1. Foundation Engineering CE 483
7. Mat foundation

2. CONTENTS Introduction Common Types of Mat foundations
Analysis and Design of Mat foundations
References
CE Foundation Engineering Mat foundations

3. Introduction Definition Why do we select Mat foundations?
Problematic Soils
Three Ws  three dimensions to find a space
CE Foundation Engineering Mat foundations

4. Introduction
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).
Column
Cross section
Column
Plan view
CE Foundation Engineering Mat foundations

8. Why do we select Mat foundations?
Introduction
Why do we select Mat foundations?
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;
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;
The Engineer wishes to minimize the differential settlement in variable soils, or if pockets of extremely weak soils are known to be present;
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.
In some cases of Problematic Soils (see next slide).

9. Introduction
Problematic Soils
Some Problematic Soils 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.
Crack
Soft ground

12. Introduction
Problematic Soils
Some Problematic Soils may necessitate the Use of Mat Foundations:
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.

13. Introduction
Problematic Soils
Some Problematic Soils may necessitate the Use of Mat Foundations:
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.

14. Common Types of Mat foundations
Flat Plate
Thickened Flat Plate
Beams and slab
Flat plates with pedestals
Slab with basement walls
Three Ws  three dimensions to find a space
CE Foundation Engineering Mat foundations

15. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations
Common Types of Mat foundations
Flat Plate
The mat is of uniform thickness
CE Foundation Engineering Settlement of shallow foundations

16. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations
Common Types of Mat foundations
Thickened Flat Plate
Flat Plate thickened under columns
CE Foundation Engineering Settlement of shallow foundations

17. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations
Common Types of Mat foundations
Beams and slab
Beams and slab: the beam run both ways, and the columns are located at the intersection of the beams.
CE Foundation Engineering Settlement of shallow foundations

18. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations
Common Types of Mat foundations
Flat plates with pedestals
Pedestals
CE Foundation Engineering Settlement of shallow foundations

19. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations
Common Types of Mat foundations
Slab with basement walls
Slab with basement walls as a part of the mat, where the walls act as stiffeners for the mat.
walls
CE Foundation Engineering Settlement of shallow foundations

20. Analysis and Design of Mat foundations
Bearing capacity and settlement
Analysis of Rigid Mats
Analysis and Design Procedures for Rigid Mats
Three Ws  three dimensions to find a space
CE Foundation Engineering Mat foundations

21. Bearing capacity and settlement
Analysis and Design of Mat foundations
Bearing capacity and settlement

22. Bearing capacity and settlement
Analysis and Design of Mat foundations
Bearing capacity and settlement

23. Bearing capacity and settlement
Analysis and Design of Mat foundations
Bearing capacity and settlement 2B 2b B
q= 100 kPa
0.1 q
0.2 q
Ds =
Pressure bulbs under large
and small round foundations

24. Bearing capacity and settlement
Analysis and Design of Mat foundations
Bearing capacity and settlement

25. Bearing capacity and settlement
Analysis and Design of Mat foundations
Bearing capacity and settlement

26. Bearing capacity and settlement
Analysis and Design of Mat foundations
Bearing capacity and settlement
Compensated mat foundation

27. Analysis and Design of Mat foundations
The analysis of mat foundation depends on rigidity and type of soil
Analysis of Rigid Mats

28. Analysis and Design of Mat foundations
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,
Note. This equation gives stress value – only at the edges of the mat.
This equation gives max and min of sigma .. The other one is more general gives sigma in any x and y

29. Analysis and Design Procedures for Rigid Mats
Analysis and Design of Mat foundations
Analysis and Design Procedures for Rigid Mats
(Independent Strip Method)

30. Analysis and Design Procedures for Rigid Mats
Analysis and Design of Mat foundations
Analysis and Design Procedures for Rigid Mats

31. Analysis and Design Procedures for Rigid Mats
Analysis and Design of Mat foundations
Analysis and Design Procedures for Rigid Mats
(see Section 6.8 of Das’s book for detailed information)

32. The plan of a mat foundation is shown in the figure 6. 14
The plan of a mat foundation is shown in the figure Calculate the soil pressure at points A, B, C, D, E, and F. (note: all column sections are planned to be 0.5x0.5m).

33. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations

34. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations

37. Divide the mat shown in Figure 6
Divide the mat shown in Figure 6.14 into three strips, such as AGHF (B1=4.25m), GIJH (B1=8m), and ICDJ (B1=4.25m). Use the result of example 6.5 and determine the followings:
Shear and moment diagrams for strips
Minimum thickness of mat
(assume f’c=20.7 MN/m2, fy=413.7 MN/m2, and the load factor is 1.7).

45. CE 483 - Foundation Engineering - 5. Settlement of shallow foundations
References
Braja M Das, 2011, Principles of Foundation Engineering, 7th ed, Chapter- 6.
Previous course materials and presentations at KSU.
Geotechnical on the web:
Andrew Bond and Andrew Harris, 2008, Decoding Eurocode 7, London.
The Institution of Structural Engineers library:
CE Foundation Engineering Settlement of shallow foundations