Geotechnical Engineering and Weight-Volume Relationships

Flashcards reviewing the history of geotechnical engineering and fundamental weight-volume relationships in soil mechanics.

How is soil defined in geotechnical engineering?

Soil is an uncemented aggregate of mineral grains and decayed organic matter with liquid and gas in the empty spaces between the solid particles.

What is the definition of soil mechanics?

Soil mechanics is the branch of science that deals with the study of the physical properties of soil and the behavior of soil masses subjected to various types of forces.

What is soil engineering?

Soil engineering is the application of the principles of soil mechanics to practical problems.

What is geotechnical engineering?

Geotechnical engineering is a subdiscipline of civil engineering that involves natural materials found close to the surface of the earth.

What structure shown in the image is a famous historical example of a soil-bearing capacity failure constructed prior to the 18th century?

The Leaning Tower of Pisa in Italy.

During the Preclassical Period of Soil Mechanics (1700–1776), what was the natural slope of soil when tipped in a heap called?

The angle of repose.

What contribution did French scientist Charles Augustin Coulomb make during Classical Soil Mechanics–Phase I (1776–1856)?

He used principles of calculus for maxima and minima to determine the true position of the sliding surface in soil behind a retaining wall.

Whose publication in 1857 on earth pressure and equilibrium of earth masses marked the end of Phase I of classical soil mechanics?

William John Macquorn Rankine.

What major study did French engineer Henri Philibert Gaspard Darcy publish during Classical Soil Mechanics–Phase II (1856–1910)?

He published a study on the permeability of sand filters and defined the coefficient of permeability of soil.

During the Modern Soil Mechanics period (1910–1927), how were clay-sized fractions defined?

Clay-sized fractions were defined as the percentage by weight of particles smaller than $2\,\mu m$ (2 microns) in size.

Who developed the stability analysis of undrained saturated clay slopes assuming that the critical sliding surface is the arc of a circle?

Wolmar Fellenius.

Which book published by Karl Terzaghi established a new era in the development of soil mechanics?

Erdbaumechanik auf Bodenphysikalisher Grundlage.

Which major engineering projects did Ralph B. Peck provide consulting for?

Rapid transit systems in Chicago, San Francisco, and Washington D.C., the Alaskan pipeline system, and the Dead Sea dikes.

Why is soil considered a three-phase system?

Because a given volume of soil consists of solid particles and void spaces filled with air, water, or both.

How do dry soil, saturated soil, and moist soil differ regarding their void space?

Dry soil has no water in the void space ($S = 0$), saturated soil has its entire void space filled with water ($S = 1$), and moist soil has its void space partially filled with water.

What is the formula for the total volume $V$ of a soil element?

$V = V_s + V_v = V_s + V_w + V_a$, where $V_s$ is volume of soil solids, $V_v$ is volume of voids, $V_w$ is volume of water, and $V_a$ is volume of air.

What is void ratio ($e$) and its mathematical formula?

Void ratio is the ratio of the volume of voids to the volume of soil solids: $e = \frac{V_v}{V_s}$.

What is porosity ($n$) and its mathematical formula?

Porosity is the ratio of the volume of voids to the total volume: $n = \frac{V_v}{V}$.

What formulas express the conversion between void ratio ($e$) and porosity ($n$)?

$n = \frac{e}{1+e}$ and $e = \frac{n}{1-n}$.

What is degree of saturation ($S$) and its mathematical formula?

Degree of saturation is the ratio of the volume of water to the volume of voids: $S = \frac{V_w}{V_v}$.

What is moisture content ($w$) and how is it defined?

Moisture content (or water content) is the ratio of the weight of water to the weight of soil solids in a given volume of soil: $w = \frac{W_w}{W_s}$.

What is unit weight ($\gamma$) of soil and how is it defined?

Unit weight (also called moist unit weight) is the weight of soil per unit volume: $\gamma = \frac{W}{V}$.

What is dry unit weight ($\gamma_d$) of soil?

Dry unit weight is the weight per unit volume of soil, excluding water: $\gamma_d = \frac{W_s}{V}$.

What is the formula for unit weight ($\gamma$) in terms of specific gravity ($G_s$), moisture content ($w$), void ratio ($e$), and unit weight of water ($\gamma_w$)?

$\gamma = \frac{(1+w)G_s \gamma_w}{1+e}$.

What is the formula for dry unit weight ($\gamma_d$) in terms of specific gravity ($G_s$), void ratio ($e$), and unit weight of water ($\gamma_w$)?

$\gamma_d = \frac{G_s \gamma_w}{1+e}$.

What is saturated unit weight ($\gamma_{\text{sat}}$) and its formula in terms of void ratio?

It is the unit weight when void spaces are completely filled with water ($S = 1$), expressed as $\gamma_{\text{sat}} = \frac{(G_s + e)\gamma_w}{1+e}$.

What is submerged or buoyant unit weight ($\gamma_b$ or $\gamma'$) and how is it calculated?

It is the effective unit weight of soil when submerged in water, calculated as $\gamma_b = \gamma_{\text{sat}} - \gamma_w$.

What are the standard SI units for unit weight ($\gamma$) and mass density ($\rho$) of soil?

The standard SI unit for unit weight is kilo Newtons per cubic meter ($\text{kN/m}^3$) and for mass density is kilograms per cubic meter ($\text{kg/m}^3$).

What does relative density ($D_r$) measure?

Relative density indicates the in-situ denseness or looseness of granular soil.

What is the formula for relative density ($D_r$) in terms of void ratio?

$D_r = \frac{e_{\text{max}} - e}{e_{\text{max}} - e_{\text{min}}}$, where $e_{\text{max}}$ is void ratio in the loosest state, $e_{\text{min}}$ is void ratio in the densest state, and $e$ is in-situ void ratio.

What is the formula for relative density ($D_r$) in terms of dry unit weight?

$D_r = \left[ \frac{\gamma_d - \gamma_{d(\text{min})}}{\gamma_{d(\text{max})} - \gamma_{d(\text{min})}} \right] \left[ \frac{\gamma_{d(\text{max})}}{\gamma_d} \right]$.

What are typical lower and upper practical limits for relative density ($D_r$) in soils?

In-place soils seldom have relative densities less than $20\%$ to $30\%$, and compacting granular soil to a relative density greater than about $85\%$ is difficult.