The Design of Reinforced Earth Walls DGS 28-11-2013...Danish Geotechnical Society Seminar on...

Danish Geotechnical Society Seminar on Reinforced Earth – 28/11/2013

The Design of Reinforced Earth WallsJérémy PLANCQ – Design Engineer, Terre Armée France


Fundamental Mechanisms

The Reinforced Earth is a composite material with an anisotropic artificial cohesion

Layers of pebbles separated by sheets of cardboard: The friction of the pebbles on the

cardboard And the resistance of the cardboard

sheets to traction Make it possible to build a “stack”

The reinforcements (cardboard sheets) act as a binding



If a confined dry sand, subject to confining stress 3 is loaded with a vertical stress 1 it will undergo an axial compression v and a lateral expansion h/2

If several layers of reinforcement are inserted into the soil, the magnitude of these deformations will reduce

This is a result of the confining stress generated by an interaction between the soil and the reinforcement

The factors involved define the basic principles of reinforced soil



When an vertical load is applied to reinforced soil this generates a vertical compressive strain and a resulting lateral tensile strain

If the tensile stiffness of the reinforcement is greater than that of the soil, movement will only occur if the soil can move relative to the reinforcement

Provided the surface of the soil reinforcement is sufficiently rough, movement of the soil, relative to the reinforcement, will generate shear stresses at the soil/reinforcement interface (soil/structure interaction)

These shear stresses induce tensile loads in the reinforcement which are redistributed back into the soil in the form of an internal confining stress

T T+dT

dL

σv



Shear strength

Stress Confining stress 3 Compressive

stress 1

Failure envelopeAn unreinforced soil subject to increasing compressive stress fails when shear strength is reached



When a soil is reinforced, increased compressive stress leads to increase in confining stressPractical limit is imposed on reinforced soil by tensile rupture of soil reinforcement or loss of adherence strength

Shear strength

Stress

Confining stress 3 Compressive

stress 1

Failure envelope



The internal friction makes it possible to space out the reinforcements Arch effect

A facing linked to the reinforcements is needed for: Local stability of the fill between two

reinforcements Protection against erosion

The facing is NOT there to take all applied load at the back (earth pressure, live loads) as for common CIP concrete walls


Behaviour of Reinforced Earth

The first structures were designed very simply

A research program was launched in 1969

Scale models Small models (bidimensional, three-

dimensional) for study of failure modes Bigger models (≥ 1m) for measurement of

stresses



Measurements on true scale structures Operational or experimental structures Stress along the reinforcing strips Stress in the soil inside and around the

Reinforced Earth mass

Instrumentation Strain gauges Pressure cells…

Loads Measurements during and after construction

of the structure Application of loads, vibrations…


Experimental structures

Milville, USA, 1970’sFremersdorf, Germany, 1980Fontainebleau, France, 1988: 6m high + beam Vertical and horizontal loadings applied by cables jacked and tied-back 129 tensile points 31 Glötzl cells to measure vertical stress horizontal inclinometers


Experimental structures

Fontainebleau, France, 1988

Incremental tension in the strips (for Qv=2025kN to Qv=4050kN)



Finite elements modelsSofware Rosalie (LCPC) 1982-85 50 models of walls 50 models of true abutments Parameters :

height, slenderness, shape, loads, reinforcements distribution, type of facing, deformation modulus of the subsoil…

Software Superflush (EET, USA) Walls subjected to seismic loadings

This research program led to the current semi-empirical method for the design of Reinforced Earth

Null distance

Null distance

STRIP TENSION AS A FUNCTION OF DEPTH

TENSION ALONG THE STRIPS

STRIP LAYER n°3

STRIP LAYER n°6


Evolution of Design Standards

1973: Technical Note LCPC : “La Terre Armée”1979: Guide from French National Road Administration: “Recommendations and good practice for Reinforced Earth structures”1992/1998: French standard NF P 94-220 “Soil reinforcement – Backfilled structures with quasi-inextensible and flexible reinforcing strips or sheets”

Up-to-date standard: NF P 94-270:2009 “Geotechnical design – Retaining structures – Reinforced and soil nailing structures”, French national application standard for Reinforced Earth structures derived from Eurocode 7

I addition, European standard for execution of special geotechnical works for reinforced fill: EN 14475:2006

Specific standards for Reinforced Earth also exist in other countries: Germany, UK (British Standard), USA (AASHTO), Japan, Australia…


Design Procedure

The design of a Reinforced Earth wall requires the verification of: Internal stability, local equilibrium justification for each reinforcing strip layer,

checking: The tensile strength, The soil/strip adherence.

External stability, performed by considering the RE wall as a block: Sliding on the base, Bearing capacity of the subsoil.

Compound (or combined) stability, Global stability.

These verifications are made at Ultimate Limit StateServiceability Limit State is only considered for settlements


Design Approach 2

Approach 2 is used for internal and external stability verificationsElementary actions (weight and earth pressure) Calculated with characteristic values γk , φ’k and c’k Then weighted

Rv

Load case 1(max. tension)

Load case 2(min. adherence)

W 1.35 1.00

P 1.35 1.35

Q1 1.50 -

Q2 / Pq 1.50 1.50

W

P

Pq

Q1

φ1’

φ3’ c3’ or cu3

φ2’

Q2


Design Approach 3

Approach 3 is used for compound and global stability verificationsSoil parameters Reduced

Permanent actions Not weighted: γG = 1.0

Variable actions Weighted: γQ = 1.3

Rv

q

φ1’

φ3’ c3’ ou cu3

φ2’

γφ’ 1.25

γ c’ 1.25

γ cu 1.40


External stability (approach 2)

Similar to standard retaining wallsSliding on the base: Horizontal resultant Hd must be compatible

with: Maximum allowable frictional resistance inside

RE fill under vertical resultant Vd (function of φ1k) Maximum allowable frictional resistance in

foundation soil under vertical resultant Vd(function of φfk, cfk on width L)

Partial safety factor on resistance: γR;h = 1.1

Hd

Vd φ1k

φfk, cfk

L


External stability (approach 2)

Bearing capacity of foundation soil: Vertical resultant Vd, spread on reduced

width 2x (Meyerhof’s model) must be compatible with the bearing capacity of the foundation soil on this reduced width

Partial safety factor on resistance: γR;v = 1.4

Rv

x

Vd


Embedment depth

The embedment depth D at the foot of a Reinforced Earth wall is a function of the pressure at the base of the wall (qref) and of the angle of the slope at the bottom of the wall (βp), with a minimum value of 0.4m (except on rock or concrete):

Slope βp of ground in front

D/qref(m/kPa)

0 1.5 x 10-3

18° (tan βp = 1/3) 3.0 x 10-3

27° (tan βp = 1/2) 4.5 x 10-3

34° (tan βp = 2/3) 6.4 x 10-3


Internal stability (approach 2)

Semi-empirical method

Maximum tension line Linking the points where tension in the strips

reaches its maximum Boundary between “active zone” and

“resistant zone” Line defined by the sketch, for standard

shape of RE wall Usually 0.5 Hm ≤ L ≤ 0.7 Hm

0.2Hm

0.3Hm

0.6Hm

0.4Hm

L

tm



Maximum tension tm In the strips with vertical spacing sv, on

which applies horizontal stress σh:

On maximum tension line, σh and σv are linked by:

At each strip level, σv is calculated as for the pressure at the base

For reinforcing strips z ≥ 6m K = Ka

z < 6m Ka ≤ K ≤ 1.6 Ka

z

K1.6Ka

Ka

6m

sv

tmvh K σσ ⋅=

vhm st ⋅= σ

φ1k

−=

24tan 12 k

aKϕπ



Allowable tensile strength Maximum tension tm must be lower than the

long term allowable tensile strength of the strip layer Allowable tensile strength is calculated

considering the required service life of the structure

Partial safety factor: 1.00 on yield stress (steel reinforcements) 1.25 on tensile failure

vhm st ∗σ=

Rv

x2x

σv


Allowable tensile strength

The allowable tensile strength for one strip (Tr) is given by:

where: Tlim: initial ultimate tensile strength (respectively yield strength) of the strip, ρend: reduction factor due to installation damage (= 1 for steel strips), ρflu: reduction factor due to creep (= 1 for steel strips), ρdeg: reduction factor due to environmental chemical and biological degradation. For

steel strips, this factor represents the loss of strength due to the loss of thickness with time.

γM;t = 1.25 (resp. 1.00): partial safety coefficient on ultimate (resp. yield) tensile limit of the strip material.

Calculation of ρdeg for steel strips is detailed in NF P 94-270 standardReduction factors for geosynthetic strips are derived from laboratory tests

tMfluendr

TT;

limdeg γ

ρρρ ⋅⋅⋅=



Tension at the facing The tension in one strip at the facing is equal to:

t0 = αi.tm where αi is given by:

Full height rigidfacing

Z

0.75

1.00 αi

Z0.

85

0.4H

1.00 αi

Z

1.00 αi

Flexiblefacing

Concretepanels



Pull-out capacity (soil/strip adherence) The strips are anchored in the resistant zone The pull-out capacity (rf) is a function of:

Adherence length La

Total horizontal surface of the strips (nb2) n strips of b width on 2 faces on 1m

Average vertical stress (σv) along La

Friction coefficient µ*

La

σv


La

ha


Soil/strip adherence The friction coefficient µ* depends on the

type of reinforcement High adherence (HA) or smooth steel strips Welded mesh Geosynthetic strips

µ* is derived from pull-out tests

For HA steel strips, µ* varies with the average depth (ha) on the adherence length La

ha ≥ 6m ha < 6m

with

(function of the fill characteristics)

φ1k

h

µ*

µ0*

µ1*

6m

k11 tanϕ=μ=μ ∗∗

∗∗∗ μ≤μ<μ 01

5.22.1 0 << ∗μ


Friction coefficient

Experimental measurements Pull-out tests of strip samples:

Experimental or operational structures Laboratory device

Database for various types of strips, fills (grain size distribution), depths…

Conservative envelope

PRESSUREMETER

JACK

SUPPORT

STRIP SAMPLE

HA

Smooth

µ*Influence of type of strip

HA

Smooth

µ* Influence of earth pressure


Friction coefficient

Dilatancy of soils Increase in volume of a compacted granular material

subjected to shear

The dilatancy effect: Increases with the density, i.e. the compacity Decreases with the increase of confining stress At low depth, the “impeded dilatancy” leads to a local

increase of the vertical stress and to an increase of the apparent friction coefficient

h

µ*

µ0*

µ1*

6m

strips

Real σv

γh



Pull-out capacity Maximum tension tm must be lower than

pull-out capacity rf

Partial safety factor: 1.35

h

µ*

µ0*

µ1*

6m

La

ha

σv

φ1k


Compound stability (approach 3)

Checking of structure stability along potential failure surfaces which are crossing the reinforcing strip layers

Partial factor on global shear resistance: 1.1Partial factors on reinforcements: Tensile strength :

1.00 on yield stress 1.25 on tensile failure

Adherence : 1.10


Global stability (approach 3)

Checking of structure stability along potential failure surfaces which are not crossing the reinforcing strip layers

Partial factor on global shear resistance: 1.1


Thank you !

The Design of Reinforced Earth Walls DGS 28-11-2013...Danish Geotechnical Society Seminar on...

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