Environmental and Engineering Geoscience; August 2007; v. 13; no. 3;
p. 197-203; DOI: 10.2113/gseegeosci.13.3.197
© 2007 Association of Engineering Geologists
Determination of Organic Soil Permeability Using The Piezocone Dissipation Test
Stefan. VAN BAARS1 and
Henke C. VAN DE GRAAF2
1 Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
2 Lankelma Geotechniek-Zuid, P.O. Box 38, 5688 ZG Oirschot, The Netherlands
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ABSTRACT
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Among other parameters, the hydraulic conductivity needed to predict time-dependant settlement can be estimated using a piezocone dissipation test. This test is commonly used along with cone penetration tests, soil borings, and laboratory tests in foundation site investigations. The piezocone dissipation test is based on the fact that the rate of decay of the large excess pore water pressures generated during penetration of the piezocone through saturated clays and silts depends on the hydraulic conductivity of the material. However, interpretation of the dissipation curve is often problematic, as existing methods of analysis assume a continuous decrease of pore pressure with time, whereas actual dissipation curves often exhibit nonstandard behavior, the interpretation of which is more complex. This article presents a new method of interpretation that can be used to estimate the hydraulic conductivity regardless of the shape of the dissipation curve. Examples of results using the new analysis method are compared with results obtained using laboratory odometer testing.
Key Words: Cone Penetration Test • Dissipation • Hydraulic Conductivity • Permeability • Piezocone • Site Investigation
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Introduction
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In a piezocone test, the surrounding soil is compressed by the penetration of the cone tip, which creates excess pore water pressures. At the same time, the shearing of the soil by the cone tip may also result in dilatant behavior, which results in a negative excess pore pressure. Depending on the relative magnitudes of the pore pressures created by the compression and shearing actions, the resultant excess pore pressure may be less than, equal to, or greater than the initial hydrostatic pressure. In clean sands and gravels, drained response is essentially observed, and measured pore pressures are hydrostatic. In most other cases, an initial undrained response occurs that is followed by drainage. Once penetration has stopped, the excess pressures will dissipate with time and eventually reach the pretest hydrostatic value. Since the rate at which the pressures dissipate depends on the hydraulic conductivity of the surrounding medium, the pressure dissipation curve can be used to estimate the hydraulic conductivity of the medium.
The shape of the pressure dissipation versus time curve, however, depends on several factors, including the geometry of the cone tip, the location of the pore-pressure sensor on the cone (Figure 1), and the dilatancy of the soil. Consequently, a wide range of dissipation curves can be obtained, as shown in Figure 2.
The response also depends on whether the pore-pressure sensor is located on the mid-face of the cone (u1) or on the shoulder behind the cone (u2). The excess pore pressure measured at the shoulder is typically less than that measured at the mid-face location (Figure 3). This observation can be explained as follows:
- The soil is more compressed at the cone tip than at other locations.
- As a result of symmetry, soil below the cone tip is not subject to shear, which does occur adjacent to the rods.
- As the distance from the cone tip increases, the dissipation of the pressure and deformations induced by the cone tip increase.
Calculation of The Hydraulic Conductivity
The problem is to understand how all of these different results can lead to a hydraulic conductivity, k, or a consolidation coefficient, cv. As shown in Figure 3, the pressure can vary significantly over a small distance in the beginning of the measurement. For this reason, the pressures at the beginning of the curve should not be used for the calculation of the coefficients. It is more appropriate to use the data obtained as the pore pressure nears final equilibrium, in which case the pressures are the same for all measuring points around the cone.
Occasionally the measurements are concluded before final equilibrium is reached, especially in the case of a low-permeability soil, in which the dissipation time may exceed 24 hours, rendering a complete dissipation test economically unattractive. Figures 2b and 3 are examples of unfinished dissipation tests. For these cases, an approximation of the equilibrium pore pressure u0 must be obtained by other tests or calculations (see Figure 3).
Pore water pressure dissipation consists of two phenomena, the groundwater flow and the conservation or storage of water. The groundwater flow can be described by Darcy's Law:
where q = specific discharge, i = hydraulic gradient, Q = total discharge, A = cross section, h = hydraulic head, and x = flow distance.
The hydraulic head depends on the pressure:
where 
w = unit weight of water and z = vertical coordinate of hydraulic head location.
Combining Eq. 1 and Eq. 2, we obtain the relation between pressure and specific discharge:
The increase of the water volume in the incremental volume 
V is for a small time step:
In the same area, storage of water can be obtained by determining the compressibility of water:
The storage capacity depends on the change in pressure p, the compressibility of water ß, and the ratio of water in the soil, which is the porosity, n (at saturation).
Considering the Law of Conservation of Mass and assuming that soil solids are incompressible, the sum of Eq. 4 and Eq. 5 must be zero:
For one-dimensional groundwater flow (q = 
q/x), the incremental volume element V can be defined as:
By inserting Eq. 7 into Eq. 6, we find:
By combining Eq. 3 and Eq. 8, we obtain the following diffusion equation:
or:
The dissipation constant cd is a diffusion coefficient, which determines the rate of the excess pore water dissipation.
For two-dimensional axisymmetric (radial) groundwater flow (r = x), the relation is identical, except that the flow cross section A depends on the distance r from the origin, the angle 
(in radians, see Figure 4), and the height b:
For a constant specific discharge q and a small time step t, the difference between the discharge entering the area and the discharge leaving the area is q x A x t. This gives the following equation for axisymmetric groundwater flow:
For three-dimensional groundwater flow around the cone tip, the flow cross-section is:
This gives the following diffusion equation:
Near the shoulder element at the shaft (u2), the dissipation process will be approximately the average of the two-dimensional and three-dimensional processes, as shown in Figure 4. This average is:
The solution to this differential equation consists of Bessel functions. Because of the complexity of the analytical solution, it is customary to evaluate the dissipation constant cd by plotting the excess pore pressure versus the logarithm of time. If the relative pore pressure is plotted for one specific distance from the origin (r = 2.5 cm, as in Figure 5) for several dissipation constants, then it becomes clear that the distribution in time depends linearly on the dissipation constant.
This means that if the distance from the origin is known, theoretically speaking, each clear point of the curve can be used to calculate the dissipation constant, for example, the top of the curve or the tangent of the ascending or descending parts of the curve.
As the rate of pore pressure dissipation is a function of the radius from the cone r, it is found that, especially at the start of the dissipation, the results depend strongly on the position of the pore pressure elements, as shown in Figure 6.
As the distance from the origin increases, the pore pressure change decreases, and the maximum pressure change occurs at a progressively longer delay from the onset of the test. To ensure consistent behavior, regardless of the distance from the origin, it is best to calculate the dissipation constant from the tangent to the descending portion of the curves. An example of the calculation procedure is now described with the aid of Figure 7. The dissipation constant cd is related to the point of intersection of the diagonal tangential line with the horizontal line of the pore water pressure at equilibrium u0. Please note that the corresponding time of this intersection point, which is called t100%, does not actually represent 100 percent dissipation, as the pore pressure approaches u0 asymptotically.
As Figure 5 shows, the reciprocal value of this time t100% depends linearly on the dissipation constant. Hence:
In this case, the value of the constant X was derived from Eq. 15 numerically (shown in Figures 5 and 6). This equation is based on a relatively thin cone with respect to the dissipation area. With a calibration of the core penetration test (CPT) cone the value of X can be determined more precisely.
The diffusion process of a dissipation test looks very similar to a one-dimensional compression test. However, the dissipation constant cd is different from the consolidation coefficient cv:
Note that in soil mechanics textbooks it is commonly assumed that the pore space compressibility term nß is small compared to mv. The (mv + nß) term represents the "storativity" of the porous medium (Bear, 1979).
The similarity is that both coefficients depend linearly on the permeability and the unit weight of water. The greatest difference is that the one-dimensional compression test depends mainly on the compressibility of the soil mv. The dissipation process does not, because during this test the cone is stationary and the soil is not being compressed. The dissipation process depends linearly on the porosity n and the compressibility of the pore water ß. Substituting Eq. 16 into Eq. 17 we obtain:
From comparison of the two relationships in Eq. 18 it is clear that the consolidation coefficient can also be estimated if the compressibility of the soil mv is known. This can be found, for example, with a one-dimensional compression test, which is unfortunately not an in situ test. However, the compressibility of the soil can be determined in situ using the Menard pressure meter test or empirical CPT correlations.
In the calculation of the permeability from the dissipation time, there can be some inaccuracy. First, the in situ porosity is not known, although one can assume, roughly, that n 
0.4 for sand, n 0.6 for clay, and n 0.8 for peat. This can lead to errors of 10–20 percent in k, which is generally acceptable. Second, the in situ compressibility of the pore water is not known. The compressibility ß depends on the degree of saturation S and the pressure p (Verruijt, 2005):
If there is no air (or methane for peat) in the soil then the compressibility of the pore water is ß0 = 0.5 x 10–9 m2/N. If there is 1 percent air or methane in the water then the compressibility is ß = 1.0 x 10–7 m2/N for shallow samples close to atmospheric conditions: p = 100 kPa. This means that a small amount of (nondissolved) air or methane can change the compressibility and the permeability of the soil by a factor of 200.
This is not a severe limitation, because the amount of nondissolved air and methane in organic materials is primarily below 1 percent. Nonorganic materials (pure clay and sand) have almost no air in the pore water, which results in a compressibility approaching ß0.
The validity of the approach is demonstrated in the following three examples from The Netherlands, examples that concern organic silty clays.
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Example 1: Pannerden
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Figure 8 shows a dissipation curve obtained near Pannerden in The Netherlands for a new train line. Borings show an organic silty clay layer at a depth of 18 m below mean sea level. Although no actual measurement data are available, the amount of nondissolved air and methane in the silty organic clay is estimated to be low, about 0.2 percent, which results in a compressibility that approximates ß = 2.0 x 10–8 m2/N. According to a one-dimensional compression test (log-t method), the permeability of this layer is approximately k = 5.9 x 10–8 cm/s (boring 28). A nearby dissipation test showed a reduced hydrostatic pressure due to dilitant behavior, resulting in a dissipation time of t100% = 210 seconds (see Figure 8). Using Eq. 18 yields an estimated hydraulic conductivity of:
This value is comparable to the value of the one-dimensional compression test, even though the amount of nondissolved air and methane was estimated.
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Example 2: Rijswijk
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Figure 9 shows a dissipation curve obtained near Rijswijk. Both u1 and u2 dissipation tests were carried out on the same organic silty clay. Both tests resulted in a hydraulic conductivity of:
This value falls between the values from the one-dimensional compression test obtained using the log-t method (k = 3.6 x 10–8 cm/s) and the 
-t method (k = 6.7 x 10–8 cm/s).
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Example 3: Rotterdam
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In Rotterdam in The Netherlands, Kort (2002) conducted a u2 dissipation test on organic silty clay. Figure 10 is a plot of the results. The water content, w, was measured to be about 50 percent, which results in a porosity of n = 0.57. There are about 14 m of peat and organic clay producing methane below the depth tested. During excavation of a building pit, methane was even bubbling up from the ground. Therefore, the amount of nondissolved gas was estimated to measure around 1 percent. Eq. 19 gives an estimation of the pore water compressibility of:
Based on this assumed compressibility and based on the dissipation time of 1,210 seconds, the dissipation test results in a permeability of:
This value agrees well with the values obtained from the one-dimensional compression test using both the log-t and the -t methods (k = 5.2 x 10–7 mm/s), despite the rough estimation of the amount of gas.
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Comparison Between The New Interpretation Method and The Classical Interpretation Methods
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The new interpretation method differs fundamentally from classical methods, which are presented by Lunne and others (1997). The new method is based on the concept of dissipation of the excess pore pressure for a constant soil volume. The soil volume is constant because the penetration has ceased at the beginning of the dissipation test. In this way, the dissipation time depends on the permeability. The classical methods are all based on an assumed changing volume during the test (which is incorrect), such that the dissipation time depends on the consolidation coefficient. The hydraulic conductivity and the consolidation coefficient are fundamentally different parameters. Therefore, it is impossible to compare directly the results of the two different approaches.
Additionally, the classical methods can only directly interpret curves that continuously descend in time. To evaluate other curve shapes requires a trial-and-error approach (Mayne, 2002). The new method, however, can be used to directly obtain the hydraulic conductivity for all dissipation curve shapes.
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Conclusions
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The new interpretation method for the dissipation test, presented in this article, can be used to determine the hydraulic conductivity for all dissipation curve shapes, which is not the case for the classical interpretation methods. Another important point is that the new method results in a hydraulic conductivity instead of a consolidation coefficient, because during the CPT the cone is stationary and the soil is not being compressed, as it is during consolidation.
The values of hydraulic conductivity obtained with this new method correspond well with values obtained from one-dimensional compression tests, for the limited number of tests on organic soils for which data were available. However, caution should be exercised when using this method for nonorganic soils.
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REFERENCES CITED
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Bear, J., 1979, Hydraulics of Groundwater, McGraw-Hill New York.
Kort, D.A., 2002, Rotterdam Sheet Pile Wall Field Test, CUR Publication 207 Gouda.
Lunne, T., Robertson, P.K., and Powell, J.J.M., 1997, Cone Penetration Testing in Geotechnical Practice, Blackie Academic and Professional London.
Mayne, P.W., 2002, Flow Properties from Piezocone Dissipation Tests, Electronic document, available at http://www.ce.gatech.edu/
geosys.
Shiyo Chen, B., and Mayne, P.W., 1994, Profiling the Overconsolidation Ratio of Clays by Piezocone Tests, Report GIT-CEEGEO-94-1, National Science Foundation, Arlington, VA.
Verruijt, A., 2005, Grondmechanica, VSSD Delft, The Netherlands.
Copyright © 2009 by Association of Engineering Geologists
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ABSTRACT
Introduction
