3.2 DESIGN OF SHALLOW FOUNDATIONS ON SOILS
3.2.1 Determination of Bearing Capacity of Soils
3.2.1.1 General
There are a variety of methods for determining the bearing capacity of shallow foundations on soils. A preliminary estimate of allowable bearing pressure may be obtained on the basis of soil descriptions. Other methods include correlating bearing pressures with results of insitu field tests, such as SPT N value and tip resistance of CPT. For example, the presumed allowable bearing pressures given in the Code of Practice for Foundations (BD, 2004a) are based on soil descriptions. Typical undrained shear strength and SPT N values of various material types are also provided. The presumed allowable bearing pressures are usually based on empirical correlations and are intended to be used without resorting to significant amount of testing and design evaluation.
Methods based on engineering principles can be used to compute the bearing capacity of soils and estimate the foundation settlement. This would require carrying out adequate ground investigation to characterise the site, obtaining samples for laboratory tests to determine geotechnical parameters and establishing a reliable engineering geological model.
Designs following this approach normally result in bearing pressures higher than the presumed allowable bearing pressures given in codes of practice.
3.2.1.2 Empirical methods
The allowable bearing pressure of a soil can be obtained from correlations with SPT N values. For example, Terzaghi & Peck (1967) proposed bearing pressure of 10 N (kPa) and 5 N (kPa) for non-cohesive soils in dry and submerged conditions respectively. This was based on limiting the settlement of footings of up to about 6 m wide to less than 25 mm, even if it is founded on soils with compressible sand pockets. Based on back-analysis of more than 200 settlement records of foundations on soils and gravel, Burland & Burbidge (1985) proposed a correlation between soil compressibility, width of foundation and average SPT N value. This generally results in an allowable bearing pressure greater than that proposed by Terzaghi & Peck (1967).
3.2.1.3 Bearing capacity theory
The ultimate bearing capacity of a shallow foundation resting on soils can be computed as follows (GEO, 1993) :
qu = Qu
Bf'Lf' = c' Nc ζcs ζci ζct ζcg + 0.5 Bf' γs' Nγ ζγs ζγi ζγt ζγg +q Nq ζqs ζqi ζqt ζqg [3.1]
where Nc, Nγ, Nq = general bearing capacity factors which determine the capacity of a long strip footing acting on the surface of a soil in a homogenous half-space Qu = ultimate resistance against bearing capacity failure
qu = ultimate bearing capacity of foundation
q = overburden pressure at the level of foundation base c' = effective cohesion of soil
γs' = effective unit weight of the soil Bf = least dimension of footing Lf = longer dimension of footing Bf' = Bf – 2eB
Lf' = Lf – 2eL
eL = eccentricity of load along L direction eB = eccentricity of load along B direction
ζcs, ζγs, ζqs = influence factors for shape of shallow foundation ζci, ζγi, ζqi = influence factors for inclination of load
ζcg, ζγg, ζqg = influence factors for ground surface
ζct, ζγt, ζqt = influence factors for tilting of foundation base
Figure 3.1 shows the generalised loading and geometric parameters for the design of a shallow foundation. The bearing capacity factors are given in Table 3.1. Equation [3.1] is applicable for the general shear type of failure of a shallow foundation, which is founded at a depth less than the foundation width. This failure mode is applicable to soils that are not highly compressible and have a certain shear strength, e.g. in dense sand. If the soils are highly compressible, e.g. in loose sands, punching failure may occur. Vesic (1975) recommended using a rigidity index of soil to define whether punching failure is likely to occur. In such case, the ultimate bearing capacity of the foundation can be evaluated based on Equation [3.1] with an additional set of influence factors for soil compressibility (Vesic, 1975).
In selecting φ' value for foundation design, attention should be given to the stress- dependency of the strength envelope of soils.
Kimmerling (2002) suggested using the actual dimensions, Bf and Lf, to compute the influence factors for shape of shallow foundation. The equations for computing shape factors given in Table 3.1 use the full dimensions of a shallow foundation. No depth factors are included in Equation [3.1] as the beneficial effect of foundation embedment is unreliable because of possible construction activities in future (GEO, 1993).
The ultimate bearing capacity depends on the effective unit weight of the soil. Where the groundwater level is at a distance greater than Bf' below the base of the foundation, the effective unit weight of the soil can be taken as the bulk unit weight, γ. Where the groundwater level is at the same level as the foundation base, the effect of groundwater should be considered in bearing capacity evaluation. For static groundwater, the submerged unit weight of the soil can be used in Equation [3.1]. Where the groundwater flows under an upward hydraulic gradient, the effective unit weight of the soil should be taken as γ – γw (1 + ί) where ί is the upward hydraulic gradient and γw is the unit weight of water. For intermediate groundwater levels, the ultimate bearing capacity may be interpolated between the above limits.
An effective groundwater control measure is needed in case the groundwater is above the proposed excavated level of a shallow foundation. The effect of softening or loosening of foundation soils due to excessive ingress of groundwater into the excavations should be assessed. For fine-grained soils, the effect of softening due to swelling should be considered, which may occur in the foundation upon excavation resulting in a reduction of effective stress.
P H
0.5Bf 0.5Bf
eB
q ω
αf
Df
ắ
ắ ắ ắ
(a) Force Acting on a Spread Foundation
(b) Effective Dimensions of Foundation Base 0.5Bf 0.5Bf
0.5Lf0.5Lf
0.5Bf' 0.5Bf'
0.5L
f '
0.5L
f '
eB
eL
Point of application of P
Figure 3.1 – Generalised Loading and Geometric Parameters for a Spread Shallow Foundation
Table 3.1 – Bearing Capacity Factors for Computing Ultimate Bearing Capacity of Shallow Foundations Parameters c' – φ' soil For undrained condition (φ = 0)
Bearing
capacity factors Nc = ( Nq – 1 )cot φ' Nγ = 2 ( Nq + 1 ) tan φ' Nq = eπ tan φ' tan2 ( 45° + φ'
2 )
Nc = 2 + π Nγ = 0 Nq = 1 Shape factors
ζcs = 1 + Bf
Lf
Nq
Nc
ζγs = 1 – 0.4 Bf
Lf
ζqs = 1 + Bf
Lf tan φ'
ζcs = 1 + 0.2 Bf
Lf ζqs = 1
Inclination
factors ζci = ζqi – 1 - ζqi
Nc tan φ' ζγi = ⎝⎛
⎠⎞
1 – H
P + Bf'Lf' c' cot φ' mi+1
ζqi = ⎝⎛
⎠⎞
1 – H
P + Bf'Lf' c' cot φ' mi
ζci = 0.5 + 0.5 1 – H c' Bf'Lf' ζqi = 1
Tilt factors
ζct = ζqt– 1 - ζqt
Nc tan φ'
ζγt = ( 1 – αf tan φ' )2 for αf < 45°
ζqt ≈ ζγt
ζct = 1 – 2αf π + 2 ζqt = 1
Ground sloping
factors ζcg = e -2ω tan φ' ζγg ≈ ζqg
ζqg = ( 1 – tan ω )2 for ω ≤ 45°
ζqg = 0 for ω > 45°
ζcg = 1 – 2ω π + 2 ζqg = 1
where Bf and Lf = dimensions of the footing
Bf' and Lf' = effective dimensions of the footing
P and H = vertical and horizontal component of the applied load φ' = angle of shearing resistance
Df = depth from ground surface to the base of shallow foundation αf = inclination of the base of the footing
ω = sloping inclination in front of the footing mi =
2 + Bf' Lf' 1 + Bf'
Lf'
= load inclination along dimension Bf'; mi = 2 + Lf'
Bf' 1 + Lf'
Bf'
= load inclination along dimension Lf'
Equation [3.1] is generally applicable to homogenous isotopic soils. The presence of geological features such as layering or weak discontinuities can result in failure mechanisms different from that assumed for the derivation of the equation. Therefore, the presence of geological features, in particular weak soil layers, should be checked in ground investigations.
The evaluation of bearing capacity should take into account the geological characteristics of the ground.
The effect of load inclination and eccentricity are approximated and included as influence factors in Equation [3.1]. In reality, the problem of bearing capacity under combined loading conditions is essentially a three-dimensional problem. Recent research work (Murff, 1994; Bransby & Randolph, 1998; Taiebat & Carter, 2000) have suggested that for any foundation, there is a surface in a three-dimensional load space that defines a failure envelope for the foundation. The axes of the three-dimensional space represent the vertical load, horizontal load and moment. Any combination of loads outside this envelope causes failure of the foundation. Solutions are largely applicable to undrained failure in fine-grained soils. Further work are needed to extend their applications to granular soils, which are more appropriate to local ground conditions.