Bender Elements Successfully Quantified Stiffness ...docs.trb.org/prp/17-03736.pdf · Revised Manuscript No. 17-03736. Bender Elements Successfully Quantified Stiffness Enhancement

Revised Manuscript No. 17-03736

Bender Elements Successfully Quantified Stiffness Enhancement Provided by Geogrid-Aggregate Interlock

Accepted for Presentation and Re-review for Publication 96th Annual Meeting of the Transportation Research Board

Washington, DC, January 2017

by

Yong-Hoon Byun, Ph.D., Post-Doctoral Research Associate Phone: (217) 751-2420 / Email: [email protected]

and

Erol Tutumluer, Ph.D., Professor (Corresponding Author)

Paul F. Kent Endowed Faculty Scholar Phone: (217) 333-8637 / Email: [email protected]

Department of Civil and Environmental Engineering

University of Illinois at Urbana-Champaign 205 North Mathews Avenue, Urbana, IL 61801

Word Count: 4,232 words + 2 Tables (*250) + 11 Figures (*250) = 7,482

November 15, 2016

mailto:[email protected]

mailto:[email protected]

Byun and Tutumluer 1

Bender Elements Successfully Quantified Stiffness Enhancement Provided by Geogrid-1 Aggregate Interlock 2 3 Yong-Hoon Byun – Post-Doctoral Research Associate 4 Erol Tutumluer – Professor, Paul F. Kent Endowed Faculty Scholar 5 University of Illinois at Urbana-Champaign 6 7 8 ABSTRACT 9 10 Lateral restraint is a primary mechanism of geogrid base reinforcement contributing to the performance 11 improvement of flexible pavements, and the interlocking between the geogrid and aggregate is responsible 12 for the stiffness enhancement in a zone formed around the geogrid. This paper introduces a novel 13 application of bender elements as shear wave transducers for quantifying local stiffness increase in the 14 vicinity of a geogrid. Several triaxial test specimens of a dense-graded granite type aggregate were prepared 15 at two different moisture contents for resilient modulus testing. Reinforced specimens also included a 16 punched and drawn geogrid piece and placed at specimen mid-height. Two pairs of bender elements 17 installed on the membrane at two different heights enabled the measurement of shear waves horizontally 18 across the specimen. Shear wave velocities and axial resilient strains were recorded under the applied stress 19 states. The test results show that the resilient modulus of the reinforced specimen was similar to that of the 20 unreinforced one tested at the same moisture content. The 1:1 aspect ratio of specimen restricted the bulging 21 at specimen mid-height, and the interaction between the geogrid and aggregate, in turn, was less intensified. 22 In contrast, the shear moduli obtained at mid-height of reinforced specimen were always greater than those 23 obtained from unreinforced specimen thus clearly indicating a local stiffness increase in the vicinity of the 24 geogrid. Further, in the reinforced specimens, the shear moduli obtained near the upper end were always 25 less than those obtained from the specimen mid-height. The small-strain shear modulus determination by 26 bender elements was quite effective for evaluating the stiffness enhancement provided by geogrid-27 aggregate interlock. 28 29 30 31 32 33 34 35 36 37 38 39 40 Key Words: Aggregate, Bender element, Geogrid, Interlock, Shear modulus, Shear wave 41 42 43 44 45


INTRODUCTION 1 2 Base reinforcement is a common application of geogrids, which can provide potential benefits of reducing 3 the unbound aggregate base course thickness or extending the pavement life. To better account for geogrid 4 functions, three reinforcement mechanisms have been recognized for the geogrid-aggregate composite 5 system as the tensioned membrane effect, increased bearing capacity, and lateral restraint. Although the 6 tensioned membrane effect was considered a main mechanism in the past, it is more applicable to large 7 deformations in an unpaved road surface or a construction working platform. Traffic induced rut depth 8 generated in an asphalt surfaced pavement is generally smaller and this effect can be negligible. Secondly, 9 in case of the geogrid reinforcement placed towards the bottom of base course, the failure envelope can be 10 limited within the base course, which leads to an increase in the bearing capacity of the pavement system. 11 Most of all, the lateral restraint resulting from the interlocking between geogrid and aggregate particles has 12 been acknowledged to develop a relatively “stiffer” layer surrounding the geogrid to make it a primary 13 mechanism for the geogrid-reinforced base. 14

Many researchers have investigated the interlocking action between geogrid and granular materials 15 (1-5). Konietzky et al. (1) reported a significant increase in contact forces in a restricted area around the 16 geogrid during the pullout test simulated by discrete element method. Chen et al. (2) also demonstrated the 17 reinforced zone in the ballast particles around the geogrid by discrete element method. Perkins et al. (3) 18 measured the radial displacement at different levels of the aggregate specimens in permanent deformation 19 testing and established the zone influenced by geogrid reinforcement. The results of field tests performed 20 by Kwon and Tutumluer (4) validated a stiffer layer development around the geogrid predicted by their 21 finite element modeling considering compaction-induced residual stresses. Zhou et al. (5) also observed the 22 shear zone around the geogrid using micro-image analysis and identified the increase in shear zone 23 thickness with an increase in the applied stress. Nevertheless, the stiffened zone around the geogrid has not 24 been quantified and thus new experimental approaches are required. 25

The current problem with evaluating aggregate-geogrid interlock and the effectiveness of currently 26 available geogrid products is that there is no representative laboratory test to quantify the stiffness 27 enhancement provided by the interlock in the geogrid-aggregate composite system. For example, for 28 unbound aggregates, the properties that seem to be influential may include gradation, angularity, hardness, 29 density, and surface texture/friction as outlined by Giroud (6). For a geogrid, the properties that can have 30 great influence on performance include aperture size and geometry, junction strength, and rib shape and 31 stiffness (6). 32

The bender element test, commonly carried out for the evaluation of shear modulus of soils through 33 the shear wave propagation, may have potential to study the geogrid-aggregate composite system. The 34 bender element which has optimal coupling with soils and compatible operating frequency is widely used 35 as a shear wave transducer (7). Many attempts have been made to apply the bender element in several 36 laboratory tests, such as triaxial test and oedometer test (8-10). Lee and Santamarina (11) monitored the 37 shear wave velocities during the liquefaction by using a series of bender elements horizontally installed at 38 different levels of a sand specimen. Byun et al. (12) also characterized the evolution of shear wave velocities 39 according to horizontal displacement by using bender elements mounted at different layers in direct shear 40 boxes. 41

A few attempts have also been made to apply the bender element to studying aggregate materials. 42 Souto et al. (13) developed a resonant column testing device with bender elements and evaluated the shear 43 modulus in a series of sands and gravels. The test results showed the shear modulus measured by bender 44 element and resonant column tests gave similar values up to the confining pressure of 100 kPa. Davich et 45 al. (14) incorporated the bender elements into a repeated load triaxial testing device in order to compare the 46 resilient and elastic moduli of aggregate specimens. However, the vertical arrangement of bender elements 47 mounted at top cap and pedestal caused some damage to the bender element due to the potential migration 48 of large aggregates under the repeated load. The use of a wire mesh and fine sand around the bender 49 elements could protect the bender elements from migrating large aggregates. 50


The objective of this paper is to describe the successful application of the bender elements for 1 quantifying local stiffness increase in the vicinity of a geogrid where it is properly interlocked with 2 aggregate particles to prevent any movement, and hence the enhanced stiffness when such small-strain 3 behavior is realized in laboratory triaxial test specimens. First, the basic concept of shear wave velocity 4 measurement is introduced as a novel approach for evaluating geogrid-reinforced aggregate system. Then, 5 installation of the bender elements on the membrane at different specimen heights and the required 6 equipment and the operation of wave measurement system are briefly explained. Properties of a granite 7 type aggregate material and the punched and drawn geogrid used are described with further details given 8 on the specimen preparation procedure, followed by the resilient modulus test procedure recommended by 9 AASHTO T307. The shear moduli obtained from the measured shear waves are compared with the resilient 10 modulus test results. Finally, the effectiveness of shear modulus determination horizontally across the 11 specimen for quantifying the local stiffness enhancement in the vicinity of geogrid is demonstrated. 12

13 14

SHEAR WAVE TRANSMISSION 15 16 Shear Wave Velocity 17 18 Shear wave velocity is generally estimated from the measurement of shear waves by using two wave 19 transducers. To measure the shear waves, a pair of wave transducers (bender elements or BE here) is 20 embedded in a geomaterial as shown in Figure 1(a). Then, a shear wave generated at a transducer (as a 21 sender) propagates through the material and can be detected at the other transducer (as a receiver). Figure 22 1(b) shows typical waveforms of input and output signals. After trigger of input signal, the elapsed time up 23 to the completion of a first small bump of output signal is recorded as a first arrival time. Provided that the 24 travel distance between two transducers (dtravel) and the first arrival time (t1st arrival) are recorded, the shear 25 wave velocity can be estimated directly using Equation 1 as follows: 26 27 V𝑠𝑠 = 𝑑𝑑𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

𝑡𝑡1𝑠𝑠𝑡𝑡 𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡 (1) 28

29

(a) (b)

30 FIGURE 1: Propagation of shear waves in a particular geomaterial 31

32 33 Bender Elements 34 35 A pair of bender elements (BEs), each having 6-mm width and 16-mm length, was used as a set of shear 36 wave transducers in this study. Figure 2 shows the BE mounted at a brass base. One end of the BE was 37 fixed at the mounting base by using a high strength-epoxy, while the other end of the BE was designed to 38 be inserted into a specimen to generate and detect the shear waves. To prevent the bender elements from 39

BEBE

Specimen

d travel

Shear wave

Sender Receiver

Input signal

Output signal

t 1st arrival


any damage during specimen preparation and testing, the mounting base includes a pair of protection bar 1 above and below the BE. 2 3

(a) (dimensions in mm) (b)

4 FIGURE 2: Bender element used as a shear wave transducer (a) mounted at base (schematic 5

drawing); (b) mounted at base (photo) 6 7 8 Measurement System 9 10 For characterization of local stiffness of a triaxial specimen, two pairs of BE were attached to a cylindrical 11 membrane and arranged at two different heights of a specimen as shown in Figure 3. To transmit and 12 measure the shear waves, a signal generator, oscilloscope, and filter-amplifier were used in this study. An 13 input square signal of 10 V with a 20 Hz frequency was triggered from the signal generator to a BE used as 14 a transmitter. The output signal detected at the other BE used as a receiver was filtered by passing only 15 frequencies ranging from 1 kHz to 50 kHz. Simultaneously, the filtered output signal was amplified to 16 maximize the signal/noise ratio. 17

18

19

FIGURE 3: Shear wave measurement system (dimensions in mm) 20 21

11Mounting

base

Coaxialcable

Protection bar

BE

1 1816

6

10

5

Oscilloscope

Signal generator

Filter & amplifier

Input

Output

Computer

Specimen

BE BE

Geogrid(if used)

55

75

150

150


MATERIAL PROPERTIES 1 2 Aggregate 3 4 A high quality crushed granite commonly used in North Carolina for unbound aggregate base course was 5 obtained from a quarry for this study. To investigate the grain size distribution of the aggregate, wet sieving 6 and dry sieving were carried out according to ASTM C117 (15) and ASTM C136/C136M (16), respectively. 7 Figure 4(a) shows the gradation curve of the well-graded aggregate with a maximum particle size of 38 8 mm, average particle size (D50) of 4 mm and approximately 12% passing the No. 200 sieve, all satisfying 9 requirements of North Carolina (NC) DOT specification. 10

To establish the moisture-density characteristics, aggregate specimens were compacted at four 11 different moisture contents. The compaction test was performed in accordance with North Carolina DOT 12 practice using drop hammers and similar to the modified compaction test method specified in ASTM D1557 13 (17). Compared to 56 blows per layer specified in ASTM D1557, 86 blow counts per layer were applied by 14 using a modified compaction hammer according to NCDOT procedures (18). The moisture-density 15 relationship is presented in Figure 4(b) and the results show that the optimum moisture content and the 16 maximum dry density for this compactive effort are 24.3 kN/m3 and a water content of 5.6 %, respectively. 17 After the compaction of each specimen, unsoaked California Bearing Ratio (CBR) tests were performed to 18 evaluate the strength characteristics of the aggregate (19). 19

20 Geogrid 21 22 A triangular aperture geogrid was used for the reinforcement of the aggregate and the dimensions of this 23 punched and drawn geogrid are summarized in Table 1. Sarsby (20) and Jewell et al. (21) recommended 24 that the ratio of aperture size to average particle size had to be greater than approximately 3.5. Considering 25 the grain size distribution of the aggregate, the geogrid used in this study is appropriate for aggregate 26 reinforcement. 27 28

TABLE 1: Dimensions of the geogrid used 29 Rib pitch [mm] Mid depth [mm] Mid width [mm]

Longitudinal Diagonal Diagonal Transverse Diagonal Transverse 40 40 1.3 1.2 0.9 1.2

30 31 32 RESILIENT MODULUS TESTING OF GEOGRID REINFORCED AGGREGATES 33 34 Specimen Preparation 35 36 Using the granite type aggregate and the geogrid selected, geogrid-reinforced and unreinforced specimens 37 were prepared for resilient modulus testing. First, a membrane including two pairs of BEs was placed in a 38 compaction mold, and the levels of two pairs of BEs were adjusted to two different heights of the cylindrical 39 specimen, as previously shown in Figure 3. Then, the aggregate was compacted in the mold with a rammer 40 producing a modified compactive effort of approximately 2,700 kN∙m/m3. Each specimen was filled in four 41 layers applying 56 blows per layer. Figure 5(a) shows the geogrid arranged at the mid-height of the 42 reinforced specimen. The compacted specimens were prepared at two different moisture contents: 3% and 43 5%. For the water content of 3%, the geogrid-reinforced and unreinforced specimens had the dry unit 44 weights of 23.1 kN/m3 and 23.3 kN/m3, respectively. For the moisture content of 5%, the dry unit weights 45 of 23.4 kN/m3 and 23.5 kN/m3 were accomplished in the reinforced and unreinforced ones, respectively. 46 The dry unit weights of the specimens prepared for the resilient modulus tests are smaller than those 47


prepared for the moisture-density tests due to the difference in the blow counts applied between the two 1 tests. After finishing the specimen preparation, the specimen including the two pairs of BEs was placed in 2 the triaxial test rig for the repeated load testing [see Figure 5(b)]. 3

4 5

(a)

(b)

6 FIGURE 4: Granite aggregate material properties (a) gradation; (b) moisture-density and 7

unsoaked CBR test results 8

0

20

40

60

80

100

0.01 0.1 1 10 100

Cum

ulat

ive

Perc

ent P

assi

ng [%

]

Particle Size [mm]

Aggregate used

NCDOT specification band

2 3 4 5 6 7 823.8

24.0

24.2

24.4 Dry density CBR

Moisture Content [%]

Dry

Dens

ity [k

N/m

^3]

0

50

100

150

200

250

300

CBR

[%]


1

(a) (b)

2 FIGURE 5: Configuration of specimen including bender elements (a) in compaction mold with 3

geogrid; (b) setup for repeated load triaxial testing using the University of Illinois FastCell 4 5 6 Resilient Modulus Test Procedure 7 8 Figure 6 shows the configuration of the compacted specimens when the oil-filled confining cell is lowered 9 on the instrumented specimen. Before applying the horizontal confining pressure, there is a small gap 10 between the specimen and confining cell where the mounting base of BE is located as shown in Figure 6(a). 11 A pair of linear variable differential transformers (LVDTs) diametrically embedded in the confining cell is 12 used for the measurement of radial specimen displacement and subsequently, for the correction of the travel 13 distance of shear waves according to deformation of the specimen. After applying the confining pressure, 14 the membrane incorporated with the confining cell is inflated, and it rests on the mounting base of BE as 15 shown in Figure 6(b). Consequently, the confining pressure helps the BE to be fixed on the specimen 16 membrane during resilient modulus testing. 17

The resilient modulus tests were conducted using an advanced triaxial testing device, referred to as 18 the University of Illinois FastCell (UI-FastCell), presenting unique capabilities for independent pulsing in 19 the vertical and horizontal directions. Further details about the capabilities of the UI-FastCell can be found 20 elsewhere (22). Four cylindrical specimens having equal dimensions of 150-mm height and 150-mm 21 diameter were prepared at the two different moisture contents for resilient modulus testing. Two of them 22 were geogrid-reinforced and the other two were unreinforced specimens. According to the AASHTO T307 23 procedure, the specimens were first conditioned by applying 1000 repetitions of 103.4-kPa repeated load 24 deviator stress under the confining pressure of 103.4 kPa. After that, three deviator stresses were pulsed for 25 100 load repetitions at each of the five different confining pressures for a total of 15 stress states applied 26 according to the resilient modulus test procedure specified for base/subbase materials. Output signals from 27 the BE pairs were obtained at the two locations, i.e. specimen mid-height and near the upper end of 28 specimen, as shown in Figure 3. The signals were recorded after each 100 load repetitions were completed 29 at each of the 15 stress states. 30 31

32

Confining cell

BE

BE

Geogrid

Compaction mold


(a) (b)

1 FIGURE 6: Configuration of the confining cell lowered on to cylindrical specimen (a) before 2

applying confining pressure; (b) after applying confining pressure 3 (Note: 2nd membrane belongs to the confinement cell filled with oil, lowered on to the specimen) 4

5

6

INTERPRETATION OF TEST RESULTS 7 8 Resilient Modulus 9 10 Figure 7 shows the resilient moduli obtained for all specimens as a function of the bulk stress, θ = σ1 +2 σ3, 11 where σ1 and σ3 are the applied vertical and horizontal stresses, respectively. The average axial resilient 12 strains, measured from the last 5 cycles of the 100 load repetitions at each stress state, were used to compute 13 the resilient moduli. In general, the resilient modulus increases with an increase in the bulk stress and this 14 expected trend is commonly known as the stress-hardening behavior. Figure 7 indicates the resilient moduli 15 of the geogrid-reinforced and unreinforced specimens which are quite similar to each other. To better show 16 any differences in the overall resilient modulus behavior, the resilient moduli trend lines were represented 17 by the K-θ model suggested by Hicks and Monismith (23). The solid and dashed lines indicate again quite 18 similar trends fitted in the reinforced and unreinforced specimens, respectively. In addition, there is a little 19 difference among the resilient moduli at the moisture contents of 3% and 5% and the drier specimens at 3% 20 moisture content had slightly higher resilient moduli. 21 22 23 24

Confining cell

Specimen

2nd MembraneLVDT

LVDT

BE BE

1st Membrane

S-waveBE BE

LVDT

LVDT

σ3σ3

σ3σ3

Confining cell


1

FIGURE 7: Resilient modulus results of the four specimens tested 2 3

Waveform 4 5 Figure 8 shows the typical waveforms recorded at each confining pressure for the reinforced specimen at 6 the moisture content of 3%. The signals shown in Figure 8 are the output signals averaged by stacking 128 7 signals, and each signal was normalized with its maximum amplitude. As the confining pressure increases, 8 the first arrival time increases, regardless of the distance from the geogrid. Also, signal/noise ratio increases 9 with an increase in the confining pressure, because the amplitude of shear wave increases with a confining 10 pressure. 11

12

Shear Modulus 13 14 Shear wave velocity can be calculated by the first-arrival time and the travel distance between two BEs, as 15 mentioned earlier. Subsequently, a shear modulus (Gmax) of a specimen can be estimated by multiplying a 16 bulk density (ρ) by the shear wave velocity (Vs) as follows. 17 18 G𝑚𝑚𝑚𝑚𝑚𝑚 = 𝜌𝜌V𝑠𝑠2 (2) 19 20 Figure 9 shows the variations in shear moduli as a function of the bulk stress for the four specimens. In 21 general, the shear modulus increases with an increase in the bulk stress, regardless of the geogrid 22 reinforcement. In case of the 3% moisture content, the shear moduli obtained at mid-height of the reinforced 23 specimen is always the highest among the others, while the shear moduli obtained at the middle and near 24 the upper end of the unreinforced specimen and also near the upper end of the reinforced specimen are all 25 similar to each other. Furthermore, to better indicate the dependence of shear modulus on the applied 26 stresses, Figure 9 shows the trend lines for shear modulus estimated as power functions of bulk stress. The 27 solid and dashed lines represent the trend lines fitted at the middle and near upper end of the reinforced and 28 unreinforced specimens, respectively. Also, in case of the moisture content of 5% [see Figure 9(b)], the 29 shear moduli obtained at the middle of the reinforced specimen is obviously higher than the others. 30

0

50

100

150

200

250

0 100 200 300 400 500 600 700

Res

ilient

Mod

ulus

[MPa

]

Bulk Stress [kPa]

Reinforced - 3%Unreinforced - 3%Reinforced - 5%Unreinforced - 5%


1

(a)

(b)

2 FIGURE 8: Typical waveforms shown for the reinforced specimen at 3% moisture content 3

(a) 5 mm away from geogrid (middle); (b) 55 mm away from geogrid (upper) – [1 psi=6.9 kPa] 4 5

Time [ms]

σc= 3 psi

σc= 5 psi

σc= 10 psi

σc= 15 psi

σc= 30 psi

0 0.2 0.4 0.6 0.8 1

Time [ms]

σc= 3 psi

σc= 5 psi

σc= 10 psi

σc= 15 psi

σc= 30 psi

0 0.2 0.4 0.6 0.8 1


(a)

(b)

1 FIGURE 9: Shear moduli computed from measured shear wave velocities during the resilient 2

modulus testing – (a) moisture content of 3 %; (b) moisture content of 5 % 3 4

5 Note that these good results clearly quantifying the local shear modulus increase in the vicinity of 6

the geogrid were obtained despite the fact that the UI-FastCell specimens had 1:1 ratio of height to diameter 7 of the specimens, i.e., specimens used in this study were shorter compared to the 2:1 ratio of height to 8 diameter of standard triaxial specimens. This undoubtedly restricted the bulging of the specimen under 9 repeated loading. Accordingly, the shorter specimen used in this study is considered to less mobilize the 10 interaction between the geogrid and aggregate at the mid-specimen height and the effect of geogrid 11

0

100

200

300

400

0 100 200 300 400 500 600 700

Shea

r Mod

ulus

[MPa

]

Bulk Stress [kPa]

Reinforced - upperReinforced - middleUnreinforced - upperUnreinforced - middle

0

100

200

300

400

0 100 200 300 400 500 600 700

Shea

r Mod

ulus

[MPa

]

Bulk Stress [kPa]



reinforcement on the specimen deformations was less intensified. When the innovative approach using the 1 bender element is applied to standard longer specimens, one may therefore expect more pronounced results 2 and better quantification of the stiffness enhancement provided by the interlock mechanism of the geogrid 3 and aggregate composite system. 4 5 6 DISCUSSION 7 8 The resilient modulus is an important property for defining the resilient behavior of the base course in 9 pavement design. Similarly, the resilient modulus obtained from the standard resilient modulus test 10 represents the stiffness of a whole aggregate specimen. In contrast, the bender elements can be used to 11 evaluate the local stiffness around the zone these instruments are placed, and the shear modulus obtained 12 from bender element testing determines the local stiffness within that zone/layer of aggregate specimen. 13 To investigate the relationship between the resilient and the shear moduli obtained in this study, 14 the moduli computed at each of the 15 stress states are presented and compared in Figure 10. For all the 15 specimens, the magnitudes of shear moduli are generally greater than those of resilient moduli. Note that 16 shear modulus is estimated at small-strain level, while resilient modulus is estimated at larger-strain levels 17 (24). Since the shear modulus estimated at small-strain level decreases with an increase in the strain level, 18 the shear modulus at small-strain should be greater than the resilient modulus at larger strain. In the current 19 study, the bender elements successfully enabled the periodic monitoring of shear waves for the evaluation 20 of local stiffness, without any disturbance of the aggregate specimen. 21 A comparison between the shear modulus and the resilient modulus (Mr) can be established using 22 a linear relationship as follows. 23 24 G𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑎𝑎M𝑟𝑟 (3) 25 26 where a is the correlation coefficient and stands for the slope of any straight line shown in Figure 10. The 27 slope of straight line estimated at the middle of the reinforced specimen is the steepest. The results mean 28 that especially at the middle of the reinforced specimen, the shear modulus is more sensitive to the effect 29 of geogrid reinforcement than the resilient modulus, and the shear modulus can be a more useful parameter 30 to quantify the local stiffness enhancement provided by geogrid-reinforced aggregate. 31

The values of the correlation coefficient a are summarized in Table 2. The coefficients of 32 determination (R2) over 0.94 represented that the relationship between the shear modulus and the resilient 33 modulus is highly reliable. Figure 11 clearly shows that the coefficient a estimated at the middle of the 34 reinforced specimen is much higher (up to 70%) than others, regardless of the moisture contents of the 35 tested specimens. Thus, the shear modulus evaluation by the bender elements can be effectively used for 36 the quantification of stiffness enhancement of geogrid-reinforced aggregate. 37 38 39

TABLE 2: Correlation coefficient between the shear and resilient moduli 40 41

Moisture content = 3 % Moisture content = 5 % Reinforced Unreinforced Reinforced Unreinforced Upper Middle Upper Middle Upper Middle Upper Middle

a 1.25 1.72 1.30 1.17 1.38 1.70 1.18 1.20 R2 0.96 0.96 0.97 0.97 0.95 0.95 0.96 0.94

42 43


(a)

(b)

1 FIGURE 10: Comparisons of the shear and resilient moduli obtained in this study 2

(a) moisture content = 3 %; (b) moisture content = 5 % 3 4 5 6

0

100

200

300

400

0 100 200 300 400

Shea

r Mod

ulus

[MPa

]

Resilient Modulus [MPa]


0

100

200

300

400

0 100 200 300 400

Shea

r Mod

ulus

[MPa

]

Resilient Modulus [MPa]



1 FIGURE 11: Correlation coefficients determined for the relationship between the shear and 2

resilient moduli from the four preliminary tests conducted in this study 3 4

5 SUMMARY AND CONCLUSIONS 6 7 A new innovative approach based on the use of bender elements and shear wave propagation was presented 8 in this paper to evaluate the stiffness enhancement of a geogrid-aggregate composite system such as in the 9 case of base course reinforcement application of geogrids in flexible pavements. Fundamental principle of 10 shear wave transmission and the estimation method for shear wave velocity were introduced. Bender 11 elements optimized for the application of base course aggregate specimens in resilient modulus testing were 12 configured with wave measurement devices. A representative granite type crushed stone and a punched and 13 drawn geogrid commonly used for unbound base course and its reinforcement were adopted for the 14 specimens of resilient modulus tests. Four different reinforced and unreinforced specimens were prepared 15 by following a modified compaction procedure, and two pairs of bender elements were installed at two 16 different specimen heights, i.e. in the middle and upper end of the specimen. The resilient modulus tests 17 were conducted with the bender element instrumentation to properly quantify the local shear moduli near 18 the geogrid and far away from the geogrid. 19

The results of the resilient modulus tests indicated that the resilient moduli of the geogrid reinforced 20 and unreinforced specimens were quite similar at any moisture content. From the measurement of shear 21 waves, the shear modulus was estimated at the middle and upper end positions of the four specimens. At 22 both near optimum and dry of optimum moisture contents, the shear modulus obtained at the middle of the 23 reinforced specimen was always greater than those obtained at its upper layer, as well as those obtained 24 from the unreinforced specimens. Overall, the shear moduli were greater than the resilient moduli at 25 approximately 20%-40% due to the modulus degradation behavior with strain level. This difference was 26 the greatest (up to 70%) for the shear modulus measured at the mid-specimen height where the geogrid was 27 placed. The small-strain shear modulus determination using bender elements can be useful for the 28 evaluation of an elastic stiffness increase in a local zone. Therefore, based on the preliminary findings of 29 this research study, the bender element application can be effectively used for the quantification of the 30 stiffness enhancement provided by the interlock between geogrid and aggregate, and for development of 31 better and more effective geogrid products for base reinforcement. 32 33 34

1

1.2

1.4

1.6

1.8

upper middle upper middle

Coe

ffici

ent a

wc = 3 %

wc = 5 %

Reinforced Unreinforced


1 ACKNOWLEDGEMENTS 2 3 The authors would like to acknowledge Mr. Joe Inglis for providing a filter-amplifier set used in this 4 research study. Special thanks go to graduate student Issam Qamhia and research engineer James Meister 5 at the Illinois Center for Transportation for their help with conducting the laboratory experiments. The 6 contributions of Darold Marrow and Tim Prunkard of the UIUC CEE Department machine shop during the 7 manufacturing of the mounting bases for bender elements are greatly acknowledged. 8 9 10 REFERENCES 11

12 1. Konietzky, H., te Kamp, L., Gro¨ger, T., and C. Jenner. Use of DEM to Model the Interlocking 13

Effect of Geogrids under Static and Cyclic Loading. In Numerical Modeling in Micromechanics via 14 Particle Methods, ed. Y. Shimizu, R. Hart and P. Cundall, 2004, pp. 3–12. 15

2. Chen, Cheng, G. R. McDowell, and N. H. Thom. Investigating Geogrid-Reinforced Ballast: 16 Experimental Pull-out Tests and Discrete Element Modelling. Soils and Foundations Vol. 54, No. 17 1, 2014, pp. 1–11 18

3. Perkins, S. W., Christopher, B. R., Cuelho, E. L., Eiksund, G. R., Hoff, I., Schwartz, C. W., Svano, 19 G., and A. Want. Development of Design Methods for Geosynthetic Reinforced Flexible Pavements, 20 FHWA Report DTFH61-01-X-00068, 2004. 21

4. Kwon, J. and E. Tutumluer. Geogrid Base Reinforcement with Aggregate Interlock and Modeling 22 of Associated Stiffness Enhancement in Mechanistic Pavement Analysis. In Transportation 23 Research Record: Journal of the Transportation Research Board, No. 2116, Transportation 24 Research Board of the National Academies, Washington, D.C., 2009, pp. 85–95. 25

5. Zhou, J., Chen, J. F., Xue, J. F., and J. Q. Wang. Micro-mechanism of the Interaction between Sand 26 and Geogrid Transverse Ribs. Geosynthetics International Vol. 19, No. 6, 2012, pp. 426–437. 27

6. Giroud, J.P. (2009). “An Assessment of the Use of Geogrids in Unpaved Roads and Unpaved 28 Areas,” In Proceedings of the Jubilee Symposium on Polymer Geogrid Reinforcement, September 29 8, 2009, London, UK, (http://www.tensar.co.uk/jubilee-symposium/index.html). 30

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