Fundamentals of foundation

A foundation is the part of a structure that transfers loads safely to the ground. It must not fail in shear (bearing capacity failure) and must not settle excessively or unevenly. The choice between a simple footing and a pile depends on soil strength, depth of good strata, loads, water table and cost. In Nepal, isolated and combined footings dominate residential buildings, mat foundations suit larger buildings on soft Kathmandu Valley lake sediments, and piles or wells support major river bridges.

Key concepts

Definition and functions

• Foundation = substructure (footing + soil beneath) that receives loads from the superstructure.
• Functions:
  • Distribute load over a large area so soil pressure stays within allowable bearing capacity.
  • Limit total and differential settlement.
  • Provide a level, firm base for construction.
  • Resist overturning, sliding, uplift and lateral loads (wind, earthquake).
  • Reach below frost, scour, shrink-swell zones and seasonal water-level changes.
  • Anchor structure against earthquake forces (tie beams, plinth beams).

Types of foundation

Shallow foundations (depth $D_f$ ≤ width $B$, Terzaghi's definition):

Type	Description
Spread/isolated footing	Separate pad under each column (square, rectangular, circular; plain, stepped, sloped)
Wall (strip) footing	Continuous under load-bearing walls
Combined footing	One footing for two or more columns (rectangular or trapezoidal) — when columns are close or near a boundary
Strap (cantilever) footing	Two footings joined by a strap beam — boundary columns
Mat (raft)	Single slab under entire building

Deep foundations ($D_f > B$):

• Piles: end-bearing, friction, compaction, tension, batter piles; driven or bored cast-in-situ; concrete, steel, timber.
• Piers (drilled shafts) and well (caisson) foundations — bridge foundations on rivers with deep scour.

Factors affecting choice of foundation

• Type and magnitude of loads; structural system.
• Soil profile, bearing capacity and compressibility; depth to firm stratum.
• Groundwater level and possibility of scour.
• Permissible total and differential settlement.
• Seismic zone (liquefaction risk in loose saturated sands), expansive or collapsible soils.
• Adjacent structures, construction method, equipment, time and cost.

Site investigation of foundation

• Gather soil profile, water table, SPT/CPT values, laboratory strength and consolidation parameters, chemical tests (sulphates, chlorides).
• Plate load test for allowable pressure on granular soils.
• Results decide foundation type, depth and allowable bearing pressure.

Minimum depth of foundation

Rankine's formula for cohesionless soils: $D_{min} = \frac{q}{\gamma}\left(\frac{1-\sin\phi}{1+\sin\phi}\right)^2$ $q$ = gross bearing pressure (kPa), $\gamma$ = unit weight (kN/m³). In practice, footings are founded not less than about 1–1.5 m below ground for buildings, below topsoil and seasonal moisture change.

Concept of spread foundation

• Spreads concentrated column load over area $A = \dfrac{P}{q_a}$.
• Designed for: bearing pressure, punching (two-way) shear, one-way shear, bending moment, and development length of bars.
• Contact pressure distribution: on sand, rigid footing has maximum pressure at centre; on clay, maximum at edges. Uniform pressure is assumed in design.

Concept of mat (raft) foundation

• Used when: required footing area exceeds about 50% of the building plan area, soil is soft or erratic, differential settlement must be controlled, or basements need water-tightness.
• Types: flat plate, plate thickened under columns, beam–slab (two-way), cellular raft, raft on piles (piled raft).
• Floating (compensated) foundation: excavated soil weight balances building load, so net pressure ≈ 0: depth $D_f = Q/(A\gamma)$.
• Mats can tolerate larger total settlement than isolated footings because they reduce differential settlement.

High-yield points

• Shallow foundation: $D_f \le B$; deep: $D_f > B$ (Terzaghi).
• Use a mat when footings would cover more than about half the plan area.
• Combined or strap footings serve boundary (property-line) columns.
• Rigid footing contact pressure: maximum at the centre on sand, at the edges on clay.
• Well (caisson) foundations suit river bridges with deep scour.

Formulas

• Footing area $A = P/q_a$ (include self-weight in $P$).
• Rankine minimum depth: $D_{min} = \dfrac{q}{\gamma}\left(\dfrac{1-\sin\phi}{1+\sin\phi}\right)^2$.
• Floating foundation depth: $D_f = Q/(A\gamma)$.

Worked example

A column carries 900 kN. Allowable bearing pressure is 150 kPa. Find the size of a square footing (ignore self-weight). If the footing self-weight is 10% of the load, what size is needed?

• $A = 900/150 = 6$ m² → $B = \sqrt6 = 2.45$ m
• With self-weight: $A = 990/150 = 6.6$ m² → $B = 2.57$ m → adopt 2.6 m × 2.6 m.

Exam tips

• Shallow: $D_f \le B$; deep: $D_f > B$ (Terzaghi).
• Mat is preferred when isolated footings would cover more than about half the plan area.
• Combined or strap footings are used for property-line (boundary) columns.
• Contact pressure under rigid footing: maximum at centre for sand, at edges for clay.
• Floating foundation reduces net load by excavating soil of equal weight.

Exam-style questions

From Calmon's question bank, which has 24 questions on this topic.

1. During the reconnaissance stage of site investigation for a foundation, the engineer mainly

• A. Carries out pile load tests
• B. Inspects the site and studies existing maps, records and nearby structures
• C. Performs triaxial tests on undisturbed samples
• D. Designs the reinforcement of footings

Answer: B. Reconnaissance is a preliminary visual study of the site, topography, drainage, existing structures, and available geological maps and records, used to plan detailed exploration.

2. A friction pile transfers most of its load to the soil by

• A. Lateral earth pressure on the pile cap
• B. Bearing on a rock stratum at its tip
• C. Skin friction (adhesion) along its embedded length
• D. Buoyancy of the surrounding water

Answer: C. Friction piles derive their capacity mainly from shaft resistance along the surface in contact with the soil, unlike end-bearing piles which rest on a hard stratum.

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