Profiling of K 0 lateral stress coefficient in soils using paired directional G 0 ratios Taeseo Ku ⁎, Paul W. Mayne Geosystems Engineering Division, School of Civil & Environmental Engineering, Georgia Institute of Technology, 790 Atlantic Drive, Atlanta, GA 30332, USA abstract article info Article history: Received 7 December 2012 Accepted 6 April 2013 Available online 15 April 2013 Keywords: Anisotropy In-situ measurements Lateral stress coefficient Overconsolidation Shear modulus Shear wave velocity Using a special database compiled from directional shear wave velocity measurements at 12 well-documented sites, the geostatic stress state and stress history are evaluated from shear stiffness ratios. At each site, a benchmark profile of lateral stress coefficient (K 0 ) was detailed using direct in-situ methods (i.e., self-boring pressuremeter, total stress cells, and/or hydraulic fracture), and/or laboratory methods (i.e., suction, consolidometer, and/or triaxial stress path testing). Also, the yield stress ratio (YSR), or more common parameter: overconsolidation ratio (OCR), was available either from series of consolidation tests on undisturbed samples procured from various depths and/or engineering geology studies, or both. Statistical expressions are derived to relate both K 0 and OCR in terms of the ratio G 0,HH /G 0,VH as well as other factors. Published by Elsevier B.V. 1. Introduction The shear modulus at very small strains is an important soil property for geotechnical design problems related to ground deformation predic- tions and dynamic response analysis. The small-strain shear modulus (G 0 or G max ), which represents the initial stiffness in soils, is a baseline reference value for stress–strain–strength curves for both static and dynamic loading (Burland, 1989; Fahey, 1998; Mayne et al., 2009). To understand comprehensive ground movement response, it is necessary to determine an accurate G 0 profile and appropriate modulus reduction curves that capture the non-linear stiffness response of the geomaterial. The value of G 0 can be obtained from various in-situ geophysical methods conducted in the field and/or from laboratory testing programs on undisturbed samples, such as resonant column tests and bender element tests. The G 0 measurements should best be carefully evaluated from in-situ field tests because there are often difficulties in laboratory G 0 measurements due to sample disturbance effects, stress relief, and aging effects (Clayton, 2011; Santagata, 2008; Tatsuoka and Shibuya, 1992). For instance, based on 40 intact samples, Stokoe and Santamarina (2000) showed that the ratio of laboratory G 0 to field G 0 values (i.e., G 0,lab /G 0,field ) generally decreases when the magni- tude of corresponding field G 0 increases. Therefore, the magnitude of G 0 assessed from in-situ geophysical methods is preferable, if at all possible. The geophysical methods provide in-situ shear wave velocity profiles whereby the stiffness G 0 is directly calculated as follows: G 0;ij ¼ ρ t ⋅ V 2 s;ij ð1Þ where, ρ t is a total mass density of soil, V s is shear wave velocity, ‘i’ is propagation direction and ‘j’ is the particle motion direction of shear wave. Assuming cross-anisotropy in soils, the directional G 0 in different planes can be defined. Herein, the subscripts V and H refer to vertical and horizontal, respectively. Field geophysics usually generates three different G 0 types: (1) G 0,VH from downhole testing (VH) using a horizontal surface source, (2) G 0,HV from standard crosshole (HV) test using an up–down hammer source, and (3) G 0,HH from crosshole arrays using a special rotary hammer, torsional apparatus, or hori- zontal solenoid device (HH waves). With respect to the three types of in-situ V s measurements, Fig. 1 depicts the general set-up and wave directions for different geophysical tests. Since the geostatic stress state is represented by the at-rest lateral stress coefficient K 0 = σ ho ′/σ vo ′, it follows logically that the stiffness anisotropy of the ground might afford a means to quantify this parameter. As such, this study develops a relationship between K 0 and its associated stress history (i.e., OCR =overconsolidation ratio), in terms of a paired shear modulus ratio, specifically the stiffness ratio (G 0,HH /G 0,VH ) in dif- ferent planes. 2. Shear stiffness anisotropy A good number of prior studies have examined the initial stiffness in soils and relevant factors affecting its magnitude (e.g., Hardin and Blandford, 1989; Jamiolkowski et al., 1995; Santagata et al., 2005; Journal of Applied Geophysics 94 (2013) 15–21 ⁎ Corresponding author. Tel.: +1 561 972 0837; fax: +1 404 894 2281. E-mail addresses: taeseo@gatech.edu (T. Ku), paul.mayne@gatech.edu (P.W. Mayne). 0926-9851/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.jappgeo.2013.04.002 Contents lists available at SciVerse ScienceDirect Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo