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geotechnical engineering (soil mechanics)

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geotechnical engineering (soil mechanics)

  1. 1. Length: 1 ft ϭ 0.3048 m 1 ft ϭ 30.48 cm 1 ft ϭ 304.8 mm 1 in. ϭ 0.0254 m 1 in. ϭ 2.54 cm 1 in. ϭ 25.4 mm Area: 1 ft2 ϭ 929.03 ϫ 10Ϫ4 m2 1 ft2 ϭ 929.03 cm2 1 ft2 ϭ 929.03 ϫ 102 mm2 1 in.2 ϭ 6.452 ϫ 10Ϫ4 m2 1 in.2 ϭ 6.452 cm2 1 in.2 ϭ 645.16 mm2 Volume: 1 ft3 ϭ 28.317 ϫ 10Ϫ3 m3 1 ft3 ϭ 28.317 ϫ 103 cm3 1 in.3 ϭ 16.387 ϫ 10Ϫ6 m3 1 in.3 ϭ 16.387 cm3 Section 1 in.3 ϭ 0.16387 ϫ 105 mm3 modulus: 1 in.3 ϭ 0.16387 ϫ 10Ϫ4 m3 Hydraulic 1 ft/min ϭ 0.3048 m/min conductivity: 1 ft/min ϭ 30.48 cm/min 1 ft/min ϭ 304.8 mm/min 1 ft/sec ϭ 0.3048 m/sec 1 ft/sec ϭ 304.8 mm/sec 1 in./min ϭ 0.0254 m/min 1 in./sec ϭ 2.54 cm/sec 1 in./sec ϭ 25.4 mm/sec Coefficient of 1 in.2 /sec ϭ 6.452 cm2 /sec consolidation: 1 in.2 /sec ϭ 20.346 ϫ 103 m2 /yr 1 ft2 /sec ϭ 929.03 cm2 /sec Force: 1 lb ϭ 4.448 N 1 lb ϭ 4.448 ϫ 10Ϫ3 kN 1 lb ϭ 0.4536 kgf 1 kip ϭ 4.448 kN 1 U.S. ton ϭ 8.896 kN 1 lb ϭ 0.4536 ϫ 10Ϫ3 metric ton 1 lb/ft ϭ 14.593 N/m Stress: 1 lb/ft2 ϭ 47.88 N/m2 1 lb/ft2 ϭ 0.04788 kN/m2 1 U.S. ton/ft2 ϭ 95.76 kN/m2 1 kip/ft2 ϭ 47.88 kN/m2 1 lb/in.2 ϭ 6.895 kN/m2 Unit weight: 1 lb/ft3 ϭ 0.1572 kN/m3 1 lb/in.3 ϭ 271.43 kN/m3 Moment: 1 lb-ft ϭ 1.3558 N · m 1 lb-in. ϭ 0.11298 N · m Energy: 1 ft-lb ϭ 1.3558 J Moment of 1 in.4 ϭ 0.4162 ϫ 106 mm4 inertia: 1 in.4 ϭ 0.4162 ϫ 10Ϫ6 m4 CONVERSION FACTORS FROM ENGLISH TO SI UNITS
  2. 2. Length: 1 m ϭ 3.281 ft 1 cm ϭ 3.281 ϫ 10Ϫ2 ft 1 mm ϭ 3.281 ϫ 10Ϫ3 ft 1 m ϭ 39.37 in. 1 cm ϭ 0.3937 in. 1 mm ϭ 0.03937 in. Area: 1 m2 ϭ 10.764 ft2 1 cm2 ϭ 10.764 ϫ 10Ϫ4 ft2 1 mm2 ϭ 10.764 ϫ 10Ϫ6 ft2 1 m2 ϭ 1550 in.2 1 cm2 ϭ 0.155 in.2 1 mm2 ϭ 0.155 ϫ 10Ϫ2 in.2 Volume: 1 m3 ϭ 35.32 ft3 1 cm3 ϭ 35.32 ϫ 10Ϫ4 ft3 1 m3 ϭ 61,023.4 in.3 1 cm3 ϭ 0.061023 in.3 Force: 1 N ϭ 0.2248 lb 1 kN ϭ 224.8 lb 1 kgf ϭ 2.2046 lb 1 kN ϭ 0.2248 kip 1 kN ϭ 0.1124 U.S. ton 1 metric ton ϭ 2204.6 lb 1 N/m ϭ 0.0685 lb/ft Stress: 1 N/m2 ϭ 20.885 ϫ 10Ϫ3 lb/ft2 1 kN/m2 ϭ 20.885 lb/ft2 1 kN/m2 ϭ 0.01044 U.S. ton/ft2 1 kN/m2 ϭ 20.885 ϫ 10Ϫ3 kip/ft2 1 kN/m2 ϭ 0.145 lb/in.2 Unit weight: 1 kN/m3 ϭ 6.361 lb/ft3 1 kN/m3 ϭ 0.003682 lb/in.3 Moment: 1 N · m ϭ 0.7375 lb-ft 1 N · m ϭ 8.851 lb-in. Energy: 1 J ϭ 0.7375 ft-lb Moment of 1 mm4 ϭ 2.402 ϫ 10Ϫ6 in.4 inertia: 1 m4 ϭ 2.402 ϫ 106 in.4 Section 1 mm3 ϭ 6.102 ϫ 10Ϫ5 in.3 modulus: 1 m3 ϭ 6.102 ϫ 104 in.3 Hydraulic 1 m/min ϭ 3.281 ft/min conductivity: 1 cm/min ϭ 0.03281 ft/min 1 mm/min ϭ 0.003281 ft/min 1 m/sec ϭ 3.281 ft/sec 1 mm/sec ϭ 0.03281 ft/sec 1 m/min ϭ 39.37 in./min 1 cm/sec ϭ 0.3937 in./sec 1 mm/sec ϭ 0.03937 in./sec Coefficient of 1 cm2 /sec ϭ 0.155 in.2 /sec consolidation: 1 m2 /yr ϭ 4.915 ϫ 10Ϫ5 in.2 /sec 1 cm2 /sec ϭ 1.0764 ϫ 10Ϫ3 ft2 /sec CONVERSION FACTORS FROM SI TO ENGLISH UNITS
  3. 3. Principles of Geotechnical Engineering Seventh Edition BRAJA M. DAS Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
  4. 4. Principles of Geotechnical Engineering, 7th Edition Braja M. Das Executive Director, Global Publishing Program: Chris Carson Senior Developmental Editor: Hilda Gowans Editorial Assistant: Nancy Saundercook Associate Marketing Manager: Lauren Betsos Director, Content and Media Production: Barbara Fuller Jacobsen Content Project Manager: Emily Nesheim Production Service: RPK Editorial Services Copyeditor: Shelly Gerger-Knechtl Proofreader: Nancy Benziger Indexer: Braja M. Das Compositor: Integra Software Services Senior Art Director: Michelle Kunkler Internal Designer: Carmela Pereira Cover Designer: Andrew Adams Cover Images: H. Turan Durgunog˘lu, Zetas, Istanbul, Turkey Permissions Account Manager, Text: Mardell Glinski Shultz Permissions Account Manager, Images: Deanna Ettinger Text and Images Permissions Researcher: Kristiina Paul Senior First Print Buyer: Doug Wilke Printed in the United States of America 1 2 3 4 5 6 7 13 12 11 10 09 © 2010, 2006 Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means—graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, information storage and retrieval systems, or in any other manner—except as may be permitted by the license terms herein. For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706. For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions. Further permissions questions can be emailed to permissionrequest@cengage.com. Library of Congress Control Number: 2009930622 ISBN-13: 978-0-495-41130-7 ISBN-10: 0-495-41130-2 Cengage Learning 200 First Stamford Place, Suite 400 Stamford, CT 06902 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: international.cengage.com/region. Cengage Learning products are represented in Canada by Nelson Education Ltd. For your course and learning solutions, visit www.cengage.com/engineering. Purchase any of our products at your local college store or at our preferred online store www.ichapters.com.
  5. 5. To our granddaughter Elizabeth Madison
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  7. 7. v Contents Preface xiii 1 Geotechnical Engineering—A Historical Perspective 1 1.1 Geotechnical Engineering Prior to the 18th Century 1 1.2 Preclassical Period of Soil Mechanics (1700–1776) 4 1.3 Classical Soil Mechanics—Phase I (1776–1856) 4 1.4 Classical Soil Mechanics—Phase II (1856–1910) 5 1.5 Modern Soil Mechanics (1910–1927) 5 1.6 Geotechnical Engineering after 1927 7 1.7 End of an Era 10 References 12 2 Origin of Soil and Grain Size 15 2.1 Rock Cycle and the Origin of Soil 15 2.2 Soil–Particle Size 24 2.3 Clay Minerals 26 2.4 Specific Gravity (Gs) 34 2.5 Mechanical Analysis of Soil 35 2.6 Particle–Size Distribution Curve 42 2.7 Particle Shape 46 2.8 Summary 47 Problems 47 References 50 3 Weight–Volume Relationships 51 3.1 Weight–Volume Relationships 51 3.2 Relationships among Unit Weight, Void Ratio, Moisture Content, and Specific Gravity 54
  8. 8. 3.3 Relationships among Unit Weight, Porosity, and Moisture Content 57 3.4 Various Unit-Weight Relationships 59 3.5 Relative Density 64 3.6 Comments on emax and emin 67 3.7 Summary 68 Problems 69 References 72 4 Plasticity and Structure of Soil 73 4.1 Introduction 73 4.2 Liquid Limit (LL) 74 4.3 Plastic Limit (PL) 78 4.4 Shrinkage Limit (SL) 81 4.5 Liquidity Index and Consistency Index 83 4.6 Activity 84 4.7 Plasticity Chart 87 4.8 Soil Structure 88 4.9 Summary 93 Problems 93 References 94 5 Classification of Soil 95 5.1 Textural Classification 95 5.2 Classification by Engineering Behavior 98 5.3 AASHTO Classification System 98 5.4 Unified Soil Classification System 102 5.5 Summary and Comparison between the AASHTO and Unified Systems 104 Problems 112 References 113 6 Soil Compaction 114 6.1 Compaction—General Principles 114 6.2 Standard Proctor Test 115 6.3 Factors Affecting Compaction 118 6.4 Modified Proctor Test 122 6.5 Structure of Compacted Clay Soil 127 6.6 Effect of Compaction on Cohesive Soil Properties 129 vi Contents
  9. 9. 6.7 Field Compaction 132 6.8 Specifications for Field Compaction 136 6.9 Determination of Field Unit Weight of Compaction 140 6.10 Compaction of Organic Soil and Waste Materials 144 6.11 Special Compaction Techniques 147 6.12 Summary and General Comments 155 Problems 155 References 157 7 Permeability 160 7.1 Bernoulli’s Equation 160 7.2 Darcy’s Law 162 7.3 Hydraulic Conductivity 164 7.4 Laboratory Determination of Hydraulic Conductivity 166 7.5 Relationships for Hydraulic Conductivity—Granular Soil 172 7.6 Relationships for Hydraulic Conductivity—Cohesive Soils 177 7.7 Directional Variation of Permeability 180 7.8 Equivalent Hydraulic Conductivity in Stratified Soil 182 7.9 Permeability Test in the Field by Pumping from Wells 187 7.10 In Situ Hydraulic Conductivity of Compacted Clay Soils 189 7.11 Summary and General Comments 192 Problems 193 References 196 8 Seepage 198 8.1 Laplace’s Equation of Continuity 198 8.2 Continuity Equation for Solution of Simple Flow Problems 200 8.3 Flow Nets 204 8.4 Seepage Calculation from a Flow Net 205 8.5 Flow Nets in Anisotropic Soils 209 8.6 Mathematical Solution for Seepage 211 8.7 Uplift Pressure Under Hydraulic Structures 213 8.8 Seepage Through an Earth Dam on an Impervious Base 214 8.9 L. Casagrande’s Solution for Seepage Through an Earth Dam 217 8.10 Filter Design 219 8.11 Summary 222 Problems 222 References 225 Contents vii
  10. 10. 9 In Situ Stresses 226 9.1 Stresses in Saturated Soil without Seepage 226 9.2 Stresses in Saturated Soil with Upward Seepage 231 9.3 Stresses in Saturated Soil with Downward Seepage 233 9.4 Seepage Force 235 9.5 Heaving in Soil Due to Flow Around Sheet Piles 237 9.6 Use of Filters to Increase the Factor of Safety Against Heave 240 9.7 Effective Stress in Partially Saturated Soil 242 9.8 Capillary Rise in Soils 243 9.9 Effective Stress in the Zone of Capillary Rise 245 9.10 Summary and General Comments 248 Problems 249 References 252 10 Stresses in a Soil Mass 253 10.1 Normal and Shear Stresses on a Plane 253 10.2 The Pole Method of Finding Stresses Along a Plane 258 10.3 Stresses Caused by a Point Load 260 10.4 Vertical Stress Caused by a Line Load 262 10.5 Vertical Stress Caused by a Horizontal Line Load 264 10.6 Vertical Stress Caused by a Strip Load (Finite Width and Infinite Length) 266 10.7 Vertical Stress Due to Embankment Loading 267 10.8 Vertical Stress Below the Center of a Uniformly Loaded Circular Area 273 10.9 Vertical Stress at Any Point Below a Uniformly Loaded Circular Area 275 10.10 Vertical Stress Caused by a Rectangularly Loaded Area 278 10.11 Stress Isobars 285 10.12 Influence Chart for Vertical Pressure 285 10.13 Summary and General Comments 288 Problems 289 References 293 11 Compressibility of Soil 294 11.1 Contact Pressure and Settlement Profile 294 11.2 Relations for Elastic Settlement Calculation 296 11.3 Fundamentals of Consolidation 304 11.4 One-Dimensional Laboratory Consolidation Test 308 viii Contents
  11. 11. 11.5 Void Ratio–Pressure Plots 310 11.6 Normally Consolidated and Overconsolidated Clays 313 11.7 Effect of Disturbance on Void Ratio–Pressure Relationship 316 11.8 Calculation of Settlement from One-Dimensional Primary Consolidation 317 11.9 Compression Index (Cc) 319 11.10 Swell Index (Cs) 320 11.11 Secondary Consolidation Settlement 326 11.12 Time Rate of Consolidation 330 11.13 Coefficient of Consolidation 338 11.14 Calculation of Consolidation Settlement Under a Foundation 345 11.15 A Case History—Settlement Due to a Preload Fill for Construction of Tampa VA Hospital 347 11.16 Methods for Accelerating Consolidation Settlement 351 11.17 Precompression 354 11.18 Summary and General Comments 357 Problems 358 References 362 12 Shear Strength of Soil 365 12.1 Mohr–Coulomb Failure Criterion 365 12.2 Inclination of the Plane of Failure Caused by Shear 367 12.3 Laboratory Tests for Determination of Shear Strength Parameters 368 12.4 Direct Shear Test 369 12.5 Drained Direct Shear Test on Saturated Sand and Clay 373 12.6 General Comments on Direct Shear Test 376 12.7 Triaxial Shear Test—General 380 12.8 Consolidated-Drained Triaxial Test 381 12.9 Consolidated-Undrained Triaxial Test 389 12.10 Unconsolidated-Undrained Triaxial Test 395 12.11 Unconfined Compression Test on Saturated Clay 397 12.12 Empirical Relationships Between Undrained Cohesion (cu) and Effective Overburden Pressure ( ) 398 12.13 Sensitivity and Thixotropy of Clay 401 12.14 Strength Anisotropy in Clay 403 12.15 Vane Shear Test 406 12.16 Other Methods for Determining Undrained Shear Strength 411 12.17 Shear Strength of Unsaturated Cohesive Soils 412 sœ o Contents ix
  12. 12. 12.18 Stress Path 414 12.19 Summary and General Comments 418 Problems 419 References 422 13 Lateral Earth Pressure: At-Rest, Rankine, and Coulomb 424 13.1 At-Rest, Active, and Passive Pressures 424 13.2 Earth Pressure At-Rest 426 13.3 Earth Pressure At-Rest for Partially Submerged Soil 429 13.4 Rankine’s Theory of Active Pressure 432 13.5 Theory of Rankine’s Passive Pressure 434 13.6 Yielding of Wall of Limited Height 436 13.7 A Generalized Case for Rankine Active and Passive Pressures—Granular Backfill 438 13.8 Diagrams for Lateral Earth-Pressure Distribution Against Retaining Walls 442 13.9 Rankine’s Pressure for cЈ–fЈ Soil—Inclined Backfill 454 13.10 Coulomb’s Active Pressure 457 13.11 Graphic Solution for Coulomb’s Active Earth Pressure 461 13.12 Coulomb’s Passive Pressure 466 13.13 Active Force on Retaining Walls with Earthquake Forces 468 13.14 Common Types of Retaining Walls in the Field 479 13.15 Summary and General Comments 482 Problems 483 References 486 14 Lateral Earth Pressure: Curved Failure Surface 488 14.1 Retaining Walls with Friction 488 14.2 Properties of a Logarithmic Spiral 490 14.3 Procedure for Determination of Passive Earth Pressure (Pp)—Cohesionless Backfill 492 14.4 Coefficient of Passive Earth Pressure (Kp) 494 14.5 Passive Force on Walls with Earthquake Forces 498 14.6 Braced Cuts—General 499 14.7 Determination of Active Thrust on Bracing Systems of Open Cuts—Granular Soil 503 14.8 Determination of Active Thrust on Bracing Systems for Cuts—Cohesive Soil 504 x Contents
  13. 13. 14.9 Pressure Variation for Design of Sheetings, Struts, and Wales 505 14.10 Summary 509 Problems 509 References 511 15 Slope Stability 512 15.1 Introduction—Modes of Slope Failure 512 15.2 Factor of Safety 514 15.3 Stability of Infinite Slopes 515 15.4 Finite Slopes—General 519 15.5 Analysis of Finite Slopes with Plane Failure Surfaces (Culmann’s Method) 520 15.6 Analysis of Finite Slopes with Circular Failure Surfaces—General 523 15.7 Mass Procedure—Slopes in Homogeneous Clay Soil with f ϭ 0 524 15.8 Mass Procedure—Stability of Saturated Clay Slopes (f ϭ 0 Condition) with Earthquake Forces 532 15.9 Mass Procedure—Slopes in Homogeneous cЈ–fЈ Soil 535 15.10 Ordinary Method of Slices 544 15.11 Bishop’s Simplified Method of Slices 548 15.12 Stability Analysis by Method of Slices for Steady-State Seepage 550 15.13 Other Solutions for Steady-State Seepage Condition 557 15.14 A Case History of Slope Failure 561 15.15 Morgenstern’s Method of Slices for Rapid Drawdown Condition 565 15.16 Fluctuation of Factor of Safety of Slopes in Clay Embankment on Saturated Clay 568 Problems 571 References 574 16 Soil-Bearing Capacity for Shallow Foundations 576 16.1 Ultimate Soil-Bearing Capacity for Shallow Foundations 577 16.2 Terzaghi’s Ultimate Bearing Capacity Equation 579 16.3 Effect of Groundwater Table 584 16.4 Factor of Safety 586 16.5 General Bearing Capacity Equation 589 16.6 A Case History for Evaluation of the Ultimate Bearing Capacity 593 Contents xi
  14. 14. xii Contents 16.7 Ultimate Load for Shallow Foundations Under Eccentric Load 597 16.8 Bearing Capacity of Sand Based on Settlement 602 16.9 Plate-Load Test 604 16.10 Summary and General Comments 607 Problems 608 References 610 17 Landfill Liners and Geosynthetics 611 17.1 Landfill Liners—Overview 611 17.2 Compaction of Clay Soil for Clay Liner Construction 612 17.3 Geosynthetics 616 17.4 Geotextiles 616 17.5 Geomembranes 619 17.6 Geonets 621 17.7 Single Clay Liner and Single Geomembrane Liner Systems 622 17.8 Recent Advances in the Liner Systems for Landfills 623 17.9 Leachate Removal Systems 624 17.10 Closure of Landfills 627 17.11 Summary and General Comments 628 References 628 18 Subsoil Exploration 629 18.1 Planning for Soil Exploration 629 18.2 Boring Methods 631 18.3 Common Sampling Methods 635 18.4 Sample Disturbance 639 18.5 Correlations for Standard Penetration Test 639 18.6 Other In Situ Tests 644 18.7 Rock Coring 648 18.8 Soil Exploration Report 650 Problems 652 References 653 Answers to Selected Problems 655 Index 662
  15. 15. Principles of Geotechnical Engineering was originally published with a 1985 copyright and was intended for use as a text for the introductory course in geotechnical engineering taken by practically all civil engineering students, as well as for use as a reference book for practicing engineers. The book was revised in 1990, 1994, 1998, 2002, and 2006. This Seventh Edition is the twenty-fifth anniversary edition of the text. As in the previous editions of the book, this new edition offers an overview of soil properties and mechanics, together with coverage of field practices and basic engineering procedures without chang- ing the basic philosophy in which the text was written originally. Unlike the Sixth Edition that had 17 chapters, this edition has 18 chapters. For bet- ter understanding and more comprehensive coverage, Weight-Volume Relationships and Plasticity and Structure of Soil are now presented in two separate chapters (Chapters 3 and 4). Most of the example and homework problems have been changed and/or modified. Other noteworthy changes for the Seventh Edition are • New scanning electron micrographs for quartz, mica, limestone, sand grains, and clay minerals such as kaolinite and montmorillonite have been added to Chapter 2. • A summary of recently published empirical relationships between liquid limit, plastic limit, plasticity index, activity, and clay-size fractions in a soil mass have been incorporated in Chapter 4. • The USDA Textural Classification of Soil has now been added to Chapter 5 (Classification of Soil). • Additional empirical relationships for hydraulic conductivity for granular and cohesive soils have been added, respectively, to Chapter 7 (Permeability) and Chapter 17 (Landfill Liners and Geosynthetics). • The presentation of the filter design criteria has been improved in Chapter 8 (Seepage). • In Chapter 11 (Compressibility of Soil), the procedure for estimating elastic settlement of foundations has been thoroughly revised with the inclusions of theories by Steinbrenner (1934) and Fox (1948). A case study related to the consolidation settlement due to a preload fill for construction of the Tampa VA Hospital is also added to this chapter. xiii Preface
  16. 16. xiv Preface • The presentation on estimation of active force on retaining walls with earthquake forces in Chapter 13 (Lateral Earth Pressure: At-Rest, Rankine, and Coulomb) has been improved. • Chapter 14 (Lateral Earth Pressure: Curved Failure Surface) now includes the procedure to estimate the passive earth pressure on retaining walls with inclined backface and horizontal granular backfill using the method of triangular slices. It also includes the relationships for passive earth pressure on retaining walls with a horizontal granular backfill and vertical backface under earthquake conditions determined by using the pseudo-static method. • Chapter 15 (Slope Stability) now includes a case history of slope failure in relation to a major improvement program of Interstate Route 95 in New Hampshire. • A method to calculate the ultimate bearing capacity of eccentrically loaded shallow strip foundations in granular soil using the reduction factor has been added to Chapter 16 (Soil-Bearing Capacity for Shallow Foundations). I am grateful to my wife Janice for her help in getting the manuscript ready for pub- lication. Finally, many thanks are due to Christopher Carson, Executive Director, Global Publishing Programs; Hilda Gowans, Senior Development Editor; and the production staff of Cengage Learning (Engineering) for the final development and production of the book. Braja M. Das Henderson, Nevada
  17. 17. 1 For engineering purposes, soil is defined as the uncemented aggregate of mineral grains and decayed organic matter (solid particles) with liquid and gas in the empty spaces between the solid particles. Soil is used as a construction material in various civil engi- neering projects, and it supports structural foundations. Thus, civil engineers must study the properties of soil, such as its origin, grain-size distribution, ability to drain water, com- pressibility, shear strength, and load-bearing capacity. Soil mechanics is the branch of sci- ence that deals with the study of the physical properties of soil and the behavior of soil masses subjected to various types of forces. Soils engineering is the application of the prin- ciples of soil mechanics to practical problems. Geotechnical engineering is the subdisci- pline of civil engineering that involves natural materials found close to the surface of the earth. It includes the application of the principles of soil mechanics and rock mechanics to the design of foundations, retaining structures, and earth structures. 1.1 Geotechnical Engineering Prior to the 18th Century The record of a person’s first use of soil as a construction material is lost in antiquity. In true engineering terms, the understanding of geotechnical engineering as it is known today began early in the 18th century (Skempton, 1985). For years, the art of geotechnical engi- neering was based on only past experiences through a succession of experimentation with- out any real scientific character. Based on those experimentations, many structures were built—some of which have crumbled, while others are still standing. Recorded history tells us that ancient civilizations flourished along the banks of rivers, such as the Nile (Egypt), the Tigris and Euphrates (Mesopotamia), the Huang Ho (Yellow River, China), and the Indus (India). Dykes dating back to about 2000 B.C. were built in the basin of the Indus to protect the town of Mohenjo Dara (in what became Pakistan after 1947). During the Chan dynasty in China (1120 B.C. to 249 B.C.) many dykes were built for irrigation purposes. There is no evidence that measures were taken to stabilize the foun- dations or check erosion caused by floods (Kerisel, 1985). Ancient Greek civilization used isolated pad footings and strip-and-raft foundations for building structures. Beginning around 2750 B.C., the five most important pyramids were built in Egypt in a period of less than a century (Saqqarah, Meidum, Dahshur South and North, and Cheops). This posed formidable challenges regarding foundations, stability of slopes, and construction of 1 Geotechnical Engineering— A Historical Perspective
  18. 18. Figure 1.1 Leaning Tower of Pisa, Italy (Courtesy of Braja M. Das, Henderson, Nevada) underground chambers. With the arrival of Buddhism in China during the Eastern Han dynasty in 68 A.D., thousands of pagodas were built. Many of these structures were con- structed on silt and soft clay layers. In some cases the foundation pressure exceeded the load-bearing capacity of the soil and thereby caused extensive structural damage. One of the most famous examples of problems related to soil-bearing capacity in the construction of structures prior to the 18th century is the Leaning Tower of Pisa in Italy. (See Figure 1.1.) Construction of the tower began in 1173 A.D. when the Republic of Pisa was flourishing and continued in various stages for over 200 years. The structure weighs about 15,700 metric tons and is supported by a circular base having a diameter of 20 m (Ϸ 66 ft). The tower has tilted in the past to the east, north, west and, finally, to the south. Recent inves- tigations showed that a weak clay layer exists at a depth of about 11 m (Ϸ 36 ft) below the ground surface compression, which caused the tower to tilt. It became more than 5 m (Ϸ 16.5 ft) out of plumb with the 54 m (Ϸ 179 ft) height. The tower was closed in 1990 because it was feared that it would either fall over or collapse. It recently has been stabilized by excavating soil from under the north side of the tower. About 70 metric tons of earth were removed in 41 separate extractions that spanned the width of the tower. As the ground 2 Chapter 1: Geotechnical Engineering—A Historical Perspective
  19. 19. Figure 1.2 Tilting of Garisenda Tower (left) and Asinelli Tower (right) in Bologna, Italy (Courtesy of Braja M. Das, Henderson, Nevada) gradually settled to fill the resulting space, the tilt of the tower eased. The tower now leans 5 degrees. The half-degree change is not noticeable, but it makes the structure considerably more stable. Figure 1.2 is an example of a similar problem. The towers shown in Figure 1.2 are located in Bologna, Italy, and they were built in the 12th century. The tower on the left is usually referred to as the Garisenda Tower. It is 48 m (Ϸ 157 ft) in height and weighs about 4210 metric tons. It has tilted about 4 degrees. The tower on the right is the Asinelli Tower, which is 97 m high and weighs 7300 metric tons. It has tilted about 1.3 degrees. After encountering several foundation-related problems during construction over centuries past, engineers and scientists began to address the properties and behaviors of soils in a more methodical manner starting in the early part of the 18th century. Based on the emphasis and the nature of study in the area of geotechnical engineering, the time span extending from 1700 to 1927 can be divided into four major periods (Skempton, 1985): 1. Pre-classical (1700 to 1776 A.D.) 2. Classical soil mechanics—Phase I (1776 to 1856 A.D.) 3. Classical soil mechanics—Phase II (1856 to 1910 A.D.) 4. Modern soil mechanics (1910 to 1927 A.D.) 1.1 Geotechnical Engineering Prior to the 18th Century 3
  20. 20. Brief descriptions of some significant developments during each of these four periods are discussed below. 1.2 Preclassical Period of Soil Mechanics (1700 –1776) This period concentrated on studies relating to natural slope and unit weights of various types of soils, as well as the semiempirical earth pressure theories. In 1717 a French royal engineer, Henri Gautier (1660–1737), studied the natural slopes of soils when tipped in a heap for formulating the design procedures of retaining walls. The natural slope is what we now refer to as the angle of repose. According to this study, the natural slope of clean dry sand and ordinary earth were 31Њ and 45Њ, respectively. Also, the unit weight of clean dry sand and ordinary earth were recommended to be 18.1 kN/m3 (115 lb/ft3 ) and 13.4 kN/m3 (85 lb/ft3 ), respectively. No test results on clay were reported. In 1729, Bernard Forest de Belidor (1671–1761) published a textbook for military and civil engineers in France. In the book, he proposed a theory for lateral earth pressure on retaining walls that was a follow-up to Gautier’s (1717) original study. He also specified a soil classification system in the manner shown in the following table. Unit weight Classification kN/m3 lb/ft3 Rock — — Firm or hard sand 16.7 to 106 to Compressible sand 18.4 117 Ordinary earth (as found in dry locations) 13.4 85 Soft earth (primarily silt) 16.0 102 Clay 18.9 120 Peat — — The first laboratory model test results on a 76-mm-high (Ϸ 3 in.) retaining wall built with sand backfill were reported in 1746 by a French engineer, Francois Gadroy (1705–1759), who observed the existence of slip planes in the soil at failure. Gadroy’s study was later summarized by J. J. Mayniel in 1808. 1.3 Classical Soil Mechanics—Phase I (1776–1856) During this period, most of the developments in the area of geotechnical engineering came from engineers and scientists in France. In the preclassical period, practically all theoretical considerations used in calculating lateral earth pressure on retaining walls were based on an arbitrarily based failure surface in soil. In his famous paper presented in 1776, French scien- tist Charles Augustin Coulomb (1736–1806) used the principles of calculus for maxima and minima to determine the true position of the sliding surface in soil behind a retaining wall. In this analysis, Coulomb used the laws of friction and cohesion for solid bodies. In 1820, special cases of Coulomb’s work were studied by French engineer Jacques Frederic Francais (1775–1833) and by French applied mechanics professor Claude Louis Marie Henri Navier 4 Chapter 1: Geotechnical Engineering—A Historical Perspective
  21. 21. (1785–1836). These special cases related to inclined backfills and backfills supporting sur- charge. In 1840, Jean Victor Poncelet (1788–1867), an army engineer and professor of mechanics, extended Coulomb’s theory by providing a graphical method for determining the magnitude of lateral earth pressure on vertical and inclined retaining walls with arbitrarily broken polygonal ground surfaces. Poncelet was also the first to use the symbol f for soil friction angle. He also provided the first ultimate bearing-capacity theory for shallow foun- dations. In 1846 Alexandre Collin (1808–1890), an engineer, provided the details for deep slips in clay slopes, cutting, and embankments. Collin theorized that in all cases the failure takes place when the mobilized cohesion exceeds the existing cohesion of the soil. He also observed that the actual failure surfaces could be approximated as arcs of cycloids. The end of Phase I of the classical soil mechanics period is generally marked by the year (1857) of the first publication by William John Macquorn Rankine (1820–1872), a pro- fessor of civil engineering at the University of Glasgow. This study provided a notable the- ory on earth pressure and equilibrium of earth masses. Rankine’s theory is a simplification of Coulomb’s theory. 1.4 Classical Soil Mechanics—Phase II (1856–1910) Several experimental results from laboratory tests on sand appeared in the literature in this phase. One of the earliest and most important publications is one by French engineer Henri Philibert Gaspard Darcy (1803–1858). In 1856, he published a study on the permeability of sand filters. Based on those tests, Darcy defined the term coefficient of permeability (or hydraulic conductivity) of soil, a very useful parameter in geotechnical engineering to this day. Sir George Howard Darwin (1845–1912), a professor of astronomy, conducted labora- tory tests to determine the overturning moment on a hinged wall retaining sand in loose and dense states of compaction. Another noteworthy contribution, which was published in 1885 by JosephValentin Boussinesq (1842–1929), was the development of the theory of stress distribu- tion under loaded bearing areas in a homogeneous, semiinfinite, elastic, and isotropic medium. In 1887, Osborne Reynolds (1842–1912) demonstrated the phenomenon of dilatency in sand. 1.5 Modern Soil Mechanics (1910 –1927) In this period, results of research conducted on clays were published in which the funda- mental properties and parameters of clay were established. The most notable publications are described next. Around 1908, Albert Mauritz Atterberg (1846–1916), a Swedish chemist and soil scientist, defined clay-size fractions as the percentage by weight of particles smaller than 2 microns in size. He realized the important role of clay particles in a soil and the plasticity thereof. In 1911, he explained the consistency of cohesive soils by defining liq- uid, plastic, and shrinkage limits. He also defined the plasticity index as the difference between liquid limit and plastic limit (see Atterberg, 1911). In October 1909, the 17-m (56-ft) high earth dam at Charmes, France, failed. It was built between 1902–1906. A French engineer, Jean Fontard (1884–1962), carried out investigations to determine the cause of failure. In that context, he conducted undrained 1.5 Modern Soil Mechanics (1910 –1927) 5
  22. 22. double-shear tests on clay specimens (0.77 m2 in area and 200 mm thick) under constant vertical stress to determine their shear strength parameters (see Frontard, 1914). The times for failure of these specimens were between 10 to 20 minutes. Arthur Langley Bell (1874–1956), a civil engineer from England, worked on the design and construction of the outer seawall at Rosyth Dockyard. Based on his work, he developed relationships for lateral pressure and resistance in clay as well as bearing capac- ity of shallow foundations in clay (see Bell, 1915). He also used shear-box tests to mea- sure the undrained shear strength of undisturbed clay specimens. Wolmar Fellenius (1876–1957), an engineer from Sweden, developed the stability analysis of saturated clay slopes (that is, ␾ ϭ 0 condition) with the assumption that the critical surface of sliding is the arc of a circle. These were elaborated upon in his papers published in 1918 and 1926. The paper published in 1926 gave correct numerical solutions for the stability numbers of circular slip surfaces passing through the toe of the slope. Karl Terzaghi (1883–1963) of Austria (Figure 1.3) developed the theory of consoli- dation for clays as we know today. The theory was developed when Terzaghi was teaching 6 Chapter 1: Geotechnical Engineering—A Historical Perspective Image not available due to copyright restrictions
  23. 23. at the American Roberts College in Istanbul, Turkey. His study spanned a five-year period from 1919 to 1924. Five different clay soils were used. The liquid limit of those soils ranged between 36 to 67, and the plasticity index was in the range of 18 to 38. The consolidation theory was published in Terzaghi’s celebrated book Erdbaumechanik in 1925. 1.6 Geotechnical Engineering after 1927 The publication of Erdbaumechanik auf Bodenphysikalisher Grundlage by Karl Terzaghi in 1925 gave birth to a new era in the development of soil mechanics. Karl Terzaghi is known as the father of modern soil mechanics, and rightfully so. Terzaghi was born on October 2, 1883 in Prague, which was then the capital of the Austrian province of Bohemia. In 1904 he graduated from the Technische Hochschule in Graz, Austria, with an undergraduate degree in mechanical engineering. After graduation he served one year in the Austrian army. Following his army service, Terzaghi studied one more year, concen- trating on geological subjects. In January 1912, he received the degree of Doctor of Technical Sciences from his alma mater in Graz. In 1916, he accepted a teaching position at the Imperial School of Engineers in Istanbul. After the end of World War I, he accepted a lectureship at the American Robert College in Istanbul (1918–1925). There he began his research work on the behavior of soils and settlement of clays and on the failure due to piping in sand under dams. The publication Erdbaumechanik is primarily the result of this research. In 1925, Terzaghi accepted a visiting lectureship at Massachusetts Institute of Technology, where he worked until 1929. During that time, he became recognized as the leader of the new branch of civil engineering called soil mechanics. In October 1929, he returned to Europe to accept a professorship at the Technical University of Vienna, which soon became the nucleus for civil engineers interested in soil mechanics. In 1939, he returned to the United States to become a professor at Harvard University. The first conference of the International Society of Soil Mechanics and Foundation Engineering (ISSMFE) was held at Harvard University in 1936 with Karl Terzaghi pre- siding. The conference was possible due to the conviction and efforts of Professor Arthur Casagrande of Harvard University. About 200 individuals representing 21 countries attended this conference. It was through the inspiration and guidance of Terzaghi over the preceding quarter-century that papers were brought to that conference covering a wide range of topics, such as • Effective stress • Shear strength • Testing with Dutch cone penetrometer • Consolidation • Centrifuge testing • Elastic theory and stress distribution • Preloading for settlement control • Swelling clays • Frost action • Earthquake and soil liquefaction • Machine vibration • Arching theory of earth pressure 1.6 Geotechnical Engineering after 1927 7
  24. 24. For the next quarter-century, Terzaghi was the guiding spirit in the development of soil mechanics and geotechnical engineering throughout the world. To that effect, in 1985, Ralph Peck wrote that “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. Within the next few years he would be engaged on proj- ects on every continent save Australia and Antarctica.” Peck continued with, “Hence, even today, one can hardly improve on his contemporary assessments of the state of soil mechan- ics as expressed in his summary papers and presidential addresses.” In 1939, Terzaghi delivered the 45th James Forrest Lecture at the Institution of Civil Engineers, London. His lecture was entitled “Soil Mechanics—A New Chapter in Engineering Science.” In it, he proclaimed that most of the foundation failures that occurred were no longer “acts of God.” Following are some highlights in the development of soil mechanics and geo- technical engineering that evolved after the first conference of the ISSMFE in 1936: • Publication of the book Theoretical Soil Mechanics by Karl Terzaghi in 1943 (Wiley, New York); • Publication of the book Soil Mechanics in Engineering Practice by Karl Terzaghi and Ralph Peck in 1948 (Wiley, New York); • Publication of the book Fundamentals of Soil Mechanics by Donald W. Taylor in 1948 (Wiley, New York); • Start of the publication of Geotechnique, the international journal of soil mechanics in 1948 in England; After a brief interruption for World War II, the second conference of ISSMFE was held in Rotterdam,The Netherlands, in 1948.There were about 600 participants, and seven volumes of proceedings were published. In this conference,A.W. Skempton presented the landmark pa- per on ␾ ϭ 0 concept for clays. Following Rotterdam, ISSMFE conferences have been organ- ized about every four years in different parts of the world. The aftermath of the Rotterdam con- ference saw the growth of regional conferences on geotechnical engineering, such as • European Regional Conference on Stability of Earth Slopes, Stockholm (1954) • First Australia-New Zealand Conference on Shear Characteristics of Soils (1952) • First Pan American Conference, Mexico City (1960) • Research conference on Shear Strength of Cohesive Soils, Boulder, Colorado, (1960) Two other important milestones between 1948 and 1960 are (1) the publication of A. W. Skempton’s paper on A and B pore pressure parameters which made effective stress calculations more practical for various engineering works and (2) publication of the book entitled The Measurement of Soil Properties in the Triaxial Text by A. W. Bishop and B. J. Henkel (Arnold, London) in 1957. By the early 1950’s, computer-aided finite difference and finite element solutions were applied to various types of geotechnical engineering problems. They still remain an important and useful computation tool in our profession. Since the early days, the profes- sion of geotechnical engineering has come a long way and has matured. It is now an estab- lished branch of civil engineering, and thousands of civil engineers declare geotechnical engineering to be their preferred area of speciality. In 1997, the ISSMFE was changed to ISSMGE (International Society of Soil Mechanics and Geotechnical Engineering) to reflect its true scope. These international conferences have been instrumental for exchange of information regarding new 8 Chapter 1: Geotechnical Engineering—A Historical Perspective
  25. 25. developments and ongoing research activities in geotechnical engineering. Table 1.1 gives the location and year in which each conference of ISSMFE/ISSMGE was held, and Table 1.2 gives a list of all of the presidents of the society. In 1997, a total of 30 technical committees of ISSMGE was in place. The names of these technical committees are given in Table 1.3. 1.6 Geotechnical Engineering after 1927 9 Table 1.1 Details of ISSMFE (1936–1997) and ISSMGE (1997–present) Conferences Conference Location Year I Harvard University, Boston, U.S.A. 1936 II Rotterdam, the Netherlands 1948 III Zurich, Switzerland 1953 IV London, England 1957 V Paris, France 1961 VI Montreal, Canada 1965 VII Mexico City, Mexico 1969 VIII Moscow, U.S.S.R. 1973 IX Tokyo, Japan 1977 X Stockholm, Sweden 1981 XI San Francisco, U.S.A. 1985 XII Rio de Janeiro, Brazil 1989 XIII New Delhi, India 1994 XIV Hamburg, Germany 1997 XV Istanbul, Turkey 2001 XVI Osaka, Japan 2005 XVII Alexandria, Egypt 2009 Table 1.2 Presidents of ISSMFE (1936–1997) and ISSMGE (1997–present) Conferences Year President 1936–1957 K. Terzaghi (U. S. A.) 1957–1961 A. W. Skempton (U. K.) 1961–1965 A. Casagrande (U. S. A.) 1965–1969 L. Bjerrum (Norway) 1969–1973 R. B. Peck (U. S. A.) 1973–1977 J. Kerisel (France) 1977–1981 M. Fukuoka (Japan) 1981–1985 V. F. B. deMello (Brazil) 1985–1989 B. B. Broms (Singapore) 1989–1994 N. R. Morgenstern (Canada) 1994–1997 M. Jamiolkowski (Italy) 1997–2001 K. Ishihara (Japan) 2001–2005 W. F. Van Impe (Belgium) 2005–2009 P. S. Sˆeco e Pinto (Portugal)
  26. 26. Table 1.3 ISSMGE Technical Committees for 1997–2001 (based on Ishihara, 1999) Committee number Committee name TC-1 Instrumentation for Geotechnical Monitoring TC-2 Centrifuge Testing TC-3 Geotechnics of Pavements and Rail Tracks TC-4 Earthquake Geotechnical Engineering TC-5 Environmental Geotechnics TC-6 Unsaturated Soils TC-7 Tailing Dams TC-8 Frost TC-9 Geosynthetics and Earth Reinforcement TC-10 Geophysical Site Characterization TC-11 Landslides TC-12 Validation of Computer Simulation TC-14 Offshore Geotechnical Engineering TC-15 Peat and Organic Soils TC-16 Ground Property Characterization from In-situ Testing TC-17 Ground Improvement TC-18 Pile Foundations TC-19 Preservation of Historic Sites TC-20 Professional Practice TC-22 Indurated Soils and Soft Rocks TC-23 Limit State Design Geotechnical Engineering TC-24 Soil Sampling, Evaluation and Interpretation TC-25 Tropical and Residual Soils TC-26 Calcareous Sediments TC-28 Underground Construction in Soft Ground TC-29 Stress-Strain Testing of Geomaterials in the Laboratory TC-30 Coastal Geotechnical Engineering TC-31 Education in Geotechnical Engineering TC-32 Risk Assessment and Management TC-33 Scour of Foundations TC-34 Deformation of Earth Materials 1.7 End of an Era In Section 1.6, a brief outline of the contributions made to modern soil mechanics by pio- neers such as Karl Terzaghi, Arthur Casagrande, Donald W. Taylor, Laurits Bjerrum, and Ralph B. Peck was presented. The last of the early giants of the profession, Ralph B. Peck, passed away on February 18, 2008, at the age of 95. Professor Ralph B. Peck (Figure 1.4) was born in Winnipeg, Canada to American parents Orwin K. and Ethel H. Peck on June 23, 1912. He received B.S. and Ph.D. degrees in 1934 and 1937, respectively, from Rensselaer Polytechnic Institute, Troy, New York. During the period from 1938 to 1939, he took courses from Arthur Casagrande at Harvard University in a new subject called “soil mechanics.” From 1939 to 1943, Dr. Peck worked as an assistant to Karl Terzaghi, the “father” of modern soil mechanics, on the Chicago 10 Chapter 1: Geotechnical Engineering—A Historical Perspective
  27. 27. 1.7 End of an Era 11 Subway Project. In 1943, he joined the University of Illinois at Champaign-Urban and was a professor of foundation engineering from 1948 until he retired in 1974. After retirement, he was active in consulting, which included major geotechnical projects in 44 states in the United States and 28 other countries on five continents. Some examples of his major con- sulting projects include • Rapid transit systems in Chicago, San Francisco, and Washington, D.C. • Alaskan pipeline system • James Bay Project in Quebec, Canada • Heathrow Express Rail Project (U.K.) • Dead Sea dikes His last project was the Rion-Antirion Bridge in Greece. On March 13, 2008, The Times of the United Kingdom wrote, “Ralph B. Peck was an American civil engi- neer who invented a controversial construction technique that would be used on some of the modern engineering wonders of the world, including the Channel Tunnel. Known as Image not available due to copyright restrictions
  28. 28. ‘the godfather of soil mechanics,’ he was directly responsible for a succession of cele- brated tunneling and earth dam projects that pushed the boundaries of what was believed to be possible.” Dr. Peck authored more than 250 highly distinguished technical publications. He was the president of the ISSMGE from 1969 to 1973. In 1974, he received the National Medal of Science from President Gerald R. Ford. Professor Peck was a teacher, mentor, friend, and counselor to generations of geotechnical engineers in every country in the world. The 16th ISSMGE Conference in Osaka, Japan (2005) would be the last major con- ference of its type that he would attend. During his trip to Osaka, even at the age of 93, he was intent on explaining to the author the importance of field testing and sound judgment in the decision-making process involved in the design and construction of geotechnical engineering projects (which he had done to numerous geotechnical engineers all over the world) (Figure 1.5). This is truly the end of an era. References ATTERBERG, A. M. (1911). “Über die physikalische Bodenuntersuchung, und über die Plasti- zität de Tone,” International Mitteilungen für Bodenkunde, Verlag für Fachliteratur. G.m.b.H. Berlin, Vol. 1, 10–43. 12 Chapter 1: Geotechnical Engineering—A Historical Perspective Figure 1.5 Professor Ralph B. Peck (right) with the author, Braja Das, during his trip to attend the XVI ISSMGE Conference in Osaka, Japan—the last conference of its type that he would attend (Courtesy of Braja M. Das, Henderson, Nevada)
  29. 29. BELIDOR, B. F. (1729). La Science des Ingenieurs dans la Conduite des Travaux de Fortification et D’Architecture Civil, Jombert, Paris. BELL, A. L. (1915). “The Lateral Pressure and Resistance of Clay, and Supporting Power of Clay Foundations,” Min. Proceeding of Institute of Civil Engineers, Vol. 199, 233–272. BISHOP, A. W. and HENKEL, B. J. (1957). The Measurement of Soil Properties in the Triaxial Test, Arnold, London. BOUSSINESQ, J. V. (1885). Application des Potentiels â L’Etude de L’Équilibre et du Mouvement des Solides Élastiques, Gauthier-Villars, Paris. COLLIN, A. (1846). Recherches Expérimentales sur les Glissements Spontanés des Terrains Argileux Accompagnées de Considérations sur Quelques Principes de la Mécanique Terrestre, Carilian-Goeury, Paris. COULOMB, C. A. (1776). “Essai sur une Application des Règles de Maximis et Minimis à Quelques Problèmes de Statique Relatifs à L’Architecture,” Mèmoires de la Mathèmatique et de Phisique, présentés à l’Académie Royale des Sciences, par divers savans, et lûs dans sés Assemblées, De L’Imprimerie Royale, Paris, Vol. 7, Annee 1793, 343–382. DARCY, H. P. G. (1856). Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris. DARWIN, G. H. (1883). “On the Horizontal Thrust of a Mass of Sand,” Proceedings, Institute of Civil Engineers, London, Vol. 71, 350–378. FELLENIUS, W. (1918). “Kaj-och Jordrasen I Göteborg,” Teknisk Tidskrift. Vol. 48, 17–19. FRANCAIS, J. F. (1820). “Recherches sur la Poussée de Terres sur la Forme et Dimensions des Revêtments et sur la Talus D’Excavation,” Mémorial de L’Officier du Génie, Paris, Vol. IV, 157–206. FRONTARD, J. (1914). “Notice sur L’Accident de la Digue de Charmes,” Anns. Ponts et Chaussées 9th Ser., Vol. 23, 173–292. GADROY, F. (1746). Mémoire sur la Poussée des Terres, summarized by Mayniel, 1808. GAUTIER, H. (1717). Dissertation sur L’Epaisseur des Culées des Ponts . . . sur L’Effort et al Pesanteur des Arches . . . et sur les Profiles de Maconnerie qui Doivent Supporter des Chaussées, des Terrasses, et des Remparts. Cailleau, Paris. ISHIHARA, K. (1999). Personal communication. KERISEL, J. (1985). “The History of Geotechnical Engineering up until 1700,” Proceedings, XI International Conference on Soil Mechanics and Foundation Engineering, San Francisco, Golden Jubilee Volume, A. A. Balkema, 3–93. MAYNIEL, J. J. (1808). Traité Experimentale, Analytique et Pratique de la Poussé des Terres. Colas, Paris. NAVIER, C. L. M. (1839). Leçons sur L’Application de la Mécanique à L’Establissement des Constructions et des Machines, 2nd ed., Paris. PECK, R. B. (1985). “The Last Sixty Years,” Proceedings, XI International Conference on Soil Mechanics and Foundation Engineering, San Francisco, Golden Jubilee Volume, A. A. Balkema, 123–133. PONCELET, J.V. (1840). Mémoire sur la Stabilité des Revêtments et de seurs Fondations, Bachelier, Paris. RANKINE, W. J. M. (1857). “On the Stability of Loose Earth,” Philosophical Transactions, Royal Society, Vol. 147, London. REYNOLDS, O. (1887). “Experiments Showing Dilatency, a Property of Granular Material Possibly Connected to Gravitation,” Proceedings, Royal Society, London, Vol. 11, 354–363. SKEMPTON, A. W. (1948). “The f ϭ 0 Analysis of Stability and Its Theoretical Basis,” Proceedings, II International Conference on Soil Mechanics and Foundation Engineering, Rotterdam, Vol. 1, 72–78. SKEMPTON, A. W. (1954). “The Pore Pressure Coefficients A and B,” Geotechnique, Vol. 4, 143–147. SKEMPTON, A. W. (1985). “A History of Soil Properties, 1717–1927,” Proceedings, XI International Conference on Soil Mechanics and Foundation Engineering, San Francisco, Golden Jubilee Volume, A. A. Balkema, 95–121. References 13
  30. 30. TAYLOR, D. W. (1948). Fundamentals of Soil Mechanics, John Wiley, New York. TERZAGHI, K. (1925). Erdbaumechanik auf Bodenphysikalisher Grundlage, Deuticke, Vienna. TERZAGHI, K. (1939). “Soil Mechanics—A New Chapter in Engineering Science,” Institute of Civil Engineers Journal, London, Vol. 12, No. 7, 106–142. TERZAGHI, K. (1943). Theoretical Soil Mechanics, John Wiley, New York. TERZAGHI, K., and PECK, R. B. (1948). Soil Mechanics in Engineering Practice, John Wiley, New York. 14 Chapter 1: Geotechnical Engineering—A Historical Perspective
  31. 31. 2 In general, soils are formed by weathering of rocks. The physical properties of soil are dic- tated primarily by the minerals that constitute the soil particles and, hence, the rock from which it is derived. This chapter provides an outline of the rock cycle and the origin of soil and the grain-size distribution of particles in a soil mass. 2.1 Rock Cycle and the Origin of Soil The mineral grains that form the solid phase of a soil aggregate are the product of rock weathering. The size of the individual grains varies over a wide range. Many of the phys- ical properties of soil are dictated by the size, shape, and chemical composition of the grains. To better understand these factors, one must be familiar with the basic types of rock that form the earth’s crust, the rock-forming minerals, and the weathering process. On the basis of their mode of origin, rocks can be divided into three basic types: igneous, sedimentary, and metamorphic. Figure 2.1 shows a diagram of the formation cycle of different types of rock and the processes associated with them. This is called the rock cycle. Brief discussions of each element of the rock cycle follow. Igneous Rock Igneous rocks are formed by the solidification of molten magma ejected from deep within the earth’s mantle. After ejection by either fissure eruption or volcanic eruption, some of the molten magma cools on the surface of the earth. Sometimes magma ceases its mobil- ity below the earth’s surface and cools to form intrusive igneous rocks that are called plu- tons. Intrusive rocks formed in the past may be exposed at the surface as a result of the continuous process of erosion of the materials that once covered them. The types of igneous rock formed by the cooling of magma depend on factors such as the composition of the magma and the rate of cooling associated with it. After con- ducting several laboratory tests, Bowen (1922) was able to explain the relation of the rate of magma cooling to the formation of different types of rock. This explanation—known as Bowen’s reaction principle—describes the sequence by which new minerals are formed as magma cools. The mineral crystals grow larger and some of them settle. The crystals that remain suspended in the liquid react with the remaining melt to form a new mineral 15 Origin of Soil and Grain Size
  32. 32. 16 Chapter 2: Origin of Soil and Grain Size Lower resistance to weathering Olivine Augite Hornblende Biotite (black mica) Orthoclase (potassium feldspar) Muscovite (white mica) Quartz Sodium feldspar Higher resistance to weathering Continuous plagioclase feldspar series Calcium feldspar Crystallization at higher temperature Crystallization at lower temperature Discontinuous ferromagnesian series Figure 2.2 Bowen’s reaction series Transportation,Erosion,Weathering Compaction, Cementation, Crystallization Metamorphic rock Igneous rock Sedimentary rock Sediments Magma Metamorphism M elting Figure 2.1 Rock cycle
  33. 33. 2.1 Rock Cycle and the Origin of Soil 17 at a lower temperature. This process continues until the entire body of melt is solidified. Bowen classified these reactions into two groups: (1) discontinuous ferromagnesian reac- tion series, in which the minerals formed are different in their chemical composition and crystalline structure, and (2) continuous plagioclase feldspar reaction series, in which the minerals formed have different chemical compositions with similar crystalline structures. Figure 2.2 shows Bowen’s reaction series. The chemical compositions of the minerals are given in Table 2.1. Figure 2.3 is a scanning electron micrograph of a fractured surface of quartz showing glass-like fractures with no discrete planar cleavage. Figure 2.4 is a scan- ning electron micrograph that shows basal cleavage of individual mica grains. Thus, depending on the proportions of minerals available, different types of igneous rock are formed. Granite, gabbro, and basalt are some of the common types of igneous rock generally encountered in the field. Table 2.2 shows the general composition of some igneous rocks. Table 2.1 Composition of Minerals Shown in Bowen’s Reaction Series Mineral Composition Olivine (Mg, Fe)2SiO4 Augite Ca, Na(Mg, Fe, Al)(Al, Si2O6) Hornblende Complex ferromagnesian silicate of Ca, Na, Mg, Ti, and Al Biotite (black mica) K(Mg, Fe)3AlSi3O10(OH)2 Orthoclase (potassium feldspar) K(AlSi3O8) Muscovite (white mica) KAl3Si3O10(OH)2 Quartz SiO2 Ca1Al2Si2O82 Na1AlSi3O82 Plagioclase e calcium feldspar sodium feldspar Table 2.2 Composition of Some Igneous Rocks Name Mode of of rock occurrence Texture Abundant minerals Less abundant minerals Granite Intrusive Coarse Quartz, sodium feldspar, Biotite, muscovite, potassium feldspar hornblende Rhyolite Extrusive Fine Gabbro Intrusive Coarse Plagioclase, Hornblende, biotite, pyroxines, olivine magnetite Basalt Extrusive Fine Diorite Intrusive Coarse Plagioclase, Biotite, pyroxenes hornblende (quartz usually absent) Andesite Extrusive Fine Syenite Intrusive Coarse Potassium feldspar Sodium feldspar, biotite, hornblende Trachyte Extrusive Fine Peridotite Intrusive Coarse Olivine, pyroxenes Oxides of iron
  34. 34. Figure 2.3 Scanning electron micrograph of fractured surface of quartz showing glass-like fractures with no discrete planar surface (Courtesy of David J. White, Iowa State University, Ames, Iowa) Figure 2.4 Scanning electron micrograph show- ing basal cleavage of individual mica grains (Courtesy of David J. White, Iowa State University, Ames, Iowa) 18
  35. 35. Weathering Weathering is the process of breaking down rocks by mechanical and chemical pro- cesses into smaller pieces. Mechanical weathering may be caused by the expansion and contraction of rocks from the continuous gain and loss of heat, which results in ultimate disintegration. Frequently, water seeps into the pores and existing cracks in rocks. As the temperature drops, the water freezes and expands. The pressure exerted by ice because of volume expansion is strong enough to break down even large rocks. Other physical agents that help disintegrate rocks are glacier ice, wind, the running water of streams and rivers, and ocean waves. It is important to realize that in mechanical weath- ering, large rocks are broken down into smaller pieces without any change in the chem- ical composition. Figure 2.5 shows several examples of mechanical erosion due to ocean waves and wind at Yehliu in Taiwan. This area is located at a long and narrow sea cape at the northwest side of Keelung, about 15 kilometers between the north coast of Chin Shan and Wanli. In chemical weathering, the original rock minerals are transformed into new min- erals by chemical reaction. Water and carbon dioxide from the atmosphere form car- bonic acid, which reacts with the existing rock minerals to form new minerals and soluble salts. Soluble salts present in the groundwater and organic acids formed from decayed organic matter also cause chemical weathering. An example of the chemical weathering of orthoclase to form clay minerals, silica, and soluble potassium carbonate follows: Orthoclase Silica Kaolinite (clay mineral) Most of the potassium ions released are carried away in solution as potassium carbonate is taken up by plants. The chemical weathering of plagioclase feldspars is similar to that of orthoclase in that it produces clay minerals, silica, and different soluble salts. Ferromagnesian minerals also form the decomposition products of clay minerals, silica, and soluble salts. Additionally, the iron and magnesium in ferromagnesian minerals result in other products such as hematite and limonite. Quartz is highly resistant to weathering and only slightly soluble in water. Figure 2.2 shows the susceptibility of rock-forming minerals to weather- ing. The minerals formed at higher temperatures in Bowen’s reaction series are less resist- ant to weathering than those formed at lower temperatures. The weathering process is not limited to igneous rocks. As shown in the rock cycle (Figure 2.1), sedimentary and metamorphic rocks also weather in a similar manner. Thus, from the preceding brief discussion, we can see how the weathering process changes solid rock masses into smaller fragments of various sizes that can range from large boulders to very small clay particles. Uncemented aggregates of these small grains in var- ious proportions form different types of soil. The clay minerals, which are a product of chemical weathering of feldspars, ferromagnesians, and micas, give the plastic property to soils. There are three important clay minerals: (1) kaolinite, (2) illite, and (3) montmoril- lonite. (We discuss these clay minerals later in this chapter.) 2K1AlSi3O8 2 ϩ 2Hϩ ϩ H2O S 2Kϩ ϩ 4SiO2 ϩ Al2Si2O51OH24 Carbonic acid H2O ϩ CO2 S H2CO3 S Hϩ ϩ 1HCO3 2Ϫ 2.1 Rock Cycle and the Origin of Soil 19
  36. 36. 20 Figure 2.5 Mechanical erosion due to ocean waves and wind at Yehliu, Taiwan (Courtesy of Braja M. Das, Henderson, Nevada)
  37. 37. Figure 2.5 (Continued) 21
  38. 38. Transportation of Weathering Products The products of weathering may stay in the same place or may be moved to other places by ice, water, wind, and gravity. The soils formed by the weathered products at their place of origin are called resid- ual soils. An important characteristic of residual soil is the gradation of particle size. Fine- grained soil is found at the surface, and the grain size increases with depth. At greater depths, angular rock fragments may also be found. The transported soils may be classified into several groups, depending on their mode of transportation and deposition: 1. Glacial soils—formed by transportation and deposition of glaciers 2. Alluvial soils—transported by running water and deposited along streams 3. Lacustrine soils—formed by deposition in quiet lakes 4. Marine soils—formed by deposition in the seas 5. Aeolian soils—transported and deposited by wind 6. Colluvial soils—formed by movement of soil from its original place by gravity, such as during landslides Sedimentary Rock The deposits of gravel, sand, silt, and clay formed by weathering may become compacted by overburden pressure and cemented by agents like iron oxide, calcite, dolomite, and quartz. Cementing agents are generally carried in solution by ground-water. They fill the spaces between particles and form sedimentary rock. Rocks formed in this way are called detrital sedimentary rocks. All detrital rocks have a clastic texture. The following are some examples of detrital rocks with clastic texture. Particle size Sedimentary rock Granular or larger (grain size 2 mm–4 mm or larger) Conglomerate Sand Sandstone Silt and clay Mudstone and shale In the case of conglomerates, if the particles are more angular, the rock is called breccia. In sandstone, the particle sizes may vary between mm and 2 mm. When the grains in sandstone are practically all quartz, the rock is referred to as orthoquartzite. In mudstone and shale, the size of the particles are generally less than mm. Mudstone has a blocky aspect; whereas, in the case of shale, the rock is split into platy slabs. Sedimentary rock also can be formed by chemical processes. Rocks of this type are classified as chemical sedimentary rock. These rocks can have clastic or nonclastic texture. The following are some examples of chemical sedimentary rock. Composition Rock Calcite (CaCO3) Limestone Halite (NaCl) Rock salt Dolomite [CaMg(CO3)] Dolomite Gypsum (CaSO4 ؒ 2H2O) Gypsum 1 16 1 16 22 Chapter 2: Origin of Soil and Grain Size
  39. 39. Limestone is formed mostly of calcium carbonate deposited either by organisms or by an inorganic process. Most limestones have a clastic texture; however, nonclastic textures also are found commonly. Figure 2.6 shows the scanning electron micrograph of a fractured sur- face of Limestone. Individual grains of calcite show rhombohedral cleavage. Chalk is a sed- imentary rock made in part from biochemically derived calcite, which are skeletal fragments of microscopic plants and animals. Dolomite is formed either by chemical dep- osition of mixed carbonates or by the reaction of magnesium in water with limestone. Gypsum and anhydrite result from the precipitation of soluble CaSO4 due to evaporation of ocean water. They belong to a class of rocks generally referred to as evaporites. Rock salt (NaCl) is another example of an evaporite that originates from the salt deposits of seawater. Sedimentary rock may undergo weathering to form sediments or may be subjected to the process of metamorphism to become metamorphic rock. Metamorphic Rock Metamorphism is the process of changing the composition and texture of rocks (without melt- ing) by heat and pressure. During metamorphism, new minerals are formed, and mineral grains are sheared to give a foliated-texture to metamorphic rock. Gneiss is a metamorphic rock derived from high-grade regional metamorphism of igneous rocks, such as granite, gab- bro, and diorite. Low-grade metamorphism of shales and mudstones results in slate. The clay minerals in the shale become chlorite and mica by heat; hence, slate is composed primarily of mica flakes and chlorite. Phyllite is a metamorphic rock, which is derived from slate with 2.1 Rock Cycle and the Origin of Soil 23 Figure 2.6 Scanning electron micrograph of the fractured surface of limestone (Courtesy of David J. White, Iowa State University, Ames, Iowa)
  40. 40. further metamorphism being subjected to heat greater than 250 to 300ЊC. Schist is a type of metamorphic rock derived from several igneous, sedimentary, and low-grade metamorphic rocks with a well-foliated texture and visible flakes of platy and micaceous minerals. Metamorphic rock generally contains large quantities of quartz and feldspar as well. Marble is formed from calcite and dolomite by recrystallization. The mineral grains in marble are larger than those present in the original rock. Green marbles are colored by hornblends, serpentine, or talc. Black marbles contain bituminous material, and brown marbles contain iron oxide and limonite. Quartzite is a metamorphic rock formed from quartz-rich sandstones. Silica enters into the void spaces between the quartz and sand grains and acts as a cementing agent. Quartzite is one of the hardest rocks. Under extreme heat and pressure, metamorphic rocks may melt to form magma, and the cycle is repeated. 2.2 Soil-Particle Size As discussed in the preceding section, the sizes of particles that make up soil vary over a wide range. Soils generally are called gravel, sand, silt, or clay, depending on the pre- dominant size of particles within the soil. To describe soils by their particle size, several organizations have developed particle-size classifications. Table 2.3 shows the particle-size classifications developed by the Massachusetts Institute of Technology, the U.S. Department of Agriculture, the American Association of State Highway and Transportation Officials, and the U.S. Army Corps of Engineers and U.S. Bureau of Reclamation. In this table, the MIT system is presented for illustration purposes only. This system is important in the history of the development of the size limits of particles present in soils; however, the Unified Soil Classification System is now almost universally accepted and has been adopted by the American Society for Testing and Materials (ASTM). Figure 2.7 shows the size limits in a graphic form. Gravels are pieces of rocks with occasional particles of quartz, feldspar, and other minerals. Sand particles are made of mostly quartz and feldspar. Other mineral grains also 24 Chapter 2: Origin of Soil and Grain Size Table 2.3 Particle-Size Classifications Grain size (mm) Name of organization Gravel Sand Silt Clay Massachusetts Institute of Technology Ͼ2 2 to 0.06 0.06 to 0.002 Ͻ0.002 (MIT) U.S. Department of Agriculture Ͼ2 2 to 0.05 0.05 to 0.002 Ͻ0.002 (USDA) American Association of State 76.2 to 2 2 to 0.075 0.075 to 0.002 Ͻ0.002 Highway and Transportation Officials (AASHTO) Unified Soil Classification System 76.2 to 4.75 4.75 to 0.075 Fines (U.S. Army Corps of Engineers, U.S. (i.e., silts and clays) Bureau of Reclamation, and American Ͻ0.075 Society for Testing and Materials) Note: Sieve openings of 4.75 mm are found on a U.S. No. 4 sieve; 2-mm openings on a U.S. No. 10 sieve; 0.075-mm openings on a U.S. No. 200 sieve. See Table 2.5.
  41. 41. 2.2 Soil-Particle Size 25 Massachusetts Institute of Technology U.S. Department of Agriculture American Association of State Highway and Transportation Officials Unified Soil Classification System 100 10 1.0 0.1 0.01 0.001 Grain size (mm) Gravel Sand Silt Silt and clay Clay Figure 2.7 Soil-separate-size limits by various systems may be present at times. Figure 2.8 shows the scanning electron micrograph of some sand grains. Note that the larger grains show rounding that can occur as a result of wear during intermittent transportation by wind and/or water. Figure 2.9 is a higher magnification of the grains highlighted in Figure 2.8, and it reveals a few small clay particles adhering to larger sand grains. Silts are the microscopic soil fractions that consist of very fine quartz Figure 2.8 Scanning electron micrograph of some sand grains (Courtesy of David J. White, Iowa State University, Ames, Iowa)
  42. 42. 26 Chapter 2: Origin of Soil and Grain Size Figure 2.9 Higher magnification of the sand grains highlighted in Figure 2.8 (Courtesy of David J. White, Iowa State University, Ames, Iowa) grains and some flake-shaped particles that are fragments of micaceous minerals. Clays are mostly flake-shaped microscopic and submicroscopic particles of mica, clay minerals, and other minerals. As shown in Table 2.3 and Figure 2.7, clays generally are defined as particles smaller than 0.002 mm. However, in some cases, particles between 0.002 and 0.005 mm in size also are referred to as clay. Particles classified as clay on the basis of their size may not necessarily contain clay minerals. Clays have been defined as those particles “which develop plasticity when mixed with a limited amount of water” (Grim, 1953). (Plasticity is the putty-like property of clays that contain a certain amount of water.) Nonclay soils can contain particles of quartz, feldspar, or mica that are small enough to be within the clay classification. Hence, it is appropriate for soil particles smaller than 2 microns (2 mm), or 5 microns (5 mm) as defined under different systems, to be called clay-sized particles rather than clay. Clay particles are mostly in the colloidal size range (Ͻ1 mm), and 2 mm appears to be the upper limit. 2.3 Clay Minerals Clay minerals are complex aluminum silicates composed of two basic units: (1) silica tetra- hedron and (2) alumina octahedron. Each tetrahedron unit consists of four oxygen atoms surrounding a silicon atom (Figure 2.10a). The combination of tetrahedral silica units gives
  43. 43. and Oxygen Hydroxyl Aluminum Silicon and Oxygen (a) Silicon (b) and Hydroxyl (c) (d) Aluminum (e) Figure 2.10 (a) Silica tetrahedron; (b) silica sheet; (c) alumina octahedron; (d) octahedral (gibb- site) sheet; (e) elemental silica-gibbsite sheet (After Grim, 1959. With permission from ASCE.) a silica sheet (Figure 2.10b). Three oxygen atoms at the base of each tetrahedron are shared by neighboring tetrahedra. The octahedral units consist of six hydroxyls surrounding an aluminum atom (Figure 2.10c), and the combination of the octahedral aluminum hydroxyl units gives an octahedral sheet. (This also is called a gibbsite sheet—Figure 2.10d.) 2.3 Clay Minerals 27
  44. 44. 28 Chapter 2: Origin of Soil and Grain Size Sometimes magnesium replaces the aluminum atoms in the octahedral units; in this case, the octahedral sheet is called a brucite sheet. In a silica sheet, each silicon atom with a positive charge of four is linked to four oxygen atoms with a total negative charge of eight. But each oxygen atom at the base of the tetrahedron is linked to two silicon atoms. This means that the top oxygen atom of each tetrahedral unit has a negative charge of one to be counterbalanced. When the silica sheet is stacked over the octahedral sheet, as shown in Figure 2.10e, these oxygen atoms replace the hydroxyls to balance their charges. Of the three important clay minerals, kaolinite consists of repeating layers of ele- mental silica-gibbsite sheets in a 1:1 lattice, as shown in Figures 2.11 and 2.12a. Each layer is about 7.2 Å thick. The layers are held together by hydrogen bonding. Kaolinite occurs as platelets, each with a lateral dimension of 1000 to 20,000 Å and a thickness of 100 to 1000 Å. The surface area of the kaolinite particles per unit mass is about 15 m2 /g. The surface area per unit mass is defined as specific surface. Figure 2.13 shows a scanning elec- tron micrograph of a kaolinite specimen. Illite consists of a gibbsite sheet bonded to two silica sheets—one at the top and another at the bottom (Figures 2.14 and 2.12b). It is sometimes called clay mica. The illite layers are bonded by potassium ions. The negative charge to balance the potassium ions comes from the substitution of aluminum for some silicon in the tetrahedral sheets. Substitution of one element for another with no change in the crystalline form is known as Figure 2.11 Atomic structure of montmorillonite (After Grim, 1959. With permission from ASCE.) Oxygen Hydroxyl Aluminum Silicon
  45. 45. 2.3 Clay Minerals 29 nH2O and exchangeable cations (c)(b)(a) Basal spacing variable—from 9.6 Å to complete separation 7.2 Å 10 Å Gibbsite sheet Silica sheet Potassium Gibbsite sheet Gibbsite sheet Silica sheet Silica sheet Potassium Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet Silica sheet Gibbsite sheet Silica sheet Silica sheet Figure 2.12 Diagram of the structures of (a) kaolinite; (b) illite; (c) montmorillonite Figure 2.13 Scanning electron micrograph of a kaolinite specimen (Courtesy of David J. White, Iowa State University, Ames, Iowa) isomorphous substitution. Illite particles generally have lateral dimensions ranging from 1000 to 5000 Å and thicknesses from 50 to 500 Å. The specific surface of the particles is about 80 m2 /g. Montmorillonite has a structure similar to that of illite—that is, one gibbsite sheet sandwiched between two silica sheets. (See Figures 2.15 and 2.12c.) In montmorillonite there is isomorphous substitution of magnesium and iron for aluminum in the octahedral
  46. 46. 30 Chapter 2: Origin of Soil and Grain Size sheets. Potassium ions are not present as in illite, and a large amount of water is attracted into the space between the layers. Particles of montmorillonite have lateral dimensions of 1000 to 5000 Å and thicknesses of 10 to 50 Å. The specific surface is about 800 m2 /g. Figure 2.16 is a scanning electron micrograph showing the fabric of montmorillonite. Besides kaolinite, illite, and montmorillonite, other common clay minerals generally found are chlorite, halloysite, vermiculite, and attapulgite. The clay particles carry a net negative charge on their surfaces. This is the result both of isomorphous substitution and of a break in continuity of the structure at its edges. Larger neg- ative charges are derived from larger specific surfaces. Some positively charged sites also occur at the edges of the particles. A list of the reciprocal of the average surface densities of the neg- ative charges on the surfaces of some clay minerals follows (Yong and Warkentin, 1966): Reciprocal of average surface density of charge Clay mineral (Å2 /electronic charge) Kaolinite 25 Clay mica and chlorite 50 Montmorillonite 100 Vermiculite 75 Figure 2.14 Atomic structure of illite PotassiumOxygen Hydroxyl Aluminum Silicon
  47. 47. 2.3 Clay Minerals 31 Exchangeable cations nH2O Oxygen Hydroxyl Aluminum, iron, magnesium Silicon, occasionally aluminum Figure 2.15 Atomic structure of montmorillonite (After Grim, 1959. With permission from ASCE.) In dry clay, the negative charge is balanced by exchangeable cations like Ca2ϩ , Mg2ϩ , Naϩ , and Kϩ surrounding the particles being held by electrostatic attraction. When water is added to clay, these cations and a few anions float around the clay particles. This configuration is referred to as a diffuse double layer (Figure 2.17a). The cation concentration decreases with the distance from the surface of the particle (Figure 2.17b). Water molecules are polar. Hydrogen atoms are not axisymmetric around an oxygen atom; instead, they occur at a bonded angle of 105Њ (Figure 2.18). As a result, a water mol- ecule has a positive charge at one side and a negative charge at the other side. It is known as a dipole. Dipolar water is attracted both by the negatively charged surface of the clay particles and by the cations in the double layer. The cations, in turn, are attracted to the soil par- ticles. A third mechanism by which water is attracted to clay particles is hydrogen bond- ing, where hydrogen atoms in the water molecules are shared with oxygen atoms on the
  48. 48. 32 Chapter 2: Origin of Soil and Grain Size Figure 2.16 Scanning electron micrograph showing the fabric of montmorillonite (Courtesy of David J. White, Iowa State University, Ames, Iowa) Surface of clay particle (b) Cations Anions Distance from the clay particle Concentrationofions (a) Ϫ ϩ ϩ ϩ Ϫ Ϫ ϩ Ϫ ϩ ϩ ϩ Ϫ ϩ ϩ Ϫ Ϫ Ϫ Ϫ ϩ ϩ ϩ Ϫ Ϫ ϩ ϩ ϩ Ϫ ϩ Ϫ Ϫ ϩ ϩ ϩ ϩ ϩ Ϫ ϩ Ϫ ϩ Ϫ ϩ Ϫ ϩ Figure 2.17 Diffuse double layer surface of the clay. Some partially hydrated cations in the pore water are also attracted to the surface of clay particles. These cations attract dipolar water molecules. All these pos- sible mechanics of attraction of water to clay are shown in Figure 2.19. The force of attrac- tion between water and clay decreases with distance from the surface of the particles. All
  49. 49. 2.3 Clay Minerals 33 105° Hydrogen Hydrogen Oxygen Figure 2.18 Dipolar character of water Dipolar water molecule Dipolar water molecule Cation Clay particle Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ ϩ Ϫ Ϫ Ϫ Ϫ Ϫ ϪϪ ϪϪ Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩϩ ϩ ϩ ϩϩ ϩϩ ϩ ϩ ϩϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ Figure 2.19 Attraction of dipolar molecules in diffuse double layer the water held to clay particles by force of attraction is known as double-layer water. The innermost layer of double-layer water, which is held very strongly by clay, is known as adsorbed water. This water is more viscous than free water is. Figure 2.20 shows the absorbed and double-layer water for typical montmorillonite and kaolinite particles. This orientation of water around the clay particles gives clay soils their plastic properties. It needs to be well recognized that the presence of clay minerals in a soil aggregate has a great influence on the engineering properties of the soil as a whole. When moisture is present, the engineering behavior of a soil will change greatly as the percentage of clay mineral content increases. For all practical purposes, when the clay content is about 50% or more, the sand and silt particles float in a clay matrix, and the clay minerals primarily dictate the engineering properties of the soil.
  50. 50. 34 Chapter 2: Origin of Soil and Grain Size 200 Å 200 Å 10 Å Typical montmorillonite particle, 1000 Å by 10 Å (a) Typical kaolinite particle, 10,000 Å by 1000 Å (b) 1000 Å 400 Å 400 Å 10ϩ Å 10ϩ Å Montmorillonite crystal Adsorbed water Double-layer waterKaolinite crystal Figure 2.20 Clay water (Redrawn after Lambe, 1958. With permission from ASCE.) 2.4 Specific Gravity (Gs) Specific gravity is defined as the ratio of the unit weight of a given material to the unit weight of water. The specific gravity of soil solids is often needed for various calculations in soil mechanics. It can be determined accurately in the laboratory. Table 2.4 shows the specific gravity of some common minerals found in soils. Most of the values fall within a range of 2.6 to 2.9. The specific gravity of solids of light-colored sand, which is mostly made of quartz, may be estimated to be about 2.65; for clayey and silty soils, it may vary from 2.6 to 2.9.
  51. 51. 2.5 Mechanical Analysis of Soil 35 2.5 Mechanical Analysis of Soil Mechanical analysis is the determination of the size range of particles present in a soil, expressed as a percentage of the total dry weight. Two methods generally are used to find the particle-size distribution of soil: (1) sieve analysis—for particle sizes larger than 0.075 mm in diameter, and (2) hydrometer analysis—for particle sizes smaller than 0.075 mm in diameter. The basic principles of sieve analysis and hydrometer analysis are described briefly in the following two sections. Sieve Analysis Sieve analysis consists of shaking the soil sample through a set of sieves that have progressively smaller openings. U.S. standard sieve numbers and the sizes of openings are given in Table 2.5. Table 2.4 Specific Gravity of Common Minerals Mineral Specific gravity, Gs Quartz 2.65 Kaolinite 2.6 Illite 2.8 Montmorillonite 2.65–2.80 Halloysite 2.0–2.55 Potassium feldspar 2.57 Sodium and calcium feldspar 2.62–2.76 Chlorite 2.6–2.9 Biotite 2.8–3.2 Muscovite 2.76–3.1 Hornblende 3.0–3.47 Limonite 3.6–4.0 Olivine 3.27–3.7 Table 2.5 U.S. Standard Sieve Sizes Sieve no. Opening (mm) Sieve no. Opening (mm) 4 4.75 35 0.500 5 4.00 40 0.425 6 3.35 50 0.355 7 2.80 60 0.250 8 2.36 70 0.212 10 2.00 80 0.180 12 1.70 100 0.150 14 1.40 120 0.125 16 1.18 140 0.106 18 1.00 170 0.090 20 0.850 200 0.075 25 0.710 270 0.053 30 0.600
  52. 52. 36 Chapter 2: Origin of Soil and Grain Size The sieves used for soil analysis are generally 203 mm (8 in.) in diameter. To con- duct a sieve analysis, one must first oven-dry the soil and then break all lumps into small particles. The soil then is shaken through a stack of sieves with openings of decreasing size from top to bottom (a pan is placed below the stack). Figure 2.21 shows a set of sieves in a shaker used for conducting the test in the laboratory. The smallest-sized sieve that should be used for this type of test is the U.S. No. 200 sieve. After the soil is shaken, the mass of soil retained on each sieve is determined. When cohesive soils are analyzed, breaking the lumps into individual particles may be difficult. In this case, the soil may be mixed with water to make a slurry and then washed through the sieves. Portions retained on each sieve are collected separately and oven-dried before the mass retained on each sieve is measured. 1. Determine the mass of soil retained on each sieve (i.e., M1, M2, · · · Mn) and in the pan (i.e., Mp) 2. Determine the total mass of the soil: M1 ϩ M2 ϩ · · · ϩ Mi ϩ · · · ϩ Mn ϩ Mp ϭ ͚ M 3. Determine the cumulative mass of soil retained above each sieve. For the ith sieve, it is M1 ϩ M2 ϩ · · · ϩ Mi Figure 2.21 A set of sieves for a test in the laboratory (Courtesy of Braja M. Das, Henderson, Nevada)
  53. 53. 2.5 Mechanical Analysis of Soil 37 4. The mass of soil passing the ith sieve is ͚ M Ϫ (M1 ϩ M2 ϩ · · · ϩ Mi) 5. The percent of soil passing the ith sieve (or percent finer) is Once the percent finer for each sieve is calculated (step 5), the calculations are plot- ted on semilogarithmic graph paper (Figure 2.22) with percent finer as the ordinate (arith- metic scale) and sieve opening size as the abscissa (logarithmic scale). This plot is referred to as the particle-size distribution curve. Hydrometer Analysis Hydrometer analysis is based on the principle of sedimentation of soil grains in water. When a soil specimen is dispersed in water, the particles settle at different velocities, depending on their shape, size, weight, and the viscosity of the water. For simplicity, it is assumed that all the soil particles are spheres and that the velocity of soil particles can be expressed by Stokes’ law, according to which (2.1) D ϭ diameter of soil particles h ϭ viscosity of water rw ϭ density of water rs ϭ density of soil particles where v ϭ velocity v ϭ rs Ϫ rw 18h D2 F ϭ ͚ M Ϫ 1M1 ϩ M2 ϩ p ϩ Mi 2 ͚ M ϫ 100 Particle size (mm) — log scale Percentpassing 100 80 60 40 20 0 0.51.010.0 5.0 0.050.1 Figure 2.22 Particle-size distribution curve
  54. 54. 38 Chapter 2: Origin of Soil and Grain Size Thus, from Eq. (2.1), (2.2) where Note that (2.3) Thus, combining Eqs. (2.2) and (2.3) gives (2.4) If the units of h are (g и sec)/cm2 , rw is in g/cm3 , L is in cm, t is in min, and D is in mm, then or Assume rw to be approximately equal to 1 g/cm3 , so that (2.5) where (2.6) Note that the value of K is a function of Gs and h, which are dependent on the temperature of the test. Table 2.6 gives the variation of K with the test temperature and the specific grav- ity of soil solids. K ϭ B 30h 1Gs Ϫ 12 D 1mm2 ϭ K B L 1cm2 t 1min2 D ϭ B 30h 1Gs Ϫ 12rw B L t D1mm2 10 ϭ B 18h 3 1g # sec2/cm2 4 1Gs Ϫ 12rw 1g/cm3 2 B L 1cm2 t 1min2 ϫ 60 D ϭ B 18h 1Gs Ϫ 12rw B L t rs ϭ Gs rw v ϭ Distance Time ϭ L t . D ϭ B 18hv rs Ϫ rw ϭ B 18h rs Ϫ rw B L t
  55. 55. 2.5 Mechanical Analysis of Soil 39 In the laboratory, the hydrometer test is conducted in a sedimentation cylin- der usually with 50 g of oven-dried sample. Sometimes 100-g samples also can be used. The sedimentation cylinder is 457 mm (18 in.) high and 63.5 mm (2.5 in.) in di- ameter. It is marked for a volume of 1000 ml. Sodium hexametaphosphate generally is used as the dispersing agent. The volume of the dispersed soil suspension is increased to 1000 ml by adding distilled water. Figure 2.23 shows an ASTM 152H type of hydrometer. When a hydrometer is placed in the soil suspension at a time t, measured from the start of sedimentation it measures the specific gravity in the vicinity of its bulb at a depth L (Figure 2.24). The specific gravity is a function of the amount of soil particles present per unit volume of suspension at that depth. Also, at a time t, the soil particles in sus- pension at a depth L will have a diameter smaller than D as calculated in Eq. (2.5). The larger particles would have settled beyond the zone of measurement. Hydrometers are designed to give the amount of soil, in grams, that is still in suspension. They are cali- brated for soils that have a specific gravity, Gs, of 2.65; for soils of other specific grav- ity, a correction must be made. By knowing the amount of soil in suspension, L, and t, we can calculate the per- centage of soil by weight finer than a given diameter. Note that L is the depth measured from the surface of the water to the center of gravity of the hydrometer bulb at which the density of the suspension is measured. The value of L will change with time t. Hydrometer analysis is effective for separating soil fractions down to a size of about Text not available due to copyright restrictions
  56. 56. 40 Chapter 2: Origin of Soil and Grain Size 0.5 mm. The value of L (cm) for the ASTM 152H hydrometer can be given by the expression (see Figure 2.24) (2.7) The value of L1 is 10.5 cm for a reading of R ϭ 0 and 2.3 cm for a reading of R ϭ 50. Hence, for any reading R, L1 ϭ 10.5 Ϫ 110.5 Ϫ 2.32 50 R ϭ 10.5 Ϫ 0.164R 1cm2 A ϭ cross-sectional area of the sedimentation cylinder ϭ 27.8 cm2 VB ϭ volume of the hydrometer bulb ϭ 67 cm3 L2 ϭ length of the hydrometer bulb ϭ 14 cm bulb to the mark for a hydrometer reading 1cm2 where L1 ϭ distance along the stem of the hydrometer from the top of the L ϭ L1 ϩ 1 2 aL2 Ϫ VB A b L L1 L2 Figure 2.24 Definition of L in hydrometer test 0 60 Figure 2.23 ASTM 152H hydrometer (Courtesy of ELE International)
  57. 57. 2.5 Mechanical Analysis of Soil 41 Table 2.7 Variation of L with Hydrometer Reading— ASTM 152H Hydrometer Hydrometer Hydrometer reading, R L (cm) reading, R L (cm) 0 16.3 31 11.2 1 16.1 32 11.1 2 16.0 33 10.9 3 15.8 34 10.7 4 15.6 35 10.6 5 15.5 36 10.4 6 15.3 37 10.2 7 15.2 38 10.1 8 15.0 39 9.9 9 14.8 40 9.7 10 14.7 41 9.6 11 14.5 42 9.4 12 14.3 43 9.2 13 14.2 44 9.1 14 14.0 45 8.9 15 13.8 46 8.8 16 13.7 47 8.6 17 13.5 48 8.4 18 13.3 49 8.3 19 13.2 50 8.1 20 13.0 51 7.9 21 12.9 52 7.8 22 12.7 53 7.6 23 12.5 54 7.4 24 12.4 55 7.3 25 12.2 56 7.1 26 12.0 57 7.0 27 11.9 58 6.8 28 11.7 59 6.6 29 11.5 60 6.5 30 11.4 Thus, from Eq. (2.7), (2.8) where R ϭ hydrometer reading corrected for the meniscus. On the basis of Eq. (2.8), the variations of L with the hydrometer readings R are given in Table 2.7. In many instances, the results of sieve analysis and hydrometer analysis for finer fractions for a given soil are combined on one graph, such as the one shown in Figure 2.25. When these results are combined, a discontinuity generally occurs in the range where they overlap. This discontinuity occurs because soil particles are generally irregular in shape. L ϭ 10.5 Ϫ 0.164R ϩ 1 2 a14 Ϫ 67 27.8 b ϭ 16.29 Ϫ 0.164R
  58. 58. 42 Chapter 2: Origin of Soil and Grain Size Sieve analysis gives the intermediate dimensions of a particle; hydrometer analysis gives the diameter of an equivalent sphere that would settle at the same rate as the soil particle. 2.6 Particle-Size Distribution Curve A particle-size distribution curve can be used to determine the following four parameters for a given soil (Figure 2.26): 1. Effective size (D10): This parameter is the diameter in the particle-size dis- tribution curve corresponding to 10% finer. The effective size of a granular soil is a good measure to estimate the hydraulic conductivity and drainage through soil. 2. Uniformity coefficient (Cu): This parameter is defined as (2.9) where D60 ϭ diameter corresponding to 60% finer. 3. Coefficient of gradation (Cc): This parameter is defined as (2.10)Cc ϭ D30 2 D60 ϫ D10 Cu ϭ D60 D10 Particle diameter (mm)—log scale Unified classification Sand Sieve analysis 10 16 30 40 60 100 200 Hydrometer analysis Sieve no. Silt and clay Percentfiner 100 80 60 40 20 0 0.5 0.2 0.1 0.0515 2 0.005 0.002 0.0010.010.02 Sieve analysis Hydrometer analysis Figure 2.25 Particle-size distribution curve—sieve analysis and hydrometer analysis
  59. 59. 2.6 Particle-Size Distribution Curve 43 4. Sorting coefficient (S0): This parameter is another measure of uniformity and is gen- erally encountered in geologic works and expressed as (2.11) The sorting coefficient is not frequently used as a parameter by geotechnical engineers. The percentages of gravel, sand, silt, and clay-size particles present in a soil can be obtained from the particle-size distribution curve. As an example, we will use the particle- size distribution curve shown in Figure 2.25 to determine the gravel, sand, silt, and clay size particles as follows (according to the Unified Soil Classification System—see Table 2.3): Size (mm) Percent finer 76.2 100 100 Ϫ 100 ϭ 0% gravel 4.75 100 100 Ϫ 62 ϭ 38% sand 0.075 62 62 Ϫ 0 ϭ 62% silt and clay — 0 The particle-size distribution curve shows not only the range of particle sizes present in a soil, but also the type of distribution of various-size particles. Such types of distributions are demonstrated in Figure 2.27. Curve I represents a type of soil in which most of the soil grains are the same size. This is called poorly graded soil. Curve II represents a soil in which the par- ticle sizes are distributed over a wide range, termed well graded. A well-graded soil has a uni- formity coefficient greater than about 4forgravelsand6forsands,andacoefficientofgradation between 1 and 3 (for gravels and sands). A soil might have a combination of two or more uni- formlygraded fractions. Curve III represents such a soil. This type of soil is termed gap graded. S0 ϭ B D75 D25 Particle size (mm)—log scale Percentfiner 100 80 60 40 30 25 75 20 10 0 0.5 0.1 0.051.010.0 5.0 D75 D30 D25 D10D60 Figure 2.26 Definition of D75, D60, D30, D25, and D10
  60. 60. 44 Example 2.1 Following are the results of a sieve analysis. Make the necessary calculations and draw a particle-size distribution curve. Mass of soil retained U.S. sieve no. on each sieve (g) 4 0 10 40 20 60 40 89 60 140 80 122 100 210 200 56 Pan 12 Solution The following table can now be prepared. Mass Cumulative mass U.S. Opening retained on retained above Percent sieve (mm) each sieve (g) each sieve (g) finera (1) (2) (3) (4) (5) 4 4.75 0 0 100 10 2.00 40 0 + 40 ϭ 40 94.5 20 0.850 60 40 + 60 ϭ 100 86.3 40 0.425 89 100 + 89 ϭ 189 74.1 60 0.250 140 189 + 140 ϭ 329 54.9 80 0.180 122 329 + 122 ϭ 451 38.1 100 0.150 210 451 + 210 ϭ 661 9.3 200 0.075 56 661 + 56 ϭ 717 1.7 Pan – 12 717 + 12 ϭ 729 ϭ ⌺M 0 a g M Ϫ col. 4 g M ϫ 100 ϭ 729 Ϫ col. 4 729 ϫ 100 100 80 60 40 20 0 Percentfiner I II III 2.0 1.0 0.5 0.2 0.1 0.05 0.02 0.01 0.005 Particle diameter (mm)—log scale Well graded Poorly graded Gap graded Figure 2.27 Different types of particle-size distribution curves
  61. 61. 2.6 Particle-Size Distribution Curve 45 The particle-size distribution curve is shown in Figure 2.28. Figure 2.28 Particle-size distribution curve ■ Particle size (mm) D60 ϭ 0.27 mm D30 ϭ 0.17 mm D10 ϭ 0.15 mm Percentfiner 100 60 40 30 80 20 10 0 10 5 3 1 0.5 0.3 0.1 0.05 Example 2.2 For the particle-size distribution curve shown in Figure 2.28 determine a. D10, D30, and D60 b. Uniformity coefficient, Cu c. Coefficient of gradation, Cz Solution Part a From Figure 2.28, D10 ϭ 0.15 mm D30 ϭ 0.17 mm D60 ϭ 0.27 mm Part b ■Cz ϭ D2 30 D60 ϫ D10 ϭ 10.1722 10.27210.152 ϭ 0.71 Cu ϭ D60 D10 ϭ 0.27 0.15 ϭ 1.8
  62. 62. 46 Chapter 2: Origin of Soil and Grain Size 2.7 Particle Shape The shape of particles present in a soil mass is equally as important as the particle-size dis- tribution because it has significant influence on the physical properties of a given soil. However, not much attention is paid to particle shape because it is more difficult to mea- sure. The particle shape generally can be divided into three major categories: 1. Bulky 2. Flaky 3. Needle shaped Bulky particles are formed mostly by mechanical weathering of rock and minerals. Geologists use such terms as angular, subangular, subrounded, and rounded to describe the shapes of bulky particles. These shapes are shown qualitatively in Figure 2.29. Small sand particles located close to their origin are generally very angular. Sand particles carried by Figure 2.29 Shape of bulky particles Angular Subrounded Subangular Rounded Example 2.3 For the particle-size distribution curve shown in Figure 2.28, determine the percent- ages of gravel, sand, silt, and clay-size particles present. Use the Unified Soil Classification System. Solution From Figure 2.28, we can prepare the following table. Size (mm) Percent finer 76.2 100 100 Ϫ 100 ϭ 0% gravel 4.75 100 100 Ϫ 1.7 ϭ 98.3% sand 0.075 1.7 1.7 Ϫ 0 ϭ 1.7% silt and clay – 0
  63. 63. Problems 47 wind and water for a long distance can be subangular to rounded in shape. The shape of gran- ular particles in a soil mass has a great influence on the physical properties of the soil, such as maximum and minimum void ratios, shear strength parameters, compressibility, etc. The angularity, A, is defined as (2.12) The sphericity of bulky particles is defined as (2.13) Flaky particles have very low sphericity—usually 0.01 or less. These particles are predominantly clay minerals. Needle-shaped particles are much less common than the other two particle types. Examples of soils containing needle-shaped particles are some coral deposits and atta- pulgite clays. 2.8 Summary In this chapter, we discussed the rock cycle, the origin of soil by weathering, the particle- size distribution in a soil mass, the shape of particles, and clay minerals. Some important points include the following: 1. Rocks can be classified into three basic categories: (a) igneous, (b) sedimentary, and (c) metamorphic. 2. Soils are formed by chemical and mechanical weathering of rocks. 3. Based on the size of the soil particles, soil can be classified as gravel, sand, silt, or clay. 4. Clays are mostly flake-shaped microscopic and submicroscopic particles of mica, clay minerals, and other minerals. 5. Clay minerals are complex aluminum silicates that develop plasticity when mixed with a limited amount of water. 6. Mechanical analysis is a process for determining the size range of particles present in a soil mass. Sieve analysis and hydrometer analysis are two tests used in the mechanical analysis of soil. Problems 2.1 For a soil, suppose that D10 ϭ 0.08 mm, D30 ϭ 0.22 mm, and D60 ϭ 0.41 mm. Calculate the uniformity coefficient and the coefficient of gradation. 2.2 Repeat Problem 2.1 with the following: D10 ϭ 0.24 mm, D30 ϭ 0.82 mm, and D60 ϭ 1.81 mm. Lp ϭ length of particle V ϭ volume of particle where De ϭ equivalent diameter of the partilce ϭ 3 B 6V p S ϭ De Lp A ϭ Average radius of corners and edges Radius of the maximum inscribed sphere
  64. 64. 48 Chapter 2: Origin of Soil and Grain Size 2.3 Repeat Problem 2.1 with the following: D10 ϭ 0.18 mm, D30 ϭ 0.32 mm, and D60 ϭ 0.78 mm. 2.4 The following are the results of a sieve analysis: Mass of soil U.S. sieve no. retained (g) 4 0 10 18.5 20 53.2 40 90.5 60 81.8 100 92.2 200 58.5 Pan 26.5 a. Determine the percent finer than each sieve and plot a grain-size distribution curve. b. Determine D10, D30, and D60 from the grain-size distribution curve. c. Calculate the uniformity coefficient, Cu. d. Calculate the coefficient of gradation, Cc. 2.5 Repeat Problem 2.4 with the following: Mass of soil U.S. sieve no. retained (g) 4 0 10 44 20 56 40 82 60 51 80 106 100 92 200 85 Pan 35 2.6 Repeat Problem 2.4 with the following: Mass of soil U.S. sieve no. retained (g) 4 0 10 41.2 20 55.1 40 80.0 60 91.6 100 60.5 200 35.6 Pan 21.5
  65. 65. Problems 49 2.7 Repeat Problem 2.4 with the following results of a sieve analysis: Mass of soil retained on U.S. sieve no. each sieve (g) 4 0 6 0 10 0 20 9.1 40 249.4 60 179.8 100 22.7 200 15.5 Pan 23.5 2.8 The following are the results of a sieve and hydrometer analysis. Sieve number/ Percent Analysis grain size finer than Sieve 40 100 80 97 170 92 200 90 Hydrometer 0.04 mm 74 0.015 mm 42 0.008 mm 27 0.004 mm 17 0.002 mm 11 a. Draw the grain-size distribution curve. b. Determine the percentages of gravel, sand, silt, and clay according to the MIT system. c. Repeat part b according to the USDA system. d. Repeat part b according to the AASHTO system. 2.9 The particle-size characteristics of a soil are given in this table. Draw the particle- size distribution curve. Size (mm) Percent finer 0.425 100 0.033 90 0.018 80 0.01 70 0.0062 60 0.0035 50 0.0018 40 0.001 35
  66. 66. 50 Chapter 2: Origin of Soil and Grain Size Determine the percentages of gravel, sand, silt, and clay: a. According to the USDA system. b. According to the AASHTO system. 2.10 Repeat Problem 2.9 with the following data: Size (mm) Percent finer 0.425 100 0.1 92 0.052 84 0.02 62 0.01 46 0.004 32 0.001 22 2.11 In a hydrometer test, the results are as follows: Gs ϭ 2.60, temperature of water ϭ 24 °C, and R ϭ 43 at 60 min after the start of sedimentation (see Figure 2.24). What is the diameter, D, of the smallest-size particles that have settled beyond the zone of measurement at that time (that is, t ϭ 60 min)? 2.12 Repeat Problem 2.11 with the following values: Gs ϭ 2.70, temperature ϭ 23 °C, t ϭ 120 min, and R ϭ 25. References AMERICAN SOCIETY FOR TESTING AND MATERIALS (2007). ASTM Book of Standards, Sec. 4, Vol. 04.08, West Conshohocken, Pa. BOWEN, N. L. (1922). “The Reaction Principles in Petrogenesis,” Journal of Geology, Vol. 30, 177–198. GRIM, R. E. (1953). Clay Mineralogy, McGraw-Hill, New York. GRIM, R. E. (1959). “Physico-Chemical Properties of Soils: Clay Minerals,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 85, No. SM2, 1–17. LAMBE, T. W. (1958). “The Structure of Compacted Clay,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 84, No. SM2, 1655–1 to 1655–35. YONG, R. N., and WARKENTIN, B. P. (1966). Introduction of Soil Behavior, Macmillan, New York.
  67. 67. 3 Chapter 2 presented the geologic processes by which soils are formed, the description of limits on the sizes of soil particles, and the mechanical analysis of soils. In natural occur- rence, soils are three-phase systems consisting of soil solids, water, and air. This chapter discusses the weight–volume relationships of soil aggregates. 3.1 Weight–Volume Relationships Figure 3.1a shows an element of soil of volume V and weight W as it would exist in a nat- ural state. To develop the weight–volume relationships, we must separate the three phases (that is, solid, water, and air) as shown in Figure 3.1b. Thus, the total volume of a given soil sample can be expressed as (3.1) where Vs ϭ volume of soil solids Vv ϭ volume of voids Vw ϭ volume of water in the voids Va ϭ volume of air in the voids Assuming that the weight of the air is negligible, we can give the total weight of the sample as (3.2) where Ws ϭ weight of soil solids Ww ϭ weight of water The volume relationships commonly used for the three phases in a soil element are void ratio, porosity, and degree of saturation. Void ratio (e) is defined as the ratio of the vol- ume of voids to the volume of solids. Thus, (3.3)e ϭ Vv Vs W ϭ Ws ϩ Ww V ϭ Vs ϩ Vv ϭ Vs ϩ Vw ϩ Va 51 Weight–Volume Relationships

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