Geotechnical Engineering II_2.1_1723632296246.pptx

Geotech engineering ppt

1. UNIT II STRESSES IN SOILS

2. STRESSES IN A SOIL MASS A stress on the soil depends on the load per unit area. Construction of a foundation mainly increases the stresses on the soil. It is necessary to estimate the net increase of vertical stresses acting upon the soil as a result of construction of a foundation so that we can calculate the settlement strategy. As the stress increases in the soil, the soil can be deformed by the stress.

3. INTRODUCTION What is stress? Stress is defined as the force across a small boundary per unit area of that boundary, for all orientations of the boundary. Stress in soil is caused by the first or both of the following :- (a) self weight of soil. (B) structural loads, applied at or below the surface. The estimation of vertical stresses at any point in a soil mass due to external loading is essential to the prediction of settlements of buildings, bridges and pressure.

4. GEOSTATIC STRESSES Stresses due to self weight are known as geostatic stresses. When the ground surface is horizontal the stresses due to self wt of soil are normal to the horizontal and vertical planes, and are no shearing stresses on these places. This planes are principle planes. Types of stresses: Vertical Stresses: The vertical stress at depth z below ground surface due to self weight of soil is given by σ Z = γ *Z Where σ Z = vertical stress Z = depth below surface γ = unit weight of soil

5. CONTENT Introduction Geostatic Stresses Boussinesq’s Equation Vertical Stresses Under A Circular Area Vertical Stresses Under A Rectangular Area Equation Point Load Method Newmark’s Influence Chart

6. (2) Horizontal Stresses The horizontal stresses at any point in soil mass are highly variable. the horizontal stress is given by σ x = σ y = k * σ Z Where k = coefficient of lateral earth pressure at rest. = ϻ 1 − ϻ ϻ = Poison’s ratio.

7. BOUSSINESQ’S EQUATION Boussinesq published in 1885 a solution for the stresses beneath a point load on the surface of a material which had the following properties: Semi-infinite – this means infinite below the surface therefore providing no boundaries of the material apart from the surface Homogeneous – the same properties at all locations Isotropic –the same properties in all directions Elastic –a linear stress-strain relationship.

8. Assumptions made by boussinesq. The soil medium is an elastic, homogeneous, isotropic and semi infinite medium, which extends infinitely in all directions from a level surface The self weight of the soil is ignored. The soil is initially unstressed The change in volume of the soil upon application of the loads on to it is neglected. The top surface of the medium is free of shear stress and is subjected to only the point load at a specified location . The stresses are distributed symmetrically with respect to z axis.

9. Stresses due to point load vertical stress due to point load

10. Stresses due to line load

11. Stresses due to strip load

12. Stresses due to strip load The state of stress encountered in this case also is that of a plane strain condition. Such conditions are found for structures extended very much in one direction, such as strip and wall foundations, foundations of retaining walls, embankments, dams and the like. For such structures the distribution of stresses in any section (except for the end portions of 2 to 3 times the widths of the structures from its end) will be the same as in the neighboring sections, provided that the load does not change in directions perpendicular to the plane considered. Fig. 6.4(a) shows a load q per unit area acting on a strip of infinite length and of constant width B. The vertical stress at any arbitrary point P due to a line load of qdx acting at jc = x can be written from Eq. (6.4) as

13. Stresses due to strip load

14. Vertical stress under circular uniform load: Circular uniform load shown in Fig(8) At point A we can calculate the vertical stress. Assume small element with area rdφ . dr of the uniform load q from Boussinesq’s theory dQ = qdr . rdφ

15. Vertical stress under circular uniform load Circular uniform load shown in Fig(8) At point A we can calculate the vertical stress. Assume small element with area rdφ . dr of the uniform load q from Boussinesq’s theory dQ = qdr . rdφ

16. Vertical stress under circular uniform load

17. Vertical stress under circular uniform load

18. VERTICAL STRESS UNDER ON CIRCULAR AREA       3/ 2  2     1   ( R / z )  1    q  1 Where:  = Change in Vertical Stress q = Load per Unit Area z = Depth R = Radius

19. Pressure Bulb

20. P σz Bulbs of pressure Lines or Contours of equal stress increase

21. Pressure Bulb Stress isobar or pressure Bulb concept An isobar is a stress contour or a line which connects all points below the ground surface at which the vertical pressure is the same in fact an isobar is a spatial curved, surface and resembles a bulb in shape, this is because the vertical pressure at all points in a horizontal plane at equal radial distances from the load is the same. Thus, the stress isobar is also called the bulb of pressure or simply the pressure bulb. The vertical pressure at each point on the pressure bulb is the same.

22. Pressure Bulb Pressure at points inside the bulb are greater than that at a point on the surface of the bulb and pressures at points outside the bulb are smaller than that value.

23. N EWMARK I NFLUENCE C HARTS Newmark’s chart is a graphical representation of Boussinesq’s theory. Newmark developed a graphical procedure for determining the vertical stress below the uniformly loaded area. The chart developed by Newmark’s is also called “Influence Chart”. Based on the Boussinesq’s equation which expresses vertical stress   underneath the center of a circular area loaded with a uniformly distributed load ( q ), Newmark developed influence charts to compute the vertical stress (and also the horizontal stress and shear stress) due to loaded area of any shape, irregular or geometric, below any point either outside or inside of the loaded area.

24. N EWMARK I NFLUENCE C HARTS Newmark (1942) constructed influence chart , based on the Boussinesq solution to determine the vertical stress increase at any point below an area of any shape carrying uniform pressure. Chart consists of influence areas which has a influence value of 0.005 per unit pressure The loaded area is drawn on tracing paper to a scale such that the length of the scale line on the chart is equal to the depth z Position the loaded area on the chart such that the point at which the vertical stress required is at the center of the chart. Then count the number of influence areas covered by the scale drawing , N .

25. Write the Boussinesq’s equation to find vertical stress  at point  O  directly below the center of the loaded area and at depth  z  as follows.

26. LIMITATIONS OF N EWMARK I NFLUENCE C HARTS There are however limitations to these theories that one must realize when they are applied to an actual soil. Generally, soil deposits are not homogeneous, perfectly elastic, and isotropic. This being the case, some variation from the theoretical stress calculations should be expected in the field. One could expect up to a 30% difference between theoretical estimates and field values.

27. Westergaards Theory The Boussinesq theory assumes that the soil mass is isotropic. Actual sedimentary soils are generally anisotropic. Thin layers of sand are usually embedded in a homogeneous clay deposit. Westergaard’s theory assumes that thin sheets of rigid material are sandwiched in a homogeneous soil mass. These thin sheets are closely spaced and are of infinite rigidity; hence, they are incompressible. These thin sheets of sand permit only downward displacement of the soil mass without lateral deformation.

28. Westergaards Theory As per Westergaard’s theory, vertical stress due to a point load is given by

29. Pressure distribution diagrams

30. Contact Pressure Distribution under Footings The stability of structure is majorly depends upon soil – foundation interaction. Even though they are of different physical nature, they both must be act together to get required stability. So, It is important to know about the contact pressure developed between soil and foundation and its distribution in different conditions which is briefly explained below.

31. What is Foundation Contact Pressure? Generally loads from the structure are transferred to the soil through footing. A reaction to this load, soil exerts an upward pressure on the bottom surface of the footing which is termed as contact pressure.

32. Contact Pressure Distribution under Footings The distribution of contact pressure under different types of footings on different types of soils are explained below. Under Flexible Footing Under Rigid Footing

33. Contact Pressure Distribution under Flexible Footing For flexible footing on cohesive soil, settlement is maximum at center of footing and minimum at the edges which forms bowl like shape as shown in below figure. But the contact pressure is distributed uniformly along the settlement line or deflected line

34. Fig 1: C.P Distribution - Flexible Footing - Cohesive Soil

35. Contact Pressure Distribution under Flexible Footing When a flexible footing is laid on the Cohesionless soil, settlement at center becomes minimum while at edges it is maximum which exact opposite case of the settlement of flexible footing over cohesive soil. But in this case also contact pressure is uniform along the settlement line which .is shown in below image

36. Fig 2: C.P Distribution - Flexible Footing - Cohesionless Soil

37. 2. Contact Pressure Distribution under Rigid Footing For rigid footings resting on cohesive soils, settlement is uniform but contact pressure varies. At edges contact pressure is maximum and at center it is minimum which forms inverted bowl shape as shown in below figure. The values of stresses at edges becomes finite when plastic flow occurs in real soils.

38. Fig 3: C.P Distribution - Rigid Footing - Cohesive Soil

39. Contact Pressure Distribution under Rigid Footing If the footing is resting on Cohesionless soils, contact pressure is maximum at center and gradually reduces to zero towards edges. Settlement is uniform in this case also. If the footing is embedded, then there may be some amount of contact pressure at the edges of rigid footing

40. Fig 4: C.P Distribution - Rigid Footing - Cohesionless Soil