Unit-3-Design of shallow foundation.pdf

SHALLOW FOUNDATIONS
by
Dr. V. Vignesh
Assistant Professor
Sanjivani College of Engineering, Kopargaon

SETTLEMENT OF FOUNDATION
The Allowable bearing capacity for the design of the footing is governed
by
• Bearing capacity of soil
• Permissible Settlement
Total Settlement St in general case for any type of soil is given by
St= Si+Sc+Ss
Si=Immediate settlement or Elastic settlement
Sc=Consolidation settlement or Primary settlement
Ss=Secondary consolidation settlement

Immediate settlement or Elastic settlement (Si)
• It takes place during or immediately after the construction of the
structure.
• The settlement is not truly elastic. It is computed using elastic theory
for cohesive soils.
Consolidation settlement (Sc)
• This component of the settlement occurs due to gradual expulsion of
water from the voids of the soil.
• This settlement of determined by using Terzhaghi’s theory of
consolidation.
Secondary Consolidation Settlement (Ss).
• This component of the settlement is due to secondary consolidation.
This settlement occurs after completion of the primary consolidation.

Causes of Settlement
(1) Underground erosion.
(2) Structural collapse of soil.
(3) Thermal changes.
(4) Frost heave.
(5) Vibration and Shocks.
(6) Mining subsidence.
(7) Land slides.
(8) Creep.
(9) Changes in the vicinity.

IMMEDIATE SETTLEMENT OF COHESIVE SOILS
The linear theory of elasticity is used to determine the elastic settlement
of the footings on saturated clay.
where q = uniformly distributed load, B = characteristic length of the loaded area, Es =
modulus of elasticity of the soil, μ = Poisson’s ratio (0.50 for saturated clay), I =
influence factor.

CONSOLIDATION SETTLEMENT IN COHESIVE SOILS

SETTLEMENT OF FOUNDATION ON COHESIONLESS SOIL:
Static cone penetration method:
The settlement of each small layer is estimated using the following equation:
(or) 𝑆 = 2.303
𝐻
𝐶
𝑙𝑜𝑔10(
σ°+∆𝜎
𝜎°
)
Where, C=Compressibility coefficient
qc=Cone resistance in kN/m2
Standard penetration Test method:
The average value of N to be used in assessment of settlement and bearing capacity is given by
𝑁 =
3𝑁1 +2𝑁2 +𝑁3
6
Where, N1 = Corrected SPT value at foundation level.
N2 = Corrected SPT value at depth 1.5B
N3 = Corrected SPT value at depth 2B
From Terzhaghi’s and Peck corelation of settlement with SPT values, Teng proposed the
following equation,
𝑆 =
0.722𝑞
𝑁 − 3
2𝐵
𝐵 + 0.3
2

PROBLEM SOLVING
1. A Column footing 5mX5m if founded at 3m depth in a stratum of medium dense
sand giving SPT value of 20. Determine the settlement of the footing from
Terzhaghi and Peck correlation at the surface of the centre point, If the column load
is 100 tonnes.
2. In a normally consolidated clay of liquid limit 65.5% and 5m thickness, the
overburden pressure is increased from 250 kN/m2 by 120 kN/m2. Estimate the
settlement that can takes place. Assume Saturated water content of 45%.
ALLOWABLE SETTLEMENT
• The allowable maximum settlement depends upon the type of soil, the type of
foundation and the structural framing system.
• The maximum settlement ranging from 20 mm to 300 mm is generally permitted for
various structures.
• IS : 1904 (1966) permits a maximum settlement for isolated foundations
40 mm on sand
65 mm on clay.
For Mat foundations
40 mm to 65 mm on sand
65 to 100 mm on clay

• According to general practice, the maximum differential settlement is limited to 25
mm in sandy soils and 40 mm in clayey soils..
IS : 1904—1978 gives the safe values of the maximum and differential settlements of
different types of building:

PRINCIPLES OF DESIGN OF FOOTINGS:
The footing is designed using the following procedure.
(1) The safe bearing capacity is determined using the methods discussed in
previous chapter.
(2) The footing is proportioned making use of the safe bearing capacity
determined in Step (1).
(3) The maximum settlement of the footing and the differential settlement
between various footings are estimated.
(4) Angular distortion is determined between various parts of the structure.
(5) The maximum settlement, the differential settlement and the angular
distortion obtained in the step (3) and (4) are compared with the given
allowable values.
(6) If the values are not within the allowable limits, the safe bearing
capacity is revised and the procedure repeated.
(7) The stability of the footing is checked against sliding and overturning.
(8) The factor of safety against sliding should not be less than 1.5, and
against overturning it is 2.

DESIGN OF STRIP FOOTINGS
(a) Plain Concrete Footings
1. The width (B) of the footing is determined from the relation
𝐵 =
𝑄
𝑞𝑛𝑎
Where, Q = load per m run, qna = allowable soil pressure.
2. If the actual width provided is different from the theoretical width, the actual
pressure is given by
𝑞𝑎 =
𝑄
𝐴𝑐𝑡𝑢𝑎𝑙 𝑤𝑖𝑑𝑡ℎ
3. The thickness at the edge of the footing should be at least 15 cm. On cohesive soils,
generally a minimum thickness of 30 cm.
4. A 45° load distribution is also commonly used.

(b) Reinforced Concrete Footings
1. Footings carrying heavy loads on weak soils are reinforced in the transverse direction. The
width of the footing is determined using
𝐵 =
𝑄
𝑞𝑛𝑎
2. For computing the bending moment for which the footing is to be designed, the critical section
is taken as follows (IS 456 - 1978).
(i) At the face of the monolithic wall
(ii) Half-way between the centre line and the edge of the wall for footings under
masonry walls.

3. For monolithic walls, the maximum bending moment is given by
where B = width of footing, b = width of wall, qo = actual soil pressure.
4. For checking the diagonal shear, the critical section is taken at a
distance equal to the effective depth (d) of footing from the face of the
wall.
The diagonal shear is given by

DESIGN OF SPREAD FOOTINGS
(a) Plain Concrete Footings.
1. The area (A) of the footing is determined from the relation
𝐴 =
𝑄
𝑞𝑛𝑎
Where, Q = load per m run, qna = allowable soil pressure.
2. If the area actually provided is more, the actual pressure is given by
𝑞𝑎 =
𝑄
𝐴𝑐𝑡𝑢𝑎𝑙 𝑎𝑟𝑒𝑎
The design is similar to that of a plain concrete strip footing.
(b) Reinforced Concrete Footings.
1. The area of the footing is obtained using
𝐴 =
𝑄
𝑞𝑛𝑎
The shape of the footing may be square, circular or rectangular.
2. The maximum B.M. is given by,

3. For checking the diagonal shear F, the critical section is taken at a distance equal to
the effective depth (d) of the footing from the face of the column.
4. For punching shear, the critical section is taken at a distance of d/2 from the face of
the column. Generally the overall depth (do) of the footing is determined from the
punching shear considerations.

5. The Maximum Force of bond is given by

COMBINED FOOTINGS
• The footing is proportioned such that the centre of gravity of the
footing lies on the line of action of the resultant of the column
loads. The pressure distribution thus becomes uniform.
• A combined footing is generally rectangular in plan if sufficient
space is available beyond each column.
• If one of the columns is near the property line, the rectangular
footing can still be provided if the interior column is relatively
heavier.
• However, if the interior column is lighter, a trapezoidal footing is
required to keep the resultant of the column loads through the centroid
of the footing

Rectangular combined footings
The design of a combined footing consists of selecting length and width of the footing
such that the centroid of the fooling and the resultant of the column loads coincide

STEP 1: Determine the total column loads,
𝑄 = 𝑄1 + 𝑄2
where Q1 and Q2 are the exterior and interior columns loads, respectively
STEP 2: Find the base area of the footings.
STEP 3: Locate the line of action of the resultant of the column loads measured from
one of the column, say exterior column
where x2 is the distance between columns.
STEP 4: Determine the total length of the footings.
Where, b1 = width of the exterior column.
STEP 5: Find the width of the footing.
STEP 6: As the actual length and width that are provided may be slightly more due to
rounding off, the actual pressure is given by
𝐴 =
𝑄
𝑞𝑛𝑎

STEP 7: Draw the shear force and the bending moment diagrams along
the length of the footing, considering the pressure q0.
STEP 8: Determine the bending moments at the face of the columns and
the maximum bending moment at the point of zero shear.
STEP 9: Find the thickness of footing for the maximum bending
moment.
Check for diagonal shear and punching shear, as in the case of an
isolated footings.
STEP 10: Determine the longitudinal reinforcement for the maximum
bending moment.

Problem Solving:
1. Design a rectangular footing for two columns as shown in figure .
Take allowable soil pressure as 100 kN/m2
.

TRAPEZOIDAL FOOTING
• Trapezoidal combined footings are provided to avoid eccentricity of loading with
respect to the base.
• Trapezoidal footings are required when the space outside the exterior column is
limited and the exterior column carries the heavier load.

Design procedure:
STEP 1: Determine the total column loads
𝑄 = 𝑄1 + 𝑄2
STEP 2: Find the base area of the footing
STEP 3: Locate the line of action of resultant of the column loads
STEP 4: Determine the distance x' of the resultant from the outer face of the exterior column
A trapezoidal footing is required if
where L is the length of the trapezoidal footing, determined from
If x’= L/2, a rectangular footing is provided. However, if x’ < L/3, a combined footing cannot be
provided. In such a case, a strap footing is suitable.
𝐴 =
𝑄
𝑞𝑛𝑎

STEP 5: Determine the widths B1 and B2 from the following relations.
STEP 6: Once the dimensions B1 and B2 have been found, the rest of the design can be
done as in the case of a rectangular combined footing.

Design a trapezoidal footing for the two columns shown in Fig. Take allowable soil
pressure as 200 kN/m2.

PRINCIPLES OF DESIGN OF MAT FOUNDATIONS
• A mat (or raft) is a thick reinforced concrete slab which supports all the load-bearing
walls and column loads of a structure or a large portion of structure.
• A mat is required when the loads are heavy and the soil is very weak or highly
compressible.
• A mat is more economical than individual footings when the total base area required
for the individual footings exceeds about one-half of the area covered by the
structure.
COMMON TYPES OF MAT FOUNDATIONS
There are several types of mat foundations.
(1) Flat Plate Type: In this type of mat foundation, a
mat of uniform thickness is provided. This type is most
suitable when the column loads are relatively light and
the spacing of columns is relatively small and uniform.

(2) Flat Plate Thickened Under Columns: When the
column loads are heavy, this type is more suitable than
the flat plate type. A portion of slab under the column
is thickened to provide enough thickness for
negative bending moment and diagonal shear.
(3) Beam and Slab Construction: In this type of
construction, the beams run in two perpendicular
directions and a slab is provided between the beams.
The columns are located at the intersection of beams.
This type is suitable when the bending stresses arc
high because of large column spacing and unequal
column loads.

(4) Box Structures. In this type of mat foundation,
a box structure is provided in which the basement
walls act as stiffeners for the mat. This type of mat
foundation can resist very high bending stresses
(5) Mats placed on Piles. The mat is supported on
piles in this type of construction. This type of mat
is used where the soil is highly compressible and
the water table is high. This method of
construction reduces the settlement and also
controls buoyancy.

CONVENTIONAL DESIGN OF RAFT FOUNDATIONS
STEP 1: Determine the line of action of all the loads acting on the raft. The self weight
of the raft is not considered, as it is taken directly by the soil.
STEP 2: Determine the contact pressure distribution as under.
(a) If the resultant passes through the centre of the raft, the contact pressure is given by
q = Q/A
(b) If the resultant has an eccentricity of ex and ey in x-and y-directions
The maximum contact pressure should be less than the allowable soil pressure.
STEP 3: Divide the slab into strips (bands) in x-and y-directions. Each strip is assumed
to act as independent beam subjected to the contact pressure and the column loads.
STEP 4: Draw the shear force and bending moment diagrams for each strip.
STEP 5: Determine the modified column loads as explained below.

STEP 6: The bending moment and shear force diagrams are drawn for the modified column
loads and the modified average soil pressure
STEP 7: Design the individual strips for the bending moment and shear force found in step 6.
The raft is designed as an inverted floor supported at columns.

The plan of a mat foundation with 9 columns is shown in Fig. Assuming that the mat is
rigid, determine the soil pressure distribution. All the columns are of the size 0.6 m x
0.6 m.
Draw the S.F. and B.M. diagrams for the strip ABFE.

Unit-3-Design of shallow foundation.pdf

More Related Content

What's hot (20)

Similar to Unit-3-Design of shallow foundation.pdf (20)

More from Sanjivani College of Engineering, Kopargaon (7)

Recently uploaded (20)

Unit-3-Design of shallow foundation.pdf