Geotechnical Engineering $($CEGR $3278)$

Phase Diagram Relationships

Example $1$: The specific gravity of the soil solids of a saturated sample is $2\mathrm{.}75.$ The porosity of the specimen is $30\%.$ What is the total unit weight and density of this soil specimen?

GIVEN:

$,s=2\mathrm{.}75=$

spectlity $G_s=2\mathrm{.}75=\frac{y_s}{y_w}=\frac{w_s}{v_s}(\frac{1}{y_w})=\frac{w_s}{v_s}(\frac{1}{9\mathrm{.}81})$

$2\mathrm{.}75=\frac{y_5}{y_w}=9\mathrm{.}81$

$yw$

$n\%=30\%=\frac{V_v}{v}100=\frac{v_w}{V}100$ saturated

$y_s=26\mathrm{.}971$

$cs=\frac{P_s}{P_w}$

$y_w=9\mathrm{.}81\frac{kn}{m^3}=w_w,V=\mathrm{.}30=\frac{V_v}{(V)}$

$2\mathrm{.}75=\frac{ps}{100}$

$S^{0,}0=\frac{v_w}{v_v}100=100,y_w=\frac{w_w}{V_w}$

$p_s=275$

Yis

FIND:

SOLUTION:

Phase Diagram Solution Method

Determine number of phases and DRAW phase diagram

Include all given info on the diagram $($weight or mass, volume$)$

$W_a$ and $M_a=0($negligible$)$

Define all EQUATIONS and variables

${}_w$ and ${}_w$ are KNOWN CONSTANTS $-$ write out full equation!

Break down the $G_s$ equation if this value is given

Don't confuse subscripts: ${}_d{}_s$

Don't confuse mass with weight

ASSUME a volume $($but only if needed$)$

MANIPULATE the equations to soLve