinehart (2009). 4.1 Roller-Induced Stress Paths and Levels In current pavement design procedures, laboratory- determined resilient modulus (M r ) serves as one key per- formance indicator for unbound materials. In addition, mechanistic-empirical (M-E) pavement design promotes the use of layered analysis and nonlinear modulus functions. To enable performance-based QA, the relationship between roller-measured soil stiffness and soil modulus must be bet- ter understood, including the relationship between the stress state/stress path induced by vibratory roller loading and the stress state/stress path used in laboratory M r testing (AAS- HTO T307). A considerable amount of testing has been performed to characterize the stress-dependent nature of M r . The consen- sus model describing M r of granular soils that reflects the confining and deviator stress dependence of soil (Uzan 1985, Witczak & Uzan 1988) is given by: M k p p q p k k r a a a = ï£« ï£ï£¬ ï£¶ ï£¸ï£· ï£« ï£ï£¬ ï£¶ ï£¸ï£·1 Î¸ 2 3 (4.1) table 4.1. Summary of roller parameters. Roller Characteristic Ammann AC110 Bomag BW213 Sakai SV510 Drum width, m (ft) 2.20 (7.22) 2.13 (7.00) 2.13 (7.00) Drum radius, m (ft) 0.75 (2.46) 0.75 (2.46) 0.75 (2.46) Static mass, kg (lb) 11,500 (25,350) 14,900 (32,850) 12,500 (27,600) Static linear load, kN/m (kip/ft) 31.5 (2.2) 42.4 (2.9) 32.2 (2.2) Operating frequency (Hz) 20â34 28 37, 28c Vertical eccentric force F ev , kN (kip) 0â277 (0â62)a 0â365 (0â82)b 186, 245 (42, 55)c a One hundred preprogrammed amplitude settings. b Six preprogrammed amplitude settings. c Low- and high-amplitude settings.
Î¸ Ï Ï Ï= = + +( )3p z x y (4.2) q z x x y y z zx xy = ( ) +( ) +( ) + + + 1 2 6 6 2 2 2 2 2 Ï Ï Ï Ï Ï Ï Ï Ï â â â 6 2Ï yz (4.3) where p is the mean normal stress, q is the deviator stress, the bulk stress Î¸ = 3p, p a is atmospheric pressure, and k i are best-fit parameters determined by evaluation of laboratory data. Santha (1994) determined model parameters k i for a wide range of granular and cohesive soils. Average Â± standard deviation values of k 1 , k 2 , and k 3 were found to be 420 Â± 173, 0.34 Â± 0.09, and -0.37 Â± 0.10, respectively, for granular ma- terials. For cohesive soil, average Â± standard deviation values were reported to be 645 Â± 252, 0, and -0.26 Â± 0.13 for k 1 , k 2 , and k 3 , respectively. The deviator stress q is equivalent to the von Mises stress commonly used in solid mechanics and can be related to the octahedral shear stress Ï oct via q = 3 2Ï oct / . For assessment of laboratory M r data, Equation 4.3 reduces to the commonly observed form q = (Ï z â Ï x ). Commercially available earth pressure cells (EPCs) and lin- ear voltage displacement transducers (LVDTs; see Figure 4.1) were used to measure total normal stresses Ï x , Ï y , and Ï z and normal strains Îµ x , Îµ y , and Îµ z induced by static and vibratory roller compactors. The sign convention used throughout in- cludes z positive downward from the soil surface, x positive in the direction of roller travel, and y positive to the roller operatorâs right. Total stresses were measured and assumed equal to effective stress. This is similar to the methodology employed in lab testing of M r , where total stresses are also measured and used to determine M r . While suction-induced pore pressures likely exist, their influence is considered mini- mal compared to the high roller-induced normal stresses. A complete discussion of in situ measurement of stress and strain, including sensor dimensions, sensor calibration, field installation techniques, and measurement uncertainty is pro- vided in Rinehart & Mooney (2009a). To complement the measured in situ stresses from dis- crete depths during vibratory roller passes, the complete state of stress was investigated with a boundary element method (BEM) approach (see Rinehart et al. 2008, 2009). The boundary element formulation used is appropriate for two- dimensional plane-strain conditions and can accommodate general anisotropy (Ting 1996). Experimental results show that plane strain conditions exist beneath the center of the 2.1-m (6.9-ft)-long drum but not at the edges (Rinehart et al. 2008). The two-dimensional approach offered by the bound- ary element tool used here is a good first step in character- izing the stresses induced by the vibrating drum. Results from low-vibration amplitude roller passes over two different soils are discussed: clayey sand subgrade [A-6(1)] and granular subbase (A-1-b). To compare stress paths in the field and laboratory (i.e., during M r testing per AASHTO T-307), profiles of mean normal stress p and deviator stress q were cal- culated according to Equations 4.2 and 4.3. Figure 4.2 presents p-q stress paths from four depths during low-excitation force (F ev , see Section 2.1.1) vibratory roller loading on a clayey sand subgrade and granular subbase. The paths shown represent the least squares best fit to the in-ground sensor measurements determined by BEM analysis (see Rinehart et al. 2009 for more detail). The paths are not strictly linear, but it is a reasonable assumption. For the medium stiff subgrade of TB MN29, the maximum value of roller-induced q is much greater than that used in M r testing. Figure 4.2 also shows that for base materials the slope of the p-q loading line m in M r testing is very similar to that induced by the roller, 3.0 and 3.1, respectively. For sub- grade materials, m varies between 1.8 and 2.2, lower than the value of 3.0 used in M r testing. In general, inspection of the p and q profiles with depth (see Rinehart et al. 2009) reveals that for z < 0.5 m (1.6 ft), levels of q observed in the subgrade material are greater than the highest value of q used in AASHTO T307 lab M r testing by a factor of 1 to 3. For z > 0.5 m (1.6 ft), values of q observed in the field are similar to those used in lab testing. Levels of p in the subgrade material are greater than the highest lab value by a factor of 1 to 5 for z < 0.25 m (0.8 ft). Levels of p in the field are similar to lab levels at depths between z = 0.25 (0.8 ft) and 0.5 m (1.6 ft); for z > 0.5 m (1.6 ft), lab levels of p are greater than those used in the field. For the subbase material [i.e., z = 0.25 m (0.8 ft) in Figure 4.2b], the levels of roller-induced q are greater than the highest value of q used in the lab by a factor of 1 to 2.5. Levels of p in the lab are greater than those observed in the field by a factor of 1 to 5. Figure 4.1. LVDT strain sensor (top) and EPC (bottom).
â 4.2 Measurement Depth in Vertically Homogeneous Embankments Roller MVs from typical highway construction earthwork rollers (11 to 15 tons) measure to depths significantly greater than a typical 15- to 30-cm (6- to 12-in)-thick lift and to depths greater than the 20- to 50-cm (8- to 20-in) depths of traditional spot tests [e.g., nuclear gauge, static PLT, and LWD; Mooney & Miller 2008]. Pavement earthwork involves various combinations and thicknesses of embankment sub- grade, subbase, and base course materials; therefore, roller- measured stiffness of homogeneous and layered structures will be significantly influenced by measurement depth. This section presents an investigation of roller measurement depth and how it is influenced by F ev . 4.2.1 measurement depth from layer Buildup experiments One approach to experimentally assess measurement depth is to monitor roller-measured stiffness as successive layers of a stiff material are placed and compacted above a softer sub- surface. Roller-measured stiffness provides a composite mea- sure of the soil from the surface to the measurement depth and therefore should increase with increasing thickness of the overlying stiff material. Beyond a critical stiff soil thick- ness H c , the roller-measured stiffness should remain constant, indicating it is no longer sensing the underlying soft mate- rial. Figures 4.3a and b show how this layer buildup approach was used to investigate measurement depth. The study is de- scribed in detail in Rinehart & Mooney (2009b). These data suggest that the measurement depth (i.e., H c ) reflected by the roller-measured stiffness is approximately 1.0 to 1.2 m (3.3 to 3.9 ft) for this 11,500-kg (25,350-lb) Ammann roller when operated on this crushed stone (A-1-a) material. Within the 0.1- to 0.2-m (0.3- to 0.6-ft) uncertainty associ- ated with this approach (i.e., one-half layer thickness), H c does not depend strongly on F ev . This finding contradicts previous literature that indicates measurement depth varies consider- ably with vibration amplitude (Anderegg & Kaufmann 2004, Kopf & Erdmann 2005); for example, H c should have varied by 1.0 m (3.3 ft) over the range of F ev tested here per the re- lationship suggested by Anderegg and Kaufmann. In Section 4.2.2 below, it is shown that H c does vary slightly with F ev . It is also worth noting that the roller-measured stiffness does not begin to increase until the third lift of crushed stone [H > 0.5 m (1.6 ft)], suggesting that roller-based stiffness measures are insensitive to âthinâ layers of stiff soil over softer mate- rial, which are common in pavement earthwork construction (e.g., base over subgrade). This critical point is discussed in more detail in Section 4.4. Figures 4.4a and b show how the layer buildup approach was employed during a second experimental investigation of measurement depth. Seven layers of the crushed rock base material [totaling 1.72 m (5.64 ft) thick] were placed and compacted within a trench cut into a sandy silt embank- ment (TB MD4). Several 15-ton Bomag roller-measured E vib records measured during the buildup of base course layers over subgrade are presented in Figure 4.4c. The embankment subgrade in TB MD4 had two distinct stiffness zones, as evi- denced by the H = 0 m MV record. Figure 4.4d shows that the roller-measured stiffness values increase substantially with H and plateau at approximately H = 1.2 to 1.4 m (3.9 to 4.6 ft) Figure 4.2. Stress paths due to vibratory roller load- ing and laboratory Mr testing per AASHTO T307: (a) subgrade soil, A-6(1) [f = 30 Hz, Fev = 87 kN (19.6 kip), v = 0.5 m/s (1.6 ft/s)] and (b) subbase material, A-1- b [f = 28 Hz, Fev = 88 kN (19.8 kip), v = 1.0 m/s (3.3 ft/s)]; selected AASHTO T307 subgrade (S) and base (B) loading sequences shown for reference (adapted from Rinehart et al. 2009).
Figure 4.3. (a) photo and (b) schematic of stiff-layer buildup portion of TB MN29, (c) roller-measured stiffness records at three values of stone thickness H, and (d) variation of roller-measured stiffness with H for three levels of Fev (adapted from Rinehart & Mooney 2009b). for the stiffer section and at approximately H = 1.1 to 1.3 m (3.6 to 4.3 ft) for the softer section. These data suggest that the measurement depth (i.e., H c ) reflected by the roller-measured stiffness is approximately 1.1 to 1.4 m (3.6 to 4.6 ft) for this 14,900-kg (32,850-lb) Bomag roller when operating on this crushed rock (A-1-b) mate- rial. Similar to results from MN29, within the 0.1- to 0.2-m (0.3- to 0.6-ft) uncertainty of this technique, H c does not vary strongly over these low, medium, and high F ev values. The base-to-subgrade stiffness ratio does not appreciably affect H c . An inspection of Figure 4.4d data shows that H c was the same for both the soft and stiff subgrade sections [within the 0.1- to 0.2-m (0.3- to 0.6-ft) uncertainty]. For H > H c, the roller-measured stiffness is not influenced by the underlying subgrade material. For base course thickness more typical of practice (i.e., H < H c ), Figures 4.4d and e illustrate that roller-measured stiff- ness is clearly a composite measure of the underlying sub- grade and overlying base material. The relative contribution of each material to roller MV is a function of layer thickness, base/subgrade modulus ratio, F ev , and other roller/soil inter- action factors (contact area, dynamics). A comparison of Fig- ures 4.4d and e illustrates that the base-to-subgrade stiffness ratio influences the roller-measured stiffness for H < H c . This is described further in Section 4.4. 4.2.2 measurement depth from profiles of vertical Stress and Strain Profiles of vertical stress and strain measured during roller passes on TB MN29 clayey sand and during the buildup of MD4 crushed rock over silt were examined to determine a mechanistic rationale for H c . Magnitudes of Ï z,peak and Îµ z,peak at the experimentally determined H c [1.2 m (3.9 ft)] were identified from the TB MD4 theoretical profiles. Total and cyclic Ï z,peak and Îµ z,peak at z = 1.2 m (3.9 ft) were found to be 8% to 12% of their maximum values (termed Ï z,max and Îµ z,max ) at or near z = 0 (see Table 4.2). The observed ratios of Ï z,peak and Îµ z,peak to their maximum values increased slightly with F ev . Specifically, cyclic Îµ z,peak values increased from 9% of maxi- mum at low F ev to 11% of maximum at high F ev . These results suggest that H c does increase slightly with F ev . Further, these
â Figure 4.4. (a) photo and (b) schematic of stiff-layer buildup portion of TB MD4, (c) roller-measured stiffness re- cords at three values of H, and (dâe) variation of roller-measured stiffness with H for three levels of Fev (adapted from Rinehart & Mooney 2009b). results show that measurement depth is a function of stress and strain decay and that H c is reached when stress or strain has decayed to about 10% of its peak value (i.e., at or near the surface). The relationship between H c and cyclic Îµ z reduction to approximately 10% of maximum is consistent with classi- cal settlement analysis used in foundation engineering. Given that roller MVs are based on cyclic deformation, the following analysis focuses on the decay of cyclic strain. The 10% cyclic Îµ z,peak criterion for estimating H c was applied to the profiles of cyclic Îµ z,peak from the TB MN29 clayey sand. Figure 4.5a presents the variation of estimated H c as a function of actual vertical drum displacement z d from several IC roller passes. These values of z d reflect the range of low to high F ev . Figure 4.5a shows that measurement depth increases from 0.8 m (2.6 ft) at low F ev and z d to 1.2 m (3.9 ft) at high F ev and z d . Here, a 0.1 mm (0.004 in) increase in z d corresponds to a 3-cm (1.2-in) increase in measurement depth. This is considerably less than the 0.1 mm (0.004 in) = 10 cm (3.9 in)
rule of thumb reported in the literature (e.g., Anderegg and Kaufmann 2004). Using the 10% cyclic Îµ z,peak criteria, measurement depth was estimated from data collected during IC roller passes on the MN29 clayey sand and on the MD4 crushed rock over silt (see Figure 4.5b). Two different IC rollers were used. Measurement depth is plotted versus F ev because actual drum deflection values (z d ) were not reported by both rollers. There is very good agreement across the two materials and rollers using the cyclic strain criteria. Additionally, the range of H c observed experimentally in the layer build-up experiments agree rea- sonably well and within the 0.1-0.2 m (0.3-0.6 ft) uncertainty of that technique. Regarding the measurement volume of roller MVs (i.e., 3D), Rinehart and Mooney (2009b) shows that peak stress and strain propagate roughly twice as far in the vertical direction than in the horizontal direction. The results presented here along with those in the literature show that a given roller-measured stiffness value is representative of soil approximately 0.25-0.3 m (0.8-1.0 ft) in front of and behind the center of the drum and to a depth of 0.8-1.2 m (3.0-3.9 ft). This area of influence is important to consider when performing correlations of roller-measured stiffness to spot-test measurements that reflect a much smaller volume. 4.3 Relating Roller-Based Stiffness to In Situ Response An important objective of this study was to understand the nature of roller-measured stiffness through its relationship to in situ soil modulus. This relationship holds the key to the development of performance-based specifications and the prediction of pavement performance using roller-measured soil properties. A more detailed presentation of these results is available in Mooney and Rinehart (2009). As illustrated in Figure 4.6g-i, roller-based stiffness is de- rived from cyclic drum deformation z d and is indirectly influ- table 4.2. Ïz and Îµz decay at the experimentally determined measurement depth. F ev (kN) Ï z z=1.2m Ï z ,max ï£« ï£ï£¬ ï£¶ ï£¸ï£· (%) Ï z z=1.2m Ï z ,max ï£« ï£ï£¬ ï£¶ ï£¸ï£· Cyclic (%) Îµ z z=1.2m Îµ z ,max ï£« ï£ï£¬ ï£¶ ï£¸ï£· (%) Îµ z z=1.2m Îµ z ,max ï£« ï£ï£¬ ï£¶ ï£¸ï£· Cyclic (%) 88 8.3 6.5 11.7 9.2 175 9.7 7.8 12.0 10.4 248 10.5 8.7 9.4 11.0 Mean 9.5 7.7 11.0 10.2 Figure 4.5. Variation of measurement depth with (a) actual vertical drum displacement zd from TB MN29 and (b) Fev from both TB MN29 and TB MD4 (adapted from Rinehart & Mooney, 2009b).
â enced by the soil response in the x and y directions. Similarly, a vertical dynamic deformation modulus M can be extracted from the cyclic in situ Ï z -Îµ z response to vibratory loading. As illustrated in Figure 4.6a-d, the cyclic soil response is cal- culated by subtracting the portion due to the static roller weight. Figures 4.6e and f show individual cyclic Ï z -Îµ z paths and illustrate the measures of M evaluated in this study as determined from the Ï z -Îµ z response during vibratory roller passes over clayey sand subgrade and granular base material, respectively. M L is the tangent modulus of the loading por- tion of the Ï z -Îµ z response, and M S is the secant modulus from zero Ï z -Îµ z through the point of maximum Îµ z . The extracted M values are not constitutive (e.g., Youngâs modulus); rather, M is akin to a partially constrained dynamic modulus that is influenced by the Ï y -Îµ y and Ï x -Îµ x fields. In Figures 4.6h-i, k 1 is equivalent to the stiffness term used by Bomag to determine E vib (see Section 2.2.2) and is comparable to M L . The stiffness term k 2 in Figures 4.6h-i is equivalent to Ammann k s (see Sec- tion 2.2.1) and is comparable to M S (Mooney and Rinehart 2009). 4.3.1 embankment Situations Roller-measured stiffness was related to in situ moduli M from multiple depths within a 1-m (3.3-ft)-deep vertically homogeneous subgrade soil (TB MN29). Instrumentation was installed at four depths during construction of a clayey sand embankment test bed (see Figure 4.7a). Four lifts of the clayey sand subgrade soil (A-6(1)) were placed and com- pacted with the IC roller with instrumentation in place, re- sulting in a 1.0-m (3.3-ft)-thick layer of subgrade soil above the underlying crushed stone. This 1.0 m (3.3 ft) of subgrade soil extends beyond the measurement depth of the IC roller at low-medium amplitude levels (see Section 4.2). Therefore, roller MVs reflect the clayey sand only, and this test bed rep- resents a vertically homogeneous embankment situation. Roller MVs and in situ stress-strain data were collected simultaneously during Ammann IC roller passes using vari- ous excitation frequency and amplitude combinations. Fig- ures 4.7b and c present M L and M S values determined at three depths during vibratory passes. The M versus vertical excita- tion force amplitude F ev (see Equation 2.1) data were char- acterized statistically with power relationships (M L = b(F ev )c) at each depth. Figure 4.7d shows that roller-measured k s de- creases as F ev increases. Figures 4.7e and f illustrate the re- lationship of in-situ M L and M S (from three depths) to the roller-measured k s . The data were collected over the range of F ev shown using three excitation frequencies and four eccen- tric mass moments. As shown in Figures 4.7b and c, M L and M S generally in- creased with depth and decreased with increasing F ev . The sensitivity of M S values to depth and to F ev was similar to that shown by M L . M varied by a factor of two for these low to high amplitude F ev values typically employed in the field. M values also varied by a factor of two over the depths mea- sured (0.14-0.65m [0.46-2.1 ft]). The variability of M with depth coupled with the varying stiffness along the length of the drum illustrate that roller-measured stiffnessâeven at low F ev âprovides a composite reflection of a field of spa- tially varying modulus, i.e., there is not just one value of soil modulus reflected in a roller MV. For performance-related specifications, this nonlinear variation in modulus should be taken into consideration together with the differences be- tween roller-induced and traffic-induced stress conditions and their effect on modulus. The observed M L and M S behavior as a function of F ev are a field manifestation of the stress dependence of soil modulus that has been well established in the laboratory (e.g., Ishihara 1996, Andrei et al. 2004). Generally, modulus increases with increasing confining stress and decreases with increasing shear (deviatoric) stress. For fine-grained cohesionless and cohesive soils, the decrease in modulus with increasing shear stress typically outweighs the increase in modulus due to in- creasing effective confining stress (Andrei et al. 2004). Roller vibration induces both confining and shear stresses. Dur- ing vibratory loading here, the substantial levels of Ï z and Ï y coupled with very low values of Ï x at x = 0 (see Rinehart and Mooney 2009a) lead to the significant levels of devia- toric stress that results in the decrease in M with increasing F ev . The decrease in roller-measured stiffness with increasing F ev has been documented previously for embankment granu- lar material and attributed to stress-induced softening (e.g., Mooney & Rinehart 2007); these results now confirm this hypothesis. Figures 4.7e and f show that roller-measured stiffness is positively correlated with M L and M S implying that changes in roller-measured stiffness are representative of the response of the soil. The strength of the M versus roller-measured stiff- ness relationship (evidenced by R2) and the sensitivity of M to roller-measured stiffness (evidenced by slope of the best fit line) were found to be greater at z = 0.36 (1.2 ft) and 0.65 m (2.1 ft) than at z = 0.14 m (0.46 ft), implying that the roller MV is less reflective of soil very near the surface. The results illustrate one mechanism by which roller- measured stiffness varies with F ev during operation on vertically homogeneous embankment soil, a situation commonly encountered in earthwork. Generalizing to all vertically homogeneous embankments, the relationship between roller-measured stiffness and F ev (or amplitude A) will be dictated by the stress-dependent modulus relation- ship of the involved soil. Because the modulus relationship varies across soils, the relationship between roller-measured
0 Figure 4.6. Total roller-induced (a) Ïz , (b) ez , cyclic roller-induced (c) Ïz , (d) Îµz , individual Ïz-Îµz paths showing extraction of the vertical deformation moduli ML and MS for (e) subgrade soil, (f) base material, (g) free body diagram of roller drum, and Fs-zd paths showing extraction of roller-measured stiffness for (h) contact operation and (i) partial loss of contact operation (adapted from Mooney & Rinehart, 2009 and Rinehart & Mooney, 2009b).
â Figure 4.7. (a) MN29 embankment test bed schematic, (b-c) variation of in situ vertical deformation modulus with Fev , (d) variation of roller-measured stiffness with Fev and (e-f) correlation between roller-measured stiff- ness and in situ vertical deformation modulus (adapted from Mooney & Rinehart, 2009). stiffness and F ev will not be unique and may change as the soil is compacted. The considerable variation of stress with depth combined with the stress dependent soil modulus indicates that the modulus field may vary significantly with depth. To inves- tigate this, Equation 4.1 was used to calculate soil modulus based on the stress profiles calculated with the BEM model and typical k i values for cohesive and granular soils (e.g., from Santha, 1994). Average k i values are taken to be 420, 0.25 and -0.30 for k 1 , k 2 , and k 3 , respectively. Applying Equa- tion 4.1 with average k i values to data from TB MN29 shows a relatively constant modulus profile, with only 10% varia- tion from z = 0.25 to z = 1.0 m (0.8-3.3 ft) (see Figure 4.8a). However, results presented earlier from analysis of M L and M S from in-ground instrumentation revealed that the modulus in TB MN29 was a factor of two greater at z = 0.65 m (2.13 ft) than at z = 0.14 m (0.46 ft). Using k i values more typical of a cohesive soil (e.g., 420, 0 and -0.6 for k 1 , k 2 , and k 3 , respec- tively) results in a modulus profile more representative of the observed behavior (see Figure 4.8d) with modulus ranging from 37 MPa at z = 0.25 m to 71 MPa at z = 1.0 m (0.8-3.3 ft). Figure 4.8 illustrates that the modulus profile with depth can vary considerably and is strongly dependent on modulus function parameters (Rinehart et al. 2009). 4.3.2 layered earthwork Another common earthwork situation is the layered sys- tem involving a base course overlying a subbase or subgrade, or a subbase course overlying a subgrade. In these situations, roller MVs provide a composite measure of the involved lay- ers. In layered systems, the dependence of roller MV on F ev does not always parallel in situ modulus behavior as was the case in the homogeneous embankment discussed earlier. The structure of the layered system plays a significant role in the nature of the roller MV. As illustrated in Figure 4.9a, TB MD4 was constructed by compacting several lifts of crushed rock subbase material (A-1-b) over a sandy silt subgrade A-4(0). In-ground instrumentation was installed in the subgrade and the first lift of subbase material to measure Ï z and Îµ z . Roller MV data (E vib ) were collected during operation on the sub- grade and on the first three lifts of subbase material. Figures 4.9(b-d) illustrate the relationships observed be- tween in situ M and F ev and between roller-measured stiffness and F ev observed during testing on MD4. Within the data from each lift, roller-measured stiffness values increased with F ev (Figure 4.9d), however, M L and M S in the crushed rock both decrease with increasing F ev (Figures 4.9b and c). Focusing on M L behavior because it more closely parallels the definition
Figure 4.9. (a) TB MD4 layered test bed schematic, (b-c) variation of M with Fev , (d) variation of roller-measured stiffness with Fev , and (e-f) correlation between roller-measured stiffness and M (adapted from Mooney & Rine- hart 2009). Figure 4.8. Modulus variation with depth in clayey sand subgrade (TB MN29) (adapted from Rinehart et al. 2009). of the roller-based stiffness measurement E vib , the decrease in M L with increasing F ev at z = 0.39 and 0.63 m (1.3, 2.1 ft) is consistent with shear stress-dependent modulus behavior. Similar to clayey sand behavior (TB MN29 presented earlier), the M L versus F ev sensitivity increased with depth, and was reasonably insensitive at z = 0.23 m (0.75 ft). The layered structure is the primary cause for the increase in roller-measured stiffness with increasing F ev despite the decrease in base course M L . As described in significant detail elsewhere (Mooney & Rinehart 2009), the stiffer base ma- terial takes on a greater portion of the load with increasing F ev . Vibratory roller interaction with layered earthwork is in-
â fluenced by a number of factors including stress-dependent modulus of each material, drum/soil contact width, the stiff- ness ratios of the involved layers, and roller/soil dynamics. The topic is not fully understood and is an area of ongoing research. Modulus profiles determined from the p and q distribu- tions in TB MD4 are presented in Figure 4.10. The value of k 1 for the subbase material (z = 0-0.3 m [0-1 ft]) was increased beyond the range presented by Santha (1994) to account for the high stiffness of this material. Analysis of TB MD4 data shows that the modulus profile with average k i values is nearly constant with depth within the base layer. However, the k i parameters have a significant influence on the variation of modulus with depth. Depending on k i parameters selected, the modulus can vary more than 100% within only a 0.3-m (1.0-ft)-thick base layer (Rinehart et al. 2009). In layered base over subbase or subgrade structures, roller MVs are a composite measure of the two materials. The modulus in the underlying subgrade material is considerably lower than the base course modulus (Figure 4.10), and mod- ulus in base and subgrade materials can both vary signifi- cantly with depth given the roller-induced stress states shown here. Therefore, knowledge of the roller-induced stresses and material specific k i parameters combined with the appropri- ate numerical analysis tools to predict performance is impor- tant if roller MVs are to be used in pavement performance prediction. 4.4 Sensitivity of Roller-Based Stiffness to Thin Lifts Using typical highway construction rollers (11-15 ton) with low to high amplitude vibration, the measurement depth for vertically homogeneous embankment conditions was found to be 0.8-1.2 m (2.6-3.9 ft). The total thickness of most base- subbase-subgrade structures is on this order, and therefore, roller MVs will reflect a composite action of these layers. As described in Sections 4.2 and 4.3, roller MVs on layered struc- Figure 4.10. Modulus variation with depth in TB MD4 (adapted from Rinehart et al. 2009).
tures are a function of layer thickness, the relative stiffness of the layers, vibration amplitude or F ev , and other drum/soil interaction factors. This section addresses the instrumented rollerâs ability to sense stiff layers atop a softer subsurface, i.e., to what degree are roller MVs representative of a relatively thin layer or lift of base or subbase material atop subgrade? To address this question, several layered test beds were con- structed. The stiff layer buildup experiments described earlier represent layered test beds, particularly when the first few lay- ers of stiff material are being compacted (before the test beds approach the embankment condition). In addition, TB FL1-6 and TB NC6-10 involved placement and compaction of thin lifts of aggregate base course material atop subgrade. Figure 4.4 presented roller MV data records versus H for the crushed rock subbase (A-1-b) over soft and stiff sections of sandy silt subgrade (A-4(0)) (TBMD4). For H < H c , the roller MV is a composite measure of both the underlying sub- grade and overlying stiff subbase layer. The contribution of the subbase increases with H. The roller-measured stiffness is more sensitive to the crushed rock base atop the stiffer sub- grade than atop the softer subgrade. For the stiff subgrade (base/subgrade stiffness ratio â 4), E vib increased by 110% to 170% from the subgrade to the first layer of subbase. By contrast, E vib increases 65% to 90% from the subgrade to the first layer of subbase on the soft subgrade portion of the test bed (base/subgrade stiffness ratio â 10). This trend contin- ues with the second lift of subbase material. Similar results are found by examining Figure 4.3d where the stiffness ratio of crushed stone (A-1-a) to clayey sand (A-6(1)) subgrade is also 10. This indicates that the roller MV is more sensitive to thin lifts when the subgrade is stiff. Figure 4.4 also showed that an increase in amplitude (F ev ) results in increased sensitivity to the stiff, overlying layer. This is in part attributable to an increased portion of stress being taken by the stiff material (Mooney & Rinehart 2009). How- ever, as described earlier, roller-measured stiffness is ampli- tude dependent, and it is unclear how the interplay of these two factors affects the results presented in Figure 4.4. TBs FL1-6 were created to further explore the influence of layer stiffness ratio on roller-measured stiffness. As shown in Figure 4.11a, four 15-cm (6-in)-thick lifts of aggregate base material (A-1-b) were placed and compacted atop 30-cm (12-in)-thick granular subgrade (A-3) and ash-stabilized granular subgrade material (A-3). The ash-stabilized sub- grade was prepared by in-place mixing 8 cm (3 in) of bed ash with 22 cm (9 in) of the native granular subgrade material. Figures 4.11b and c present roller-measured stiffness data and LWD modulus results collected during compaction of the stabilized subgrade and base material layers. Roller-measured stiffness k s-CSM (computed from independent instrumentation installed by the research team on the Sakai CCC roller) was reported every 4 cm (1.6 in), and the data presented are the average of the MV over 1.0 m (3.3 ft) distance (the trends presented are representative of the test strip as a whole). The Prima LWD with a 300-mm (12-in), diameter plate was used (E LWD-P3 ). The average of five locations across the width of the drum is reported. Figure 4.11a shows the roller-measured stiffness on the 30-cm (12-in)-thick stabilized subgrade increases from less than 40 MPa after pass 2 to more than 60 MPa after pass 11. LWD test results show a similar trend during compaction of the stabilized subgrade with E LWD-P3 increasing from less than 50 MPa after the second pass to more than 70 MPa after the 12th (and final) pass. However, roller-measured stiffness data collected during compaction of the first lift of aggregate base material (Base L1 in Figure 4.11a), remain at approximately Figure 4.11. Roller MV and LWD test results during compaction of TB FL1-6.
â 80 MPa throughout compaction, while E LWD-P3 increases from about 75 MPa after the second pass to 90 MPa after the sixth (and final) pass for the first lift of base material. Testing with the nuclear gauge revealed that unit weight increased from 16.83 kN/m3 (107.1 pcf) after pass 2 to 17.44 kN/m3 (111.0 pcf) after pass 6. The spot-test results indicate that compaction took place and the base material stiffened with consecutive roller passes. Therefore, the roller-measured stiff- ness was insensitive to the compaction-induced stiffness in- crease in this 15-cm (6-in) lift. Similar results were observed for the second 15-cm (6-in)-thick base lift. Note that the base: stabilized subgrade modulus ratio (based on roller-measured stiffness and LWD testing) was about 2:1. Figure 4.11b also shows that the roller-measured stiffness increased from 60 MPa to 110 MPa during compaction of the third 15-cm (6-in)-thick lift of base material (base L3). Here, the roller-measured stiffness was sensitive to compaction of a 15-cm (6-in)-thick layer atop existing (stiff) base material. These results show that the stiffness contrast between layers is critical. The sensitivity of roller MVs to compaction of thin lifts of subbase or base material improves as the stiffness con- trast between the two layers decreases. This is consistent with previous findings (e.g., Mooney et al. 2005). The influence of base course thickness on roller-measured stiffness was further examined on TB NC6-10. TB NC6-10 involved compacting 15- and 30-cm (6-, 12-in) lifts of ag- gregate base material atop a silty sand subgrade (see Figure 4.12a). After compaction of the first 15-cm (6-in)-thick lift it was scarified (loosened) before an additional 15 cm (6 in) was placed. This 30 cm (12 in) of loose material formed the second lift of base material. This sequence was repeated for the third and fourth lifts. Figure 4.12b shows roller-measured stiffness data collected during compaction of the four distinct lifts of base material. The roller MV (E vib ) was found to be fairly insensitive to compaction of the 15-cm (6-in)-thick lift directly atop the subgrade (Base L1). The roller MV sensitiv- ity increases for the 30-cm (12- in)-thick lift placed directly atop the subgrade (Base L2). Roller MV sensitivity decreases for the 15 cm Base L3 and then increases significantly for the 30 cm Base L4. Results from LWD testing (not shown here) confirm that compaction took place for all lifts. Note that the base:stabilized subgrade modulus ratio (based on roller- measured stiffness and LWD testing) was about 4:1. These re- sults corroborate those presented in Figure 4.11 and illustrate that the sensitivity of roller-based stiffness to compaction of base course material over subgrade improves with increased lift thickness and as the modulus ratio decreases. For the two base over subgrade situations examined here, roller MVs were not sensitive to compaction of 15 cm (6 in) of base material placed directly atop subgrade material. Generalizing these findings to all layered situations is chal- lenging due to the interplay of several factors including lift/ layer thickness, stiffness contrast between the layers, stress de- pendency of the materials involved and the amplitude of vi- bration. The results presented above indicate that CCC-based QA of thin base layers directly atop softer subgrade might be unreliable as roller-measured stiffness can be insensitive to these layers. With more knowledge of the roller-induced stress-strain field in layered situations and the ability to per- form dynamic analysis of the roller-induced stress-strain field, it should be possible to more accurately predict each layerâs contribution to the composite stiffness. Figure 4.12. Roller-measured stiffness data collected during compaction of TB NC7-10.
4.5 Conclusions The following conclusions can be drawn from the results presented in this chapter. â¢ Vibratory and static rolling induces a complex three- dimensional stress-strain-modulus state in the soil. For vertically homogeneous embankment conditions and the 11-15 ton smooth drum vibratory rollers used in this study (and commonly used in practice), the volume of soil re- flected in a roller MV is cylindrically shaped extending to 0.8-1.2 m (2.6-3.9 ft) deep and 0.2-0.3 m (0.7-1.0 ft) in front of and behind the drum. Therefore, for typical base, subbase, and subgrade structures, roller MVs are a com- posite reflection of these layers. The contribution of each layer to the roller MV is influenced by layer thickness, rela- tive stiffness of the layers, vibration amplitude, the stress- dependent modulus function for each soil, and drum/soil interaction issues (contact area, dynamics). Sublift mate- rial properties contribute significantly to roller MVs. â¢ For embankment situations, the measurement depth of roller MVs is controlled by relative decay of roller- induced cyclic stress and strain and is reached when values have decayed to about 10% of their peak. The measurement depth was mildly influenced by vibration amplitude, i.e., a 0.1 mm (0.004 in) increase in A yielded a 3-cm (1.2-in) increase in measurement depth. â¢ Roller MVs were found to be insensitive to the compac- tion of thin lifts (e.g., 15 cm [6 in]) of stiff base material placed directly over a soft subsurface. Roller MVs were more sensitive to compaction of 30-cm (12-in) lifts of the same stiff material over soft subgrade. Further, roller MVs were sensitive to compaction of 15-cm (6-in) lifts of base material placed atop similar (stiff) base material. The sen- sitivity of roller MVs to compaction of thin lifts improves as the modulus ratio of the overlying stiff to underlying soft layer decreases and as layer thickness increases. These results imply that CCC-based QA of thin base layers atop softer subgrade may be unreliable. â¢ In situ stress-strain-modulus measurements at depths to 1 m (3.3 ft) beneath the roller indicate highly nonlinear modulus behavior within the bulb of soil reflected in roller MVs. In base, subbase, and subgrade structures, modulus varies widely from layer to layer and within layers. Modulus values increased by a factor of two with depth in vertically homogeneous embankment test beds. In situ modulus is strongly influenced by the vibratory loading. A change in vibration amplitude from low to high created a two-fold change in modulus. â¢ The amplitude (A) dependence of roller MVsâparticularly stiffness measures such as E vib and k s âis a result of stress- dependent soil modulus, layer interaction, and drum/soil contact mechanics. For vertically homogeneous embank- ment conditions, the nature of the MV-A dependence, that is, positive, negative, or neutral, depends on the modulus function parameters of the soil. Coarse granular soils (i.e., gravels) that are governed by mean effective stress-induced hardening may generally exhibit a positive roller MV-A dependence (i.e., increase in A yields an increase in roller MV). Conversely, finer grained granular soils (i.e., sands) and cohesive soils governed by shear stress-induced soften- ing may generally exhibit a negative roller MV-A depen- dence. (i.e., increase in A yields a decrease in roller MV). â¢ The roller MV-A dependence of layered structures is more complex and is influenced by stress-dependent soil modu- lus (modulus function parameters), layer thickness, relative stiffness of layers, and drum/soil interaction issues. Both positive and negative roller MV-A dependence is possible, even within the same material. The roller MV-A relation- ship is site dependent and cannot be predicted a priori. â¢ Levels of vibratory roller-induced deviator stress were found to be considerably greater than those used in M r test- ing, while levels of confining stress are considerably less. Even during low excitation force associated with finishing passes and proof rolling of compacted soil, estimated devi- ator stresses q from z = 0-0.5 m (0-1.6 ft) in the clayey sand were up to three times greater than the maximum q values used for laboratory M r testing of subgrade soils. Similarly, estimated q values in the crushed rock base course were up to 2.5 times greater than the maximum q used for labora- tory M r testing of base materials. For z > 0.5 m, field and maximum laboratory q values were reasonably similar. Conversely, values of p observed in the field were approxi- mately 0.3-0.5 of those used during laboratory M r testing (below z = 0.25 m). â¢ The extraction of mechanistic material parameters using roller-based measurements for performance-based speci- fications consistent with M-Eâbased design (e.g., AAS- HTO 2007 Pavement Design Guide) is possible. However, the extraction of appropriate parameters must account for the three-dimensional nature of the roller/soil inter- action, the influence of layers, the nonlinear modulus of each involved material, and the dynamics of the drum/ soil interaction.