a large scale resonant column testing system

Resonant Column Testing System 541

A LARGE SCALE RESONANT COLUMN TESTING SYSTEM FOR EVALUATING DYNAMIC PROPERTIES OF GRAVELLY FILL MATERIALS

OF DAMS

Nam-Ryong Kim1 Dong-Hoon Shin2

Ik-Soo Ha3 Min-Seub Kim4

ABSTRACT

This article introduces a large scale resonant column testing apparatus to evaluate small-strain shear modulus, damping ratio, and the modulus reduction curve corresponding to shear strain level of gravelly soils. These key parameters are important for the seismic analysis of geotechnical systems such as earth embankment dams and the main purpose of this new testing system is focusing on the characterization of gravelly fill materials for dam construction. Detailed configurations of the fixed-free Stokoe type resonant column testing apparatus which can test 200mm in diameter specimen are introduced, and the system was calibrated. A series of tests for gravelly fill material have been conducted on large scale specimens 200mm in diameter and 400mm in height. The result and applicability of this testing apparatus to evaluate dynamic properties of gravelly fill materials is addressed. Finally, the applicability of this new system is discussed.

INTRODUCTION Recently geomaterials with large coarse grains are frequently used as fill materials of large geosystems such as embankment dams, and demands for coarse materials continue to increase in mega construction projects. For the design of this type of infrastructure, it is important to evaluate and understand the material characteristics to verify and predict the safety and the performance of the systems. However, evaluation of strength and/or deformation characteristics of the coarse material is not easy in the lab because it requires large scale testing equipment. For example, fill materials for concrete faced rock-fill dams sometimes contain massive rubbles and it is almost impossible to directly evaluate the material properties as granular material or continuum because a small sample with relatively large rubbles cannot be considered as representing whole granular system. While most of design criteria for geotechnical structures depend on the strength parameters, deformation characteristics or stiffness is more important in the performance evaluation or prediction of deformation under service conditions. Especially in the seismic analysis of geosystems, the key soil parameters are shear modulus and damping ratio. For example, small-strain shear modulus (or shear wave velocity), modulus

1 K-water Institute, 462-1 Jeonmin, Yuseong, Daejeon, Korea, +82-42-870-7632, [email protected] 2 K-water Institute, 462-1 Jeonmin, Yuseong, Daejeon, Korea, +82-42-870-7600, [email protected] 3 K-water Institute, 462-1 Jeonmin, Yuseong, Daejeon, Korea, +82-42-870-7603, [email protected] 4 K-water Institute, 462-1 Jeonmin, Yuseong, Daejeon, Korea, +82-42-870-7613, [email protected]

542 Innovative Dam and Levee Design and Construction

reduction curve and damping characteristics are the key parameters for site response analysis or multi-dimensional seismic analysis of geotechnical systems. It is same for the dams constructed with coarse gravels. Therefore, it is strongly recommended to evaluate the dynamic deformation characteristics of coarse or gravelly materials reliably for seismic analysis of earth structures constructed with these kinds of materials. For this purpose, several large scale resonant column testing systems have been developed to evaluate deformation characteristics of gravelly soil (Woods, 19991; Prange, 1981), but only a few systems are capable to use specimens larger than 150mm in diameter (Richter & Huber, 2003; Menq, 2003; Hardin & Kalinski, 2005). Resonant column testing is the preferred method to evaluate dynamic properties of soils, since it directly measures shear modulus and damping ratio (Clayton et al., 2009). However, the diameter of specimen to be tested is normally less than 100mm. The main purpose of large scale resonant column testing systems is to evaluate dynamic deformation characteristics of fill materials for dams as well as ballast materials for railway construction. These materials generally contain relatively large gravel particles or even crushed rubbles. Therefore, the size of testing system has to be as large as possible to reliably evaluate the dynamic deformation characteristics of these materials. Alternative methods to estimate the strength parameters of original coarse materials using small samples by adjusting grain size distributions have been introduced and adopted (Hou et al., 2004), however the effect of this adjustment on stiffness parameters is not clear. To investigate and extrapolate the stiffness measurement result from reduced particle size sample to the original sample, samples with various particle size conditions must be compared in the same testing environment. The specimens of these samples must also be considered as homogeneous continuum. Therefore, the large scale resonant column testing system was developed not only to investigate the effect of largest particle size but also to directly evaluate dynamic deformation characteristics of gravelly materials. In this article, development of the K-water large scale resonant column (LSRC) testing equipment is introduced. The main feature of the system is applicability to coarse materials with maximum grain sizes over 30mm. Gravelly materials often used as fill materials for geotechnical systems such as dams can be tested in the new system. The dynamic characteristics of the system have been investigated and the applicability of the system on gravelly material has been examined and verified this study. LARGE SCALE RESONANT COLUMN TESTING APPARATUS IN K-WATER

General Design and Specifications The K-water large scale resonant column (LSRC) testing apparatus has been designed as a Stokoe type system and its boundary conditions are fixed at the bottom and free at the top with additional mass which is consist of top cap and driving plate . The standard for resonant column test (ASTM D4015) recommends that the largest grain size must be smaller than 1/6 of the diameter of the testing specimen and the height of the specimen must be about 2 to 3 times of the diameter when the specimen is tested under high confining pressure. The basic configuration of the testing system introduced here fits to a


200mm in diameter and 400mm in height specimen. Therefore, the test can be conducted for maximum 33mm grain size samples. Figure 1 illustrates the design of the LSRC testing apparatus developed in at K-water. The parts were designed with cautious analysis, such as deformation induced by the reaction force during applying torsional excitation, to ensure precise operation.

Coil-magnet system

Driving plate

Proximitor targetProximitor

Proximitor support

Accelerometer

Base plate

Driving system support

Driving system leveling part

Specimen

Bottom pedestal

Top cap

Figure 1. Design of the K-water LSRC testing apparatus.

The system was designed to satisfy the requirements for the general resonant column test method. The main features of the testing system are listed as follows:

- Gravelly soil sample with maximum grain size over 30mm can be tested in an appropriate manner.

- Solid cylinder type specimen with 200mm in diameter and 400mm in height is used with standard configurations.

- The maximum dimensions of testing specimen can be enlarged up to 300mm in diameter and 600mm in height.

- Maximum 2MPa pneumatic confining pressure can be applied to the testing specimen.

- Coil-magnet driving system provides torsional cyclic load at the top of the specimen and it is controlled by sinusoidal current regulated by the amplifier.

- The maximum torsional load generated by coil-magnet system is up to 500Nm, which can characterize deformation modulus of 800MPa shear modulus sample.

- Cyclic torsional shear test can be conducted in the same testing configuration by directly measuring shear strain using a pair of proximitors at the top of the sample.

Driving and Measurement System


The basic principles for operation of the LSRC testing system are to apply cyclic excitation load to the driving plate, and to measure the dynamic response of the specimen. The configuration of operation and measurement system of the K-water LSRC testing system is illustrated in Figure 2. Once sinusoidal current is provided to 4 pairs of coils in the driving system, the interaction between magnetic field generated by the current through the coils and the magnets attached to the driving plate acts as a loading mechanism hence it provides cyclic torque at the top of the specimen. By sweeping the excitation frequency, frequency response can be acquired and the resonant column test software seeks the resonant frequency to find the shear modulus or shear wave velocity.

Figure 2. Control and measurement system configuration of LSRC testing system.

Figure 3. LSRC testing system.

For accurate control of the driving system, an arbitrary waveform generator (Agilent 33220A) is employed in the system and it generates precise sinusoidal excitation signal according to the commands from the control software. Since the testing system focuses on applications on gravelly materials under high confining pressure and uses a large

specimen, the strain level corresponding to 10Vp excitation can be smaller than 0.0001%, which is generally smaller than elastic threshold strain of gravelly material. Therefore, a power amplifier which can provide precisely regulated electric current to the coil system is implemented and it is confirmed that the response of gravelly soil specimen


under maximum excitation shows shear strain level up to 0.01% at maximum loading level. The response of the specimen caused by the cyclic torsional excitation is measured using an accelerometer (PCB 353B15) attached at the top of the driving plate. The signal from the accelerometer is collected by the A/D board (NI USB-6251) and the frequency response curve is plotted by measurement software. The shear strain level is determined from the acceleration measurement and the shear modulus is calculated from the resonance frequency. The software also has a capability to evaluate damping ratio by both half-power bandwidth and free vibration decay methods. Once a single step of the test is completed, we can increase the output voltage from the waveform generator to increase the strain level hence it is possible to obtain the modulus reduction and damping curves at specific confining stress levels.

SYSTEM VERIFICATIONS To measure dynamic deformation properties of geomaterials using resonant column testing system, it is important to evaluate dynamic characteristics of the testing system. The dynamic characteristic of the system is a key factor in calculating the shear modulus from the governing equation. The shear modulus of the testing specimen is calculated by the equation derived by elastic theory and it is expressed as Equation (1)

S

n

S

n

Vl

Vl

II

tan0

= (1)

where I is the mass polar moment of inertia of the specimen, I0 is the mass polar moment of inertia of the system attached at the top of the specimen, n is the natural frequency of the specimen, l is the height of the specimen, and VS is the shear wave velocity of the testing material. While the mass polar moment of inertia I of the specimen can be easily calculated, that is not in case for I0, which is the key factor to solve the Equation (1) to calculate VS. Therefore, the I0 of testing system is usually evaluated by experimental method. The system characteristics of the K-water LSRC equipment have been evaluated using metal specimens, and the performance and accuracy were verified by using urethane specimens. Calibrations using Metal Specimens To evaluate I0 of driving system, total three metal specimens were prepared and LSRC tests were conducted. The main part of the metal specimen is a single aluminum rod and large rigid metal disk can be attached at the top of the specimen. The torsional stiffness of the system can be solely fixed by the rod while the polar moment of inertia of the system can be changed by substituting the metal flange disks. For the specimen installed in the LSRC testing system, the response characteristic of the single degree-of-freedom (SDOF) system can be determined by following equation


=nKI

(2)

where n is the natural frequency of the system, K is the torsional stiffness of the specimen, or the rod, and I is the polar moment of inertia of the specimen. If the specimen is tested in the LSRC testing system, Equation (2) can be rewritten as

0 2+ = 'n

KI I (3)

Figure 4. LSRC testing system with metal specimen for calibration.

Therefore I0 can be calculated by solving simultaneous equations from two tests with different flanges since I of specimens can be easily calculated for each case and K does not change. Figure 4 shows the installation of the metal specimen in the LSRC testing system employed to measure I0 and the circular flange at the top can be replaced by larger sizes. Table 1 shows I values for each specimen with different flanges calculated and the natural frequencies fr measured from LSRC testing system. With the results in Table 1, I0 was calculated from three combinations of the results as listed in Table 2. The difference in each I0 from these 3 cases is around 2% and the average I0 is similar to the result from numerical estimation. Therefore, the I0 value of the testing system could be successfully evaluated and this parameter can be used to evaluate the deformation characteristics of soil specimen.

Table 1. Mass polar moment of inertia of each specimen and corresponding resonant frequencies from LSRC test.

Specimen ID I (kgmm2) fn (Hz) #1 10,683.74 37.7 #2 65.303.82 27.7 #3 132,316.39 22.1

Table 2. Determination of mass polar moment of inertia of the driving system from

LSRC test of 3 metal specimens.

Specimens K (Nm) I0 (kgmm2) I0 (average) #1 - #2 3,595.6 53,398 52,817


#2 - #3 3,555.0 52,057 #3 - #1 3,573.2 52,997

System Verification using Urethane Specimens The system compliance of testing equipment for evaluating mechanical properties of materials must be evaluated to verify its applicability (Kwon, 1999). To confirm this issue, three sets of urethane specimens with different rigidity were tested in the K-water LSRC testing system. Urethane specimen for system verification is known that the deformation modulus doesnt change with strain or confining stress level. Additionally, there is no effect of loading history on the deformation characteristics, so it is often used for verification of material testing equipment (Stokoe et al., 1990, Kwon, 1999). In this study, each urethane specimen with three different hardness and/or deformation moduli was cured in two different sizes to fit to normal resonant column (D=50mm, H=100mm) and the K-water LSRC (D=200mm, H=400mm) testing systems. Since the specimens in two different dimensions are made of same material, the test result can be directly compared and the accuracy of new LSRC testing system can be verified. Figure 5 shows the frequency response functions evaluated from the LSRC test of the hardest urethane specimen. A series of tests have been conducted increasing the excitation level to increase shear strain and the shear strain level ranged from 0.0001 to 0.01%. In the result, the resonance frequency doesnt change because stiffness of urethane specimen has no strain dependency as expected, while general geomaterials shows strain dependent stiffness characteristics. The experimental results from the LSRC test for three different urethane specimens are summarized in Table 3. In case of U60, it was difficult to evaluate the modulus and damping in broad strain range because the material was too soft to measure the response precisely.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

50 60 70 80 90 100

ACC.

am

plitu

de (V

rms)

Frequency (Hz)

fr

Figure 5. Frequency response of a urethane specimen U95 from LSRC test.

Table 3. LSRC test result of urethane specimen.

Specimen Strain range (%) fr (Hz) G (MPa) VS (m/s) D (%) U60 0.01 0.03 8.3 0.7 24.2 5.28 U80 0.002 0.05 32.2 11.9 106.1 2.72


U95 0.0001 0.01 72.5 52.9 223.1 8.08

Figure 6. Comparison of RC test results for large and normal scale urethane specimens.

For these three urethane materials with different hardness, results from both RC and LSRC tests are plotted together and compared in Figure 6. The shear moduli evaluated by two different systems are similar in all cases but LSRC test results tend to be slightly smaller than RC result except for U60 case which is too soft to be evaluated precisely. Even though the difference from these two testing systems is about 5%, the modulus and damping measured from the LSRC system is still in reasonable range. So the applicability and the system compliance could be verified and it can evaluate the deformation characteristics of the tested material precisely.

MEASUREMENT OF DYNAMIC DEFORMATION CHARACTERISTICS OF GRAVELLY MATERIAL

The performance and applicability of this system for evaluating deformation characteristics of gravelly materials have to be examined. The testing procedure and the results from a series of test are discussed in this section. Sample Preparations The first testing material to investigate the applicability of the K-water LSRC testing system has been chosen considering the maximum grain size which can be tested by preparing 200mm diameter specimen. The testing material is from the fill material of a newly constructed concrete faced rockfill dam (CFRD) in Korea, and is made by crushing sound granite. Originally the maximum grain size of rock fill material for the dam is about 1,500mm however it can never be tested by general lab testing equipment even by the new system. Therefore the material was prepared by parallel shifting of the grain size distribution to satisfy the maximum grain size requirement of the K-water LSRC testing system. The particle size distributions of the original and selected material for the test are shown in Figure 7. The maximum grain size of the tested material is 26mm and D50 is 2.3mm.


Figure 7. Grain size distribution of the fill material; original distribution and distribution

of tested material prepared by parallel shifting method

Figure 8 shows the sample and the preparation process for LSRC test. The grains from dried original sample were separated by sieve and then they were mixed all together to satisfy the parallel shifted distribution according to the maximum grain size 26mm. The sample was poured into a latex membrane in the steel mold. The sample was compacted by in five layers and the unit weight of the sample is 1.95kg/cm2. The sample prepared in the mold was moved and installed to the baseplate, and the driving system was installed at the top of the specimen.

(a) (b)

(c) (d)

Figure 8. Sample preparations for LSRC test; (a) testing material, (b) mold for sample preparation, (c) installation of the specimen, and (d) testing setup


Test Results After the specimen and the pressure chamber is secured in the testing system, the LSRC test is conducted with increasing confining pressure. The small strain shear modulus Gmax and the nonlinear deformation characteristics are highly dependent of effective stress level so the effect of confining stress needs to be verified. The test has been conducted from 25kPa confining stress and every test set has been conducted by increasing the confining stress twice up to 400kPa. During the test, it was difficult to determine the frequency response of the specimen in small strain level when specimen was tested under low confining pressure. The frequency response was too noisy to determine the modulus or damping ratio in this case and it is considered that the signal to noise ratio from the acceleration signal is too low. On the other hand, the largest shear strain level for the 400kPa case was limited to only 0.01% even though the excitation input was applied as maximum capacity of the driving system. Therefore, it will be necessary to improve the driving capacity to evaluate the nonlinear deformation characteristics of dense materials. Figure 9 and 10 show the result from LSRC test; shear modulus reduction and damping characteristics corresponding to shear stress level. The maximum shear modulus Gmax at small strain is generally expressed as a function of void ratio and effective stress (Hardin, 1978): 1-max = ( ) ( ') = '( ')

n n naG A F e P A (4)

and A is determined as 8.17 and n is determined as 0.595 from the experimental result. The elastic threshold strain, which means the shear strain level that shear modulus starts decreasing and the nonlinearity appears, for gravel is generally around 0.0001% (Seed et al., 1986) and these from the experimental result are between 0.0001 to 0.001%. Damping ratio starts increasing from near the elastic threshold strain and it generally decreases with confining stress. This trend could be observed in the experimental result.

0

50

100

150

200

250

300

350

0.00001 0.0001 0.001 0.01 0.1

Shea

r mod

ulus

(MPa

)

Shear strain (%)

25kPa

50kPa

100kPa

200kPa

400kPa

Figure 9. Modulus reduction curves of gravelly material at each confining stress level.


0

1

2

3

4

5

6

7

8

9

0.00001 0.0001 0.001 0.01 0.1

Dam

ping

ratio

(%)

Shear strain (%)

25kPa

50kPa

100kPa

200kPa

400kPa

Figure 10. Damping ratio of gravelly material at each confining stress level measured by

free vibration decay method

During the LSRC test for the gravelly material, it was difficult to precisely determine the frequency response and the damping ratio at low confining pressure. This problem is considered as the effect of not only low signal-to-noise ratio due to small response but also the mechanical noise caused by frictional behavior between the coarse grains. This irregularity can also make it difficult to measure reliable damping ratio in small strain range. The modulus reduction curve such as Figure 9 is often normalized by Gmax value to investigate the nonlinear deformation characteristics or to find deformation model parameters. Figure 11 shows the normalized modulus reduction curve derived from Figure 9. The elastic threshold strain of cohesionless soil, including gravel, generally tends to increase with confining pressure. However the result from this experiment shows an opposite trend. The reason for this phenomenon has to be investigated further. However, this trend could come from the effect of fine content in the soil sample. The tested material contains more than 30% of fine grain material which passes #200 sieve and this fine grained material can weaken the strong frictional behavior of coarse grains. Therefore, the modulus reduction characteristics in low confining pressure can be similar with sandy soil. On the other hand, the interactions and stresses through the chains of coarse grains can increase with the higher confining pressure so the deformation characteristics can be more similar to pure gravels. This hypothesis may explain the reason that the modulus reduction curve tends to decrease with confining pressure, but further investigation is necessary for clearer interpretation.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00001 0.0001 0.001 0.01 0.1

Nor

mal

ized

shea

r mod

ulus

(G/G

max

)

Shear strain (%)

25kPa

50kPa

100kPa

200kPa

400kPa

Figure 11. Normalized modulus reduction curves of the tested gravelly material.

CONCLUSIONS Dynamic deformation characteristics such as modulus reduction and damping characteristics of fill materials are the key parameters for seismic design and performance evaluation of dams. The K-water large scale resonant column testing system has been developed for this purpose and the application and its characteristics have been introduced in this article. The LSRC testing system was calibrated, and the applicability and system compliance were verified. The shear modulus reduction and damping curves of gravelly material in practical shear strain range could be evaluated using the testing system, and the applicability of the newly developed system could be confirmed. However, the deformation characteristics of the gravelly material have to be investigated in detail, especially when the sample is prepared by parallel shifting of grain size distribution. Furthermore, wide range of research on the effect of the soil classification parameters such as maximum grain size, fine content and grain size distribution on the deformation characteristic is required to better understand the deformation behavior of gravelly fill materials for dams.

ACKNOWLEDGEMENTS This study was supported by a grant from the Construction Technology Innovation Program (09-CTIP-F045) funded by the Minister of Land, Transport, and Maritime Affairs (MLTM) of the South Korean government. This financial assistance is gratefully acknowledged. Special thanks are to the reviewers for their revisions and helpful suggestions.

REFERENCES ASTM (2003) Standard test methods for modulus and damping of soils by resonant-column method, ASTM D4015


Clayton, C.R.I., Priest, M.B., Zervos, A., and Kim, S.G. (2009) The Stokoe resonant column apparatus: effects of stiffness, mass and specimen fixity, Geotechnique 59(5), pp. 429-437. Hardin, B.O. (1978) The nature of stress-strain behavior of soils, Proceedings of the ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, Pasadena, pp. 3-90. Hardin, B.O. and Kalinski, M.E. (2005) Estimating the shear modulus of gravelly soils, ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 131, No. 7, pp. 867-875. Hou, Y.J., Xu, Z.P., and Liang, J.H. (2004) Centrifuge modeling of cutoff wall for CFRD built in deep overburden. Proceedings of International Conference of Hydropower, Yichan, China, pp. 86-92. Kwon, G.C. (1999) Alternative MR testing methods for subgrade and subbase materials considering deformational characteristics of soils, Ph.D thesis, KAIST, Daejeon, Korea. Menq, F.Y. (2003) Dynamic properties of sandy and gravelly soils, Ph.D thesis, The University of Texas at Austin. Prange, B. (1981) Stochastic excitation of rock masses, Proceedings of 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Vo. 4, pp. 89-880. Richter, S. and Huber G. (2003) Resonant column tests with cohesive and non-cohesive granular materials, Geotechnical Measurement and Modelling, Natau, Fecker & Pimentel Eds. pp. 381-387. Seed, H.B., Wong, R.T., Idriss, I.M., and Tokimatsu, K. (1986). Moduli and damping factors for dynamic analyses of cohesionless soils, Journal of Geotechnical Engineering, ASCE, 112(11), pp. 1016-1032. Stokoe, K.H., Kim, D.S., and Andrus, R. (1990) Development of synthetic specimens for calibration and evaluation of MR equipment, Transportation Research Record 1278, TRB, National Research Council, Washington D.C., pp. 63-71. Woods, R.D. (1991) Field and laboratory determination of soil properties at low and high strains, Proceedings of 2nd International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, Missouri, Vol. 3, pp. 1727-1741.

a large scale resonant column testing system

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