Principles of foundation engineering 7th edition

Sách của ông BRAJA DAS tập hợp tất cả công thức cơ học đất nền móng, hố đào sâu trong ngành xây dựng và cầu đường (tái bản lần thứ 7) bản gốc màu rất đẹp. Dùng để tra thông số đầu vào cho các phần mềm tính toán cơ đất như Plaxis, Slope, Sheet Pile, ...

conductivity: 1

111111Coefficient ofconsolidation:

in.>sec 5 2.54 cm>sec

in.>sec 5 0.0254 m>min

in.>min 5 304.8 mm>sec

Seventh Edition

Author Braja M Das

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Association of Foundation Drillers, Dallas, Texas

D B M Contractors, Inc., Federal Way,

Washington

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1.9 Soil Classification Systems 17

1.10 Hydraulic Conductivity of Soil 25

1.11 Steady-State Seepage 28

1.12 Effective Stress 30

1.13 Consolidation 32

1.14 Calculation of Primary Consolidation Settlement 37

1.15 Time Rate of Consolidation 38

1.16 Degree of Consolidation Under Ramp Loading 44

1.17 Shear Strength 47

1.18 Unconfined Compression Test 52

1.19 Comments on Friction Angle, 54

1.20 Correlations for Undrained Shear Strength, C u 57

2 Natural Soil Deposits and Subsoil Exploration 64

2.11 Purpose of Subsurface Exploration 74

2.12 Subsurface Exploration Program 74

2.13 Exploratory Borings in the Field 77

2.14 Procedures for Sampling Soil 81

2.15 Split-Spoon Sampling 81

2.16 Sampling with a Scraper Bucket 89

2.17 Sampling with a Thin-Walled Tube 90

2.18 Sampling with a Piston Sampler 92

2.19 Observation of Water Tables 92

2.20 Vane Shear Test 94

2.21 Cone Penetration Test 98

3.5 Modification of Bearing Capacity Equations for Water Table 142

3.6 The General Bearing Capacity Equation 143

3.7 Case Studies on Ultimate Bearing Capacity 148

3.8 Effect of Soil Compressibility 153

3.9 Eccentrically Loaded Foundations 157

3.10 Ultimate Bearing Capacity under Eccentric Loading—One-Way

Eccentricity 159

3.11 Bearing Capacity—Two-way Eccentricity 165

3.12 Bearing Capacity of a Continuous Foundation Subjected to

Eccentric Inclined Loading 173Problems 177

4.6 Bearing Capacity of Foundations on Top of a Slope 203

4.7 Seismic Bearing Capacity of a Foundation at the Edge

of a Granular Soil Slope 209

4.8 Bearing Capacity of Foundations on a Slope 210

5.2 Stress Due to a Concentrated Load 224

5.3 Stress Due to a Circularly Loaded Area 224

5.4 Stress below a Rectangular Area 226

5.5 Average Vertical Stress Increase Due to a Rectangularly

Loaded Area 232

5.6 Stress Increase under an Embankment 236

5.7 Westergaard’s Solution for Vertical Stress Due to a

Point Load 240

5.8 Stress Distribution for Westergaard Material 241

5.9 Elastic Settlement of Foundations on Saturated Clay (␮S⫽ 0.5) 243

5.10 Settlement Based on the Theory of Elasticity 245

5.11 Improved Equation for Elastic Settlement 254

5.12 Settlement of Sandy Soil: Use of Strain Influence Factor 258

5.13 Settlement of Foundation on Sand Based on Standard Penetration

Resistance 263

5.14 Settlement in Granular Soil Based on Pressuremeter Test

5.15 Primary Consolidation Settlement Relationships 273

5.16 Three-Dimensional Effect on Primary Consolidation

Settlement 274

5.17 Settlement Due to Secondary Consolidation 278

5.18 Field Load Test 280

5.19 Presumptive Bearing Capacity 282

5.20 Tolerable Settlement of Buildings 283Problems 285

References 288

6.1 Introduction 291

6.2 Combined Footings 291

6.3 Common Types of Mat Foundations 294

6.4 Bearing Capacity of Mat Foundations 296

6.5 Differential Settlement of Mats 299

6.6 Field Settlement Observations for Mat Foundations 300

6.7 Compensated Foundation 300

6.8 Structural Design of Mat Foundations 304Problems 322

References 323

7 Lateral Earth Pressure 324

7.1 Introduction 324

7.2 Lateral Earth Pressure at Rest 325

7.3 Rankine Active Earth Pressure 328

7.4 A Generalized Case for Rankine Active Pressure 334

7.5 Coulomb’s Active Earth Pressure 340

7.6 Active Earth Pressure Due to Surcharge 348

7.7 Active Earth Pressure for Earthquake Conditions 350

7.8 Active Pressure for Wall Rotation about the Top: Braced Cut 355

7.9 Active Earth Pressure for Translation of Retaining

Wall—Granular Backfill 357

7.10 Rankine Passive Earth Pressure 360

7.11 Rankine Passive Earth Pressure: Vertical Backface

and Inclined Backfill 363

7.12 Coulomb’s Passive Earth Pressure 365

7.13 Comments on the Failure Surface Assumption for Coulomb’s

8.2 Proportioning Retaining Walls 377

8.3 Application of Lateral Earth Pressure Theories to Design 378

8.4 Stability of Retaining Walls 380

8.5 Check for Overturning 382

8.6 Check for Sliding along the Base 384

8.7 Check for Bearing Capacity Failure 387

8.8 Construction Joints and Drainage from Backfill 396

8.9 Gravity Retaining-Wall Design for Earthquake Conditions 399

8.10 Comments on Design of Retaining Walls and a Case Study 402

8.11 Soil Reinforcement 405

8.12 Considerations in Soil Reinforcement 406

8.13 General Design Considerations 409

8.14 Retaining Walls with Metallic Strip Reinforcement 410

8.15 Step-by-Step-Design Procedure Using Metallic Strip

Reinforcement 417

8.16 Retaining Walls with Geotextile Reinforcement 422

8.17 Retaining Walls with Geogrid Reinforcement—General 428

8.18 Design Procedure fore Geogrid-Reinforced

Retaining Wall 428Problems 433

References 435

9.1 Introduction 437

9.2 Construction Methods 441

9.3 Cantilever Sheet Pile Walls 442

9.4 Cantilever Sheet Piling Penetrating Sandy Soils 442

9.5 Special Cases for Cantilever Walls Penetrating

a Sandy Soil 449

9.6 Cantilever Sheet Piling Penetrating Clay 452

9.7 Special Cases for Cantilever Walls Penetrating Clay 457

9.8 Anchored Sheet-Pile Walls 460

9.9 Free Earth Support Method for Penetration

of Sandy Soil 461

9.10 Design Charts for Free Earth Support Method (Penetration into

Sandy Soil) 465

9.11 Moment Reduction for Anchored Sheet-Pile Walls 469

9.12 Computational Pressure Diagram Method for Penetration into

Sandy Soil 472

9.13 Fixed Earth-Support Method for Penetration

into Sandy Soil 476

9.14 Field Observations for Anchor Sheet Pile Walls 479

9.15 Free Earth Support Method for Penetration of Clay 482

9.16 Anchors 486

9.17 Holding Capacity of Anchor Plates in Sand 488

9.18 Holding Capacity of Anchor Plates in Clay

10 Braced Cuts 501

10.1 Introduction 501

10.2 Pressure Envelope for Braced-Cut Design 502

10.3 Pressure Envelope for Cuts in Layered Soil 506

10.4 Design of Various Components of a Braced Cut 507

10.5 Case Studies of Braced Cuts 515

10.6 Bottom Heave of a Cut in Clay 520

10.7 Stability of the Bottom of a Cut in Sand 524

10.8 Lateral Yielding of Sheet Piles and Ground Settlement 529

Problems 531

References 533

11.1 Introduction 535

11.2 Types of Piles and Their Structural Characteristics 537

11.3 Estimating Pile Length 546

11.4 Installation of Piles 548

11.5 Load Transfer Mechanism 551

11.6 Equations for Estimating Pile Capacity 554

11.7 Meyerhof’s Method for Estimating Q p 557

11.8 Vesic’s Method for Estimating Q p 560

11.9 Coyle and Castello’s Method for Estimating Q pin Sand 563

11.10 Correlations for Calculating Q pwith SPT

and CPT Results 567

11.11 Frictional Resistance (Q s) in Sand 568

11.12 Frictional (Skin) Resistance in Clay 575

11.13 Point Bearing Capacity of Piles Resting on Rock 579

11.14 Pile Load Tests 583

11.15 Elastic Settlement of Piles 588

11.16 Laterally Loaded Piles 591

11.17 Pile-Driving Formulas 606

11.18 Pile Capacity For Vibration-Driven Piles 611

11.19 Negative Skin Friction 613

11.20 Group Efficiency 617

11.21 Ultimate Capacity of Group Piles

in Saturated Clay 621

11.22 Elastic Settlement of Group Piles 624

11.23 Consolidation Settlement of Group Piles 626

11.24 Piles in Rock 629Problems 629

12.4 Other Design Considerations 645

12.5 Load Transfer Mechanism 646

12.6 Estimation of Load-Bearing Capacity 646

12.7 Drilled Shafts in Granular Soil: Load-Bearing

Capacity 648

12.8 Load-Bearing Capacity Based on Settlement 652

12.9 Drilled Shafts in Clay: Load-Bearing Capacity 661

12.10 Load-Bearing Capacity Based on Settlement 663

12.11 Settlement of Drilled Shafts at Working Load 668

12.12 Lateral Load-Carrying Capacity—Characteristic Load

and Moment Method 670

12.13 Drilled Shafts Extending into Rock 679Problems 681

References 685

13.1 Introduction 686

13.2 Definition and Types of Collapsible Soil 686

13.3 Physical Parameters for Identification 687

13.4 Procedure for Calculating Collapse Settlement 691

13.5 Foundation Design in Soils Not Susceptible

to Wetting 692

13.6 Foundation Design in Soils Susceptible to Wetting 694

13.7 General Nature of Expansive Soils 695

13.8 Unrestrained Swell Test 699

13.9 Swelling Pressure Test 700

13.10 Classification of Expansive Soil on the Basis

of Index Tests 705

13.11 Foundation Considerations for Expansive Soils 708

13.12 Construction on Expansive Soils 711

13.13 General Nature of Sanitary Landfills 716

13.14 Settlement of Sanitary Landfills 717

Preface

Soil mechanics and foundation engineering have developed rapidly during the last fiftyyears Intensive research and observation in the field and the laboratory have refined andimproved the science of foundation design Originally published in the fall of 1983 with a

1984 copyright, this text on the principles of foundation engineering is now in the seventhedition The use of this text throughout the world has increased greatly over the years; italso has been translated into several languages New and improved materials that havebeen published in various geotechnical engineering journals and conference proceedingshave been incorporated into each edition of the text

Principles of Foundation Engineering is intended primarily for undergraduate civil

engineering students The first chapter, on Geotechnical Properties of Soil, reviews the ics covered in the introductory soil mechanics course, which is a prerequisite for the foun-dation engineering course The text is composed of fourteen chapters with examples andproblems, and an answer section for selected problems The chapters are mostly devoted tothe geotechnical aspects of foundation design Both Systéime International (SI) units andEnglish units are used in the text

top-Because the text introduces the application of fundamental concepts of foundationanalysis and design to civil engineering students, the mathematical derivations are notalways presented; instead, just the final form of the equation is given A list of referencesfor further information and study is included at the end of each chapter

Each chapter contains many example problems that will help students understandthe application of the equations and graphs For better understanding and visualization

of the ideas and field practices, about thirty new photographs have been added in thisedition

A number of practice problems also are given at the end of each chapter Answers tosome of these problems are given at the end of the text

The following is a brief overview of the changes from the sixth edition

• In several parts of the text, the presentation has been thoroughly reorganized for better understanding

• A number of new case studies have been added to familiarize students with the deviations from theory to practice

• In Chapter 1 on Geotechnical Properties of Soil, new sections on liquidity index andactivity have been added The discussions on hydraulic conductivity of clay, relativedensity, and the friction angle of granular soils have been expanded

• Expanded treatment of the weathering process of rocks is given in Chapter 2, NaturalSoil Deposits and Subsoil Exploration

• In Chapter 3 (Shallow Foundations: Ultimate Bearing Capacity), a new case study onbearing capacity failure in soft saturated clay has been added Also included is the

reduction factor method for estimating the ultimate bearing capacity of eccentrically

loaded strip foundations on granular soil

• Chapter 4, Ultimate Bearing Capacity of Shallow Foundations: Special Cases, hasnew sections on the ultimate bearing capacity of weaker soil underlain by a strongersoil, the seismic bearing capacity of foundations at the edge of a granular slope,foundations on rocks, and the stress characteristics solution for foundations located

on the top of granular slopes

• Stress distribution due to a point load and uniformly loaded circular and rectangularareas located on the surface of a Westergaard-type material has been added toChapter 5 on Allowable Bearing Capacity and Settlement Also included in this chapter is the procedure to estimate foundation settlement based on Pressuremetertest results

• Lateral earth pressure due to a surcharge on unyielding retaining structures is nowincluded in Chapter 7 (Lateral Earth Pressure) Also included in this chapter is thesolution for passive earth pressure on a retaining wall with inclined back face andhorizontal granular backfill using the method of triangular slices

• Chapter 8 on Retaining Walls has a new case study A more detailed discussion isprovided on the design procedure for geogrid-reinforced retaining walls

• Chapter 9 on Sheet Pile Walls has an added section on the holding capacity of plateanchors based on the stress characteristics solution

• Two case studies have been added to the chapter on Braced Cuts (Chapter 10)

• The chapter on Pile Foundations (Chapter 11) has been thoroughly reorganized forbetter understanding

• Based on recent publications, new recommendations have been made to estimate theload-bearing capacity of drilled shafts extending to rock (Chapter 12)

As my colleagues in the geotechnical engineering area well know, foundation sis and design is not just a matter of using theories, equations and graphs from a textbook.Soil profiles found in nature are seldom homogeneous, elastic, and isotropic The educatedjudgment needed to properly apply the theories, equations, and graphs to the evaluation ofsoils, foundations, and foundation design cannot be overemphasized or completely taught

analy-in the classroom Field experience must supplement classroom work

The following individuals were kind enough to share their photographs which havebeen included in this new edition

• Professor A S Wayal, K J Somayia Polytechnic, Mumbai, India

• Professor Sanjeev Kumar, Southern Illinois University, Carbondale, Illinois

• Mr Paul J Koszarek, Professional Service Industries, Inc., Waukesha, Wisconsin

• Professor Khaled Sobhan, Florida Atlantic University, Boca Raton, Florida

• Professor Jean-Louis Briaud, Texas A&M University, College Station, Texas

• Dr Dharma Shakya, Geotechnical Solutions, Inc., Irvine, California

• Mr Jon Ridgeway, Tensar International, Atlanta, Georgia

• Professor N Sivakugan, James Cook University, Townsville, Queensland, Australia

• Professor Anand J Puppala, University of Texas at Arlington, Arlington, Texas

• Professor Thomas M Petry, Missouri University of Science and Technology,Rolla, Missouri

Thanks are due to Neill Belk, graduate student at the University of North Carolina atCharlotte, and Jennifer Nicks, graduate student at Texas A&M University, College Station,Texas, for their help during the preparation of this revised edition I am also grateful forseveral helpful suggestions of Professor Adel S Saada of Case Western Reserve University,Cleveland, Ohio

Thanks are due to Chris Carson, Executive Director, Global Publishing Program;and Hilda Gowans, Senior Developmental Editor, Engineering, Cengage Learning; LaurenBetsos, Marketing Manager; and Rose Kernan of RPK Editorial Services for their interestand patience during the revision and production of the manuscript

For the past twenty-seven years, my primary source of inspiration has been theimmeasurable energy of my wife, Janice I am grateful for her continual help in thedevelopment of the original text and its six subsequent revisions

Braja M Das

The design of foundations of structures such as buildings, bridges, and dams generallyrequires a knowledge of such factors as (a) the load that will be transmitted by the super-structure to the foundation system, (b) the requirements of the local building code, (c) thebehavior and stress-related deformability of soils that will support the foundation system,and (d) the geological conditions of the soil under consideration To a foundation engineer,the last two factors are extremely important because they concern soil mechanics.The geotechnical properties of a soil—such as its grain-size distribution, plasticity,compressibility, and shear strength—can be assessed by proper laboratory testing In addi-

tion, recently emphasis has been placed on the in situ determination of strength and

defor-mation properties of soil, because this process avoids disturbing samples during fieldexploration However, under certain circumstances, not all of the needed parameters can

be or are determined, because of economic or other reasons In such cases, the engineermust make certain assumptions regarding the properties of the soil To assess the accuracy

of soil parameters—whether they were determined in the laboratory and the field orwhether they were assumed—the engineer must have a good grasp of the basic principles

of soil mechanics At the same time, he or she must realize that the natural soil deposits onwhich foundations are constructed are not homogeneous in most cases Thus, the engineermust have a thorough understanding of the geology of the area—that is, the origin andnature of soil stratification and also the groundwater conditions Foundation engineering

is a clever combination of soil mechanics, engineering geology, and proper judgmentderived from past experience To a certain extent, it may be called an art

When determining which foundation is the most economical, the engineer must sider the superstructure load, the subsoil conditions, and the desired tolerable settlement

con-In general, foundations of buildings and bridges may be divided into two major categories:

(1) shallow foundations and (2) deep foundations Spread footings, wall footings, and mat

foundations are all shallow foundations In most shallow foundations, the depth of ment can be equal to or less than three to four times the width of the foundation Pile and drilled shaft foundations are deep foundations They are used when top layers have poor

embed-1

Geotechnical Properties of Soil

Table 1.1 U.S Standard Sieve Sizes

Sieve No Opening (mm)

This chapter serves primarily as a review of the basic geotechnical properties of soils

It includes topics such as grain-size distribution, plasticity, soil classification, effective stress,consolidation, and shear strength parameters It is based on the assumption that you havealready been exposed to these concepts in a basic soil mechanics course

In any soil mass, the sizes of the grains vary greatly To classify a soil properly, you must

know its grain-size distribution The grain-size distribution of coarse-grained soil is erally determined by means of sieve analysis For a fine-grained soil, the grain-size distri- bution can be obtained by means of hydrometer analysis The fundamental features of

gen-these analyses are presented in this section For detailed descriptions, see any soil ics laboratory manual (e.g., Das, 2009)

mechan-Sieve Analysis

A sieve analysis is conducted by taking a measured amount of dry, well-pulverized soil andpassing it through a stack of progressively finer sieves with a pan at the bottom Theamount of soil retained on each sieve is measured, and the cumulative percentage of soil

passing through each is determined This percentage is generally referred to as percent

finer Table 1.1 contains a list of U.S sieve numbers and the corresponding size of their

openings These sieves are commonly used for the analysis of soil for classificationpurposes

The percent finer for each sieve, determined by a sieve analysis, is plotted on

semilog-arithmic graph paper, as shown in Figure 1.1 Note that the grain diameter, D, is plotted on

the logarithmic scale and the percent finer is plotted on the arithmetic scale.

Two parameters can be determined from the grain-size distribution curves of

coarse-grained soils: (1) the uniformity coefficient and (2) the coefficient of gradation, or

For the grain-size distribution curve shown in Figure 1.1,

and Thus, the values of and are

Figure 1.2 Hydrometer analysis

Parameters and are used in the Unified Soil Classification System, which is described

later in the chapter

Hydrometer Analysis

Hydrometer analysis is based on the principle of sedimentation of soil particles in water

This test involves the use of 50 grams of dry, pulverized soil A deflocculating agent is

always added to the soil The most common deflocculating agent used for hydrometeranalysis is 125 cc of 4% solution of sodium hexametaphosphate The soil is allowed tosoak for at least 16 hours in the deflocculating agent After the soaking period, distilledwater is added, and the soil–deflocculating agent mixture is thoroughly agitated The sam-ple is then transferred to a 1000-ml glass cylinder More distilled water is added to thecylinder to fill it to the 1000-ml mark, and then the mixture is again thoroughly agitated

A hydrometer is placed in the cylinder to measure the specific gravity of the soil–watersuspension in the vicinity of the instrument’s bulb (Figure 1.2), usually over a 24-hourperiod Hydrometers are calibrated to show the amount of soil that is still in suspension at

any given time t The largest diameter of the soil particles still in suspension at time t can

be determined by Stokes’ law,

Cc

Cu

Table 1.2 Soil-Separate Size Limits

Classification system Grain size (mm)

Unified Gravel: 75 mm to 4.75 mm

Sand: 4.75 mm to 0.075 mm Silt and clay (fines): mm

Sand: 2 mm to 0.05 mm Silt: 0.05 mm to 0.002 mm Clay: ,0.002 mm

,0.075

weight of watereffective length (i.e., length measured from the water surface in the cylinder to thecenter of gravity of the hydrometer; see Figure 1.2)

Soil particles having diameters larger than those calculated by Eq (1.3) would have settledbeyond the zone of measurement In this manner, with hydrometer readings taken at various

times, the soil percent finer than a given diameter D can be calculated and a grain-size

dis-tribution plot prepared The sieve and hydrometer techniques may be combined for a soilhaving both coarse-grained and fine-grained soil constituents

Several organizations have attempted to develop the size limits for gravel, sand, silt, and

clay on the basis of the grain sizes present in soils Table 1.2 presents the size limits

rec-ommended by the American Association of State Highway and Transportation Officials(AASHTO) and the Unified Soil Classification systems (Corps of Engineers, Department

of the Army, and Bureau of Reclamation) The table shows that soil particles smaller than

0.002 mm have been classified as clay However, clays by nature are cohesive and can be rolled into a thread when moist This property is caused by the presence of clay minerals such as kaolinite, illite, and montmorillonite In contrast, some minerals, such as quartz and feldspar, may be present in a soil in particle sizes as small as clay minerals, but these particles will not have the cohesive property of clay minerals Hence, they are called clay-

size particles, not clay particles.

In nature, soils are three-phase systems consisting of solid soil particles, water, and air (or

gas) To develop the weight–volume relationships for a soil, the three phases can be

sepa-rated as shown in Figure 1.3a Based on this separation, the volume relationships can then

be defined

The void ratio, e, is the ratio of the volume of voids to the volume of soil solids in a

given soil mass, or

V 5 total volume of soil

n 5VvV

Vs5 volume

Vv5 volume

(1.6)

The degree of saturation, S, is the ratio of the volume of water in the void spaces to

the volume of voids, generally expressed as a percentage, or

(1.7)where

of water

Note that, for saturated soils, the degree of saturation is 100%

The weight relationships are moisture content, moist unit weight, dry unit weight, and saturated unit weight, often defined as follows:

(1.8)where

of the soil solids

of water

(1.9)where

weight of the soil

The weight of air, in the soil mass is assumed to be negligible

(1.10)

When a soil mass is completely saturated (i.e., all the void volume is occupied by

water), the moist unit weight of a soil [Eq (1.9)] becomes equal to the saturated unit

More useful relations can now be developed by considering a representative soil

spec-imen in which the volume of soil solids is equal to unity, as shown in Figure 1.3b Note that

if then, from Eq (1.4), and the weight of the soil solids is

where

gravity of soil solids

unit weight of water (9.81 kN>m3)

Dry unit weight5 gd5Ws

Also, from Eq (1.8), the weight of water Thus, for the soil specimen underconsideration, Now, for the general relation for moist unit weightgiven in Eq (1.9),

According to Eq (1.7), degree of saturation is

Now, referring to Fig 1.3(b),

In SI units, Newton or kiloNewton is weight and is a derived unit, and g or kg ismass The relationships given in Eqs (1.11), (1.12) and (1.16) can be expressed as moist,dry, and saturated densities as follow:

be obtained by considering a representative soil specimen with a unit volume (Figure 1.3c).These relationships are

(1.20)(1.21)and

Except for peat and highly organic soils, the general range of the values of specificgravity of soil solids found in nature is rather small Table 1.4 gives some represen-tative values For practical purposes, a reasonable value can be assumed in lieu of running

a test

In granular soils, the degree of compaction in the field can be measured according to the

relative density, defined as

(1.23)

wherevoid ratio of the soil in the loosest statevoid ratio in the densest state

void ratioThe relative density can also be expressed in terms of dry unit weight, or

(1.24)

where

dry unit weight

dry unit weight in the densest state; that is, when the void ratio is dry unit weight in the loosest state; that is, when the void ratio is

The denseness of a granular soil is sometimes related to the soil’s relative density.Table 1.5 gives a general correlation of the denseness and For naturally occurringsands, the magnitudes of and [Eq (1.23)] may vary widely The main reasons forsuch wide variations are the uniformity coefficient,Cu,and the roundness of the particles

Table 1.4 Specific Gravities of Some Soils

Table 1.5 Denseness of a Granular Soil

Relative density, D r (%) Description

a Moist unit weight (kN/m3)

b Dry unit weight (kN/m3)

Part dFrom Eq (1.6),

Part eFrom Eq (1.14),

Part fFrom Eq (1.12),

Given: n⫽ 0.387 From Eq (1.6),

Specific gravity of soil solidsFrom Eq (1.18),

5 17.49 kN >m 3

w 5 9.8%

a The moist density of the soil in the field (kg/m3)

b The dry density of the soil in the field (kg/m3)

c The mass of water, in kilograms, to be added per cubic meter of soil in the field

for saturation

Solution

Part aFrom Eq (1.8),

From Eq (1.17),

Part bFrom Eq (1.18),

rd5 Gsrw

11 e5

(2.68) (1000)1.83 5 1468.48 kg >m 3

405.76 5 14.6%

From Eq (1.24),

■

When a clayey soil is mixed with an excessive amount of water, it may flow like a semiliquid.

If the soil is gradually dried, it will behave like a plastic, semisolid, or solid material,

depend-ing on its moisture content The moisture content, in percent, at which the soil changes from

a liquid to a plastic state is defined as the liquid limit (LL) Similarly, the moisture content,

in percent, at which the soil changes from a plastic to a semisolid state and from a semisolid

to a solid state are defined as the plastic limit (PL) and the shrinkage limit (SL), respectively These limits are referred to as Atterberg limits (Figure 1.4):

• The liquid limit of a soil is determined by Casagrande’s liquid device (ASTM Test

Designation D-4318) and is defined as the moisture content at which a grooveclosure of 12.7 mm occurs at 25 blows

• The plastic limit is defined as the moisture content at which the soil crumbles when

rolled into a thread of 3.18 mm in diameter (ASTM Test Designation D-4318)

g 5 gd(1 1 w) 5 16.11a1 1 8

100b 5 17.4 kN,m 3

gd5 16.11 kN>m3

0.75 c gd2 14.217.12 14.2d c17.1g

Solid state

Volume of the soil–water mixture

Semisolid state

Plastic state

Semiliquid

moisture content

Moisture content

LL PL

SL

Figure 1.4 Definition of Atterberg limits

• The shrinkage limit is defined as the moisture content at which the soil does not

undergo any further change in volume with loss of moisture (ASTM TestDesignation D-427)

The difference between the liquid limit and the plastic limit of a soil is defined as the

plasticity index (PI), or

(1.25)

The relative consistency of a cohesive soil in the natural state can be defined by a ratio

called the liquidity index, which is given by

(1.26)

where w⫽ in situ moisture content of soil.

The in situ moisture content for a sensitive clay may be greater than the liquid limit.

In this case,

LI⬎ 1These soils, when remolded, can be transformed into a viscous form to flow like aliquid

LI5 w 2 PL

LL2 PL

PI5 LL 2 PL

Soil deposits that are heavily overconsolidated may have a natural moisture contentless than the plastic limit In this case,

LI⬍ 0

Because the plasticity of soil is caused by the adsorbed water that surrounds the clay ticles, we can expect that the type of clay minerals and their proportional amounts in a soilwill affect the liquid and plastic limits Skempton (1953) observed that the plasticity index

par-of a soil increases linearly with the percentage par-of clay-size fraction (% finer than 2␮m byweight) present The correlations of PI with the clay-size fractions for different clays plotseparate lines This difference is due to the diverse plasticity characteristics of the varioustypes of clay minerals On the basis of these results, Skempton defined a quantity called

may be expressed as

(1.27)Activity is used as an index for identifying the swelling potential of clay soils.Typical values of activities for various clay minerals are given in Table 1.6

Soil classification systems divide soils into groups and subgroups based on common

engi-neering properties such as the grain-size distribution, liquid limit, and plastic limit The two major classification systems presently in use are (1) the American Association of State

Highway and Transportation Officials (AASHTO) System and (2) the Unified Soil Classification System (also ASTM) The AASHTO system is used mainly for the classifi-

cation of highway subgrades It is not used in foundation construction

(% of clay-size fraction, by weight)

Table 1.6 Activities of Clay Minerals

Table 1.7 AASHTO Soil Classification System

Granular materials General classification (35% or less of total sample passing No 200 sieve)

Group classification A-1-a A-1-b A-3 A-2-4 A-2-5 A-2-6 A-2-7

Sieve analysis (% passing)

No 40 sieve 30 max 50 max 51 min

No 200 sieve 15 max 25 max 10 max 35 max 35 max 35 max 35 max For fraction passing

No 40 sieve

Plasticity index (PI) 6 max Nonplastic 10 max 10 max 11 min 11 min Usual type of material Stone fragments, Fine sand Silty or clayey gravel and sand

gravel, and sand

Silt–clay materials General classification (More than 35% of total sample passing No 200 sieve)

For fraction passing

No 40 sieve

Usual types of material Mostly silty soils Mostly clayey soils

aIf the classification is A-7-5.

bIf PI LL 2 30, the classification is A-7-6.

PI < LL 2 30,

AASHTO System

The AASHTO Soil Classification System was originally proposed by the Highway ResearchBoard’s Committee on Classification of Materials for Subgrades and Granular Type Roads(1945) According to the present form of this system, soils can be classified according to eightmajor groups, A-1 through A-8, based on their grain-size distribution, liquid limit, and plas-ticity indices Soils listed in groups A-1, A-2, and A-3 are coarse-grained materials, and those

in groups A-4, A-5, A-6, and A-7 are fine-grained materials Peat, muck, and other highlyorganic soils are classified under A-8 They are identified by visual inspection

The AASHTO classification system (for soils A-1 through A-7) is presented inTable 1.7 Note that group A-7 includes two types of soil For the A-7-5 type, the plasticity

index of the soil is less than or equal to the liquid limit minus 30 For the A-7-6 type, theplasticity index is greater than the liquid limit minus 30.

For qualitative evaluation of the desirability of a soil as a highway subgrade

mater-ial, a number referred to as the group index has also been developed The higher the value

of the group index for a given soil, the weaker will be the soil’s performance as a subgrade

A group index of 20 or more indicates a very poor subgrade material The formula for thegroup index is

(1.29)

The group index is rounded to the nearest whole number and written next to the soil group

in parentheses; for example, we have

The group index for soils which fall in groups A-1-a, A-1-b, A-3, A-2-4, and A-2-5 isalways zero

Unified System

The Unified Soil Classification System was originally proposed by A Casagrande in

1942 and was later revised and adopted by the United States Bureau of Reclamationand the U.S Army Corps of Engineers The system is currently used in practically allgeotechnical work

In the Unified System, the following symbols are used for identification:

Description Gravel Sand Silt Clay Organic silts Peat and highly High Low Well Poorly

and clay organic soils plasticity plasticity graded graded

A-4

()*

Z Group indexSoil group

The plasticity chart (Figure 1.5) and Table 1.8 show the procedure for determining thegroup symbols for various types of soil When classifying a soil be sure to provide the groupname that generally describes the soil, along with the group symbol Figures 1.6, 1.7, and1.8 give flowcharts for obtaining the group names for coarse-grained soil, inorganic fine-grained soil, and organic fine-grained soil, respectively.

Liquid limit, LL

0 0

20

PI  0.9 (LL  8)

ML or OL

CL or OL

U-line

CH or OH

MH or OH 10

70 60 50 40 30

Figure 1.5 Plasticity chart