Immediate settlement: elastic solutions

General expression

In soil mechanics, it is common to apply solutions from the theory of elasticity to the evaluation of the stresses induced in a soil formation by loads applied at the surface. Such application is valid particularly under the two following conditions:

Figure 6.9 Foundation time-settlement generic curve (Perloff, 1975).

Table 6.S Typical relative importance of the three settlement components as a function of foundation soil type.

i) the loading is essentially monotonic, i.e., it increases up to a certain value and then has relatively small variations from that value;

the stress transmitted to the soil is relatively small in relation to the bearing capacity for vertical loading.

Most shallow foundations of civil engineering structures, namely buildings and bridges, satisfy these two conditions. In particular, the second is verified due to the great convenience, discussed later in this chapter, of limiting the ground-induced deformation, by keeping settlements within tight bounds. This circumstance leads to the adoption of relatively low pressure values in the foundation-soil contact surface, which ensure a reasonable proportionality in relation to the deformations produced in the soil mass.

The Annex A6.2 to this chapter contains some of the more useful elastic solutions for the evaluation of shallow foundation settlements (Boussinesq, 1885; Flamant, 1892; Giroud, 1970; Poulos and Davis, 1974). The induced stress distribution is not particularly sensitive to the variation with depth of the soil elastic properties. This means that, for stratified formations, one can employ, with reasonable accuracy, solutions for the stress distribution in homogeneous elastic media.

Consider the formation represented in Figure 6.10, comprising n layers, all with elastic behavior, loaded at the surface by a surcharge Aq_s, uniformly distributed in a given area. If the stress increments induced by that load at the center of layer /', with thickness h_f, and elastic parameters and v_p are Ao_zj, Aa_xj, and Ao_yj, respectively, the immediate settlement, Sj, at the surface, can be calculated by applying Flooke’s law as:

Figure 6.10 Surface loading of a stratified elastic formation.