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The influence of the scale effect, in this case, affects only parameter σ c , but not
the other parameters m HB , S , and a .
3.2.2.3.4. Link between grain breakage and curvature of the shear strength envelope:
linear envelope
These results raise the question of the influence of the scale effect on a linear
shear strength envelope, such as the Mohr-Coulomb criterion. An interesting answer
can be obtained by making the values of b and a converge towards 1 in equations
[3.32] and [3.35], where these two exponents control the curvature of the envelope.
In both cases, the envelope becomes linear; the scale effect disappears from the
friction angle and only affects the value of the pseudo-cohesion 3 .
The integration of the scale effect in the expression of the shear strength
envelope allows us to analyze its incidence on the stability of engineering
construction, in a second step, and to take it into account in the design and
optimization of embankment works.
3.3. Practical applications to construction design
3.3.1. A new method for rational assessment of rockfill shear strength envelope
Rockfill materials are seldom tested to determine their shear strength (see for
instance ICOLD (International Commision on Large Dams) [ICO 02]) because of
the size of the apparatus required for this purpose and the corresponding costs and
duration of the tests (for a 0−250 mm rockfill, a representative sample for a triaxial
test should measure 1.5 m in diameter and 3 m in height, and weigh approximately 3
tons!). The construction trend towards higher rockfill dams with steeper slopes
requires better knowledge of their shear strength for stability assessment. In this
situation, the above results on scale effects give access to a new method by which to
assess the shear strength of a given rockfill. The procedure for applying this method
can be divided into four steps, including (see Figure 3.13) classical laboratory
testing:
− preparation of a “reduced” material that is geometrically similar to the rockfill,
coming from the same mineral stock, but with smaller grains limited to gravel size;
− realization of a series of normalized crushing tests (Protodiakonov or Franklin
test) on grains of different sizes in order to obtain a Weibull's distribution of the
statistics of grain crushing strength;
3 This result can also be found directly by applying equation [3.31] to a linear expression of
the shear strength envelope.
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