Geogrids are stiffer material than geotextiles. Since the mid 1980's, a number of laboratory model studies have been reported relating to the evaluation of the ultimate and allowable bearing capacities of shallow foundations supported by soil reinforced with multiple layers of geogrids. The results obtained so far seem promising. In this section the general parameters of the problem are defined.

Figure 7.16 shows the  general parameters of  a rectangular surface foundation on a soil layer reinforced with several layers of geogrid. The size of the foundation is B × L (width × length) and the size of the geogrid layers is b × l (width × length). The first layer of geogrid is located at a depth u below the foundation, and the vertical distance between consecutive layers of geogrid is h. The total depth of reinforcement d can be given as

where N = number of reinforcement layers

The beneficial effects of reinforcement to increase the bearing capacity can be expressed in terms of a nondimensional parameter called the bearing capacity ratio (BCR). The bearing capacity ratio can be expressed with respect to the ultimate bearing capacity or the allowable bearing capacity (at a given settlement level of the foundation). Figure 7.17 shows the general nature of the load-settlement curve of a foundation both with and without geogrid reinforcement. Based on this concept the bearing capacity ratio can be defined as


For a given foundation and given values of b/B,  l/B, u/B, and h/B, the magnitude of BCRu increases with d/B and reaches a maximum value at (d/B)cr beyond which the bearing capacity remains practically constant. The term (d/B)cr  is the critical-reinforcement-depth ratio. For given values of  l/B, u/B, h/B, and d/B, BCRu attains a maximum value at (b/B)cr, which is called the critical-width ratio. Similarly, a critical-length ratio (l/B)cr can be established (for given values of b/B, u/B, h/B, and d/B) for a maximum value of BCRu. This concept is schematically illustrated in Fig. 7.18.  As  an  example,  Fig.  7.19 shows the variation of BCRu with d/B for four model foundations (B/L = 0, 1/3, 1/2, and 1) as reported by Omar et al. [6]. It was also shown from laboratory model tests [6,7] that for a given foundation, if b/B, l/B, d/B, and h/B are kept constant, the nature of variation of BCRu with u/B will be as shown in Fig. 7.20.

Initially (Zone 1) BCRu increases with u/B to a maximum value at (u/B)cr . For u/B > (u/B)cr the magnitude of BCRu decreases (Zone 2).  For u/B > (u/B)max the plot of BCRu versus u/B generally flattens out (Zone 3).

The present understanding (in general) among investigators is that, in Zones 1 and 2, the nature of the failure surface in soil will be as shown in Fig. 7.21a. In Zone 1 the initial increase in BCRu with u/B is due to the increase in confining pressure on the geogrid layers. In Zone 3 [that is, u/B " (u/B)max ] the failure surface in soil below the foundation is located fully above the first layer  of  geogrid, which acts as a semi-rigid rough base (Fig. 7.21b).

FIGURE 7.16 Geometric parameters of a rectangular foundation
supported by geogrid-reinforced soil

FIGURE 7.17 General nature of the load-settlement curves
for unreinforced and geogrid-reinforced soil
supporting a foundation

FIGURE 7.18  Definition  of  critical  nondimensional  parameters —           
(d/B)cr ,  (b/B)cr , and (l /B)cr

FIGURE 7.19 Variation of BCRu with d/B (after Omar et al. [6])

FIGURE 7.20 Nature of variation of BCRu with u/B
FIGURE 7.21 Failure surface in geogrid-reinforced soil under a
foundation (a) u/B < (u/B)max ; (b) u/B = (u/B)max


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