1 INTRODUCTION

Prediction of soil properties from piezocone test (CPTU) data in cohesive soils is routinely carried out in geotechnical design. This is possible because there is a general recognition that analytical and numerical analysis techniques and constitutive models of soil behaviour are now sufficiently developed to produce good agreement between cone parameters and independently measured soil properties (e.g. Lunne et al, 1997; Yu, 2004; Schnaid, 2009). A theoretical frame is essential, because the CPTU cannot measure the undrained shear strength directly and therefore CPTU assessment of Su rely on a combination of theory and empirical correlations.

Since penetration tests in clay are generally undrained, and therefore excess pore pressures are generat-

ed, the cone tip resistance qc can be related to Su as follows:

𝑞! = 𝑁!" ∙ 𝑆! + 𝜎! (1) where Nkt is a theoretical cone factor and σo is the in situ total stress. The cone factor may be deter-

mined using simple bearing capacity formulations, cavity expansion or strain path method (e.g. Terzaghi,

Using piezocone dissipation test to estimate the undrained shear strength in cohesive soil

F.M. Mantaras Geoforma Engenhaira Ltda, Joinville, Brazil E. Odebrecht Geoforma Engeharia Ltda- State Univ. of Santa Catarina – UDESC, Joinville, Brazil F. Schnaid Federal University of Rio Grande do Sul – UFRGS, Porto Alegre, Brazil

ABSTRACT: A method is developed to link the measured piezocone dissipation excess pore-water pressure (Δu) to the soil undrained shear strength (Su). In cohesive soils both Δu and Su are dependent on the same variables (stress state, stress history, soil stiffness), which allows them to be related by the theoretical cavity expansion-critical state framework. A mathematical derivation is presented to demonstrate that the ratio of normalized maximum excess pore pressure measured during a dissipa-tion test and the normalized undrained shear strength fluctuates around a mean value, being affected by soil stiffness and independent on stress history and soil friction angle. The predicted Su values ob-tained from the proposed approach are calibrated against field vane shear strength in both normally consolidated (monotonic dissipation tests) and overconsolidated soils (dilatory dissipation tests). Re-ported results are consistent and encourage the use of the method in engineering practice.

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1943; Meyerhof, 1956; Caquot & Kerisel, 1953; Baligh, 1985; Teh & Houlsby, 1991; Yu & Whittle, 1999; Abu-Farsakh et al, 2003). Yu (2004) pointed out that while each theory may be used alone for cone penetration analysis, better predictions of cone penetration mechanisms may be achieved if some of the methods are used in combination. A combination of strain path analysis and finite element calculations was used by Teh & Houlsby (1991) to model cone penetration in a Von Mises soil. Yu & Whittle (1999) proposed a cone factor estimated from both strain path analysis and cavity expansion methods. In this approach, the strain path solution developed by Baligh (1986) was used to estimate the size of the plastic zone produced by penetration. Once the plastic zone is established, spherical cavity expansion was used to determine the stress distribution and therefore cone resistance. Burns & Mayne (1998) use cavity expan-sion-critical state framework to model monotonic and dilatory response with regard to time.

Whereas theoretical solutions have been contributing in the understanding of the fundamental mechan-

ics of cone penetration, empirical correlations are still widely used in practice to estimate Su from cone re-sistance. Values of cone factor (Nkt) often fall in the range from 10 to 20 and are influenced by soil plastic-ity, overconsolidation ratio, sample disturbance, strain rate and scale effects, as well as the reference test from which Su has been established (e.g. Aas et al, 1986; Mesri, 1975; 2001; Lunne et al, 1997). However in overconsolidated clays the values of Nkt often fall outside the predicted range and there are no constitu-tive modes to support empirical evidences.

A potential alternative to overcome the existing uncertainty related to Nkt is to use the excess pore pres-

sure to estimate Su. Several relationships have been proposed based on theoretical or semi-theoretical ap-proaches using cavity expansion theory (Battaglio et al. 1986; Campanella et al. 1985; Massarsch and Broms 1981; Randolph and Wroth 1979; Vesic 1972):

𝑆! =𝑢! − 𝑢!𝑁∆!

(2)

where NΔu is shown from cavity expansion to vary in the range of 2 to 20. Lunne et al. (1997) recom-

mend using a value of NΔu of between 7 and 10. It has been advocated that these methods have the ad-vantage of increased accuracy in the measurement of Δu, mainly in soft clays where Δu can be very large (e.g. Campanella et al, 1985).

The rationality in using equation (2) is that cone resistance and excess pore pressures generated during cone penetration into fine grained soils will be dependent on the same parameters - stress state, stress his-tory, soil stiffness - and can therefore be associated in CPTU predictions. Proposed semi-empirical solu-tions (Massarch & Broms, 1981; Campanella et al., 1985) attempt to capture the reduction in excess pore pressures with increasing overconsolidation ratio. We recall that by definition NΔu = Bq Nkt, but no global correlation has been identified between these quantities given opposite trend between Bq and Su in respect to the increase in OCR.

The present analysis advocates a different approach using dissipation tests linking the measured piezo-

cone maximum excess pore-water pressure measured during dissipation test (Δumax) to the undrained shear strength (Su). The mathematical solution proposed by Burns & Mayne (1998) is used as reference given the fact that excess pore water pressures are computed through a combination of the octahedral and the shear-induced components, allowing both normally and overconsolidated clays to be modeled from pore pressures measured immediately behind the cone shoulder (u2).

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The magnitude of the generated pore water pressure during penetration and subsequent dissipation is influenced by pore pressure filter location and rate of penetration. The method discussed here is valid strictly for filter elements positioned at the cone shoulder (u2 measurements) for tests carried out at the standardized penetration of 20 mm/s.

2 MATHEMATICAL FORMULATION

The mathematical solution proposed by Burns & Mayne (1998) is based on the cavity expansion-critical state framework for the monotonic and dilatory response with regard to time. The excess pore water pres-sures, Δu, at any time can be compared with the initial values during penetration, Δui =u2 - u0, represented as:

Δui = (Δuoc)i + (Δuτ)i where: (Δuoc)i =(2/3)Mσ’vo(OCR/2)Λln(Ir) is the octahedral component during penetration and (Δuτ)I =

σ’vo[1-(OCR/2)]Λ is the shear-induced component during penetration, with OCR the overconsolidation ra-tio, φ’ the effective friction angle, M=(6sinφ’)/(3-sinφ’) and Λ the compressibility ratio (1-CC/CR). This concept has been used by Burns & Mayne (1998) to derive the following equation for the normalized ex-cess pore pressure:

Δ𝑢𝜎!!

=23𝑀 ∙ 𝑙𝑛 𝐼!

𝑂𝐶𝑅2

!

1+ 50 ∙ 𝑇∗ +1− 𝑂𝐶𝑅

2!

1+ 5000 ∙ 𝑇∗ (3)

where; Ir is the rigidity index and T* the modified time factor T*=[ch t /(r2 Ir0.5)] a dimensionless time fac-tor. For monotonic dissipation, Δumax is the same as Δu2, where Δu2 is the difference between the meas-ured pore pressure and equilibrium pore pressure during the cone penetration. For non-monotonic dissipa-tion tests (e.g. overconsolidated clays) Δumax is the difference between the maximum value of pore pressure measured during dissipation test and the equilibrium pore pressure.

By taking the first derivative of equation (3) in respect to T* and setting the gradient of the objective

function equal to zero, it is possible to determine the maximum value of the normalized excess pore pres-sure. Figure 1 shows values of Δu/σ’vo versus T* and typical values T*

max form Burns & Mayne’s (1998) for Λ =0.75; φ’ = 25o ; Ir = 100 and 1< OCR < 15.

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Figure 1 – Δu/σ’vo versus T* derived from Burns & Mayne’s (1998). The maximum value of T* combined to Δumax and related to the normalized undrained shear strength

from DSS undrained test (Wroth, 1984) yields the maximum undrained pore pressure ratio (Δumax/Su) de-fined as the ratio of the maximum excess pore pressure measured during dissipation test and the undrained shear strength:

Δ𝑢!"#𝑆!

=

23𝑀 ∙ ln  (𝐼!)

𝑂𝐶𝑅2

!

1+ 50 ∙ 𝑇∗!"#+

1− 𝑂𝐶𝑅2

!

1+ 5000 ∙ 𝑇∗!"#12 𝑠𝑖𝑛 𝜙 ∙ 𝑂𝐶𝑅!

(4)

To narrowing the band of predicted data, a log(Ir) term was introduced in equation 4 and, for simplicity

2/3⋅M⋅ln(Ir) was defined as α.

Δ𝑢!"#𝑆! ∙ log   𝐼!

=

𝛼 𝑂𝐶𝑅2

!

1+ 50 ∙ 𝑇∗!"#+

1− 𝑂𝐶𝑅2

!

1+ 5000 ∙ 𝑇∗!"#12 𝑠𝑖𝑛 𝜙 ∙ 𝑂𝐶𝑅! ∙ 𝑙𝑜𝑔 𝐼!

(5)

Because the procedure of using the derivate of Burns & Mayne (1998) model to find T*

max exhibits a nonphysical meaning for OCR < 2, in present work it has been assumed that T*

max must be set as equal to zero for OCR = 1 (e.g. monotonic decay of pore pressure readings in a pore-pressure dissipation test). Within this hypothesis, the calculated (Δumax/Su⋅log(Ir)) values range from 5.39 (for Λ=0,75; φ=24o; Ir =

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50) to 4.98 (for Λ=0,75; φ=30o; Ir = 500). For OCRs greater than 2 the procedure is rigorously consistent with Burns & Mayne (1998) model.

Based on equation 5 the derived formulation shows some sensitivity to variations on OCR and φ’, and

for typical soil parameters can be reduced to a relatively simple expression (as illustrated on Figure 2). Advantages of interpreting pore pressures measurements compared to the more conventional piezocone penetration data are: (a) maximum undrained pore pressure ratio (Δumax/Su) is less affected by soil rigidity and stress history because measurements result from pore pressure flow around the probe rather than of complete soil displacement caused by the cone penetration test and (b) well-defined failure mechanisms of flow around the probe allow for sound theoretical analysis of pore pressure dissipation and shear strength.

From the mathematical viewpoint the above expression is rigorously consistent, expressing the ratio be-

tween a value of pore pressure measured during piezocone dissipation and the undrained shear strength in DSS conditions.

Figure 2 – (Δumax/Su⋅log(Ir)) against OCR.

3 CASE STUDIES

Two case studies are reported to exemplify the possibilities offered by the new approach. The first exam-ple illustrated in Figure 2 is from the Barra da Tijuca soft clay deposit in Rio de Janeiro (Teixeira, 2012; Teixeira et al, 2012). Undrained shear strength values predicted from umax (φ’ = 26o and Ir = 50) are ap-proximately the same as those obtained from qt (Nkt = 11) and are consistent with the geological history of the site.

It interesting to note that piezocone predictions are useful for non-textbook materials such as bauxite tailings (Bedin, 2010; Nierwinski, 2013; Klahold, 2013). Monotonic dissipation test results shown in Fig-

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ure 4 yielded Su values of the same order of magnitude as those calculated from other methods ((Δumax/Su⋅log(Ir)) ≅ 5, with Ir equal to 100).

   a)Geotechnical profile. b) Dissipation tests.  

Figure 3 – Barra da Tijuca soft clay deposit in Rio de Janeiro, Brazil.

   a)Geotechnical profile. b) Dissipation tests.

Figure 4 – Bauxite tailings in Northern Brazil

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4 CLOSING REMARKS

The paper describes a new method that is easily applicable to estimate the undrained shear strength from piezocone dissipation tests. Stress history, shear strength and compressibility are the critical factors affect-ing the accuracy of predictions and are properly taken into account. The core of the method is a mathemat-ical expression derived from the principles of cavity expansion and critical state framework that can be simplified to the following equation:

𝑆! =∆𝑢!"#

4.2(±0.2) ∙ log  (𝐼!) (6)

For low OCR (<2) values the maximum undrained pore pressure ratio ranges from about 4.0⋅log(Ir) to

5.0⋅log(Ir), but with a slight increasese in OCR the ratio approaches a constant value about 4.2⋅log(Ir) (8.4 ≅ 4.2⋅log(100)) which is within the range of early recommended values (e.g. Massarch & Broms, 1981). Reported case studies encourage the use of the method in engineering practice.

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