Pe Test Geotechnical Rerview


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Pe Test Geotechnical Rerview

  1. 1. PE Refresher Course Geotechnical Component Class 1 Notes available at:
  2. 2. <ul><li>Organization </li></ul><ul><li>Lecture No. 1 </li></ul><ul><ul><li>Basics ( Chapter 35 ) </li></ul></ul><ul><ul><ul><li>Soil classification </li></ul></ul></ul><ul><ul><ul><li>Phase diagrams </li></ul></ul></ul><ul><ul><ul><li>Soil properties </li></ul></ul></ul><ul><ul><ul><ul><li>Compaction </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Permeability </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Consolidation </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Shear strength </li></ul></ul></ul></ul><ul><ul><li>Applications ( Chapter 35, 40 ) </li></ul></ul><ul><ul><ul><li>Settlement problems </li></ul></ul></ul><ul><ul><ul><li>Magnitude of settlement </li></ul></ul></ul><ul><ul><ul><li>Rate of settlement </li></ul></ul></ul>
  3. 3. <ul><li>Organization </li></ul><ul><li>Lecture No. 2 </li></ul><ul><li>Applications ( Chapters 36, 37, 38, 39, 40 ) </li></ul><ul><ul><li>Seepage problems </li></ul></ul><ul><ul><li>Slope stability problems </li></ul></ul><ul><ul><li>Foundations </li></ul></ul><ul><ul><ul><li>Shallow Foundation </li></ul></ul></ul><ul><ul><ul><li>Deep foundations </li></ul></ul></ul><ul><ul><li>Retaining structures </li></ul></ul><ul><ul><ul><li>Retaining walls </li></ul></ul></ul><ul><ul><ul><li>Braced excavations </li></ul></ul></ul>
  4. 4. <ul><li>Grain Size and Plasticity Characteristics </li></ul><ul><li>Grain Size Characteristics </li></ul><ul><ul><li>Sieve Analysis </li></ul></ul><ul><ul><li>Coefficient of Uniformity </li></ul></ul><ul><ul><ul><li>C u = D 60 /D 10 </li></ul></ul></ul><ul><ul><li>Coefficient of Curvature </li></ul></ul><ul><ul><ul><li>C z = (D 30 ) 2 / (D 60 x D 10 ) </li></ul></ul></ul>1-3 1-3 >4 5-10 4-6 15-300 25-1000 Gravel Fine sand Coarse sand Mixture of silty sand and gravel Mixture of clay, sand, silt and gravel Cz Cu Soil
  5. 5. <ul><li>Grain Size and Plasticity Characteristics </li></ul><ul><li>Hydrometer Analysis </li></ul><ul><ul><li>Relates particle size to settling velocity </li></ul></ul><ul><ul><li>Used to determine size of -#200 fraction </li></ul></ul><ul><li>Plasticity Characteristics </li></ul><ul><ul><li>Plastic Limit - lowest water content at which soil exhibits plastic behavior </li></ul></ul><ul><ul><li>Liquid limit - highest water content at which soil exhibits plastic behavior </li></ul></ul><ul><ul><li>Plasticity Index </li></ul></ul><ul><ul><ul><li>Pl = LL - PL </li></ul></ul></ul><ul><ul><li>Classification of fine-grained soils often based on plasticity characteristics as described by liquid limit and plasticity index </li></ul></ul>
  6. 6. <ul><li>Initial classification generally based on grain size </li></ul><ul><ul><li>Gravel Large grain size ( 4.75mm – 75mm) </li></ul></ul><ul><ul><li>Sand </li></ul></ul><ul><ul><li>Silt </li></ul></ul><ul><ul><li>Clay </li></ul></ul><ul><ul><li>Organics small grain size (.075mm – 4.75mm) </li></ul></ul>
  7. 7. <ul><li>USDA (US Department of Agriculture) </li></ul><ul><ul><li>Triangle identification chart - easy to use </li></ul></ul><ul><ul><li>Good for gardening (plant in loam) </li></ul></ul><ul><li>AASHTO (Am Assoc of State Highway Trans Officials) </li></ul><ul><li>Based on suitability of soil for use as pavement base </li></ul><ul><ul><li>Divides soil types into 8 groups, A-1 through A-8 </li></ul></ul><ul><ul><li>Granular soils (gravels and sands) fall into A-1 through A-3 </li></ul></ul><ul><ul><li>Differentiated primarily on basis of grain size distribution </li></ul></ul><ul><ul><li>Fine-grained soils (silts and clays) fall into A-4 through A-7. </li></ul></ul><ul><ul><li>Differentiated primarily on basis of plasticity characteristics </li></ul></ul><ul><ul><li>Highly organic soils fall into A-8 </li></ul></ul><ul><li>Subgroups depend on grain size and plasticity characteristics - See Table 9.2 </li></ul><ul><li>Group index added in parentheses after group and subgroup classification. </li></ul><ul><li>Group index calculated by Eq. 35.3 ( sub-grade suitability decreases with </li></ul><ul><li>increasing group index). </li></ul>Soil Classification (Section 9.3)
  8. 9. <ul><li>USCS (Unified Soil Classification System) </li></ul><ul><li>soils are classified on basis of parameters which influence their engineering properties . </li></ul><ul><li>Coarse – grained soils (gravels and sands) classified on basis of grain size characteristics </li></ul><ul><li>Fine-grained soils (silts and clays) classified on basis of plasticity characteristics . </li></ul><ul><li>Symbols: </li></ul><ul><ul><li>G Gravel </li></ul></ul><ul><ul><li>S Sand </li></ul></ul><ul><ul><li>M silt </li></ul></ul><ul><ul><li>C Clay </li></ul></ul><ul><ul><li>O Organic </li></ul></ul><ul><li>Modifiers: </li></ul><ul><ul><li>W Well Graded </li></ul></ul><ul><ul><li>P Poorly Graded </li></ul></ul><ul><ul><li>H High Plasticity </li></ul></ul><ul><ul><li>L Low Plasticity </li></ul></ul><ul><li>Examples: </li></ul><ul><ul><li>GW Well-graded gravel </li></ul></ul><ul><ul><li>SP Poorly-graded (uniform) sand </li></ul></ul><ul><ul><li>MH Highly plastic silt </li></ul></ul><ul><ul><li>CL Low plasticity clay </li></ul></ul><ul><ul><li>GM Silty gravel </li></ul></ul>
  9. 13. Given: Sieve analysis and plasticity data for the following three soils classify the soils Example * non-plastic 77 NP* 5 PI 47 - 15 PL 124 - 20 LL 97 5 60 No. 200 99 8 78 No. 100 100 40 86 No. 40 100 90 92 No. 10 100 97 99 No. 4 Soil 3, % Finer Soil 2, % Finer Soils 1, % Finer Sieve Size
  10. 15. Soil 1 > 50% passes #200 - Fine-grained LL=20, Pl=5 - plots in CL-ML (p. 35.6) Soil 2 < 50% passes #200 - Coarse-grained > 50% passes #4 - Sand D 60 = 0.71 mm D 30 = 0.34 mm D 10 = 0.18 mm SP - SM Soil 3 > 50% passes #200 - Fine -grained LL=124 Pl=77 - Off the chart - Extrapolating gives CH Could be CH-MH
  11. 16. Aggregate Soil Properties (Phase Diagrams) <ul><li>Phase Diagrams </li></ul><ul><ul><li>Solid, Water, and Gas phases shown separately </li></ul></ul><ul><ul><li>Volumes indicated on left side of phase diagram </li></ul></ul><ul><ul><li>Weights indicated on right side of phase diagram </li></ul></ul><ul><li>Definitions </li></ul><ul><ul><li>Void Ratio e = V v /V s </li></ul></ul><ul><ul><li>Porosity n = V v /V t </li></ul></ul><ul><ul><li>Water Content w = W w /W s </li></ul></ul><ul><ul><li>Degree of Saturation S = V w /W v </li></ul></ul><ul><ul><li>Density* ρ= Mass/Volume </li></ul></ul><ul><ul><li>Unit Weight* γ= weight/Volume </li></ul></ul><ul><ul><li>Specific Gravity G = ρ s /ρ w </li></ul></ul><ul><ul><li>*Review text lumps density and unit weight together and uses symbol ρ </li></ul></ul>Gas Water Solid V g V w V s V v V t O W w W s W t
  12. 17. Common practice is to assume V s = 1, then express other volumes and weights accordingly. From definitions Gas Water Solid wG s 1 e wG s ρ w G s ρ w ρ sub = ρ sat - ρ w Buoyant unit weight ρ sat = ρ m for S=100% Saturated unit weight ρ d = W s /V t Dry unit weight (dry density) ρ m = W t /V t Moist unit weight
  13. 18. Table 35.7 - Useful for rapid calculation of phase relationships
  14. 19. Given : e = 0.62 w = 15% G s = 2.65 Calculate : a. ⍴ d b. ⍴ m c. w for S = 100% d. ⍴ sat for S = 100% Example Gas Water Solid wG s 1 e wG s ρ w= S e ρ w G s ρ w
  15. 20. <ul><li>Standard Penetration Test </li></ul><ul><ul><li>140lb hammer dropped 30&quot; to drive standard sampler. Number of blows </li></ul></ul><ul><ul><li>required for 12&quot; penetration measured as standard penetration resistance, N. </li></ul></ul><ul><ul><li>Crude test but useful index of soil characteristics. </li></ul></ul><ul><ul><li>More useful in sands than in fine-grained soils. </li></ul></ul><ul><li>Moisture-Density Tests and Relationships </li></ul><ul><ul><li>Compaction Tests </li></ul></ul><ul><ul><ul><li>Proctor Test </li></ul></ul></ul><ul><ul><ul><li>Modified Proctor Test </li></ul></ul></ul><ul><ul><li>Density of soil for given compactive effort Influenced by water content </li></ul></ul><ul><ul><li>Density of soil for given water content influenced by level of compactive effort </li></ul></ul>Soil Testing and Mechanical Properties ⍴ d w Increasing E ⍴ d w opt w ( ⍴ d ) max
  16. 23. Field Density Tests
  17. 24. Direct Backscattering
  18. 27. Consolidation Test <ul><li>Procedure: </li></ul><ul><li>Apply vertical load in increments. </li></ul><ul><li>During each increment, measure change in </li></ul><ul><li>height of specimen as function of time . </li></ul><ul><li>At end of each increment when settlement stops, </li></ul><ul><li>measure change in height of specimen as function of vertical stress. </li></ul>
  19. 28. <ul><li>Measure deformation of sample with time </li></ul><ul><li>Plot: </li></ul><ul><li>Change in equilibrium void ratio w/ stress </li></ul><ul><ul><li> settlement magnitude information </li></ul></ul>e Change in void ratio w/time for stress Increment  settlement rate information <ul><li>Apply increment of stress </li></ul>e 0 e f P 0 P f Log p Initial equilibrium Final equilibrium e 0 e f time Initial equilibrium Final equilibrium Fast rate Slow rate
  20. 29. Consolidation Parameters <ul><li>Compression Index, C c </li></ul><ul><ul><li>Given by slope of e-log p curve (NC portion) </li></ul></ul><ul><li>Recompression Index, C r </li></ul><ul><ul><li>Given by slope of rebound portion of curve (OC portion) </li></ul></ul>Coefficient of Consolidation, C v e i e f High C v (fast settlement) Low C v (slow settlement) time e C c C r Log p e Normally consolidated Over-consolidated
  21. 30. <ul><ul><li>Shear strength influenced by pore fluid drainage </li></ul></ul><ul><ul><ul><li>Free drainage during loading  drained </li></ul></ul></ul><ul><ul><ul><li>No drainage during loading  undrained </li></ul></ul></ul><ul><ul><li>Mohr – Coulomb Failure Criterion </li></ul></ul>Shear Strength of soils friction cohesion c s For drained loading, c = 0 S Typical for sands For un-drained loading , S Typical for clays c S nc
  22. 31. Shear Strength and Principal Stresses Ϭ 3 Ϭ 1 Ϭ Շ c Փ Failure surface is always oriented at 45 + Փ/2 angle to minor principal stress axis At failure Shear strength Shear stress failure 45+  /2
  23. 32. <ul><ul><li>Generally fall into one (or both) of two categories: </li></ul></ul><ul><ul><li>Magnitude of settlement </li></ul></ul><ul><ul><li>Rate of settlement </li></ul></ul><ul><li>Must be able to : </li></ul><ul><li>Evaluate initial effective stress conditions </li></ul><ul><li>Evaluate change in effective stress due to imposed loading </li></ul><ul><li>Determine appropriate soil properties </li></ul><ul><li>Perform calculations </li></ul>APPLICATIONS Settlement Problems
  24. 33. Evaluation of Initial Effective Stresses <ul><li>For effective stresses, use ρ m above water table </li></ul><ul><li> ρ sub below water table </li></ul><ul><li>or calculate total stress and subtract water pressure </li></ul><ul><li>For total stresses, use ρ m above water table </li></ul><ul><li>ρ sat below water table </li></ul><ul><li>For water pressure, take product of ρ w and depth below water table </li></ul>Groundwater level Density of soil layers Thickness of soil layers Need to know
  25. 34. Example 10’ e = 0.40 w = 10% z Layer 1 Layer 2 5 ' 15' e = 0.60 S = 20% S = 100% First, calculate soil densities Then, calculate stresses
  26. 35. <ul><li>Change in effective stresses can be caused by: </li></ul><ul><li>External loading </li></ul><ul><ul><ul><li>Placement of fill ( Ϭ ‘ v up )  settlement </li></ul></ul></ul><ul><ul><ul><li>Construction of structure ( Ϭ ‘ v up )  settlement </li></ul></ul></ul><ul><ul><ul><li>Excavation ( Ϭ ‘ v down )  rebound </li></ul></ul></ul><ul><li>Change in groundwater conditions </li></ul><ul><ul><ul><li>Drawdown of water level – ( Ϭ ‘ v up )  settlement </li></ul></ul></ul><ul><ul><ul><li>Rising water level ( Ϭ ‘ v down )  rebound </li></ul></ul></ul><ul><li>Calculation of final effective stresses  after u excess dissipates </li></ul><ul><ul><li>Based on assumption of hydrostatic water pressures, u = ρ w (z-z w ) </li></ul></ul><ul><ul><li>Proceed in same way as for initial effective stresses </li></ul></ul><ul><li>Two important cases: </li></ul><ul><li>1. Areal loads – vertical stress = f (z) only </li></ul><ul><li>(large areal extent w /r /t thickness of soil layer) </li></ul><ul><li>2. Local loads – vertical stress = f (x, y, z) </li></ul><ul><ul><li>Must compute stress distribution </li></ul></ul>Evaluation of Change in Effective Stresses
  27. 36. <ul><ul><li>Areal Load </li></ul></ul><ul><ul><ul><li>Assume 5-ft-thick fill placed on top of </li></ul></ul></ul><ul><ul><ul><li>previous two-layered soil deposit. </li></ul></ul></ul><ul><ul><ul><li>Tests show ρ m =120 pcf. </li></ul></ul></ul>The increase in stress produced by an areal load is constant with depth Local Load Spread footing imposes uniform load of 1,000 psf over 10 ft x 10 ft area What is σ v '  different below edge of footing than below center. Different at depth than shallow Examples Z=20’ 5 ‘ ρ m = 120 10 ‘ z ρ m = 132 5 ‘ ρ m = 110 15 ‘ ρ sub = 66
  28. 37. Stress Distribution <ul><li>Important to be able to calculate subsurface stresses caused by loads or loaded areas on the ground surface. </li></ul><ul><li>Usually interested for settlement calculation problems. </li></ul><ul><li>Generally accomplished by stress distribution methods based on theory of elasticity. </li></ul><ul><li>Can use principle of superposition very useful. </li></ul><ul><li>Boussinesq – stresses caused by point load on surface. </li></ul><ul><li>Boussinesq solution widely used </li></ul><ul><li>For point load, use Eq. 40.1 </li></ul><ul><ul><li>Example 1 </li></ul></ul><ul><li>For strip footing loads, use Appendix 40a (left) </li></ul><ul><ul><li>Example 2 </li></ul></ul><ul><li>For square footing loads, use Appendix 40a (right) </li></ul><ul><ul><li>Example 3 </li></ul></ul><ul><li>For circular loaded areas, use Appendix 40b </li></ul><ul><ul><li>Example 4 </li></ul></ul><ul><li>For loaded areas of arbitrary shape, use (Newmark) </li></ul><ul><ul><li>Influence chart method – see Fig 40 3 </li></ul></ul><ul><li>Influence Chart </li></ul><ul><ul><li>Represents entire ground surface </li></ul></ul><ul><ul><li>Divided into number of “squares” – see Fig 40.3 </li></ul></ul><ul><ul><li>Squares set up so that uniform load on each </li></ul></ul><ul><ul><li>would cause same stress on subsurface </li></ul></ul><ul><ul><li>point below center of chart </li></ul></ul>
  29. 38. Example 1 Calculate vertical stress 5 ft. below and 2 ft. to the side of a surface point load of 1,000 lbs. 1000 lbs 5 ' 2 ' 5 ' P v Example 2 Calculate the vertical stress at a depth of 15 feet below the edge of a 5-foot-wide strip footing which imposes a bearing pressure of 2,000 psf on the ground surface. 15 ' P v 0.2p Chart in Appendix 40A p. A-69 (left side) 2,000 psf
  30. 39. PLOT 40.A
  31. 40. Example 3 Calculate the vertical stress at a depth of 14 feet below the center of a 4 ft. square footing that applies 10,000 psf bearing pressure to the ground surface 4 ' 14 ' P v 0.04p 10,000 psf p. 40.A Right side
  32. 41. PLOT 40.A
  33. 42. Example 3 Calculate the vertical stress at a depth of 14 feet below the center of a 4 ft. square footing that applies 10,000 psf bearing pressure to the ground surface 4 ' p. 40.A Right side Example 4 A 16 ft diameter water tank contains 20 feet of water. Calculate the vertical stress caused by the tank at a point 8 feet below the ground surface and 10 feet from the center of the tank. 8 ' P v 16 ft 10 ' 14 ' P v 0.04p 10,000 psf I = 0.2 Appendix D p. 40.B
  34. 43. PLOT 40.B
  35. 44. Determination of appropriate soil properties Compute C c or C r from e-log p curve Consolidation test C c applies to normally consolidated range C r applies to over-consolidated range Initial Conditions Final Conditions C c or C r e e 1 e 2 p 1 p 2 Log p
  36. 45. Pre-consolidation Pressure, P p <ul><li>Maximum effective stress under which soil has ever been in equilibrium </li></ul><ul><li>Soil is normally consolidated when current effective stress is equal to current value of pre-consolidation pressure. </li></ul><ul><li>Settlement behavior controlled by C c </li></ul><ul><li>Soil is over-consolidated when current effective stress is less than current value of pre-consolidation pressure. </li></ul><ul><li>Settlement behavior controlled by C r . </li></ul>Pre-consolidation Pressure, P ' p P ' 1 P ' 2 Log p e e 1 e 2 C r C c
  37. 46. Pre-consolidation Pressure, P p Disturbance Effects
  38. 47. Pre-consolidation Pressure, P p Casagrande Method
  39. 48. Calculation of Settlement Magnitude <ul><li>Need: </li></ul><ul><li>Initial and final effective stresses </li></ul><ul><li>Definition of C c and C r </li></ul>3. Definition of vertical strain P ‘ 1 P ‘ 2 Log p e e 1 e 2 P ‘ p e p OC NC initial final
  40. 49. First, calculate initial effective stress at center of soft clay layer  before new fill placed Next, calculate final stress after placement of new fill Then, calculate ultimate settlement as Example 5 Calculate the ultimate settlement of the soft clay layer due to placement of the new fill 4 ' 3 ' 2 ' 5 ' New Fill  = 125 pcf; w= 10% Old Fill Same properties as new fill Soft Clay C c =1.06 e o =2.53   sub = 30 pcf Dense Sand
  41. 50. Now, what would happen if half of the new fill was removed ? Since effective stress is decreasing, use C r Assuming C r = 0.10 rebound
  42. 51. Let’s now assume that 4 more feet of new fill is placed, bringing the total thickness Of new fill to 6 ft. Then
  43. 52. Time Rate of Primary Consolidation <ul><li>Rate controlled by coefficient of consolidation, C v </li></ul><ul><ul><li>High C v  rapid consolidation </li></ul></ul><ul><ul><li>Low C v  slow consolidation </li></ul></ul><ul><li>Degree of consolidation </li></ul><ul><ul><li>Fraction of ultimate settlement which has occurred by time t </li></ul></ul>Fraction of ultimate settlement which has occurred by time t Time required to reach given degree of consolidation Dimensionless time factor Settlement at given time t Where T v (t) and U(t) are related by Eq 40.23 and Table 40.1 50 90 100 .2 .85 T v 0% U Length of longest drainage path
  44. 53. Degree of Consolidation curves
  45. 54. Example 6 If C v for the soft clay of Example 5 was 10ft 2 /yr, how long would it take for 2 in of settlement to occur? What if the soft clay was underlain by impermeable bedrock? Then z= 5 ft Double drainage Single drainage