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Influence of Density on Mechanical Properties for Coarse-grained soil Based on Percolation Theory Yidan HUANG1, a, Lingkan YAO1,b , Jian Wang1,c 1School of Civil Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China ahuangyidan@home.swjtu.edu.cn, byaolk@home.swjtu.edu.cn, ccrest01@qq.com Keywords: percolation; coarse-grained soil; renormalization group; density Abstract.
Coarse-grained soil is the main material of embankment dams, it is one of the major study objectives of soil mechanics.
The natural structure of coarse-grained soil is featured with the point-to-point single-grained structure among particles.
From the definition of fixed points in renormalization group, it can be obtained that (2) When various numbers of h（0≤h≤0.5）are substituted into Formula(2), the corresponding points can be obtained.
On the other hand, for the sandy soil with bigger particle diameter, it is general with the property of uniform-sized particles and obvious single grain structure, which is similar to the established model with the balls of the same diameter as the background.

For individual grain volumes, a “grain radius” corresponding to the radius of a sphere, R(t), that had the same volume of the grain could be calculated from Eq. 1.
Initially, a simultaneous transformation was considered with number of nuclei N1 = N2 = 64 and growth rates, G1 = G2.
In these cases, the number of nuclei and growth rates are equal, so phase 1 of the sequential transformation dominates the transformation, with only a relatively small advantage over phase 2, initially transformed to a volume fraction of 0.1.
Grain growth is affected only by its encounter with the neighboring grains, the impingement, so the grain that is situated farther away or has a smaller number of neighboring grains, grows more.
Following of the evolution of the grains one could demonstrate that each grain evolves in a particular way, as expected.

Petal-like icosahedral quasicrystal grains (i-phase grains) morphology usually has been observed in as-solidified quasicrystalline alloys.
In their observation, a very interesting phenomenon that pentagonal dodecahedral Al-Pd-Mn quasicrystal grains connecting each other to form a single i-phase grain has been observed.
(a) 20μm (c) (b) Figs .1(a) single i-phase grain morphology [1] , (b)the attached i-phase grains morphology [2] and (c)petal-like i-phase grains morphology (observed by cross-section) , respectively Now the problem is why the coherent process can take place for i-phase grains?
Consequently, the coherent i-phase grains could be regarded as the connected clusters independently growing largely into the connected i-phase grains.
Some key factors, such as alloy composition and the cooling rate, may directly influence the numbers of i-phase clusters in liquids and the probability of them connecting each other.

Unfortunate accidents as well as the rising number of terrorist attacks in urban infrastructures have influenced the increasing number of "accidents" related to fires and consequent damage not only to concrete buildings [1].
The concrete with designation B contained aggregate grain size 8/16 and 11/22 mm, while the concrete with designation C contained coarse aggregate with the grain size of only 4/8 mm.
The number of AE events indicates the probable number of newly created cracks and other defects, and the duration of the AE signal indicates the influence of the quality of the internal structure on the propagation of the mechanical wave.
The acoustic emission method revealed that concrete B exhibits a higher number of AE events, which is again probably due to the negative impact of the higher grain size of the aggregate.
This is similarly true when analysing the parameters of the AE signals where the higher grain size of the aggregate appears to be disadvantageous because the higher number of AE events probably means the formation of a higher number of micro-cracks in the internal structure of the concrete.

Total grinding forces are defined by average number of grain in contact zone.
Calculation of cutting forces for single diamond grain.
The forces affecting a single worn diamond grain Fig. 1 shows: - reaction force of the machined material affecting the diamond grain on the wear area
The number of the cutting grains contacting the machined material can be calculated by the proposal of A.N.
Thus, for rough grinding the grain wear may be 30-40% from the average diameter of the grain, and for the finishing grinding – 10-20%.

In the as-pressed condition, the microstructure was reasonably homogeneous and the grain size was reduced to an ultrafine grain size of ~0.3 µm.
This alloy contains MgZn2 and Al3Zr precipitates which restrict grain growth.
First, there must be a small and stable grain size, typically less than ~10 µm.
Summary and Conclusions (1) A spray-cast Al-7034 alloy with an initial grain size of ~2.1 µm was processed by ECAP to reduce the grain size to ~0.3 µm.
Langdon, Ultrafine Grained Materials III (Y.T.

Modifier and grain refiners are to be added to the molten Al-Si alloys to get combined grain refinement and modification effects.
In aluminium alloys, grain refining on efficient nuclei such as Al 3Ti, Al2 Sr3 particles is facilitated by the addition of grain refining master alloys.
Supersaturated levels of dispersoid forming elements in solid solution will increase the number of nucleation sites which form fine dispersoids during preheating of the cast alloy.
The grain size: 120µm to 180 µm.
Conclusions The addition of 0.30 wt% Mn, 0.15wt%Ti and 0.10 wt%Sr to grain refined aluminium alloy has a sensible effect on grain size.

Microstructure characterization indicated that a large number of tiny grains are distributed around the large grains.
The majority of these grains are equiaxed grains, and the few twins could be observeded.
It can be seen from Fig. 4, the grain size of rolled AZ31 magnesium alloy sheet is not uniform, that a large number of tiny grains are distributed around the larger grains.
For the recovery and recrystallization of magnesium alloy sheet occur after hot rolling, the majority of grains are the equiaxed grains, and the twins almost disappear.
A large number of tiny grains are distributed in large grains.

The effect of interstitial and substitutional impurities on grain boundary (GB) cohesion in the series of B2-TiMe alloys is studied from first principles using pseudopotential approach.
The TiMe(310) surface was simulated by a slab model with 10 atomic layers of Ti and Me and the same number of layers for vacuum gap between slabs.
The number of sites for H atoms at the surface where they can be trapped is larger than at the grain boundary because they are limited to the space between matrix atoms.
Boron in TiMe alloys prefers to segregate towards the grain boundary rather than the surface.
The grain boundary expansion and hence the IS contribution is small for H and B but it is larger for C.

The grain refinement of pearlite was more obvious when the applied electric current density was higher.
Grain refinement strengthening has been utilized for many kinds of steels.
By means of this treatment some perfect fine-grains were obtained, as later called spark annealing.
It can be seen that electropulsing treatment has obvious effect on grain refinement.
The nucleation is easy to occur on defects, grain boundaries, sub-grain boundaries.