User:Egm3520.s13.Jeandona/Direct Shear Test Calculations and Variables

=Direct Shear Test=

Summary:
$$\tau = \sigma' tan \phi'+c'$$

$$\phi'$$

$$\sigma'$$

$$\tau$$

Calculations:
$$ V=A \cdot H$$ \begin{equation} V=A \cdot H \end{equation}

$$Ex: \mbox{ } V=(4.897)(1.104) \mbox{ } = \mbox{ } 5.406 in^3$$

$$A=\pi(\frac{d}{2})^2$$

$$\mbox{ } \mbox{ } Ex: \mbox{ } A=\pi(\frac{6.342 cm \cdot \frac{1 in}{2.54 cm}}{2})^2 \mbox{ } = 4.897 \mbox{ }$$

$$\sigma' = \frac{N}{A} \mbox{ }(psi)$$

$$\mbox{ } \mbox{ } Ex: \mbox{ } \sigma' = \frac{10 \cdot 8 + 483.30}{4.897}=115.03 \mbox{ }psi$$

$$\tau = \frac{T}{A} \mbox{ }(psi)$$

$$\mbox{ } \mbox{ } Ex: \mbox{ } \tau = \frac{T}{A} \mbox{ }(psi)$$

$$\rho = \frac{m}{A \cdot H} \mbox{ } (\frac{g}{cm^3})$$

$$\mbox{ } \mbox{ } Ex: \mbox{ } \rho = \frac{150.00g}{5.406 in^3} \cdot \frac{1 in^3}{16.387cm^3} \mbox{ } = \mbox{ } 1.693 \frac{g}{cm^3}$$

$$\gamma = \rho \cdot g \mbox{ } (pcf)$$

$$\mbox{ } \mbox{ } Ex: \mbox{ } \gamma = 1.693 \frac{g}{cm^3} \cdot \frac{1 Ib}{453.59 g} \cdot \frac{16.387 cm^3}{1in^3} \cdot \frac{1728 in^3}{1 ft^3} \mbox{ }= \mbox{ } 105.69 pcf$$

$$t= (\frac{0.001 \frac{in}{div}}{0.05 \frac{in}{min}})(160 div) \mbox{ } = \mbox{ } 3.2 min$$

Legend of Variable:
$$\sigma':$$ Normal stress ($$psi$$)

$$\tau:$$ Shear stress ($$psi$$)

$$\rho:$$ Density ($$\frac{g}{cm^3}$$)

$$\gamma:$$ Unit Weight ($$pcf$$)

$$N:$$ Normal force on sample; tentimes hanger weight plus mass of the platen ($$Ibs$$)

$$T:$$ Shear force on sample, from proving ring ($$Ibs$$)

$$d:$$ Sample diameter ($$in$$)

$$A:$$ Sample cross sectional area ($$in^2$$)

$$V:$$ Sample volume ($$in^3$$)

$$H:$$ Initial height of soil sample ($$in$$)

$$\delta:$$ Horizontal displacement of box ($$in$$)

$$\Delta:$$ Vertical displacement of platen ($$in$$)

$$m:$$ Mass of sand ($$g$$)

$$t:$$ Length of test ($$min$$)