The Design of Reinforced Earth Walls

Transcription

1 The Design of Reinforced Earth Walls Jérémy PLANCQ Design Engineer, Terre Armée France

2 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

3 Fundamental Mechanisms 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

4 Fundamental Mechanisms 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) T σ v T+dT These shear stresses induce tensile loads in the reinforcement which are redistributed back into the soil in the form of an internal confining stress dl

5 Fundamental Mechanisms Shear strength Failure envelope An unreinforced soil subject to increasing compressive stress fails when shear strength is reached Confining stress 3 Stress Compressive stress 1

6 Fundamental Mechanisms Shear strength Failure envelope When a soil is reinforced, increased compressive stress leads to increase in confining stress Practical limit is imposed on reinforced soil by tensile rupture of soil reinforcement or loss of adherence strength Confining stress 3 Stress Compressive stress 1

7 Fundamental Mechanisms 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

8 Behaviour of Reinforced Earth The first structures were designed very simply A research program was launched in 1969 Scale models Small models (bidimensional, threedimensional) for study of failure modes Bigger models ( 1m) for measurement of stresses

9 Behaviour of Reinforced Earth 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

10 Experimental structures Milville, USA, 1970 s Fremersdorf, Germany, 1980 Fontainebleau, 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

11 Experimental structures Fontainebleau, France, 1988 Incremental tension in the strips (for Q v =2025kN to Q v =4050kN)

12 Behaviour of Reinforced Earth Finite elements models Sofware Rosalie (LCPC) 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 Null distance Null distance STRIP LAYER n 3 This research program led to the current semi-empirical method for the design of Reinforced Earth STRIP TENSION AS A FUNCTION OF DEPTH STRIP LAYER n 6 TENSION ALONG THE STRIPS

13 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 Soil reinforcement Backfilled structures with quasi-inextensible and flexible reinforcing strips or sheets Up-to-date standard: NF P :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

14 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 State Serviceability Limit State is only considered for settlements

15 Design Approach 2 Approach 2 is used for internal and external stability verifications Elementary actions (weight and earth pressure) Q 1 Q 2 Calculated with characteristic values γ k, φ k and c k Then weighted W Pq Load case 1 (max. tension) Load case 2 (min. adherence) φ 2 W P R v φ 1 P Q Q 2 / P q φ 3 c 3 or c u3

16 Design Approach 3 Approach 3 is used for compound and global stability verifications Soil parameters Reduced q γ φ 1.25 γ c 1.25 γ cu 1.40 Permanent actions Not weighted: γ G = 1.0 Variable actions Weighted: γ Q = 1.3 R v φ 1 φ 3 c 3 ou c u3 φ 2

17 External stability (approach 2) Similar to standard retaining walls Sliding on the base: Horizontal resultant H d must be compatible with: Maximum allowable frictional resistance inside RE fill under vertical resultant V d (function of φ 1k ) Maximum allowable frictional resistance in foundation soil under vertical resultant V d (function of φ fk, c fk on width L) Partial safety factor on resistance: γ R;h = 1.1 V d φ 1k H d φ fk, c fk L

18 External stability (approach 2) Bearing capacity of foundation soil: Vertical resultant V d, 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: γ R;v = 1.4 VR dv x

19 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 (q ref ) and of the angle of the slope at the bottom of the wall (β p ), with a minimum value of 0.4m (except on rock or concrete): Slope β p of ground in front D/q ref (m/kpa) x (tan β p = 1/3) 3.0 x (tan β p = 1/2) 4.5 x (tan β p = 2/3) 6.4 x 10-3

20 Internal stability (approach 2) Semi-empirical method 0.3H m 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 H m L 0.7 H m 0.6H m 0.4H m t m 0.2H m L

21 Internal stability (approach 2) Maximum tension t m In the strips with vertical spacing s v, on which applies horizontal stress σ h : t m = σ s h v 1.6K a K On maximum tension line, σ h and σ v are linked by: σ h = K σ v At each strip level, σ v is calculated as for the pressure at the base 6m K a t m φ 1k s v For reinforcing strips z 6m K = K a K a = z < 6m K a K 1.6 K a z tan π ϕ k

22 Internal stability (approach 2) Allowable tensile strength Maximum tension t m 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 R v t m = σ h x 2x s v σ v

23 Allowable tensile strength The allowable tensile strength for one strip (Tr) is given by: where: T r = ρ end ρ flu ρ deg T lim : initial ultimate tensile strength (respectively yield strength) of the strip, ρ end : reduction factor due to installation damage (= 1 for steel strips), ρ flu : reduction factor due to creep (= 1 for steel strips), ρ deg : 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. γ M;t = 1.25 (resp. 1.00): partial safety coefficient on ultimate (resp. yield) tensile limit of the strip material. Calculation of ρ deg for steel strips is detailed in NF P standard T γ lim M ; t Reduction factors for geosynthetic strips are derived from laboratory tests

24 Internal stability (approach 2) Tension at the facing The tension in one strip at the facing is equal to: t 0 = α i.t m where α i is given by: Flexible facing Concrete panels Full height rigid facing α i α i 1.00 α i 0.4H Z Z Z

25 Internal stability (approach 2) Pull-out capacity (soil/strip adherence) The strips are anchored in the resistant zone The pull-out capacity (r f ) is a function of: Adherence length L a Total horizontal surface of the strips (n b 2) n strips of b width on 2 faces on 1m σ v Average vertical stress (σ v ) along L a Friction coefficient µ* L a

26 Internal stability (approach 2) 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 0 * µ* h a µ* is derived from pull-out tests 6m For HA steel strips, µ* varies with the average depth (h a ) on the adherence length L a h a 6m μ = μ1 = tan ϕ 1k h a < 6m μ1 < μ μ0 1.2 < μ 0 < 2.5 with (function of the fill characteristics) h µ 1 * φ 1k L a

27 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 Influence of type of strip µ* µ* Influence of earth pressure HA HA Smooth Smooth

28 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 Real σ v 6m µ 0 * µ * γ h µ 1 * strips h

29 Internal stability (approach 2) Pull-out capacity Maximum tension t m must be lower than pull-out capacity r f Partial safety factor: 1.35 µ 0 * µ* h a 6m σ v µ 1 * L a φ 1k h

30 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: 1.1 Partial factors on reinforcements: Tensile strength : 1.00 on yield stress 1.25 on tensile failure Adherence : 1.10

31 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

32 Thank you!