Introduction to Soil Mechanics

About the AuthorsBéla Bodó B.Sc., B.A., C.Eng., M.I.C.E, was born in Hungary and studied at Budapest Technical University, the University of London and the Open University. He developed his expertise in Soil Mechanics during his employment with British Rail and British Coal. Colin Jones B.Sc, C.Eng., M.I.C.E, P.G.C.E, studied at the University of Dundee, and worked at British Coal where he and Béla were colleagues. He has recently retired from the University of Wales, Newport where he was Programme Director for the Civil Engineering provision, specializing in Soil Mechanics and Geotechnics.

• Preface xiiDedication and Acknowledgments xiiiList of Symbols xiv1 Soil Structure 11.1 Volume relationships 11.1.1 Voids ratio (e) 21.1.2 Porosity (n) 31.1.3 Degree of saturation (Sr) 31.2 Weight−volume relationships 61.2.1 Bulk densities 71.2.2 Dry densities 81.2.3 Saturated densities 81.2.4 Submerged densities (γ′) 91.2.5 Density of solids (γs) 101.2.6 Specific gravity (Gs) 101.2.7 Moisture content (m) 111.2.8 Partially saturated soil 121.2.9 Relative density (Dr) 181.3 Alteration of soil structure by compaction 201.3.1 Laboratory compaction tests 211.3.2 Practical considerations 261.3.3 Relative compaction (Cr) 271.3.4 Compactive effort 271.3.5 Under- and overcompaction 281.3.6 Site tests of compaction 281.4 California bearing ratio (CBR) test 301.5 The pycnometer 35Supplementary problems for Chapter 1 392 Classification of Cohesive Soils 432.1 Atterberg Limits 432.1.1 Liquid Limit (LL) 432.1.2 Plastic Limit 482.1.3 Shrinkage Limit 502.1.4 Swelling of cohesive soils 562.1.5 Saturation Limit (Z%) 562.1.6 Relationship between the limits 572.1.7 Linear shrinkage and swelling 592.2 Consistency indices 642.2.1 Plasticity index (PI) 642.2.2 Relative consistency index (RI) 642.2.3 Liquidity index (LI) 642.3 Classification of soils by particle size 692.3.1 Sieve analysis 692.3.2 Uniformity coefficient (U) 732.3.3 Filter design 742.3.4 Typical problems 772.3.5 Combination of materials 782.3.6 Sedimentation tests 85Supplementary problems for Chapter 2 913 Permeability and Seepage 923.1 Coefficient of permeability (k) 933.2 Seepage velocity (us) 943.3 Determination of the value of k 963.3.1 Constant head test 963.3.2 Falling head test 983.4 Field pumping tests 1023.4.1 Unconfined layer 1023.4.2 Radius of influence (R) 1043.4.3 Confined layer under artesian pressure (σA) 1063.5 Permeability of stratified soil 1073.6 Flow nets 1083.6.1 Flow lines (FL) 1093.6.2 Head loss in a flow channel 1113.6.3 Equipotential lines (EPL) 1113.6.4 Flow net construction 1133.6.5 Application of flow nets 1143.6.6 Seepage flowrate (Q) 1143.6.7 Seepage pressure 1153.6.8 Seepage force (S) 1193.7 Erosion due to seepage 1213.8 Prevention of piping 1283.9 Flow net for earth dams 129Supplementary problems for Chapter 3 1354 Pressure at Depth Due to Surface Loading 1394.1 Concentrated point load 1404.2 Concentrated line load 1424.3 Uniform strip loading (Michell’s solution) 1444.4 Bulb of pressure diagrams 1474.5 Vertical pressure under triangular strip load 1514.6 Vertical pressure under circular area 1564.7 Rectangular footing 1594.8 Footings of irregular shape 1634.9 Pressure distribution under footings 1674.9.1 Influence of footing 1674.9.2 Influence of loading 1704.10 Linear dispersion of pressure 170Supplementary problems for Chapter 4 1735 Effective Pressure (σ′) 1755.1 Unloaded state 1755.2 Loaded state 1775.3 Flooded state 1805.4 Types of problem 1825.5 Effect of seepage on shallow footings 1945.6 Ground water lowering (at atmospheric pressure) 1955.7 Reduction of artesian pressure 1965.8 Capillary movement of water 1995.8.1 Equilibrium moisture content (mE) 2045.8.2 Soil suction (Ss) 208Supplementary problems for Chapter 5 2146 Shear Strength of Soils 2196.1 Coulomb–Mohr Theory 2206.1.1 Stresses on the plane of failure 2216.1.2 Friction and cohesion 2236.1.3 Apparent cohesion 2246.2 Stress path 2246.2.1 Stress path failure envelope 2256.2.2 Variation of stress path 2316.3 Effect of saturation 2346.3.1 Effective Mohr’s circle 2346.3.2 Effective stress path (ESP) 2346.4 Measurement of shear strength 2386.4.1 Triaxial tests 2386.4.2 Variation of pore pressure 2406.4.3 Total excess pore pressure 2416.4.4 Unconsolidated–undrained tests 2426.4.5 Quick-undrained test 2486.4.6 Consolidated–undrained (CU) test 2506.4.7 Consolidated–drained (CD) test 2526.4.8 Unconfined compression strength of clays 2536.4.9 Standard shear box test 2566.4.10 The Vane shear test 2596.4.11 Residual shear strength 2616.5 Thixotropy of clay 2636.6 Undrained cohesion and overburden pressure 263Supplementary problems for Chapter 6 2657 Consolidation and Settlement 2687.1 Consolidation 2687.2 The pressure–voids ratio curve 2707.2.1 Analytical solution 2707.2.2 Equation of the σ′−e curve 2717.2.3 Alternative conventional procedure 2747.2.4 Graphical solution 2767.3 Forms of the σ′−e curve 2797.3.1 Normally consolidated clay 2807.3.2 Overconsolidated clays 2807.4 Coefficient of Compressibility (av) 2817.5 Coefficient of Volume Change (mv) 2827.5.1 Voids ratio method 2827.5.2 Direct method 2827.6 Estimation of settlement 2847.6.1 Voids ratio method 2867.6.2 Method Using mv 2887.6.3 Direct method 2897.7 Rate of consolidation 2917.7.1 Variation of excess pore pressure with time 2927.7.2 Typical pore pressure distributions 2937.7.3 Estimation of time 2947.7.4 Coefficient of Consolidation (cv) 2957.8 Pore pressure isochrones 3017.8.1 Average percentage consolidation 3027.9 Coefficient of permeability (k) 3107.10 Time from similarity 3107.11 Total settlement 3117.11.1 Initial compression 3117.11.2 Primary consolidation 3117.11.3 Secondary consolidation 312Supplementary problems for Chapter 7 3148 Lateral Earth Pressure 3198.1 Resistance to active expansion 3208.2 The value of K0 3218.3 Stress path representation 3228.4 Rankine’s theory of cohesionless soil 3248.4.1 Stress path representation (Lambe) 3308.5 Rankine-Bell theory for c − φ soil 3348.5.1 Tension cracks 3358.5.2 Effect of surcharge (q kN/m) on z0 3368.5.3 Water in the cracks only 3368.6 Rankine−Bell theory for c–soil 3368.7 Pressure−force and its line of action 3368.7.1 Triangular diagram for uniform soil 3378.7.2 Triangular diagram for water 3378.7.3 Rectangular diagram for surcharge only 3388.8 Wall supporting sloping surface 3428.9 General formulae for c − φ soil 3428.9.1 Active case 3438.9.2 Passive case (with surcharge) 3458.10 Formulae for pure clay (φ = 0) 3498.11 Height of unsupported clay 3508.12 Wedge theories 3508.12.1 Procedure for cohesionless soil 3518.12.2 Procedure for cohesive soil 3558.12.3 Point of application of Pa(x) 3598.12.4 Effect of static water table 3608.13 Stability of retaining walls 3608.13.1 Gravity walls 3608.13.2 Cantilever walls 3618.13.3 Buttress and counterfort walls 3618.13.4 Stability check 3628.14 Sheet piles 3688.14.1 Cantilever sheet pile walls 3698.14.2 Factor of safety 3708.14.3 Bending of sheet piles 3748.14.4 Sheet pile in cohesive soils 3758.15 Anchored sheet pile walls 3758.15.1 Free-earth support method 3768.15.2 Fixed-earth support method 3848.15.3 Anchorage 3908.15.4 Length of tie rod (L) 3908.15.5 Stability of anchors 3908.16 Effect of ground water 3938.17 Stability of deep trenches 4008.17.1 Horizontal bracing 4008.18 Bentonite slurry support 4068.18.1 Trench in clay 4078.18.2 Trench in sand 408Supplementary problems for Chapter 8 4139 Bearing Capacity of Soils 4209.1 Terminology 4209.1.1 Foundation pressure (σ) 4209.1.2 Net foundation pressure (σn) 4219.1.3 Effective overburden pressure (σ′0) 4219.1.4 Ultimate bearing capacity (qu) 4219.1.5 Net ultimate bearing capacity (qn) 4219.1.6 Safe net bearing capacity (qsn) 4229.1.7 Safe bearing capacity (qs) 4229.1.8 Allowable foundation pressure (σa) 4229.1.9 Presumed bearing values 4249.2 Shallow strip footing 4249.2.1 Terzaghi’s equation for qu 4259.2.2 Effect of static water table 4289.3 Influence of footing shape 4359.4 Shallow rectangular footing 4369.4.1 Method of Fellenius 4389.5 Deep foundations 4399.5.1 Moderately deep foundations 4399.6 Standard penetration test (SPT) 4439.7 Pile foundations z/B > 4459.7.1 Types of pile 4469.8 Some reasons for choosing piles 4499.9 Some reasons for not choosing piles 4519.10 Effects necessitating caution 4519.11 Negative skin friction 4539.12 Stress distribution around piles 4559.13 Load-carrying capacity of piles 4559.13.1 Static formulae 4569.13.2 End-bearing resistance (Qe) 4569.13.3 Shaft resistance (Qs) 4579.13.4 Ultimate carrying capacity of pile 4589.13.5 Allowable carrying capacity of piles (Qa) 4589.13.6 Negative skin friction (Qf) 4589.14 End bearing resistance and SPT 4649.15 Influence of pile section on Qu 4659.16 Group of piles 4659.16.1 Eccentrically loaded pile group 4689.16.2 Settlement of pile groups 4719.16.3 Raking piles 472Supplementary problems for Chapter 9 47410 Stability of Slopes 47910.1 Short-term and long-term stability 47910.2 Total stress analysis (cohesive soils) 48010.2.1 Homogeneous, pure clay (φu = 0) 48010.2.2 Increasing the value of Fs 48110.2.3 Minimum value of Fs 48210.2.4 Potential slip surface 48210.2.5 Determination of the factor of safety 48310.2.6 Homogeneous c − φ soil (total stress analysis) 49710.2.7 Stratified slopes 50010.2.8 Slopes under water 50110.2.9 Taylor’s stability numbers 50510.3 Effective stress analysis (cohesive soils) 51310.3.1 Method of slices (radial procedure) 51310.3.2 Bishop’s conventional method 51810.3.3 Bishop’s rigorous iterative method 51910.4 Stability of infinite slopes 523Supplementary problems for Chapter 10 52811 Eurocode 7 53011.1 Introduction 53011.2 Recommended units 53011.3 Limit states 53111.4 Design procedures 53111.5 Verification procedures 53211.6 Application of partial factors 534AppendicesAppendix A Mass and Weight 552Appendix B Units, Conversion Factors and Unity Brackets 556Appendix C Simpson’s Rule 562Appendix D Resultant Force and Its Eccentricity 567Appendix E References 570Index 572