menard pressuremeter modulus: relationship and ... · symposium international isp7/pressio 2015 . 1...

Symposium International ISP7/PRESSIO 2015

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MENARD PRESSUREMETER MODULUS: RELATIONSHIP AND CORRELATIONS BETWEEN ELASTIC, PSEUDO ELASTIC AND CYCLIC E-MODULUS AS DEFINED BY L. MÉNARD MODULES ELASTIQUES, PSEUDO-ELASTIQUES ET CYCLIQUES DANS L’ESSAI PRESSIOMETRIQUE MÉNARD : HISTORIQUE ET PERTINENCE ACTUELLE

Jean - Pierre BAUD1, Michel GAMBIN2, Robert HEINTZ3, 1Eurogéo, Avrainville, France, [email protected] 2Apagéo, Magny les Hameaux, France, [email protected] 3Eurasol, Luxembourg, Grand-Duché, [email protected]

Translated from French version for ISP7 (S. Varaksin, Apageo, and the authors)

RÉSUMÉ – Dès la définition du module pressiométrique dans une plage expérimentale assez large pour aller de la pression des terres au repos à la pression de fluage, Louis Ménard a qualifié ce module de « pseudo-élastique » pour rappeler que son module était à la fois analogue à un module d’Young, mais non pas élastique, et caractéristique d’une phase de déformation faible à modérée mais non linéaire et non réversible. L’existence d’une proportionnalité constante entre le module EM et un supposé « module d’Young » du sol est démentie par la pratique des essais pressiométriques en autoforage sans déplacement ni décompression du sol. ABSTRACT – With his PMT Louis Ménard introduced a pressuremeter E-modulus within a rather large pressure range bounded by the earth pressure at rest and the creep pressure. He called it a “pseudo-elastic” modulus, thus claiming it is like a Young’s modulus, but not elastic, characterizing small to moderate, non-linear and non-reversible strains,. No proportionality is observed between the EM modulus and an assumed “Young’s modulus” of the soil when realizing self-bored PMT by the RotoSTAF selfboring method, preventing borehole wall displacement and decompression. 1. The pressuremeter modulus, towards an unifying soil mechanics concept Civil engineers specialized in geotechnique are used to identify the behavior of actual soils with “continuum mechanics”, unfortunately reduced most of the time to elasticity and elastoplasticity, which exactly apply only to a homogeneous, isotropic, that is an ideal medium. However the history of soil mechanics warns us about some fundamental risks linked to this practice: indeed the many failed projects remind us that the upper layer of the Earth's crust is neither continuous nor isotropic. By creating measuring devices, first for the oedometric modulus on samples, secondly in situ for the pressuremeter modulus, and making soil compressibility measurements possible, Terzaghi (1920) and Menard (1955) pioneered and were in the same time the first to encourage the review of the real soil behavior on the survey site, avoiding the adoption of models based on inappropriate simplifications. Thus it doesn't seem adequate still to consider systematically that the forecast of the behavior of a structure in a soil is reduced to a site modelling of soil elements characterized by an elastic Young’s modulus and a friction angle coupled with a cohesion, whereas:

- soils behavior do not resume in a single deformation modulus, but in an infinite number of moduli depending on the considered stress level and the deformation under increasing or decreasing stresses always occurs in an elastoplastic mode (Ménard 1961, Ménard et Rousseau, 1961);

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- the compression modulus is not equal to the traction modulus (Briaud 2013), thus soils have no Young’s modulus (Schlosser 2014);

- granular soils and overconsolidated clays exhibit a phenomenon of dilatancy in certain stress conditions;

- soils get different behaviors depending the applied stress level; they can be perfectly elastic, pseudo-elastic, plastic, quasi liquid, and the transition between those different phases is progressive, variable in space and time during the application of stresses imposed by the construction and earthworks.

Due to automatization and computer improvements, the measuring equipment as well as the interpretation of pressuremeter tests have greatly evolved. Thus a new type of pressure volume regulator, the GeoPac® coupled with a new recording rugged computer and GeoVision software, has been presented during the 6th International Symposium on Pressuremeter ISP6 included in the 18th ICSMG in Paris (Arsonnet and al. 2013a). Mainly four prominent breakthroughs are currently possible with the help of this new equipment: - a precise automatic compensation of the membrane resistance of the probe taking into

account the gap of time between the pressure generated in the measuring cell and in the guard cells due to the head losses;

- a complete automatization of the test procedure; the automatic calibration of the initial volume of the probe, so to bring the pressure for the first pressure hold of the test into equilibrium with the earth pressure at rest, this being equivalent to the “lift-off” of the Cambridge Insitu Ltd probes;

- a (p, V) diagram showing no inflection point any more. As a result the precision of the average radial deformation is of the order of 10-5. All those developments, together with the self-boring procedures already described elsewhere (Whittle 1999, Dalton 2005, Arsonnet and al. 2005, 2013a) and the automatization of the running of the test, must be considered as a capital gain, for good test practice that renders the behaviour of the soil more representative. The foundation design of a simple construction can be conducted following the "direct" method proposed by Ménard (Ménard 1963, 1965), by merely taking in account the pressuremeter modulus EM and the conventional limit pressure pLM, as a result of the interpretation of the pressuremeter curve. However, for major civil engineering projects, it is generally necessary to verify soil displacements not only during loading conditions but also during unloading that occurs in deep excavations, tunnels, during the life of a structure, vibrations or dynamic impacts generated under the foundation of wind mills for example (Gambin, 2009). These complex constructions require more detailed study of every pressuremeter curve.

2. Measurement of initial pressuremeter moduli for very small deformations. Example of a test performed by the use of the "RotoSTAF" self-boring method and the "GeoPAC" pressure regulator for high precision measurements.

First of all, we want to submit a typical test performed using the equipment that we described above. We have chosen a test that has already been published in order to illustrate a simple hyperbolic model (Baud and al. 2013b) with the details of the measured data that allows us to determine the corresponding soil properties. It has to be noted that this test was performed according to more rigorous regulations than those usually applied: - for example the contact pressure of the probe in the slotted, tube is regulated in order to

make sure that the initial point of the test curve corresponds to an experimental value p0 quite close to the conventionally calculated value of the earth pressure at rest;


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- moreover the initial part of the test is performed with very small pressure increments in order to be able to measure the corresponding very small strains*.

Figure 1: Example of the results of a Ménard type test, performed by using the self-boring RotoStaf drill technique measuring p0 by very small pressure steps close to p0, then continued by standard pressure increments up to the phase of large deformations, close to pLM. Stiff sandy clay, belonging to the Cenomanian stratigraphic stage, located at the west border of the Parisian Basin (Le Mans). The test is performed at 18 meters depth. In the above figure 1 where the classical V=f(p) curve is replaced by dR/R0= f(p), it already appeared that the hyperbolic model fits well with to the pressure volume curve, this for a visual precision, when plotting the points of test in a rectangle of approximately. 100 cm², according to the format of printing. The computation of the secant modulus and, the tangent modulus by derivation of this hyperbolic model is also quite close to the results obtained by computation considering the test points except for small initial deformations for which the moduli are substantially higher the closer you get to the initial measurement. The diagram of figure 2 represents the decreasing of moduli as a function of the deformation. It clearly shows the difference between the measurements of small strains and deformations, and the usual measuring range of the modulus EM. It has been verified that this is not an artifact linked to this type of test, but that the results are it is repeatable in various types of soils on condition that the probe has been installed successfully using the self-drilling method of the a slotted tube and thus avoiding any * This test procedure was not a one-off, in one borehole or during a single site investigation. It has been verified in different types of soils during other soil investigations surveys.


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deformation of the initial state of the soil, neither through compression nor through relaxation. It also means you have to start the test by very small pressure increments at least until the middle of the pseudo-elastic phase is reached. Further on the way to increasing plasticity the number of test points has no influence any more on the results of the modelisation based on these points.

Figure2. Test pressure and moduli as a function of ε on a logarithmic scale. On the left: test of the figure 1; exploitation of the pressuremeter test presenting the test points and the tangent and secant moduli as a function of the strain. On the right: figure three from a paper ahead of its time (Ménard 1961), that can be compared to the traditional decreasing curve of the secant modulus (Atkinson and al. 1991). It exemplifies how advanced Ménard's soil deformation concept was, that is very well confirmed by the tests performed using self-boring methods for the probe placement. From the same set of experimental data, the detailed study of the test can be continued to model the decrease of the modulus. The inverted S-shaped "pressure, modulus" curves (Fig.1, right-hand ordinate), plotted both by the secant modulus and the tangent modulus, are fitted to the double-hyperbola model (Baud et al. 1992) in accordance with EN ISO 22476-4. This model is commonly used for the V = f (p) curve of any PMT and also fits very well on the point data series: V = f (p). The two asymptotes of this adjustment do take place as following: the right on the right merges with the asymptote of the direct hyperbolic curve of the test, which is the true limit pressure pL. The other on the left is simply limited to the p = 0 value being the asymptotic curve portion between 0 and p0 being obviously virtual. In figure 2 the results of these fittings on the same test are represented in a semi-logarithmic diagram. The strains on the x-axis in a logarithmic scale, the secant and tangent moduli and the


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stress values on the y-axis in an arithmetic scale. It clearly shows that the module decay curve, as a function of the strain, is not as regular as its representation by Atkinson and al. (1991), which has become a classic, would suggest: indeed it reveals a distinct phase of lesser decrease, which corresponds to the “pseudo elastic” phase, as defined by Ménard, to determine the pressuremeter modulus EM. The slope change between the phase of micro deformations and Ménard's classic “pseudo-elastic” phase is well indicated by the "zoom" on the initial points of small strain in figure 3.

Figure 3: Shape of the pressuremeter curve at the beginning of the test, generated by small pressure increments and very small deformations. The representation of the module decay curve as a function of the applied pressure, based on the experimental data, can relatively simply be transposed, in graphic form, in a “deformation/relative modulus” cartesian diagram. The algebraic expression that is also possible, would be long to be detailed. It is sufficient to note that, for extremely small strains, when the deformation tends towards zero, the modulus has a tendency to reach a finite Gmax value. This allows us to express the reduced moduli values G/Gmax in a range going from 1 and 0. The complete "S" shaped curve presented in figure 4, is obtained by means of a single pressuremeter test performed from an in situ measure of p0 up to an expansion of the probe close to pLM It could be represented in a diagram with three axis: G/Gmax, ε, p. To simplify here, the characteristic points of the test are indexed through their p value. Several remarkable properties can be observed. First of all, for deformations of the order of 10-2, the module decay curve is not quick and monotonous, as it could be supposed by looking at the curves proposed by Atkinson and al. (1991) and later by Tani (1994) and Tatsuoka and al. (1997). On the contrary the curve exhibits a flat section exactly like Ménard had foreseen and declared as the section in which his pseudo-elastic modulus is measured. Next, the tendency for the values of ε close to zero and G close to Gmax allows to extrapolate the value of p0 so that G/Gmax is exactly 1: in our case, this value is approximately 4% less than the in-situ measurement. It is compatible with an assumed value K0 = 0,5 and an average density of 1,94 Mg/m3 of the saturated, sandy clay in which our test was performed at 18 meters depth. This Cenomanian soil layer in the region of Le Mans, is considered to be only slightly


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overconsolidated after having received during Quaternary the stress of the ice cap, and then post-glacial rebound and superimposition of the river network. The quite precise knowledge of a p0 value, obtained by extrapolation, allows us to indicate as well the decreasing evolution of p0/p during the test, according to the same abscissa ε. Thus, this “S” shaped curve has a rapid and regular decrease between 10-3 and 10-1. When comparing it with the module decay curve, three phases become apparent. First, in the phase of a small deformations, as much as 10-2, the overlapping of the two curves indeed corresponds to the linear elastic behavior at the origin. Then, the curves distinctly diverge during the Ménard pseudo elastic phase, until ε = 10-1. Finally during the large deformations in the plastic phase, the two curves join and cross each other slightly above the conventional value of the doubling of the volume of the cavity.

Figure 4: The first complete E/Emax “S" shaped curve” as a function of ε, measured and interpreted, based on a single pressuremeter test. 3. Cyclic pressuremeter moduli After finalizing his theory on settlement calculation, based on his pressuremeter modulus, L. Ménard (1961) began to perform cyclic pressuremeter tests and adopted the ratio between the pseudo-elastic modulus and the unload modulus to define his rheological coefficient alpha (Ménard and Rousseau 1961, Baud and Gambin 2013a). Ménard pointed out that the unload modulus is characterized by elastic behaviour of the soil and called it modulus of micro-deformation. As this modulus had not been codified in foundation design, cyclic tests were not often performed in the current pressuremeter practice. At the same time, the performance of cyclic tests in small deformation ranges had become almost current practice for those who used the self-boring probes of Cambridge Insitu, mainly because of the automatization of a strain controlled test. However, this practice did not lead to a rational use of the measured cyclic moduli to forecast the deformation of the foundation ground. Between 1960 and 1970, Ménard initiated research on cyclic pressuremeter tests with some of J. Biarez's students at the “Ecole centrale de Paris” in order to study the use of cycling the pressure during a standard pressuremeter test (Bisgambiglia 1976, Saadé 1981).


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In the general manuel D60 of the interpretation of PMTs, initially edited in 1967, Ménard already recommended to use the results of cyclic pressuremeter tests for settlement calculation of structures founded in deep excavations and for the definition of the subgrade reaction coefficients under vibrating machines (Ménard 1975). Only 34 years later a first attempt was made to normalize a stress controlled cyclic Ménard pressuremeter test. Nevertheless it did not surpass the experimental stage of the normalization procedure (NFP XP 94-110-2 2001) despite the intentions to introduce cyclic tests in the current investigation practice (Canepa et Combarieu 2001) and despite the conviction expressed by analysts of the pressuremeter curve that the reload curve would be is most useful for the determination of the intrinsic parameters of the soil (Monnet 1990). The precision of measurements of 1/ 50th cm3 reached by a G type manual- controlled pressuremeter, operating in high sensibility mode (Ménard 1961), has been improved nowadays by an automatized test performance conducted by GeoPAC type and HyperPAC type pressuremeters, able to run cyclic tests according to various predefined loading and unloading operation modes. The curves of the second to the nth loading phases, cycled between two chosen pressures in the pseudo-elastic part of the test, always tend to become more or less linear, thus inciting theoreticians to recognize a nearly linear elastic soil reaction and the possibility to measure “the” Young’s modulus of the soil (J. Monnet 1999, 2013). However real soil behaviour does not generate perfectly linear moduli. All the cycles remain 'almond-shaped', which means that they have a hyperbolic unload - reload curvature, as shown by the examples here below. When after one or several cycles the volume of the probe is held constant for some hours or tens of hours, the soil will relax till the stabilization of the pressure decrease is reached, thus indicating the value of earth pressure at rest. When up from this point a second test is carried out the first load moduli EM obtained before and after the relaxation are equal not only in their value but also in the shape of the curve, point by point. This ascertainment, that was verified in the Fontainebleau sand and in the smectite clays of the "Rupélian" stage in the region of Hurepoix (C. Saade, 1981), seems to be attributable to most kinds of soils. The measurement of the first virgin loading module, under conditions of self-drilling without disturbance neither decompression at the probe-borehole interface, remains an essential soil characteristic. It is more relevant than the multiple loading measurements. The contribution of cyclic loadings is certainly interesting and perhaps fundamental (Ménard and Rousseau 1961) but one should not base on the unload-reload the hope of eliminating the imperfections of the hole from the decompression and the absence of perfect support of the wall before starting the test.


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Figure 5. Single cycle test. Fontainebleau sand, self-drilling STAF depth 5 meters, Bruyère-le-Châtel (91).

Figure 6. Test with 14 cycles at the same pressure level. Fontainebleau sand, self-drilling STAF, depth 8 meters, Bruyère-le-Châtel (91). 4. Pressuremeter moduli in very stiff soils and rocks For this purpose, the precision of volume measurement is compulsory in order to obtain a representative measurement of very high moduli. This from the first loading, either when the second loading induces deformation three to four time smaller than the first one. The two exemples here below exhibit test with cycles:

- Figure 7 in a calcareous rock with very few fissures and relatively soft. The core calcareous deposits being the historical construction material of Paris. Some creep in this material is observed as soon as 7 MPa.

- Figure 8 in a sedimentary rock of much higher resistance, the Urgonien of Alpilles, dolomitic calcareous deposit that does not exhibit any creep at 25 MPa.

Figure 7. Test with a cycle between one and five MPa in soft rock (cores calcareous deposits Sartrouville, 78) and zoom on the loading unloading cycle. In these “nears elastic” loops, the difference in volume between two points of measurement is between 0.1 and 1 cm², or a slope dV/dP of 0.2 and 0.3 cm²/MPa, or a deformation of the borehole of 10-5 to 10-4.


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Figure 8. With three loading cycles between 0 and 25 MPa, without creep neither failure of the Urgonien calcareous deposit. Those examples do illustrate how one switches, from the domain of soils with a (p, V) or (p,ε) exhibiting a hyperbolic curve from the origin, to the domain of rock with cementation and fracturatio. The (p, V) relation becomes with an initial inverse curvature, the concavity towards axis of pressure indicating a precise pressuremeter measurement of the closing under radial stress of the fractures and micro fissures and the inter granular porosity. Under a stress of 25 MPa (calcareous deposit of figure 8) or until 50 MPa (sand stone of figure 1, Baud and al. 2013c), the closing of the fissures is not terminated and the rock did not exhibit the beginning of the expansion behaviour. It is in this type of rock that the test should proceed as far as possible to obtain an initial shearing of the rock matrix, after complete closing of the fissures; this will be tried with the Hyperpac prototype to 100 MPa. 5. Conclusion The behavior of cyclic test in rock without reaching failure may help to compare and understand the nature of cyclic moduli in soils and rocks: - the strain reached during the first loading in rock is the same at maximum pressure after the second and third cycle and most probably in case of next cycles, identical with of gap of only 10-6.This is within the range of the experimental error. - In rock, the increase of secant modulus according to cycles (here between 2 and 25 MPa) is only due to a partial and incomplete reopening of fissures which have been closed by the first loading. - In soils, the increase of the modulus partially originates from the reorganization of grains under the influence of micro shears, after which there is no return to initial conditions further to the successive unloading phases, this when they are relatively quickly performed after the first loading. - The important difference as compared to firm rocks is that, for soils and weak rocks, there is a reinitiation of shear immediately at the beginning of successive loadings. This is observed by the hyperbolic shape of the curve.


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- This irreversibility however is limited in time, since a long phase of rest after loading cycles allows soil to return to the initial structure of soil grains or rock elements. At the end, recovery will be complete 6. Expression of thanks Many thanks to the clients which leave available their sites for the performance of tests: Eiffage for the figures 1 to 4, CEA-DAM for the figures 5 and 6, Colas-DTP for the figure 7, Botte Fondations for the figure 8. 7. References Arsonnet G., Baud J.-P. & Gambin M. (2005) Réalisation du forage pour essais

pressiométriques par un système de tube fendu autoforé (STAF), ISP5 – PRESSIO 2005, Actes Symp. Intern. Paris, Gambin, M.P., Magnan, J.-P., Mestat, P. (eds.) 22-24 août 2005, Paris : Presses des Ponts. vol.1 pp 31-45.

Arsonnet G., Baud J.-P., Gambin M. & Youssef W. (2013a) Le GéoPAC®, un contrôleur pression-volume automatisé pour les essais pressiométriques de qualité. Actes d’ISP6, CFMS, XVIIIème CIMSG, Paris, consultable sur http://www.geotech-fr.org/ressources-documentaires/congres/symposium-isp6.

Arsonnet G., Baud J.-P. & Gambin M. (2013b) RotoSTAF®, une amélioration déterminante de l’autoforage du pressiomètre Ménard. Actes d’ISP6, CFMS, XVIIIème CIMSG, Paris, consultable sur http://www.geotech-fr.org/ressources-documentaires/congres/symposium-isp6.

Atkinson J.H. & Sällfors G. (1991) Experimental determination of soil properties. 10e ECSMFE, Firenze, 3, pp 915-956.

Baud J.-P., Gambin M. & Uprichard S. (1992) Modeling and Automatic Analysis of a Ménard Pressuremeter Test, Géotechnique et Informatique, Actes du Colloque ENPC, 29 septembre – 1er octobre 1992, Paris, Presses des Ponts, pp 25-32

Baud J.-P. & Gambin M. (2013a) Détermination du coefficient rhéologique α de Ménard dans le diagramme Pressiorama®. Actes du 18ème CISMG, Paris 2013.

Baud J.-P., Gambin M. & Schlosser F. (2013b) Courbes hyperboliques contrainte–déformation au pressiomètre Ménard autoforé, diagramme Pressiorama®. Actes du 18ème CISMG, Paris 2013.

Baud J.-P., Gambin M. & Heintz R. (2013c) 50 MPa Ménard PMTs Help Linking Soil and Rock Classifications. Actes d’ISP6, pendant le 18ème CIMSG, Paris, disponible sur http://www.cfms-sols.org/actes-du-colloque. Ce document est également disponible sur le site d’ISP6 http://www.geotech-fr.org/ressources-documentaires/congres/symposium-isp6.

Bisgambiglia J.-A. (1976) Essais pressiométriques cycliques. Le Pressiomètre dynamique. Essais alternés. Mémoire de fin d’étude. Ecole Centrale des Arts et Manufactures, Sèvres.

Bourgeois E., Coquillay S. & Mestat P., (2005) Exemples d’utilisation d’un modèle élasto-plastique avec élasticité non-linéaire pour la modélisation d’ouvrages géotechniques, Bull. Liaison P&C n°256-257, Paris.

Briaud J.-L. (2013) The Pressuremeter Test: Expanding its Use, para. 7, Proc. 18th ICSMGE, Paris, consultable sur http://www.cfms-sols.org/actes-du-colloque.

Combarieu O. & Canepa Y (2001) L’essai cyclique au pressiomètre, Bull. Liaison des P & C, n° 233, pp 37-65.

Dalton C. (2005), United Kingdom Experience with Pressuremeter 1982-2005, Symposium ISP5-Pressio2005, Presses des Ponts, Paris, vol.2, pp 201-208.

Gambin M. (2009, 2012) Réflexions sur les fondations des éoliennes, document transmis au CFMS, non publié. Disponible par http://www.apageo.com/upload/medias/documents/8_michel-gambin---communication-recentes-fruk---2010_321.pdf

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Ménard L. (1961) Influence de l’amplitude et de l’histoire d’un champ de contrainte sur le tassement d’un sol de fondation, Actes du 5ème Congrès International de la SIMSTF, Paris.

Ménard L. (1963) Calcul de la force portante des fondations sur la base des résultats des essais pressiométriques, Sols-Soils n°5, Paris.

Ménard L. (1965) Règles pour le calcul de la force portante et du tassement des fondations en fonction des résultats pressiométriques, Actes du 6ème Congrès International de la SIMSTF, Montréal.

Ménard L. & Rousseau J. (1961) L’évaluation des tassements, tendances nouvelles. Sols-Soils, n°1, Paris.

Monnet J. (1990) Theoretical study of elasto-plastic equilibrium around pressuremeter in sands, ISP3, 3th International Symposium on Pressuremeters, Oxford, pp 137-148.

Monnet J. (2013) Caractérisation mécanique des sols par l’essai pressiométrique, Actes d’ISP6, CFMS, XVIIIème CIMSG, Paris.

Saadé C. (1981) Essais pressiométriques et essais cycliques. Mémoire D.E.A., Ecole Centrale des Arts et Manufactures, Sèvres.

Schlosser F. (2014) Détermination des paramètres géotechniques des sols, retours d’expérience. Lecture 4ème Conférence Franco-Maghrébine en Ingénierie Géotechnique, Sousse, Tunisie, 12-14 nov. 2014.

Tani K. (1995) General Report: Measurement of Shear Deformation of Geomaterial – Field Tests, Proc. 1st Int. Symposium on Prefailure Deformation of Geomaterials, Sapporo, A.A. Balkema pp 1115-1131.

Tatsuoka F., Jardine R.J., Lo Presti D., Di Benedetto H., (1997) Characterizing the Prefailure Deformation Properties of Geomaterials, Proc. 14th ICSMGE, Hambourg, vol.4, pp 2129-2164.

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Terzaghi K. & Peck R.B. (1948) Soil Mechanics in Engineering practice. J. Wiley, New York. Whittle R.W. (1999) Using non-linear elasticity to obtain the engineering properties of clay – a

new solution for the self boring pressuremeter. Ground Engineering, vol.32, n°5, pp 30-34.

menard pressuremeter modulus: relationship and ... · symposium international isp7/pressio 2015 . 1...

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