1. Soil Physics 2010 Outline Announcements Basic rheology Soil strength Triaxial test

2. Soil Physics 2010 Announcements New Homework, due Feb. 8 Alert: Exam Feb. 12

3. Soil Physics 2010 Basic rheology The study of how materials flow and deform Strength of materials Pitch drop experiment: 1 drop every ~9 years!

4. Soil Physics 2010 Stress Stress is a force per unit area: N m -2 This is also a pressure. The SI unit of pressure is the Pascal: 1 Pa = 1 N m -2 1 N is the force required to accelerate 1 kg by 1 m s -2, so in earth’s gravity (g = 9.81 m s -2 ), 1/9.81 kg would exert a pressure of 1 Pa if applied over 1 m 2. 0.1 kg 1 m 1 g

5. Soil Physics 2010 Pressure 1 Pa = 1 N m -2 = 1 (kg m)/(s 2 m 2 ) = 1 kg m -1 s -2 What is atmospheric pressure? g * (Mass of atmosphere above 1 m 2 ) = 101,325 Pa ≈ 101.3 kPa ≈ 0.1 MPa Same force as a column of water 10.1 m high ≈ 14.7 psi (pounds / inch 2 ) 0.1 kg 1 m 1 g

6. Soil Physics 2010 Stresses 4 Stresses commonly encountered: Compressive  Tensile  Shear  Torsion (not typical in soil)

7. Soil Physics 2010 Kinds of behavior under stress Elastic materials regain their pre-stress form Example: rubber Plastic materials remain in stressed form Example: modeling clay Viscous materials deform slowly Example: tar Brittle materials fracture under stress Example: brick Soils have aspects of all of these

8. Soil Physics 2010 Strain (elastic & plastic) Strain is deformation (e.g. in response to stress) Often given as  ≡  L / L 0 : a relative change in length (dimensionless) Young’s modulus is the ratio: E ≡  /  L    L L0L0 LL Original height L 0 –  L : Height after compression

9. Soil Physics 2010 Stress – strain curves I Hooke’s Law:  For elastic materials: L0L0 LL F Strain ,  L/L 0 Stress , F/A Slope is E: Young’s modulus E ≡  / , so  =  / E

10. L0L0 LL F Strain ,  L/L 0 Stress , F/A Soil Physics 2010 Stress – strain curves II For many materials (including soil, sometimes): Elastic Failure Plastic Material has sheared or fractured

11. Soil strength saturation, mass basis w bb 100% 75% 90% Soil Physics 2010 Proctor Compaction Test Water gets in the way No lubrication Optimal Soil strength is resistance to shear stress Strength depends mainly on: 1. Bulk density

12. Soil strength w bb 100% 75% 90% Soil Physics 2010 More force needed Less force needed Harder to compact when dry Soil strength is resistance to shear stress Strength depends mainly on: 1. Bulk density 2.Wetness

13. Soil strength Soil strength is resistance to shear stress Strength depends mainly on: 1. Bulk density 2.Wetness Soil Physics 2010 When the soil is saturated, some stress is borne by the water:  e =  t – p  e : effective stress (Terzaghi’s  t : total stress equation)  p : water pressure tttt

14. Soil Physics 2010 Soil strength Soil strength is resistance to shear stress Strength depends mainly on: 1. Bulk density 2.Wetness 3.Particle size distribution 10 1 10 0 10 -1 10 -2 10 -3 10 -4 Gradual Abrupt Poorly Graded Gradual distributions tend to be stronger: tighter grain packing

15. Soil Physics 2010 Basic laws of friction: Pull 1. friction  normal force Normal force Support Friction 2. friction is not affected by contact area (ideal case) 3. friction is not affected by velocity (for small velocities)

16. Soil Physics 2010 Shear test How strong is this soil? How hard is it to break this soil? Measure force needed to break Repeat for different normal forces Apply normal force

17. Soil Physics 2010 Direct shear (unconfined shear)

18. Soil Physics 2010 Direct shear (unconfined shear)

19. Soil Physics 2010 A better shear test (Allen presents the triaxial test)