2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010

Estimation of u1/u2 conversion factor for piezocone

J. Peuchen Fugro, Leidschendam, Netherlands J.F. Vanden Berghe & C. Coulais Fugro, Brussels, Belgium

ABSTRACT: The use of piezocones with a pore pressure filter at the u2 position (lo- cated just above the cone tip) suits a wide range of soil conditions. For more demand- ing conditions, such as highly stratified and heavily overconsolidated soils, the u1 po- sition located on the face of the cone tip can offer more effective and robust piezocone penetration test (CPTU) profiling. In these conditions, the pore pressure measuring system at u2 position can lose saturation where the u1 position will not. Loss of saturation leads to sluggish pore pressure response and reliable pore pressure data may not be consistently obtained.

A simple-to-use equation is presented for obtaining the so-called K-factor required for calculating total (or corrected) cone resistance from measurements obtained with an u1 piezocone penetrometer. No input is required from laboratory tests or other sources external to the CPTU. Equation results compare well with field measure- ments.

1 INTRODUCTION

Measuring pore water pressure during a piezocone penetration test (CPTU) allows (1) greater sensitivity in the detection of soil behaviour types (SBT) and layer boundaries and (2) harmonizing results from different cone penetrometer designs. The pore water pressure may be measured at different positions on the cone penetrometer, as shown on Figure 1a. The common location is just above the cone tip, at the shoulder be- tween the cone and the friction sleeve. This location is called the u2 location. Meas- urements at the u2 location are used directly to derive the corrected (or total) cone re- sistance qt, by correcting for the effect of water pressure on the cone force measurement. In highly stratified or heavily overconsolidated soil conditions, the tendency for soil dilation can generate pore water suction at the u2 location. This can cause de- saturation of the pore pressure measuring system. In these circumstances, it may be preferable to measure the pore pressure on the face of the cone, at the u1 location. 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010

However, the interpretation of such test results requires a correlation to be used to deduce the magnitude of pore water pressure at the u2 location. This publication presents a simple-to-use equation for computing pore water pres- sure at the u2 location from measurements obtained with an u1 piezocone penetrome- ter. The focus is on accurately predicting qt in soils where u2 contributes significantly to qt. A significant u2 contribution typically applies to soils with Qt < 20, where Qt is the normalized cone resistance as defined in Figure 2.

1(a) 1(b) Figure 1. Typical pore pressure sensor locations and pore water pressure distribution in saturated soil during CPTUs based on field measurements (adapted from Robertson et al. 1986).

2 ASSESSMENT OF U2 BASED ON U1

2.1 K-factor correlation In a saturated soil loaded in an undrained manner, an increase in the total normal stress will generate positive water pressure, while an increase in shear stress may yield either positive or negative pore pressure, depending on the SBT and its stress history or relative density. During penetration, the pore water pressure distribution in the soil around the cone penetrometer is complex and depends on the soil behaviour type. Both the zone be- neath the cone and the zone around the friction sleeve are subjected to shear stresses. However, in the zone beneath the cone, the large increase in normal stress dominates the pore water pressure response. Around the friction sleeve, immediately behind the 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010 cone itself, there is typically a zone of normal stress relief in which shear stresses dominate the pore water pressure behaviour. The consequence of the above is a sig- nificant reduction in pore water pressure at the cone shoulder in most soil behaviour types (see Fig. 1b). Figure 1 also illustrates some complications with the u2 location. The gradient of u/u0 is relatively small for normally consolidated clay. This means that permissible tolerances in filter geometries for u2 incorporated in CPT standards (e.g. ISO, 2010) will have little influence on qt when comparing results from different cone penetro- meters. The high gradients for many other SBTs imply probable u2 scatter when comparing results from different penetrometers. The u1 location is more robust in this regard. Another u2 complication is the standardized assumption of the measured u2 value being equal to the pore pressure acting in the groove between the cone tip and the friction sleeve. This assumption ignores combined contributions from (1) relative movements between cone tip and friction sleeve when penetrating layered soils, (2) possibility of gas trapped in the groove and (3) the presence of rubber rings that pre- vent soil ingress into the groove. The u2-versus-groove assumption probably offers a reasonable approximation for a range of SBTs but will inevitably lead to scatter when comparing qt results from different penetrometers. Based on the variations on Figure 1b, Sandven et al. (1988) suggested a correlation to assess u2 when only u1 was measured. This correlation is based on a K-factor de- fined as the ratio of the pore pressure u2 to the pore pressure u1 relative to the in-situ equilibrium pore pressure u0: − uu K = 02 (1) − uu 01 From Equation 1, the K-factor represents the drop in pore water pressure at the cone shoulder with respect to the pore pressure measured on the cone itself. As would be expected from Figure 1b, K varies considerably with SBT, stress history, soil strength and sensitivity. Sandven (1990) proposed typical values for K depending on SBT.

2.2 K-factor function To expand the set of K-values proposed by Sandven (1990) to all SBTs, expected variations of the K-factor were plotted on the Robertson (1990) classification chart for CPTU data. Those variations are described below and illustrated on Figure 2: − A K-factor of 0.8 was assigned to normally consolidated clay as high excess pore water pressure is expected in such soil at the u2 location. − As no excess pore water pressure is expected during penetration in coarse clean soils (pure sand, gravel), the lower bound of the K-value range for dense sand was attributed to sand zones (i.e. most of zone 7 and zone 8). − Overconsolidated or very stiff fine grained soils dilate when sheared. Therefore, K is expected to decrease as OCR or stiffness increase. Very low or negative excess pore water pressure is expected in zone 9. A K value of 0 was chosen. − In loose sand, especially with a high fines content (i.e. zone 5 and left part of zone 6), some excess pore water pressure is expected as loose sand is compressible and fines reduce the soil permeability. A K-factor of 0.4 was selected. The K-factor is expected to be lower with low fines content and to decrease when the relative density increases. 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010

− A highly sensitive soil would yield to significant strain softening during cone pe- netration and result in disturbed soil around the friction sleeve. This phenomenon should result in a low excess pore water pressure at the u2 location. K is thus ex- pected to decrease when the sensitivity increases.

Figure 2. General trends for K-factor variation within the Robertson Classification Chart (adapted from Lunne et al. 1997 and Sandven 1990).

Based on these general considerations, a continuous mathematical expression of K was developed, related to Qt and Fr. K values are limited to the range 0 to 1 and may be evaluated over the complete range of combinations of Qt and Fr (even outside the Robertson classification ranges). This function accounts mainly for SBT, stress his- tory and soil strength and sensitivity. ⎛ ⎞ 0.47 ⎜ 1 ⎟ ⋅= e0.91K −0.09Q t − e −2Fr (2) ⎜ 1 ⎟ ⎜ 3 ⎟ ⎝ r (0.17F1 ++ 0.061(Q t − )21.6) ⎠ The above expression is plotted on the Robertson classification chart on Figure 3. 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010

Figure 3. Continuous K-factor function in Robertson (1990) classification chart.

3 VALIDATION EXAMPLES

The proposed correlation was tested for 4 sites with 18 CPTU profiles for which si- multaneous measurements of u1 and u2 were available. Soil conditions encountered include normally consolidated or slightly overconsolidated clay, layered silty clay and clayey silt, and interbedded soft soils with dilative thin layers (sand or overcon- solidated clay). For each CPTU, K derived from the measured u2 (using Eq. 1) and K values com- puted with the correlation (Eq. 2) were compared. The measured pore water pressures u1 and u2 and the calculated pore water pressure u2 using the correlation were also compared. Figure 4 shows an example. The results for all CPTU profiles are plotted together on Figure 5. The data was sorted based on the value of the measured K-factor. For easy comparison, the limits of the coloured zones presented in Figure 3 are also indicated on Figure 5 (for K = 0.2, 0.4, 0.6 and 0.8). 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010

Cone resistance qc [MPa] Pore Pressure [MPa] K [-] Friction Ratio Fr [% ] 012345 00.511.52 00.511.52 0 0 0

5 5 5

10 10 10 Depth [m] Depth

15 15 15

20 20 20

Measured u Cone Resistance 1 Measured K Measured u 2 Friction Ratio Calculated u 2 Calculated K 25 25 25 Figure 4. Measured and calculated results for uniform soil.

The following observations can be deduced from Figure 5: − The highest K values are concentrated in zone 3 of the Robertson chart (normally consolidated clay). − The K values tend to decrease as the normalized friction ratio Fr increases, and toward zone 4 on the Robertson chart (clay-silt mixture). − In zone 5 (sand) and zone 6 (sand-silt mixture), measured K oscillates between very low (<0.1 or negative) to very high (> 1) values and no clear trend can be found. − The correlation matches well the measured data in normally consolidated to slightly overconsolidated clay (zone 3, low Fr). The results exhibit an average er- ror on the u2 pore pressure from 0 to 20%. − The error between the computed and the measured u2 increases as the degree of consolidation in the clay increases (zone 3, high Fr). The relative error on u2 is of the order 60% to 100% for overconsolidated clay. − In zone 4, the correlation provides generally good results. − In zones 5 and 6, the average error on u2 is higher than 80%.

Figure 6 indicates that the error of the correlation on qt is typically below 3% (for 80% of the data – about 5400 data points). 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010

c

Measured data 0.0 < K < 0.2 0.2 < K < 0.4 0.4 < K < 0.6 0.6 < K < 0.8 0.8 < K < 1.0

Correlation K = 0.2 K = 0.4 K = 0.6 K = 0.8

Figure 5. Measured K values in Robertson (1990) classification chart.

30 5400 data points 25

20

15

10 Frequency [%] Frequency 5

0 -10 -8 -6 -4 -2 0 2 4 6 8 10

Relative Error on qt [%]

Figure 6. Relative error on qt. 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, May 2010

4 SUMMARY AND CONCLUSIONS

A mathematical equation is presented for computing the pore water pressure in a CPTU at the location u2 when only the one at the location u1 is measured. The equation provides a continuous variation of K computed from normalized fric- tion ratio Fr and normalized cone resistance Qt, with limiting K-values to a range from 0 to 1. The equation requires iterative processing of CPTU results since Qt uses qt. The correlation results were compared with CPTU field data at 4 sites where both u1 and u2 were measured. In clayey soils, the calculated pore water pressure u2 shows good agreement with the measured values. Less agreement is observed for soils with a complex structure, especially when dilative layers are imbedded in softer soil. This may be partly attributed to complications with the standardized u2 location, notably dependency on precise cone penetrometer design. The relative error on the corrected total cone resistance qt was found to be less than 3% for 80% of the available data.

REFERENCES

Campanella, R.G., Robertson, P.K., Gillespie, D & Grieg, J. 1985. Recent developments in in-situ test- ing of soils. Proceedings of the Eleventh International Conference on Soil Mechanics and Founda- tion Engineering. San Francisco, 12-16 August 1985. Vol. 2. pp. 849-854. Campanella, R.G., Robertson, P.K. & Gillespie, D. 1986. Factors affecting the pore water pressure and its measurement around a penetrating cone. Proceedings of the 39th Canadian Geotechnical Con- ference, Ottawa, August 1986. ISO International Organization for Standardization (2010), “Geotechnical investigation and testing – Field testing – Part 1: Electrical cone and piezocone penetration tests”, ISO/NP 22476-1. Lunne, T., Robertson, P.K. and Powell, J.J.M. 1997. Cone penetration testing in geotechnical practice. Blackie Academic & Professional. London. Sandven, R., Senneset, K. & Janbu, N. 1988. Interpretation of piezocone tests in cohesive soils. De Ruiter, J. (Ed.), Penetration testing 1988, Proceedings of the First International Symposium on Pe- netration Testing, ISOPT-1, Orlando, 20-24 March 1988. Vol. 2. pp. 939-953. Sandven, R. 1990. Strength and deformation properties of fine grained soils obtained from piezocone tests. Thesis. Norwegian Institute of Technology. Department of Civil Engineering. Trondheim. Robertson, P.K., Campanella, R.G., Gillespie, D. & Greig, J. (1986). Use of piezometer cone data. in Clemence, S.P. (Ed.), Use of in situ tests in geotechnical engineering: proceedings of In Situ ’86, Blacksburg, Virginia, June 23-25, 1986, Geotechnical Special Publication, No. 6, American Soci- ety of Civil Engineers, New York, pp. 1263-1280. Robertson, P.K. 1990. Soil classification using the cone penetration test. Canadian Geotechnical Jour- nal, Vol. 27 (1), pp. 151-158.