an improved technique for evaluating the cpt friction ... · an improved technique for evaluating...
TRANSCRIPT
An Improved Technique for Evaluating the CPT Friction Ratio
by
M. B. Jaksa, W. S. Kaggwa and P. I. Brooker
Department of Civil and Environmental Engineering
University of Adelaide
Research Report No. R 166
January, 2000
i
ABSTRACT
This report examines a statistical technique known as the cross-correlationfunction (CCF) for determining the shift distance associated with the conepenetration test (CPT). When evaluating the friction ratio, FR (= fs/qc), for soilclassification purposes, it is essential that the measured values of qc and fs areshifted relative to one another because of the depth discrepancy between thecone and the friction sleeve. Generally, the shift distance is estimated by meansof empirical and subjective methods. Using a series of case studies, this reportdemonstrates that the CCF is a very useful and objective technique forestimating the shift distance. In addition, a phenomenon, associated with sleevefriction measurements which is related to elastic rebound of clay soils, isdiscussed. Finally, in iterative technique is proposed for determining thelayering of a soil profile based on the CPT.
ACKNOWLEDGMENTS
The authors wish to acknowledge the Department of Transport, in particular,R. Washyn, R. Herraman and I. Forrester, for the use of the Department’sdrilling rigs and technical staff, in carrying out the research at the SouthParklands site and The City of Adelaide, and in particular, A. A. Taylor andM. Underhill, for providing access to this site. The authors also acknowledgeAustralian National, and in particular P. Gaskill, for their assistance and accessto the Keswick site.
Furthermore, the authors would like to thank the technical staff of theDepartment of Civil and Environmental Engineering, University of Adelaide:T. Sawosko, C. Haese, L. Collins, R. Kelman and B. Lucas. Thanks are duealso to R. Jha and the first author’s former undergraduate students, J. Cathro,P. Do, R. Hawtin, L. Lim, S. Potter, D. van Holst Pellekaan for performingsome of the cone penetration testing.
ii
CONTENTS
ABSTRACT ...................................................................................................i
ACKNOWLEDGMENTS..............................................................................i
CONTENTS ..................................................................................................ii
1. INTRODUCTION .......................................................................................1
2. CONE PENETRATION TEST..................................................................1
2.1 Friction Ratio ........................................................................................4
3. CROSS-CORRELATION FUNCTION....................................................7
4. CASE STUDIES ..........................................................................................9
5. DISCUSSION.............................................................................................12
5.1 Rebound Phenomenon ........................................................................17
6. SUMMARY AND CONCLUSIONS........................................................23
7. REFERENCES ..........................................................................................23
8. NOTATION ...............................................................................................24
1
1. INTRODUCTION
The electrical cone penetration test (CPT), since its formalisation in the mid1960s, has become one of the most widely used and respected forms of in situtesting currently in regular use in geotechnical engineering. Lunne et al. (1997)stated that the CPT has the highest applicability in different ground conditionsof any of the in situ tests in current use. The three main advantages of the CPTare:
1. Continuous or near continuous data (with depth);
2. Repeatable and reliable penetration data, Jaksa et al. (1997) demonstratedthat the CPT has the lowest random measurement error associated with any ofthe in situ test methods in regular use in geotechnical engineering; and
3. Cost effectiveness.
Another important benefit of the CPT is that it provides an accurate andcontinuous profile of soil stratification (de Ruiter, 1981). Soil classification ofthe subsurface profile is achieved by means of the friction ratio, FR, andempirically derived charts. This report examines the friction ratio and suggeststhe use of a statistically based technique, known as the cross-correlationfunction, to assist in better estimating this parameter.
Before discussing the cross-correlation function, it is necessary first to examinethe cone penetration test.
2. CONE PENETRATION TEST
The electric cone penetrometer consists, essentially, of two strain gauge loadcells; one being attached to the cone tip and measuring cone tip resistance, qc,and the other, connected to the side, or sleeve, of the cone penetrometer andmeasuring sleeve friction, fs. The cone tip resistance, qc, is defined as the totalforce acting on the cone tip, Fc, divided by the cross-sectional area of the baseof the cone, Ab, and is usually expressed in units of MPa. The sleeve friction,fs, is defined as the total force on the friction sleeve, Fs, divided by the surfacearea of the sleeve, As, and is usually expressed in units of kPa. A schematicrepresentation of the electric cone penetrometer is shown in Figure 1.
The load cells contain a number of electrical resistance strain gauges which arearranged in such a manner that automatic compensation is made for bending
2
Figure 1. Schematic diagram of the electric cone penetrometer.(Source: Holtz and Kovacs, 1981).
stresses and only axial stress is measured (de Ruiter, 1971). The push rods,used to advance the electric cone penetrometer into the subsurface profile, areusually of a standard length of one metre with a tapered thread, male at thelower end and female at the upper. In addition, the rods have a hollow core sothat the cone penetrometer cable can pass through each rod enabling the
3
electronics of the cone to be connected to the recording instruments located atthe ground surface.
The recording devices generally consist of two types: analogue and digital; themajority of the modern systems being digital and incorporating automaticcomputer-based data acquisition. These instruments record qc and fs, and inmost cases, depth of the cone penetrometer.
The equipment and procedure of the CPT vary throughout the world. Lunne etal. (1997) suggested that the most widely referred to international standard isthe ISSMFE International Reference Test Procedure for the Cone PenetrationTest (ISSMFE, 1989). Relevant details of the CPT equipment, as specified byISSMFE (1989) are summarised briefly below.
• The standard cone has a base diameter of 35.7 mm and an apex angle of 60°resulting in a projected area of 1000 mm2 (10 cm2). The gap between thecone and other elements of the penetrometer shall not be greater than 5 mm.
• The diameter of the standard friction sleeve is 35.7 mm and has a surface areaof 15,000 mm2 (150 cm2). The friction sleeve is located immediately abovethe cone.
• Both the cone and sleeve shall be made from steel of a type and hardnesssuitable to resist wear due to abrasion by soil. The cone shall have, andmaintain with use, a roughness of ≤ 1 µm, and the friction sleeve shall have aroughness of 0.5 µm ± 50%.
• The thrust machine shall have a stroke of at least one metre and shall push therods into the soil at a constant rate of penetration. The thrust machine shallbe anchored and/or ballasted such that it does not move relative to the soilsurface during the pushing action.
• The rate of penetration shall be 20 mm/s ± 5 mm/s.• The interval between depth readings shall not exceed 200 mm and the
accuracy of depth measurements shall be at least 100 mm. Lunne et al.(1997) stated that most data acquisitions systems collect data at depthintervals of 10 to 50 mm.
• Where narrow local protuberances outside the push rod surface are placedabove the penetrometer tip in order to reduce friction on the push rods,known as friction reducers, these shall be located at least one metre above thebase of the cone.
• Care shall be taken to calculate the friction ratio from measurements of qc andfs at the same depth. Attention is drawn to the fact that, because of the depthdiscrepancy between the cone and the friction sleeve, these parameters shallnot be calculated from measurements made at the same time.
4
2.1 Friction Ratio
As mentioned above, the friction ratio, FR, is often used in conjunction with qc,in empirically derived charts to assist in soil classification. An example of sucha chart is given in Figure 2. The friction ratio is defined as the ratio between fs
and qc, and is usually expressed as a percentage:
%100 ×=c
sR q
fF (1)
Figure 3 shows a schematic of the CPT measurements. Because of the depthdiscrepancy between the cone and the friction sleeve, and the fact that dataacquisition systems measure qc and fs at the same time, the derived values of FR,and hence the inferred soil classification, are incorrect unless some form ofdepth correction is applied to the data. The question arises as to what is theappropriate depth correction.
Schmertmann (1978) recommended that this shift distance, dfs, be the distancebetween the base of the cone and the mid-height of the sleeve which, instandard electric cone penetrometers, is approximately 75 mm. Campanella etal. (1983) stated that the shift distance, also termed the friction-bearing offset, is100 mm and is dependent on the type of soil being penetrated. Campanella etal. (1983) suggested that, for heavily interbedded soils and relatively stiff soils,the shift distance may be significantly greater than this standard shift distance of100 mm.
In actual fact, it is difficult to know the ‘true’ shift distance, as it is a complexvariable which involves the extent of the zones of soil contributing to themeasurements of qc and fs, and the distance between these zones, as shown inFigure 3. The evaluation of the shift distance is made more difficult because theextent of these zones is a function of the rigidity of the soil. As the conepenetrometer is advanced into the ground it causes a zone of soil to fail anddeform plastically ahead of it. Teh and Houlsby (1991) used finite elementmodelling to quantify the extent of this failure zone, the results of which aregiven in Figures 4 and 5.
As shown in Figure 4, ac is the radius of the base of the cone, usually 17.9 mm;rp is the radial distance of the plastic boundary from the axis of penetration,measured at a large enough distance above the cone tip; zp is the distancebetween the cone tip and the plastic boundary measured along the axis of thepenetrometer; and β is the angle of the cone base, usually 60º. Teh and Houlsby
5
(1991) used the rigidity index, Ir (= uu Es 3 ), to describe the soil type, as shownin Figure 5. Figure 5 quantifies the location and extent of the boundarybetween the plastic and elastic regions, shown diagrammatically in Figure 4,with respect to Ir and β. The two solid curves define the solutions obtainedusing cylindrical (Vesic, 1972) and spherical cavity expansion theory Teh andHoulsby (1991).
Figure 2. Soil classification chart from CPT.(After Lunne et al., 1997).
6
Figure 3. Schematic representation of qc and fs measurement.
In general, the shift distance is determined, either by using a fixed value, suchas 75 or 100 mm, or visually by means of overlapping the qc and fs soundingsand moving one relative to the other until a good match is achieved. Forexample, Campanella et al. (1983) developed a data presentation computerprogram which enables the user to input any value for the shift distance. Inaddition, the program provides a facility for the evaluation of the shift distance,whereby the peaks and troughs of the qc and fs profiles may be matched bymeans of the graphical capabilities of a computer. Such a technique is based ontrial-and-error and is somewhat subjective. An alternative, quantitative,approach is proposed which uses the statistical relationship known as the cross-correlation function. Such an approach was originally suggested by Li (1993).
7
Figure 4. Schematic representation of cone test penetration.(Adapted from Teh and Houlsby, 1991).
3. CROSS-CORRELATION FUNCTION
The cross-correlation function (CCF) enables two data series to be comparedand to determine positions of strong correlation. Consider two separate dataseries nXXXXX ,,,, 321 K= and nYYYYY ,,,, 321 K= . The cross-covariancecoefficients, between X and Y, at lag k,
XYkc , are given by (Box and Jenkins,
1970):
( )( )[ ] K ,2 ,1 ,0 E =−−= + kYYXXc kiikXY(2)
and the cross-covariance between Y and X at lag k, YXkc , is:
( )( )[ ] K ,2 ,1 ,0 E =−−= + kXXYYc kiikYX(3)
8
Figure 5. Location of the elasto-plastic boundary in cone penetration.(After Teh and Houlsby, 1991).
where, in general, YXXY kk cc ≠ . However, since:
( )( )[ ] ( )( )[ ]YXXY kkiiikik cXXYYYYXXc −−− =−−=−−= EE (4)
XYkc need only be calculated for k = 0, ± 1, ± 2, ± ...
Since the data series, X and Y, may be expressed in different units, it is useful todefine the cross-correlation coefficient at lag k,
XYkρ , as:
K ,2 ,1 ,0 ±±±=σσ
=ρ kc
YX
kk
XY
XY(5)
Since the true cross-covariance and cross-correlation function are never known,but only ever estimated by means of a sample population, the sample cross-
covariance coefficient at lag k, *XYkc , and the sample cross-correlation
coefficient at lag k, XYkr , are defined as:
9
( )( )
( )( )
−−=−−
=−−
=
∑
∑
+
=−
−
=+
K
K
,2 ,1 ,0 1
,2 ,1 ,0 1
1
1*
kXXXXn
kXXXXn
ckn
ikii
kn
ikii
kXY
(6)
K ,2 ,1 ,0 *
±±±== kss
cr
YX
kk
XY
XY(7)
where: sX is the sample standard deviation of X *0XX
c= ;
sY is the sample standard deviation of Y *0YY
c= .
If one assigns X to be the qc recording and Y the fs recording, it is possible to usethe CCF to provide the best statistical estimate of the shift distance. This isexamined in the next section.
4. CASE STUDIES
Jaksa (1995) performed 224 vertical CPTs in a 50 × 50 m area of the SouthParklands, as shown in Figure 6. These CPTs were drilled mainly into a stiff,overconsolidated clay known as Keswick Clay. Cox (1970) demonstrated thatthe geotechnical properties of Keswick Clay are remarkably similar to those ofLondon Clay.
All CPTs discussed in this paper were carried out using a standard 60°, 10 cm2
base area type penetrometer, whose dimensions and test procedure conformed tothe relevant international standard (ISSMFE, 1989). The data were obtainedusing a micro-computer based data acquisition system which allows CPTmeasurements to be recorded at 5 mm increments, and stored on disk forsubsequent analyses (Jaksa and Kaggwa, 1994). Each CPT was penetrated to atypical depth of approximately 5 metres below ground, yielding of the order of1,000 measurements of qc and fs.
To illustrate the CCF and its application to the evaluation of shift distance, anexample CPT sounding, C8, (Figure 7) is examined. The location and details ofCPT sounding C8, as well as the complete data set, are given in Jaksa (1995).
10
5 m
50 m
50 m
5 m
1 m
1 m
0 1 2 3 4 5 6 7 8 9 10A
B
C
D
E
F
G
H
I
J
K
2.5 m
CD1
CD50
0.5 m
Legend
Continuous core sample
3.3
2.4
1.6
2.3
1.1
2.2
2.2
2.3
1.0 Depth to top of Keswick Clay
Unsuccessful soundings
Successful soundings
Triaxial samples
Figure 6. Layout of vertical CPTs at South Parklands, Adelaide.
Substituting these qc and fs data into Equation (6) yields the corresponding CCFwhich is shown in Figure 8. The computations were facilitated by means of theWindows-based computer program SemiAuto (Jaksa, 1995).
11
6000
5000
4000
3000
2000
1000
00 0.5 1 1.5 2 2.5
Cone Tip Resistance, qc (MPa)
6000
5000
4000
3000
2000
1000
00 50 100 150 200
Sleeve Friction, fs (MPa)
Figure 7. Measured data from CPT sounding C8.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
−130
Figure 8. Sample cross-correlation function of cone tip resistance andsleeve friction measurements from CPT C8.
12
It can be seen from Figure 8 that the maximum value of the cross-correlationcoefficient occurs at a distance of −130 mm. (A negative value of spacingimplies that the sleeve friction measurements are shifted upwards relative to thecone tip resistance values). This implies that the optimal shift distance is130 mm, somewhat larger than the actual physical spacing of 75 mm, and thevalue of 100 mm suggested by Campanella et al. (1983).
The results from the CCFs from 9 investigations are summarised in Table 1. Itis evident from these results that the shift distance is generally greater than thephysical separation distance of 75 mm, and, particularly for overconsolidatedclays, greater than the value of 100 mm suggested by Campanella et al. (1983).Interestingly, on occasion, the shift distance is less than the physical separationdistance of 75 mm, which suggests that the centroid of the plastic failure regionassociated with the cone tip is above the tip of the penetrometer.
5. DISCUSSION
The majority of the CPT data yielded CCFs that enabled a relativelystraightforward and unambiguous value of the shift distance to be determined.Three such examples are given in Figures 8 to 10. As can be seen from thesefigures, a single and relatively obvious maximum value for the correlationcoefficient is given, which can readily be associated with an appropriate shiftdistance.
Table 1. Summary of CCF analyses performed on various soil types.
Soil Type Location No. of Shift Distance*, dfs (mm)
CPTs Mean Range and (CV)
Clay Profile (includes KeswickClay) (Figs. 7 and 8)
South Parklands 216 −110 −40 to –180 (22%)
Keswick Clay South Parklands 48 −120 −80 to –165 (14%)Keswick Clay (Horizontal CPT) Keswick 1 −120Calcareous Sand (Fig. 9) Gillman 1 −65Clay Profile (Fig. 10) Victoria Square 4 −75 −60 to –90Clay Profile Light Square 1 −75Red Brown Earth Clays (Fig. 18) Eastwood 1 −105Black Earth Clays Woodcroft 2 −55 −50 to –55River Alluvium (Sands & Clays) Adelaide 1 −95*: A negative value of dfs implies that the fs data are shifted up relative to the qc data
13
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
−65
Figure 9. Sample cross-correlation function of cone tip resistance andsleeve friction measurements in calcareous sand.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
−75
Figure 10. Sample cross-correlation function of cone tip resistance andsleeve friction measurements from Victoria Square.
14
In approximately 7% of the 303 CPT soundings examined, the cross-correlationanalyses yielded CCFs with the characteristics as shown in Figures 11 and 12.As is evident from these plots, the global maximum value of the cross-correlation coefficient yield unrealistically high values for the shift distance.Yet, these graphs clearly demonstrate that local maxima occur at shift distancesconsistent with those given in Table 1. It will be demonstrated in the followingsection, that such CCFs can be attributed to a phenomenon exhibited in the fs
measurements, which is related to elastic rebound of the clay.
In approximately 9% of the cases no meaningful shift distance could beevaluated from the CCF obtained from the complete CPT sounding. The CCFsexhibited either uncharacteristically high negative values, Figure 13, orirrational positive values, Figure 14. However, in every case, the measured datacontained a large number of values (5–10%) that exceeded the upper and/orlower bounds of the apparatus; in this case qc = 0, qc > 15 MPa, fs = 0, orfs > 500 kPa. Figures 15 and 16 show the sleeve friction measurements thatwere used to evaluate the CCFs shown in Figures 13 and 14, respectively. It isevident from Figures 15 and 16 that many of the measurements of fs have beentruncated to 500 kPa, as they exceed the limits of the measuring apparatus.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
Global maximumat -870 mm
Local maximumat -120 mm
Figure 11. Sample cross-correlation function of cone tip resistance andsleeve friction measurements from CPT A1.
15
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
Global maximumat -400 mm Local maximum
at -130 mm
Figure 12. Sample cross-correlation function of cone tip resistance andsleeve friction measurements from CPT CD40.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
−305
Figure 13. Sample cross-correlation function of cone tip resistance andsleeve friction measurements from CPT A10a.
16
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
+155
Figure 14. Sample cross-correlation function of cone tip resistance andsleeve friction measurements from CPT RB1 (red brown earth).
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
00 100 200 300 400 500
Sleeve Friction, fs (MPa)
Figure 15. Sleeve friction measurements from CPT A10a.
17
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
00 100 200 300 400 500
Sleeve Friction, fs (MPa)
Figure 16. Sleeve friction measurements from CPT RB1 (red brown earth).
In order to examine the influence of these truncated values on the resultingCCF, they will be deleted from the data set and the CCF recalculated. In thecase of CPT A10a, the upper 2 metres of data are removed and the resultingCCF is given in Figure 17. Similarly, the upper 2.5 m are removed from theRB1 data set. The corresponding CCF is shown in Figure 18. It can be clearlyseen from these figures that the CCFs yield appropriate shift distances, inaccordance with those given in Table 1.
5.1 Rebound Phenomenon
Figure 19 shows the sleeve friction measurements for CPT I1 performed at theSouth Parklands (Jaksa, 1995). This CPT, as were the majority of the 224 CPTsperformed at this site, was achieved by penetration in two stages. Firstly, a drillstem consisting of 4 × 1 m rods was driven into the subsurface. At a depth ofapproximately 3.2 to 3.6 m, penetration was temporarily halted to allow anadditional 2 m of rods to be added to the drill stem. Within approximately 5–10minutes, penetration was continued until a total sounding depth of 5 m wasachieved. It can be seen from Figure 19, that at a depth of 3.2 m, the depthcorresponding to the temporary cessation of the CPT, upon recommencement of
18
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-800 -600 -400 -200 0 200 400 600 800
Cross-Correlation Coefficient
Distance (mm)
−90
Figure 17. Sample cross-correlation function from CPT A10a with upper2 m of data removed.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-400 -300 -200 -100
0
100 200 300 400
Cross-Correlation Coefficient
Distance (mm)
−105
Figure 18. Sample cross-correlation function from CPT RB1 with upper2.5 m of data removed.
19
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
00 100 200 300 400 500
Sleeve Friction, fs (MPa)
3500
3400
3300
3200
3100
3000100 120 140 160 180 200
Sleeve Friction, fs (MPa)
Rebound Phenomenon
ENLARGEMENT
Figure 19. Sleeve friction measurements from CPT I1.
the test, the measured values of fs are substantially higher than those prior to thetest being halted. Due to the overconsolidated nature of the Keswick Clay, it isbelieved that this behaviour, known as rebound phenomenon, is a manifestationof elastic rebound of the soil. Such behaviour is apparent in each of the CPTsperformed at the South Parklands site, within Keswick Clay, as well as CPTsperformed at other locations in this clay. This phenomenon has not beenobserved in any of the CPTs performed in the other soils mentioned in thispaper and, to the authors’ knowledge, has not been reported in the literature.
The CCF for CPT I1 is given in Figure 20. The CCF exhibits a globalmaximum at –515 mm and a local maximum at –110 mm. In order toinvestigate the influence of the rebound phenomenon on the CCF, two subsetsof the CPT I1 data are examined. Firstly, data below 3.2 m are discarded, asthese include measurements associated with the rebound phenomenon, and dataabove 1.2 m are discarded, as these include values of fs which exceed the limitsof the apparatus, i.e. 500 kPa. The resulting CCF is given in Figure 21.Comparing this CCF with that given in Figure 20, it can be clearly seen that themaximum at –515 mm has disappeared and the local maximum of –110 mm hasbecome the global maximum of –115 mm.
20
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1500 -1000 -500
0
500 1000 1500
Cross-Correlation Coefficient
Distance (mm)
−110
Figure 20. Sample cross-correlation function of cone tip resistance andsleeve friction measurements from CPT I1.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1000 -750 -500 -250
0
250 500 750 1000
Cross-Correlation Coefficient
Distance (mm)
−115
Figure 21. Sample cross-correlation function from CPT I1 with databetween 1.2 and 3.2 m.
21
Secondly, only data associated with Keswick Clay will be examined. The uppersurface of this clay layer is conservatively estimated to occur at a depth of 2.1 mbelow ground. Hence, discarding data above 2.1 m and below 3.2 m, yields theCCF shown in Figure 22. The resulting shift distance is unambiguously evidentand equal to –125 mm, which is consistent with the results given in Table 1.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-300 -200 -100
0
100 200 300
Cross-Correlation Coefficient
Distance (mm)
−125
Figure 22. Sample cross-correlation function from CPT I1, between 2.1and 3.2 m, containing only Keswick Clay data.
This example has demonstrated that the presence of rebound phenomena in thesleeve friction measurements, causes the CCFs to be undular in nature, as inFigure 10, and in a number of cases, results in the global maximum suggestingan inappropriate shift distance, as in Figures 11, 12 and 17. Removing therebound phenomena from the fs data, results in the CCF adopting its morecharacteristic shape, as in Figure 8. Whilst only one example has beenpresented here, this conclusion is supported by analyses performed on otherCPT data also exhibiting undular CCFs.
This example also demonstrates that the CCF obtained from CPT data incorpor-ating more than one soil layer (Figure 20, dfs = –110 mm) yields a shift distancesomewhat different from that which incorporates only one layer (Figure 22, dfs
= –125 mm), as one would expect. This suggests an iterative approach may be
22
needed to determine the appropriate shift distance for each soil layer. It isproposed that the following technique be adopted.
1. The entire CPT data for each sounding are used as input to determine dfs,using the CCF and Equation (6).
2. The value of dfs is checked to determine whether it is appropriate or not. Itis suggested that an appropriate value of dfs lies between –30 and –200 mm,remembering that a negative value indicates that the fs data are shifted uprelative to the qc data. There are a number of situations that may lead tounsatisfactory values of dfs. These include:
(a) The qc or fs data contain a significant number (5–10%) of values equalto zero, or the upper limit of the testing and measuring apparatus. If so,these values may be removed with the values above or below the depthat which they occur. Provided that there are sufficient data, in excessof 50 qc or fs measurements, the modified data set can then be used asinput in Step 1.
(b) The CPT data contains one or more rebound phenomena. These maybe removed as in (a), again provided that the data above or below arealso discarded, and that the remaining data set has sufficient data.
(c) The values of qc and/or fs data contain measurement errors such as out-of-calibration errors, noise or other random interference. In such cases,the CPT data are suspect and the location retested.
3. With an appropriate dfs, the friction ratio, FR, can then be correctlyevaluated which, in turn, can be used to determine the likely soil layering.The original, unshifted CPT data file is then divided into a series of subsets,one for each soil layer.
4. Provided that there are sufficient data, each subset is individually input intoEquation (6) and a dfs for each layer is determined from the resulting CCF.
5. The values of dfs from Step 5 are used to re-evaluate the layering, and theprocess is repeated until the layering agrees, say within 10%.
It is expected that this technique will yield, in the majority of cases, satisfactoryresults after one or two iterations. In heavily layered soil profiles, it isanticipated that this process may be cumbersome and, in such situations, onecycle will suffice.
23
6. SUMMARY AND CONCLUSIONS
This report has demonstrated that the cross-correlation function (CCF) is auseful, robust and objective technique for estimating the shift distanceassociated with the cone penetration test (CPT). The results obtained fromCCFs of CPT data performed in a number of different soil profiles indicate thatthe shift distance is generally larger than the physical separation distance of75 mm and, particularly for overconsolidated clays, greater than the value of100 mm suggested by Campanella et al. (1983). In addition, occasionally, theshift distance estimated from the CCF is less than the physical separationdistance of 75 mm, which suggests that the centroid of the plastic failure regionassociated with the cone tip is above the tip of the penetrometer. Such anobservation has not been previously reported.
In addition, the rebound phenomenon has been observed which influences themeasured values of sleeve friction and, hence, the resulting CCF and shiftdistance. Once these effects have been removed, appropriate shift distances areobserved.
Finally, an iterative technique has been proposed for determining theappropriate layering of a soil profile estimated by means of the CPT inconjunction with the CCF. Whilst this technique requires more effort than thecurrent practice of either carrying out no shift or a shift of constant value, it isexpected that more accurate soil profiles will be obtained.
7. REFERENCES
Box, G. E. P. and Jenkins, G. M. (1970). Time Series Analysis Forecastingand Control, Holden-Day, San Fransisco, Calif.
Campanella, R. G., Robertson, P. K. and Gillespie, D. (1983). ConePenetration Testing in Deltaic Soils. Canadian Geotech. J., Vol. 20, No. 1, pp.23–35.
De Ruiter, J. (1971). Electric Penetrometer for Site Investigations. J. SoilMechanics & Foundations Div, ASCE, Vol. 97, No. SM2, pp. 457–472.
De Ruiter, J. (1981). Current Penetrometer Practice. In Cone PenetrationTesting and Experience, Geotech. Engrg. Div., ASCE, St. Louis, Missouri, pp.1–48.
Holtz, R. D. and Kovacs, W. D. (1981). An Introduction to GeotechnicalEngineering, Prentice Hall, New Jersey.
24
ISSMFE (1989). Appendix A: International Reference Test Procedure for theCone Penetration Test (CPT). Report of ISSMFE Tech. Comm. on PenetrationTesting of Soils, TC-16, With Reference to Test Procedures, Swedish Geotech.Institute, Linköping, Sweden, Information, 7, pp. 6–16.
Jaksa, M. B. (1995). The Influence of Spatial Variability on the GeotechnicalDesign Properties of a Stiff, Overconsolidated Clay, Ph.D. Thesis, Faculty ofEngineering, The University of Adelaide, Australia.
Jaksa, M. B. and Kaggwa, W. S. (1994). A Micro-Computer Based DataAcquisition System for the Cone Penetration Test. Research Report No. R 116,Dept. Civil & Environmental Engrg, University of Adelaide, Australia.
Jaksa, M. B., Brooker, P. I. and Kaggwa, W. S. (1997). InaccuraciesAssociated with Estimation of Random Measurement Errors. J. Geotech. andGeoenv. Engrg., ASCE, Vol.123, No. 5, pp. 393–401.
Kaggwa, W. S., Jha, R. K. and Jaksa, M. B. (1996). Use of Dilatometer andCone Penetration Tests to Estimate Settlements of Shallow Footings onCalcareous Sand. Proceedings 7th Australia New Zealand Conf. onGeomechanics, Adelaide, pp. 909–914.
Li, K. S (1993). Spatial Variability of Soils. Workshop on ProbabilisticMethods in Geotechnical Engineering, Canberra. (Unpublished).
Lunne, T., Robertson, P .K. and Powell, J. J. M. (1997). Cone PenetrationTesting in Geotechnical Engineering Practice, Blackie Academic andProfessional, New York.
Schmertmann, J. H. (1978). Guidelines for Cone Penetration Test:Performance and Design. Report No. FHWA-TS-78-209, U.S. Dept.Transportation, Federal Highway Administration, Washington.
Teh, C. I. and Houlsby, G. T. (1991). An Analytical Study of the ConePenetration Test in Clay. Géotechnique, 41, No. 1, pp. 17–34.
Vesic, A. S. (1972). Expansion of Cavities in Infinite Soil Mass. J. Soil Mech.Fndn. Engrg. Div., ASCE, Vol. 98, pp. 265–290.
8. NOTATION
The following symbols are used in this report:
Ab; As = area of the base of the cone, usually 1000 mm2; surface areaof the friction sleeve;
25
ac = radius of the electric cone penetrometer;CV = coefficient of variation;
* ;XYXY kk cc = cross-covariance coefficient between data series X and Y at
lag k; sample cross-covariance coefficient at lag k;dfs = sleeve friction shift distance;E[…] = expected value;Eu = undrained Young’s modulus of elasticity;Fc; Fs = total force acting on the cone tip and the friction sleeve;FR = friction ratio = ( ) %100 ×cs qf ;fs = sleeve friction, as measured by the cone penetration test;G = shear modulus;Ir = rigidity index = uuu sEsG 3= ;k = lag;n = number of pairs of observations;qc = cone tip resistance, as measured by the cone penetration test;rp = the radial distance of the plastic boundary from the axis of
penetration measured at a large enough distance above thecone penetrometer tip;
su = undrained shear strength;sX = sample standard deviation of data series X ;Xi, X = value of the property X at location i, mean value of X;zp = the distance between the cone tip and the plastic boundary
measured along the axis of the cone penetrometer;β = apex angle of the cone penetrometer tip;
XYkρ = cross-correlation coefficient between data series X and Y at
lag k; andσX = standard deviation of data series X.