**FAILURE MODE**

Binquet and Lee [2,3] conducted several laboratory tests and proposed a theory for designing a continuous foundation on sand reinforced with metallic strips.

**Figure 7.2**defines the general parameters in this design procedure. In

**Fig. 7.2**, the width of the continuous foundation is B. The first layer of reinforcement

is placed at a distance u measured from the bottom of the foundation. The distance between each layer of reinforcement is h. It was experimentally shown [2, 3] that the most beneficial effect of reinforced earth is obtained when u/B is less than about 2/3 B and the number of layers of reinforcement (N) is greater than 4 but no more than 6 to 7. If the length of the ties (that is, reinforcement strips) is sufficiently long, failure occurs when the upper ties break. This phenomenon is shown in

**Fig. 7.3**.

**Figure 7.4**shows an idealized condition for the development of a failure surface in reinforced earth which consists of two zones. Zone I is immediately below the foundation which settles with the foundation during the application of load. In zone II the soil is pushed outward and upward.

Points A1, A2, A3,. . . , and B1, B2, B3 , . . . , which define the limits of zones I and II, are points at which maximum shear stress, τmax, occurs in the xz plane. The distance x = x' of the points measured from the center line of the foundation where maximum shear stress occurs is a function of z/B. This is shown in a nondimensional form in

**Fig. 7.5**.

**FIGURE 7.5**Variation of x'/B with z/B

**FIGURE 7.6**Assumptions to calculate the force in reinforcement ties

**FIGURE 7.2**Foundation on metallic strip reinforced granular soil

**Figure 7.3**Failure in reinforced earth by tie break (u/B < 2/3 and N >= 4)

**FIGURE 7.4**Failure surface in reinforced earth at ultimate load

**FORCE IN REINFORCEMENT TIES**

In order to obtain the forces in the reinforcement ties, Binquet and Lee [3]

made the following assumptions.

**1.**Under the application of bearing pressure by the foundation, the rein-

forcing ties at points A1, A2, A3, . . . , and B1, B2, B3, . . . , (

**Fig. 7.4**) take the shape shown in

**Fig. 7.6a**.

That is, the tie takes two right angle turns on each side of zone I around two frictionless rollers.

**2.**For N reinforcing layers, the ratio of the load per unit area on the foundation supported by reinforced earth qR to the load per unit area on the foundation supported by unreinforced earth qo is constant, irrespective of the settlement level, Se (see

**Fig. 7.6b**). Binquet and Lee [2] proved this relation by laboratory experimental results.

The variations of α and β with z/B are shown in

**Figs. 7.7**and

**7.8**respectively.

**FIGURE 7.7**Variation of " with z/B

**FIGURE 7.8**Variation of β with z/B

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