Stuart  assumed the geometry of the rupture surface in the soil mass to be the same as that assumed by Terzaghi (Fig. 2.1). According to Stuart, the following conditions may arise (Fig. 2.38)
1. Case 1 (Fig. 2.38a): If the center-to-center spacing of the two foundations is x >= x1, the rupture surface in the soil under each foundation will not overlap. So the ultimate bearing capacity of each continuous foundation can be given by Terzaghi’s equation [Eq.(2.31)]. For c = 0
where Nq , Nγ = Terzaghi’s bearing capacity factors (Table 2.1)
2. Case 2 (Fig. 2.38b): If the center-to-center spacing of the two foundations (x = x2 < x1) are such that the Rankine passive zones just overlap, then the magnitude of qu will still be given by Eq. (2.114).
However, the foundation settlement at ultimate load will change (compared to the case of an isolated foundation).
3. Case 3 (Fig. 2.38c): This is the case where the center-to-center spacing of the two continuous foundations is x = x3 < x2. Note that the triangular wedges in the soil under the foundation make angles of
180º - 2Φ" at points d1 and d2. The area of the logarithmic spirals d1 g1 and d1 e are tangent to each other at point d1. Similarly, the arcs of the logarithmic spirals d2 g2 and d2 e are tangent to each other at point d2. For this case, the ultimate bearing capacity of each foundation can be given as (c = 0)
The efficiency ratios are functions of x/B and soil friction angle ".
The theoretical variations of ζq and ζγ are given in Figs. 2.39 and 2.40.
4. Case 4 (Fig. 2.38d): If the spacing of the foundation is further reduced such that x = x4 < x3, blocking will occur, and the pair of foundations will act as a single foundation. The soil between the individual units will form an inverted arch which travels down with the foundation as the load is applied.
When the two foundations touch, the zone of arching disappears and the system behaves as a single foundation with a width equal to 2B. The ultimate bearing capacity for this case can be given by Eq. (2.114), with B being replaced by 2B in the third term.
Das and Larbi-Cherif  conducted laboratory model tests to determine the interference efficiency ratios (ζq and ζγ) of two rough continuous foundations resting on sand extending to a great depth. The sand used in the model tests was highly angular, and the tests were conducted at a relative density of about 60%. The angle of friction " at this relative density of compaction was 39". Load-displacement curves obtained from the model tests were of local shear type. The experimental variations of ζq and ζγ obtained from these tests
are given in Figs. 2.41 and 2.42. From these figures it may be seen that, although the general trend of the experimental efficiency ratio variations is similar to those predicted by theory, there is a large variation in the magnitudes between the theory and experimental results. Figure 2.43 shows the experimental variations of Su /B with x/B (Su = settlement at ultimate load).
The elastic settlement of the foundation decreases with the increase in the center-to-center spacing of the foundation and remains constant at x > about 4B.
FIGURE 2.1 Failure surface in soil at ultimate load for a continuous rough rigid foundation as assumed by Terzaghi
FIGURE 2.38 Assumptions for the failure surface in granular soil under two closely spacedrough continuous foundations rough continuous foundations
FIGURE 2.39 Stuart’s interference factor εq
FIGURE 2.40 Stuart’s interference factor εy
FIGURE 2.41 Comparison of experimental and theoretical εq
FIGURE 2.42 Comparison of experimental and theoretical εy
FIGURE 2.43 Variation of experimental elastic settlement (Si /B)
with center-to-center spacing of two continuous rough foundations
TABLE 2.1 Terzaghi’s Bearing Capacity Factors—Eqs. (2.32), (2.33), and (2.34)