undrained strength properties of clays derived from pressuremeter tests

Revue. Volume X – n° x/année, pages 1 à X

Undrained strength properties of clays derived from pressuremeter tests Ramdane Bahar* — Fawzia Baidi* — Ouarda Belhassani* Eric Vincens**

* Laboratoire de Géomatériaux, Environnement et Aménagement, Université Mouloud Mammeri de Tizi-Ouzou, BP RP 17, 15000 Tizi-Ouzou, Algérie

[email protected]

** Université de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France

[email protected]

ABSTRACT. The behaviour of saturated clays under undrained conditions around pressuremeter path is studied by means of a theoretical and a numerical analysis based on the generalised elastoplastic Prager’s model with the Von Mises Criterion which is suitable for these cases of soils and gives a realistic response when unloading is considered. The soil constitutive model is described depending only on three parameters. The model response on pressuremeter path and its identification from experimental data lead to the determination of the undrained cohesion and the initial Young modulus of clays. Comparisons between the undrained cohesions determined with the proposed method and those obtained by other means illustrate the applicability of the method. An application to predict the bearing capacity and the settlement of bored piles using parameters derived from the proposed approach is also presented with a comparison to the measured data.

RÉSUMÉ. Le comportement des argiles saturées en conditions non drainées sur un chemin pressiométrique est étudié au moyen d'une analyse théorique et numérique basée sur le modèle élastoplastique du Prager généralisé avec prise compte du critère Von Mises. Ce critère est bien adapté aux sols considérés et donne une réponse réaliste en déchargement. Le modèle constitutif de sol proposé est défini seulement par trois paramètres. Cette approche permet la détermination de la cohésion non drainée et le module de Young initial des argiles saturées à partir d’essais pressiométriques. La comparaison entre les cohésions non drainées déterminées avec la méthode proposée et celles obtenues par d'autres moyens illustrent son applicabilité. Une application de l’approche proposée pour prévoir la capacité portante et le tassement d’un pieu foré soumis à une charge axiale centrée est également présentée avec une comparaison avec les mesures expérimentales.

KEYWORDS: undrained cohesion, clay, pressuremeter, behaviour, bored pile.

MOTS-CLÉS : cohésion non drainée, argile, pressiomètre, comportement, pieu foré.

Undrained strength properties of clays 2

1. Introduction

In the recent year, the use of the pressuremeter as an in situ testing device by practising geotechnical engineers has increasingly become popular in Algeria and others countries. Indeed, it provides the measurement of in situ stress-strain response of soils, and it is an useful and economical way for obtaining reliable in situ properties of soils. From this test, the design of foundations can be performed by using the limit pressure and the pressuremeter modulus. They are derived from the pressuremeter curve or deduced from existing correlations with undrained cohesion and internal angle friction (Ménard, 1957; Amar et al., 1972). In particular, these parameters are used to evaluate the bearing capacity of soil foundations and the expected settlements. But they can also help to identify usual soil parameters required by simple constitutive models (eg. Mohr-Coulomb model) for soils in numerical calculations.

For saturated clays with low permeability, several empirical, analytical or numerical methods based on pressuremeter tests have been proposed to evaluate the undrained shear strength and the stress-strain behaviour. The empirical methods give relationships between soil properties and pressuremeter parameters (Ménard, 1957; Amar et al., 1972). The analytical ones are based on the cavity expansion theory assuming idealised behaviour of soils, axial symmetry and plane strain, soil homogeneity, isotropy and undrained conditions (Baguelin et al., 1972; Ladanyi, 1972; Palmer, 1972; Gibson et al., 1961; Prévost et al., 1975; Denby, 1978; Ferreira et al., 1992; Monnet et al., 1994). Numerical solutions are used if a more precise solution of the pressuremeter test involving complex constitutive model for soils is required (Boubanga, 1990; Bahar, 1992; Zentar et al., 2001, Monnet, 2007). Boubanga (1990) and Bahar (1992) have developed a methodology called “Pressident, Pressuremeter Identification” to analyse pressuremeter tests using a very simple axisymmetric plane finite element method independent of the used constitutive model for soil. This program allows identifying the model parameters, taken into account the whole pressuremeter curve. It has successfully been used to define the soil parameters using non-viscous and viscous models for soil (Cambou et al., 1993; Bahar et al., 1995; Bahar, 1998; Bahar et al., 2005).

In this paper, the behaviour of saturated clays under undrained conditions (constant volumetric deformations) is studied by means of both a theoretical and a numerical analysis based on the generalised elastoplastic Prager’s model with the Von Mises criterion which is suitable for these kind of soils and gives a realistic response when unloading is considered along with Bauschinger effect (Iwan, 1967).

In the first part, the soil constitutive model is described. Based on the analytical representation of the stress-strain curves obtained from triaxial tests proposed by Olivari (Olivari et al., 1995) and modified by Bahar (Bahar et al., 1999), it is shown how the parameters of the generalised Prager model, composed of a large number of elastoplastic slip elements associated in series, can be identified. Also, by introducing the assumptions of incompressibility for the material and plane strain


condition for the calculation, it is shown that the proposed model depends only on three parameters, and the response of the pressuremeter test with a cycle of unloading-reloading is found to be realistic.

In the second part of the paper, the numerical program developed to simulate the pressuremeter test and taking into account the proposed model is described. This program allows the soil constitutive model parameters to be defined using pressuremeter tests. A parametric study is carried on to define the model constants that could reasonably be identified from pressuremeter tests. Then a strategy for the identification of the three parameters is presented. The model response on the pressuremeter path and its comparison with experimental data, lead to the determination of the undrained cohesion and the elastic Young modulus of clays. The validity of this method, which helps to obtain in situ mechanical properties, is compared to usual methods able to provide these properties. The comparison between the undrained cohesion determined with the proposed method and with other means illustrates the applicability of the previously described procedure.

In the third part, an application to predict the bearing capacity and settlement of a bored pile using the mechanical properties derived from this approach is presented and compared with the results obtained with the “Pressident” approach and with the experimental data.

2. Elasto-plastic model with multiple yield surfaces

Many plasticity models have been able to predict the nonlinear stress–strain behaviour of soils. Based on the use of a kinematic hardening function, a bilinear stress-strain behaviour can be simply described by means of a single internal variable (Figure 1(a)). Combining the idea of kinematic hardening and multiple internal variables together, a piecewise linear stress–strain response can be described (Figure 1(b)), the stress-strain curve is approximated by linear segments along which the tangent shear modulus is assumed to be constant. Each linear segment is associated with a yield surface in the stress space. Iwan (1967) proposed a model based on the assumption that a general hysteretic system can be constructed from a large number of ideal elasto-plastic Prager elements having different yield levels. A purely kinematic hardening rule is adopted for the movement of the yield surfaces in the stress space when the plasticity is activated, say, the sizes of the yield surfaces are assumed to remain constant while they translate in the stress space. Initially, all the yield surfaces are symmetrically arranged with respect to the origin. In this study, a collection of (n) elasto-plastic Prager elements connected in series is considered (Figure 2). The model is defined by the compliance of (n) elastic elements and their associated (n) yield surfaces. Eventually, a single linear spring elastic element of compliance (Jo) and a single yield surface of threshold stress (S∞) can be introduced and connected in series to the collection of elements to represent the initial elastic strain and failure respectively. Thus the model is defined by (2n+2) parameters that can be represented by a discrete spectrum of compliance (Figure 3).


(a) (b)

Figure 1. Stress-strain relationships: (a) bilinear; (b) piecewise linear.

Figure 2. Multiple surface model.

Figure 3. Compliance spectrum of the model.

Threshold stresses

Jo Sk

S∞ kk C

J1~ =

ε

σ

ε

σ

p1ε p

2ε pnεeε

p∞ε

pp

i

n

i

e∞=

++= ∑ εεεε1

Jo S∞ σ σ

Sn

J1 J2 Jn

S1 S2


During the initial loading, before the stress reaches the value of the first slip stress k1, the behaviour is linear elastic and is governed by the elongation of the E-spring. After the stress reaches the value of the slip stress k1, the first sliding element slip and the J1-spring becomes active. The corresponding behaviour is elasto-plastic with a linear hardening characterized by the tangent modulus E1. After the stress reaches the value of the slip stress kn*, the n*th sliding slips and the Jn*-spring become active. The corresponding behaviour is elasto-plastic with a linear hardening characterized by the tangent modulus En*.

The constitutive equations are:

– The elastic component of strain (εij) is calculated according to Hooke’s law:

ijkkijeij

E

v

Eδσσνε −+= 1

[1]

where E and ν denote the Young modulus and the Poisson ratio respectively.

– The equation of the kth yield surface fk in the stress space is given by:

( ) 2k

kijijk SXsf =− [2]

where (k) is a superscript denoting the kth element of the collection, sij denotes the components of the deviatoric stress tensor, Sk is the threshold stress of the kth yield surface, and k

ijX is the tensor specifying the position of the center of the kth yield surface in the stress space.

The total plastic strain is the sum of the plastic strain developed by each element. The number of activated elements is (n*) and, of course, 0 ≤ n*≤ n. Moreover, the components of the tensors Xij that specify the state of the model must be initially given. In the virgin state, all the residual stresses are equal to zero, hence for each cell, the hardening variables are also equal to zero, Xij(k) = 0. Since each of the (n) Prager elements will individually obey a linear work-hardening law, their combined action leads to a piecewise linear behaviour with kinematics hardening for the material as a whole.

The advantage of the multiple surface models is clearly that they are able to fit more accurately the non linear behaviour of certain materials across a wide range of strain amplitudes. This is important, for instance, for the modelling of geotechnical materials. The drawback is of course that a large number of material parameters, associated with each yield surface must be identified.


3. Modelling of the undrained behaviour of clays

3.1. Assumptions

The framework of the short-term behaviour of an incompressible medium is adopted. The considered stresses are thus total stresses. Viscous effects are also supposed to be negligible which justifies the use of an elastoplastic model as a first approximation of the true behaviour of the material. The material is supposed to be isotropic and normally consolidated or with a low value of the overconsolidation ratio.

3.2. Yield criterion

The used criterion obeys the condition of plastic incompressibility. Referring to the results of Habib (1953), obtained on Provins’s clay, it is admitted that the failure happens for the same value of the deviatoric stress in compression and in tension. Therefore the undrained cohesion is sufficient to characterise the plastic flow criterion. Consequently, the Von-Mises criterion is used:

( )( ) kkijij

kijij kXsXs =−−

2

3 [3]

where k = 2cu, cu is the undrained cohesion.

3.3. Spectrum compliance

The response of this proposed model on a triaxial path is a polygonal line that can be considered as a discretisation of the experimental curve. Then, if an analytical representation of the experimental test results for a triaxial stress path is chosen, the parameters of the Prager model can be easily identified. The following relationship is used (Olivari et al., 1995; Bahar et al., 1999):

( ) ( )

−−+−−=

R

RRRLnAp

d 1211ε [4]

( ) f

R31

31

σσσσ

−−

= [5]

σ1 and σ3 are the principal total stresses, (σ1 - σ3)f is the asymptotic value for the difference between the major and the minor principal stresses that is related closely to the strength of the soil, and A is a positive parameter defining the curvature of the curve as shown in Figure 4.


0 1 2 3 4 5 6 7 8 9 10 11 12Deviatoric plastic strain εd

p (%)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R =

(σ1

- σ 3

) /(σ

1 -

σ 3) f

A = 2.00

A = 1.00

A = 0.50

A = 0.10

A = 0.05

A = 0.01

A = 0.001

Figure 4. Theoretical curve for different values of parameter A.

As a consequence to this expression, the non-dimensional yields of the different links are fractions of the units of the chosen discretisation. Then, the compliance kJ

~

can easily be obtained from the successive secant modulus of the experimental curve. The compliances intervening in the constitutive law are written as:

EJ

10 = [6]

uk

kk c

JJ

ρ2

~

3

2= with 0 <ρk <1 [7]

Consequently, the (2n+2) parameters of the proposed model are totally defined with only three parameters: the initial Young modulus E, the curvature parameter A, and the undrained cohesion cu. Poisson ratio is equal to 0.5.

4. Model response on a pressuremeter path

The expansion of a pressuremeter probe in a homogeneous soil is considered. The hypothesis of soil incompressibility and plane strain in the axial direction is assumed. The axisymmetry imposes that the stress increments in the directions r, θ and z are principal (Figure 5). The boundary conditions can be specified either in displacements or in stresses.

– Along the wall cavity r = ro:

∆ur = ∆uo or ∆σr = ∆po [8]


– At an infinite distance r = r ∞ :

∆ur = 0 and ∆σr = 0 [9]

where ro is the initial borehole radius and uo is the radial displacement at the cavity wall.

There are two concentric annular zones around the probe (Figure 5). The first one is bounded by a circle of radius re in which the material is subject to elasto-plastic straining (r0 < r < r e). The second one is located beyond re in which the material behaves elastically (r > r e).

The pressuremeter loading is then governed by the following equilibrium equation:

0=−

+∂

∂rr

rr θσσσ [10]

σr and σθ are the radial stress and the circumferential stress respectively.

Figure 5. Equilibrium of a soil element.

rσ

θσ

zσ

r r+dr

z

rO

dz

r

Elastic zone

Elasto-plastic zone re

r∞ σr

σθ

ro


4.1. Solution of the problem in the elastic zone

Taking into account the radius re of the elastic outside zone with a Poisson ratio ν = 0.5, we obtain:

ee

r dur

rd

2=ε e

e dur

rd

2−=θε 0=zdε [11]

ee

r dur

rEd

23

2=σ ee du

r

rEd

23

2−=θσ 0=zdσ [12]

The straining takes place without volume change and at constant mean stress.

4.2. Solution of the problem in the elasto-plastic zone

The plastic incompressibility implies that the yield surfaces are represented by cylinders in the principal stress space (Von-Mises criterion). Thus, the incremental strain vector p

ijdε is normal to the sections of the yield surfaces characterised by the circles of radius Sk and center p

ijX . Furthermore, the condition of plane strain imposes that the strain path is normal to the εz axis. The two conditions lead to the following relationships between the deviatoric increments:

rr dsrCd )(=ε rdd εεθ −= 0=zdε [13]

( )( )krr

krr

n

k k

k XsXsS

J

ErC −−+= ∑

=

*

12

22

3)( [14]

Sk being a constant proportional to the threshold stress of the kth yield surface, which is a function of the undrained cohesion cu. The coefficient C(r) is a function depending on the distance r from the studied point of the soil mass to the axis of the borehole, because the number, n*, of activated links of the model depends upon this distance.

Further, to solve the problem completely, an unknown isotropic mean stress p(r) may be introduced:

)()(

rC

drdpd r

rεσ += [15]

)()(

rC

drdpd rε

σ θ −= [16]

)(rdpd z =σ [17]


This pressure dp(r) is determined from the equilibrium equation (equation [10]) and the boundary conditions (equations [8] and [9]). Therefore, the following expressions are deduced:

+

∆= ∫

ee r

r

r

r

oorCr

dr

rCrurrdp

)(2

)(

1)(

32 [18]

∫+

∆=∆

er

r

oe

o

oo

rCr

drr

rCr

r

pu

)(2

)( 32

[19]

∆po and ∆uo are the pressures applied to the cavity wall and displacement at cavity wall respectively.

5. Numerical program

From the analysis of the pressuremeter test results, a computer code called “Clayident” is developed in order to automatically identify the three parameters of the proposed model, particularly, the undrained cohesion cu. This code can be used in two different ways:

– Given the parameters of the model, the corresponding pressuremeter curve can be deduced;

– Given the experimental pressuremeter curve, parameters of the model can be identified by means of an optimisation method by comparing simulated curve to the experimental curve.

5.1. Evaluation of the proposed model from pressuremeter test

The simplex algorithm is used to optimise the parameters A, E and cu to produce the best fitting curve to the data (Nelder et al., 1965). At the beginning of the optimisation procedure, initial values for E, cu and A must be defined. For this purpose, analytical formulations taking into account analytical simplifying assumptions are considered:

– A study within the elastic zone of the soil around the pressuremeter allows the initial value of E to be determined from the measured Menard pressuremeter modulus or secant pressuremeter modulus at 2% for self boring pressuremeter.

– A study within the elastoplastic zone of the soil around pressuremeter allows the initial value of cu to be determined from the measured conventional limit pressure and elastic modulus using the simplified formulation of Salençon (1966).


– Using the Duncan et al. (1970) representation of the stress-strain curve for the undrained response of the soil, and after some algebraic manipulations, the following relationship can be obtained for the initial value of parameter A (Bahar et al., 1999):

( ) ( ) ( )

−−+−−

=

i

iiifi

iuf

R

RRRLnRRE

RcRA

12111

6 2

[20]

where Ei and cu are the initial values of Young’s modulus and undrained cohesion previously defined, Rf is a reduction factor usually less than one (Rf = 0.7). A numerical study suggests that there is a relationship between Ri and parameter β used to classify the soils according to Baguelin et al. (1978). Ri is defined from the pressuremeter test which is a factor describing the first curvature of experimental pressuremeter curve:

oi pp

ppR

−−

=lim

0%5 [21]

where po, p5% and plim are the initial total horizontal pressure in the ground, applied pressure at 5% volume change and conventional limit pressure respectively.

Figure 6 compares, for a typical optimisation case, the responses associated with the initial and optimal values of the three parameters with the experimental data. The optimal theoretical response is very close to the experimental data, indicating that the constitutive model is able to describe the undrained stress-strain behaviour of clays around the pressuremeter adequately. Figure 6 also compares the results obtained using the proposed approach and those obtained from “Pressident” finite element program taking into account the non linear elastic model (Duncan et al., 1970). It can be noted that the numerical and theoretical curves are very close.

5.2. Influence of the model parameters on the simulated curve

In order to understand the influence of the model parameters on the numerical response, we carried out a sensitivity study of the three parameters changing the value of one parameter by ±50% of its initial value. The reference parameters are identified from results of self boring pressuremeter test carried out on the clay of Cran site (France), at 3.0 m depth (Figure 6). The results are presented in Figures 7(a), 7(b) and 7(c). It may be observed that all the three parameters influence the response. The elastic modulus E has a preponderant influence not only on the beginning of the curve but also when large strains are developing. The parameter A that describes the curvature has a similar influence on the pressuremeter curve. Finally, the undrained cohesion cu has a negligible influence on the initial tangent of the curve, but an important influence on the failure behaviour. These observations


indicate that none of the three parameters of the model can be fixed to an average value. The three parameters must be determined by the proposed optimisation procedure.

0 250 500 750 1000 1250 1500 1750Volume change (cm3)

0

20

40

60

80

100

120

140

Pre

ssur

e (k

Pa)

Optimal parameters (E=4700 kPa, Cu=25 kPa, A=0.067)

Test

Bahar & Olivari approach with optimal parameters

Bahar & Olivari approach with initial parameters

Pressident approach

Figure 6. Experimental, theoretical and finite element computation pressure expansion curves.

5.3. Distribution of total stresses at various levels of cavity expansion

Experimental data simulating the pressuremeter test using a large hollow cylindrical specimen indicate that the total vertical stress does change during expansion cavity (Thevanayagam et al., 1994). The results of other analytical studies simulating a plane strain cylindrical cavity expansion in normally consolidated clays also indicate changes in total vertical stresses in all elements surrounding the cavity. An example of results for the total stresses σr, σθ and σz, using the proposed model is shown in Figures 8(a), 8(b) and 8(c). The figures show that the evolution of these stresses is important until a radius of approximately 50 cm around the probe (SBP, Self Boring Pressuremeter, ro = 8 cm and L/D=4). Figure 8(c) indicates that the total vertical stress σz initially decreases at very low strain levels and subsequently increases.


0 400 800 1200 1600 2000Volume change (cm3)

0

20

40

60

80

100

120

140

160

Pre

ssur

e (k

Pa)

0.50 E (- 50%)

E = 4700 kPa (reference)

1.5 E (+ 50%)

0 400 800 1200 1600 2000

Volume change (cm3)

0

20

40

60

80

100

120

140

160

Pre

ssur

e (k

Pa)

0.50A (- 50%)

A=0.067 (reference)

1.5A (+ 50%)

(a) (b)

0 400 800 1200 1600 2000Volume change (cm3)

0

20

40

60

80

100

120

140

160

Pre

ssur

e (k

Pa)

0.50cu (- 50%)

cu=25 kPa (reference)

1.5cu (+ 50%)

(c)

Figure 7. Influence of the parameters E, A and cu.

5.4. Response of the model on an unloading path

The unloading response of the proposed model on the pressuremeter path is very easy to obtain. Indeed, the Prager model complies with the Masing rule, so that the unloading curve has the same shape as the first loading curve, except that the scale is increased by a factor of two. This result seems to be acceptable for isotropic clays, as shown in Figure 9 (clay of Cran site). The unloading part of the curve can be used in a very profitable way to confirm the elastic value for the modulus of the soil.


(a) 0.00 0.25 0.50 0.75 1.00 1.25 1.50

Radius r (m)

405060708090

100110120

Rad

ial t

otal

str

ess

(kP

a)

1

520% limit pressure (1)

100 % limit pressure (5)

(b) 0.00 0.25 0.50 0.75 1.00 1.25 1.50

Radius r (m)

20

30

40

50

60

70

Cir

cum

fere

ntia

l str

ess

(kP

a)

1



(c) 0.00 0.25 0.50 0.75 1.00 1.25 1.50

Radius r (m)

405060708090

100

Tot

al v

ertic

al s

tres

s (k

Pa)

1

5 20% limit pressure (1)

100% limit pressure (5)

Figure 8. Distribution of total stresses at various levels of cavity.

6. Application of the proposed method to identify undrained cohesion of clays

The proposed method has been used to determine the undrained cohesion of some clay in Algeria. The results obtained are compared to those derived using “Pressident” method, the empirical methods proposed by Menard (1957) and Amar et al. (1971) and others in situ tests. The two empirical methods are established by correlation between the limit pressure obtained from pressuremeter tests and the undrained shear strength obtained from field vane and triaxial tests for soft cohesive soils.

– Pressident (Pressuremeter Identification) is a numerical program developed at the Ecole Centrale de Lyon, France, which uses the non linear elastic model of Duncan (Bahar et al., 1993).

σr

σθ

σz


0 250 500 750 1000 1250 1500 1750Volume change (cm3)

0

50

100

150

200

250

300

350

400

450

500

Pre

ssure

(kP

a)

Simulation

Test

Figure 9. Pressuremeter test with unloading (Cran clay).

– The method of Menard (1957) is an empirical relationship often used in the analysis of Menard pressuremeter data. It is given by:

5.5

_ olu

ppc = [22]

– The method of Amar et al. (1972) is an empirical relationship given by:

2510

_+= ol

u

ppc (kPa) [23]

pl, po, and cu are the limit pressure, the in situ total horizontal stress and the undrained shear strength respectively.

– The undrained shear strength was also determined from cone penetration tests using an empirical relationship cu=(qc-qo)/Nk. qc, qo and Nk are the cone resistance, the in situ vertical stress and an empirical factor respectively. The value of Nk ranges between 10 and 15 for cohesive soils (Cassan, 1988).

6.1. Very soft to soft clay of Annaba

The site is located in the east of Algeria. The soil stratigraphy encountered on site consists on muddy soft to very soft brownish clays. The thickness of the clay layer is about 25 to 30 m. The ground water table was about 5 m depth from the ground surface. The clays are saturated. The natural water content wn varies between


18% and 60%. The plasticity index varies between 26% and 35%. The shear strength parameters derived from consolidated undrained triaxial tests with pore pressure measurement range from 10° to 21° for the friction angle and from 11 kPa to 36 kPa for cohesion. A conventional limit pressure ranging from 200 kPa to 800 kPa characterizes the clays. Consolidation testing indicates that the soils are unconsolidated with a high compressibility index, Cc ranging from 11% to 41%.

Figure 10 shows an identification example concerned with the test realised at 4 m depth, in borehole SP6. The undrained cohesion obtained using the proposed method and the one obtained using “Pressident” method and empirical methods mentioned above are presented in Figures 11(a) and 11(b). It can be noted that the proposed method gives a values relatively similar to those deduced by “Pressident” method. In these figures, it can also be noted that, for limit pressure less than 300 kPa, the undrained cohesion values deduced from the proposed approach are close to those obtained from the empirical methods. For limit pressure ranging between 300 kPa and 700 kPa the undrained cohesion values deduced from the proposed approach were on the average 170% higher than those deduced from the empirical methods. There are number factors that can explain the observed difference in the values of cu obtained by different methods. The two empirical methods are established by correlation between limit pressure obtained from pressuremeter tests and undrained shear strength obtained from field vane and triaxial tests for soft cohesive soils. In general, pressuremeter undrained shear strength obtained using cavity expansion methods are significantly higher than the values obtained using other in situ or laboratory tests.

0 50 100 150 200 250 300 350Pressure (kPa)

0

100

200

300

400

500

600

Vol

ume

chan

ge (

cm3 )

Site of AnnabaBorehole SP6

Test (Depth : 4 m)

Simulation

Model parametersA = 0.0087E = 8676 kPacu = 76 kPa

po = 32 kPa

vo = 135 cm3

Figure 10. Example of identification of the proposed model parameters.


0 20 40 60 80 100Undrained cohesion cu (kPa)

24

22

20

18

16

14

12

10

8

6

4

2

0

Dep

th (

m)

Empirical relationship of Amar et al.

Empirical relationship of Menard

Pressident method

Bahar & Olivari method

Annaba siteBorehole SP3

0 20 40 60 80 100 120Undrained cohesion cu (kPa)

24

22

20

18

16

14

12

10

8

6

4

2

0

Dep

th (

m)



Pressident method


Annaba siteBorehole SP6

a) b)

Figure 11. Undrained cohesion of very soft to soft clays, site of Annaba (Algeria).

6.2. Stiff to very stiff clay of Bab Ezzouar

The site is located in Algiers. The soil stratigraphy encountered on the site consists on stiff to very stiff clays, which overlies a layer of sandstone material. The thickness of the clay is about 15 to 18 m. The clays are saturated. The natural water content wn varied between 7% and 21%. The plasticity index varied between 22% and 27%. The shear strength parameters derived from consolidated undrained triaxial tests with pore pressure measurement range from 7° to 21° for the friction angle and from 14 kPa to 126 kPa for the cohesion. A conventional limit pressure ranging from 500 kPa to 2600 kPa and pressuremeter moduli ranging from 4700 kPa to 44000 kPa characterizes the clays. Consolidation testing indicates that the soils are normally consolidated to slightly overconsolidated with medium compressibility, Cc ranging from 10% to 17%.

Figure 12 shows an identification example concerned with the test realised at 10 m depth, in borehole SP1. The undrained cohesions, obtained using the proposed


method, are presented in Figures 13(a), 13(b). These figures also show the comparison of the obtained results to those obtained by “Pressident” method, by empirical relationships and from cone penetration tests. It can be noted that the proposed method gives values relatively similar to those deduced by “Pressident” method and by the cone penetration test. It is also observed that, in common with the findings of others investigators, for stiff to very stiff clay the cu values obtained from the proposed method are consistently higher than the corresponding cu values obtained by empirical relationships and triaxial tests (factor between 1.35 and 2.30). Furthermore, the interpreted soil parameters had reasonable values when compared with the cone penetration test results.

High undrained shear strengths from pressuremeter tests have been frequently observed. The measured cu will be affected by the in situ or laboratory method used and the stress path followed during the test (Wroth, 1984). Wroth (1984) showed that the undrained shear strength derived from pressuremeter tests should be larger than the strengths derived from field vane tests due to the nature of the different stress paths. As explained by other researchers (Baguelin et al, 1978), this difference is due to disturbance during boring prior testing and also possibly due to the difference in the mode of failure during the test. It has also been recognized by many researchers that some drainage and creep takes place during pressuremeter tests in clay (Wroth, 1984). The effect of drainage and creep can result in overestimation of the undrained shear strength.

0 250 500 750 1000 1250 1500 1750 2000Pressure (kPa)

0

100

200

300

400

500

600

Vol

ume

chan

ge (

cm3 )

Site of Bab EzzouarBorehole SP1

Test (Depth : 10 m)

Simulation

Model parametersA = 0.009E = 44332 kPacu = 496 kPa

po = 100 kPa

vo = 110 cm3

Figure 12. Example of identification of the proposed model parameters.



22

20

18

16

14

12

10

8

6

4

2

0

Dep

th (

m)



Triaxial tests (UU)

CPT (Nk=10)

CPT (Nk=15)

Pressident method


Bab Ezzouar SiteBorehole SP1


22

20

18

16

14

12

10

8

6

4

2

0

Dep

th (

m)



Triaxial tests (UU)

CPT (Nk=10)

CPT (Nk=15)

Pressident method


Bab Ezzouar siteBorehole SP2

a) b)

Figure 13. Undrained cohesion of stiff to very stiff clays, site of Bab Ezzouar (Algeria).

6.3. Clay of Cran site (France)

The proposed approach was applied to identify the undrained cohesion of clay of Cran site (Boubanga, 1990; Cambou et al., 1993). Figure 14(a) shows optimised simulations of different pressuremeter tests performed at different depths leading in each case to the best set of parameters. The results obtained by the proposed method agree well with the experimental data. Figure 14(b) shows the profiles of cu obtained for Cran clay as a function of depth, and lead to a comparison with different methods used to obtain cu. It appears that the proposed method gives values of cu slightly greater than those obtained by undrained triaxial tests. Furthermore, it can be seen that the proposed method gives values in rather good agreement with field vane test results and larger than the strength derived from triaxial test. For soft clay of Cran site, the proposed method had reasonable values when compared with the cone penetration test results. The self boring pressuremeter and the field vane test shear strengths are similar and appear to increase at the same rate.


3m 6 m 9 m

11m13m

0 50 100 150 200 250 300 350 400Pressure (kPa)

0

400

800

1200

1600

2000

Vol

ume

Cha

nge

(cm

3 )

Simulation

Test

(a)

0 10 20 30 40 50 60 70 80 90 100Undrained Cohesion (kPa)

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

Dep

th (

m)

Vane test

Triaxial test

Pressident approach

Bahar & Olivari approach

(b)

Figure 14. Soft clay of Cran site. (a) best set of parameters for simulations of pressuremeter tests performed at different depths, (b) undrained cohesion profiles.

6.4. Identification of the model parameters using the results of a pressuremeter test with unloading

The proposed approach is used to interpret the Fucino soft clay (Ferreira et al., 1992) and the obtained results are compared to those obtained by using Ferreira et al. (1992) and Jefferies (1988) methods. The clay deposit is described as soft, homogeneous, highly structured and cemented. Ferreira et al. (1992) method is an extension of Jefferies (1988) method incorporating the unloading portion of the pressuremeter test to derive the initial shear modulus and undrained shear strength. The soil behaviour is represented by a hyperbolic (non linear elastic) relationship between the shear stress and the circumferential strain. Jefferies (1988) method is an extension of the Gibson-Anderson (1961) theory for pressuremeter test performed in clays incorporating the complete loading and unloading portion of the test. The method was based on an ideal elastic perfectly plastic soil model and assumed that the installation was carried out with minimum disturbance. The ratio of the unloading strength of the clay was assumed to be known. Commonly, the pressuremeter results are plotted in terms of radial pressure σr versus loge(∆V/V), where ∆V/V is a measurement of the cavity strain related to the deformed state. Jefferies (1988) used computer-aided modelling techniques to visually compare the measured response with the numerically derived curves.


The best simulated curve leading to the best set of model parameters is shown in Figure 15(a) and Table 1. Table 1 and Figure 15(b) compare the derived parameters using Jefferies (1988), Ferreira et al. (1992) and proposed methods. The set of derived parameters leads to a curve which is very close to results provided by other techniques used to identify the undrained shear strength of clays.

0 1 2 3 4 5 6 7 8 9 10 11 12Cavity strain (%)

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550

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650

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850

Pre

ssur

e (k

Pa)

Simulation

Test (V2P14 - depth : 26m)

ParametersE=30282 kPaA=0.0076cu=114 kPa

0 2 4 6 8 10 12

Cavity strain (%)

0

20

40

60

80

100

120

140

She

ar s

tren

gth

(kP

a)

Ferreira et al. (1992)

Jefferies (1988)

Bahar & Olivari

(a) (b)

Figure 15. Fucino clay test (V2P14, 26m depth), (a) Identification with the proposed method, (b) Comparison of stress-strain curves using different methods.

Table 1. Results obtained using different methods.

Test V2P10 (18 m) Test V2P14 (26 m) Methods

G (kPa) cu (kPa) G (kPa) cu (kPa)

Jefferies (1988) 4300 55 6800 100

Ferreira et al., (1992) 5952 93 11188 112

Proposed method 6068 60 10094 114

7. Load-settlement prediction of a bored pile

The proposed method has been used to predict the load-settlement curve of a bored pile of case test which was organised for the International Symposium ISP5-2005, taking place at the occasion of the “50 years of pressuremeters” (Reiffsteck, 2006). The pile diameter is D=0.5 m and its length is 12m. The pile is embedded in a 9.6 m thick clay layer, below a 2.4 m thick silt layer. The water table is located 1.8 m below ground level (Figure 16). The laboratory tests carried out on soil samples extracted close to the pile location showed that the site physical properties were


relatively homogeneous. The shear strength parameters derived from consolidated undrained triaxial tests with pore pressure measurements are c’=57 kPa and ϕ’=23°. The Young modulus at 0.2% strain derived from unconsolidated undrained triaxial tests is E=50 MPa. The results of three Menard pressuremeter boreholes, given in the exercise, are used to define the soil parameters by means of the proposed method and by the “Pressident” approach. The corresponding best curve and the best set of parameters are given in Figures 17(a) and 17(b). Figures 18(a) and 18(b) summarize the evolution of undrained cohesion evaluated by means of the proposed method, by the “Pressident” approach, by the empirical relationships proposed by Ménard and Amar et al., and by triaxial tests. The proposed method and the “Pressident” approach give very close results.

For this site, the calculation of the bearing capacity and settlements of a bored pile using the parameters derived from the proposed method was achieved using FLAC3D software (Itasca, 2005) considering an elastoplastic model with Mohr Coulomb criterion. Figure 19 gives the parameters used for achieving the calculations. Figure 20 compares the results obtained by the proposed method to those obtained using the parameters derived from “Pressident” approach an experimental data (Reiffsteck, 2006). For this case again, one can note that the proposed method is in very good agreement with the measured load-settlement curve on site.

Figure 16. Pile and soil sketch (Reiffsteck, 2006).


0 400 800 1200 1600Pressure (kPa)

0

100

200

300

400

500

600

700

Vol

ume

chan

ge (

cm3 )

Borehole SP1

Test

Simulation

Depth : 1.0 mpo = 10.8 kPa

Vo = 117 cm3

A = 0.0055E = 6526 kPacu = 63 kPa

Depth : 14.0 mPo = 151 kPa

Vo = 28 cm3

A = 0.0037E = 65 205 kPacu = 248 kPa

0 100 200 300 400 500 600 700

Pressure (kPa)

0

100

200

300

400

500

600

700

Vol

ume

chan

ge (

cm3 )

Borehole SP2

Test

Simulation

Depth : 1.0 mPo = 10.8 kPa

Vo = 135 cm3

Model parametersk = 251, n = 0.5kb = 4190, m = 0.5

cu = 111 kPa, ϕ =0

Rf =0.7

(a) (b)

Figure 17. Identification of model parameters from pressuremeter test results, best fit curve: (a) proposed method, (b) Pressident method.

0 50 100 150 200 250 300Undrained cohesion (kPa)

20

18

16

14

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8

6

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0

Dep

th (

m)

Pressident method


Menard empirical relationship

Amar et al. empirical relationship

Triaxial UU

Borehole SP1

0 50 100 150 200 250 300Undrained cohesion (kPa)

20

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16

14

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6

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0

Dep

th (

m)

Pressident method


Menard empirical relationship

Amar et al. empirical relationship

Triaxial UU

Borehole SP3

(a) borehole SP1 (b) borehole SP3

Figure 18. Profile for undrained cohesion derived from different methods.


Figure 19. Pile and model parameters of soils.

0 200 400 600 800 1000 1200 1400Load (kN)

50

45

40

35

30

25

20

15

10

5

0

Set

tlem

ent

(mm

)

Measured

Bahar & Olivari approach

Pressident approach

Figure 20. Comparison of measured and calculated load-settlement curves.

γ = 18 kN/m3 E = 12860 kPa, ν = 0.5 Cu = 80 kPa, A = 0.04

2.4

0 m

γ = 18 kN/m3 E = 100325 kPa ν = 0.5 Cu = 240 kPa A = 0.003

γ = 18 kN/m3 E = 32257 kPa ν = 0.5 Cu = 174 kPa A= 0.006

Q

Layer 1 Silt

Layer 2 Clay

Layer 3 Clay

γ = 18 kN/m3 E = 7972 kPa, ν = 0.49 Cu = 78 kPa , ϕu = 0

γ = 18 kN/m3 E = 39312 kPa ν = 0.49 Cu = 177 kPa ϕu = 0

γ = 18 kN/m3 E = 79023 kPa ν = 0.49 Cu = 241 kPa ϕu = 0

Layer 1 Silt

Layer 2 Clay

Layer 3 Clay

Soil parameters identified from Pressident approach

Soil parameters identified from Bahar & Olivari approach

6.6

0 m

12

m


8. Conclusions

A method to interpret pressuremeter test results carried out in saturated clays is proposed. The proposed model is specifically developed to describe the undrained behaviour of clays. Introducing an analytical formulation of the total stress-strain curve obtained during an undrained triaxial test, the model depends only on three parameters. The response of the model on the pressuremeter path is in good agreement with experimental data. An example of application of the proposed method has shown realistic results compared to those obtained by other methods. However, further researches are needed to verify these conclusions for various clay types with both field and laboratory test results.

Acknowledgements

The authors thank the Construction and Testing Engineering Laboratory (CTELAB) and Laboratoire de l’Habitat et de la construction du Centre (LHCC) especially for some data available for scientific use. They thank also Pr. B. Cambou and Dr. G. Olivari for their comments and discussions.

9. Bibliographie

Amar S., Jézéquel J.F., “Essais en place et en laboratoire sur sols cohérents: comparaison des résultats”, Bulletin de Liaison des Ponts et Chaussées, vol. 58, 1972, p. 97-108.

Baguelin F., Jezequel J.F., Lemée E., LeMéhauté A., “Expansion of cylindrical probes in cohesive soils”, J. of the Soil Mechanics and Foundations Division, vol. 98, n° 11, 1972, p. 1129-1142.

Baguelin F., Jezequel J.F., Shields D.H., The pressuremeter and foundation engineering, Switzerland, Trans Tech Publications, 1978.

Bahar R., Analyse numérique de l’essai pressiométrique : application à l’identification de paramètres de comportement des sols, Thèse de doctorat. Ecole Centrale de Lyon, 1992.

Bahar R., Cambou B., Fry J.J., “Forecast of creep settlements of heavy structures using pressuremeter tests”, Computers and Geotechnics, vol. 17, 1995, p. 507-521.

Bahar, R., “Interpretation of pressuremeter tests carried out in stiff clays”, Proceeding of 1st Intern. Conf. on Site Characterization ISC’98, Atlanta, USA, 26-28 mai 1998, p. 735-740.

Bahar R., Abed Y., Olivari G., “Theoretical analysis of the behaviour of clays around a pressuremeter”, Proceeding of 12th African Regional Conference, Durban, South Africa, October 25-27 1999, p. 135-142.

Bahar R., Aissaoui T. & Kelanemer S., “Comparison of some methods to evaluate the undrained cohesion of clays”, Proceeding of the 16th Inter. Conference on Soil Mechanics and Geotechnical Engineering, Osaka, Japan. vol. 2, September 12-16 2005, p. 667-670.

Boubanga A., Identification de paramètres de comportement des sols à partir de l'essai pressiométrique. Thèse de doctorat. Ecole Centrale de Lyon, 1990.


Cambou B., Bahar R., “Utilisation de l'essai pressiométrique pour l'identification de paramètres intrinsèques du comportement d'un sol”, Revue Française de Géotechnique, 63, 1993, p. 39-50.

Cassan M., Les essais in situ en mécanique des sols, vol. 1, Paris, Eyrolles (Eds), 1978.

Denby, G.M., Self-boring pressuremeter study of the San Francisco Bay mud, Ph.D thesis, Stanford University, California. 1978.

Duncan J.M., Chang C.Y., “Non linear analysis of stress and strain in soils”, Journal of Geotechnical Engineering Division., SM5, 1970, p. 1629-1653.

Ferreira R., Robertson P.K., “Interpretation of undrained self-boring pressuremeter test results incorporating unloading.” Canadian Geotechnical Journal, vol 29, 1992, p. 918-928.

Gibson R.E., Anderson W.F., “In-situ measurement of soils properties with the pressuremeter” Civ. Engng. Publ. Wks. Rev., Vol. 56, 1961, p. 615-618.

Habib P., La résistance au cisaillement des sols, Thèse de doctorat, 1953, Paris.

Iwan W.D., “On a class of models for the yielding behaviour of continuous and composite systems” Journal of Applied Mechanics, 1967, p. 612-617.

Itasca, FLAC3D, Fast Lagrangian Analysis of Continua. Itasca Consulting Group, User’s manual, Minneapolis, 2005.

Jefferies M.G., “Determination of horizontal geostatic stress in clay with self bored pressuremeter”, Canadian Geotechnical Journal, vol. 25, 1988, p. 559 - 573.

Ladanyi B., “In-situ determination of undrained stress-strain behaviour of sensitive clays with the pressuremeter” Canadian Geotechnical Journal, Vol. 9, N° 3, 1972, p. 313-319.

Ménard L., “Mesures in situ des propriétés physiques des sols”, Annales des Ponts et Chaussées, l.3, 1957, p. 357-376.

Monnet J., Chemaa T., “Etude théorique et expérimentale de l’équilibre élasto-plastique d’un sol cohérent autour du pressiomètre”, Revue française de Géotechnique, n° 73, 1995, p. 15-26.

Monnet J., “Numerical validation of an elastoplastic formulation of the conventional limit pressure measured with the pressuremeter test in cohesive soil”, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 133, Issue 9, September 2007, p. 1119-1127.

Nelder J..A., Mead R., “A simplex method for function minimisation” , The Computer Journal, vol. 7, 1965, p. 308-313.

Olivari G., Bahar R., “Response of generalized Prager's model on pressuremeter path”, Proc. 4th Int. Sym. on Pressuremeter. Sherbrooke, Canada, 17-19 mai 1995, p. 207-213.

Palmer A.C., “Undrained plain strain expansion of a cylindrical cavity in clays: a simple interpretation of the pressuremeter test”, Geotechnique, vol. 22, n° 3, 1972, p. 451-457.

Paraharam S., Chameau J.L., Alischaefel A.G., Holtz R.D. “Effect of disturbance on pressuremeter results in clays” Journal of Geotechnical Engineering, vol. 116, n° 1, 1990, p. 35-53.

Prevost J.H., Hoeg K., “Analysis of pressuremeter in strain-softening soil”, J. Geotech. Engng. Div. vol. 101, GT8 , 1975, p. 717-731.


Reiffsteck P., “Portance et tassements d’une fondation profonde - Présentation des résultats du concours de prévision”. Comptes rendus Symposium international 50 ans de pressiomètres (ISP 5), Marne-la-Vallée, 22-24 août 2005, vol. 2, 2006, p. 521-535.

Salençon J., “Expansion quasi-statique d’une cavité à symétrie sphérique ou cylindrique dans un milieu élastoplastique”, Annales des Ponts et Chaussées, vol. 3, 1966, p. 175-187.

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