Settlement Estimation 1 General

Estimation of total and differential settlement is a fundamental aspect of the design of a shallow foundation. Differential settlement and relative rotation between adjacent structural elements should be evaluated. Settlements are considered tolerable if they do not significantly affect the serviceability and stability of the structures under the design load. These performance-based design criteria are best validated with building settlement monitoring.

The total settlement of a shallow foundation usually comprises primary and secondary settlement. The primary settlement results from the compression of the soil in response to the application of foundation loads. In granular soils, the primary settlement that results from an increase in stress is associated with immediate compression. Primary consolidation settlement in fine-grained soils depends on the rate of dissipation of excess pore water pressure caused by the application of foundation loads. The primary consolidation completes when excess pore water pressure is dissipated. Soils continue to deform after the primary settlement and this process is termed as secondary compression, or creep.

Foundation settlement may be estimated based on theory of elasticity or stress-strain behaviour. Most methods tend to over-predict the settlement, as the stiffness of the structure is seldom included in the computation. It is prudent to carry out sensitivity analysis to account for the variability of the ground and loading, and uncertainty of the settlement estimation.

Tilting of a rigid foundation base can be estimated by calculating the settlements at the front and rear edges of the foundation respectively, assuming a linear ground bearing pressure distribution. In addition, Poulos & Davis (1974) provided elastic solutions for assessing the rigidity of the foundation and tilting of the foundation due to an applied moment.

Ground heave due to excavation for foundation construction should be taken into account in evaluating the total settlement. Heave is caused by relief of vertical stress in soils, as the overburden is removed. The response is largely elastic. The net uplift is practically reduced to zero when a ground bearing pressure equal to that of the original overburden is applied. Therefore, the total settlement of a shallow foundation should be assessed using the net loading intensity.

3.2.4.2 Foundations on granular soils

Most methods for computing settlements of foundations on granular soils are based on elastic theory or empirical correlations. Empirical correlations between results of insitu tests and foundation settlement, such as that given by Burland & Burbidge (1985) based on standard penetration tests, generally provide an acceptable solution for predicting the settlement of a shallow foundation on granular soils.

Briaud & Gibbens (1997) reported the results of full-scale loading tests for five square footings founded on sands. The footings ranged in size from 1 m by 1 m to 3 m by 3 m. The measured settlement data from the loading tests were compared with the settlement estimated using various methods, which are empirical correlations based on different types of tests, including SPT, CPT, pressuremeter test, dilatometer test, triaxial test and borehole shear test. They opined that the methods proposed by Burland & Burbidge (1985) using SPT and Briaud (1992) using pressuremeter tests respectively gave reasonably conservative settlement estimation.

Poulos (2000) reviewed various methods for computing settlement of shallow foundations. He noted that although soil behaviour is generally non-linear and highly dependent on effective stress level and stress history and hence should be accounted for in settlement analysis, the selection of geotechnical parameters, such as the shear and Young's modulus of soils, and site characterisation are more important than the choice of the method of analysis. Simple elasticity-based methods are capable of providing reasonable estimates of settlements.

Based on elastic theory, the settlement, δf, of a shallow foundation can be calculated using an equation of the following general form :

δf = qnet _E Bf' f

s [3.2]

where qnet = mean net ground bearing pressure Bf' = effective width of the foundation Es = Young’s modulus of soil

f = a coefficient whose value depends on the shape and dimensions of the foundation, the variation of soil stiffness with depth, the thickness of compressible strata, Poisson’s ratio, the distribution of ground bearing pressure and the point at which the settlement is calculated

Poulos & Davis (1974) gave a suite of elastic solutions for determining the coefficient 'f' for various load applications and stress distributions in soils and rocks.

The increase of stress in soils due to foundation load can be calculated by assuming an angle of stress dispersion from the base of a shallow foundation. This angle may be approximated as a ratio of 2 (vertical) to 1 (horizontal) (Bowles, 1992; French, 1999). The settlement of the foundation can then be computed by calculating the vertical compressive strains caused by the stress increases in individual layers and summing the compression of the layers.

Schmertmann (1970) proposed to estimate the settlement based on a simplified distribution of vertical strain under the centre of a shallow foundation, expressed in the form of a strain influence factor. In this method, the compressive strain in each sub-layer due to the applied stress is evaluated. The settlement of the shallow foundation is then calculated by summing the compression in each sub-layer.

A time correction factor has been proposed by Burland & Burbidge (1985) for the estimation of secondary settlement. Terzaghi et al (1996) also give an equation for estimating secondary settlement in a similar form. The commencement of secondary settlement is assumed to commence when the primary settlement completes, which is taken as the end of construction.

3.2.4.3 Foundationson fine-grained soils

For fine-grained soils, an estimate of the consolidation settlement can be made using the settlement-time curve obtained from an oedometer test. Consolidation settlement may be considered to consist of primary consolidation and secondary consolidation stage. Reference may be made to Duncan & Poulos (1981) and Terzaghi et al (1996) on the methods for determining the primary consolidation of fine-grained soils beneath shallow foundations. The traditional approach of one-dimensional analysis (Terzaghi et al, 1996) has the limitations that only vertical strains are considered and lateral dissipation of excess porewater pressure is ignored. Despite these limitations, Poulos et al (2002) reported that the one- dimensional analysis gave reasonable estimate of the rate of consolidation settlement for soft clay or overconsolidated clay with a Poisson's ratio less than 0.35.

The three-dimensional effect can be simulated by using an equivalent coefficient of consolidation in the one-dimensional analysis (Davis & Poulos, 1972). The equivalent coefficient is obtained by multiplying the coefficient of consolidation with a geometrical rate factor. This method may be adopted where sophisticated three-dimensional analysis is not warranted.

The traditional method proposed by Buisman (1936) is practical in estimating secondary consolidation settlement (Terzaghi et al, 1996; Poulos et al, 2002). In this method, the magnitude of secondary consolidation is assumed to vary linearly with the logarithm of time. It is usually expressed as :

sc = _{1 + e}Cα

o Ho log ts

tp [3.3]

where sc = secondary consolidation C_{α =} secondary compression index eo = initial void ratio

Ho = thickness of soils subject to secondary consolidation tp = time when primary consolidation completes

ts = time for which secondary consolidation is allowed

compression index, Cc, at the same vertical effective stress of a soil. They reported that the Cα/Cc ratio is constant for a soil deposit and falls within a narrow range for geotechnical materials (see Table 3.2).

The time at which secondary consolidation is assumed to commence is not well defined. A pragmatic approach is to assume that the secondary consolidation settlement commences when 95% of the primary consolidation is reached (Terzaghi et al, 1996).

Table 3.2 – Values of Cα/Cc for Geotechnical Materials (Mesri et al, 1994)

Material Cα/Cc

Granular soils 0.02 ± 0.01

Shale and mudstone 0.03 ± 0.01 Inorganic clays and silts 0.04 ± 0.01 Organic clays and silts 0.05 ± 0.01 Peat and muskeg 0.06 ± 0.01