Traduction technique français anglais de la thèse de doctorat de Bassels Seif El Dine intitulée « Etude du comportement mécanique de sols grossiers à matrice »
Université : École des ponts ParisTech (École nationale des ponts et chaussées)
Copyright : Bassels Seif El Dine 2010
French english scientific translation series : Phd thesis entitled : « A study of the mechanical behavior of matrix coarse-grained soils ».
Phd Student : Bassels Seif El Dine
University : École des ponts ParisTech (former : École nationale des ponts et chaussées), FRANCE
Chapter 1 : Bibliographic Elements (II)
The case of triaxial devices
Several researchers used various different-sized devices to study the effect of the geometric scale of shear devices.
Holtz and Gibbs  studied the effect of test tube size on the behavior of a fluviatile alluviation. Figure I.8 below presents the grading curves of the studied materials. The first contains 50% gravels and the second 20%. The authors conducted their tests both, on a fine portion of material (0/4.76 mm) and on a coarser portion (0/19 mm). They used four test tube sizes with the following diameters: 35 mm; 82.5 mm; 152 mm and 229 mm.
Figure I.9 shows that the angle of friction varies little with a size ratio Ø/dmax greater than 4. Consequently, a test tube with a diameter only 4 times larger than dmax seems sufficient to eliminate the effect of device size.
However, Fukuoka  shows that failure characteristics of a small test tube (Ø/dmax = 4) are lower than those of a large test tube (Ø/dmax = 6). Fumagalli  conducted triaxial tests with a test tube diameter of 100 mm on a limestone sample destined to be used by the cement industry of Bergame. The results are shown in Table I.1.
Fumagalli obtained a decrease in the internal angle of friction with an increase of the Ø/dmax ratio (Figure I.10 and Figure I.11).
Pedro  conducted two triaxial tests to study the influence of test tube size, the first on large test tubes (a diameter of 300 mm and a height of 600 mm) and the second on smaller sized test tubes: 100 mm in diameter and a height of 200 mm. The test sample is composed of a mixture of Fontainebleau sand and 20% of 8/10 mm gravel. The initial test conditions were identical for both triaxial tests.
Pedro observed that the behavior of test tubes was the same, whether in terms of shear strength or volume variation (matrix + 20% of an 8/10 mm gravel) regardless of tube size (Figure I.12).
Generally speaking, researchers who conducted triaxial tests on coarse-grained soils maintained minimal size ratios of 5 to 6 (Leslie ; Marchi, Chan and Seed ; Valle ).
The case of direct shear box tests
Several researchers also studied the influence of the L/dmax or L0/dmax ratios (where L and L0 designate the length or side of the direct shear box) on the mechanical behavior of soils. They showed that this ratio plays an important role in the shear strength of coarse-grained soils.
Fry et al  conducted direct shear tests in square boxes with a side of 1.2 m and in cylinders with a diameter of 100 mm, in which they compared device size L0 with the diameter of the largest particle dmax on a soil sample composed of a siliceous cement with maximum particle size of 160 mm. The tests showed the strong influence of device size on the results obtained. This influence on the angle of friction is expressed as a function of L0/dmax. The values of L0/dmax vary between 8 and 240. The angle of friction decreases when L0/dmax increases and becomes stable at values above 50. We observe a sharp increase in the angle of friction for L0/dmax values below 25 (Figure I.13).
Santos, Martinez and Garcia  studied the influence of the L0/dmax parameter on peak and minimal strength of a chalky gravel soil sample with a dmax of 25 mm at constant uniformity coefficients and soil bulk density. Starting with a sample having a dmax of 25 mm, the authors prepared three materials with parallel grading curves to conduct direct shear tests with a shear bow 300 mm large. They also conducted direct shear tests on a sand sample using 300 mm and 60 mm square boxes. They observed a 180 decrease of the Øpeak value and a 120 decrease of the Øfloor value when the L0/dmax parameter moves from 30 to 150. The authors conclude that an L0/dmax ratio below 25 produces a scale effect that has a significant impact on the results (Figure I.14).
Valle  studied the influence of shear box size on shear strength for evened out soil with a dmax of 25 mm using three shear boxes whose respective side lengths are 100 mm, 250 mm and 500 mm. He noticed that the two bigger boxes (those whose side length are 25 and 50 times bigger than dmax) have almost identical failure characteristics while those of the small 100 mm side length test tube were higher (Figure I.15).
Afriani  conducted experiments on the effect of scale relative to the dimensions of the shear box. He conducted tests on the large 500 x 500 mm shear box and on the small 250 x 250 mm shear box using material meant for reuse (coarse-grained soil from Criquebeuf-sur-seine originally extracted from the embankment of Rouen city‘s CER having been subjected to refinement up to refinement reducing it to a maximum grain size of 25 mm) as well as the natural soil of Criquebeuf-sur-seine (0/200 mm) with spacing t = 12 mm separating the two boxes.
She conducted three tests on the reused material and five tests on the natural soil with the following three normal stresses: 50 kPa, 100 kPa, and 150 kPa. The results of these tests completed by Valle  are listed in Table I.2 below.
Figure I.16 shows the results obtained. We observe that:
- For the reused material extracted from the embankment, the value of c increases with the box’s dimension while the internal angle of friction φ decreases. The observed variations between the 500 mm and the 250 mm boxes are 10.9 kPa and 4.8 degrees respectively.
- For the case of the natural material, the cohesion value varies little for both boxes. However, the value of the angle of friction is smaller than 4.5 degrees for the bigger box.
Afriani concludes then, that size ratio has an effect on cohesion and angle of friction as measured at the shear box.
In Figure I.17, Afriani  collected several measurements of cohesion and internal angle of friction as a function of shear box dimension L. Most of the given results come from previous research listed in the bibliography. Maximum grain diameter ranges from 5 mm to 80 mm for the various soils studied. Due to the widely different natures of these soils, we can observe scattered results, especially those related to cohesion. Essentially, cohesion decreases with increasing size ratio (L/dmax) whereas the internal angle of friction remains relatively constant across all box sizes.
For shear box tests, the ratios dmax divided by test tube size vary across researchers: Fukuoka  and Bourdeau et al.  use shear boxes whose side is 5 and 7 times larger than dmax while Valle , Shirdam et al.  and Wiseman et al.  use shear boxes that are respectively 20, 15 and 13 times bigger than dmax. It then seems reasonable to conclude that soil volume is representative for size ratios higher than 10.