Recommendations for the design, construction and control of rigid inclusion ground improvements

Citation preview

FOREWORD

These Recommendations on the improvement of foundation soils by inserting vertical rigid inclusions embody the achievement of the ASIRI National Project, whose research activities and studies were conducted between 2005 and 2011 with a total budget allocation of €2. 7 million. This collective effort has relied on input from 39 partner firms and organizations; it has received the financial support of the French Government and steady backing from IREX for all project management aspects. This project arose from a personal initiative coordinated through IREX's Soil Specialist Cluster, in conjunction with public works contractors and engineering companies within France, for the purpose of accompanying the development of a new ground improvement technique. This technique first appeared in France during the 1990's and consists of associating a network of vertical rigid inclusions with a granular layer in order to compose the foundation platform for civil engineering works (rafts, reservoirs, ground slabs, embankments) and construction works (ground slabs). Though previous uses were already familiar and this technique beneath embankments had already been practiced in other European countries, the increasing application of such procedures for civil engineering structures and buildings had become something of a French national specificity, owing to the dynamic role of actors within the sector (construction companies and consulting engineers). Yet in the absence ofregulatory references, a set of dedicated and adapted guidelines needed to be developed and implemented. The ASIR1 National Project has focused on designing, conducting and interpreting a series of physical experiments and numerical models as a fundamental step to understanding the mechanisms acting in this innovative foundation system. The applied research program presented herein has been facilitated by project participants' broad range of competences, stemming from both academia and the professional world; the program has also greatly benefited from the physical and human resources each partner organization made available. A project database with an exceptional collection of experimental recordings and numerical results has provided a valuable support tool for nine doctoral theses performed within the scope of this very Project. A full slate of observations and model output could thus be compared for a number of varied structures. New orientations were introduced, revealing the extent to which associating such distinct elements (soil, inclusions, load transfer platform) produces an efficient and highly economical composite foundation system. These Recommendations are derived from the project's layout, which has yielded a set of practical rules for the design, construction and control of these structures, intended for all industry actors interested in further developing this technique. Another specificity of these Project Recommendations lies in the proposed design strategy, which conforms to the general Limit State design framework set forth in the Eurocodes, especially Eurocode 7-1 relative to geotechnical design. This application of general principles to devise a method for ground improvement design constitutes an original and forward-looking

Foreword

approach, given that it was necessary to adopt specific rules for structures not easily identified from the foundation categories established in Eurocode 7-1. The novelty of this technique has been well substantiated, and the field of applications foreseen thanks to this breakthrough is now wide open. This valuable contribution was made possible thanks to the support of all partner organizations, as well as to the tremendous motivation on the part of all who drove this work program so enthusiastically. Gratitude is extended to each and every one of them. B. SIMON Director of the Scientific and Technical Connnittee

ASIRJ National Project

Summary

Foreword ..................................................................................................................................... 3 Partners ..... ......... ....................... ......... ....................... ......... ....................... ......... ......................... 5 Notations ..................................................................................................................................... 7 Chapter 1. Description, history, initial developments and launching of the national project ............................................................................................ 19 Chapter 2. Operating mechanisms ........................................................................................... 41 Chapter 3. Design methods ..................................................................................................... 91 Chapter 4. Design considerations .......................................................................................... 145 Chapter 5. Justifications ........................................................................................................ 155 Chapter 6. Geotechnical investigations ................................................................................. 245 Chapter 7. Execution conditions ............................................................................................ 263 Chapter 8. Controls and instrumentation ............................................................................... 293

ASIRI National Project partners

ANTEA Group, BALINEAU, BOTTE Fondations, BOTTE Sondages, BOUYGUES TP, CNAM (Conservatoire national des arts et metiers), DURMEYER, EDF SEPTEN, EGIS, EIFFAGE CONSTRUCTION, Ecole des Ponts-ParisTech (formerly ENPC), ESTP (Ecole speciale des travaux publics), FFB (Federation frarn;aise du batiment), FNTP (Federation nationale des travaux publics), FONDASOL, FRANK.I Fondations (groupe FAYAT), GTM (groupe VINCI), GTS, ICE, IFSTTAR (formerly LCPC), INCLUSOL, !NERIS, INSA Lyon, KELLER Fondations Speciales, 3SR formerly LIRIGM (Universite Joseph-Fourier), MENARD, NAVIER Laboratory (formerly CERMES), PIEUX QUEST, PINTO, GRAND Port Maritime du HAVRE, QUILLE, RFF (Reseau Ferre de France), RINCENT BTP, SAIPEM, SNCF (Societe Nationale des Chemins de Fer frarn;ais), SOLETANCHE BACHY, SPIE Fondations, TENCATE (formerly BIDIM Geosynthetiques), TERRASOL.

This National Project also featured an Executive Committee, presided by Frarn;ois SCHLOSSER assisted by his Vice President Olivier COMBARIEU, along with a Scientific and Technical Committee headed by Bruno SIMON. The research activities involved in this project, organized around 5 major topic areas, were coordinated by: Laurent BRIAN(;ON (full-scale testing), Elisabeth HAZA-ROSIER (field tests), Luc THOREL (physical models), Daniel DIAS (numerical modeling) and Olivier COMBARIEU (Project recommendations). Valuable contributions to this project were also appreciated from: Conseil general de Seine-et-Mame (77), Ports de PARIS, SOCOTEC, SOREDAL and AXSOL France. The Recommendations comprise 8 chapters; they were crafted by five working groups, overseen by the Scientific Committee and validated by a Review Panel. The following individuals helped assemble and draft the recommendations set forth herein: Scientific and Technical Committee Director: B. SIMON

Working groups Coordinators 0. COMBARIEU (Expert), Cl. PLUMELLE (Expert), J.-P. IORIO (Saipem), C. POILPRE (XAmsol), L. CARPINTEIRO (Socotec) and S. LAMBERT (Keller Fondations Speciales) Member P. BERTHELOT (Veritas), T. BRET (Keller Fondations Speciales), L. BRIAN(;ON (Cnam), S. BRULE(Menard), C. COPAL(KellerFondations Speciales), J. CREPET (Soredal), D. DIAS (INSA Lyon), J.B. DROUET (Menard), J.-R. GAUTHEY (Spie Fondations), M. GLANDY (Soletanche Bachy), J. GRIPON (Franki Fondations), V KELLER (Durmeyer), E. LAVEDER (Axsol France), B. LEGER (Quille), F. MASSE (Menard), A NANCEY (Tencate), U. OKYAY (Pinto), C. PLOMTEUX (Menard), J. RACINAIS (Menard), C. SIMON (EDF), and S. TURLE (Inclusol). Partners

Review Panel President: F. SCHLOSSER (Professor Emeritus) R. KASTNER (Professor Emeritus), A GUILLOUX (Terrasol), P. LIAUSU (Menard), P. AGUADO (Apave) and F. BAGUELIN (Fondasol). Figures: Mr. ANIC ANTIC (Terrasol) English translation: R. SACHS

ASIRJ National Project

Notations

Notation

Descriptif

Description

Dimension

Unites/ Units

A

Aire d'une maille (une inclusion + sol alentour)

Surface area of a mesh (inclusion + surrounding soil)

L2

(m2)

Ac

Aire de la section comprimee d'une inclusion

Surface area of the compressed cross-section of an inclusion

L2

(m2)

As

Aire du sol compressible

Surface area of the soft soil

L2

(m2)

Ap

Aire de la tete d'inclusion (dallette)

Surface area of the inclusion head

L2

(m2)

a

Longueur caracteristique de la dallette (tete d'inclusion)

Inclusion cap width

L

(m)

a,b

Espacement des inclusions dans une maille rectangulaire

Spacing between inclusions within a rectangular mesh

L

(m)

B

Dimension de reference d'une fondation superficielle

Reference dimension of a shallow foundation

L

(m)

cc

lndice de compression

Compression index

Cd

Valeur limite de calcul de l'effet d'une action

Limiting design value of the effect of an action

Cmax

Valeur maximale de la resistance a la compression d'une inclusion tenant compte de la consistance qu'il est necessaire de donner au beton, coulis ou mortier frais suivant la technique utilisee

Maximum value of the compressive strength of an inclusion, in recognition of the consistency that must be applied to the fresh concrete, grout or mortar depending on the technique employed

Cs

lndice de recompression

Recompression index

(-)

Ca

Taux de consolidation secondaire

Rate of secondary consolidation

(-)

Cae

lndice de fluage

Creep index

(-)

c'

Cohesion ( en termes de contrainte effective)

Cohesion (in terms of effective stress)

ck

Cu

Notations

(-)

ML-1r 2

ML-1r 2

Coefficient de variation du loga- Coefficient of variation of the log rithme de la permeabilite of permeability avec l'indice des vides with the void index Cohesion non drainee

Undrained shear strength

(Pa)

(Pa)

(-) ML-1r 2

(Pa)

Cuu

Cohesion apparente d'un sol non sature

Apparent cohesion of an unsaturated soil

ML-1r 2

(Pa)

Cv

Coefficient de consolidation verticale

Coefficient of consolidation in the vertical direction

L2r-1

(m 2/s)

D

Diametre d'une inclusion

Inclusion diameter

L

(m)

OP

Diametre equivalent en pointe pour une inclusion de section non circulaire

Equivalent tip diameter for an inclusion with a non-circular cross-section

L

(m)

Ds

Diametre equivalent du tot pour une inclusion de section non circulaire

Equivalent diameter of the shaft for an inclusion with a non-circular cross-section

L

(m)

dmax

Diametre nominal du plus gros grain d'un sol

Maximum soil grain diameter

L

(m)

d;

Distance horizontale entre l'axe Horizontal distance between the d'une inclusion et le centre de la axis of an inclusion and the cenfondation ter of the foundation

L

(m)

dn

Dimension a n % (n % des parti- n percent dimension (n% of partides by weight with a dimencules en poids ont des dimension of less than dn) sions inferieures a dn)

L

(m)

E

Efficacite en terme de charge

Load efficiency

(-)

Etass

Efficacite en terme de tassement

Settlement efficiency

(-)

Ev

Efficacite selon le modele Hewlett et Randolph lorsqu'elle est controlee par la rupture au sommet de la voOte

Efficiency according to the Hewlett and Randolph model when controlled by failure at the arch summit

(-)

Er

Efficacite selon le modele Efficiency according to the Hewlett et Randolph lorsqu'elle Hewlett and Randolph model est controlee par la rupture au when controlled by failure at the pied de la voOte base of the arch

(-)

EQp

Proportion of total load to be Fraction de la charge totale a appliquer en tete de la applied at the head of a fictitious colonne fictive d'un modele ana- column associated with an analytique d'une maille courante lytical model of a common mesh

(-)

Ed

Valeur de calcul de l'effet d'une action

Design value of the effect of actions

E

Module d'Young

Young's modulus, Modulus of elasticity

ML-1r 2

(Pa)

E*

Module de deformation apparent du sol renforce sous chargement vertical

Apparent deformation modulus of the reinforced soil subjected to vertical loading

ML-1r 2

(Pa)

EM

Module conventionnel determine lors de l'essai pressiometrique Menard normalise

Normalized Menard pressuremeter modulus

ML-1r 2

(Pa)

E;

Module tangent du premier chargement

Tangent modulus for initial loading

ML-1r 2

(Pa)

ASIRJ National Project

ML-1r 2

(Pa)

Valeur de reference du module Reference value of the tangent oedornetrique tangent dans le oedornetric modulus in the "Hardening soil" model rnodele Hardening soil

ML-1T-2

(Pa)

Eoedo *

Module oedornetrique equivalent du volume de sol renforce par inclusions

Equivalent oedornetric modulus of the soil volume reinforced by inclusions

ML-1T-2

(Pa)

Ep

Module d'Young de !'inclusion

Young's modulus of the inclusion

ML-1r 2

(Pa)

Es

Module de deformation apparent du sol

Apparent deformation modulus of the soil

ML-1T-2

(Pa)

Esol

Module de deformation du sol non renforce

Deformation modulus of the non-reinforced soil

ML-1r 2

(Pa)

ref

Valeur de reference du module secant a 50 % du deviateur a rupture dans le rnodele Hardening soil

Reference value of the secant modulus at 50% strength in the "Hardening soil" model

ML-1r 2

(Pa)

E ref ur

Valeur de reference du module de recornpression dans le rnodele Hardening soil

Reference value of the unloading-reloading modulus in the "Hardening soil" model

ML-1r 2

(Pa)

e

lndice des vides

Void ratio

(-)

ea

lndice des vides initial

Initial void ratio

(-)

emax

lndice des vides maximal (dans l'etat le plus lache)

Maximum void ratio (in the loosest state)

(-)

emin

lndice des vides minimal (dans l'etat le plus dense)

Minimum void ratio (in the densest state)

(-)

FN

Resultante du frotternent negatif

Resultant of negative friction

Eoed

Eoed

E50

ref

Module redornetrique

Oedornetric modulus

MLr2

(N)

fed

Design value of the comp resValeur de calcul de la resistance sive strength of the concrete, a la compression du beton, cou- grout or mortar used on an inclulis ou rnortier d'une inclusion sion

ML-1r 2

(Pa)

fck

Resistance caracteristique en Characteristic value of the corncompression du beton, coulis ou pressive strength of the conrnortier rnesuree sur cylindres a crete, grout or mortar measured 28jours on cylinders at 28 days

ML-1r 2

(Pa)

fck (t)

Resistance caracteristique en Characteristic value of the corncompression du beton, coulis ou pressive strength of the conrnortier rnesuree sur cylindres crete, grout or mortar measured on cylinders at t days at jours

ML-1r 2

(Pa)

fck*

Resistance caracteristique a la compression du beton, coulis ou rnortier d'une inclusion

Characteristic value of the cornpressive strength of the concrete, grout or mortar used on an inclusion

ML-1r 2

(Pa)

fcvd

Valeur de calcul de la resistance en cisaillernent et en cornpression du beton, coulis ou rnortier d'une inclusion

Design value of the shear and compressive strength of the concrete, grout or mortar used on an inclusion

ML-1r 2

(Pa)

Notations

fctd

Valeur de calcul de la resistance a la traction du beton, coulis ou rnortier d'une inclusion

Design value of the tensile strength of the concrete, grout or mortar used on an inclusion

ML-1r 2

(Pa)

fc28

Valeur caracteristique de la resistance a la compression a 28 j du beton d'un dallage

Characteristic value of the cornpressive strength value at 28 days for the ground slab concrete

ML-1r 2

(Pa)

ftrendage28

Valeur caracteristique de la resistance en traction par fendage a 28 j du beton d'un dallage

Characteristic value of the tensile strength value by splitting at 28 days for the ground slab concrete

ML-1r 2

(Pa)

fn

Frotternent negatif unitaire

Negative skin friction

ML-1r 2

(Pa)

G

Taux marginal de report d'effort Marginal load efficiency ratio on sur la tete d'une inclusion the inclusion head

G

Module de cisaillernent

Shear modulus

G11,G12,

Qualificatif des missions geotechniques norrnalisees (norrne NF P 94-500)

Qualifier of standardized geotechnical missions (NF P 94-500 Standard)

Module de cisaillernent equivalent du sol renforce

Equivalent shear modulus of the reinforced soil

Acceleration de la pesanteur terrestre

Acceleration due to earth gravity

G2,G3

G4 G*

g

(g

=

9,81 rn/s 2)

(g

=9.81

rn/s 2)

(-) ML-1r 2

(Pa)

ML-1r 2

(Pa)

Lr2

(rn/s 2)

g

Part perrnanente d'une surcharge

Permanent component of a surcharge

ML-1r 2

(Pa)

g (z)

Deplacernent lateral impose du sol autour d'une inclusion

Imposed lateral displacement of the soil around an inclusion

L

(rn)

9max

Valeur rnaxirnale du deplacernent lateral impose autour d'une inclusion

Maximum imposed lateral displacement value around an inclusion

L

(rn)

H

Hauteur du sol compressible

Height of the soft soil

L

(rn)

He

Hauteur du plan d'egal tassernent

Height of the equal settlement plane

L

(rn)

HRou hR

Hauteur du rernblai

Embankment height

L

(rn)

HMouhm

Hauteur du rnatelas

Platform height

L

(rn)

HM

Hauteur du rnodele nurnerique plan

Height of the numerical model plane

L

(rn)

H,Hs

Epaisseur du sol compressible

Soft soil thickness

L

(rn)

h

Epaisseur d'un dallage

Thickness of a ground slab

L

(rn)

he

Hauteur d'action du frotternent negatif dans la couche cornpressible (hauteur critique)

Height of negative friction action taking place in the soft layer ( critical height)

L

(rn)

ASIRJ National Project

h;

Distance verticale entre le point d'intersection d'un rnecanisrne de rupture avec une inclusion et le centre de la fondation

Vertical distance between the point of intersection of a failure mechanism with an inclusion and the foundation center

L

(rn)

h,, ha

Hauteur d'application du frotternent negatif sur la colonne fictive surrnontant la tete d'inclusion

Height of negative friction application on the fictitious column positioned on top of the inclusion head

L

(rn)

I

Produit d'inertie d'une section

Product of inertia for a crosssection

L4

(rn4)

lo

lndice de densite

Density index

(-)

le

lndice de consistance

Consistency index

(-)

IP

lndice de plasticite

Plasticity index

(-)

J

Raideur d'une nappe geosynthetique

Stiffness of a geosynthetic layer

k

Coefficient de la loi de variation Coefficient of the modulus variadu module dans le rnodele rheo- tion law in the "Hardening soil" logique Hardening soil rheological model

Ks ou ks

Module de reaction du sol corn- Coefficient of subgrade reaction pressible (sol support) of soft soil (supporting soil)

Mr2

(N/rn)

(-) ML-2r 2

(kN/rn 3)

K

Rapport entre contraintes horizontale et verticale

Ratio between horizontal and vertical stresses

(-)

Ko

Facteur depression des terres au repos

Coefficient of earth pressure at rest

(-)

Ka

Coefficient de poussee des terres

Coefficient of active earth pressure

(-)

Kp

Coefficient de butee des terres

Coefficient of passive earth pressure

(-)

Kq

Coefficient de transmission d'une surcharge dans un massif non pesant

Coefficient of surcharge transmission within a weightless medium

(-)

Kx

Impedance horizontale d'une fondation superficielle

Horizontal impedance of a shallow foundation

MT-2

(kN/rn)

kh,kv

Coefficients de perrneabilite horizontale et verticale

Coefficients of horizontal and vertical permeability

Lr1

(mis)

k;

Module de reaction en sous face d'un dallage a proxirnite de l'axe d'une inclusion rigide (r < rk)

Coefficient of subgrade reaction on the underside of a ground slab adjacent to the axis of a rigid inclusion (r < rk)

ML-2r 2

(kN/rn 3 )

ks

Module de reaction du sol corn- Coefficient of subgrade reaction pressible ou module de reaction of the soft soil or coefficient of en sous face d'un dallage a dis- subgrade reaction on the undertance de !'inclusion side of a ground slab removed from the inclusion (r > rk) (r> rk)

ML-2T-2

(kN/rn 3 )

Notations

k-c, kq

Pentes des lois de mobilisation de Frank et Zhao pour le frotternent et la pointe

Slopes of the Frank and Zhao mobilization laws for both the friction and the tip

ML-1r 2

(Pa)

k1

Empirical coefficient for deterrniCoefficient ernpirique pour la ning the design value of the determination de la valeur de compressive strength of the calcul de la resistance en cornconcrete, mortar or grout on a pression du beton, du rnortier ou deep foundation (NF P 94 262 coulis d'une fondation profonde Standard); this coefficient (norrne NF P 94 262) ; tient accounts for the mode of placecornpte du mode de rnise en rnent in the soil as well as possiplace dans le sol ainsi que des ble cross-section variations variations possibles de section depending on the technique selon la technique utilisee employed

(-)

k2

Empirical coefficients for deterCoefficient ernpirique pour la determination de la valeur de mining the design value of the calcul de la resistance en corncompressive strength of the pression du beton, du rnortier ou concrete, mortar or grout on a coulis d'une fondation profonde deep foundation (NF P 94 262 (norrne NF P 94 262) ; tient Standard); this coefficient cornpte des difficultes de beton- accounts for concreting difficulties tied to the inclusion geonage liees a la geornetrie de !'inclusion. rnetry

(-)

k3

Coefficient ernpirique pour la determination de la valeur de calcul de la resistance en cornpression du beton, du rnortier ou coulis d'une fondation profonde (norrne NF P 94 262) ; tient cornpte des controles d'integrite effectues

Empirical coefficients for determining the design value of the compressive strength of the concrete, mortar or grout on a deep foundation (NF P 94 262 Standard); this coefficient accounts for the structural integrity testing conducted

(-)

L

Dimension de reference d'une fondation superficielle

Reference dimension for a shallow foundation

L

(rn)

L

Longueur d'une inclusion

Inclusion length

L

(rn)

L

(rn)

L

(rn)

Lat

Longueur necessaire a la rnobiLength required to mobilize lisation des efforts d'ancrage anchorage forces, measured as cornptee a partir de la derniere of the last inclusion in the inclusion dans la direction longi- embankment longitudinal directudinale tion

L

(rn)

Lat

Longueur necessaire a la rnobiLength required to mobilize lisation des efforts d'ancrage anchorage forces, measured as cornptee a partir de la derniere of the last inclusion in the inclusion dans la direction embankment transverse transversale direction

L

(rn)

L1

L1, L2

Largeur de la spirale logarithrniWidth of the logarithmic spiral in que dans le rnecanisrne de the Prandtl mechanism Prandtl Dimensions de reference d'un dallage

Reference dimensions of a ground slab

ASIRJ National Project

Lrr

Longueur d'ancrage d'une nappe geosynthetique comptee a partir de la tete du talus

Anchorage length of a geosynthetic layer, measured from the top of the slope

L

(m)

Lht

Longueur disponible pour l'ancrage d'une nappe geosynthetique comptee a partir de la tete du talus

Length available for the anchorage of a geosynthetic layer, measured from the top of the slope

L

(m)

LM

Demi-largeur du modele numerique plan

Half-width of the numerical plane-strain model

L

(m)

ML-1r 2

(Pa)

Lmax

Width of the Prandtl mechanism, Largeur du mecanisme de Prandtl comptee depuis le bord measured from the outer edge exterieur de !'inclusion of the inclusion

M

Moment d'un torseur d'effort

Net moment of a system of loads

ML2r 2

(Nm)

M

Moment flechissant

Bending moment

ML2r 2

(Nm)

Md

Valeur de calcul du moment d'un torseur d'effort

Design value of net moment of a system of loads

ML2r 2

(Nm)

MR

Moment du torseur des reactions developpees dans les inclusions pour la verification de portance ELU

Net moment of reactions developed in inclusions, for verification of ULS load-bearing capacity

ML2r 2

(Nm)

Mr

Moment radial dans une plaque

Radial moment in a plate

ML2r 2

(Nm)

Mx

Moment de flexion dans une plaque autour de l'axe (Oy)

Bending moment in a plate around the (Oy) axis

ML2r 2

(Nm)

My

Moment de flexion dans une plaque autour de l'axe (Ox)

Bending moment in a plate around the (Ox) axis

ML2r 2

(Nm)

Msup

Moment flechissant qui sollicite la fibre superieure du dallage en traction

Bending moment that loads the upper fiber of the ground slab in tension

ML2r 2

(Nm)

Minf

Moment flechissant qui sollicite la fibre inferieure du dallage en traction

Bending moment that loads the lower fiber of the ground slab in tension

ML2r 2

(Nm)

MO

Teneur en matieres organiques

Organic matter content

m

(-)

Exposant de la loi de variation Exponent of the modulus variadu module dans le modele rheo- tion law used in the "Hardening soil" rheological model logique Hardening soil

(-)

ma

Moment calcule dans un dallage continu sur sol homogeneise equivalent

Computed moment in a continuous ground slab on an equivalent homogenized soil

ML2r 2

(Nm)

mb

Terme correctif representant !'influence des inclusions rigides sur un dallage continu

Corrective term representing the influence of rigid inclusionson a continuous ground slab

ML2r 2

(Nm)

me

Terme correctif representant les interactions entre les inclusions rigides et les joints

Corrective term representing the interactions between rigid inclusions and joints

ML2r 2

(Nm)

Notations

m-c,mq

Coefficients des lois de Frank et Zhao de mobilisation du frottement et du terme de pointe

Coefficients of Frank and Zhao mobilization laws for both friction and the tip term

(-)

Nc,Nq,N

Facteurs de capacite portante

Bearing capacity factors

(-)

Nk

Facteur de correlation entre la cohesion non drainee cu et la resistance de pointe qc

Correlation factor between undrained cohesion Cu and cone resistance qc

(-)

Correlation factors between undrained cohesion Cu and corrected piezocone resistance qt

(-) (-)

Nkt

Facteurs de correlation entre la cohesion non drainee cu et la resistance de pointe piezocone

qt

n

Porosite

Porosity

p

Perimetre de !'inclusion

Inclusion perimeter

L

(m)

p

Contrainte horizontale contre une inclusion

Horizontal stress against an inclusion

ML-1r 2

(Pa)

Contrainte moyenne effective

Effective mean stress

= (cr/ + cr2'+ 0-3')/3

= (cr1' + cr2'+ cr3')/3

ML-1r 2

(Pa)

p'

P1

Pression limite conventionnelle Standard limit pressure determideterminee lors de l'essai pres- ned when conducting the stansiometrique Menard normalise dard Menard pressuremeter test

ML-1r 2

(Pa)

Pi*

Pression limite conventionnelle comptee a partir de la contrainte totale horizontale regnant dans le sol lors de l'essai

Standard net limit pressure corrected from the total horizontal stress acting in the soil at test elevation

ML-1r 2

(Pa)

Valeur ultime de la contrainte Ultimate value of the lateral soil horizontale contre une inclusion pressure against an inclusion

ML-1r 2

(Pa)

P1im

Q

Resultante verticale d'un torseur d'effort

Vertical net force of a system of loads

MLr2

(N)

Qd

Valeur de calcul de la resultante verticale d'un torseur d'effort

Design value of the vertical net force of a system of loads

MLr2

(N)

Q*

Resultante verticale des efforts appliques (en !'absence d'inclusions)

Vertical net force of applied loads (in the absence of inclusions)

MLr2

(N)

Q* p

Resultante verticale des efforts appliques sur l'aire d'une tete inclusion (en !'absence d'inclusions)

Vertical net forces of applied loads over the inclusion head area (in the absence of inclusions)

MLr2

(N)

MLr2

(N)

MLr2

(N)

QR

Q5 (z)

Resultante verticale du torseur Vertical net force of reactions des reactions developpees dans developed in inclusions, for verification of ULS load-bearing les inclusions pour la verification de portance ELU capacity Resultante verticale des efforts appliques a la section d'inclusion placee a la profondeur z sous la tete

Vertical net force of loads applied to the inclusion crosssection placed at depth z below the head

ASIRJ National Project

Os

Load applied at the corner (or Charge appliquee en angle (ou edge) of the ground slab serving en bord) de dallage qui annule to cancel out the lifting due to le soulevernent dO au retrait difthe differential shrinkage and ferentiel et au gradient de terntemperature gradient perature (DTU 13.3) (DTU 13.3)

MLr2

(N)

Os*

Resultante verticale des efforts appliques sur l'aire cornplernentaire d'une tete d'inclusion (en !'absence d'inclusions)

Vertical net force of loads applied on the complementary area of an inclusion head (in the absence of inclusions)

MLT2

(N)

Resultante verticale des efforts appliques en tete d'une inclusion

Vertical net force of loads applied at the head of an inclusion

MLr2

(N)

Resultante verticale des efforts appliques a la surface du sol compressible

Vertical net force of loads applied to the soft soil surface

MLr2

(N)

q

Deviateur des contraintes

Equivalent shear stress

ML-1r 2

(Pa)

q

Part variable d'une surcharge

Variable component of a surcharge

ML-1r 2

(Pa)

qo

Contrainte appliquee en tete du profil (surcharge)

Stress applied at the profile head (excess surface load)

ML-1r 2

(Pa)

q*

Contrainte verticale s'exen;_:ant sur le sol compressible non renforce (sans inclusion)

Vertical stress acting upon the non-reinforced soft soil (without inclusion)

ML-1r 2

(Pa)

qa

Valeur asyrnptotique du deviaAsymptotic value of the hyperteur dans l'ajusternent hyperbobolic fitting of stress-strain curve lique de la courbe effortin primary triaxial loading deformation d'un essai triaxial

qc

Resistance de pointe (ou resistance de cone)

Cone resistance

ML-1r 2

(Pa)

qp

Resistance lirnite en pointe d'une inclusion

Limit value of point resistance of an inclusion

ML-1r 2

(Pa)

qs

Frotternent lateral unitaire lirnite

Limit value of skin friction

ML-1r 2

(Pa)

qt

Resistance de pointe (ou resistance de cone) du piezocone

Cone resistance corrected for pore water pressure (piezocone testing)

ML-1r 2

(Pa)

*

qp

Contrainte appliquee sur le sol compressible a !'emplacement ou se trouverait la tete d'inclusion si elle etait en place

Stress applied on the soft soil at the location of the inclusion head (provided an inclusion had been placed)

ML-1r 2

(Pa)

qs*

contrainte appliquee sur le sol compressible (sans inclusion)

Stress applied on the soft soil (without an inclusion)

ML-1r 2

(Pa)

q/

contrainte appliquee sur la tete de !'inclusion

Stress applied on the inclusion head

ML-1T-2

(Pa)

q/(P)

Valeur lirnite de la contrainte sur la tete de !'inclusion calculee avec le rnecanisrne de Prandtl

Limit value of stress on the inclusion head, as calculated using the Prandtl mechanism

ML-1r 2

(Pa)

Op(O)

OU

Op+

0 5 (0)

OU

Os+

Notations

q/(L)

+

qp,d

Valeur lirnite de la contrainte sur Limit value of stress on the la tete de !'inclusion calculee inclusion head, as calculated for pour un debord L de la sernelle an overhang length L of the toopar rapport au bord de l'incluting relative to the inclusion sion edge

ML-1r 2

(Pa)

Valeur lirnite de calcul de la conDesign limit value of the stress trainte appliquee sur la tete de applied on the inclusion head !'inclusion

ML-1r 2

(Pa)

q/

Contrainte appliquee a la surface du sol compressible

Stress applied to the soft soil surface

ML-1r 2

(Pa)

R

Rayon de la rnaille equivalente

Radius of the equivalent mesh

L

(rn)

R

Rayon d'une sernelle circulaire

Radius of a circular footing

L

(rn)

Re

Seuil dans la courbe chargedeplacernent d'une fondation sur inclusions

Threshold in the load-displacernent curve of a foundation built on inclusions

MLr2

(N)

Rb

Resistance ultirne de pointe de !'inclusion

Ultimate point resistance of the inclusion

MLr2

(N)

L

(rn)

Re

Rayon maximal du cone de dif- Maximum radius of the diffusion fusion cone

Rd

Valeur de calcul de la resistance a une action

Design value of the resistance to an action

Rr

Rapport q/qa

q/qa ratio

Rk

Valeur caracteristique de resistance

Characteristic resistance value

Rs

Resistance ultirne rnobilisee par frotternent sur le tot d'une inclusion

Ultimate resistance mobilized by friction on the shaft of an inclusion

Roe

Rapport de surconsolidation

Overconsolidation ratio

(-)

MLr2

(N)

(-)

Re.er; d

Valeur de calcul de la resistance Design critical ground bearing critique (fluage) en cornpres- resistance value (creep) in cornsion du terrain pour une inclupression for an isolated inclusion isolee sion

MLr2

(N)

Rt;k

Characteristic value of shortValeur caracteristique de la resistance de traction a court term tensile strength of the geoterrne du geosynthetique rnesu- synthetic, as measured accorree suivant la norrne NF EN ISO ding to the NF EN ISO 10319 10319 Standard

Mr2

(N/rn)

Rt;d

Valeur de calcul de la resistance Design value of the ultimate tenultirne de traction du geosynthesile strength of the geosynthetic tique

Mr2

(N/rn)

Rt-L; d

Valeur de calcul de la resistance Design value of the ultimate tenultirne de traction du geosynthe- sile strength of the geosynthetic in the longitudinal direction of tique dans le sens longitudinal du rernblai the embankment

Mr2

(N/rn)

Rt-T; d

Valeur de calcul de la resistance Design value of the ultimate tenultirne de traction du geosynthe- sile strength of the geosynthetic tique dans le sens transversal in the transverse direction of the du rernblai embankment

MT-2

(N/rn)

ASIRJ National Project

Rv;d

Valeur de calcul de la resistance Design value of the ground bearing resistance beneath a shaldu terrain sous une fondation superficielle low foundation

L

(m)

rk

Rayon definissant la distribution Radius defining the distribution of coefficients of subgrade reacdes coefficients de reaction tion k; and ks k; et ks

L

(m)

rp

Rayon de !'inclusion

Inclusion radius

L

(m)

s

Aire de la semelle

Footing area

L

(m)

s,

Degre de saturation

Saturation ratio, degree of saturation

(-)

SRR

Taux de reduction des contraintes

Stress reduction ratio

(-)

s

Sc, Sy, Sq

Entraxe des inclusions dans une Center-to-center distance of the maille carree inclusions in a square mesh Coefficients de forme pour le calcul de la capacite portante

L

Shape coefficients for computation of the load-bearing capacity

(m)

(-)

T

Resultante horizontale d'un tor- Horizontal net force of a system seur d'effort of loads

MLr2

(N)

Td

Valeur de calcul de la resultante horizontale d'un torseur d'effort

Design value of the horizontal net force of a system of loads

MLr2

(N)

Td

Valeur de calcul de la traction dans le geosynthetique

Design value of tension in the geosynthetic

Mr2

(N/m)

Td; mesh

Valeur de calcul de la traction Design value of tension in the dans le geosynthetique resultant geosynthetic resulting from verdes charges verticales sur une tical loads on a mesh maille

Mr2

(N/m)

Td; thrust

Design value of tension in the Valeur de calcul de la traction geosynthetic resulting from horidans le geosynthetique resultant zontal outward thrust of the des efforts de poussee du talus, embakment fill, as evaluated on evaluee au nu exterieur the external unfinished side of de la derniere tete d'inclusion the last inclusion head

Mr2

(N/m)

Design value of tension in the Valeur de calcul de la traction geosynthetic resulting from horidans le geosynthetique resultant zontal outward thrust of the Td; thrust; des efforts de poussee du talus, embakment fill, as evaluated in max evaluee a l'aplomb de la crete alignment with the slope ridge du talus line

Mr2

(N/m)

Mr2

(N/m)

Tgeo

Valeur de calcul de la resistance de la nappe geosynthetique

Design value of geosynthetic layer resistance

Tgeo, long

Valeur de calcul de la resistance Design value of geosynthetic layer resistance in the longitudide la nappe geosynthetique dans le sens longitudinal nal direction

Mr2

(N/m)

Tgeo, trans

Valeur de calcul de la resistance de la nappe geosynthetique dans le sens transversal

Mr2

(N/m)

Notations

Design value of geosynthetic layer resistance in the transverse direction

TR

Resultante horizontale du tor- Horizontal net force of the reacseur des reactions developpees tions developed in inclusions, dans les inclusions pour la verifi- for verification of ULS load-beacation de portance ELU ring capacity

MLr2

(N)

T

Effort tranchant dans une inclusion

Shear force in an inclusion

MLr2

(N)

Tv

Facteur temps redometrique

Time factor

u

Degre de consolidation

Degree of consolidation, consolidation ratio

u

Pression interstitielle, surpression interstitielle

Pore pressure, excess pore pressure

ML-1r 2

(Pa)

V

Vitesse d'un bloc rigide

Velocity of a rigid block

Lr1

(mis)

V

Volume specifique

= (1

+ e)

Specific volume

= (1

(-)

+ e)

(g/100 g of soil)

Vas

Valeur de bleu de methylene d'un sol

Methylene blue value of a soil

V;

Effort vertical applique en pied d'un rack

Vertical force applied at foot of a rack

MLT"2

(N)

V

Deplacement lateral

Lateral displacement

L

(m)

w

Poids du volume de matelas d'une maille elementaire

Weight of the load platform for a unit cell

MLT-2

(N)

WP

Poids du matelas supporte Weight of the load platform suppar la tete d'une inclusion dans ported by an inclusion head in a une maille unit cell

MLr2

(N)

WT

Charge verticale supportee par une nappe geosynthetique entre deux inclusions

Vertical load supported by a geosynthetic layer placed between two inclusions

MLr2

(N)

w(z)

Deplacement relatif entre le sol et !'inclusion ; =y5 (z) - Yp(z)

Relative displacement between the soil and the inclusion =y5 (z) - Yp(z)

L

(m)

w

Teneur en eau

Water content

(-)

Wn

Teneur en eau naturelle

Natural water content

(-)

WL

Limite de liquidite

Liquid limit

(-)

Wp

Limite de plasticite

Plastic limit

(-)

y

Tassement

Settlement

L

(m)

Ys

Tassement du sol

Soil settlement

L

(m)

Yp

Tassement de !'inclusion

Inclusion settlement

L

(m)

YM

Tassement a la surface du matelas

Settlement at the load platform surface

L

(m)

ASIRJ National Project

a

Taux de couverture

Coverage area ratio/Area replacement ratio/Area ratio

(-)

a

Deformation angulaire d'une fondation

Angular deformation of a foundation

(rad)

a

Coefficient reducteur du frottement de !'interface sol-geosynthetique

Reduction coefficient of friction at the soil-geosynthetic interface

(-)

ace

Coefficient pour le calcul de la resistance caracteristique du beton

Coefficient for the characteristic concrete strength computation

(-)

13

Angle de diffusion des efforts

Diffusion angle of forces

(°)

13

Coefficient correcteur pour evaluer le module apparent du sol renforce

Correction coefficient for evaluating the apparent modulus of reinforced soil

(-)

13

Rotation relative d'une fondation

Relative foundation rotation

(-)

~

Deflexion d'une fondation

Foundation deflection

(-)

E

Deformation

Strain

(-)

E1 OU Ea

Deformation axiale

Axial strain

(-)

Ev

Deformation volumique

Volume strain

(-)

qi'

Angle de frottement interne effectif

Angle of shearing resistance (in terms of effective stress),effective angle of shearing resistance

(°)