DYNAMIC PROPERTIES OF SOLANI SAND UNDER CYCLIC LOADS ...
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Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
DYNAMIC PROPERTIES OF SOLANI SAND UNDER CYCLIC LOADS Suresh S. Kale1, B.K. Maheshwari2 and A.M. Kaynia3 ABSTRACT Roorkee is seismically vulnerable area under subduction zone of Himalayan region. This city has experienced earthquakes in the past and faces the danger of severe seismic threat in future also. Dynamic soil properties are very essential input parameters for any geotechnical earthquake engineering problem such as ground response analysis, soil structure interaction, and liquefaction. There is an imperative need for the studies on dynamic properties of soil in this region. Major area of Roorkee is covered by soil from the bed of Solani river i.e. Solani sand. In this paper, the strength characteristics of Solani sand are investigated by a series of cyclic triaxial tests, which has been never reported in the literature. Strain controlled undrained cyclic triaxial tests were performed to evaluate dynamic properties of the soil viz. shear modulus and damping ratio. The paper presents, effect of parameters such as relative density, amplitude of cyclic shear strain, confining pressure and frequency of cyclic loading on dynamic soil properties of Solani sand. The effect of cyclic shear strain on shear modulus and damping ratio are investigated. For this purpose, first hysteresis loop of the soil is evaluated. Modulus reduction curves are presented and compared with those available in the literature. INTRODUCTION Dynamic analyses to evaluate the response of the earth structures to dynamic stress applications, such as those produced by earthquakes, blasting, wind loading or machine vibrations are finding increased applications in civil engineering practice. Various idealized models and analytical techniques may be used to represent a soil deposit and its response, but whatever procedure is followed; it is first necessary to evaluate the appropriate dynamic properties of the soils in the deposit. The objective of the present study is to evaluate the strain dependent dynamic properties such as shear modulus and damping ratios of soils in strain controlled tests with the variation of various parameters. The parameters are, relative density of the sample, confining pressure and frequency of loading. Cyclic triaxial tests were carried out on the sand samples collected from bed of Solani River. Tests were 1
M. Tech Student, Dept. of Earthquake Engg., IIT Roorkee, [email protected] Associate Professor, Dept. of Earthquake Engg., IIT Roorkee, [email protected] 3 Discipline Leader, Earthquake Engineering, NGI, Oslo, Norway, [email protected] 2
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Fig. 1: Grain size distribution for Solani sand
conducted on Solani Sand Samples by varying different parameters such as number of cycles applied, relative density of soil specimen, confining pressure, frequency of loading and shear strain amplitude. INDEX PROPERTIES OF SOLANI SAND Fig. 1 presents grain size distribution (according to IS 2720 Part 4-1983) for Solani sand. Figure shows that the 80 % of the particle size falls in medium sand range and less than 5 % is passing through 0.075 mm sieve therefore as per Unified Soil Classification System, the soil can be classified as poorly graded sand i.e. SP type. The index properties are shown in Table 1. Specific gravity of the sample is determined according to IS: 2720 Part 3-1980. The maximum and minimum void ratios were determined in accordance with the procedure laid down in Indian Standard IS.: 2720 (Part-14-1986). Table 1: Index Properties of Solani River Sand Sr. No.
Particulars
Notations
1
Soil Type
SP
2 3 4
Specific Gravity of Grains Uniformity Co-efficient Co-efficient of Curvature
5
Grain Size
6 7
Maximum Void Ratio Minimum Void Ratio
G Cu Cc D50 D10 D30 D60 emax emin
Value Poorly graded Sand with little fines 2.64 1.769 1.207 0.215 0.13 0.19 0.23 0.927 0.553
SAMPLE PREPARATION There are three types of procedure widely used for the sample preparation for triaxial testing of saturated sands namely, (i) moist placement method (wet tamping), (ii) dry deposition method and (iii) water sedimentation method.
Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
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Fig. 2: Sample preparation by water sedimentation method
Primary need of all these methods is to obtain homogeneous samples with uniform distribution of void ratio to cover a wide range of density in samples reconstituted by an identical method. Different methods of sample reconstitution have been known to create different fabrics, thereby yielding different responses to load application (Ishihara 1993). The water sedimentation method has been used for sample preparation for this study (Fig. 2). For the preparation of saturated sample of sand at a particular relative density (Dr), the following sequential procedure has been evolved. a) The relative density (Dr) of sand is defined by a mathematical equation given by
Dr =
emax − e emax − emin
(1)
where Dr. is the relative density, emax is the maximum void ratio, emin is the minimum void ratio and e is the desired void ratio at a particular relative density of sand. b) The void ratio (e) corresponding to a relative density (Dr) of sand was calculated as
e = emax − Dr (emax − emin )
(2) The values of emax and emin are given in corresponding tables for various types of soil samples. c) Knowing the value of void ratio (e) obtained, dry unit weight of sand (γd) was determined by the following equation:
γd =
G γw 1+ e
(3)
where γ w is the unit weight of water (taken as 10 kN/m3) and Gs is the specific gravity of solids. d) Water content (w) required for 100 % saturation i.e. Sr = 1.0 was determined by
w=
e × Sr Gs
i.e.
w=
e Gs
e) Knowing the values of γ d equation:
Wd = γ d × V where, V is volume of the sample.
(4) and V, the dry weight of sand (Wd) was determined by the (5)
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f) Quantity of water (Ww) required for saturation was determined from
WW = w × Wd
g)
h) i)
j) k) l)
(6) Mould of desired size was fixed to the base pedal of corresponding triaxial cell with rubber membrane attached tightly to it, porous stone and wet filter paper was placed at the bottom of the mould. The amount of water required to achieve saturation is added into the mould. Quantity of water required for the particular Dr can be determined by equation 3.6 The quantity of dry sand (Wd) obtained in step (e) was poured into the water through funnel with a plastic tube attached to the end, keeping the tip of the funnel at a constant height from the water surface. The sample was prepared in four layers and tamped gently at each layer. Filter paper and porous stone was placed on top of the sample. Top cap with vacuum ring was placed on porous stone and rubber membrane is pulled over this assembly. Then rubber membrane was sealed with o-ring. Fig. 3 shows a sample of sand ready for testing.
Cyclic triaxial test were carried out on Solani sand sample of 70 mm diameter and 140 mm height with 3 different relative densities viz. 35%, 45% and 55%, three cell pressures i.e 100 kPa, 150 kPa and 200 kPa and three frequencies viz. 0.5 Hz, 1Hz and 1.5 Hz. 7 levels of axial strains were used for each combination of the parameters. Axial strain on which samples were tested are 0.025%, 0.05%, 0.075%, 0.1%, 0.2%, 0.5% and 0.7%. The combinations are given in Table 2. A total 49 samples were tested. Evaluation of Dynamic Properties of Soil When cyclic triaxial test are performed on soil specimen, a hysteresis loop similar to the one shown in Fig. 4 will be formed in the plot of deviator stress, σd, versus axial strain, є. The slope of the
Fig. 3: Sand sample ready for testing
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Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia Table 2: Combination of Parameters for Triaxial Testing on Solani Sand Test No.
Dr
Cell Pressure
Frequency
1 to 7
35 %
100 kPa
1.0 Hz
8 to 14
45 %
100 kPa
1.0 Hz
15 to 21
0.5 Hz
22 to 28 29 to 35
100 kPa
1.0 Hz 1.5 Hz
55%
36 to 42
150 kPa
1.0 Hz
43 to 49
200 kPa
1.0 Hz
secant line connecting the extreme points on the hysteresis loop is the dynamic Young’s modulus, E, which is given by, E = σd/є (7) Further, γ = (1+ν) є (8)
Fig. 4: Hysteretic stress-strain relationship for cyclic loading
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where G is the shear modulus, γ is the shear strain and ν is the Poisson’s ratio that may be taken as 0.5 for saturated undrained specimen. The damping ratio, D, is a measure of dissipated energy versus elastic strain energy and is computed by
D=
1 AL 4π AT
(9)
where, AL = Area enclosed by the hysteresis loop and AT = Area of the shaded triangle. EFFECT OF NUMBER OF CYCLES OF LOADING Fig 5 (a) show the typical deviatoric stress versus the axial strain plot for the first cycle of loading obtained from the strain controlled cyclic triaxial test on Solani sand for relative density of 55%. Frequency of the test was 1 Hz and the data was collected at every 4 millisecond i.e. 250 points were collected for one cycle. Fig 5 (b) shows shear stress versus shear strain plot. Slope of the line connecting maximum and minimum point of the loop shown in Fig 5 (b) gives shear modulus for the first cycle of the test.
G=
7.2 + 8.2 = 183.33 kPa 0.043 + 0.041
Damping ratio is calculated for the loop shown in Fig 5 (a). The area of the loop and the triangle is determined by using AOTOCAD software.
D=
1 767.93 1 AL × = = 0.2235 i.e. 22.3 % 4π 273.3 4π AT
Fig. 5 (a): Deviator stress vs. axial strain relationship at first cycle for Solani sand
Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
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Fig. 5 (a): Deviator stress vs. axial strain relationship at first cycle for Solani sand
Fig. 6 (a): Variation of shear modulus with number of cycles subjected to different axial strains
Fig 6 (a) and Fig 6 (b) show variation in shear modulus with number of cycles and variation of damping ratio with number of cycles, respectively. Figures show that, as the number of cycles increases the shear modulus and damping ratio of the soil decreases. The shear modulus decreases with increasing axial strain whereas damping ratio increases with increasing axial strain.
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Fig. 6 (b): Variation of damping ratio with number of cycles subjected to different axial strains
EFFECT OF RELATIVE DENSITY OF SOIL Effect of relative density on dynamic properties is examined with three different relative densities of 35 %, 45 % and 55 % at the same confining pressure of 100 kPa and frequency of 1 Hz. Table 3 illustrates the effect of relative density on dynamic properties of Solani sand samples. The effect of relative density on shear modulus becomes significant in the range of shear strains tested. However, the reduction in shear modulus and increase in damping vary significantly over a range of shear strain tested i.e. 0.03 % to 1.0 %. It can be noticed that shear modulus is increased with the increase in relative density for low shear strain level and it falls in a narrow band at high shear strain values. No particular pattern is seen for the damping ratios at lower shear strain values but they are almost same in the range of 0.1 % to 1 % shear strain. Comparing these results with the RaviShankar et al. (2005), GovindaRaju (2004), we can say that these are in close agreement. Also the effect of Dr on damping ratio is not very significant. Table 3: Effect of relative density on dynamic properties of Solani sand Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12
RD (%)
Dr = 35%
Dr = 45%
Dr = 55%
Shear Strain Level (%) 0.038 0.075 0.105 0.150 0.038
Shear Modulus G (kPa) 14338 8684 7306 637 20586
Damping Ratio 7.73 9.10 9.47 10.00 9.97
0.075
112066
8.30
0.113 0.150 0.038 0.075 0.113 0.150
95406 76306 22885 13785 11436 8694
8.84 10.03 9.81 9.65 10.85 11.00
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EFFECT OF CONFINING PRESSURE The influence of confining stress on the strain dependent shear modulus is particularly important when dealing in problem in which pore water pressure build up occurs in the sand in the course of cyclic loading. Strain controlled cyclic tests were carried out on Solani sand at a relative density of 55 % subjected to confining pressure of 100 kPa, 150 kPa and 200 kPa. All the tests were conducted at a loading frequency of 1 Hz with sinusoidal wave. The influence of confining stress on the shear modulus values of Solani sand are illustrated in Table 4. A considerable effect of confining pressure on the shear modulus can be noticed at low strain level. As the confining pressure increases shear modulus increases significantly. Further, the damping ratio decreases with increase in confining pressure. Higher values of damping are noticed at lower confining pressure. Table 4: Effect of confining pressure on dynamic properties of Solani sand Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Confining Pressure (kPa) 100
150
200
Axial Strain Level (%)
Shear Strain Level (%)
0.025 0.050 0.075 0.100 0.025 0.050 0.075 0.100 0.200 0.025 0.050 0.075 0.100 0.200
0.038 0.075 0.113 0.150 0.038 0.075 0.113 0.150 0.300 0.038 0.075 0.113 0.150 0.300
Shear Modulus G (kPa) 22885 13785 11436 8694 29902 28314 26578 22863 4496 46252 45054 43850 40440 27792
Damping Ratio 9.81 9.65 10.85 11.00 8.50 8.20 9.00 9.50 13.00 7.11 6.70 7.10 8.07 11.32
The values of shear modulus are found to be converging at high shear strain level. At high shear strain, values of shear modulus are in the same range irrespective of the confining pressure. However there is small variation in damping ratio with confining pressure. The results are in close agreement with the results reported by Kokusho (1980), Silver and Seed (1971) and Hardin and Drnevich (1972) EFFECT OF FREQUENCY OF EXCITATION Strain controlled cyclic triaxial tests were carried out on saturated Solani sand of 55 % relative density at confining pressure of 100 kPa. All the samples were subjected to cyclic loading in undrained condition with harmonic sinusoidal loading frequencies of 0.5 Hz, 1.0 Hz and 1.5 Hz. Table 5 illustrates variation of shear modulus and damping ratio with shear strain at various frequencies.From the Table 5, it is found that the range of frequencies used in the testing does not
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significantly affect the shear modulus values. These findings are in close agreement with the results reported by Govindaraju (2005), Drnevich and Richart (1970) and Iwasaki et al. (1978) leading to the conclusion that the frequency of loading in the ranges tested does not affect the response of sands to cyclic loading. Further, It is observed that the damping ratios are affected to some extent by the frequency of loading. Higher damping ratios are noticed at higher frequencies in the range of shear strains tested. Table 5: Effect of frequency of loading on dynamic properties of Solani sand Samples Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Freqency (Hz)
0.5
1
1.5
Shear Strain Level (%) 0.038 0.075 0.113 0.150 0.300 0.750 0.038 0.075 0.113 0.150 0.750 0.038 0.075 0.113 0.150 0.300 0.750
Shear Modulus G (kPa) 23740 15876 13574 9907 5686 2633 22885 13784 11436 8694 841 22531 14890 14337 9408 6845 2080
Damping Ratio 7.46 8.33 8.07 9.45 13.45 15.45 9.81 9.65 10.85 11.00 15.37 10.30 11.34 10.95 13.20 16.04 16.49
CONCLUSION As the number of cycles of loading increases the shear modulus and the damping ratio of the soil decreases. Relative density has significant effect on shear modulus values at lower shear strain levels but at large strain levels the effect is not so significant. Also, relative density does not significantly affect damping properties of the sand. Studies on Solani sand related to the effect of confining pressure on strain dependent dynamic properties, demonstrates that as the confining pressure increases the shear modulus increases significantly and the damping ratio decreases correspondingly in the range of shear strain tested. The effect of frequency on the dynamic properties of Solani sand indicates that frequency of loading does not significantly affect the shear modulus value in the range of shear strain tested. However, the damping ratios are affected to some extent by the frequency of loading. Higher damping ratios are noticed at higher frequencies.
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ACKNOWLEDGEMENT The Cyclic Triaxial System used for experiments was procured from the financial assistance received from Seismology Division, Ministry of Earth Science, Govt. of India. This support is gratefully acknowledged. The preparation of soil samples and use of triaxial testing system was learned during second author’s visit to NGI, Oslo. This interaction is thankfully acknowledged. REFERENCES 1.
2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13.
ASTM D3999-91 (2003), “Test method for the determination of the modulus and damping properties of soils using the cyclic triaxial aapparatus”, Annual book of ASTM standards, ASTM international, West Cnhohocken, PA. Drnevich, V. P. and Richart, F. E. Jr. (1970), “Dynamic prestraining of dry sand”, Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. SM6, June , pp. 603-624. Govindaraju, L. (2005), “liquefaction and dynamic properties of sandy soils”, Ph. D. Thesis, IISC Bangalore, Karnataka, India. Hardin, B. O. and Drnevich, V. P. (1972), “Shear modulus and damping in soils: Measurement and Parameters effects”, Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 96, No. SM2, March, pp. 453-469. IS: 1498-1970, “Classification and Identification of Soil for General Engineering Purposes”, BIS, New Delhi, India. IS: 2720 (Part 3) -1980, “Methods of test for Soils-Determination of Specific Gravity”, BIS, New Delhi, India. IS: 2720 (Part 4) -1983, “Methods of Test for Soils Grain Size Analysis”, BIS, New Delhi, India. IS: 2720 (Part 14) -1986, “Methods of Test for Soils-Determination of Density Index (Relative Density) of Cohesionless Soils”, BIS, New Delhi, India. Ishihara, K. (1993), “Liquefaction and flow failure during earthquakes”, Geotechnique, Vol. 43, No. 3, pp. 351-415. Iwasaki, T., Tatsuoka, F. and Takagi, Y. (1978), “Shear moduli of sands under cyclic torsional shear loading”, Soils and Foundations, Vol. 18, No. 1, pp. 39-56. Kokusho, T. (1980), “Cyclic triaxiaal test of dynamic soil properties for wide strain range”, Soils and Foundations, Vol. 20, No. 2, pp. 45-59. RaviShankar, B. V., Sitharam, T. G. and Govindaraju, L. (2005), “Dynamic properties of Ahmedabad sands at large strains”, IGC, Ahmedabad, pp. 369-372. Silver, M. L. and Seed, H. B. (1971), “Volume changes in sands during cyclic loading”, Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM9, Proc. Paper No. 1171.
Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
DYNAMIC PROPERTIES OF SOLANI SAND UNDER CYCLIC LOADS Suresh S. Kale1, B.K. Maheshwari2 and A.M. Kaynia3 ABSTRACT Roorkee is seismically vulnerable area under subduction zone of Himalayan region. This city has experienced earthquakes in the past and faces the danger of severe seismic threat in future also. Dynamic soil properties are very essential input parameters for any geotechnical earthquake engineering problem such as ground response analysis, soil structure interaction, and liquefaction. There is an imperative need for the studies on dynamic properties of soil in this region. Major area of Roorkee is covered by soil from the bed of Solani river i.e. Solani sand. In this paper, the strength characteristics of Solani sand are investigated by a series of cyclic triaxial tests, which has been never reported in the literature. Strain controlled undrained cyclic triaxial tests were performed to evaluate dynamic properties of the soil viz. shear modulus and damping ratio. The paper presents, effect of parameters such as relative density, amplitude of cyclic shear strain, confining pressure and frequency of cyclic loading on dynamic soil properties of Solani sand. The effect of cyclic shear strain on shear modulus and damping ratio are investigated. For this purpose, first hysteresis loop of the soil is evaluated. Modulus reduction curves are presented and compared with those available in the literature. INTRODUCTION Dynamic analyses to evaluate the response of the earth structures to dynamic stress applications, such as those produced by earthquakes, blasting, wind loading or machine vibrations are finding increased applications in civil engineering practice. Various idealized models and analytical techniques may be used to represent a soil deposit and its response, but whatever procedure is followed; it is first necessary to evaluate the appropriate dynamic properties of the soils in the deposit. The objective of the present study is to evaluate the strain dependent dynamic properties such as shear modulus and damping ratios of soils in strain controlled tests with the variation of various parameters. The parameters are, relative density of the sample, confining pressure and frequency of loading. Cyclic triaxial tests were carried out on the sand samples collected from bed of Solani River. Tests were 1
M. Tech Student, Dept. of Earthquake Engg., IIT Roorkee, [email protected] Associate Professor, Dept. of Earthquake Engg., IIT Roorkee, [email protected] 3 Discipline Leader, Earthquake Engineering, NGI, Oslo, Norway, [email protected] 2
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Fig. 1: Grain size distribution for Solani sand
conducted on Solani Sand Samples by varying different parameters such as number of cycles applied, relative density of soil specimen, confining pressure, frequency of loading and shear strain amplitude. INDEX PROPERTIES OF SOLANI SAND Fig. 1 presents grain size distribution (according to IS 2720 Part 4-1983) for Solani sand. Figure shows that the 80 % of the particle size falls in medium sand range and less than 5 % is passing through 0.075 mm sieve therefore as per Unified Soil Classification System, the soil can be classified as poorly graded sand i.e. SP type. The index properties are shown in Table 1. Specific gravity of the sample is determined according to IS: 2720 Part 3-1980. The maximum and minimum void ratios were determined in accordance with the procedure laid down in Indian Standard IS.: 2720 (Part-14-1986). Table 1: Index Properties of Solani River Sand Sr. No.
Particulars
Notations
1
Soil Type
SP
2 3 4
Specific Gravity of Grains Uniformity Co-efficient Co-efficient of Curvature
5
Grain Size
6 7
Maximum Void Ratio Minimum Void Ratio
G Cu Cc D50 D10 D30 D60 emax emin
Value Poorly graded Sand with little fines 2.64 1.769 1.207 0.215 0.13 0.19 0.23 0.927 0.553
SAMPLE PREPARATION There are three types of procedure widely used for the sample preparation for triaxial testing of saturated sands namely, (i) moist placement method (wet tamping), (ii) dry deposition method and (iii) water sedimentation method.
Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
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Fig. 2: Sample preparation by water sedimentation method
Primary need of all these methods is to obtain homogeneous samples with uniform distribution of void ratio to cover a wide range of density in samples reconstituted by an identical method. Different methods of sample reconstitution have been known to create different fabrics, thereby yielding different responses to load application (Ishihara 1993). The water sedimentation method has been used for sample preparation for this study (Fig. 2). For the preparation of saturated sample of sand at a particular relative density (Dr), the following sequential procedure has been evolved. a) The relative density (Dr) of sand is defined by a mathematical equation given by
Dr =
emax − e emax − emin
(1)
where Dr. is the relative density, emax is the maximum void ratio, emin is the minimum void ratio and e is the desired void ratio at a particular relative density of sand. b) The void ratio (e) corresponding to a relative density (Dr) of sand was calculated as
e = emax − Dr (emax − emin )
(2) The values of emax and emin are given in corresponding tables for various types of soil samples. c) Knowing the value of void ratio (e) obtained, dry unit weight of sand (γd) was determined by the following equation:
γd =
G γw 1+ e
(3)
where γ w is the unit weight of water (taken as 10 kN/m3) and Gs is the specific gravity of solids. d) Water content (w) required for 100 % saturation i.e. Sr = 1.0 was determined by
w=
e × Sr Gs
i.e.
w=
e Gs
e) Knowing the values of γ d equation:
Wd = γ d × V where, V is volume of the sample.
(4) and V, the dry weight of sand (Wd) was determined by the (5)
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f) Quantity of water (Ww) required for saturation was determined from
WW = w × Wd
g)
h) i)
j) k) l)
(6) Mould of desired size was fixed to the base pedal of corresponding triaxial cell with rubber membrane attached tightly to it, porous stone and wet filter paper was placed at the bottom of the mould. The amount of water required to achieve saturation is added into the mould. Quantity of water required for the particular Dr can be determined by equation 3.6 The quantity of dry sand (Wd) obtained in step (e) was poured into the water through funnel with a plastic tube attached to the end, keeping the tip of the funnel at a constant height from the water surface. The sample was prepared in four layers and tamped gently at each layer. Filter paper and porous stone was placed on top of the sample. Top cap with vacuum ring was placed on porous stone and rubber membrane is pulled over this assembly. Then rubber membrane was sealed with o-ring. Fig. 3 shows a sample of sand ready for testing.
Cyclic triaxial test were carried out on Solani sand sample of 70 mm diameter and 140 mm height with 3 different relative densities viz. 35%, 45% and 55%, three cell pressures i.e 100 kPa, 150 kPa and 200 kPa and three frequencies viz. 0.5 Hz, 1Hz and 1.5 Hz. 7 levels of axial strains were used for each combination of the parameters. Axial strain on which samples were tested are 0.025%, 0.05%, 0.075%, 0.1%, 0.2%, 0.5% and 0.7%. The combinations are given in Table 2. A total 49 samples were tested. Evaluation of Dynamic Properties of Soil When cyclic triaxial test are performed on soil specimen, a hysteresis loop similar to the one shown in Fig. 4 will be formed in the plot of deviator stress, σd, versus axial strain, є. The slope of the
Fig. 3: Sand sample ready for testing
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Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia Table 2: Combination of Parameters for Triaxial Testing on Solani Sand Test No.
Dr
Cell Pressure
Frequency
1 to 7
35 %
100 kPa
1.0 Hz
8 to 14
45 %
100 kPa
1.0 Hz
15 to 21
0.5 Hz
22 to 28 29 to 35
100 kPa
1.0 Hz 1.5 Hz
55%
36 to 42
150 kPa
1.0 Hz
43 to 49
200 kPa
1.0 Hz
secant line connecting the extreme points on the hysteresis loop is the dynamic Young’s modulus, E, which is given by, E = σd/є (7) Further, γ = (1+ν) є (8)
Fig. 4: Hysteretic stress-strain relationship for cyclic loading
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where G is the shear modulus, γ is the shear strain and ν is the Poisson’s ratio that may be taken as 0.5 for saturated undrained specimen. The damping ratio, D, is a measure of dissipated energy versus elastic strain energy and is computed by
D=
1 AL 4π AT
(9)
where, AL = Area enclosed by the hysteresis loop and AT = Area of the shaded triangle. EFFECT OF NUMBER OF CYCLES OF LOADING Fig 5 (a) show the typical deviatoric stress versus the axial strain plot for the first cycle of loading obtained from the strain controlled cyclic triaxial test on Solani sand for relative density of 55%. Frequency of the test was 1 Hz and the data was collected at every 4 millisecond i.e. 250 points were collected for one cycle. Fig 5 (b) shows shear stress versus shear strain plot. Slope of the line connecting maximum and minimum point of the loop shown in Fig 5 (b) gives shear modulus for the first cycle of the test.
G=
7.2 + 8.2 = 183.33 kPa 0.043 + 0.041
Damping ratio is calculated for the loop shown in Fig 5 (a). The area of the loop and the triangle is determined by using AOTOCAD software.
D=
1 767.93 1 AL × = = 0.2235 i.e. 22.3 % 4π 273.3 4π AT
Fig. 5 (a): Deviator stress vs. axial strain relationship at first cycle for Solani sand
Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
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Fig. 5 (a): Deviator stress vs. axial strain relationship at first cycle for Solani sand
Fig. 6 (a): Variation of shear modulus with number of cycles subjected to different axial strains
Fig 6 (a) and Fig 6 (b) show variation in shear modulus with number of cycles and variation of damping ratio with number of cycles, respectively. Figures show that, as the number of cycles increases the shear modulus and damping ratio of the soil decreases. The shear modulus decreases with increasing axial strain whereas damping ratio increases with increasing axial strain.
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Fig. 6 (b): Variation of damping ratio with number of cycles subjected to different axial strains
EFFECT OF RELATIVE DENSITY OF SOIL Effect of relative density on dynamic properties is examined with three different relative densities of 35 %, 45 % and 55 % at the same confining pressure of 100 kPa and frequency of 1 Hz. Table 3 illustrates the effect of relative density on dynamic properties of Solani sand samples. The effect of relative density on shear modulus becomes significant in the range of shear strains tested. However, the reduction in shear modulus and increase in damping vary significantly over a range of shear strain tested i.e. 0.03 % to 1.0 %. It can be noticed that shear modulus is increased with the increase in relative density for low shear strain level and it falls in a narrow band at high shear strain values. No particular pattern is seen for the damping ratios at lower shear strain values but they are almost same in the range of 0.1 % to 1 % shear strain. Comparing these results with the RaviShankar et al. (2005), GovindaRaju (2004), we can say that these are in close agreement. Also the effect of Dr on damping ratio is not very significant. Table 3: Effect of relative density on dynamic properties of Solani sand Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12
RD (%)
Dr = 35%
Dr = 45%
Dr = 55%
Shear Strain Level (%) 0.038 0.075 0.105 0.150 0.038
Shear Modulus G (kPa) 14338 8684 7306 637 20586
Damping Ratio 7.73 9.10 9.47 10.00 9.97
0.075
112066
8.30
0.113 0.150 0.038 0.075 0.113 0.150
95406 76306 22885 13785 11436 8694
8.84 10.03 9.81 9.65 10.85 11.00
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Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
EFFECT OF CONFINING PRESSURE The influence of confining stress on the strain dependent shear modulus is particularly important when dealing in problem in which pore water pressure build up occurs in the sand in the course of cyclic loading. Strain controlled cyclic tests were carried out on Solani sand at a relative density of 55 % subjected to confining pressure of 100 kPa, 150 kPa and 200 kPa. All the tests were conducted at a loading frequency of 1 Hz with sinusoidal wave. The influence of confining stress on the shear modulus values of Solani sand are illustrated in Table 4. A considerable effect of confining pressure on the shear modulus can be noticed at low strain level. As the confining pressure increases shear modulus increases significantly. Further, the damping ratio decreases with increase in confining pressure. Higher values of damping are noticed at lower confining pressure. Table 4: Effect of confining pressure on dynamic properties of Solani sand Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Confining Pressure (kPa) 100
150
200
Axial Strain Level (%)
Shear Strain Level (%)
0.025 0.050 0.075 0.100 0.025 0.050 0.075 0.100 0.200 0.025 0.050 0.075 0.100 0.200
0.038 0.075 0.113 0.150 0.038 0.075 0.113 0.150 0.300 0.038 0.075 0.113 0.150 0.300
Shear Modulus G (kPa) 22885 13785 11436 8694 29902 28314 26578 22863 4496 46252 45054 43850 40440 27792
Damping Ratio 9.81 9.65 10.85 11.00 8.50 8.20 9.00 9.50 13.00 7.11 6.70 7.10 8.07 11.32
The values of shear modulus are found to be converging at high shear strain level. At high shear strain, values of shear modulus are in the same range irrespective of the confining pressure. However there is small variation in damping ratio with confining pressure. The results are in close agreement with the results reported by Kokusho (1980), Silver and Seed (1971) and Hardin and Drnevich (1972) EFFECT OF FREQUENCY OF EXCITATION Strain controlled cyclic triaxial tests were carried out on saturated Solani sand of 55 % relative density at confining pressure of 100 kPa. All the samples were subjected to cyclic loading in undrained condition with harmonic sinusoidal loading frequencies of 0.5 Hz, 1.0 Hz and 1.5 Hz. Table 5 illustrates variation of shear modulus and damping ratio with shear strain at various frequencies.From the Table 5, it is found that the range of frequencies used in the testing does not
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significantly affect the shear modulus values. These findings are in close agreement with the results reported by Govindaraju (2005), Drnevich and Richart (1970) and Iwasaki et al. (1978) leading to the conclusion that the frequency of loading in the ranges tested does not affect the response of sands to cyclic loading. Further, It is observed that the damping ratios are affected to some extent by the frequency of loading. Higher damping ratios are noticed at higher frequencies in the range of shear strains tested. Table 5: Effect of frequency of loading on dynamic properties of Solani sand Samples Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Freqency (Hz)
0.5
1
1.5
Shear Strain Level (%) 0.038 0.075 0.113 0.150 0.300 0.750 0.038 0.075 0.113 0.150 0.750 0.038 0.075 0.113 0.150 0.300 0.750
Shear Modulus G (kPa) 23740 15876 13574 9907 5686 2633 22885 13784 11436 8694 841 22531 14890 14337 9408 6845 2080
Damping Ratio 7.46 8.33 8.07 9.45 13.45 15.45 9.81 9.65 10.85 11.00 15.37 10.30 11.34 10.95 13.20 16.04 16.49
CONCLUSION As the number of cycles of loading increases the shear modulus and the damping ratio of the soil decreases. Relative density has significant effect on shear modulus values at lower shear strain levels but at large strain levels the effect is not so significant. Also, relative density does not significantly affect damping properties of the sand. Studies on Solani sand related to the effect of confining pressure on strain dependent dynamic properties, demonstrates that as the confining pressure increases the shear modulus increases significantly and the damping ratio decreases correspondingly in the range of shear strain tested. The effect of frequency on the dynamic properties of Solani sand indicates that frequency of loading does not significantly affect the shear modulus value in the range of shear strain tested. However, the damping ratios are affected to some extent by the frequency of loading. Higher damping ratios are noticed at higher frequencies.
Suresh S. Kale, B.K. Maheshwari and A.M. Kaynia
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ACKNOWLEDGEMENT The Cyclic Triaxial System used for experiments was procured from the financial assistance received from Seismology Division, Ministry of Earth Science, Govt. of India. This support is gratefully acknowledged. The preparation of soil samples and use of triaxial testing system was learned during second author’s visit to NGI, Oslo. This interaction is thankfully acknowledged. REFERENCES 1.
2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13.
ASTM D3999-91 (2003), “Test method for the determination of the modulus and damping properties of soils using the cyclic triaxial aapparatus”, Annual book of ASTM standards, ASTM international, West Cnhohocken, PA. Drnevich, V. P. and Richart, F. E. Jr. (1970), “Dynamic prestraining of dry sand”, Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. SM6, June , pp. 603-624. Govindaraju, L. (2005), “liquefaction and dynamic properties of sandy soils”, Ph. D. Thesis, IISC Bangalore, Karnataka, India. Hardin, B. O. and Drnevich, V. P. (1972), “Shear modulus and damping in soils: Measurement and Parameters effects”, Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 96, No. SM2, March, pp. 453-469. IS: 1498-1970, “Classification and Identification of Soil for General Engineering Purposes”, BIS, New Delhi, India. IS: 2720 (Part 3) -1980, “Methods of test for Soils-Determination of Specific Gravity”, BIS, New Delhi, India. IS: 2720 (Part 4) -1983, “Methods of Test for Soils Grain Size Analysis”, BIS, New Delhi, India. IS: 2720 (Part 14) -1986, “Methods of Test for Soils-Determination of Density Index (Relative Density) of Cohesionless Soils”, BIS, New Delhi, India. Ishihara, K. (1993), “Liquefaction and flow failure during earthquakes”, Geotechnique, Vol. 43, No. 3, pp. 351-415. Iwasaki, T., Tatsuoka, F. and Takagi, Y. (1978), “Shear moduli of sands under cyclic torsional shear loading”, Soils and Foundations, Vol. 18, No. 1, pp. 39-56. Kokusho, T. (1980), “Cyclic triaxiaal test of dynamic soil properties for wide strain range”, Soils and Foundations, Vol. 20, No. 2, pp. 45-59. RaviShankar, B. V., Sitharam, T. G. and Govindaraju, L. (2005), “Dynamic properties of Ahmedabad sands at large strains”, IGC, Ahmedabad, pp. 369-372. Silver, M. L. and Seed, H. B. (1971), “Volume changes in sands during cyclic loading”, Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM9, Proc. Paper No. 1171.
