# SOIL MECHANICS

## HOMEWORK ASSIGNMENTS

### Correlation of Maximum Dry Unit Weight and Grain Size of Granular Soils:

It is practically impossible to predict accurately the maximum dry unit weight of compaction of soil due to the existence of several variables. So any type of empirical or semiempirical formulation for prediction of the maximum value of Yd has to be considered as an estimation only. Korfiatis and Manikopoulos (1982) have developed a parametric relationship for the prediction of the maximum modified Proctor dry unit weight of compaction of granular soils. This can be explained by referring to Figure 1, which is a typical grain-size distribution curve of a soil in which F is equal to the percent of fines (that is, the percent of soil passing through the no. 200 sieve). D50 is the mean grain size which corresponds to 50% finer. The slope

of the grain-size distribution curve in a log-normal plot at point A can be given as

The definitions of D1 and D2 are shown in Figure 1. Once the magnitude of S is determined, the value of Yd(max) (based on the modified Proctor test) can be estimated as

Based on statistical relationships,

a 0.6682 + 0.0101

c 0.8565 + 0.0238

d 0.3282 + 0.0267

q 0.7035 + 0.0477

*************************************

Sand Cone Method (ASTM Designation D-7556):

The sand cone consists of a glass or plastic jar with a metal cone attached at its top (Figure 2). The jar with the cone is filled with a poorly graded dry Ottawa sand. The weight of the jar, cone, and the sand filling the jar is determined (W1). In the field, a small hole is excavated in the area where the soil has been compacted. If the weight of the moist soil excavated from the hole (W2) is determined, and the moisture content of the excavated soil is known, the dry weight of the soil W3 can be obtained as:

where Wc = moisture content

After excavation of the hole, the cone with the sand-filled jar attached to it is placed over the hole (Figure 2). Sand is allowed to flow out of the jar to fill the hole and the cone. After that, the weight of the jar, cone, and the remaining sand in the jar is determined (W4). So

where W5 = weight of sand to fill the hole and cone

The volume of the hole excavated can now be determined as

where Wc = weight of sand to fill the cone only

d(sand) = dry unit weight of sand used

The values of Wc and d(sand) are determined from the calibration done in the laboratory. The dry unit weight of compaction made in the field can now be determined as

Due Date 2/