Reinforcement and prestressing systems of concrete at the execution of structural elements

This research presents the consolidation, stabilization and fixing system of anchors with protected long strands joined together in soil, by injecting grout with special additives. Dynamic response to earthquakes, in case of anchoring system with strands must be able to reach high allowable values of total displacement (elongation of strands) in order to achieve an adequate degree of stability of ground massive.


Introduction
Consolidation of the natural soil in order to avoid slipping is the process that is undertaken effectively with anchors with long steel strands and that form a bulb at the end of the embedded attachment.
For a versant are used more anchors with length of at least 10 m, and a density distribution such that static load could be taken over.
In case of earthquake, the anchors behaviour, when the earthquake acceleration for the first vibration mode is ,one must consider the working between anchor and equivalent support mass.
This article presents the capacity to resist with elastic elongation to seismic action.

Dynamic model
Figure 1 shows the whole consolidation with a single steel strand length L, which is fixed by a bulb in A and in B fix a plate taking over the mass m of the slope.In case of a horizontal seismic motion ,, the anchor has as elastic element the steel strand and should take the inertial force F i = m • a .The position of strand 1 inside a protective pipe 2, as well as the existence of fixing mortar 3 there.In this space there is oil for the cable that makes the linear viscous force evident.The dynamic model is in figure 2 where k, c and m are constant.The motion equation of mass m is: (2) or numeric , it is: (5) We mark and we have: Critical damping fraction is: or Therefore from ( 6) we obtain the value of amplitude A for and : Critical damping fraction is: or Therefore from (6) we obtain the value of amplitude A for and : The dissipated energy in the integrally joined srandtube system, when the harmonic deformation occurs with represent the damping equivalent with the viscous one and has the meaning of hysteretic damping.represent the damping equivalent with the viscous one and has the meaning of hysteretic damping.We find that is the structural parameter of the system and it is dependent on the physical quantities m, c, k without the influence of dynamic vibration regime for instance ω or Ω.For , namely under harmonic vibration regime, the structural equivalent damping depends essentially of pulsation ω and Ω.
At resonance, for , critical damping fraction is equal with structural damping , ie .

Bearing capacity
Dynamic force F i of seismic movement must be taken by the strand-bulb system in order to keep in contact with the allowed deflection.So, in dynamic regime we have to determine the force from bulb In this case, the transmitted force is determined on the relation transmissibility as follows:  We note that the stiffness it is less then stiffness as 80 times, so less wires n=3 with diameter d=0,5 mm, so the deformation would be As a result the solution is not possible for , where T 1, so we'll have in bulb always .

Conclusions
The anchors system with steel strands having lengths of over 10 m secure the fixation of slopes in static and dynamic regime to seismic forces.
Transmitted force to the bulb can be 5% ... 25% bigger than the excitation force, with low elongation.
The structural damping of the system for , what makes that during the cyclic loading the dissipated energy is relatively low and without external heat transfer.
Anchor strength is provided both by good elongation and relatively low stiffness, as well as by rigid fixing of the bulb with grout fuelled under pressure into the tube locations.
amplitude A and pulsation ω = 0.5 π rad / s, can be calculated as follows or Taking into account that the hysteretic energy loss factor

Fig 3
Fig 3 Curve family for with discrete values ; 0,25; 0,35The optimization condition of force Q 0 results only for T<1, ieIn this case, we choose for =0,52 so we have:

Figure 4 Fig 4
Figure 4 shows the new configuration of curves , and at , for .So we have,