Mat foundation

Er. Nirdesh Singh Karki — Mon, 31 Mar 2025 04:47:44 +0000

1.1 Introduction and types of mat foundation

Mat foundation:

A large footing which covers the entire area below a structure and supports arrangement of all wall and column.
Resist the differential settlement.

Types of mat foundation:

1. Flat slab mat

Single slab of uniform thickness.
Suitable for closed spaced.

2. Flat slab thickedd under column

Column is subjected to very heavy load.

3. Rigid frame

Used to carry extremely heavy load.

4. Piled raft mat

If soil is highly compressive then this is used.

5. Flat slab with pedestals

Same as flat slab but pedestals are provided at base.

1.2 Bearing capacity and settlements

1. For cohesive soil

In cohesive soil net ultimate bearing capacity is determined by skempton’s equation.

q_nu= CN_c[1+0.2(D_f/B)]*[1+0.2(B/L)]

∴ q_nu= 5C[1+0.2(D_f/B)]*[1+0.2(B/L)]

Let,

Q = Total superimposed load

Gross pressure (q_g) = Q/A
In term of net ultimate bearing capacity;

∴ q_g = q_ns + γ D_f= Q/A – γ D_f

2. For cohesion less soil

Bearing capacity of cohesionless soil depends upon width of footing.

Safe bearing capacity is determined as:

∴ q_ns = 0.22 N²BRw₁ + 0.67 (100+N²)D_fRw₂

Safe settlement pressure for a settlement 25 mm is

∴ q_ns = 17.5 (N-5)Rw₁

Q_np = 22 Rw₁ (for 50 mm settlement)

∴ Above equation is applicable for 5 ≤ N ≤50.

1.3 Compensated foundation (Floating foundation)

When structure in soil is nearly equal to the total excavated soil from ground including weight of water in soil.

i.e Excavated weight = Structural weight

Settlement of sub soil is prevented.
Rigid raft foundation is provided when floating foundation is needed.

Diffulties during construction of floating foundation:

Excavation: Should be done carefully.
Dewatering: If depth of excavation is below water table dewatering is necessary.
Critical depth: If soil has low shear strength the limited depth is excavated i.e called as critical depth.
Bottom heave: Excavation of foundation reduce pressure in below of foundation results in heaving of bottom of excavation.

1.4 Conventional method of analysis

Determine the line of action of all loads acting on the raft.
Determine the contact pressure.

a. If e = 0 , q = Q/A

b. If resultant has an ecentricity e_x & e_y in x & y direction.

Then,

q = (Q/A) ± Q(e_x/I_yy)x ± Q(e_y/I_xx)y

Divide the mat into number of beam or strip to analyze each beam separately.
Draw shear force and bending moment diagram of each strip and calculate q_av below the beam.
Determine modified column load.

Q_av = ½ (downward load + upward load)

or, Q_av = ½ (Q₁ + Q₂ + Q₃ + q_av *B₁*x

Modified average soil pressure

q_av= Q_av/x₁* B

Column load modified factor

F = Q_av / (Q₁+Q₂+Q₃)

All the column load are multiplied by ‘F’ for the strip.

For strip

FQ₁, FQ₂ & FQ₃

Draw BMD and SFD for modified column load.
Find maximum bending moment and shear force.
Find thickness of slab and reinforcement using BM_maxand SF_max.

References:

Terzaghi, Karl, Peck, R.B & John, Wiley (1969) Soil mechanics in engineering practice, New York.
Arora , K.R (2008), Soil mechanics and foundation engineering, Delhi: Standard Publisher Distribution.

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mat foundation Archives - OnlineEngineeringNotes

Mat foundation

1.1 Introduction and types of mat foundation

1.2 Bearing capacity and settlements

1.3 Compensated foundation (Floating foundation)

1.4 Conventional method of analysis