Calculo Muros Tierra Reforzada

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Steep reinforced slopes
Pietro Rimoldi Angelo Ricciuti Piergiorgio Recalcati Director, Geosynthetics Division Design Eng., Geosynthetics Division Design Eng., Geosynthetics Division

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Geogrids and reinforced soil

Reinforced soil is a composite material which combines the typical resistance of two different materials in such a way to minimize the weakness of each one.Particularly, a relative large quantity of the cheapest and compression resistant material, the soil, is improved in its engineering characteristics by the combination with a relatively small quantity of a more expensive and highly tensile resistant material, the geogrids. Thus, a sinergy is developed between the tensile and compressive resistance of the two materials: this fact improves the globalcharacteristics of the composite material, like with concrete and steel (Fig. 1).

Reinforcement layers

Fig. 1 - Typical base and slope reinforcement for an embankment A relevant number of projects has already been realized worldwide, allowing the development of the techniques of design and construction of reinforced soil.

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Basic theory of reinforced soil

A simple model helpsto explain the principle on which the reinforced soil techniques are based (Jewell, 1980). Let us consider the soil element in Fig. 2a, which is part of an infinite mass of soil: the application of a vertical stress σv causes a deformation in the element and the consequent horizontal stress σh caused by the lateral compression suffered by the adjacent soil. Horizontally the soil element undergoesa "tensile deformation" εh, which is one of the principal causes of local failure. When, as in Fig. 2b, a reinforcing element is put in the soil, the application of a vertical stress is followed by the deformation of the soil element and the extension of the reinforcement. This extension then generates a tensile strength T in the reinforcement, which in turn produces a horizontal stress σh*. Thisstress, which also provides a confinement action on the soil granules, greatly contributes to resist the horizontal forces and to reduce the horizontal deformations. Therefore the inclusion of a geogrid into the soil mass reduces the stresses and strains applied to the soil; or, on the other hand, the vertical stress σv applied to the soil mass can be increased, compared to the unreinforced soil,at equal deformations.

σv

a) σh εh

σv σh* σh* F σh εh

b)

F σh

Fig. 2 - Stresses and strain in an unreinforced and a reinforced soil element

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With regards to the resistance to the shear stresses, according to Fig. 3 in a non-cohesive soil element we have:

(τ )
yx

max

= σ y ⋅ tan φ max

(1)

where φmax = maximum angle of shear resistance of soil;(τyx)max = maximum overall shear stress provided by the soil.

σy τxy

τxy σy

Fig. 3 - Shear stresses in an unreinforced soil element When the soil element is crossed by a reinforcement element which makes a θ angle with the shearing direction (fig. 4), the state of stress is modified because the tension T generates a shear stress produced by the tangential component T·senθ, meanwhile thenormal component T·cosθ generates another τ^yx caused by the friction angle φmax in the soil (Jewell, 1980). Therefore:

(τ )
yxr

max

= σ yr ⋅ tan φ max + ( T / AS ) ⋅ cosθ ⋅ tan φ max + ( T / AS ) ⋅ sin θ
+ shear stress caused by the normal component of T + shear stress caused by the tangential component of T

(2)

Total = shear shear resistance resistance of soil alone

where As =area of the soil element (τyxr )max = maximum overall shear stress of the reinforced soil

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τyxr

σyr

T

ϑ

τyxr T σyr

Fig. 4 - Shear stresses in a reinforced soil element So the normal stress on the soil element is increased by: ) σ y = (T / As ) ⋅ cosθ while the maximum shear stress which the soil can carry is increased. The main advantages of a reinforced soil...