1. FOOTINGS AND RAFT

2. UNIT III FOOTINGS AND RAFTS
Types of footings – Contact pressure distribution: Isolated footing – Combined footings – Types and proportioning – Mat foundation – Types and applications – Proportioning – Floating foundation – Seismic force consideration – Codal Provision.

6. A combined footing is usually used to support two columns of unequal loads. In such a case, the resultant of the applied loads would not coincide with the centroid of the footing, and the consequent the soil pressure would not be uniform.
Another case where a combined footing is an efficient foundation solution is when there are two interior columns which are so close to each other that the two isolated footings stress zones in the soil areas would overlap.
The area of the combined footing may be proportioned for a uniform settlement by making its centroid coincide with the resultant of the column loads supported by the footing.
There are many instances when the load to be carried by a column and the soil bearing capacity are such that the standard spread footing design will require an extension of the column foundation beyond the property line. In such a case, two or more columns can be supported on a single rectangular foundation. If the net allowable soil pressure is known, the size of the foundation B x L can be determined.

7. Combined Footings

8. Combined Footings

12. Rectangular Combined Footings

13. Rectangular Combined Footings

14. Trapezoidal Combined Footing

15. Trapezoidal Combined Footing

16. Example on Trapezoidal Combined Footing
Design a trapezoid-shaped footing, with columns at ends of footing as shown below, where qall = 120 kPa and L = 7 m.

17. Cantilever or Strap Footings

18. Cantilever or Strap Footings

19. MAT FOUNDATIONS

20. Definition
A mat foundation is primarily a shallow foundation. In essence, it is an expanded continuous footing and is usually analyzed in the same way.
Mat foundations are sometimes referred to as raft foundations (especially in the UK).

21. Why we select Mat foundations?
1. The area covered by the individual footings exceeds 50% of the structural plan area. This is usually the case for buildings higher than 10-stories, and/or on relatively weak soils where q < 150 kPa;
2. The building requires a deep basement and below the phreatic surface (WT). Basements may be required to build several levels of parking, or to install mechanical systems, access to a subway station, etc;
3. The Engineer wishes to minimize the differential settlement in variable soils, or if pockets of extremely weak soils are known to be present;
4. The Engineer wishes to take full advantage of the soil’s increasing bearing capacity with depth by excavating basements, and thereby seek a fully or a partially compensated foundation.

22. Problem Soils That May Necessitate the Use of Mat Foundations.
1. Compressible soils occur in highly organic soils including some glacial deposits and certain flood plain areas. Highly plastic clays in some glacial deposits and in coastal plains and offshore areas there can be significant amounts of compressible soils. Problems involved are excessive settlements, low bearing capacity, and low shear strength.
2. Collapsing soils such as the settlement of loose sands and silts. Densification occurs by the movement of grains to reduce the volume. Typically includes shallow subsidence. May occur in sandy coastal plain area, sandy glacial deposits, and alluvial deposits. In arid and Semi-arid region.
3. Expansive soils, containing swelling clays, mainly from the Montmorillite/Smectite group, which increase in volume when absorbing water and shrink when loosing it. Climate is closely related to the severity of the problem. Semi-arid and semi-humid areas with swelling clays are the most severe because the soil moisture active zone has the greatest thickness under such conditions. Foundation supports should be placed below the active soil zone.

25. Types of Mat foundations

26. Types of Mat foundations

28. Flat plate type
Mat of uniform thickness is provided. Suitable when column loads are relatively light and the spacing between them is small and uniform
Flat plate thickened under column
When columns are very heavy this is more suitable. The portion of slab under the column is thickened to provide enough thickness for negative bending moment and diagonal shear.
Beam and slab construction
Beams runs in two perpendicular directions and the slab is provided between the beams. The columns are located at the intersection of beams. This type is suitable when bending stresses are high because of large column spacing and unequal column loads
Box structures
A box structure is provided in which basement walls acts as stiffeners.
Boxes made of cellular construction or rigid frames consisting of slabs and basement walls .This type can resist higher bending stress
Mat placed on piles
Mat foundation supported on piles. This type is used where soil is highly compressible and water table is high. Method of construction reduces settlement and also controls buoyancy.

30. Compensated mat foundation

31. Analysis of Rigid Mats
The analysis of a mat by assuming that it is rigid simplifies the soil pressures to either a uniform condition or varying linearly. This is attained by not permitting R (the resultant force) to fall outside the kern of the mat. Hence, the corner stress is,

32. Analysis and Design Procedure for Rigid Mats

39. Floating foundation
The floating foundation is a special type of foundation construction useful in locations where deep deposits of compressible cohesive soils exist and the use of piles is impractical. The concept of a floating foundation requires that the substructure be assembled as a combination of a raft and caisson to create a rigid box.
This foundation is installed at such a depth that the total weight of the soil excavated for the rigid box equals the total weight of the planned structure. Theoretically speaking, therefore, the soil below the structure is not subjected to any increase in stress; consequently, no settlement is to be expected. However, some settlement does occur usually because the soil at the bottom of the excavation expands after excavation and gets recompressed during and after construction.

42. F R

43. Contact Pressure
On the underside of the footing, the soil reaction produce a upward pressure which is assumed uniform in deriving different relationship for soil-structure interaction problem. This pressure is called contact pressure. But actually a footing are not flexible as well as contact pressure is not uniform, necessitating more investigation for actual contact pressure distribution.
Factor Influencing Contact Pressure
The actual distribution of contact pressure depends upon a number of factors such as
1) Elastic properties of footing
2) Elastic properties of soil
3) Thickness of footing

44. Contact Pressure On Saturated Clay
Flexible Footing When a footing is flexible, it deforms into shape of bowel, with the maximum deflection at the center. The contact pressure distribution is uniform.
Rigid Footing
When a footing is rigid, the settlement is uniform. The contact pressure distribution is minimum at the center and the maximum at the edges. The stresses at the edges in real soils can not be infinite as theoretically determined for an elastic mass. In real soils, beyond a certain limiting value of stress, the plastic flow occurs and the pressure becomes finite

45. Contact pressure on sand
Flexible footing
In this case, the edges of flexible footing undergo a large settlement than at the centre. The soil at the centre is confined and, therefore, has a high modulus of elasticity and deflects less for the same contact pressure. The contact pressure is uniform. 
Rigid footing
If the footing is rigid, the settlement is uniform. The contact pressure increases from zero at the edges to a maximum at the centre. The soil, being unconfined at edges, has low modulus of elasticity. However, if the footing is embedded, there would be finite contact pressure at edges.

46. Thus it is observed that the contact pressure distribution for flexible footing is uniform for both clay and sand. The contact pressure for rigid footing is maximum at the edges for footing on clay, but for rigid footings on sand, it is minimum at the edges

47. Consequence of assuming uniformity in pressure
For convenience, the contact pressure is assumed to be uniform for all types of footings and all types of soils if load is symmetric.
The above assumption of uniform pressure distribution will result in a slightly unsafe design for rigid footing on clays, as the maximum bending moment at centre is underestimated. It will give a conservative design for rigid footings on sandy (cohessionless) soils, as the maximum bending moment is overestimated. However, at the ultimate stage just before failure, the soil behaves as an elasto-plastic material ( and not an elastic material) and the contact pressure is uniform and the assumption is justified at the ultimate stage.