CE 240Soil Mechanics & Foundations

Lecture 1

Historical Perspective of Soil Mechanics and Geotechnical Engineering

Fundamentals of math and physics for geotechnical engineering

(Das, Ch. 1)

Outline of this lecture

1, go through the syllabus

2, labs and homeworks

3, Historical Perspective of Soil Mechanics and Geotechnical Engineering

4, Fundamentals of math and physics for geotechnical engineering

A Syllabus of CE 240: Soil Mechanics & FoundationsFall Semester, 2006

Course number: CE 240 (3 Credit Units)Instructor: Prof. Lanbo Liu, Lanbo.Liu@ uconn.eduTA: Matthew Pruett, matthew.pruett@huskymail.uconn.eduWeb: http://www.engr.uconn.edu/~lanboLecture: Monday, Wednesday, and Friday, 11:00-11:50 amLecture Location: Castleman Building, Room 212Lab: Thursday (one in the following 3 sessions: 8-11, 11-2, 2-5)Lab Location: Castleman Building, Room 105Textbook: Principles of Geotechnical Engineering, 6th Edition, by B. M. Das, Thomson Press, 2006Grading:Lab: 30%; Midterm I: 20%; Midterm II: 20%;Final: 30%

Aims:

1, To describe soil as an engineering material and to understand the nature of stresses induced in the soil and by the soil;

2, To give an appreciation of the function and forms of shallow and deep foundations;

3, To analyze bearing capacity and settlements of foundations;

4, To consider the relevance of site and ground investigation to soil and foundation engineering.

(08/28) Mon. Introduction and the syllabus, history of Geotechnical Engineering.(08/30) Wed. Rock cycle, rock types, and origin of soil.(09/01) Fri. Soil particles.Reading: Chapter 1, 2

(09/04) Mon. Official holiday of the Labor Day, no class.(09/06) Wed. weight-volume relationships.(09/07) Thu. Lab 01:(09/08) Fri. Soil consistency.Reading: Chapter 3

(09/11) Mon. Atterberg limits(09/13) Wed. Engineering classification of soil(09/14) Thu. Lab 02: (09/15) Fri. Soil compaction.Reading: Chapter 4, 5

(09/18) Mon. Soil compaction.(09/20) Wed. Proctor test (09/21) Thu. Lab 03:(09/22) Fri. Compaction techniques.Reading: Chapter 5

(09/25) Mon. Permeability I.(09/27) Wed. Permeability II.

(09/29) Fri. Midterm Exam IReading: Chapter 6

(10/02) Mon. Groundwater flow, Seepage I.(10/04) Wed. Groundwater flow, Seepage II.(10/05) Thu. Lab 04:(10/06) Fri. Groundwater flow, Seepage II.Reading: Chapter 7

(10/09) Mon. In situ stresses I.(10/11) Wed. In situ stresses II.(10/12) Thu. Lab 05:(10/13) Fri. In situ stresses III.Reading: Chapter 8(10/16) Mon. Stress in a soil mass I.(10/18) Wed. Stress in a soil mass II. (10/19) Thu. Lab 06:(10/20) Fri. Stress in a soil mass III.Reading: Chapters 9

(10/23) Mon. Compressibility of soil I.(10/25) Wed. Compressibility of soil II.(10/26) Thu. Lab 07:(10/27) Fri. Compressibility of soil III.Reading: Chapter 10

(10/30) Mon. Shear strength of soil I.(11/01) Wed. Shear strength of soil II.(11/03) Fri. Midterm Exam II.Reading: Chapter 11

(11/06) Mon. Lateral Earth Pressure I.(11/08) Wed. Lateral Earth Pressure II.(11/09) Thu. Lab 08:(11/10) Fri. Lateral Earth Pressure III.Reading: Chapter 12, 13

(11/13) Mon. Slope stability I.(11/15) Wed. Slope stability II.(11/16) Thu. Lab 09:(11/17) Fri. Slope stability III.Reading: Chapter 14

(11/27) Mon. Soil-bearing capacity.(11/29) Wed. foundations.(12/01) Fri. Soil-bearing capacity for shallow foundations.Reading: Chapter 15

(12/04) Mon. Subsoil Exploration I.(12/06) Wed. Subsoil Exploration II.(12/08) Fri. Course summary and reviews.Reading: Chapter 17

Labs:1, 12-13 students form a group, 3 groups for the class of CE240 fall semester 2006.2, Safety first: work on your lab, no fool around.3, work out the lab by group effort, but submit the lab report (or data sheet) individually and the grade is on individual base.4, Towards the end of the semester, there may be 1-2 labs will be graded based on group effort.

HWs:There will be HW assignment, but no grading. I will post the

right answers on my web page upon the due date. Midterms and final exam will cover the contents covered by HWs and labs.

Historical Perspective of Soil Mechanics and Geotechnical Engineering

The record of the first use of soil as a construction material by man kind is lost in antiquity.

In true engineering sense, there is no ‘Geotechnical Engineering’ prior to the 18th Century.

One of the most famous example of problems related to soil bearing capacity and foundations in the construction of structures prior to 18th century is the Leaning Tower of Pisa in Italy. The construction of the Tower began in 1173 A.D. and last over 200 years.

The Leaning Tower of Pisa, Italy. Morning, 1 March 2004. SW view

Height: 54 m;Max tilt: 5 m out of plumbTilt direction: E, N, W, and S.Weight: 15,700 tons;Base: φ = 20 m;Reason: a weak clay layer at 11 m depthSolution: excavation of soil from north side for about 70 tons.

Tilting of Garisenda Tower (left) in Bologna, Italy (built in 12th Century)

Study of soil behavior in a more methodical manner in the area of geotechnical engineering started in the early part of the 18th century, and last to 1927. The development of soil mechanics can be divided into four phases, according to Skempton (1985):

1, Preclassical period (1700-1776);rough classification of soils;

2, Classical soil mechanics – Phase I (1776-1856)started from French scientist Coulomb’s presentation on determining the sliding surface in soil behind a retaining wall;ended by the publication of Rankine’s paper on earth lateral pressure. Rankin’s theory is a simplification of Coulomb’s theory.

3, Classical soil mechanics – Phase II (1856-1910)started from the publication of a paper on the permeability of sand filters by French engineer Darcy in 1856.

4, Modern soil mechanics (1910-1927)marked by a series of important studies and publications related to the mechanic behavior of clays, most noticeable,Atterberg (1911) on consistency of clayey soils, the Atterberg limits;Bell (1915) on lateral pressure and resistance of clays;Terzaghi (1925) on theory of consolidation for clays.

Geotechnical Engineering after 1927

The development of Geotechnical Engineering as a branch of Civil Engineering is absolutely impacted by one single professional individual – Karl Terzaghi (1883-1963). His contribution has spread to almost every topic in soil mechanics and geotechnical engineering covered by the test book:

Effective stress (Ch. 8);Elastic stress distribution (Ch. 9);Consolidation settlement (Ch. 10);Shear strength (Ch. 11);in situ testing (Ch. 17).

Born: October 2, 1883 in Prague

Died: October 25, 1963 in Winchester, Massachusetts

He was married to Ruth D. Terzaghi, a geologist.

He won the Norman Medal of ASCE four times (1930, 1943, 1946, and 1955).

He was given nine honorary doctorate degrees from universities in eight different countries.

He started modern soil mechanics with his theories of consolidation, lateral earth pressures, bearing capacity, and stability.

“ Few people during Terzaghi’s lifetime would have disagreed that he was not only the guiding spirit in soil mechanics, but that he was the clearing house for research and application throughout the world.”

- Ralph B. Peck

Photo: Acceptance remarks from life long educator Ralph B. Peck at the OPAL & 41st Annual OCEA Awards gala held on April 28, 2001, Washington, DC.

Fundamentals

• Basic mathematics– Derivation, integration, differential equation

• Basic mechanics– Hooke’s law, and Darcy’s law

• Basic units and constants– Force, pressure, stress, strain, etc.

Definition of The Derivation

The derivative of a function f(x) at the point is given and denoted by

x

f(x)

f’(x)

h

x0

In the table below, u,v, and w are functions of the variable x. a, b, c, and n are constants (with some restrictions whenever they apply). designate the natural logarithmic function and e the natural base for . Recall that .

Integration

∫=b

adxxfy )(

a b

Area=y

f(x)

∫=π

0)sin( dxxy

n Sum of areas ofinscribed rectangles

Sum of areas ofcircumscribed rectangles Average of the Two Sums

2 0 3.14159265 1.570796334 1.11072073 2.68151706 1.896118908 1.58153252 2.36693068 1.97423160

16 1.79722080 2.18991988 1.9935703432 1.90021859 2.09656813 1.9983933664 1.95051100 2.04868577 1.99959839

128 1.97535591 2.02444329 1.99989960256 1.98770306 2.01224674 1.99997490512 1.99385780 2.00612964 1.99999372

1024 1.99693047 2.00306640 1.99999844

Differential equations are the relations with physical basis, and expressed by derivatives of a quantity (usually with physical meanings) with respect to a variable (in physics, usually the space or time).

An example, the differential equation describes the forced, and damped oscillation.

SIdtdIh

dtId

=++ 2002

2

2 ωω

A simplified case for the wave equation is the plane wave propagating in 1 direction, say the x-direction. In this case, the wave equation can be written as

2

2

22

2 1tu

vxu

∂∂

=∂∂ (1)

One solution for a plane wave propagating in an unbounded, uniform medium can be expressed as )cos(0 kxtuu += ω (2) This plane wave can be viewed as the wave generated by a plane source occupying the entire yz-plane to generate wave propagation in the x-direction. In this equation, u0 is the amplitude, ω is the angular frequency; k is called the wave number. We will show the relationship of k with respect to angular frequency ω by demonstrating Eqn (2) does satisfy the 1-D wave equation (1). Taking the secondary derivative of u with respect to space, here the x-coordinate, is

)cos(02

2

2

kxtukxu

+−=∂∂ ω

and putting the second derivative of u with respect to time on the right hand side of Eqn (1) gives

)cos(102

2

2

2

2 kxtuvt

uv

+−=∂∂ ωω

comparing the last 2 equation leads to

v

k ω=

SI Unit System

• SI – Le Systeme International d’Unites• Base units• Derived units

SI base units The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1.

Table 1. SI base units

Base quantityName Symbol

length meter mmass kilogram kgtime second sElectric current ampere Athermodynamic temperature

Kelvin K

amount of substance mole molluminous intensity candela cd

Table 2. Examples of SI derived units

Derived quantityName Symbol

Area Square meter m2

Volume Cubic meter m3

Speed, velocity meter per second m/sAcceleration meter per second

squaredm/ s2

Density kilogram per cubic meter kg/m3

Specific volume cubic meter per kilogram m3/kgAmount-of-substance concentration

mole per cubic meter mol/m3

Luminance candela per square meter cd/m2

Frequency Revolution per second 1/secAngular frequency Radian per sec Radian/secWave number Radian per meter Radian/mWave length meter m

Some extremes of length, mass, and time:Length:

The length of the major axis of the Milky Way is 6 x 1019 meter;

The size of a virus is about 10-8 meter (0.01 micron);

Mass:The mass of the Milky Way is ~ 1041 kg;The mass of the Earth is ~ 1024 kg;The mass of the virus is ~ 10-13 kg;The mass of the electron is ~ 10-30 kg;

Time:The earth was formed 4.61 billion (109)years ago;1 year=365 x 24 x 60 x60 = 3.1536 x 107 seconds.The sampling rate of the ground penetrating radar can be as short as 10-10 second (0.1 nanosec).

Some basic constants:

Gravitational acceleration: g = 9.81 m/sec/sec

Universal attraction constant: G = 6.67 x 10-11 Nm2/kg2

The base of the natural logarithm: e = 2.71828

Bulk density of crustal material: ρ = 2.5-2.7 g/cm3

sound wave velocity in the air: v = 340 m/secsound wave velocity in water: v = 1500 m/secThe speed of light: c = 300,000,000 m/sec

Hooke’s law in macroscopic form

kuf −=

Hooke’s law in microscopic form

εσ M=

Physics of Groundwater Flow: Darcy’s law

dxdHk

dxdP

gkqw

−=−=ρ

x

H1 H2

Water flow

Common mechanic properties:

Density;

Elastic properties:

- elastic modulii

stress:force per unit area;

Special case: stress in fluid is called pressure, the stress at a given point in all directions are the same – isotropic stress.

Strain: deformation in a unit length, area, or volume.

Young’s modulus E

Young’s modulus is the stress needed to compress the solid to shorten in a unit strain.

Poisson’s ration ν

Poisson’s measures the relativity of the expansion in the lateral directions and compression in the direction in which the uni-axial compression applies.

zzzzAFE

/// 1

∆=

∆=

σ

zzrr

//

∆∆

−=ν

Bulk Modulus K

Imagine you have a small cube of the material making up the medium and that you subject this cube to pressure by squeezing it on all sides. If the material is not very stiff, you can image that it would be possible to squeeze the material in this cube into a smaller cube. The bulk modulus describes the ratio of the pressure applied to the cube to the amount of volume change that the cube undergoes. If k is very large, then the material is very stiff, meaning that it doesn't compress very much even under large pressures. If K is small, then a small pressure can compress the material by large amounts. For example, gases have very small Bulk Modulus . Solids and liquids have large Bulk Modulus.

vvAFK

//

∆= ∆v

σ

Shear Modulus µ

The shear modulus describes how difficult it is to deform a cube of the material under an applied shearing force. For example, imagine you have a cube of material firmly cemented to a table top. Now, push on one of the top edges of the material parallel to the table top. If the material has asmall shear modulus, you will be able to deform the cube in the direction you are pushing it so that the cube will take on the shape of a parallelogram. If the material has a large shear modulus, it will take a large force applied in this direction to deform the cube. Gases and fluids can not support shear forces. That is, they have shear modulii of zero. From the equations given above, notice that this implies that fluids and gases do not allow the propagation of S waves.

xyAF

//

∆=µ

Shear Modulus µ (cont.)

yxAF

//

∆=µ

Seismic wave (elastic wave) Velocities related to material properties:

Vp- P-wave (compressive wave) velocityVs- S-wave (shear wave) velocity

So, seismic velocities are determined by the mechanic properties of the materials in which the seismic waves propagate through.

From: Sheriff and Geldart, Exploration Seismology, p69.

Readings: Textbook by Das: Chapter 1.