Granular Materials in Civil Engineering: Recent Advances in the Physics of Their Mechanical Behavior and Applications to Engineering Works - Multiscale Geomechanics: From Soil to Engineering Projects - page 55

3.2.1.3. Centraltrendinthestatisticsoffailure
In the wide range of materials investigated by Marsal, values of exponent λ
(lambda) between 1.2 and 1.8 were found, which corresponds to values of Weibull's
parameter, m , between 4 and 15, with a mean value of λ equal to 1.5 and a
corresponding mean value of m equal to 6. The subject of the suitability of
Weibull's theory to natural grains has recently been updated by Lobo-Guerrero
Vallejo [LOB 06].
This central value of λ = 1.5 has physical meaning. It corresponds to the
configuration of a microcrack distribution within grains, which verifies the
geometrical similarity with their diameter. For this specific distribution, the size of
the significant cracks is statistically proportional to the grain diameter. In this case,
the failure stress given by fracture mechanics in equation [3.21] becomes inversely
proportional to the square root of the grain diameter. If we also assume that the
significant stress in a grain is proportional to the average macroscopic stress within
the granular medium, then the maximum macroscopic stress endurable by the
granular medium before significant grain crushing develops is inversely proportional
to the square root of a characteristic grain diameter.
These central assumptions are the core of the “clastic process” theory developed
by Bolton and McDowell [BOL 98], which provides a clear relation between the
compressibility of granular materials and grain breakage, depending on well defined
material parameters.
3.2.2. Scaleeffectinshearstrength
3.2.2.1. Shearstrengthofrockfill
Numerous experimental results on the shear strength of rockfill have been
gathered and published by different authors, such as Leps [LEP 70], Charles and
Watts [CHA 80] (see Figure 3.10), Duncan [DUN 04] and others. They show a wide
dispersion of the values and a pronounced curvature of the shear strength envelope:
the friction angle measured in triaxial compression tests significantly decreases
when the confining stress increases. This reduction of the friction angle has been
attributed to grain breakage that induces a decrease in dilative behavior (see sections
3.1.3.2 and 3.1.3.3). The amplitude of grain breakage was measured by comparing
the grain size distribution before and after testing.
In Figure 3.10, the results presented by Charles and Watts - curves A, B1, and C
- appear shifted towards the upper right-hand side of the diagram when compared to
the results obtained by Marsal or Marachi [MAR 69]. This remark also holds for
material B2, which corresponds to very weak grain strength and was chosen by the