Soil Mechanics I

Homework No $2$

Consider a container with volume equal to $1m^3($that is$,$ the total volume is $1m^3),$ filled with wet

sand. The specific gravity of the sand is $2\mathrm{.}65.$ The net weight of the wet sand is $18\mathrm{.}63kN,$ the dry

weight of the sand is $16\mathrm{.}57kN.$ Find:

a$.$ water content, $w$

b$.$ the dry unit weight, ${}_d$

c$.$ porosity, $n$

d$.$ degree of saturation, $S$

e$.$ saturated unit weight, ${}_{\text{s}\text{a}\text{t}},$ corresponding to a degree of saturation of $100\%.$

For a saturated soil, given $w=40\%$ and $G_s=2\mathrm{.}71,$ determine the saturated and dry unit weights in

$pcf$ and $k\frac{N}{m^3}.$

The soil from a pit has the following in situ properties: $w=12\%,e=0\mathrm{.}54,G_s=2\mathrm{.}65.$ This soil will

be used for the construction of an embankment, which will have a total volume of $44,000m^3$ at

completion. The soil will be compacted $($this operation densifies the material by reducing void size

without changing the amount of solid particles or water$)$ during construction to a dry unit weight ${}_d=$

$18\mathrm{.}3k\frac{N}{m^3}.$ The soil is transported from the pit to the embankment location by trucks. Each truck can

carry $62kN$ of soil. Determine:

a$.$ degree of saturation, total unit weight in situ, dry unit weight in situ;

b$.$ the number of truck loads necessary to transport all the soil;

c$.$ the volume excavated in the pit.

A sand having an initial porosity of $37\%$ is loaded isotropically to $3000$kPa. At this load, e $=0\mathrm{.}290$

and the sand occupies a volume of $73c{m}^3.$ What was the initial volume of sand?

For a given soil, the following are given: $G_s=2\mathrm{.}67,$ total unit weight ${}_t=17\mathrm{.}6k\frac{N}{m^3}$ and water

content, $w=10\mathrm{.}8\%.$ Determine:

a$.{}_d(k\frac{N}{m^3})$

b$.$ Void ratio and porosity, $e$ and $n$

c$.$ Degree of saturation, $S$