Examination of the Potential of the Seismic Dilatometer ( SDMT ) to Estimate In Situ Stiffness Decay Curves in Various Soil Types

This paper illustrates the use of the seismic dilatometer (SDMT) to assess the decay of in-situ stiffness with strain level in different soil types. The approach adopted in this study relies on the ability of the SDMT to provide routinely at each test depth both a small strain stiffness (G0 from VS) and a working strain stiffness (constrained modulus MDMT derived from the usual DMT interpretation). At various test sites, working strain DMT moduli are compared with reference stiffness decay curves back-figured from (i) the behavior observed under a full-scale test embankment (at Treporti) or footings (in Texas), (ii) from laboratory tests (at L’Aquila, Fucino plain and Po plain) and (iii) various combinations of insitu and laboratory testing techniques (Western Australia). Typical ranges of the shear strains DMT associated with working strain DMT moduli are inferred to assist construction of stiffness strain decay curves for different soil types.

The seismic dilatometer (SDMT) is the combination of the flat dilatometer (DMT) with an add-on seismic module for the measurement of the shear wave velocity V S .The approach adopted in this study relies on the ability of the SDMT to provide routinely, at each test depth, both the stiffness at small strains (the small strain shear modulus G 0 obtained from the shear wave velocity V S as G 0 = r V S 2 ) and the stiffness at operative strains (as represented by the constrained modulus M DMT obtained by the usual DMT interpretation).The potential for these two stiffness values to provide guidance when selecting the G-g curve of a soil element is examined.

Flat Dilatometer Test (DMT)
The flat dilatometer, introduced by Marchetti (1980), consists of a steel blade having a thin, expandable, circular steel membrane mounted on one face.When at rest, the membrane is flush with the surrounding flat surface of the blade.The blade is connected, by an electro-pneumatic tube running through the insertion rods, to a control unit on the surface (Figs.1a and 1b).The control unit is equipped with pressure gauges, an audio-visual signal, a valve for regulating gas pressure (provided by a tank) and vent valves.The blade is advanced into the ground using common field equipment, i.e. penetrometers normally used for the cone penetration test (CPT) or drill rigs.
The test starts by inserting the dilatometer into the ground.When the blade has advanced to the desired test depth, the penetration is stopped.The operator inflates the membrane and takes, in about 30 sec, two readings: the A pressure, required to just begin to move the membrane ("lift-off" pressure), and the B pressure, required to expand the membrane center of 1.1 mm against the soil.A third reading C ("closing pressure") can also optionally be taken by slowly deflating the membrane soon after B is reached.The blade is then advanced to the next test depth, with a depth increment of typically 20 cm.
The interpretation proceeds as follows.First the field readings are used to derive the DMT intermediate parameters material index I D , horizontal stress index K D , dilatometer modulus E D .Then I D , K D , E D are used, by means of commonly used correlations, to estimate the constrained modulus M, the undrained shear strength s u , the in situ earth pressure coefficient K 0 (clays), the overconsolidation ratio OCR (clays), the friction angle j' (sands), the bulk unit weight g.Consolidation and permeability coefficients may be estimated by performing dissipation tests.The C-reading, in sand, approximately equals the equilibrium pore pressure.
More detailed information on the DMT equipment, test procedure and all the interpretation formulae may be found in the comprehensive report by ISSMGE Technical Committee TC16 (Marchetti et al., 2001).

Seismic Dilatometer Test (SDMT)
The seismic dilatometer (SDMT) is a combination of the mechanical flat dilatometer (DMT) with an add-on seismic module for measuring the shear wave velocity V S .First introduced by Hepton (1988), the SDMT was subsequently improved at Georgia Tech, Atlanta, USA (Martin & Mayne, 1997, 1998;Mayne et al., 1999).A new SDMT system (Figs.1b and 1c) has been more recently developed in Italy (Marchetti et al., 2008).
The seismic module (Fig. 1b) is a cylindrical element placed above the DMT blade, equipped with two receivers spaced at 0.50 m.The shear wave source, located at ground surface, is an automatic hammer or a pendulum hammer (» 10 kg) which hits horizontally a steel rectangular plate pressed vertically against the soil (by the weight of the truck) and oriented with its long axis parallel to the axis of the receivers, so that they can offer the highest sensitivity to the generated shear wave.When a shear wave is generated at the surface (Fig. 1c), it reaches first the upper receiver, then, after a delay, the lower receiver.The seismograms acquired by the two receivers, amplified and digitized at depth, are transmitted to a PC at the surface, which determines the delay.V S is obtained as the ratio between the difference in distance between the source and the two receivers (S 2 -S 1 ) and the delay of the arrival of the impulse from the first to the second receiver (Dt).
The determination of the delay from SDMT seismograms, normally obtained using a cross-correlation algorithm rather than relying on the first arrival time or specific single points in the seismogram, is generally well conditioned.The true-interval test configuration with two receivers avoids possible inaccuracy in the determination of the "zero time" at the hammer impact, sometimes observed in the pseudo-interval one-receiver configuration.Moreover, the couple of seismograms recorded by the two receivers at a given test depth corresponds to the same hammer blow and not to different blows in sequence, which are not necessarily identical.Hence the repeatability of V S measurements is considerably improved (observed V S repeatability » 1%, i.e. a few m/s).V S measurements are taken every 0.50 m of depth (while the mechanical DMT readings are taken every 0.20 m).Validations of V S measurements by SDMT by comparison with V S measured by other in situ seismic tests at various research sites are reported by Marchetti et al. (2008).

4.Tentative Method for Deriving in situ G-g
Decay Curves from SDMT Marchetti et al. (2008) first proposed the possible use of the SDMT for deriving in situ elemental soil stiffness variations with strain level (G-g curves or similar).Such curves could be tentatively constructed by fitting "reference typical-shape" laboratory G-g curves through two points, both obtained by SDMT: (1) the initial small strain modulus G 0 (obtained as G 0 = r V S 2 ), and (2) a working strain modulus G DMT .
To locate the second point on the G-g curve it is necessary to know, at least approximately, the elemental shear strain corresponding to G DMT .Indications by Mayne (2001) locate the DMT moduli at an intermediate level of strain (g » 0.05-0.1%)along the G-g curve.Similarly Ishihara (2001) classified the DMT within the group of methods of measurement of soil deformation characteristics involving an intermediate level of strain (0.01-1%).The above qualitative indications are investigated in this paper.(Marchetti et al., 2001;Marchetti et al., 2008).
As suggested by Marchetti et al. (2008), a working strain shear modulus G DMT can be derived from the constrained modulus M DMT provided by the usual DMT interpretation (Marchetti, 1980, Marchetti et al., 2001).As a first approximation, by referring to linear elasticity: where n = Poisson's ratio.E.g. assuming a typical drained n of 0.2 (noting that M DMT is a drained modulus), the working strain shear modulus may be obtained from Eq. 1 as G DMT = 0.375 M DMT .It should be noted that correlations between the DMT parameters (E D and K D ) and M DMT proposed by Marchetti (1980) are based on the assumption that M DMT represents a reasonable estimate of the "operative" or drained working strain modulus (i.e. the modulus that, when introduced into the linear elasticity formulae, provides realistic estimates of the settlement of a shallow foundation under working loads).This assumption is supported by the good agreement observed in a large number of well documented comparisons between measured and DMTpredicted settlements or moduli (see Monaco et al., 2006;Marchetti et al., 2008).
The use of the SDMT to assess the in situ decay of stiffness at various test sites is explored in the following sections using data obtained in different soil types and where both SDMT data and "reference" stiffness decay curves were available.Such stiffness decay curves were: (a) back-figured from the observed behavior under a fullscale test embankment (Treporti) or footings (Texas), (b) obtained by laboratory tests (L'Aquila, Fucino plain, Po plain), or (c) reconstructed by the combined use of different in situ/laboratory techniques (Western Australia).The procedure adopted in all cases is as follows, and is shown schematically on Fig. 2: 1) Using SDMT data obtained at the same depth of each available reference stiffness decay curve, a working strain modulus G DMT (or E DMT ) is derived from M DMT and normalized by its small strain value G 0 (or E 0 ) derived from V S .
2) The G DMT /G 0 (or E DMT /E 0 ) horizontal ordinate line is superimposed to the same-depth experimental stiffness decay curve, in such a way that the data point ordinate matches the curve; 3) The "intersection" of the G DMT /G 0 (or E DMT /E 0 ) horizontal ordinate line with the stiffness decay curve provides a shear strain value referred to here as g DMT .

Treporti, Venice (Italy)
A full-scale vertically-walled cylindrical test embankment (40 m diameter, 6.7 m height, applied load 106 kPa) was constructed at the site of Treporti, Venice (Italy) where ground conditions are typical of the highly heterogeneous, predominantly silty deposits of the Venice lagoon.Pore pressures, surface settlements, horizontal movements and vertical displacements were monitored continuously and at various depths; see Simonini (2006).The Treporti test site was investigated extensively by means of piezocone tests (Gottardi & Tonni, 2004), flat dilatometer tests (Marchetti et al., 2004), seismic piezocone tests and seismic dilatometer tests (McGillivray & Mayne, 2004), continuous coring boreholes and high quality laboratory tests (Simonini et al., 2006).Significant results of the experimental program at Treporti have already been published by various research groups.
Figure 3 shows the profiles of the DMT parameters at Treporti, namely the material index I D , the constrained modulus M DMT , the undrained shear strength s u and the horizontal stress index K D from DMT 14 at the centre of the embankment, as well as the profiles of V S obtained from SDMT 14 (McGillivray & Mayne, 2004), before starting the construction of the embankment (2002).
The Treporti embankment research has provided a unique opportunity to investigate the decay of soil stiffness in situ (Monaco et al., 2014).Besides the moduli at the end of construction, moduli were also back-calculated in the elements on the centerline from local vertical strains e v measured during construction, under each load increment (from small to working strains).The stiffness considered in this section is the Young's modulus E.
In situ secant Young's moduli E were back-calculated at the mid-height of each 1 m soil layer as E = (Ds v -2 n Ds r )/e v , assuming vertical and radial stress increments Ds v and Ds r according to the theory of elasticity, e v obtained from extensometer data at the centre of the embankment under each load increment during construction (Marchetti et al., 2006).Figure 4a shows the moduli corresponding to the first construction step (H = 0.5 m), to half-bank (H = 3.5 m) and to the construction end (H = 6.7 m).In the same figure, the small strain modulus E 0 , derived from V S measured by SDMT, and the modulus E DMT derived from M DMT are shown for comparative purposes, assuming elasticity theory and a Poisson's ratio n = 0.15 for both cases (hence E DMT = 0.95 M DMT ). Figure 4a shows the progressive reduction of the back-calculated moduli E under increasing load.Such reduction should reflect the combined effects of the increase in stiffness with stress level and the reduction in stiffness with strain level.
In order to separate the two effects, the dependence of E on current stress level was taken into account, as a first approximation, by use of the Janbu's relation: where K E = modulus number, p a = reference atmospheric pressure (100 kPa), s' v = current vertical effective stress, and n = exponent, generally varying between 0.5 to 1 and assumed here to equal 0.5, following the observations of Cola & Simonini (2002).The variation of the modulus number K E in Eq. 2 corresponding to E back-calculated under each load increment is represented in Fig. 4b, which even more clearly shows the decay of stiffness, normalized for the effect of stress level, with increasing strain.In situ decay curves of soil stiffness with strain level (Fig. 5) were reconstructed from the back-calculated moduli at the mid-height of each 1 m soil layer.To account for the effect of varying stress level, such in situ curves are expressed in terms of variation of the ratio K E /K E0 , where K E and K E0 are respectively the modulus number corresponding to E back-calculated for each load increment and to the initial modulus E 0 (K E0 is obtained by Eq. 2 for E = E 0 and s' v = s' v0 ).The two sets of curves in Fig. 5 are representative of two distinct soil layers: (a) the sand layer between 2 to 8 m depth, and (b) the low plasticity (plasticity index PI = 8-12%, Simonini et al., 2006) silt layer between 8 to 20 m depth (which contributed most of the observed settlement).Note that the initial part of the curves in Fig. 5 at small strains is missing, since the extensometers did not provide reliable measurements of e v less than about 0.01-0.5%.
At Treporti test site, using SDMT results obtained at the depth of each back-figured in situ stiffness decay curve in Fig. 5, Young's moduli E DMT were derived from M DMT us-ing elasticity theory and normalized by their small strain values E 0 derived from V S .The E DMT moduli were derived from the constrained moduli M DMT , using the theory of elasticity, by Eq. 3: assuming n = 0.15, hence E DMT = 0.95 M DMT .
The dots in Fig. 5 are the intersection between the in situ decay curve at a given depth and the horizontal line having as ordinate the ratio K E /K E0 corresponding to E DMT /E 0 at the same depth.Such "intersections" provided the values of the associated abscissas, i.e. the vertical strains e v in this case.The rectangular shaded areas in Figs.5a and 5b denote, for each soil layer, the range of values of the ratio K E /K E0 corresponding to E DMT /E 0 and the associated range of vertical strains: e v » 0.01 to 0.1% in sand, » 0.3 to 1% in silt (Monaco et al., 2014).
Hence, the ratio G DMT /G 0 was calculated by using the theory of elasticity (Eq.4), while the corresponding shear strain g DMT was obtained by Eqs. 5, 6, as introduced by Atkinson (2000): assuming n = 0.15, hence G DMT = 0.43 E DMT .
e ne (5) where e s = shear strain for the individual soil elements.
The values of the normalized working strain shear modulus G DMT /G 0 range from 0.18 to 0.24 in sand and 0.02 to 0.12 in silt, while the range of values of the shear strain g DMT are 0.02% to 0.14% in sand, 0.50% to 1.65% in silt.

Texas A&M University National Geotechnical Experimentation Site (U.S.A.)
In 1994 a Spread Footing Prediction Symposium was conducted at the Texas A&M University National Geotechnical Experimentation Site, as part of the ASCE Geotechnical Specialty Conference Settlement '94.Five square footings, ranging in size from 1 to 3 m, were constructed and tested to obtain the complete load-settlement curves (Gibbens & Briaud, 1994a).The test site, composed of medium dense silty fine sand, was extensively investigated by several in situ tests (SPT, CPTU, DMT, borehole pressuremeter, Cross-Hole, borehole shear test and step blade test).Laboratory triaxial and resonant column tests were executed on reconstituted samples (Gibbens & Briaud, 1994b).Figure 6 plots the DMT profiles (DMT 1, DMT 2), in terms of the material index I D , the constrained modulus M, the friction angle j' and the horizontal stress index K D .
Figure 7 shows the in situ stiffness decay curve reconstructed by Berardi (1999) based on the observed performance of the footings.The Young's modulus E was backfigured from the observed load-settlement curves by use of a non linear iterative approach.The influence of current stress level was considered "implicit" in the E values determined over a limited influence depth, assumed within B and 2B (B = footing width).In Fig. 7 the decay of E, normalized to its initial value E 0 , is plotted as a function of the relative displacement w/B% (footing settlement w/ width B).
From the results of two DMTs executed at the Texas A&M University test site, Young's moduli E DMT (average values over an influence depth assumed within B and 2B) were derived from M DMT by Eq. 3, assuming n = 0.2.The initial values of E 0 over the same depth interval were derived from V S measured by Cross-Hole via elasticity theory (for n = 0.2).In Fig. 7 the data points corresponding to E DMT /E 0 for each footing size (3 m, 2 m, 1.5 m and 1 m) are superimposed to the E/E 0 -w/B curve reconstructed by Berardi (1999).The "intersection" of the DMT data points with the observed in situ decay curve indicates that the moduli estimated from DMT are located in a range of relative displacement w/B » 0.25 to 0.45%.
Hence, the ratio G DMT /G 0 was calculated by using the theory of elasticity (Eq.4), while the corresponding shear strain g DMT was obtained by Eqs. 6, 7, as introduced by Atkinson ( 2000): The values of the normalized working strain shear modulus G DMT /G 0 range from 0.20% to 0.25%, while the range of values of the shear strain g DMT are 0.02 to 0.14% in sand, 0.13 to 0.23% in silt.

L'Aquila (Italy)
Following the destructive April 6, 2009 earthquake (moment magnitude M w = 6.3), the area of L'Aquila was extensively investigated by a variety of geotechnical and geophysical testing techniques, involving several working groups.Soon after the earthquake site investigations, including Down-Hole, surface wave tests and SDMT, were concentrated at a number of sites selected for the construction of new temporary houses for the homeless people (C.A.S.E.Project).Advanced cyclic/dynamic laboratory tests, including resonant column/torsional shear tests (RC-CTS) and double sample direct simple shear tests (DSDSS), were carried out on undisturbed samples from several C.A.S.E.sites, in medium-to fine-grained soils, by a network of Italian soil dynamics laboratories.Details and data are reported in Monaco et al. (2012); Santucci de Magistris et al. (2013); Monaco et al. (2013).The availability of both SDMT and laboratory test results at three C.A.S.E.sites (Cese di Preturo, Pianola, Roio Piano) permitted some calibration of empirical estimates of nonlinear parameters from SDMT (Amoroso et al., 2012).
Coupled data from SDMT and resonant column/torsional shear tests were also obtained from an extensive geotechnical investigation performed in the Southern part of the city centre of L'Aquila for the reconstruction of several damaged buildings (Totani et al., 2012;Amoroso et al., 2015).(Berardi, 1999) and superimposed E DMT /E 0 data points (Amoroso et al., 2012).
Table 1 reports the values of the shear wave velocity V S measured by SDMT, the small strain shear modulus G 0 in situ obtained from V S , the constrained modulus M DMT obtained from the SDMT at the depth of the samples tested in the laboratory, the working strain shear modulus G DMT calculated using Eq. 1, assuming n = 0.2, and the plasticity index PI.The values of the normalized working strain shear modulus G DMT /G 0 , also reported in Table 1, result 0.10 to 0.23 in silt and clay, 0.37 in silty sand.Figure 8 plots the SDMT profiles, in terms of the material index I D , the constrained modulus M, the undrained shear strength s u , the horizontal stress index K D and the shear wave velocity V S at the four mentioned sites.In Fig. 9 each G DMT /G 0 data point (grey symbols) is superimposed on the corresponding same-depth laboratory G/G 0 curve (RC tests by University of Napoli Federico II, DSDSS tests by University of Roma La Sapienza).The range of values of the shear strain g DMT resulting from the "intersection" of the G DMT /G 0 data points with the laboratory curves (rectangular areas in Fig. 9) are g DMT = 0.24 to 0.52% in silt and clay, g DMT = 0.16% in silty sand; these are also reported in Table 1.

Fucino plain (Italy)
In 1986 a comprehensive investigation, involving static and dynamic loading effects, was carried out in the national research site of Fucino, Italy (Burghignoli et al., 1991).In situ tests (SPT, CPT, DMT, self-boring pressumeter, vane test, Down-Hole, Cross-Hole, Spectral Analy-sis of Surface Waves) and laboratory tests (static and dynamic) were carried out to investigate the homogeneous lacustrine clay deposit to a depth of 40 m.Resonant column/torsional shear tests (RC-CTS) were executed on twelve undisturbed samples recovered from depths ranging between 3 and 37 m (effective vertical stress between 30 and 250 kPa).Although the data points pertain to a wide range of consolidation stresses, the results define, within a narrow band, the strong dependence of the stiffness on the strain level (Burghignoli et al., 1991).In 2004 the same site in the Fucino plain was investigated by seismic dilatometer (Marchetti et al., 2008) and the results are illustrated in Fig. 10.
Table 2 reports the values of the shear wave velocity V S measured by SDMT, the small strain shear modulus G 0 in situ obtained from V S , the constrained modulus M DMT obtained by SDMT at the depth of the samples tested in the laboratory, the working strain shear modulus G DMT calculated by Eq. 1, assuming n = 0.2, and the plasticity index PI.The values of the normalized working strain shear modulus G DMT /G 0 , also reported in Table 2, result 0.04 to 0.13 in clay.In Fig. 11 each G DMT /G 0 data point (grey symbols) is superimposed on the corresponding same-depth laboratory G/G 0 curve (RC tests).The range of values of the shear strain g DMT resulting from the "intersection" of the G DMT /G 0 data points with the laboratory curves (rectangular areas in Fig. 11) are g DMT = 1.10 to 1.70% in clay; these are also reported in Table 2.

Po plain (Italy)
The seismic sequence which affected northern Italy in May 2012, in particular the two main shocks that occurred on May 20, 2012 (M w = 5.8) and May 29, 2012 (M w = 5.6), induced several cases of liquefaction and related ground deformations.
An extensive site investigation program was subsequently planned by the "Liquefaction Working Group" promoted by the Emilia Romagna regional government and by the national Department of Civil Protection, in addition to the existing soil investigation data base, to characterize the soils and to define the input data necessary for site seismic response analyses and for assessment of liquefaction hazard (Regione Emilia Romagna -Liquefaction Working Group, 2012).The available results of this investigation programme, illustrated in various reports and papers (e.g.Facciorusso et al., 2012, Fioravante et al., 2013), include borehole logs, results of piezocone/seismic piezocone penetration tests (CPTU/SCPTU) and laboratory tests on samples, including resonant column/torsional shear tests (RC-CTS).An additional investigation involving seismic dilatometer (SDMTs), as illustrated in Fig. 12, as well as resonant column tests (RC) was carried out by the Working Group S2-UR4 ( 2013) and focused only on the area of San Carlo; see also Romeo et al. (2015).The town of San Carlo was constructed above the abandoned channel of the Reno River, and sand is the prevailing lithology in the band near this paleo-channel.Part of the town was built on the ancient banks of the Reno River.
The availability of results from both SDMT and laboratory resonant column (RC) tests on undisturbed samples taken in nearby boreholes in the area of San Carlo permitted some calibration of empirical estimates of non-linear parameters from SDMT.
Table 3 reports the values of the shear wave velocity V S measured by SDMT, the small strain shear modulus G 0 in situ obtained from V S , the constrained modulus M DMT obtained from SDMTs performed at the depth of the samples tested in the laboratory, the working strain shear modulus G DMT calculated by Eq. 1, assuming n = 0.2, and the plasticity index PI.The values of the normalized working strain shear modulus G DMT /G 0 range from 0.07 to 0.10 in silt and clay, and 0.06 to 0.32 in silty sand; see Table 3.In Fig. 13 each G DMT /G 0 data point (black and grey symbols) is superimposed on the corresponding same-depth laboratory G/G 0 curve (RC tests).The range of values of the shear strain g DMT resulting from the "intersection" of the G DMT /G 0 data points with the laboratory curves (rectangular areas in Fig. 13) are g DMT = 0.32% to 0.47% in silt and clay, g DMT = 0.07 to 0.30% in silty sand; see Table 3.

Western Australia
The G/G 0 -g decay curves presented in this section were obtained at five different test sites in Western Australia (Shenton Park, Ledge Point, Perth CBD, East Perth, Margaret River).Such curves were constructed based on the results of several in situ tests, including flat/seismic dilatometer tests (DMT/SDMT), seismic cone penetration tests (SCPT), self-boring pressuremeter tests (SBP) and  Figure 14 shows the SDMT profiles, in terms of the material index I D , the constrained modulus M DMT , the inferred friction angle j' or the undrained shear strength s u , the horizontal stress index K D and the shear wave velocity V S at the three mentioned sites.
The in situ normalized G/G 0 -g decay curves shown in Fig. 15 (Shenton Park, silica sand), Fig. 16 (Ledge Point, calcareous sand) and Fig. 17 (Perth CBD, alluvial silty clay) were reconstructed by combining the information resulting from SCPT and SBP.In particular: • the initial part of the curves (g £ 0.001%) was characterized by the small strain shear modulus G 0 obtained from V S measured by SCPT (no SDMT data were available at these sites); • the non-linear G/G 0 -g decay at medium to large shear strains (g ³ 0.01%) was estimated based on SBP data, according to the procedure proposed by Jardine (1992); • the central part of the curves (0.001% > g > 0.01%) was defined by simply connecting the initial part obtained from SCPT (G 0 ) and the final part obtained from SBP.
The working strain shear modulus G DMT was calculated from M DMT obtained by DMT at the same depths of the SCPT and SBP data used to define the G/G 0 -g curve, by use of Eq. 1, assuming n = 0.      (Amoroso, 2011).
from in situ SDMT and laboratory triaxial tests.In this case: • the initial part of the curves (g £ 0.001%) was characterized by G 0 derived from V S measured by SDMT; • the non-linear G/G 0 -g decay at medium to large shear strains (g ³ 0.1% at Margaret River, g ³ 0.5% at East Perth) was estimated from triaxial tests according to Atkinson (2000); • the central part of the curves (0.001% > g > 0.5% at East Perth, 0.001% > g > 0.1% at Margaret River) was defined by simply connecting the initial part obtained from SDMT (G 0 ) and the final part obtained from triaxial tests.
The working strain shear modulus G DMT was calculated from M DMT obtained by SDMT at the same depths of the samples tested in the laboratory by use of Eq. 1, assuming n = 0.2 at both sites.The values of G DMT /G 0 vary from 0.04 in soft clay to 0.07 in silty clay; see Table 4.The values of the shear strain g DMT resulting from the "intersection" of the G DMT /G 0 data points with the reconstructed reference G/G 0 -g decay curves (dot symbols in Figs.18 and 19) are 5.5% in soft clay and vary from 0.23% to 1.50% in silty clay; see Table 4.

Summary of results at various test sites
Over the past decades, numerous studies have been conducted regarding the dynamic soil properties and the       parameters affecting them, such as the mean effective confining pressure, the soil type and the plasticity.Various investigators have proposed non linear curves for sands (for example Darendeli, 2001;Seed et al., 1986;Iwasaki et al., 1978;Kokusho, 1980), clays and silts with different plasticity (for example Darendeli 2001;Vucetic & Dobry, 1991;Sun et al., 1988).Figure 20 summarizes the upper and lower ranges of these typical curves, obtained for different values of the mean effective confining pressure, as-sumed between 25 and 1600 kPa, and a plasticity index PI ranging between 0% and 100%.Figure 20 shows that the curves proposed by Darendeli (2001) including all the other reference curves.
Figure 21 depicts the possible use of the SDMT for calibrating the selection of in situ G/G 0 -g decay curves in various soil types.The results obtained at all the test sites previously described were superimposed on the Darendeli (2001) G/G 0 -g stiffness decay curves.The rectangular shaded areas in Fig. 21 represent the range of values of the normalized working strain shear modulus G DMT /G 0 determined in different soil types (sand, silt and clay) and the corresponding shear strain g DMT determined by the "intersection" procedure.Based on the available information, the "typical range" of shear strain associated to the working strain moduli G DMT can be approximately assumed as: g DMT » 0.01-0.45% in sand, g DMT » 0.1-1.9% in silt and clay.In soft clay the values of g DMT > 2% (not shown in Fig. 21) are too high to attempt an interpolation using a reference stiffness decay curve.
These observations are in agreement with preliminary literature indications (Mayne, 2001;Ishihara, 2001).Moreover, the calculated values of the ratio G DMT /G 0which could be regarded as the shear modulus decay factor at working strains -are in line with the trends observed by Marchetti et al. (2008), who investigated the experimental interrelationship between small strain and working strain stiffness using SDMT in sand, silt and clay.In particular, the diagrams of the ratio G DMT /G 0 vs. the DMT horizontal stress index K D (related to OCR) constructed by Marchetti et al. (2008) using the SDMT results at 34 different sites, in a variety of soil types, indicated that the G decay in sands is more significant at lower strains than in silts and clays, and that the decay curves in silts and clays are very similar.

Proposed numerical G-g decay curves from SDMT
Several authors (Hardin & Drnevich, 1972;Bellotti et al., 1989;Byrne et al., 1990;Fahey & Carter, 1993;Fahey, 1998) introduced a hyperbolic model to represent the non-linear stress-strain behaviour of soil in pressuremeter tests.In this respect, the SDMT experimental data determined at all the investigated test sites (Fig. 22) were used to assist the construction of a hyperbolic stress-strain equation (Eq.bolic G vs g curves have been seen to be particularly relevant for dynamic/cyclic applications.

Conclusions
The results presented in this paper support the possible use of the SDMT to assess the decay of in situ stiffness with strain level and to address the selection of elemental G-g curves in various soil types.This potential stems from the ability of the SDMT to provide routinely, at each test depth, both a small strain stiffness (G 0 from V S ) and a working strain stiffness G DMT (derived via standard DMT correlations)."Reference typical-shape" laboratory G-g curves may be tentatively fitted through these two stiffness values.A significant premise of this approach is that, to locate the second point on the G-g curve, it is necessary to know (at least approximately) the shear strain g DMT corresponding to working strain modulus G DMT .
Typical ranges of g DMT in different soil types have been inferred from the "intersection" of the SDMT data points with same-depth reference stiffness decay curves -backfigured from the observed field behavior under full-scale loading, or obtained by cyclic/dynamic laboratory tests or reconstructed by the combined use of different in situ/laboratory techniques -at various test sites.
Based on the available information, g DMT is typically about 0.1% in sand, about 0.5 to 1.0% in silt and clay and greater than 2% in soft clay.The proposed hyperbolic relationship, together with an estimate of g DMT from Fig. 21, can provide a useful first order estimate of a soil's G-g degradation curve.

Figure 2 -
Figure 2 -Procedure to derive in situ G-g decay curves from SDMT.

Figure 4 -
Figure 4 -Variation of (a) secant Young's modulus E, and (b) corresponding modulus number K E (Eq. 2), back-calculated from local e v measured at the center under various embankment loads throughout construction (Monaco et al., 2014, with permission from ASCE).

Figure 5 -
Figure 5 -Curves of decay of soil stiffness with vertical strain back-calculated from local e v measurements (curves labeled "In situ curves") in the sand layer 2 to 8 m depth (box a) and in the silt layer 8 to 20 m depth (box b).The dots are the intersection between the curve at a given depth and the horizontal line having as ordinate the ratio K E /K E0 corresponding to E DMT /E 0 at the same depth.Such "intersections" provided the values of the associated abscissas e v (Monaco et al., 2014, with permission from ASCE).
Figure14shows the SDMT profiles, in terms of the material index I D , the constrained modulus M DMT , the inferred friction angle j' or the undrained shear strength s u , the horizontal stress index K D and the shear wave velocity V S at the three mentioned sites.The in situ normalized G/G 0 -g decay curves shown in Fig. 15 (Shenton Park, silica sand), Fig. 16 (Ledge Point, calcareous sand) and Fig. 17(Perth CBD, alluvial silty clay) were reconstructed by combining the information resulting from SCPT and SBP.In particular:• the initial part of the curves (g £ 0.001%) was characterized by the small strain shear modulus G 0 obtained from V S measured by SCPT (no SDMT data were available at these sites); • the non-linear G/G 0 -g decay at medium to large shear strains (g ³ 0.01%) was estimated based on SBP data, according to the procedure proposed by Jardine (1992); • the central part of the curves (0.001% > g > 0.01%) was defined by simply connecting the initial part obtained from SCPT (G 0 ) and the final part obtained from SBP.The working strain shear modulus G DMT was calculated from M DMT obtained by DMT at the same depths of the SCPT and SBP data used to define the G/G 0 -g curve, by use of Eq. 1, assuming n = 0.2 in sand in silty clay.The values

Figure 21 -
Figure 21 -Possible use of the SDMT for calibrating the selection of in situ G/G 0 -g decay curves in various soil types.
Figure 23 -Comparison between hyperbolic and "measured" stiffness decay curves at Shenton Park (a) and Roio Piano (b).

Figure 22 -
Figure 22 -SDMT experimental data used to assist the construction of a hyperbolic equation.

Table 1 -
Amoroso et al., 2012) DMT /G 0 obtained from SDMT and corresponding shear strain g DMT determined from the intersection with the G/G 0 -g laboratory curves (afterAmoroso et al., 2012).

Table 2 -
Fucino plain -Values of G DMT /G 0 obtained from SDMT and corresponding shear strain g DMT determined from the intersection with the G/G 0 -g laboratory curves.

Table 3 -
Po plain -Values of G DMT /G 0 obtained from SDMT and corresponding shear strain g DMT determined from the intersection with the G/G 0 -g laboratory curves (after Working Group S2-UR4, 2013).

Table 4 -
(Amoroso et al., 2012)ues of G DMT /G 0 obtained from SDMT (or DMT + SCPT) and corresponding shear strain g DMT determined from the intersection with the G/G 0 -g reference curves at five test sites(Amoroso et al., 2012).