Shallow footings
The general bearing-capacity equation with every correction factor, elastic settlement, base sliding, and eccentric tilt.
A shallow footing carries a column load by spreading it onto the soil a short distance below grade. The design question is twofold: will the soil shear (a bearing failure), and will the footing settle more than the structure can tolerate? PileCalc answers both with the general bearing-capacity equation for shear and an elastic check for settlement, plus a base-sliding check for footings that carry horizontal load. This page explains the method and every input on the footing tool.
The bearing-capacity equation
Ultimate bearing capacity is the average pressure at which the soil beneath the footing shears. PileCalc uses the general bearing-capacity equation, summing a cohesion term, an overburden (surcharge) term, and a self-weight term — each multiplied by a dimensionless bearing factor and by shape, depth, and load-inclination corrections:
Here q = γ·Df is the effective overburden pressure at the footing base, and N_c, N_q, N_γ are the bearing-capacity factors. The s, d, and i terms are the shape (from the B/L ratio), depth (from the embedment Df), and load-inclination (from any horizontal shear) factors.
The bearing factors grow exponentially with the friction angle φ, so a few degrees moves capacity a great deal. For clay (φ = 0) the N_q and N_γ contributions collapse and the c·N_c cohesion term dominates the result.
When the load is eccentric the bearing area itself shrinks. PileCalc applies the effective-width method — see Loads & factors — replacing B with a reduced effective width B′ before evaluating the equation above.
Geometry
The footing is a rectangular pad of plan dimensions B × L founded at depth Df below grade.
The footing width in the load direction — the shorter plan side.
Why it matters. Width drives the self-weight 0.5·γ·B·N_γ term and sets the B/L shape factors. It is also the dimension that eccentric moment erodes through B′ = B − 2e, so it controls how much an overturning moment costs you.
The other plan dimension of the footing.
Why it matters. With the width it sets the B/L ratio behind the shape factors and the plan area carrying load. A square footing (B = L) and a strip footing (L ≫ B) sit at the two ends of that range.
The embedment of the footing base below grade.
Why it matters. Deeper footings gain capacity two ways: more overburden in the q·N_q term (with q = γ·Df) and larger depth factors d. Embedment also helps resist sliding and frost.
Soil at the base
Bearing capacity and settlement are governed by the soil at the footing base. Strength (c and φ) sets the shear capacity; stiffness (Es) sets the settlement.
The soil cohesion at the footing base.
Why it matters. It scales the c·N_c term, which is the dominant contribution for clay (φ = 0). Use the undrained shear strength for a short-term (undrained) clay check.
The friction angle of the bearing soil.
Why it matters. The bearing factors N_c, N_q, N_γ grow exponentially with φ — small changes move capacity a lot. Set it to 0 for an undrained clay analysis.
The unit weight of the soil.
Why it matters. It sets both the overburden q = γ·Df and the self-weight 0.5·γ·B·N_γ term. Use the buoyant (effective) unit weight below the water table.
The elastic (Young's) modulus of the soil.
Why it matters. It controls elastic settlement — softer soil settles more under the same pressure. It has no effect on the bearing-capacity (shear) check.
Loads & factors
The footing carries a vertical load, an optional overturning moment, and an optional horizontal shear, checked against a factor of safety. The moment is what makes the loading eccentric.
The vertical (compression) load on the footing.
Why it matters. It is the demand checked against the allowable bearing load, and together with the moment it sets the eccentricity e = M/Q.
The applied overturning moment.
Why it matters. It creates an eccentricity e = M/Q. When e > B/6 the resultant leaves the middle third of the base and part of the footing tends to lift; the effective-width method then shrinks the bearing area to B′ = B − 2e (and L′ = L − 2e′ for biaxial moment), re-centering the pressure block on the reduced area before the bearing equation is evaluated.
The horizontal load at the base.
Why it matters. It drives the base-sliding check and reduces bearing capacity through the load-inclination factors i.
The friction coefficient between the footing base and soil (≈ tan δ).
Why it matters. It sets the sliding resistance Pf = k_f·(Q + W) checked against the applied shear.
The weight of the footing plus the soil above it.
Why it matters. It adds to the normal force resisting sliding, raising Pf = k_f·(Q + W).
The factor of safety applied to the ultimate bearing capacity.
Why it matters. The allowable load is the ultimate (net) capacity divided by this — allowable = q_net × area / FS. A value of about 3 is typical for shallow footings.
Eccentric loads also tilt the footing
Settlement
Passing the bearing check means the soil will not shear — it says nothing about how far the footing moves. PileCalc estimates the immediate elastic settlement at the footing center from the soil modulus Es: under the same pressure, softer soil (lower Es) settles more. For shallow footings this serviceability limit is often what actually governs the size, not bearing capacity.
Because an eccentric load presses harder on one edge, the footing also tilts. PileCalc reports that base rotation separately: the resulting differential settlement can be the controlling check for moment-loaded footings.
Sliding
A footing that carries horizontal shear must not slide across its base. The resisting force is the base friction acting on the total normal load — the vertical load plus the footing weight:
This resistance Pf must exceed the applied shear P. The sliding factor of safety is Pf / P, and a value of at least 1.5 is typically required. Set a base friction to enable the check; with no shear there is nothing to resist.
Reading the results
The tool reports a bearing block, a settlement block, and a sliding block.
Bearing capacity
- Ultimate bearing — the gross pressure from the bearing equation, and net bearing, with the existing overburden removed.
- Allowable load — the net capacity over the plan area divided by the factor of safety.
- Applied pressure — Q over the plan area, to compare against the net capacity.
- The bearing factors N_c, N_q, N_γ, plus the eccentricity e and the effective width B′ that the moment produced.
Settlement & sliding
- Elastic settlement — the immediate settlement at the footing center, and tilt — the base rotation from any eccentric load.
- Sliding resistance Pf and the sliding FS against the applied shear.
Units