User:Egm3520.s13.Jeandona/Unconfined Compression

=Unconfined Compression Test=

Summary:
$$c_u$$

$$q_u$$

$$A$$

$$\tau_{max}$$

Calculations:
$$c_u = \frac{q_u}{2}$$

$$c_u = \frac{8349.1}{2} = 4174.6 psf$$

$$L_o = 7.256 cm \cdot \frac{1 in}{2.54 cm} = 2.857 in$$

$$d = 3.318 cm \cdot \frac{1 in}{2.54cm} = 1.306 in$$

$$M_d = M_{cd}-M_c$$

$$Ex: M_d = 35.34-11.14=24.2g$$

$$M_w = M_{cw}-M_{cd}$$

$$Ex: M_w = 38.93-35.34=3.58g$$

$$A_o = \pi {\frac{d}{2}}^2$$

$$Ex: A_o = \pi {\frac{1.306}{2}}^2 = 1.34in^2$$

$$w = \frac{M_w}{M_d}$$

$$Ex: w = \frac{3.58}{24.2} = 14.8%$$

$$A = \frac{A_o}{1-\epsilon_a}$$

$$Ex: A = \frac{1.34in^2 \cdot \frac{1 ft^2}{144 in^2}}{1-0.00175}=0.00932 ft^2$$

$$\epsilon_a = \frac{ \delta}{L_o}$$

$$Ex: \epsilon_a = \frac{0.005 in}{2.857 in} = 0.00175$$

$$\sigma_a = \frac{P}{A}$$

$$Ex: \sigma_a = \frac{28.49 Ibs}{0.00929 ft^2} = 3066.89 psf$$

$$\gamma = \frac{M_s}{A_o L_o (1+w)}$$

$$Ex: \gamma = \frac{124.94g}{1+0.148} \cdot \frac{1 Ib}{453.593g} \cdot \frac{1}{1.34in^2 \cdot 2.857in} \cdot \frac{1728 in^3}{1 ft^3} = 108.30 pcf$$

$$P = 94 div \cdot \frac{0.3031}{1 div} = 28.49 Ibs$$

Variables:
$$c_u:\text{shear strength (psf)}$$

$$q_u:$$ unconfined compressive strength (psf)

$$L_o:$$ initial length of sample(in)

$$d:$$ initial diameter of sample (in)

$$A_o:$$ initial cross-sectional area of sample (in2)

$$A:$$ corrected area of sample (in2)

$$\epsilon_a:$$ axial strain (%)

$$\sigma:$$ axial stress (psf)

$$C:$$ undrained shear strength (psf)

$$M_s:$$ mass of sample (g)

$$M_c:$$ mass of Can (g)

$$M_{cw}:$$ mass of Can + Wet soil (g)

$$M_{cd}:$$ mass of Can + Dry soil (g)

$$M_d:$$ mass of dry soil (g)

$$M_w:$$ mass of water (g)

$$w:$$ water content (%)

$$\gamma:$$ unit weight (pcf)

$$P:$$ proving ring force