TALREN 97  TERRASOL

PRESENTATION ARTICLETALREN 97  Stability analysis of geotechnical structuresTALREN 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 soilinclusion interaction and the design of actual structures. 1. CALCULATION METHOD1.1 General principlesThe 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 t_{max} to the mobilized shear stress t along the failure surface. The system equilibrium of the soil is determined using the reduced strength parameters c / G_{c} and tanf / G_{f} (c is the cohesion and f is the internal friction angle). 1.2 GeometryTALREN 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. 1.3 Failure surfacesThe program can analyze circular and all types of polygonal failure
surfaces (figure 3). 1.4 Hydraulic conditionsFour possible options exist for computing pore pressures along the failure surfaces (figures 4a, 4b, and 4c):
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).
1.5 SurchargesThree types of surcharges can be applied (figure 6):
1.6 Seismic loadingsSeismic loads are treated with a pseudostatic approach by introducing the forces associated with the horizontal and/or vertical accelerations (figure 7). One should note that:
1.7 Reinforcement1.7.1 Forces in the reinforcing elementsWhen 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). The forces taken into account are:
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). 1.7.2 Determination of the mobilized forces
 for an anchor: T_{n} = min[T_{a}/G_{mR}, T_{s}/G_{qs}]
if the failure surface intersects the anchor before the fictitious anchorage point;
where: T_{a} = tensile strength of the anchor  for a brace: T_{n} = T_{a}/G_{mR}
where: T_{a }= compressive strength of the brace  for a reinforcing strip: T_{n} = min[T_{a}/G_{mR}, (2 B m* s_{v} L_{a})/G_{S1}]
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 T_{c} in a reinforcement is computed by the subgrade reaction method or more generally from the reaction curve: T_{c} = min(T_{c1},T_{c2},T_{c3}) where: T_{c1} = maximum shear force when the soil
plastifies before the inclusion;
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).
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 multicriteria 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 T_{n}, T_{c} 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 T_{n}, T_{c} 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 (T_{n}, T_{c}), mobilized at failure, is perpendicular to the direction of d. This allows the determination of the forces T_{n} and T_{c} along the failure surface. 1.7.3 System equilibrium considering reinforcementThe forces T_{n} and T_{c}, mobilized at failure in the inclusions, completely modify the stress state (s, t) 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 soilinclusion interaction. The increase in stresses (Ds, Dt) are then considered in the equilibrium of the slices (see figure 11) by the following expression:
1.8 Analysis at the Ultimate Limit StateThe 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: G_{S3} t £ t_{max} To change the expression into an equality, an additional coefficient G is incorporated, which gives: G G_{S3} t = t_{max} where:
soil reinforcement
soil reinforcement G_{S3} = coefficient inherent to the
uncertainty of the analysis method;
2. REFERENCESTALREN 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 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 Retaining works for sensitive buildings (reinforced soil walls) 1984 Aurillac : Hospital  excavation adjacent to a church. Other noteworthy studies 1980 Highway A40: study of the natural slopes, and nailed and anchored
retaining walls.
3. BIBLIOGRAPHIC REFERENCESRAULIN P., ROUQUES G., TOUBOL A. (1974)  Calcul de stabilité des
pentes en rupture non circulaire  Rapport de recherche LCPC no. 36 (June). 