Shallow Foundation & Bearing Capacity - Civil Engineering SSC JE (Technical)

Foundation

Foundation is the lowest part of a building or civil structure that is in direct contact with the ground and transfers structural loads safely to the soil. Foundations are broadly classified into two types:

• Shallow foundation
• Deep foundation

Shallow foundation

Shallow foundations are those in which the depth of foundation (D_f) measured from the ground surface to the base of the footing is small compared with the width of the footing (B). In many practical guides shallow foundations are considered when the ratio D_f/B is small (see figure above).

Deep foundation

Deep foundations transfer loads to deeper, stronger strata and are used when surface soils are weak or when large loads must be carried at depths where suitable bearing strata exist. They are used when the depth is large relative to the footing width; the figure above indicates situations when the depth-to-width ratio may be significantly greater than unity.

In the above, D_f is the depth of footing and B is the width (or least lateral dimension) of the footing.

Types Of Footings

• Strip footing (Continuous footing) (L » B): Provided for load-bearing walls or rows of columns spaced so closely that individual footings would overlap.

• Combined footing: Provided to support two or more columns where individual footings would overlap or when columns are close to property lines.

• Spread footing (Isolated footing): Provided to support an individual column. Common shapes are circular, square and rectangular.

• Raft (Mat) foundation: A single heavily reinforced concrete slab that underlies the entire structure or a major portion of it. Raft foundations distribute loads over a large area and are economical for structures founded on relatively weak soils.

Bearing Capacity

Bearing capacity is the load-carrying capacity of soil expressed as pressure (force per unit area). The key definitions are:

• Ultimate (gross) bearing capacity (q_u): the least gross pressure which will cause shear failure of the soil immediately below the footing.
• Net ultimate bearing capacity (q_nu): the net pressure that can be applied to the footing by external loads that will just cause failure. It equals the ultimate bearing capacity minus the stress due to the weight of the soil and footing (surcharge). Assuming the unit weight of footing and adjacent soil are comparable,

q_nu = q_u - γD_f

where γ is the unit weight of soil and D_f is the depth of the footing.

• Safe bearing capacity: bearing capacity after applying an appropriate factor of safety (FS). Safe values may be expressed as:

Safe net bearing capacity (q_ns): the net soil pressure that can be safely applied considering shear failure only.

Safe gross bearing capacity (q_s) is the maximum gross pressure which the soil can safely carry without shear failure, and

q_s = q_ns + γD_f

Bearing capacity of footing

Methods To Determine Bearing Capacity

(i) Rankine's Method (1885)

Rankine considered the equilibrium of soil elements beneath and adjacent to the footing and derived relations for bearing capacity. For cohesionless soils Rankine proposed an expression for ultimate bearing capacity in terms of the soil's passive earth pressure coefficient (K_p):

In practice Rankine's bearing capacity expression gives zero ultimate capacity when the foundation depth is zero, which is not realistic. Therefore Rankine's equations are rarely used to give design values of bearing capacity; instead they are used to estimate minimum depths of foundation by using active earth pressure considerations.

In the expression above, K_a is Rankine's coefficient of active earth pressure and q is the maximum pressure at the base of foundation used to compute required minimum depth.

(ii) Terzaghi's Method

Terzaghi's bearing capacity theory is a classical method to estimate the ultimate bearing capacity under a strip footing and applies to shallow foundations. The main assumptions are:

• The base of the strip footing is rough.
• The foundation is shallow (depth ≤ breadth).
• Shear strength of soil above the base is neglected and replaced by a uniform surcharge (γD_f).
• Loads are uniformly distributed and act vertically.
• The footing is of indefinite (infinite) length.
• Soil shear strength follows the Mohr-Coulomb criterion.

For a strip footing Terzaghi's equation for ultimate bearing capacity can be written as:

where:

• c = cohesion of soil (kN/m²)
• q = total surcharge at the base of footing = q_appl + γ_a D_f (kN/m²)
• q_appl = applied surcharge (kN/m²)
• γ_a = unit weight of the overburden material above the base causing surcharge (kN/m³)
• D_f = depth of embedment (m)
• γ = unit weight of soil under the footing (kN/m³)
• B_f = footing width (least lateral dimension) (m)
• N_q, N_c, N_γ = bearing capacity factors depending on the angle of internal friction (φ)

The bearing capacity factors are related to φ by expressions such as:

Terzaghi proposed shape factors to account for footing geometry. The general form with shape factors is:

Common shape factor values are:

• For long (strip) footings: s_c = s_q = s_γ = 1
• For square footings: s_c = 1.3, s_q = 1.0, s_γ = 0.8
• For circular footings: s_c = 1.3, s_q = 1.0, s_γ = 0.6

For rectangular footings of length L and width B the shape factors are given by expressions such as:

(iii) Skempton's Method (cohesive soils)

Skempton (1951) observed that the bearing capacity factor N_c in Terzaghi's relation increases with depth for cohesive soils. For rectangular footings and for various depth-to-width ratios he gave adjustment expressions:

For (D_f/B) > 2.5, an alternative expression is given:

For square and circular footings the expression is:

The analysis leads to a maximum practical value of N_c ≈ 9. The Skempton corrections permit the use of Terzaghi's form for a wider range of embedment depths.

(iv) Meyerhof's Method

Meyerhof extended bearing-capacity theory to include effects of depth, footing shape and load inclination by introducing depth and inclination factors in addition to shape factors. For a strip footing the ultimate bearing capacity may be written as:

q_u = cN_cs_cd_ci_c + q₀N_qs_qd_qi_q + 0.5γBN_γs_γd_γi_γ

where the symbols s, d and i represent shape, depth and inclination factors respectively. For strip footings s_c, s_q, s_γ = 1. The factors N_c, N_q, N_γ depend on φ and on the footing roughness, depth and shape as well as loading inclination.

Effect Of Water Table

The position of the groundwater table significantly affects the bearing capacity of soil. If the groundwater table rises close to or above the footing level, the effective stresses are reduced and the bearing capacity falls.

In the expression above, R_w1 and R_w2

are water-table correction factors. These correction factors are obtained from relations depending on the distance of the water table from the base of foundation.

When the water table is below the base of foundation at a distance b, the correction R_w2 is:

When b = 0, R_w2 = 0.5.

When the water table rises above the base of foundation, the correction factor R_w1 applies and is given by:

When a = D_f, R_w1 = 0.5.

Plate Load Test

The plate load test is an in-situ test to determine the ultimate bearing capacity of soil and the settlement of foundations under load. It is performed for both clayey and sandy soils and helps to select and design foundations. Safe bearing capacity is obtained by dividing the ultimate load by an appropriate factor of safety (commonly between 2 and 3).

• Bearing-capacity calculation for clayey soils: the ultimate bearing capacity of the foundation (q_u,f) is taken equal to the ultimate plate load (q_u,p).
• Bearing-capacity calculation for sandy soils: q_u,f/q_u,p = B_f/B_p, where B_f is the foundation width and B_p is the plate width.

Finally,

Safe bearing capacity = Ultimate bearing capacity / Factor of safety

The factor of safety typically ranges from 2 to 3.

Foundation settlement from plate tests

• For clayey soils: S_f = S_p × B_f/B_p, where S_p is the plate settlement and S_f is the foundation settlement.
• For sandy soils: relationships equate settlements by geometric similarity; see figure and relations obtained from plate tests for details.

where q_uf = ultimate bearing capacity of foundation, q_up = ultimate bearing capacity of plate, S_f = settlement of foundation, S_p = settlement of plate, B_f = width of foundation and B_p = width of plate.

Housel's Approach (Settlement-based Design)

Housel proposed a method to determine safe bearing pressure based on plate load test results by using an empirical relation that accounts for both area and perimeter effects:

Q = A_p m + P_p n

where Q is the load applied on a given plate, A_p is the contact area of the plate, P_p is the plate perimeter, m is a constant corresponding to bearing pressure and n is a constant corresponding to perimeter shear.

For a prototype foundation the corresponding expression is:

Q_f = m A_f + n P_f

where A_f is the area of the foundation and P_f is its perimeter. Knowing A_f and P_f one can determine the required foundation size for a given permissible settlement.

Standard Penetration Test (Spt)

The Standard Penetration Test is an in-situ dynamic penetrometer test performed in a borehole to obtain an index value of soil resistance (the N value). Empirical correlations relate N to soil properties used for design.

Procedure

• A standard split-spoon sampler is placed at the test depth in the borehole once the desired depth is reached.
• A drop hammer of mass 63.5 kg is allowed to fall through a height of 750 mm at the rate of about 30 blows per minute (as per IS 2131:1963).
• The sampler is first driven 150 mm (the seating drive) and the blows are ignored. It is then driven two successive 150 mm increments and the number of blows for each 150 mm is recorded.
• The sum of the blows for the last two 150 mm increments (i.e., for 300 mm penetration after seating) is the Standard Penetration Number N.
• If the number of blows required for any 150 mm increment exceeds 50, this is taken as refusal and the test is discontinued.

Corrections in SPT

Before using SPT N in correlations or design charts, corrections are applied (as per IS 2131 - 1981). The common corrections are:

1. Dilatancy correction

The corrected penetration number for dilatancy is given by:

N_c = 15 + 0.5 (N_r - 15)

where N_r is the recorded value and N_c is the corrected value. If N_r ≤ 15, then N_c = N_r.

2. Overburden pressure correction

The corrected SPT value accounting for overburden is:

N_c = C_n N

where C_n is a correction factor that depends on the effective overburden pressure; charts or formulae are used to obtain C_n for a given site condition.

After applying necessary corrections, the adjusted N-value can be used with empirical correlations to estimate bearing capacity, settlement and other design parameters.