Amy L. Crook and Dr. Travis Gerber, Civil and Environmental Engineering
Introduction
An important soil parameter in geotechnical engineering is relative density. Relative density is a measure of the compactness of a cohesionless soil when compared to the loosest and densest state of the soil.
Three separate parameters are needed to calculate relative density: maximum density, minimum density, and in-place density. These parameters are also known as minimum void ratio, maximum void ratio, and in-place void ratio, respectively. The maximum density or minimum void ratio is the densest state of the soil. The minimum density or maximum void ratio is the loosest state of the soil.
The minimum and maximum densities are defined by standard laboratory procedures set by the American Society for Testing and Materials (ASTM). Standard D 4254-00 summarizes procedures for calculating the maximum void ratio. The basic procedure consists filling a mold of known volume with a soil in the loosest possible state. This is accomplished by using a funnel or scoop so as to minimize the segregation of particles and to prevent bulking. The mass of the soil is then determined. The index density, used in calculating the relative density, is calculated as the ratio of the mass of the soil to the volume that it fills. The ASTM standard summarizing the calculations for the maximum index density of a soil is D 4253-00. Soil is placed in a mold in the same manner as discussed in ASTM D 4254-00. A surcharge load placed on top of the soil, and the soil, mold, and surcharge load are placed on a vibrating table with a dial gage placed to calculate the change in volume of the soil. The mold assembly is then vibrated for approximately 8 minutes. The dial gage reading is recorded as well as the mass of the soil and the maximum index density is calculated.
According to Tavenas (1973) the observed coefficient of variability for determining the minimum and maximum density through laboratory testing is on the order of 2.5 percent a piece for each density. This leads to a coefficient of variability for the calculated relative density on the order of 40 percent. The purpose of this research is to assess whether computer simulation can be used to overcome shortcomings in laboratory testing for relative density of soils. By reducing the segregation of the sample and reducing the inconsistency of the operator it is hoped that variability in the laboratory testing can also be lessened. Of the three parameters maximum void ratio is the focus of this research.
Methods of Investigation
The computer software used for this research is S3D PorouStructure developed by Smart Imaging Technologies. This program was developed for modeling and analyzing pores and porous structures. The capabilities of this program consist of 3-dimensional modeling and measure the geometrical parameters of the pores of the model.
The particle distributions used for this research were chosen to represent a range of values for the coefficient of uniformity (Cu). The coefficient of uniformity is a descriptor of the soil’s gradation. As the particles become a uniform size Cu approaches 1.
Results and Interpretation
The results of the various simulations were plotted with the uniformity coefficient (Cu) versus the maximum void ratio (emax). Distributions 1-4 are normally distributed and the trend of the results tends to show that as emax decreases Cu increases, which was to be expected. The results of B, E, and F, which are skewed from being normally distributed, tend to follow the some general trend. There was no apparent trend with Cc.
Conclusions
The minimum density or maximum void ratio of spheres is represented well using computer simulation. Charts can be constructed using these results to correlate between maximum void ratio and the coefficient of uniformity. If the coefficient of uniformity of a soil can be quantified then it can be used to determine the maximum void ratio from charts. If the maximum void ratio could be determined from charts with the same degree or greater precision than laboratory tests then this representation could be used as a tool in determining relative density.
It is recommended that additional work be performed. This continued research should consider particles that are non-spherical and take into account the effects kinematic disturbances have on the packing of particles to estimate minimum void ratio or maximum density.
I have enjoyed working on this research. There have been times that the process has become frustrating because things didn’t work as expected. The most frustrating was the computational time for each of the simulations. Some of the simulations took several days to run. Working on a one on one basis with Dr. Gerber has helped me to improve my writing and creative thinking. I look forward to continue working on research for a thesis with Dr. Gerber
References
- Holtz, W.G. (1973). “The Relative Density Approach—Uses, Testing Requirements, Reliability, and Shortcomings.” Evaluation of Relative Density and Its Role in Geotechnical Projects Involving Cohesionless Soils, ASTM STP 523, American Society for Testing and Materials, 5-17.
- ASTM. (2000b). “Standard Test Methods for Minimum Index Density and Unit Weight of Soils and Calculation of Relative Density.” D 4254-00, West Conshohocken, Pa.
- ASTM. (2000a). “Standard Test Methods for Maximum Index Density and Unit Weight of Soils Using a Vibratory Table.” D 4253-00, West Conshohochen, Pa.
- Tavenas, F.A., Ladd, R.S., La Rochelle, P. (1973). “Accuracy of Relative Density Measurements: Results of a Comparative Test Program.” Evaluation of Relative Density and Its Role in Geotechnical Projects Involving Cohesionless Soils, ASTM STP 523, American Society for Testing and Materials, 18-60.