EFFECT OF STRONG MOTION PARAMETERS ON THE RESPONSE OF SOIL USING CYCLIC TRIAXIAL TESTS

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1 ICOVP, 13 th International Conference on Vibration Problems 29 th November 2 nd December, 217, Indian Institute of Technology Guwahati, INDIA EFFECT OF STRONG MOTION PARAMETERS ON THE RESPONSE OF SOIL USING CYCLIC TRIAXIAL TESTS SHIV SHANKAR KUMAR CR, PR, A. MURALI KRISHNA, ARINDAM DEY Indian Institute of Technology Guwahati, Assam 78139, India k.shiv@iitg.ernet.in, amurali@iitg.ernet.in, arindam.dey@iitg.ernet.in Abstract. Dynamic response of soil is significantly affected by stress history and the frequency contents of irregular vibration corresponding to PGA levels. This paper addresses the effect of strong motion parameters on the response of saturated sandy soil. Stress-controlled cyclic triaxial tests have been conducted at different relative densities (3%-9%) and confining pressures (5-15kPa). Cyclic loading in terms of irregular stress, evaluated using simplified procedure proposed by Seed and Idriss (1971), was applied on the test specimens. The responses have been presented in terms of excess pore-water pressure ratio and shear strain accumulation in the soil specimens. The results indicated that the accumulated shear strains and excess porewater pressures in the soil specimens is significantly affected by the increase in confining depth and simultaneous changes in the relative density. Further, the study emphasized that the strong motions scaled to the same PGA levels produce substantially differing soil response due to the variation in the associated strong motion parameters. Keywords: Irregular seismic excitation, Strong motion parameters, Cyclic triaxial test, Cohesionless soil,, Excess pore-water pressure 1. Introduction Dynamic behaviour of soils and associated liquefaction aspects are very important considerations in earthquake geotechnical engineering. To study the dynamic behaviour and subsequent evaluation of dynamic soil properties, different laboratory tests using variety of test specimen and loading conditions are conducted (Seed and Idriss, 197; Hardin and Drnevich, 1972; Iwasaki et al., 1978; Kokusho et al., 1982; Seed et al., 1986; Chung et al., 1989; Vucetic and Dobry, 1991; Ishibashi and Zhang, 1993; Stokoe et al., 1995; Sitharam and Govindaraju, 23). Most of the tests, in general, use regular harmonic excitations as cyclic loading. However, it is very well established that the behaviour of soil under real earthquake excitation (irregular) is largely different in comparison to the regular harmonic excitations. This is mainly due to wide range of frequency content and associated ground motion parameters in the irregular motions. Shear stresses induced by real-time strong motions are extremely irregular and possesses erratic temporal variation of magnitude and frequency. Hence, it is very essential to study the behaviour of soil under real seismic excitations. Instances of investigation of soil response in the laboratory using real earthquake motion are very limited (Ishihara and Yasuda, 1972, 1973, 1975; Tsukamoto et al., 24; Sawada et al., 26). The dynamic behaviour of soils is influenced by various parameters, namely stress or strain levels (magnitude of earthquake), soil type, saturation state of soil and in-situ stress conditions. Several researchers have performed cyclic triaxial tests under variety of test conditions to anticipate the effect of the abovementioned parameters (Seed and Lee, 1966; Dobry et al., 1982; Vucetic and Dobry, 1988;

2 2 Kumar, Krishna, Dey Ladd et al., 1989; Ishihara, 1996). Due to the versatility in simulating medium to large strains in the soil sample, cyclic triaxial tests have been extensively used for investigating the dynamic behaviour of soil. In most of the literatures, tests were conducted with different irregular excitations at either a particular relative density or a particular confining pressure. The present study deals with the effect of relative density, confining pressure and the strong motion parameters on the response of soil in terms of accumulated shear strains and excess pore-water pressure. In the present study, response of Brahmaputra sand subjected to irregular seismic excitations has been investigated through cyclic triaxial tests. The tests have been conducted at different confining pressures (σʹc = 5, 1, and 15 kpa) on the specimens prepared at different relative densities (Dr = 3, 6 and 9%). Test specimens subjected to different confining pressures represent the soils in the field located at different confining depths i.e. 5 m, 1 m and 15 m. The specimens were subjected to three different real earthquake excitations, namely Kobe (1995; PGA =.834g), Bhuj (21; PGA =.13g), and Tezpur (212; Scaled PGA =.36g) strong motions. The results were reported in terms of the excess pore-water pressure and shear strain accumulations. 2. Experimental Investigation 2.1. Soil Characteristics Brahmaputra river sand (BS), collected from Guwahati region, Assam (India) has been used for the present study. The particle size distribution of the sand, obtained from sieve analysis (IS: 272-IV), is shown in Fig. 1 which reflects that the soil falls within the zone of severely liquefaction susceptible soils (Tsuchida, 197; Ishihara et al. 198; Xenaki and Athanasopoulos, 23). The specific gravity of the sand was found to be 2.7 (IS: 272-III). The minimum and maximum dry unit weight (IS: 272-XIV) were found to be kn/m 3 and kn/m 3, respectively. The physical properties of the sand are summarized in Table 1. Based on the obtained results, BS classified as poorly graded sand (SP) (ASTM D2487). Percentage finer Boundry for partially liquefiable zone Boundry for severely liquefiable zone Brahmaputra sand 1E Praticle size (mm) Figure.1. Particle size distribution 2.2. Testing Apparatus Cyclic triaxial apparatus, facilitating both monotonic as well as cyclic loading, was used for the experimental investigations. The apparatus consists a loading frame of 1 kn, fitted with a pneumatic dynamic actuator, having a displacement range and operational

3 Effect of strong motion parameters on the response of soil using cyclic triaxial tests 3 frequency range of -3 mm and.1-1 Hz, respectively. The details of instrumentations available with the apparatus has been described in Kumar et al. (217a) Sample Preparation Figure.2. Cyclic triaxial setup and components Dry pluviation technique was adopted to prepare the cylindrical specimens of BS having 7 mm diameter and 14 mm height (ASTM D5311). A nominal vacuum pressure of 15-2 kpa has been used to maintain verticality of the specimen (Ishihara et al. 1978). In order to achieve a quick saturation and a substantial replacement of the pore-air, carbon dioxide (CO2), in gaseous form, was flushed through the specimen, for 1-15 minutes, with a pressure lesser than the applied cell pressure, followed by flushing with de-aired water. To attain the saturation, the cell pressure (CP) and back pressure (BP) were then gradually increased in stages while maintaining an almost constant differential pressure of 1 kpa and checking the pore pressure parameter (B) after each increment of CP. The saturation process was terminated as the back pressure (BP) reached 2 kpa and the corresponding B-value was obtained to be greater than.96. The test specimens were consolidated to the targeted effective stress levels, and were subsequently subjected to cyclic loading Irregular Seismic Excitations Three different irregular stress time histories, computed from the acceleration histories of Bhuj (21; PGA =.13g), Tezpur (212; Scaled PGA =.36g) and Kobe (1995; PGA =.834g) strong motions, have been used to evaluate the dynamic response of soil. The associated ground motion parameters of these earthquakes obtained from seismosignal are presented in Table 1. Figure 3 represents the acceleration histories and their corresponding frequency content obtained by the Fast Fourier Transformations (FFT) of the strong motions. Frequency-domain representation indicates the variation of energy content over a frequency band. It is observed that the significant energy content of Bhuj and Kobe strong motions are congregated over a frequency band of.5-4 Hz, while the same for Tezpur motion is found to be at 2-15 Hz. Apart from these acceleration histories of different PGA, all the ground motions were scaled to similar PGA levels (.13 g and.36 g) for few of

4 4 Kumar, Krishna, Dey the tests. Table 2 presents the ground motion parameters of scaled PGA to.13g of different earthquake motions. It can be observed that the three scaled ground motions (PGA =.13g) are also different because of the associated ground motion parameters such as predominant period (fundamental frequency), duration and energy levels. Acceleration (g) Bhuj (.13g) Tezpur (.36g) Kobe (.834g) Time (s) FFT (g-s) Hz Bhuj motion Hz.12 Tezpur motion Hz.6.4 Kobe motion Frequency (Hz) Figure.3. Acceleration time histories and frequency domain representation of input motion Table.1. Strong motion parameters for different earthquakes used for the analysis Strong Tezpur Bhuj motion parameters Tezpur (Scaled motion) Kobe Magnitude Station Ahmadabad TZP TZP KJMA Site Class B B B B Distance from source 238 km km Max. PGA (g) Predominant period (sec) Mean period (sec) Bracketed duration (sec) Significant duration (sec) Arias intensity (m/sec) Specific energy density (cm 2 /sec) Cumulative absolute velocity (cm/sec) v max/a max (sec) Table.2. Ground motion parameters of scaled PGA =.13g of different earthquake motions Strong motion parameters 21 Bhuj 212 Tezpur 1995 Kobe Predominant period (s) Mean period (s) Bracketed duration (s) Significant duration (s) Arias intensity (m/s) Specific energy density (cm 2 /s) v max/a max (s) Cyclic loading has been applied on the test specimen in terms of cyclic stress history, which was evaluated based on the accelerations and the effective stress on the sample. It was considered that the specimens tested at different effective confining stress are assumed to be located at different confining depths below the ground level. To evaluate the irregular shear stress ( ) history induced by a real-time earthquake at any depth z within a soil

5 Effect of strong motion parameters on the response of soil using cyclic triaxial tests 5 deposit, the approach proposed by Seed and Idriss (1971), as exhibited by Eqn. 1, has been adopted. acc. ( g) = ' c rd (1) g r z; for z 9.15 m (2a) d r z; for 9.15 z 23m (2b) d acc. ( g) d 2 = 2 ' c r (3) d g where, acc. (g) is the acceleration time history, σʹc is the effective confining stress and rd is the stress reduction factor (Eqn. 2; Youd et al. 21) accounting for the deformable characteristics of the soil specimen. The deviatoric stress history, to be applied during the experiment, was evaluated from the strong motion stress histories as per Eqn. 3. Cyclic stress ratio (CSR) of the cyclic loading can be evaluated as /σʹc. Figure 4 shows typical applied deviatoric stress time histories of different ground motions with different PGA for a test specimen at 1 kpa confining stress i.e.at an approximated confining depth of 1 m. Deviatoric stress (kpa) Bhuj motion (.13g) ' c = 1kPa -4 Tezpur motion (.36g) Kobe motion (.834g) Time (s) Figure.4. Typical variation of deviator stress at σʹc = 1 kpa for input excitations Table.3. Investigation parameters of irregular excitations Soil Irregular excitation PGA (g) D r (%) Confining depth (m) Bhuj.13 Tezpur , 1, 15 Kobe.834 Bhuj.13 Tezpur , 15 Sand Kobe.834 Bhuj Tezpur Kobe Bhuj.13 3, 6, 9 1 Tezpur Kobe

6 6 Kumar, Krishna, Dey 3. Results and Discussions Three strong motion excitations (Bhuj, Tezpur and Kobe motions as described earlier) have been chosen to study the behaviour of BS specimens under irregular seismic excitations at different relative densities and confining depths. Stress-controlled cyclic triaxial tests at undrained condition were conducted on BS specimens, summarized in Table 3. Test specimens were prepared at different relative densities (3, 6 and 9%) and were subjected to different confining pressures i.e. 5, 1 and 15 kpa representing the approximate soil confining depths to be 5, 1 and 15 m, respectively. Cyclic loading was applied on the soil specimens in the form of irregular excitations as explained earlier. Test results were presented in terms of developed shear strains and excess pore water pressures. Excess pore-water pressures (ue) are represented as excess pore-water pressure ratio (ru = ue /σʹc) Effect of relative density Relative density, indicates the compactness of soil specimen and also an indicative of the degree of inter-particle interaction, plays a major role in defining the dynamic behaviour of cohesionless soils. The effect of relative density on the onset of liquefaction of the BS specimens at a confining stress of 1 kpa and subjected to Bhuj motion is presented in Fig. 5. It can be observed that ru decreases with the increase in Dr; maximum ru values of.13,.9 and.8 are obtained for test specimens at Dr of 3%, 6% and 9%, respectively. Owing to the higher ratio of solid particles in a fixed volume representing a denser state, the quantity of induced pore-water pressure decreases and hence, a reduced ru was observed during the dynamic shaking. As a consequence, tests conducted at higher relative densities revealed lesser shear strain accumulation (<.4%). Specimens when subjected to Bhuj motion, no liquefaction was observed suggested by ru << 1. Similar observations were observed, when the BS specimens subjected to Tezpur and Kobe motions, respectively, although depicting larger strains and excess pore-water pressure ratios (Kumar et al. 217b). This feature is attributed to the impulsive nature of Tezpur and Kobe strong motions, where the PGA is reached suddenly, unlike the Bhuj motion which shows a gradual attainment of PGA (Fig. 3). Therefore, it can be stated that the relative density plays a significant role in governing the onset of liquefaction of cohesionless specimens subjected to seismic shaking. Table 4 enumerates the findings of the experimental investigations conducted on BS specimens prepared at different relative densities. It can be noticed that for a given earthquake motion, variation in the relative density of the specimen showed significant difference in maximum shear strain values; the difference being larger (3 times) for higher PGA motion (Kobe). For BS specimens subjected to Tezpur motion, it can be observed that the specimen prepared at Dr = 9% attained a near-liquefaction state with maximum ru, value (ru,max) of.9, whereas the specimen prepared at Dr = 6% showed a distinct onset of liquefaction; although, the difference in the maximum shear strains (γmax) are marginal,.5 and.52, respectively. From this observation, it may be stated that the threshold shear strain manifesting the onset of liquefaction for these set of tests may be about.5 % and the corresponding maximum cyclic stress ratio (CSRmax) being.32. Table 4 clearly indicates that the specimens prepared at higher relative density resulting reduction in ru. This effect being more pronounced at lower PGA level. At higher PGA levels, though there is significant reduction in the resulting shear strains, liquefaction condition becomes inevitable since the excess pore-water pressure ratio reaches 1.. Table 4 also listed the

7 Effect of strong motion parameters on the response of soil using cyclic triaxial tests 7 shear modulus (G) of different specimens, evaluated as a ratio of the maximum shear stress (applied) to the maximum shear strains (observed) for a given test, and as obvious, the shear modulus is found to increase with the increase in the relative density. Higher PGA also reflects lesser value of G because of the significant increase in ru. (%) Bhuj motion (.13g) ' c = 1 kpa Dr = 3% Dr = 6% Dr = 9% Time (s) ru Excess pore pressure ratio (ru ) Figure.5. Strain accumulation and excess PWP ratio in BS specimens confined at 1 kpa for different Dr subjected Bhuj motion Table.4. Summary of investigations on BS specimens prepared at different relative density Input motion Bhuj Tezpur Kobe 3.2. Effect of confining depth D r σʹc γ CSR max τ max G (%) (kpa) max (%) (kpa) (MPa) r u,max Liquefaction Effect of confining depth has been represented in terms of different confining pressures and the resulting shear stresses due to a given earthquake motion. In this attempt, the test specimens prepared at Dr = 3% are considered for different confining depths. Figure 6 shows the results of such specimens subjected to different irregular stress loadings. Figure 6a illustrates the accumulation of shear strain (γ) and development of ru in the BS specimen subjected to Bhuj motion (PGA =.13g). It is observed that the γmax is nearly.1%,.3% and.3% at confining depths of 5 m, 1 m and 15 m, respectively. An increase in the confining depth implies that the sample has been subjected to higher shear stress, which resulted in increased shear strain. Maximum excess pore pressures observed are very low (ru,max =.1<< 1) which is due to the low CSR values (.97,.92 and.78 at 5, 1 and 15m depth due to.13g PGA). It is also observed that the specimens at two No Yes Yes

8 8 Kumar, Krishna, Dey different depths, 1 and 15 m (with σʹc = 1 and 15 kpa) showed identical response in terms of shear strain and pore pressure, which is again attributed to the low PGA level. BS specimens at different depths subjected to scaled Tezpur motion (PGA =.36g) with CSR ranging between exhibited higher peak shear strains in the range of.6-1.8% (Fig. 6). Specimens subjected to confining stresses 1 and 15 kpa exhibited a clear onset of liquefaction as ru reaches nearly 1, while it was significantly lesser (ru,max =.25 << 1) for 5 kpa confining pressure. This behaviour indicates that a homogeneous BS stratum in the field located at a particular depth, corresponding to the above stated range of confining stresses (1-15 kpa), is likely to liquefy. It was also observed that as the specimen liquefies; a significant residual shear strain is manifested indicating the strength reduction of soil. Similar response of larger residual shear strain (> 6%) has also been reported from ground response analysis studies using SHAKE and DEEPSOIL (Suetomi and Yoshida, 1998; Kumar et al. 214a,b; Singhai et al. 216). Specimens subjected to Kobe motion (PGA =.834g with CSR range of.65-.8) exhibited ru = 1 at any of the confining pressures and a substantial residual shear strain (> 5%), thus clearly exhibiting the occurrence of liquefaction in the specimen. From the above illustration, it can be stated that the behaviour of BS specimens at different confining pressure is indicative of their supposed behaviour at different depths in the field subjected to strong motions. (%) Tezpur motion (.36g); D.1 r = 3%.6 '.5 c = 5 kpa ru 'c = 1 kpa ru ' c = 15 kpa ru -3 Time (s) Figure.6. Strain accumulation and excess PWP ratio histories of BS specimens at Dr = 3% and different σʹc for Tezpur motion Table. 5. Summary of investigations on BS specimen subjected to different σʹc Input motion Bhuj (.13g) Tezpur (.36g) Kobe (.834g) σʹc D r γ CSR max τ max G (kpa) (%) max (%) (kpa) (MPa) r u,max Liquefaction No No Yes Yes Table 5 summarizes the results demonstrating the effect of confining pressures (depth) and PGA levels of chosen strong motions. It can be stated that the BS specimens will manifest Excess pore pressure ratio (ru )

9 Effect of strong motion parameters on the response of soil using cyclic triaxial tests 9 the onset of liquefaction behaviour beyond a PGA value of.36g. It has been noticed that the developed maximum shear strain (γmax) exceeds.5% for soils exhibiting liquefaction. Furthermore, at particular Dr and confining depth, the input motion of higher PGA reflect higher strain accumulation. Table 5 also illustrates that for a particular Dr, generation of excess PWP or liquefaction susceptibility of soil increases with the increase of confining depth for all input motions. a (%) b (%) Dr = 6%, ' c = 1 kpa Bhuj motion (.13g) r u Tezpur motion (.13g) r u Kobe motion (.13g).2.15 r u Time (s) 4 Dr = 6%, ' c = 1 kpa 3 Bhuj motion (.36g) ru Tezpur motion (.36g) 2. ru Kobe motion (.36g) 2 ru Time (s) Figure.7. Strain accumulation and excess PWP ratio from scaled earthquake motion of PGA.13g and.36g at Dr = 6% and σʹc = 1 kpa Excess pore pressure ratio (ru ) Excess pore pressure ratio (ru ) 3.3. Effect of similarly scaled strong motions The results obtained from the experimental investigations conducted on the BS specimens based on irregular stress loading evaluated from scaled PGA to.13g and.36g, of different strong motions. Figure 7 depicts the effect of the three earthquake motions (with same PGA) on the BS specimens prepared at Dr = 6% and subjected to σʹc = 1 kpa (1 m depth). It was observed that none of the ground motions, when scaled to PGA =.13g, could initiate liquefaction in the BS specimen; while, liquefaction was observed in the

10 1 Kumar, Krishna, Dey specimens for any of ground motions scaled to.36g. Though the PGA is same, the specimens exhibited different shear strain levels under different excitations. The overall behaviour of the specimens can clearly observed from the summary of the results presented in Table 6. It can be noted that BS specimens, prepared at particular Dr and σʹc, subjected to the similarly scaled strong motions results in different magnitudes of maximum shear strain due to the variation in the associated strong motion parameters. From the table, it can be stated that Tezpur motion shows lowest values of γmax and ru,max in comparison to the Bhuj and Kobe motion, the highest magnitudes being manifested by the Bhuj motion. The reason for such behaviour is attributed to the varying strong motion parameters (Table 2) such as arias intensity, specific energy density, which exhibited similar trend of variation as that observed from the response of test results. Although other strong motions parameters such as predominant period, mean period, bracketed duration and significant duration (Table 2) might have a direct or indirect effect on the observed responses, however, the study of their individual effects is outside the scope of the present attempt. Table.6. Summary of results subjected to ground motions with same PGA Input Scaled D r σʹc τ CSR max γ max G motion PGA(g) (%) (kpa) max (kpa) (%) (MPa) r u,max Bhuj Tezpur Kobe Bhuj Tezpur Kobe Conclusions Liquefaction The present study illustrates the effect of irregular seismic excitations (Bhuj, Tezpur and Kobe motion) on the dynamic response of Brahmaputra sand. The generation of excess pore water pressure, accumulation of shear strain due to cyclic loading and the onset of liquefaction was observed to be significantly affected by the state of the specimen manifested in terms of relative density and confining depth. Based on the present study, the following conclusions can be drawn: 1. Due to higher inter-particle interaction and degree of compactness, an increase in the relative density leads to the decrement of the accumulated shear strain and the excess pore-water pressure ratio. The effect on accumulated shear strain is more prominent for higher PGA of the input motions, while lower PGA induces prominent effect on the developed excess pore-water pressure. 2. BS specimens subjected to any of the strong motions exhibited onset of liquefaction when the maximum shear strain exceeded.5%, and hence, this magnitude of shear strain can be stated as the threshold shear strain for liquefaction. 3. The time taken for the onset of liquefaction is governed by the nature of the applied strong motion. An impulsive strong motion, e.g. Tezpur/Kobe motion will exhibit a quick liquefaction phenomenon, while Bhuj motion will exhibit a gradual attainment of the onset due to its gradual rise towards PGA. 4. An increase in the confining depth leads to the enhancement in the accumulated shear strain and excess pore-water pressure ratio, and hence, increases the liquefaction susceptibility of the sample. Such effect gets more pronounced with higher PGA of the input motion. No Yes

11 Effect of strong motion parameters on the response of soil using cyclic triaxial tests Based on the results of BS specimens subjected to similarly scaled strong motions, it can be stated that specimens at any relative density will liquefy under the following optimum conditions: PGA >.36g, CSR >.3 and γmax >.5%. 6. Cohesionless soil specimens subjected to similarly scaled strong motions exhibits varying accumulated shear strains and excess pore-water pressure ratios due to the variation of the other associated strong motion parameters such as arias intensity, specific energy density, predominant period, mean period, bracketed duration and significant duration. Individual and simultaneous effect of the strong motion parameters is bound to affect the dynamic response of cohesionless soil and needs to be studied in rigorous and minute detail. Reference [1] ASTM D2487, Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System), ASTM International, West Conshohocken, PA, 26. [2] ASTM D5311, Test Method for Load Controlled Cyclic Triaxial Strength of Soil, Annual book of ASTM standards. ASTM International, West Conshohocken, PA, 211. [3] Chang C.Y., Power M.S., Tang Y.K., Mok C.M., Evidence of Nonlinear Soil Response during a Moderate Earthquake, Proceeding of the 12th International Conference on Soil Mechanics and Foundation Engineering. Rio de Janeiro, 3, 1 4, [4] Dobry R., Ladd R.S., Yokel F.Y., Chung R.M., Powell D., Prediction of Pore Water Pressure Buildup and Liquefaction of Sands During Earthquakes by the Cyclic Strain Method, US Department of Commerce, National Bureau of Standards, 138, [5] Hardin B.O., Drnevich V.P., Shear Modulus and Damping in Soils: Measurement and Parameter Effects, Journal of Soil Mechanics and Foundations Division, 98, , [6] IS: 272 part-3, Methods of the Tests for Soils, Part 3: Determination of Specific Gravity-Fine, Medium and Coarse Grained Soils, Bureau of Indian standard, New Delhi, [7] IS: 272 part-4, Methods of the Tests for Soils, Part 4: Grain Size Analysis. Bureau of Indian standard, New Delhi, [8] IS: 272 part-14, Methods of the Tests for Soils, Part 14: Determination of Density Index of Cohesionless Soils. Bureau of Indian standard, New Delhi, [9] Ishibashi I., Zhang X., Unified Dynamic Shear Moduli and Damping Ratios of Sand and Clay, Soils and Foundations, 33, , [1] Ishihara K., Troncoso J., Kawase Y., Takahashi Y., Cyclic Strength Characteristics of Tailings Materials, Soils and Foundations, 2, , 198. [11] Ishihara K., Soil Behaviour in Earthquake Geotechnics, Clarendon Press, Oxford University Press, [12] Ishihara K., Yasuda S., Soil Liquefaction due to Irregular Excitation, Soils and Foundations, 12, 65 77, [13] Ishihara K., Yasuda S., Soil Liquefaction under Random Earthquake Loading Condition, Proceeding 5 th world conference on earthquake engineering, Rome, ASCE, , [14] Ishihara K., Yasuda S., Sand Liquefaction in Hollow Cylinder Torsion under Irregular Excitation, Soils and Foundations, 15, 45 59, [15] Iwasaki T., Tatsuoka F., Takagi Y., Shear Modulus of Sands under Torsional Shear Loading, Soils and Foundations, 18, 39 56, [16] Kokusho T., Yoshida Y., Esashi Y., Dynamic Properties of Soft Clay for Wide Strain Range, Soils and Foundations, 22, 1 18, [17] Kumar S.S., Dey A., Krishna A.M., Equivalent Linear and Nonlinear Ground Response Analysis of Two Typical Sites at Guwahati City, Proceedings of Indian Geotechnical Conference, Kakinada, 18-2 December 214. [18] Kumar SS, Krishna AM, Dey A., Nonlinear Site-Specific Ground Response Analysis: Case Study of Amingaon, Guwahati, 15 th Symposium on earthquake engineering, IIT Roorke, December 214. [19] Kumar S.S., Krishna A.M., Dey A., Evaluation of Dynamic Properties of Sandy Soil at High Cyclic Strains, Soil Dynamics and Earthquake Engineering, 99, , 217a.

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