Foundations and Piles

Requirements of a foundation

A foundation must:

1. be safe against shear failure of the soil (adequate bearing capacity with a factor of safety);
2. keep total and differential settlement within permissible limits;
3. be placed at a depth safe from seasonal moisture changes, frost, scour and the effect of adjacent construction;
4. be structurally strong and durable against aggressive soil and water;
5. be economical and practical to construct.

Types of shallow foundations

Depth of foundation

Factors governing depth

• Stratum of adequate bearing capacity and acceptable settlement.
• Seasonal volume change zone in expansive clays (often 1.5–3.5 m in black cotton soils).
• Frost penetration in cold regions.
• Scour depth for bridge foundations near water.
• Ground water level, adjacent foundations and future excavations.
• A minimum depth of about 0.5 m (practice often uses 0.8–1.0 m for buildings) to remove topsoil and vegetation and protect against weathering.

Rankine's minimum depth (cohesionless soil)

For a footing with pressure $q$ on soil with $\gamma$, $\varphi$:

Proportioning footings for uniform settlement

Footings of different sizes carrying the same pressure settle differently (larger footings settle more on clay because the pressure bulb is deeper). To reduce differential settlement, footings may be proportioned on the basis of the dead load plus the average (sustained) part of the live load rather than the full design load: the footing with the highest ratio of live to dead load is sized for the allowable pressure under full load, and the same "service" pressure is used for all others.

Combined footings

For two columns with loads $P_1$ (exterior, at property line) and $P_2$, spaced $s$ apart:

1. Locate the resultant: $\bar{x}=\frac{P_{2}s}{P_1+P_2}$ from column 1.
2. Make the centroid of the footing coincide with the resultant so pressure is uniform.
3. Rectangular footing: length $L=2\times$ (distance from property line to resultant); width $B=\frac{P_1+P_2}{q_{a}L}$.
4. If the length is restricted at both ends or loads are very unequal, use a trapezoidal footing (wider under the heavier load).
5. Design longitudinally as an inverted beam (upward soil pressure, columns as supports) and transversely for local bending under each column.

When piles are used

A pile is a long, slender member that transfers load to deeper, stronger strata or distributes it through skin friction. Piles are used when:

• the soil near the surface is too weak or compressible for shallow foundations;
• loads are very heavy or concentrated (bridges, tall buildings, industrial plants);
• there are uplift or lateral forces (towers, offshore structures, retaining structures);
• scour may undermine shallow foundations (bridge piers);
• expansive or collapsible soils must be bypassed;
• future excavation next to the structure is expected.

Classification

Driven piles densify loose sands (increasing capacity) but cause noise and vibration and may heave clays; bored piles are quiet and suitable near existing structures and in clays, but may loosen sands.

Static capacity

Ultimate capacity = base (point) resistance + shaft (skin) resistance:

Piles in clay (undrained, total stress)

$\alpha$ = adhesion factor (about 1.0 for soft clays, reducing to about 0.3–0.5 for stiff clays; bored piles lower than driven); ${\bar{c}}_u$ = average undrained strength along the shaft.

Piles in sand (effective stress)

$K$ = earth pressure coefficient on the shaft (depends on installation: higher for driven displacement piles); $\delta$ = pile–soil friction angle. Field results show that base and shaft resistances do not keep increasing linearly with depth — beyond a critical depth (roughly 15–20 pile diameters) ${\sigma }_v^{\prime }$ is usually limited in these calculations.

Safe load: $Q_{safe}=Q_u/F$, with $F$ commonly 2.5 (IS 2911), or separate factors on base and shaft.

Dynamic formulas (driven piles)

Based on the energy of the hammer and the penetration (set) per blow at the end of driving:

Dynamic formulas are unreliable in clays (driving resistance differs greatly from static capacity because of pore pressures and remoulding) — use static analysis and load tests.

Pile load test (IS 2911 Part 4)

• Initial test — on test piles before the job, to decide design capacity (loaded to about 2.5 times the design load or to failure).
• Routine test — on working piles during construction (to about 1.5 times the design load).
• Loads applied in increments by a jack against kentledge or reaction piles; settlements recorded.

Other tests: cyclic load test (separates base and shaft resistance), lateral load test, pull-out test, dynamic pile testing (PDA), low-strain integrity tests.

Pile groups

Piles are used in groups under a pile cap.

• Minimum spacing (centre to centre): commonly about 2.5 to 3 times the pile diameter; wider for friction piles in clay to reduce overlap of stress zones; closer spacing permitted for end-bearing piles on rock.
• Stress zones of friction piles overlap, so group capacity may be less than the sum of individual capacities.

Group efficiency

Group capacity in clay

Check both:

1. Sum of individual capacities × efficiency (or simply $n{Q}_u$), and
2. Block failure of the group acting as a single large pier:

($N_c$ ≈ 9 for deep blocks, $B_g$, $L_g$ = plan dimensions of the group, $L$ = pile length).

The smaller value governs. In loose sand driven groups can have efficiency > 1 (densification).

Group settlement

Settlement of a group exceeds that of a single pile under the same load per pile (deeper stressed zone). For friction piles in clay, the group load is assumed to act on an equivalent raft at two-thirds of the pile length below the cap, spreading at 2 vertical : 1 horizontal; consolidation settlement is computed for layers below. For end-bearing groups, the equivalent raft is at the pile tips.