# 16.2: Chapter2- Basic Soil Mechanics

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

# 16.2.1. MC: Mohr Circles 1

Which of the following statements are true?

The bold green answers are true.

1. The Mohr circle gives the relation between normal stress and tensile stress.

2. In the τ-σ diagram for soil the positive horizontal axis gives tensile stress.

3. In the τ-σ diagram for soil the positive horizontal axis gives compressive stress.

4. The Mohr circle gives the relation between normal stress and shear stress.

5. In the τ-σ diagram for steel the positive horizontal axis gives compressive stress.

6. In the τ-σ diagram for steel the positive horizontal axis gives tensile stress.

7. In the Mohr circle real angles are shown by a factor 2.

8. In the Mohr circle real angles are shown by a factor 1/2.

# 16.2.2. MC: Mohr Circles 2

Which of the following statements are true?

The bold green answers are true.

1. The Mohr circle gives the relation between normal stress and shear stress.

2. In the τ-σ diagram for soil the positive horizontal axis gives tensile stress.

3. In the τ-σ diagram for steel the positive horizontal axis gives compressive stress.

4. On the plane of a principle normal stress there is no shear stress.

5. The largest shear stress is always on a plane with an angle of 45 degrees with respect to the principal stresses.

6. In the Mohr circle the angle between the two principal stresses is 180 degrees.

7. Mohr circles can cross the failure line/curve.

8. Tensile failure occurs on a plane with an angle of 90 degrees with the plane with the largest shear stress.

# 16.2.3. MC: Mohr Circles 3

Which of the following statements are true?

The bold green answers are true.

1. The Mohr circle is based on a force equilibrium.

2. The Mohr circle is based on a stress equilibrium.

3. In the Mohr circle real angles are shown by a factor 2.

4. In the Mohr circle real angles are shown by a factor 1/2.

5. With 1 Mohr circle the angle of internal friction can be determined.

6. At least 2 (different confining pressures) Mohr circles are required to determine the angle of internal friction.

7. Fundamentally the Mohr circle is valid in a point.

8. Fundamentally the Mohr circle is valid in an area.

# 16.2.4. MC: Active/Passive Soil Failure 1

Which of the following statements are true?

The bold green answers are true.

1. Passive soil failure is the failure where the soil is passive, the outside world is active.

2. Active soil failure is the failure where the outside world is active, the soil is passive.

3. Passive soil failure is the failure where the soil is active, the outside world is passive.

4. Active soil failure is the failure where the outside world is passive, the soil is active.

5. The stresses with passive failure are larger than with active failure.

6. The stresses with active failure are larger than with passive failure.

7. Excavating soil in dredging is a typical example of active failure.

8. Excavating soil in dredging is a typical example of passive failure.

# 16.2.5. MC: Active/Passive Soil Failure 2

Which of the following statements are true? (Active failure means the horizontal stress is smaller than the vertical stress, passive failure means the horizontal stress is larger than the vertical stress).

The bold green answers are true.

1. The failure of a dike, because it’s too high, is passive failure.

2. At low tide a quay wall is pushed into to the water, this is active failure.

3. A bulldozer pushes a hole in a dike, this is active failure.

4. A very heavy truck drives over a dike. The dike collapses under the weight of the truck. This is active failure.

5. Cutting processes in general are an example of active failure.

6. Forces occurring with active failure are always larger than with passive failure.

7. The cutting process of a cutter head is a typical example of passive failure.

8. The cutting process of a clamshell is a typical example of active failure.

# 16.2.6. MC: Active/Passive Soil Failure 3

Which of the following statements are true? (Active mode means the horizontal stress is smaller than the vertical stress, passive mode means the horizontal stress is larger than the vertical stress).

The bold green answers are true.

1. Settled or sedimented sand is in active mode.

2. Settled or sedimented sand is in passive mode.

3. Glacial sand, after the ice has melted is in passive mode.

4. Glacial sand, after the ice has melted is in active mode.

5. Glacial sand, when the layer of ice is the thickest is in active mode.

6. Glacial sand, when the layer of ice is the thickest is in passive mode.

7. Sand with a building on top is in passive mode.

8. Sand with a building on top is in active mode.

# 16.2.7. MC: Active/Passive Soil Failure 4

Which of the following statements are true?

The bold green answers are true.

1. The active soil pressure coefficient increases with increasing internal friction angle.

2. The passive soil pressure coefficient increases with increasing internal friction angle.

3. The active soil pressure coefficient decreases with increasing internal friction angle.

4. The passive soil pressure coefficient decreases with increasing internal friction angle.

5. Passive soil failure is the failure where the soil is passive, the outside world is active.

6. Active soil failure is the failure where the outside world is active, the soil is passive.

7. Passive soil failure is the failure where the soil is active, the outside world is passive.

8. Active soil failure is the failure where the outside world is passive, the soil is active.

# 16.2.8. Calc.: Bulldozer 1

A bulldozer with a blade height of 0.5 m and a blade width of 3 m and a blade angle of 90 degrees is pushing sand. The internal friction angle of the sand is 45 degrees. The sand has no cohesion or adhesion and the friction between the sand and the blade is assumed to be zero, so a smooth blade. The bulldozer has a maximum forward speed of 1.5 m/sec.

1. What is the coefficient of passive failure for this sand?

$$\ \mathrm{K_{p}=\frac{1+\sin (\varphi)}{1-\sin (\varphi)}=\frac{1+\sin (\pi / 4)}{1-\sin (\pi / 4)}=5.826}\quad(-)$$

2. What is the pushing force of the bulldozer?

The density of the dry sand ρs with 40% porosity is about 1.6 ton/m3.

$$\ \mathrm{F}=\frac{\mathrm{1}}{2} \cdot \rho_{\mathrm{s}} \cdot \mathrm{g} \cdot \mathrm{h}^{2} \cdot \mathrm{w} \cdot \mathrm{K}_{\mathrm{p}}=\frac{\mathrm{1}}{2} \cdot \mathrm{1 .6} \cdot \mathrm{9 .8 1} \cdot \mathrm{0 .5}^{2} \cdot \mathrm{3} \cdot \mathrm{5 .8 2 6}=\mathrm{3 4. 3}\quad(\mathrm{KN})$$

3. What is the pushing power of the bulldozer?

$$\ \mathrm{P}=\mathrm{F} \cdot \mathrm{v}=34.3 \cdot \mathrm{1 .5}=\mathrm{5 1 .4 5} \quad(\mathrm{kW})$$

4. Suppose a total efficiency of 1/3 of the whole drive system of the bulldozer, what is the installed power of the bulldozer.

$$\ \mathrm{P_{\text {installed }}=\frac{P}{\eta}=\frac{51.45}{0.3333}=154.35} \quad(\mathrm{kW})$$

5. What is the coefficient of active failure of this sand?

$$\ \mathrm{K}_{\mathrm{a}}=\frac{\mathrm{1}-\sin (\varphi)}{1+\sin (\varphi)}=\frac{1-\sin (\pi / 4)}{1+\sin (\pi / 4)}=\mathrm{0 .1 7 1 6}\quad(-)$$

6. What is the force the bulldozer has to exert on the sand not to make it fail in active mode?

$$\ \mathrm{F}=\frac{\mathrm{1}}{2} \cdot \rho_{\mathrm{s}} \cdot \mathrm{g} \cdot \mathrm{h}^{2} \cdot \mathrm{w} \cdot \mathrm{K}_{\mathrm{a}}=\frac{\mathrm{1}}{2} \cdot \mathrm{1 .6} \cdot \mathrm{9 .8 1} \cdot \mathrm{0 .5}^{2} \cdot \mathrm{3} \cdot \mathrm{0 .1 7 1 6}=\mathrm{1 .0 1}\quad(\mathrm{kN})$$

# 16.2.9. Calc.: Bulldozer 2

A bulldozer with a blade height of 1.0 m and a blade angle of 90 degrees is pushing dry sand. The internal friction angle of the sand is 45 degrees. The sand has no cohesion or adhesion and the friction between the sand and the blade is assumed to be zero, so a smooth blade. The bulldozer has a maximum forward speed of 1.0 m/sec. The bulldozer has a maximum pushing force of 100 kN.

1. What is the coefficient of passive failure for this sand?

$$\ \mathrm{K_{p}=\frac{1+\sin (\varphi)}{1-\sin (\varphi)}=\frac{1+\sin (\pi / 4)}{1-\sin (\pi / 4)}=5.826}\quad(-)$$

2. What is the maximum width of the bulldozer blade?

The density of the dry sand ρs with 40% porosity is about 1.6 ton/m3.

$$\ \begin{array}{left}\mathrm{F}=\frac{\mathrm{1}}{2} \cdot \rho_{\mathrm{s}} \cdot \mathrm{g} \cdot \mathrm{h}^{2} \cdot \mathrm{w} \cdot \mathrm{K}_{\mathrm{p}}=\mathrm{10 0} \mathrm{k} \mathrm{N}\\ \mathrm{w}=\frac{\mathrm{1 0 0}}{\frac{1}{2} \cdot \rho_{\mathrm{s}} \cdot \mathrm{g} \cdot \mathrm{h}^{2} \cdot \mathrm{K}_{\mathrm{p}}}=\frac{\mathrm{1 0 0}}{\mathrm{0 . 5} \cdot \mathrm{1 .6} \cdot \mathrm{9 .8 1} \cdot \mathrm{1}^{2} \cdot \mathrm{5 .8 2 6}}=\mathrm{2. 1 8 7} \mathrm{~ m}\end{array}$$

This page titled 16.2: Chapter2- Basic Soil Mechanics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Sape A. Miedema (TU Delft Open Textbooks) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.