TALREN 97 - logo.bmp (26678 octets) TERRASOL
Geotechnical Consultants

 

PRESENTATION ARTICLE

TALREN 97 - Stability analysis of geotechnical structures

TALREN 97, developed by TERRASOL, is a stability analysis program for geotechnical structures along potential failure surfaces. The program considers hydraulic and seismic data, in addition to various types of soil inclusions (nail, anchor, brace, reinforcing strip, geotextile, pile, micropile, sheetpile, etc.). Its development was carried out concurrently with experimental research on soil-inclusion interaction and the design of actual structures.

1. CALCULATION METHOD

1.1 General principles

The program allows determination of the stability of a geotechnical structure (excavation, fill, etc.), with or without reinforcement (nails, anchors, reinforcing strips, braces, piles, etc.). TALREN 97 is based on classical slope stability methods considering a failure surface at limit equilibrium. The validity of these methods has been proven for nearly 40 years by more than a thousand actual structures. The equilibrium of the active soil mass, located between the slope surface and a circular, polygonal or any shape failure surface, is analyzed by conventional methods, i.e.: Fellenius or Bishop slice methods, or the Perturbation method.

In these methods, the soil is divided into discrete or elemental vertical slices, for which the static equilibrium is analyzed (see figure 1). The safety factor G, assumed constant along the failure surface, is defined as the ratio of the maximum shear strength tmax to the mobilized shear stress t along the failure surface. The system equilibrium of the soil is determined using the reduced strength parameters c / Gc and tanf / Gf (c is the cohesion and f is the internal friction angle).

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1.2 Geometry

TALREN 97 accepts all possible slope and soil profile geometries (figure 2). The geometry is defined by points and segments, using open or closed polygonal lines. This allows the definition of complex geometries.

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1.3 Failure surfaces

The program can analyze circular and all types of polygonal failure surfaces (figure 3).
Each failure surface is discretized by segments (maximum number = 49).

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1.4 Hydraulic conditions

Four possible options exist for computing pore pressures along the failure surfaces (figures 4a, 4b, and 4c):

a phreatic surface geometrically defined by points, with the possibility of introducing seepage by imposing the equipotential line at each point;
pore pressures given at every point along a non-circular failure surface;
pore pressures defined at every node of a triangular mesh, whose values were obtained, for example, from finite element seepage analysis;
ru coefficient given for certain soils.

Fig3_4a_4b.gif (68328 octets) Fig3_4a_4b.gif (68328 octets)Fig4c.gif (40376 octets)

The program can also treat external water tables by considering the horizontal forces, equal to the hydrostatic pressure applied at the endpoints of the failure surface, in the global equilibrium (figure 5).

Fig5.gif (42930 octets)

1.5 Surcharges

Three types of surcharges can be applied (figure 6):

Vertical distributed surcharges, which increase the weight of each soil slice on which they are applied (discretization of the failure surface) in proportion to the slice thickness;
Line loads which induce additional soil stresses along the failure surface. This increase is taken into account by considering the shear stress (Dt) and normal stress (Ds) increments in the equilibrium equations;
Additional moments which are added to or subtracted from the driving moment. For circular failure surfaces, additional moments can only be considered when the Fellenius or Bishop analysis methods are used.

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1.6 Seismic loadings

Seismic loads are treated with a pseudo-static approach by introducing the forces associated with the horizontal and/or vertical accelerations (figure 7). One should note that:

the vertical coefficient is applied to the soil, the surcharges and the water;
the horizontal coefficient is only applied to the soil and the water located within the soil.

fig7.gif (24974 octets)

1.7 Reinforcement

1.7.1 Forces in the reinforcing elements

When reinforcement are introduced in the soil, the mobilized forces in these elements, at the intersection with the failure surfaces, should be considered in the static equilibrium (figure 8).

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The forces taken into account are:

the axial force for nails, anchors, braces or reinforcing strips;
the shear force and bending moment for nails working in coupled tension/shear or pure shear (piles and micropiles work in shear and bending when used for slope stabilization).

These forces depend on the mechanical characteristics of the soil since they are mobilized by soil/inclusion interaction (lateral friction, lateral pressure between the soil and the nails).

TALREN 97 considers all criteria associated with the different soil/ inclusion interaction mechanisms, for the various types of reinforcement currently used in practice (figure 9).

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1.7.2 Determination of the mobilized forces

Axial force with no shear or bending moment

- for a nail:    Tn = min[Ta/GmR, (qs p D La)/Gqs]
    where:       Ta = tensile strength of the nail
                     qs = limit soil/inclusion lateral friction
                    D = grouted diameter (for grouted bar) or equivalent diameter                            of the inclusion (for driven element)
                    La = active length beyond the failure surface
                    GmR= partial safety factor applied to Ta
                    Gqs = partial safety factor applied to qs

- for an anchor:   Tn = min[Ta/GmR, Ts/Gqs] if the failure surface intersects the anchor before the fictitious anchorage point;
                            Tn = 0 if the failure surface intersects the anchor beyond the fictitious anchorage point;
                            Tn is a function of the grouted length beyond the failure surface (optional).

            where:      Ta = tensile strength of the anchor
                           Ts = limit tensile resistance of the lateral friction over the length of                                      the anchor
                            GmR =partial safety factor applied to Ta
                            Gqs = partial safety factor applied to qs

- for a brace: Tn = Ta/GmR

            where:  Ta = compressive strength of the brace
                        GmR = partial safety factor applied to Ta

- for a reinforcing strip: Tn = min[Ta/GmR, (2 B m* sv La)/GS1]
            where:  Ta = tensile strength of the strip
                        B = strip width
                        m* = soil/strip interface friction coefficient (according to the specifications)
                        sv = normal stress applied to the strip
                        La = active length beyond the failure surface
                        GmR = partial safety factor applied to Ta
                        GS1 = partial safety factor applied to sv

Shear force and bending moment without axial force

The mobilization of a shear force or bending moment requires that the reinforcing element possesses a certain stiffness. Therefore, anchors and flexible strips cannot mobilize shear forces because of their low transversal rigidity. When nails, piles or micropiles are oriented to resist landslides, one can consider that the axial forces are negligible compared to the mobilized shear forces and bending moments. In TALREN 97, the maximum shear force Tc in a reinforcement is computed by the subgrade reaction method or more generally from the reaction curve:

Tc = min(Tc1,Tc2,Tc3)   where:

    Tc1 = maximum shear force when the soil plastifies before the inclusion;
    Tc2 = maximum shear force when the inclusion plastifies before the soil;
    Tc3 = maximum shear force corresponding to the intrinsic shear strength of the inclusion.


Tc1 = pl* B Lo/2 (long inclusion; L* ³ 2 Lo)
Tc1 = pl* B L*/4 (short inclusion)
Tc2 = (0.24) pl* B Lo + (1.62) Mmax/Lo (long inclusion)
Tc2 = (0.10) pl* B L* + (4.05) Mmax/L* (short inclusion)
Tc3 = Rc = Rn/2 (shear resistance equal to half the tensile resistance, Tresca criterion)
with: Rn = tensile resistance of the inclusion factored by GaNai
pl* = soil limit pressure reduced by a safety factor equal to Gpl
B = application width of the soil lateral pressure on the inclusion
Lo = transfer length of the inclusion
L* = active length of the inclusion
Mmax = allowable moment of the inclusion factored by GmR

Details on these criteria are found in the article "TALREN : Méthode de calcul des ouvrages en terre renforcée" (Blondeau, Christiansen, Guilloux, and Schlosser 1984), and in the Recommendations Clouterre 91 edited by Presses de l'Ecole Nationale des Ponts et Chaussées and the Federal Highway Administration (USA).

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Combination of axial force, shear force and bending moment:

All the above mentioned criteria can be taken in account when the inclusions work in both tension or compression, and coupled bending/shear. This is the basic principle behind the multi-criteria analysis (F. Schlosser 1982, 1983) in which the maximum plastic work rule is applied. An experimental 7.5 m high soil nailed mass (no. 1 of C.E.B.T.P.) showed that at failure, the nails work not only in tension but also in bending. This results in a shearing zone within the soil adjacent to the failure surface.

In the Tn, Tc plane, combination of the various criteria results in the limit envelope represented on figure 10 for the point of zero bending moment. By plotting the displacement d of the soil along the failure surface on the same Tn, Tc axis system, it can be shown from the principle of maximum work that the tangent to the yield surface at the application point of the force T (Tn, Tc), mobilized at failure, is perpendicular to the direction of d. This allows the determination of the forces Tn and Tc along the failure surface.

1.7.3 System equilibrium considering reinforcement

The forces Tn and Tc, mobilized at failure in the inclusions, completely modify the stress state (st) in the soil along the failure surface. The modification of the stresses (Ds, Dt) is taken into account by means of a diffusion cone which allows the distribution of the effect of soil-inclusion interaction. The increase in stresses (Ds, Dt) are then considered in the equilibrium of the slices (see figure 11) by the following expression:

fig11.gif (40692 octets)

1.8 Analysis at the Ultimate Limit State

The analysis method at the Ultimate Limit State consists in comparing the shear stresses, generated by the loads, to the mobilized shear resistance. Each parameter is factored by a weighting factor (for loads) or by a partial safety factor (for resisting forces). The static equilibrium is thus given by:

GS3 t £ tmax

To change the expression into an equality, an additional coefficient G is incorporated, which gives:

G GS3 t = tmax

where:

        

 

              soil           reinforcement

 

    

           

                   soil             reinforcement

GS3 = coefficient inherent to the uncertainty of the analysis method;
GS1 = weighting factor on the soil unit weights;
GQ = weighting factor on the loads;
GmR   = partial safety factor on the reinforcement effect (Gqs for the soil/inclusion lateral friction, Gp1 for the soil limit pressure, GmR for the tensile or compressive strength of the reinforcement);
Gf = partial safety factor on the soil internal friction angle (tan f);
Gc = partial safety factor on the soil cohesion;
G = additional coefficient to obtain an equality and whose minimum value Gmin for the set of failure surfaces should be greater or equal to 1.

 

2. REFERENCES

TALREN benefits from years of experience acquired in the practice of designing reinforced soil structures. The program has been calibrated on failed structures (either occurring naturally or artificially pushed to failure); the main cases are listed below :

1978 Madrid                                                  provoked failure
1981 Les Eparris                                            repair after failure
1984 Orchard Station                                     repair after failure
1984 Experimental nailed wall CEBTP              provoked failure

From among the hundred or more structures studied to date by TERRASOL using the TALREN program, the notable cases include:

High structures (reinforced soil walls)

1980 La Clusaz             Parking                              14 meters
1981 Ferrières/Ariège Hydropower station              17 meters
1984 Monaco                Le Florestan Bldg.               38 meters
1984 Singapore             Orchard station                    16 meters
1986 Nice                     La Bornala Bldg.                  24 meters
1995 Monaco                Underground train station    18 meters

Retaining works for sensitive buildings (reinforced soil walls)

1984 Aurillac : Hospital - excavation adjacent to a church.
1986 Paris : The Grand Louvre - excavation at the base of the facades - Maximum charge 3500 kN/m2.
1989 Paris 13 : Charles Fourier - excavation adjacent to heavy buildings 6 to 7 stories. H = 12 m.
1990 Toulouse : Avenue Jean Rieux - excavation adjacent to heavy buildings 6 to 7 stories - H = 12 m.

Other noteworthy studies

1980 Highway A40: study of the natural slopes, and nailed and anchored retaining walls.
1981-87 Nice seaport and airport: investigation into the cause of failure.
1983-88 Sète port: analysis of new wharfs.
1983-88 Transgabonese railroad: analysis of numerous unstable excavations.
1987 EDF hydroelectric power station in Génissiat: stabilization of an unstable natural slope by sub-horizontal drains and anchored diaphragm walls .
1988-91 Highway A4: stabilization of 8 Reinforced Earth abutments.
1988 Marseille: Hotel de Région - 17 m high retaining structure in a sensitive zone.
1988 Honfleur: reinforcement of a slope by soldier piles and soil nailing after failure.
1988 Martinique: RD1 Fond St DENIS - study and stabilization of a major slide.
1989 Paris 18: Place des Abbesses - study of a 22 m high temporary excavation.
1989 Paris Sud: Grand Mare - SNCF 17 m deep trench.
1989 Marne Reservoir Dam: instability analysis of the dam slopes.
1989 SNCF Paris/Lyon line: stabilization of a fill located above a deep slide with 800 mm diameter piles.
1990 Biarritz: stability analysis of the Cote des Basques - a 35 m high slope.
1990 Highway A34: stabilization of over 900 m of Reinforced Earth walls by soil nailing.
1990 Nice: Jardin de Babylone - stability analysis of a 20 m high anchored retaining structure below an existing building.
1991 Paris 14: Didot-Pierre Larousse - stability analysis of a 10 m high anchored retaining structure.
1991-93 TGV interconnection: Section 46A (Valenton) - embankment construction in areas containing filled in ballast quarries.
1994 Monaco - Condamine dike : stability analysis and verification of the treatment techniques (compaction grouting, inclusions).
1994-95 Highway A29 near Le Havre : fill placement on compressible soils (preloading and rigid inclusions) and excavation works (retaining structure using treated chalk, soil nailing).
1994-95 St. Martin de Queyrières : retaining structures on sloped embankments (soil nailing, Paraweb reinforcement) with soil consolidation (jet-grouting).

 

3. BIBLIOGRAPHIC REFERENCES

RAULIN P., ROUQUES G., TOUBOL A. (1974) - Calcul de stabilité des pentes en rupture non circulaire - Rapport de recherche LCPC no. 36 (June).
SCHLOSSER F., GUILLOUX A. (1981) - Le frottement dans le renforcement des sols - Revue Française de Géotechnique no. 16 (August).
SCHLOSSER F. (1982) - Behavior and design of soil nailing - Symposium on recent developments in in ground improvement techniques, Bangkok.
SCHLOSSER F., GUILLOUX A. (1982) - Soil Nailing : practical applications - Symposium on recent developments in ground improvement techniques, Bangkok.
SCHLOSSER F. (1983) - Analogies et différences dans le comportement et le calcul des ouvrages de soutènement en terre armée et par clouage des sols - Annales de l'ITBTP (418), Série Sols et Fondations 184.
BLONDEAU F., CHRISTANSEN M., GUILLOUX A., SCHLOSSER F. (1984) - TALREN : Méthode de calcul des ouvrages en terre renforcée - Colloque international : Renforcement en place des sols et des roches, Paris.
PROJET NATIONAL CLOUTERRE. Recommendations Clouterre 1991 (English translation). Presses de l'Ecole Nationale des Ponts et Chaussées and FHWA (USA).

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