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Stress-strain-strength-flow parameters from enhanced in-situ tests
Paul W. MayneGeorgia Institute of Technology, Atlanta, Georgia USA
Proceedings, International Conference on In-Situ Measurement of Soil Properties & Case Histories [In-Situ 2001],Bali,Indonesia, May 21-24, 2001, pp. 27-48.
ABSTRACT: Seismic piezocone penetration tests (SCPTu) with dissipation phases are particularly useful forgeotechnical site characterization as they provide four independent readings with depth from a single sounding,as well as time-rate information. The penetration data (qt, fs, ub) reflect failure states of stress, the shear wave (Vs)provides the small-strain stiffness, and dissipations give flow properties. Taken together, an entire stress-strain-strength-flow representation can be derived for all depths in the soil profile. A similar approach is obtainablefrom seismic flat dilatometer soundings. Methods of evaluating the degree of preconsolidation, stress state,strength, stiffness, and permeability characteristics of sands and clays are reviewed with example applications.For clays, a combined cavity expansion and critical-state model has proven useful. For sands, chamber test resultshave guided the interpretation of parameters.
1 INTRODUCTION
The complexities of soil behavior are many andinclude the inherent aspects of natural fabric,anisotropy, nonlinear stress-strain behavior, porewaterresponse, cementation, and sensitivity, as well asrheological effects such as aging, strain rate, creep,and thixotropy. Thus, the overreliance of some inusing the single N-value from the standard penetrationtest to provide most of the geotechnical data neededfor engineering analysis is not very realistic. Manyvaried and useful tests have been developed tomeasure and assess the in-situ properties andparameters of soils, as discussed in Jamiolkowski, etal. (1985) and Lunne, et al. (1994). Of particular noteis the seismic piezocone penetrometer test (SCPTu)that is a hybrid field method, combining the virtues ofthe CPT with downhole geophysics (Robertson, et al.,1986), as illustrated in Figure 1. In a similar manner,the seismic flat dilatometer (SDMT) provides bothpenetration and wave velocity data from the samesounding (Hepton, 1988).
The SCPTu and SDMT obtain measurements attwo opposite ends of the stress-strain spectrum,including failure states corresponding to the strengthcharacteristics (Jmax) of the material, as well as thenondestructive properties associated with elastic wavepropagation and soil stiffness (E or G). In addition,both of these tests can also be halted periodically tomonitor the decay rate of readings with time. This isparticularly advantageous in fine-grained soils, where
excess porewater pressures are induced by theinstallation of the probe. These readings providedirect information about the flow properties of the soil,namely the coefficient of consolidation andpermeability.
Figure 1. Setup and procedure for seismic piezocone testing
d = 35.7 mm
CONE TIP STRESS SLEEVE FRICTION PORE PRESSURE SHEAR W AVE VELOCITY
0
5
10
15
20
25
30
35
0 10 20 30 40
qt (MPa)D
epth
(m)
0 100 200 300
fs (kPa)0 1000 2000 3000
u2 (kPa)0 100 200 300 400
Vs (m/sec)
qt
fs
u2
Vs
Figure 2. Illustrative results of SCPTu for geostratigraphic profiling of soil layers in Memphis, Tennessee.
Of interest to geotechnical exploration, the SCPTu andSDMT provide optimization of data collection forgeostratigraphy and the evaluation of soil parameters.
1.1 Geostratigraphic profilingThe cone penetrometer provides continuous readingswith depth, thus is unsurpassed in its ability todelineate changes in soil strata, layer boundaries, andthe presence of seams, lenses, and inclusions. Thebasic readings include: cone tip stress (qc), sleevefriction (fs), and penetration porewater pressures (u).An example of the detailed profiling capability isshown in Figure 2 for Memphis, Tennessee, whichindicates an 11-meter thick sand layer overlaying adouble marine clay layer. The unusual feature at 20 to22 m depth is believed to be a buried desiccated crustof the lower clay unit.
A visual examination of the individual penetrationrecords is often sufficient for determining stratigraphyand soil classification. If necessary, the use ofempirical soil behavioral charts can be implemented,such as that by Robertson (1990).
1.2 CPT measurement corrections
The tip stresses must be corrected for porewatereffects on the back of the cone tip (Lunne et al., 1997),thus designated qT. This correction requires theporewater pressures to be measured at the shoulder (ub
or u2), therefore, this is the standard piezoconegeometry. The tip stress correction is paramount forsoundings taken in soft to firm to stiff intact clayswhere positive )u are generated. In the case of sandswhere pore pressures are near hydrostatic (u2 . u0) andmuch smaller than qc, the correction is often small(therefore, qT . qc). In the special case of fissured andoverconsolidated materials, the measured ub can bezero or negative, again diminishing the need forcorrection. In this situation, a midface porewaterpressure element (ut or u1) provides more interestingdata for stratigraphic mapping (Mayne, et al. 1995).
A similar correction occurs for sleeve readings, yetis not demanded from a practical standpoint becauseadditional channels of porewater pressures must beobtained (Jamiolkowski, et al., 1985).
A nice feature concerning porewater readings isthat corrections are not required, provided that propersaturation techniques are followed and clogging of thefilter does not occur. In general, plastic porous filterssaturated under vacuum with glycerine are excellentfor the shoulder element. Other filter types includeceramic, sintered brass, and steel, that can be saturatedwith water, silicon, and/or special greases (Campanella& Robertson, 1988).
The importance of taking accurate baselinereadings before and after each sounding should benoted. As electronics in both the penetrometer andfield data acquisition unit can be affected by changes
in temperature, humidity, electromagneticinterference, power drops/surges, and otherhappenstance, initial baseline values of each channelmust be carefully established prior to advancing thesounding.
Finally, the use of different class penetrometersshould be considered with regard to datainterpretation, especially on critical projects or wherehigh-quality results are expected. The use of class 1cones are sufficient for routine exploration ofsubsurface strata and layering sequences across a site,yet the interpretation of soil parameters and propertiesmay necessitate a class 3 penetrometer (Lunne, et al.1997) at select sounding locations for calibration andverification with laboratory triaxial shear,consolidation, and resonant column results. 1.3 DMT measurement correctionsThe flat plate dilatometer provides two pressurereadings at either 20-cm or 30-cm depth intervals:contact pressure (“A”) and expansion pressure (“B”).Both readings require a correction for the membranestiffness taken in air, per Schmertmann (1986). Thecorrected “A” and “B” are designated p0 and p1,respectively.
1.4 Corrections to geophysical dataWith modern electronics, the early-reported problemsof timing delays associated with trigger switches andoscilloscopes now appear minimized. For pseudo-interval downhole tests conducted with a singlehorizontal geophone, the individual wave trains fromthe geophysical surveys do require an assessment ofthe shear wave arrivals that are made difficult,however, due to the pre-arrival of the P-wave(Campanella, 1994).
Traditionally, the identification of the S-wavearrival has relied upon polarized wave-generation andpaired sets of right & left strikes to assess a singlepoint on the time of arrival (ts). Today, with availablesoftware packages such as Mathcad, it is relativelysimple to conduct cross-correlation over thousands ofpoints on the wave train to evaluate the interval time.This then represents a correction in data evaluationprocedures. Of course, the true-interval method withtwo downhole geophones approach (e.g., Burghignoli,et al. 1991) avoids this issue and with the advent ofnew digital cones, may in fact become the futuremanner for SCPTu.
Since the same energy source is used for eachseparate event, as downhole tests advance with depth,the amplitude of the wave arrival decreases, thus theshear strain can be measured as the peak particlevelocity divided by the shear wave velocity, (s = ç/Vs.
As such, a correction for the derived small-strain shearmodulus (G0 = DTVs
2) based on the measured strainlevel is available (Larsson & Mulabdiƒ, 1991a).
2 SOIL STRENGTH
For saturated geomaterials, it is common to assumethat either the drained strength or undrained strengthconditions prevail during penetration. For clean sands,fully-drained penetration is the usual considerationwith direct assessment focused on the effective stressfriction angle (Nr) and an assumed nil value for theeffective cohesion intercept (cr = 0). For clays, totalstress analyses with no volume change are the normalassumptions, with penetration data giving theundrained shear strength (cu or su).
The undrained strength of soil is greatly affectedby many factors, including initial stress state (Ko),anisotropy, boundary conditions, strain rate, directionof loading, degree of disturbance, and other variables.Because of its non-uniqueness for a given clay, it isbest to relate in-situ test results to a more stableparameter. Consequently, it is recommended that thepreconsolidation stress (Fpr) obtained from laboratoryone-dimensional consolidation (oedometer) tests beused as a unique and consistent reference forbenchmarking in-situ penetration test data in clays.Then, the normalized form, or overconsolidation ratio(OCR = Fpr/Fvor), can be related to a suite ofundrained strengths via either an empirical stresshistory approach (Ladd, 1991) or constitutiverelationships, such as critical state soil mechanics(Wroth, 1984).
2.1 Drained strength of sands
The drained strength of sands can be expressed interms of the Mohr-Coulomb criterion as a peak frictionangle (Nr). Here, perhaps, the standard penetrationtest (SPT) can be used, provided that energycorrections are made properly to the measured N-values. Energy measurements from donut, safety, andauto-hammers show, on average, an energy efficiencyof 60%, yet this varies with operator, equipment, andpractice in a particular country.
Recent findings from high-quality frozen sandspecimens and associated N-values in soil boringshave been reported by Hatanaka & Uchida (1996).These results have been adjusted from the Japanese78% efficiency to an equivalent 60% value(designated N60) and normalized to a stress-level ofone atmosphere, designated (N1)60, and related to thetriaxial-measured value of Nr, as shown by Figure 3.
Triaxial Database with SPT-N Values
20
25
30
35
40
45
50
55
0 10 20 30 40 50 60Normalized (N1)60
Frict
ion
Ang
le,
φ' (d
eg)
Sand (SP and SP-SM)
Sand Fill (SP to SM)
SM (Piedmont)
H&T (1996)
φ' = [15.4(N1)60]0.5+20ο
25
30
35
40
45
50
55
10 100 1000Normalized Tip Stress, qt/σvo'
Frict
ion
Ang
le,
φ' (de
g)
Frankston Sand
Ticino Sand
Edgar Sand
Hokksund Sand
Lone Star Sand
R&C (1983)
φ' =arctan[0.1+0.38 log(qt/σvo')]
Figure 3. Peak friction angle of sands from SPT data. (Modifiedafter Hatanaka & Uchida, 1996).
Additional results from residual silty sand in Atlanta,Georgia (30% fines) reported by Mayne (1998) havealso been included and appear to fit this relationship.The expression for peak Nr is given by:
where the energy-corrected and stress-normalized N-value is obtained from:
Figure 4. Peak friction angle of clean quartz sands from CPT(after Robertson & Campanella, 1983).
The parameter Fatm = 1 bar = 100 kPa = referencestress equal to one atmosphere.
For the CPT, several separate theories of bearingcapacity and wedge plasticity were evaluated in lightof calibration chamber test data from several quartzsands that were compiled by Robertson & Campanella(1983). The recommended relationship for unaged,uncemented quartz sands is shown in Figure 4. Theexpression for peak Nr from CPT is given by:
Nr = arctan [0.1 + 0.38 log (qc/Fvor)] (3)
that shows good agreement between experimentalresults and the equation. In essence, this is an inversesolution to the well-known bearing capacity factor fora deep foundation: Nq = qc/Fvor = fctn(Nr). Yet, forclean sands, it has been observed experimentally thatthe measured tip resistance increases in proportion tothe square root of effective overburden stress (e.g.,Olsen, 1994). An alternative expression that accounts for thenonlinear normalization of qc with stress level andconsistent with (1) has been proposed (Kulhawy &Mayne, 1990):
Nr = 17.6° + 11.0 log(qc1) (4)
where qc1 = (qc)/(Fvor/Fatm)0.5 = normalized cone tipresistance. For the silty sand [Piedmont geology], (4)provides excellent agreement with consolidatedtriaxial tests on recovered samples (Figure 5). Twocommercial labs gave consistent results withcharacteristic parameters: cN= 0 and Nr = 35°±1°.
Figure 5. CPT profiling of Nr in silty sand (30% fines) inAtlanta, Georgia, USA.
30
32
34
36
38
40
42
44
46
1 2 3 4 5 6 7 8 9 10
Lateral Stress Index, KD
Effe
ctiv
e φ'
(deg
)
Active McDonald Farm SandAt-Rest (NC) Po River SandPassive Piedmont Silty Sand
φ '= 20o + 1/(0.04+0.06/KD)
WEDGE PLASTICITY
THEORY
1
10
100
20 30 40 50Effective Friction φ' (deg.)
Resist
ance
Num
ber,
Nm
Bq = 0.1
0.2 0.4 0.6 0.8 1.0
Bq = (u2-u0)/(qt-σvo)
NM = ∆(qt-σvo)/∆σvo'
β = 0
The peak angle of friction in sands can also beassessed by flat plate dilatometer tests. A wedgeplasticity solution for the CPT was presented byMarchetti (1985) that was later cross-correlated forCPT-DMT relationships by Campanella & Robertson(1991). The wedge solutions relate the DMT lateralstress index (KD) as a function of Nr and lateral stressstate, including active, at-rest (NC), and passiveconditions. For this approach, the passive caseappears to provide a generally conservative evaluationof peak Nr when compared with a data from threefield sites (see Figure 6). Results from the silty sandappear low in this case and perhaps affected bycapillarity effects in the soil.
Figure 6. Evaluation of peak Nr of sands from DMT data(Modified after Marchetti, 1997).
The expression for the Kp case can be approximated bya hyperbola of the form:
where KD = (p0-u0)/Fvor = lateral stress index.
2.2 Effective Strength of SoilsOf special interest is the possibility in evaluating theeffective stress strength parameters of all soil typesfrom the CPT, since porewater pressures aremeasured. An effective stress formulation coupledwith plasticity
Figure 7. Effective stress parameter determination for all soiltypes from CPTu data (Senneset, et al. 1989).
theory for interpretation of piezocone data has beendeveloped that relates effective Nr to the coneresistance number (Nm = )qnet/)Fvor) and normalizedporewater pressure parameter (Bq = )u2/)qnet), whereqnet = (qt-Fvo). Figure 7 shows a summary graph forone case and full details on the calculations are givenelsewhere (e.g., Senneset, et al., 1989).
2.3. Undrained strength of clays & siltsThe undrained shear strength (su, also cu) is a totalstress parameter that is often used in defining therelative consistency of fine-grained soils. The oldarchaic term “cohesion” (c) should no longer be used,as it results in confusion with the effective cohesionintercept (cr).
The undrained shear strength depends on initialstress state, direction of loading, rate, stress history,degree of fissuring, boundary conditions, and otherfactors. Each laboratory test (i.e., triaxial, plane strain,simple shear) provides a different value of su on thesame clay because of these effects. Moreover, each ofthe in-situ tests is traditionally assessed using adifferent theoretical basis in order to interpret su. Forinstance, limit equilibrium is applied to vane sheartests to obtain su from maximum torque readings,whereas cavity expansion theory is used to get su frompressuremeter tests. The result is that a matrix ofinterrelationships and calibrations would be requiredto connect all of the various laboratory strength modesto the individual in-situ tests. Instead, a stress historyapproach is followed herein.
0
0.1
0.2
0.3
0.4
0.5
0.6
NC
Und
rained
She
ar S
tren
gth
Ratio
15 20 25 30 35 40 45 Effective Stress Friction Angle (deg)
CIUC
KoPSC
CKoUC
SS
DSS
KoPSE
CKoUE
Wroth-Prevost Constitutive Model
The normalized undrained shear strength toeffective overburden ratio (su/Fvor) has been related tooverconsolidation ratio (OCR) both experimentally(e.g., Ladd, 1991) and theoretically (e.g., Wroth,1984). Extensive calibration efforts have been madeusing data from triaxial compression (CIUC andCAUC), triaxial extension (CIUC and CAUE), planestrain active (PSA) and extension (PSE), and directsimple shear (DSS), as well as special cuboidal triaxialand hollow cylinder tests (Kulhawy & Mayne, 1990).In as much as the modified Cam Clay has an isotropicyield surface, the distinction between compression andextension type loadings cannot be made without morerigorous considerations, a hybrid Wroth-Prevost modelwas produced to represent the interrelationshipsbetween the laboratory shearing modes, as indicatedby Figure 8.
The isotropically-consolidated undrained triaxialcompression test (CIUC) with porewater pressuremeasurements should be considered the minimumlevel of effort to be undertaken in the labcharacterization of su. The CIUC provides a directmeasurement of both a total stress parameter (su) aswell as effective stress parameter (Nr). Anisotropically-consolidated triaxial, plane strain, simple shear, andextension modes generally require a relatively highlevel of technical expertise. Since most commerciallabs can conduct CIUC tests, this provides aconvenient and practical reference. The su from CIUCtests are the highest, however, and should be reducedappropriately via Figure 8.
Figure 8. Normalized (su/Fvor)NC ratios with effective Nr fromWroth-Prevost calibrated model.
An internally-consistent critical-state model by Ohta,et al. (1985) provides similar interrelationships fordifferent testing methods. Assuming the normally-consolidated at-rest state can be approximated by K0(NC) = 1 - sinNr, the anisotropic bullet Cam-claymodel gives the curves shown in Figure 9.
Figure 9. Normalized (su/Fvor)NC ratios with effective Nr fromOhta critical-state model compared with modified Cam-clay.
Thus, a hierarchy of undrained strength ratios can beconsidered for a given clay, depending on the properloading case. For each mode, the overconsolidatedstrength is obtained from:
(su/Fvor)OC = (su/Fvor)NC OCR7 (6)
where 7 = 1 - 6/8 = plastic volumetric strain ratio, 8= Cc/2.3 = isotropic compression index, 6 . Cs/2.3 =isotropic swelling index. For many clays of low tomedium sensitivity, a value of 7 . 0.8 is appropriate,while for highly structured and/or cemented clays, avalue of 7 . 0.9+ may apply, yet for remolded and/orartificial materials, lower values are found (e.g., forWeald clay, 7 . 0.6).
If the CIUC test is adopted as a reference value,then the undrained strength of intact clays can berepresented in terms of stress history and effectivestress by (Wroth & Houlsby, 1985):
(su/Fvor)CIUC = (M/2) (OCR/2)7 (7)
where M = 6sin Nr/(3-sin Nr) in triaxial compression.For fissured geomaterials, consideration should begiven to reducing the strength given by (7) by up to afactor of 2, depending on the extent of cracking anddiscontinuities. An additional adjustment for strainrate can also be made (Kulhawy & Mayne, 1990).
Figure 10. Undrained DSS strength ratio with OCR and Nr
For many cases, the appropriate mode of undrainedstrength (TX, PS, DSS) will not be known beforehand,particularly during the time of the site characterizationphase. In these cases, the simple shear is considereda representative and intermediate value that can beused in engineering analyses involving embankmentstability, foundation bearing capacity, and excavationproblems. A simplifed expression for the DSS modeis given by:
(su/Fvor)DSS = ½ sinNr OCR7 (8)
The calibration of (8) with data from a variety of claysis shown in Figure 10 and seen to be reasonable.
3 STRESS HISTORY
As the stress history is needed for obtaining su in claysand silts, the utilization of in-situ test data will nowfocus towards the interpretation of the OCR of theformation. Statistical trends and correlative methodshave been reported elsewhere based on regressionanalyses of databases collected by piezocone (e.g.,Larsson & Mulabdiƒ, 1991b; Chen & Mayne, 1996),flat dilatometer (Pool, 1994), field vane (Mayne &Mitchell, 1988), as well as other devices (Mayne,1995). Herein, an analytical model based on cavityexpansion and critical-state concepts will be reviewedto express the OCR in terms of piezocone and flatdilatometer results.
3.1 Piezocone evaluation of OCR in clays The cone tip stress can be formulated in terms of theVesiƒ spherical cavity expansion theory:
qT = Fvo +su [(4/3)(ln IR +1)+B/2+1] (9)
where IR = G/su = rigidity index, and G = shearmodulus at the appropriate level of strain. For thesolution, the undrained strength from critical-state soilmechanics given by (7) has been used.
The measured excess porewater pressures arerepresented as a combination of changes due tooctahedral (normal) stresses and shear-inducedresponse:
)umeas = )uoct + )ushear (10)
The normal stress component is associated with a largefailure zone of soil that is disturbed around the probeand represented by spherical cavity expansion:
)uoct = (4/3) su ln IR (11)
For spherical cavities, the size of the zone of plasticdisturbance is given by rplastic/rprobe = (IR)0.33 .
The shear component is an interface value thatreflects a thin annulus zone that is highly-shearedimmediately adjacent to the probe as it punchesthrough the clay. For a piezocone with midface filterelement (type 1), the shear term was originallyneglected but later was modified (Mayne & Chen,1994). For shoulder filter elements (type 2), the shearcomponent is evaluated from CSSM:
Type 1: )ushear . 2 Fvor (12)
Type 2: )ushear = Fvor[1- (OCR/2)7] (13)
The above can be collected and rearranged to expressthe overconsolidation ratio in terms of a normalizedform of the effective cone tip resistance, (qT - u)/Fvor,and material constants M and 7 (Mayne, 1991, 1993):
Piezocone Readings (MN/m 2 )
0
5
10
15
20
25
30
0 2 4 6 8
Dep
th (m)
qTub
Amherst Lower 232rdBrent Cross MadingleyTaranto Boston BlueCretaceous Baton RougeVarennes St. J. VianneyPontida YorktownSt. Alban Strong PitCornell HagaBothkennar GloucesterOtttawa STP Emmerstad
0
10
20
30
40
50
0 10 20 30 40 50 Effective Cone Stress, (qt-u2)/σvo'
Ove
rcon
solid
ation
Ratio,
OCR
Λ = 0.75: φ' = 20o 30o 40o
Λ = 0.88
SCE-CSSM Model
OCRM
q uT
vo=
+−
2
1195 1
2
1
. '
/
σ
Λ
Figure
11. Analytical model for evaluating OCR from type 2 piezoconedata in clays.
The use of (15) for the direct assessment of degree ofoverconsolidation ratio in clays from type 2 CPTus isshown in Figure 11 for 20 clay sites. Parametricranges of the input parameters are shown for 20° < Nr< 40° and 0.75 < 7 < 0.88.
It should be emphasized that a class level 3penetrometer will be most valued as a qualityinstrument in providing OCRs in clay deposits becauseof the high accuracy of numbers needed. In thissituation, a type 1 cone cannot provide the accuratecorrection of tip stresses, particularly in soft clays.Moreover, because of the general closeness of the qTand u1 readings, the use of (14) may result in someinstability of estimates, excepting very stiff to hardoverconsolidated and/or fissured materials where thecorrection for qT may actually be small and/or thedifference between qT and u1 is large. When in doubt,always conduct type 2 soundings first to determine thelevel of the correction.
Results from the ongoing Cooper River Bridgeproject in Charleston, South Carolina will be presentedusing a class 3 cone. Figure 12 shows the measuredprofiles of qT and u2 with depth. Of particular interestis the clay deposit encountered below depths of 13 m.
Figure12. Piezocone data for Cooper River Bridge in South Carolinaindicating marl below depths of 13 meters.
This marine deposit is locally termed “Cooper Marl”and consists of a sandy calcareous plastic clay ofOligocene age. Groundwater is about 1 m deep. Themarl has an average 40 percent sand fraction that iscomposed of highly- broken shell fragments. Over thedepth range encountered from 13 m to the finalinvestigation depths of 60 m, a summary of the indexproperties are given in Table 1. The percent of CaCO3ranges between 50 to 80 percent.
A fairly comprehensive set of consolidated triaxialtests (CD and CU) indicated a consistently higheffective stress friction angle of Nr . 43° to 45°.Using the NTH effective piezocone method ofSenneset et al. (1989) in Fig. 7, an evaluation of theprocessed data from Figure 12 gives mean values forthe cone resistance number Nm = 18.3 ± 2.5 and porepressure parameter Bq = 0.56 ± 0.07. Assuming noadhesion and $ = 0, the interpreted Nr .46.4°. Whilesome might question the reasonableness of thesevalues, high frictional parameters in triaxialcompression have been observed for Mexico City claywith Nr .43° (Diaz-Rodriguez, et. al. 1992) andBothkennar clay with 37° < Nr < 45° (Smith, et al.1992).
12
14
16
18
20
22
24
26
28
30
32
0 2 4 6 8 10 12Overconsolidation Ratio, OCR
Dep
th (m)
CE-CSSM
Oed. (1998)
Consol. (1993)
OCR from CPTu
COOPERMARL
Table 1. Index properties of Cooper Marl, South Carolina
Index Mean Range
water content, wn 46.9 35 - 66
liquid limit, LL 82.9 60 - 129
plasticity index, PI 51.5 37 - 80
void ratio, e0 1.27 0.93 - 1.66
percent fines, PF 66.8 42 - 93
clay fraction, CF 12.4 5 - 22
yield stress, Fpr (kPa) 682 616 - 785
shear wave, Vs (m/s) 440 384 - 555
Figure 13. Measured and Predicted OCRs for Cooper Marl inCharleston, South Carolina, USA.
The SCE-CSSM approach has been used to evaluatethe profile of overconsolidation ratio in the CooperMarl per equation (15) with Nr = 43° and 7 = 0.8.The summary results shown in Figure 13 indicate goodagreement with two different sets of consolidationtests performed on recovered tube samples.
Empirical estimates of the preconsolidation stresscan also be made directly, yet these are dependentupon the plasticity and mineralogy of the clay, as wellas other likely factors such as age, degree of fissuring,and sensitivity. For piezocone tests, a variety ofparameters for obtaining Fpr has been explored(Larsson & Mulabdiƒ, 1991b). One such trend for alarge database is presented in Figure 14 using the netcone tip resistance.
Figure 14. Empirical trend for Fpr and net tip stress in clays.(After Chen & Mayne, 1996).
The mean trend from regression analysis on intactclays is given by:
Fpr . 0.305 (qT-Fvo) (16)
It can be noted that the separate category of fissuredgeomaterials at high OCRs lies above this line, thusreflecting the added influence of the macrofabric ofdiscontinuities on the penetration readings. In thesecases, the preconsolidation stress will be under-estimated by (16).
The estimate for intact soils is improved if the clayplasticity index (PI or IP) is considered. For type 2cones, three trends can be realized from multipleregression analyses:
Fpr . 0.65 (qT-Fvo) (IP)-0.23 (17)
Fpr . 0.94 (u2-uo) (IP)-0.20 (18)
Fpr . (qT-u2) (IP)-0.18 (19)
The ratio Fpr/(qT-Fvo) does not uniquely decrease withplasticity index, however, as the organic clays ofSweden appear to show a more rapid rate of decreasewith IP than Japanese marine clays (Mayne, Robertson,& Lunne, 1998). The trends given by (17) through(19) thus do not include effects of geologic origin,organic content, and mineralogy.
These empirical correlations are neverthelessuseful in providing an approximate check on the dataand indication of reasonableness, as well as warning of
10
15
20
25
30
0 500 1000σp' (kPa)
Dep
th (m)
10
15
20
25
30
0 500 1000σp' (kPa)
10
15
20
25
30
0 500 1000σp' (kPa)
fctn (qt-σvo) fctn (∆u2) fctn (qt-u2)
Figure 15. Empirical estimates of preconsolidation for theCooper marl from piezocone correlations with plasticity index
anomalous behavior. For Cooper marl, the applicationsare shown in Figure 15 using an average IP = 52.
3.2 Dilatometer evaluation of OCR in claysAlthough the geometry of the flat plate dilatometer isnon-axisymmetric, lab chamber experiments by Huang(1991) have shown excess porewater pressuresgenerated in clays are essentially symmetric early on,just after installation of the blade. The observedmagnitudes of )u become directional later asdissipation occurs. Since the p0 and p1 readings aretaken fairly early (within 15 to 45 seconds ofpenetration, respectively), cavity expansion can beused to approximate the level of induced pressures.
The contact pressures of the DMT are noted to bedominated by current porewater pressures (Mayne &Bachus, 1989). An analytical formulation usingcylindrical cavity expansion and undrained strengthfrom critical-state theory gives:
The evaluations of OCR with lateral stress index (KD)and its possible variations with Nr and rigidity index(IR) are evidenced in Figure 16. For this case, theanalysis considers that passive failure may occur athigh OCRs with the likely manifestations that anetwork of cracks and fissures are propagated in thesoil mass. The limiting OCR can be estimated from aK0-OCR relationship when K0 reaches the passivestress coefficient (Kp), as discussed subsequently. Athigher OCRs, then the operational undrained strengthis reduced by a factor of two.
Figure 16. Cavity expansion-critical state relationships for OCRin terms of dilatometer KD, rigidity index IR, and Nr for clays.
Figure 17. Calibration of OCR-KD expression with DMT data.
The data tend to confirm the generalized relationshipbetween OCR and KD, including the effect of thefissuring macrofabric at high OCRs. In theaforementioned discussion of piezocone profiling,perhaps the negative porewater pressures observed infissured materials already takes these effects intoaccount. An alternative empirical approach for aquick evaluation of stress history in intact clays is(Mayne, 1995):
Fpr . 0.51 (p0 - u0) (21)
4 INITIAL STRESS STATE
The initial state of stress is represented by the lateralstress coefficient, K0 = Fhor/Fvor and remains one ofthe most difficult parameters to measure accurately byeither lab or field tests. Instead, for soils that haveexperienced a simple stress history caused by load-unloading, the following provides an estimate:
K0 = (1-sinNr) OCRsinNr (22)
This expression was developed on the basis ofinstrumented oedometer tests, special triaxial stress-path tests, and other laboratory devices on clays, silts,sands, and gravels (Mayne & Kulhawy, 1982). Morerecently, field calibration by push-in spade cells, self-boring pressuremeter, and hydraulic fracturing testshave been carried out in clays, as summarized inFigure 18 (data compiled by Lunne, et al. 1990). Forsands, the difficulty in sampling restricts the usualdetermination of associated preconsolidation,however, for a few well-characterized sands, Figure 19appears to confirm that K0 increases with OCR byfield PMT.
Eventually, during unloading, the value of K0increases to reach the passive failure state. If aconservative Rankine criterion is adopted, then themaximum lateral stress state is given by:
Kp = (1+sinNr)/(1-sinNr) (23)
When (22) is equated to (23), a limiting OCR can begiven by:
OCRlimit . [(1+sinNr)/(1-sinNr)2]1/sinNr (24)
The limiting OCR can be greater than allowed by (24)if a proper assessment of the effective cohesionintercept (cr) is taken into account. Many triaxial testsover a wide range of stresses and different stress pathsare needed to define the yield surface, however. Thegeneralized expression for Kp is then:
The relevant value of cr appears to be controlled byrate effects, age, test mode, and other factors. It is alsothe intercept of a forced fit of a linear Mohr-Coulombcriterion to a curved yield surface, and thus dependson stress level (Mesri & Abdel-Ghaffar, 1994). In thiscase, the following is recommended for estimatingshort-term situations:
0.02 < (cr /Fpr) < 0.04 (26)
Figure 18. Field data from K0 measurements in clays. (Datacompiled by Lunne et. al., 1990).
Figure 19. Field data from PMT K0 measurements in sands.
4.1 Geostatic stress state of clays
Although correlations for estimating K0 in clays arepossible from the DMT KD index (e.g., Marchetti,1980) or CPTu parameters (e.g., Mayne & Kulhawy,1990), a more consistent approach is achieved by firstassessing the OCR and then using (22) for claysprestressed by mechanical overconsolidation.Notably, more research is still needed in quantifyingthe magnitudes of K0 caused by desiccation, aging,cyclic loading, and cementation.
4.2 Geostatic stress state and OCR of sands
The in-situ K0 in sands may be assessed indirectly byin-situ penetration tests such as the DMT, as discussedelsewhere (e.g., Schmertmann, 1986; Mayne &Martin, 1998). For the CPT, a statistical evaluation ofa large database (n = 590) compiled from 26 separateseries of calibration chamber tests has produced theempirical relationship shown in Figure 20 for both NCand OC sands. If the expression for effectivehorizontal stress is normalized by the effective verticalstress, the relevant K0 can be expressed by thefollowing regression equation (r2 = 0.871):
K0 = 1.33(qT)0.22 (Fvor)-0.31 OCR0.27 (27)
where qT is in MPa and Fvor in kPa. Of course, theformulation applies only to unaged and uncementedquartzitic sands and has been verified by a limitednumber of field test sites (Mayne, 1995b). If anassumed K0 - OCR relationship is assumed apriori, itmight take the general form: K0 = K0NC OCR" (28)
Solving (27) and (28) provides the following directsolution for OCR:
If (22) is an estimator for (28), then K0NC = (1-sinNr)and " = sinNr. The profile of OCR (and associated K0values) can be then be obtained directly with depth.
An example use of (29) is given in Figure 21 forStockholm sand (Dahlberg, 1974). Originally, a 24-mthick deposit of glacial sand was available that wassubsequently quarried for construction use. After 16m of excavation, a large test program employing manydifferent types of in-situ tests was conducted,including SPT, CPT, PMT, screw plate tests, inplacedensities, as well as laboratory testing.
In the original citation, the deduced profile of OCRwas ascertained by calculation of the mechanicaloverburden removed: OCR = ()Fv+Fvor)/Fvor that wasverified with preconsolidation stresses interpretedfrom screw plate tests. In addition, the correspondingK0 profile was assessed and agreed with lift-offpressures from PMTs.. Figure 21 shows the CPTapproach applied to Stockholm obtained using (3) toobtain Nr with depth (Nr. 40° ± ) and (29) to generatethe OCR profiles from two nearby soundings.
Figure 20. CPT calibration chamber relationship for evaluatingteral stresses in unaged clean quartz sands.
Figure 21. CPT-evaluated profile of OCR in Stockholm sanddeposit (data reported by Dahlberg, 1974).
Of recent, the use of paired (or more) sets of
directional shear wave velocity measurements havebeen explored for deciphering the in-situ geostaticstate of stress in soils and further work in this directionwill be interesting (e.g., Fioravante, et al. 1998; Sully& Campanella, 1995). The downhole Vs from SCPTand SDMT provides at least one vertically-directedprofile and could be coupled with data from surfaceSASW series (e.g., Butcher & Powell, 1995).
5 DEFORMATION PARAMETERS
The deformation characteristics of soils include theconsolidation indices (Cc, Cs, Cr) and elastic moduli(E, G, K, B), as well as rate and creep parameters.The discussions herein will focus on elastic parametersto represent soil stiffness under monotonic loading.The stiffness of soils is needed in evaluatingdeflections of shallow & deep foundations, retainingwalls, and excavations, and embankments. Stiffnesscan be measured in-situ using the pressuremeter, plateload test, dilatometer, screw plate, and geophysicalmethods, albeit these all provide moduli at differentpoints along the stress-strain curve.
With the recent interest in enhanced in-situ testingfor geotechnical site characterization, it is timely todiscuss the use of seismic piezocone (SCPTu) anddilatometer (SDMT) for the evaluation of stiffnessover a range of stress-strain-strength responses, sincedata are collected at two opposite ends of the curve. Amodified hyperbola (Fahey & Carter, 1993) can beused to conveniently degrade the initial stiffness (E0)with increasing load level and provide nonlinear load-displacement-capacity results.
Despite the repeated attempts to estimatedeformation parameters from routine penetration testdata, the stiffness of soils is not really well-representedat the peak resistances that occur at failure strains orbeyond (Figure 22). In fact, most of the activity ofinterest in earthwork deformations takes place close tothe in-situ K0 state and corresponding small-strainregion characterized by Gmax (Burland, 1989).
Figure 22. Conceptual stress-strain response of soils
5.1 Small-strain stiffnessRecent research has found that the small-strainstiffness from shear wave velocity (Vs) measurementsapplies to the initial static monotonic loading, as wellas the dynamic loading of geomaterials (Tatsuoka &Shibuya, 1992; Jardine, et al., 1991). Thus, theoriginal dynamic shear modulus (Gdyn) has been re-termed the maximum shear modulus (designated Gmax),or alternatively, the small-strain shear modulus (G0),that provides an upper limit stiffness given by:
G0 = DT Vs2 (30)
where DT = (T/g = total mass density, (T = soil unitweight, and g = 9.8 m/s2 = gravitational constant. Themodulus G0 is a fundamental stiffness of all solids incivil engineering and can be measured in all soil typesfrom colloids, clays, silts, sands, gravels, to bouldersand fractured rocks. Interestingly, G0 applies todrained and undrained soil behavior, because at suchsmall strains, porewater pressures have not yet beengenerated. The concept of a threshold strain wouldmark the onset of )u. The corresponding equivalentelastic Young’s modulus is found from:
E0 = 2G0 (1+<) (31)
where 0.1 # < # 0.2 is the appropriate range of valuesfor Poisson’s ratio of geomaterials at small strains.
5.2 Shear wave measurementsThe shear wave velocity can be measured inconventional cased boreholes using the crosshole test(CHT) and downhole test (DHT), or with improvedsurface techniques such as spectral analysis of surfacewaves (SASW), seismic refraction (SR), and reflectionsurveys. Also available is the suspension logger anddownhole methods of SCPTu and SDMT. The latterare convenient in that they can map thegeostratigraphic profiles, strength characteristics, andobtain a DH measurement of Vs within the samesounding.
A representative SCPTu (one of 15) obtained insoft varved clay at the National GeotechnicalExperimentation Site (NGES) in Amherst, MA isshown in Figure 23. A companion SDMT at the samesite has been presented elsewhere (Mayne, et al.1999a). The site profile consists of 1 m of clay fillover a 3-m desiccated clay crust, underlain by varvedlacustrine silty clay. Groundwater lies 1 m deep.High excess porewater readings are evidence of claymaterials. The procedure of individual rod breaks at1-m intervals can be noted here as well.
0
2
4
6
8
10
12
14
16
0 1 2 3 4
Tip Stress, qt (MPa)Dep
th (m)
0
2
4
6
8
10
12
14
16
0 20 40 60 80
Sleeve fs (kPa)
0
2
4
6
8
10
12
14
16
-0.2 0 0.2 0.4 0.6
Porewater ub (MPa)
0
2
4
6
8
10
12
14
16
0 100 200 300 400
Shear Wave,VS (m/s)
Unit Weight Estimation
10
12
14
16
18
20
22
24
26
28
10 100 1000 10000Shear Wave Velocity, Vs (m/s)
Satu
rate
d U
nit W
eigh
t, γ T
(kN
/m3 )
Intact Clays
Fissured Clays
Silts
Peat
Sands
Gravels
WeatheredRocksIntact Rocks
Saturated Soil Materials:γT (kN/m3) = 8.32 log Vs - 1.61 Log z
with Vs (m/s) and depth z (m)n = 727 r2 = 0.808 S.E. = 1.05
z (m) = 1
10
100
Fgure 23. Respresentative seismic piezocone results in varved clay at NGES in Amherst, Massachusetts.
In order to obtain the initial stiffness Gmax, an estimateor measurement of mass density or unit weight isneeded. A global compilation of VS data from alltypes of saturated geomaterials ranging from clays togravels to rocks finds the the following trend:
((sat) = 8.32 logVS - 1.61 log z (32)
where ((sat) is in kN/m3, VS (m/s),and z (meters).The estimate is also handy for calculating Fvo and Fvor.
Figure 24. Correlation for unit weight from depth and VS.
5.3 Intermediate stiffness of soilsThe stress-strain-strength-time response of soils iscomplex, highly nonlinear, and depends upon loadingdirection, anisotropy, rate effects, stress level, strainhistory, time effects, and other factors. It is thereforea difficult issue to recommend a single test, or even asuite of tests, that directly obtains the relevant Es forall possible types of analyses in every soil type. Thisis because the modulus varies considerably with strainlevel (or stress level).
In certain geologic settings and types ofgeomaterials, it has in fact been possible to developcalibrated correlations between specific tests (e.g.,PMT, DMT) with performance monitored dataobtained from full-scale structures, includingfoundations and embankments, or with referencevalues from laboratory test. These tests will providea modulus somewhere along the stress-strain-strengthcurve (Fig. 25), generally at an intermediate level ofstrain. Of particular note, the small-strain modulusfrom shear wave velocity measurements provides anexcellent reference value, as this is the maximumstiffness that the soil can exhibit at a given void ratioand effective confining state. Herein, a generalizedapproach based on the small strain stiffness from shearwave measurements will be discussed, whereby theinitial modulus (E0) is degraded to an appropriatestress level, or current factor of safety (FS).
0
0.2
0.4
0.6
0.8
1
Mod
ulus
Rat
io,
G/Go
1E-06 1E-05 0.0001 0.001 0.01 0.1
Shear Strain
CyclicLoading
Monotonic(Static)Loading
Laboratory Modulus Degradation Data
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Mobilization Factor, q/qult
Nor
malized
Mod
ulus
, E/
E 0 Toyoura Sand (eo =0.67)Toyoura Sand (eo =0.83)Kaolin
Pisa Clay
Ticino Sand (NC)
Figure 25. Reduction of shear modulus with level of strain.
The shear modulus decreases with shear strain leveland is commonly shown in normalized form, withcurrent G divided by the maximum Gmax (or G0). Therelationship between G/G0 and logarithm of shearstrain is well recognized for dynamic loadingconditions (e.g., Vucetic and Dobry, 1991), however,the monotonic static loading curves show a more rapiddecay with strain, as depicted in Figure 26. The cyclicresponse is representative of data obtained fromlaboratory resonant column tests, whereas themonotonic curve has been only more recentlyaddressed with the advent of special internal & localstrain measurements in triaxial tests, as well as bytorsional shear devices (Jamiolkowski, et al. 1994).
Laboratory monotonic shear tests with high-resolution deformation instrumentation have shownthat strain data obtained external to the triaxial cellsare flawed because of seating errors, bedding problemswith the filter stone, and boundary effects at thespecimen ends. Thus, old strain data showgeomaterials generally softer than they really are.New internal measurements are now available thataccurately measure the soil stiffness at small- tointermediate- to large-strains (LoPresti, et al. 1993,1995; Tatsuoka & Shibuya, 1992). Figure 27 showsa selection of normalized secant moduli (E/E0) at theircorresponding mobilized stress level (q/qult) obtainedfrom lab tests on uncemented and unstructuredgeomaterials.
5.4 Stress-strain-strength representation
A modified hyperbola can be used as a simple meansto reduce the small-strain stiffness (E0) to secantvalues of E at working load levels, in terms of themobilized
Figure 26. Modulus reduction for monotonic & cyclic loading
strength (q/qult). Figure 28 illustrates the representativemodulus reduction scheme for unstructured clays anduncemented sands. The generalized form may be givenas (Fahey & Carter, 1993; Fahey et al. 1994):
E/E0 = 1 - f (q/qult)g (33)
where f and g are fitting parameters. Values of f = 1and g = 0.3 appear reasonable first-order estimates forunstructured and uncemented geomaterials (Mayne, etal. 1999a) and these provide a general fit for the datashown in Figure 27. The mobilized stress level can
Figure 27. Modulus degradation in terms of mobilized stressfrom instrumented laboratory test specimens.
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0Mobilization Factor, q/qult
Nor
malized
Mod
ulus
, E/
Emax
g = 0.2g = 0.3g = 0.4
Modified Hyperbola:
E/Emax = 1 - (q/qult)g
DSS Data from Amherst
0.0
0.1
0.2
0.3
0.4
0 1 2 3 4 5 6
Shear Strain, γs (%)
Nor
m.S
hear
Str
ess,
τ/σ
vo' G91
G92Depth = 8.61 meters
Modified Hyperbolafrom SCPTu Data: qT = 565 kPa u2 = 414 kPa Vs = 141 m/s
Figure 28. Modified hyperbolic curves to represent modulusreduction from small-strain region to intermediate strains.
also be considered as an inverse factor of safety, or(q/qult) = 1/FS. That is, for a stress level half ofultimate, (q/qult) = 0.5 and the corresponding FS = 2.
Modulus reduction has been addressed using anumber of different numerical schemes (e.g., Duncan& Chang, 1970; Hardin & Drnevich, 1972; Prevost &Keane, 1990; Tatsuoka & Shibuya, 1992). Several ofthese approaches have a more fundamental basis or abetter fitting algorithm over the full range of strainsfrom small- to intermediate- to large-ranges (e.g.,Puzrin & Burland, 1996, 1998). Herein, only anapproximate approach has been sought so that the VSdata may be incorporated into stress-strain estimations,starting from the initial stiffness and quickly reducingthese values to intermediate- and high-strain regions ofsoil stiffness.
From the SCPTu field data in soft Amherst claygiven in Figure 23, the degree of overconsolidationand derived shear strengths for simple shear have beenevaluated. The initial stiffness has been taken fromthe VS data and a modified hyperbola used to connectthe two ends of the curve. Measured results from twolaboratory DSS tests (nos. G91 and G92) onspecimens taken from the same depths are shown to bein nice agreement with the predicted curves in Figure29. Since data are taken along the entire depth of thesounding, it is possible to generate nonlinear J-(scurves for all depths, if desired. Illustrative stress-strain comparisons are made from SCPTu (Burns &Mayne, 1996) and SDMT data (Mayne, et al., 1999).
Figure 29. Applied modified hyperbola to SCPTu data andcomparison with laboratory DSS data on Amherst soft clay.
6 FLOW CHARACTERISTICS
The hydraulic conductivity (k) and coefficient ofconsolidation (cv) represent the flow characteristics offluids through the soil mass. In this regard, the excessporewater pressures generated during probeinstallation can be monitored with time at periodicstops in the sounding. Several methods of interpretingpiezocone dissipation tests have been available for thispurpose (e.g. Teh & Houlsby, 1991), however, priorderivations have been developed solely to addressmonotonic decay of porewater pressures with time.With type 2 penetrometers, a dilatory response canoccur in overconsolidated fissured materials, wherebythe porewater values initially increase duringdissipation, reach a peak, and then subsequently decaywith time. In addition, existing approaches only matcha single point (usually 50%) of the recordeddissipation.
6.1 CE-CSSM approachUsing the hybrid cavity expansion-critical stateformulation described earlier, the octahedral normaland shear-induced components can be allowed todissipate separately. The summation of theirresponses given (Figure 30) provides the type ofmeasured behavior during porewater dissipation. Theoctahedral component is obtained from (11) andalways a positive value, whereas shear-induced valuesfrom (13) can be positive or negative depending uponthe degree of OCR and frictional qualities. Moreover,
Amherst - Piezocone Dissipations (NGES)
0
100
200
300
400
500
600
0.01 0.1 1 10 100 1000
Time (minutes)
Pore
wate
r u 2
(kP
a)
M easured Response at 12.2 m
Approx. CE-CSSM M ethod
Hydrostatic uo
the large octahedral zone will require long times todecay because of the noted soil volume influenced. Incontrast, the shear zone occurs as a thin annulus thatwill decay more rapidly. It is possible, therefore, torepresent both monotonic and dilatory responses withthis approach. Full details are given elsewhere on thesolving of the second-order differential equation forradial flow and consolidation (Burns & Mayne, 1998).Herein, only a brief review of the features will bediscussed and an approximate closed-form given forpractical use.
F ig u
re 30. Normal- and shear-induced components of excessporewater pressures around the cone.
In lieu of merely matching one point on the dissipationcurve (i.e, t50), the entire curve is matched to providethe best overall value of the horizontal coefficient ofconsolidation (ch). The excess porewater pressures )utat any time t can be compared with the initial valuesduring penetration ()ui). measured initial excessporewater pressure ()ui = u2-uo) is given by:
)ui = ()uoct)i + ()ushear)i (34)
where ()uoct)i = (2/3)MFvor(OCR/2)7 lnIR = theoctahedral component during the penetration and()ushear)i = Fvor[1 - (OCR/2)7 ] is the shear-inducedcomponent. For practical use, an approximate closed-form expression is presented here. The porewaterpressures at any time (t) are obtained in terms of themodified time factor T* from:
where the modified time factor is defined here by:
and a = probe radius. Using a spreadsheet, log valuesof T* are established and used to generatecorresponding times t for given IR and a. Trial & erroris performed on the value of ch to give the best fit.
6.1 Monotonic DissipationsA representative look at monotonic dissipation isshown in Figure 31 for the Amherst site (z = 12.2 m).Using (35) and (36) with the following inputparameters (OCR = 1.8, IR = 227, Nr = 33°, 7 = 0.8),the predicted response is also indicated using a trial &error for the entire )u recording with time todetermine a best fit ch = 0.5 cm2/min.
Figure 31. Measured and fitted montonic dissipations in soft clayat Amherst site (data from Lutenegger, 2000).
6.2. Dilatory Dissipations
In contrast, a dilatory type curve is shown in Figure 32for the hard Taranto clay (data from Pane, et al. 1995).Here, the CE-CSSM model used the following inputparameters (OCR = 28, IR = 12, Nr = 28°, 7 = 0.8) toobtain the fit for ch.
A summary comparison of measured cv fromlaboratory oedometer and consolidation tests with thepiezocone fitted ch values using the rigorous method ispresented in Figure 33. The categories include intactclays, desiccated crustal clays, and fissured materials.Curves showing normalized excess porewaterpressures from the rigorous method for various OCRand Nr have also been given (Burns & Mayne, 1998).
Taranto, Italy - Piezocone Dissipations
0
500
1000
1500
2000
2500
0.01 0.1 1 10 100 1000
Time (minutes)
Pore
wate
r u 2
(kP
a)
M eas. u2 at 12 m
Approx. CE-CSSM
Hydrostatic uo
0.001
0.01
0.1
1
10
0.001 0.01 0.1 1 10
Piezocone ch (cm2/min)
Oed
omet
er c
v (c
m2 /m
in)
Intact
Crust
Fissured
Keaveny & Mitchell (1986): CK 0 UC Triaxial Data
0
50
100
150
200
250
300
1 10
Overconsolidation Ratio, OCR
Rigidity
Ind
ex, I R
50 =
G/s
u
2 5
PI = 10
20
30
40 50 > 50
Keaveny & Mitchell (1986): CK 0 UC Triaxial Data
Figure 32. Measured and fitted dilatory response in the hardoverconsolidated Taranto clay (data from Pane, et al. 1995).
Figure 33. Comparison of consolidation coefficients fromoedometer and piezocone for clays (Burns & Mayne, 1998).
Figure 34. Empirical rigidity estimate from PI and OCR.
6.3 Undrained Rigidity IndexFor the evaluation of ch from piezocone dissipationtests using any of the cavity expansion or strain pathmethods, an evaluation of undrained rigidity index isrequired. If quality samples are available, the value ofIR = G/su can be assess at 50% of the peak strength.Results from pressuremeter tests (PMT) can also beused. In many cases, the site exploration may solelyrely on soil borings with SPTs and companions seriesof CPTs. Thus, some direction towards the evaluationof IR is warranted.
An empirical approach between IR, OCR, and PIhas been published on the basis of CAUC triaxial testdata (Keaveny & Mitchell, 1986). Figure 34 presentsthe empirical curves that show IR, decreasing with OCRand PI which may approximately be expressed by:
Alternatively, a Cam-clay derivation has beensuggested that depends on routine soil parameters forinput (Kulhawy & Mayne, 1990). Figure 35 illustratesthe curves obtained by this approach (7 = 0.8) whichcan be calculated from:
Figure 35. Rigidity index from Cam-clay derivation.
0
5
10
15
20
Dept
h (m
eter
s)
0 20 40 60 80
Backcalculated Ir
Bothkennar, Grangemouth, Scotla
PowellQuarterman,& Lunne (1988)
0.1
1
10
100
1 10 100 1000Shear Modulus, Go (MPa)
Cons
traine
d M
odulus
, D' (M
Pa)
Bothkennar
Brent Cross
Drammen
Fucino
Hutchinson
Madingley
Montalto
Onsoy
Pentre
Pisa
St Alban
Ska Edeby
D' = Go/10
D' = Go/20
The third and final method discussed is areformulation of the SCE-CSSM method forpiezocone penetration. Interestingly, thebackcalculation of soil rigidity index (IR = G/su) from(9) is accomplished using (7) and (15) to provide adirect evaluation as:
(39)IM
qq uR
t v
t= +
−−
−
exp
.. .
152 925 2 925
2
σ ο
The expression is somewhat sensitive to the quality ofinput data because of the exponential form, thus theimportance in using class 3 penetrometers (Lunne, etal., 1997) for this purpose. An example evaluationusing piezocone data from the UK test site atBothkennar, Scotland is presented below in Figure 36.The profile compares well with the aforementionedempirical approach using PI and OCR that give goodestimates of ch.
Figure 36. Direct rigidity index from CPTu measurements.
6.4 PermeabilityOnce the coefficient of consolidation has beendetermined, the hydraulic conductivity or permeability(k) can be evaluated from:
k = ch (w/Dr (40)
where Dr = 1/mv = constrained modulus, as definedfrom one-dimensional oedometer tests and (w = 9.8kN/m3 = unit weight of water. In lieu of a directmeasure of Dr, it seems possible that this stiffnessmight correlate with the small-strain modulus from
shear wave velocity measurements. As such, Figure 37presents a compiled database on clays where bothlaboratory consolidation moduli (Dr) and field valuesof G0 were available. A conservative trend appears tobe defined by:
Dr = 0.1 G0 (41)
Figure 37. Relationship for constrained modulus from small-strain shear modulus in clays.
Alternatively, a first-order estimate on the constrainedmodulus is obtained from the net tip resistance(Kulhawy & Mayne, 1990):
Dr = 8.25 (qT-Fvo) (42)
Using the aforementioned value ch = 0.5 cm2/s for z =12.2 m at the Amherst site and the SCPTu data fromFigure 23 (qT = 690 kPa; VS = 140 m/s), the evaluatedparameters are (T = 16.1 kN/m3, Gmax = 32.2 MPa, andDr = 3.2 MPa (per eqn 41), giving a permeability k =2.53·10-7 cm/s. This corresponds well to the reportedvalue from laboratory testing (and other field methods)of k = 4 ·10-7 cm/s at z = 12.2 m given by DeGroot &Lutenegger (1994).
As a check, an empirical estimate of k can be madedirectly from the t50 reading(Parez & Fauriel, 1988).This is conveniently approximated by:
k (cm/s) = (251" t50)-1.25 (43)
where t50 is in seconds (Finke & Mayne, 2001). Fort50 = 600 s scaled from Fig. 31, (43) provides anotherreasonable estimate of k = 3.37·10-7 cm/s.
0
2
4
6
8
10
12
0 2 4 6 8qt (MPa)
Dep
th (m
eter
s)0
2
4
6
8
10
12
0 100 200 300
fs (kPa)
0
2
4
6
8
10
12
-100 0 100 200u2 (kPa)
0
2
4
6
8
10
12
0 100 200 300 400Vs (m /s)
SCPTu
SDMT
CHT
SASWuo
0
5
10
15
20
25
30
0 1 2 3Axial Load, Q (MN)
Top
Def
lect
ion
(mm)
Qtotal = Qs + QbPred. QsPred. QbMeas. TotalMeas. ShaftMeas. Base
Figure 38. Results of seismic piezocone tests in residuum at Opelika NGES, Alabama, USA (Schneider, et al., 1999).
7 DIRECT APPLICATIONS
Another approach to utilization of SCPTu and SDMTdata is the direct application of the measuredresistances to foundation analyses (e.g., Robertson, etal., 1988). Along these lines, full-scale load tests fromthe new National Geotechnical Experimentation Site(NGES) at Opelika, Alabama will be presented. Adrilled shaft was constructed under slurry installationmethods with a diameter d = 0.914 m and embeddedlength L = 11.0 m. The soil profile consists of residualsoils (ML and SM) of the Piedmont geology derivedfrom the inplace weathering of metamorphic andigneous rocks, primarily schist, gneiss, and granites.
Results from a representative seismic piezoconesounding at the site are shown in Figure 38. Thenegative porewater pressures are typical in thisgeology (Finke & Mayne, 2001). The downhole shearwaves from CHT, DHT, and SASW compare well(Schneider et al., 1999). At this site, the DHT valueswere obtained using both series of seismic cone andseismic dilatometer tests.
The side friction component was calculated on thebasis of measured CPT fs and )u2 per the method ofTakesue, et al. (1998) and the end bearing capacitybased upon the approach of Eslami & Fellenius (1997)using the effective tip stress (qt-u2). The soil-pilestiffness is obtained from the shear wave measurementand the modulus reduction procedure per (33) utilized
in an elastic continuum analysis of the axially-loadedpile. The comparison of measured and predicted axialpile response is shown in Figure 39. In addition togiving nonlinear load-displacement-capacityrepresentation, the associated load-transfer for thedrilled shaft is also obtained with good agreement.
Figure 39. Measured & predicted Q-* from SCPTu data.
Figure 40. Concept of seismic piezocone pressuremeter with dissipation phases for site exploration.
8 CONCLUSIONS
Results from hybrid penetration tests (SCPTu andSDMT) incorporating downhole geophysics anddissipation phases provide an optimization for datacollection during field exploration since information iscollected at two opposite ends of the stress-strain-strength curve. The data can be utilized to evaluatethe geostratigraphy and soil parameters including: unitweight ((t), effective strength parameters (Nr), totalstress parameters (su), stress history (OCR and Fpr),geostatic horizontal stresses (K0), small-strain stiffness(Gmax), intermediate-strain moduli (Dr, Er, Gr), andrigidity index (IR), as well as the horizontal coefficientof consolidation (ch) and permeability (k).
Direct measurements of stiffness at intermediatestrains (i.e., cone pressuremeter) would be valuable intailoring the fitting parameter of the modifiedhyperbola used here, or for more robust degradationand reduction schemes (e.g., Puzrin & Burland, 1996,1998). New directions for enhanced geotechnical sitecharacterization might include the seismic piezoconepressuremeter (SCPMTu), as seen in Fig. 40, as wellas added sensors such as dielectric (permittivity) andresistivity to further improve and optimize theamounts and types of data recorded.
9 ACKNOWLEDGMENTS
The author acknowledges the funding support receivedfrom the National Science Foundation (NSF), UnitedStates Geological Survey (USGS), the Mid-AmericaEarthquake Center (MAE), International Associationof Foundation Drilling (ADSC), and Federal HighwayAdministration (FHWA) towards research efforts onin-situ testing. Additional thanks to Alan Luteneggerand Dan Brown for providing access & data at theNGES sites at Amherst/MA and Opelika/AL.
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