Unit Cell Testing of Reinforced Soils - Reinforced Soil Engineering: Advances in Research and Practice - page 51

respectively:

A R
A s R ð

cos u tan f 0 Þ DS R ¼ sin u þ ð 26 Þ

A R
A s R ð

sin c tan f 0 Þ

DS R ¼ cos c þ ð 27 Þ

where

1

tan 2 1

¼ ð Þ

c 28

k þ 1 = tan 2 1 i

DS R : shear strength increase due to reinforcement,
s R : tensile stress in reinforcement at shear plane,
A R /A: reinforcement area to total area in the shear plane,
u: angle of shear distortion,
i: initial angle of inclination wrt shear plane,

k( ¼ x/z ): distortion ratio,

x is the horizontal shear displacement and z is the thickness of the
shear zone.

It is necessary to assume the distribution of tensile stress in the
reinforcement, either linear or parabolic, in order to estimate the strength increase
based on the above equations. Moreover, the thickness of the shear zone should
be assumed in using the equations.
Direct shear tests were performed on dry sand reinforced with different types
of discrete reinforcement. The effect due to the reinforcement stiffness, diameter,
orientation; reinforcement area ratio; friction between sand and reinforcement;
and the angle of friction and density of sandwere investigated. It was found that the
shear strength increase was proportional to the fiber area ratio up to a certain limit
and that an inclination of 60 produced the greatest increase in shear strength.

While McGown et al., 1978 reported that the increase in strength was more
significant for loose sand than dense sand, Gray and Ohashi (1983) reported that
the increase was approximately the same for sand in the loose and dense states.
These findings were found to be applicable to other types of reinforcement.
There was a critical confining pressure in the failure envelope, similar to that
reported by Yang (1972) for a triaxial compression test, below which failure
occurred by the pullout of reinforcement. Above this confining pressure, the failure
envelopes are parallel to each other due to the rupture strength of reinforcements.
Jewell and Wroth (1987) manufactured a direct shear box for investigating
the behavior of both unreinforced and reinforced sand. Leighton Buzzard sand
was used. Reinforcement with different stiffness was aligned during shearing as
shown in Fig. 9a. Figure 9b shows the effect of reinforcement stiffness on the
shear stress-displacement relationship of the composite. At the initial stage of

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