# GSP 131 Contemporary Issues in Foundation Engineering

concern for design of a micropile if the compression load that produces yielding of the pile material exceeds the value of P_{cr}.

# Cadden and Gómez (2002) re-arranged Equation 7 as follows:

E_{s }≤

⋅ 4

1

^{I }⋅ A^{2 }

E y f 2

(Equation 8)

where:

A = cross-sectional area of the pile [length^{2}] f_{y }= yield stress of the pile material [force/area]

The first of the two terms inside the brackets represents the geometric properties of the pile, while the second term represents its material properties. The combination of these two terms is referred to as the pile factor and is given in units of [stress^{-1}]. Table 3 lists some of the sections and steel types (solid and hollow core bars and casing) often used for micropile work in the United States. Pile factors are also listed for each section.

The value of E_{s }calculated using Equation 8 can be defined as the critical or limiting lateral reaction modulus. If the critical E_{s }value is less than the actual soil E_{s}, then the geotechnical and structural axial strength of the pile will control the pile capacity. If the critical E_{s }is greater than the actual soil stiffness, buckling should be evaluated

further.

Equation 8 is represented graphically in Figure 2.

Any given combination of

micropile and soil can be represented by a point in the diagram. An undamaged pile represented by a point located to the right of the line will fail under compression before it buckles. A pile represented by a point to the left of the line may buckle before it fails in compression. Figure 2 thus becomes a tool for checking whether buckling of a given pile section should be explored further for a given site.

It can be seen that, according to the theoretical background described previously, buckling does not control the design of micropiles except for very soft soils.

Figure 2 may be used for an approximate determination of whether or not buckling may occur in a micropile. If, according to Figure 2, a particular combination of soil and micropile type may be susceptible to buckling, then the minimum critical load can be estimated using numerical procedures. This chart assumes that the pile has constant cross-sectional properties, and there are no horizontal loads or moments applied to the top of the pile. In addition, the soil is assumed to have a constant value of lateral reaction modulus throughout the length of the pile, behaving as a non- yielding, linear elastic material.

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