Dynamic soil properties for microzonation of Delhi, India

C Hanumantharao1,∗ and G V Ramana2,∗∗

1Civil Engineering Group, Birla Institute of Technology and Science Pilani, Pilani 333 031, India.2Civil Engineering Department, Indian Institute of Technology Delhi, New Delhi 110 016, India.

∗e-mail: hrao@bits-pilani.ac.in∗∗e-mail: ramana@civil.iitd.ac.in

Delhi, the capital of India, has experienced mild seismic shaking during several earthquakes inthe past. The large variations of depth to bedrock and ground water table coupled with differentsoil types at different locations of Delhi necessitate a seismic microzonation study. Dynamic soilproperties such as shear wave velocity, modulus reduction and damping characteristics of local soilsare the basic and essential input parameters for conducting even a preliminary ground responseanalysis which is an essential input in microzonation studies. Shear wave velocity is not measuredroutinely due to its high cost and lack of the required expertise. Several researchers in the pastdeveloped correlations between shear wave velocity (Vs) and routinely measured N values. In thepresent study, shear wave velocity profiles measured in the field at more than 80 borehole locationsto a depth of about 20 to 32 m using Spectral Analysis of Surface Waves (SASW) are presented andcorrelations between shear wave velocity and N values are also presented for use by engineers anddesigners. Results of strain and stress controlled cyclic triaxial tests on remoulded samples of sand-silt mixtures in the high strain range are used for generating the modulus reduction and dampingcurves and are compared with the well-known curves in the literature. The results presented inthis article can be used for microzonation studies as well as site specific ground response analysesat Delhi.

1. Introduction

The extensive loss of life and damage caused bythe recent earthquakes (Uttarkashi (1991, Mw 7.0),Jabalpur (1997, Mw 5.8), Chamoli (1999, Mw 6.5),and Bhuj (2001, Mw 7.6)) has demonstrated theseismic hazard being faced by India. If a major citylike Delhi is subjected to such earthquakes, it wouldcertainly result in higher devastation and majorloss of life. Several earthquakes of magnitudes rang-ing from 3 to 7.7 have been observed in and aroundDelhi during the past three centuries (Srivastavaand Somayajulu 1966; Parvez et al 2004). Delhi liesin seismic zone IV as per the seismic hazard map ofIndia (IS: 1893–2002) with an expected zero periodacceleration of 0.24 g. It has been a well establishedfact that a detailed dynamic analysis and design

of built environment that takes into account thebehaviour of local soil deposits reduces the loss oflife and damage to infrastructure.

Shear wave velocity or shear modulus at verylow strains is the most important input para-meter in the analysis of engineering problemsinvolving earthquake engineering, particularly inmicrozonation studies. It is widely accepted thatthe shear wave velocity profile of a site is a fun-damental parameter to estimate the site-specificamplification factor. In most geotechnical investi-gation programs, dynamic in situ tests are usu-ally not conducted due to cost considerations andlack of specialized personnel. For this reason manyattempts have been made in the past to correlatevalues of shear wave velocity (Vs) or shear modulusto other readily available soil parameters such as N

Keywords. Shear wave velocity; modulus reduction curves; damping curves.

J. Earth Syst. Sci. 117, S2, November 2008, pp. 719–730© Printed in India. 719

720 C Hanumantharao and G V Ramana

Figure 1. Geological map of Delhi (modified from Parvezet al 2004).

value. Several empirical equations have been pro-posed for estimating the shear wave velocity by useof several soil indexes, so as to avoid in situ mea-surement and also to examine the physical relationbetween soil indices and shear wave velocity. Themost common relations are based on the N valueobtained from the standard penetration test. Onsimilar lines, empirical correlations are developedbetween shear wave velocity and N values for sandsand silty sand/sandy slit to represent the two pre-dominant types of soils encountered in Delhi, asshown in figure 1.

It is also widely accepted that the shear mod-ulus and damping ratio of soils is a function ofthe amplitude of shear strain under cyclic loading.Modulus reduction and damping curves of localsoils are an essential input for carrying out groundresponse analysis using the most commonly usedequivalent linear technique. Hence strain depen-dent modulus reduction and damping curves aregenerated using cyclic triaxial tests for differentsand-silt mixtures.

2. Measurement of shear wavevelocity (VsVsVs)

In situ measurement of Vs using geophysicalmethods is the best method for measuring the lowstrain shear modulus, Gmax (Rollins et al 1998b).

Geophysical methods are based on the fact thatthe velocity of propagation of a wave in an elasticbody is a function of the modulus of elasticity, Pois-son’s ratio and density of the material (Hvorslev1949). Methods employing wave propagation prin-ciples in determining Vs variation with depth iseither intrusive or non-intrusive. Spectral Analysisof Surface Waves (SASW) method (Nazarian andStokoe 1984), a non-intrusive and non-destructivetesting technique is used in the present study tomeasure Vs. Comparison of SASW test results withthose of crosshole, downhole, and suspension logsat the same test sites have been reported in theliterature (Nazarian and Stokoe 1984; Dennis et al1988; Stokoe et al 1988, 1999; Brown et al 2002)and the difference in measured shear wave velocityresults between these methods is of the order of10 to 15 per cent. In general, SASW results werereported to be on the lower side at the surface(Brown et al 2002).

The SASW method is an established methodfor measuring shear wave velocity and is beingincreasingly used. This test comprises three steps,namely: (i) field testing (ii) dispersion calcula-tions, and (iii) inversion. A detailed descriptionof the test procedures, factors affecting the resultsand the details on inversion processes are well doc-umented in literature (e.g., Nazarian and Stokoe1984; Ignacio et al 1987; Salinero et al 1987; Stokoeet al 1999; Rao and Ramana 2004). In the cur-rent work, as a first approximation in the inversionprocess, the thickness of the layer is assumed to beapproximately equal to half of the wavelength andshear wave velocity as approximately 1.1 times thephase velocity. By trial and error, attempts weremade to obtain a close match between the theo-retical and experimental curve (Joh 1992). In theinversion process, a Poisson’s ratio of 0.33 is con-sidered for the soils above ground water table andcompression wave velocity of 1500 m/s is adoptedfor the soils below ground water table (Ignacio et al1987; Rix et al 1991; Brown et al 2002). The unitweight of the soil is taken from the nearest bore-hole. Typical shear wave velocity measured at threerepresentative sites is shown in figure 2.

3. Standard penetration tests

More than 2000 borelogs are available at severallocations for Delhi from various public as well asprivate organizations. However, a large scatter wasobserved between the results from different agen-cies at the same test location and the reportedN value is not consistent between different orga-nizations. In view of this, no attempts were madefor developing the regression correlation based onthe entire dataset and N values from locations

Dynamic soil properties for Delhi 721

Figure 2. Typical SPT borelogs and shear wave velocity profiles used for Vs–N correlation (Vs is in m/s, depth is in m,CL: clayey silt, SP-SM: fine sand with mica, SP: fine sand, MI: sandy silt, and SM: silty fine sand).

where tests were conducted under the supervisionof Indian Institute of Technology, Delhi only areused.

Standard penetration tests are conducted in theboreholes of 150 mm diameter and were advancedusing shell and auger method in accordance withIS: 1892–1979. SPT values are measured at 1.5 mdepth intervals by connecting a split spoon samplerto A-rods and a 63.5 kg hammer falling freely froma height of 750 mm is used to drive it to 450 mmpenetration. All the tests are conducted in accor-dance with IS: 2131–1981. The number of blowsfor each 150 mm of penetration of the split spoonsampler is recorded. The blows required to pene-trate the initial 150 mm of the split spoon (seatingdrive) are ignored due to the possible presence ofloose materials or cuttings from the drilling oper-ation. The cumulative number of blows requiredto penetrate the remaining 300 mm of the 450 mmsampling interval is termed the SPT value or Nvalue. Typical borelogs are shown in figure 2. In theborelogs, CL represents clayey silt, SP-SM repre-sents fine sand with mica, SP represents fine sand,MI represents sandy silt, and SM represents siltyfine sand.

4. Correlation between VsVsVs and NNN value

In the literature several correlations are reportedbetween Vs and N values measured in the field and

are comprehensively summarized in table 1. Theserelations are often expressed in the following form:

Vs = ANB , (1)

where A, B are constant parameters and are oftenaccompanied by a correlation coefficient R. Usu-ally the trend observed is that if A increases Bdecreases for the same type of soil (Ohsaki andIwasaki 1973; Imai 1977; Ohta and Goto 1978; Imaiand Tonouchi 1982).

Geologic age and soil type are often used by sev-eral researchers (Ohsaki and Iwasaki 1973; Imai1977; Ohta and Goto 1978; Imai and Tonouchi1982; Pitikilas et al 1992; Raptakis et al 1995;Rollins et al 1998a) to enhance correlationsbetween shear wave velocity and N value. Theempirical correlations for cohesive soils are moreconsistent than those for sandy soils and alsoshowed higher shear wave velocities than sand(Ohsaki and Iwasaki 1973). In contradiction to thisobservation, Imai (1977) reported that the sandysoils showed better correlation and higher velocitiesthan cohesive soils. Ohta and Goto (1978) used soiltype as an additional parameter in correlation andobserved that the Vs, gravel ≥ Vs, sand ≥ Vs, clay. Imaiand Tonouchi (1982) observed that Vs is greatestin tertiary, less in diluvial, and least in alluvial lay-ers. They also reported that the clayey soils showhigher Vs than sands. Rollins et al (1998b) reported

722 C Hanumantharao and G V Ramana

Table 1. Vs–N correlations reported in literature.

Author (s) Correlation Soil Country

Imai and Yoshimura (1970)$ Vs = 76.0N0.39 All Japan

Ohba and Toriumi (1970)$ Vs = 84.0N0.31 Alluvial Japan

Shibata (1970)∗ Vs = 32.0N0.50 Sands Japan

Ohta et al (1972)$ Vs = 87.0N0.36 Sands Japan

Ohsaki and Iwasaki (1973) Vs = 82.0N0.39 All Japan

Ohsaki and Iwasaki (1973) Vs = 59.0N0.47 Cohesionless Japan

Imai et al (1975)∗ Vs = 90.0N0.34 All Japan

Imai (1977) Vs = 91.0N0.34 All Japan

Ohta and Goto (1978) Vs = 85.3N0.35 All Japan

JRA (1980)∗ Vs = 100.0N0.33 Clays Japan

JRA (1980)∗ Vs = 80.0N0.33 Sands Japan

Imai and Tonouchi (1982) Vs = 97.0N0.31 All Japan

Yokota et al (1991)∗ Vs = 121.0N0.27 All Japan

Seed and Idriss (1981)∗ Vs = 61.0N0.50 All USA

Seed et al (1983) Vs = 56.4N0.50 Sands USA

Sykora and Stokoe (1983) Vs = 106.7N0.27 Granular USA

Fumal and Tinsley (1985) Vs = 152 + 5.1N0.27 Sands and USAgravelly sands

Sykora and Koester (1988) Vs = 63.0N0.43 Holocene gravels USA

Sykora and Koester (1988) Vs = 132.0N0.32 Pleistocene gravels USA

Lee (1990) Vs = 57.0N0.49 Sands USA

Lee (1990) Vs = 114.0N0.31 Clays USA

Lee (1990) Vs = 106.0N0.32 Silts USA

Rollins et al (1998a, b) Vs = 63.0N0.4360 Holocene gravel USA

Rollins et al (1998a, b) Vs = 132.0N0.3260 Pleistocene gravel USA

Rollins et al (1998a, b) Vs = 222.0N0.06 Recent fill USA

Andrus et al (2004) Vs1cs = 87.8N0.251,60cs All USA

Pitikilas et al (1992) Vs = 155.1N0.17 Debris fill Greece

Pitikilas et al (1992) Vs = 162.0N0.17 Silty sand Greece

Pitikilas et al (1992) Vs = 165.7N0.19 Soft clays Greece

Pitikilas et al (1992) Vs = 357.5N0.19 Hard clays Greece

Kalteziotis et al (1992)∼ Vs = 76.2N0.24 All soils Greece

Kalteziotis et al (1992)∼ Vs = 76.6N0.45 Cohesive soil Greece

Kalteziotis et al (1992)∼ Vs = 49.1N0.50 Cohesionless soil Greece

Athanasopoulos (1995) Vs = 107.6N0.36 All soils Greece

Raptakis et al (1995) Vs = 123.4N0.29 Loose sand Greece

Raptakis et al (1995) Vs = 100.0N0.24 Medium dense sand Greece

Raptakis et al (1995) Vs = 105.7N0.33 Soft clays Greece

Raptakis et al (1995) Vs = 184.2N0.17 Stiff clays Greece

Raptakis et al (1995) Vs = 192.4N0.13 Gravel Greece

Jafari et al (1997)∗ Vs = 22.0N0.85 All soils Iran

Jafari et al (2002) Vs = 27.0N0.73 Clays Iran

Jafari et al (2002) Vs = 22.0N0.77 Silts Iran

Jafari et al (2002) Vs = 19.0N0.85 Fine grained soil Iran

Chein et al (2000) Vs = 22.0N0.76 Silty sand Taiwan

Kayabali (1996) Vs = 175 + 3.75N Granular soils Turkey

$Adopted from Ohsaki and Iwasaki (1973);∗Adopted from Jafari et al (2002);∼Adopted from Athanasopoulos (1995).

that the estimation of shear wave velocity can beimproved, if the effective stress is included in theregression equation.

While developing the correlations, N values lessthan 2 and more than 50 are rejected in the regres-sion analysis because of poor reliability (e.g., Ohta

Dynamic soil properties for Delhi 723

Figure 3. Correlation developed between Vs and N for(A) sand, (B) sandy silt/silty sand and (C) all soils ofDelhi.

and Goto 1978). Uncorrected N values are usedfor developing the regression correlation with theuncorrected shear wave velocity at same depth(Sykora and Koester 1988; Rollins et al 1998a).Correlations are developed based on N values alone(did not consider other parameters such as soiltype, geological age, depth, effective stress, etc.)and are developed for two different soil types: oneconsisting of predominately sand and the othercomprising sandy silt to silty sand.

The general criteria used for selecting the pene-tration and Vs measurements are: (i) penetrationtest locations are within 6m of the Vs test

locations, and (ii) at least two Vs measurementsand the corresponding test intervals are within theuniform layer. N values are measured at every1.5 m interval, but shear wave velocity profile isdeveloped based on the layer formations observedfrom SPT and experimental dispersion curves fromSASW testing. As the shear wave velocity for a par-ticular layer is constant from the test results, shearwave velocity profile is also transferred to 1.5 minterval using weighted average method. The entiredatabase for each group is made into pairs of Vs

and N to develop the regression equations betweenN and Vs. Simple linear power regression analy-sis as suggested by several previous researchers iscarried out for developing the correlation betweenVs and N . The developed correlations satisfactorilypredict the measured Vs values with the measuredN values of up to 40, since most of the data-base used in the regression analysis fall in thisrange. Estimated shear wave velocities for N val-ues between 40 and 50 should be used with engi-neering judgement. However, these correlations arenot applicable for N values above 50. It may bebecause of power regression used in the presentstudy. The datasets used to develop correlationsbetween Vs–N are shown in figure 3 along with thecorrelation coefficient. The developed correlationsare compared with the available correlations fromliterature in figure 4.

The following empirical correlations between Vs

and N are recommended for Delhi region and theseequations are applicable for N values up to 40, andcan also be used with engineering judgement forN values in between 40 and 50. However, thesecorrelations cannot be used for N values above 50.

Vs = 79.0N 0.434 m/s (for sand), (2)

Vs = 86.0N 0.42 m/s (for silty sand/sandy silt),(3)

Vs = 82.6N 0.43 m/s (for all soils). (4)

5. Strain dependent modulus reduction(G/GmaxG/GmaxG/Gmax) and damping curves

In general, damping ratio decreases with theincrease in depth (Seed and Idriss 1970; Elgamalet al 2005). At larger depths (> 60m), the soilresponse was practically linear (Elgamal et al 1996)and it maintains the same stiffness and responsepatterns throughout the earthquake. Relative den-sity has no significant influence on the dynamicproperties of soils in the large strain (> 1%) levels,

724 C Hanumantharao and G V Ramana

Figure 4. Comparison of Vs–N correlations for the soils of Delhi with other correlations reported in the literature.

but it has considerable influence at small strain lev-els (Sitharam et al 2004a, b). The seismic geophys-ical tests do not provide a realistic estimation ofmaterial damping, which can be determined accu-rately only by laboratory testing (Boominathan2004).

In order to characterize the dynamic propertiesof Delhi soils, undrained strain and stress con-trolled cyclic triaxial tests were conducted on spec-imens formed using various mixtures of Yamunasand and non-plastic fines (obtained from wash-ing Delhi silt). In general, soils of Delhi consistof Yamuna sand and silt in different proportions,along with some minor fraction of clay and kankar.These minor constituents are not considered inthe current study. Clean Yamuna sand (S100M00)and Yamuna sand mixed with 15% (S85M15), 30%(S70M30), and 50% (S50M50) fines are used torepresent the different soil mixtures encounteredin different parts of Delhi. In the present study,the different sand-silt mixtures are referred to asS(x)M (100-x) where S and M represent sand andsilt respectively and x refers to the percentage byweight of sand in the sand-silt mixture. The per-centage of sand by weight is taken so as to be rep-resentative of field conditions encountered in Delhi(Tuli 1994). The fines present in Delhi are non-plastic, and even if there is some clay present, theplasticity index of Delhi silt is usually below 10.

Figure 5. Grain size distribution curves of differentsand-silt mixtures used.

5.1 Grain size distribution

Grain size distribution for the different sand-siltmixtures used in the present study is shown infigure 5 and the grain size parameters are givenin table 2 along the other index properties. Thenon-plastic silt fraction is obtained by washingDelhi silt through 0.075 mm sieve. As reported byTuli (1994), it is observed that the fines are non-plastic in most of the places, particularly in flu-vial beds. Hence in this study, fines are considered

Dynamic soil properties for Delhi 725

Table 2. Index properties of sand-silt mixtures.

Geotechnical FC = 0% FC = 15% FC = 30% FC = 50% FC = 100%properties (S100M00) (S85M15) (S70M30) (S50M50) (S00M100)

Specific gravity 2.660 2.668 2.675 2.685 2.710(Gs)

Uniformity 2.0 5.3 19 28 10.7coefficient (Cu)

Coefficient of 1.20 2.30 1.90 1.30 1.04curvature (Cc)

D10 (mm) 0.110 0.040 0.010 0.005 0.003

D50 (mm) 0.210 0.185 0.160 0.078 0.026

Maximum density, 17.2 18.2 19.1 19.7 17.0γdmax (kN/m3)

Minimum density, 13.2 14.1 14.2 14.0 12.2γdmin (kN/m3)

Maximum void 1.015 0.892 0.884 0.918 1.221ratio (emax)

Minimum void ratio 0.546 0.466 0.401 0.363 0.594(emin)

primarily as non-plastic and insignificant clay con-tent encountered at few locations is not taken intoaccount.

5.2 Sample preparation

The modulus reduction and damping curves areless sensitive to specimen preparation method,degree of saturation and drainage conditions(Tatsuoka et al 1979; Kokusho 1980). Remouldedspecimens are prepared using moist tamping undercompaction method (Ladd 1978; Chan 1985) inseven layers. Membrane correction is not consid-ered for fine grained soils (Frydman et al 1973;Silver 1977; Erten and Maher 1995; Polito andMartin 2000) since the membrane penetration perunit area is negligible. Area correction is also notconsidered to the cyclic triaxial loading data inaccordance with standard practice as outlined byChan (1985).

5.3 Saturation and consolidation

All the specimens were saturated by passing car-bon dioxide as well as deaired water so as to achievehigher saturation at lower back pressure and in lesstime. Incremental back pressure saturation as perBS: 1377 (1990) is adopted for saturation and allthe specimens are saturated using a back pressureof 313 ± 1 kPa to achieve Skempton pore pres-sure parameter B in excess of 0.98. Back pres-sure is kept constant for all the tests to eliminatethe effect of back pressure on modulus and dam-ping. All the specimens are tested at a void ratio(e) of 0.75 and are isotropically consolidated toan effective confining pressures (σ′

3c) of 100 and150 kPa.

5.4 Cyclic loading

Strain and stress controlled undrained cyclic tri-axial tests are conducted on remoulded speci-mens of 70 mm diameter and 140 mm height undera sinusoidal loading at 1 Hz frequency as perASTM D3999B for evaluating the modulus reduc-tion and damping curves. Since the fines presentin Delhi are non-plastic and percentage of non-plastic fines changes the void ratio only, thesefines do not influence the damping and modulusreduction behaviour significantly (Sun et al 1988;Vucetic and Dobry 1991). Hence clean Yamunasand (S100M00) and Yamuna sand mixed withequal proportions (S50M50) of non-plastic fines areonly used for strain controlled testing. For othermixtures (S85M15; S70M30) stress controlled testswere used to evaluate the modulus reduction anddamping curves. As all the tests are conductedon saturated samples in undrained condition, Pois-son’s ratio (υ) is considered as 0.5 (Rollins et al1998b).

5.5 Estimation of Gmax

One of the most reliable methods to characte-rize small strain shear modulus (Gmax) is in situmeasurement of shear wave velocity (Vs) in the fieldat small strains using seismic methods (Rollins et al1998b). Since the SASW test is performed on theground surface at strain levels less than 0.001%,small strain shear modulus, Gmax, can be deter-mined from the measured shear wave velocity (Vs)profile by assuming the density, ρ as:

Gmax = ρV 2s . (5)

726 C Hanumantharao and G V Ramana

Figure 6. (A) Applied axial strain, (B) induced deviatorstress and (C) Pore pressure ratio variation with number ofcycles for S100M00 (σ′

3c = 146 ± 1 kPa, f = 1Hz, e = 0.75,εDA = 0.4%).

Figure 7. Effective stress path for S100M00 (σ′3c =

146 ± 1 kPa, f = 1Hz, e = 0.75, εDA = 0.4%).

Gmax can also be estimated directly from N valuein the field as:

Gmax = aN b, (6)

Figure 8. Hysteresis loop for S100M00 (σ′3c = 146± 1 kPa,

f = 1Hz, e = 0.75, εDA = 0.4%).

where a, b are correlation coefficients (e.g., a = 1.2and b = 0.8 (Ohsaki and Iwasaki 1973)). Similarly,number of correlations given for Vs and N in table 1can also be used to estimate Gmax by assuming thedensity of soil, since slight variation of density doesnot influence the estimated value.

5.6 Normalised modulus reductionand damping curves

A typical test result at a double amplitude strain(εDA) of 0.4% for clean Yamuna sand is pre-sented and explained here. For the double ampli-tude strain applied, the resulting deviator stressand generated excess pore pressure ratio are shownin figure 6(a), (b), and (c) respectively. It can beobserved that with increasing number of cycles ofstrain application, the pore pressure increased asthe specimen is saturated. It can also be observedfrom figure 7 that both mean normal effective stressand deviator stress reached zero at the end of 40cycles of strain application. The stiffness of thesoil decreased during successive cycles of strainapplication, as is evident from figure 8 is primarilybecause of tests were conducted on saturatedspecimens.

Kokusho (1980) reported that the stiffness isnot changing significantly with number of cycleswhen the strain amplitude is low. However, themodulus will decrease significantly if the strainis large because of pore pressure development. Itwas observed that for pore pressure ratio of about0.2, the maximum closure error criteria as speci-fied in ASTM D3999 is also satisfied. In view ofthis modulus reduction and associated damping inthis study are reported for the cycle where the porepressure ratio has attained a value of about 0.2.

Figures 9 and 10 show the hysteresis loopsobtained and used for estimation of shear modulusand damping at different strains for clean Yamunasand (S100M00) and sand-silt mixture (S50M50)respectively.

Dynamic soil properties for Delhi 727

Figure 9. Hysteresis loops forS100M00 at double amplitudestrain of (A) 0.2%, (B) 0.4%,(C) 0.5%, (D) 0.75%, and (E) 1%(σ′

3c = 146 kPa, e = 0.75, f =1Hz, ru = 0.2).

Figure 11 shows the estimated shear modulusand damping curves for different sand-silt mixturesusing standard procedures (as outlined in differ-ent codes of practice). These values are normalizedwith reference to the Gmax, which was obtainedfrom the in situ measured shear wave velocity soas to plot them on modulus reduction and dam-ping curves for sands as given by Seed and Idriss(1970). By considering the shear wave velocity of240 m/s and saturated unit weight of 20 kN/m3,Gmax is estimated as 118 MPa, and is used in thepresent study.

Figures 12 and 13 show the modulus reduc-tion and damping behaviour of Yamuna sand anddifferent sand-silt mixtures superimposed on therange of values reported by Seed and Idriss (1970).As reported in the literature, modulus reductionand damping behaviour of non-plastic soils is rel-atively independent of confining pressure, compo-sition and loading frequency (Mitchell 1993) andhence the tests in the current study are conducted

at a particular void ratio, confining pressure andfrequency of cyclic loading. The curves generatedin the current study indicate that soils of Delhi,in general, can be represented using lower boundestimates of Seed and Idriss (1970).

6. Conclusions

Based on extensive well-planned field andlaboratory testing that takes into account thedifferent soil conditions encountered in Delhi,dynamic soil properties required for a meaning-ful microzonation from geotechnical earthquakeengineering perspective are presented. ExtensiveSASW testing coupled with judicially selectedborelogs are used for developing Vs–N correla-tion for Delhi region and are compared with otherreported values in the literature. Strain and stresscontrolled cyclic triaxial tests as per ASTM D3999indicated that the modulus reduction and damping

728 C Hanumantharao and G V Ramana

Figure 10. Hysteretic loops forS50M50 at double amplitude strainof (A) 0.2%, (B) 0.5%, (C) 0.75%,(D) 1%, and (E) 2% (σ′

3c =100 kPa, e = 0.75, f = 1Hz, ru =0.2).

Figure 11. Variation of shear modulus with shear strain fordifferent sand-silt mixtures.

behaviour can be approximated by lower boundSeed and Idriss (1970) values for sand. This con-clusion is based on measurements at large strainsonly and no attempt was made to estimate themodulus reduction and damping behaviour at low

Figure 12. Normalized shear modulus (G/Gmax) versusshear strain.

strains due to the lack of appropriate equipment.The results presented in this paper can be usedfor estimation of site period, site classification,soil amplification factor, and liquefaction hazardassessment. The present results can be used to

Dynamic soil properties for Delhi 729

Figure 13. Variation of damping ratio with shear strain.

further refine the first cut microzonation map forDelhi developed by different government agenciessuch as Department of Science and Technologyand Indian Meteorological Department. However,before using the correlations to estimate shearwave velocity based on N values, a few confirma-tory boreholes at the site of interest need to bedrilled.

Acknowledgement

The authors greatly acknowledge the financial sup-port provided by Seismology Division, Depart-ment of Science and Technology for Cyclic Triaxialsystem facility at IIT Delhi.

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MS received 30 September 2007; revised 29 December 2007; accepted 6 March 2008