16.9: Chapter 9- Hyperbaric Rock Cutting

Last updated
Save as PDF

Page ID: 35241

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

16.9.1. MC: Soil Mechanical Parameters

Which material/environmental properties play a dominant role in the hyperbaric cutting of rock/stone at high cutting velocities?

The bold green answers are true.

The ratio of the hydrostatic pressure to the cohesion of the rock.
The external shear strength or adhesion of the rock.
The external friction angle of the rock.
The hydrostatic pressure to adhesion ratio.
The permeability of the rock.
The tensile strength of the rock.
The shear strength or cohesion of the rock.
The internal friction angle of the rock.

1.1.1 Exercise 2

Consider a rock with a compressive strength of 30 MPa and a tensile strength of -2 MPa. The angle of internal friction is 20 degrees, the angle of external friction is 13 degrees. A blade angle of 60 degrees is used and a blade height of 0.1 m and blade width w=0.05 m. The layer thickness is 0.01 m. The water depth is 1000 m.

What is the hydrostatic pressure to cohesion ratio r_z?

The cohesion or shear strength is according to equation (8-117) (eqn 8.77, 1^st edition):

\(\ \mathrm{c=\frac{U C S}{2} \cdot\left(\frac{1-\sin (\varphi)}{\cos (\varphi)}\right)=10.5} \text{ MPa}\)

The hydrostatic pressure to cohesion ratio r_z is according to equation (9-29) (eqn 9-27, 1^st edition):

\(\ \mathrm{r}_{\mathrm{z}}=\frac{\rho_{\mathrm{l}} \cdot \mathrm{g} \cdot(\mathrm{z}+\mathrm{1 0})}{\mathrm{c}}=\frac{\mathrm{1 .0 2 5} \cdot \mathrm{9 . 8 1} \cdot(\mathrm{1 0 0 0}+\mathrm{1 0})}{\mathrm{1 0 5 0 0}}=\mathrm{0 .9 6 7}\)

What is the mobilized blade height h_b,m?

The ratio h_b,m/h_i=0.65, see Figure 9-17 (Figure 9-16, 1^st edition).

\(\ \mathrm{h}_{\mathrm{b}, \mathrm{m}}=\mathrm{0 .6 5} \cdot \mathrm{h}_{\mathrm{i}}=\mathrm{0. 6 5} \cdot \mathrm{0 .0 1}=\mathrm{0 .0 0 6 5}(\mathrm{m})\)

So what is the cutting mechanism with the original blade height of 0.1 m?

Since the mobilized blade height h_b,m is smaller than the blade height h_b, the Curling Type will occur.

What are the horizontal and the vertical cutting forces?

The horizontal force coefficient is about 2.9 according to Figure 9-19 (Figure 9-18, 1^st edition) and the vertical force coefficient is about 0.68 Figure 9-20 (Figure 9-19, 1^st edition).

\(\ \begin{array}{left} \text{Horizontal }& \mathrm{F_{h}=\lambda_{H C} \cdot c \cdot h_{i} \cdot w=2.9 \cdot 10500 \cdot 0.01 \cdot 0.05=15.23} \quad(\mathrm{kN})\\
\text{Vertical } & \mathrm{F_{v}=\lambda_{V C} \cdot c \cdot h_{i} \cdot w=0.68 \cdot 10500 \cdot 0.01 \cdot 0.05=3.57}\quad(\mathrm{kN})\end{array}\)

What is the shear angle β?

The shear angle is β=41°, according to Figure 9-18 (Figure 9-17, 1^st edition).